LMFDB - Embedded newform 231.2.u.a.20.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(20,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6]))

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

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

chi := DirichletCharacter("231.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.u (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			20.5
Character	$\chi$	$=$	231.20
Dual form			231.2.u.a.104.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64177 - 0.533443i) q^{2} +(-1.71497 - 0.242653i) q^{3} +(0.792810 + 0.576010i) q^{4} +(0.0901224 + 0.277368i) q^{5} +(2.68614 + 1.31322i) q^{6} +(2.64157 + 0.148745i) q^{7} +(1.03500 + 1.42455i) q^{8} +(2.88224 + 0.832286i) q^{9} +O(q^{10})$	\(q+(-1.64177 - 0.533443i) q^{2} +(-1.71497 - 0.242653i) q^{3} +(0.792810 + 0.576010i) q^{4} +(0.0901224 + 0.277368i) q^{5} +(2.68614 + 1.31322i) q^{6} +(2.64157 + 0.148745i) q^{7} +(1.03500 + 1.42455i) q^{8} +(2.88224 + 0.832286i) q^{9} -0.503450i q^{10} +(-1.91881 - 2.70521i) q^{11} +(-1.21987 - 1.18022i) q^{12} +(-3.95370 - 1.28464i) q^{13} +(-4.25750 - 1.65333i) q^{14} +(-0.0872528 - 0.497546i) q^{15} +(-1.54496 - 4.75490i) q^{16} +(-2.04829 - 6.30398i) q^{17} +(-4.28799 - 2.90393i) q^{18} +(2.21414 + 3.04750i) q^{19} +(-0.0883170 + 0.271812i) q^{20} +(-4.49411 - 0.896078i) q^{21} +(1.70717 + 5.46491i) q^{22} -1.41628i q^{23} +(-1.42931 - 2.69420i) q^{24} +(3.97627 - 2.88893i) q^{25} +(5.80578 + 4.21815i) q^{26} +(-4.74099 - 2.12673i) q^{27} +(2.00858 + 1.63950i) q^{28} +(2.24789 - 3.09395i) q^{29} +(-0.122164 + 0.863401i) q^{30} +(-5.52136 - 1.79400i) q^{31} +5.10892i q^{32} +(2.63427 + 5.10496i) q^{33} +11.4423i q^{34} +(0.196807 + 0.746092i) q^{35} +(1.80566 + 2.32004i) q^{36} +(-5.91329 - 4.29626i) q^{37} +(-2.00944 - 6.18441i) q^{38} +(6.46875 + 3.16249i) q^{39} +(-0.301848 + 0.415459i) q^{40} +(8.01488 - 5.82315i) q^{41} +(6.90029 + 3.86851i) q^{42} -0.184966 q^{43} +(0.0369769 - 3.24997i) q^{44} +(0.0289045 + 0.874449i) q^{45} +(-0.755503 + 2.32520i) q^{46} +(-2.89934 + 2.10649i) q^{47} +(1.49577 + 8.52940i) q^{48} +(6.95575 + 0.785839i) q^{49} +(-8.06920 + 2.62184i) q^{50} +(1.98307 + 11.3082i) q^{51} +(-2.39457 - 3.29585i) q^{52} +(-3.02722 - 0.983603i) q^{53} +(6.64913 + 6.02065i) q^{54} +(0.577412 - 0.776017i) q^{55} +(2.52212 + 3.91699i) q^{56} +(-3.05769 - 5.76363i) q^{57} +(-5.34096 + 3.88043i) q^{58} +(2.44032 + 