LMFDB - Embedded newform 69.7.f.a.34.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

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, 19]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			34.7
Character	$\chi$	$=$	69.34
Dual form			69.7.f.a.67.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.47034 + 4.15823i) q^{2} +(2.21847 - 15.4298i) q^{3} +(-2.01221 + 4.40612i) q^{4} +(-59.1450 - 201.429i) q^{5} +(49.8064 + 109.061i) q^{6} +(-482.533 + 418.118i) q^{7} +(-75.3556 - 524.109i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})$	\(q+(-6.47034 + 4.15823i) q^{2} +(2.21847 - 15.4298i) q^{3} +(-2.01221 + 4.40612i) q^{4} +(-59.1450 - 201.429i) q^{5} +(49.8064 + 109.061i) q^{6} +(-482.533 + 418.118i) q^{7} +(-75.3556 - 524.109i) q^{8} +(-233.157 - 68.4610i) q^{9} +(1220.28 + 1057.38i) q^{10} +(-86.0016 + 133.821i) q^{11} +(63.5215 + 40.8228i) q^{12} +(1172.26 - 1352.86i) q^{13} +(1383.52 - 4711.85i) q^{14} +(-3239.23 + 465.730i) q^{15} +(2463.93 + 2843.53i) q^{16} +(173.246 - 79.1189i) q^{17} +(1793.28 - 526.554i) q^{18} +(1077.38 + 492.024i) q^{19} +(1006.53 + 144.718i) q^{20} +(5380.98 + 8372.97i) q^{21} -1223.48i q^{22} +(10377.4 + 6351.84i) q^{23} -8254.07 q^{24} +(-23931.1 + 15379.6i) q^{25} +(-1959.40 + 13628.0i) q^{26} +(-1573.59 + 3445.68i) q^{27} +(-871.319 - 2967.44i) q^{28} +(13126.2 + 28742.5i) q^{29} +(19022.3 - 16482.9i) q^{30} +(-146.265 - 1017.30i) q^{31} +(4748.69 + 1394.34i) q^{32} +(1874.04 + 1623.86i) q^{33} +(-791.967 + 1232.32i) q^{34} +(112761. + 72466.9i) q^{35} +(770.808 - 889.559i) q^{36} +(-13042.2 + 44417.8i) q^{37} +(-9016.97 + 1296.45i) q^{38} +(-18273.7 - 21088.9i) q^{39} +(-101114. + 46177.3i) q^{40} +(-105518. + 30982.9i) q^{41} +(-69633.5 - 31800.6i) q^{42} +(123596. + 17770.4i) q^{43} +(-416.579 - 648.209i) q^{44} +51013.8i q^{45} +(-93557.6 + 2053.03i) q^{46} -45074.7 q^{47} +(49341.2 - 31709.7i) q^{48} +(41273.0 - 287060. i) q^{49} +(90890.4 - 199022. i) q^{50} +(-836.447 - 2848.68i) q^{51} +(3602.02 + 7887.33i) q^{52} +(85053.7 - 73699.4i) q^{53} +(-4146.29 - 28838.1i) q^{54} +(32042.1 + 9408.40i) q^{55} +(255501. + 221393. i) q^{56} +(9981.96 - 15532.2i) q^{57} +(-204449. - 131391. i) q^{58} +(253356. - 292389. i) q^{59} +(4465.93 - 15209.6i) q^{60} +(-19371.4 + 2785.19i) q^{61} +(5176.55 + 5974.06i) q^{62} +(141131. - 64452.2i) q^{63} +(-267571. + 78566.1i) q^{64} +(-341838. - 156112. i) q^{65} +(-18878.1 - 2714.26i) q^{66} +(34468.0 + 53633.2i) q^{67} +922.548i q^{68} +(121029. - 146029. i) q^{69} -1.03093e6 q^{70} +(-33369.0 + 21445.0i) q^{71} +(-18311.4 + 127359. i) q^{72} +(-200778. + 439642. i) q^{73} +(-100312. - 341631. i) q^{74} +(184213. + 403371. i) q^{75} +(-4335.83 + 3757.02i) q^{76} +(-14454.3 - 100532. i) q^{77} +(205930. + 60466.4i) q^{78} +(64545.8 + 55929.3i) q^{79} +(427042. - 664490. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(553902. - 639237. i) q^{82} +(-239789. + 816647. i) q^{83} +(-47720.0 + 6861.10i) q^{84} +(-26183.5 - 30217.4i) q^{85} +(-873601. + 398960. i) q^{86} +(472611. - 138771. i) q^{87} +(76617.6 + 34990.1i) q^{88} +(650900. + 93585.2i) q^{89} +(-212127. - 330076. i) q^{90} +1.14294e6i q^{91} +(-48868.4 + 32942.8i) q^{92} -16021.2 q^{93} +(291648. - 187431. i) q^{94} +(35386.3 - 246117. i) q^{95} +(32049.2 - 70178.0i) q^{96} +(216656. + 737864. i) q^{97} +(926612. + 2.02900e6i) q^{98} +(29213.4 - 25313.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$1$

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 $

$2$	−6.47034	+	4.15823i	−0.808792	+	0.519779i	−0.878474	−	0.477790i	$-0.841438\pi$
$2$	−6.47034	+	4.15823i	−0.808792	+	0.519779i	0.0696820	+	0.997569i	$0.477802\pi$
$3$	2.21847	−	15.4298i	0.0821655	−	0.571474i
$3$	2.21847	−	15.4298i	0.0821655	−	0.571474i
$4$	−2.01221	+	4.40612i	−0.0314408	+	0.0688457i
$5$	−59.1450	−	201.429i	−0.473160	−	1.61144i	−0.757584	−	0.652737i	$-0.773621\pi$
$5$	−59.1450	−	201.429i	−0.473160	−	1.61144i	0.284424	−	0.958699i	$-0.408198\pi$
$6$	49.8064	+	109.061i	0.230585	+	0.504911i
$7$	−482.533	+	418.118i	−1.40680	+	1.21900i	−0.463921	+	0.885877i	$0.653558\pi$
$7$	−482.533	+	418.118i	−1.40680	+	1.21900i	−0.942883	+	0.333125i	$0.891897\pi$
$8$	−75.3556	−	524.109i	−0.147179	−	1.02365i
$9$	−233.157	−	68.4610i	−0.319831	−	0.0939109i
$10$	1220.28	+	1057.38i	1.22028	+	1.05738i
$11$	−86.0016	+	133.821i	−0.0646143	+	0.100542i	−0.872057	−	0.489404i	$-0.837214\pi$
$11$	−86.0016	+	133.821i	−0.0646143	+	0.100542i	0.807443	+	0.589946i	$0.200851\pi$
$12$	63.5215	+	40.8228i	0.0367601	+	0.0236243i
$13$	1172.26	−	1352.86i	0.533572	−	0.615774i	−0.423405	−	0.905941i	$-0.639165\pi$
$13$	1172.26	−	1352.86i	0.533572	−	0.615774i	0.956976	+	0.290166i	$0.0937106\pi$
$14$	1383.52	−	4711.85i	0.504200	−	1.71715i
$15$	−3239.23	+	465.730i	−0.959771	+	0.137994i
$16$	2463.93	+	2843.53i	0.601546	+	0.694221i
$17$	173.246	−	79.1189i	0.0352628	−	0.0161040i	−0.397706	−	0.917513i	$-0.630193\pi$
$17$	173.246	−	79.1189i	0.0352628	−	0.0161040i	0.432968	+	0.901409i	$0.357466\pi$
$18$	1793.28	−	526.554i	0.307490	−	0.0902871i
$19$	1077.38	+	492.024i	0.157076	+	0.0717341i	0.492402	−	0.870368i	$-0.336119\pi$
$19$	1077.38	+	492.024i	0.157076	+	0.0717341i	−0.335326	+	0.942102i	$0.608846\pi$
$20$	1006.53	+	144.718i	0.125817	+	0.0180897i
$21$	5380.98	+	8372.97i	0.581037	+	0.904111i
$22$		−	1223.48i		−	0.114903i
$23$	10377.4	+	6351.84i	0.852912	+	0.522055i
$23$	10377.4	+	6351.84i	0.852912	+	0.522055i
$24$	−8254.07			−0.597083
$25$	−23931.1	+	15379.6i	−1.53159	+	0.984294i
$26$	−1959.40	+	13628.0i	−0.111482	+	0.775373i
$27$	−1573.59	+	3445.68i	−0.0799467	+	0.175059i
$28$	−871.319	−	2967.44i	−0.0396920	−	0.135179i
$29$	13126.2	+	28742.5i	0.538204	+	1.17850i	0.962076	+	0.272780i	$0.0879431\pi$
$29$	13126.2	+	28742.5i	0.538204	+	1.17850i	−0.423873	+	0.905722i	$0.639330\pi$
$30$	19022.3	−	16482.9i	0.704528	−	0.610477i
$31$	−146.265	−	1017.30i	−0.00490972	−	0.0341478i	0.987219	−	0.159368i	$-0.0509455\pi$
$31$	−146.265	−	1017.30i	−0.00490972	−	0.0341478i	−0.992129	+	0.125220i	$0.960036\pi$
$32$	4748.69	+	1394.34i	0.144919	+	0.0425519i
$33$	1874.04	+	1623.86i	0.0521479	+	0.0451864i
$34$	−791.967	+	1232.32i	−0.0201498	+	0.0313537i
$35$	112761.	+	72466.9i	2.62999	+	1.69019i
$36$	770.808	−	889.559i	0.0165211	−	0.0190663i
$37$	−13042.2	+	44417.8i	−0.257482	+	0.876904i	0.724715	+	0.689049i	$0.241972\pi$
$37$	−13042.2	+	44417.8i	−0.257482	+	0.876904i	−0.982197	+	0.187855i	$0.939847\pi$
$38$	−9016.97	+	1296.45i	−0.164327	+	0.0236267i
$39$	−18273.7	−	21088.9i	−0.308058	−	0.355518i
$40$	−101114.	+	46177.3i	−1.57991	+	0.721520i
$41$	−105518.	+	30982.9i	−1.53100	+	0.449542i	−0.935356	−	0.353708i	$-0.884921\pi$
$41$	−105518.	+	30982.9i	−1.53100	+	0.449542i	−0.595642	+	0.803250i	$0.703102\pi$
$42$	−69633.5	−	31800.6i	−0.939876	−	0.429227i
$43$	123596.	+	17770.4i	1.55453	+	0.223508i	0.865382	−	0.501113i	$-0.167076\pi$
$43$	123596.	+	17770.4i	1.55453	+	0.223508i	0.689148	+	0.724621i	$0.257985\pi$
$44$	−416.579	−	648.209i	−0.00489034	−	0.00760952i
$45$			51013.8i			0.559822i
$46$	−93557.6	+	2053.03i	−0.961182	+	0.0210922i
$47$	−45074.7			−0.434149			−0.217075	−	0.976155i	$-0.569651\pi$
$47$	−45074.7			−0.434149			−0.217075	+	0.976155i	$0.569651\pi$
$48$	49341.2	−	31709.7i	0.446156	−	0.286727i
$49$	41273.0	−	287060.i	0.350815	−	2.43997i
$50$	90890.4	−	199022.i	0.727123	−	1.59218i
$51$	−836.447	−	2848.68i	−0.00630562	−	0.0214750i
$52$	3602.02	+	7887.33i	0.0256175	+	0.0560945i
$53$	85053.7	−	73699.4i	0.571302	−	0.495036i	−0.320631	−	0.947204i	$-0.603895\pi$
$53$	85053.7	−	73699.4i	0.571302	−	0.495036i	0.891933	+	0.452169i	$0.149349\pi$
$54$	−4146.29	−	28838.1i	−0.0263317	−	0.183141i
$55$	32042.1	+	9408.40i	0.192589	+	0.0565494i
$56$	255501.	+	221393.i	1.45488	+	1.26066i
$57$	9981.96	−	15532.2i	0.0539003	−	0.0838705i
$58$	−204449.	−	131391.i	−1.04786	−	0.673416i
$59$	253356.	−	292389.i	1.23360	−	1.42365i	0.362914	−	0.931823i	$-0.381782\pi$
$59$	253356.	−	292389.i	1.23360	−	1.42365i	0.870690	−	0.491832i	$-0.163673\pi$
$60$	4465.93	−	15209.6i	0.0206756	−	0.0704147i
$61$	−19371.4	+	2785.19i	−0.0853439	+	0.0122706i	−0.184854	−	0.982766i	$-0.559181\pi$
$61$	−19371.4	+	2785.19i	−0.0853439	+	0.0122706i	0.0995106	+	0.995037i	$0.468272\pi$
$62$	5176.55	+	5974.06i	0.0217203	+	0.0250665i
$63$	141131.	−	64452.2i	0.564417	−	0.257760i
$64$	−267571.	+	78566.1i	−1.02070	+	0.299706i
$65$	−341838.	−	156112.i	−1.24475	−	0.568456i
$66$	−18878.1	−	2714.26i	−0.0656638	−	0.00944102i
$67$	34468.0	+	53633.2i	0.114602	+	0.178324i	0.893816	−	0.448434i	$-0.148018\pi$
$67$	34468.0	+	53633.2i	0.114602	+	0.178324i	−0.779214	+	0.626758i	$0.784382\pi$
$68$			922.548i			0.00293401i
$69$	121029.	−	146029.i	0.368420	−	0.444522i
$70$	−1.03093e6			−3.00564
$71$	−33369.0	+	21445.0i	−0.0932328	+	0.0599171i	−0.586427	−	0.810002i	$-0.699466\pi$
$71$	−33369.0	+	21445.0i	−0.0932328	+	0.0599171i	0.493194	+	0.869919i	$0.335829\pi$
$72$	−18311.4	+	127359.i	−0.0490596	+	0.341217i
$73$	−200778.	+	439642.i	−0.516116	+	1.13014i	0.454773	+	0.890607i	$0.349720\pi$
$73$	−200778.	+	439642.i	−0.516116	+	1.13014i	−0.970889	+	0.239529i	$0.923007\pi$
$74$	−100312.	−	341631.i	−0.247547	−	0.843066i
$75$	184213.	+	403371.i	0.436654	+	0.956139i
$76$	−4335.83	+	3757.02i	−0.00987716	+	0.00855860i
$77$	−14454.3	−	100532.i	−0.0316610	−	0.220207i
$78$	205930.	+	60466.4i	0.433945	+	0.127418i
$79$	64545.8	+	55929.3i	0.130914	+	0.113438i	0.717857	−	0.696191i	$-0.245123\pi$
$79$	64545.8	+	55929.3i	0.130914	+	0.113438i	−0.586943	+	0.809628i	$0.699669\pi$
$80$	427042.	−	664490.i	0.834065	−	1.29783i
