LMFDB - Embedded newform 69.8.e.a.4.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,8,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.5545667584$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$14$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			4.6
Character	$\chi$	$=$	69.4
Dual form			69.8.e.a.52.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.75287 - 8.21765i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(30.3765 - 35.0564i) q^{4} +(42.6731 + 27.4244i) q^{5} +(159.733 + 184.342i) q^{6} +(138.669 + 964.463i) q^{7} +(-1511.60 - 443.845i) q^{8} +(613.274 - 394.127i) q^{9} +O(q^{10})$	\(q+(-3.75287 - 8.21765i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(30.3765 - 35.0564i) q^{4} +(42.6731 + 27.4244i) q^{5} +(159.733 + 184.342i) q^{6} +(138.669 + 964.463i) q^{7} +(-1511.60 - 443.845i) q^{8} +(613.274 - 394.127i) q^{9} +(65.2168 - 453.593i) q^{10} +(3287.95 - 7199.61i) q^{11} +(-520.278 + 1139.25i) q^{12} +(87.6906 - 609.901i) q^{13} +(7405.21 - 4759.04i) q^{14} +(-1314.11 - 385.859i) q^{15} +(1180.48 + 8210.45i) q^{16} +(9776.81 + 11283.0i) q^{17} +(-5540.34 - 3560.56i) q^{18} +(9277.78 - 10707.1i) q^{19} +(2257.66 - 662.909i) q^{20} +(-10928.9 - 23930.9i) q^{21} -71503.1 q^{22} +(-57973.3 - 6627.09i) q^{23} +42536.1 q^{24} +(-31385.4 - 68724.4i) q^{25} +(-5341.04 + 1568.27i) q^{26} +(-12889.6 + 14875.4i) q^{27} +(38022.9 + 24435.8i) q^{28} +(-109762. - 126673. i) q^{29} +(1760.85 + 12247.0i) q^{30} +(-112074. - 32907.9i) q^{31} +(-106601. + 68508.1i) q^{32} +(-30412.9 + 211526. i) q^{33} +(56028.9 - 122686. i) q^{34} +(-20532.4 + 44959.6i) q^{35} +(4812.46 - 33471.4i) q^{36} +(-418437. + 268913. i) q^{37} +(-122806. - 36059.0i) q^{38} +(2367.65 + 16467.3i) q^{39} +(-52332.4 - 60394.8i) q^{40} +(-67774.3 - 43555.9i) q^{41} +(-155641. + 179619. i) q^{42} +(-664409. + 195088. i) q^{43} +(-152516. - 333963. i) q^{44} +36979.0 q^{45} +(163107. + 501275. i) q^{46} +1.33801e6 q^{47} +(-93037.0 - 203723. i) q^{48} +(-120776. + 35463.1i) q^{49} +(-446968. + 515828. i) q^{50} +(-339109. - 217932. i) q^{51} +(-18717.2 - 21600.8i) q^{52} +(-142183. - 988902. i) q^{53} +(170614. + 50096.8i) q^{54} +(337752. - 217060. i) q^{55} +(218460. - 1.51943e6i) q^{56} +(-158906. + 347956. i) q^{57} +(-629026. + 1.37738e6i) q^{58} +(226588. - 1.57596e6i) q^{59} +(-53445.1 + 34347.1i) q^{60} +(-1.54837e6 - 454643. i) q^{61} +(150174. + 1.04448e6i) q^{62} +(465163. + 536827. i) q^{63} +(1.85623e6 + 1.19293e6i) q^{64} +(20468.2 - 23621.6i) q^{65} +(1.85238e6 - 543908. i) q^{66} +(-587834. - 1.28718e6i) q^{67} +692528. q^{68} +(1.55229e6 - 269307. i) q^{69} +446517. q^{70} +(-1.93589e6 - 4.23901e6i) q^{71} +(-1.10195e6 + 323563. i) q^{72} +(2.06294e6 - 2.38076e6i) q^{73} +(3.78018e6 + 2.42937e6i) q^{74} +(1.33585e6 + 1.54165e6i) q^{75} +(-93526.4 - 650491. i) q^{76} +(7.39970e6 + 2.17275e6i) q^{77} +(126437. - 81256.3i) q^{78} +(-364723. + 2.53670e6i) q^{79} +(-174791. + 382740. i) q^{80} +(220769. - 483416. i) q^{81} +(-103579. + 720405. i) q^{82} +(-4.78436e6 + 3.07472e6i) q^{83} +(-1.17091e6 - 343810. i) q^{84} +(107777. + 749605. i) q^{85} +(4.09661e6 + 4.72774e6i) q^{86} +(3.80711e6 + 2.44668e6i) q^{87} +(-8.16556e6 + 9.42356e6i) q^{88} +(8.39310e6 - 2.46444e6i) q^{89} +(-138778. - 303880. i) q^{90} +600387. q^{91} +(-1.99335e6 + 1.83103e6i) q^{92} +3.15375e6 q^{93} +(-5.02138e6 - 1.09953e7i) q^{94} +(689548. - 202470. i) q^{95} +(2.24050e6 - 2.58568e6i) q^{96} +(-9.47656e6 - 6.09021e6i) q^{97} +(744681. + 859407. i) q^{98} +(-821147. - 5.71120e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) $ 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9 + 1322 * q^10 + 7892 * q^11 - 19980 * q^12 + 39810 * q^13 - 26296 * q^14 + 135 * q^15 - 142164 * q^16 - 97081 * q^17 - 11664 * q^18 + 120905 * q^19 + 124755 * q^20 + 26406 * q^21 - 837266 * q^22 - 224688 * q^23 - 60264 * q^24 - 180624 * q^25 + 385108 * q^26 - 275562 * q^27 + 1121760 * q^28 - 375654 * q^29 + 35694 * q^30 + 505029 * q^31 - 661528 * q^32 - 360423 * q^33 - 1872759 * q^34 - 964610 * q^35 - 1269189 * q^36 - 28802 * q^37 - 1459868 * q^38 + 1074870 * q^39 + 5371901 * q^40 - 1557480 * q^41 + 883116 * q^42 + 1160786 * q^43 - 4521825 * q^44 - 2009124 * q^45 - 4123580 * q^46 + 811422 * q^47 - 1563111 * q^48 - 10960262 * q^49 + 16636695 * q^50 + 4413852 * q^51 - 4843791 * q^52 + 4291672 * q^53 - 98415 * q^54 + 2093539 * q^55 - 12548382 * q^56 - 4007907 * q^57 - 7414367 * q^58 + 2955424 * q^59 + 7289973 * q^60 + 4919292 * q^61 + 16083211 * q^62 + 712962 * q^63 - 1673596 * q^64 - 13246221 * q^65 + 7219449 * q^66 + 148565 * q^67 - 23039568 * q^68 - 657018 * q^69 + 12781104 * q^70 - 7247645 * q^71 - 600696 * q^72 + 32596055 * q^73 + 32550658 * q^74 - 10061874 * q^75 + 12150569 * q^76 - 43349150 * q^77 - 17201700 * q^78 + 4815410 * q^79 + 36529590 * q^80 - 7440174 * q^81 + 20862470 * q^82 + 35160800 * q^83 - 5346540 * q^84 + 48578363 * q^85 + 76972708 * q^86 + 1505088 * q^87 - 35912212 * q^88 + 1401264 * q^89 + 963738 * q^90 - 91970208 * q^91 - 74293537 * q^92 + 555606 * q^93 - 32520253 * q^94 + 79436789 * q^95 + 41519736 * q^96 + 18296816 * q^97 - 38956823 * q^98 - 9731421 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−3.75287	−	8.21765i	−0.331710	−	0.726344i	0.668133	−	0.744042i	$-0.267094\pi$
$2$	−3.75287	−	8.21765i	−0.331710	−	0.726344i	−0.999843	+	0.0176976i	$0.994366\pi$
$3$	−25.9063	+	7.60678i	−0.553964	+	0.162658i
$3$	−25.9063	+	7.60678i	−0.553964	+	0.162658i
$4$	30.3765	−	35.0564i	0.237317	−	0.273878i
$5$	42.6731	+	27.4244i	0.152672	+	0.0981164i	0.614746	−	0.788725i	$-0.289258\pi$
$5$	42.6731	+	27.4244i	0.152672	+	0.0981164i	−0.462074	+	0.886841i	$0.652895\pi$
$6$	159.733	+	184.342i	0.301901	+	0.348413i
$7$	138.669	+	964.463i	0.152804	+	1.06278i	0.911490	+	0.411321i	$0.134933\pi$
$7$	138.669	+	964.463i	0.152804	+	1.06278i	−0.758686	+	0.651456i	$0.774158\pi$
$8$	−1511.60	−	443.845i	−1.04381	−	0.306490i
$9$	613.274	−	394.127i	0.280418	−	0.180214i
$10$	65.2168	−	453.593i	0.0206234	−	0.143439i
$11$	3287.95	−	7199.61i	0.744820	−	1.63093i	−0.0306401	−	0.999530i	$-0.509755\pi$
$11$	3287.95	−	7199.61i	0.744820	−	1.63093i	0.775460	−	0.631397i	$-0.217518\pi$
$12$	−520.278	+	1139.25i	−0.0869162	+	0.190320i
$13$	87.6906	−	609.901i	0.0110701	−	0.0769942i	−0.983537	−	0.180704i	$-0.942162\pi$
$13$	87.6906	−	609.901i	0.0110701	−	0.0769942i	0.994608	+	0.103710i	$0.0330714\pi$
$14$	7405.21	−	4759.04i	0.721256	−	0.463523i
$15$	−1314.11	−	385.859i	−0.100534	−	0.0295195i
$16$	1180.48	+	8210.45i	0.0720510	+	0.501126i
$17$	9776.81	+	11283.0i	0.482643	+	0.556999i	0.943885	−	0.330275i	$-0.107141\pi$
$17$	9776.81	+	11283.0i	0.482643	+	0.556999i	−0.461242	+	0.887274i	$0.652596\pi$
$18$	−5540.34	−	3560.56i	−0.223915	−	0.143901i
$19$	9277.78	−	10707.1i	0.310318	−	0.358125i	−0.579071	−	0.815277i	$-0.696585\pi$
$19$	9277.78	−	10707.1i	0.310318	−	0.358125i	0.889389	+	0.457151i	$0.151130\pi$
$20$	2257.66	−	662.909i	0.0631036	−	0.0185289i
$21$	−10928.9	−	23930.9i	−0.257518	−	0.563885i
$22$	−71503.1			−1.43168
$23$	−57973.3	−	6627.09i	−0.993530	−	0.113573i
$23$	−57973.3	−	6627.09i	−0.993530	−	0.113573i
$24$	42536.1			0.628085
$25$	−31385.4	−	68724.4i	−0.401733	−	0.879673i
$26$	−5341.04	+	1568.27i	−0.0595963	+	0.0174991i
$27$	−12889.6	+	14875.4i	−0.126028	+	0.145444i
$28$	38022.9	+	24435.8i	0.327334	+	0.210365i
$29$	−109762.	−	126673.i	−0.835720	−	0.964473i	0.164038	−	0.986454i	$-0.447548\pi$
$29$	−109762.	−	126673.i	−0.835720	−	0.964473i	−0.999758	+	0.0219815i	$0.993003\pi$
$30$	1760.85	+	12247.0i	0.0119069	+	0.0828144i
$31$	−112074.	−	32907.9i	−0.675677	−	0.198397i	−0.0741477	−	0.997247i	$-0.523624\pi$
$31$	−112074.	−	32907.9i	−0.675677	−	0.198397i	−0.601530	+	0.798850i	$0.705442\pi$
$32$	−106601.	+	68508.1i	−0.575089	+	0.369587i
$33$	−30412.9	+	211526.i	−0.147319	+	1.02463i
$34$	56028.9	−	122686.i	0.244476	−	0.535327i
$35$	−20532.4	+	44959.6i	−0.0809470	+	0.177249i
$36$	4812.46	−	33471.4i	0.0171913	−	0.119568i
$37$	−418437.	+	268913.i	−1.35808	+	0.872783i	−0.998186	−	0.0602117i	$-0.980822\pi$
$37$	−418437.	+	268913.i	−1.35808	+	0.872783i	−0.359891	+	0.932994i	$0.617186\pi$
$38$	−122806.	−	36059.0i	−0.363058	−	0.106603i
$39$	2367.65	+	16467.3i	0.00639132	+	0.0444526i
$40$	−52332.4	−	60394.8i	−0.129289	−	0.149207i
$41$	−67774.3	−	43555.9i	−0.153575	−	0.0986969i	0.461596	−	0.887090i	$-0.347277\pi$
$41$	−67774.3	−	43555.9i	−0.153575	−	0.0986969i	−0.615172	+	0.788393i	$0.710913\pi$
$42$	−155641.	+	179619.i	−0.324153	+	0.374093i
$43$	−664409.	+	195088.i	−1.27437	+	0.374189i	−0.847825	−	0.530276i	$-0.822088\pi$
$43$	−664409.	+	195088.i	−1.27437	+	0.374189i	−0.426547	+	0.904465i	$0.640270\pi$
$44$	−152516.	−	333963.i	−0.269917	−	0.591036i
$45$	36979.0			0.0604939
$46$	163107.	+	501275.i	0.247071	+	0.759318i
$47$	1.33801e6			1.87982			0.939911	−	0.341420i	$-0.110908\pi$
$47$	1.33801e6			1.87982			0.939911	+	0.341420i	$0.110908\pi$
$48$	−93037.0	−	203723.i	−0.121426	−	0.265886i
$49$	−120776.	+	35463.1i	−0.146654	+	0.0430616i
$50$	−446968.	+	515828.i	−0.505686	+	0.583593i
$51$	−339109.	−	217932.i	−0.357967	−	0.230051i
$52$	−18717.2	−	21600.8i	−0.0184599	−	0.0213039i
$53$	−142183.	−	988902.i	−0.131184	−	0.912405i	−0.944014	−	0.329904i	$-0.892984\pi$
$53$	−142183.	−	988902.i	−0.131184	−	0.912405i	0.812830	−	0.582500i	$-0.197926\pi$
$54$	170614.	+	50096.8i	0.147447	+	0.0432944i
$55$	337752.	−	217060.i	0.273734	−	0.175918i
$56$	218460.	−	1.51943e6i	0.166232	−	1.15617i
$57$	−158906.	+	347956.i	−0.113652	+	0.248864i
$58$	−629026.	+	1.37738e6i	−0.423322	+	0.926946i
$59$	226588.	−	1.57596e6i	0.143634	−	0.998993i	−0.782730	−	0.622362i	$-0.786173\pi$
$59$	226588.	−	1.57596e6i	0.143634	−	0.998993i	0.926363	−	0.376631i	$-0.122918\pi$
$60$	−53445.1	+	34347.1i	−0.0319432	+	0.0205286i
$61$	−1.54837e6	−	454643.i	−0.873416	−	0.256458i	−0.185848	−	0.982578i	$-0.559503\pi$
$61$	−1.54837e6	−	454643.i	−0.873416	−	0.256458i	−0.687568	+	0.726120i	$0.741321\pi$
$62$	150174.	+	1.04448e6i	0.0800248	+	0.556585i
$63$	465163.	+	536827.i	0.234376	+	0.270484i
