LMFDB - Embedded newform 37.8.f.a.16.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.10
Character	$\chi$	$=$	37.16
Dual form			37.8.f.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.25018 - 1.54694i) q^{2} +(-41.1038 + 14.9605i) q^{3} +(-82.3827 - 69.1273i) q^{4} +(-92.7474 + 525.997i) q^{5} +197.841 q^{6} +(9.66574 - 54.8172i) q^{7} +(532.674 + 922.618i) q^{8} +(-209.638 + 175.907i) q^{9} +O(q^{10})$	\(q+(-4.25018 - 1.54694i) q^{2} +(-41.1038 + 14.9605i) q^{3} +(-82.3827 - 69.1273i) q^{4} +(-92.7474 + 525.997i) q^{5} +197.841 q^{6} +(9.66574 - 54.8172i) q^{7} +(532.674 + 922.618i) q^{8} +(-209.638 + 175.907i) q^{9} +(1207.88 - 2092.10i) q^{10} +(-2796.10 - 4842.99i) q^{11} +(4420.42 + 1608.90i) q^{12} +(-1376.96 - 1155.41i) q^{13} +(-125.880 + 218.030i) q^{14} +(-4056.93 - 23008.0i) q^{15} +(1553.63 + 8811.07i) q^{16} +(11629.7 - 9758.45i) q^{17} +(1163.11 - 423.339i) q^{18} +(4466.97 - 1625.84i) q^{19} +(44001.5 - 36921.7i) q^{20} +(422.796 + 2397.80i) q^{21} +(4392.12 + 24909.0i) q^{22} +(20502.0 - 35510.5i) q^{23} +(-35697.8 - 29954.0i) q^{24} +(-194657. - 70849.4i) q^{25} +(4064.98 + 7040.76i) q^{26} +(53816.8 - 93213.4i) q^{27} +(-4585.65 + 3847.82i) q^{28} +(95164.8 + 164830. i) q^{29} +(-18349.3 + 104064. i) q^{30} +93640.6 q^{31} +(30706.4 - 174145. i) q^{32} +(187384. + 157234. i) q^{33} +(-64523.9 + 23484.8i) q^{34} +(27937.2 + 10168.3i) q^{35} +29430.5 q^{36} +(-33264.6 + 306309. i) q^{37} -21500.5 q^{38} +(73883.8 + 26891.5i) q^{39} +(-534698. + 194614. i) q^{40} +(40983.2 + 34389.0i) q^{41} +(1912.28 - 10845.1i) q^{42} -828283. q^{43} +(-104432. + 592266. i) q^{44} +(-73083.1 - 126584. i) q^{45} +(-142070. + 119211. i) q^{46} +(171333. - 296757. i) q^{47} +(-195678. - 338925. i) q^{48} +(770966. + 280609. i) q^{49} +(717727. + 602245. i) q^{50} +(-332032. + 575095. i) q^{51} +(33567.6 + 190371. i) q^{52} +(-178016. - 1.00958e6i) q^{53} +(-372926. + 312922. i) q^{54} +(2.80673e6 - 1.02157e6i) q^{55} +(55724.0 - 20281.9i) q^{56} +(-159286. + 133656. i) q^{57} +(-149485. - 847772. i) q^{58} +(-444188. - 2.51911e6i) q^{59} +(-1.25626e6 + 2.17591e6i) q^{60} +(-291252. - 244389. i) q^{61} +(-397989. - 144856. i) q^{62} +(7616.41 + 13192.0i) q^{63} +(172709. - 299140. i) q^{64} +(735450. - 617116. i) q^{65} +(-553185. - 958144. i) q^{66} +(290814. - 1.64929e6i) q^{67} -1.63266e6 q^{68} +(-311453. + 1.76634e6i) q^{69} +(-103008. - 86434.1i) q^{70} +(323531. - 117755. i) q^{71} +(-273963. - 99714.5i) q^{72} +399138. q^{73} +(615222. - 1.25041e6i) q^{74} +9.06108e6 q^{75} +(-480391. - 174848. i) q^{76} +(-292505. + 106463. i) q^{77} +(-272420. - 228587. i) q^{78} +(437609. - 2.48180e6i) q^{79} -4.77869e6 q^{80} +(-713621. + 4.04714e6i) q^{81} +(-120988. - 209558. i) q^{82} +(-4.43708e6 + 3.72315e6i) q^{83} +(130922. - 226764. i) q^{84} +(4.05429e6 + 7.02224e6i) q^{85} +(3.52035e6 + 1.28130e6i) q^{86} +(-6.37758e6 - 5.35143e6i) q^{87} +(2.97882e6 - 5.15947e6i) q^{88} +(-2.20731e6 - 1.25183e7i) q^{89} +(114799. + 651058. i) q^{90} +(-76645.5 + 64313.2i) q^{91} +(-4.14376e6 + 1.50820e6i) q^{92} +(-3.84898e6 + 1.40091e6i) q^{93} +(-1.18726e6 + 996229. i) q^{94} +(440888. + 2.50040e6i) q^{95} +(1.34315e6 + 7.61739e6i) q^{96} +(194163. - 336299. i) q^{97} +(-2.84266e6 - 2.38527e6i) q^{98} +(1.43808e6 + 523420. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) $ 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−4.25018	−	1.54694i	−0.375666	−	0.136731i	0.147285	−	0.989094i	$-0.452947\pi$
$2$	−4.25018	−	1.54694i	−0.375666	−	0.136731i	−0.522951	+	0.852363i	$0.675169\pi$
$3$	−41.1038	+	14.9605i	−0.878936	+	0.319907i	−0.741780	−	0.670643i	$-0.766018\pi$
$3$	−41.1038	+	14.9605i	−0.878936	+	0.319907i	−0.137156	+	0.990550i	$0.543796\pi$
$4$	−82.3827	−	69.1273i	−0.643615	−	0.540057i
$5$	−92.7474	+	525.997i	−0.331823	+	1.88186i	0.124767	+	0.992186i	$0.460182\pi$
$5$	−92.7474	+	525.997i	−0.331823	+	1.88186i	−0.456590	+	0.889677i	$0.650929\pi$
$6$	197.841			0.373928
$7$	9.66574	−	54.8172i	0.0106510	−	0.0604051i	−0.979019	−	0.203769i	$-0.934681\pi$
$7$	9.66574	−	54.8172i	0.0106510	−	0.0604051i	0.989670	+	0.143364i	$0.0457920\pi$
$8$	532.674	+	922.618i	0.367829	+	0.637099i
$9$	−209.638	+	175.907i	−0.0958562	+	0.0804329i
$10$	1207.88	−	2092.10i	0.381964	−	0.661582i
$11$	−2796.10	−	4842.99i	−0.633401	−	1.09708i	−0.986852	−	0.161629i	$-0.948325\pi$
$11$	−2796.10	−	4842.99i	−0.633401	−	1.09708i	0.353451	−	0.935453i	$-0.385008\pi$
$12$	4420.42	+	1608.90i	0.738464	+	0.268779i
$13$	−1376.96	−	1155.41i	−0.173828	−	0.145859i	0.551723	−	0.834027i	$-0.313971\pi$
$13$	−1376.96	−	1155.41i	−0.173828	−	0.145859i	−0.725551	+	0.688168i	$0.758415\pi$
$14$	−125.880	+	218.030i	−0.0122605	+	0.0212358i
$15$	−4056.93	−	23008.0i	−0.310369	−	1.76019i
$16$	1553.63	+	8811.07i	0.0948260	+	0.537785i
$17$	11629.7	−	9758.45i	0.574111	−	0.481737i	−0.308896	−	0.951096i	$-0.599959\pi$
$17$	11629.7	−	9758.45i	0.574111	−	0.481737i	0.883007	+	0.469359i	$0.155515\pi$
$18$	1163.11	−	423.339i	0.0470076	−	0.0171094i
$19$	4466.97	−	1625.84i	0.149408	−	0.0543802i	−0.266233	−	0.963909i	$-0.585779\pi$
$19$	4466.97	−	1625.84i	0.149408	−	0.0543802i	0.415642	+	0.909528i	$0.363557\pi$
$20$	44001.5	−	36921.7i	1.22988	−	1.03199i
$21$	422.796	+	2397.80i	0.00996239	+	0.0564995i
$22$	4392.12	+	24909.0i	0.0879418	+	0.498743i
$23$	20502.0	−	35510.5i	0.351357	−	0.608569i	−0.635130	−	0.772405i	$-0.719054\pi$
$23$	20502.0	−	35510.5i	0.351357	−	0.608569i	0.986488	+	0.163836i	$0.0523869\pi$
$24$	−35697.8	−	29954.0i	−0.527111	−	0.442298i
$25$	−194657.	−	70849.4i	−2.49161	−	0.906872i
$26$	4064.98	+	7040.76i	0.0453578	+	0.0785620i
$27$	53816.8	−	93213.4i	0.526193	−	0.911392i
$28$	−4585.65	+	3847.82i	−0.0394773	+	0.0331254i
$29$	95164.8	+	164830.i	0.724575	+	1.25500i	0.959149	+	0.282902i	$0.0912971\pi$
$29$	95164.8	+	164830.i	0.724575	+	1.25500i	−0.234574	+	0.972098i	$0.575370\pi$
$30$	−18349.3	+	104064.i	−0.124078	+	0.703681i
$31$	93640.6			0.564544			0.282272	−	0.959334i	$-0.408912\pi$
$31$	93640.6			0.564544			0.282272	+	0.959334i	$0.408912\pi$
$32$	30706.4	−	174145.i	0.165655	−	0.939476i
$33$	187384.	+	157234.i	0.907683	+	0.761636i
$34$	−64523.9	+	23484.8i	−0.281543	+	0.102473i
$35$	27937.2	+	10168.3i	0.110140	+	0.0400876i
$36$	29430.5			0.105133
$37$	−33264.6	+	306309.i	−0.107963	+	0.994155i
$37$	−33264.6	+	306309.i	−0.107963	+	0.994155i
$38$	−21500.5			−0.0635631
$39$	73883.8	+	26891.5i	0.199445	+	0.0725920i
$40$	−534698.	+	194614.i	−1.32099	+	0.480800i
$41$	40983.2	+	34389.0i	0.0928672	+	0.0779248i	0.688039	−	0.725673i	$-0.258472\pi$
$41$	40983.2	+	34389.0i	0.0928672	+	0.0779248i	−0.595172	+	0.803598i	$0.702916\pi$
$42$	1912.28	−	10845.1i	0.00398272	−	0.0225871i
$43$	−828283.			−1.58869			−0.794345	−	0.607467i	$-0.792186\pi$
$43$	−828283.			−1.58869			−0.794345	+	0.607467i	$0.792186\pi$
$44$	−104432.	+	592266.i	−0.184821	+	1.04817i
$45$	−73083.1	−	126584.i	−0.119556	−	0.207078i
$46$	−142070.	+	119211.i	−0.215203	+	0.180577i
$47$	171333.	−	296757.i	0.240712	−	0.416926i	−0.720205	−	0.693761i	$-0.755952\pi$
$47$	171333.	−	296757.i	0.240712	−	0.416926i	0.960917	+	0.276835i	$0.0892857\pi$
$48$	−195678.	−	338925.i	−0.255387	−	0.442343i
$49$	770966.	+	280609.i	0.936157	+	0.340733i
$50$	717727.	+	602245.i	0.812016	+	0.681362i
$51$	−332032.	+	575095.i	−0.350496	+	0.607078i
$52$	33567.6	+	190371.i	0.0331061	+	0.187754i
$53$	−178016.	−	1.00958e6i	−0.164245	−	0.931482i	−0.949839	−	0.312739i	$-0.898753\pi$
$53$	−178016.	−	1.00958e6i	−0.164245	−	0.931482i	0.785593	−	0.618743i	$-0.212358\pi$
$54$	−372926.	+	312922.i	−0.322289	+	0.270432i
$55$	2.80673e6	−	1.02157e6i	2.27474	−	0.827937i
$56$	55724.0	−	20281.9i	0.0424018	−	0.0154330i
$57$	−159286.	+	133656.i	−0.113924	+	0.0955934i
$58$	−149485.	−	847772.i	−0.100600	−	0.570533i
$59$	−444188.	−	2.51911e6i	−0.281569	−	1.59686i	−0.717290	−	0.696774i	$-0.754618\pi$
$59$	−444188.	−	2.51911e6i	−0.281569	−	1.59686i	0.435722	−	0.900081i	$-0.356493\pi$
$60$	−1.25626e6	+	2.17591e6i	−0.750845	+	1.30050i
$61$	−291252.	−	244389.i	−0.164291	−	0.137857i	0.556936	−	0.830556i	$-0.311977\pi$
$61$	−291252.	−	244389.i	−0.164291	−	0.137857i	−0.721227	+	0.692699i	$0.756421\pi$
$62$	−397989.	−	144856.i	−0.212080	−	0.0771909i
$63$	7616.41	+	13192.0i	0.00383759	+	0.00664690i
$64$	172709.	−	299140.i	0.0823539	−	0.142641i
$65$	735450.	−	617116.i	0.332167	−	0.278721i
$66$	−553185.	−	958144.i	−0.236846	−	0.410230i
$67$	290814.	−	1.64929e6i	0.118128	−	0.669938i	−0.867026	−	0.498264i	$-0.833971\pi$
$67$	290814.	−	1.64929e6i	0.118128	−	0.669938i	0.985154	−	0.171674i	$-0.0549177\pi$
$68$	−1.63266e6			−0.629672
$69$	−311453.	+	1.76634e6i	−0.114135	+	0.647294i
$70$	−103008.	−	86434.1i	−0.0358946	−	0.0301191i
$71$	323531.	−	117755.i	0.107278	−	0.0390460i	−0.287823	−	0.957683i	$-0.592932\pi$
$71$	323531.	−	117755.i	0.107278	−	0.0390460i	0.395102	+	0.918637i	$0.370709\pi$
$72$	−273963.	−	99714.5i	−0.0865025	−	0.0314843i
$73$	399138.			0.120086			0.0600430	−	0.998196i	$-0.480876\pi$
$73$	399138.			0.120086			0.0600430	+	0.998196i	$0.480876\pi$
$74$	615222.	−	1.25041e6i	0.176490	−	0.358708i
$75$	9.06108e6			2.48008
$76$	−480391.	−	174848.i	−0.125530	−	0.0456891i
$77$	−292505.	+	106463.i	−0.0730157	+	0.0265756i
$78$	−272420.	−	228587.i	−0.0649991	−	0.0545407i
$79$	437609.	−	2.48180e6i	0.0998600	−	0.566334i	−0.893289	−	0.449482i	$-0.851609\pi$
$79$	437609.	−	2.48180e6i	0.0998600	−	0.566334i	0.993149	−	0.116852i	$-0.0372803\pi$
$80$	−4.77869e6			−1.04350
$81$	−713621.	+	4.04714e6i	−0.149200	+	0.846157i
$82$	−120988.	−	209558.i	−0.0242323	−	0.0419716i
$83$	−4.43708e6	+	3.72315e6i	−0.851772	+	0.714722i	−0.960179	−	0.279385i	$-0.909870\pi$
$83$	−4.43708e6	+	3.72315e6i	−0.851772	+	0.714722i	0.108407	+	0.994107i	$0.465425\pi$
$84$	130922.	−	226764.i	0.0241010	−	0.0417442i
$85$	4.05429e6	+	7.02224e6i	0.716059	+	1.24025i
$86$	3.52035e6	+	1.28130e6i	0.596817	+	0.217224i
$87$	−6.37758e6	−	5.35143e6i	−1.03834	−	0.871269i
$88$	2.97882e6	−	5.15947e6i	0.465967	−	0.807078i
