LMFDB - Embedded newform 384.2.v.a.157.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			157.10
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.706338 - 1.22519i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.00217 + 1.73079i) q^{4} +(-0.708130 + 0.378503i) q^{5} +(1.28852 - 0.582847i) q^{6} +(-0.234536 - 1.17909i) q^{7} +(2.82842 + 0.00532616i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.706338 - 1.22519i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.00217 + 1.73079i) q^{4} +(-0.708130 + 0.378503i) q^{5} +(1.28852 - 0.582847i) q^{6} +(-0.234536 - 1.17909i) q^{7} +(2.82842 + 0.00532616i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.963917 + 0.600241i) q^{10} +(-2.55728 + 3.11605i) q^{11} +(-1.62423 - 1.16700i) q^{12} +(1.09905 - 2.05618i) q^{13} +(-1.27895 + 1.12019i) q^{14} +(-0.307272 - 0.741820i) q^{15} +(-1.99130 - 3.46911i) q^{16} +(-2.92955 + 7.07255i) q^{17} +(0.453743 + 1.33945i) q^{18} +(-0.0109526 - 0.0361057i) q^{19} +(0.0545578 - 1.60495i) q^{20} +(1.19640 - 0.117835i) q^{21} +(5.62406 + 0.932163i) q^{22} +(-6.86147 + 4.58469i) q^{23} +(-0.282534 + 2.81428i) q^{24} +(-2.41967 + 3.62129i) q^{25} +(-3.29551 + 0.105813i) q^{26} +(0.290285 - 0.956940i) q^{27} +(2.27581 + 0.775722i) q^{28} +(2.83755 - 2.32872i) q^{29} +(-0.691831 + 0.900441i) q^{30} +(-6.28384 + 6.28384i) q^{31} +(-2.84379 + 4.89008i) q^{32} +(-2.85039 - 2.85039i) q^{33} +(10.7345 - 1.40636i) q^{34} +(0.612372 + 0.746178i) q^{35} +(1.32058 - 1.50202i) q^{36} +(3.55263 + 1.07768i) q^{37} +(-0.0365001 + 0.0389218i) q^{38} +(1.93855 + 1.29530i) q^{39} +(-2.00491 + 1.06680i) q^{40} +(-4.73246 - 7.08262i) q^{41} +(-0.989436 - 1.38259i) q^{42} +(-0.229727 - 2.33246i) q^{43} +(-2.83041 - 7.54895i) q^{44} +(0.768365 - 0.233081i) q^{45} +(10.4636 + 5.16826i) q^{46} +(7.57923 + 3.13942i) q^{47} +(3.64759 - 1.64168i) q^{48} +(5.13190 - 2.12570i) q^{49} +(6.14587 + 0.406696i) q^{50} +(-6.75135 - 3.60867i) q^{51} +(2.45738 + 3.96288i) q^{52} +(-0.642068 - 0.526932i) q^{53} +(-1.37747 + 0.320270i) q^{54} +(0.631449 - 3.17451i) q^{55} +(-0.657087 - 3.33622i) q^{56} +(0.0370054 - 0.00736084i) q^{57} +(-4.85739 - 1.83167i) q^{58} +(1.13528 + 2.12396i) q^{59} +(1.59188 + 0.211608i) q^{60} +(11.4311 + 1.12587i) q^{61} +(12.1374 + 3.26038i) q^{62} +1.20219i q^{63} +(7.99994 + 0.0301292i) q^{64} +1.87204i q^{65} +(-1.47893 + 5.50561i) q^{66} +(-9.62036 - 0.947523i) q^{67} +(-9.30522 - 12.1584i) q^{68} +(-3.89007 - 7.27781i) q^{69} +(0.481667 - 1.27732i) q^{70} +(-4.05482 + 0.806554i) q^{71} +(-2.77304 - 0.557022i) q^{72} +(1.41126 - 7.09488i) q^{73} +(-1.18900 - 5.11385i) q^{74} +(-3.36668 - 2.76297i) q^{75} +(0.0734680 + 0.0172276i) q^{76} +(4.27389 + 2.28444i) q^{77} +(0.217713 - 3.29001i) q^{78} +(3.50792 - 1.45303i) q^{79} +(2.72317 + 1.70287i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-5.33483 + 10.8009i) q^{82} +(-14.3601 + 4.35608i) q^{83} +(-0.995055 + 2.18882i) q^{84} +(-0.602485 - 6.11713i) q^{85} +(-2.69544 + 1.92897i) q^{86} +(2.03938 + 3.05214i) q^{87} +(-7.24966 + 8.79990i) q^{88} +(3.20933 + 2.14441i) q^{89} +(-0.828294 - 0.776759i) q^{90} +(-2.68219 - 0.813635i) q^{91} +(-1.05877 - 16.4704i) q^{92} +(-5.63766 - 6.86951i) q^{93} +(-1.50712 - 11.5035i) q^{94} +(0.0214220 + 0.0214220i) q^{95} +(-4.58779 - 3.30941i) q^{96} +(-5.54866 + 5.54866i) q^{97} +(-6.22925 - 4.78609i) q^{98} +(3.11605 - 2.55728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	−0.706338	−	1.22519i	−0.499456	−	0.866339i
$2$	−0.706338	−	1.22519i	−0.499456	−	0.866339i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	−1.00217	+	1.73079i	−0.501087	+	0.865397i
$5$	−0.708130	+	0.378503i	−0.316685	+	0.169272i	−0.622079	−	0.782954i	$-0.713712\pi$
$5$	−0.708130	+	0.378503i	−0.316685	+	0.169272i	0.305394	+	0.952226i	$0.401212\pi$
$6$	1.28852	−	0.582847i	0.526037	−	0.237946i
$7$	−0.234536	−	1.17909i	−0.0886463	−	0.445655i	−0.999461	−	0.0328389i	$-0.989545\pi$
$7$	−0.234536	−	1.17909i	−0.0886463	−	0.445655i	0.910814	−	0.412816i	$-0.135455\pi$
$8$	2.82842	+	0.00532616i	0.999998	+	0.00188308i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	0.963917	+	0.600241i	0.304817	+	0.189813i
$11$	−2.55728	+	3.11605i	−0.771049	+	0.939526i	−0.999420	−	0.0340482i	$-0.989160\pi$
$11$	−2.55728	+	3.11605i	−0.771049	+	0.939526i	0.228371	+	0.973574i	$0.426660\pi$
$12$	−1.62423	−	1.16700i	−0.468875	−	0.336883i
$13$	1.09905	−	2.05618i	0.304822	−	0.570282i	−0.682143	−	0.731219i	$-0.738952\pi$
$13$	1.09905	−	2.05618i	0.304822	−	0.570282i	0.986965	+	0.160937i	$0.0514517\pi$
$14$	−1.27895	+	1.12019i	−0.341813	+	0.299383i
$15$	−0.307272	−	0.741820i	−0.0793372	−	0.191537i
$16$	−1.99130	−	3.46911i	−0.497824	−	0.867278i
$17$	−2.92955	+	7.07255i	−0.710520	+	1.71535i	−0.0118212	+	0.999930i	$0.503763\pi$
$17$	−2.92955	+	7.07255i	−0.710520	+	1.71535i	−0.698699	+	0.715416i	$0.746237\pi$
$18$	0.453743	+	1.33945i	0.106948	+	0.315711i
$19$	−0.0109526	−	0.0361057i	−0.00251269	−	0.00828323i	0.955675	−	0.294424i	$-0.0951276\pi$
$19$	−0.0109526	−	0.0361057i	−0.00251269	−	0.00828323i	−0.958188	+	0.286140i	$0.907628\pi$
$20$	0.0545578	−	1.60495i	0.0121995	−	0.358878i
$21$	1.19640	−	0.117835i	0.261077	−	0.0257138i
$22$	5.62406	+	0.932163i	1.19905	+	0.198738i
$23$	−6.86147	+	4.58469i	−1.43072	+	0.955974i	−0.432185	+	0.901785i	$0.642257\pi$
$23$	−6.86147	+	4.58469i	−1.43072	+	0.955974i	−0.998531	+	0.0541888i	$0.982743\pi$
$24$	−0.282534	+	2.81428i	−0.0576721	+	0.574463i
$25$	−2.41967	+	3.62129i	−0.483934	+	0.724258i
$26$	−3.29551	+	0.105813i	−0.646303	+	0.0207517i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	2.27581	+	0.775722i	0.430088	+	0.146598i
$29$	2.83755	−	2.32872i	0.526920	−	0.432432i	−0.332951	−	0.942944i	$-0.608044\pi$
$29$	2.83755	−	2.32872i	0.526920	−	0.432432i	0.859870	+	0.510512i	$0.170544\pi$
$30$	−0.691831	+	0.900441i	−0.126311	+	0.164397i
$31$	−6.28384	+	6.28384i	−1.12861	+	1.12861i	−0.138208	+	0.990403i	$0.544134\pi$
$31$	−6.28384	+	6.28384i	−1.12861	+	1.12861i	−0.990403	+	0.138208i	$0.955866\pi$
$32$	−2.84379	+	4.89008i	−0.502716	+	0.864452i
$33$	−2.85039	−	2.85039i	−0.496190	−	0.496190i
$34$	10.7345	−	1.40636i	1.84095	−	0.241190i
$35$	0.612372	+	0.746178i	0.103510	+	0.126127i
$36$	1.32058	−	1.50202i	0.220096	−	0.250337i
$37$	3.55263	+	1.07768i	0.584049	+	0.177169i	0.568463	−	0.822709i	$-0.307538\pi$
$37$	3.55263	+	1.07768i	0.584049	+	0.177169i	0.0155866	+	0.999879i	$0.495038\pi$
$38$	−0.0365001	+	0.0389218i	−0.00592110	+	0.00631395i
$39$	1.93855	+	1.29530i	0.310417	+	0.207414i
$40$	−2.00491	+	1.06680i	−0.317003	+	0.168675i
$41$	−4.73246	−	7.08262i	−0.739086	−	1.10612i	−0.990402	−	0.138215i	$-0.955864\pi$
$41$	−4.73246	−	7.08262i	−0.739086	−	1.10612i	0.251317	−	0.967905i	$-0.419136\pi$
$42$	−0.989436	−	1.38259i	−0.152673	−	0.213338i
$43$	−0.229727	−	2.33246i	−0.0350331	−	0.355697i	−0.996681	−	0.0814093i	$-0.974058\pi$
$43$	−0.229727	−	2.33246i	−0.0350331	−	0.355697i	0.961648	−	0.274288i	$-0.0884421\pi$
$44$	−2.83041	−	7.54895i	−0.426700	−	1.13805i
$45$	0.768365	−	0.233081i	0.114541	−	0.0347457i
$46$	10.4636	+	5.16826i	1.54278	+	0.762018i
$47$	7.57923	+	3.13942i	1.10554	+	0.457931i	0.859401	−	0.511302i	$-0.170837\pi$
$47$	7.57923	+	3.13942i	1.10554	+	0.457931i	0.246143	+	0.969233i	$0.420837\pi$
$48$	3.64759	−	1.64168i	0.526484	−	0.236955i
$49$	5.13190	−	2.12570i	0.733129	−	0.303672i
$50$	6.14587	+	0.406696i	0.869157	+	0.0575155i
$51$	−6.75135	−	3.60867i	−0.945378	−	0.505315i
$52$	2.45738	+	3.96288i	0.340778	+	0.549553i
$53$	−0.642068	−	0.526932i	−0.0881948	−	0.0723796i	0.589263	−	0.807941i	$-0.299418\pi$
$53$	−0.642068	−	0.526932i	−0.0881948	−	0.0723796i	−0.677458	+	0.735562i	$0.736918\pi$
$54$	−1.37747	+	0.320270i	−0.187450	+	0.0435832i
$55$	0.631449	−	3.17451i	0.0851446	−	0.428051i
$56$	−0.657087	−	3.33622i	−0.0878069	−	0.445821i
$57$	0.0370054	−	0.00736084i	0.00490149	−	0.000974967i
$58$	−4.85739	−	1.83167i	−0.637806	−	0.240510i
$59$	1.13528	+	2.12396i	0.147801	+	0.276516i	0.944917	−	0.327310i	$-0.106142\pi$
$59$	1.13528	+	2.12396i	0.147801	+	0.276516i	−0.797116	+	0.603826i	$0.793642\pi$
$60$	1.59188	+	0.211608i	0.205510	+	0.0273185i
$61$	11.4311	+	1.12587i	1.46360	+	0.144152i	0.798227	−	0.602357i	$-0.205771\pi$
$61$	11.4311	+	1.12587i	1.46360	+	0.144152i	0.665376	+	0.746509i	$0.268271\pi$
$62$	12.1374	+	3.26038i	1.54145	+	0.414068i
$63$			1.20219i			0.151462i
$64$	7.99994	+	0.0301292i	0.999993	+	0.00376616i
$65$			1.87204i			0.232198i
$66$	−1.47893	+	5.50561i	−0.182043	+	0.677694i
$67$	−9.62036	−	0.947523i	−1.17531	−	0.115758i	−0.508554	−	0.861030i	$-0.669820\pi$
$67$	−9.62036	−	0.947523i	−1.17531	−	0.115758i	−0.666761	+	0.745272i	$0.732320\pi$
$68$	−9.30522	−	12.1584i	−1.12842	−	1.47442i
$69$	−3.89007	−	7.27781i	−0.468309	−	0.876145i
$70$	0.481667	−	1.27732i	0.0575702	−	0.152670i
$71$	−4.05482	+	0.806554i	−0.481219	+	0.0957203i	−0.429738	−	0.902954i	$-0.641394\pi$
$71$	−4.05482	+	0.806554i	−0.481219	+	0.0957203i	−0.0514807	+	0.998674i	$0.516394\pi$
$72$	−2.77304	−	0.557022i	−0.326805	−	0.0656456i
$73$	1.41126	−	7.09488i	0.165175	−	0.830392i	−0.805980	−	0.591943i	$-0.798361\pi$
$73$	1.41126	−	7.09488i	0.165175	−	0.830392i	0.971155	−	0.238449i	$-0.0766390\pi$
$74$	−1.18900	−	5.11385i	−0.138218	−	0.594473i
$75$	−3.36668	−	2.76297i	−0.388751	−	0.319040i
$76$	0.0734680	+	0.0172276i	0.00842735	+	0.00197614i