$64$	1.85623e6	+	1.19293e6i	0.885119	+	0.568832i
$65$	20468.2	−	23621.6i	0.00924448	−	0.0106687i
$66$	1.85238e6	−	543908.i	0.793098	−	0.232875i
$67$	−587834.	−	1.28718e6i	−0.238777	−	0.522849i	0.751868	−	0.659314i	$-0.229153\pi$
$67$	−587834.	−	1.28718e6i	−0.238777	−	0.522849i	−0.990645	+	0.136465i	$0.956426\pi$
$68$	692528.			0.267089
$69$	1.55229e6	−	269307.i	0.568853	−	0.0986906i
$70$	446517.			0.155595
$71$	−1.93589e6	−	4.23901e6i	−0.641914	−	1.40559i	−0.898457	−	0.439062i	$-0.855311\pi$
$71$	−1.93589e6	−	4.23901e6i	−0.641914	−	1.40559i	0.256543	−	0.966533i	$-0.417416\pi$
$72$	−1.10195e6	+	323563.i	−0.347936	+	0.102163i
$73$	2.06294e6	−	2.38076e6i	0.620664	−	0.716284i	−0.355169	−	0.934802i	$-0.615577\pi$
$73$	2.06294e6	−	2.38076e6i	0.620664	−	0.716284i	0.975833	+	0.218518i	$0.0701222\pi$
$74$	3.78018e6	+	2.42937e6i	1.08443	+	0.696920i
$75$	1.33585e6	+	1.54165e6i	0.365632	+	0.421961i
$76$	−93526.4	−	650491.i	−0.0244392	−	0.169978i
$77$	7.39970e6	+	2.17275e6i	1.84713	+	0.542365i
$78$	126437.	−	81256.3i	0.0301678	−	0.0193877i
$79$	−364723.	+	2.53670e6i	−0.0832277	+	0.578861i	0.904946	+	0.425526i	$0.139911\pi$
$79$	−364723.	+	2.53670e6i	−0.0832277	+	0.578861i	−0.988174	+	0.153336i	$0.950998\pi$
$80$	−174791.	+	382740.i	−0.0381685	+	0.0835773i
$81$	220769.	−	483416.i	0.0461572	−	0.101070i
$82$	−103579.	+	720405.i	−0.0207454	+	0.144287i
$83$	−4.78436e6	+	3.07472e6i	−0.918440	+	0.590246i	−0.912205	−	0.409735i	$-0.865621\pi$
$83$	−4.78436e6	+	3.07472e6i	−0.918440	+	0.590246i	−0.00623566	+	0.999981i	$0.501985\pi$
$84$	−1.17091e6	−	343810.i	−0.215549	−	0.0632909i
$85$	107777.	+	749605.i	0.0190353	+	0.132393i
$86$	4.09661e6	+	4.72774e6i	0.694512	+	0.801510i
$87$	3.80711e6	+	2.44668e6i	0.619838	+	0.398346i
$88$	−8.16556e6	+	9.42356e6i	−1.27731	+	1.47410i
$89$	8.39310e6	−	2.46444e6i	1.26199	−	0.370555i	0.418757	−	0.908098i	$-0.362466\pi$
$89$	8.39310e6	−	2.46444e6i	1.26199	−	0.370555i	0.843236	+	0.537543i	$0.180648\pi$
$90$	−138778.	−	303880.i	−0.0200664	−	0.0439394i
$91$	600387.			0.0835192
$92$	−1.99335e6	+	1.83103e6i	−0.266886	+	0.245153i
$93$	3.15375e6			0.406572
$94$	−5.02138e6	−	1.09953e7i	−0.623556	−	1.36540i
$95$	689548.	−	202470.i	0.0825148	−	0.0242285i
$96$	2.24050e6	−	2.58568e6i	0.258462	−	0.298281i
$97$	−9.47656e6	−	6.09021e6i	−1.05426	−	0.677534i	−0.105790	−	0.994389i	$-0.533737\pi$
$97$	−9.47656e6	−	6.09021e6i	−1.05426	−	0.677534i	−0.948474	+	0.316854i	$0.897373\pi$
$98$	744681.	+	859407.i	0.0799243	+	0.0922376i
$99$	−821147.	−	5.71120e6i	−0.0850546	−	0.591568i
$100$	−3.36261e6	−	987351.i	−0.336261	−	0.0987351i
$101$	4.75091e6	−	3.05322e6i	0.458830	−	0.294872i	−0.290734	−	0.956804i	$-0.593899\pi$
$101$	4.75091e6	−	3.05322e6i	0.458830	−	0.294872i	0.749564	+	0.661932i	$0.230263\pi$
$102$	−518255.	+	3.60454e6i	−0.0483552	+	0.336318i
$103$	−2.18460e6	+	4.78360e6i	−0.196989	+	0.431345i	−0.982189	−	0.187897i	$-0.939833\pi$
$103$	−2.18460e6	+	4.78360e6i	−0.196989	+	0.431345i	0.785200	+	0.619242i	$0.212560\pi$
$104$	−403254.	+	883003.i	−0.0351530	+	0.0769743i
$105$	189920.	−	1.32092e6i	0.0160106	−	0.111356i
$106$	−7.59285e6	+	4.87963e6i	−0.619205	+	0.397939i
$107$	−4.92169e6	−	1.44514e6i	−0.388393	−	0.114042i	0.0817055	−	0.996657i	$-0.473963\pi$
$107$	−4.92169e6	−	1.44514e6i	−0.388393	−	0.114042i	−0.470098	+	0.882614i	$0.655781\pi$
$108$	129936.	+	903727.i	0.00992539	+	0.0690326i
$109$	1.27480e7	+	1.47120e7i	0.942867	+	1.08813i	0.995983	+	0.0895378i	$0.0285390\pi$
$109$	1.27480e7	+	1.47120e7i	0.942867	+	1.08813i	−0.0531168	+	0.998588i	$0.516916\pi$
$110$	−3.05126e6	−	1.96093e6i	−0.218577	−	0.140471i
$111$	8.79460e6	−	1.01495e7i	0.610359	−	0.704392i
$112$	−7.75498e6	+	2.27707e6i	−0.521576	+	0.153148i
$113$	−5.20812e6	−	1.14042e7i	−0.339552	−	0.743516i	0.660421	−	0.750896i	$-0.270378\pi$
$113$	−5.20812e6	−	1.14042e7i	−0.339552	−	0.743516i	−0.999973	+	0.00738031i	$0.997651\pi$
$114$	3.45573e6			0.218461
$115$	−2.29216e6	−	1.87268e6i	−0.140541	−	0.114821i
$116$	−7.77489e6			−0.462478
$117$	−186600.	−	408598.i	−0.0107711	−	0.0235855i
$118$	−1.38010e7	+	4.05234e6i	−0.773257	+	0.227049i
$119$	−9.52633e6	+	1.09940e7i	−0.518217	+	0.598054i
$120$	1.81515e6	+	1.16653e6i	0.0958910	+	0.0616254i
$121$	−2.82624e7	−	3.26165e7i	−1.45031	−	1.67374i
$122$	2.07475e6	+	1.44302e7i	0.103444	+	0.719470i
$123$	2.08710e6	+	612829.i	0.101129	+	0.0296942i
$124$	−4.55806e6	+	2.92928e6i	−0.214686	+	0.137970i
$125$	1.10940e6	−	7.71602e6i	0.0508044	−	0.353353i
$126$	2.66575e6	−	5.83719e6i	0.118720	−	0.259960i
$127$	1.15993e7	−	2.53988e7i	0.502478	−	1.10027i	−0.473178	−	0.880967i	$-0.656893\pi$
$127$	1.15993e7	−	2.53988e7i	0.502478	−	1.10027i	0.975656	−	0.219306i	$-0.0703794\pi$
$128$	528548.	−	3.67613e6i	0.0222766	−	0.154937i
$129$	1.57284e7	−	1.01080e7i	0.645091	−	0.414574i
$130$	−270928.	−	79551.7i	−0.0108156	−	0.00317576i
$131$	3.00491e6	+	2.08996e7i	0.116784	+	0.812248i	0.961060	+	0.276340i	$0.0891216\pi$
$131$	3.00491e6	+	2.08996e7i	0.116784	+	0.812248i	−0.844276	+	0.535908i	$0.819969\pi$
$132$	6.49150e6	+	7.49159e6i	0.245661	+	0.283508i
$133$	1.16132e7	+	7.46333e6i	0.428026	+	0.275075i
$134$	−8.37149e6	+	9.66122e6i	−0.300563	+	0.346869i
$135$	−957990.	+	281291.i	−0.0335114	+	0.00983984i
$136$	−9.77067e6	−	2.13948e7i	−0.333072	−	0.729326i
$137$	5.02281e7			1.66888			0.834440	−	0.551099i	$-0.185791\pi$
$137$	5.02281e7			1.66888			0.834440	+	0.551099i	$0.185791\pi$
$138$	−8.03860e6	−	1.17455e7i	−0.260378	−	0.380446i
$139$	−9.91039e6			−0.312996			−0.156498	−	0.987678i	$-0.550021\pi$
$139$	−9.91039e6			−0.312996			−0.156498	+	0.987678i	$0.550021\pi$
$140$	952419.	+	2.08551e6i	0.0293346	+	0.0642338i
$141$	−3.46629e7	+	1.01779e7i	−1.04135	+	0.305769i
$142$	−2.75695e7	+	3.18169e7i	−0.808016	+	0.932500i
$143$	−4.10273e6	−	2.63666e6i	−0.117327	−	0.0754013i
$144$	3.95992e6	+	4.56999e6i	0.110514	+	0.127540i
$145$	−1.20999e6	−	8.41569e6i	−0.0329606	−	0.229246i
$146$	−2.73062e7	−	8.01782e6i	−0.726149	−	0.213217i
$147$	2.85911e6	−	1.83744e6i	0.0742368	−	0.0477091i
$148$	−3.28354e6	+	2.28375e7i	−0.0832582	+	0.579073i
$149$	804780.	−	1.76222e6i	0.0199308	−	0.0436424i	−0.899405	−	0.437117i	$-0.856000\pi$
$149$	804780.	−	1.76222e6i	0.0199308	−	0.0436424i	0.919336	+	0.393474i	$0.128727\pi$
$150$	7.65549e6	−	1.67632e7i	0.185205	−	0.405543i
$151$	−2.84557e6	+	1.97913e7i	−0.0672588	+	0.467796i	0.928160	+	0.372182i	$0.121390\pi$
$151$	−2.84557e6	+	1.97913e7i	−0.0672588	+	0.467796i	−0.995419	+	0.0956134i	$0.969519\pi$
$152$	−1.87765e7	+	1.20670e7i	−0.433674	+	0.278705i
$153$	1.04428e7	+	3.06629e6i	0.235721	+	0.0692138i
$154$	−9.91526e6	−	6.89621e7i	−0.218767	−	1.52156i
$155$	−3.88008e6	−	4.47785e6i	−0.0836911	−	0.0965847i
$156$	649206.	+	417219.i	0.0136914	+	0.00879890i
$157$	−4.27834e7	+	4.93746e7i	−0.882320	+	1.01825i	0.117363	+	0.993089i	$0.462556\pi$
$157$	−4.27834e7	+	4.93746e7i	−0.882320	+	1.01825i	−0.999683	+	0.0251628i	$0.991990\pi$
$158$	2.22145e7	−	6.52276e6i	0.448060	−	0.131562i
$159$	1.12058e7	+	2.45372e7i	0.221081	+	0.484101i
$160$	−6.42778e6			−0.124063
$161$	−1.64751e6	−	5.68321e7i	−0.0311127	−	1.07326i
$162$	−4.80106e6			−0.0887226
$163$	2.65762e7	+	5.81937e7i	0.480657	+	1.05249i	0.982282	+	0.187407i	$0.0600085\pi$
$163$	2.65762e7	+	5.81937e7i	0.480657	+	1.05249i	−0.501625	+	0.865085i	$0.667264\pi$
$164$	−3.58566e6	+	1.05285e6i	−0.0634769	+	0.0186385i
$165$	−7.09878e6	+	8.19243e6i	−0.123024	+	0.141977i
$166$	4.32221e7	+	2.77772e7i	0.733378	+	0.471313i
$167$	1.05559e7	+	1.21822e7i	0.175383	+	0.202403i	0.836635	−	0.547761i	$-0.184520\pi$
$167$	1.05559e7	+	1.21822e7i	0.175383	+	0.202403i	−0.661251	+	0.750164i	$0.729974\pi$
$168$	5.89843e6	+	4.10245e7i	0.0959741	+	0.667515i
$169$	5.98425e7	+	1.75713e7i	0.953687	+	0.280028i
$170$	5.75552e6	−	3.69885e6i	0.0898490	−	0.0577424i
$171$	1.46985e6	−	1.02230e7i	0.0224795	−	0.156348i
$172$	−1.33434e7	+	2.92179e7i	−0.199947	+	0.437824i
$173$	1.68898e7	−	3.69835e7i	0.248007	−	0.543059i	−0.744157	−	0.668005i	$-0.767149\pi$
$173$	1.68898e7	−	3.69835e7i	0.248007	−	0.543059i	0.992164	+	0.124946i	$0.0398758\pi$
$174$	5.81836e6	−	4.04676e7i	0.0837294	−	0.582351i
$175$	6.19300e7	−	3.98000e7i	0.873510	−	0.561371i
$176$	6.29934e7	+	1.84965e7i	0.870965	+	0.255738i
$177$	6.11789e6	+	4.25509e7i	0.0829268	+	0.576769i
$178$	−5.17501e7	−	5.97228e7i	−0.687766	−	0.793725i
$179$	−5.55624e6	−	3.57078e6i	−0.0724095	−	0.0465347i	0.503935	−	0.863741i	$-0.331885\pi$
$179$	−5.55624e6	−	3.57078e6i	−0.0724095	−	0.0465347i	−0.576345	+	0.817207i	$0.695521\pi$
$180$	1.12329e6	−	1.29635e6i	0.0143562	−	0.0165679i
$181$	−1.11687e8	+	3.27942e7i	−1.40000	+	0.411076i	−0.892683	−	0.450684i	$-0.851180\pi$
$181$	−1.11687e8	+	3.27942e7i	−1.40000	+	0.411076i	−0.507315	+	0.861761i	$0.669362\pi$
$182$	−2.25318e6	−	4.93377e6i	−0.0277042	−	0.0606637i
$183$	4.35710e7			0.525556
$184$	8.46909e7	+	3.57486e7i	1.00225	+	0.423055i
$185$	−2.52308e7			−0.292975
$186$	−1.18356e7	−	2.59164e7i	−0.134864	−	0.295311i
$187$	1.13379e8	−	3.32911e7i	1.26791	−	0.372291i
$188$	4.06441e7	−	4.69058e7i	0.446113	−	0.514842i
$189$	−1.61342e7	−	1.03688e7i	−0.173832	−	0.111715i
$190$	−4.25161e6	−	4.90662e6i	−0.0449693	−	0.0518973i
$191$	9.62933e6	+	6.69735e7i	0.0999953	+	0.695482i	0.976724	+	0.214498i	$0.0688115\pi$
$191$	9.62933e6	+	6.69735e7i	0.0999953	+	0.695482i	−0.876729	+	0.480984i	$0.840279\pi$
$192$	−5.71624e7	−	1.67844e7i	−0.582849	−	0.171140i
$193$	1.15642e8	−	7.43188e7i	1.15789	−	0.744129i	0.186693	−	0.982418i	$-0.440223\pi$
$193$	1.15642e8	−	7.43188e7i	1.15789	−	0.744129i	0.971194	+	0.238289i	$0.0765867\pi$
$194$	−1.44829e7	+	1.00731e8i	−0.142413	+	0.990504i
$195$	−350571.	+	767644.i	−0.00338575	+	0.00741377i
$196$	−2.42555e6	+	5.31122e6i	−0.0230099	+	0.0503846i
$197$	1.26053e7	−	8.76719e7i	0.117469	−	0.817013i	−0.842858	−	0.538136i	$-0.819129\pi$
$197$	1.26053e7	−	8.76719e7i	0.117469	−	0.817013i	0.960327	−	0.278877i	$-0.0899621\pi$
$198$	−4.38510e7	+	2.81813e7i	−0.401468	+	0.258008i
$199$	1.00013e8	+	2.93666e7i	0.899648	+	0.264160i	0.698677	−	0.715437i	$-0.253772\pi$
$199$	1.00013e8	+	2.93666e7i	0.899648	+	0.264160i	0.200971	+	0.979597i	$0.435590\pi$