$81$	49675.2	+	31924.3i	0.0934726	+	0.0600712i
$82$	553902.	−	639237.i	1.00460	−	1.15937i
$83$	−239789.	+	816647.i	−0.419368	+	1.42824i	0.431146	+	0.902282i	$0.358110\pi$
$83$	−239789.	+	816647.i	−0.419368	+	1.42824i	−0.850513	+	0.525953i	$0.823709\pi$
$84$	−47720.0	+	6861.10i	−0.0805123	+	0.0115759i
$85$	−26183.5	−	30217.4i	−0.0426355	−	0.0492040i
$86$	−873601.	+	398960.i	−1.37347	+	0.627241i
$87$	472611.	−	138771.i	0.717704	−	0.210737i
$88$	76617.6	+	34990.1i	0.112430	+	0.0513448i
$89$	650900.	+	93585.2i	0.923302	+	0.132751i	0.587539	−	0.809196i	$-0.300097\pi$
$89$	650900.	+	93585.2i	0.923302	+	0.132751i	0.335763	+	0.941946i	$0.391006\pi$
$90$	−212127.	−	330076.i	−0.290984	−	0.452780i
$91$			1.14294e6i			1.51670i
$92$	−48868.4	+	32942.8i	−0.0627574	+	0.0423055i
$93$	−16021.2			−0.0199180
$94$	291648.	−	187431.i	0.351136	−	0.225662i
$95$	35386.3	−	246117.i	0.0412729	−	0.287059i
$96$	32049.2	−	70178.0i	0.0362246	−	0.0793208i
$97$	216656.	+	737864.i	0.237387	+	0.808464i	0.988879	+	0.148723i	$0.0475162\pi$
$97$	216656.	+	737864.i	0.237387	+	0.808464i	−0.751492	+	0.659742i	$0.770666\pi$
$98$	926612.	+	2.02900e6i	0.984509	+	2.15577i
$99$	29213.4	−	25313.5i	0.0301076	−	0.0260884i
$100$	−19610.0	−	136390.i	−0.0196100	−	0.136390i
$101$	−734687.	−	215724.i	−0.713080	−	0.209379i	−0.0949805	−	0.995479i	$-0.530279\pi$
$101$	−734687.	−	215724.i	−0.713080	−	0.209379i	−0.618099	+	0.786100i	$0.712097\pi$
$102$	17257.6	+	14953.8i	0.0162622	+	0.0140913i
$103$	729723.	−	1.13547e6i	0.667800	−	1.03912i	−0.327740	−	0.944768i	$-0.606287\pi$
$103$	729723.	−	1.13547e6i	0.667800	−	1.03912i	0.995539	−	0.0943485i	$-0.0300768\pi$
$104$	−797381.	−	512446.i	−0.708869	−	0.455562i
$105$	1.36830e6	−	1.57911e6i	1.18199	−	1.36409i
$106$	−243866.	+	830533.i	−0.204755	+	0.697331i
$107$	1.45508e6	−	209209.i	1.18778	−	0.170777i	0.480037	−	0.877248i	$-0.340623\pi$
$107$	1.45508e6	−	209209.i	1.18778	−	0.170777i	0.707741	+	0.706472i	$0.249714\pi$
$108$	−12015.7	−	13866.9i	−0.00953845	−	0.0110080i
$109$	−1.55408e6	+	709725.i	−1.20004	+	0.548038i	−0.912241	−	0.409654i	$-0.865649\pi$
$109$	−1.55408e6	+	709725.i	−1.20004	+	0.548038i	−0.287795	+	0.957692i	$0.592922\pi$
$110$	−246445.	+	72362.9i	−0.185158	+	0.0543673i
$111$	656423.	+	299779.i	0.479971	+	0.219195i
$112$	−2.37786e6	−	341885.i	−1.69251	−	0.243347i
$113$	−918792.	−	1.42967e6i	−0.636769	−	0.990832i	−0.998289	−	0.0584679i	$-0.981378\pi$
$113$	−918792.	−	1.42967e6i	−0.636769	−	0.990832i	0.361520	−	0.932364i	$-0.382258\pi$
$114$			142006.i			0.0958501i
$115$	665677.	−	2.46599e6i	0.437693	−	1.62143i
$116$	−153056.			−0.0980562
$117$	−365938.	+	235174.i	−0.228481	+	0.146836i
$118$	−423480.	+	2.94537e6i	−0.257743	+	1.79264i
$119$	−50516.1	+	110615.i	−0.0299771	+	0.0656406i
$120$	488187.	+	1.66261e6i	0.282516	+	0.962160i
$121$	725421.	+	1.58845e6i	0.409481	+	0.896639i
$122$	113758.	−	98572.1i	0.0626474	−	0.0542843i
$123$	243971.	+	1.69685e6i	0.131106	+	0.911862i
$124$	4776.66	+	1402.55i	0.00250530	+	0.000735621i
$125$	2.03429e6	+	1.76273e6i	1.04156	+	0.902516i
$126$	−645156.	+	1.00388e6i	−0.322517	+	0.501847i
$127$	−1.47309e6	−	946698.i	−0.719148	−	0.462169i	0.129192	−	0.991620i	$-0.458762\pi$
$127$	−1.47309e6	−	946698.i	−0.719148	−	0.462169i	−0.848340	+	0.529451i	$0.822398\pi$
$128$	1.19716e6	−	1.38159e6i	0.570849	−	0.658794i
$129$	548388.	−	1.86764e6i	0.255458	−	0.870008i
$130$	2.86096e6	−	411344.i	1.30221	−	0.187230i
$131$	218628.	+	252310.i	0.0972506	+	0.112233i	0.802289	−	0.596936i	$-0.203616\pi$
$131$	218628.	+	252310.i	0.0972506	+	0.112233i	−0.705038	+	0.709170i	$0.749070\pi$
$132$	−10925.9	+	4989.69i	−0.00475046	+	0.00216946i
$133$	−725597.	+	213054.i	−0.308419	+	0.0905598i
$134$	−446039.	−	203699.i	−0.185378	−	0.0846593i
$135$	787132.	+	113172.i	0.319924	+	0.0459981i
$136$	−54522.0	−	84837.9i	−0.0216748	−	0.0337267i
$137$			103562.i			0.0402752i	0.999797	+	0.0201376i	$0.00641044\pi$
$137$			103562.i			0.0402752i	−0.999797	+	0.0201376i	$0.993590\pi$
$138$	−175877.	+	1.44813e6i	−0.0669223	+	0.551023i
$139$	−3.68208e6			−1.37103			−0.685517	−	0.728056i	$-0.740424\pi$
$139$	−3.68208e6			−1.37103			−0.685517	+	0.728056i	$0.740424\pi$
$140$	−546196.	+	351019.i	−0.199051	+	0.127922i
$141$	−99996.8	+	695493.i	−0.0356721	+	0.248105i
$142$	126736.	−	277512.i	0.0442623	−	0.0969209i
$143$	80224.8	+	273220.i	0.0274347	+	0.0934340i
$144$	−379812.	−	831672.i	−0.127198	−	0.278525i
$145$	5.01323e6	−	4.34399e6i	1.64442	−	1.42490i
$146$	−529034.	−	3.67951e6i	−0.169991	−	1.18231i
$147$	−4.33771e6	−	1.27367e6i	−1.36555	−	0.400963i
$148$	−169466.	−	146844.i	−0.0522756	−	0.0452970i
$149$	837355.	−	1.30295e6i	0.253134	−	0.393885i	−0.691309	−	0.722559i	$-0.742966\pi$
$149$	837355.	−	1.30295e6i	0.253134	−	0.393885i	0.944443	+	0.328675i	$0.106602\pi$
$150$	−2.86923e6	−	1.84394e6i	−0.850143	−	0.546354i
$151$	−3.79758e6	+	4.38264e6i	−1.10300	+	1.27293i	−0.143985	+	0.989580i	$0.545992\pi$
$151$	−3.79758e6	+	4.38264e6i	−1.10300	+	1.27293i	−0.959016	+	0.283352i	$0.908554\pi$
$152$	176688.	−	601743.i	0.0503124	−	0.171348i
$153$	−45810.1	+	6586.50i	−0.0127905	+	0.00183899i
$154$	511559.	+	590371.i	0.140066	+	0.161645i
$155$	−196263.	+	89630.3i	−0.0527040	+	0.0240691i
$156$	129691.	−	38080.7i	0.0341614	−	0.0100307i
$157$	6.16425e6	+	2.81512e6i	1.59287	+	0.727441i	0.997128	−	0.0757317i	$-0.0241293\pi$
$157$	6.16425e6	+	2.81512e6i	1.59287	+	0.727441i	0.595746	+	0.803173i	$0.296857\pi$
$158$	−650200.	−	93484.7i	−0.164845	−	0.0237011i
$159$	−948478.	−	1.47586e6i	−0.235959	−	0.367159i
$160$		−	1.03899e6i		−	0.253661i
$161$	−7.66325e6	+	1.27399e6i	−1.83626	+	0.305273i
$162$	−454164.			−0.106824
$163$	−700440.	+	450146.i	−0.161737	+	0.103942i	−0.619005	−	0.785387i	$-0.712464\pi$
$163$	−700440.	+	450146.i	−0.161737	+	0.103942i	0.457269	+	0.889329i	$0.348828\pi$
$164$	75809.8	−	527269.i	0.0171867	−	0.119536i
$165$	216254.	−	473530.i	0.0481407	−	0.105413i
$166$	−1.84429e6	−	6.28108e6i	−0.403186	−	1.37312i
$167$	3.39515e6	+	7.43434e6i	0.728970	+	1.59622i	0.800890	+	0.598811i	$0.204360\pi$
$167$	3.39515e6	+	7.43434e6i	0.728970	+	1.59622i	−0.0719202	+	0.997410i	$0.522913\pi$
$168$	3.98287e6	−	3.45117e6i	0.839978	−	0.727845i
$169$	230892.	+	1.60589e6i	0.0478353	+	0.332702i
$170$	295067.	+	86639.6i	0.0600585	+	0.0176348i
$171$	−217514.	−	188477.i	−0.0435011	−	0.0376939i
$172$	−327000.	+	508821.i	−0.0642631	+	0.0999954i
$173$	5.56890e6	+	3.57891e6i	1.07555	+	0.691215i	0.953526	−	0.301312i	$-0.0974246\pi$
$173$	5.56890e6	+	3.57891e6i	1.07555	+	0.691215i	0.122026	+	0.992527i	$0.461061\pi$
$174$	−2.48091e6	+	2.86312e6i	−0.470937	+	0.543490i
$175$	5.11708e6	−	1.74272e7i	0.954791	−	3.25172i
$176$	−592427.	+	85178.1i	−0.108667	+	0.0156239i
$177$	−3.94943e6	−	4.55789e6i	−0.712222	−	0.821947i
$178$	−4.60069e6	+	2.10106e6i	−0.815761	+	0.372545i
$179$	1.09372e6	−	321146.i	0.190699	−	0.0559942i	−0.184989	−	0.982741i	$-0.559225\pi$
$179$	1.09372e6	−	321146.i	0.190699	−	0.0559942i	0.375687	+	0.926746i	$0.377407\pi$
$180$	−224773.	−	102650.i	−0.0385413	−	0.0176012i
$181$	6.05089e6	+	869987.i	1.02043	+	0.146716i	0.632167	−	0.774832i	$-0.282166\pi$
$181$	6.05089e6	+	869987.i	1.02043	+	0.146716i	0.388264	+	0.921548i	$0.373075\pi$
$182$	−4.75261e6	−	7.39520e6i	−0.788348	−	1.22669i
$183$			305076.i			0.0497800i
$184$	2.54706e6	−	5.91753e6i	0.408871	−	0.949920i
$185$	9.71844e6			1.53490
$186$	103662.	−	66619.8i	0.0161095	−	0.0103530i
$187$	−4311.67	+	29988.4i	−0.000659358	+	0.00458593i
$188$	90699.6	−	198604.i	0.0136500	−	0.0298893i
$189$	−681390.	−	2.32060e6i	−0.100928	−	0.343728i
$190$	794451.	+	1.73961e6i	0.115826	+	0.253624i
$191$	−1.17619e6	+	1.01918e6i	−0.168802	+	0.146268i	−0.735165	−	0.677888i	$-0.762895\pi$
$191$	−1.17619e6	+	1.01918e6i	−0.168802	+	0.146268i	0.566363	+	0.824156i	$0.308350\pi$
$192$	618659.	+	4.30287e6i	0.0874073	+	0.607931i
$193$	−8.57312e6	−	2.51730e6i	−1.19252	−	0.350157i	−0.375534	−	0.926809i	$-0.622541\pi$
$193$	−8.57312e6	−	2.51730e6i	−1.19252	−	0.350157i	−0.816990	+	0.576652i	$0.804359\pi$
$194$	−4.47005e6	−	3.87332e6i	−0.612219	−	0.530491i
$195$	−3.16714e6	+	4.92816e6i	−0.427133	+	0.664632i
$196$	1.18177e6	+	759478.i	0.156951	+	0.100867i
$197$	−7.92492e6	+	9.14585e6i	−1.03656	+	1.19626i	−0.0563312	+	0.998412i	$0.517940\pi$
$197$	−7.92492e6	+	9.14585e6i	−1.03656	+	1.19626i	−0.980233	+	0.197847i	$0.936605\pi$
$198$	−83760.8	+	285263.i	−0.0107906	+	0.0367494i
$199$	−3.58426e6	+	515339.i	−0.454821	+	0.0653934i	−0.365919	−	0.930647i	$-0.619245\pi$
$199$	−3.58426e6	+	515339.i	−0.454821	+	0.0653934i	−0.0889028	+	0.996040i	$0.528336\pi$
$200$	9.86393e6	+	1.13836e7i	1.23299	+	1.42295i
$201$	904015.	−	412850.i	0.111324	−	0.0508398i
$202$	5.65070e6	−	1.65920e6i	0.685564	−	0.201300i
$203$	−1.83516e7	−	8.38089e6i	−2.19374	−	1.00185i
$204$	14234.7	+	2046.64i	0.00167671	+	0.000241075i
$205$	1.24817e7	+	1.94219e7i	1.44881	+	2.25440i
$206$			1.03812e7i			1.18754i
$207$	−1.98470e6	−	2.19142e6i	−0.223761	−	0.247067i
$208$	6.73525e6			0.748452
$209$	−158500.	+	101862.i	−0.0173616	+	0.0111576i
$210$	−2.28709e6	+	1.59071e7i	−0.246960	+	1.71764i
$211$	1.28619e6	−	2.81636e6i	0.136917	−	0.299806i	−0.828737	−	0.559639i	$-0.810940\pi$
$211$	1.28619e6	−	2.81636e6i	0.136917	−	0.299806i	0.965654	+	0.259832i	$0.0836673\pi$
$212$	153583.	+	523055.i	0.0161189	+	0.0548959i
$213$	256863.	+	562452.i	0.0265805	+	0.0582032i
$214$	−8.54491e6	+	7.40421e6i	−0.871899	+	0.755505i
$215$	−3.73060e6	−	2.59469e7i	−0.375374	−	2.61078i
$216$	1.92449e6	+	565082.i	0.190966	+	0.0560725i
$217$	495928.	+	429724.i	0.0485333	+	0.0420543i