$77$	4.27389	+	2.28444i	0.487055	+	0.260336i
$78$	0.217713	−	3.29001i	0.0246511	−	0.372521i
$79$	3.50792	−	1.45303i	0.394672	−	0.163479i	−0.176516	−	0.984298i	$-0.556483\pi$
$79$	3.50792	−	1.45303i	0.394672	−	0.163479i	0.571188	+	0.820819i	$0.306483\pi$
$80$	2.72317	+	1.70287i	0.304459	+	0.190387i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−5.33483	+	10.8009i	−0.589134	+	1.19276i
$83$	−14.3601	+	4.35608i	−1.57622	+	0.478142i	−0.952763	−	0.303714i	$-0.901773\pi$
$83$	−14.3601	+	4.35608i	−1.57622	+	0.478142i	−0.623460	+	0.781856i	$0.714273\pi$
$84$	−0.995055	+	2.18882i	−0.108569	+	0.238820i
$85$	−0.602485	−	6.11713i	−0.0653486	−	0.663496i
$86$	−2.69544	+	1.92897i	−0.290657	+	0.208006i
$87$	2.03938	+	3.05214i	0.218644	+	0.327224i
$88$	−7.24966	+	8.79990i	−0.772817	+	0.938072i
$89$	3.20933	+	2.14441i	0.340188	+	0.227307i	0.713915	−	0.700232i	$-0.246920\pi$
$89$	3.20933	+	2.14441i	0.340188	+	0.227307i	−0.373727	+	0.927539i	$0.621920\pi$
$90$	−0.828294	−	0.776759i	−0.0873098	−	0.0818775i
$91$	−2.68219	−	0.813635i	−0.281170	−	0.0852921i
$92$	−1.05877	−	16.4704i	−0.110384	−	1.71716i
$93$	−5.63766	−	6.86951i	−0.584598	−	0.712335i
$94$	−1.50712	−	11.5035i	−0.155447	−	1.18649i
$95$	0.0214220	+	0.0214220i	0.00219785	+	0.00219785i
$96$	−4.58779	−	3.30941i	−0.468239	−	0.337765i
$97$	−5.54866	+	5.54866i	−0.563381	+	0.563381i	−0.930266	−	0.366885i	$-0.880424\pi$
$97$	−5.54866	+	5.54866i	−0.563381	+	0.563381i	0.366885	+	0.930266i	$0.380424\pi$
$98$	−6.22925	−	4.78609i	−0.629249	−	0.483468i
$99$	3.11605	−	2.55728i	0.313175	−	0.257016i
$100$	−3.84278	−	7.81711i	−0.384278	−	0.781711i
$101$	5.18030	−	17.0772i	0.515459	−	1.69924i	−0.182589	−	0.983189i	$-0.558448\pi$
$101$	5.18030	−	17.0772i	0.515459	−	1.69924i	0.698048	−	0.716051i	$-0.254052\pi$
$102$	0.347431	+	10.8206i	0.0344008	+	1.07140i
$103$	−2.67401	+	4.00194i	−0.263478	+	0.394323i	−0.939495	−	0.342563i	$-0.888705\pi$
$103$	−2.67401	+	4.00194i	−0.263478	+	0.394323i	0.676016	+	0.736887i	$0.263705\pi$
$104$	3.11953	−	5.80989i	0.305895	−	0.569707i
$105$	−0.802608	+	0.536285i	−0.0783265	+	0.0523361i
$106$	−0.192074	+	1.15885i	−0.0186558	+	0.112557i
$107$	18.4494	−	1.81711i	1.78357	−	0.175667i	0.848282	−	0.529544i	$-0.177637\pi$
$107$	18.4494	−	1.81711i	1.78357	−	0.175667i	0.935292	+	0.353877i	$0.115137\pi$
$108$	1.36535	+	1.46144i	0.131381	+	0.140627i
$109$	1.35154	+	4.45544i	0.129454	+	0.426754i	0.997575	−	0.0695995i	$-0.0221721\pi$
$109$	1.35154	+	4.45544i	0.129454	+	0.426754i	−0.868121	+	0.496353i	$0.834672\pi$
$110$	−4.33539	+	1.46863i	−0.413363	+	0.140029i
$111$	−1.42071	+	3.42989i	−0.134848	+	0.325551i
$112$	−3.62337	+	3.16155i	−0.342377	+	0.298739i
$113$	1.69590	+	4.09425i	0.159536	+	0.385155i	0.983354	−	0.181700i	$-0.0581600\pi$
$113$	1.69590	+	4.09425i	0.159536	+	0.385155i	−0.823818	+	0.566855i	$0.808160\pi$
$114$	−0.0351567	−	0.0401394i	−0.00329273	−	0.00375940i
$115$	3.12349	−	5.84364i	0.291267	−	0.544923i
$116$	1.18681	+	7.24499i	0.110193	+	0.672681i
$117$	−1.47907	+	1.80226i	−0.136740	+	0.166619i
$118$	1.80036	−	2.89117i	0.165737	−	0.266154i
$119$	9.02628	+	1.79544i	0.827438	+	0.164588i
$120$	−0.865143	−	2.09982i	−0.0789764	−	0.191686i
$121$	−1.02412	−	5.14861i	−0.0931021	−	0.468056i
$122$	−6.69482	−	14.8005i	−0.606121	−	1.33997i
$123$	7.51238	−	4.01545i	0.677368	−	0.362061i
$124$	−4.57854	−	17.1735i	−0.411165	−	1.54223i
$125$	0.736279	−	7.47556i	0.0658548	−	0.668635i
$126$	1.47291	−	0.849154i	0.131217	−	0.0756486i
$127$	2.60665			0.231303			0.115651	−	0.993290i	$-0.463104\pi$
$127$	2.60665			0.231303			0.115651	+	0.993290i	$0.463104\pi$
$128$	−5.61375	−	9.82272i	−0.496190	−	0.868214i
$129$	2.34375			0.206355
$130$	2.29360	−	1.32229i	0.201162	−	0.115973i
$131$	−1.43500	+	14.5698i	−0.125376	+	1.27297i	0.702348	+	0.711834i	$0.252135\pi$
$131$	−1.43500	+	14.5698i	−0.125376	+	1.27297i	−0.827724	+	0.561135i	$0.810365\pi$
$132$	7.79003	−	2.07685i	0.678035	−	0.180767i
$133$	−0.0400032	+	0.0213822i	−0.00346872	+	0.00185407i
$134$	5.63433	+	12.4560i	0.486732	+	1.07604i
$135$	0.156646	+	0.787512i	0.0134819	+	0.0677782i
$136$	−8.32367	+	19.9886i	−0.713749	+	1.71401i
$137$	−15.8803	−	3.15879i	−1.35675	−	0.269874i	−0.537476	−	0.843279i	$-0.680622\pi$
$137$	−15.8803	−	3.15879i	−1.35675	−	0.269874i	−0.819272	+	0.573405i	$0.805622\pi$
$138$	−6.16899	+	9.90666i	−0.525139	+	0.843311i
$139$	−0.251702	+	0.306700i	−0.0213491	+	0.0260139i	−0.783576	−	0.621297i	$-0.786606\pi$
$139$	−0.251702	+	0.306700i	−0.0213491	+	0.0260139i	0.762226	+	0.647310i	$0.224106\pi$
$140$	−1.90518	+	0.312091i	−0.161017	+	0.0263765i
$141$	−3.86720	+	7.23502i	−0.325677	+	0.609298i
$142$	3.85225	+	4.39822i	0.323274	+	0.369090i
$143$	3.59659	+	8.68293i	0.300762	+	0.726103i
$144$	1.27624	+	3.79094i	0.106354	+	0.315911i
$145$	−1.12793	+	2.72306i	−0.0936692	+	0.226137i
$146$	−9.68938	+	3.28232i	−0.801899	+	0.271647i
$147$	1.61245	+	5.31555i	0.132993	+	0.438419i
$148$	−5.42559	+	5.06885i	−0.445981	+	0.416657i
$149$	2.72805	−	0.268690i	0.223491	−	0.0220119i	0.0143481	−	0.999897i	$-0.495433\pi$
$149$	2.72805	−	0.268690i	0.223491	−	0.0220119i	0.209143	+	0.977885i	$0.432933\pi$
$150$	−1.00714	+	6.07641i	−0.0822324	+	0.496137i
$151$	11.6737	−	7.80011i	0.949991	−	0.634764i	0.0190057	−	0.999819i	$-0.493950\pi$
$151$	11.6737	−	7.80011i	0.949991	−	0.634764i	0.930986	+	0.365055i	$0.118950\pi$
$152$	−0.0307862	−	0.102181i	−0.00249709	−	0.00828794i
$153$	4.25304	−	6.36513i	0.343838	−	0.514590i
$154$	−0.219939	−	6.84991i	−0.0177232	−	0.551982i
$155$	2.07132	−	6.82823i	0.166373	−	0.548457i
$156$	−4.18467	+	2.05712i	−0.335041	+	0.164702i
$157$	3.80109	−	3.11948i	0.303360	−	0.248961i	−0.470381	−	0.882464i	$-0.655883\pi$
$157$	3.80109	−	3.11948i	0.303360	−	0.248961i	0.773741	+	0.633502i	$0.218383\pi$
$158$	−4.25801	−	3.27154i	−0.338749	−	0.260269i
$159$	0.587328	−	0.587328i	0.0465781	−	0.0465781i
$160$	0.162861	−	4.53919i	0.0128753	−	0.358855i
$161$	7.01503	+	7.01503i	0.552862	+	0.552862i
$162$	−0.183712	−	1.40223i	−0.0144338	−	0.110170i
$163$	−5.14221	−	6.26580i	−0.402769	−	0.490775i	0.531644	−	0.846968i	$-0.321575\pi$
$163$	−5.14221	−	6.26580i	−0.402769	−	0.490775i	−0.934412	+	0.356193i	$0.884075\pi$
$164$	17.0013	−	1.09289i	1.32758	−	0.0853405i
$165$	3.09733	+	0.939565i	0.241127	+	0.0731450i
$166$	15.4801	+	14.5169i	1.20149	+	1.12673i
$167$	−2.30151	−	1.53782i	−0.178096	−	0.119000i	0.463327	−	0.886187i	$-0.346656\pi$
$167$	−2.30151	−	1.53782i	−0.178096	−	0.119000i	−0.641423	+	0.767188i	$0.721656\pi$
$168$	3.38456	−	0.326916i	0.261125	−	0.0252221i
$169$	4.20245	+	6.28941i	0.323265	+	0.483801i
$170$	−7.06908	+	5.05892i	−0.542174	+	0.388001i
$171$	0.00369823	+	0.0375487i	0.000282810	+	0.00287142i
$172$	4.26724	+	1.93992i	0.325374	+	0.147918i
$173$	10.3468	−	3.13866i	0.786651	−	0.238628i	0.128695	−	0.991684i	$-0.458921\pi$
$173$	10.3468	−	3.13866i	0.786651	−	0.238628i	0.657956	+	0.753056i	$0.271421\pi$
$174$	2.29896	−	4.65446i	0.174284	−	0.352854i
$175$	4.83733	+	2.00369i	0.365668	+	0.151465i
$176$	15.9022	+	2.66650i	1.19868	+	0.200995i
$177$	−2.22501	+	0.921630i	−0.167242	+	0.0692739i
$178$	0.360430	−	5.44671i	0.0270154	−	0.408248i
$179$	12.7564	+	6.81843i	0.953456	+	0.509633i	0.873318	−	0.487151i	$-0.161964\pi$
$179$	12.7564	+	6.81843i	0.953456	+	0.509633i	0.0801384	+	0.996784i	$0.474464\pi$
$180$	−0.366620	+	1.56347i	−0.0273263	+	0.116534i
$181$	0.924467	+	0.758691i	0.0687151	+	0.0563930i	0.668124	−	0.744050i	$-0.267098\pi$
$181$	0.924467	+	0.758691i	0.0687151	+	0.0563930i	−0.599409	+	0.800443i	$0.704598\pi$
$182$	0.897679	+	3.86089i	0.0665404	+	0.286189i
$183$	−2.24089	+	11.2657i	−0.165651	+	0.832785i
$184$	−19.4316	+	12.9309i	−1.43251	+	0.953278i
$185$	−2.92363	+	0.581546i	−0.214949	+	0.0427561i
$186$	−4.43435	+	11.7594i	−0.325142	+	0.862240i
$187$	−14.5468	−	27.2151i	−1.06377	−	1.99017i
$188$	−13.0294	+	9.97184i	−0.950266	+	0.727271i
$189$	−1.19640	−	0.117835i	−0.0870255	−	0.00857127i
$190$	0.0111148	−	0.0413771i	0.000806353	−	0.00300181i
$191$			11.0518i			0.799679i	0.916585	+	0.399839i	$0.130934\pi$
$191$			11.0518i			0.799679i	−0.916585	+	0.399839i	$0.869066\pi$
$192$	−0.814116	+	7.95847i	−0.0587537	+	0.574353i
$193$			12.9246i			0.930333i	0.885223	+	0.465166i	$0.154005\pi$
$193$			12.9246i			0.930333i	−0.885223	+	0.465166i	$0.845995\pi$
$194$	10.7174	+	2.87893i	0.769463	+	0.206695i
$195$	−1.86302	−	0.183492i	−0.133414	−	0.0131401i
$196$	−1.46390	+	11.0126i	−0.104564	+	0.786614i
$197$	8.02636	+	15.0163i	0.571854	+	1.06986i	0.987092	+	0.160151i	$0.0511982\pi$
$197$	8.02636	+	15.0163i	0.571854	+	1.06986i	−0.415238	+	0.909713i	$0.636302\pi$
$198$	−5.33414	−	2.01145i	−0.379081	−	0.142948i
$199$	−11.4197	+	2.27152i	−0.809520	+	0.161024i	−0.582462	−	0.812858i	$-0.697911\pi$
$199$	−11.4197	+	2.27152i	−0.809520	+	0.161024i	−0.227058	+	0.973881i	$0.572911\pi$
$200$	−6.86313	+	10.2296i	−0.485297	+	0.723345i
$201$	1.88592	−	9.48116i	0.133023	−	0.668750i
$202$	−24.5818	+	5.71540i	−1.72957	+	0.402134i
$203$	−3.41128	−	2.79957i	−0.239425	−	0.196491i
$204$	13.0119	−	8.06868i	0.911015	−	0.564921i
$205$	6.03199	+	3.22416i	0.421292	+	0.225185i
$206$	6.79189	+	0.449446i	0.473214	+	0.0313144i
$207$	7.62406	−	3.15799i	0.529909	−	0.219495i
$208$	−9.32166	+	0.281732i	−0.646341	+	0.0195346i
$209$	0.140516	+	0.0582037i	0.00971971	+	0.00402604i
$210$	1.22396	+	0.604547i	0.0844614	+	0.0417177i