1.77299i) q^{59} +(0.217417 - 0.444718i) q^{60} +(13.9451 - 4.53104i) q^{61} +(8.10781 + 5.89067i) q^{62} +(7.48983 + 2.62726i) q^{63} +(-0.364604 + 1.12214i) q^{64} -1.21241i q^{65} +(-1.60166 - 9.78640i) q^{66} -14.5349 q^{67} +(2.00725 - 6.17769i) q^{68} +(-0.343664 + 2.42887i) q^{69} +(0.0748856 - 1.32990i) q^{70} +(-0.913804 + 0.296913i) q^{71} +(1.79747 + 4.96730i) q^{72} +(2.91589 - 4.01338i) q^{73} +(7.41645 + 10.2079i) q^{74} +(-7.52020 + 3.98957i) q^{75} +3.69145i q^{76} +(-4.66628 - 7.43141i) q^{77} +(-8.93319 - 8.64279i) q^{78} +(3.95957 - 12.1863i) q^{79} +(1.17962 - 0.857046i) q^{80} +(7.61460 + 4.79769i) q^{81} +(-16.2649 + 5.28479i) q^{82} +(2.76762 + 8.51786i) q^{83} +(-3.04683 - 3.29908i) q^{84} +(1.56393 - 1.13626i) q^{85} +(0.303671 + 0.0986686i) q^{86} +(-4.60581 + 4.76057i) q^{87} +(1.86775 - 5.53332i) q^{88} -9.27676 q^{89} +(0.419014 - 1.45106i) q^{90} +(-10.2529 - 3.98154i) q^{91} +(0.815790 - 1.12284i) q^{92} +(9.03365 + 4.41643i) q^{93} +(5.88373 - 1.91174i) q^{94} +(-0.645736 + 0.888779i) q^{95} +(1.23970 - 8.76164i) q^{96} +(2.36507 + 0.768458i) q^{97} +(-11.0005 - 5.00066i) q^{98} +(-3.27896 - 9.39406i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	$ 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) $ 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−1.64177	−	0.533443i	−1.16091	−	0.377201i	−0.335665	−	0.941982i	$-0.608961\pi$
$2$	−1.64177	−	0.533443i	−1.16091	−	0.377201i	−0.825241	+	0.564780i	$0.808961\pi$
$3$	−1.71497	−	0.242653i	−0.990138	−	0.140096i
$3$	−1.71497	−	0.242653i	−0.990138	−	0.140096i
$4$	0.792810	+	0.576010i	0.396405	+	0.288005i
$5$	0.0901224	+	0.277368i	0.0403040	+	0.124043i	0.969184	−	0.246338i	$-0.0792273\pi$
$5$	0.0901224	+	0.277368i	0.0403040	+	0.124043i	−0.928880	+	0.370381i	$0.879227\pi$
$6$	2.68614	+	1.31322i	1.09661	+	0.536120i
$7$	2.64157	+	0.148745i	0.998418	+	0.0562203i
$7$	2.64157	+	0.148745i	0.998418	+	0.0562203i
$8$	1.03500	+	1.42455i	0.365926	+	0.503654i
$9$	2.88224	+	0.832286i	0.960746	+	0.277429i
$10$		−	0.503450i		−	0.159205i
$11$	−1.91881	−	2.70521i	−0.578543	−	0.815652i
$11$	−1.91881	−	2.70521i	−0.578543	−	0.815652i
$12$	−1.21987	−	1.18022i	−0.352147	−	0.340700i
$13$	−3.95370	−	1.28464i	−1.09656	−	0.356294i	−0.295782	−	0.955256i	$-0.595580\pi$
$13$	−3.95370	−	1.28464i	−1.09656	−	0.356294i	−0.800778	+	0.598962i	$0.795580\pi$
$14$	−4.25750	−	1.65333i	−1.13786	−	0.441871i
$15$	−0.0872528	−	0.497546i	−0.0225286	−	0.128466i