$218$	7.10423e6	−	1.10544e7i	0.685721	−	1.06700i
$219$	6.33817e6	+	4.07329e6i	0.603436	+	0.387805i
$220$	−105930.	+	122250.i	−0.00994834	+	0.0114810i
$221$	96052.6	−	327125.i	0.00889881	−	0.0303066i
$222$	−5.49383e6	+	789893.i	−0.502130	+	0.0721954i
$223$	1.24479e7	+	1.43657e7i	1.12249	+	1.29542i	0.950639	+	0.310298i	$0.100429\pi$
$223$	1.24479e7	+	1.43657e7i	1.12249	+	1.29542i	0.171849	+	0.985123i	$0.445026\pi$
$224$	−2.87440e6	+	1.31270e6i	−0.255743	+	0.116794i
$225$	6.63260e6	−	1.94751e6i	0.582286	−	0.170975i
$226$	1.18898e7	+	5.42989e6i	1.03003	+	0.470398i
$227$	2.36418e6	+	339917.i	0.202117	+	0.0290600i	0.242629	−	0.970119i	$-0.421990\pi$
$227$	2.36418e6	+	339917.i	0.202117	+	0.0290600i	−0.0405128	+	0.999179i	$0.512899\pi$
$228$	48351.1	+	75235.8i	0.00407946	+	0.00634776i
$229$			9.15730e6i			0.762537i	0.924464	+	0.381269i	$0.124513\pi$
$229$			9.15730e6i			0.762537i	−0.924464	+	0.381269i	$0.875487\pi$
$230$	5.94701e6	+	1.87238e7i	0.488782	+	1.53890i
$231$	−1.58325e6			−0.128444
$232$	1.40751e7	−	9.04550e6i	1.12716	−	0.724383i
$233$	−160788.	+	1.11831e6i	−0.0127112	+	0.0884083i	−0.995189	−	0.0979687i	$-0.968765\pi$
$233$	−160788.	+	1.11831e6i	−0.0127112	+	0.0884083i	0.982478	+	0.186377i	$0.0596746\pi$
$234$	1.38983e6	−	3.04331e6i	0.108471	−	0.237519i
$235$	2.66594e6	+	9.07937e6i	0.205422	+	0.699604i
$236$	778495.	+	1.70467e6i	0.0592270	+	0.129689i
$237$	1.00617e6	−	871851.i	0.0755834	−	0.0654934i
$238$	−133106.	−	925773.i	−0.00987341	−	0.0686710i
$239$	1.80352e7	+	5.29560e6i	1.32107	+	0.387902i	0.864879	−	0.501980i	$-0.167395\pi$
$239$	1.80352e7	+	5.29560e6i	1.32107	+	0.387902i	0.456192	+	0.889881i	$0.349213\pi$
$240$	−9.30556e6	−	8.06331e6i	−0.673145	−	0.583283i
$241$	−1.32016e6	+	2.05421e6i	−0.0943138	+	0.146755i	−0.885204	−	0.465203i	$-0.845981\pi$
$241$	−1.32016e6	+	2.05421e6i	−0.0943138	+	0.146755i	0.790890	+	0.611958i	$0.209618\pi$
$242$	−1.12989e7	−	7.26134e6i	−0.797240	−	0.512355i
$243$	602788.	−	695654.i	0.0420093	−	0.0484814i
$244$	26707.5	−	90957.3i	0.00183850	−	0.00626135i
$245$	−6.02634e7	+	8.66457e6i	−4.09785	+	0.589181i
$246$	−8.63448e6	−	9.96473e6i	−0.580004	−	0.669360i
$247$	1.92861e6	−	880765.i	0.127983	−	0.0584479i
$248$	−522154.	+	153318.i	−0.0342329	+	0.0100517i
$249$	1.20687e7	+	5.51160e6i	0.781741	+	0.357009i
$250$	−2.04924e7	−	2.94636e6i	−1.31151	−	0.188567i
$251$	2.71308e6	+	4.22163e6i	0.171570	+	0.266968i	0.916381	−	0.400308i	$-0.131097\pi$
$251$	2.71308e6	+	4.22163e6i	0.171570	+	0.266968i	−0.744811	+	0.667276i	$0.767460\pi$
$252$			751530.i			0.0469618i
$253$	−1.74248e6	+	842444.i	−0.107599	+	0.0520211i
$254$	1.34680e7			0.821867
$255$	−524336.	+	336970.i	−0.0316220	+	0.0203222i
$256$	538945.	−	3.74844e6i	0.0321236	−	0.223425i
$257$	−5.05299e6	+	1.10645e7i	−0.297680	+	0.651828i	−0.998081	−	0.0619216i	$-0.980277\pi$
$257$	−5.05299e6	+	1.10645e7i	−0.297680	+	0.651828i	0.700401	+	0.713749i	$0.253004\pi$
$258$	4.21782e6	+	1.43646e7i	0.245600	+	0.836437i
$259$	−1.22785e7	−	2.68863e7i	−0.706720	−	1.54750i
$260$	1.37570e6	−	1.19205e6i	0.0782715	−	0.0678226i
$261$	−1.09274e6	−	7.60014e6i	−0.0614601	−	0.427465i
$262$	−2.46376e6	−	723426.i	−0.136992	−	0.0402245i
$263$	3.14589e6	+	2.72593e6i	0.172932	+	0.149847i	0.737027	−	0.675864i	$-0.236229\pi$
$263$	3.14589e6	+	2.72593e6i	0.172932	+	0.149847i	−0.564094	+	0.825710i	$0.690775\pi$
$264$	709863.	−	1.10457e6i	0.0385801	−	0.0600317i
$265$	−1.98757e7	−	1.27734e7i	−1.06804	−	0.686385i
$266$	3.80893e6	−	4.39573e6i	0.202375	−	0.233554i
$267$	2.88800e6	−	9.83563e6i	0.151727	−	0.516735i
$268$	−305671.	+	43948.9i	−0.0158800	+	0.00228320i
$269$	−8.95020e6	−	1.03291e7i	−0.459807	−	0.530646i	0.477741	−	0.878501i	$-0.341456\pi$
$269$	−8.95020e6	−	1.03291e7i	−0.459807	−	0.530646i	−0.937548	+	0.347855i	$0.886910\pi$
$270$	−5.56361e6	+	2.54081e6i	−0.282660	+	0.129087i
$271$	1.25807e7	−	3.69404e6i	0.632118	−	0.185607i	0.0500501	−	0.998747i	$-0.484062\pi$
$271$	1.25807e7	−	3.69404e6i	0.632118	−	0.185607i	0.582068	+	0.813140i	$0.302244\pi$
$272$	651844.	+	297687.i	0.0323920	+	0.0147929i
$273$	1.76353e7	+	2.53558e6i	0.866753	+	0.124620i
$274$	−430634.	−	670080.i	−0.0209342	−	0.0325743i
$275$		−	4.52516e6i		−	0.217588i
$276$	399887.	+	827112.i	0.0190200	+	0.0393402i
$277$	2.73427e7			1.28648			0.643238	−	0.765666i	$-0.277590\pi$
$277$	2.73427e7			1.28648			0.643238	+	0.765666i	$0.277590\pi$
$278$	2.38243e7	−	1.53109e7i	1.10888	−	0.712635i
$279$	−35542.5	+	247203.i	−0.00163657	+	0.0113826i
$280$	2.94834e7	−	6.45597e7i	1.34309	−	2.94095i
$281$	−4.25021e6	−	1.44749e7i	−0.191554	−	0.652374i	−0.998123	−	0.0612341i	$-0.980496\pi$
$281$	−4.25021e6	−	1.44749e7i	−0.191554	−	0.652374i	0.806569	−	0.591140i	$-0.201322\pi$
$282$	−2.24501e6	−	4.91588e6i	−0.100108	−	0.219207i
$283$	−1.72050e7	+	1.49082e7i	−0.759094	+	0.657758i	−0.945834	−	0.324651i	$-0.894753\pi$
$283$	−1.72050e7	+	1.49082e7i	−0.759094	+	0.657758i	0.186740	+	0.982409i	$0.440208\pi$
$284$	−27343.7	−	190180.i	−0.00119372	−	0.00830251i
$285$	−3.71903e6	−	1.09201e6i	−0.160655	−	0.0471727i
$286$	−1.65520e6	−	1.43423e6i	−0.0707540	−	0.0613087i
$287$	3.79614e7	−	5.90692e7i	1.60582	−	2.49871i
$288$	−1.01173e6	−	650200.i	−0.0423534	−	0.0272189i
$289$	−1.57830e7	+	1.82145e7i	−0.653877	+	0.754614i
$290$	−1.43740e7	+	4.89532e7i	−0.589363	+	2.00719i
$291$	1.18657e7	−	1.70603e6i	0.481521	−	0.0692323i
$292$	−1.53311e6	−	1.76930e6i	−0.0615779	−	0.0710647i
$293$	−1.66404e7	+	7.59943e6i	−0.661548	+	0.302119i	−0.717750	−	0.696300i	$-0.754828\pi$
$293$	−1.66404e7	+	7.59943e6i	−0.661548	+	0.302119i	0.0562022	+	0.998419i	$0.482101\pi$
$294$	3.33627e7	−	9.79616e6i	1.31286	−	0.385491i
$295$	−7.38805e7	−	3.37401e7i	−2.87782	−	1.31426i
$296$	2.42626e7	+	3.48843e6i	0.935539	+	0.134510i
$297$	−325774.	−	506914.i	−0.0124350	−	0.0193493i
$298$			1.19124e7i			0.450145i
$299$	2.07581e7	−	6.59312e6i	0.776557	−	0.246648i
$300$	−2.14798e6			−0.0795547
$301$	−6.70693e7	+	4.31029e7i	−2.45937	+	1.58054i
$302$	6.34758e6	−	4.41484e7i	0.230456	−	1.60285i
$303$	−4.95845e6	+	1.08575e7i	−0.178245	+	0.390303i
$304$	1.25551e6	+	4.27588e6i	0.0446890	+	0.152197i
$305$	1.70674e6	+	3.73725e6i	0.0601546	+	0.131720i
$306$	269019.	−	233106.i	0.00938897	−	0.00813559i
$307$	6.68849e6	+	4.65195e7i	0.231160	+	1.60775i	0.693099	+	0.720842i	$0.256245\pi$
$307$	6.68849e6	+	4.65195e7i	0.231160	+	1.60775i	−0.461939	+	0.886912i	$0.652846\pi$
$308$	472041.	+	138604.i	0.0161558	+	0.00474376i
$309$	−1.59012e7	−	1.37785e7i	−0.538958	−	0.467010i
$310$	897184.	−	1.39605e6i	0.0301159	−	0.0468613i
$311$	3.56232e7	+	2.28937e7i	1.18427	+	0.761087i	0.976167	−	0.217019i	$-0.0696334\pi$
$311$	3.56232e7	+	2.28937e7i	1.18427	+	0.761087i	0.208107	+	0.978106i	$0.433270\pi$
$312$	−9.67589e6	+	1.11666e7i	−0.318586	+	0.367668i
$313$	6.12631e6	−	2.08643e7i	0.199787	−	0.680410i	−0.797262	−	0.603634i	$-0.793719\pi$
$313$	6.12631e6	−	2.08643e7i	0.199787	−	0.680410i	0.997048	−	0.0767767i	$-0.0244629\pi$
$314$	−5.15907e7	+	7.41762e6i	−1.66641	+	0.239594i
$315$	−2.13298e7	−	2.46159e7i	−0.682424	−	0.787559i
$316$	−376311.	+	171855.i	−0.0119257	+	0.00544631i
$317$	−1.60496e7	+	4.71260e6i	−0.503834	+	0.147939i	−0.523766	−	0.851862i	$-0.675473\pi$
$317$	−1.60496e7	+	4.71260e6i	−0.503834	+	0.147939i	0.0199320	+	0.999801i	$0.493655\pi$
$318$	1.22739e7	+	5.60532e6i	0.381683	+	0.174309i
$319$	−4.97523e6	−	715330.i	−0.153264	−	0.0220361i
$320$	3.16510e7	+	4.92500e7i	0.965913	+	1.50299i
$321$		−	2.29157e7i		−	0.692816i
$322$	4.42862e7	−	4.01087e7i	1.32648	−	1.20135i
$323$	225581.			0.00669414
$324$	−240619.	+	154637.i	−0.00707449	+	0.00454650i
$325$	−7.24703e6	+	5.04042e7i	−0.211110	+	1.46831i
$326$	2.66027e6	−	5.82519e6i	0.0767845	−	0.168135i
$327$	7.50323e6	+	2.55537e7i	0.214588	+	0.730819i
$328$	2.41898e7	+	5.29682e7i	0.685504	+	1.50104i
$329$	2.17500e7	−	1.88465e7i	0.610762	−	0.529229i
$330$	569813.	+	3.96313e6i	0.0158559	+	0.110280i
$331$	−2.58829e7	−	7.59991e6i	−0.713722	−	0.209568i	−0.0953395	−	0.995445i	$-0.530394\pi$
$331$	−2.58829e7	−	7.59991e6i	−0.713722	−	0.209568i	−0.618383	+	0.785877i	$0.712212\pi$
$332$	−3.11574e6	−	2.69980e6i	−0.0851426	−	0.0737765i
$333$	6.08177e6	−	9.46343e6i	0.164702	−	0.256281i
$334$	−5.28815e7	−	3.39849e7i	−1.41927	−	0.912108i
$335$	8.76470e6	−	1.01150e7i	0.233132	−	0.269049i
$336$	−1.05504e7	+	3.59314e7i	−0.278133	+	0.947233i
$337$	−6.90774e6	+	993183.i	−0.180487	+	0.0259501i	−0.231966	−	0.972724i	$-0.574516\pi$
$337$	−6.90774e6	+	993183.i	−0.180487	+	0.0259501i	0.0514786	+	0.998674i	$0.483607\pi$
$338$	−8.17161e6	−	9.43054e6i	−0.211620	−	0.244223i
$339$	−2.40978e7	+	1.10051e7i	−0.618555	+	0.282485i
$340$	185828.	−	54564.1i	0.00472797	−	0.00138826i
$341$	148715.	+	67915.9i	0.00375052	+	0.00171281i
$342$	2.19112e6	+	315036.i	0.0547758	+	0.00787557i
$343$	5.94980e7	+	9.25807e7i	1.47442	+	2.29424i
$344$		−	6.61169e7i		−	1.62419i
$345$	−3.65729e7	−	1.57420e7i	−0.890640	−	0.383356i
$346$	−5.09146e7			−1.22918
$347$	−1.62280e7	+	1.04291e7i	−0.388398	+	0.249608i	−0.720237	−	0.693728i	$-0.755967\pi$
$347$	−1.62280e7	+	1.04291e7i	−0.388398	+	0.249608i	0.331839	+	0.943336i	$0.392331\pi$
$348$	−339549.	+	2.36162e6i	−0.00805684	+	0.0560366i
$349$	2.70609e7	−	5.92551e7i	0.636599	−	1.39396i	−0.266209	−	0.963915i	$-0.585771\pi$
$349$	2.70609e7	−	5.92551e7i	0.636599	−	1.39396i	0.902809	−	0.430043i	$-0.141501\pi$
$350$	3.93570e7	+	1.34038e8i	0.917949	+	3.12625i
$351$	2.81686e6	+	6.16806e6i	0.0651394	+	0.142635i
$352$	−594987.	+	515559.i	−0.0136421	+	0.0118209i
$353$	−2.64606e6	−	1.84038e7i	−0.0601556	−	0.418392i	−0.997540	−	0.0700957i	$-0.977670\pi$