$211$	−8.66194	+	2.62757i	−0.596312	+	0.180889i	−0.573991	−	0.818861i	$-0.694606\pi$
$211$	−8.66194	+	2.62757i	−0.596312	+	0.180889i	−0.0223211	+	0.999751i	$0.507106\pi$
$212$	1.55547	−	0.583211i	0.106830	−	0.0400551i
$213$	−0.405228	−	4.11435i	−0.0277658	−	0.281911i
$214$	−15.2578	−	21.3205i	−1.04300	−	1.45744i
$215$	1.04552	+	1.56473i	0.0713039	+	0.106714i
$216$	0.826144	−	2.70509i	0.0562120	−	0.184058i
$217$	8.88302	+	5.93544i	0.603019	+	0.402924i
$218$	4.50411	−	4.80294i	0.305057	−	0.325296i
$219$	6.92238	+	2.09988i	0.467771	+	0.141897i
$220$	4.86160	+	4.27432i	0.327769	+	0.288174i
$221$	11.3227	+	13.7968i	0.761649	+	0.928072i
$222$	5.20577	−	0.682028i	0.349388	−	0.0457747i
$223$	6.19167	+	6.19167i	0.414625	+	0.414625i	0.883346	−	0.468721i	$-0.155285\pi$
$223$	6.19167	+	6.19167i	0.414625	+	0.414625i	−0.468721	+	0.883346i	$0.655285\pi$
$224$	6.43283	+	2.20619i	0.429811	+	0.147407i
$225$	3.07965	−	3.07965i	0.205310	−	0.205310i
$226$	3.81836	−	4.96972i	0.253993	−	0.330581i
$227$	−0.610813	+	0.501281i	−0.0405411	+	0.0332712i	−0.654446	−	0.756109i	$-0.727098\pi$
$227$	−0.610813	+	0.501281i	−0.0405411	+	0.0332712i	0.613905	+	0.789380i	$0.289598\pi$
$228$	−0.0243458	+	0.0714256i	−0.00161234	+	0.00473028i
$229$	−5.45636	+	17.9872i	−0.360566	+	1.18863i	0.569734	+	0.821829i	$0.307046\pi$
$229$	−5.45636	+	17.9872i	−0.360566	+	1.18863i	−0.930300	+	0.366799i	$0.880454\pi$
$230$	−9.36581	+	0.300720i	−0.617563	+	0.0198289i
$231$	−2.69236	+	4.02940i	−0.177144	+	0.265115i
$232$	8.03819	−	6.57148i	0.527733	−	0.431439i
$233$	0.717014	−	0.479093i	0.0469731	−	0.0313865i	−0.531862	−	0.846831i	$-0.678507\pi$
$233$	0.717014	−	0.479093i	0.0469731	−	0.0313865i	0.578835	+	0.815445i	$0.303507\pi$
$234$	3.25283	+	0.539142i	0.212644	+	0.0352448i
$235$	−6.55536	+	0.645646i	−0.427624	+	0.0421173i
$236$	−4.81389	−	0.163640i	−0.313357	−	0.0106521i
$237$	1.10220	+	3.63345i	0.0715953	+	0.236018i
$238$	−4.17585	−	12.3271i	−0.270680	−	0.799046i
$239$	9.80730	−	23.6769i	0.634381	−	1.53153i	−0.199681	−	0.979861i	$-0.563990\pi$
$239$	9.80730	−	23.6769i	0.634381	−	1.53153i	0.834062	−	0.551671i	$-0.186010\pi$
$240$	−1.96159	+	2.54314i	−0.126620	+	0.164159i
$241$	6.80136	+	16.4199i	0.438114	+	1.05770i	0.976600	+	0.215066i	$0.0689967\pi$
$241$	6.80136	+	16.4199i	0.438114	+	1.05770i	−0.538485	+	0.842635i	$0.681003\pi$
$242$	−5.58464	+	4.89140i	−0.358995	+	0.314431i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	−13.4046	+	18.6566i	−0.858141	+	1.19436i
$245$	−2.82947	+	3.44772i	−0.180768	+	0.220267i
$246$	−10.2260	−	6.36782i	−0.651983	−	0.405997i
$247$	−0.0862774	−	0.0171616i	−0.00548970	−	0.00109197i
$248$	−17.8068	+	17.7399i	−1.13073	+	1.12648i
$249$	−2.92757	−	14.7179i	−0.185527	−	0.932709i
$250$	−9.67903	+	4.37819i	−0.612156	+	0.276901i
$251$	10.4324	−	5.57622i	0.658486	−	0.351968i	−0.108072	−	0.994143i	$-0.534468\pi$
$251$	10.4324	−	5.57622i	0.658486	−	0.351968i	0.766558	+	0.642175i	$0.221968\pi$
$252$	−2.08075	−	1.20481i	−0.131075	−	0.0758956i
$253$	3.26056	−	33.1051i	0.204990	−	2.08130i
$254$	−1.84117	−	3.19363i	−0.115526	−	0.200386i
$255$	6.14673			0.384923
$256$	−8.06948	+	13.8161i	−0.504342	+	0.863504i
$257$	−20.2919			−1.26578			−0.632888	−	0.774243i	$-0.718131\pi$
$257$	−20.2919			−1.26578			−0.632888	+	0.774243i	$0.718131\pi$
$258$	−1.65548	−	2.87153i	−0.103066	−	0.178774i
$259$	0.437463	−	4.44164i	0.0271826	−	0.275990i
$260$	−3.24011	−	1.87611i	−0.200943	−	0.116351i
$261$	−3.23734	+	1.73039i	−0.200386	+	0.107109i
$262$	18.8643	−	8.53305i	1.16544	−	0.527174i
$263$	−3.40713	−	17.1288i	−0.210093	−	1.05621i	−0.931513	−	0.363709i	$-0.881510\pi$
$263$	−3.40713	−	17.1288i	−0.210093	−	1.05621i	0.721420	−	0.692498i	$-0.243490\pi$
$264$	−8.04693	−	8.07730i	−0.495254	−	0.497123i
$265$	0.654113	+	0.130111i	0.0401818	+	0.00799266i
$266$	0.0544530	+	0.0339085i	0.00333873	+	0.00207906i
$267$	−2.44865	+	2.98369i	−0.149855	+	0.182599i
$268$	11.2812	−	15.7013i	0.689111	−	0.959108i
$269$	−3.06166	+	5.72797i	−0.186673	+	0.349240i	−0.957797	−	0.287444i	$-0.907195\pi$
$269$	−3.06166	+	5.72797i	−0.186673	+	0.349240i	0.771125	+	0.636684i	$0.219695\pi$
$270$	0.854205	−	0.748170i	0.0519853	−	0.0455322i
$271$	1.09438	+	2.64206i	0.0664787	+	0.160494i	0.953627	−	0.300990i	$-0.0973172\pi$
$271$	1.09438	+	2.64206i	0.0664787	+	0.160494i	−0.887149	+	0.461484i	$0.847317\pi$
$272$	30.3691	−	3.92062i	1.84140	−	0.237722i
$273$	1.07262	−	2.58953i	0.0649178	−	0.156725i
$274$	7.34676	+	21.6876i	0.443834	+	1.31019i
$275$	−5.09637	−	16.8005i	−0.307322	−	1.01311i
$276$	16.4949	+	0.560718i	0.992877	+	0.0337513i
$277$	−28.4820	+	2.80523i	−1.71132	+	0.168550i	−0.905709	−	0.423899i	$-0.860661\pi$
$277$	−28.4820	+	2.80523i	−1.71132	+	0.168550i	−0.805608	+	0.592449i	$0.798161\pi$
$278$	0.553551	+	0.0917487i	0.0331998	+	0.00550272i
$279$	7.38902	−	4.93718i	0.442369	−	0.295581i
$280$	1.72807	+	2.11377i	0.103272	+	0.126322i
$281$	−15.1021	+	22.6020i	−0.900918	+	1.34832i	0.0362136	+	0.999344i	$0.488470\pi$
$281$	−15.1021	+	22.6020i	−0.900918	+	1.34832i	−0.937132	+	0.348975i	$0.886530\pi$
$282$	11.5958	−	0.372321i	0.690520	−	0.0221714i
$283$	5.25377	−	17.3194i	0.312304	−	1.02953i	−0.650540	−	0.759472i	$-0.725457\pi$
$283$	5.25377	−	17.3194i	0.312304	−	1.02953i	0.962844	−	0.270057i	$-0.0870426\pi$
$284$	2.66766	−	7.82637i	0.158296	−	0.464409i
$285$	−0.0234185	+	0.0192191i	−0.00138719	+	0.00113844i
$286$	8.09782	−	10.5396i	0.478834	−	0.623219i
$287$	−7.24113	+	7.24113i	−0.427431	+	0.427431i
$288$	3.74315	−	4.24132i	0.220567	−	0.249922i
$289$	−29.4180	−	29.4180i	−1.73047	−	1.73047i
$290$	4.13295	−	0.541475i	0.242695	−	0.0317965i
$291$	−4.97808	−	6.06581i	−0.291820	−	0.355584i
$292$	10.8654	+	9.55289i	0.635852	+	0.559041i
$293$	−19.0688	−	5.78444i	−1.11401	−	0.337931i	−0.320962	−	0.947092i	$-0.604006\pi$
$293$	−19.0688	−	5.78444i	−1.11401	−	0.337931i	−0.793046	+	0.609161i	$0.791506\pi$
$294$	5.37361	−	5.73013i	0.313395	−	0.334188i
$295$	−1.60785	−	1.07433i	−0.0936128	−	0.0625501i
$296$	10.0426	+	3.06705i	0.583714	+	0.178269i
$297$	2.23954	+	3.35171i	0.129951	+	0.194486i
$298$	−2.25612	−	3.15259i	−0.130694	−	0.182625i
$299$	1.88584	+	19.1472i	0.109061	+	1.10731i
$300$	8.15612	−	3.05806i	0.470894	−	0.176557i
$301$	−2.69631	+	0.817916i	−0.155413	+	0.0471439i
$302$	−17.8022	−	8.79296i	−1.02440	−	0.505978i
$303$	16.4872	+	6.82921i	0.947163	+	0.392328i
$304$	−0.103445	+	0.109893i	−0.00593298	+	0.00630279i
$305$	−8.52085	+	3.52945i	−0.487902	+	0.202096i
$306$	−10.8026	−	0.714848i	−0.617542	−	0.0408651i
$307$	−14.3186	−	7.65345i	−0.817206	−	0.436806i	0.00914715	−	0.999958i	$-0.497088\pi$
$307$	−14.3186	−	7.65345i	−0.817206	−	0.436806i	−0.826353	+	0.563153i	$0.809588\pi$
$308$	−8.23708	+	5.10782i	−0.469351	+	0.291045i
$309$	−3.72057	−	3.05340i	−0.211656	−	0.173702i
$310$	−9.82892	+	2.28528i	−0.558245	+	0.129795i
$311$	3.44271	−	17.3077i	0.195218	−	0.981429i	−0.751590	−	0.659631i	$-0.770713\pi$
$311$	3.44271	−	17.3077i	0.195218	−	0.981429i	0.946808	−	0.321798i	$-0.104287\pi$
$312$	5.47615	+	3.67398i	0.310026	+	0.207998i
$313$	17.2027	−	3.42182i	0.972353	−	0.193413i	0.316742	−	0.948512i	$-0.397411\pi$
$313$	17.2027	−	3.42182i	0.972353	−	0.193413i	0.655611	+	0.755099i	$0.272411\pi$
$314$	−6.50680	−	2.45365i	−0.367200	−	0.138468i
$315$	−0.455034	−	0.851308i	−0.0256382	−	0.0479658i
$316$	−1.00065	+	7.52768i	−0.0562911	+	0.423465i
$317$	10.9099	+	1.07453i	0.612762	+	0.0603518i	0.399637	−	0.916673i	$-0.369136\pi$
$317$	10.9099	+	1.07453i	0.612762	+	0.0603518i	0.213124	+	0.977025i	$0.431636\pi$
$318$	−1.13444	−	0.304736i	−0.0636162	−	0.0170887i
$319$			14.7971i			0.828481i
$320$	−5.67640	+	3.00667i	−0.317320	+	0.168078i
$321$			18.5387i			1.03473i
$322$	3.63976	−	13.5497i	0.202836	−	0.755097i
$323$	0.287446	+	0.0283109i	0.0159939	+	0.00157526i
$324$	−1.58823	+	1.21553i	−0.0882352	+	0.0675294i
$325$	4.78669	+	8.95526i	0.265518	+	0.496748i
$326$	−4.04465	+	10.7259i	−0.224012	+	0.594055i
$327$	−4.56646	+	0.908325i	−0.252526	+	0.0502305i
$328$	−13.3477	−	20.0579i	−0.737001	−	1.10751i
$329$	1.92406	−	9.67292i	0.106077	−	0.533285i
$330$	−1.03662	−	4.45846i	−0.0570639	−	0.245430i
$331$	0.149538	+	0.122723i	0.00821937	+	0.00674546i	0.638494	−	0.769627i	$-0.279558\pi$
$331$	0.149538	+	0.122723i	0.00821937	+	0.00674546i	−0.630275	+	0.776372i	$0.717058\pi$
$332$	6.85181	−	29.2199i	0.376042	−	1.60365i
$333$	−3.27412	−	1.75006i	−0.179421	−	0.0959025i
$334$	−0.258475	+	3.90600i	−0.0141431	+	0.213727i
$335$	7.17110	−	2.97037i	0.391799	−	0.162289i
$336$	−2.79118	−	3.91581i	−0.152271	−	0.213625i
$337$	20.9217	+	8.66607i	1.13968	+	0.472071i	0.871060	−	0.491176i	$-0.163433\pi$
$337$	20.9217	+	8.66607i	1.13968	+	0.472071i	0.268619	+	0.963247i	$0.413433\pi$
$338$	4.73736	−	9.59124i	0.257679	−	0.521695i
$339$	−4.24077	+	1.28642i	−0.230327	+	0.0698689i
$340$	11.1913	+	5.08765i	0.606933	+	0.275916i
$341$	−3.51125	−	35.6503i	−0.190145	−	1.93057i
$342$	0.0433921	−	0.0310531i	0.00234637	−	0.00167916i
$343$	−8.38533	−	12.5495i	−0.452766	−	0.677611i
$344$	−0.637343	−	6.59841i	−0.0343632	−	0.355762i
$345$	5.50935	+	3.68123i	0.296613	+	0.198191i
$346$	−11.1538	−	10.4598i	−0.599630	−	0.562322i
$347$	−6.86478	−	2.08241i	−0.368521	−	0.111789i	0.100592	−	0.994928i	$-0.467926\pi$
$347$	−6.86478	−	2.08241i	−0.368521	−	0.111789i	−0.469113	+	0.883138i	$0.655426\pi$
$348$	−7.32644	+	0.470964i	−0.392738	+	0.0252463i