$89$	−2.20731e6	−	1.25183e7i	−0.331893	−	1.88226i	−0.455985	−	0.889988i	$-0.650713\pi$
$89$	−2.20731e6	−	1.25183e7i	−0.331893	−	1.88226i	0.124092	−	0.992271i	$-0.460398\pi$
$90$	114799.	+	651058.i	0.0165993	+	0.0941392i
$91$	−76645.5	+	64313.2i	−0.0106621	+	0.00894654i
$92$	−4.14376e6	+	1.50820e6i	−0.554800	+	0.201931i
$93$	−3.84898e6	+	1.40091e6i	−0.496198	+	0.180601i
$94$	−1.18726e6	+	996229.i	−0.147434	+	0.123712i
$95$	440888.	+	2.50040e6i	0.0527589	+	0.299211i
$96$	1.34315e6	+	7.61739e6i	0.154944	+	0.878733i
$97$	194163.	−	336299.i	0.0216005	−	0.0374132i	−0.855023	−	0.518590i	$-0.826457\pi$
$97$	194163.	−	336299.i	0.0216005	−	0.0374132i	0.876624	+	0.481177i	$0.159790\pi$
$98$	−2.84266e6	−	2.38527e6i	−0.305094	−	0.256004i
$99$	1.43808e6	+	523420.i	0.148957	+	0.0542159i
$100$	1.11388e7	+	1.92929e7i	1.11388	+	1.92929i
$101$	−1.95559e6	+	3.38718e6i	−0.188866	+	0.327125i	−0.944872	−	0.327439i	$-0.893814\pi$
$101$	−1.95559e6	+	3.38718e6i	−0.188866	+	0.327125i	0.756007	+	0.654564i	$0.227148\pi$
$102$	2.30083e6	−	1.93063e6i	0.214676	−	0.180135i
$103$	8.30245e6	+	1.43803e7i	0.748645	+	1.29669i	0.948472	+	0.316860i	$0.102628\pi$
$103$	8.30245e6	+	1.43803e7i	0.748645	+	1.29669i	−0.199828	+	0.979831i	$0.564038\pi$
$104$	332529.	−	1.88586e6i	0.0289876	−	0.164397i
$105$	−1.30045e6			−0.109630
$106$	−805156.	+	4.56627e6i	−0.0656613	+	0.372384i
$107$	1.49660e7	+	1.25580e7i	1.18103	+	0.991005i	0.999972	+	0.00753277i	$0.00239778\pi$
$107$	1.49660e7	+	1.25580e7i	1.18103	+	0.991005i	0.181062	+	0.983472i	$0.442047\pi$
$108$	−1.08772e7	+	3.95896e6i	−0.830869	+	0.302412i
$109$	−2.17765e7	−	7.92601e6i	−1.61063	−	0.586221i	−0.629065	−	0.777352i	$-0.716562\pi$
$109$	−2.17765e7	−	7.92601e6i	−1.61063	−	0.586221i	−0.981565	+	0.191131i	$0.938784\pi$
$110$	−1.35094e7			−0.967746
$111$	−3.21525e6	−	1.30881e7i	−0.223144	−	0.908337i
$112$	498015.			0.0334949
$113$	−1.39796e7	−	5.08817e6i	−0.911425	−	0.331732i	−0.156603	−	0.987662i	$-0.550054\pi$
$113$	−1.39796e7	−	5.08817e6i	−0.911425	−	0.331732i	−0.754822	+	0.655930i	$0.772277\pi$
$114$	883750.	−	321659.i	0.0558679	−	0.0203343i
$115$	1.67769e7	+	1.40775e7i	1.02865	+	0.863144i
$116$	3.55434e6	−	2.01576e7i	0.211425	−	1.19905i
$117$	491907.			0.0283944
$118$	−2.00904e6	+	1.13938e7i	−0.112564	+	0.638384i
$119$	−422521.	−	731828.i	−0.0229845	−	0.0398102i
$120$	1.90666e7	−	1.59988e7i	1.00725	−	0.845185i
$121$	−5.89280e6	+	1.02066e7i	−0.302394	+	0.523761i
$122$	859817.	+	1.48925e6i	0.0428693	+	0.0742518i
$123$	−2.19904e6	−	800386.i	−0.106553	−	0.0387821i
$124$	−7.71436e6	−	6.47312e6i	−0.363349	−	0.304886i
$125$	3.44568e7	−	5.96809e7i	1.57794	−	2.73307i
$126$	−11963.9	−	67850.5i	−0.000532813	−	0.00302173i
$127$	−5.24678e6	−	2.97560e7i	−0.227290	−	1.28902i	−0.858259	−	0.513216i	$-0.828454\pi$
$127$	−5.24678e6	−	2.97560e7i	−0.227290	−	1.28902i	0.630969	−	0.775808i	$-0.282657\pi$
$128$	−1.85358e7	+	1.55533e7i	−0.781223	+	0.655524i
$129$	3.40455e7	−	1.23916e7i	1.39636	−	0.508232i
$130$	−4.08043e6	+	1.48516e6i	−0.162894	+	0.0592885i
$131$	6.38172e6	−	5.35490e6i	0.248021	−	0.208114i	−0.510299	−	0.859997i	$-0.670465\pi$
$131$	6.38172e6	−	5.35490e6i	0.248021	−	0.208114i	0.758319	+	0.651883i	$0.226021\pi$
$132$	−4.56805e6	−	2.59067e7i	−0.172871	−	0.980401i
$133$	−45947.5	−	260581.i	−0.00169348	−	0.00960423i
$134$	−3.78736e6	+	6.55989e6i	−0.135978	+	0.235521i
$135$	4.40386e7	+	3.69528e7i	1.54051	+	1.29264i
$136$	1.51981e7	+	5.53167e6i	0.518089	+	0.188569i
$137$	−1.88241e7	−	3.26043e7i	−0.625449	−	1.08331i	−0.988454	−	0.151522i	$-0.951582\pi$
$137$	−1.88241e7	−	3.26043e7i	−0.625449	−	1.08331i	0.363005	−	0.931787i	$-0.381751\pi$
$138$	4.05614e6	−	7.02545e6i	0.131382	−	0.227561i
$139$	−2.49094e7	+	2.09015e7i	−0.786704	+	0.660123i	−0.944927	−	0.327280i	$-0.893868\pi$
$139$	−2.49094e7	+	2.09015e7i	−0.786704	+	0.660123i	0.158223	+	0.987403i	$0.449423\pi$
$140$	−1.59863e6	−	2.76891e6i	−0.0492380	−	0.0852828i
$141$	−2.60277e6	+	1.47611e7i	−0.0781933	+	0.443456i
$142$	−1.55722e6			−0.0456396
$143$	−1.74550e6	+	9.89925e6i	−0.0499166	+	0.283091i
$144$	−1.87563e6	−	1.57384e6i	−0.0523453	−	0.0439229i
$145$	−9.55265e7	+	3.47688e7i	−2.60217	+	0.947112i
$146$	−1.69640e6	−	617441.i	−0.0451123	−	0.0164195i
$147$	−3.58877e7			−0.931825
$148$	2.39148e7	−	2.29351e7i	0.606387	−	0.581547i
$149$	6.80778e7			1.68598			0.842992	−	0.537926i	$-0.180792\pi$
$149$	6.80778e7			1.68598			0.842992	+	0.537926i	$0.180792\pi$
$150$	−3.85112e7	−	1.40169e7i	−0.931682	−	0.339105i
$151$	1.58413e7	−	5.76577e6i	0.374431	−	0.136282i	−0.147948	−	0.988995i	$-0.547267\pi$
$151$	1.58413e7	−	5.76577e6i	0.374431	−	0.136282i	0.522379	+	0.852713i	$0.325045\pi$
$152$	3.87947e6	+	3.25526e6i	0.0896024	+	0.0751853i
$153$	−721438.	+	4.09148e6i	−0.0162847	+	0.0923549i
$154$	1.40789e6			0.0310632
$155$	−8.68492e6	+	4.92546e7i	−0.187329	+	1.06240i
$156$	−4.22781e6	−	7.32278e6i	−0.0891619	−	0.154433i
$157$	1.84672e7	−	1.54959e7i	0.380849	−	0.319571i	−0.432186	−	0.901784i	$-0.642258\pi$
$157$	1.84672e7	−	1.54959e7i	0.380849	−	0.319571i	0.813036	+	0.582214i	$0.197813\pi$
$158$	−5.69911e6	+	9.87115e6i	−0.114950	+	0.199099i
$159$	2.24210e7	+	3.88343e7i	0.442349	+	0.766170i
$160$	8.87517e7	+	3.23030e7i	1.71300	+	0.623480i
$161$	−1.74842e6	−	1.46710e6i	−0.0330183	−	0.0277056i
$162$	9.29370e6	−	1.60972e7i	0.171746	−	0.297472i
$163$	−5.56337e6	−	3.15514e7i	−0.100619	−	0.570640i	−0.992880	−	0.119120i	$-0.961993\pi$
$163$	−5.56337e6	−	3.15514e7i	−0.100619	−	0.570640i	0.892261	−	0.451521i	$-0.149118\pi$
$164$	−999089.	−	5.66611e6i	−0.0176869	−	0.100307i
$165$	−1.00084e8	+	8.39804e7i	−1.73449	+	1.45541i
$166$	2.46178e7	−	8.96016e6i	0.417707	−	0.152033i
$167$	3.51881e6	−	1.28074e6i	0.0584640	−	0.0212792i	−0.312623	−	0.949877i	$-0.601208\pi$
$167$	3.51881e6	−	1.28074e6i	0.0584640	−	0.0212792i	0.371087	+	0.928598i	$0.378985\pi$
$168$	−1.98704e6	+	1.66732e6i	−0.0323313	+	0.0271292i
$169$	−1.03351e7	−	5.86133e7i	−0.164707	−	0.934099i
$170$	−6.36849e6	−	3.61175e7i	−0.0994181	−	0.563828i
$171$	−650447.	+	1.12661e6i	−0.00994777	+	0.0172300i
$172$	6.82362e7	+	5.72569e7i	1.02250	+	0.857983i
$173$	−1.15595e8	−	4.20731e7i	−1.69737	−	0.617794i	−0.701853	−	0.712322i	$-0.747644\pi$
$173$	−1.15595e8	−	4.20731e7i	−1.69737	−	0.617794i	−0.995522	+	0.0945281i	$0.969866\pi$
$174$	1.88275e7	+	3.26102e7i	0.270939	+	0.469279i
$175$	−5.76527e6	+	9.98574e6i	−0.0813179	+	0.140847i
$176$	3.83278e7	−	3.21609e7i	0.529932	−	0.444666i
$177$	5.59451e7	+	9.68998e7i	0.758326	+	1.31346i
$178$	−9.98353e6	+	5.66194e7i	−0.132683	+	0.752481i
$179$	−8.24564e7			−1.07458			−0.537290	−	0.843397i	$-0.680552\pi$
$179$	−8.24564e7			−1.07458			−0.537290	+	0.843397i	$0.680552\pi$
$180$	−2.72960e6	+	1.54803e7i	−0.0348855	+	0.197846i
$181$	2.44524e7	+	2.05180e7i	0.306511	+	0.257194i	0.783048	−	0.621961i	$-0.213664\pi$
$181$	2.44524e7	+	2.05180e7i	0.306511	+	0.257194i	−0.476537	+	0.879154i	$0.658108\pi$
$182$	425245.	−	154777.i	0.00522865	−	0.00190307i
$183$	1.56278e7	+	5.68804e6i	0.188503	+	0.0686094i
$184$	4.36835e7			0.516958
$185$	−1.58032e8	−	4.59065e7i	−1.83504	−	0.533056i
$186$	1.85260e7			0.211099
$187$	−7.97779e7	−	2.90368e7i	−0.892148	−	0.324715i
$188$	−3.46289e7	+	1.26039e7i	−0.380090	+	0.138341i
$189$	−4.58952e6	−	3.85106e6i	−0.0494482	−	0.0414920i
$190$	1.99411e6	−	1.13092e7i	0.0210917	−	0.119617i
$191$	5.30280e7			0.550666			0.275333	−	0.961349i	$-0.411212\pi$
$191$	5.30280e7			0.550666			0.275333	+	0.961349i	$0.411212\pi$
$192$	−2.62368e6	+	1.48796e7i	−0.0267520	+	0.151718i
$193$	4.36558e7	+	7.56140e7i	0.437110	+	0.757097i	0.997465	−	0.0711555i	$-0.0226687\pi$
$193$	4.36558e7	+	7.56140e7i	0.437110	+	0.757097i	−0.560355	+	0.828252i	$0.689335\pi$
$194$	−1.34546e6	+	1.12897e6i	−0.0132301	+	0.0111014i
$195$	−2.09974e7	+	3.63685e7i	−0.202789	+	0.351240i
$196$	−4.41165e7	−	7.64121e7i	−0.418509	−	0.724879i
$197$	1.64426e8	+	5.98460e7i	1.53228	+	0.557703i	0.964178	−	0.265256i	$-0.0854566\pi$
$197$	1.64426e8	+	5.98460e7i	1.53228	+	0.557703i	0.568100	+	0.822960i	$0.307679\pi$
$198$	−5.30241e6	−	4.44925e6i	−0.0485451	−	0.0407342i
$199$	6.84654e7	−	1.18586e8i	0.615865	−	1.06671i	−0.374367	−	0.927281i	$-0.622140\pi$
$199$	6.84654e7	−	1.18586e8i	0.615865	−	1.06671i	0.990232	−	0.139429i	$-0.0445267\pi$
$200$	−3.83218e7	−	2.17334e8i	−0.338720	−	1.92098i
$201$	1.27207e7	+	7.21427e7i	0.110490	+	0.626623i
$202$	1.35514e7	−	1.13709e7i	0.115679	−	0.0970659i
$203$	9.95536e6	−	3.62346e6i	0.0835259	−	0.0304009i
$204$	6.71084e7	−	2.44255e7i	0.553441	−	0.201436i
$205$	−2.18896e7	+	1.83675e7i	−0.177459	+	0.148906i
$206$	−1.30415e7	−	7.39620e7i	−0.103942	−	0.589486i
$207$	1.94855e6	+	1.10508e7i	0.0152692	+	0.0865958i
$208$	8.04108e6	−	1.39276e7i	0.0619574	−	0.107313i
$209$	−2.03640e7	−	1.70875e7i	−0.154295	−	0.129469i
$210$	5.52713e6	+	2.01171e6i	0.0411843	+	0.0149899i
$211$	7.58927e7	+	1.31450e8i	0.556175	+	0.963323i	0.997811	+	0.0661289i	$0.0210648\pi$
$211$	7.58927e7	+	1.31450e8i	0.556175	+	0.963323i	−0.441636	+	0.897194i	$0.645602\pi$
$212$	−5.51240e7	+	9.54776e7i	−0.397343	+	0.688218i
$213$	−1.15366e7	+	9.68039e6i	−0.0817995	+	0.0686379i
$214$	−4.41817e7	−	7.65250e7i	−0.308173	−	0.533771i
$215$	7.68211e7	−	4.35674e8i	0.527164	−	2.98970i
$216$	1.14667e8			0.774196
$217$	905106.	−	5.13311e6i	0.00601299	−	0.0341013i
$218$	8.02930e7	+	6.73739e7i	0.524904	+	0.440447i
$219$	−1.64061e7	+	5.97132e6i	−0.105548	+	0.0384163i
$220$	−3.01844e8	−	1.09862e8i	−1.91119	−	0.695615i
$221$	−2.72886e7			−0.170062
$222$	−6.58111e6	+	6.06006e7i	−0.0403704	+	0.371742i
$223$	−6.23253e6			−0.0376355			−0.0188177	−	0.999823i	$-0.505990\pi$
$223$	−6.23253e6			−0.0376355			−0.0188177	+	0.999823i	$0.505990\pi$
$224$	−9.24932e6	−	3.36648e6i	−0.0549847	−	0.0200128i
$225$	5.32703e7	−	1.93888e7i	0.311779	−	0.113478i
$226$	5.15448e7	+	4.32512e7i	0.297033	+	0.249241i
$227$	1.38894e7	−	7.87708e7i	0.0788122	−	0.446966i	−0.919709	−	0.392601i	$-0.871575\pi$
$227$	1.38894e7	−	7.87708e7i	0.0788122	−	0.446966i	0.998521	−	0.0543654i	$-0.0173136\pi$
$228$	2.23617e7			0.124949