$200$	1.69391e7	+	1.17814e8i	0.149722	+	1.04134i
$201$	2.50199e7	+	2.88745e7i	0.217320	+	0.250800i
$202$	−4.29199e7	−	2.75829e7i	−0.366377	−	0.235456i
$203$	1.06950e8	−	1.23427e8i	0.897318	−	1.03556i
$204$	−1.79408e7	+	5.26791e6i	−0.147958	+	0.0434443i
$205$	−1.69765e6	−	3.71734e6i	−0.0137629	−	0.0301365i
$206$	4.75085e7			0.378648
$207$	−3.81654e7	+	1.87846e7i	−0.299071	+	0.147200i
$208$	5.11108e6			0.0393814
$209$	−4.65822e7	−	1.02001e8i	−0.352946	−	0.772844i
$210$	−1.15676e7	+	3.39656e6i	−0.0861938	+	0.0253088i
$211$	3.81717e7	−	4.40525e7i	0.279739	−	0.322836i	−0.598441	−	0.801167i	$-0.704213\pi$
$211$	3.81717e7	−	4.40525e7i	0.279739	−	0.322836i	0.878179	+	0.478331i	$0.158758\pi$
$212$	−3.89863e7	−	2.50550e7i	−0.281020	−	0.180600i
$213$	8.23970e7	+	9.50912e7i	0.584229	+	0.674236i
$214$	6.59484e6	+	4.58681e7i	0.0459998	+	0.319936i
$215$	−3.37026e7	−	9.89598e6i	−0.231275	−	0.0679085i
$216$	2.60863e7	−	1.67646e7i	0.176126	−	0.113189i
$217$	1.61973e7	−	1.12655e8i	0.107605	−	0.748411i
$218$	7.30563e7	−	1.59971e8i	0.477595	−	1.04579i
$219$	−3.53332e7	+	7.73690e7i	−0.227315	+	0.497751i
$220$	2.65039e6	−	1.84339e7i	0.0167815	−	0.116718i
$221$	7.73887e6	−	4.97347e6i	0.0482286	−	0.0309946i
$222$	−1.16410e8	−	3.41811e7i	−0.714094	−	0.209677i
$223$	−6.13677e6	−	4.26822e7i	−0.0370572	−	0.257739i	0.962868	−	0.269973i	$-0.0870148\pi$
$223$	−6.13677e6	−	4.26822e7i	−0.0370572	−	0.257739i	−0.999925	+	0.0122341i	$0.996106\pi$
$224$	−8.08557e7	−	9.33124e7i	−0.480665	−	0.554717i
$225$	−4.63340e7	−	2.97771e7i	−0.271182	−	0.174278i
$226$	−7.41702e7	+	8.55970e7i	−0.427415	+	0.493263i
$227$	−2.78337e8	+	8.17271e7i	−1.57936	+	0.463741i	−0.949707	−	0.313139i	$-0.898619\pi$
$227$	−2.78337e8	+	8.17271e7i	−1.57936	+	0.463741i	−0.629649	+	0.776880i	$0.716801\pi$
$228$	7.37106e6	+	1.61404e7i	0.0411868	+	0.0901865i
$229$	−7.01955e7			−0.386265			−0.193132	−	0.981173i	$-0.561865\pi$
$229$	−7.01955e7			−0.386265			−0.193132	+	0.981173i	$0.561865\pi$
$230$	−6.78684e6	+	2.58641e7i	−0.0367807	+	0.140168i
$231$	−2.08226e8			−1.11146
$232$	1.09694e8	+	2.40195e8i	0.576731	+	1.26286i
$233$	−2.53165e8	+	7.43359e7i	−1.31117	+	0.384993i	−0.861297	−	0.508102i	$-0.830347\pi$
$233$	−2.53165e8	+	7.43359e7i	−1.31117	+	0.384993i	−0.449868	+	0.893095i	$0.648529\pi$
$234$	−2.65742e6	+	3.06683e6i	−0.0135583	+	0.0156471i
$235$	5.70971e7	+	3.66941e7i	0.286996	+	0.184441i
$236$	−4.83644e7	−	5.58155e7i	−0.239516	−	0.276416i
$237$	−9.84751e6	−	6.84910e7i	−0.0480515	−	0.334206i
$238$	1.26096e8	+	3.70250e7i	0.606291	+	0.178023i
$239$	−2.49415e8	+	1.60289e8i	−1.18176	+	0.759473i	−0.975710	−	0.219068i	$-0.929698\pi$
$239$	−2.49415e8	+	1.60289e8i	−1.18176	+	0.759473i	−0.206053	+	0.978541i	$0.566062\pi$
$240$	1.61678e6	−	1.12450e7i	0.00754940	−	0.0525072i
$241$	1.32635e8	−	2.90430e8i	0.610378	−	1.33654i	−0.311937	−	0.950103i	$-0.600978\pi$
$241$	1.32635e8	−	2.90430e8i	0.610378	−	1.33654i	0.922315	−	0.386439i	$-0.126295\pi$
$242$	−1.61966e8	+	3.54656e8i	−0.734632	+	1.60862i
$243$	−2.04206e6	+	1.42029e7i	−0.00912950	+	0.0634971i
$244$	−6.29723e7	+	4.04699e7i	−0.277514	+	0.178348i
$245$	−6.12645e6	−	1.79889e6i	−0.0266151	−	0.00781489i
$246$	−2.79662e6	−	1.94509e7i	−0.0119774	−	0.0833044i
$247$	−5.71672e6	−	6.59744e6i	−0.0241383	−	0.0278571i
$248$	1.54805e8	+	9.94870e7i	0.644471	+	0.414176i
$249$	1.00556e8	−	1.16048e8i	0.412774	−	0.476367i
$250$	−6.75709e7	+	1.98406e7i	−0.273508	+	0.0803092i
$251$	5.79626e7	+	1.26920e8i	0.231361	+	0.506610i	0.989332	−	0.145679i	$-0.0465365\pi$
$251$	5.79626e7	+	1.26920e8i	0.231361	+	0.506610i	−0.757971	+	0.652288i	$0.773809\pi$
$252$	3.29492e7			0.129701
$253$	−2.38326e8	+	3.95596e8i	−0.925230	+	1.53578i
$254$	−2.52249e8			−0.965854
$255$	−8.49419e6	−	1.85997e7i	−0.0320798	−	0.0702449i
$256$	2.38799e8	−	7.01178e7i	0.889597	−	0.261209i
$257$	2.99942e8	−	3.46151e8i	1.10223	−	1.27204i	0.142902	−	0.989737i	$-0.454357\pi$
$257$	2.99942e8	−	3.46151e8i	1.10223	−	1.27204i	0.959326	−	0.282302i	$-0.0910979\pi$
$258$	−1.42091e8	−	9.13163e7i	−0.515107	−	0.331039i
$259$	−3.17381e8	−	3.66277e8i	−1.13509	−	1.30997i
$260$	−206334.	−	1.43508e6i	−0.000728053	−	0.00506372i
$261$	−1.17240e8	−	3.44246e7i	−0.408162	−	0.119847i
$262$	1.60469e8	−	1.03127e8i	0.551233	−	0.354256i
$263$	−2.86787e6	+	1.99464e7i	−0.00972106	+	0.0676115i	−0.994105	−	0.108426i	$-0.965419\pi$
$263$	−2.86787e6	+	1.99464e7i	−0.00972106	+	0.0676115i	0.984383	+	0.176038i	$0.0563280\pi$
$264$	1.39857e8	−	3.06243e8i	0.467810	−	1.02436i
$265$	2.10526e7	−	4.60988e7i	0.0694937	−	0.152170i
$266$	1.77482e7	−	1.23442e8i	0.0578189	−	0.402139i
$267$	−1.98688e8	+	1.27689e8i	−0.638825	+	0.410548i
$268$	−6.29801e7	−	1.84926e7i	−0.199863	−	0.0586850i
$269$	4.72277e7	+	3.28476e8i	0.147933	+	1.02889i	0.919597	+	0.392863i	$0.128515\pi$
$269$	4.72277e7	+	3.28476e8i	0.147933	+	1.02889i	−0.771664	+	0.636030i	$0.780575\pi$
$270$	5.90677e6	+	6.81677e6i	0.0182632	+	0.0210768i
$271$	3.94298e8	+	2.53400e8i	1.20346	+	0.773417i	0.979552	−	0.201194i	$-0.0644820\pi$
$271$	3.94298e8	+	2.53400e8i	1.20346	+	0.773417i	0.223908	+	0.974610i	$0.428118\pi$
$272$	−8.10974e7	+	9.35914e7i	−0.244352	+	0.281997i
$273$	−1.55538e7	+	4.56701e6i	−0.0462666	+	0.0135851i
$274$	−1.88500e8	−	4.12757e8i	−0.553584	−	1.21218i
$275$	−5.97983e8			−1.73390
$276$	3.77121e7	−	6.25981e7i	0.107969	−	0.179217i
$277$	3.97926e8			1.12492			0.562462	−	0.826823i	$-0.309854\pi$
$277$	3.97926e8			1.12492			0.562462	+	0.826823i	$0.309854\pi$
$278$	3.71924e7	+	8.14401e7i	0.103824	+	0.227343i
$279$	−8.17020e7	+	2.39899e7i	−0.225226	+	0.0661323i
$280$	5.09917e7	−	5.88475e7i	0.138818	−	0.160205i
$281$	1.48176e8	+	9.52269e7i	0.398387	+	0.256028i	0.724460	−	0.689317i	$-0.242089\pi$
$281$	1.48176e8	+	9.52269e7i	0.398387	+	0.256028i	−0.326073	+	0.945345i	$0.605725\pi$
$282$	2.13724e8	+	2.46651e8i	0.567521	+	0.654954i
$283$	5.50799e7	+	3.83089e8i	0.144458	+	1.00473i	0.925094	+	0.379739i	$0.123986\pi$
$283$	5.50799e7	+	3.83089e8i	0.144458	+	1.00473i	−0.780636	+	0.624986i	$0.785105\pi$
$284$	−2.07410e8	−	6.09011e7i	−0.537298	−	0.157765i
$285$	−1.63235e7	+	1.04905e7i	−0.0417692	+	0.0268434i
$286$	−6.27015e6	+	4.36098e7i	−0.0158488	+	0.110231i
$287$	3.26099e7	−	7.14057e7i	0.0814259	−	0.178298i
$288$	−3.83745e7	+	8.40284e7i	−0.0946605	+	0.207278i
$289$	2.66763e7	−	1.85538e8i	0.0650105	−	0.452158i
$290$	−6.46162e7	+	4.15263e7i	−0.155578	+	0.0999839i
$291$	2.91829e8	+	8.56889e7i	0.694231	+	0.203844i
$292$	−2.07959e7	−	1.44638e8i	−0.0488806	−	0.339972i
$293$	6.33233e7	+	7.30790e7i	0.147071	+	0.169729i	0.824505	−	0.565854i	$-0.191454\pi$
$293$	6.33233e7	+	7.30790e7i	0.147071	+	0.169729i	−0.677434	+	0.735583i	$0.736908\pi$
$294$	−2.58293e7	−	1.65995e7i	−0.0592784	−	0.0380959i
$295$	5.28889e7	−	6.10370e7i	0.119946	−	0.138426i
$296$	7.51864e8	−	2.20767e8i	1.68507	−	0.494781i
$297$	6.47168e7	+	1.41710e8i	0.143341	+	0.313872i
$298$	−1.75016e7			−0.0383107
$299$	−9.12559e6	+	3.47769e7i	−0.0197429	+	0.0752387i
$300$	9.46234e7			0.202336
$301$	−2.80288e8	−	6.13746e8i	−0.592410	−	1.29720i
$302$	1.73317e8	−	5.08906e7i	0.362091	−	0.106320i
$303$	−9.98533e7	+	1.15237e8i	−0.206212	+	0.237981i
$304$	9.88625e7	+	6.35351e7i	0.201825	+	0.129705i
$305$	−5.36056e7	−	6.18642e7i	−0.108183	−	0.124850i
$306$	−1.39929e7	−	9.73227e7i	−0.0279179	−	0.194173i
$307$	4.93768e8	+	1.44983e8i	0.973955	+	0.285979i	0.729727	−	0.683739i	$-0.239647\pi$
$307$	4.93768e8	+	1.44983e8i	0.973955	+	0.285979i	0.244228	+	0.969718i	$0.421465\pi$
$308$	3.00946e8	−	1.93406e8i	0.586895	−	0.377175i
$309$	2.02071e7	−	1.40543e8i	0.0389627	−	0.270991i
$310$	−2.22359e7	+	4.86899e7i	−0.0423925	+	0.0928267i
$311$	1.01004e8	−	2.21167e8i	0.190404	−	0.416926i	−0.790221	−	0.612822i	$-0.790034\pi$
$311$	1.01004e8	−	2.21167e8i	0.190404	−	0.416926i	0.980625	+	0.195896i	$0.0627616\pi$
$312$	3.73001e6	−	2.59428e7i	0.00695296	−	0.0483589i
$313$	5.25236e8	−	3.37549e8i	0.968166	−	0.622202i	0.0419194	−	0.999121i	$-0.486653\pi$
$313$	5.25236e8	−	3.37549e8i	0.968166	−	0.622202i	0.926246	+	0.376919i	$0.123016\pi$
$314$	5.66304e8	+	1.66282e8i	1.03228	+	0.303104i
$315$	5.12784e6	+	3.56649e7i	0.00924373	+	0.0642916i
$316$	7.78486e7	+	8.98421e7i	0.138786	+	0.160168i
$317$	−9.84477e7	−	6.32685e7i	−0.173579	−	0.111553i	0.450966	−	0.892541i	$-0.351079\pi$
$317$	−9.84477e7	−	6.32685e7i	−0.173579	−	0.111553i	−0.624546	+	0.780988i	$0.714716\pi$
$318$	1.59584e8	−	1.84170e8i	0.278289	−	0.321162i
$319$	−1.27289e9	+	3.73754e8i	−2.19545	+	0.644641i
$320$	4.64959e7	+	1.01812e8i	0.0793213	+	0.173689i
$321$	1.38496e8			0.233705
$322$	−4.60843e8	+	2.26822e8i	−0.769233	+	0.378608i
$323$	2.11516e8			0.349248
$324$	−1.02406e7	−	2.24238e7i	−0.0167270	−	0.0366271i
$325$	−4.46673e7	+	1.31155e7i	−0.0721769	+	0.0211930i
$326$	3.78478e8	−	4.36787e8i	0.605033	−	0.698245i
$327$	−4.42165e8	−	2.84162e8i	−0.699307	−	0.449417i
$328$	8.31153e7	+	9.59202e7i	0.130054	+	0.150090i
$329$	1.85540e8	+	1.29046e9i	0.287245	+	1.99783i
$330$	9.39633e7	+	2.75901e7i	0.143933	+	0.0422625i
$331$	3.47214e8	−	2.23141e8i	0.526258	−	0.338206i	−0.250385	−	0.968146i	$-0.580557\pi$
$331$	3.47214e8	−	2.23141e8i	0.526258	−	0.338206i	0.776643	+	0.629941i	$0.216921\pi$
$332$	−3.75437e7	+	2.61122e8i	−0.0563058	+	0.391616i
$333$	−1.50631e8	+	3.29835e8i	−0.223542	+	0.489488i
$334$	6.04938e7	−	1.32463e8i	0.0888378	−	0.194528i
$335$	1.02153e7	−	7.10488e7i	0.0148455	−	0.103252i
$336$	1.83582e8	−	1.17981e8i	0.264023	−	0.169677i
$337$	−2.86011e8	−	8.39805e7i	−0.407079	−	0.119529i	0.0717812	−	0.997420i	$-0.477132\pi$
$337$	−2.86011e8	−	8.39805e7i	−0.407079	−	0.119529i	−0.478860	+	0.877891i	$0.658950\pi$
$338$	−8.01862e7	−	5.57707e8i	−0.112951	−	0.785593i
$339$	2.21672e8	+	2.55824e8i	0.309039	+	0.356650i
$340$	2.95523e7	+	1.89921e7i	0.0407770	+	0.0262058i
$341$	−6.05419e8	+	6.98690e8i	−0.826829	+	0.954211i
$342$	−8.95253e7	+	2.62870e7i	−0.121019	+	0.0355345i
$343$	2.82397e8	+	6.18363e8i	0.377859	+	0.827397i
$344$	1.09091e9			1.44489
$345$	7.36265e7	+	3.10783e7i	0.0965311	+	0.0407465i
$346$	−3.67303e8			−0.476714
$347$	−2.89694e8	−	6.34341e8i	−0.372209	−	0.815023i	−0.999348	−	0.0361158i	$-0.988501\pi$
