LMFDB - Embedded newform 770.2.bi.a.27.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(27,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 10, 8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("770.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bi (of order $20$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$48$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			27.3
Character	$\chi$	$=$	770.27
Dual form			770.2.bi.a.713.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(-0.442024 - 2.79083i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.523489 - 2.17393i) q^{5} +(2.68732 + 0.873164i) q^{6} +(-2.62728 + 0.312118i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-4.74017 + 1.54018i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.442024 - 2.79083i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.523489 - 2.17393i) q^{5} +(2.68732 + 0.873164i) q^{6} +(-2.62728 + 0.312118i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-4.74017 + 1.54018i) q^{9} +(1.69932 + 1.45337i) q^{10} +(-3.05087 - 1.30084i) q^{11} +(-1.99801 + 1.99801i) q^{12} +(-1.20936 + 2.37351i) q^{13} +(0.914659 - 2.48262i) q^{14} +(-6.29845 - 0.500040i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.85026 + 3.63134i) q^{17} +(0.779687 - 4.92275i) q^{18} +(-3.09109 - 2.24581i) q^{19} +(-2.06644 + 0.854291i) q^{20} +(2.03239 + 7.19432i) q^{21} +(2.54412 - 2.12778i) q^{22} +(1.65248 - 1.65248i) q^{23} +(-0.873164 - 2.68732i) q^{24} +(-4.45192 - 2.27605i) q^{25} +(-1.56577 - 2.15510i) q^{26} +(2.54523 + 4.99529i) q^{27} +(1.79678 + 1.94205i) q^{28} +(4.72889 + 6.50875i) q^{29} +(3.30498 - 5.38495i) q^{30} +(10.0404 - 3.26232i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.28186 + 9.08946i) q^{33} -4.07555 q^{34} +(-0.696827 + 5.87490i) q^{35} +(4.03223 + 2.92959i) q^{36} +(-4.00867 - 0.634911i) q^{37} +(3.40436 - 1.73461i) q^{38} +(7.15862 + 2.32598i) q^{39} +(0.176967 - 2.22905i) q^{40} +(1.60620 - 2.21075i) q^{41} +(-7.33287 - 1.45528i) q^{42} +(-6.71998 + 6.71998i) q^{43} +(0.740858 + 3.23282i) q^{44} +(0.866803 + 11.1111i) q^{45} +(0.722162 + 2.22259i) q^{46} +(-3.97381 + 0.629390i) q^{47} +(2.79083 + 0.442024i) q^{48} +(6.80516 - 1.64004i) q^{49} +(4.04911 - 2.93338i) q^{50} +(9.31660 - 6.76891i) q^{51} +(2.63105 - 0.416718i) q^{52} +(-7.63326 - 3.88934i) q^{53} -5.60634 q^{54} +(-4.42502 + 5.95140i) q^{55} +(-2.54610 + 0.719272i) q^{56} +(-4.90134 + 9.61942i) q^{57} +(-7.94621 + 1.25856i) q^{58} +(-0.0640985 + 0.0465703i) q^{59} +(3.29760 + 5.38947i) q^{60} +(3.50599 + 1.13917i) q^{61} +(-1.65149 + 10.4271i) q^{62} +(11.9730 - 5.52596i) q^{63} +(0.951057 - 0.309017i) q^{64} +(4.52674 + 3.87157i) q^{65} +(-7.06283 - 6.15968i) q^{66} +(-5.40239 - 5.40239i) q^{67} +(1.85026 - 3.63134i) q^{68} +(-5.34224 - 3.88136i) q^{69} +(-4.91822 - 3.28803i) q^{70} +(-0.616665 + 1.89790i) q^{71} +(-4.44088 + 2.26274i) q^{72} +(-7.15418 - 1.13311i) q^{73} +(2.38561 - 3.28351i) q^{74} +(-4.38422 + 13.4306i) q^{75} +3.82080i q^{76} +(8.42150 + 2.46543i) q^{77} +(-5.32240 + 5.32240i) q^{78} +(-11.1735 + 3.63049i) q^{79} +(1.90576 + 1.16965i) q^{80} +(0.719245 - 0.522562i) q^{81} +(1.24059 + 2.43480i) q^{82} +(-10.4774 + 5.33848i) q^{83} +(4.62572 - 5.87295i) q^{84} +(8.86287 - 2.12137i) q^{85} +(-2.93674 - 9.03835i) q^{86} +(16.0745 - 16.0745i) q^{87} +(-3.21681 - 0.807561i) q^{88} -7.47380 q^{89} +(-10.2935 - 4.27199i) q^{90} +(2.43651 - 6.61332i) q^{91} +(-2.30819 - 0.365582i) q^{92} +(-13.5427 - 26.5790i) q^{93} +(1.24328 - 3.82643i) q^{94} +(-6.50038 + 5.54416i) q^{95} +(-1.66086 + 2.28597i) q^{96} +(7.16274 + 3.64960i) q^{97} +(-1.62819 + 6.80801i) q^{98} +(16.4652 + 1.46732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 4 q^{7}+O(q^{10}) $ 384 * q - 4 * q^7	$ 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) $ 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	−0.442024	−	2.79083i	−0.255203	−	1.61129i	−0.698975	−	0.715146i	$-0.746360\pi$
$3$	−0.442024	−	2.79083i	−0.255203	−	1.61129i	0.443772	−	0.896140i	$-0.353640\pi$
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	0.523489	−	2.17393i	0.234111	−	0.972210i
$5$	0.523489	−	2.17393i	0.234111	−	0.972210i
$6$	2.68732	+	0.873164i	1.09709	+	0.356468i
$7$	−2.62728	+	0.312118i	−0.993017	+	0.117970i
$7$	−2.62728	+	0.312118i	−0.993017	+	0.117970i
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−4.74017	+	1.54018i	−1.58006	+	0.513392i
$10$	1.69932	+	1.45337i	0.537374	+	0.459597i
$11$	−3.05087	−	1.30084i	−0.919873	−	0.392217i
$11$	−3.05087	−	1.30084i	−0.919873	−	0.392217i
$12$	−1.99801	+	1.99801i	−0.576777	+	0.576777i
$13$	−1.20936	+	2.37351i	−0.335417	+	0.658292i	−0.995691	−	0.0927323i	$-0.970440\pi$
$13$	−1.20936	+	2.37351i	−0.335417	+	0.658292i	0.660275	+	0.751024i	$0.270440\pi$
$14$	0.914659	−	2.48262i	0.244453	−	0.663508i
$15$	−6.29845	−	0.500040i	−1.62625	−	0.129110i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	1.85026	+	3.63134i	0.448755	+	0.880730i	0.998955	+	0.0456979i	$0.0145512\pi$
$17$	1.85026	+	3.63134i	0.448755	+	0.880730i	−0.550201	+	0.835032i	$0.685449\pi$
$18$	0.779687	−	4.92275i	0.183774	−	1.16030i
$19$	−3.09109	−	2.24581i	−0.709146	−	0.515225i	0.173752	−	0.984789i	$-0.444411\pi$
$19$	−3.09109	−	2.24581i	−0.709146	−	0.515225i	−0.882898	+	0.469565i	$0.844411\pi$
$20$	−2.06644	+	0.854291i	−0.462071	+	0.191025i
$21$	2.03239	+	7.19432i	0.443503	+	1.56993i
$22$	2.54412	−	2.12778i	0.542409	−	0.453644i
$23$	1.65248	−	1.65248i	0.344567	−	0.344567i	−0.513514	−	0.858081i	$-0.671657\pi$
$23$	1.65248	−	1.65248i	0.344567	−	0.344567i	0.858081	+	0.513514i	$0.171657\pi$
$24$	−0.873164	−	2.68732i	−0.178234	−	0.548547i
$25$	−4.45192	−	2.27605i	−0.890384	−	0.455211i
$26$	−1.56577	−	2.15510i	−0.307073	−	0.422650i
$27$	2.54523	+	4.99529i	0.489829	+	0.961343i
$28$	1.79678	+	1.94205i	0.339560	+	0.367014i
$29$	4.72889	+	6.50875i	0.878132	+	1.20865i	0.976935	+	0.213538i	$0.0684988\pi$
$29$	4.72889	+	6.50875i	0.878132	+	1.20865i	−0.0988024	+	0.995107i	$0.531501\pi$
$30$	3.30498	−	5.38495i	0.603403	−	0.983153i
$31$	10.0404	−	3.26232i	1.80331	−	0.585930i	0.803352	−	0.595505i	$-0.203048\pi$
$31$	10.0404	−	3.26232i	1.80331	−	0.585930i	0.999954	+	0.00957484i	$0.00304781\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.28186	+	9.08946i	−0.397221	+	1.58227i
$34$	−4.07555			−0.698952
$35$	−0.696827	+	5.87490i	−0.117785	+	0.993039i
$36$	4.03223	+	2.92959i	0.672039	+	0.488265i
$37$	−4.00867	−	0.634911i	−0.659021	−	0.104379i	−0.182038	−	0.983291i	$-0.558269\pi$
$37$	−4.00867	−	0.634911i	−0.659021	−	0.104379i	−0.476982	+	0.878913i	$0.658269\pi$
$38$	3.40436	−	1.73461i	0.552260	−	0.281391i
$39$	7.15862	+	2.32598i	1.14630	+	0.372454i
$40$	0.176967	−	2.22905i	0.0279809	−	0.352444i
$41$	1.60620	−	2.21075i	0.250847	−	0.345261i	−0.664961	−	0.746878i	$-0.731552\pi$
$41$	1.60620	−	2.21075i	0.250847	−	0.345261i	0.915808	+	0.401617i	$0.131552\pi$
$42$	−7.33287	−	1.45528i	−1.13149	−	0.224555i
$43$	−6.71998	+	6.71998i	−1.02479	+	1.02479i	−0.0251025	+	0.999685i	$0.507991\pi$
$43$	−6.71998	+	6.71998i	−1.02479	+	1.02479i	−0.999685	+	0.0251025i	$0.992009\pi$
$44$	0.740858	+	3.23282i	0.111688	+	0.487366i
$45$	0.866803	+	11.1111i	0.129215	+	1.65634i
$46$	0.722162	+	2.22259i	0.106477	+	0.327702i
$47$	−3.97381	+	0.629390i	−0.579640	+	0.0918059i	−0.439368	−	0.898307i	$-0.644798\pi$
$47$	−3.97381	+	0.629390i	−0.579640	+	0.0918059i	−0.140272	+	0.990113i	$0.544798\pi$
$48$	2.79083	+	0.442024i	0.402821	+	0.0638007i
$49$	6.80516	−	1.64004i	0.972166	−	0.234292i
$50$	4.04911	−	2.93338i	0.572630	−	0.414843i
$51$	9.31660	−	6.76891i	1.30459	−	0.947837i
$52$	2.63105	−	0.416718i	0.364861	−	0.0577883i
$53$	−7.63326	−	3.88934i	−1.04851	−	0.534242i	−0.157166	−	0.987572i	$-0.550236\pi$
$53$	−7.63326	−	3.88934i	−1.04851	−	0.534242i	−0.891343	+	0.453330i	$0.850236\pi$
$54$	−5.60634			−0.762926
$55$	−4.42502	+	5.95140i	−0.596670	+	0.802487i
$56$	−2.54610	+	0.719272i	−0.340238	+	0.0961168i
$57$	−4.90134	+	9.61942i	−0.649198	+	1.27412i
$58$	−7.94621	+	1.25856i	−1.04339	+	0.165257i
$59$	−0.0640985	+	0.0465703i	−0.00834492	+	0.00606294i	−0.591950	−	0.805975i	$-0.701642\pi$
$59$	−0.0640985	+	0.0465703i	−0.00834492	+	0.00606294i	0.583605	+	0.812038i	$0.301642\pi$
$60$	3.29760	+	5.38947i	0.425718	+	0.695778i
$61$	3.50599	+	1.13917i	0.448896	+	0.145855i	0.524736	−	0.851265i	$-0.324164\pi$
$61$	3.50599	+	1.13917i	0.448896	+	0.145855i	−0.0758401	+	0.997120i	$0.524164\pi$
$62$	−1.65149	+	10.4271i	−0.209740	+	1.32424i
$63$	11.9730	−	5.52596i	1.50846	−	0.696206i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	4.52674	+	3.87157i	0.561473	+	0.480209i
$66$	−7.06283	−	6.15968i	−0.869374	−	0.758204i
$67$	−5.40239	−	5.40239i	−0.660007	−	0.660007i	0.295375	−	0.955382i	$-0.404556\pi$
$67$	−5.40239	−	5.40239i	−0.660007	−	0.660007i	−0.955382	+	0.295375i	$0.904556\pi$
$68$	1.85026	−	3.63134i	0.224377	−	0.440365i
$69$	−5.34224	−	3.88136i	−0.643130	−	0.467261i
$70$	−4.91822	−	3.28803i	−0.587840	−	0.392994i
$71$	−0.616665	+	1.89790i	−0.0731846	+	0.225239i	−0.980957	−	0.194223i	$-0.937781\pi$
$71$	−0.616665	+	1.89790i	−0.0731846	+	0.225239i	0.907773	+	0.419462i	$0.137781\pi$
$72$	−4.44088	+	2.26274i	−0.523362	+	0.266666i
$73$	−7.15418	−	1.13311i	−0.837333	−	0.132621i	−0.276981	−	0.960875i	$-0.589334\pi$
$73$	−7.15418	−	1.13311i	−0.837333	−	0.132621i	−0.560352	+	0.828255i	$0.689334\pi$