$229$	−5.80594e6	+	3.29271e7i	−0.0319483	+	0.181188i	−0.996606	−	0.0823178i	$-0.973768\pi$
$229$	−5.80594e6	+	3.29271e7i	−0.0319483	+	0.181188i	0.964658	+	0.263506i	$0.0848788\pi$
$230$	−4.95278e7	−	8.57847e7i	−0.268412	−	0.464903i
$231$	1.04303e7	−	8.75208e6i	0.0556745	−	0.0467164i
$232$	−1.01384e8	+	1.75601e8i	−0.533040	+	0.923252i
$233$	−86162.4	−	149238.i	−0.000446244	−	0.000772917i	0.865802	−	0.500386i	$-0.166809\pi$
$233$	−86162.4	−	149238.i	−0.000446244	−	0.000772917i	−0.866248	+	0.499613i	$0.833475\pi$
$234$	−2.09069e6	−	760949.i	−0.0106668	−	0.00388240i
$235$	1.40203e8	+	1.17644e8i	0.704723	+	0.591333i
$236$	−1.37546e8	+	2.38237e8i	−0.681171	+	1.17982i
$237$	1.91418e7	+	1.08558e8i	0.0934035	+	0.529717i
$238$	663697.	+	3.76401e6i	0.00319117	+	0.0180981i
$239$	2.62765e8	−	2.20486e8i	1.24502	−	1.04469i	0.247903	−	0.968785i	$-0.420259\pi$
$239$	2.62765e8	−	2.20486e8i	1.24502	−	1.04469i	0.997115	−	0.0759087i	$-0.0241858\pi$
$240$	1.96422e8	−	7.14918e7i	0.917173	−	0.333824i
$241$	1.03751e8	−	3.77623e7i	0.477456	−	0.173780i	−0.0920711	−	0.995752i	$-0.529349\pi$
$241$	1.03751e8	−	3.77623e7i	0.477456	−	0.173780i	0.569527	+	0.821973i	$0.307126\pi$
$242$	4.08344e7	−	3.42642e7i	0.185214	−	0.155413i
$243$	9.66086e6	+	5.47895e7i	0.0431911	+	0.244949i
$244$	7.10014e6	+	4.02669e7i	0.0312898	+	0.177453i
$245$	−2.19104e8	+	3.79500e8i	−0.951852	+	1.64866i
$246$	8.10817e6	+	6.80356e6i	0.0347256	+	0.0291382i
$247$	−8.02934e6	−	2.92244e6i	−0.0339032	−	0.0123398i
$248$	4.98799e7	+	8.63945e7i	0.207656	+	0.359671i
$249$	1.26680e8	−	2.19417e8i	0.520009	−	0.900682i
$250$	−2.38770e8	+	2.00352e8i	−0.966473	+	0.810967i
$251$	−1.79535e8	−	3.10964e8i	−0.716624	−	1.24123i	−0.962330	−	0.271884i	$-0.912353\pi$
$251$	−1.79535e8	−	3.10964e8i	−0.716624	−	1.24123i	0.245707	−	0.969344i	$-0.420980\pi$
$252$	284467.	−	1.61329e6i	0.00111977	−	0.00635056i
$253$	−2.29303e8			−0.890200
$254$	−2.37309e7	+	1.34585e8i	−0.0908649	+	0.515320i
$255$	−2.71703e8	−	2.27986e8i	−1.02613	−	0.861029i
$256$	6.12932e7	−	2.23089e7i	0.228335	−	0.0831072i
$257$	−2.60075e8	−	9.46597e7i	−0.955726	−	0.347856i	−0.183369	−	0.983044i	$-0.558700\pi$
$257$	−2.60075e8	−	9.46597e7i	−0.955726	−	0.347856i	−0.772357	+	0.635188i	$0.780922\pi$
$258$	−1.63869e8			−0.594055
$259$	1.64695e7	+	4.78418e6i	0.0589021	+	0.0171103i
$260$	−1.03248e8			−0.364313
$261$	−4.89449e7	−	1.78145e7i	−0.170398	−	0.0620199i
$262$	−3.54071e7	+	1.28871e7i	−0.121629	+	0.0442692i
$263$	1.54733e8	+	1.29836e8i	0.524489	+	0.440099i	0.866193	−	0.499709i	$-0.166560\pi$
$263$	1.54733e8	+	1.29836e8i	0.524489	+	0.440099i	−0.341704	+	0.939808i	$0.611004\pi$
$264$	−4.52523e7	+	2.56638e8i	−0.151365	+	0.858436i
$265$	5.47546e8			1.80742
$266$	−207818.	+	1.17859e6i	−0.000677014	+	0.00383954i
$267$	2.78009e8	+	4.81525e8i	0.893859	+	1.54821i
$268$	−1.37969e8	+	1.15770e8i	−0.437834	+	0.367386i
$269$	2.26814e8	−	3.92853e8i	0.710454	−	1.23054i	−0.254233	−	0.967143i	$-0.581823\pi$
$269$	2.26814e8	−	3.92853e8i	0.710454	−	1.23054i	0.964687	−	0.263399i	$-0.0848437\pi$
$270$	−1.30008e8	−	2.25181e8i	−0.401974	−	0.696239i
$271$	−3.16087e8	−	1.15046e8i	−0.964747	−	0.351139i	−0.188855	−	0.982005i	$-0.560478\pi$
$271$	−3.16087e8	−	1.15046e8i	−0.964747	−	0.351139i	−0.775892	+	0.630866i	$0.782700\pi$
$272$	1.04051e8	+	8.73088e7i	0.313511	+	0.263067i
$273$	2.18826e6	−	3.79017e6i	0.00650922	−	0.0112743i
$274$	2.95689e7	+	1.67694e8i	0.0868377	+	0.492481i
$275$	2.01158e8	+	1.14082e9i	0.583275	+	3.30792i
$276$	1.47760e8	−	1.23986e8i	0.423035	−	0.354969i
$277$	−1.35626e8	+	4.93638e7i	−0.383410	+	0.139550i	−0.526532	−	0.850155i	$-0.676508\pi$
$277$	−1.35626e8	+	4.93638e7i	−0.383410	+	0.139550i	0.143122	+	0.989705i	$0.454286\pi$
$278$	1.38203e8	−	5.03016e7i	0.385797	−	0.140419i
$279$	−1.96306e7	+	1.64720e7i	−0.0541151	+	0.0454080i
$280$	5.49994e6	+	3.11917e7i	0.0149729	+	0.0849154i
$281$	−1.09438e8	−	6.20652e8i	−0.294235	−	1.66869i	−0.670295	−	0.742095i	$-0.733832\pi$
$281$	−1.09438e8	−	6.20652e8i	−0.294235	−	1.66869i	0.376060	−	0.926595i	$-0.377279\pi$
$282$	3.38967e7	−	5.87108e7i	0.0900089	−	0.155900i
$283$	7.21423e6	+	6.05345e6i	0.0189207	+	0.0158764i	0.652199	−	0.758048i	$-0.273847\pi$
$283$	7.21423e6	+	6.05345e6i	0.0189207	+	0.0158764i	−0.633278	+	0.773924i	$0.718291\pi$
$284$	−3.47934e7	−	1.26638e7i	−0.0901329	−	0.0328057i
$285$	−5.55296e7	−	9.61800e7i	−0.142091	−	0.246109i
$286$	2.27322e7	−	3.93734e7i	0.0574593	−	0.0995225i
$287$	2.28124e6	−	1.91419e6i	0.00569619	−	0.00477967i
$288$	2.41960e7	+	4.19088e7i	0.0596857	+	0.103379i
$289$	−3.12327e7	+	1.77129e8i	−0.0761145	+	0.431667i
$290$	4.59789e8			1.10705
$291$	−2.94959e6	+	1.67279e7i	−0.00701675	+	0.0397940i
$292$	−3.28820e7	−	2.75913e7i	−0.0772892	−	0.0648533i
$293$	−2.82569e8	+	1.02847e8i	−0.656277	+	0.238865i	−0.648628	−	0.761105i	$-0.724657\pi$
$293$	−2.82569e8	+	1.02847e8i	−0.656277	+	0.238865i	−0.00764890	+	0.999971i	$0.502435\pi$
$294$	1.52529e8	+	5.55160e7i	0.350055	+	0.127410i
$295$	1.36624e9			3.09850
$296$	−3.00326e8	+	1.32472e8i	−0.673087	+	0.296896i
$297$	−6.01909e8			−1.33316
$298$	−2.89343e8	−	1.05312e8i	−0.633367	−	0.230527i
$299$	−6.92595e7	+	2.52084e7i	−0.149841	+	0.0545376i
$300$	−7.46477e8	−	6.26368e8i	−1.59622	−	1.33938i
$301$	−8.00597e6	+	4.54041e7i	−0.0169212	+	0.0959649i
$302$	−7.62477e7			−0.159295
$303$	2.97080e7	−	1.68483e8i	0.0613514	−	0.347941i
$304$	2.12654e7	+	3.68328e7i	0.0434127	+	0.0751929i
$305$	1.55561e8	−	1.30531e8i	0.313943	−	0.263430i
$306$	9.39550e6	−	1.62735e7i	0.0187454	−	0.0324680i
$307$	−3.20662e8	−	5.55402e8i	−0.632503	−	1.09553i	−0.987038	−	0.160485i	$-0.948694\pi$
$307$	−3.20662e8	−	5.55402e8i	−0.632503	−	1.09553i	0.354535	−	0.935043i	$-0.384639\pi$
$308$	3.14569e7	+	1.14494e7i	0.0613463	+	0.0223282i
$309$	−5.56398e8	−	4.66874e8i	−1.07283	−	0.900212i
$310$	1.13106e8	−	1.95906e8i	0.215636	−	0.373492i
$311$	1.26325e8	+	7.16425e8i	0.238138	+	1.35055i	0.835904	+	0.548875i	$0.184944\pi$
$311$	1.26325e8	+	7.16425e8i	0.238138	+	1.35055i	−0.597767	+	0.801670i	$0.703945\pi$
$312$	1.45454e7	+	8.24909e7i	0.0271134	+	0.153768i
$313$	3.23785e8	−	2.71688e8i	0.596831	−	0.500800i	−0.293594	−	0.955930i	$-0.594852\pi$
$313$	3.23785e8	−	2.71688e8i	0.596831	−	0.500800i	0.890425	+	0.455130i	$0.150407\pi$
$314$	−1.02460e8	+	3.72924e7i	−0.186767	+	0.0679778i
$315$	−7.64536e6	+	2.78268e6i	−0.0137820	+	0.00501622i
$316$	−2.07612e8	+	1.74207e8i	−0.370124	+	0.310571i
$317$	5.63948e7	+	3.19831e8i	0.0994332	+	0.563914i	0.993298	+	0.115578i	$0.0368720\pi$
$317$	5.63948e7	+	3.19831e8i	0.0994332	+	0.563914i	−0.893865	+	0.448336i	$0.852017\pi$
$318$	−3.52189e7	−	1.99736e8i	−0.0614159	−	0.348307i
$319$	5.32181e8	−	9.21764e8i	0.917893	−	1.58984i
$320$	1.41329e8	+	1.18589e8i	0.241104	+	0.202311i
$321$	−8.03032e8	−	2.92280e8i	−1.35508	−	0.493209i
$322$	5.16158e6	+	8.94012e6i	0.00861563	+	0.0149227i
$323$	3.60836e7	−	6.24987e7i	0.0595801	−	0.103196i
$324$	3.38558e8	−	2.84084e8i	0.553001	−	0.464023i
$325$	1.86175e8	+	3.22465e8i	0.300836	+	0.521064i
$326$	−2.51628e7	+	1.42705e8i	−0.0402251	+	0.228128i
$327$	1.01367e9			1.60318
$328$	−9.89722e6	+	5.61299e7i	−0.0154866	+	0.0878286i
$329$	−1.46113e7	−	1.22604e7i	−0.0226206	−	0.0189809i
$330$	5.55287e8	−	2.02108e8i	0.850587	−	0.309588i
$331$	−5.36380e7	−	1.95226e7i	−0.0812969	−	0.0295897i	0.301052	−	0.953608i	$-0.402662\pi$
$331$	−5.36380e7	−	1.95226e7i	−0.0812969	−	0.0295897i	−0.382348	+	0.924018i	$0.624885\pi$
$332$	6.22910e8			0.934204
$333$	−4.69084e7	−	7.00654e7i	−0.0696138	−	0.103980i
$334$	−1.69368e7			−0.0248725
$335$	8.40548e8	+	3.05934e8i	1.22153	+	0.444602i
$336$	−2.04703e7	+	7.45057e6i	−0.0294399	+	0.0107152i
$337$	−6.49072e8	−	5.44636e8i	−0.923822	−	0.775179i	0.0508758	−	0.998705i	$-0.483799\pi$
$337$	−6.49072e8	−	5.44636e8i	−0.923822	−	0.775179i	−0.974698	+	0.223526i	$0.928243\pi$
$338$	−4.67451e7	+	2.65105e8i	−0.0658458	+	0.373430i
$339$	6.50737e8			0.907208
$340$	1.51425e8	−	8.58774e8i	0.208940	−	1.18496i
$341$	−2.61829e8	−	4.53501e8i	−0.357583	−	0.619352i
$342$	4.50731e6	−	3.78208e6i	0.00609292	−	0.00511257i
$343$	4.57545e7	−	7.92491e7i	0.0612215	−	0.106039i
$344$	−4.41205e8	−	7.64189e8i	−0.584367	−	1.01215i
$345$	−9.00201e8	−	3.27646e8i	−1.18025	−	0.429575i
$346$	4.26215e8	+	3.57637e8i	0.553174	+	0.464168i
$347$	−5.25156e8	+	9.09597e8i	−0.674738	+	1.16868i	0.301807	+	0.953369i	$0.402410\pi$
$347$	−5.25156e8	+	9.09597e8i	−0.674738	+	1.16868i	−0.976545	+	0.215312i	$0.930923\pi$
$348$	1.55473e8	+	8.81730e8i	0.197755	+	1.12152i
$349$	1.03300e8	+	5.85845e8i	0.130081	+	0.737724i	0.978160	+	0.207854i	$0.0666480\pi$
$349$	1.03300e8	+	5.85845e8i	0.130081	+	0.737724i	−0.848079	+	0.529869i	$0.822241\pi$
$350$	3.99507e7	−	3.35226e7i	0.0498065	−	0.0417927i
$351$	−1.81803e8	+	6.61709e7i	−0.224402	+	0.0816756i
$352$	−9.29240e8	+	3.38216e8i	−1.13561	+	0.413328i
$353$	−2.39185e8	+	2.00700e8i	−0.289416	+	0.242849i	−0.775923	−	0.630828i	$-0.782715\pi$
$353$	−2.39185e8	+	2.00700e8i	−0.289416	+	0.242849i	0.486507	+	0.873677i	$0.338271\pi$
$354$	−8.78787e7	−	4.98385e8i	−0.105286	−	0.597109i
$355$	3.19324e7	+	1.81098e8i	0.0378819	+	0.214839i
$356$	−6.83510e8	+	1.18387e9i	−0.802916	+	1.39069i
$357$	2.83158e7	+	2.37597e7i	0.0329374	+	0.0276378i
$358$	3.50454e8	+	1.27555e8i	0.403683	+	0.146929i
$359$	−2.63078e8	−	4.55665e8i	−0.300092	−	0.519774i	0.676065	−	0.736842i	$-0.263684\pi$
$359$	−2.63078e8	−	4.55665e8i	−0.300092	−	0.519774i	−0.976156	+	0.217068i	$0.930351\pi$
$360$	7.78589e7	−	1.34856e8i	0.0879528	−	0.152339i
$361$	−6.67435e8	+	5.60045e8i	−0.746679	+	0.626538i
$362$	−7.21870e7	−	1.25032e8i	−0.0799796	−	0.138529i
$363$	8.95195e7	−	5.07690e8i	0.0982300	−	0.557090i
$364$	1.07601e7			0.0116939
$365$	−3.70190e7	+	2.09945e8i	−0.0398473	+	0.225986i
$366$	−5.76217e7	−	4.83503e7i	−0.0614330	−	0.0515484i
$367$	−1.50833e9	+	5.48988e8i	−1.59282	+	0.579738i	−0.977940	−	0.208885i	$-0.933017\pi$
$367$	−1.50833e9	+	5.48988e8i	−1.59282	+	0.579738i	−0.614877	+	0.788623i	$0.710794\pi$
$368$	3.44738e8	+	1.25474e8i	0.360597	+	0.131247i
$369$	−1.46409e7			−0.0151696