$347$	−2.89694e8	−	6.34341e8i	−0.372209	−	0.815023i	0.627139	−	0.778907i	$-0.284226\pi$
$348$	2.01419e8	−	5.91419e7i	0.256196	−	0.0752259i
$349$	−5.98752e8	+	6.90997e8i	−0.753977	+	0.870136i	−0.994948	−	0.100396i	$-0.967989\pi$
$349$	−5.98752e8	+	6.90997e8i	−0.753977	+	0.870136i	0.240970	+	0.970532i	$0.422534\pi$
$350$	−5.59478e8	−	3.59554e8i	−0.697501	−	0.448256i
$351$	7.94224e6	+	9.16583e6i	0.00980320	+	0.0113135i
$352$	1.42734e8	+	9.92735e8i	0.174432	+	1.21320i
$353$	−1.22623e9	−	3.60053e8i	−1.48375	−	0.435667i	−0.563206	−	0.826317i	$-0.690432\pi$
$353$	−1.22623e9	−	3.60053e8i	−1.48375	−	0.435667i	−0.920539	+	0.390650i	$0.872250\pi$
$354$	3.26708e8	−	2.09963e8i	0.391425	−	0.251554i
$355$	3.36416e7	−	2.33982e8i	0.0399096	−	0.277577i
$356$	1.68559e8	−	3.69093e8i	0.198005	−	0.433571i
$357$	1.63163e8	−	3.57278e8i	0.189795	−	0.415592i
$358$	−8.49153e6	+	5.90599e7i	−0.00978127	+	0.0680302i
$359$	−6.43933e7	+	4.13831e7i	−0.0734531	+	0.0472055i	−0.576852	−	0.816849i	$-0.695719\pi$
$359$	−6.43933e7	+	4.13831e7i	−0.0734531	+	0.0472055i	0.503399	+	0.864054i	$0.332083\pi$
$360$	−5.58973e7	−	1.64129e7i	−0.0631440	−	0.0185408i
$361$	9.86458e7	+	6.86097e8i	0.110358	+	0.767556i
$362$	6.88638e8	+	7.94731e8i	0.762977	+	0.880522i
$363$	9.80281e8	+	6.29988e8i	1.07567	+	0.691289i
$364$	1.82377e7	−	2.10474e7i	0.0198205	−	0.0228741i
$365$	1.53323e8	−	4.50197e7i	0.165037	−	0.0484593i
$366$	−1.63516e8	−	3.58051e8i	−0.174332	−	0.381734i
$367$	1.01495e8			0.107180			0.0535901	−	0.998563i	$-0.482934\pi$
$367$	1.01495e8			0.107180			0.0535901	+	0.998563i	$0.482934\pi$
$368$	−1.40252e7	−	4.83810e8i	−0.0146704	−	0.506067i
$369$	−5.87308e7			−0.0608518
$370$	9.46880e7	+	2.07338e8i	0.0971827	+	0.212800i
$371$	9.34043e8	−	2.74260e8i	0.949638	−	0.278839i
$372$	9.58000e7	−	1.10559e8i	0.0964862	−	0.111351i
$373$	−2.26932e8	−	1.45840e8i	−0.226420	−	0.145511i	0.422513	−	0.906357i	$-0.361148\pi$
$373$	−2.26932e8	−	1.45840e8i	−0.226420	−	0.145511i	−0.648933	+	0.760846i	$0.724784\pi$
$374$	−6.99072e8	−	8.06772e8i	−0.690989	−	0.797444i
$375$	2.99537e7	+	2.08332e8i	0.0293319	+	0.204008i
$376$	−2.02253e9	−	5.93868e8i	−1.96217	−	0.576146i
$377$	−8.68829e7	+	5.58363e7i	−0.0835103	+	0.0536688i
$378$	−2.46577e7	+	1.71498e8i	−0.0234818	+	0.163319i
$379$	−3.13609e8	+	6.86708e8i	−0.295904	+	0.647940i	−0.997937	−	0.0642048i	$-0.979549\pi$
$379$	−3.13609e8	+	6.86708e8i	−0.295904	+	0.647940i	0.702032	+	0.712145i	$0.252276\pi$
$380$	1.38482e7	−	3.03234e7i	0.0129465	−	0.0283488i
$381$	−1.07291e8	+	7.46223e8i	−0.0993858	+	0.691243i
$382$	5.14227e8	−	3.30473e8i	0.471990	−	0.303330i
$383$	1.56837e9	+	4.60516e8i	1.42644	+	0.418841i	0.901678	−	0.432408i	$-0.142336\pi$
$383$	1.56837e9	+	4.60516e8i	1.42644	+	0.418841i	0.524763	+	0.851249i	$0.324154\pi$
$384$	1.42708e7	+	9.92555e7i	0.0128614	+	0.0894531i
$385$	2.56182e8	+	2.95650e8i	0.228790	+	0.264037i
$386$	−1.04472e9	−	6.71399e8i	−0.924577	−	0.594189i
$387$	−3.30575e8	+	3.81504e8i	−0.289923	+	0.334589i
$388$	−5.01366e8	+	1.47214e8i	−0.435756	+	0.127950i
$389$	−8.56829e8	−	1.87619e9i	−0.738024	−	1.61605i	−0.786778	−	0.617236i	$-0.788252\pi$
$389$	−8.56829e8	−	1.87619e9i	−0.738024	−	1.61605i	0.0487539	−	0.998811i	$-0.484475\pi$
$390$	7.62388e6			0.00650803
$391$	−4.92020e8	−	7.18907e8i	−0.416260	−	0.608211i
$392$	1.98305e8			0.166277
$393$	−2.36825e8	−	5.18574e8i	−0.196813	−	0.430960i
$394$	−7.67763e8	+	2.25436e8i	−0.632398	+	0.185689i
$395$	−8.51313e7	+	9.82468e7i	−0.0695024	+	0.0802100i
$396$	−2.25158e8	−	1.44700e8i	−0.182202	−	0.117094i
$397$	−1.32627e9	−	1.53060e9i	−1.06381	−	1.22771i	−0.972749	−	0.231861i	$-0.925518\pi$
$397$	−1.32627e9	−	1.53060e9i	−1.06381	−	1.22771i	−0.0910649	−	0.995845i	$-0.529027\pi$
$398$	−1.34013e8	−	9.32084e8i	−0.106551	−	0.741079i
$399$	−3.57626e8	−	1.05009e8i	−0.281854	−	0.0827598i
$400$	5.27208e8	−	3.38816e8i	0.411882	−	0.264700i
$401$	5.76305e7	−	4.00829e8i	0.0446320	−	0.310423i	−0.955261	−	0.295766i	$-0.904425\pi$
$401$	5.76305e7	−	4.00829e8i	0.0446320	−	0.310423i	0.999893	−	0.0146571i	$-0.00466566\pi$
$402$	1.43384e8	−	3.13967e8i	0.110080	−	0.241042i
$403$	−2.98984e7	+	6.54684e7i	−0.0227552	+	0.0498269i
$404$	3.72811e7	−	2.59296e8i	0.0281290	−	0.195642i
$405$	2.26783e7	−	1.45744e7i	0.0169636	−	0.0109018i
$406$	−1.41565e9	−	4.15674e8i	−1.04982	−	0.308256i
$407$	5.60269e8	+	3.89676e9i	0.411923	+	2.86499i
$408$	4.15867e8	+	4.79936e8i	0.303141	+	0.349843i
$409$	−1.00655e9	−	6.46870e8i	−0.727450	−	0.467504i	0.123771	−	0.992311i	$-0.460501\pi$
$409$	−1.00655e9	−	6.46870e8i	−0.727450	−	0.467504i	−0.851221	+	0.524807i	$0.824138\pi$
$410$	−2.41767e7	+	2.79014e7i	−0.0173242	+	0.0199932i
$411$	−1.30123e9	+	3.82074e8i	−0.924498	+	0.271457i
$412$	1.01335e8	+	2.21893e8i	0.0713872	+	0.156316i
$413$	1.55137e9			1.08366
$414$	2.97596e8	+	2.43134e8i	0.206122	+	0.168401i
$415$	−2.88486e8			−0.198133
$416$	3.24353e7	+	7.10234e7i	0.0220898	+	0.0483698i
$417$	2.56742e8	−	7.53862e7i	0.173388	−	0.0509115i
$418$	−6.63390e8	+	7.65593e8i	−0.444275	+	0.512721i
$419$	3.93162e8	+	2.52670e8i	0.261109	+	0.167805i	0.664645	−	0.747159i	$-0.268583\pi$
$419$	3.93162e8	+	2.52670e8i	0.261109	+	0.167805i	−0.403536	+	0.914964i	$0.632219\pi$
$420$	−4.05376e7	−	4.67829e7i	−0.0266984	−	0.0308116i
$421$	−7.97820e7	−	5.54896e8i	−0.0521096	−	0.362430i	−0.999147	−	0.0413055i	$-0.986848\pi$
$421$	−7.97820e7	−	5.54896e8i	−0.0521096	−	0.362430i	0.947037	−	0.321124i	$-0.104061\pi$
$422$	−5.05261e8	−	1.48358e8i	−0.327282	−	0.0960987i
$423$	8.20566e8	−	5.27346e8i	0.527135	−	0.338769i
$424$	−2.23996e8	+	1.55793e9i	−0.142712	+	0.992582i
$425$	4.68571e8	−	1.02603e9i	0.296084	−	0.648333i
$426$	4.72200e8	−	1.03397e9i	0.295933	−	0.648002i
$427$	2.23776e8	−	1.55639e9i	0.139096	−	0.967435i
$428$	−2.00165e8	+	1.28638e8i	−0.123406	+	0.0793080i
$429$	1.26343e8	+	3.70977e7i	0.0772594	+	0.0226854i
$430$	4.51600e7	+	3.14094e8i	0.0273914	+	0.190511i
$431$	3.11382e7	+	3.59354e7i	0.0187337	+	0.0216198i	0.765039	−	0.643984i	$-0.222720\pi$
$431$	3.11382e7	+	3.59354e7i	0.0187337	+	0.0216198i	−0.746305	+	0.665604i	$0.768174\pi$
$432$	−1.37350e8	−	8.82694e7i	−0.0819662	−	0.0526765i
$433$	9.88730e8	−	1.14106e9i	0.585289	−	0.675459i	−0.383444	−	0.923564i	$-0.625262\pi$
$433$	9.88730e8	−	1.14106e9i	0.585289	−	0.675459i	0.968733	+	0.248105i	$0.0798077\pi$
$434$	−9.86542e8	+	2.89675e8i	−0.579297	+	0.170097i
$435$	9.53627e7	+	2.08815e8i	0.0555477	+	0.121633i
$436$	9.02991e8			0.521772
$437$	−6.08821e8	+	5.59243e8i	−0.348983	+	0.320565i
$438$	7.68392e8			0.436942
$439$	−6.21536e8	−	1.36097e9i	−0.350623	−	0.767758i	−0.999974	−	0.00726823i	$-0.997686\pi$
$439$	−6.21536e8	−	1.36097e9i	−0.350623	−	0.767758i	0.649350	−	0.760489i	$-0.275041\pi$
$440$	−6.06886e8	+	1.78198e8i	−0.339643	+	0.0997281i
$441$	−6.00919e7	+	6.93498e7i	−0.0333642	+	0.0385044i
$442$	−6.99132e7	−	4.49305e7i	−0.0385107	−	0.0247493i
$443$	−9.10939e8	−	1.05128e9i	−0.497825	−	0.574520i	0.450115	−	0.892971i	$-0.351383\pi$
$443$	−9.10939e8	−	1.05128e9i	−0.497825	−	0.574520i	−0.947940	+	0.318450i	$0.896838\pi$
$444$	−8.86557e7	−	6.16614e8i	−0.0480691	−	0.334328i
$445$	4.25745e8	+	1.25010e8i	0.229029	+	0.0672489i
$446$	−3.27717e8	+	2.10611e8i	−0.174915	+	0.112411i
$447$	−7.44405e6	+	5.17745e7i	−0.00394215	+	0.0274182i
$448$	−8.93132e8	+	1.95569e9i	−0.469292	+	1.02761i
$449$	3.57235e8	−	7.82235e8i	0.186248	−	0.407826i	−0.793358	−	0.608756i	$-0.791669\pi$
$449$	3.57235e8	−	7.82235e8i	0.186248	−	0.407826i	0.979606	+	0.200930i	$0.0643963\pi$
$450$	−7.08117e7	+	4.92506e8i	−0.0366320	+	0.254781i
$451$	−5.36424e8	+	3.44739e8i	−0.275354	+	0.176959i
$452$	−5.57995e8	−	1.63842e8i	−0.284214	−	0.0834527i
$453$	−7.68303e7	−	5.34366e8i	−0.0388319	−	0.270082i
$454$	1.71617e9	+	1.98056e9i	0.860724	+	0.993329i
$455$	2.56204e7	+	1.64652e7i	0.0127511	+	0.00819461i
$456$	3.94640e8	−	4.55439e8i	0.194906	−	0.224933i
$457$	1.55357e9	−	4.56168e8i	0.761418	−	0.223573i	0.122103	−	0.992517i	$-0.461036\pi$
$457$	1.55357e9	−	4.56168e8i	0.761418	−	0.223573i	0.639315	+	0.768945i	$0.279218\pi$
$458$	2.63435e8	+	5.76841e8i	0.128128	+	0.280561i
$459$	−2.93859e8			−0.141839
$460$	−1.35277e8	+	2.34693e7i	−0.0647996	+	0.0112421i
$461$	9.58976e8			0.455884			0.227942	−	0.973675i	$-0.426800\pi$
$461$	9.58976e8			0.455884			0.227942	+	0.973675i	$0.426800\pi$
$462$	7.81447e8	+	1.71113e9i	0.368683	+	0.807303i
$463$	1.89502e9	−	5.56428e8i	0.887319	−	0.260540i	0.193854	−	0.981030i	$-0.437901\pi$
$463$	1.89502e9	−	5.56428e8i	0.887319	−	0.260540i	0.693465	+	0.720490i	$0.256083\pi$
$464$	9.10466e8	−	1.05073e9i	0.423108	−	0.488292i
$465$	1.34580e8	+	8.64896e7i	0.0620721	+	0.0398913i
$466$	1.56096e9	+	1.80144e9i	0.714564	+	0.824651i
$467$	3.19321e8	+	2.22092e9i	0.145083	+	1.00908i	0.924121	+	0.382100i	$0.124799\pi$
$467$	3.19321e8	+	2.22092e9i	0.145083	+	1.00908i	−0.779037	+	0.626977i	$0.784292\pi$
$468$	−1.99922e7	−	5.87025e6i	−0.00901573	−	0.00264726i
$469$	1.15992e9	−	7.45435e8i	0.519186	−	0.333661i
$470$	8.72607e7	−	6.06912e8i	0.0387683	−	0.269639i
$471$	7.32777e8	−	1.60456e9i	0.323146	−	0.707591i
$472$	−1.04199e9	+	2.28164e9i	−0.456107	+	0.998735i
$473$	−7.79987e8	+	5.42493e9i	−0.338902	+	2.35711i
$474$	−5.25878e8	+	3.37961e8i	−0.226809	+	0.145761i
$475$	−1.02703e9	−	3.01563e8i	−0.439698	−	0.129107i
$476$	9.60320e7	+	6.67918e8i	0.0408124	+	0.283856i
$477$	−4.76950e8	−	5.50429e8i	−0.201214	−	0.232213i
$478$	2.25323e9	+	1.44806e9i	0.943641	+	0.606442i
$479$	−6.69581e8	+	7.72737e8i	−0.278374	+	0.321261i	−0.877669	−	0.479268i	$-0.840902\pi$
$479$	−6.69581e8	+	7.72737e8i	−0.278374	+	0.321261i	0.599295	+	0.800528i	$0.295448\pi$
$480$	1.66520e8	−	4.88947e7i	0.0687261	−	0.0201798i
$481$	1.27318e8	+	2.78787e8i	0.0521652	+	0.114226i
$482$	−2.88442e9			−1.17326
$483$	4.74990e8	+	1.45978e9i	0.191809	+	0.589484i
$484$	−2.00193e9			−0.802584
$485$	−2.37374e8	−	5.19777e8i	−0.0944795	−	0.206881i
$486$	1.24378e8	−	3.65206e7i	0.0491491	−	0.0144315i
$487$	1.88191e9	−	2.17184e9i	0.738324	−	0.852071i	−0.255059	−	0.966926i	$-0.582095\pi$
$487$	1.88191e9	−	2.17184e9i	0.738324	−	0.852071i	0.993382	+	0.114855i	$0.0366402\pi$