$74$	2.38561	−	3.28351i	0.277321	−	0.381700i
$75$	−4.38422	+	13.4306i	−0.506246	+	1.55083i
$76$			3.82080i			0.438276i
$77$	8.42150	+	2.46543i	0.959719	+	0.280962i
$78$	−5.32240	+	5.32240i	−0.602643	+	0.602643i
$79$	−11.1735	+	3.63049i	−1.25712	+	0.408463i	−0.860467	−	0.509507i	$-0.829828\pi$
$79$	−11.1735	+	3.63049i	−1.25712	+	0.408463i	−0.396652	+	0.917969i	$0.629828\pi$
$80$	1.90576	+	1.16965i	0.213071	+	0.130771i
$81$	0.719245	−	0.522562i	0.0799161	−	0.0580624i
$82$	1.24059	+	2.43480i	0.137000	+	0.268878i
$83$	−10.4774	+	5.33848i	−1.15004	+	0.585975i	−0.921814	−	0.387633i	$-0.873293\pi$
$83$	−10.4774	+	5.33848i	−1.15004	+	0.585975i	−0.228227	+	0.973608i	$0.573293\pi$
$84$	4.62572	−	5.87295i	0.504707	−	0.640791i
$85$	8.86287	−	2.12137i	0.961313	−	0.230095i
$86$	−2.93674	−	9.03835i	−0.316677	−	0.974631i
$87$	16.0745	−	16.0745i	1.72337	−	1.72337i
$88$	−3.21681	−	0.807561i	−0.342913	−	0.0860863i
$89$	−7.47380			−0.792222			−0.396111	−	0.918203i	$-0.629640\pi$
$89$	−7.47380			−0.792222			−0.396111	+	0.918203i	$0.629640\pi$
$90$	−10.2935	−	4.27199i	−1.08503	−	0.450307i
$91$	2.43651	−	6.61332i	0.255416	−	0.693264i
$92$	−2.30819	−	0.365582i	−0.240646	−	0.0381146i
$93$	−13.5427	−	26.5790i	−1.40431	−	2.75611i
$94$	1.24328	−	3.82643i	0.128235	−	0.394666i
$95$	−6.50038	+	5.54416i	−0.666925	+	0.568819i
$96$	−1.66086	+	2.28597i	−0.169510	+	0.233311i
$97$	7.16274	+	3.64960i	0.727266	+	0.370561i	0.778095	−	0.628147i	$-0.216186\pi$
$97$	7.16274	+	3.64960i	0.727266	+	0.370561i	−0.0508286	+	0.998707i	$0.516186\pi$
$98$	−1.62819	+	6.80801i	−0.164472	+	0.687713i
$99$	16.4652	+	1.46732i	1.65481	+	0.147471i
$100$	0.775407	+	4.93951i	0.0775407	+	0.493951i
$101$	−13.1907	+	4.28592i	−1.31252	+	0.426465i	−0.879921	−	0.475120i	$-0.842405\pi$
$101$	−13.1907	+	4.28592i	−1.31252	+	0.426465i	−0.432603	+	0.901585i	$0.642405\pi$
$102$	1.80149	+	11.3742i	0.178374	+	1.12621i
$103$	7.75864	+	1.22885i	0.764481	+	0.121082i	0.526485	−	0.850184i	$-0.323509\pi$
$103$	7.75864	+	1.22885i	0.764481	+	0.121082i	0.237996	+	0.971266i	$0.423509\pi$
$104$	−0.823174	+	2.53347i	−0.0807189	+	0.248427i
$105$	16.7039	−	0.652120i	1.63013	−	0.0636404i
$106$	6.93085	−	5.03556i	0.673184	−	0.489097i
$107$	−1.52914	−	9.65462i	−0.147828	−	0.933347i	−0.944399	−	0.328802i	$-0.893355\pi$
$107$	−1.52914	−	9.65462i	−0.147828	−	0.933347i	0.796571	−	0.604545i	$-0.206645\pi$
$108$	2.54523	−	4.99529i	0.244914	−	0.480672i
$109$		−	18.0547i		−	1.72933i	−0.502349	−	0.864665i	$-0.667531\pi$
$109$		−	18.0547i		−	1.72933i	0.502349	−	0.864665i	$-0.332469\pi$
$110$	−3.29382	−	6.64460i	−0.314053	−	0.633538i
$111$			11.4682i			1.08851i
$112$	0.515031	−	2.59514i	0.0486659	−	0.245218i
$113$	−6.99075	+	1.10723i	−0.657634	+	0.104159i	−0.476328	−	0.879268i	$-0.658033\pi$
$113$	−6.99075	+	1.10723i	−0.657634	+	0.104159i	−0.181306	+	0.983427i	$0.558033\pi$
$114$	−6.34580	−	8.73425i	−0.594339	−	0.818038i
$115$	−2.72732	−	4.45744i	−0.254324	−	0.415658i
$116$	2.48612	−	7.65150i	0.230831	−	0.710424i
$117$	2.07697	−	13.1135i	0.192016	−	1.21234i
$118$	−0.0123943	−	0.0782547i	−0.00114099	−	0.00720393i
$119$	−5.99456	−	8.96305i	−0.549520	−	0.821641i
$120$	−6.29913	+	0.491412i	−0.575030	+	0.0448596i
$121$	7.61564	+	7.93738i	0.692331	+	0.721580i
$122$	−2.60669	+	2.60669i	−0.235999	+	0.235999i
$123$	−6.87980	−	3.50544i	−0.620331	−	0.316074i
$124$	−8.54086	−	6.20530i	−0.766992	−	0.557252i
$125$	−7.27850	+	8.48666i	−0.651009	+	0.759070i
$126$	−0.511973	+	13.1768i	−0.0456102	+	1.17388i
$127$	−7.55415	+	3.84903i	−0.670322	+	0.341546i	−0.755808	−	0.654793i	$-0.772756\pi$
$127$	−7.55415	+	3.84903i	−0.670322	+	0.341546i	0.0854858	+	0.996339i	$0.472756\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	21.7247	+	15.7839i	1.91275	+	1.38970i
$130$	−5.50469	+	2.27570i	−0.482793	+	0.199592i
$131$		−	16.1155i		−	1.40802i	−0.710190	−	0.704010i	$-0.751391\pi$
$131$		−	16.1155i		−	1.40802i	0.710190	−	0.704010i	$-0.248609\pi$
$132$	8.69477	−	3.49659i	0.756783	−	0.304339i
$133$	8.82212	+	4.93558i	0.764975	+	0.427969i
$134$	7.26620	−	2.36093i	0.627704	−	0.203953i
$135$	12.1918	−	2.91816i	1.04930	−	0.251155i
$136$	2.39555	+	3.29719i	0.205417	+	0.282732i
$137$	−8.98611	+	4.57865i	−0.767735	+	0.391180i	−0.793565	−	0.608486i	$-0.791777\pi$
$137$	−8.98611	+	4.57865i	−0.767735	+	0.391180i	0.0258298	+	0.999666i	$0.491777\pi$
$138$	5.88365	−	2.99787i	0.500849	−	0.255195i
$139$	16.1479	−	11.7321i	1.36965	−	0.995107i	0.371883	−	0.928280i	$-0.378712\pi$
$139$	16.1479	−	11.7321i	1.36965	−	0.995107i	0.997765	−	0.0668277i	$-0.0212878\pi$
$140$	5.16248	−	2.88943i	0.436309	−	0.244202i
$141$	3.51304	+	10.8120i	0.295851	+	0.910536i
$142$	−1.41108	−	1.41108i	−0.118415	−	0.118415i
$143$	6.77715	−	5.66808i	0.566734	−	0.473989i
$144$		−	4.98411i		−	0.415343i
$145$	16.6251	−	6.87300i	1.38064	−	0.570771i
$146$	4.25754	−	5.86000i	0.352356	−	0.484977i
$147$	−7.58512	−	18.2671i	−0.625610	−	1.50665i
$148$	1.84258	+	3.61627i	0.151459	+	0.297256i
$149$	2.64514	+	0.859457i	0.216698	+	0.0704095i	0.415354	−	0.909660i	$-0.363658\pi$
$149$	2.64514	+	0.859457i	0.216698	+	0.0704095i	−0.198656	+	0.980069i	$0.563658\pi$
$150$	−9.97637	−	10.0037i	−0.814567	−	0.816802i
$151$	−7.00097	−	5.08650i	−0.569730	−	0.413933i	0.265277	−	0.964172i	$-0.414537\pi$
$151$	−7.00097	−	5.08650i	−0.569730	−	0.413933i	−0.835007	+	0.550239i	$0.814537\pi$
$152$	−3.40436	−	1.73461i	−0.276130	−	0.140695i
$153$	−14.3635	−	14.3635i	−1.16122	−	1.16122i
$154$	−6.01999	+	6.38433i	−0.485105	+	0.514464i
$155$	−1.83602	−	23.5348i	−0.147472	−	1.89036i
$156$	−2.32598	−	7.15862i	−0.186227	−	0.573148i
$157$	−5.49794	+	0.870789i	−0.438784	+	0.0694965i	−0.371918	−	0.928266i	$-0.621300\pi$
$157$	−5.49794	+	0.870789i	−0.438784	+	0.0694965i	−0.0668654	+	0.997762i	$0.521300\pi$
$158$	1.83787	−	11.6039i	0.146213	−	0.923155i
$159$	−7.48040	+	23.0223i	−0.593234	+	1.82579i
$160$	−1.90736	+	1.16704i	−0.150790	+	0.0922623i
$161$	−3.82576	+	4.85730i	−0.301512	+	0.382809i
$162$	0.139076	+	0.878090i	0.0109268	+	0.0689892i
$163$	9.20897	+	4.69220i	0.721302	+	0.367522i	0.775789	−	0.630993i	$-0.217352\pi$
$163$	9.20897	+	4.69220i	0.721302	+	0.367522i	−0.0544866	+	0.998515i	$0.517352\pi$
$164$	−2.73264			−0.213383
$165$	18.5653	+	9.71883i	1.44531	+	0.756610i
$166$		−	11.7590i		−	0.912677i
$167$	−5.74066	−	2.92501i	−0.444225	−	0.226344i	0.217546	−	0.976050i	$-0.430195\pi$
$167$	−5.74066	−	2.92501i	−0.444225	−	0.226344i	−0.661771	+	0.749706i	$0.730195\pi$
$168$	3.13280	+	6.78781i	0.241701	+	0.523691i
$169$	3.47023	+	4.77637i	0.266941	+	0.367413i
$170$	−2.13351	+	8.85996i	−0.163632	+	0.679528i
$171$	18.1113	+	5.88471i	1.38500	+	0.450015i
$172$	9.38648	+	1.48667i	0.715713	+	0.113358i
$173$	1.99571	+	12.6004i	0.151731	+	0.957990i	0.939632	+	0.342188i	$0.111168\pi$
$173$	1.99571	+	12.6004i	0.151731	+	0.957990i	−0.787901	+	0.615802i	$0.788832\pi$
$174$	7.02483	+	21.6202i	0.532551	+	1.63902i
$175$	12.4068	+	4.59029i	0.937867	+	0.346994i
$176$	2.17994	−	2.49957i	0.164319	−	0.188412i
$177$	0.158303	+	0.158303i	0.0118988	+	0.0118988i
$178$	3.39304	−	6.65921i	0.254319	−	0.499129i
$179$	−14.7035	+	20.2376i	−1.09899	+	1.51263i	−0.262275	+	0.964993i	$0.584473\pi$
$179$	−14.7035	+	20.2376i	−1.09899	+	1.51263i	−0.836716	+	0.547638i	$0.815527\pi$
$180$	8.47954	−	7.23217i	0.632027	−	0.539054i
$181$	−3.31529	−	1.07720i	−0.246423	−	0.0800678i	0.183201	−	0.983075i	$-0.441354\pi$
$181$	−3.31529	−	1.07720i	−0.246423	−	0.0800678i	−0.429624	+	0.903008i	$0.641354\pi$
$182$	4.78636	+	5.17333i	0.354788	+	0.383473i
$183$	1.62949	−	10.2882i	0.120455	−	0.760523i
$184$	1.37363	−	1.89064i	0.101266	−	0.139380i
$185$	−3.47874	+	8.38218i	−0.255762	+	0.616270i
$186$	29.8303			2.18726
$187$	−0.921123	−	13.4857i	−0.0673592	−	0.986169i
$188$	2.84493	+	2.84493i	0.207488	+	0.207488i
$189$	−8.24613	−	12.3296i	−0.599818	−	0.896845i
$190$	−1.98877	−	8.30888i	−0.144280	−	0.602790i
$191$	−3.41636	+	2.48213i	−0.247199	+	0.179601i	−0.704485	−	0.709719i	$-0.748822\pi$
$191$	−3.41636	+	2.48213i	−0.247199	+	0.179601i	0.457285	+	0.889320i	$0.348822\pi$
$192$	−1.28280	−	2.51764i	−0.0925784	−	0.181695i
$193$	11.1664	+	21.9153i	0.803776	+	1.57750i	0.816335	+	0.577578i	$0.196002\pi$
$193$	11.1664	+	21.9153i	0.803776	+	1.57750i	−0.0125592	+	0.999921i	$0.503998\pi$
$194$	−6.50363	+	4.72517i	−0.466934	+	0.339247i
$195$	8.80396	−	14.3447i	0.630464	−	1.02724i
$196$	−5.32680	−	4.54150i	−0.380486	−	0.324393i
$197$	−7.10754	−	7.10754i	−0.506391	−	0.506391i	0.407025	−	0.913417i	$-0.366566\pi$
$197$	−7.10754	−	7.10754i	−0.506391	−	0.506391i	−0.913417	+	0.407025i	$0.866566\pi$
$198$	−8.78242	+	14.0044i	−0.624140	+	0.995252i
$199$	15.8079			1.12059			0.560295	−	0.828293i	$-0.310688\pi$
$199$	15.8079			1.12059			0.560295	+	0.828293i	$0.310688\pi$
$200$	−4.75316	−	1.55160i	−0.336099	−	0.109714i
$201$	−12.6892	+	17.4651i	−0.895024	+	1.23190i
$202$	2.16967	−	13.6988i	0.152658	−	0.963842i
$203$	−14.4556	−	15.6243i	−1.01458	−	1.09661i
$204$	−10.9523	−	3.55862i	−0.766816	−	0.249154i
$205$	−3.96518	−	4.64907i	−0.276940	−	0.324705i
$206$	−4.61726	+	6.35511i	−0.321700	+	0.442782i
$207$	−5.28794	+	10.3782i	−0.367538	+	0.721333i
$208$	−1.88362	−	1.88362i	−0.130606	−	0.130606i
$209$	6.50910	+	10.8727i	0.450244	+	0.752080i
$210$	−7.00235	+	15.1793i	−0.483208	+	1.04747i
$211$	−3.27593	−	10.0823i	−0.225525	−	0.694093i	−0.998238	−	0.0593382i	$-0.981101\pi$