$370$	6.00652e8	+	4.39577e8i	0.616477	+	0.451158i
$371$	−5.70629e7			−0.0580156
$372$	4.13931e8	+	1.50659e8i	0.416896	+	0.151738i
$373$	−1.91196e8	+	6.95897e7i	−0.190765	+	0.0694327i	−0.435636	−	0.900123i	$-0.643476\pi$
$373$	−1.91196e8	+	6.95897e7i	−0.190765	+	0.0694327i	0.244871	+	0.969556i	$0.421254\pi$
$374$	2.94152e8	+	2.46823e8i	0.290751	+	0.243969i
$375$	−5.23445e8	+	2.96860e9i	−0.512579	+	2.90698i
$376$	3.65058e8			0.354164
$377$	5.94079e7	−	3.36919e8i	0.0571017	−	0.323840i
$378$	1.35489e7	+	2.34674e7i	0.0129028	+	0.0223482i
$379$	−1.49415e8	+	1.25374e8i	−0.140980	+	0.118296i	−0.710550	−	0.703646i	$-0.751554\pi$
$379$	−1.49415e8	+	1.25374e8i	−0.140980	+	0.118296i	0.569570	+	0.821943i	$0.307110\pi$
$380$	1.36524e8	−	2.36467e8i	0.127634	−	0.221069i
$381$	6.60828e8	+	1.14459e9i	0.612140	+	1.06026i
$382$	−2.25378e8	−	8.20310e7i	−0.206867	−	0.0752933i
$383$	3.90090e8	+	3.27324e8i	0.354788	+	0.297702i	0.802709	−	0.596371i	$-0.203391\pi$
$383$	3.90090e8	+	3.27324e8i	0.354788	+	0.297702i	−0.447921	+	0.894073i	$0.647836\pi$
$384$	5.29203e8	−	9.16606e8i	0.476939	−	0.826082i
$385$	−2.88702e7	−	1.63731e8i	−0.0257832	−	0.146224i
$386$	−6.85745e7	−	3.88906e8i	−0.0606886	−	0.344182i
$387$	1.73639e8	−	1.45701e8i	0.152286	−	0.127783i
$388$	−3.92431e7	+	1.42833e7i	−0.0341077	+	0.0124142i
$389$	1.59456e9	−	5.80372e8i	1.37346	−	0.499900i	0.453273	−	0.891372i	$-0.350256\pi$
$389$	1.59456e9	−	5.80372e8i	1.37346	−	0.499900i	0.920190	+	0.391472i	$0.128034\pi$
$390$	1.45502e8	−	1.22091e8i	0.124206	−	0.104222i
$391$	−1.08096e8	−	6.13043e8i	−0.0914516	−	0.518648i
$392$	1.51779e8	+	8.60780e8i	0.127265	+	0.721757i
$393$	−1.82200e8	+	3.15580e8i	−0.151417	+	0.262262i
$394$	−6.06259e8	−	5.08712e8i	−0.499369	−	0.419021i
$395$	1.26483e9	+	4.60362e8i	1.03263	+	0.375846i
$396$	−8.22906e7	−	1.42532e8i	−0.0665913	−	0.115339i
$397$	−3.95591e8	+	6.85184e8i	−0.317307	+	0.549592i	−0.979925	−	0.199365i	$-0.936112\pi$
$397$	−3.95591e8	+	6.85184e8i	−0.317307	+	0.549592i	0.662618	+	0.748958i	$0.269445\pi$
$398$	−4.74435e8	+	3.98098e8i	−0.377212	+	0.316519i
$399$	5.78705e6	+	1.00235e7i	0.00456092	+	0.00789974i
$400$	3.21834e8	−	1.82521e9i	0.251433	−	1.42595i
$401$	−8.71209e8			−0.674710			−0.337355	−	0.941377i	$-0.609532\pi$
$401$	−8.71209e8			−0.674710			−0.337355	+	0.941377i	$0.609532\pi$
$402$	5.75350e7	−	3.26297e8i	0.0441714	−	0.250508i
$403$	−1.28939e8	−	1.08193e8i	−0.0981336	−	0.0823439i
$404$	3.95254e8	−	1.43861e8i	0.298223	−	0.108544i
$405$	−2.06260e9	−	7.50724e8i	−1.54284	−	0.561549i
$406$	−4.79173e7			−0.0355346
$407$	1.57646e9	−	6.95372e8i	1.15905	−	0.511254i
$408$	−7.07458e8			−0.515692
$409$	−9.21142e8	−	3.35268e8i	−0.665725	−	0.242304i	−0.0130191	−	0.999915i	$-0.504144\pi$
$409$	−9.21142e8	−	3.35268e8i	−0.665725	−	0.242304i	−0.652706	+	0.757611i	$0.726366\pi$
$410$	1.21448e8	−	4.42035e7i	0.0870256	−	0.0316747i
$411$	1.26152e9	+	1.05854e9i	0.896288	+	0.752075i
$412$	3.10090e8	−	1.75861e9i	0.218448	−	1.23888i
$413$	−1.42384e8			−0.0994572
$414$	8.81319e6	−	4.99821e7i	0.00610424	−	0.0346189i
$415$	−1.54684e9	−	2.67920e9i	−1.06237	−	1.84008i
$416$	−2.43490e8	+	2.04312e8i	−0.165826	+	0.139145i
$417$	7.11172e8	−	1.23179e9i	0.480285	−	0.831877i
$418$	6.01175e7	+	1.04127e8i	0.0402610	+	0.0697340i
$419$	5.46507e8	+	1.98912e8i	0.362950	+	0.132103i	0.517056	−	0.855951i	$-0.327028\pi$
$419$	5.46507e8	+	1.98912e8i	0.362950	+	0.132103i	−0.154107	+	0.988054i	$0.549250\pi$
$420$	1.07134e8	+	8.98963e7i	0.0705596	+	0.0592065i
$421$	−1.06176e9	+	1.83903e9i	−0.693490	+	1.20116i	0.277197	+	0.960813i	$0.410594\pi$
$421$	−1.06176e9	+	1.83903e9i	−0.693490	+	1.20116i	−0.970687	+	0.240347i	$0.922739\pi$
$422$	−1.19212e8	−	6.76087e8i	−0.0772196	−	0.437934i
$423$	1.62838e7	+	9.23501e7i	0.0104608	+	0.0593261i
$424$	8.36631e8	−	7.02017e8i	0.533032	−	0.447267i
$425$	−2.95518e9	+	1.07560e9i	−1.86734	+	0.679655i
$426$	6.40077e7	−	2.32969e7i	0.0401143	−	0.0146004i
$427$	−1.62119e7	+	1.36034e7i	−0.0100771	+	0.00845571i
$428$	−3.64841e8	−	2.06912e9i	−0.224932	−	1.27565i
$429$	−7.63513e7	−	4.33010e8i	−0.0466892	−	0.264787i
$430$	−1.00046e9	+	1.73285e9i	−0.606823	+	1.05105i
$431$	−1.77928e8	−	1.49299e8i	−0.107047	−	0.0898229i	0.587693	−	0.809084i	$-0.300036\pi$
$431$	−1.77928e8	−	1.49299e8i	−0.107047	−	0.0898229i	−0.694740	+	0.719261i	$0.744481\pi$
$432$	9.04921e8	+	3.29364e8i	0.540030	+	0.196555i
$433$	5.58719e8	+	9.67730e8i	0.330739	+	0.572857i	0.982657	−	0.185432i	$-0.0593686\pi$
$433$	5.58719e8	+	9.67730e8i	0.330739	+	0.572857i	−0.651918	+	0.758290i	$0.726035\pi$
$434$	−1.17875e7	+	2.04165e7i	−0.00692160	+	0.0119886i
$435$	3.40634e9	−	2.85826e9i	1.98415	−	1.66490i
$436$	1.24611e9	+	2.15832e9i	0.720032	+	1.24713i
$437$	3.38472e7	−	1.91957e8i	0.0194016	−	0.110032i
$438$	7.89659e7			0.0449035
$439$	5.01026e8	−	2.84146e9i	0.282641	−	1.60294i	−0.430952	−	0.902375i	$-0.641822\pi$
$439$	5.01026e8	−	2.84146e9i	0.282641	−	1.60294i	0.713593	−	0.700561i	$-0.247067\pi$
$440$	2.43759e9	+	2.04538e9i	1.36419	+	1.14469i
$441$	−2.10984e8	+	7.67920e7i	−0.117143	+	0.0426365i
$442$	1.15981e8	+	4.22137e7i	0.0638866	+	0.0232528i
$443$	−1.98879e9			−1.08686			−0.543432	−	0.839453i	$-0.682876\pi$
$443$	−1.98879e9			−1.08686			−0.543432	+	0.839453i	$0.682876\pi$
$444$	−6.39865e8	+	1.30050e9i	−0.346935	+	0.705129i
$445$	6.78929e9			3.65228
$446$	2.64894e7	+	9.64134e6i	0.0141384	+	0.00514595i
$447$	−2.79825e9	+	1.01848e9i	−1.48187	+	0.539357i
$448$	−1.47287e7	−	1.23588e7i	−0.00773910	−	0.00649387i
$449$	−9.50469e7	+	5.39038e8i	−0.0495537	+	0.281033i	−0.999508	−	0.0313551i	$-0.990018\pi$
$449$	−9.50469e7	+	5.39038e8i	−0.0495537	+	0.281033i	0.949955	+	0.312388i	$0.101129\pi$
$450$	−2.56402e8			−0.132641
$451$	5.19523e7	−	2.94636e8i	0.0266678	−	0.151241i
$452$	7.99948e8	+	1.38555e9i	0.407453	+	0.705729i
$453$	−5.64879e8	+	4.73990e8i	−0.285504	+	0.239566i
$454$	−1.80886e8	+	3.13304e8i	−0.0907214	+	0.157134i
$455$	−2.67199e7	−	4.62802e7i	−0.0132982	−	0.0230332i
$456$	−2.08161e8	−	7.57645e7i	−0.102807	−	0.0374187i
$457$	−2.19978e9	−	1.84583e9i	−1.07813	−	0.904661i	−0.0823687	−	0.996602i	$-0.526249\pi$
$457$	−2.19978e9	−	1.84583e9i	−1.07813	−	0.904661i	−0.995764	+	0.0919408i	$0.970693\pi$
$458$	7.56125e7	−	1.30965e8i	0.0367760	−	0.0636979i
$459$	−2.83747e8	−	1.60921e9i	−0.136958	−	0.776727i
$460$	−4.08988e8	−	2.31948e9i	−0.195911	−	1.11106i
$461$	−1.23753e9	+	1.03841e9i	−0.588306	+	0.493647i	−0.887663	−	0.460494i	$-0.847672\pi$
$461$	−1.23753e9	+	1.03841e9i	−0.588306	+	0.493647i	0.299357	+	0.954141i	$0.403228\pi$
$462$	−5.78697e7	+	2.10628e7i	−0.0273026	+	0.00993733i
$463$	−3.33816e9	+	1.21499e9i	−1.56305	+	0.568904i	−0.971433	−	0.237314i	$-0.923733\pi$
$463$	−3.33816e9	+	1.21499e9i	−1.56305	+	0.568904i	−0.591618	+	0.806218i	$0.701511\pi$
$464$	−1.30448e9	+	1.09459e9i	−0.606212	+	0.508672i
$465$	−3.79893e8	−	2.15448e9i	−0.175217	−	0.993705i
$466$	135344.	+	767575.i	6.19568e−5	+	0.000351374i
$467$	1.17056e9	−	2.02746e9i	0.531843	−	0.921179i	−0.467466	−	0.884011i	$-0.654833\pi$
$467$	1.17056e9	−	2.02746e9i	0.531843	−	0.921179i	0.999309	−	0.0371682i	$-0.0118337\pi$
$468$	−4.05246e7	−	3.40042e7i	−0.0182750	−	0.0153346i
$469$	−8.75983e7	−	3.18832e7i	−0.0392095	−	0.0142711i
$470$	−4.13898e8	−	7.16892e8i	−0.183887	−	0.318501i
$471$	−5.27247e8	+	9.13218e8i	−0.232509	+	0.402718i
$472$	2.08757e9	−	1.75168e9i	0.913786	−	0.766758i
$473$	2.31596e9	+	4.01137e9i	1.00628	+	1.74292i
$474$	8.65772e7	−	4.91004e8i	0.0373404	−	0.211768i
$475$	−9.84716e8			−0.421583
$476$	−1.57809e7	+	8.94977e7i	−0.00670666	+	0.0380354i
$477$	2.14911e8	+	1.80331e8i	0.0906658	+	0.0760777i
$478$	−1.45788e9	+	5.30624e8i	−0.610553	+	0.222223i
$479$	4.19072e9	+	1.52530e9i	1.74227	+	0.634133i	0.999377	−	0.0352809i	$-0.0112326\pi$
$479$	4.19072e9	+	1.52530e9i	1.74227	+	0.634133i	0.742889	+	0.669414i	$0.233455\pi$
$480$	−4.13130e9			−1.70507
$481$	3.99716e8	−	3.83342e8i	0.163773	−	0.157065i
$482$	−4.99376e8			−0.203125
$483$	9.38151e7	+	3.41459e7i	0.0378842	+	0.0137887i
$484$	1.19102e9	−	4.33496e8i	0.477486	−	0.173791i
$485$	1.58884e8	+	1.33320e8i	0.0632390	+	0.0530638i
$486$	4.36955e7	−	2.47810e8i	0.0172667	−	0.0979245i
$487$	−6.92163e8			−0.271555			−0.135777	−	0.990739i	$-0.543353\pi$
$487$	−6.92163e8			−0.271555			−0.135777	+	0.990739i	$0.543353\pi$
$488$	7.03358e7	−	3.98894e8i	0.0273973	−	0.155378i
$489$	7.00702e8	+	1.21365e9i	0.270989	+	0.469368i
$490$	1.51829e9	−	1.27400e9i	0.583002	−	0.489196i
$491$	1.24420e9	−	2.15501e9i	0.474355	−	0.821608i	−0.525213	−	0.850971i	$-0.676015\pi$
$491$	1.24420e9	−	2.15501e9i	0.474355	−	0.821608i	0.999569	+	0.0293629i	$0.00934784\pi$
$492$	1.25834e8	+	2.17952e8i	0.0476345	+	0.0825054i
$493$	2.71522e9	+	9.88260e8i	1.02057	+	0.371456i
$494$	2.96053e7	+	2.48418e7i	0.0110491	+	0.00927126i
$495$	−4.08696e8	+	7.07882e8i	−0.151454	+	0.262327i
$496$	1.45483e8	+	8.25074e8i	0.0535335	+	0.303604i
$497$	−3.32786e6	−	1.88732e7i	−0.00121595	−	0.00689602i
$498$	−8.77837e8	+	7.36593e8i	−0.318501	+	0.267254i
$499$	2.08063e9	−	7.57286e8i	0.749622	−	0.272840i	0.0611754	−	0.998127i	$-0.480515\pi$
$499$	2.08063e9	−	7.57286e8i	0.749622	−	0.272840i	0.688447	+	0.725287i	$0.258293\pi$
$500$	−6.96422e9	+	2.53477e9i	−2.49160	+	0.906867i
$501$	−1.25476e8	+	1.05287e8i	−0.0445788	+	0.0374060i
$502$	2.82014e8	+	1.59938e9i	0.0994964	+	0.564272i
$503$	−2.92952e7	−	1.66141e8i	−0.0102638	−	0.0582090i	0.979246	−	0.202677i	$-0.0649641\pi$
$503$	−2.92952e7	−	1.66141e8i	−0.0102638	−	0.0582090i	−0.989509	+	0.144468i	$0.953853\pi$
$504$	−8.11412e6	+	1.40541e7i	−0.00282315	+	0.00488985i
$505$	−1.60027e9	−	1.34279e9i	−0.552935	−	0.463967i
$506$	9.74578e8	+	3.54717e8i	0.334418	+	0.121718i
$507$	1.30170e9	+	2.25461e9i	0.443591	+	0.768322i
$508$	−1.62471e9	+	2.81407e9i	−0.549859	+	0.952385i
$509$	4.68010e8	−	3.92707e8i	0.157305	−	0.131995i	−0.560738	−	0.827993i	$-0.689482\pi$
$509$	4.68010e8	−	3.92707e8i	0.157305	−	0.131995i	0.718043	+	0.695999i	$0.245038\pi$
$510$	8.02107e8	+	1.38929e9i	0.267754	+	0.463764i