$349$	17.1980	+	20.9558i	0.920588	+	1.12174i	0.992243	+	0.124310i	$0.0396716\pi$
$349$	17.1980	+	20.9558i	0.920588	+	1.12174i	−0.0716560	+	0.997429i	$0.522828\pi$
$350$	−0.961895	−	7.34193i	−0.0514155	−	0.392443i
$351$	−1.64860	−	1.64860i	−0.0879960	−	0.0879960i
$352$	−7.96539	−	21.3667i	−0.424557	−	1.13885i
$353$	−19.9037	+	19.9037i	−1.05937	+	1.05937i	−0.0612457	+	0.998123i	$0.519507\pi$
$353$	−19.9037	+	19.9037i	−1.05937	+	1.05937i	−0.998123	+	0.0612457i	$0.980493\pi$
$354$	2.70078	+	2.07508i	0.143545	+	0.110289i
$355$	2.56606	−	2.10591i	0.136192	−	0.111770i
$356$	−6.92783	+	3.40562i	−0.367174	+	0.180498i
$357$	−2.67152	+	8.80683i	−0.141392	+	0.466107i
$358$	−0.656456	−	20.4451i	−0.0346948	−	1.08056i
$359$	−0.985880	+	1.47547i	−0.0520327	+	0.0778725i	−0.856574	−	0.516024i	$-0.827411\pi$
$359$	−0.985880	+	1.47547i	−0.0520327	+	0.0778725i	0.804541	+	0.593897i	$0.202411\pi$
$360$	2.17450	−	0.655159i	0.114606	−	0.0345299i
$361$	15.7967	−	10.5550i	0.831407	−	0.555529i
$362$	0.276553	−	1.66854i	0.0145353	−	0.0876964i
$363$	5.22420	−	0.514539i	0.274200	−	0.0270063i
$364$	4.09626	−	3.82692i	0.214702	−	0.200585i
$365$	1.68608	+	5.55826i	0.0882534	+	0.290933i
$366$	15.3854	−	5.21188i	0.804210	−	0.272430i
$367$	−14.0137	+	33.8321i	−0.731511	+	1.76602i	−0.0940128	+	0.995571i	$0.529969\pi$
$367$	−14.0137	+	33.8321i	−0.731511	+	1.76602i	−0.637498	+	0.770452i	$0.720031\pi$
$368$	29.5680	+	14.6737i	1.54134	+	0.764922i
$369$	3.25977	+	7.86979i	0.169697	+	0.409685i
$370$	2.77757	+	3.17123i	0.144399	+	0.164864i
$371$	−0.470713	+	0.880642i	−0.0244382	+	0.0457207i
$372$	17.5396	−	2.87319i	0.909387	−	0.148968i
$373$	−19.7399	+	24.0532i	−1.02209	+	1.24543i	−0.0530371	+	0.998593i	$0.516890\pi$
$373$	−19.7399	+	24.0532i	−1.02209	+	1.24543i	−0.969058	+	0.246834i	$0.920610\pi$
$374$	−23.0687	+	37.0456i	−1.19286	+	1.91558i
$375$	7.36740	+	1.46547i	0.380451	+	0.0756764i
$376$	21.4205	+	8.91997i	1.10468	+	0.460012i
$377$	−1.66965	−	8.39390i	−0.0859913	−	0.432308i
$378$	0.700694	+	1.54905i	0.0360398	+	0.0796746i
$379$	12.0305	−	6.43045i	0.617967	−	0.330310i	−0.132535	−	0.991178i	$-0.542312\pi$
$379$	12.0305	−	6.43045i	0.617967	−	0.330310i	0.750502	+	0.660868i	$0.229812\pi$
$380$	−0.0585456	+	0.0156085i	−0.00300332	+	0.000800698i
$381$	−0.255496	+	2.59410i	−0.0130895	+	0.132900i
$382$	13.5405	−	7.80629i	0.692793	−	0.399405i
$383$	−18.8456			−0.962968			−0.481484	−	0.876455i	$-0.659902\pi$
$383$	−18.8456			−0.962968			−0.481484	+	0.876455i	$0.659902\pi$
$384$	10.3257	−	4.62392i	0.526929	−	0.235964i
$385$	−3.89114			−0.198311
$386$	15.8351	−	9.12913i	0.805983	−	0.464660i
$387$	−0.229727	+	2.33246i	−0.0116777	+	0.118566i
$388$	−4.04287	−	15.1643i	−0.205245	−	0.769851i
$389$	24.2368	−	12.9548i	1.22885	−	0.656835i	0.276259	−	0.961083i	$-0.410905\pi$
$389$	24.2368	−	12.9548i	1.22885	−	0.656835i	0.952593	+	0.304248i	$0.0984052\pi$
$390$	1.09111	+	2.41216i	0.0552506	+	0.122145i
$391$	−12.3245	−	61.9592i	−0.623274	−	3.13341i
$392$	14.5265	−	5.98506i	0.733700	−	0.302291i
$393$	−14.3590	−	2.85618i	−0.724315	−	0.144075i
$394$	12.7284	−	20.4403i	0.641249	−	1.02977i
$395$	−1.93409	+	2.35669i	−0.0973145	+	0.118578i
$396$	1.30330	+	7.95609i	0.0654932	+	0.399808i
$397$	−5.90303	+	11.0438i	−0.296264	+	0.554272i	−0.985378	−	0.170381i	$-0.945500\pi$
$397$	−5.90303	+	11.0438i	−0.296264	+	0.554272i	0.689114	+	0.724653i	$0.258000\pi$
$398$	10.8492	+	12.3868i	0.543821	+	0.620895i
$399$	−0.0173582	−	0.0419064i	−0.000868998	−	0.00209795i
$400$	17.3809	+	1.18304i	0.869047	+	0.0591521i
$401$	5.35389	−	12.9254i	0.267360	−	0.645465i	−0.731997	−	0.681308i	$-0.761412\pi$
$401$	5.35389	−	12.9254i	0.267360	−	0.645465i	0.999357	+	0.0358428i	$0.0114116\pi$
$402$	−12.9483	+	4.38630i	−0.645803	+	0.218769i
$403$	6.01445	+	19.8270i	0.299601	+	0.987652i
$404$	24.3655	+	26.0803i	1.21223	+	1.29754i
$405$	−0.799073	+	0.0787019i	−0.0397063	+	0.00391073i
$406$	−1.02048	+	6.15690i	−0.0506455	+	0.305562i
$407$	−12.4432	+	8.31427i	−0.616786	+	0.412123i
$408$	−19.0765	−	10.2428i	−0.944425	−	0.507095i
$409$	−7.00667	+	10.4862i	−0.346458	+	0.518510i	−0.963247	−	0.268618i	$-0.913433\pi$
$409$	−7.00667	+	10.4862i	−0.346458	+	0.518510i	0.616789	+	0.787128i	$0.288433\pi$
$410$	−0.310412	−	9.66767i	−0.0153302	−	0.477452i
$411$	4.70013	−	15.4942i	0.231840	−	0.764274i
$412$	−4.24672	−	8.63881i	−0.209221	−	0.425604i
$413$	2.23808	−	1.83675i	0.110129	−	0.0903804i
$414$	−9.25429	−	7.11030i	−0.454824	−	0.349452i
$415$	8.52000	−	8.52000i	0.418231	−	0.418231i
$416$	6.92941	+	11.2218i	0.339743	+	0.550194i
$417$	−0.280552	−	0.280552i	−0.0137387	−	0.0137387i
$418$	−0.0279414	−	0.213270i	−0.00136666	−	0.0104314i
$419$	19.3028	+	23.5205i	0.943003	+	1.14905i	0.988671	+	0.150096i	$0.0479583\pi$
$419$	19.3028	+	23.5205i	0.943003	+	1.14905i	−0.0456681	+	0.998957i	$0.514542\pi$
$420$	−0.123847	−	1.92660i	−0.00604312	−	0.0940084i
$421$	−19.7160	−	5.98078i	−0.960898	−	0.291485i	−0.229403	−	0.973332i	$-0.573677\pi$
$421$	−19.7160	−	5.98078i	−0.960898	−	0.291485i	−0.731496	+	0.681846i	$0.761177\pi$
$422$	9.33752	+	8.75655i	0.454543	+	0.426262i
$423$	−6.82113	−	4.55773i	−0.331655	−	0.221604i
$424$	−1.81323	−	1.49381i	−0.0880584	−	0.0725456i
$425$	−18.5232	−	27.7220i	−0.898509	−	1.34471i
$426$	−4.75463	+	3.40260i	−0.230362	+	0.164857i
$427$	−1.35351	−	13.7424i	−0.0655008	−	0.665041i
$428$	−15.3445	+	33.7532i	−0.741704	+	1.63152i
$429$	−8.99365	+	2.72819i	−0.434218	+	0.131718i
$430$	1.17860	−	2.38619i	0.0568372	−	0.115072i
$431$	28.6063	+	11.8491i	1.37792	+	0.570752i	0.943924	−	0.330164i	$-0.107104\pi$
$431$	28.6063	+	11.8491i	1.37792	+	0.570752i	0.433994	+	0.900916i	$0.357104\pi$
$432$	−3.89778	+	0.898521i	−0.187532	+	0.0432301i
$433$	−12.3944	+	5.13394i	−0.595638	+	0.246721i	−0.660074	−	0.751201i	$-0.729475\pi$
$433$	−12.3944	+	5.13394i	−0.595638	+	0.246721i	0.0644363	+	0.997922i	$0.479475\pi$
$434$	0.997624	−	15.0758i	0.0478875	−	0.723662i
$435$	−2.59939	−	1.38940i	−0.124631	−	0.0666167i
$436$	−9.06593	−	2.12588i	−0.434179	−	0.101811i
$437$	0.240684	+	0.197524i	0.0115135	+	0.00944888i
$438$	−2.31679	−	9.96445i	−0.110701	−	0.476120i
$439$	−5.23898	+	26.3382i	−0.250043	+	1.25705i	0.627903	+	0.778292i	$0.283914\pi$
$439$	−5.23898	+	26.3382i	−0.250043	+	1.25705i	−0.877946	+	0.478760i	$0.841086\pi$
$440$	1.80291	−	8.97549i	0.0859505	−	0.427890i
$441$	−5.44800	+	1.08367i	−0.259429	+	0.0516036i
$442$	8.90599	−	23.6177i	0.423615	−	1.12338i
$443$	−2.64195	−	4.94273i	−0.125523	−	0.234836i	0.811309	−	0.584618i	$-0.198756\pi$
$443$	−2.64195	−	4.94273i	−0.125523	−	0.234836i	−0.936831	+	0.349782i	$0.886256\pi$
$444$	−4.51264	−	5.89630i	−0.214161	−	0.279826i
$445$	−3.08429	−	0.303776i	−0.146209	−	0.0144003i
$446$	3.21255	−	11.9594i	0.152119	−	0.566292i
$447$			2.74125i			0.129657i
$448$	−1.84075	−	9.43974i	−0.0869673	−	0.445986i
$449$			17.3357i			0.818123i	0.912507	+	0.409062i	$0.134144\pi$
$449$			17.3357i			0.818123i	−0.912507	+	0.409062i	$0.865856\pi$
$450$	−5.94843	−	1.59788i	−0.280412	−	0.0753248i
$451$	34.1721	+	3.36565i	1.60910	+	0.158482i
$452$	−8.78589	−	1.16791i	−0.413254	−	0.0549337i
$453$	6.61833	+	12.3820i	0.310956	+	0.581758i
$454$	1.04560	+	0.394287i	0.0490727	+	0.0185048i
$455$	2.20730	−	0.439060i	0.103480	−	0.0205835i
$456$	0.104706	−	0.0206225i	0.00490332	−	0.000965735i
$457$	−3.22557	+	16.2161i	−0.150886	+	0.758555i	0.829039	+	0.559190i	$0.188888\pi$
$457$	−3.22557	+	16.2161i	−0.150886	+	0.758555i	−0.979925	+	0.199365i	$0.936112\pi$
$458$	25.8918	−	6.01998i	1.20984	−	0.281295i
$459$	5.91761	+	4.85646i	0.276210	+	0.226680i
$460$	6.98386	+	11.2625i	0.325624	+	0.525115i
$461$	−32.1605	−	17.1901i	−1.49786	−	0.800624i	−0.500004	−	0.866023i	$-0.666668\pi$
$461$	−32.1605	−	17.1901i	−1.49786	−	0.800624i	−0.997859	+	0.0653988i	$0.979168\pi$
$462$	6.83848	+	0.452529i	0.318155	+	0.0210536i
$463$	12.1743	−	5.04275i	0.565786	−	0.234356i	−0.0814087	−	0.996681i	$-0.525942\pi$
$463$	12.1743	−	5.04275i	0.565786	−	0.234356i	0.647195	+	0.762324i	$0.275942\pi$
$464$	−13.7290	−	5.20661i	−0.637352	−	0.241711i
$465$	6.59233	+	2.73063i	0.305712	+	0.126630i
$466$	−1.09343	−	0.540075i	−0.0506523	−	0.0250185i
$467$	−6.77453	+	2.05503i	−0.313488	+	0.0950954i	−0.443108	−	0.896468i	$-0.646124\pi$
$467$	−6.77453	+	2.05503i	−0.313488	+	0.0950954i	0.129620	+	0.991564i	$0.458624\pi$
$468$	−1.63705	−	4.36615i	−0.0756725	−	0.201825i
$469$	1.13910	+	11.5655i	0.0525990	+	0.534046i
$470$	5.42134	+	7.57551i	0.250068	+	0.349432i
$471$	2.73188	+	4.08855i	0.125878	+	0.188390i
$472$	3.19974	+	6.01350i	0.147280	+	0.276794i
$473$	7.85556	+	5.24892i	0.361199	+	0.241345i
$474$	3.67314	−	3.91684i	0.168713	−	0.179907i
$475$	0.157251	+	0.0477015i	0.00721517	+	0.00218870i
$476$	−12.1534	+	13.8233i	−0.557052	+	0.633589i
$477$	0.526932	+	0.642068i	0.0241265	+	0.0293983i
$478$	−35.9359	+	4.70811i	−1.64367	+	0.215344i
$479$	−7.54715	−	7.54715i	−0.344838	−	0.344838i	0.513345	−	0.858183i	$-0.328406\pi$
$479$	−7.54715	−	7.54715i	−0.344838	−	0.344838i	−0.858183	+	0.513345i	$0.828406\pi$
$480$	4.50137	+	0.606995i	0.205459	+	0.0277054i
$481$	6.12043	−	6.12043i	0.279068	−	0.279068i
$482$	15.3135	−	19.9310i	0.697509	−	0.907831i
$483$	−7.66885	+	6.29366i	−0.348945	+	0.286372i
$484$	9.93754	+	3.38726i	0.451706	+	0.153966i
$485$	1.82899	−	6.02936i	0.0830499	−	0.273779i
$486$	1.41349	−	0.0453845i	0.0641170	−	0.00205868i