$211$	−3.27593	−	10.0823i	−0.225525	−	0.694093i	0.772713	−	0.634755i	$-0.218899\pi$
$212$	1.34018	+	8.46153i	0.0920436	+	0.581140i
$213$	5.56929	+	0.882089i	0.381602	+	0.0604398i
$214$	9.29655	+	3.02063i	0.635499	+	0.206486i
$215$	11.0909	+	18.1266i	0.756394	+	1.23622i
$216$	3.29532	+	4.53562i	0.224218	+	0.308610i
$217$	−25.3606	+	11.7048i	−1.72159	+	0.794574i
$218$	16.0869	+	8.19668i	1.08954	+	0.555149i
$219$			20.4669i			1.38303i
$220$	7.41575	+	0.0817747i	0.499970	+	0.00551325i
$221$	−10.8567			−0.730298
$222$	−10.2182	−	5.20643i	−0.685800	−	0.349433i
$223$	−4.42361	−	27.9296i	−0.296227	−	1.87030i	−0.465950	−	0.884811i	$-0.654287\pi$
$223$	−4.42361	−	27.9296i	−0.296227	−	1.87030i	0.169723	−	0.985492i	$-0.445713\pi$
$224$	2.07847	+	1.63706i	0.138873	+	0.109381i
$225$	24.6084	+	3.93214i	1.64056	+	0.262143i
$226$	2.18719	−	6.73147i	0.145490	−	0.447771i
$227$	3.00749	−	18.9885i	0.199614	−	1.26031i	−0.660739	−	0.750616i	$-0.729757\pi$
$227$	3.00749	−	18.9885i	0.199614	−	1.26031i	0.860353	−	0.509698i	$-0.170243\pi$
$228$	10.6632	−	1.68889i	0.706188	−	0.111849i
$229$	−5.86116	−	18.0388i	−0.387316	−	1.19204i	−0.934786	−	0.355212i	$-0.884409\pi$
$229$	−5.86116	−	18.0388i	−0.387316	−	1.19204i	0.547469	−	0.836826i	$-0.315591\pi$
$230$	5.20978	−	0.406429i	0.343523	−	0.0267991i
$231$	3.15809	−	24.5927i	0.207787	−	1.61808i
$232$	5.68886	+	5.68886i	0.373492	+	0.373492i
$233$	2.92303	+	1.48936i	0.191494	+	0.0975709i	0.547109	−	0.837062i	$-0.315728\pi$
$233$	2.92303	+	1.48936i	0.191494	+	0.0975709i	−0.355615	+	0.934633i	$0.615728\pi$
$234$	10.7413	+	7.80398i	0.702178	+	0.510162i
$235$	−0.711997	+	8.96825i	−0.0464456	+	0.585024i
$236$	0.0753524	+	0.0244835i	0.00490502	+	0.00159374i
$237$	15.0711	+	29.5786i	0.978970	+	1.92134i
$238$	10.7076	−	1.27205i	0.694071	−	0.0824550i
$239$	−7.70850	+	10.6098i	−0.498622	+	0.686294i	−0.981949	−	0.189146i	$-0.939428\pi$
$239$	−7.70850	+	10.6098i	−0.498622	+	0.686294i	0.483327	+	0.875440i	$0.339428\pi$
$240$	2.42190	−	5.83566i	0.156333	−	0.376691i
$241$		−	8.89062i		−	0.572695i	−0.958126	−	0.286348i	$-0.907559\pi$
$241$		−	8.89062i		−	0.572695i	0.958126	−	0.286348i	$-0.0924412\pi$
$242$	−10.5297	+	3.18209i	−0.676874	+	0.204552i
$243$	10.1165	+	10.1165i	0.648976	+	0.648976i
$244$	−1.13917	−	3.50599i	−0.0729276	−	0.224448i
$245$	−0.00290521	−	15.6525i	−0.000185607	−	1.00000i
$246$	6.24673	−	4.53852i	0.398277	−	0.289365i
$247$	9.06870	−	4.62073i	0.577028	−	0.294010i
$248$	9.40643	−	4.79282i	0.597309	−	0.304344i
$249$	19.5300	+	26.8808i	1.23767	+	1.70350i
$250$	−4.25730	−	10.3381i	−0.269255	−	0.653836i
$251$	6.05851	−	1.96853i	0.382410	−	0.124252i	−0.111503	−	0.993764i	$-0.535566\pi$
$251$	6.05851	−	1.96853i	0.382410	−	0.124252i	0.493912	+	0.869512i	$0.335566\pi$
$252$	−11.5082	−	6.43830i	−0.724946	−	0.405575i
$253$	−7.19113	+	2.89190i	−0.452103	+	0.181812i
$254$		−	8.47822i		−	0.531971i
$255$	−9.83798	−	23.7971i	−0.616078	−	1.49023i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−0.0916692	+	0.578776i	−0.00571817	+	0.0361031i	−0.990382	−	0.138357i	$-0.955818\pi$
$257$	−0.0916692	+	0.578776i	−0.00571817	+	0.0361031i	0.984664	+	0.174460i	$0.0558179\pi$
$258$	−23.9264	+	12.1911i	−1.48959	+	0.758985i
$259$	10.7300	+	0.416907i	0.666733	+	0.0259054i
$260$	0.471412	−	5.93786i	0.0292357	−	0.368251i
$261$	−32.4404	−	23.5693i	−2.00801	−	1.45890i
$262$	14.3590	+	7.31629i	0.887104	+	0.452002i
$263$	9.49409	−	9.49409i	0.585431	−	0.585431i	−0.350960	−	0.936390i	$-0.614145\pi$
$263$	9.49409	−	9.49409i	0.585431	−	0.585431i	0.936390	+	0.350960i	$0.114145\pi$
$264$	−0.831859	+	9.33452i	−0.0511974	+	0.574500i
$265$	−12.4511	+	14.5581i	−0.764863	+	0.894299i
$266$	−8.40279	+	5.61986i	−0.515208	+	0.344576i
$267$	3.30360	+	20.8581i	0.202177	+	1.27650i
$268$	−1.19518	+	7.54607i	−0.0730072	+	0.460950i
$269$	4.55069	−	14.0056i	0.277461	−	0.853936i	−0.711097	−	0.703094i	$-0.751801\pi$
$269$	4.55069	−	14.0056i	0.277461	−	0.853936i	0.988558	−	0.150842i	$-0.0481985\pi$
$270$	−2.93486	+	12.1878i	−0.178610	+	0.741724i
$271$	−3.01827	−	4.15429i	−0.183347	−	0.252355i	0.707444	−	0.706770i	$-0.249848\pi$
$271$	−3.01827	−	4.15429i	−0.183347	−	0.252355i	−0.890790	+	0.454415i	$0.849848\pi$
$272$	−4.02538	+	0.637557i	−0.244074	+	0.0386576i
$273$	−19.5336	−	3.87665i	−1.18223	−	0.234625i
$274$		−	10.0853i		−	0.609278i
$275$	10.6215	+	12.7352i	0.640498	+	0.767960i
$276$			6.60337i			0.397476i
$277$	2.43905	−	4.78690i	0.146548	−	0.287617i	−0.806050	−	0.591847i	$-0.798399\pi$
$277$	2.43905	−	4.78690i	0.146548	−	0.287617i	0.952599	+	0.304230i	$0.0983990\pi$
$278$	3.12242	+	19.7142i	0.187270	+	1.18238i
$279$	−42.5686	+	30.9279i	−2.54852	+	1.85160i
$280$	0.230789	+	5.91158i	0.0137923	+	0.353284i
$281$	6.88063	−	21.1764i	0.410464	−	1.26328i	−0.505782	−	0.862662i	$-0.668796\pi$
$281$	6.88063	−	21.1764i	0.410464	−	1.26328i	0.916246	−	0.400617i	$-0.131204\pi$
$282$	−11.2285	−	1.77841i	−0.668645	−	0.105903i
$283$	−4.46032	−	28.1614i	−0.265139	−	1.67402i	−0.656919	−	0.753961i	$-0.728141\pi$
$283$	−4.46032	−	28.1614i	−0.265139	−	1.67402i	0.391781	−	0.920059i	$-0.371859\pi$
$284$	1.89790	−	0.616665i	0.112620	−	0.0365923i
$285$	18.3461	+	15.6908i	1.08673	+	0.929443i
$286$	1.97353	+	8.61174i	0.116697	+	0.509223i
$287$	−3.52993	+	6.30958i	−0.208365	+	0.372442i
$288$	4.44088	+	2.26274i	0.261681	+	0.133333i
$289$	0.229159	−	0.315410i	0.0134799	−	0.0185535i
$290$	−1.42374	+	17.9333i	−0.0836050	+	1.05308i
$291$	7.01931	−	21.6032i	0.411479	−	1.26640i
$292$	3.28841	+	6.45388i	0.192440	+	0.377684i
$293$	−6.22250	−	0.985547i	−0.363522	−	0.0575762i	−0.0279983	−	0.999608i	$-0.508913\pi$
$293$	−6.22250	−	0.985547i	−0.363522	−	0.0575762i	−0.335524	+	0.942032i	$0.608913\pi$
$294$	19.7197	+	1.53470i	1.15008	+	0.0895057i
$295$	0.0676856	+	0.163725i	0.00394081	+	0.00953241i
$296$	−4.05864			−0.235903
$297$	−1.26710	−	18.5509i	−0.0735245	−	1.07643i
$298$	−1.96665	+	1.96665i	−0.113925	+	0.113925i
$299$	1.92373	+	5.92063i	0.111252	+	0.342399i
$300$	13.4426	−	4.34741i	0.776107	−	0.250998i
$301$	15.5578	−	19.7527i	0.896738	−	1.13853i
$302$	7.71048	−	3.92868i	0.443688	−	0.226070i
$303$	17.7919	+	34.9185i	1.02212	+	2.00602i
$304$	3.09109	−	2.24581i	0.177286	−	0.128806i
$305$	4.31181	−	7.02543i	0.246894	−	0.402275i
$306$	19.3188	−	6.27707i	1.10438	−	0.358836i
$307$	−15.0429	+	15.0429i	−0.858546	+	0.858546i	−0.991167	−	0.132621i	$-0.957661\pi$
$307$	−15.0429	+	15.0429i	−0.858546	+	0.858546i	0.132621	+	0.991167i	$0.457661\pi$
$308$	−2.95546	−	8.26228i	−0.168403	−	0.470787i
$309$		−	22.1962i		−	1.26270i
$310$	21.8032	+	9.04870i	1.23834	+	0.513931i
$311$	−5.39250	+	7.42214i	−0.305781	+	0.420871i	−0.934060	−	0.357117i	$-0.883760\pi$
$311$	−5.39250	+	7.42214i	−0.305781	+	0.420871i	0.628279	+	0.777988i	$0.283760\pi$
$312$	7.43434	+	1.17748i	0.420887	+	0.0666619i
$313$	21.9365	−	11.1772i	1.23992	−	0.631773i	0.293890	−	0.955839i	$-0.405050\pi$
$313$	21.9365	−	11.1772i	1.23992	−	0.631773i	0.946034	+	0.324067i	$0.105050\pi$
$314$	1.72014	−	5.29403i	0.0970729	−	0.298760i
$315$	−5.74529	−	28.9213i	−0.323711	−	1.62953i
$316$	9.50476	+	6.90561i	0.534684	+	0.388471i
$317$	3.05378	−	5.99338i	0.171517	−	0.336622i	−0.789207	−	0.614128i	$-0.789508\pi$
$317$	3.05378	−	5.99338i	0.171517	−	0.336622i	0.960724	+	0.277506i	$0.0895079\pi$
$318$	−17.1170	−	17.1170i	−0.959873	−	0.959873i
$319$	−5.96039	−	26.0089i	−0.333718	−	1.45622i
$320$	−0.173913	−	2.22929i	−0.00972204	−	0.124621i
$321$	−26.2685	+	8.53515i	−1.46616	+	0.476385i
$322$	−2.59103	−	5.61395i	−0.144392	−	0.312853i
$323$	2.43598	−	15.3802i	0.135542	−	0.855776i
$324$	−0.845523	−	0.274727i	−0.0469735	−	0.0152626i
$325$	10.7862	−	7.81409i	0.598311	−	0.433447i
$326$	−8.36157	+	6.07504i	−0.463105	+	0.336465i
$327$	−50.3877	+	7.98062i	−2.78644	+	0.441329i
$328$	1.24059	−	2.43480i	0.0685002	−	0.134439i
$329$	10.2439	−	2.89388i	0.564762	−	0.159545i
$330$	−17.0880	+	12.1296i	−0.940664	+	0.667710i
$331$	6.43115			0.353488			0.176744	−	0.984257i	$-0.443443\pi$
$331$	6.43115			0.353488			0.176744	+	0.984257i	$0.443443\pi$
$332$	10.4774	+	5.33848i	0.575020	+	0.292987i
$333$	19.9796	−	3.16446i	1.09488	−	0.173412i
$334$	5.21241	−	3.78704i	0.285210	−	0.207217i
$335$	−14.5725	+	8.91631i	−0.796180	+	0.487150i
$336$	−7.47024	−	0.290250i	−0.407535	−	0.0158345i
$337$	−17.0321	−	2.69762i	−0.927799	−	0.146949i	−0.325794	−	0.945441i	$-0.605631\pi$
$337$	−17.0321	−	2.69762i	−0.927799	−	0.146949i	−0.602006	+	0.798492i	$0.705631\pi$
$338$	−5.83123	+	0.923576i	−0.317177	+	0.0502359i
$339$	6.18016	+	19.0206i	0.335660	+	1.03306i
$340$	−6.92569	−	5.92330i	−0.375598	−	0.321236i
$341$	−34.8757	−	3.10800i	−1.88862	−	0.168307i
$342$	−13.4657	+	13.4657i	−0.728139	+	0.728139i
$343$	−17.3672	+	6.43286i	−0.937739	+	0.347342i
$344$	−5.58601	+	7.68848i	−0.301177	+	0.414535i
$345$	−11.2344	+	9.58179i	−0.604840	+	0.515866i
$346$	−12.1331	−	3.94227i	−0.652277	−	0.211938i
$347$	−22.5224	+	11.4757i	−1.20906	+	0.616049i	−0.938041	−	0.346524i	$-0.887362\pi$
$347$	−22.5224	+	11.4757i	−1.20906	+	0.616049i	−0.271023	+	0.962573i	$0.587362\pi$
$348$	−22.4530	−	3.55620i	−1.20360	−	0.190632i
$349$	8.46735	+	6.15189i	0.453247	+	0.329303i	0.790876	−	0.611976i	$-0.209625\pi$
$349$	8.46735	+	6.15189i	0.453247	+	0.329303i	−0.337630	+	0.941279i	$0.609625\pi$
$350$	−9.72256	+	8.97061i	−0.519693	+	0.479499i
$351$	−14.9344			−0.797141
$352$	1.23746	+	3.07712i	0.0659569	+	0.164011i