$353$	−2.64606e6	−	1.84038e7i	−0.0601556	−	0.418392i	0.937385	−	0.348296i	$-0.113240\pi$
$354$	4.45069e7	+	1.30684e7i	1.00327	+	0.294587i
$355$	6.29326e6	+	5.45314e6i	0.140667	+	0.121888i
$356$	−1.72209e6	+	2.67963e6i	−0.0381686	+	0.0593916i
$357$	1.59470e6	+	1.02485e6i	0.0350488	+	0.0225245i
$358$	−5.74135e6	+	6.62587e6i	−0.125131	+	0.144409i
$359$	1.98950e7	−	6.77562e7i	0.429992	−	1.46442i	−0.405081	−	0.914281i	$-0.632757\pi$
$359$	1.98950e7	−	6.77562e7i	0.429992	−	1.46442i	0.835073	−	0.550139i	$-0.185425\pi$
$360$	2.67368e7	−	3.84417e6i	0.573062	−	0.0823939i
$361$	−2.98898e7	−	3.44947e7i	−0.635334	−	0.733214i
$362$	−4.27689e7	+	1.95319e7i	−0.901576	+	0.411736i
$363$	2.61188e7	−	7.66917e6i	0.546051	−	0.160335i
$364$	−5.03593e6	−	2.29983e6i	−0.104418	−	0.0476861i
$365$	1.00432e8	+	1.44399e7i	2.06535	+	0.296952i
$366$	−1.26858e6	−	1.97394e6i	−0.0258746	−	0.0402617i
$367$		−	1.38049e7i		−	0.279277i	−0.990203	−	0.139639i	$-0.955406\pi$
$367$		−	1.38049e7i		−	0.279277i	0.990203	−	0.139639i	$-0.0445941\pi$
$368$	7.50753e6	+	4.51589e7i	0.150645	+	0.906150i
$369$	2.67233e7			0.531877
$370$	−6.28815e7	+	4.04115e7i	−1.24142	+	0.797811i
$371$	−1.02262e7	+	7.11249e7i	−0.200260	+	1.39284i
$372$	32238.0	−	70591.3i	0.000626237	−	0.00137127i
$373$	1.55628e6	+	5.30021e6i	0.0299890	+	0.102133i	0.973128	−	0.230267i	$-0.0739599\pi$
$373$	1.55628e6	+	5.30021e6i	0.0299890	+	0.102133i	−0.943139	+	0.332400i	$0.892142\pi$
$374$	−96800.6	−	211964.i	−0.00185039	−	0.00405179i
$375$	3.17115e7	−	2.74782e7i	0.601344	−	0.521068i
$376$	3.39663e6	+	2.36241e7i	0.0638976	+	0.444417i
$377$	5.42718e7	+	1.59356e7i	1.01286	+	0.297403i
$378$	1.40584e7	+	1.21817e7i	0.260292	+	0.225545i
$379$	1.94833e7	−	3.03165e7i	0.357885	−	0.556880i	−0.614895	−	0.788609i	$-0.710802\pi$
$379$	1.94833e7	−	3.03165e7i	0.357885	−	0.556880i	0.972781	+	0.231728i	$0.0744381\pi$
$380$	1.01322e6	+	651156.i	0.0184651	+	0.0118668i
$381$	−1.78754e7	+	2.06293e7i	−0.323206	+	0.373000i
$382$	3.37239e6	−	1.14853e7i	0.0604989	−	0.206040i
$383$	5.32181e7	−	7.65161e6i	0.947247	−	0.136194i	0.348658	−	0.937250i	$-0.386637\pi$
$383$	5.32181e7	−	7.65161e6i	0.947247	−	0.136194i	0.598589	+	0.801056i	$0.295728\pi$
$384$	−1.86618e7	−	2.15369e7i	−0.329580	−	0.380355i
$385$	−1.93952e7	+	8.85749e6i	−0.339869	+	0.155213i
$386$	6.59385e7	−	1.93613e7i	1.14651	−	0.336645i
$387$	−2.76007e7	−	1.26048e7i	−0.476197	−	0.217472i
$388$	−3.68707e6	−	530121.i	−0.0631229	−	0.00907570i
$389$	−2.17346e7	−	3.38197e7i	−0.369235	−	0.574541i	0.606068	−	0.795413i	$-0.292746\pi$
$389$	−2.17346e7	−	3.38197e7i	−0.369235	−	0.574541i	−0.975303	+	0.220872i	$0.929110\pi$
$390$		−	4.50566e7i		−	0.759564i
$391$	2.30039e6	+	279385.i	0.0384833	+	0.00467383i
$392$	−1.53561e8			−2.54931
$393$	4.37811e6	−	2.81364e6i	0.0721289	−	0.0463544i
$394$	1.32463e7	−	9.21304e7i	0.216575	−	1.50631i
$395$	7.44824e6	−	1.63094e7i	0.120854	−	0.264634i
$396$	52751.1	+	179654.i	0.000849466	+	0.00289302i
$397$	2.13685e7	+	4.67904e7i	0.341509	+	0.747800i	0.999988	−	0.00479859i	$-0.00152745\pi$
$397$	2.13685e7	+	4.67904e7i	0.341509	+	0.747800i	−0.658480	+	0.752598i	$0.728800\pi$
$398$	2.10485e7	−	1.82386e7i	0.333866	−	0.289296i
$399$	1.67767e6	+	1.16685e7i	0.0264112	+	0.183694i
$400$	−1.02697e8	−	3.01546e7i	−1.60464	−	0.471165i
$401$	−6.39477e7	−	5.54110e7i	−0.991726	−	0.859335i	−0.00166827	−	0.999999i	$-0.500531\pi$
$401$	−6.39477e7	−	5.54110e7i	−0.991726	−	0.859335i	−0.990057	+	0.140663i	$0.955076\pi$
$402$	−4.13256e6	+	6.43038e6i	−0.0636122	+	0.0989825i
$403$	−1.54772e6	−	994659.i	−0.0236470	−	0.0151970i
$404$	2.42885e6	−	2.80304e6i	0.0368346	−	0.0425094i
$405$	3.49245e6	−	1.18942e7i	0.0525734	−	0.179048i
$406$	1.53591e8	−	2.20830e7i	2.29502	−	0.329974i
$407$	−4.82238e6	−	5.56533e6i	−0.0715284	−	0.0825482i
$408$	−1.42999e6	+	653053.i	−0.0210548	+	0.00961542i
$409$	−3.87532e7	+	1.13790e7i	−0.566419	+	0.166316i	−0.552390	−	0.833586i	$-0.686284\pi$
$409$	−3.87532e7	+	1.13790e7i	−0.566419	+	0.166316i	−0.0140295	+	0.999902i	$0.504466\pi$
$410$	−1.61522e8	−	7.37645e7i	−2.34358	−	1.07028i
$411$	1.59794e6	+	229749.i	0.0230162	+	0.00330924i
$412$	3.53467e6	+	5.50005e6i	0.0505425	+	0.0786457i
$413$			2.47020e8i			3.50657i
$414$	2.19541e7	+	5.92637e6i	0.309396	+	0.0835194i
$415$	1.78679e8			2.49994
$416$	7.45303e6	−	4.78977e6i	0.103527	−	0.0665326i
$417$	−8.16857e6	+	5.68137e7i	−0.112652	+	0.783510i
$418$	601982.	−	1.31816e6i	0.00824242	−	0.0180484i
$419$	−3.00507e7	−	1.02343e8i	−0.408519	−	1.39129i	−0.865097	−	0.501604i	$-0.832743\pi$
$419$	−3.00507e7	−	1.02343e8i	−0.408519	−	1.39129i	0.456578	−	0.889683i	$-0.349075\pi$
$420$	4.20443e6	+	9.20641e6i	0.0567491	+	0.124263i
$421$	−5.26861e7	+	4.56528e7i	−0.706074	+	0.611816i	−0.932056	−	0.362315i	$-0.881986\pi$
$421$	−5.26861e7	+	4.56528e7i	−0.706074	+	0.611816i	0.225982	+	0.974132i	$0.427441\pi$
$422$	3.38901e6	+	2.35711e7i	0.0450957	+	0.313648i
$423$	1.05095e7	+	3.08586e6i	0.138854	+	0.0407713i
$424$	−4.50358e7	−	3.90238e7i	−0.590827	−	0.511955i
$425$	−2.92916e6	+	4.55786e6i	−0.0381572	+	0.0593737i
$426$	−4.00080e6	−	2.57116e6i	−0.0517509	−	0.0332583i
$427$	8.18283e6	−	9.44349e6i	0.105104	−	0.121297i
$428$	−2.00612e6	+	6.83223e6i	−0.0255874	+	0.0871427i
$429$	4.39371e6	−	631720.i	0.0556493	−	0.00800116i
$430$	1.32032e8	+	1.52373e8i	1.66063	+	1.91647i
$431$	−1.85348e7	+	8.46455e6i	−0.231502	+	0.105724i	−0.527789	−	0.849375i	$-0.676979\pi$
$431$	−1.85348e7	+	8.46455e6i	−0.231502	+	0.105724i	0.296287	+	0.955099i	$0.404252\pi$
$432$	−1.36751e7	+	4.01538e6i	−0.169621	+	0.0498053i
$433$	1.18101e8	+	5.39349e7i	1.45476	+	0.664365i	0.976826	−	0.214034i	$-0.0686603\pi$
$433$	1.18101e8	+	5.39349e7i	1.45476	+	0.664365i	0.477929	+	0.878398i	$0.341388\pi$
$434$	−4.99572e6	−	718276.i	−0.0611123	−	0.00878662i
$435$	−5.59051e7	−	8.69901e7i	−0.679178	−	1.05682i
$436$		−	8.27559e6i		−	0.0998480i
$437$	8.05515e6	+	1.19493e7i	0.0965226	+	0.143185i
$438$	−5.79478e7			−0.689627
$439$	−7.78066e7	+	5.00033e7i	−0.919651	+	0.591024i	−0.912556	−	0.408951i	$-0.865895\pi$
$439$	−7.78066e7	+	5.00033e7i	−0.919651	+	0.591024i	−0.00709439	+	0.999975i	$0.502258\pi$
$440$	2.51648e6	−	1.75025e7i	0.0295417	−	0.205467i
$441$	−2.92755e7	+	6.41044e7i	−0.341341	+	0.747433i
$442$	738769.	+	2.51602e6i	0.00855544	+	0.0291371i
$443$	−3.04559e7	−	6.66892e7i	−0.350317	−	0.767086i	−0.999976	−	0.00686130i	$-0.997816\pi$
$443$	−3.04559e7	−	6.66892e7i	−0.350317	−	0.767086i	0.649660	−	0.760225i	$-0.274911\pi$
$444$	−2.64172e6	+	2.28906e6i	−0.0301813	+	0.0261523i
$445$	−1.96467e7	−	1.36645e8i	−0.222951	−	1.55065i
$446$	−1.40278e8	−	4.11893e7i	−1.58119	−	0.464280i
$447$	−1.82466e7	−	1.58108e7i	−0.204296	−	0.177023i
$448$	9.62623e7	−	1.49787e8i	1.07059	−	1.66587i
$449$	−1.26777e8	−	8.14744e7i	−1.40055	−	0.900082i	−0.400685	−	0.916216i	$-0.631228\pi$
$449$	−1.26777e8	−	8.14744e7i	−1.40055	−	0.900082i	−0.999870	+	0.0161342i	$0.994864\pi$
$450$	−3.48170e7	+	4.01809e7i	−0.382079	+	0.440943i
$451$	4.92855e6	−	1.67851e7i	0.0537266	−	0.182976i
$452$	8.14810e6	−	1.17152e6i	0.0882350	−	0.0126863i
$453$	5.91984e7	+	6.83186e7i	0.636818	+	0.734927i
$454$	−1.67105e7	+	7.63141e6i	−0.178575	+	0.0815525i
$455$	2.30222e8	−	6.75992e7i	2.44406	−	0.717641i
$456$	−8.89279e6	−	4.06120e6i	−0.0937872	−	0.0428312i
$457$	8.73655e7	+	1.25613e7i	0.915358	+	0.131609i	0.583867	−	0.811849i	$-0.301539\pi$
$457$	8.73655e7	+	1.25613e7i	0.915358	+	0.131609i	0.331492	+	0.943458i	$0.392448\pi$
$458$	−3.80782e7	−	5.92508e7i	−0.396351	−	0.616734i
$459$			721452.i			0.00746053i
$460$	9.52597e6	+	7.89514e6i	0.0978669	+	0.0811122i
$461$	−7.99970e7			−0.816528			−0.408264	−	0.912864i	$-0.633866\pi$
$461$	−7.99970e7			−0.816528			−0.408264	+	0.912864i	$0.633866\pi$
$462$	1.02442e7	−	6.58353e6i	0.103885	−	0.0667626i
$463$	−9.66301e6	+	6.72077e7i	−0.0973575	+	0.677136i	0.881439	+	0.472299i	$0.156576\pi$
$463$	−9.66301e6	+	6.72077e7i	−0.0973575	+	0.677136i	−0.978796	+	0.204837i	$0.934333\pi$
$464$	−4.93879e7	+	1.08144e8i	−0.494387	+	1.08256i
$465$	947573.	+	3.22714e6i	0.00942440	+	0.0320966i
$466$	−3.60982e6	−	7.90441e6i	−0.0356721	−	0.0781109i
$467$	4.40492e7	−	3.81689e7i	0.432501	−	0.374765i	−0.411229	−	0.911532i	$-0.634900\pi$
$467$	4.40492e7	−	3.81689e7i	0.432501	−	0.374765i	0.843730	+	0.536768i	$0.180355\pi$
$468$	−299862.	−	2.08558e6i	−0.00292539	−	0.0203465i
$469$	−3.90569e7	−	1.14681e7i	−0.378599	−	0.111167i
$470$	−5.50037e7	−	4.76609e7i	−0.529783	−	0.459060i
$471$	5.71119e7	−	8.88679e7i	0.546593	−	0.850515i
$472$	−1.72336e8	−	1.10753e8i	−1.63889	−	1.05325i
$473$	−1.30075e7	+	1.50115e7i	−0.122917	+	0.141853i
$474$	−2.88490e6	+	9.82506e6i	−0.0270892	+	0.0922572i
$475$	−3.33501e7	+	4.79502e6i	−0.311183	+	0.0447414i
$476$	−385734.	−	445160.i	−0.00357657	−	0.00412758i
$477$	−2.48764e7	+	1.13607e7i	−0.229209	+	0.104676i
$478$	−1.38714e8	+	4.07301e7i	−1.27010	+	0.372934i
$479$	6.23155e6	+	2.84585e6i	0.0567009	+	0.0258944i	0.443564	−	0.896243i	$-0.353714\pi$
$479$	6.23155e6	+	2.84585e6i	0.0567009	+	0.0258944i	−0.386863	+	0.922137i	$0.626441\pi$
$480$	−1.60315e7	−	2.30498e6i	−0.144960	−	0.0208422i
$481$	4.48020e7	+	6.97133e7i	0.402590	+	0.626442i
$482$		−	1.87809e7i		−	0.167717i
$483$	2.65674e6	+	1.21069e8i	0.0235780	+	1.07446i
$484$	−8.45861e6			−0.0746041
$485$	1.35813e8	−	8.72819e7i	1.19047	−	0.765066i
$486$	−1.00755e6	+	7.00765e6i	−0.00877722	+	0.0610469i
$487$	−2.76668e7	+	6.05819e7i	−0.239537	+	0.524512i	−0.990775	−	0.135519i	$-0.956730\pi$
$487$	−2.76668e7	+	6.05819e7i	−0.239537	+	0.524512i	0.751238	+	0.660031i	$0.229457\pi$
$488$	2.91949e6	+	9.94287e6i	0.0251216	+	0.0855564i