$487$	5.24089	−	7.84355i	0.237487	−	0.355425i	−0.693512	−	0.720445i	$-0.743938\pi$
$487$	5.24089	−	7.84355i	0.237487	−	0.355425i	0.931000	+	0.365020i	$0.118938\pi$
$488$	32.3260	+	3.24531i	1.46333	+	0.146908i
$489$	6.73965	−	4.50329i	0.304778	−	0.203646i
$490$	6.22266	+	1.03138i	0.281111	+	0.0465929i
$491$	33.0800	−	3.25810i	1.49288	−	0.147036i	0.681613	−	0.731713i	$-0.261279\pi$
$491$	33.0800	−	3.25810i	1.49288	−	0.147036i	0.811266	+	0.584677i	$0.198779\pi$
$492$	−0.578791	+	17.0266i	−0.0260939	+	0.767617i
$493$	8.15724	+	26.8908i	0.367384	+	1.21110i
$494$	0.0399147	+	0.117828i	0.00179585	+	0.00530133i
$495$	−1.23863	+	2.99032i	−0.0556724	+	0.134405i
$496$	34.3123	+	9.28636i	1.54067	+	0.416970i
$497$	1.90200	+	4.59184i	0.0853165	+	0.205972i
$498$	−15.9643	+	13.9826i	−0.715379	+	0.626577i
$499$	−1.84937	+	3.45992i	−0.0827889	+	0.154887i	−0.919909	−	0.392132i	$-0.871738\pi$
$499$	−1.84937	+	3.45992i	−0.0827889	+	0.154887i	0.837120	+	0.547019i	$0.184238\pi$
$500$	12.2008	+	8.76616i	0.545635	+	0.392034i
$501$	1.75600	−	2.13969i	0.0784523	−	0.0955944i
$502$	−14.2007	−	8.84294i	−0.633809	−	0.394680i
$503$	−15.7620	−	3.13526i	−0.702793	−	0.139794i	−0.169257	−	0.985572i	$-0.554137\pi$
$503$	−15.7620	−	3.13526i	−0.702793	−	0.139794i	−0.533535	+	0.845778i	$0.679137\pi$
$504$	−0.00640306	+	3.40031i	−0.000285215	+	0.151462i
$505$	2.79543	+	14.0536i	0.124395	+	0.625377i
$506$	−42.8630	+	19.3886i	−1.90549	+	0.861926i
$507$	−6.67104	+	3.56574i	−0.296271	+	0.158360i
$508$	−2.61231	+	4.51157i	−0.115903	+	0.200169i
$509$	2.19620	−	22.2984i	0.0973448	−	0.988359i	−0.815144	−	0.579258i	$-0.803342\pi$
$509$	2.19620	−	22.2984i	0.0973448	−	0.988359i	0.912489	−	0.409101i	$-0.134158\pi$
$510$	−4.34167	−	7.53090i	−0.192252	−	0.333474i
$511$	−8.69650			−0.384711
$512$	22.6271	+	0.127827i	0.999984	+	0.00564922i
$513$	−0.0377304			−0.00166584
$514$	14.3330	+	24.8615i	0.632200	+	1.09659i
$515$	0.378800	−	3.84602i	0.0166919	−	0.169476i
$516$	−2.34884	+	4.05654i	−0.103402	+	0.178579i
$517$	−29.1648	+	15.5889i	−1.28267	+	0.685600i
$518$	−5.75084	+	2.60132i	−0.252677	+	0.114295i
$519$	2.10938	+	10.6046i	0.0925917	+	0.465490i
$520$	−0.00997076	+	5.29491i	−0.000437247	+	0.232197i
$521$	6.79613	+	1.35183i	0.297744	+	0.0592249i	0.341702	−	0.939808i	$-0.388997\pi$
$521$	6.79613	+	1.35183i	0.297744	+	0.0592249i	−0.0439580	+	0.999033i	$0.513997\pi$
$522$	4.40671	+	2.74411i	0.192877	+	0.120106i
$523$	−26.4355	+	32.2117i	−1.15594	+	1.40852i	−0.259280	+	0.965802i	$0.583485\pi$
$523$	−26.4355	+	32.2117i	−1.15594	+	1.40852i	−0.896661	+	0.442717i	$0.854015\pi$
$524$	−23.7792	−	17.0852i	−1.03880	−	0.746368i
$525$	−2.46818	+	4.61765i	−0.107720	+	0.201531i
$526$	−18.5794	+	16.2731i	−0.810101	+	0.709540i
$527$	−26.0340	−	62.8516i	−1.13406	−	2.73786i
$528$	−4.21236	+	15.5643i	−0.183319	+	0.677350i
$529$	17.2587	−	41.6662i	0.750379	−	1.81157i
$530$	−0.302614	−	0.893314i	−0.0131447	−	0.0388031i
$531$	−0.699102	−	2.30463i	−0.0303385	−	0.100013i
$532$	0.00308205	−	0.0906660i	0.000133624	−	0.00393087i
$533$	−19.7644	+	1.94662i	−0.856090	+	0.0843175i
$534$	5.38515	+	0.892565i	0.233038	+	0.0386251i
$535$	−12.3768	+	8.26992i	−0.535096	+	0.357540i
$536$	−27.2054	−	2.73123i	−1.17509	−	0.117971i
$537$	−8.03594	+	12.0266i	−0.346776	+	0.518987i
$538$	9.18041	−	0.294767i	0.395796	−	0.0127083i
$539$	−6.49991	+	21.4273i	−0.279971	+	0.922940i
$540$	−1.52001	−	0.518102i	−0.0654107	−	0.0222955i
$541$	15.8761	−	13.0292i	0.682568	−	0.560169i	−0.227933	−	0.973677i	$-0.573197\pi$
$541$	15.8761	−	13.0292i	0.682568	−	0.560169i	0.910500	+	0.413508i	$0.135697\pi$
$542$	2.46402	−	3.20701i	0.105839	−	0.137753i
$543$	−0.845651	+	0.845651i	−0.0362904	+	0.0362904i
$544$	−26.2543	−	34.4386i	−1.12565	−	1.47654i
$545$	−2.64347	−	2.64347i	−0.113234	−	0.113234i
$546$	−3.93029	+	0.514923i	−0.168201	+	0.0220367i
$547$	29.1814	+	35.5577i	1.24771	+	1.52034i	0.764173	+	0.645012i	$0.223147\pi$
$547$	29.1814	+	35.5577i	1.24771	+	1.52034i	0.483535	+	0.875325i	$0.339353\pi$
$548$	21.3821	−	24.3199i	0.913396	−	1.03889i
$549$	−10.9918	−	3.33433i	−0.469119	−	0.142306i
$550$	−16.9840	+	18.1108i	−0.724200	+	0.772248i
$551$	−0.115159	−	0.0769465i	−0.00490592	−	0.00327803i
$552$	−10.9640	−	20.6054i	−0.466659	−	0.877026i
$553$	−2.53599	−	3.79538i	−0.107841	−	0.161396i
$554$	23.5549	+	32.9144i	1.00075	+	1.39840i
$555$	−0.292180	−	2.96655i	−0.0124023	−	0.125923i
$556$	−0.278585	−	0.743010i	−0.0118146	−	0.0315107i
$557$	−3.09145	+	0.937780i	−0.130989	+	0.0397350i	−0.355098	−	0.934829i	$-0.615553\pi$
$557$	−3.09145	+	0.937780i	−0.130989	+	0.0397350i	0.224110	+	0.974564i	$0.428053\pi$
$558$	−11.2681	−	5.56562i	−0.477018	−	0.235611i
$559$	−5.04845	−	2.09113i	−0.213526	−	0.0884456i
$560$	1.36916	−	3.61025i	0.0578576	−	0.152561i
$561$	28.5099	−	11.8092i	1.20369	−	0.498585i
$562$	38.3589	+	2.53836i	1.61807	+	0.107074i
$563$	−29.8359	−	15.9476i	−1.25743	−	0.672111i	−0.298139	−	0.954523i	$-0.596366\pi$
$563$	−29.8359	−	15.9476i	−1.25743	−	0.672111i	−0.959293	+	0.282411i	$0.908866\pi$
$564$	−8.64672	−	13.9441i	−0.364093	−	0.587151i
$565$	−2.75060	−	2.25736i	−0.115719	−	0.0949679i
$566$	−24.9304	+	5.79646i	−1.04790	+	0.243643i
$567$	0.234536	−	1.17909i	0.00984959	−	0.0495172i
$568$	−11.4730	+	2.25968i	−0.481398	+	0.0948140i
$569$	−9.70426	+	1.93030i	−0.406824	+	0.0809223i	−0.394260	−	0.918999i	$-0.628999\pi$
$569$	−9.70426	+	1.93030i	−0.406824	+	0.0809223i	−0.0125634	+	0.999921i	$0.503999\pi$
$570$	0.0400884	+	0.0151169i	0.00167912	+	0.000633179i
$571$	−4.56411	−	8.53885i	−0.191002	−	0.357340i	0.768132	−	0.640291i	$-0.221186\pi$
$571$	−4.56411	−	8.53885i	−0.191002	−	0.357340i	−0.959134	+	0.282952i	$0.908686\pi$
$572$	−18.6328	−	2.47685i	−0.779076	−	0.103562i
$573$	−10.9986	−	1.08326i	−0.459472	−	0.0452540i
$574$	13.9864	+	3.75707i	0.583783	+	0.156817i
$575$		−	35.9408i		−	1.49884i
$576$	−7.84035	−	1.59026i	−0.326681	−	0.0662609i
$577$		−	0.771951i		−	0.0321367i	−0.999871	−	0.0160684i	$-0.994885\pi$
$577$		−	0.771951i		−	0.0321367i	0.999871	−	0.0160684i	$-0.00511494\pi$
$578$	−15.2635	+	56.8216i	−0.634879	+	2.36347i
$579$	−12.8624	−	1.26683i	−0.534541	−	0.0526477i
$580$	−3.58267	−	4.68118i	−0.148762	−	0.194376i
$581$	8.50418	+	15.9102i	0.352813	+	0.660066i
$582$	−3.91555	+	10.3836i	−0.162305	+	0.430414i
$583$	3.28390	−	0.653208i	0.136005	−	0.0270531i
$584$	4.02942	−	20.0598i	0.166739	−	0.830080i
$585$	0.365216	−	1.83607i	0.0150998	−	0.0759120i
$586$	6.38195	+	27.4486i	0.263636	+	1.13389i
$587$	31.2378	+	25.6362i	1.28932	+	1.05812i	0.994734	+	0.102493i	$0.0326821\pi$
$587$	31.2378	+	25.6362i	1.28932	+	1.05812i	0.294587	+	0.955625i	$0.404818\pi$
$588$	−10.8161	−	2.53628i	−0.446048	−	0.104594i
$589$	0.295707	+	0.158059i	0.0121844	+	0.00651269i
$590$	−0.180573	+	2.72876i	−0.00743407	+	0.112341i
$591$	−15.7307	+	6.51586i	−0.647073	+	0.268026i
$592$	−3.33575	−	14.4705i	−0.137099	−	0.594732i
$593$	−15.1406	−	6.27146i	−0.621752	−	0.257538i	0.0494923	−	0.998775i	$-0.484240\pi$
$593$	−15.1406	−	6.27146i	−0.621752	−	0.257538i	−0.671244	+	0.741237i	$0.734240\pi$
$594$	2.52460	−	5.11130i	0.103586	−	0.209719i
$595$	−7.07136	+	2.14507i	−0.289897	+	0.0879394i
$596$	−2.26894	+	4.99097i	−0.0929392	+	0.204438i
$597$	−1.14125	−	11.5873i	−0.0467084	−	0.474239i
$598$	22.1269	−	15.8349i	0.904838	−	0.647538i
$599$	−19.5288	−	29.2270i	−0.797927	−	1.19418i	−0.977603	−	0.210456i	$-0.932505\pi$
$599$	−19.5288	−	29.2270i	−0.797927	−	1.19418i	0.179677	−	0.983726i	$-0.442495\pi$
$600$	−9.50768	−	7.83276i	−0.388150	−	0.319771i
$601$	5.61881	+	3.75437i	0.229196	+	0.153144i	0.664866	−	0.746962i	$-0.268489\pi$
$601$	5.61881	+	3.75437i	0.229196	+	0.153144i	−0.435670	+	0.900106i	$0.643489\pi$
$602$	2.90661	+	2.72576i	0.118464	+	0.111094i
$603$	9.25066	+	2.80616i	0.376716	+	0.114275i
$604$	1.80132	+	28.0218i	0.0732947	+	1.14019i
$605$	2.67398	+	3.25825i	0.108713	+	0.132467i
$606$	−3.27844	−	25.0236i	−0.133178	−	1.01651i
$607$	30.2628	+	30.2628i	1.22833	+	1.22833i	0.964595	+	0.263734i	$0.0849542\pi$
$607$	30.2628	+	30.2628i	1.22833	+	1.22833i	0.263734	+	0.964595i	$0.415046\pi$
$608$	0.207707	+	0.0491182i	0.00842362	+	0.00199201i
$609$	3.12045	−	3.12045i	0.126447	−	0.126447i
$610$	10.3428	+	7.94666i	0.418769	+	0.321751i
$611$	14.7852	−	12.1339i	0.598144	−	0.490884i
$612$	6.75444	+	13.7401i	0.273032	+	0.555411i
$613$	9.30002	−	30.6581i	0.375624	−	1.23827i	−0.541851	−	0.840475i	$-0.682276\pi$
$613$	9.30002	−	30.6581i	0.375624	−	1.23827i	0.917475	−	0.397793i	$-0.130224\pi$
$614$	0.736849	+	22.9489i	0.0297368	+	0.926143i
$615$	−3.79988	+	5.68692i	−0.153226	+	0.229319i
$616$	12.0762	+	6.48413i	0.486564	+	0.261253i
$617$	1.78218	−	1.19081i	0.0717477	−	0.0479403i	−0.519179	−	0.854665i	$-0.673762\pi$
$617$	1.78218	−	1.19081i	0.0717477	−	0.0479403i	0.590927	+	0.806725i	$0.298762\pi$
$618$	−1.11300	+	6.71514i	−0.0447716	+	0.270122i
$619$	−7.32238	+	0.721192i	−0.294311	+	0.0289871i	−0.244095	−	0.969751i	$-0.578491\pi$
$619$	−7.32238	+	0.721192i	−0.294311	+	0.0289871i	−0.0502160	+	0.998738i	$0.515991\pi$
$620$	9.74244	+	10.4281i	0.391266	+	0.418803i
$621$	2.39549	+	7.89688i	0.0961278	+	0.316891i
$622$	−23.6369	+	8.00710i	−0.947753	+	0.321056i
$623$	1.77575	−	4.28704i	0.0711439	−	0.171757i
$624$	0.633307	−	9.30439i	0.0253526	−	0.372474i
$625$	−6.02534	−	14.5465i	−0.241014	−	0.581858i
$626$	−16.3433	−	18.6596i	−0.653209	−	0.745786i