$488$	2.13872e9	+	1.37447e9i	0.833077	+	0.535386i
$489$	−1.13116e9	−	1.30542e9i	−0.437463	−	0.504860i
$490$	8.20917e6	+	5.70960e7i	0.00315219	+	0.0219240i
$491$	2.32787e8	+	6.83525e7i	0.0887512	+	0.0260597i	0.325807	−	0.945436i	$-0.394364\pi$
$491$	2.32787e8	+	6.83525e7i	0.0887512	+	0.0260597i	−0.237056	+	0.971496i	$0.576182\pi$
$492$	8.48825e7	−	5.45507e7i	0.0321322	−	0.0206501i
$493$	3.56126e8	−	2.47691e9i	0.133856	−	0.930991i
$494$	−3.27613e7	+	7.17373e7i	−0.0122269	+	0.0267732i
$495$	1.21585e8	−	2.66235e8i	0.0450570	−	0.0986612i
$496$	1.37887e8	−	9.59026e8i	0.0507385	−	0.352894i
$497$	3.81992e9	−	2.45491e9i	1.39575	−	0.896993i
$498$	−1.33102e9	−	3.90823e8i	−0.482927	−	0.141800i
$499$	5.17888e7	+	3.60199e8i	0.0186588	+	0.129775i	0.997022	−	0.0771213i	$-0.0245729\pi$
$499$	5.17888e7	+	3.60199e8i	0.0186588	+	0.129775i	−0.978363	+	0.206896i	$0.933664\pi$
$500$	−2.36796e8	−	2.73277e8i	−0.0847188	−	0.0977707i
$501$	−3.66132e8	−	2.35299e8i	−0.130078	−	0.0835963i
$502$	8.25461e8	−	9.52632e8i	0.291228	−	0.336095i
$503$	−2.83358e9	+	8.32015e8i	−0.992769	+	0.291503i	−0.737485	−	0.675363i	$-0.763987\pi$
$503$	−2.83358e9	+	8.32015e8i	−0.992769	+	0.291503i	−0.255283	+	0.966866i	$0.582169\pi$
$504$	−4.64871e8	−	1.01793e9i	−0.161743	−	0.354168i
$505$	2.86469e8			0.0989824
$506$	4.14527e9	+	4.73858e8i	1.42242	+	0.162600i
$507$	−1.68396e9			−0.573857
$508$	−5.38046e8	−	1.17816e9i	−0.182094	−	0.398731i
$509$	2.70807e9	−	7.95161e8i	0.910223	−	0.267265i	0.207088	−	0.978322i	$-0.433601\pi$
$509$	2.70807e9	−	7.95161e8i	0.910223	−	0.267265i	0.703135	+	0.711057i	$0.251783\pi$
$510$	−1.20968e8	+	1.39604e8i	−0.0403808	+	0.0466019i
$511$	2.58222e9	+	1.65949e9i	0.856091	+	0.550176i
$512$	−1.78370e9	−	2.05850e9i	−0.587322	−	0.677806i
$513$	3.96859e7	+	2.76022e8i	0.0129785	+	0.0902677i
$514$	−3.97019e9	−	1.16575e9i	−1.28956	−	0.378648i
$515$	−2.24411e8	+	1.44220e8i	−0.0723967	+	0.0465265i
$516$	1.23423e8	−	8.58428e8i	0.0395479	−	0.275062i
$517$	4.39931e9	−	9.63315e9i	1.40013	−	3.06585i
$518$	−1.81885e9	+	3.98272e9i	−0.574966	+	1.25900i
$519$	−1.56227e8	+	1.08658e9i	−0.0490536	+	0.341175i
$520$	−4.14239e7	+	2.66215e7i	−0.0129193	+	0.00830274i
$521$	−3.47484e9	−	1.02030e9i	−1.07647	−	0.316081i	−0.305005	−	0.952351i	$-0.598658\pi$
$521$	−3.47484e9	−	1.02030e9i	−1.07647	−	0.316081i	−0.771466	+	0.636270i	$0.780476\pi$
$522$	1.57096e8	+	1.09262e9i	0.0483412	+	0.336221i
$523$	4.04502e9	+	4.66821e9i	1.23642	+	1.42690i	0.867498	+	0.497441i	$0.165727\pi$
$523$	4.04502e9	+	4.66821e9i	1.23642	+	1.42690i	0.368920	+	0.929461i	$0.379728\pi$
$524$	8.23944e8	+	5.29517e8i	0.250172	+	0.160776i
$525$	−1.30163e9	+	1.50216e9i	−0.392581	+	0.453063i
$526$	1.74676e8	−	5.12894e7i	0.0523338	−	0.0153666i
$527$	−7.24426e8	−	1.58627e9i	−0.215604	−	0.472107i
$528$	−1.77263e9			−0.524081
$529$	3.31699e9	+	7.68389e8i	0.974202	+	0.225676i
$530$	−4.57832e8			−0.133580
$531$	−4.82167e8	−	1.05580e9i	−0.139755	−	0.306020i
$532$	6.14405e8	−	1.80406e8i	0.176915	−	0.0519468i
$533$	−3.25080e7	+	3.75162e7i	−0.00929918	+	0.0107318i
$534$	1.79495e9	+	1.15355e9i	0.510104	+	0.327824i
$535$	−1.70392e8	−	1.96643e8i	−0.0481073	−	0.0555188i
$536$	3.17261e8	+	2.20660e9i	0.0889897	+	0.618937i
$537$	1.71104e8	+	5.02406e7i	0.0476815	+	0.0140005i
$538$	2.52206e9	−	1.62083e9i	0.698260	−	0.448744i
$539$	−1.41786e8	+	9.86142e8i	−0.0390007	+	0.271256i
$540$	−1.92394e7	+	4.21283e7i	−0.00525790	+	0.0115132i
$541$	−5.83327e8	+	1.27731e9i	−0.158388	+	0.346821i	−0.972144	−	0.234386i	$-0.924692\pi$
$541$	−5.83327e8	+	1.27731e9i	−0.158388	+	0.346821i	0.813756	+	0.581207i	$0.197419\pi$
$542$	6.02600e8	−	4.19117e9i	0.162567	−	1.13068i
$543$	2.64394e9	−	1.69916e9i	0.708683	−	0.455443i
$544$	−1.81519e9	−	5.32989e8i	−0.483422	−	0.141946i
$545$	1.40531e8	+	9.77414e8i	0.0371864	+	0.258637i
$546$	9.59016e7	+	1.10676e8i	0.0252146	+	0.0290992i
$547$	8.00546e8	+	5.14480e8i	0.209137	+	0.134404i	0.641016	−	0.767527i	$-0.278513\pi$
$547$	8.00546e8	+	5.14480e8i	0.209137	+	0.134404i	−0.431879	+	0.901931i	$0.642149\pi$
$548$	1.52576e9	−	1.76082e9i	0.396053	−	0.457069i
$549$	−1.12876e9	+	3.31435e8i	−0.291139	+	0.0854860i
$550$	2.24415e9	+	4.91401e9i	0.575153	+	1.25941i
$551$	−2.37465e9			−0.604741
$552$	−2.46596e9	−	2.81891e8i	−0.624021	−	0.0713335i
$553$	−2.49713e9			−0.627919
$554$	−1.49337e9	−	3.27002e9i	−0.373149	−	0.817082i
$555$	6.53637e8	−	1.91925e8i	0.162297	−	0.0476548i
$556$	−3.01043e8	+	3.47423e8i	−0.0742792	+	0.0857228i
$557$	−3.62629e9	−	2.33047e9i	−0.889138	−	0.571414i	0.0144122	−	0.999896i	$-0.495412\pi$
$557$	−3.62629e9	−	2.33047e9i	−0.889138	−	0.571414i	−0.903550	+	0.428482i	$0.859049\pi$
$558$	5.03758e8	+	5.81367e8i	0.122744	+	0.141655i
$559$	6.07221e7	+	4.22332e8i	0.0147030	+	0.102262i
$560$	−3.93376e8	−	1.15506e8i	−0.0946564	−	0.0277936i
$561$	−2.68400e9	+	1.72490e9i	−0.641818	+	0.412472i
$562$	2.26455e8	−	1.57503e9i	0.0538153	−	0.374293i
$563$	−5.41067e7	+	1.18477e8i	−0.0127783	+	0.0279805i	−0.915914	−	0.401376i	$-0.868532\pi$
$563$	−5.41067e7	+	1.18477e8i	−0.0127783	+	0.0279805i	0.903135	+	0.429356i	$0.141259\pi$
$564$	−6.96136e8	+	1.52433e9i	−0.163387	+	0.357768i
$565$	9.05059e7	−	6.29482e8i	0.0211109	−	0.146830i
$566$	2.94138e9	−	1.89031e9i	0.681858	−	0.438204i
$567$	4.96850e8	+	1.45888e8i	0.114468	+	0.0336109i
$568$	1.04482e9	+	7.26690e9i	0.239234	+	1.66391i
$569$	−2.04877e9	−	2.36441e9i	−0.466231	−	0.538059i	0.473129	−	0.880993i	$-0.343125\pi$
$569$	−2.04877e9	−	2.36441e9i	−0.466231	−	0.538059i	−0.939359	+	0.342934i	$0.888579\pi$
$570$	1.47467e8	+	9.47713e7i	0.0333529	+	0.0214346i
$571$	2.03119e9	−	2.34412e9i	0.456588	−	0.526930i	−0.480045	−	0.877244i	$-0.659380\pi$
$571$	2.03119e9	−	2.34412e9i	0.456588	−	0.526930i	0.936632	+	0.350314i	$0.113925\pi$
$572$	−2.17059e8	+	6.37342e7i	−0.0484943	+	0.0142392i
$573$	−7.58913e8	−	1.66179e9i	−0.168520	−	0.369007i
$574$	−7.09167e8			−0.156515
$575$	1.36407e9	+	4.19218e9i	0.299227	+	0.919607i
$576$	1.60854e9			0.350714
$577$	1.57768e9	+	3.45463e9i	0.341903	+	0.748663i	0.999991	−	0.00427804i	$-0.00136175\pi$
$577$	1.57768e9	+	3.45463e9i	0.341903	+	0.748663i	−0.658088	+	0.752941i	$0.728634\pi$
$578$	−1.62480e9	+	4.77084e8i	−0.349987	+	0.102765i
$579$	−2.43054e9	+	2.80499e9i	−0.520388	+	0.600560i
$580$	−3.31779e8	−	2.13221e8i	−0.0706075	−	0.0453767i
$581$	−3.62890e9	−	4.18797e9i	−0.767642	−	0.885906i
$582$	−3.91038e8	−	2.71973e9i	−0.0822221	−	0.571868i
$583$	−7.58720e9	−	2.22780e9i	−1.58577	−	0.465625i
$584$	−4.17502e9	+	2.68312e9i	−0.867388	+	0.557436i
$585$	3.24271e6	−	2.25535e7i	0.000669673	−	0.00465768i
$586$	3.62893e8	−	7.94624e8i	0.0744966	−	0.163125i
$587$	−5.11269e8	+	1.11952e9i	−0.104332	+	0.228455i	−0.954597	−	0.297899i	$-0.903714\pi$
$587$	−5.11269e8	+	1.11952e9i	−0.104332	+	0.228455i	0.850266	+	0.526354i	$0.176441\pi$
$588$	2.24359e7	−	1.56045e8i	0.00455116	−	0.0316540i
$589$	−1.39215e9	+	8.94679e8i	−0.280725	+	0.180411i
$590$	−7.00066e8	−	2.05558e8i	−0.140332	−	0.0412052i
$591$	3.40344e8	+	2.36714e9i	0.0678206	+	0.471702i
$592$	−2.70186e9	−	3.11811e9i	−0.535225	−	0.617682i
$593$	1.67341e9	+	1.07543e9i	0.329541	+	0.211783i	0.694940	−	0.719068i	$-0.255431\pi$
$593$	1.67341e9	+	1.07543e9i	0.329541	+	0.211783i	−0.365399	+	0.930851i	$0.619067\pi$
$594$	9.21648e8	−	1.06364e9i	0.180432	−	0.208229i
$595$	−7.08021e8	+	2.07894e8i	−0.137796	+	0.0404606i
$596$	−3.73307e7	−	8.17429e7i	−0.00722278	−	0.0158157i
$597$	−2.81436e9			−0.541340
$598$	3.20031e8	−	5.55224e7i	0.0611981	−	0.0106173i
$599$	−4.23228e7			−0.00804600			−0.00402300	−	0.999992i	$-0.501281\pi$
$599$	−4.23228e7			−0.00804600			−0.00402300	+	0.999992i	$0.501281\pi$
$600$	−1.33501e9	−	2.92327e9i	−0.252322	−	0.552509i
$601$	6.85344e9	−	2.01235e9i	1.28780	−	0.378132i	0.435028	−	0.900417i	$-0.356738\pi$
$601$	6.85344e9	−	2.01235e9i	1.28780	−	0.378132i	0.852771	+	0.522285i	$0.174920\pi$
$602$	−3.99166e9	+	4.60662e9i	−0.745703	+	0.860587i
$603$	−8.67814e8	−	5.57710e8i	−0.161182	−	0.103585i
$604$	6.07375e8	+	7.00948e8i	0.112157	+	0.129436i
$605$	−3.11557e8	−	2.16693e9i	−0.0571997	−	0.397833i
$606$	1.32171e9	+	3.88090e8i	0.241259	+	0.0708399i
$607$	−3.74565e9	+	2.40718e9i	−0.679778	+	0.436867i	−0.834439	−	0.551101i	$-0.814208\pi$
$607$	−3.74565e9	+	2.40718e9i	−0.679778	+	0.436867i	0.154661	+	0.987968i	$0.450572\pi$
$608$	−2.55492e8	+	1.77699e9i	−0.0461015	+	0.320643i
$609$	−1.83181e9	+	4.01110e9i	−0.328639	+	0.719619i
$610$	−3.07203e8	+	6.72681e8i	−0.0547988	+	0.119993i
$611$	1.17331e8	−	8.16054e8i	0.0208098	−	0.144735i
$612$	4.24709e8	−	2.72944e8i	0.0748965	−	0.0481331i
$613$	6.74197e9	+	1.97962e9i	1.18216	+	0.347113i	0.813005	−	0.582256i	$-0.197830\pi$
$613$	6.74197e9	+	1.97962e9i	1.18216	+	0.347113i	0.369152	+	0.929369i	$0.379648\pi$
$614$	−6.61627e8	−	4.60172e9i	−0.115352	−	0.802288i
$615$	7.22568e7	+	8.33888e7i	0.0125261	+	0.0144559i
$616$	−1.02210e10	−	6.56863e9i	−1.76182	−	1.13225i
$617$	4.61146e9	−	5.32191e9i	0.790388	−	0.912156i	−0.207426	−	0.978251i	$-0.566509\pi$
$617$	4.61146e9	−	5.32191e9i	0.790388	−	0.912156i	0.997813	+	0.0660948i	$0.0210540\pi$
$618$	−1.23077e9	+	3.61386e8i	−0.209757	+	0.0615903i
$619$	−1.63980e9	−	3.59066e9i	−0.277890	−	0.608495i	0.718297	−	0.695737i	$-0.244922\pi$
$619$	−1.63980e9	−	3.59066e9i	−0.277890	−	0.608495i	−0.996187	+	0.0872416i	$0.972195\pi$
$620$	−2.74840e8			−0.0463137
$621$	8.45835e8	−	7.76957e8i	0.141731	−	0.130190i
$622$	−2.19652e9			−0.365990
$623$	3.54072e9	+	7.75309e9i	0.586655	+	1.28460i
$624$	−1.32409e8	+	3.88789e7i	−0.0218159	+	0.00640571i
$625$	−3.60636e9	+	4.16196e9i	−0.590866	+	0.681896i
$626$	−4.74500e9	−	3.04943e9i	−0.773083	−	0.496831i
$627$	1.98267e9	+	2.28813e9i	0.321229	+	0.370718i
$628$	4.31286e8	+	2.99966e9i	0.0694875	+	0.483296i
$629$	−7.12514e9	−	2.09213e9i	−1.14161	−	0.335206i
$630$	2.73837e8	−	1.75985e8i	0.0436316	−	0.0280403i
$631$	−9.39385e8	+	6.53357e9i	−0.148847	+	1.03526i	0.769264	+	0.638932i	$0.220623\pi$
$631$	−9.39385e8	+	6.53357e9i	−0.148847	+	1.03526i	−0.918111	+	0.396324i	$0.870286\pi$
$632$	1.67721e9	−	3.67259e9i	0.264289	−	0.578712i
$633$	−6.53790e8	+	1.43160e9i	−0.102453	+	0.224341i