$16$	−1.54496	−	4.75490i	−0.386240	−	1.18873i
$17$	−2.04829	−	6.30398i	−0.496782	−	1.52894i	−0.814160	−	0.580640i	$-0.802802\pi$
$17$	−2.04829	−	6.30398i	−0.496782	−	1.52894i	0.317378	−	0.948299i	$-0.397198\pi$
$18$	−4.28799	−	2.90393i	−1.01069	−	0.684463i
$19$	2.21414	+	3.04750i	0.507958	+	0.699144i	0.983573	−	0.180509i	$-0.0577746\pi$
$19$	2.21414	+	3.04750i	0.507958	+	0.699144i	−0.475615	+	0.879653i	$0.657775\pi$
$20$	−0.0883170	+	0.271812i	−0.0197483	+	0.0607790i
$21$	−4.49411	−	0.896078i	−0.980696	−	0.195540i
$22$	1.70717	+	5.46491i	0.363969	+	1.16512i
$23$		−	1.41628i		−	0.295314i	−0.989039	−	0.147657i	$-0.952827\pi$
$23$		−	1.41628i		−	0.295314i	0.989039	−	0.147657i	$-0.0471732\pi$
$24$	−1.42931	−	2.69420i	−0.291757	−	0.549952i
$25$	3.97627	−	2.88893i	0.795255	−	0.577786i
$26$	5.80578	+	4.21815i	1.13861	+	0.827247i
$27$	−4.74099	−	2.12673i	−0.912405	−	0.409289i
$28$	2.00858	+	1.63950i	0.379586	+	0.309836i
$29$	2.24789	−	3.09395i	0.417422	−	0.574532i	−0.547587	−	0.836749i	$-0.684454\pi$
$29$	2.24789	−	3.09395i	0.417422	−	0.574532i	0.965009	+	0.262217i	$0.0844535\pi$
$30$	−0.122164	+	0.863401i	−0.0223039	+	0.157635i
$31$	−5.52136	−	1.79400i	−0.991666	−	0.322212i	−0.232135	−	0.972683i	$-0.574571\pi$
$31$	−5.52136	−	1.79400i	−0.991666	−	0.322212i	−0.759531	+	0.650472i	$0.774571\pi$
$32$			5.10892i			0.903138i
$33$	2.63427	+	5.10496i	0.458568	+	0.888659i
$34$			11.4423i			1.96234i
$35$	0.196807	+	0.746092i	0.0332665	+	0.126113i
$36$	1.80566	+	2.32004i	0.300944	+	0.386674i
$37$	−5.91329	−	4.29626i	−0.972139	−	0.706300i	−0.0162009	−	0.999869i	$-0.505157\pi$
$37$	−5.91329	−	4.29626i	−0.972139	−	0.706300i	−0.955938	+	0.293568i	$0.905157\pi$
$38$	−2.00944	−	6.18441i	−0.325973	−	1.00324i
$39$	6.46875	+	3.16249i	1.03583	+	0.506404i
$40$	−0.301848	+	0.415459i	−0.0477264	+	0.0656898i
$41$	8.01488	−	5.82315i	1.25171	−	0.909424i	0.253394	−	0.967363i	$-0.418453\pi$
$41$	8.01488	−	5.82315i	1.25171	−	0.909424i	0.998320	+	0.0579391i	$0.0184529\pi$
$42$	6.90029	+	3.86851i	1.06474	+	0.596924i
$43$	−0.184966			−0.0282070			−0.0141035	−	0.999901i	$-0.504489\pi$
$43$	−0.184966			−0.0282070			−0.0141035	+	0.999901i	$0.504489\pi$
$44$	0.0369769	−	3.24997i	0.00557448	−	0.489952i
$45$	0.0289045	+	0.874449i	0.00430884	+	0.130355i
$46$	−0.755503	+	2.32520i	−0.111393	+	0.342832i
$47$	−2.89934	+	2.10649i	−0.422912	+	0.307263i	−0.778808	−	0.627262i	$-0.784175\pi$