$511$	3.85796e6	−	2.18796e7i	0.00127904	−	0.00725381i
$512$	2.80216e9			0.922674
$513$	8.88474e7	−	5.03879e8i	0.0290559	−	0.164784i
$514$	9.58934e8	+	8.04641e8i	0.311471	+	0.261355i
$515$	−8.33400e9	+	3.03333e9i	−2.68861	+	0.978575i
$516$	−3.66136e9	−	1.33263e9i	−1.17319	−	0.427006i
$517$	−1.91626e9			−0.609869
$518$	−6.25974e7	−	4.58108e7i	−0.0197880	−	0.0144815i
$519$	5.38083e9			1.68952
$520$	9.61117e8	+	3.49818e8i	0.299754	+	0.109101i
$521$	4.24705e9	−	1.54580e9i	1.31569	−	0.478874i	0.413618	−	0.910450i	$-0.364265\pi$
$521$	4.24705e9	−	1.54580e9i	1.31569	−	0.478874i	0.902076	+	0.431577i	$0.142043\pi$
$522$	1.80466e8	+	1.51429e8i	0.0555328	+	0.0465976i
$523$	−8.30527e8	+	4.71015e9i	−0.253862	+	1.43972i	0.545114	+	0.838362i	$0.316486\pi$
$523$	−8.30527e8	+	4.71015e9i	−0.253862	+	1.43972i	−0.798977	+	0.601362i	$0.794625\pi$
$524$	−8.95913e8			−0.272023
$525$	8.75821e7	−	4.96703e8i	0.0264154	−	0.149809i
$526$	−4.56792e8	−	7.91188e8i	−0.136858	−	0.237044i
$527$	1.08901e9	−	9.13787e8i	0.324111	−	0.271962i
$528$	−1.09427e9	+	1.89534e9i	−0.323525	+	0.560361i
$529$	8.61748e8	+	1.49259e9i	0.253096	+	0.438375i
$530$	−2.32717e9	−	8.47019e8i	−0.678988	−	0.247131i
$531$	5.36248e8	+	4.49965e8i	0.155430	+	0.130421i
$532$	−1.42280e7	+	2.46436e7i	−0.00409688	+	0.00709600i
$533$	−1.66990e7	−	9.47045e7i	−0.00477688	−	0.0270910i
$534$	−4.36697e8	−	2.47663e9i	−0.124104	−	0.703828i
$535$	−7.99350e9	+	6.70734e9i	−2.25683	+	1.89370i
$536$	1.67657e9	−	6.10222e8i	0.470268	−	0.171164i
$537$	3.38927e9	−	1.23359e9i	0.944487	−	0.343765i
$538$	−1.57172e9	+	1.31883e9i	−0.435147	+	0.365132i
$539$	−7.96714e8	−	4.51839e9i	−0.219150	−	1.24286i
$540$	−1.07357e9	−	6.08854e9i	−0.293396	−	1.66393i
$541$	−1.69936e9	+	2.94338e9i	−0.461419	+	0.799201i	−0.999032	−	0.0439910i	$-0.985993\pi$
$541$	−1.69936e9	+	2.94338e9i	−0.461419	+	0.799201i	0.537613	+	0.843192i	$0.319326\pi$
$542$	1.16545e9	+	9.77933e8i	0.314411	+	0.263822i
$543$	−1.31205e9	−	4.77546e8i	−0.351682	−	0.128002i
$544$	−1.34228e9	−	2.32489e9i	−0.357476	−	0.619166i
$545$	6.18877e9	−	1.07193e10i	1.63763	−	2.83646i
$546$	−1.51636e7	+	1.27238e7i	−0.00398684	+	0.00334536i
$547$	5.27617e8	+	9.13860e8i	0.137836	+	0.238739i	0.926677	−	0.375858i	$-0.122652\pi$
$547$	5.27617e8	+	9.13860e8i	0.137836	+	0.238739i	−0.788841	+	0.614597i	$0.789319\pi$
$548$	−7.03066e8	+	3.98729e9i	−0.182501	+	1.03501i
$549$	1.04047e8			0.0268366
$550$	9.09827e8	−	5.15989e9i	0.233179	−	1.32242i
$551$	6.93086e8	+	5.81568e8i	0.176505	+	0.148105i
$552$	−1.79556e9	+	6.53529e8i	−0.454373	+	0.165378i
$553$	−1.31816e8	−	4.79770e7i	−0.0331458	−	0.0120641i
$554$	6.52796e8			0.163115
$555$	7.18252e9	−	4.77324e8i	1.78341	−	0.118519i
$556$	3.49696e9			0.862838
$557$	−2.08415e9	−	7.58567e8i	−0.511016	−	0.185995i	0.0736260	−	0.997286i	$-0.476543\pi$
$557$	−2.08415e9	−	7.58567e8i	−0.511016	−	0.185995i	−0.584642	+	0.811291i	$0.698765\pi$
$558$	1.08915e8	−	3.96417e7i	0.0265379	−	0.00965901i
$559$	1.14051e9	+	9.57004e8i	0.276159	+	0.231725i
$560$	−4.61896e7	+	2.61954e8i	−0.0111144	+	0.0630329i
$561$	3.71358e9			0.888019
$562$	−4.94980e8	+	2.80717e9i	−0.117628	+	0.667102i
$563$	−1.59996e9	−	2.77122e9i	−0.377860	−	0.654473i	0.612891	−	0.790168i	$-0.290007\pi$
$563$	−1.59996e9	−	2.77122e9i	−0.377860	−	0.654473i	−0.990751	+	0.135695i	$0.956673\pi$
$564$	1.23482e9	−	1.03613e9i	0.289818	−	0.243186i
$565$	3.97293e9	−	6.88133e9i	0.926706	−	1.60510i
$566$	−2.12974e7	−	3.68882e7i	−0.00493707	−	0.00855126i
$567$	2.14955e8	+	7.82373e7i	0.0495230	+	0.0180249i
$568$	2.80980e8	+	2.35770e8i	0.0643362	+	0.0539845i
$569$	2.49268e9	−	4.31744e9i	0.567248	−	0.982503i	−0.429588	−	0.903025i	$-0.641341\pi$
$569$	2.49268e9	−	4.31744e9i	0.567248	−	0.982503i	0.996837	−	0.0794779i	$-0.0253253\pi$
$570$	8.72259e7	+	4.94683e8i	0.0197280	+	0.111883i
$571$	−2.60819e8	−	1.47918e9i	−0.0586290	−	0.332502i	0.941359	−	0.337407i	$-0.109550\pi$
$571$	−2.60819e8	−	1.47918e9i	−0.0586290	−	0.332502i	−0.999988	+	0.00490510i	$0.998439\pi$
$572$	8.28107e8	−	6.94865e8i	0.185012	−	0.155244i
$573$	−2.17965e9	+	7.93328e8i	−0.484000	+	0.176162i
$574$	−1.26568e7	+	4.60670e6i	−0.00279339	+	0.00101671i
$575$	−6.50676e9	+	5.45982e9i	−1.42734	+	1.19768i
$576$	1.64146e7	+	9.30917e7i	0.00357891	+	0.0202970i
$577$	2.59685e8	+	1.47275e9i	0.0562771	+	0.319163i	0.999931	−	0.0117715i	$-0.00374708\pi$
$577$	2.59685e8	+	1.47275e9i	0.0562771	+	0.319163i	−0.943654	+	0.330935i	$0.892636\pi$
$578$	4.06753e8	−	7.04517e8i	0.0876159	−	0.151755i
$579$	−2.92564e9	−	2.45491e9i	−0.626392	−	0.525605i
$580$	1.02732e10	+	3.73914e9i	2.18629	+	0.795744i
$581$	1.61205e8	+	2.79215e8i	0.0341006	+	0.0590639i
$582$	3.84134e7	−	6.65339e7i	0.00807703	−	0.0139898i
$583$	−4.39163e9	+	3.68502e9i	−0.917880	+	0.770193i
$584$	2.12610e8	+	3.68251e8i	0.0441712	+	0.0765067i
$585$	−4.56231e7	+	2.58741e8i	−0.00942191	+	0.0534343i
$586$	1.36006e9			0.279201
$587$	7.83457e8	−	4.44321e9i	0.159876	−	0.906699i	−0.794316	−	0.607504i	$-0.792171\pi$
$587$	7.83457e8	−	4.44321e9i	0.159876	−	0.906699i	0.954192	−	0.299195i	$-0.0967181\pi$
$588$	2.95652e9	+	2.48082e9i	0.599736	+	0.503239i
$589$	4.18289e8	−	1.52245e8i	0.0843477	−	0.0307000i
$590$	−5.80677e9	−	2.11349e9i	−1.16400	−	0.423661i
$591$	−7.65384e9			−1.52519
$592$	−2.75059e9	+	1.82795e8i	−0.544879	+	0.0362107i
$593$	−4.87192e9			−0.959420			−0.479710	−	0.877427i	$-0.659258\pi$
$593$	−4.87192e9			−0.959420			−0.479710	+	0.877427i	$0.659258\pi$
$594$	2.55822e9	+	9.31116e8i	0.500824	+	0.182285i
$595$	4.24127e8	−	1.54370e8i	0.0825442	−	0.0300436i
$596$	−5.60843e9	−	4.70603e9i	−1.08512	−	0.910527i
$597$	−1.04008e9	+	5.89860e9i	−0.200059	+	1.13459i
$598$	3.33361e8			0.0637472
$599$	1.57499e9	−	8.93221e9i	0.299422	−	1.69811i	−0.349242	−	0.937032i	$-0.613561\pi$
$599$	1.57499e9	−	8.93221e9i	0.299422	−	1.69811i	0.648664	−	0.761075i	$-0.275328\pi$
$600$	4.82660e9	+	8.35992e9i	0.912246	+	1.58006i
$601$	2.57306e9	−	2.15906e9i	0.483493	−	0.405698i	−0.368195	−	0.929749i	$-0.620024\pi$
$601$	2.57306e9	−	2.15906e9i	0.483493	−	0.405698i	0.851687	+	0.524050i	$0.175580\pi$
$602$	1.04264e8	−	1.80591e8i	0.0194781	−	0.0337371i
$603$	2.29155e8	+	3.96909e8i	0.0425618	+	0.0737191i
$604$	−1.70362e9	−	6.20068e8i	−0.314590	−	0.114501i
$605$	−4.82211e9	−	4.04623e9i	−0.885306	−	0.742860i
$606$	−3.86897e8	+	6.70125e8i	−0.0706221	+	0.122321i
$607$	−1.09973e9	−	6.23688e9i	−0.199584	−	1.13190i	−0.905738	−	0.423839i	$-0.860682\pi$
$607$	−1.09973e9	−	6.23688e9i	−0.199584	−	1.13190i	0.706154	−	0.708059i	$-0.250429\pi$
$608$	−1.45967e8	−	8.27822e8i	−0.0263386	−	0.149374i
$609$	−3.54994e8	+	2.97875e8i	−0.0636884	+	0.0534409i
$610$	−8.63085e8	+	3.14137e8i	−0.153957	+	0.0560357i
$611$	−5.78794e8	+	2.10664e8i	−0.102655	+	0.0373633i
$612$	3.42267e8	−	2.87196e8i	0.0603580	−	0.0506464i
$613$	1.44337e9	+	8.18573e9i	0.253084	+	1.43531i	0.800943	+	0.598740i	$0.204332\pi$
$613$	1.44337e9	+	8.18573e9i	0.253084	+	1.43531i	−0.547859	+	0.836571i	$0.684557\pi$
$614$	5.03696e8	+	2.85660e9i	0.0878171	+	0.498036i
$615$	6.24956e8	−	1.08246e9i	0.108339	−	0.187649i
$616$	−2.54035e8	−	2.13161e8i	−0.0437886	−	0.0367430i
$617$	−2.80093e9	−	1.01946e9i	−0.480070	−	0.174731i	0.0906387	−	0.995884i	$-0.471109\pi$
$617$	−2.80093e9	−	1.01946e9i	−0.480070	−	0.174731i	−0.570708	+	0.821153i	$0.693331\pi$
$618$	1.64257e9	+	2.84501e9i	0.279939	+	0.484868i
$619$	5.85184e8	−	1.01357e9i	0.0991687	−	0.171765i	−0.812172	−	0.583418i	$-0.801715\pi$
$619$	5.85184e8	−	1.01357e9i	0.0991687	−	0.171765i	0.911341	+	0.411653i	$0.135048\pi$
$620$	4.12033e9	−	3.45737e9i	0.694322	−	0.582605i
$621$	−2.20670e9	−	3.82212e9i	−0.369763	−	0.640448i
$622$	5.71361e8	−	3.24035e9i	0.0952016	−	0.539915i
$623$	−7.07551e8			−0.117233
$624$	−1.22155e8	+	6.92775e8i	−0.0201263	+	0.114142i
$625$	1.57988e10	+	1.32568e10i	2.58848	+	2.17199i
$626$	−1.79643e9	+	6.53846e8i	−0.292684	+	0.106528i
$627$	1.09268e9	+	3.97702e8i	0.177033	+	0.0644349i
$628$	−2.59257e9			−0.417707
$629$	2.60225e9	+	3.88689e9i	0.416938	+	0.622766i
$630$	3.67988e7			0.00586329
$631$	3.62356e8	+	1.31887e8i	0.0574160	+	0.0208977i	0.370568	−	0.928805i	$-0.379163\pi$
$631$	3.62356e8	+	1.31887e8i	0.0574160	+	0.0208977i	−0.313152	+	0.949703i	$0.601385\pi$
$632$	2.52286e9	−	9.18246e8i	0.397542	−	0.144694i
$633$	−5.08604e9	−	4.26769e9i	−0.797015	−	0.668775i
$634$	2.55070e8	−	1.44658e9i	0.0397510	−	0.225439i
$635$	1.61382e10			2.50119
$636$	8.37407e8	−	4.74917e9i	0.129073	−	0.732012i
$637$	−7.37372e8	−	1.27717e9i	−0.113031	−	0.195776i
$638$	−3.68778e9	+	3.09441e9i	−0.562202	+	0.471743i
$639$	−4.71102e7	+	8.15972e7i	−0.00714269	+	0.0123715i
$640$	−6.46186e9	−	1.11923e10i	−0.974379	−	1.68767i
$641$	−1.03205e9	−	3.75636e8i	−0.154774	−	0.0563332i	0.263471	−	0.964667i	$-0.415133\pi$
$641$	−1.03205e9	−	3.75636e8i	−0.154774	−	0.0563332i	−0.418245	+	0.908334i	$0.637355\pi$
$642$	2.96089e9	+	2.48448e9i	0.441621	+	0.370564i
$643$	−1.46320e9	+	2.53433e9i	−0.217052	+	0.375945i	−0.953905	−	0.300107i	$-0.902977\pi$
$643$	−1.46320e9	+	2.53433e9i	−0.217052	+	0.375945i	0.736853	+	0.676053i	$0.236311\pi$
$644$	4.26230e7	+	2.41727e8i	0.00628844	+	0.0356635i
$645$	3.36029e9	+	1.90571e10i	0.493080	+	2.79639i
$646$	−2.50043e8	+	2.09811e8i	−0.0364923	+	0.0306207i
$647$	−1.10417e10	+	4.01885e9i	−1.60277	+	0.583361i	−0.979992	−	0.199038i	$-0.936218\pi$
$647$	−1.10417e10	+	4.01885e9i	−1.60277	+	0.583361i	−0.622778	+	0.782399i	$0.713996\pi$
$648$	−4.11410e9	+	1.49741e9i	−0.593966	+	0.216186i
$649$	−1.09581e10	+	9.19490e9i	−1.57354	+	1.32035i
$650$	−2.92444e8	−	1.65853e9i	−0.0417683	−	0.236880i
$651$	3.95909e7	+	2.24531e8i	0.00562421	+	0.0318965i
$652$	−1.72274e9	+	2.98387e9i	−0.243418	+	0.421613i
$653$	−7.30031e8	−	6.12569e8i	−0.102600	−	0.0860912i	0.590045	−	0.807370i	$-0.299110\pi$
$653$	−7.30031e8	−	6.12569e8i	−0.102600	−	0.0860912i	−0.692644	+	0.721279i	$0.743554\pi$
$654$	−4.30830e9	−	1.56809e9i	−0.602259	−	0.219204i
$655$	2.22477e9	+	3.85342e9i	0.309343	+	0.535798i
$656$	−2.39331e8	+	4.14533e8i	−0.0331006	+	0.0573319i
$657$	−8.36742e7	+	7.02110e7i	−0.0115110	+	0.00965887i