$489$	5.39175e6	+	1.18063e7i	0.0461108	+	0.100969i
$490$	3.53895e8	−	3.06652e8i	3.00806	−	2.60650i
$491$	−1.18711e7	−	8.25652e7i	−0.100287	−	0.697513i	−0.976489	−	0.215568i	$-0.930840\pi$
$491$	−1.18711e7	−	8.25652e7i	−0.100287	−	0.697513i	0.876201	−	0.481945i	$-0.160069\pi$
$492$	−7.96746e6	−	2.33946e6i	−0.0668998	−	0.0196435i
$493$	4.54815e6	+	3.94099e6i	0.0379572	+	0.0328901i
$494$	−8.81630e6	+	1.37184e7i	−0.0731317	+	0.113795i
$495$	−6.82672e6	−	4.38727e6i	−0.0562855	−	0.0361725i
$496$	2.53233e6	−	2.92247e6i	0.0207527	−	0.0239499i
$497$	7.13515e6	−	2.43001e7i	0.0581211	−	0.197942i
$498$	−1.01007e8	+	1.45226e7i	−0.817832	+	0.117587i
$499$	1.56855e8	+	1.81020e8i	1.26240	+	1.45689i	0.832517	+	0.554000i	$0.186899\pi$
$499$	1.56855e8	+	1.81020e8i	1.26240	+	1.45689i	0.429881	+	0.902886i	$0.358555\pi$
$500$	−1.18602e7	+	5.41638e6i	−0.0948817	+	0.0433310i
$501$	1.22242e8	−	3.58936e7i	0.972095	−	0.285433i
$502$	−3.51090e7	−	1.60338e7i	−0.277529	−	0.126743i
$503$	1.19565e8	+	1.71908e7i	0.939505	+	0.135080i	0.595019	−	0.803711i	$-0.297144\pi$
$503$	1.19565e8	+	1.71908e7i	0.939505	+	0.135080i	0.344485	+	0.938792i	$0.388053\pi$
$504$	−4.44150e7	−	6.91111e7i	−0.346927	−	0.539829i
$505$			1.60747e8i			1.24815i
$506$	7.77136e6	−	1.26965e7i	0.0599854	−	0.0980017i
$507$	2.52908e7			0.194061
$508$	7.13543e6	−	4.58566e6i	0.0544289	−	0.0349793i
$509$	−2.63357e7	+	1.83169e8i	−0.199706	+	1.38899i	0.605431	+	0.795898i	$0.293001\pi$
$509$	−2.63357e7	+	1.83169e8i	−0.199706	+	1.38899i	−0.805137	+	0.593089i	$0.797908\pi$
$510$	1.99143e6	−	4.36062e6i	0.0150125	−	0.0328729i
$511$	−8.69401e7	−	2.96091e8i	−0.651565	−	2.21902i
$512$	6.07028e7	+	1.32921e8i	0.452271	+	0.990336i
$513$	−3.39072e6	+	2.93807e6i	−0.0251153	+	0.0217626i
$514$	−1.33142e7	−	9.26026e7i	−0.0980454	−	0.681921i
$515$	−2.71877e8	−	7.98302e7i	−1.99045	−	0.584448i
$516$	7.12557e6	+	6.17434e6i	0.0518645	+	0.0449409i
$517$	3.87649e6	−	6.03194e6i	0.0280522	−	0.0436501i
$518$	1.91246e8	+	1.22906e8i	1.37595	+	0.884269i
$519$	6.75763e7	−	7.79872e7i	0.483384	−	0.557855i
$520$	−5.60605e7	+	1.90925e8i	−0.398701	+	1.35785i
$521$	−3.96721e7	+	5.70399e6i	−0.280525	+	0.0403335i	−0.281141	−	0.959666i	$-0.590713\pi$
$521$	−3.96721e7	+	5.70399e6i	−0.280525	+	0.0403335i	0.000616038		1.00000i	$0.499804\pi$
$522$	3.86735e7	+	4.46316e7i	0.271896	+	0.313784i
$523$	1.82958e8	−	8.35543e7i	1.27893	−	0.584069i	0.344025	−	0.938961i	$-0.388210\pi$
$523$	1.82958e8	−	8.35543e7i	1.27893	−	0.584069i	0.934907	+	0.354892i	$0.115482\pi$
$524$	−1.55164e6	+	455601.i	−0.0107844	+	0.00316658i
$525$	−2.57546e8	−	1.17617e8i	−1.77982	−	0.812817i
$526$	−3.16900e7	−	4.55633e6i	−0.217753	−	0.0313082i
$527$	−105827.	−	164671.i	−0.000723047	−	0.00112508i
$528$			9.32998e6i			0.0633839i
$529$	6.73442e7	+	1.31831e8i	0.454918	+	0.890533i
$530$	1.81717e8			1.22059
$531$	−7.90890e7	+	5.08274e7i	−0.528241	+	0.339480i
$532$	521308.	−	3.62578e6i	0.00346226	−	0.0240805i
$533$	−8.17787e7	+	1.79070e8i	−0.540081	+	1.18261i
$534$	2.22125e7	+	7.56488e7i	0.145873	+	0.496796i
$535$	−1.28202e8	−	2.80722e8i	−0.837205	−	1.83322i
$536$	2.55123e7	−	2.21065e7i	0.165674	−	0.143558i
$537$	−2.52882e6	−	1.75884e7i	−0.0163304	−	0.113580i
$538$	1.00861e8	+	2.96156e7i	0.647707	+	0.190184i
$539$	3.48651e7	+	3.02108e7i	0.222651	+	0.192928i
$540$	−2.08252e6	+	3.24047e6i	−0.0132254	+	0.0205791i
$541$	5.04888e7	+	3.24472e7i	0.318862	+	0.204920i	0.690274	−	0.723548i	$-0.257490\pi$
$541$	5.04888e7	+	3.24472e7i	0.318862	+	0.204920i	−0.371412	+	0.928468i	$0.621126\pi$
$542$	−6.60409e7	+	7.62153e7i	−0.414778	+	0.478679i
$543$	2.68474e7	−	9.14340e7i	0.167689	−	0.571095i
$544$	933012.	−	134147.i	0.00579549	−	0.000833266i
$545$	2.34876e8	+	2.71061e8i	1.45094	+	1.67447i
$546$	−1.24650e8	+	5.69257e7i	−0.765798	+	0.349728i
$547$	−1.20275e8	+	3.53160e7i	−0.734876	+	0.215779i	−0.627694	−	0.778460i	$-0.716001\pi$
$547$	−1.20275e8	+	3.53160e7i	−0.734876	+	0.215779i	−0.107182	+	0.994239i	$0.534183\pi$
$548$	−456306.	−	208388.i	−0.00277278	−	0.00126628i
$549$	4.70726e6	+	676802.i	0.0284480	+	0.00409020i
$550$	1.88167e7	+	2.92793e7i	0.113098	+	0.175984i
$551$			3.74251e7i			0.223721i
$552$	−8.56556e7	−	5.24285e7i	−0.509259	−	0.311710i
$553$	−5.45306e7			−0.322452
$554$	−1.76916e8	+	1.13697e8i	−1.04049	+	0.668684i
$555$	2.15600e7	−	1.49953e8i	0.126116	−	0.877157i
$556$	7.40911e6	−	1.62237e7i	0.0431064	−	0.0943898i
$557$	1.65530e7	+	5.63742e7i	0.0957878	+	0.326223i	0.993421	−	0.114520i	$-0.0365330\pi$
$557$	1.65530e7	+	5.63742e7i	0.0957878	+	0.326223i	−0.897633	+	0.440744i	$0.854715\pi$
$558$	−797958.	−	1.74728e6i	−0.00459280	−	0.0100568i
$559$	1.68927e8	−	1.46376e8i	0.967083	−	0.837982i
$560$	7.17730e7	+	4.99192e8i	0.408693	+	2.84252i
$561$	453149.	+	133056.i	0.00256656	+	0.000753611i
$562$	8.76903e7	+	7.59841e7i	0.494018	+	0.428069i
$563$	9.39641e6	−	1.46211e7i	0.0526546	−	0.0819322i	−0.813928	−	0.580966i	$-0.802675\pi$
$563$	9.39641e6	−	1.46211e7i	0.0526546	−	0.0819322i	0.866583	+	0.499033i	$0.166311\pi$
$564$	−2.86321e6	−	1.84007e6i	−0.0159594	−	0.0102565i
$565$	−2.33635e8	+	2.69630e8i	−1.29537	+	1.49493i
$566$	4.93303e7	−	1.68004e8i	0.272060	−	0.926551i
$567$	−3.73181e7	+	5.36553e6i	−0.204724	+	0.0294349i
$568$	1.37541e7	+	1.58730e7i	0.0750560	+	0.0866193i
$569$	−1.31711e8	+	6.01502e7i	−0.714964	+	0.326513i	−0.739473	−	0.673187i	$-0.764925\pi$
$569$	−1.31711e8	+	6.01502e7i	−0.714964	+	0.326513i	0.0245088	+	0.999700i	$0.492198\pi$
$570$	2.86042e7	−	8.39896e6i	0.154456	−	0.0453525i
$571$	−249529.	−	113956.i	−0.00134033	−	0.000612109i	0.414745	−	0.909938i	$-0.363871\pi$
$571$	−249529.	−	113956.i	−0.00134033	−	0.000612109i	−0.416085	+	0.909326i	$0.636598\pi$
$572$	−1.36527e6	−	196296.i	−0.00729509	−	0.00104888i
$573$	1.31163e7	+	2.04094e7i	0.0697186	+	0.108484i
$574$			5.40050e8i			2.85561i
$575$	−3.46031e8	+	7.59333e6i	−1.82017	+	0.0399419i
$576$	6.77648e7			0.354598
$577$	−1.30714e8	+	8.40047e7i	−0.680447	+	0.437297i	−0.834678	−	0.550738i	$-0.814346\pi$
$577$	−1.30714e8	+	8.40047e7i	−0.680447	+	0.437297i	0.154231	+	0.988035i	$0.450710\pi$
$578$	2.63810e7	−	1.83484e8i	0.136618	−	0.950197i
$579$	−5.78606e7	+	1.26697e8i	−0.298090	+	0.652725i
$580$	9.05248e6	+	3.08299e7i	0.0463963	+	0.158011i
$581$	−2.25748e8	−	4.94319e8i	−1.15105	−	2.52046i
$582$	−6.96812e7	+	6.03791e7i	−0.353465	+	0.306279i
$583$	2.54779e6	+	1.77202e7i	0.0128575	+	0.0894260i
$584$	2.45550e8	+	7.21001e7i	1.23283	+	0.361990i
$585$	6.90143e7	+	5.98012e7i	0.344724	+	0.298705i
$586$	7.60690e7	−	1.18366e8i	0.378020	−	0.588210i
$587$	−2.05072e8	−	1.31792e8i	−1.01389	−	0.651589i	−0.0754944	−	0.997146i	$-0.524054\pi$
$587$	−2.05072e8	−	1.31792e8i	−1.01389	−	0.651589i	−0.938398	+	0.345557i	$0.887690\pi$
$588$	1.43403e7	−	1.65496e7i	0.0705386	−	0.0814059i
$589$	342951.	−	1.16798e6i	0.00167837	−	0.00571599i
$590$	6.18331e8	−	8.89025e7i	3.01068	−	0.432871i
$591$	1.23537e8	+	1.42570e8i	0.598461	+	0.690660i
$592$	−1.58439e8	+	7.23565e7i	−0.763653	+	0.348748i
$593$	3.02040e8	−	8.86869e7i	1.44844	−	0.425300i	0.539414	−	0.842041i	$-0.318646\pi$
$593$	3.02040e8	−	8.86869e7i	1.44844	−	0.425300i	0.909025	+	0.416741i	$0.136828\pi$
$594$	4.21573e6	+	1.92526e6i	0.0201147	+	0.00918607i
$595$	2.52689e7	+	3.63311e6i	0.119960	+	0.0172476i
$596$	4.05602e6	+	6.31130e6i	0.0191585	+	0.0298112i
$597$			5.64477e7i			0.265292i
$598$	−1.06896e8	+	1.28977e8i	−0.499871	+	0.603125i
$599$	−1.79620e7			−0.0835746			−0.0417873	−	0.999127i	$-0.513305\pi$
$599$	−1.79620e7			−0.0835746			−0.0417873	+	0.999127i	$0.513305\pi$
$600$	1.97529e8	−	1.26944e8i	0.914487	−	0.587705i
$601$	2.29487e7	−	1.59612e8i	0.105715	−	0.735261i	−0.866161	−	0.499765i	$-0.833420\pi$
$601$	2.29487e7	−	1.59612e8i	0.105715	−	0.735261i	0.971875	−	0.235496i	$-0.0756713\pi$
$602$	2.54730e8	−	5.57780e8i	1.16759	−	2.55666i
$603$	−4.36466e6	−	1.48647e7i	−0.0199066	−	0.0677958i
$604$	−1.16689e7	−	2.55514e7i	−0.0529566	−	0.115959i
$605$	2.77056e8	−	2.40070e8i	1.25113	−	1.08411i
$606$	−1.30651e7	−	9.08700e7i	−0.0587078	−	0.408322i
$607$	−1.04408e8	−	3.06569e7i	−0.466838	−	0.137076i	0.0398495	−	0.999206i	$-0.487312\pi$
$607$	−1.04408e8	−	3.06569e7i	−0.466838	−	0.137076i	−0.506688	+	0.862130i	$0.669130\pi$
$608$	4.43011e6	+	3.83871e6i	0.0197108	+	0.0170795i
$609$	−1.70028e8	+	2.64568e8i	−0.752780	+	1.17135i
$610$	−2.65836e7	−	1.70842e7i	−0.117118	−	0.0752671i
$611$	−5.28391e7	+	6.09796e7i	−0.231650	+	0.267338i
$612$	63158.6	−	215098.i	0.000275536	−	0.000938389i
$613$	1.11843e8	−	1.60805e7i	0.485541	−	0.0698102i	0.104803	−	0.994493i	$-0.466579\pi$
$613$	1.11843e8	−	1.60805e7i	0.485541	−	0.0698102i	0.380738	+	0.924683i	$0.375670\pi$
$614$	−2.36716e8	−	2.73184e8i	−1.02264	−	1.18019i
$615$	3.27367e8	−	1.49503e8i	1.40737	−	0.642726i
$616$	−5.16005e7	+	1.51513e7i	−0.220756	+	0.0648197i
$617$	1.32178e8	+	6.03639e7i	0.562736	+	0.256993i	0.676410	−	0.736525i	$-0.263535\pi$
$617$	1.32178e8	+	6.03639e7i	0.562736	+	0.256993i	−0.113674	+	0.993518i	$0.536262\pi$
$618$	1.60180e8	+	2.30304e7i	0.678646	+	0.0975746i
$619$	−3.45499e7	−	5.37607e7i	−0.145672	−	0.226670i	0.760748	−	0.649047i	$-0.224832\pi$
$619$	−3.45499e7	−	5.37607e7i	−0.145672	−	0.226670i	−0.906420	+	0.422377i	$0.861196\pi$
$620$		−	1.04511e6i		−	0.00438519i
$621$	−3.82162e7	+	2.57620e7i	−0.159578	+	0.107573i
$622$	−3.25692e8			−1.35343
$623$	−3.53210e8	+	2.26995e8i	−1.46073	+	0.938753i
$624$	1.49419e7	−	1.03924e8i	0.0614969	−	0.427720i
$625$	5.01013e7	−	1.09706e8i	0.205215	−	0.449358i
$626$	4.71193e7	+	1.60474e8i	0.192077	+	0.654155i
$627$	1.22008e6	+	2.67159e6i	0.00494976	+	0.0108385i
$628$	−2.48075e7	+	2.14958e7i	−0.100162	+	0.0867912i