$634$	−1.50456e8	+	1.04645e9i	−0.0234476	+	0.163081i
$635$	1.19152e9	−	7.65746e8i	0.184669	−	0.118680i
$636$	1.20058e9	+	3.52522e8i	0.185051	+	0.0543358i
$637$	1.10380e7	+	7.67713e7i	0.00169202	+	0.0117682i
$638$	7.84836e9	+	9.05749e9i	1.19648	+	1.38081i
$639$	−2.85794e9	−	1.83669e9i	−0.433311	−	0.278472i
$640$	1.23370e8	−	1.42377e8i	0.0186029	−	0.0214689i
$641$	5.35940e9	−	1.57366e9i	0.803735	−	0.235998i	0.146037	−	0.989279i	$-0.453348\pi$
$641$	5.35940e9	−	1.57366e9i	0.803735	−	0.235998i	0.657698	+	0.753281i	$0.271530\pi$
$642$	−5.19757e8	−	1.13811e9i	−0.0775224	−	0.169750i
$643$	−4.09161e9			−0.606955			−0.303477	−	0.952839i	$-0.598148\pi$
$643$	−4.09161e9			−0.606955			−0.303477	+	0.952839i	$0.598148\pi$
$644$	−2.04237e9	−	1.66861e9i	−0.301325	−	0.246180i
$645$	9.48387e8			0.139164
$646$	−7.93792e8	−	1.73816e9i	−0.115849	−	0.253674i
$647$	1.51597e9	−	4.45129e8i	0.220052	−	0.0646132i	−0.169848	−	0.985470i	$-0.554328\pi$
$647$	1.51597e9	−	4.45129e8i	0.220052	−	0.0646132i	0.389900	+	0.920857i	$0.372509\pi$
$648$	−5.48274e8	+	6.32742e8i	−0.0791563	+	0.0913512i
$649$	−1.06013e10	−	6.81302e9i	−1.52230	−	0.978325i
$650$	2.75409e8	+	3.17839e8i	0.0393353	+	0.0453953i
$651$	4.37327e8	+	3.04168e9i	0.0621259	+	0.432095i
$652$	2.84735e9	+	8.36058e8i	0.402323	+	0.118133i
$653$	7.70340e9	−	4.95067e9i	1.08265	−	0.695774i	0.127478	−	0.991841i	$-0.459312\pi$
$653$	7.70340e9	−	4.95067e9i	1.08265	−	0.695774i	0.955167	+	0.296067i	$0.0956753\pi$
$654$	−6.75756e8	+	4.69998e9i	−0.0944643	+	0.657013i
$655$	−4.44930e8	+	9.74260e8i	−0.0618653	+	0.135466i
$656$	2.77607e8	−	6.07875e8i	0.0383943	−	0.0840718i
$657$	3.26825e8	−	2.27312e9i	0.0449610	−	0.312711i
$658$	9.90824e9	−	6.36764e9i	1.35583	−	0.871340i
$659$	4.74049e9	+	1.39193e9i	0.645245	+	0.189461i	0.587951	−	0.808896i	$-0.299935\pi$
$659$	4.74049e9	+	1.39193e9i	0.645245	+	0.189461i	0.0572935	+	0.998357i	$0.481753\pi$
$660$	7.15607e7	+	4.97715e8i	0.00968881	+	0.0673872i
$661$	3.02990e9	+	3.49669e9i	0.408059	+	0.470926i	0.922162	−	0.386803i	$-0.126421\pi$
$661$	3.02990e9	+	3.49669e9i	0.408059	+	0.470926i	−0.514103	+	0.857728i	$0.671875\pi$
$662$	−3.13674e9	−	2.01586e9i	−0.420219	−	0.270058i
$663$	−1.62654e8	+	1.87712e8i	−0.0216754	+	0.0250147i
$664$	8.59673e9	−	2.52423e9i	1.13958	−	0.334611i
$665$	2.90893e8	+	6.36967e8i	0.0383582	+	0.0839927i
$666$	3.27576e9			0.429688
$667$	5.52383e9	+	8.07104e9i	0.720775	+	1.05315i
$668$	7.47715e8			0.0970551
$669$	4.83655e8	+	1.05906e9i	0.0624517	+	0.136750i
$670$	−6.22191e8	+	1.82692e8i	−0.0799212	+	0.0234670i
$671$	−8.36423e9	+	9.65284e9i	−1.06880	+	1.23346i
$672$	2.80448e9	+	1.80233e9i	0.356500	+	0.229109i
$673$	−4.42546e9	−	5.10725e9i	−0.559636	−	0.645854i	0.403465	−	0.914995i	$-0.367806\pi$
$673$	−4.42546e9	−	5.10725e9i	−0.559636	−	0.645854i	−0.963101	+	0.269141i	$0.913260\pi$
$674$	3.83242e8	+	2.66551e9i	0.0482129	+	0.335328i
$675$	1.42685e9	+	4.18961e8i	0.178573	+	0.0524337i
$676$	2.43379e9	−	1.56410e9i	0.303019	−	0.194739i
$677$	7.62660e8	−	5.30441e9i	0.0944649	−	0.657018i	−0.886485	−	0.462757i	$-0.846860\pi$
$677$	7.62660e8	−	5.30441e9i	0.0944649	−	0.657018i	0.980950	−	0.194261i	$-0.0622307\pi$
$678$	1.27036e9	−	2.78170e9i	0.156539	−	0.342773i
$679$	4.55968e9	−	9.98431e9i	0.558972	−	1.22398i
$680$	1.69793e8	−	1.18094e9i	0.0207080	−	0.144027i
$681$	6.58900e9	−	4.23449e9i	0.799474	−	0.513791i
$682$	8.01365e9	+	2.35302e9i	0.967353	+	0.284040i
$683$	2.50390e8	+	1.74150e9i	0.0300708	+	0.209147i	0.999317	−	0.0369448i	$-0.0117626\pi$
$683$	2.50390e8	+	1.74150e9i	0.0300708	+	0.209147i	−0.969246	+	0.246092i	$0.920853\pi$
$684$	−3.13733e8	−	3.62068e8i	−0.0374856	−	0.0432607i
$685$	2.14339e9	+	1.37747e9i	0.254791	+	0.163744i
$686$	4.02169e9	−	4.64127e9i	0.475635	−	0.548912i
$687$	1.81851e9	−	5.33961e8i	0.213976	−	0.0628292i
$688$	−2.38609e9	−	5.22480e9i	−0.279336	−	0.611660i
$689$	−6.15600e8			−0.0717021
$690$	−2.09205e7	−	7.21669e8i	−0.00242438	−	0.0836308i
$691$	3.87487e9			0.446770			0.223385	−	0.974730i	$-0.428289\pi$
$691$	3.87487e9			0.446770			0.223385	+	0.974730i	$0.428289\pi$
$692$	−7.83454e8	−	1.71553e9i	−0.0898757	−	0.196800i
$693$	5.39438e9	−	1.58393e9i	0.615708	−	0.180788i
$694$	−4.12561e9	+	4.76121e9i	−0.468522	+	0.540703i
$695$	−4.22908e8	−	2.71786e8i	−0.0477858	−	0.0307101i
$696$	−4.66887e9	−	5.38816e9i	−0.524903	−	0.605771i
$697$	−1.71174e8	−	1.19054e9i	−0.0191479	−	0.133177i
$698$	7.92541e9	+	2.32711e9i	0.882120	+	0.259014i
$699$	5.99311e9	−	3.85154e9i	0.663715	−	0.426544i
$700$	4.85975e8	−	3.38003e9i	0.0535513	−	0.372458i
$701$	−3.20601e9	+	7.02019e9i	−0.351522	+	0.769725i	0.648442	+	0.761264i	$0.275421\pi$
$701$	−3.20601e9	+	7.02019e9i	−0.351522	+	0.769725i	−0.999964	+	0.00846157i	$0.997307\pi$
$702$	4.55153e7	−	9.96647e7i	0.00496567	−	0.0108733i
$703$	−1.00288e9	+	6.97518e9i	−0.108869	+	0.757202i
$704$	1.46918e10	−	9.44185e9i	1.58698	−	1.01989i
$705$	−1.75830e9	−	5.16283e8i	−0.188986	−	0.0554914i
$706$	1.64309e9	+	1.14279e10i	0.175729	+	1.22222i
$707$	3.60353e9	+	4.15869e9i	0.383495	+	0.442577i
$708$	1.67752e9	+	1.07808e9i	0.177644	+	0.114165i
$709$	−1.26612e9	+	1.46118e9i	−0.133418	+	0.153972i	−0.818527	−	0.574468i	$-0.805209\pi$
$709$	−1.26612e9	+	1.46118e9i	−0.133418	+	0.153972i	0.685109	+	0.728440i	$0.259754\pi$
$710$	−2.04904e9	+	6.01652e8i	−0.214855	+	0.0630872i
$711$	7.76108e8	+	1.69944e9i	0.0809802	+	0.177322i
$712$	−1.37808e10			−1.43085
$713$	6.27923e9	+	2.65051e9i	0.648773	+	0.273852i
$714$	−3.54832e9			−0.364820
$715$	−1.02768e8	−	2.25030e8i	−0.0105144	−	0.0230233i
$716$	−2.93958e8	+	8.63138e7i	−0.0299288	+	0.00878789i
$717$	5.24214e9	−	6.04975e9i	0.531119	−	0.612944i
$718$	5.81732e8	+	3.73856e8i	0.0586526	+	0.0376937i
$719$	6.28054e9	+	7.24813e9i	0.630153	+	0.727235i	0.977602	−	0.210464i	$-0.0674975\pi$
$719$	6.28054e9	+	7.24813e9i	0.630153	+	0.727235i	−0.347449	+	0.937699i	$0.612952\pi$
$720$	4.36531e7	+	3.03614e8i	0.00435865	+	0.0303151i
$721$	−4.91654e9	−	1.44363e9i	−0.488525	−	0.143444i
$722$	5.26790e9	−	3.38547e9i	0.520903	−	0.334764i
$723$	−1.22685e9	+	8.53291e9i	−0.120728	+	0.839678i
$724$	−2.24301e9	+	4.91152e9i	−0.219658	+	0.480984i
$725$	−5.26057e9	+	1.15190e10i	−0.512684	+	1.12262i
$726$	1.49815e9	−	1.04199e10i	0.145304	−	1.01061i
$727$	−1.69404e10	+	1.08870e10i	−1.63514	+	1.05084i	−0.690184	+	0.723634i	$0.742470\pi$
$727$	−1.69404e10	+	1.08870e10i	−1.63514	+	1.05084i	−0.944953	+	0.327205i	$0.893893\pi$
$728$	−9.07543e8	−	2.66479e8i	−0.0871781	−	0.0255978i
$729$	−5.51357e7	−	3.83477e8i	−0.00527092	−	0.0366601i
$730$	−9.45357e8	−	1.09100e9i	−0.0899427	−	0.103799i
$731$	−8.69699e9	−	5.58922e9i	−0.823490	−	0.529225i
$732$	1.32354e9	−	1.52744e9i	0.124723	−	0.143938i
$733$	1.26047e10	−	3.70108e9i	1.18214	−	0.347108i	0.369142	−	0.929373i	$-0.379652\pi$
$733$	1.26047e10	−	3.70108e9i	1.18214	−	0.347108i	0.812999	+	0.582265i	$0.197833\pi$
$734$	−3.80899e8	−	8.34053e8i	−0.0355528	−	0.0778497i
$735$	1.72398e8			0.0160149
$736$	6.63400e9	−	3.26519e9i	0.613343	−	0.301881i
$737$	−1.11999e10			−1.03057
$738$	2.20409e8	+	4.82629e8i	0.0201852	+	0.0441994i
$739$	−7.34433e9	+	2.15649e9i	−0.669417	+	0.196558i	−0.598743	−	0.800941i	$-0.704333\pi$
$739$	−7.34433e9	+	2.15649e9i	−0.669417	+	0.196558i	−0.0706734	+	0.997500i	$0.522515\pi$
$740$	−7.66424e8	+	8.84501e8i	−0.0695278	+	0.0802393i
$741$	1.98284e8	+	1.27430e8i	0.0179029	+	0.0115055i
$742$	−5.75911e9	−	6.64637e9i	−0.517538	−	0.597270i
$743$	7.76121e8	+	5.39804e9i	0.0694175	+	0.482809i	0.994641	+	0.103387i	$0.0329680\pi$
$743$	7.76121e8	+	5.39804e9i	0.0694175	+	0.482809i	−0.925224	+	0.379422i	$0.876123\pi$
$744$	−4.76720e9	−	1.39977e9i	−0.424383	−	0.124610i
$745$	8.26704e7	−	5.31290e7i	0.00732492	−	0.00470744i
$746$	−3.46817e8	+	2.41216e9i	−0.0305854	+	0.212726i
$747$	−1.72229e9	+	3.77130e9i	−0.151177	+	0.331031i
$748$	2.27700e9	−	4.98593e9i	0.198933	−	0.435603i
$749$	7.11298e8	−	4.94718e9i	0.0618536	−	0.430201i
$750$	1.59959e9	−	1.02799e9i	0.138450	−	0.0889767i
$751$	1.88822e9	+	5.54432e8i	0.162672	+	0.0477649i	0.362055	−	0.932157i	$-0.382075\pi$
$751$	1.88822e9	+	5.54432e8i	0.162672	+	0.0477649i	−0.199382	+	0.979922i	$0.563894\pi$
$752$	1.57950e9	+	1.09857e10i	0.135443	+	0.942027i
$753$	−2.46705e9	−	2.84713e9i	−0.210570	−	0.243010i
$754$	7.84903e8	+	5.04427e8i	0.0666832	+	0.0428547i
$755$	−6.64194e8	+	7.66521e8i	−0.0561670	+	0.0648201i
$756$	−8.53593e8	+	2.50638e8i	−0.0718497	+	0.0210970i
$757$	−5.70044e9	−	1.24822e10i	−0.477609	−	1.04582i	−0.983114	−	0.182995i	$-0.941421\pi$
$757$	−5.70044e9	−	1.24822e10i	−0.477609	−	1.04582i	0.505504	−	0.862824i	$-0.331306\pi$
$758$	6.82006e9			0.568782
$759$	3.16494e9	−	1.20613e10i	0.262736	−	1.00126i
$760$	−1.13218e9			−0.0935554
$761$	−7.83448e9	−	1.71551e10i	−0.644412	−	1.41107i	−0.896361	−	0.443326i	$-0.853799\pi$
$761$	−7.83448e9	−	1.71551e10i	−0.644412	−	1.41107i	0.251948	−	0.967741i	$-0.418929\pi$
$762$	6.53484e9	−	1.91880e9i	0.535048	−	0.157104i
$763$	−1.24214e10	+	1.43351e10i	−1.01236	+	1.16833i
$764$	2.64035e9	+	1.69685e9i	0.214208	+	0.137663i
$765$	3.61537e8	+	4.17236e8i	0.0291969	+	0.0336951i
$766$	−2.10155e9	−	1.46166e10i	−0.168942	−	1.17502i
$767$	−9.41309e8	−	2.76393e8i	−0.0753266	−	0.0221179i
$768$	−5.65304e9	+	3.63299e9i	−0.450316	+	0.289401i
$769$	4.41703e8	−	3.07211e9i	0.0350258	−	0.243610i	−0.964785	−	0.263038i	$-0.915275\pi$
$769$	4.41703e8	−	3.07211e9i	0.0350258	−	0.243610i	0.999811	+	0.0194281i	$0.00618456\pi$
$770$	1.46813e9	−	3.21475e9i	0.115890	−	0.253764i
$771$	−5.13729e9	+	1.12491e10i	−0.403686	+	0.883950i
$772$	9.07464e8	−	6.31155e9i	0.0709854	−	0.493714i
$773$	2.30294e9	−	1.48001e9i	0.179331	−	0.115249i	−0.447896	−	0.894086i	$-0.647826\pi$
$773$	2.30294e9	−	1.48001e9i	0.179331	−	0.115249i	0.627226	+	0.778837i	$0.284190\pi$
$774$	4.37567e9	+	1.28481e9i	0.339197	+	0.0995971i
$775$	1.25591e9	+	8.73506e9i	0.0969177	+	0.674077i
$776$	1.16216e10	+	1.34121e10i	0.892792	+	1.03034i
$777$	1.10084e10	+	7.07465e9i	0.841878	+	0.541042i
$778$	−1.22023e10	+	1.40822e10i	−0.928996	+	1.07212i
$779$	−1.09515e9	+	3.21566e8i	−0.0830030	+	0.0243719i
$780$	1.62617e7	+	3.56081e7i	0.00122697	+	0.00268669i