$627$	−0.0716965	+	0.134135i	−0.00286328	+	0.00535682i
$628$	1.58982	+	9.70516i	0.0634406	+	0.387278i
$629$	−18.0295	+	21.9691i	−0.718885	+	0.875964i
$630$	−0.721605	+	1.15881i	−0.0287494	+	0.0461682i
$631$	46.7517	+	9.29948i	1.86115	+	0.370207i	0.992197	−	0.124681i	$-0.0397906\pi$
$631$	46.7517	+	9.29948i	1.86115	+	0.370207i	0.868957	+	0.494887i	$0.164791\pi$
$632$	9.92962	−	4.09110i	0.394979	−	0.162735i
$633$	−1.76590	−	8.87777i	−0.0701882	−	0.352860i
$634$	−6.38958	−	14.1257i	−0.253763	−	0.561003i
$635$	−1.84584	+	0.986624i	−0.0732501	+	0.0391530i
$636$	0.427939	+	1.60515i	0.0169689	+	0.0636483i
$637$	1.26939	−	12.8884i	0.0502953	−	0.510656i
$638$	18.1293	−	10.4518i	0.717746	−	0.413790i
$639$	4.13426			0.163549
$640$	7.69319	+	4.83094i	0.304100	+	0.190960i
$641$	37.0785			1.46451			0.732256	−	0.681030i	$-0.238468\pi$
$641$	37.0785			1.46451			0.732256	+	0.681030i	$0.238468\pi$
$642$	22.7134	−	13.0946i	0.896427	−	0.516802i
$643$	0.159482	−	1.61925i	0.00628936	−	0.0638570i	−0.991528	−	0.129895i	$-0.958536\pi$
$643$	0.159482	−	1.61925i	0.00628936	−	0.0638570i	0.997817	+	0.0660382i	$0.0210359\pi$
$644$	−19.1719	+	5.11130i	−0.755477	+	0.201413i
$645$	−1.65968	+	0.887116i	−0.0653497	+	0.0349302i
$646$	−0.168348	−	0.372172i	−0.00662355	−	0.0146429i
$647$	−1.96530	−	9.88022i	−0.0772638	−	0.388431i	−0.999996	−	0.00298864i	$-0.999049\pi$
$647$	−1.96530	−	9.88022i	−0.0772638	−	0.388431i	0.922732	−	0.385443i	$-0.125951\pi$
$648$	2.61108	+	1.08731i	0.102573	+	0.0427136i
$649$	−9.52161	−	1.89397i	−0.373756	−	0.0743447i
$650$	7.59086	−	12.1900i	0.297738	−	0.478132i
$651$	−6.77755	+	8.25847i	−0.265633	+	0.323675i
$652$	15.9982	−	2.62069i	0.626538	−	0.102634i
$653$	−0.139763	+	0.261478i	−0.00546935	+	0.0102324i	−0.884641	−	0.466273i	$-0.845597\pi$
$653$	−0.139763	+	0.261478i	−0.00546935	+	0.0102324i	0.879172	+	0.476505i	$0.158097\pi$
$654$	4.33833	+	4.95319i	0.169642	+	0.193685i
$655$	−4.49855	−	10.8605i	−0.175773	−	0.424353i
$656$	−15.1467	+	30.5210i	−0.591379	+	1.19165i
$657$	−2.76828	+	6.68323i	−0.108001	+	0.260737i
$658$	−13.2102	+	4.47501i	−0.514987	+	0.174454i
$659$	6.63122	+	21.8602i	0.258316	+	0.851553i	0.986158	+	0.165808i	$0.0530232\pi$
$659$	6.63122	+	21.8602i	0.258316	+	0.851553i	−0.727842	+	0.685744i	$0.759477\pi$
$660$	−4.73026	+	4.41923i	−0.184125	+	0.172018i
$661$	−4.15427	+	0.409160i	−0.161583	+	0.0159145i	−0.178485	−	0.983943i	$-0.557120\pi$
$661$	−4.15427	+	0.409160i	−0.161583	+	0.0159145i	0.0169023	+	0.999857i	$0.494620\pi$
$662$	0.0447341	−	0.269896i	0.00173864	−	0.0104898i
$663$	−14.8402	+	9.91588i	−0.576344	+	0.385101i
$664$	−40.6396	+	12.2444i	−1.57712	+	0.475173i
$665$	0.0202343	−	0.0302827i	0.000784651	−	0.00117431i
$666$	0.168490	+	5.24755i	0.00652884	+	0.203338i
$667$	−8.79333	+	28.9877i	−0.340479	+	1.12241i
$668$	4.96816	−	2.44227i	0.192224	−	0.0944944i
$669$	−6.76874	+	5.55496i	−0.261695	+	0.214767i
$670$	−8.70448	−	6.68787i	−0.336283	−	0.258375i
$671$	−32.7408	+	32.7408i	−1.26394	+	1.26394i
$672$	−2.82609	+	6.18561i	−0.109019	+	0.238615i
$673$	17.8028	+	17.8028i	0.686247	+	0.686247i	0.961400	−	0.275153i	$-0.0887286\pi$
$673$	17.8028	+	17.8028i	0.686247	+	0.686247i	−0.275153	+	0.961400i	$0.588729\pi$
$674$	−4.16025	−	31.7542i	−0.160247	−	1.22313i
$675$	2.76297	+	3.36668i	0.106347	+	0.129584i
$676$	−15.0973	+	0.970493i	−0.580664	+	0.0373267i
$677$	44.2210	+	13.4143i	1.69955	+	0.515553i	0.983253	−	0.182243i	$-0.0583358\pi$
$677$	44.2210	+	13.4143i	1.69955	+	0.515553i	0.716296	+	0.697796i	$0.245836\pi$
$678$	4.57152	+	4.28709i	0.175568	+	0.164645i
$679$	7.84374	+	5.24102i	0.301015	+	0.201132i
$680$	−1.67150	−	17.3050i	−0.0640991	−	0.663618i
$681$	−0.438997	−	0.657006i	−0.0168224	−	0.0251765i
$682$	−41.1983	+	29.4831i	−1.57756	+	1.12897i
$683$	0.815532	+	8.28024i	0.0312055	+	0.316834i	0.998098	+	0.0616499i	$0.0196362\pi$
$683$	0.815532	+	8.28024i	0.0312055	+	0.316834i	−0.966892	+	0.255185i	$0.917864\pi$
$684$	−0.0686954	−	0.0312295i	−0.00262663	−	0.00119409i
$685$	12.4409	−	3.77392i	0.475344	−	0.144194i
$686$	−9.45267	+	19.1378i	−0.360905	+	0.730686i
$687$	−17.3658	−	7.19314i	−0.662546	−	0.274435i
$688$	−7.63412	+	5.44157i	−0.291048	+	0.207458i
$689$	−1.78913	+	0.741083i	−0.0681605	+	0.0282330i
$690$	0.618738	−	9.35018i	0.0235549	−	0.355955i
$691$	16.2221	+	8.67090i	0.617118	+	0.329857i	0.750162	−	0.661254i	$-0.229975\pi$
$691$	16.2221	+	8.67090i	0.617118	+	0.329857i	−0.133044	+	0.991110i	$0.542475\pi$
$692$	−4.93689	+	21.0536i	−0.187672	+	0.800338i
$693$	−3.74610	−	3.07434i	−0.142302	−	0.116785i
$694$	2.29751	+	9.88153i	0.0872123	+	0.375098i
$695$	0.0621508	−	0.312453i	0.00235751	−	0.0118520i
$696$	5.75196	+	8.64361i	0.218027	+	0.327635i
$697$	63.9562	−	12.7217i	2.42251	−	0.481868i
$698$	13.5272	−	35.8727i	0.512013	−	1.35780i
$699$	0.406507	+	0.760521i	0.0153755	+	0.0287655i
$700$	−8.31582	+	6.36438i	−0.314309	+	0.240551i
$701$	23.0985	+	2.27500i	0.872418	+	0.0859257i	0.524309	−	0.851528i	$-0.324324\pi$
$701$	23.0985	+	2.27500i	0.872418	+	0.0859257i	0.348110	+	0.937454i	$0.386824\pi$
$702$	−0.855379	+	3.18432i	−0.0322842	+	0.120185i
$703$		−	0.140074i		−	0.00528298i
$704$	−20.5520	+	24.8512i	−0.774582	+	0.936615i
$705$		−	6.58708i		−	0.248084i
$706$	38.4446	+	10.3271i	1.44688	+	0.388664i
$707$	−21.3505	−	2.10284i	−0.802968	−	0.0790855i
$708$	0.634696	−	4.77467i	0.0238533	−	0.179443i
$709$	10.0358	+	18.7756i	0.376902	+	0.705134i	0.996833	−	0.0795225i	$-0.0253395\pi$
$709$	10.0358	+	18.7756i	0.376902	+	0.705134i	−0.619931	+	0.784656i	$0.712840\pi$
$710$	−4.39264	−	1.65642i	−0.164853	−	0.0621643i
$711$	−3.72399	+	0.740748i	−0.139661	+	0.0277802i
$712$	9.06592	+	6.08238i	0.339760	+	0.227947i
$713$	14.3069	−	71.9259i	0.535799	−	2.69365i
$714$	12.6770	−	2.94748i	0.474426	−	0.110307i
$715$	−5.83337	−	4.78732i	−0.218156	−	0.179036i
$716$	−24.5854	+	15.2454i	−0.918799	+	0.569748i
$717$	22.6016	+	12.0808i	0.844073	+	0.451166i
$718$	2.50410	+	0.165706i	0.0934521	+	0.00618409i
$719$	2.42235	−	1.00337i	0.0903382	−	0.0374193i	−0.337057	−	0.941484i	$-0.609431\pi$
$719$	2.42235	−	1.00337i	0.0903382	−	0.0374193i	0.427395	+	0.904065i	$0.359431\pi$
$720$	−2.33863	−	2.20141i	−0.0871555	−	0.0820418i
$721$	5.34582	+	2.21431i	0.199089	+	0.0824652i
$722$	−24.0898	−	11.8986i	−0.896528	−	0.442818i
$723$	−17.0075	+	5.15917i	−0.632516	+	0.191872i
$724$	−2.23961	+	0.839723i	−0.0832346	+	0.0312080i
$725$	1.56703	+	15.9103i	0.0581980	+	0.590894i
$726$	−4.32046	−	6.03719i	−0.160347	−	0.224061i
$727$	0.229210	+	0.343037i	0.00850093	+	0.0127225i	0.835696	−	0.549193i	$-0.185065\pi$
$727$	0.229210	+	0.343037i	0.00850093	+	0.0127225i	−0.827195	+	0.561915i	$0.810065\pi$
$728$	−7.58204	−	2.31559i	−0.281009	−	0.0858214i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	5.61897	−	5.99177i	0.207967	−	0.221765i
$731$	17.1695	+	5.20830i	0.635035	+	0.192636i
$732$	−17.2529	−	15.1687i	−0.637684	−	0.560652i
$733$	−1.68587	−	2.05424i	−0.0622690	−	0.0758750i	0.740944	−	0.671566i	$-0.234378\pi$
$733$	−1.68587	−	2.05424i	−0.0622690	−	0.0758750i	−0.803213	+	0.595691i	$0.796878\pi$
$734$	51.3492	−	6.72746i	1.89533	−	0.248315i
$735$	−3.15378	−	3.15378i	−0.116329	−	0.116329i
$736$	−2.90691	−	46.5910i	−0.107150	−	1.71737i
$737$	27.5545	−	27.5545i	1.01498	−	1.01498i
$738$	7.33947	−	9.55257i	0.270170	−	0.351635i
$739$	30.1447	−	24.7391i	1.10889	−	0.910044i	0.112394	−	0.993664i	$-0.464148\pi$
$739$	30.1447	−	24.7391i	1.10889	−	0.910044i	0.996498	+	0.0836202i	$0.0266483\pi$
$740$	1.92345	−	5.64301i	0.0707073	−	0.207441i
$741$	0.0255357	−	0.0841798i	0.000938076	−	0.00309242i
$742$	1.41144	−	0.0453187i	0.0518154	−	0.00166370i
$743$	3.59627	−	5.38219i	0.131934	−	0.197454i	−0.759620	−	0.650367i	$-0.774615\pi$
$743$	3.59627	−	5.38219i	0.131934	−	0.197454i	0.891555	+	0.452913i	$0.149615\pi$
$744$	−15.9091	−	19.4599i	−0.583256	−	0.713434i
$745$	−1.83012	+	1.22284i	−0.0670502	+	0.0448015i
$746$	43.4127	+	7.19547i	1.58945	+	0.263445i
$747$	14.9340	−	1.47087i	0.546406	−	0.0538163i
$748$	61.6822	+	2.09679i	2.25532	+	0.0766661i
$749$	−6.46960	−	21.3274i	−0.236394	−	0.779287i
$750$	−3.40840	−	10.0616i	−0.124457	−	0.367396i
$751$	−1.12953	+	2.72692i	−0.0412171	+	0.0995069i	−0.943147	−	0.332375i	$-0.892150\pi$
$751$	−1.12953	+	2.72692i	−0.0412171	+	0.0995069i	0.901930	+	0.431882i	$0.142150\pi$
$752$	−4.20149	−	32.5447i	−0.153213	−	1.18678i
$753$	4.52682	+	10.9287i	0.164967	+	0.398264i
$754$	−9.10477	+	7.97456i	−0.331576	+	0.290416i
$755$	−5.31412	+	9.94202i	−0.193401	+	0.361827i
$756$	1.40295	−	1.95264i	0.0510249	−	0.0710167i
$757$	11.2474	−	13.7051i	0.408796	−	0.498119i	−0.527391	−	0.849623i	$-0.676830\pi$
$757$	11.2474	−	13.7051i	0.408796	−	0.498119i	0.936186	+	0.351504i	$0.114330\pi$
$758$	−16.3761	−	10.1976i	−0.594808	−	0.370393i
$759$	32.6261	+	6.48973i	1.18425	+	0.235562i
$760$	0.0604763	+	0.0607045i	0.00219371	+	0.00220198i
$761$	1.86958	+	9.39903i	0.0677724	+	0.340715i	0.999763	−	0.0217675i	$-0.00692937\pi$
$761$	1.86958	+	9.39903i	0.0677724	+	0.340715i	−0.931991	+	0.362482i	$0.881929\pi$
$762$	3.35872	−	1.51928i	0.121674	−	0.0550376i
$763$	4.93639	−	2.63855i	0.178709	−	0.0955221i
$764$	−19.1284	−	11.0758i	−0.692040	−	0.400708i
$765$	−0.602485	+	6.11713i	−0.0217829	+	0.221165i
$766$	13.3114	+	23.0895i	0.480960	+	0.834256i
$767$	5.61498			0.202745
$768$	−12.9586	−	9.38483i	−0.467603	−	0.338646i