$629$	1.25477e6	+	8.72710e6i	0.00504210	+	0.0350686i
$630$	2.40369e8	+	7.05788e7i	0.961296	+	0.282262i
$631$	−1.44282e8	−	1.25021e8i	−0.574279	−	0.497616i	0.318614	−	0.947885i	$-0.396783\pi$
$631$	−1.44282e8	−	1.25021e8i	−0.574279	−	0.497616i	−0.892893	+	0.450269i	$0.851328\pi$
$632$	2.44492e7	−	3.80437e7i	0.0968530	−	0.150706i
$633$	−4.06025e7	−	2.60936e7i	−0.160082	−	0.102878i
$634$	8.42504e7	−	9.72301e7i	0.330601	−	0.381534i
$635$	−1.03567e8	+	3.52716e8i	−0.404483	+	1.37754i
$636$	8.41135e6	−	1.20937e6i	0.0326960	−	0.00470097i
$637$	−3.39968e8	−	3.92344e8i	−1.31529	−	1.51792i
$638$	3.51659e7	−	1.60597e7i	0.135413	−	0.0618410i
$639$	9.24836e6	−	2.71556e6i	0.0354456	−	0.0104078i
$640$	−3.49099e8	−	1.59428e8i	−1.33171	−	0.608170i
$641$	−4.68468e8	−	6.73556e7i	−1.77871	−	0.255740i	−0.826885	−	0.562371i	$-0.809889\pi$
$641$	−4.68468e8	−	6.73556e7i	−1.77871	−	0.255740i	−0.951829	+	0.306630i	$0.900798\pi$
$642$	9.52888e7	+	1.48272e8i	0.360111	+	0.560344i
$643$		−	4.31191e8i		−	1.62195i	−0.585084	−	0.810973i	$-0.698938\pi$
$643$		−	4.31191e8i		−	1.62195i	0.585084	−	0.810973i	$-0.301062\pi$
$644$	9.80669e6	−	3.63287e7i	0.0367168	−	0.136017i
$645$	−4.08632e8			−1.52283
$646$	−1.45958e6	+	938018.i	−0.00541416	+	0.00347947i
$647$	−2.63100e7	+	1.82990e8i	−0.0971423	+	0.675639i	0.881818	+	0.471589i	$0.156320\pi$
$647$	−2.63100e7	+	1.82990e8i	−0.0971423	+	0.675639i	−0.978961	+	0.204050i	$0.934590\pi$
$648$	1.29885e7	−	2.84409e7i	0.0477348	−	0.104525i
$649$	1.73387e7	+	5.90503e7i	0.0634283	+	0.216017i
$650$	−1.62702e8	−	3.56267e8i	−0.592450	−	1.29728i
$651$	7.73076e6	−	6.69874e6i	0.0280207	−	0.0242801i
$652$	−573965.	−	3.99201e6i	−0.00207082	−	0.0144029i
$653$	2.26798e8	+	6.65940e7i	0.814517	+	0.239164i	0.662354	−	0.749191i	$-0.269558\pi$
$653$	2.26798e8	+	6.65940e7i	0.814517	+	0.239164i	0.152164	+	0.988355i	$0.451376\pi$
$654$	−1.54806e8	−	1.34141e8i	−0.553421	−	0.479542i
$655$	3.78920e7	−	5.89610e7i	0.134841	−	0.209817i
$656$	−3.48090e8	−	2.23704e8i	−1.23305	−	0.792431i
$657$	7.69111e7	−	8.87601e7i	0.271202	−	0.312984i
$658$	−6.23619e7	+	2.12385e8i	−0.218898	+	0.745497i
$659$	1.82861e8	−	2.62914e7i	0.638947	−	0.0918666i	0.184775	−	0.982781i	$-0.440844\pi$
$659$	1.82861e8	−	2.62914e7i	0.638947	−	0.0918666i	0.454172	+	0.890914i	$0.349935\pi$
$660$	1.65128e6	+	1.90568e6i	0.00574367	+	0.00662855i
$661$	1.01609e8	−	4.64035e7i	0.351827	−	0.160674i	−0.231659	−	0.972797i	$-0.574415\pi$
$661$	1.01609e8	−	4.64035e7i	0.351827	−	0.160674i	0.583486	+	0.812123i	$0.301688\pi$
$662$	1.99073e8	−	5.84532e7i	0.686182	−	0.201481i
$663$	−4.83438e6	−	2.20779e6i	−0.0165882	−	0.00757559i
$664$	4.46082e8	+	6.41368e7i	1.52374	+	0.219080i
$665$	8.58309e7	+	1.33555e8i	0.291863	+	0.454147i
$666$			8.65210e7i			0.292886i
$667$	−4.63515e7	+	3.81647e8i	−0.156202	+	1.28613i
$668$	−3.95884e7			−0.132812
$669$	2.49274e8	−	1.60199e8i	0.832529	−	0.535034i
$670$	−1.46500e7	+	1.01893e8i	−0.0487095	+	0.338782i
$671$	1.29326e6	−	2.83184e6i	0.00428072	−	0.00937348i
$672$	1.38778e7	+	4.72636e7i	0.0457314	+	0.155747i
$673$	−1.14851e8	−	2.51488e8i	−0.376780	−	0.825033i	−0.999106	−	0.0422752i	$-0.986539\pi$
$673$	−1.14851e8	−	2.51488e8i	−0.376780	−	0.825033i	0.622326	−	0.782758i	$-0.286188\pi$
$674$	4.05655e7	−	3.51502e7i	0.132488	−	0.114802i
$675$	−1.53354e7	−	1.06660e8i	−0.0498637	−	0.346809i
$676$	−7.54035e6	−	2.21405e6i	−0.0244091	−	0.00716715i
$677$	1.43794e8	+	1.24598e8i	0.463420	+	0.401556i	0.855032	−	0.518575i	$-0.173537\pi$
$677$	1.43794e8	+	1.24598e8i	0.463420	+	0.401556i	−0.391612	+	0.920130i	$0.628083\pi$
$678$	1.10159e8	−	1.71411e8i	0.353453	−	0.549983i
$679$	−4.13058e8	−	2.65456e8i	−1.31948	−	0.847976i
$680$	−1.38642e7	+	1.60001e7i	−0.0440927	+	0.0508857i
$681$	1.04897e7	−	3.57246e7i	0.0332140	−	0.113117i
$682$	−1.24465e6	+	178953.i	−0.00392367	+	0.000564139i
$683$	−2.50147e8	−	2.88685e8i	−0.785115	−	0.906071i	0.212352	−	0.977193i	$-0.431888\pi$
$683$	−2.50147e8	−	2.88685e8i	−0.785115	−	0.906071i	−0.997468	+	0.0711219i	$0.977342\pi$
$684$	1.26814e6	−	579140.i	0.00396277	−	0.00180973i
$685$	2.08604e7	−	6.12517e6i	0.0649010	−	0.0190566i
$686$	−7.69944e8	−	3.51622e8i	−2.38499	−	1.08919i
$687$	1.41295e8	+	2.03152e7i	0.435770	+	0.0626543i
$688$	2.54002e8	+	3.95234e8i	0.779958	+	1.21364i
$689$		−	2.01460e8i		−	0.615930i
$690$	3.02098e8	−	5.02228e7i	0.919603	−	0.152881i
$691$	2.99037e8			0.906340			0.453170	−	0.891424i	$-0.350293\pi$
$691$	2.99037e8			0.906340			0.453170	+	0.891424i	$0.350293\pi$
$692$	−2.69749e7	+	1.73357e7i	−0.0814033	+	0.0523147i
$693$	−3.51240e6	+	2.44293e7i	−0.0105537	+	0.0734025i
$694$	6.16341e7	−	1.34960e8i	0.184392	−	0.403762i
$695$	2.17777e8	+	7.41679e8i	0.648719	+	2.20933i
$696$	−1.08345e8	−	2.37242e8i	−0.321352	−	0.703663i
$697$	−1.58293e7	+	1.37161e7i	−0.0467479	+	0.0405073i
$698$	7.13034e7	+	4.95926e8i	0.209674	+	1.45831i
$699$	1.68985e7	+	4.96185e6i	0.0494786	+	0.0145282i
$700$	6.64897e7	+	5.76136e7i	0.193847	+	0.167970i
$701$	8.12510e7	−	1.26429e8i	0.235871	−	0.367023i	−0.703058	−	0.711132i	$-0.748183\pi$
$701$	8.12510e7	−	1.26429e8i	0.235871	−	0.367023i	0.938930	+	0.344109i	$0.111819\pi$
$702$	−4.38743e7	−	2.81963e7i	−0.126823	−	0.0815043i
$703$	−3.59061e7	+	4.14378e7i	−0.103348	+	0.119270i
$704$	1.24978e7	−	4.25635e7i	0.0358191	−	0.121989i
$705$	1.46007e8	−	2.09926e7i	0.416684	−	0.0599101i
$706$	9.36481e7	+	1.08076e8i	0.266125	+	0.307124i
$707$	4.44709e8	−	2.03092e8i	1.25840	−	0.574690i
$708$	2.80297e7	−	8.23026e6i	0.0789803	−	0.0231907i
$709$	1.39860e8	+	6.38721e7i	0.392424	+	0.179214i	0.601848	−	0.798611i	$-0.294431\pi$
$709$	1.39860e8	+	6.38721e7i	0.392424	+	0.179214i	−0.209423	+	0.977825i	$0.567159\pi$
$710$	−6.33949e7	−	9.11482e6i	−0.177125	−	0.0254667i
$711$	−1.12203e7	−	1.74592e7i	−0.0312174	−	0.0485752i
$712$		−	3.48195e8i		−	0.964678i
$713$	4.94386e6	−	1.14859e7i	0.0136395	−	0.0316882i
$714$	−1.45798e7			−0.0400549
$715$	5.02897e7	−	3.23193e7i	0.137582	−	0.0884185i
$716$	−785789.	+	5.46528e6i	−0.00214076	+	0.0148893i
$717$	1.21720e8	−	2.66531e8i	0.330222	−	0.723086i
$718$	1.53019e8	+	5.21133e8i	0.413400	+	1.40791i
$719$	1.17403e8	+	2.57077e8i	0.315858	+	0.691633i	0.999262	−	0.0384071i	$-0.0122284\pi$
$719$	1.17403e8	+	2.57077e8i	0.315858	+	0.691633i	−0.683404	+	0.730041i	$0.739501\pi$
$720$	−1.45059e8	+	1.25695e8i	−0.388640	+	0.336759i
$721$	1.22645e8	+	8.53013e8i	0.327222	+	2.27588i
$722$	3.36834e8	+	9.89035e7i	0.894962	+	0.262785i
$723$	2.87673e7	+	2.49270e7i	0.0761173	+	0.0659560i
$724$	−1.60089e7	+	2.49104e7i	−0.0421839	+	0.0656394i
$725$	−7.56173e8	−	4.85963e8i	−1.98430	−	1.27523i
$726$	−1.37107e8	+	1.58230e8i	−0.358303	+	0.413504i
$727$	−1.42833e8	+	4.86445e8i	−0.371729	+	1.26599i	0.535206	+	0.844721i	$0.320234\pi$
$727$	−1.42833e8	+	4.86445e8i	−0.371729	+	1.26599i	−0.906935	+	0.421270i	$0.861584\pi$
$728$	5.99025e8	−	8.61269e7i	1.55257	−	0.223226i
$729$	−9.39654e6	−	1.08442e7i	−0.0242541	−	0.0279907i
$730$	−7.09873e8	+	3.24188e8i	−1.82479	+	0.833352i
$731$	2.28185e7	−	6.70012e6i	0.0584165	−	0.0171526i
$732$	−1.34420e6	−	613877.i	−0.00342714	−	0.00156512i
$733$	4.14596e8	+	5.96098e7i	1.05272	+	0.151358i	0.646884	−	0.762588i	$-0.276072\pi$
$733$	4.14596e8	+	5.96098e7i	1.05272	+	0.151358i	0.405835	+	0.913946i	$0.366981\pi$
$734$	5.74040e7	+	8.93224e7i	0.145162	+	0.225877i
$735$			9.49074e8i			2.39022i
$736$	4.04223e7	+	4.46325e7i	0.101388	+	0.111948i
$737$	−1.01416e7			−0.0253339
$738$	−1.72909e8	+	1.11122e8i	−0.430178	+	0.276459i
$739$	3.80916e7	−	2.64933e8i	0.0943834	−	0.656451i	−0.886626	−	0.462488i	$-0.846957\pi$
$739$	3.80916e7	−	2.64933e8i	0.0943834	−	0.656451i	0.981009	−	0.193963i	$-0.0621341\pi$
$740$	−1.95555e7	+	4.28206e7i	−0.0482585	+	0.105671i
$741$	−9.31146e6	−	3.17119e7i	−0.0228857	−	0.0779414i
$742$	−2.29587e8	−	5.02725e8i	−0.561998	−	1.23060i
$743$	−5.33138e8	+	4.61967e8i	−1.29979	+	1.12628i	−0.315652	+	0.948875i	$0.602223\pi$
$743$	−5.33138e8	+	4.61967e8i	−1.29979	+	1.12628i	−0.984139	+	0.177400i	$0.943231\pi$
$744$	1.20729e6	+	8.39685e6i	0.00293151	+	0.0203891i
$745$	−3.11978e8	−	9.16050e7i	−0.754493	−	0.221539i
$746$	−3.21091e7	−	2.78227e7i	−0.0773414	−	0.0670167i
$747$	1.11817e8	−	1.73990e8i	0.268254	−	0.417411i
$748$	−123456.	−	79340.6i	−0.000294991	−	0.000189579i
$749$	−6.14651e8	+	7.09345e8i	−1.46279	+	1.68815i
$750$	−9.09235e7	+	3.09657e8i	−0.215522	+	0.734001i
$751$	−4.82124e8	+	6.93190e7i	−1.13825	+	0.163656i	−0.685564	−	0.728012i	$-0.740444\pi$
$751$	−4.82124e8	+	6.93190e7i	−1.13825	+	0.163656i	−0.452689	+	0.891668i	$0.649535\pi$
$752$	−1.11061e8	−	1.28171e8i	−0.261161	−	0.301396i
$753$	7.11578e7	−	3.24967e7i	0.166662	−	0.0761121i
$754$	−4.17421e8	+	1.22566e8i	−0.973778	+	0.285927i
$755$	1.10740e9	+	5.05733e8i	2.57314	+	1.17512i
$756$	1.15960e7	+	1.66725e6i	0.0268374	+	0.00385864i
$757$	−3.59542e8	−	5.59459e8i	−0.828824	−	1.28968i	−0.954682	−	0.297627i	$-0.903805\pi$
$757$	−3.59542e8	−	5.59459e8i	−0.828824	−	1.28968i	0.125858	−	0.992048i	$-0.459832\pi$
$758$			2.77174e8i			0.636422i
$759$	9.13310e6	+	2.87551e7i	0.0208878	+	0.0657641i
$760$	−1.31659e8			−0.299923
$761$	1.81579e8	−	1.16694e8i	0.412014	−	0.264785i	−0.318173	−	0.948033i	$-0.603069\pi$
$761$	1.81579e8	−	1.16694e8i	0.412014	−	0.264785i	0.730187	+	0.683248i	$0.239433\pi$
$762$	2.98783e7	−	2.07808e8i	0.0675291	−	0.469675i
$763$	4.53148e8	−	9.92255e8i	1.02015	−	2.23383i
$764$	−2.12387e6	−	7.23324e6i	−0.00476264	−	0.0162201i
$765$	4.03615e6	+	8.83795e6i	0.00901537	+	0.0197409i
$766$	−3.12522e8	+	2.70802e8i	−0.695335	+	0.602512i
$767$	−9.85614e7	−	6.85509e8i	−0.218434	−	1.51924i