$781$	−3.68843e10			−2.77053
$782$	−4.06123e9	+	6.74122e9i	−0.303693	+	0.504098i
$783$	3.29911e9			0.245601
$784$	−4.33742e8	−	9.49763e8i	−0.0321459	−	0.0703897i
$785$	−3.17977e9	+	9.33665e8i	−0.234613	+	0.0688886i
$786$	−3.37269e9	+	3.89229e9i	−0.247740	+	0.285908i
$787$	1.00651e10	+	6.46842e9i	0.736046	+	0.473028i	0.854185	−	0.519969i	$-0.174056\pi$
$787$	1.00651e10	+	6.46842e9i	0.736046	+	0.473028i	−0.118139	+	0.992997i	$0.537693\pi$
$788$	−2.69056e9	−	3.10507e9i	−0.195885	−	0.226063i
$789$	−7.74324e7	−	5.38554e8i	−0.00561246	−	0.0390355i
$790$	1.12684e9	+	3.30871e8i	0.0813147	+	0.0238762i
$791$	1.02767e10	−	6.60445e9i	0.738307	−	0.474481i
$792$	−1.29364e9	+	8.99750e9i	−0.0925288	+	0.643552i
$793$	−4.13065e8	+	9.04487e8i	−0.0294146	+	0.0644089i
$794$	−7.60059e9	+	1.66430e10i	−0.538859	+	1.17994i
$795$	−1.94732e8	+	1.35439e9i	−0.0137453	+	0.0956004i
$796$	4.06755e9	−	2.61405e9i	0.285849	−	0.183704i
$797$	−2.93880e9	−	8.62909e8i	−0.205620	−	0.0603755i	0.177301	−	0.984157i	$-0.443264\pi$
$797$	−2.93880e9	−	8.62909e8i	−0.205620	−	0.0603755i	−0.382921	+	0.923781i	$0.625082\pi$
$798$	4.79203e8	+	3.33293e9i	0.0333818	+	0.232175i
$799$	1.30815e10	+	1.50968e10i	0.907282	+	1.04706i
$800$	8.05388e9	+	5.17592e9i	0.556148	+	0.357415i
$801$	4.17596e9	−	4.81932e9i	0.287107	−	0.331339i
$802$	−3.51015e9	+	1.03067e9i	−0.240279	+	0.0705522i
$803$	−1.03577e10	−	2.26802e10i	−0.705925	−	1.54576i
$804$	1.77225e9			0.120262
$805$	1.48828e9	−	2.47039e9i	0.100554	−	0.166909i
$806$	6.50201e8			0.0437396
$807$	−3.72214e9	−	8.15034e9i	−0.249307	−	0.545907i
$808$	−8.53661e9	+	2.50658e9i	−0.569306	+	0.167163i
$809$	−1.20510e10	+	1.39076e10i	−0.800207	+	0.923488i	−0.998393	−	0.0566767i	$-0.981950\pi$
$809$	−1.20510e10	+	1.39076e10i	−0.800207	+	0.923488i	0.198186	+	0.980164i	$0.436495\pi$
$810$	−2.04876e8	−	1.31666e8i	−0.0135455	−	0.00870514i
$811$	−1.74615e10	−	2.01517e10i	−1.14950	−	1.32660i	−0.936957	−	0.349444i	$-0.886370\pi$
$811$	−1.74615e10	−	2.01517e10i	−1.14950	−	1.32660i	−0.212544	−	0.977151i	$-0.568175\pi$
$812$	−1.07813e9	−	7.49859e9i	−0.0706687	−	0.491511i
$813$	−1.21424e10	−	3.56532e9i	−0.792476	−	0.232692i
$814$	2.99196e10	−	1.92281e10i	1.94433	−	1.24954i
$815$	−4.61836e8	+	3.21214e9i	−0.0298838	+	0.207847i
$816$	1.38901e9	−	3.04150e9i	0.0894929	−	0.195962i
$817$	−4.07541e9	+	8.92390e9i	−0.261453	+	0.572503i
$818$	−1.53830e9	+	1.06991e10i	−0.0982660	+	0.683455i
$819$	3.68202e8	−	2.36629e8i	0.0234203	−	0.0150513i
$820$	−1.81885e8	−	5.34063e7i	−0.0115199	−	0.00338255i
$821$	−3.47465e9	−	2.41667e10i	−0.219134	−	1.52411i	−0.741246	−	0.671234i	$-0.765765\pi$
$821$	−3.47465e9	−	2.41667e10i	−0.219134	−	1.52411i	0.522112	−	0.852877i	$-0.325144\pi$
$822$	8.02308e9	+	9.25913e9i	0.503837	+	0.581459i
$823$	−8.16808e9	−	5.24931e9i	−0.510764	−	0.328248i	0.259745	−	0.965677i	$-0.416362\pi$
$823$	−8.16808e9	−	5.24931e9i	−0.510764	−	0.328248i	−0.770509	+	0.637429i	$0.779998\pi$
$824$	5.42541e9	−	6.26125e9i	0.337821	−	0.389867i
$825$	1.54915e10	−	4.54872e9i	0.960518	−	0.282034i
$826$	−5.82211e9	−	1.27486e10i	−0.359460	−	0.787107i
$827$	−2.50503e10			−1.54008			−0.770041	−	0.637995i	$-0.779764\pi$
$827$	−2.50503e10			−1.54008			−0.770041	+	0.637995i	$0.779764\pi$
$828$	−5.00812e8	+	1.90855e9i	−0.0306598	+	0.116842i
$829$	−1.65113e10			−1.00656			−0.503280	−	0.864124i	$-0.667873\pi$
$829$	−1.65113e10			−1.00656			−0.503280	+	0.864124i	$0.667873\pi$
$830$	1.08265e9	+	2.37068e9i	0.0657227	+	0.143913i
$831$	−1.03088e10	+	3.02694e9i	−0.623167	+	0.182978i
$832$	8.90341e8	−	1.02751e9i	0.0535951	−	0.0618520i
$833$	−1.58094e9	−	1.01601e9i	−0.0947670	−	0.0609030i
$834$	−1.58302e9	−	1.82690e9i	−0.0944940	−	0.109052i
$835$	1.16366e8	+	8.09341e8i	0.00691707	+	0.0481093i
$836$	−4.99079e9	−	1.46543e9i	−0.295425	−	0.0867446i
$837$	1.93411e9	−	1.24298e9i	0.114010	−	0.0732697i
$838$	6.00865e8	−	4.17911e9i	0.0352714	−	0.245318i
$839$	1.00430e10	−	2.19910e10i	0.587076	−	1.28552i	−0.350117	−	0.936706i	$-0.613858\pi$
$839$	1.00430e10	−	2.19910e10i	0.587076	−	1.28552i	0.937193	−	0.348812i	$-0.113415\pi$
$840$	−8.73366e8	+	1.91241e9i	−0.0508416	+	0.111327i
$841$	−1.54325e9	+	1.07335e10i	−0.0894642	+	0.622237i
$842$	−4.26053e9	+	2.73807e9i	−0.245964	+	0.158071i
$843$	−4.56306e9	−	1.33984e9i	−0.262337	−	0.0770292i
$844$	−3.84797e8	−	2.67632e9i	−0.0220309	−	0.153229i
$845$	2.07178e9	+	2.39097e9i	0.118126	+	0.136325i
$846$	−7.41302e9	−	4.76406e9i	−0.420919	−	0.270508i
$847$	2.75383e10	−	3.17809e10i	1.55720	−	1.79711i
$848$	7.95148e9	−	2.33477e9i	0.447778	−	0.131479i
$849$	−4.34099e9	−	9.50545e9i	−0.243451	−	0.533084i
$850$	−1.01900e10			−0.569127
$851$	2.60403e10	−	1.28168e10i	1.44841	−	0.712895i
$852$	5.83649e9			0.323305
$853$	1.19331e10	+	2.61298e10i	0.658311	+	1.44150i	0.884088	+	0.467321i	$0.154781\pi$
$853$	1.19331e10	+	2.61298e10i	0.658311	+	1.44150i	−0.225777	+	0.974179i	$0.572492\pi$
$854$	−1.36297e10	+	4.00204e9i	−0.748830	+	0.219876i
$855$	3.43083e8	−	3.95939e8i	0.0187723	−	0.0216644i
$856$	6.79819e9	+	4.36893e9i	0.370455	+	0.238077i
$857$	1.72429e10	+	1.98993e10i	0.935786	+	1.07995i	0.996648	+	0.0818080i	$0.0260694\pi$
$857$	1.72429e10	+	1.98993e10i	0.935786	+	1.07995i	−0.0608625	+	0.998146i	$0.519385\pi$
$858$	−1.69294e8	−	1.17747e9i	−0.00915032	−	0.0636419i
$859$	2.44403e10	+	7.17633e9i	1.31562	+	0.386302i	0.862911	−	0.505356i	$-0.168639\pi$
$859$	2.44403e10	+	7.17633e9i	1.31562	+	0.386302i	0.452711	+	0.891657i	$0.350457\pi$
$860$	−1.37069e9	+	8.80886e8i	−0.0734841	+	0.0472254i
$861$	−3.01635e8	+	2.09791e9i	−0.0161053	+	0.112015i
$862$	1.78447e8	−	3.90743e8i	0.00948927	−	0.0207786i
$863$	−1.34424e10	+	2.94347e10i	−0.711932	+	1.55891i	0.112944	+	0.993601i	$0.463972\pi$
$863$	−1.34424e10	+	2.94347e10i	−0.711932	+	1.55891i	−0.824876	+	0.565313i	$0.808755\pi$
$864$	3.54956e8	−	2.46877e9i	0.0187230	−	0.130222i
$865$	1.73499e9	−	1.11501e9i	0.0911466	−	0.0585764i
$866$	−1.30874e10	−	3.84280e9i	−0.684762	−	0.201064i
$867$	7.20261e8	+	5.00952e9i	0.0375338	+	0.261054i
$868$	−3.45725e9	−	3.98988e9i	−0.179437	−	0.207081i
$869$	1.70641e10	+	1.09664e10i	0.882092	+	0.566886i
$870$	1.35809e9	−	1.56731e9i	0.0699213	−	0.0806935i
$871$	−8.36598e8	+	2.45647e8i	−0.0428996	+	0.0125965i
$872$	−1.27400e10	−	2.78968e10i	−0.650673	−	1.42477i
$873$	−8.21204e9			−0.417735
$874$	6.88049e9	+	2.90430e9i	0.348601	+	0.147147i
$875$	7.59565e9			0.383298
$876$	1.63898e9	+	3.58886e9i	0.0823774	+	0.180381i
$877$	−1.86642e10	+	5.48030e9i	−0.934352	+	0.274351i	−0.713258	−	0.700902i	$-0.752781\pi$
$877$	−1.86642e10	+	5.48030e9i	−0.934352	+	0.274351i	−0.221094	+	0.975252i	$0.570963\pi$
$878$	−8.85146e9	+	1.02151e10i	−0.441351	+	0.509346i
$879$	−2.19637e9	−	1.41152e9i	−0.109080	−	0.0701013i
$880$	2.18087e9	+	2.51686e9i	0.107880	+	0.124500i
$881$	−4.24951e9	−	2.95560e10i	−0.209374	−	1.45623i	−0.775205	−	0.631709i	$-0.782354\pi$
$881$	−4.24951e9	−	2.95560e10i	−0.209374	−	1.45623i	0.565831	−	0.824521i	$-0.308555\pi$
$882$	7.95409e8	+	2.33553e8i	0.0390347	+	0.0114616i
$883$	−2.05348e10	+	1.31969e10i	−1.00376	+	0.645075i	−0.935770	−	0.352611i	$-0.885294\pi$
$883$	−2.05348e10	+	1.31969e10i	−1.00376	+	0.645075i	−0.0679867	+	0.997686i	$0.521658\pi$
$884$	6.07282e7	−	4.22374e8i	0.00295670	−	0.0205643i
$885$	−9.05861e8	+	1.98356e9i	−0.0439299	+	0.0961930i
$886$	−5.22041e9	+	1.14311e10i	−0.252166	+	0.552166i
$887$	3.87382e9	−	2.69430e10i	0.186383	−	1.29632i	−0.654895	−	0.755720i	$-0.727287\pi$
$887$	3.87382e9	−	2.69430e10i	0.186383	−	1.29632i	0.841278	−	0.540603i	$-0.181804\pi$
$888$	−1.77987e10	+	1.14385e10i	−0.852987	+	0.548182i
$889$	2.61047e10	+	7.66503e9i	1.24613	+	0.365896i
$890$	−5.70479e8	−	3.96777e9i	−0.0271253	−	0.188661i
$891$	−2.75453e9	−	3.17890e9i	−0.130459	−	0.150558i
$892$	−1.68270e9	−	1.08140e9i	−0.0793833	−	0.0510165i
$893$	1.24137e10	−	1.43262e10i	0.583341	−	0.673212i
$894$	4.53401e8	−	1.33131e8i	0.0212227	−	0.00623155i
$895$	−1.39176e8	−	3.04753e8i	−0.00648908	−	0.0142091i
$896$	3.61879e9			0.168068
$897$	−2.81298e7	−	9.70357e8i	−0.00130135	−	0.0448909i
$898$	−7.76878e9			−0.358002
$899$	8.13300e9	+	1.78088e10i	0.373329	+	0.817476i
$900$	−2.45134e9	+	7.19779e8i	−0.112087	+	0.0329117i
$901$	9.76772e9	−	1.12726e10i	0.444894	−	0.513435i
$902$	4.84608e9	+	3.11438e9i	0.219871	+	0.141302i
$903$	1.19299e10	+	1.37678e10i	0.539173	+	0.622239i
$904$	2.81088e9	+	1.95501e10i	0.126547	+	0.880157i
$905$	−5.66539e9	−	1.66351e9i	−0.254074	−	0.0746028i
$906$	−4.10290e9	+	2.63677e9i	−0.183291	+	0.117794i
$907$	4.81201e9	−	3.34683e10i	0.214142	−	1.48939i	−0.544985	−	0.838446i	$-0.683465\pi$
$907$	4.81201e9	−	3.34683e10i	0.214142	−	1.48939i	0.759127	−	0.650942i	$-0.225626\pi$
$908$	−5.58985e9	+	1.22401e10i	−0.247799	+	0.542604i
$909$	1.71025e9	−	3.74493e9i	0.0755242	−	0.165375i
$910$	3.91553e7	−	2.72331e8i	0.00172245	−	0.0119799i
$911$	1.07646e10	−	6.91796e9i	0.471718	−	0.303154i	−0.283099	−	0.959091i	$-0.591362\pi$
$911$	1.07646e10	−	6.91796e9i	0.471718	−	0.303154i	0.754816	+	0.655936i	$0.227726\pi$
$912$	−3.04446e9	−	8.93934e8i	−0.132901	−	0.0390233i
$913$	6.40606e9	+	4.45551e10i	0.278576	+	1.93754i
$914$	−9.57897e9	−	1.10547e10i	−0.414961	−	0.478890i
$915$	1.85931e9	+	1.19491e9i	0.0802377	+	0.0515656i
$916$	−2.13229e9	+	2.46080e9i	−0.0916670	+	0.105789i
$917$	−1.97402e10	+	5.79625e9i	−0.845394	+	0.248230i
$918$	1.10282e9	+	2.41483e9i	0.0470494	+	0.103024i
$919$	7.34712e9			0.312257			0.156129	−	0.987737i	$-0.450099\pi$
$919$	7.34712e9			0.312257			0.156129	+	0.987737i	$0.450099\pi$
$920$	2.63364e9	+	3.84810e9i	0.111506	+	0.162925i
$921$	−1.38946e10			−0.586052
$922$	−3.59892e9	−	7.88053e9i	−0.151221	−	0.331129i
$923$	−2.75514e9	+	8.08981e8i	−0.115329	+	0.0338635i
$924$	−6.32520e9	+	7.29967e9i	−0.263768	+	0.304404i
$925$	3.16137e10	+	2.03169e10i	1.31335	+	0.844037i
$926$	−1.16843e10	−	1.34844e10i	−0.483575	−	0.558075i
$927$	5.45591e8	+	3.79467e9i	0.0224951	+	0.156457i
$928$	2.03789e10	+	5.98377e9i	0.837070	+	0.245786i
$929$	2.91043e10	−	1.87042e10i	1.19097	−	0.765392i	0.213602	−	0.976921i	$-0.431480\pi$
$929$	2.91043e10	−	1.87042e10i	1.19097	−	0.765392i	0.977372	+	0.211528i	$0.0678441\pi$