$353$	−5.58836	−	5.58836i	−0.297438	−	0.297438i	0.542571	−	0.840010i	$-0.317451\pi$
$353$	−5.58836	−	5.58836i	−0.297438	−	0.297438i	−0.840010	+	0.542571i	$0.817451\pi$
$354$	−0.212917	+	0.0691809i	−0.0113164	+	0.00367692i
$355$	3.80308	+	2.33411i	0.201846	+	0.123882i
$356$	4.39299	+	6.04643i	0.232828	+	0.320460i
$357$	−22.3646	+	20.6917i	−1.18366	+	1.09512i
$358$	−11.3566	−	22.2886i	−0.600215	−	1.17799i
$359$	9.47976	+	13.0478i	0.500323	+	0.688635i	0.982250	−	0.187576i	$-0.0600632\pi$
$359$	9.47976	+	13.0478i	0.500323	+	0.688635i	−0.481928	+	0.876211i	$0.660063\pi$
$360$	2.59428	+	10.8387i	0.136731	+	0.571248i
$361$	−1.36013	−	4.18604i	−0.0715856	−	0.220318i
$362$	2.46490	−	2.46490i	0.129552	−	0.129552i
$363$	18.7856	−	24.7625i	0.985987	−	1.29969i
$364$	−6.78243	+	1.91603i	−0.355496	+	0.100427i
$365$	−6.20843	+	14.9595i	−0.324964	+	0.783015i
$366$	8.42705	+	6.12261i	0.440489	+	0.320034i
$367$	2.89196	−	18.2591i	0.150959	−	0.953117i	−0.789633	−	0.613579i	$-0.789729\pi$
$367$	2.89196	−	18.2591i	0.150959	−	0.953117i	0.940592	−	0.339538i	$-0.110271\pi$
$368$	1.06096	+	2.08225i	0.0553064	+	0.108545i
$369$	−4.20874	+	12.9532i	−0.219098	+	0.674315i
$370$	−5.88926	−	6.90501i	−0.306168	−	0.358974i
$371$	21.2686	+	7.83589i	1.10421	+	0.406819i
$372$	−13.5427	+	26.5790i	−0.702154	+	1.37806i
$373$	14.5299	−	14.5299i	0.752330	−	0.752330i	−0.222584	−	0.974914i	$-0.571449\pi$
$373$	14.5299	−	14.5299i	0.752330	−	0.752330i	0.974914	+	0.222584i	$0.0714491\pi$
$374$	12.4340	+	5.30163i	0.642946	+	0.274141i
$375$	26.9021	+	16.5617i	1.38922	+	0.855245i
$376$	−3.82643	+	1.24328i	−0.197333	+	0.0641174i
$377$	−21.1675	+	3.35260i	−1.09018	+	0.172668i
$378$	14.7294	−	1.74984i	0.757599	−	0.0900021i
$379$	−16.5897	−	5.39034i	−0.852158	−	0.276883i	−0.149808	−	0.988715i	$-0.547866\pi$
$379$	−16.5897	−	5.39034i	−0.852158	−	0.276883i	−0.702350	+	0.711832i	$0.747866\pi$
$380$	8.30615	+	2.00015i	0.426096	+	0.102605i
$381$	14.0811	+	19.3810i	0.721397	+	0.992918i
$382$	−0.660601	−	4.17087i	−0.0337993	−	0.213400i
$383$	−5.53600	+	10.8650i	−0.282877	+	0.555177i	−0.988101	−	0.153808i	$-0.950846\pi$
$383$	−5.53600	+	10.8650i	−0.282877	+	0.555177i	0.705224	+	0.708984i	$0.250846\pi$
$384$	2.82562			0.144194
$385$	9.76822	−	17.0171i	0.497835	−	0.867272i
$386$	−24.5961			−1.25191
$387$	21.5039	−	42.2038i	1.09311	−	2.14534i
$388$	−1.25757	−	7.93996i	−0.0638433	−	0.403090i
$389$	−7.20917	−	9.92257i	−0.365520	−	0.503094i	0.586157	−	0.810198i	$-0.300640\pi$
$389$	−7.20917	−	9.92257i	−0.365520	−	0.503094i	−0.951676	+	0.307103i	$0.900640\pi$
$390$	8.78430	+	14.3567i	0.444810	+	0.726981i
$391$	9.05827	+	2.94321i	0.458096	+	0.148845i
$392$	6.46482	−	2.68441i	0.326523	−	0.135583i
$393$	−44.9757	+	7.12344i	−2.26872	+	0.359330i
$394$	9.55962	−	3.10611i	0.481607	−	0.156484i
$395$	2.04322	+	26.1909i	0.102806	+	1.31781i
$396$	−8.49090	−	14.1831i	−0.426684	−	0.712726i
$397$	−12.4629	+	12.4629i	−0.625493	+	0.625493i	−0.946931	−	0.321438i	$-0.895834\pi$
$397$	−12.4629	+	12.4629i	−0.625493	+	0.625493i	0.321438	+	0.946931i	$0.395834\pi$
$398$	−7.17662	+	14.0849i	−0.359732	+	0.706013i
$399$	9.87478	−	26.8027i	0.494357	−	1.34181i
$400$	3.54037	−	3.53069i	0.177019	−	0.176534i
$401$	−10.5082	+	32.3410i	−0.524756	+	1.61503i	0.240041	+	0.970763i	$0.422839\pi$
$401$	−10.5082	+	32.3410i	−0.524756	+	1.61503i	−0.764797	+	0.644271i	$0.777161\pi$
$402$	−9.80079	−	19.2351i	−0.488819	−	0.959361i
$403$	−4.39932	+	27.7762i	−0.219146	+	1.38363i
$404$	11.2207	+	8.15230i	0.558250	+	0.405592i
$405$	−0.759495	−	1.83714i	−0.0377396	−	0.0912882i
$406$	20.4841	−	5.78673i	1.01661	−	0.287191i
$407$	11.4040	+	7.15166i	0.565276	+	0.354495i
$408$	8.14301	−	8.14301i	0.403139	−	0.403139i
$409$	0.465814	+	1.43363i	0.0230330	+	0.0708883i	0.961912	−	0.273358i	$-0.0881344\pi$
$409$	0.465814	+	1.43363i	0.0230330	+	0.0708883i	−0.938879	+	0.344246i	$0.888134\pi$
$410$	5.94251	−	1.42237i	0.293479	−	0.0702457i
$411$	16.7503	+	23.0548i	0.826232	+	1.13721i
$412$	−3.56626	−	6.99917i	−0.175697	−	0.344824i
$413$	0.153869	−	0.142359i	0.00757141	−	0.00700505i
$414$	−6.84634	−	9.42319i	−0.336479	−	0.463124i
$415$	6.12069	+	25.5717i	0.300453	+	1.25526i
$416$	2.53347	−	0.823174i	0.124214	−	0.0403594i
$417$	−39.8802	−	39.8802i	−1.95294	−	1.95294i
$418$	−12.6427	+	0.863546i	−0.618375	+	0.0422374i
$419$	−26.6368			−1.30129			−0.650645	−	0.759382i	$-0.725502\pi$
$419$	−26.6368			−1.30129			−0.650645	+	0.759382i	$0.725502\pi$
$420$	−10.3459	−	13.1304i	−0.504826	−	0.640698i
$421$	−10.3845	−	7.54475i	−0.506107	−	0.367708i	0.305238	−	0.952276i	$-0.401264\pi$
$421$	−10.3845	−	7.54475i	−0.506107	−	0.367708i	−0.811345	+	0.584568i	$0.801264\pi$
$422$	10.4706	+	1.65838i	0.509702	+	0.0807289i
$423$	17.8672	−	9.10378i	0.868732	−	0.442641i
$424$	−8.14771	−	2.64735i	−0.395688	−	0.128567i
$425$	0.0279120	−	20.3777i	0.00135393	−	0.988466i
$426$	−3.31435	+	4.56182i	−0.160581	+	0.221021i
$427$	−9.56677	−	1.89862i	−0.462968	−	0.0918807i
$428$	−6.91195	+	6.91195i	−0.334101	+	0.334101i
$429$	−18.8143	−	16.4085i	−0.908363	−	0.792208i
$430$	−21.1861	+	1.65278i	−1.02168	+	0.0797042i
$431$	−2.92202	−	8.99307i	−0.140749	−	0.433181i	0.855691	−	0.517487i	$-0.173133\pi$
$431$	−2.92202	−	8.99307i	−0.140749	−	0.433181i	−0.996440	+	0.0843065i	$0.973133\pi$
$432$	−5.53732	+	0.877025i	−0.266414	+	0.0421959i
$433$	20.2683	+	3.21018i	0.974032	+	0.154272i	0.623111	−	0.782134i	$-0.285869\pi$
$433$	20.2683	+	3.21018i	0.974032	+	0.154272i	0.350921	+	0.936405i	$0.385869\pi$
$434$	1.08443	−	27.9104i	0.0520545	−	1.33974i
$435$	−26.5300	−	43.3597i	−1.27202	−	2.07894i
$436$	−14.6066	+	10.6123i	−0.699529	+	0.508237i
$437$	−8.81915	+	1.39682i	−0.421877	+	0.0668188i
$438$	−18.2362	−	9.29180i	−0.871358	−	0.443979i
$439$	−18.4241			−0.879333			−0.439666	−	0.898161i	$-0.644903\pi$
$439$	−18.4241			−0.879333			−0.439666	+	0.898161i	$0.644903\pi$
$440$	−3.43954	+	6.57035i	−0.163974	+	0.313229i
$441$	−29.7317	+	18.2552i	−1.41580	+	0.869296i
$442$	4.92882	−	9.67335i	0.234440	−	0.460114i
$443$	4.99221	−	0.790688i	0.237187	−	0.0375667i	−0.0367092	−	0.999326i	$-0.511688\pi$
$443$	4.99221	−	0.790688i	0.237187	−	0.0375667i	0.273896	+	0.961759i	$0.411688\pi$
$444$	9.27793	−	6.74081i	0.440311	−	0.319905i
$445$	−3.91245	+	16.2475i	−0.185468	+	0.770206i
$446$	26.8937	+	8.73830i	1.27345	+	0.413770i
$447$	1.22938	−	7.76203i	0.0581479	−	0.367131i
$448$	−2.40224	+	1.10872i	−0.113495	+	0.0523819i
$449$	37.5491	−	12.2004i	1.77205	−	0.575774i	0.773721	−	0.633527i	$-0.218393\pi$
$449$	37.5491	−	12.2004i	1.77205	−	0.575774i	0.998331	+	0.0577524i	$0.0183934\pi$
$450$	−14.6755	+	20.1411i	−0.691812	+	0.949459i
$451$	−7.77615	+	4.65530i	−0.366165	+	0.219210i
$452$	5.00482	+	5.00482i	0.235407	+	0.235407i
$453$	−11.1010	+	21.7869i	−0.521568	+	1.02364i
$454$	15.5535	+	11.3003i	0.729964	+	0.530350i
$455$	−13.1014	−	8.75880i	−0.614203	−	0.410619i
$456$	−3.33619	+	10.2677i	−0.156231	+	0.480830i
$457$	−10.8731	+	5.54010i	−0.508620	+	0.259155i	−0.689416	−	0.724366i	$-0.742133\pi$
$457$	−10.8731	+	5.54010i	−0.508620	+	0.259155i	0.180796	+	0.983521i	$0.442133\pi$
$458$	18.7336	+	2.96711i	0.875364	+	0.138644i
$459$	−13.4303	+	18.4852i	−0.626871	+	0.862814i
$460$	−2.00306	+	4.82647i	−0.0933932	+	0.225035i
$461$		−	30.4241i		−	1.41699i	−0.705714	−	0.708497i	$-0.749374\pi$
$461$		−	30.4241i		−	1.41699i	0.705714	−	0.708497i	$-0.250626\pi$
$462$	20.4786	+	13.9787i	0.952749	+	0.650350i
$463$	15.7960	−	15.7960i	0.734102	−	0.734102i	−0.237327	−	0.971430i	$-0.576271\pi$
$463$	15.7960	−	15.7960i	0.734102	−	0.734102i	0.971430	+	0.237327i	$0.0762714\pi$
$464$	−7.65150	+	2.48612i	−0.355212	+	0.115415i
$465$	−64.8702	+	15.5270i	−3.00828	+	0.720046i
$466$	−2.65405	+	1.92828i	−0.122947	+	0.0893259i
$467$	16.9036	+	33.1753i	0.782207	+	1.53517i	0.843550	+	0.537051i	$0.180462\pi$
$467$	16.9036	+	33.1753i	0.782207	+	1.53517i	−0.0613429	+	0.998117i	$0.519538\pi$
$468$	−11.8298	+	6.02759i	−0.546834	+	0.278626i
$469$	15.8798	+	12.5074i	0.733259	+	0.577537i
$470$	−7.66753	−	4.70590i	−0.353677	−	0.217067i
$471$	4.86044	+	14.9589i	0.223957	+	0.689270i
$472$	−0.0560242	+	0.0560242i	−0.00257872	+	0.00257872i
$473$	29.2434	−	11.7602i	1.34461	−	0.540734i
$474$	−33.1968			−1.52478
$475$	8.64972	+	17.0337i	0.396876	+	0.781558i
$476$	−3.72774	+	10.1180i	−0.170861	+	0.463760i
$477$	42.1732	+	6.67958i	1.93098	+	0.305837i
$478$	−5.95385	−	11.6851i	−0.272323	−	0.534464i
$479$	−3.97765	+	12.2420i	−0.181744	+	0.559349i	−0.999877	−	0.0156790i	$-0.995009\pi$
$479$	−3.97765	+	12.2420i	−0.181744	+	0.559349i	0.818133	+	0.575028i	$0.195009\pi$
$480$	4.10010	+	4.80726i	0.187143	+	0.219420i
$481$	6.35489	−	8.74676i	0.289758	−	0.398818i
$482$	7.92160	+	4.03626i	0.360819	+	0.183846i
$483$	15.2470	+	8.53000i	0.693762	+	0.388129i
$484$	1.94511	−	10.8267i	0.0884143	−	0.492121i
$485$	11.6836	−	13.6608i	0.530524	−	0.620303i
$486$	−13.6067	+	4.42109i	−0.617213	+	0.200545i
$487$	−4.52046	−	28.5411i	−0.204842	−	1.29332i	−0.848986	−	0.528415i	$-0.822787\pi$
$487$	−4.52046	−	28.5411i	−0.204842	−	1.29332i	0.644145	−	0.764904i	$-0.277213\pi$
$488$	3.64103	+	0.576683i	0.164822	+	0.0261052i
$489$	9.02456	−	27.7747i	0.408105	−	1.25602i
$490$	13.9478	+	7.10349i	0.630096	+	0.320903i
$491$	−9.41109	+	6.83756i	−0.424717	+	0.308575i	−0.779533	−	0.626361i	$-0.784543\pi$
$491$	−9.41109	+	6.83756i	−0.424717	+	0.308575i	0.354816	+	0.934936i	$0.384543\pi$