$658$	4.31347e7	+	7.47115e7i	0.00590250	+	0.0102234i
$659$	7.76959e8	−	4.40635e9i	0.105755	−	0.599764i	−0.885162	−	0.465283i	$-0.845952\pi$
$659$	7.76959e8	−	4.40635e9i	0.105755	−	0.599764i	0.990916	−	0.134480i	$-0.0429365\pi$
$660$	1.40505e10			1.90234
$661$	−4.85390e8	+	2.75278e9i	−0.0653710	+	0.370738i	0.934519	+	0.355913i	$0.115830\pi$
$661$	−4.85390e8	+	2.75278e9i	−0.0653710	+	0.370738i	−0.999890	+	0.0148245i	$0.995281\pi$
$662$	1.97770e8	+	1.65949e8i	0.0264947	+	0.0222317i
$663$	1.12166e9	−	4.08252e8i	0.149474	−	0.0544040i
$664$	−5.79856e9	−	2.11050e9i	−0.768656	−	0.279768i
$665$	1.41326e8			0.0186358
$666$	9.09821e7	+	3.70355e8i	0.0119343	+	0.0485801i
$667$	7.80427e9			1.01834
$668$	−3.78424e8	−	1.37735e8i	−0.0491202	−	0.0178783i
$669$	2.56181e8	−	9.32421e7i	0.0330792	−	0.0120398i
$670$	−3.09922e9	−	2.60055e9i	−0.398098	−	0.334044i
$671$	−3.69206e8	+	2.09387e9i	−0.0471780	+	0.267560i
$672$	4.30546e8			0.0547302
$673$	1.13168e9	−	6.41807e9i	0.143110	−	0.811618i	−0.825755	−	0.564029i	$-0.809251\pi$
$673$	1.13168e9	−	6.41807e9i	0.143110	−	0.811618i	0.968865	−	0.247589i	$-0.0796382\pi$
$674$	1.91615e9	+	3.31887e9i	0.241057	+	0.417524i
$675$	−1.70799e10	+	1.43318e10i	−2.13758	+	1.79365i
$676$	−3.20035e9	+	5.54316e9i	−0.398459	+	0.690151i
$677$	−4.18596e9	−	7.25030e9i	−0.518484	−	0.898040i	−0.999769	−	0.0214761i	$-0.993163\pi$
$677$	−4.18596e9	−	7.25030e9i	−0.518484	−	0.898040i	0.481286	−	0.876564i	$-0.340170\pi$
$678$	−2.76575e9	−	1.00665e9i	−0.340807	−	0.124044i
$679$	−1.65582e7	−	1.38940e7i	−0.00202988	−	0.00170327i
$680$	−4.31923e9	+	7.48113e9i	−0.526775	+	0.912401i
$681$	6.07547e8	+	3.44557e9i	0.0737166	+	0.418067i
$682$	4.11281e8	+	2.33249e9i	0.0496470	+	0.281562i
$683$	2.33533e8	−	1.95958e8i	0.0280463	−	0.0235337i	−0.628657	−	0.777683i	$-0.716395\pi$
$683$	2.33533e8	−	1.95958e8i	0.0280463	−	0.0235337i	0.656703	+	0.754149i	$0.271950\pi$
$684$	1.31465e8	−	4.78493e7i	0.0157077	−	0.00571715i
$685$	1.88956e10	−	6.87745e9i	2.24618	−	0.817542i
$686$	−3.17058e8	+	2.66043e8i	−0.0374977	+	0.0314643i
$687$	−2.53962e8	−	1.44029e9i	−0.0298827	−	0.169473i
$688$	−1.28684e9	−	7.29806e9i	−0.150649	−	0.854373i
$689$	−9.21353e8	+	1.59583e9i	−0.107315	+	0.185874i
$690$	3.31917e9	+	2.78511e9i	0.384642	+	0.322753i
$691$	−5.20270e9	−	1.89363e9i	−0.599868	−	0.218334i	0.0241962	−	0.999707i	$-0.492297\pi$
$691$	−5.20270e9	−	1.89363e9i	−0.599868	−	0.218334i	−0.624064	+	0.781373i	$0.714520\pi$
$692$	6.61463e9	+	1.14569e10i	0.758812	+	1.31430i
$693$	4.25925e7	−	7.37724e7i	0.00486146	−	0.00842030i
$694$	3.63910e9	−	3.05356e9i	0.413271	−	0.346776i
$695$	−8.68382e9	−	1.50408e10i	−0.981214	−	1.69951i
$696$	1.54015e9	−	8.73464e9i	0.173153	−	0.982002i
$697$	8.12204e8			0.0908554
$698$	4.67221e8	−	2.64974e9i	0.0520030	−	0.294924i
$699$	5.77428e6	+	4.84520e6i	0.000639481	+	0.000536588i
$700$	1.16525e9	−	4.24115e8i	0.128403	−	0.0467348i
$701$	1.09590e10	+	3.98874e9i	1.20159	+	0.437343i	0.863779	−	0.503870i	$-0.168091\pi$
$701$	1.09590e10	+	3.98874e9i	1.20159	+	0.437343i	0.337812	+	0.941214i	$0.390313\pi$
$702$	8.75057e8			0.0954677
$703$	3.49419e8	+	1.42236e9i	0.0379317	+	0.154406i
$704$	−1.93165e9			−0.208652
$705$	−7.52287e9	−	2.73810e9i	−0.808578	−	0.294298i
$706$	1.32705e9	−	4.83006e8i	0.141929	−	0.0516579i
$707$	1.66773e8	+	1.39940e8i	0.0177484	+	0.0148927i
$708$	2.08951e9	−	1.18502e10i	0.221273	−	1.25490i
$709$	7.10322e9			0.748503			0.374252	−	0.927327i	$-0.377900\pi$
$709$	7.10322e9			0.748503			0.374252	+	0.927327i	$0.377900\pi$
$710$	1.44428e8	−	8.19094e8i	0.0151443	−	0.0858874i
$711$	3.44827e8	+	5.97258e8i	0.0359797	+	0.0623187i
$712$	1.03738e10	−	8.70466e9i	1.07711	−	0.903799i
$713$	1.91982e9	−	3.32523e9i	0.198357	−	0.343564i
$714$	−8.35922e7	−	1.44786e8i	−0.00859452	−	0.0148861i
$715$	−5.04508e9	−	1.83626e9i	−0.516175	−	0.187872i
$716$	6.79298e9	+	5.69999e9i	0.691616	+	0.580335i
$717$	−7.50205e9	+	1.29939e10i	−0.760086	+	1.31651i
$718$	4.13244e8	+	2.34362e9i	0.0416649	+	0.236293i
$719$	2.00830e9	+	1.13896e10i	0.201501	+	1.14277i	0.902852	+	0.429952i	$0.141470\pi$
$719$	2.00830e9	+	1.13896e10i	0.201501	+	1.14277i	−0.701351	+	0.712816i	$0.747419\pi$
$720$	1.00179e9	−	8.40604e8i	0.100026	−	0.0839320i
$721$	8.68534e8	−	3.16121e8i	0.0863005	−	0.0314108i
$722$	3.70307e9	−	1.34781e9i	0.366169	−	0.133275i
$723$	−3.69962e9	+	3.10435e9i	−0.364060	+	0.305482i
$724$	−5.96101e8	−	3.38066e9i	−0.0583761	−	0.331067i
$725$	−6.84638e9	−	3.88277e10i	−0.667233	−	3.78407i
$726$	−1.16584e9	+	2.01929e9i	−0.113073	+	0.195849i
$727$	−1.21392e10	−	1.01860e10i	−1.17171	−	0.983179i	−0.171709	−	0.985148i	$-0.554929\pi$
$727$	−1.21392e10	−	1.01860e10i	−1.17171	−	0.983179i	−0.999998	+	0.00196842i	$0.999373\pi$
$728$	−1.00164e8	−	3.64565e7i	−0.00962166	−	0.00350200i
$729$	−5.71060e9	−	9.89105e9i	−0.545928	−	0.945575i
$730$	4.82109e8	−	8.35038e8i	0.0458686	−	0.0794467i
$731$	−9.63266e9	+	8.08276e9i	−0.912085	+	0.765330i
$732$	−8.94258e8	−	1.54890e9i	−0.0842702	−	0.145960i
$733$	3.12862e9	−	1.77433e10i	0.293419	−	1.66406i	−0.380138	−	0.924930i	$-0.624124\pi$
$733$	3.12862e9	−	1.77433e10i	0.293419	−	1.66406i	0.673558	−	0.739135i	$-0.264765\pi$
$734$	7.25993e9			0.677636
$735$	3.32849e9	−	1.88768e10i	0.309201	−	1.75357i
$736$	−5.55443e9	−	4.66072e9i	−0.513531	−	0.430904i
$737$	−8.80063e9	+	3.20317e9i	−0.809800	+	0.294743i
$738$	6.22263e7	+	2.26485e7i	0.00569871	+	0.00207416i
$739$	9.68512e9			0.882774			0.441387	−	0.897317i	$-0.354487\pi$
$739$	9.68512e9			0.882774			0.441387	+	0.897317i	$0.354487\pi$
$740$	9.84575e9	+	1.47063e10i	0.893178	+	1.33411i
$741$	3.73758e8			0.0337463
$742$	2.42527e8	+	8.82727e7i	0.0217945	+	0.00793255i
$743$	8.38681e9	−	3.05255e9i	0.750129	−	0.273024i	0.0614687	−	0.998109i	$-0.480422\pi$
$743$	8.38681e9	−	3.05255e9i	0.750129	−	0.273024i	0.688660	+	0.725085i	$0.258199\pi$
$744$	−3.34276e9	−	2.80491e9i	−0.297577	−	0.249697i
$745$	−6.31404e9	+	3.58087e10i	−0.559449	+	3.17279i
$746$	9.20268e8			0.0811574
$747$	2.75251e8	−	1.56102e9i	0.0241605	−	0.137021i
$748$	4.56508e9	+	7.90696e9i	0.398835	+	0.690802i
$749$	8.33049e8	−	6.99011e8i	0.0724409	−	0.0607852i
$750$	6.81697e9	−	1.18073e10i	0.590034	−	1.02197i
$751$	−4.92488e9	−	8.53014e9i	−0.424283	−	0.734880i	0.572070	−	0.820205i	$-0.306141\pi$
$751$	−4.92488e9	−	8.53014e9i	−0.424283	−	0.734880i	−0.996353	+	0.0853248i	$0.972807\pi$
$752$	2.88093e9	+	1.04857e9i	0.247042	+	0.0899160i
$753$	1.20318e10	+	1.00958e10i	1.02694	+	0.861708i
$754$	−7.73686e8	+	1.34006e9i	−0.0657302	+	0.113848i
$755$	1.56353e9	+	8.86725e9i	0.132219	+	0.749850i
$756$	1.11883e8	+	6.34522e8i	0.00941757	+	0.0534097i
$757$	−8.78528e9	+	7.37172e9i	−0.736071	+	0.617637i	−0.931779	−	0.363025i	$-0.881744\pi$
$757$	−8.78528e9	+	7.37172e9i	−0.736071	+	0.617637i	0.195708	+	0.980662i	$0.437300\pi$
$758$	8.28987e8	−	3.01727e8i	0.0691362	−	0.0251635i
$759$	9.42521e9	−	3.43050e9i	0.782429	−	0.284781i
$760$	−2.07207e9	+	1.73867e9i	−0.171221	+	0.143671i
$761$	4.87725e8	+	2.76603e9i	0.0401171	+	0.227515i	0.998274	−	0.0587282i	$-0.0187045\pi$
$761$	4.87725e8	+	2.76603e9i	0.0401171	+	0.227515i	−0.958157	+	0.286243i	$0.907593\pi$
$762$	−1.03803e9	−	5.88696e9i	−0.0849899	−	0.482002i
$763$	−6.44967e8	+	1.11712e9i	−0.0525656	+	0.0910463i
$764$	−4.36859e9	−	3.66568e9i	−0.354417	−	0.297391i
$765$	−2.08519e9	−	7.58948e8i	−0.168396	−	0.0612910i
$766$	−1.15160e9	−	1.99463e9i	−0.0925766	−	0.160347i
$767$	−2.29897e9	+	3.98194e9i	−0.183971	+	0.318648i
$768$	−2.18563e9	+	1.83396e9i	−0.174105	+	0.146092i
$769$	7.54586e9	+	1.30698e10i	0.598366	+	1.03640i	0.993062	+	0.117588i	$0.0375164\pi$
$769$	7.54586e9	+	1.30698e10i	0.598366	+	1.03640i	−0.394697	+	0.918812i	$0.629150\pi$
$770$	−1.30578e8	+	7.40547e8i	−0.0103075	+	0.0584568i
$771$	1.21062e10			0.951303
$772$	1.63051e9	−	9.24709e9i	0.127545	−	0.723343i
$773$	3.55730e9	+	2.98493e9i	0.277008	+	0.232437i	0.770698	−	0.637201i	$-0.219908\pi$
$773$	3.55730e9	+	2.98493e9i	0.277008	+	0.232437i	−0.493690	+	0.869638i	$0.664352\pi$
$774$	−9.63387e8	+	3.50644e8i	−0.0746805	+	0.0271815i
$775$	−1.82278e10	−	6.63438e9i	−1.40663	−	0.511970i
$776$	4.13701e8			0.0317812
$777$	−7.48531e8	+	4.97447e7i	−0.0572448	+	0.00380429i
$778$	−7.67496e9			−0.584316
$779$	2.38982e8	+	8.69822e7i	0.0181127	+	0.00659249i
$780$	4.24388e9	−	1.54465e9i	0.320208	−	0.116546i
$781$	−1.47491e9	−	1.23760e9i	−0.110787	−	0.0929612i
$782$	−4.88913e8	+	2.77276e9i	−0.0365601	+	0.207343i
$783$	2.04859e10			1.52506
$784$	−1.27467e9	+	7.22899e9i	−0.0944692	+	0.535762i
$785$	6.43798e9	+	1.11509e10i	0.475013	+	0.822747i
$786$	1.26257e9	−	1.05942e9i	0.0927418	−	0.0778196i
$787$	−9.39688e9	+	1.62759e10i	−0.687183	+	1.19024i	0.285563	+	0.958360i	$0.407820\pi$
$787$	−9.39688e9	+	1.62759e10i	−0.687183	+	1.19024i	−0.972745	+	0.231875i	$0.925514\pi$
$788$	−9.40883e9	−	1.62966e10i	−0.685005	−	1.18646i
$789$	−8.30251e9	−	3.02187e9i	−0.601783	−	0.219031i
$790$	−4.66362e9	−	3.91324e9i	−0.336533	−	0.282385i
$791$	−4.14042e8	+	7.17142e8i	−0.0297459	+	0.0515214i
$792$	2.83113e8	+	1.60561e9i	0.0202498	+	0.114843i
$793$	1.18673e8	+	6.73029e8i	0.00845077	+	0.0479267i
$794$	2.74127e9	−	2.30020e9i	0.194348	−	0.163077i
$795$	−2.25062e10	+	8.19158e9i	−1.58861	+	0.578206i
$796$	−1.38379e10	+	5.03657e9i	−0.972464	+	0.353948i
$797$	1.43628e10	−	1.20518e10i	1.00493	−	0.843234i	0.0172676	−	0.999851i	$-0.494503\pi$
$797$	1.43628e10	−	1.20518e10i	1.00493	−	0.843234i	0.987659	+	0.156617i	$0.0500588\pi$
$798$	−9.09032e6	−	5.15537e7i	−0.000633241	−	0.00359129i
$799$	−9.03346e8	−	5.12313e9i	−0.0626528	−	0.355322i
$800$	−1.83153e10	+	3.17230e10i	−1.26473	+	2.19058i
$801$	2.66478e9	+	2.23602e9i	0.183210	+	0.153731i
$802$	3.70279e9	+	1.34771e9i	0.253466	+	0.0922540i
$803$	−1.11603e9	−	1.93302e9i	−0.0760626	−	0.131744i
$804$	3.93906e9	−	6.82266e9i	0.267299	−	0.462975i
$805$	9.33850e8	−	7.83593e8i	0.0630945	−	0.0529426i
$806$	3.80647e8	+	6.59300e8i	0.0256065	+	0.0443517i
$807$	−3.44560e9	+	1.95410e10i	−0.230785	+	1.30885i
$808$	−4.16677e9			−0.277881