$930$	2.05678e8	−	1.43052e9i	0.00838487	−	0.0583181i
$931$	−7.40827e8	+	1.62218e9i	−0.0300880	+	0.0658834i
$932$	−5.08432e9	+	1.11331e10i	−0.205720	+	0.450465i
$933$	−9.34261e8	+	6.49793e9i	−0.0376602	+	0.261932i
$934$	1.70524e10	−	1.09589e10i	0.684812	−	0.440102i
$935$	5.75123e9	+	1.68871e9i	0.230102	+	0.0675640i
$936$	1.00710e8	+	7.00456e8i	0.00401429	+	0.0279200i
$937$	1.90311e10	+	2.19631e10i	0.755746	+	0.872177i	0.995112	−	0.0987521i	$-0.0314851\pi$
$937$	1.90311e10	+	2.19631e10i	0.755746	+	0.872177i	−0.239366	+	0.970929i	$0.576940\pi$
$938$	−1.04788e10	−	6.73429e9i	−0.414572	−	0.266429i
$939$	−1.10393e10	+	1.27400e10i	−0.435122	+	0.502158i
$940$	3.02077e9	−	8.86979e8i	0.118623	−	0.0348310i
$941$	−6.55086e9	−	1.43444e10i	−0.256292	−	0.561201i	0.737125	−	0.675756i	$-0.236183\pi$
$941$	−6.55086e9	−	1.43444e10i	−0.256292	−	0.561201i	−0.993417	+	0.114556i	$0.963456\pi$
$942$	−1.59357e10			−0.621146
$943$	3.64045e9	+	2.97423e9i	0.141372	+	0.115500i
$944$	1.32068e10			0.510970
$945$	−4.04138e8	−	8.84939e8i	−0.0155782	−	0.0341116i
$946$	4.75073e10	−	1.39494e10i	1.82449	−	0.535719i
$947$	1.73686e10	−	2.00444e10i	0.664568	−	0.766952i	−0.318948	−	0.947772i	$-0.603330\pi$
$947$	1.73686e10	−	2.00444e10i	0.664568	−	0.766952i	0.983516	+	0.180820i	$0.0578751\pi$
$948$	−2.70018e9	−	1.73530e9i	−0.102935	−	0.0661523i
$949$	−1.27113e9	−	1.46696e9i	−0.0482789	−	0.0557168i
$950$	1.37617e9	+	9.57148e9i	0.0520762	+	0.362198i
$951$	3.03169e9	+	8.90183e8i	0.114302	+	0.0335620i
$952$	1.92796e10	−	1.23902e10i	0.724216	−	0.465426i
$953$	−2.24026e9	+	1.55814e10i	−0.0838444	+	0.583151i	0.903980	+	0.427575i	$0.140632\pi$
$953$	−2.24026e9	+	1.55814e10i	−0.0838444	+	0.583151i	−0.987824	+	0.155575i	$0.950277\pi$
$954$	−2.73330e9	+	5.98510e9i	−0.101922	+	0.223178i
$955$	−1.42579e9	+	3.12205e9i	−0.0529717	+	0.115992i
$956$	−1.95720e9	+	1.36126e10i	−0.0724491	+	0.503894i
$957$	3.01328e10	−	1.93652e10i	1.11134	−	0.714215i
$958$	8.86293e9	+	2.60239e9i	0.325685	+	0.0956298i
$959$	6.96508e9	+	4.84432e10i	0.255012	+	1.77365i
$960$	−1.97900e9	−	2.28389e9i	−0.0721932	−	0.0833153i
$961$	−1.16674e10	−	7.49819e9i	−0.424075	−	0.272536i
$962$	1.81316e9	−	2.09250e9i	0.0656635	−	0.0757797i
$963$	−3.58791e9	+	1.05351e9i	−0.129464	+	0.0380141i
$964$	−6.15245e9	−	1.34720e10i	−0.221196	−	0.484353i
$965$	6.97297e9			0.249788
$966$	1.02134e10	−	9.38166e9i	0.364543	−	0.334857i
$967$	−3.04928e10			−1.08444			−0.542220	−	0.840237i	$-0.682416\pi$
$967$	−3.04928e10			−1.08444			−0.542220	+	0.840237i	$0.682416\pi$
$968$	2.82446e10	+	6.18471e10i	1.00086	+	2.19157i
$969$	−5.47960e9	+	1.60895e9i	−0.193471	+	0.0568081i
$970$	−3.38051e9	+	3.90131e9i	−0.118927	+	0.137249i
$971$	−3.46057e10	−	2.22397e10i	−1.21305	−	0.779583i	−0.231887	−	0.972743i	$-0.574490\pi$
$971$	−3.46057e10	−	2.22397e10i	−1.21305	−	0.779583i	−0.981167	+	0.193160i	$0.938126\pi$
$972$	4.35870e8	+	5.03021e8i	0.0152239	+	0.0175693i
$973$	−1.37426e9	−	9.55821e9i	−0.0478272	−	0.332645i
$974$	−2.49099e10	−	7.31422e9i	−0.863806	−	0.253636i
$975$	1.05740e9	−	6.79549e8i	0.0365361	−	0.0234804i
$976$	1.90499e9	−	1.32495e10i	0.0655873	−	0.456169i
$977$	−1.81619e10	+	3.97690e10i	−0.623061	+	1.36431i	0.290212	+	0.956963i	$0.406274\pi$
$977$	−1.81619e10	+	3.97690e10i	−0.623061	+	1.36431i	−0.913272	+	0.407350i	$0.866453\pi$
$978$	−6.48243e9	+	1.41945e10i	−0.221591	+	0.485216i
$979$	9.85312e9	−	6.85300e10i	0.335610	−	2.33422i
$980$	−2.49163e8	+	1.60127e8i	−0.00845653	+	0.00543468i
$981$	1.36164e10	+	3.99815e9i	0.460492	+	0.135213i
$982$	−3.11924e8	−	2.16948e9i	−0.0105114	−	0.0731081i
$983$	7.62486e8	+	8.79956e8i	0.0256032	+	0.0295477i	0.768407	−	0.639962i	$-0.221050\pi$
$983$	7.62486e8	+	8.79956e8i	0.0256032	+	0.0295477i	−0.742804	+	0.669509i	$0.766504\pi$
$984$	−2.88286e9	−	1.85270e9i	−0.0964584	−	0.0619901i
$985$	2.94226e9	−	3.39554e9i	0.0980965	−	0.113209i
$986$	−2.16908e10	+	6.36901e9i	−0.720622	+	0.211594i
$987$	−1.46229e10	−	3.20197e10i	−0.484087	−	1.06000i
$988$	−4.04936e8			−0.0133579
$989$	3.98109e10	−	6.90681e9i	1.30862	−	0.227034i
$990$	−2.64411e9			−0.0866078
$991$	1.41958e10	+	3.10845e10i	0.463343	+	1.01458i	0.986713	+	0.162474i	$0.0519473\pi$
$991$	1.41958e10	+	3.10845e10i	0.463343	+	1.01458i	−0.523370	+	0.852106i	$0.675325\pi$
$992$	1.42016e10	−	4.16998e9i	0.461899	−	0.135626i
$993$	−7.29765e9	+	8.42193e9i	−0.236516	+	0.272954i
$994$	−3.45093e10	−	2.21778e10i	−1.11451	−	0.716252i
$995$	3.46253e9	+	3.99597e9i	0.111433	+	0.128600i
$996$	−1.01368e9	−	7.05029e9i	−0.0325082	−	0.226099i
$997$	−2.64588e10	−	7.76899e9i	−0.845544	−	0.248274i	−0.169863	−	0.985468i	$-0.554332\pi$
$997$	−2.64588e10	−	7.76899e9i	−0.845544	−	0.248274i	−0.675682	+	0.737194i	$0.736151\pi$
$998$	2.76563e9	−	1.77736e9i	0.0880719	−	0.0566004i
$999$	1.39330e9	−	9.69062e9i	0.0442146	−	0.307519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.8.e.a.4.6	✓	140
23.6	even	11	inner	69.8.e.a.52.6	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.8.e.a.4.6	✓	140	1.1	even	1	trivial
69.8.e.a.52.6	yes	140	23.6	even	11	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.75287 - 8.21765i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(30.3765 - 35.0564i) q^{4} +(42.6731 + 27.4244i) q^{5} +(159.733 + 184.342i) q^{6} +(138.669 + 964.463i) q^{7} +(-1511.60 - 443.845i) q^{8} +(613.274 - 394.127i) q^{9} +O(q^{10})\)	\(q+(-3.75287 - 8.21765i) q^{2} +(-25.9063 + 7.60678i) q^{3} +(30.3765 - 35.0564i) q^{4} +(42.6731 + 27.4244i) q^{5} +(159.733 + 184.342i) q^{6} +(138.669 + 964.463i) q^{7} +(-1511.60 - 443.845i) q^{8} +(613.274 - 394.127i) q^{9} +(65.2168 - 453.593i) q^{10} +(3287.95 - 7199.61i) q^{11} +(-520.278 + 1139.25i) q^{12} +(87.6906 - 609.901i) q^{13} +(7405.21 - 4759.04i) q^{14} +(-1314.11 - 385.859i) q^{15} +(1180.48 + 8210.45i) q^{16} +(9776.81 + 11283.0i) q^{17} +(-5540.34 - 3560.56i) q^{18} +(9277.78 - 10707.1i) q^{19} +(2257.66 - 662.909i) q^{20} +(-10928.9 - 23930.9i) q^{21} -71503.1 q^{22} +(-57973.3 - 6627.09i) q^{23} +42536.1 q^{24} +(-31385.4 - 68724.4i) q^{25} +(-5341.04 + 1568.27i) q^{26} +(-12889.6 + 14875.4i) q^{27} +(38022.9 + 24435.8i) q^{28} +(-109762. - 126673. i) q^{29} +(1760.85 + 12247.0i) q^{30} +(-112074. - 32907.9i) q^{31} +(-106601. + 68508.1i) q^{32} +(-30412.9 + 211526. i) q^{33} +(56028.9 - 122686. i) q^{34} +(-20532.4 + 44959.6i) q^{35} +(4812.46 - 33471.4i) q^{36} +(-418437. + 268913. i) q^{37} +(-122806. - 36059.0i) q^{38} +(2367.65 + 16467.3i) q^{39} +(-52332.4 - 60394.8i) q^{40} +(-67774.3 - 43555.9i) q^{41} +(-155641. + 179619. i) q^{42} +(-664409. + 195088. i) q^{43} +(-152516. - 333963. i) q^{44} +36979.0 q^{45} +(163107. + 501275. i) q^{46} +1.33801e6 q^{47} +(-93037.0 - 203723. i) q^{48} +(-120776. + 35463.1i) q^{49} +(-446968. + 515828. i) q^{50} +(-339109. - 217932. i) q^{51} +(-18717.2 - 21600.8i) q^{52} +(-142183. - 988902. i) q^{53} +(170614. + 50096.8i) q^{54} +(337752. - 217060. i) q^{55} +(218460. - 1.51943e6i) q^{56} +(-158906. + 347956. i) q^{57} +(-629026. + 1.37738e6i) q^{58} +(226588. - 1.57596e6i) q^{59} +(-53445.1 + 34347.1i) q^{60} +(-1.54837e6 - 454643. i) q^{61} +(150174. + 1.04448e6i) q^{62} +(465163. + 536827. i) q^{63} +(1.85623e6 + 1.19293e6i) q^{64} +(20468.2 - 23621.6i) q^{65} +(1.85238e6 - 543908. i) q^{66} +(-587834. - 1.28718e6i) q^{67} +692528. q^{68} +(1.55229e6 - 269307. i) q^{69} +446517. q^{70} +(-1.93589e6 - 4.23901e6i) q^{71} +(-1.10195e6 + 323563. i) q^{72} +(2.06294e6 - 2.38076e6i) q^{73} +(3.78018e6 + 2.42937e6i) q^{74} +(1.33585e6 + 1.54165e6i) q^{75} +(-93526.4 - 650491. i) q^{76} +(7.39970e6 + 2.17275e6i) q^{77} +(126437. - 81256.3i) q^{78} +(-364723. + 2.53670e6i) q^{79} +(-174791. + 382740. i) q^{80} +(220769. - 483416. i) q^{81} +(-103579. + 720405. i) q^{82} +(-4.78436e6 + 3.07472e6i) q^{83} +(-1.17091e6 - 343810. i) q^{84} +(107777. + 749605. i) q^{85} +(4.09661e6 + 4.72774e6i) q^{86} +(3.80711e6 + 2.44668e6i) q^{87} +(-8.16556e6 + 9.42356e6i) q^{88} +(8.39310e6 - 2.46444e6i) q^{89} +(-138778. - 303880. i) q^{90} +600387. q^{91} +(-1.99335e6 + 1.83103e6i) q^{92} +3.15375e6 q^{93} +(-5.02138e6 - 1.09953e7i) q^{94} +(689548. - 202470. i) q^{95} +(2.24050e6 - 2.58568e6i) q^{96} +(-9.47656e6 - 6.09021e6i) q^{97} +(744681. + 859407. i) q^{98} +(-821147. - 5.71120e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9	\( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) 140 * q - 16 * q^2 - 378 * q^3 - 740 * q^4 - 6 * q^5 + 1647 * q^6 + 978 * q^7 - 824 * q^8 - 10206 * q^9 + 1322 * q^10 + 7892 * q^11 - 19980 * q^12 + 39810 * q^13 - 26296 * q^14 + 135 * q^15 - 142164 * q^16 - 97081 * q^17 - 11664 * q^18 + 120905 * q^19 + 124755 * q^20 + 26406 * q^21 - 837266 * q^22 - 224688 * q^23 - 60264 * q^24 - 180624 * q^25 + 385108 * q^26 - 275562 * q^27 + 1121760 * q^28 - 375654 * q^29 + 35694 * q^30 + 505029 * q^31 - 661528 * q^32 - 360423 * q^33 - 1872759 * q^34 - 964610 * q^35 - 1269189 * q^36 - 28802 * q^37 - 1459868 * q^38 + 1074870 * q^39 + 5371901 * q^40 - 1557480 * q^41 + 883116 * q^42 + 1160786 * q^43 - 4521825 * q^44 - 2009124 * q^45 - 4123580 * q^46 + 811422 * q^47 - 1563111 * q^48 - 10960262 * q^49 + 16636695 * q^50 + 4413852 * q^51 - 4843791 * q^52 + 4291672 * q^53 - 98415 * q^54 + 2093539 * q^55 - 12548382 * q^56 - 4007907 * q^57 - 7414367 * q^58 + 2955424 * q^59 + 7289973 * q^60 + 4919292 * q^61 + 16083211 * q^62 + 712962 * q^63 - 1673596 * q^64 - 13246221 * q^65 + 7219449 * q^66 + 148565 * q^67 - 23039568 * q^68 - 657018 * q^69 + 12781104 * q^70 - 7247645 * q^71 - 600696 * q^72 + 32596055 * q^73 + 32550658 * q^74 - 10061874 * q^75 + 12150569 * q^76 - 43349150 * q^77 - 17201700 * q^78 + 4815410 * q^79 + 36529590 * q^80 - 7440174 * q^81 + 20862470 * q^82 + 35160800 * q^83 - 5346540 * q^84 + 48578363 * q^85 + 76972708 * q^86 + 1505088 * q^87 - 35912212 * q^88 + 1401264 * q^89 + 963738 * q^90 - 91970208 * q^91 - 74293537 * q^92 + 555606 * q^93 - 32520253 * q^94 + 79436789 * q^95 + 41519736 * q^96 + 18296816 * q^97 - 38956823 * q^98 - 9731421 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more