$768$	−5.66420e7	−	1.66316e7i	−0.125042	−	0.0367156i
$769$	4.55255e8	+	3.94481e8i	1.00110	+	0.867455i	0.991184	−	0.132496i	$-0.0422991\pi$
$769$	4.55255e8	+	3.94481e8i	1.00110	+	0.867455i	0.00991285	+	0.999951i	$0.496845\pi$
$770$	8.86619e7	−	1.37961e8i	0.194207	−	0.302192i
$771$	1.59513e8	+	1.02513e8i	0.348043	+	0.223674i
$772$	2.83424e7	−	3.27089e7i	0.0616006	−	0.0710909i
$773$	−1.56253e8	+	5.32150e8i	−0.338291	+	1.15211i	0.598177	+	0.801364i	$0.295892\pi$
$773$	−1.56253e8	+	5.32150e8i	−0.338291	+	1.15211i	−0.936469	+	0.350751i	$0.885926\pi$
$774$	2.30999e8	−	3.32127e7i	0.498182	−	0.0716277i
$775$	1.91459e7	+	2.20956e7i	0.0411312	+	0.0474679i
$776$	3.70395e8	−	1.69154e8i	0.792647	−	0.361990i
$777$	−4.42089e8	+	1.29809e8i	−0.942425	+	0.276721i
$778$	2.81260e8	+	1.28447e8i	0.597268	+	0.272763i
$779$	−1.28927e8	−	1.85370e7i	−0.272730	−	0.0392126i
$780$	−1.53411e7	−	2.38713e7i	−0.0323276	−	0.0503028i
$781$		−	6.30978e6i		−	0.0132453i
$782$	−1.60461e7	+	7.75785e6i	−0.0335543	+	0.0162226i
$783$	−1.19693e8			−0.249335
$784$	9.17958e8	−	5.89936e8i	1.90491	−	1.22421i
$785$	2.02463e8	−	1.40816e9i	0.418540	−	2.91101i
$786$	−1.66281e7	+	3.64104e7i	−0.0342432	+	0.0749822i
$787$	1.12735e8	+	3.83940e8i	0.231278	+	0.787660i	0.990582	+	0.136924i	$0.0437216\pi$
$787$	1.12735e8	+	3.83940e8i	0.231278	+	0.787660i	−0.759304	+	0.650737i	$0.774460\pi$
$788$	−2.43511e7	−	5.33215e7i	−0.0497669	−	0.108974i
$789$	4.90395e7	−	4.24930e7i	0.0998425	−	0.0865140i
$790$	1.96255e7	+	1.36499e8i	0.0398053	+	0.276852i
$791$	1.04112e9	+	3.05700e8i	2.10364	+	0.617683i
$792$	−1.54685e7	−	1.34035e7i	−0.0311366	−	0.0269800i
$793$	−1.89403e7	+	2.94717e7i	−0.0379811	+	0.0590998i
$794$	−3.32827e8	−	2.13895e8i	−0.664900	−	0.427305i
$795$	−2.41184e8	+	2.78341e8i	−0.480006	+	0.553957i
$796$	4.94164e6	−	1.68297e7i	0.00979787	−	0.0333685i
$797$	1.07976e7	−	1.55246e6i	0.0213281	−	0.00306652i	−0.131643	−	0.991297i	$-0.542025\pi$
$797$	1.07976e7	−	1.55246e6i	0.0213281	−	0.00306652i	0.152971	+	0.988231i	$0.451116\pi$
$798$	−5.93753e7	−	6.85227e7i	−0.116841	−	0.134842i
$799$	−7.80902e6	+	3.56626e6i	−0.0153093	+	0.00699154i
$800$	−1.35086e8	+	3.96648e7i	−0.263840	+	0.0774703i
$801$	−1.45355e8	−	6.63813e7i	−0.282834	−	0.129166i
$802$	6.44175e8	+	9.26183e7i	1.24876	+	0.179545i
$803$	−4.15662e7	−	6.46782e7i	−0.0802774	−	0.124914i
$804$			4.81394e6i			0.00926259i
$805$	7.09863e8	+	1.46825e9i	1.36078	+	2.81458i
$806$	1.41503e7			0.0270246
$807$	−1.79231e8	+	1.15185e8i	−0.341030	+	0.219167i
$808$	−5.77000e7	+	4.01312e8i	−0.109381	+	0.760761i
$809$	−1.70272e8	+	3.72843e8i	−0.321586	+	0.704174i	−0.999521	−	0.0309472i	$-0.990148\pi$
$809$	−1.70272e8	+	3.72843e8i	−0.321586	+	0.704174i	0.677935	+	0.735121i	$0.262875\pi$
$810$	2.68615e7	+	9.14820e7i	0.0505447	+	0.172139i
$811$	−3.74768e8	−	8.20628e8i	−0.702587	−	1.53845i	−0.836806	−	0.547499i	$-0.815580\pi$
$811$	−3.74768e8	−	8.20628e8i	−0.702587	−	1.53845i	0.134219	−	0.990952i	$-0.457147\pi$
$812$	7.38545e7	−	6.39952e7i	0.137946	−	0.119531i
$813$	−2.90883e7	−	2.02313e8i	−0.0541310	−	0.376489i
$814$	5.43444e7	+	1.59569e7i	0.100758	+	0.0295853i
$815$	1.32100e8	+	1.14465e8i	0.244023	+	0.211447i
$816$	6.03935e6	−	9.39741e6i	0.0111153	−	0.0172957i
$817$	1.24417e8	+	7.99577e7i	0.228146	+	0.146620i
$818$	2.03430e8	−	2.34771e8i	0.371668	−	0.428928i
$819$	7.82468e7	−	2.66484e8i	0.142434	−	0.485087i
$820$	−1.10691e8	+	1.59150e7i	−0.200757	+	0.0288646i
$821$	3.91660e8	+	4.51999e8i	0.707749	+	0.816786i	0.989777	−	0.142620i	$-0.0455528\pi$
$821$	3.91660e8	+	4.51999e8i	0.707749	+	0.816786i	−0.282029	+	0.959406i	$0.591007\pi$
$822$	−1.12945e7	+	5.15805e6i	−0.0203354	+	0.00928688i
$823$	8.14794e7	−	2.39245e7i	0.146167	−	0.0429184i	−0.207831	−	0.978165i	$-0.566640\pi$
$823$	8.14794e7	−	2.39245e7i	0.146167	−	0.0429184i	0.353997	+	0.935246i	$0.384822\pi$
$824$	−6.50100e8	−	2.96891e8i	−1.16198	−	0.530658i
$825$	−6.98222e7	−	1.00389e7i	−0.124346	−	0.0178783i
$826$	−1.02717e9	−	1.59830e9i	−1.82264	−	2.83608i
$827$			4.73536e8i			0.837213i	0.908168	+	0.418607i	$0.137481\pi$
$827$			4.73536e8i			0.837213i	−0.908168	+	0.418607i	$0.862519\pi$
$828$	1.36493e7	−	4.33525e6i	0.0240447	−	0.00763701i
$829$	−2.73226e8			−0.479577			−0.239789	−	0.970825i	$-0.577078\pi$
$829$	−2.73226e8			−0.479577			−0.239789	+	0.970825i	$0.577078\pi$
$830$	−1.15611e9	+	7.42989e8i	−2.02193	+	1.29942i
$831$	6.06589e7	−	4.21892e8i	0.105704	−	0.735188i
$832$	−2.07374e8	+	4.54085e8i	−0.360067	+	0.788438i
$833$	−1.55615e7	−	5.29976e7i	−0.0269225	−	0.0916898i
$834$	−1.83391e8	−	4.01570e8i	−0.316140	−	0.692251i
$835$	1.29669e9	−	1.12359e9i	2.22729	−	1.92996i
$836$	−129880.	−	903336.i	−0.000222292	−	0.00154607i
$837$	3.73545e6	+	1.09683e6i	0.00637039	+	0.00187052i
$838$	6.20005e8	+	5.37237e8i	1.05357	+	0.912923i
$839$	2.19428e8	−	3.41437e8i	0.371540	−	0.578128i	−0.604261	−	0.796786i	$-0.706532\pi$
$839$	2.19428e8	−	3.41437e8i	0.371540	−	0.578128i	0.975802	+	0.218658i	$0.0701680\pi$
$840$	−9.30735e8	−	5.98147e8i	−1.57032	−	1.00918i
$841$	−2.64305e8	+	3.05024e8i	−0.444342	+	0.512798i
$842$	1.51062e8	−	5.14470e8i	0.253058	−	0.861835i
$843$	−2.32774e8	+	3.34678e7i	−0.388554	+	0.0558656i
$844$	9.82115e6	+	1.13342e7i	0.0163356	+	0.0188523i
$845$	3.09817e8	−	1.41489e8i	0.513494	−	0.234505i
$846$	−8.08315e7	+	2.37343e7i	−0.133496	+	0.0391981i
$847$	−1.01420e9	−	4.63169e8i	−1.66906	−	0.762236i
$848$	4.19133e8	+	6.02623e7i	0.687329	+	0.0988229i
$849$	1.91862e8	+	2.98543e8i	0.313520	+	0.487847i
$850$		−	4.16710e7i		−	0.0678543i
$851$	−4.17479e8	+	3.78098e8i	−0.677401	+	0.613502i
$852$	−2.99509e6			−0.00484275
$853$	2.22947e8	−	1.43279e8i	0.359215	−	0.230854i	−0.348568	−	0.937284i	$-0.613332\pi$
$853$	2.22947e8	−	1.43279e8i	0.359215	−	0.230854i	0.707783	+	0.706430i	$0.249696\pi$
$854$	−1.36774e7	+	9.51286e7i	−0.0219599	+	0.152735i
$855$	−2.51000e7	+	5.49613e7i	−0.0401583	+	0.0879344i
$856$	−2.19297e8	−	7.46856e8i	−0.349632	−	1.19074i
$857$	−1.48303e8	−	3.24739e8i	−0.235618	−	0.515932i	0.754478	−	0.656326i	$-0.227890\pi$
$857$	−1.48303e8	−	3.24739e8i	−0.235618	−	0.515932i	−0.990096	+	0.140394i	$0.955163\pi$
$858$	−2.58019e7	+	2.23575e7i	−0.0408499	+	0.0353966i
$859$	1.49615e8	+	1.04059e9i	0.236045	+	1.64173i	0.671130	+	0.741340i	$0.265809\pi$
$859$	1.49615e8	+	1.04059e9i	0.236045	+	1.64173i	−0.435085	+	0.900389i	$0.643282\pi$
$860$	1.21832e8	+	3.57731e7i	0.191543	+	0.0562421i
$861$	−8.27208e8	−	7.16780e8i	−1.29600	−	1.12299i
$862$	8.47287e7	−	1.31840e8i	0.132284	−	0.205838i
$863$	1.20741e8	+	7.75957e7i	0.187855	+	0.120727i	0.631188	−	0.775630i	$-0.282568\pi$
$863$	1.20741e8	+	7.75957e7i	0.187855	+	0.120727i	−0.443333	+	0.896357i	$0.646204\pi$
$864$	−1.22770e7	+	1.41684e7i	−0.0190348	+	0.0219674i
$865$	3.91526e8	−	1.33342e9i	0.604940	−	2.06024i
$866$	−9.88427e8	+	1.42114e8i	−1.52192	+	0.218819i
$867$	2.46032e8	+	2.83937e8i	0.377516	+	0.435676i
$868$	−2.89133e6	+	1.32043e6i	−0.00442118	+	0.00201909i
$869$	−1.30356e7	+	3.82759e6i	−0.0198642	+	0.00583265i
$870$	7.23450e8	+	3.30389e8i	1.09863	+	0.501727i
$871$	1.12963e8	+	1.62417e7i	0.170955	+	0.0245797i
$872$	4.89082e8	+	7.61027e8i	0.737620	+	1.14776i
$873$		−	1.86870e8i		−	0.280865i
$874$	−1.01807e8	−	4.38207e7i	−0.152491	−	0.0656364i
$875$	−1.71864e9			−2.56544
$876$	−3.07011e7	+	1.97304e7i	−0.0456712	+	0.0293511i
$877$	5.71215e7	−	3.97289e8i	0.0846839	−	0.588989i	−0.902655	−	0.430365i	$-0.858385\pi$
$877$	5.71215e7	−	3.97289e8i	0.0846839	−	0.588989i	0.987339	−	0.158625i	$-0.0507059\pi$
$878$	2.95510e8	−	6.47076e8i	0.436604	−	0.956030i
$879$	8.03413e7	+	2.73617e8i	0.118297	+	0.402881i
$880$	5.21965e7	+	1.14294e8i	0.0765937	+	0.167717i
$881$	3.43687e8	−	2.97807e8i	0.502615	−	0.435518i	−0.366287	−	0.930502i	$-0.619371\pi$
$881$	3.43687e8	−	2.97807e8i	0.502615	−	0.435518i	0.868902	+	0.494983i	$0.164826\pi$
$882$	−7.71387e7	−	5.36511e8i	−0.112426	−	0.781940i
$883$	4.11314e8	+	1.20773e8i	0.597436	+	0.175423i	0.566449	−	0.824097i	$-0.308317\pi$
$883$	4.11314e8	+	1.20773e8i	0.597436	+	0.175423i	0.0309871	+	0.999520i	$0.490135\pi$
$884$	1.24807e6	+	1.08146e6i	0.00180669	+	0.00156551i
$885$	−6.84504e8	+	1.06511e9i	−0.987521	+	1.53661i
$886$	4.74369e8	+	3.04859e8i	0.682049	+	0.438326i
$887$	3.86207e8	−	4.45707e8i	0.553413	−	0.638673i	−0.408262	−	0.912865i	$-0.633865\pi$
$887$	3.86207e8	−	4.45707e8i	0.553413	−	0.638673i	0.961675	+	0.274192i	$0.0884104\pi$
$888$	1.07652e8	−	3.66628e8i	0.153738	−	0.523584i
$889$	1.10665e9	−	1.59112e8i	1.57508	−	0.226463i
$890$	6.95324e8	+	8.02447e8i	0.986319	+	1.13827i
$891$	−8.54429e6	+	3.90205e6i	−0.0120793	+	0.00551644i
$892$	−8.83446e7	+	2.59403e7i	−0.124476	+	0.0365495i
$893$	−4.85626e7	−	2.21778e7i	−0.0681943	−	0.0311433i
$894$	1.83807e8	+	2.64274e7i	0.257246	+	0.0369864i
$895$	−1.29376e8	−	2.01314e8i	−0.180462	−	0.280805i
$896$			1.16722e9i			1.62266i
$897$	−5.56793e7	−	3.34919e8i	−0.0771466	−	0.464048i
$898$	1.15908e9			1.60060
$899$	2.73198e7	−	1.75573e7i	0.0376009	−	0.0241646i
$900$	−4.76522e6	+	3.31428e7i	−0.00653666	+	0.0454634i
$901$	8.90421e6	−	1.94975e7i	0.0121737	−	0.0266566i
$902$	3.79070e7	+	1.29099e8i	0.0516534	+	0.175915i
$903$	5.16277e8	+	1.13049e9i	0.701163	+	1.53533i
$904$	−6.80067e8	+	5.89281e8i	−0.920548	+	0.797659i
$905$	−1.82639e8	−	1.27028e9i	−0.246404	−	1.71378i
$906$	−6.67118e8	−	1.95884e8i	−0.897053	−	0.263399i
$907$	1.91068e8	+	1.65561e8i	0.256074	+	0.221889i	0.773431	−	0.633880i	$-0.218539\pi$
$907$	1.91068e8	+	1.65561e8i	0.256074	+	0.221889i	−0.517357	+	0.855769i	$0.673084\pi$
$908$	−6.25493e6	+	9.73286e6i	−0.00835535	+	0.0130012i
$909$	1.56529e8	+	1.00595e8i	0.208402	+	0.133932i