$809$	−4.19421e8	+	2.37865e9i	−0.0278503	+	0.157947i	−0.995561	−	0.0941155i	$-0.969998\pi$
$809$	−4.19421e8	+	2.37865e9i	−0.0278503	+	0.157947i	0.967711	+	0.252062i	$0.0811088\pi$
$810$	7.60508e9	+	6.38142e9i	0.502813	+	0.421910i
$811$	−9.12490e9	+	3.32119e9i	−0.600696	+	0.218636i	−0.624427	−	0.781083i	$-0.714668\pi$
$811$	−9.12490e9	+	3.32119e9i	−0.600696	+	0.218636i	0.0237311	+	0.999718i	$0.492445\pi$
$812$	−1.07063e9	−	3.89677e8i	−0.0701767	−	0.0255422i
$813$	1.47135e10			0.960283
$814$	−7.77595e9	+	5.16762e8i	−0.505322	+	0.0335819i
$815$	1.71119e10			1.10725
$816$	−5.58306e9	−	2.03207e9i	−0.359713	−	0.130925i
$817$	−3.69991e9	+	1.34666e9i	−0.237364	+	0.0863933i
$818$	3.39638e9	+	2.84990e9i	0.216960	+	0.182051i
$819$	4.75464e6	−	2.69649e7i	0.000302430	−	0.00171516i
$820$	3.07302e9			0.194633
$821$	−2.32932e9	+	1.32103e10i	−0.146902	+	0.833125i	0.818918	+	0.573911i	$0.194574\pi$
$821$	−2.32932e9	+	1.32103e10i	−0.146902	+	0.833125i	−0.965820	+	0.259214i	$0.916537\pi$
$822$	−3.72418e9	−	6.45047e9i	−0.233873	−	0.405079i
$823$	1.33021e10	−	1.11618e10i	0.831807	−	0.697969i	−0.123898	−	0.992295i	$-0.539540\pi$
$823$	1.33021e10	−	1.11618e10i	0.831807	−	0.697969i	0.955705	+	0.294326i	$0.0950953\pi$
$824$	−8.84499e9	+	1.53200e10i	−0.550747	+	0.953922i
$825$	−2.53357e10	−	4.38828e10i	−1.57089	−	2.72085i
$826$	6.05157e8	+	2.20259e8i	0.0373627	+	0.0135989i
$827$	5.99636e9	+	5.03154e9i	0.368653	+	0.309337i	0.808229	−	0.588869i	$-0.200427\pi$
$827$	5.99636e9	+	5.03154e9i	0.368653	+	0.309337i	−0.439575	+	0.898206i	$0.644871\pi$
$828$	6.03384e8	−	1.04509e9i	0.0369392	−	0.0639806i
$829$	−2.14020e9	−	1.21377e10i	−0.130471	−	0.739937i	−0.977907	−	0.209040i	$-0.932966\pi$
$829$	−2.14020e9	−	1.21377e10i	−0.130471	−	0.739937i	0.847436	−	0.530897i	$-0.178145\pi$
$830$	2.42977e9	+	1.37799e10i	0.147500	+	0.836515i
$831$	4.83622e9	−	4.05807e9i	0.292350	−	0.245311i
$832$	−5.83442e8	+	2.12355e8i	−0.0351209	+	0.0127830i
$833$	1.17044e10	−	4.26005e9i	0.701602	−	0.255362i
$834$	−4.92811e9	+	4.13517e9i	−0.294170	+	0.246838i
$835$	3.47306e8	+	1.96967e9i	0.0206447	+	0.117082i
$836$	4.96435e8	+	2.81542e9i	0.0293860	+	0.166656i
$837$	5.03944e9	−	8.72856e9i	0.297059	−	0.514521i
$838$	−2.01504e9	−	1.69082e9i	−0.118285	−	0.0992531i
$839$	−1.26178e10	−	4.59251e9i	−0.737594	−	0.268462i	−0.0542185	−	0.998529i	$-0.517267\pi$
$839$	−1.26178e10	−	4.59251e9i	−0.737594	−	0.268462i	−0.683376	+	0.730067i	$0.739489\pi$
$840$	−6.92714e8	−	1.19982e9i	−0.0403252	−	0.0698453i
$841$	−9.48773e9	+	1.64332e10i	−0.550017	+	0.952658i
$842$	7.35754e9	−	6.17371e9i	0.424757	−	0.356413i
$843$	1.37836e10	+	2.38739e10i	0.792439	+	1.37254i
$844$	2.83454e9	−	1.60755e10i	0.162287	−	0.920375i
$845$	3.17890e10			1.81250
$846$	7.36507e7	−	4.17694e8i	0.00418197	−	0.0237171i
$847$	5.02540e8	+	4.21681e8i	0.0284170	+	0.0238447i
$848$	8.61890e9	−	3.13702e9i	0.485363	−	0.176658i
$849$	−3.87095e8	−	1.40891e8i	−0.0217090	−	0.00790144i
$850$	1.42239e10			0.794425
$851$	1.01952e10	+	7.46120e9i	0.567078	+	0.415007i
$852$	1.61960e9			0.0897158
$853$	−5.22472e9	−	1.90164e9i	−0.288231	−	0.104908i	0.193858	−	0.981030i	$-0.437900\pi$
$853$	−5.22472e9	−	1.90164e9i	−0.288231	−	0.104908i	−0.482090	+	0.876122i	$0.660122\pi$
$854$	8.99470e7	−	3.27380e7i	0.00494179	−	0.00179866i
$855$	−5.32265e8	−	4.46623e8i	−0.0291237	−	0.0244377i
$856$	−3.61421e9	+	2.04972e10i	−0.196949	+	1.11696i
$857$	7.90626e9			0.429080			0.214540	−	0.976715i	$-0.431175\pi$
$857$	7.90626e9			0.429080			0.214540	+	0.976715i	$0.431175\pi$
$858$	−3.45333e8	+	1.95848e9i	−0.0186652	+	0.105856i
$859$	4.77846e9	+	8.27653e9i	0.257224	+	0.445525i	0.965497	−	0.260413i	$-0.0838588\pi$
$859$	4.77846e9	+	8.27653e9i	0.257224	+	0.445525i	−0.708273	+	0.705939i	$0.750525\pi$
$860$	−3.64457e10	+	3.05816e10i	−1.95390	+	1.63951i
$861$	−6.51302e7	+	1.12809e8i	−0.00347754	+	0.00602327i
$862$	5.25268e8	+	9.09792e8i	0.0279322	+	0.0483801i
$863$	−1.15493e10	−	4.20361e9i	−0.611673	−	0.222631i	0.0175624	−	0.999846i	$-0.494409\pi$
$863$	−1.15493e10	−	4.20361e9i	−0.611673	−	0.222631i	−0.629235	+	0.777215i	$0.716632\pi$
$864$	−1.45801e10	−	1.22342e10i	−0.769064	−	0.645322i
$865$	3.28515e10	−	5.69004e10i	1.72583	−	2.98923i
$866$	−8.77637e8	−	4.97733e9i	−0.0459200	−	0.260426i
$867$	−1.36617e9	−	7.74795e9i	−0.0711932	−	0.403757i
$868$	−4.29403e8	+	3.60312e8i	−0.0222867	+	0.0187008i
$869$	−1.32430e10	+	4.82004e9i	−0.684567	+	0.249162i
$870$	−1.88991e10	+	6.87870e9i	−0.973023	+	0.354152i
$871$	−2.30604e9	+	1.93500e9i	−0.118250	+	0.0992239i
$872$	−4.28711e9	−	2.43134e10i	−0.218956	−	1.24176i
$873$	1.84536e7	+	1.04655e8i	0.000938709	+	0.00532368i
$874$	−4.40803e8	+	7.63493e8i	−0.0223334	+	0.0386825i
$875$	−2.93849e9	−	2.46568e9i	−0.148284	−	0.124425i
$876$	1.76436e9	+	6.42173e8i	0.0886792	+	0.0322766i
$877$	1.08954e10	+	1.88714e10i	0.545439	+	0.944727i	0.998579	+	0.0532882i	$0.0169702\pi$
$877$	1.08954e10	+	1.88714e10i	0.545439	+	0.944727i	−0.453141	+	0.891439i	$0.649696\pi$
$878$	−6.52502e9	+	1.13017e10i	−0.325350	+	0.563523i
$879$	1.00760e10	−	8.45476e9i	0.500411	−	0.419895i
$880$	1.33617e10	+	2.31432e10i	0.660956	+	1.14481i
$881$	5.10080e9	−	2.89281e10i	0.251317	−	1.42529i	−0.554034	−	0.832494i	$-0.686912\pi$
$881$	5.10080e9	−	2.89281e10i	0.251317	−	1.42529i	0.805352	−	0.592797i	$-0.201976\pi$
$882$	1.01551e9			0.0498363
$883$	7.30979e8	−	4.14559e9i	0.0357308	−	0.202639i	−0.961716	−	0.274046i	$-0.911638\pi$
$883$	7.30979e8	−	4.14559e9i	0.0357308	−	0.202639i	0.997447	+	0.0714071i	$0.0227489\pi$
$884$	2.24811e9	+	1.88639e9i	0.109455	+	0.0918433i
$885$	−5.61577e10	+	2.04397e10i	−2.72338	+	0.991229i
$886$	8.45270e9	+	3.07653e9i	0.408298	+	0.148608i
$887$	−1.70120e10			−0.818509			−0.409254	−	0.912420i	$-0.634211\pi$
$887$	−1.70120e10			−0.818509			−0.409254	+	0.912420i	$0.634211\pi$
$888$	1.03627e10	−	9.93815e9i	0.496622	−	0.476278i
$889$	−1.68185e9			−0.0802845
$890$	−2.88557e10	−	1.05026e10i	−1.37204	−	0.499381i
$891$	2.15956e10	−	7.86017e9i	1.02281	−	0.372272i
$892$	5.13453e8	+	4.30838e8i	0.0242228	+	0.0203253i
$893$	2.82857e8	−	1.60416e9i	0.0132919	−	0.0753822i
$894$	1.34686e10			0.630436
$895$	7.64762e9	−	4.33718e10i	0.356571	−	2.02221i
$896$	6.73428e8	+	1.16641e9i	0.0312761	+	0.0541719i
$897$	2.46970e9	−	2.07232e9i	0.114254	−	0.0958702i
$898$	1.23782e9	−	2.14397e9i	0.0570416	−	0.0987989i
$899$	8.91128e9	+	1.54348e10i	0.409055	+	0.708504i
$900$	−5.72885e9	−	2.08513e9i	−0.261950	−	0.0953421i
$901$	−1.19222e10	−	1.00039e10i	−0.543025	−	0.455652i
$902$	−6.76591e8	+	1.17189e9i	−0.0306975	+	0.0531697i
$903$	−3.50195e8	−	1.98605e9i	−0.0158271	−	0.0897602i
$904$	−2.75215e9	−	1.56082e10i	−0.123903	−	0.702689i
$905$	−1.30603e10	+	1.09589e10i	−0.585711	+	0.491470i
$906$	3.13407e9	−	1.14071e9i	0.140010	−	0.0509596i
$907$	2.40022e9	−	8.73609e8i	0.106813	−	0.0388769i	−0.288061	−	0.957612i	$-0.593010\pi$
$907$	2.40022e9	−	8.73609e8i	0.106813	−	0.0388769i	0.394874	+	0.918735i	$0.370788\pi$
$908$	−6.58946e9	+	5.52922e9i	−0.292112	+	0.245111i
$909$	−1.85863e8	−	1.05408e9i	−0.00820767	−	0.0465480i
$910$	4.19716e7	+	2.38033e8i	0.00184634	+	0.0104711i
$911$	−3.57773e9	+	6.19680e9i	−0.156781	+	0.271552i	−0.933706	−	0.358041i	$-0.883445\pi$
$911$	−3.57773e9	+	6.19680e9i	−0.156781	+	0.271552i	0.776925	+	0.629593i	$0.216778\pi$
$912$	−1.42513e9	−	1.19582e9i	−0.0622117	−	0.0522018i
$913$	3.04377e10	+	1.10784e10i	1.32362	+	0.481759i
$914$	6.49406e9	+	1.12480e10i	0.281323	+	0.487265i
$915$	−4.44132e9	+	7.69260e9i	−0.191663	+	0.331970i
$916$	2.75447e9	−	2.31128e9i	0.118414	−	0.0993614i
$917$	−2.31856e8	−	4.01587e8i	−0.00992947	−	0.0171983i
$918$	−1.28337e9	+	7.27837e9i	−0.0547524	+	0.310516i
$919$	−2.12080e10			−0.901354			−0.450677	−	0.892687i	$-0.648817\pi$
$919$	−2.12080e10			−0.901354			−0.450677	+	0.892687i	$0.648817\pi$
$920$	−4.05153e9	+	2.29774e10i	−0.171539	+	0.972844i
$921$	2.14895e10	+	1.80319e10i	0.906397	+	0.760557i
$922$	6.86609e9	−	2.49905e9i	0.288504	−	0.105007i
$923$	−5.81544e8	−	2.11665e8i	−0.0243432	−	0.00886018i
$924$	−1.46429e9			−0.0610624
$925$	2.81770e10	−	5.72685e10i	1.17057	−	2.37914i
$926$	1.60673e10			0.664972
$927$	−4.27009e9	−	1.55419e9i	−0.176059	−	0.0640802i
$928$	3.16265e10	−	1.15111e10i	1.29907	−	0.472823i
$929$	3.49934e10	+	2.93629e10i	1.43196	+	1.20156i	0.944543	+	0.328388i	$0.106505\pi$
$929$	3.49934e10	+	2.93629e10i	1.43196	+	1.20156i	0.487417	+	0.873169i	$0.337939\pi$
$930$	−1.71824e9	+	9.74460e9i	−0.0700475	+	0.397259i
$931$	3.90010e9			0.158399
$932$	−3.21811e6	+	1.82508e7i	−0.000130210	+	0.000738458i
$933$	−1.59105e10	−	2.75579e10i	−0.641356	−	1.11086i
$934$	−8.11144e9	+	6.80630e9i	−0.325749	+	0.273336i
$935$	2.26724e10	−	3.92698e10i	0.907105	−	1.57115i
$936$	2.62026e8	+	4.53842e8i	0.0104443	+	0.0180900i
$937$	−2.93353e9	−	1.06772e9i	−0.116494	−	0.0424003i	0.283116	−	0.959086i	$-0.408632\pi$
$937$	−2.93353e9	−	1.06772e9i	−0.116494	−	0.0424003i	−0.399609	+	0.916686i	$0.630854\pi$
$938$	3.22987e8	+	2.71018e8i	0.0127784	+	0.0107223i
$939$	−9.24418e9	+	1.60114e10i	−0.364367	+	0.631102i
$940$	−3.41786e9	−	1.93837e10i	−0.134217	−	0.761181i
$941$	1.30133e9	+	7.38023e9i	0.0509126	+	0.288740i	0.999624	−	0.0274023i	$-0.00872352\pi$
$941$	1.30133e9	+	7.38023e9i	0.0509126	+	0.288740i	−0.948712	+	0.316142i	$0.897612\pi$
$942$	3.65358e9	−	3.06572e9i	0.142410	−	0.119496i
$943$	2.06141e9	−	7.50291e8i	0.0800522	−	0.0291366i
$944$	2.15060e10	−	7.82754e9i	0.832065	−	0.302847i
$945$	2.45131e9	−	2.05689e9i	0.0944903	−	0.0792868i
$946$	−3.63792e9	−	2.06317e10i	−0.139712	−	0.792347i
$947$	−1.87287e9	−	1.06216e10i	−0.0716609	−	0.406409i	−0.999446	−	0.0332932i	$-0.989400\pi$
$947$	−1.87287e9	−	1.06216e10i	−0.0716609	−	0.406409i	0.927785	−	0.373116i	$-0.121711\pi$
$948$	5.92740e9	−	1.02666e10i	0.225962	−	0.391377i
$949$	−5.49597e8	−	4.61166e8i	−0.0208743	−	0.0175156i
$950$	4.18522e9	+	1.52329e9i	0.158375	+	0.0576436i
$951$	−7.10288e9	−	1.23026e10i	−0.267795	−	0.463835i
$952$	4.50132e8	−	7.79651e8i	0.0169087	−	0.0292868i
$953$	1.91178e10	−	1.60417e10i	0.715505	−	0.600380i	−0.210633	−	0.977565i	$-0.567553\pi$