$769$	−36.5970			−1.31972			−0.659861	−	0.751387i	$-0.729385\pi$
$769$	−36.5970			−1.31972			−0.659861	+	0.751387i	$0.729385\pi$
$770$	2.74846	+	4.76738i	0.0990476	+	0.171804i
$771$	1.98896	−	20.1942i	0.0716306	−	0.727278i
$772$	−22.3698	−	12.9527i	−0.805107	−	0.466177i
$773$	33.1749	−	17.7323i	1.19322	−	0.637788i	0.249446	−	0.968389i	$-0.419751\pi$
$773$	33.1749	−	17.7323i	1.19322	−	0.637788i	0.943771	+	0.330601i	$0.107251\pi$
$774$	3.01997	−	1.36605i	0.108551	−	0.0491015i
$775$	−7.55080	−	37.9604i	−0.271233	−	1.36358i
$776$	−15.7235	+	15.6644i	−0.564441	+	0.562319i
$777$	4.37737	+	0.870713i	0.157037	+	0.0312367i
$778$	−32.9914	−	20.5441i	−1.18280	−	0.736542i
$779$	−0.203891	+	0.248442i	−0.00730515	+	0.00890135i
$780$	2.18466	−	3.04062i	0.0782233	−	0.108872i
$781$	7.85605	−	14.6976i	0.281111	−	0.525922i
$782$	−67.2065	+	58.8639i	−2.40330	+	2.10497i
$783$	−1.40475	−	3.39136i	−0.0502015	−	0.121197i
$784$	−17.5935	−	13.5702i	−0.628338	−	0.484652i
$785$	−1.51093	+	3.64772i	−0.0539276	+	0.130193i
$786$	6.64294	+	19.6099i	0.236946	+	0.699461i
$787$	3.48002	+	11.4721i	0.124049	+	0.408936i	0.996866	−	0.0791127i	$-0.0252087\pi$
$787$	3.48002	+	11.4721i	0.124049	+	0.408936i	−0.872816	+	0.488049i	$0.837709\pi$
$788$	−34.0338	−	1.15693i	−1.21241	−	0.0412138i
$789$	17.3803	−	1.71181i	0.618754	−	0.0609419i
$790$	4.25351	+	0.705001i	0.151333	+	0.0250828i
$791$	4.42975	−	2.95987i	0.157504	−	0.105241i
$792$	8.82714	−	7.21647i	0.313659	−	0.256426i
$793$	14.8784	−	22.2670i	0.528346	−	0.790725i
$794$	17.7003	−	0.568324i	0.628158	−	0.0201691i
$795$	−0.193599	+	0.638210i	−0.00686625	+	0.0226350i
$796$	7.51298	−	22.0416i	0.266291	−	0.781243i
$797$	−12.6212	+	10.3580i	−0.447066	+	0.366898i	−0.830823	−	0.556536i	$-0.812130\pi$
$797$	−12.6212	+	10.3580i	−0.447066	+	0.366898i	0.383757	+	0.923434i	$0.374630\pi$
$798$	−0.0390825	+	0.0508672i	−0.00138351	+	0.00180068i
$799$	−44.4074	+	44.4074i	−1.57102	+	1.57102i
$800$	−10.8274	−	22.1305i	−0.382805	−	0.782433i
$801$	−2.72931	−	2.72931i	−0.0964355	−	0.0964355i
$802$	−19.6177	+	2.57020i	−0.692726	+	0.0907568i
$803$	18.4990	+	22.5411i	0.652817	+	0.795460i
$804$	14.5199	+	12.7659i	0.512078	+	0.450219i
$805$	−7.62277	−	2.31234i	−0.268667	−	0.0814993i
$806$	20.0436	−	21.3734i	0.706004	−	0.752845i
$807$	−5.40029	−	3.60836i	−0.190099	−	0.127020i
$808$	14.7430	−	48.2738i	0.518658	−	1.69827i
$809$	17.0278	+	25.4839i	0.598666	+	0.895966i	0.999799	−	0.0200533i	$-0.00638360\pi$
$809$	17.0278	+	25.4839i	0.598666	+	0.895966i	−0.401133	+	0.916020i	$0.631384\pi$
$810$	0.660840	+	0.923425i	0.0232196	+	0.0324459i
$811$	−0.00493799	−	0.0501363i	−0.000173396	−	0.00176052i	0.995098	−	0.0988974i	$-0.0315316\pi$
$811$	−0.00493799	−	0.0501363i	−0.000173396	−	0.00176052i	−0.995271	+	0.0971368i	$0.969032\pi$
$812$	8.26417	−	3.09857i	0.290015	−	0.108739i
$813$	−2.73661	+	0.830141i	−0.0959770	+	0.0291143i
$814$	18.9756	+	9.37256i	0.665096	+	0.328508i
$815$	6.01298	+	2.49066i	0.210625	+	0.0872439i
$816$	0.925050	+	30.6071i	0.0323832	+	1.07146i
$817$	−0.0816992	+	0.0338409i	−0.00285829	+	0.00118394i
$818$	17.7967	+	1.17767i	0.622246	+	0.0411764i
$819$	2.47192	+	1.32127i	0.0863760	+	0.0461689i
$820$	−11.6255	+	7.20896i	−0.405979	+	0.251748i
$821$	−21.5829	−	17.7126i	−0.753248	−	0.618175i	0.177379	−	0.984143i	$-0.443238\pi$
$821$	−21.5829	−	17.7126i	−0.753248	−	0.618175i	−0.930628	+	0.365968i	$0.880738\pi$
$822$	−22.3032	+	5.18563i	−0.777915	+	0.180870i
$823$	1.90869	−	9.59562i	0.0665327	−	0.334482i	−0.933155	−	0.359474i	$-0.882956\pi$
$823$	1.90869	−	9.59562i	0.0665327	−	0.334482i	0.999688	+	0.0249920i	$0.00795602\pi$
$824$	−7.58455	+	11.3049i	−0.264220	+	0.393826i
$825$	17.2191	−	3.42509i	0.599492	−	0.119246i
$826$	−3.83120	−	1.44471i	−0.133305	−	0.0502678i
$827$	−11.7379	−	21.9601i	−0.408168	−	0.763629i	0.590902	−	0.806743i	$-0.298772\pi$
$827$	−11.7379	−	21.9601i	−0.408168	−	0.763629i	−0.999070	+	0.0431146i	$0.986272\pi$
$828$	−2.17480	+	16.3605i	−0.0755796	+	0.568568i
$829$	−48.9158	−	4.81778i	−1.69891	−	0.167328i	−0.798392	−	0.602138i	$-0.794316\pi$
$829$	−48.9158	−	4.81778i	−1.69891	−	0.167328i	−0.900522	+	0.434809i	$0.856816\pi$
$830$	−16.4566	−	4.42061i	−0.571217	−	0.153442i
$831$		−	28.6198i		−	0.992810i
$832$	8.85430	−	16.4162i	0.306968	−	0.569130i
$833$			42.5230i			1.47334i
$834$	−0.145564	+	0.541893i	−0.00504048	+	0.0187642i
$835$	2.21183	+	0.217847i	0.0765437	+	0.00753890i
$836$	−0.241560	+	0.184874i	−0.00835454	+	0.00639402i
$837$	4.18916	+	7.83737i	0.144799	+	0.270899i
$838$	15.1828	−	40.2630i	0.524480	−	1.39086i
$839$	−19.3769	+	3.85430i	−0.668965	+	0.133065i	−0.517877	−	0.855455i	$-0.673278\pi$
$839$	−19.3769	+	3.85430i	−0.668965	+	0.133065i	−0.151087	+	0.988520i	$0.548278\pi$
$840$	−2.27297	+	1.51257i	−0.0784249	+	0.0521885i
$841$	−3.02885	+	15.2271i	−0.104443	+	0.525071i
$842$	6.59857	+	28.3803i	0.227402	+	0.978048i
$843$	−21.0128	−	17.2448i	−0.723721	−	0.593942i
$844$	4.13298	−	17.6253i	0.142263	−	0.606688i
$845$	−5.35644	−	2.86308i	−0.184267	−	0.0984928i
$846$	−0.766060	+	11.5765i	−0.0263377	+	0.398007i
$847$	−5.83050	+	2.41507i	−0.200338	+	0.0829828i
$848$	−0.549437	+	3.27668i	−0.0188678	+	0.112522i
$849$	16.7210	+	6.92606i	0.573863	+	0.237702i
$850$	−20.8810	+	42.2755i	−0.716212	+	1.45004i
$851$	−29.3171	+	8.89325i	−1.00498	+	0.304857i
$852$	7.52720	+	3.42193i	0.257878	+	0.117233i
$853$	−3.48363	−	35.3699i	−0.119277	−	1.21104i	−0.849409	−	0.527735i	$-0.823041\pi$
$853$	−3.48363	−	35.3699i	−0.119277	−	1.21104i	0.730132	−	0.683307i	$-0.239459\pi$
$854$	−15.8810	+	11.3651i	−0.543436	+	0.388905i
$855$	−0.0168311	−	0.0251896i	−0.000575613	−	0.000861465i
$856$	52.1925	−	5.04129i	1.78390	−	0.172308i
$857$	19.3086	+	12.9016i	0.659570	+	0.440711i	0.839787	−	0.542916i	$-0.182680\pi$
$857$	19.3086	+	12.9016i	0.659570	+	0.440711i	−0.180217	+	0.983627i	$0.557680\pi$
$858$	9.69511	+	9.09189i	0.330986	+	0.310392i
$859$	22.8258	+	6.92412i	0.778805	+	0.236248i	0.654567	−	0.756004i	$-0.272851\pi$
$859$	22.8258	+	6.92412i	0.778805	+	0.236248i	0.124239	+	0.992252i	$0.460351\pi$
$860$	−3.75602	+	0.241448i	−0.128079	+	0.00823330i
$861$	−6.49651	−	7.91602i	−0.221400	−	0.269777i
$862$	−5.68831	−	43.4176i	−0.193745	−	1.47881i
$863$	−0.632007	−	0.632007i	−0.0215138	−	0.0215138i	0.696268	−	0.717782i	$-0.254842\pi$
$863$	−0.632007	−	0.632007i	−0.0215138	−	0.0215138i	−0.717782	+	0.696268i	$0.754842\pi$
$864$	3.85401	+	4.14085i	0.131116	+	0.140875i
$865$	−6.13886	+	6.13886i	−0.208728	+	0.208728i
$866$	15.0447	+	11.5592i	0.511239	+	0.392798i
$867$	32.1598	−	26.3928i	1.09220	−	0.896348i
$868$	−19.1754	+	9.42633i	−0.650854	+	0.319951i
$869$	−4.44302	+	14.6467i	−0.150719	+	0.496855i
$870$	0.133767	+	4.16613i	0.00453513	+	0.141245i
$871$	−12.5215	+	18.7398i	−0.424276	+	0.634975i
$872$	3.79900	+	12.6091i	0.128650	+	0.426997i
$873$	6.52453	−	4.35955i	0.220822	−	0.147549i
$874$	0.0720003	−	0.434403i	0.00243545	−	0.0146939i
$875$	−8.98706	+	0.885148i	−0.303818	+	0.0299235i
$876$	−10.5719	+	9.87677i	−0.357191	+	0.333705i
$877$	−5.84079	−	19.2545i	−0.197230	−	0.650179i	−0.998644	−	0.0520686i	$-0.983419\pi$
$877$	−5.84079	−	19.2545i	−0.197230	−	0.650179i	0.801414	−	0.598110i	$-0.204081\pi$
$878$	35.9697	−	12.1849i	1.21392	−	0.411220i
$879$	7.62565	−	18.4100i	0.257207	−	0.620952i
$880$	−12.2701	+	4.13082i	−0.413626	+	0.139250i
$881$	−7.29473	−	17.6110i	−0.245766	−	0.593331i	0.752070	−	0.659083i	$-0.229055\pi$
$881$	−7.29473	−	17.6110i	−0.245766	−	0.593331i	−0.997836	+	0.0657522i	$0.979055\pi$
$882$	5.17584	+	5.90939i	0.174279	+	0.198979i
$883$	24.7089	−	46.2270i	0.831520	−	1.55566i	0.000112297	−	1.00000i	$-0.499964\pi$
$883$	24.7089	−	46.2270i	0.831520	−	1.55566i	0.831407	−	0.555664i	$-0.187536\pi$
$884$	−35.2267	+	5.77054i	−1.18480	+	0.194084i
$885$	1.22676	−	1.49481i	0.0412370	−	0.0502474i
$886$	−4.18967	+	6.72812i	−0.140755	+	0.226036i
$887$	−8.88648	−	1.76763i	−0.298379	−	0.0593512i	0.0436308	−	0.999048i	$-0.486107\pi$
$887$	−8.88648	−	1.76763i	−0.298379	−	0.0593512i	−0.342009	+	0.939697i	$0.611107\pi$
$888$	−4.03663	+	9.69362i	−0.135460	+	0.325297i
$889$	−0.611353	−	3.07348i	−0.0205041	−	0.103081i
$890$	1.80637	+	3.99340i	0.0605495	+	0.133859i
$891$	−3.55508	+	1.90023i	−0.119100	+	0.0636601i
$892$	−16.9216	+	4.51137i	−0.566578	+	0.151052i
$893$	0.0303391	−	0.308038i	0.00101526	−	0.0103081i
$894$	3.35855	−	1.93625i	0.112327	−	0.0647579i
$895$	−11.6140			−0.388212
$896$	−10.2653	+	8.92291i	−0.342939	+	0.298094i
$897$	−19.2399			−0.642401
$898$	21.2395	−	12.2449i	0.708772	−	0.408617i
$899$	−3.19743	+	32.4640i	−0.106640	+	1.08274i
$900$	2.24390	+	8.41659i	0.0747966	+	0.280553i
$901$	5.60772	−	2.99739i	0.186820	−	0.0998576i
$902$	−20.0135	−	44.2445i	−0.666375	−	1.47318i
$903$	−0.549693	−	2.76350i	−0.0182926	−	0.0919634i
$904$	4.77490	+	11.5893i	0.158811	+	0.385455i
$905$	−0.941809	−	0.187338i	−0.0313068	−	0.00622731i
$906$	10.4955	−	16.8546i	0.348691	−	0.559956i
$907$	−27.6015	+	33.6326i	−0.916494	+	1.11675i	0.0763204	+	0.997083i	$0.475683\pi$
$907$	−27.6015	+	33.6326i	−0.916494	+	1.11675i	−0.992814	+	0.119667i	$0.961817\pi$
$908$	−0.255474	−	1.55956i	−0.00847820	−	0.0517559i
$909$	−8.41235	+	15.7384i	−0.279020	+	0.522010i
$910$	−2.09703	−	2.39424i	−0.0695160	−	0.0793683i
$911$	−18.8850	−	45.5924i	−0.625687	−	1.51054i	−0.844933	−	0.534873i	$-0.820360\pi$
$911$	−18.8850	−	45.5924i	−0.625687	−	1.51054i	0.219246	−	0.975670i	$-0.429640\pi$