$492$	1.20789	+	7.62632i	0.0544559	+	0.343821i
$493$	−14.8858	+	29.2151i	−0.670425	+	1.31578i
$494$			10.1780i			0.457932i
$495$	11.8092	−	35.0260i	0.530783	−	1.57430i
$496$			10.5571i			0.474027i
$497$	1.02778	−	5.17878i	0.0461022	−	0.232300i
$498$	−32.8174	+	5.19777i	−1.47058	+	0.232918i
$499$	16.6114	+	22.8636i	0.743628	+	1.02352i	0.998402	+	0.0565152i	$0.0179989\pi$
$499$	16.6114	+	22.8636i	0.743628	+	1.02352i	−0.254774	+	0.967001i	$0.582001\pi$
$500$	11.1440	+	0.900098i	0.498377	+	0.0402536i
$501$	−5.62570	+	17.3141i	−0.251338	+	0.773538i
$502$	−0.996533	+	6.29186i	−0.0444775	+	0.280820i
$503$	−0.126539	−	0.798936i	−0.00564210	−	0.0356228i	0.984707	−	0.174220i	$-0.0557405\pi$
$503$	−0.126539	−	0.798936i	−0.00564210	−	0.0356228i	−0.990349	+	0.138598i	$0.955741\pi$
$504$	10.9612	−	7.33092i	0.488249	−	0.326545i
$505$	2.41209	+	30.9193i	0.107337	+	1.37589i
$506$	0.688001	−	7.72024i	0.0305854	−	0.343207i
$507$	11.7961	−	11.7961i	0.523883	−	0.523883i
$508$	7.55415	+	3.84903i	0.335161	+	0.170773i
$509$	10.6106	+	7.70906i	0.470307	+	0.341698i	0.797561	−	0.603238i	$-0.206123\pi$
$509$	10.6106	+	7.70906i	0.470307	+	0.341698i	−0.327254	+	0.944936i	$0.606123\pi$
$510$	25.6697	+	2.03794i	1.13667	+	0.0902414i
$511$	19.1497	+	0.744045i	0.847131	+	0.0329146i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	3.35094	−	21.1570i	0.147948	−	0.934104i
$514$	−0.474077	−	0.344437i	−0.0209106	−	0.0151925i
$515$	6.73299	−	16.2234i	0.296691	−	0.714890i
$516$		−	26.8532i		−	1.18215i
$517$	12.9423	+	3.24910i	0.569203	+	0.142895i
$518$	−5.24281	+	9.37127i	−0.230356	+	0.411750i
$519$	34.2834	−	11.1393i	1.50487	−	0.488963i
$520$	5.07666	+	3.11576i	0.222626	+	0.136635i
$521$	−13.5704	−	18.6781i	−0.594530	−	0.818301i	0.400664	−	0.916225i	$-0.368780\pi$
$521$	−13.5704	−	18.6781i	−0.594530	−	0.818301i	−0.995194	+	0.0979245i	$0.968780\pi$
$522$	35.7280	−	18.2043i	1.56377	−	0.796782i
$523$	0.409256	−	0.208526i	0.0178955	−	0.00911821i	−0.445020	−	0.895521i	$-0.646803\pi$
$523$	0.409256	−	0.208526i	0.0178955	−	0.00911821i	0.462915	+	0.886402i	$0.346803\pi$
$524$	−13.0377	+	9.47246i	−0.569556	+	0.413807i
$525$	7.32662	−	36.6543i	0.319760	−	1.59973i
$526$	4.14907	+	12.7695i	0.180908	+	0.556778i
$527$	30.4239	+	30.4239i	1.32529	+	1.32529i
$528$	−7.93946	−	4.97897i	−0.345521	−	0.216682i
$529$			17.5386i			0.762547i
$530$	−7.31872	−	17.7032i	−0.317905	−	0.768979i
$531$	0.232112	−	0.319474i	0.0100728	−	0.0138640i
$532$	−1.19254	−	10.0383i	−0.0517033	−	0.435216i
$533$	3.30475	+	6.48593i	0.143144	+	0.280937i
$534$	−20.0845	−	6.52585i	−0.869142	−	0.282401i
$535$	−21.7889	−	1.72984i	−0.942018	−	0.0747876i
$536$	−6.18100	−	4.49076i	−0.266978	−	0.193971i
$537$	62.9790	+	32.0894i	2.71775	+	1.38476i
$538$	10.4131	+	10.4131i	0.448941	+	0.448941i
$539$	−22.8951	−	3.84886i	−0.986162	−	0.165782i
$540$	−9.52699	−	8.14811i	−0.409976	−	0.350639i
$541$	1.21933	+	3.75272i	0.0524232	+	0.161342i	0.973841	−	0.227232i	$-0.0729677\pi$
$541$	1.21933	+	3.75272i	0.0524232	+	0.161342i	−0.921417	+	0.388574i	$0.872968\pi$
$542$	5.07176	−	0.803288i	0.217851	−	0.0345042i
$543$	−1.54085	+	9.72855i	−0.0661242	+	0.417492i
$544$	1.25942	−	3.87608i	0.0539970	−	0.166186i
$545$	−39.2497	−	9.45145i	−1.68127	−	0.404856i
$546$	12.3222	−	15.6446i	0.527342	−	0.669529i
$547$	3.82113	+	24.1256i	0.163380	+	1.03154i	0.924014	+	0.382358i	$0.124888\pi$
$547$	3.82113	+	24.1256i	0.163380	+	1.03154i	−0.760635	+	0.649180i	$0.775112\pi$
$548$	8.98611	+	4.57865i	0.383867	+	0.195590i
$549$	−18.3735			−0.784163
$550$	−16.1692	+	3.68214i	−0.689455	+	0.157007i
$551$		−	30.7394i		−	1.30954i
$552$	−5.88365	−	2.99787i	−0.250425	−	0.127598i
$553$	28.2228	−	13.0258i	1.20015	−	0.553912i
$554$	3.15786	+	4.34642i	0.134164	+	0.184662i
$555$	24.9309	+	6.00345i	1.05826	+	0.254832i
$556$	−18.9830	−	6.16795i	−0.805059	−	0.261579i
$557$	−11.9545	−	1.89341i	−0.506529	−	0.0802264i	−0.102061	−	0.994778i	$-0.532544\pi$
$557$	−11.9545	−	1.89341i	−0.506529	−	0.0802264i	−0.404469	+	0.914552i	$0.632544\pi$
$558$	−8.23122	−	51.9699i	−0.348455	−	2.20006i
$559$	−7.82303	−	24.0768i	−0.330879	−	1.01834i
$560$	−5.37203	−	2.47817i	−0.227010	−	0.104722i
$561$	−37.2290	+	8.53168i	−1.57181	+	0.360208i
$562$	15.7446	+	15.7446i	0.664145	+	0.664145i
$563$	3.21166	−	6.30324i	0.135355	−	0.265650i	−0.813373	−	0.581743i	$-0.802371\pi$
$563$	3.21166	−	6.30324i	0.135355	−	0.265650i	0.948728	+	0.316093i	$0.102371\pi$
$564$	6.68220	−	9.19725i	0.281371	−	0.387274i
$565$	−1.25255	+	15.7770i	−0.0526952	+	0.663743i
$566$	27.1169	+	8.81082i	1.13981	+	0.370346i
$567$	−1.72655	+	1.59740i	−0.0725084	+	0.0670846i
$568$	−0.312176	+	1.97100i	−0.0130986	+	0.0827013i
$569$	−5.49447	+	7.56249i	−0.230340	+	0.317036i	−0.908505	−	0.417874i	$-0.862775\pi$
$569$	−5.49447	+	7.56249i	−0.230340	+	0.317036i	0.678165	+	0.734910i	$0.262775\pi$
$570$	−22.3096	+	9.22304i	−0.934446	+	0.386310i
$571$	44.2939			1.85364			0.926822	−	0.375501i	$-0.122529\pi$
$571$	44.2939			1.85364			0.926822	+	0.375501i	$0.122529\pi$
$572$	−8.56908	−	2.15122i	−0.358291	−	0.0899470i
$573$	8.43733	+	8.43733i	0.352474	+	0.352474i
$574$	−4.01932	−	6.00967i	−0.167763	−	0.250839i
$575$	−11.1179	+	3.59559i	−0.463647	+	0.149946i
$576$	−4.03223	+	2.92959i	−0.168010	+	0.122066i
$577$	17.7924	+	34.9196i	0.740708	+	1.45372i	0.885685	+	0.464286i	$0.153689\pi$
$577$	17.7924	+	34.9196i	0.740708	+	1.45372i	−0.144977	+	0.989435i	$0.546311\pi$
$578$	0.176997	+	0.347375i	0.00736209	+	0.0144489i
$579$	56.2261	−	40.8506i	2.33668	−	1.69770i
$580$	−15.3323	−	9.41012i	−0.636641	−	0.390734i
$581$	25.8607	−	17.2959i	1.07288	−	0.717553i
$582$	16.0619	+	16.0619i	0.665787	+	0.665787i
$583$	18.2287	+	21.7955i	0.754955	+	0.902678i
$584$	−7.24335			−0.299732
$585$	−27.4204	−	11.3799i	−1.13370	−	0.470502i
$586$	3.70308	−	5.09686i	0.152973	−	0.210549i
$587$	2.17597	−	13.7385i	0.0898119	−	0.567050i	−0.901213	−	0.433376i	$-0.857322\pi$
$587$	2.17597	−	13.7385i	0.0898119	−	0.567050i	0.991025	−	0.133674i	$-0.0426776\pi$
$588$	−10.3200	+	16.8736i	−0.425589	+	0.695857i
$589$	−38.3623	−	12.4647i	−1.58069	−	0.513598i
$590$	−0.176608	−	0.0140211i	−0.00727085	−	0.000577239i
$591$	−16.6942	+	22.9776i	−0.686709	+	0.945174i
$592$	1.84258	−	3.61627i	0.0757297	−	0.148628i
$593$	24.3898	+	24.3898i	1.00157	+	1.00157i	0.999999	+	0.00157124i	$0.000500142\pi$
$593$	24.3898	+	24.3898i	1.00157	+	1.00157i	0.00157124	+	0.999999i	$0.499500\pi$
$594$	17.1042	+	7.29294i	0.701795	+	0.299233i
$595$	−22.6231	+	8.33968i	−0.927456	+	0.341894i
$596$	−0.859457	−	2.64514i	−0.0352047	−	0.108349i
$597$	−6.98746	−	44.1171i	−0.285978	−	1.80559i
$598$	−6.14868	−	0.973855i	−0.251438	−	0.0398239i
$599$	34.8369	+	11.3192i	1.42340	+	0.462490i	0.916680	−	0.399623i	$-0.130859\pi$
$599$	34.8369	+	11.3192i	1.42340	+	0.462490i	0.506717	+	0.862112i	$0.330859\pi$
$600$	−2.22923	+	13.9511i	−0.0910080	+	0.569551i
$601$	−10.3934	−	14.3052i	−0.423954	−	0.583522i	0.542598	−	0.839992i	$-0.317441\pi$
$601$	−10.3934	−	14.3052i	−0.423954	−	0.583522i	−0.966552	+	0.256470i	$0.917441\pi$
$602$	10.5367	+	22.8296i	0.429442	+	0.930467i
$603$	33.9289	+	17.2876i	1.38169	+	0.704007i
$604$			8.65367i			0.352113i
$605$	21.2420	−	12.4007i	0.863610	−	0.504161i
$606$	−39.1900			−1.59198
$607$	−2.55644	−	1.30257i	−0.103763	−	0.0528696i	0.401339	−	0.915930i	$-0.368545\pi$
$607$	−2.55644	−	1.30257i	−0.103763	−	0.0528696i	−0.505101	+	0.863060i	$0.668545\pi$
$608$	0.597705	+	3.77376i	0.0242402	+	0.153046i
$609$	−37.2151	+	47.2494i	−1.50803	+	1.91464i
$610$	4.30218	+	7.03133i	0.174190	+	0.284690i
$611$	3.31191	−	10.1930i	0.133986	−	0.412366i
$612$	−3.17766	+	20.0629i	−0.128449	+	0.810996i
$613$	19.6275	−	3.10869i	0.792746	−	0.125559i	0.253089	−	0.967443i	$-0.418554\pi$
$613$	19.6275	−	3.10869i	0.792746	−	0.125559i	0.539658	+	0.841884i	$0.318554\pi$
$614$	−6.57400	−	20.2327i	−0.265305	−	0.816525i
$615$	−11.2221	+	13.1211i	−0.452517	+	0.529095i
$616$	8.70350	+	1.11766i	0.350674	+	0.0450319i
$617$	26.6488	+	26.6488i	1.07284	+	1.07284i	0.997130	+	0.0757113i	$0.0241227\pi$
$617$	26.6488	+	26.6488i	1.07284	+	1.07284i	0.0757113	+	0.997130i	$0.475877\pi$
$618$	19.7770	+	10.0769i	0.795547	+	0.405351i
$619$	−20.5533	−	14.9328i	−0.826106	−	0.600201i	0.0923486	−	0.995727i	$-0.470563\pi$
$619$	−20.5533	−	14.9328i	−0.826106	−	0.600201i	−0.918455	+	0.395525i	$0.870563\pi$
$620$	−17.9609	+	15.3188i	−0.721328	+	0.615218i
$621$	12.4606	+	4.04869i	0.500026	+	0.162468i
$622$	−4.16503	−	8.17433i	−0.167003	−	0.327761i
$623$	19.6357	−	2.33271i	0.786690	−	0.0934581i
$624$	−4.42427	+	6.08948i	−0.177112	+	0.243774i
$625$	14.6392	+	20.2656i	0.585567	+	0.810624i
$626$			24.6199i			0.984009i
$627$	27.4667	−	22.9718i	1.09691	−	0.917404i
$628$	3.93609	+	3.93609i	0.157067	+	0.157067i
$629$	−5.11151	−	15.7316i	−0.203809	−	0.627260i
$630$	28.3773	+	8.01089i	1.13058	+	0.319161i
$631$	−13.7687	+	10.0035i	−0.548122	+	0.398234i	−0.827092	−	0.562066i	$-0.810007\pi$
$631$	−13.7687	+	10.0035i	−0.548122	+	0.398234i	0.278971	+	0.960300i	$0.410007\pi$
$632$	−10.4680	+	5.33372i	−0.416395	+	0.212164i
$633$	−26.6899	+	13.5992i	−1.06083	+	0.540519i
$634$	3.95375	+	5.44187i	0.157024	+	0.216124i
$635$	4.41300	+	18.4371i	0.175125	+	0.731654i
$636$	23.0223	−	7.48040i	0.912894	−	0.296617i
$637$	−4.33726	+	18.1355i	−0.171848	+	0.718555i
$638$	25.8801	+	6.49704i	1.02460	+	0.257220i
$639$		−	9.94614i		−	0.393463i