$910$	−1.20852e9	+	1.39471e9i	−1.60372	+	1.85079i
$911$	2.19129e7	−	7.46285e7i	0.0289831	−	0.0987074i	−0.943731	−	0.330713i	$-0.892711\pi$
$911$	2.19129e7	−	7.46285e7i	0.0289831	−	0.0987074i	0.972714	+	0.232006i	$0.0745289\pi$
$912$	6.87613e7	−	9.88638e6i	0.0906483	−	0.0130333i
$913$	−8.86623e7	−	1.02322e8i	−0.116500	−	0.134448i
$914$	−6.17517e8	+	2.82010e8i	−0.808742	+	0.369340i
$915$	6.14513e7	−	1.80437e7i	0.0802173	−	0.0235539i
$916$	−4.03482e7	−	1.84264e7i	−0.0524974	−	0.0239747i
$917$	−2.10991e8	−	3.03359e7i	−0.273625	−	0.0393413i
$918$	−2.99997e6	−	4.66804e6i	−0.00387783	−	0.00603401i
$919$		−	7.17256e8i		−	0.924118i	−0.886849	−	0.462059i	$-0.847111\pi$
$919$		−	7.17256e8i		−	0.924118i	0.886849	−	0.462059i	$-0.152889\pi$
$920$	−1.34261e9	−	1.63061e8i	−1.72420	−	0.209405i
$921$	7.32624e8			0.937783
$922$	5.17607e8	−	3.32646e8i	0.660401	−	0.424414i
$923$	−1.01051e7	+	7.02825e7i	−0.0128510	+	0.0893804i
$924$	3.18583e6	−	6.97600e6i	0.00403838	−	0.00884282i
$925$	−3.71012e8	−	1.26355e9i	−0.468773	−	1.59650i
$926$	−2.16942e8	−	4.75037e8i	−0.273219	−	0.598267i
$927$	−2.47875e8	+	2.14785e8i	−0.311167	+	0.269628i
$928$	2.22557e7	+	1.54792e8i	0.0278482	+	0.193688i
$929$	−7.59085e8	−	2.22887e8i	−0.946767	−	0.277996i	−0.228327	−	0.973585i	$-0.573325\pi$
$929$	−7.59085e8	−	2.22887e8i	−0.946767	−	0.277996i	−0.718440	+	0.695589i	$0.755144\pi$
$930$	−1.95503e7	−	1.69404e7i	−0.0243055	−	0.0210608i
$931$	1.85707e8	−	2.88966e8i	0.230133	−	0.358095i
$932$	−4.60385e6	−	2.95872e6i	−0.00568688	−	0.00365473i
$933$	4.32274e8	−	4.98870e8i	0.532248	−	0.614247i
$934$	−1.26298e8	+	4.30132e8i	−0.155009	+	0.527912i
$935$	6.29555e6	−	905164.i	0.00770192	−	0.00110737i
$936$	1.50832e8	+	1.74070e8i	0.183936	+	0.212273i
$937$	−9.35352e8	+	4.27161e8i	−1.13699	+	0.519246i	−0.892787	−	0.450479i	$-0.851253\pi$
$937$	−9.35352e8	+	4.27161e8i	−1.13699	+	0.519246i	−0.244202	+	0.969724i	$0.578526\pi$
$938$	3.00399e8	−	8.82050e7i	0.363990	−	0.106877i
$939$	−3.08341e8	−	1.40815e8i	−0.372421	−	0.170079i
$940$	−4.53692e7	−	6.52311e6i	−0.0546233	−	0.00785364i
$941$	3.29121e8	+	5.12123e8i	0.394991	+	0.614618i	0.980610	−	0.195968i	$-0.0627850\pi$
$941$	3.29121e8	+	5.12123e8i	0.394991	+	0.614618i	−0.585619	+	0.810586i	$0.699149\pi$
$942$			8.12490e8i			0.971997i
$943$	−1.29180e9	−	3.48712e8i	−1.54049	−	0.415845i
$944$	1.45567e9			1.73040
$945$	−4.27137e8	+	2.74504e8i	−0.506141	+	0.325277i
$946$	2.17418e7	−	1.51217e8i	0.0256816	−	0.178619i
$947$	1.29808e8	−	2.84239e8i	0.152845	−	0.334683i	−0.817685	−	0.575666i	$-0.804743\pi$
$947$	1.29808e8	−	2.84239e8i	0.152845	−	0.334683i	0.970529	+	0.240983i	$0.0774700\pi$
$948$	1.81686e6	+	6.18765e6i	0.00213254	+	0.00726275i
$949$	3.59409e8	+	7.86997e8i	0.420524	+	0.920819i
$950$	1.95847e8	−	1.69703e8i	0.228427	−	0.197933i
$951$	3.71088e7	+	2.58097e8i	0.0431454	+	0.300083i
$952$	6.17810e7	+	1.81405e7i	0.0716051	+	0.0210251i
$953$	−9.01149e8	−	7.80850e8i	−1.04116	−	0.902171i	−0.0458551	−	0.998948i	$-0.514601\pi$
$953$	−9.01149e8	−	7.80850e8i	−1.04116	−	0.902171i	−0.995306	+	0.0967768i	$0.969147\pi$
$954$	1.13718e8	−	1.76949e8i	0.130974	−	0.203800i
$955$	2.74858e8	+	1.76641e8i	0.315572	+	0.202806i
$956$	−5.96236e7	+	6.88093e7i	−0.0682408	+	0.0787541i
$957$	−2.20748e7	+	7.51798e7i	−0.0251861	+	0.0857759i
$958$	−5.21540e7	+	7.49861e6i	−0.0593186	+	0.00852872i
$959$	−4.33010e7	−	4.99721e7i	−0.0490956	−	0.0566593i
$960$	8.30134e8	−	3.79109e8i	0.938284	−	0.428500i
$961$	8.50540e8	−	2.49741e8i	0.958351	−	0.281397i
$962$	−5.79769e8	−	2.64771e8i	−0.651223	−	0.297403i
$963$	−3.53584e8	−	5.08378e7i	−0.395926	−	0.0569256i
$964$	−6.39465e6	−	9.95028e6i	−0.00713815	−	0.0111072i
$965$			1.87577e9i			2.08736i
$966$	−5.20622e8	−	7.72307e8i	−0.577552	−	0.856759i
$967$	−1.02592e9			−1.13458			−0.567289	−	0.823519i	$-0.692008\pi$
$967$	−1.02592e9			−1.13458			−0.567289	+	0.823519i	$0.692008\pi$
$968$	7.77858e8	−	4.99899e8i	0.857579	−	0.551132i
$969$	500444.	−	3.48066e6i	0.000550027	−	0.00382552i
$970$	−5.15819e8	+	1.12949e9i	−0.565174	+	1.23756i
$971$	−5.08706e8	−	1.73249e9i	−0.555660	−	1.89240i	−0.436983	−	0.899470i	$-0.643953\pi$
$971$	−5.08706e8	−	1.73249e9i	−0.555660	−	1.89240i	−0.118676	−	0.992933i	$-0.537865\pi$
$972$	1.85220e6	+	4.05576e6i	0.00201693	+	0.00441645i
$973$	1.77673e9	−	1.53954e9i	1.92878	−	1.67129i
$974$	−7.28999e7	−	5.07030e8i	−0.0788951	−	0.548728i
$975$	7.61649e8	+	2.23640e8i	0.821752	+	0.241288i
$976$	−5.56497e7	−	4.82207e7i	−0.0598568	−	0.0518662i
$977$	−1.31304e8	+	2.04313e8i	−0.140797	+	0.219084i	−0.904490	−	0.426496i	$-0.859748\pi$
$977$	−1.31304e8	+	2.04313e8i	−0.140797	+	0.219084i	0.763693	+	0.645580i	$0.223384\pi$
$978$	−8.39797e7	−	5.39705e7i	−0.0897755	−	0.0576952i
$979$	−6.85021e7	+	7.90556e7i	−0.0730055	+	0.0842528i
$980$	8.30854e7	−	2.82963e8i	0.0882768	−	0.300643i
$981$	4.10933e8	−	5.90833e7i	0.435275	−	0.0625832i
$982$	4.20135e8	+	4.84862e8i	0.443664	+	0.512016i
$983$	4.00171e8	−	1.82752e8i	0.421294	−	0.192399i	−0.193476	−	0.981105i	$-0.561976\pi$
$983$	4.00171e8	−	1.82752e8i	0.421294	−	0.192399i	0.614770	+	0.788706i	$0.289249\pi$
$984$	8.70952e8	−	2.55735e8i	0.914132	−	0.268413i
$985$	2.31096e9	+	1.05538e9i	2.41816	+	1.10433i
$986$	−4.58156e7	−	6.58729e6i	−0.0477950	−	0.00687189i
$987$	−2.42546e8	−	3.77409e8i	−0.252257	−	0.392519i
$988$			1.02700e7i			0.0106487i
$989$	1.16973e9	+	9.69472e8i	1.20919	+	1.00218i
$990$	6.24144e7			0.0643249
$991$	−8.39769e8	+	5.39687e8i	−0.862857	+	0.554525i	−0.895560	−	0.444941i	$-0.853225\pi$
$991$	−8.39769e8	+	5.39687e8i	−0.862857	+	0.554525i	0.0327030	+	0.999465i	$0.489588\pi$
$992$	723892.	−	5.03478e6i	0.000741547	−	0.00515757i
$993$	−1.74685e8	+	3.82508e8i	−0.178406	+	0.390654i
$994$	5.48786e7	+	1.86899e8i	0.0558784	+	0.190304i
$995$	3.15796e8	+	6.91497e8i	0.320581	+	0.701974i
$996$	−4.85696e7	+	4.20858e7i	−0.0491571	+	0.0425949i
$997$	1.43484e8	+	9.97956e8i	0.144784	+	1.00699i	0.924588	+	0.380969i	$0.124409\pi$
$997$	1.43484e8	+	9.97956e8i	0.144784	+	1.00699i	−0.779804	+	0.626023i	$0.784681\pi$
$998$	−1.76763e9	−	5.19022e8i	−1.77828	−	0.522149i
$999$	−1.32526e8	−	1.14835e8i	−0.132925	−	0.115180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.34.7	✓	240
23.21	odd	22	inner	69.7.f.a.67.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.34.7	✓	240	1.1	even	1	trivial
69.7.f.a.67.7	yes	240	23.21	odd	22	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:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47034 + 4.15823i) q^{2} +(2.21847 - 15.4298i) q^{3} +(-2.01221 + 4.40612i) q^{4} +(-59.1450 - 201.429i) q^{5} +(49.8064 + 109.061i) q^{6} +(-482.533 + 418.118i) q^{7} +(-75.3556 - 524.109i) q^{8} +(-233.157 - 68.4610i) q^{9} +O(q^{10})\)	\(q+(-6.47034 + 4.15823i) q^{2} +(2.21847 - 15.4298i) q^{3} +(-2.01221 + 4.40612i) q^{4} +(-59.1450 - 201.429i) q^{5} +(49.8064 + 109.061i) q^{6} +(-482.533 + 418.118i) q^{7} +(-75.3556 - 524.109i) q^{8} +(-233.157 - 68.4610i) q^{9} +(1220.28 + 1057.38i) q^{10} +(-86.0016 + 133.821i) q^{11} +(63.5215 + 40.8228i) q^{12} +(1172.26 - 1352.86i) q^{13} +(1383.52 - 4711.85i) q^{14} +(-3239.23 + 465.730i) q^{15} +(2463.93 + 2843.53i) q^{16} +(173.246 - 79.1189i) q^{17} +(1793.28 - 526.554i) q^{18} +(1077.38 + 492.024i) q^{19} +(1006.53 + 144.718i) q^{20} +(5380.98 + 8372.97i) q^{21} -1223.48i q^{22} +(10377.4 + 6351.84i) q^{23} -8254.07 q^{24} +(-23931.1 + 15379.6i) q^{25} +(-1959.40 + 13628.0i) q^{26} +(-1573.59 + 3445.68i) q^{27} +(-871.319 - 2967.44i) q^{28} +(13126.2 + 28742.5i) q^{29} +(19022.3 - 16482.9i) q^{30} +(-146.265 - 1017.30i) q^{31} +(4748.69 + 1394.34i) q^{32} +(1874.04 + 1623.86i) q^{33} +(-791.967 + 1232.32i) q^{34} +(112761. + 72466.9i) q^{35} +(770.808 - 889.559i) q^{36} +(-13042.2 + 44417.8i) q^{37} +(-9016.97 + 1296.45i) q^{38} +(-18273.7 - 21088.9i) q^{39} +(-101114. + 46177.3i) q^{40} +(-105518. + 30982.9i) q^{41} +(-69633.5 - 31800.6i) q^{42} +(123596. + 17770.4i) q^{43} +(-416.579 - 648.209i) q^{44} +51013.8i q^{45} +(-93557.6 + 2053.03i) q^{46} -45074.7 q^{47} +(49341.2 - 31709.7i) q^{48} +(41273.0 - 287060. i) q^{49} +(90890.4 - 199022. i) q^{50} +(-836.447 - 2848.68i) q^{51} +(3602.02 + 7887.33i) q^{52} +(85053.7 - 73699.4i) q^{53} +(-4146.29 - 28838.1i) q^{54} +(32042.1 + 9408.40i) q^{55} +(255501. + 221393. i) q^{56} +(9981.96 - 15532.2i) q^{57} +(-204449. - 131391. i) q^{58} +(253356. - 292389. i) q^{59} +(4465.93 - 15209.6i) q^{60} +(-19371.4 + 2785.19i) q^{61} +(5176.55 + 5974.06i) q^{62} +(141131. - 64452.2i) q^{63} +(-267571. + 78566.1i) q^{64} +(-341838. - 156112. i) q^{65} +(-18878.1 - 2714.26i) q^{66} +(34468.0 + 53633.2i) q^{67} +922.548i q^{68} +(121029. - 146029. i) q^{69} -1.03093e6 q^{70} +(-33369.0 + 21445.0i) q^{71} +(-18311.4 + 127359. i) q^{72} +(-200778. + 439642. i) q^{73} +(-100312. - 341631. i) q^{74} +(184213. + 403371. i) q^{75} +(-4335.83 + 3757.02i) q^{76} +(-14454.3 - 100532. i) q^{77} +(205930. + 60466.4i) q^{78} +(64545.8 + 55929.3i) q^{79} +(427042. - 664490. i) q^{80} +(49675.2 + 31924.3i) q^{81} +(553902. - 639237. i) q^{82} +(-239789. + 816647. i) q^{83} +(-47720.0 + 6861.10i) q^{84} +(-26183.5 - 30217.4i) q^{85} +(-873601. + 398960. i) q^{86} +(472611. - 138771. i) q^{87} +(76617.6 + 34990.1i) q^{88} +(650900. + 93585.2i) q^{89} +(-212127. - 330076. i) q^{90} +1.14294e6i q^{91} +(-48868.4 + 32942.8i) q^{92} -16021.2 q^{93} +(291648. - 187431. i) q^{94} +(35386.3 - 246117. i) q^{95} +(32049.2 - 70178.0i) q^{96} +(216656. + 737864. i) q^{97} +(926612. + 2.02900e6i) q^{98} +(29213.4 - 25313.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more