$953$	1.91178e10	−	1.60417e10i	0.715505	−	0.600380i	0.926138	+	0.377185i	$0.123108\pi$
$954$	−6.34447e8	−	1.09889e9i	−0.0236579	−	0.0409767i
$955$	−4.91821e9	+	2.78926e10i	−0.182724	+	1.03628i
$956$	−3.68889e10			−1.36551
$957$	−8.08454e9	+	4.58497e10i	−0.298170	+	1.69100i
$958$	−1.54518e10	−	1.29656e10i	−0.567805	−	0.476445i
$959$	−1.96922e9	+	7.16738e8i	−0.0720991	+	0.0262419i
$960$	−7.58329e9	−	2.76009e9i	−0.276636	−	0.100687i
$961$	−1.87441e10			−0.681290
$962$	−2.29187e9	+	1.01093e9i	−0.0829998	+	0.0366109i
$963$	−5.34646e9			−0.192919
$964$	−1.11577e10	−	4.06107e9i	−0.401148	−	0.146006i
$965$	−4.38217e10	+	1.59498e10i	−1.56980	+	0.571359i
$966$	−3.45909e8	−	2.90252e8i	−0.0123465	−	0.0103599i
$967$	1.17125e9	−	6.64248e9i	0.0416540	−	0.236231i	−0.956872	−	0.290510i	$-0.906175\pi$
$967$	1.17125e9	−	6.64248e9i	0.0416540	−	0.236231i	0.998526	+	0.0542790i	$0.0172860\pi$
$968$	−1.25558e10			−0.444917
$969$	−5.48159e8	+	3.10876e9i	−0.0193541	+	0.109763i
$970$	−4.69049e8	−	8.12417e8i	−0.0165013	−	0.0285810i
$971$	1.94929e10	−	1.63565e10i	0.683297	−	0.573354i	−0.233671	−	0.972316i	$-0.575074\pi$
$971$	1.94929e10	−	1.63565e10i	0.683297	−	0.573354i	0.916968	+	0.398962i	$0.130629\pi$
$972$	2.99156e9	−	5.18153e9i	0.104488	−	0.180978i
$973$	9.04991e8	+	1.56749e9i	0.0314956	+	0.0545519i
$974$	2.94182e9	+	1.07073e9i	0.102014	+	0.0371300i
$975$	−1.24768e10	−	1.04692e10i	−0.431107	−	0.361742i
$976$	1.70083e9	−	2.94593e9i	0.0585582	−	0.101426i
$977$	6.89064e9	+	3.90787e10i	0.236390	+	1.34063i	0.839667	+	0.543101i	$0.182750\pi$
$977$	6.89064e9	+	3.90787e10i	0.236390	+	1.34063i	−0.603278	+	0.797531i	$0.706139\pi$
$978$	−1.10066e9	−	6.24218e9i	−0.0376243	−	0.213378i
$979$	−5.44540e10	+	4.56923e10i	−1.85477	+	1.55634i
$980$	4.42842e10	−	1.61181e10i	1.50300	−	0.547045i
$981$	5.95942e9	−	2.16905e9i	0.201540	−	0.0733547i
$982$	−8.62173e9	+	7.23449e9i	−0.290539	+	0.243791i
$983$	−8.52528e9	−	4.83493e10i	−0.286267	−	1.62350i	−0.700724	−	0.713432i	$-0.747140\pi$
$983$	−8.52528e9	−	4.83493e10i	−0.286267	−	1.62350i	0.414457	−	0.910069i	$-0.363971\pi$
$984$	−4.32922e8	−	2.45522e9i	−0.0144853	−	0.0821500i
$985$	−4.67288e10	+	8.09367e10i	−1.55797	+	2.69848i
$986$	−1.00114e10	−	8.40056e9i	−0.332603	−	0.279087i
$987$	7.84002e8	+	2.85353e8i	0.0259542	+	0.00944654i
$988$	4.59459e8	+	7.95805e8i	0.0151564	+	0.0262517i
$989$	−1.69815e10	+	2.94127e10i	−0.558197	+	0.966826i
$990$	2.83208e9	−	2.37640e9i	0.0927645	−	0.0778387i
$991$	1.18717e10	+	2.05624e10i	0.387485	+	0.671144i	0.992111	−	0.125366i	$-0.0400104\pi$
$991$	1.18717e10	+	2.05624e10i	0.387485	+	0.671144i	−0.604625	+	0.796510i	$0.706677\pi$
$992$	2.87537e9	−	1.63070e10i	0.0935196	−	0.530376i
$993$	2.49679e9			0.0809207
$994$	−1.50517e7	+	8.53625e7i	−0.000486109	+	0.00275686i
$995$	5.60257e10	+	4.70111e10i	1.80304	+	1.51293i
$996$	−2.56039e10	+	9.31907e9i	−0.821105	+	0.298858i
$997$	−2.36662e10	−	8.61378e9i	−0.756301	−	0.275271i	−0.0650462	−	0.997882i	$-0.520719\pi$
$997$	−2.36662e10	−	8.61378e9i	−0.756301	−	0.275271i	−0.691255	+	0.722611i	$0.742942\pi$
$998$	−1.00145e10			−0.318913
$999$	2.67619e10	+	1.95853e10i	0.849256	+	0.621514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.f.a.16.10	yes	132
37.7	even	9	inner	37.8.f.a.7.10	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.f.a.7.10	✓	132	37.7	even	9	inner
37.8.f.a.16.10	yes	132	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.25018 - 1.54694i) q^{2} +(-41.1038 + 14.9605i) q^{3} +(-82.3827 - 69.1273i) q^{4} +(-92.7474 + 525.997i) q^{5} +197.841 q^{6} +(9.66574 - 54.8172i) q^{7} +(532.674 + 922.618i) q^{8} +(-209.638 + 175.907i) q^{9} +O(q^{10})\)	\(q+(-4.25018 - 1.54694i) q^{2} +(-41.1038 + 14.9605i) q^{3} +(-82.3827 - 69.1273i) q^{4} +(-92.7474 + 525.997i) q^{5} +197.841 q^{6} +(9.66574 - 54.8172i) q^{7} +(532.674 + 922.618i) q^{8} +(-209.638 + 175.907i) q^{9} +(1207.88 - 2092.10i) q^{10} +(-2796.10 - 4842.99i) q^{11} +(4420.42 + 1608.90i) q^{12} +(-1376.96 - 1155.41i) q^{13} +(-125.880 + 218.030i) q^{14} +(-4056.93 - 23008.0i) q^{15} +(1553.63 + 8811.07i) q^{16} +(11629.7 - 9758.45i) q^{17} +(1163.11 - 423.339i) q^{18} +(4466.97 - 1625.84i) q^{19} +(44001.5 - 36921.7i) q^{20} +(422.796 + 2397.80i) q^{21} +(4392.12 + 24909.0i) q^{22} +(20502.0 - 35510.5i) q^{23} +(-35697.8 - 29954.0i) q^{24} +(-194657. - 70849.4i) q^{25} +(4064.98 + 7040.76i) q^{26} +(53816.8 - 93213.4i) q^{27} +(-4585.65 + 3847.82i) q^{28} +(95164.8 + 164830. i) q^{29} +(-18349.3 + 104064. i) q^{30} +93640.6 q^{31} +(30706.4 - 174145. i) q^{32} +(187384. + 157234. i) q^{33} +(-64523.9 + 23484.8i) q^{34} +(27937.2 + 10168.3i) q^{35} +29430.5 q^{36} +(-33264.6 + 306309. i) q^{37} -21500.5 q^{38} +(73883.8 + 26891.5i) q^{39} +(-534698. + 194614. i) q^{40} +(40983.2 + 34389.0i) q^{41} +(1912.28 - 10845.1i) q^{42} -828283. q^{43} +(-104432. + 592266. i) q^{44} +(-73083.1 - 126584. i) q^{45} +(-142070. + 119211. i) q^{46} +(171333. - 296757. i) q^{47} +(-195678. - 338925. i) q^{48} +(770966. + 280609. i) q^{49} +(717727. + 602245. i) q^{50} +(-332032. + 575095. i) q^{51} +(33567.6 + 190371. i) q^{52} +(-178016. - 1.00958e6i) q^{53} +(-372926. + 312922. i) q^{54} +(2.80673e6 - 1.02157e6i) q^{55} +(55724.0 - 20281.9i) q^{56} +(-159286. + 133656. i) q^{57} +(-149485. - 847772. i) q^{58} +(-444188. - 2.51911e6i) q^{59} +(-1.25626e6 + 2.17591e6i) q^{60} +(-291252. - 244389. i) q^{61} +(-397989. - 144856. i) q^{62} +(7616.41 + 13192.0i) q^{63} +(172709. - 299140. i) q^{64} +(735450. - 617116. i) q^{65} +(-553185. - 958144. i) q^{66} +(290814. - 1.64929e6i) q^{67} -1.63266e6 q^{68} +(-311453. + 1.76634e6i) q^{69} +(-103008. - 86434.1i) q^{70} +(323531. - 117755. i) q^{71} +(-273963. - 99714.5i) q^{72} +399138. q^{73} +(615222. - 1.25041e6i) q^{74} +9.06108e6 q^{75} +(-480391. - 174848. i) q^{76} +(-292505. + 106463. i) q^{77} +(-272420. - 228587. i) q^{78} +(437609. - 2.48180e6i) q^{79} -4.77869e6 q^{80} +(-713621. + 4.04714e6i) q^{81} +(-120988. - 209558. i) q^{82} +(-4.43708e6 + 3.72315e6i) q^{83} +(130922. - 226764. i) q^{84} +(4.05429e6 + 7.02224e6i) q^{85} +(3.52035e6 + 1.28130e6i) q^{86} +(-6.37758e6 - 5.35143e6i) q^{87} +(2.97882e6 - 5.15947e6i) q^{88} +(-2.20731e6 - 1.25183e7i) q^{89} +(114799. + 651058. i) q^{90} +(-76645.5 + 64313.2i) q^{91} +(-4.14376e6 + 1.50820e6i) q^{92} +(-3.84898e6 + 1.40091e6i) q^{93} +(-1.18726e6 + 996229. i) q^{94} +(440888. + 2.50040e6i) q^{95} +(1.34315e6 + 7.61739e6i) q^{96} +(194163. - 336299. i) q^{97} +(-2.84266e6 - 2.38527e6i) q^{98} +(1.43808e6 + 523420. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9}+O(q^{10}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9	\( 132 q + 15 q^{2} + 33 q^{3} - 279 q^{4} + 576 q^{5} - 12 q^{6} - 597 q^{7} - 3750 q^{8} - 3243 q^{9} - 6003 q^{10} - 15975 q^{11} - 4635 q^{12} - 15981 q^{13} - 13491 q^{14} + 38493 q^{15} - 74151 q^{16} + 37698 q^{17} - 20100 q^{18} - 66102 q^{19} - 176184 q^{20} - 142530 q^{21} + 132783 q^{22} + 140631 q^{23} - 38793 q^{24} - 544092 q^{25} - 423147 q^{26} + 130557 q^{27} + 603813 q^{28} + 22890 q^{29} - 319860 q^{30} - 1288044 q^{31} - 217866 q^{32} + 112344 q^{33} + 812019 q^{34} + 1479252 q^{35} + 8118132 q^{36} - 1664550 q^{37} + 305010 q^{38} - 1580340 q^{39} - 4681425 q^{40} - 2956593 q^{41} - 3553029 q^{42} - 1023528 q^{43} + 6409524 q^{44} + 1803336 q^{45} + 10219434 q^{46} - 2607204 q^{47} - 2984043 q^{48} - 6819531 q^{49} + 5724015 q^{50} - 1675833 q^{51} + 11768451 q^{52} + 2280177 q^{53} - 7803897 q^{54} - 3542196 q^{55} + 12168843 q^{56} - 85203 q^{57} - 12425487 q^{58} - 7014600 q^{59} + 2356788 q^{60} + 10840332 q^{61} + 6334368 q^{62} - 3331359 q^{63} - 26175624 q^{64} - 573195 q^{65} - 36720249 q^{66} + 6642918 q^{67} - 25277742 q^{68} - 1236438 q^{69} - 27401982 q^{70} + 20311041 q^{71} + 40093005 q^{72} + 38643780 q^{73} - 9531 q^{74} + 16639446 q^{75} + 5787405 q^{76} - 316971 q^{77} + 9363381 q^{78} + 17712534 q^{79} - 74410128 q^{80} - 10355109 q^{81} - 16702371 q^{82} - 31021176 q^{83} - 61626192 q^{84} + 23576445 q^{85} + 18579072 q^{86} + 104996631 q^{87} + 57279702 q^{88} - 13471320 q^{89} + 56306910 q^{90} - 2335911 q^{91} - 178133436 q^{92} + 24366258 q^{93} + 77086020 q^{94} - 26254407 q^{95} + 152523921 q^{96} + 14408415 q^{97} - 521205 q^{98} + 58375668 q^{99}+O(q^{100}) \) 132 * q + 15 * q^2 + 33 * q^3 - 279 * q^4 + 576 * q^5 - 12 * q^6 - 597 * q^7 - 3750 * q^8 - 3243 * q^9 - 6003 * q^10 - 15975 * q^11 - 4635 * q^12 - 15981 * q^13 - 13491 * q^14 + 38493 * q^15 - 74151 * q^16 + 37698 * q^17 - 20100 * q^18 - 66102 * q^19 - 176184 * q^20 - 142530 * q^21 + 132783 * q^22 + 140631 * q^23 - 38793 * q^24 - 544092 * q^25 - 423147 * q^26 + 130557 * q^27 + 603813 * q^28 + 22890 * q^29 - 319860 * q^30 - 1288044 * q^31 - 217866 * q^32 + 112344 * q^33 + 812019 * q^34 + 1479252 * q^35 + 8118132 * q^36 - 1664550 * q^37 + 305010 * q^38 - 1580340 * q^39 - 4681425 * q^40 - 2956593 * q^41 - 3553029 * q^42 - 1023528 * q^43 + 6409524 * q^44 + 1803336 * q^45 + 10219434 * q^46 - 2607204 * q^47 - 2984043 * q^48 - 6819531 * q^49 + 5724015 * q^50 - 1675833 * q^51 + 11768451 * q^52 + 2280177 * q^53 - 7803897 * q^54 - 3542196 * q^55 + 12168843 * q^56 - 85203 * q^57 - 12425487 * q^58 - 7014600 * q^59 + 2356788 * q^60 + 10840332 * q^61 + 6334368 * q^62 - 3331359 * q^63 - 26175624 * q^64 - 573195 * q^65 - 36720249 * q^66 + 6642918 * q^67 - 25277742 * q^68 - 1236438 * q^69 - 27401982 * q^70 + 20311041 * q^71 + 40093005 * q^72 + 38643780 * q^73 - 9531 * q^74 + 16639446 * q^75 + 5787405 * q^76 - 316971 * q^77 + 9363381 * q^78 + 17712534 * q^79 - 74410128 * q^80 - 10355109 * q^81 - 16702371 * q^82 - 31021176 * q^83 - 61626192 * q^84 + 23576445 * q^85 + 18579072 * q^86 + 104996631 * q^87 + 57279702 * q^88 - 13471320 * q^89 + 56306910 * q^90 - 2335911 * q^91 - 178133436 * q^92 + 24366258 * q^93 + 77086020 * q^94 - 26254407 * q^95 + 152523921 * q^96 + 14408415 * q^97 - 521205 * q^98 + 58375668 * q^99

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