$640$	2.06527	+	0.857121i	0.0816370	+	0.0338807i
$641$	3.50331	+	2.54531i	0.138373	+	0.100534i	0.654818	−	0.755786i	$-0.272745\pi$
$641$	3.50331	+	2.54531i	0.138373	+	0.100534i	−0.516446	+	0.856320i	$0.672745\pi$
$642$	4.32077	−	27.2803i	0.170527	−	1.07667i
$643$	26.3134	−	13.4073i	1.03770	−	0.528734i	0.149773	−	0.988720i	$-0.452146\pi$
$643$	26.3134	−	13.4073i	1.03770	−	0.528734i	0.887926	+	0.459986i	$0.152146\pi$
$644$	6.17837	+	0.240056i	0.243462	+	0.00945952i
$645$	45.6857	−	38.9652i	1.79887	−	1.53425i
$646$	12.5979	+	9.15293i	0.495659	+	0.360117i
$647$	−3.72000	−	1.89543i	−0.146248	−	0.0745172i	0.379335	−	0.925259i	$-0.376153\pi$
$647$	−3.72000	−	1.89543i	−0.146248	−	0.0745172i	−0.525583	+	0.850742i	$0.676153\pi$
$648$	0.628643	−	0.628643i	0.0246954	−	0.0246954i
$649$	0.256137	−	0.0586983i	0.0100543	−	0.00230411i
$650$	2.06557	+	13.1581i	0.0810182	+	0.516103i
$651$	43.8761	+	65.6034i	1.71964	+	2.57120i
$652$	−1.61682	−	10.2082i	−0.0633197	−	0.399785i
$653$	0.234099	−	1.47804i	0.00916100	−	0.0578403i	−0.982684	−	0.185288i	$-0.940678\pi$
$653$	0.234099	−	1.47804i	0.00916100	−	0.0578403i	0.991845	+	0.127447i	$0.0406784\pi$
$654$	15.7647	−	48.5189i	0.616450	−	1.89724i
$655$	−35.0340	−	8.43629i	−1.36889	−	0.329633i
$656$	1.60620	+	2.21075i	0.0627117	+	0.0863153i
$657$	35.6572	−	5.64755i	1.39112	−	0.220332i
$658$	−2.07215	+	10.4411i	−0.0807807	+	0.407038i
$659$			31.2817i			1.21856i	0.792955	+	0.609280i	$0.208542\pi$
$659$			31.2817i			1.21856i	−0.792955	+	0.609280i	$0.791458\pi$
$660$	−3.04972	−	20.7322i	−0.118710	−	0.807001i
$661$			21.7964i			0.847781i	0.905713	+	0.423890i	$0.139336\pi$
$661$			21.7964i			0.847781i	−0.905713	+	0.423890i	$0.860664\pi$
$662$	−2.91968	+	5.73020i	−0.113477	+	0.222711i
$663$	4.79890	+	30.2991i	0.186374	+	1.17672i
$664$	−9.51325	+	6.91178i	−0.369186	+	0.268229i
$665$	15.3479	−	16.5949i	0.595165	−	0.643524i
$666$	−6.25101	+	19.2386i	−0.242222	+	0.745482i
$667$	18.5700	+	2.94120i	0.719034	+	0.113884i
$668$	1.00789	+	6.36357i	0.0389964	+	0.246214i
$669$	−75.9913	+	24.6911i	−2.93799	+	0.954612i
$670$	−1.32872	−	17.0321i	−0.0513329	−	0.658008i
$671$	−9.21446	−	8.03618i	−0.355720	−	0.310233i
$672$	3.65003	−	6.52426i	0.140803	−	0.251679i
$673$	19.8381	+	10.1080i	0.764702	+	0.389635i	0.792416	−	0.609981i	$-0.208823\pi$
$673$	19.8381	+	10.1080i	0.764702	+	0.389635i	−0.0277145	+	0.999616i	$0.508823\pi$
$674$	10.1360	−	13.9510i	0.390425	−	0.537374i
$675$	0.0383958	−	28.0317i	0.00147786	−	1.07894i
$676$	1.82441	−	5.61496i	0.0701696	−	0.215960i
$677$	−14.7823	−	29.0119i	−0.568130	−	1.11502i	−0.979102	−	0.203369i	$-0.934811\pi$
$677$	−14.7823	−	29.0119i	−0.568130	−	1.11502i	0.410973	−	0.911648i	$-0.365189\pi$
$678$	−19.7532	−	3.12860i	−0.758616	−	0.120153i
$679$	−19.9576	−	7.35289i	−0.765903	−	0.282178i
$680$	8.42190	−	3.48171i	0.322965	−	0.133517i
$681$	−54.3232			−2.08167
$682$	18.6025	−	29.6635i	0.712325	−	1.13587i
$683$	−22.5080	+	22.5080i	−0.861246	+	0.861246i	−0.991483	−	0.130237i	$-0.958426\pi$
$683$	−22.5080	+	22.5080i	−0.861246	+	0.861246i	0.130237	+	0.991483i	$0.458426\pi$
$684$	−5.88471	−	18.1113i	−0.225007	−	0.692502i
$685$	5.24953	+	21.9320i	0.200574	+	0.837979i
$686$	2.15281	−	18.3947i	0.0821945	−	0.702313i
$687$	−47.7524	+	24.3311i	−1.82187	+	0.928289i
$688$	−4.31449	−	8.46767i	−0.164489	−	0.322827i
$689$	18.4627	−	13.4140i	0.703374	−	0.511031i
$690$	−3.43712	−	14.3600i	−0.130849	−	0.546675i
$691$	38.5155	−	12.5145i	1.46520	−	0.476072i	0.535546	−	0.844506i	$-0.320106\pi$
$691$	38.5155	−	12.5145i	1.46520	−	0.476072i	0.929654	+	0.368434i	$0.120106\pi$
$692$	9.02088	−	9.02088i	0.342923	−	0.342923i
$693$	−43.7166	+	1.28403i	−1.66065	+	0.0487763i
$694$		−	25.2774i		−	0.959519i
$695$	−17.0516	−	41.2460i	−0.646803	−	1.56455i
$696$	13.3620	−	18.3912i	0.506486	−	0.697118i
$697$	10.9999	+	1.74221i	0.416651	+	0.0659910i
$698$	−9.32547	+	4.75156i	−0.352974	+	0.179849i
$699$	2.86449	−	8.81599i	0.108345	−	0.333452i
$700$	−3.57892	−	12.7354i	−0.135270	−	0.481354i
$701$	3.08160	+	2.23891i	0.116390	+	0.0845625i	0.644458	−	0.764640i	$-0.277083\pi$
$701$	3.08160	+	2.23891i	0.116390	+	0.0845625i	−0.528067	+	0.849202i	$0.677083\pi$
$702$	6.78009	−	13.3067i	0.255898	−	0.502228i
$703$	10.9653	+	10.9653i	0.413563	+	0.413563i
$704$	−3.30353	−	0.294399i	−0.124507	−	0.0110956i
$705$	25.3436	−	1.97712i	0.954495	−	0.0744626i
$706$	7.51633	−	2.44220i	0.282881	−	0.0919135i
$707$	33.3179	−	15.3774i	1.25305	−	0.578325i
$708$	0.0350216	−	0.221118i	0.00131619	−	0.00831012i
$709$	−46.3700	−	15.0665i	−1.74146	−	0.565836i	−0.746437	−	0.665456i	$-0.768237\pi$
$709$	−46.3700	−	15.0665i	−1.74146	−	0.565836i	−0.995026	+	0.0996201i	$0.968237\pi$
$710$	−3.80627	+	2.32890i	−0.142847	+	0.0874021i
$711$	47.3728	−	34.4183i	1.77662	−	1.29079i
$712$	−7.38179	+	1.16916i	−0.276644	+	0.0438161i
$713$	11.2006	−	21.9825i	0.419467	−	0.823251i
$714$	−8.28310	−	29.3208i	−0.309987	−	1.09730i
$715$	−8.77423	−	17.7002i	−0.328138	−	0.661951i
$716$	25.0151			0.934857
$717$	33.0176	+	16.8233i	1.23306	+	0.628278i
$718$	−15.9294	+	2.52296i	−0.594479	+	0.0941562i
$719$	−17.4146	+	12.6524i	−0.649455	+	0.471857i	−0.863085	−	0.505058i	$-0.831471\pi$
$719$	−17.4146	+	12.6524i	−0.649455	+	0.471857i	0.213631	+	0.976915i	$0.431471\pi$
$720$	−10.8351	−	2.60913i	−0.403800	−	0.0972364i
$721$	−20.7676	−	0.806910i	−0.773427	−	0.0300509i
$722$	4.34727	+	0.688540i	0.161789	+	0.0256248i
$723$	−24.8122	+	3.92987i	−0.922776	+	0.146153i
$724$	1.07720	+	3.31529i	0.0400339	+	0.123212i
$725$	−6.23836	−	39.7396i	−0.231687	−	1.47589i
$726$	13.5350	+	27.9800i	0.502333	+	1.03844i
$727$	8.38370	−	8.38370i	0.310934	−	0.310934i	−0.534337	−	0.845271i	$-0.679439\pi$
$727$	8.38370	−	8.38370i	0.310934	−	0.310934i	0.845271	+	0.534337i	$0.179439\pi$
$728$	1.37196	−	6.91305i	0.0508484	−	0.256215i
$729$	25.3295	−	34.8630i	0.938128	−	1.29122i
$730$	−10.5104	−	12.3232i	−0.389009	−	0.456103i
$731$	−36.8363	−	11.9688i	−1.36244	−	0.442683i
$732$	−9.28109	+	4.72895i	−0.343039	+	0.174787i
$733$	−26.9395	−	4.26680i	−0.995034	−	0.157598i	−0.362378	−	0.932031i	$-0.618035\pi$
$733$	−26.9395	−	4.26680i	−0.995034	−	0.157598i	−0.632656	+	0.774433i	$0.718035\pi$
$734$	14.9561	+	10.8662i	0.552038	+	0.401079i
$735$	−43.6821	+	6.92688i	−1.61124	+	0.255502i
$736$	−2.33697			−0.0861417
$737$	9.45437	+	23.5096i	0.348256	+	0.865988i
$738$	−9.63063	−	9.63063i	−0.354508	−	0.354508i
$739$	16.2493	−	5.27973i	0.597742	−	0.194218i	0.00550885	−	0.999985i	$-0.498246\pi$
$739$	16.2493	−	5.27973i	0.597742	−	0.194218i	0.592233	+	0.805767i	$0.298246\pi$
$740$	8.82608	−	2.11256i	0.324453	−	0.0776593i
$741$	−16.9043	−	23.2667i	−0.620993	−	0.854724i
$742$	−16.6376	+	15.3931i	−0.610785	+	0.565097i
$743$	−21.0426	−	41.2984i	−0.771978	−	1.51509i	−0.855048	−	0.518549i	$-0.826472\pi$
$743$	−21.0426	−	41.2984i	−0.771978	−	1.51509i	0.0830695	−	0.996544i	$-0.473528\pi$
$744$	−17.5338	−	24.1332i	−0.642820	−	0.884766i
$745$	3.25310	−	5.30042i	0.119184	−	0.194192i
$746$	6.34980	+	19.5427i	0.232483	+	0.715508i
$747$	41.4423	−	41.4423i	1.51629	−	1.51629i
$748$	−10.3687	+	8.67188i	−0.379117	+	0.317075i
$749$	7.03086	+	24.8881i	0.256902	+	0.909391i
$750$	−26.9699	+	16.4511i	−0.984802	+	0.600708i
$751$	−32.9906	−	23.9691i	−1.20385	−	0.874645i	−0.209188	−	0.977875i	$-0.567082\pi$
$751$	−32.9906	−	23.9691i	−1.20385	−	0.874645i	−0.994657	+	0.103230i	$0.967082\pi$
$752$	0.629390	−	3.97381i	0.0229515	−	0.144910i
$753$	−8.17183	−	16.0381i	−0.297798	−	0.584462i
$754$	6.62265	−	20.3824i	0.241183	−	0.742284i
$755$	−14.7226	+	12.5569i	−0.535810	+	0.456991i
$756$	−5.12789	+	13.9184i	−0.186500	+	0.506208i
$757$	22.7536	−	44.6564i	0.826992	−	1.62306i	0.0456530	−	0.998957i	$-0.485463\pi$
$757$	22.7536	−	44.6564i	0.826992	−	1.62306i	0.781339	−	0.624106i	$-0.214537\pi$
$758$	12.3344	−	12.3344i	0.448006	−	0.448006i
$759$	11.2495	+	18.7909i	0.408330	+	0.682068i
$760$	−5.55306	+	6.49278i	−0.201431	+	0.235518i
$761$	−24.0224	+	7.80534i	−0.870810	+	0.282943i	−0.710136	−	0.704064i	$-0.751367\pi$
$761$	−24.0224	+	7.80534i	−0.870810	+	0.282943i	−0.160674	+	0.987008i	$0.551367\pi$
$762$	−23.6613	+	3.74758i	−0.857157	+	0.135760i
$763$	5.63521	+	47.4348i	0.204008	+	1.71725i
$764$	4.01618	+	1.30494i	0.145300	+	0.0472109i
$765$	−38.7442	+	23.7060i	−1.40080	+	0.857093i
$766$	−7.16751	−	9.86523i	−0.258973	−	0.356445i
$767$	−0.0330166	−	0.208459i	−0.00119216	−	0.00752700i
$768$	−1.28280	+	2.51764i	−0.0462892	+	0.0908476i
$769$	−19.0770			−0.687935			−0.343967	−	0.938982i	$-0.611771\pi$
$769$	−19.0770			−0.687935			−0.343967	+	0.938982i	$0.611771\pi$
$770$	10.7277	+	16.4292i	0.386598	+	0.592066i
$771$	1.65579			0.0596317
$772$	11.1664	−	21.9153i	0.401888	−	0.788750i
$773$	−5.70481	−	36.0188i	−0.205188	−	1.29550i	−0.848211	−	0.529658i	$-0.822320\pi$
$773$	−5.70481	−	36.0188i	−0.205188	−	1.29550i	0.643023	−	0.765847i	$-0.277680\pi$
$774$	27.8413	+	38.3203i	1.00073	+	1.37739i
$775$	−52.1242	−	8.32886i	−1.87236	−	0.299182i
$776$	7.64548	+	2.48417i	0.274457	+	0.0891764i
$777$	−3.57942	−	30.1300i	−0.128411	−	1.08091i
$778$	12.1140	−	1.91866i	0.434307	−	0.0687875i
$779$	−9.92985	+	3.22641i	−0.355774	+	0.115598i
$780$	−16.7799	+	1.30905i	−0.600818	+	0.0468714i
$781$	4.35022	−	4.98807i	0.155663	−	0.178487i
$782$	−6.73479	+	6.73479i	−0.240835	+	0.240835i
$783$	−20.4770	+	40.1884i	−0.731789	+	1.43622i
$784$	−0.543139	+	6.97890i	−0.0193978	+	0.249246i