$912$	−0.0992243	−	0.113718i	−0.00328565	−	0.00376559i
$913$	23.1489	−	55.8865i	0.766118	−	1.84957i
$914$	22.1461	−	7.50208i	0.732527	−	0.248147i
$915$	−2.67727	−	8.82576i	−0.0885077	−	0.291771i
$916$	−25.6639	−	27.4701i	−0.847960	−	0.907639i
$917$	17.5157	−	1.72515i	0.578419	−	0.0569693i
$918$	1.77024	−	10.6805i	0.0584267	−	0.352509i
$919$	−12.4060	+	8.28942i	−0.409236	+	0.273443i	−0.743103	−	0.669178i	$-0.766647\pi$
$919$	−12.4060	+	8.28942i	−0.409236	+	0.273443i	0.333866	+	0.942620i	$0.391647\pi$
$920$	8.86568	−	16.5117i	0.292293	−	0.544373i
$921$	9.02007	−	13.4995i	0.297221	−	0.444823i
$922$	1.65501	+	51.5447i	0.0545049	+	1.69753i
$923$	−2.79804	+	9.22389i	−0.0920985	+	0.303608i
$924$	−4.27585	−	8.69807i	−0.140665	−	0.286146i
$925$	−12.4988	+	10.2575i	−0.410957	+	0.337264i
$926$	−14.7775	−	11.3539i	−0.485618	−	0.373112i
$927$	3.40337	−	3.40337i	0.111781	−	0.111781i
$928$	3.31822	+	20.4982i	0.108926	+	0.672887i
$929$	−26.2781	−	26.2781i	−0.862156	−	0.862156i	0.129432	−	0.991588i	$-0.458685\pi$
$929$	−26.2781	−	26.2781i	−0.862156	−	0.862156i	−0.991588	+	0.129432i	$0.958685\pi$
$930$	−1.31087	−	10.0056i	−0.0429852	−	0.328096i
$931$	−0.132958	−	0.162009i	−0.00435751	−	0.00530964i
$932$	0.110640	+	1.72114i	0.00362412	+	0.0563778i
$933$	16.8869	+	5.12259i	0.552852	+	0.167706i
$934$	7.30290	+	6.84853i	0.238958	+	0.224091i
$935$	20.6020	+	13.7658i	0.673758	+	0.450191i
$936$	−4.19305	+	5.08967i	−0.137054	+	0.166361i
$937$	15.1139	+	22.6196i	0.493751	+	0.738950i	0.991744	−	0.128230i	$-0.0409297\pi$
$937$	15.1139	+	22.6196i	0.493751	+	0.738950i	−0.497994	+	0.867181i	$0.665930\pi$
$938$	13.3654	−	9.56478i	0.436394	−	0.312301i
$939$	1.71919	+	17.4552i	0.0561037	+	0.569630i
$940$	5.45213	−	11.9930i	0.177829	−	0.391169i
$941$	13.5868	−	4.12151i	0.442917	−	0.134357i	−0.0609459	−	0.998141i	$-0.519412\pi$
$941$	13.5868	−	4.12151i	0.442917	−	0.134357i	0.503863	+	0.863784i	$0.331912\pi$
$942$	3.07961	−	6.23497i	0.100339	−	0.203146i
$943$	64.9432	+	26.9004i	2.11484	+	0.875997i
$944$	5.10758	−	8.16785i	0.166238	−	0.265841i
$945$	0.891810	−	0.369400i	0.0290106	−	0.0120166i
$946$	0.882233	−	13.3320i	0.0286839	−	0.433462i
$947$	−16.1085	−	8.61018i	−0.523456	−	0.279793i	0.188432	−	0.982086i	$-0.439660\pi$
$947$	−16.1085	−	8.61018i	−0.523456	−	0.279793i	−0.711888	+	0.702293i	$0.752160\pi$
$948$	−7.39335	−	1.73368i	−0.240125	−	0.0563072i
$949$	−13.0373	−	10.6994i	−0.423209	−	0.347318i
$950$	−0.0526289	−	0.226355i	−0.00170751	−	0.00734394i
$951$	−2.13872	+	10.7521i	−0.0693527	+	0.348659i
$952$	25.5206	+	5.12633i	0.827126	+	0.166145i
$953$	−41.2251	+	8.20018i	−1.33541	+	0.265630i	−0.810606	−	0.585593i	$-0.800862\pi$
$953$	−41.2251	+	8.20018i	−1.33541	+	0.265630i	−0.524805	+	0.851222i	$0.675862\pi$
$954$	0.414463	−	1.09911i	0.0134187	−	0.0355849i
$955$	−4.18313	−	7.82609i	−0.135363	−	0.253246i
$956$	31.1512	+	40.7028i	1.00750	+	1.31642i
$957$	−14.7259	−	1.45037i	−0.476021	−	0.0468839i
$958$	−3.91584	+	14.5775i	−0.126515	+	0.470978i
$959$			19.4652i			0.628565i
$960$	−2.43581	−	5.94377i	−0.0786153	−	0.191834i
$961$		−	47.9734i		−	1.54753i
$962$	−11.8218	−	3.17559i	−0.381149	−	0.102385i
$963$	−18.4494	−	1.81711i	−0.594525	−	0.0585556i
$964$	−35.2357	−	4.68387i	−1.13486	−	0.150857i
$965$	−4.89200	−	9.15229i	−0.157479	−	0.294623i
$966$	13.1277	+	4.95033i	0.422377	+	0.159274i
$967$	13.2640	−	2.63838i	0.426543	−	0.0848446i	0.0228493	−	0.999739i	$-0.492726\pi$
$967$	13.2640	−	2.63838i	0.426543	−	0.0848446i	0.403693	+	0.914894i	$0.367726\pi$
$968$	−2.86923	−	14.5679i	−0.0922205	−	0.468230i
$969$	−0.0563492	+	0.283287i	−0.00181020	+	0.00910048i
$970$	−8.67898	+	2.01791i	−0.278665	+	0.0647912i
$971$	−17.8510	−	14.6499i	−0.572866	−	0.470139i	0.302802	−	0.953054i	$-0.402078\pi$
$971$	−17.8510	−	14.6499i	−0.572866	−	0.470139i	−0.875667	+	0.482915i	$0.839578\pi$
$972$	−1.05400	−	1.69973i	−0.0338072	−	0.0545188i
$973$	0.420660	+	0.224848i	0.0134858	+	0.00720828i
$974$	−13.3117	−	0.880885i	−0.426533	−	0.0282254i
$975$	−9.38131	+	3.88587i	−0.300442	+	0.124447i
$976$	−18.8570	−	41.8977i	−0.603596	−	1.34111i
$977$	45.3586	+	18.7882i	1.45115	+	0.601086i	0.962473	−	0.271378i	$-0.0874794\pi$
$977$	45.3586	+	18.7882i	1.45115	+	0.601086i	0.488678	+	0.872464i	$0.337479\pi$
$978$	−10.2779	−	5.07650i	−0.328649	−	0.162329i
$979$	−14.8892	+	4.51660i	−0.475862	+	0.144351i
$980$	−3.13167	−	8.35244i	−0.100038	−	0.266809i
$981$	−0.456360	−	4.63350i	−0.0145705	−	0.147936i
$982$	−27.3574	−	38.2279i	−0.873011	−	1.21990i
$983$	17.7062	+	26.4992i	0.564740	+	0.845194i	0.998438	−	0.0558646i	$-0.0177915\pi$
$983$	17.7062	+	26.4992i	0.564740	+	0.845194i	−0.433698	+	0.901058i	$0.642792\pi$
$984$	21.2696	−	11.3174i	0.678049	−	0.360785i
$985$	−11.3674	−	7.59545i	−0.362196	−	0.242011i
$986$	27.1846	−	28.9882i	0.865733	−	0.923171i
$987$	9.43775	+	2.86291i	0.300407	+	0.0911274i
$988$	0.116168	−	0.132129i	0.00369580	−	0.00420360i
$989$	12.2699	+	14.9509i	0.390160	+	0.475411i
$990$	4.53860	−	0.594620i	0.144246	−	0.0188983i
$991$	−33.3874	−	33.3874i	−1.06059	−	1.06059i	−0.998042	−	0.0625447i	$-0.980078\pi$
$991$	−33.3874	−	33.3874i	−1.06059	−	1.06059i	−0.0625447	−	0.998042i	$-0.519922\pi$
$992$	−12.8586	−	48.5984i	−0.408260	−	1.54300i
$993$	−0.136789	+	0.136789i	−0.00434088	+	0.00434088i
$994$	4.28241	−	5.57370i	0.135830	−	0.176787i
$995$	7.22685	−	5.93092i	0.229106	−	0.188023i
$996$	28.4076	+	9.68286i	0.900129	+	0.306813i
$997$	−12.9422	+	42.6648i	−0.409884	+	1.35121i	0.472771	+	0.881185i	$0.343254\pi$
$997$	−12.9422	+	42.6648i	−0.409884	+	1.35121i	−0.882655	+	0.470021i	$0.844246\pi$
$998$	5.54533	−	0.178051i	0.175534	−	0.00563610i
$999$	2.06255	−	3.08682i	0.0652562	−	0.0976628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.10	✓	512
128.53	even	32	inner	384.2.v.a.181.10	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.10	✓	512	1.1	even	1	trivial
384.2.v.a.181.10	yes	512	128.53	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.706338 - 1.22519i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.00217 + 1.73079i) q^{4} +(-0.708130 + 0.378503i) q^{5} +(1.28852 - 0.582847i) q^{6} +(-0.234536 - 1.17909i) q^{7} +(2.82842 + 0.00532616i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.706338 - 1.22519i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.00217 + 1.73079i) q^{4} +(-0.708130 + 0.378503i) q^{5} +(1.28852 - 0.582847i) q^{6} +(-0.234536 - 1.17909i) q^{7} +(2.82842 + 0.00532616i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.963917 + 0.600241i) q^{10} +(-2.55728 + 3.11605i) q^{11} +(-1.62423 - 1.16700i) q^{12} +(1.09905 - 2.05618i) q^{13} +(-1.27895 + 1.12019i) q^{14} +(-0.307272 - 0.741820i) q^{15} +(-1.99130 - 3.46911i) q^{16} +(-2.92955 + 7.07255i) q^{17} +(0.453743 + 1.33945i) q^{18} +(-0.0109526 - 0.0361057i) q^{19} +(0.0545578 - 1.60495i) q^{20} +(1.19640 - 0.117835i) q^{21} +(5.62406 + 0.932163i) q^{22} +(-6.86147 + 4.58469i) q^{23} +(-0.282534 + 2.81428i) q^{24} +(-2.41967 + 3.62129i) q^{25} +(-3.29551 + 0.105813i) q^{26} +(0.290285 - 0.956940i) q^{27} +(2.27581 + 0.775722i) q^{28} +(2.83755 - 2.32872i) q^{29} +(-0.691831 + 0.900441i) q^{30} +(-6.28384 + 6.28384i) q^{31} +(-2.84379 + 4.89008i) q^{32} +(-2.85039 - 2.85039i) q^{33} +(10.7345 - 1.40636i) q^{34} +(0.612372 + 0.746178i) q^{35} +(1.32058 - 1.50202i) q^{36} +(3.55263 + 1.07768i) q^{37} +(-0.0365001 + 0.0389218i) q^{38} +(1.93855 + 1.29530i) q^{39} +(-2.00491 + 1.06680i) q^{40} +(-4.73246 - 7.08262i) q^{41} +(-0.989436 - 1.38259i) q^{42} +(-0.229727 - 2.33246i) q^{43} +(-2.83041 - 7.54895i) q^{44} +(0.768365 - 0.233081i) q^{45} +(10.4636 + 5.16826i) q^{46} +(7.57923 + 3.13942i) q^{47} +(3.64759 - 1.64168i) q^{48} +(5.13190 - 2.12570i) q^{49} +(6.14587 + 0.406696i) q^{50} +(-6.75135 - 3.60867i) q^{51} +(2.45738 + 3.96288i) q^{52} +(-0.642068 - 0.526932i) q^{53} +(-1.37747 + 0.320270i) q^{54} +(0.631449 - 3.17451i) q^{55} +(-0.657087 - 3.33622i) q^{56} +(0.0370054 - 0.00736084i) q^{57} +(-4.85739 - 1.83167i) q^{58} +(1.13528 + 2.12396i) q^{59} +(1.59188 + 0.211608i) q^{60} +(11.4311 + 1.12587i) q^{61} +(12.1374 + 3.26038i) q^{62} +1.20219i q^{63} +(7.99994 + 0.0301292i) q^{64} +1.87204i q^{65} +(-1.47893 + 5.50561i) q^{66} +(-9.62036 - 0.947523i) q^{67} +(-9.30522 - 12.1584i) q^{68} +(-3.89007 - 7.27781i) q^{69} +(0.481667 - 1.27732i) q^{70} +(-4.05482 + 0.806554i) q^{71} +(-2.77304 - 0.557022i) q^{72} +(1.41126 - 7.09488i) q^{73} +(-1.18900 - 5.11385i) q^{74} +(-3.36668 - 2.76297i) q^{75} +(0.0734680 + 0.0172276i) q^{76} +(4.27389 + 2.28444i) q^{77} +(0.217713 - 3.29001i) q^{78} +(3.50792 - 1.45303i) q^{79} +(2.72317 + 1.70287i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-5.33483 + 10.8009i) q^{82} +(-14.3601 + 4.35608i) q^{83} +(-0.995055 + 2.18882i) q^{84} +(-0.602485 - 6.11713i) q^{85} +(-2.69544 + 1.92897i) q^{86} +(2.03938 + 3.05214i) q^{87} +(-7.24966 + 8.79990i) q^{88} +(3.20933 + 2.14441i) q^{89} +(-0.828294 - 0.776759i) q^{90} +(-2.68219 - 0.813635i) q^{91} +(-1.05877 - 16.4704i) q^{92} +(-5.63766 - 6.86951i) q^{93} +(-1.50712 - 11.5035i) q^{94} +(0.0214220 + 0.0214220i) q^{95} +(-4.58779 - 3.30941i) q^{96} +(-5.54866 + 5.54866i) q^{97} +(-6.22925 - 4.78609i) q^{98} +(3.11605 - 2.55728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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