$785$	−0.985080	+	12.4080i	−0.0351590	+	0.442860i
$786$	14.0715	−	43.3076i	0.501913	−	1.54473i
$787$	11.8664	+	23.2892i	0.422992	+	0.830170i	0.999911	+	0.0133675i	$0.00425515\pi$
$787$	11.8664	+	23.2892i	0.422992	+	0.830170i	−0.576918	+	0.816802i	$0.695745\pi$
$788$	−1.57241	+	9.92783i	−0.0560149	+	0.353664i
$789$	−30.6930	−	22.2998i	−1.09270	−	0.793893i
$790$	−24.2639	−	10.0699i	−0.863271	−	0.358271i
$791$	18.0210	−	5.09093i	0.640755	−	0.181013i
$792$	16.4920	−	1.12647i	0.586018	−	0.0400273i
$793$	−6.94383	+	6.94383i	−0.246583	+	0.246583i
$794$	−5.44647	−	16.7625i	−0.193288	−	0.594879i
$795$	46.1329	+	28.3138i	1.63617	+	1.00419i
$796$	−9.29163	−	12.7888i	−0.329333	−	0.453288i
$797$	−7.09929	−	13.9331i	−0.251470	−	0.493537i	0.730418	−	0.683000i	$-0.239325\pi$
$797$	−7.09929	−	13.9331i	−0.251470	−	0.493537i	−0.981888	+	0.189463i	$0.939325\pi$
$798$	19.3983	+	20.9667i	0.686692	+	0.742211i
$799$	−9.63812	−	13.2657i	−0.340972	−	0.469308i
$800$	1.53857	+	4.75739i	0.0543967	+	0.168199i
$801$	35.4271	−	11.5110i	1.25176	−	0.406720i
$802$	−24.0454	−	24.0454i	−0.849074	−	0.849074i
$803$	20.3525	+	12.7634i	0.718224	+	0.450411i
$804$	21.5881			0.761353
$805$	8.55668	+	10.8597i	0.301583	+	0.382753i
$806$	−22.7516	−	16.5300i	−0.801389	−	0.582243i
$807$	−41.0987	−	6.50940i	−1.44674	−	0.229142i
$808$	−12.3578	+	6.29663i	−0.434747	+	0.221515i
$809$	−9.96118	−	3.23658i	−0.350216	−	0.113792i	0.128626	−	0.991693i	$-0.458943\pi$
$809$	−9.96118	−	3.23658i	−0.350216	−	0.113792i	−0.478842	+	0.877901i	$0.658943\pi$
$810$	1.98171	+	0.157329i	0.0696301	+	0.00552799i
$811$	−11.9815	+	16.4912i	−0.420729	+	0.579084i	−0.965794	−	0.259310i	$-0.916505\pi$
$811$	−11.9815	+	16.4912i	−0.420729	+	0.579084i	0.545065	+	0.838394i	$0.316505\pi$
$812$	−4.14356	+	20.8786i	−0.145410	+	0.732694i
$813$	−10.2598	+	10.2598i	−0.359826	+	0.359826i
$814$	−11.5495	+	6.91427i	−0.404809	+	0.242345i
$815$	15.0213	−	17.5633i	0.526173	−	0.615216i
$816$	3.55862	+	10.9523i	0.124577	+	0.383408i
$817$	35.8639	−	5.68029i	1.25472	−	0.198728i
$818$	−1.48885	−	0.235810i	−0.0520563	−	0.00824491i
$819$	−1.36382	+	35.1009i	−0.0476557	+	1.22653i
$820$	−1.43050	+	5.94055i	−0.0499554	+	0.207453i
$821$	7.30170	−	5.30500i	0.254831	−	0.185146i	−0.453034	−	0.891493i	$-0.649658\pi$
$821$	7.30170	−	5.30500i	0.254831	−	0.185146i	0.707865	+	0.706348i	$0.249658\pi$
$822$	−28.1465	+	4.45796i	−0.981721	+	0.155489i
$823$	−42.7862	−	21.8007i	−1.49143	−	0.759924i	−0.497249	−	0.867608i	$-0.665657\pi$
$823$	−42.7862	−	21.8007i	−1.49143	−	0.759924i	−0.994185	+	0.107684i	$0.965657\pi$
$824$	7.85535			0.273654
$825$	30.8467	−	35.2719i	1.07395	−	1.22801i
$826$	0.0569880	+	0.201728i	0.00198287	+	0.00701902i
$827$	11.4711	−	22.5132i	0.398888	−	0.782862i	−0.600977	−	0.799266i	$-0.705222\pi$
$827$	11.4711	−	22.5132i	0.398888	−	0.782862i	0.999865	+	0.0164041i	$0.00522183\pi$
$828$	11.5043	−	1.82210i	0.399802	−	0.0633224i
$829$	9.41846	−	6.84291i	0.327117	−	0.237664i	−0.412090	−	0.911143i	$-0.635201\pi$
$829$	9.41846	−	6.84291i	0.327117	−	0.237664i	0.739206	+	0.673479i	$0.235201\pi$
$830$	−25.5633	−	6.15571i	−0.887314	−	0.213668i
$831$	−14.4375	−	4.69104i	−0.500833	−	0.162730i
$832$	−0.416718	+	2.63105i	−0.0144471	+	0.0912153i
$833$	18.5469	+	21.6774i	0.642612	+	0.751077i
$834$	53.6387	−	17.4283i	1.85736	−	0.603492i
$835$	−9.36393	+	10.9486i	−0.324052	+	0.378891i
$836$	4.97025	−	11.6568i	0.171900	−	0.403158i
$837$	41.8512	+	41.8512i	1.44659	+	1.44659i
$838$	12.0928	−	23.7335i	0.417740	−	0.819861i
$839$	17.7491	+	12.8955i	0.612766	+	0.445201i	0.850387	−	0.526157i	$-0.176368\pi$
$839$	17.7491	+	12.8955i	0.612766	+	0.445201i	−0.237621	+	0.971358i	$0.576368\pi$
$840$	16.3962	−	3.25715i	0.565722	−	0.112382i
$841$	−11.0400	+	33.9777i	−0.380690	+	1.17164i
$842$	11.4369	−	5.82737i	0.394140	−	0.200825i
$843$	−62.1411	−	9.84219i	−2.14025	−	0.338983i
$844$	−6.23120	+	8.57651i	−0.214487	+	0.295216i
$845$	12.2001	−	5.04366i	0.419696	−	0.173507i
$846$			20.0528i			0.689429i
$847$	−22.4858	−	18.4767i	−0.772621	−	0.634867i
$848$	6.05779	−	6.05779i	0.208025	−	0.208025i
$849$	−76.6220	+	24.8960i	−2.62966	+	0.854428i
$850$	18.1440	+	9.27617i	0.622335	+	0.318170i
$851$	−7.67344	+	5.57508i	−0.263042	+	0.191111i
$852$	−2.55992	−	5.02413i	−0.0877015	−	0.172124i
$853$	19.9144	−	10.1469i	0.681857	−	0.347423i	−0.0785137	−	0.996913i	$-0.525017\pi$
$853$	19.9144	−	10.1469i	0.681857	−	0.347423i	0.760370	+	0.649490i	$0.225017\pi$
$854$	6.03490	−	7.66210i	0.206510	−	0.262192i
$855$	22.2740	−	36.2920i	0.761754	−	1.24116i
$856$	−3.02063	−	9.29655i	−0.103243	−	0.317749i
$857$	−8.17537	+	8.17537i	−0.279265	+	0.279265i	−0.832816	−	0.553550i	$-0.813273\pi$
$857$	−8.17537	+	8.17537i	−0.279265	+	0.279265i	0.553550	+	0.832816i	$0.313273\pi$
$858$	23.1616	−	9.31439i	0.790722	−	0.317988i
$859$	27.9314			0.953007			0.476504	−	0.879172i	$-0.341904\pi$
$859$	27.9314			0.953007			0.476504	+	0.879172i	$0.341904\pi$
$860$	8.14564	−	19.6273i	0.277764	−	0.669285i
$861$	19.1693	+	7.06244i	0.653287	+	0.240687i
$862$	9.33945	+	1.47922i	0.318103	+	0.0503826i
$863$	−0.456099	−	0.895146i	−0.0155258	−	0.0304711i	0.883113	−	0.469160i	$-0.155443\pi$
$863$	−0.456099	−	0.895146i	−0.0155258	−	0.0304711i	−0.898639	+	0.438689i	$0.855443\pi$
$864$	1.73245	−	5.33195i	0.0589393	−	0.181397i
$865$	28.4371	+	2.25764i	0.966889	+	0.0767622i
$866$	−12.0619	+	16.6018i	−0.409880	+	0.564152i
$867$	−0.981550	−	0.500125i	−0.0333352	−	0.0169851i
$868$	24.3760	+	13.6373i	0.827375	+	0.462879i
$869$	38.8116	+	3.45876i	1.31660	+	0.117330i
$870$	50.6782	−	3.95354i	1.71815	−	0.134038i
$871$	19.3560	−	6.28916i	0.655855	−	0.213100i
$872$	−2.82438	−	17.8324i	−0.0956457	−	0.603883i
$873$	−39.5737	−	6.26785i	−1.33937	−	0.212135i
$874$	2.75924	−	8.49207i	0.0933327	−	0.287248i
$875$	16.4738	−	24.5686i	0.556916	−	0.830569i
$876$	16.5581	−	12.0302i	0.559447	−	0.406462i
$877$	−3.89191	−	24.5725i	−0.131420	−	0.829756i	−0.962039	−	0.272913i	$-0.912013\pi$
$877$	−3.89191	−	24.5725i	−0.131420	−	0.829756i	0.830618	−	0.556842i	$-0.187987\pi$
$878$	8.36435	−	16.4160i	0.282283	−	0.554012i
$879$			17.8016i			0.600432i
$880$	−4.29271	−	6.04753i	−0.144707	−	0.203862i
$881$		−	21.8585i		−	0.736433i	−0.929740	−	0.368216i	$-0.879969\pi$
$881$		−	21.8585i		−	0.736433i	0.929740	−	0.368216i	$-0.120031\pi$
$882$	−2.76762	−	34.7788i	−0.0931905	−	1.17106i
$883$	−38.2050	+	6.05108i	−1.28570	+	0.203635i	−0.761615	−	0.648030i	$-0.775593\pi$
$883$	−38.2050	+	6.05108i	−1.28570	+	0.203635i	−0.524086	+	0.851665i	$0.675593\pi$
$884$	6.38138	+	8.78322i	0.214629	+	0.295412i
$885$	0.427009	−	0.261269i	0.0143537	−	0.00878247i
$886$	−1.56191	+	4.80706i	−0.0524733	+	0.161496i
$887$	−6.42623	+	40.5736i	−0.215772	+	1.36233i	0.607337	+	0.794445i	$0.292238\pi$
$887$	−6.42623	+	40.5736i	−0.215772	+	1.36233i	−0.823108	+	0.567884i	$0.807762\pi$
$888$	1.79401	+	11.3270i	0.0602032	+	0.380108i
$889$	18.6455	−	12.4703i	0.625350	−	0.418239i
$890$	−12.7004	−	10.8622i	−0.425719	−	0.364103i
$891$	−2.87409	+	0.658648i	−0.0962857	+	0.0220656i
$892$	−19.9954	+	19.9954i	−0.669495	+	0.669495i
$893$	13.6969	+	6.97893i	0.458350	+	0.233541i
$894$	6.35789	+	4.61928i	0.212640	+	0.154492i
$895$	36.2980	+	42.5585i	1.21331	+	1.42257i
$896$	0.102721	−	2.64376i	0.00343167	−	0.0883217i
$897$	15.6731	−	7.98586i	0.523311	−	0.266640i
$898$	−6.17626	+	38.9954i	−0.206105	+	1.30129i
$899$	68.7135	+	49.9233i	2.29172	+	1.66503i
$900$	−11.2833	−	22.2199i	−0.376109	−	0.740662i
$901$		−	34.9153i		−	1.16320i
$902$	−0.617608	−	9.04206i	−0.0205641	−	0.301068i
$903$	−62.0033	−	34.6881i	−2.06334	−	1.15435i
$904$	−6.73147	+	2.18719i	−0.223885	+	0.0727448i
$905$	−4.07727	+	6.64329i	−0.135533	+	0.220830i
$906$	−14.3725	−	19.7820i	−0.477494	−	0.657214i
$907$	−34.4354	+	17.5457i	−1.14341	+	0.582596i	−0.919918	−	0.392110i	$-0.871745\pi$
$907$	−34.4354	+	17.5457i	−1.14341	+	0.582596i	−0.223491	+	0.974706i	$0.571745\pi$
$908$	−17.1298	+	8.72808i	−0.568473	+	0.289651i
$909$	55.9251	−	40.6320i	1.85492	−	1.34768i
$910$	13.7521	−	7.69701i	0.455876	−	0.255153i
$911$	16.9957	+	52.3075i	0.563094	+	1.73303i	0.673547	+	0.739144i	$0.264770\pi$
$911$	16.9957	+	52.3075i	0.563094	+	1.73303i	−0.110453	+	0.993881i	$0.535230\pi$
$912$	−7.63401	−	7.63401i	−0.252787	−	0.252787i
$913$	38.9096	−	2.65768i	1.28772	−	0.0879563i
$914$		−	12.2031i		−	0.403643i
$915$	−21.5127	−	8.92812i	−0.711188	−	0.295155i
$916$	−11.1486	+	15.3447i	−0.368360	+	0.507004i
$917$	5.02995	+	42.3399i	0.166103	+	1.39819i
$918$	−10.3732	−	20.3586i	−0.342367	−	0.671932i
$919$	4.27758	+	1.38987i	0.141104	+	0.0458476i	0.378718	−	0.925512i	$-0.376365\pi$
$919$	4.27758	+	1.38987i	0.141104	+	0.0458476i	−0.237613	+	0.971360i	$0.576365\pi$
$920$	−3.39104	−	3.97591i	−0.111799	−	0.131082i
$921$	48.6316	+	35.3329i	1.60247	+	1.16426i
$922$	27.1081	+	13.8123i	0.892758	+	0.454883i
$923$	−3.75890	−	3.75890i	−0.123726	−	0.123726i
$924$	−21.7522	+	11.9003i	−0.715596	+	0.391491i
$925$	16.4012	+	11.9505i	0.539267	+	0.392930i
$926$	6.90310	+	21.2456i	0.226850	+	0.698173i
$927$	−38.6699	+	6.12471i	−1.27009	+	0.201162i
$928$	1.25856	−	7.94621i	0.0413141	−	0.260847i
$929$	−6.66105	+	20.5006i	−0.218542	+	0.672603i	0.780341	+	0.625354i	$0.215045\pi$
$929$	−6.66105	+	20.5006i	−0.218542	+	0.672603i	−0.998883	+	0.0472491i	$0.984955\pi$
$930$	15.6158	−	64.8489i	0.512063	−	2.12648i
$931$	−24.7186	−	10.2136i	−0.810121	−	0.334737i
$932$	−0.513197	−	3.24020i	−0.0168103	−	0.106136i
$933$	23.0975	+	11.7688i	0.756179	+	0.385293i
$934$	−37.2335			−1.21832
$935$	−29.7990	−	5.05714i	−0.974533	−	0.165386i
$936$		−	13.2769i		−	0.433970i
$937$	−4.42349	−	2.25388i	−0.144509	−	0.0736312i	0.380241	−	0.924888i	$-0.375841\pi$
$937$	−4.42349	−	2.25388i	−0.144509	−	0.0736312i	−0.524750	+	0.851256i	$0.675841\pi$
$938$	−18.3534	+	8.47073i	−0.599260	+	0.276579i
$939$	−40.8901	−	56.2804i	−1.33440	−	1.83664i
$940$	7.67397	−	4.69539i	0.250297	−	0.153147i
$941$	26.2166	+	8.51828i	0.854636	+	0.277688i	0.703387	−	0.710808i	$-0.251670\pi$
$941$	26.2166	+	8.51828i	0.854636	+	0.277688i	0.151250	+	0.988496i	$0.451670\pi$
$942$	−15.5351	−	2.46052i	−0.506160	−	0.0801679i
$943$	−0.999003	−	6.30745i	−0.0325320	−	0.205399i
$944$	−0.0244835	−	0.0753524i	−0.000796869	−	0.00245251i
$945$	−31.1204	+	11.4721i	−1.01235	+	0.373187i
$946$	−2.79782	+	31.3951i	−0.0909649	+	1.02074i
$947$	3.57473	+	3.57473i	0.116163	+	0.116163i	0.762799	−	0.646636i	$-0.223825\pi$
$947$	3.57473	+	3.57473i	0.116163	+	0.116163i	−0.646636	+	0.762799i	$0.723825\pi$
$948$	15.0711	−	29.5786i	0.489485	−	0.960668i
$949$	11.3414	−	15.6101i	0.368158	−	0.506727i
$950$	−19.1040	−	0.0261673i	−0.619816	−	0.000848980i
$951$	−18.0763	−	5.87336i	−0.586165	−	0.190457i
$952$	−7.32289	−	7.91494i	−0.237336	−	0.256525i
$953$	−3.62942	+	22.9153i	−0.117568	+	0.742298i	0.856517	+	0.516119i	$0.172624\pi$
$953$	−3.62942	+	22.9153i	−0.117568	+	0.742298i	−0.974086	+	0.226180i	$0.927376\pi$
$954$	−25.0978	+	34.5442i	−0.812571	+	1.11841i
$955$	3.60755	+	8.72630i	0.116738	+	0.282376i
$956$	13.1145			0.424153
$957$	−69.9517	+	28.1310i	−2.26122	+	0.909346i
$958$	−9.10185	−	9.10185i	−0.294067	−	0.294067i
$959$	22.1799	−	14.8341i	0.716227	−	0.479018i
$960$	−6.14471	+	1.47076i	−0.198320	+	0.0474687i
$961$	65.0871	−	47.2885i	2.09958	−	1.52544i
$962$	4.90836	+	9.63320i	0.158252	+	0.310587i
$963$	22.1182	+	43.4094i	0.712749	+	1.39885i
$964$	−7.19266	+	5.22577i	−0.231660	+	0.168311i
$965$	53.4878	−	12.8025i	1.72183	−	0.412129i
$966$	−14.5223	+	9.71262i	−0.467247	+	0.312498i
$967$	6.64448	+	6.64448i	0.213672	+	0.213672i	0.805825	−	0.592153i	$-0.201722\pi$
$967$	6.64448	+	6.64448i	0.213672	+	0.213672i	−0.592153	+	0.805825i	$0.701722\pi$
$968$	8.76356	+	6.64831i	0.281671	+	0.213685i
$969$	−44.0002			−1.41349
$970$	6.86759	+	16.6120i	0.220505	+	0.533379i
$971$	−19.6454	+	27.0395i	−0.630450	+	0.867740i	−0.998061	−	0.0622397i	$-0.980176\pi$
$971$	−19.6454	+	27.0395i	−0.630450	+	0.867740i	0.367611	+	0.929980i	$0.380176\pi$
$972$	2.23810	−	14.1308i	0.0717871	−	0.453246i
$973$	−38.7632	+	35.8636i	−1.24269	+	1.14974i
$974$	27.4825	+	8.92961i	0.880597	+	0.286123i
$975$	−26.5755	−	26.6484i	−0.851098	−	0.853433i
$976$	−2.16682	+	2.98238i	−0.0693583	+	0.0954635i
$977$	17.4740	−	34.2947i	0.559044	−	1.09719i	−0.422574	−	0.906328i	$-0.638873\pi$
$977$	17.4740	−	34.2947i	0.559044	−	1.09719i	0.981618	−	0.190857i	$-0.0611267\pi$
$978$	20.6504	+	20.6504i	0.660327	+	0.660327i
$979$	22.8016	+	9.72221i	0.728743	+	0.310723i
$980$	−12.6614	+	9.20264i	−0.404454	+	0.293968i
$981$	27.8075	+	85.5825i	0.887824	+	2.73244i
$982$	−1.81976	−	11.4895i	−0.0580710	−	0.366646i
$983$	−48.4887	−	7.67986i	−1.54655	−	0.244949i	−0.675952	−	0.736946i	$-0.736267\pi$
$983$	−48.4887	−	7.67986i	−1.54655	−	0.244949i	−0.870597	+	0.491996i	$0.836267\pi$
$984$	−7.34347	−	2.38604i	−0.234101	−	0.0760641i
$985$	−19.1720	+	11.7306i	−0.610871	+	0.373767i
$986$	−19.2728	−	26.5268i	−0.613772	−	0.844785i
$987$	−12.6044	−	27.3097i	−0.401201	−	0.869277i
$988$	−9.06870	−	4.62073i	−0.288514	−	0.147005i
$989$			22.2093i			0.706215i
$990$	25.8471	+	26.4235i	0.821475	+	0.839794i
$991$	−30.2810			−0.961909			−0.480954	−	0.876746i	$-0.659710\pi$
$991$	−30.2810			−0.961909			−0.480954	+	0.876746i	$0.659710\pi$
$992$	−9.40643	−	4.79282i	−0.298654	−	0.152172i
$993$	−2.84272	−	17.9483i	−0.0902111	−	0.569571i
$994$	4.14772	+	3.26687i	0.131558	+	0.103619i
$995$	8.27524	−	34.3652i	0.262343	−	1.08945i
$996$	10.2676	−	31.6003i	0.325340	−	1.00129i
$997$	−2.82387	+	17.8292i	−0.0894330	+	0.564658i	0.901760	+	0.432236i	$0.142275\pi$
$997$	−2.82387	+	17.8292i	−0.0894330	+	0.564658i	−0.991193	+	0.132422i	$0.957725\pi$
$998$	−27.9130	+	4.42099i	−0.883572	+	0.139944i
$999$	−7.03140	−	21.6404i	−0.222464	−	0.684673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bi.a.27.3	✓	384
5.3	odd	4	inner	770.2.bi.a.643.46	yes	384
7.6	odd	2	inner	770.2.bi.a.27.22	yes	384
11.9	even	5	inner	770.2.bi.a.97.27	yes	384
35.13	even	4	inner	770.2.bi.a.643.27	yes	384
55.53	odd	20	inner	770.2.bi.a.713.22	yes	384
77.20	odd	10	inner	770.2.bi.a.97.46	yes	384
385.328	even	20	inner	770.2.bi.a.713.3	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bi.a.27.3	✓	384	1.1	even	1	trivial
770.2.bi.a.27.22	yes	384	7.6	odd	2	inner
770.2.bi.a.97.27	yes	384	11.9	even	5	inner
770.2.bi.a.97.46	yes	384	77.20	odd	10	inner
770.2.bi.a.643.27	yes	384	35.13	even	4	inner
770.2.bi.a.643.46	yes	384	5.3	odd	4	inner
770.2.bi.a.713.3	yes	384	385.328	even	20	inner
770.2.bi.a.713.22	yes	384	55.53	odd	20	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.442024 - 2.79083i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.523489 - 2.17393i) q^{5} +(2.68732 + 0.873164i) q^{6} +(-2.62728 + 0.312118i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-4.74017 + 1.54018i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(-0.442024 - 2.79083i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(0.523489 - 2.17393i) q^{5} +(2.68732 + 0.873164i) q^{6} +(-2.62728 + 0.312118i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-4.74017 + 1.54018i) q^{9} +(1.69932 + 1.45337i) q^{10} +(-3.05087 - 1.30084i) q^{11} +(-1.99801 + 1.99801i) q^{12} +(-1.20936 + 2.37351i) q^{13} +(0.914659 - 2.48262i) q^{14} +(-6.29845 - 0.500040i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.85026 + 3.63134i) q^{17} +(0.779687 - 4.92275i) q^{18} +(-3.09109 - 2.24581i) q^{19} +(-2.06644 + 0.854291i) q^{20} +(2.03239 + 7.19432i) q^{21} +(2.54412 - 2.12778i) q^{22} +(1.65248 - 1.65248i) q^{23} +(-0.873164 - 2.68732i) q^{24} +(-4.45192 - 2.27605i) q^{25} +(-1.56577 - 2.15510i) q^{26} +(2.54523 + 4.99529i) q^{27} +(1.79678 + 1.94205i) q^{28} +(4.72889 + 6.50875i) q^{29} +(3.30498 - 5.38495i) q^{30} +(10.0404 - 3.26232i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.28186 + 9.08946i) q^{33} -4.07555 q^{34} +(-0.696827 + 5.87490i) q^{35} +(4.03223 + 2.92959i) q^{36} +(-4.00867 - 0.634911i) q^{37} +(3.40436 - 1.73461i) q^{38} +(7.15862 + 2.32598i) q^{39} +(0.176967 - 2.22905i) q^{40} +(1.60620 - 2.21075i) q^{41} +(-7.33287 - 1.45528i) q^{42} +(-6.71998 + 6.71998i) q^{43} +(0.740858 + 3.23282i) q^{44} +(0.866803 + 11.1111i) q^{45} +(0.722162 + 2.22259i) q^{46} +(-3.97381 + 0.629390i) q^{47} +(2.79083 + 0.442024i) q^{48} +(6.80516 - 1.64004i) q^{49} +(4.04911 - 2.93338i) q^{50} +(9.31660 - 6.76891i) q^{51} +(2.63105 - 0.416718i) q^{52} +(-7.63326 - 3.88934i) q^{53} -5.60634 q^{54} +(-4.42502 + 5.95140i) q^{55} +(-2.54610 + 0.719272i) q^{56} +(-4.90134 + 9.61942i) q^{57} +(-7.94621 + 1.25856i) q^{58} +(-0.0640985 + 0.0465703i) q^{59} +(3.29760 + 5.38947i) q^{60} +(3.50599 + 1.13917i) q^{61} +(-1.65149 + 10.4271i) q^{62} +(11.9730 - 5.52596i) q^{63} +(0.951057 - 0.309017i) q^{64} +(4.52674 + 3.87157i) q^{65} +(-7.06283 - 6.15968i) q^{66} +(-5.40239 - 5.40239i) q^{67} +(1.85026 - 3.63134i) q^{68} +(-5.34224 - 3.88136i) q^{69} +(-4.91822 - 3.28803i) q^{70} +(-0.616665 + 1.89790i) q^{71} +(-4.44088 + 2.26274i) q^{72} +(-7.15418 - 1.13311i) q^{73} +(2.38561 - 3.28351i) q^{74} +(-4.38422 + 13.4306i) q^{75} +3.82080i q^{76} +(8.42150 + 2.46543i) q^{77} +(-5.32240 + 5.32240i) q^{78} +(-11.1735 + 3.63049i) q^{79} +(1.90576 + 1.16965i) q^{80} +(0.719245 - 0.522562i) q^{81} +(1.24059 + 2.43480i) q^{82} +(-10.4774 + 5.33848i) q^{83} +(4.62572 - 5.87295i) q^{84} +(8.86287 - 2.12137i) q^{85} +(-2.93674 - 9.03835i) q^{86} +(16.0745 - 16.0745i) q^{87} +(-3.21681 - 0.807561i) q^{88} -7.47380 q^{89} +(-10.2935 - 4.27199i) q^{90} +(2.43651 - 6.61332i) q^{91} +(-2.30819 - 0.365582i) q^{92} +(-13.5427 - 26.5790i) q^{93} +(1.24328 - 3.82643i) q^{94} +(-6.50038 + 5.54416i) q^{95} +(-1.66086 + 2.28597i) q^{96} +(7.16274 + 3.64960i) q^{97} +(-1.62819 + 6.80801i) q^{98} +(16.4652 + 1.46732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 4 q^{7}+O(q^{10}) \) 384 * q - 4 * q^7	\( 384 q - 4 q^{7} + 24 q^{15} + 96 q^{16} + 16 q^{22} + 16 q^{23} - 40 q^{25} + 4 q^{28} + 16 q^{30} - 32 q^{35} + 80 q^{36} - 64 q^{37} + 44 q^{42} - 80 q^{43} - 16 q^{46} - 64 q^{50} - 136 q^{51} + 80 q^{53} + 8 q^{56} - 112 q^{57} - 96 q^{58} + 68 q^{63} - 272 q^{65} + 160 q^{67} - 8 q^{70} + 16 q^{71} + 96 q^{77} + 24 q^{81} - 80 q^{85} - 16 q^{88} - 84 q^{91} + 16 q^{92} + 88 q^{93} - 184 q^{95} - 32 q^{98}+O(q^{100}) \) 384 * q - 4 * q^7 + 24 * q^15 + 96 * q^16 + 16 * q^22 + 16 * q^23 - 40 * q^25 + 4 * q^28 + 16 * q^30 - 32 * q^35 + 80 * q^36 - 64 * q^37 + 44 * q^42 - 80 * q^43 - 16 * q^46 - 64 * q^50 - 136 * q^51 + 80 * q^53 + 8 * q^56 - 112 * q^57 - 96 * q^58 + 68 * q^63 - 272 * q^65 + 160 * q^67 - 8 * q^70 + 16 * q^71 + 96 * q^77 + 24 * q^81 - 80 * q^85 - 16 * q^88 - 84 * q^91 + 16 * q^92 + 88 * q^93 - 184 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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