$47$	−2.89934	+	2.10649i	−0.422912	+	0.307263i	0.355897	+	0.934525i	$0.384175\pi$
$48$	1.49577	+	8.52940i	0.215895	+	1.23111i
$49$	6.95575	+	0.785839i	0.993679	+	0.112263i
$50$	−8.06920	+	2.62184i	−1.14116	+	0.370785i
$51$	1.98307	+	11.3082i	0.277685	+	1.58346i
$52$	−2.39457	−	3.29585i	−0.332067	−	0.457052i
$53$	−3.02722	−	0.983603i	−0.415821	−	0.135108i	0.0936323	−	0.995607i	$-0.470152\pi$
$53$	−3.02722	−	0.983603i	−0.415821	−	0.135108i	−0.509453	+	0.860499i	$0.670152\pi$
$54$	6.64913	+	6.02065i	0.904832	+	0.819307i
$55$	0.577412	−	0.776017i	0.0778582	−	0.104638i
$56$	2.52212	+	3.91699i	0.337032	+	0.523430i
$57$	−3.05769	−	5.76363i	−0.405001	−	0.763412i
$58$	−5.34096	+	3.88043i	−0.701302	+	0.509526i
$59$	2.44032	+	1.77299i	0.317702	+	0.230824i	0.735194	−	0.677856i	$-0.237091\pi$
$59$	2.44032	+	1.77299i	0.317702	+	0.230824i	−0.417492	+	0.908681i	$0.637091\pi$
$60$	0.217417	−	0.444718i	0.0280684	−	0.0574129i
$61$	13.9451	−	4.53104i	1.78549	−	0.580140i	0.786204	−	0.617967i	$-0.212043\pi$
$61$	13.9451	−	4.53104i	1.78549	−	0.580140i	0.999284	+	0.0378260i	$0.0120433\pi$
$62$	8.10781	+	5.89067i	1.02969	+	0.748115i
$63$	7.48983	+	2.62726i	0.943630	+	0.331003i
$64$	−0.364604	+	1.12214i	−0.0455755	+	0.140267i
$65$		−	1.21241i		−	0.150380i
$66$	−1.60166	−	9.78640i	−0.197151	−	1.20462i
$67$	−14.5349			−1.77571			−0.887857	−	0.460119i	$-0.847807\pi$
$67$	−14.5349			−1.77571			−0.887857	+	0.460119i	$0.847807\pi$
$68$	2.00725	−	6.17769i	0.243415	−	0.749155i
$69$	−0.343664	+	2.42887i	−0.0413723	+	0.292402i
$70$	0.0748856	−	1.32990i	0.00895054	−	0.158953i
$71$	−0.913804	+	0.296913i	−0.108449	+	0.0352371i	−0.362739	−	0.931891i	$-0.618158\pi$
$71$	−0.913804	+	0.296913i	−0.108449	+	0.0352371i	0.254290	+	0.967128i	$0.418158\pi$
$72$	1.79747	+	4.96730i	0.211834	+	0.585402i
$73$	2.91589	−	4.01338i	0.341279	−	0.469730i	−0.603536	−	0.797336i	$-0.706242\pi$
$73$	2.91589	−	4.01338i	0.341279	−	0.469730i	0.944814	+	0.327606i	$0.106242\pi$
$74$	7.41645	+	10.2079i	0.862145	+	1.18664i
$75$	−7.52020	+	3.98957i	−0.868357	+	0.460676i
$76$			3.69145i			0.423439i
$77$	−4.66628	−	7.43141i	−0.531772	−	0.846888i
$78$	−8.93319	−	8.64279i	−1.01148	−	0.978603i
$79$	3.95957	−	12.1863i	0.445487	−	1.37107i	−0.436463	−	0.899722i	$-0.643769\pi$
$79$	3.95957	−	12.1863i	0.445487	−	1.37107i	0.881949	−	0.471345i	$-0.156231\pi$
$80$	1.17962	−	0.857046i	0.131886	−	0.0958207i
$81$	7.61460	+	4.79769i	0.846067	+	0.533077i
$82$	−16.2649	+	5.28479i	−1.79616	+	0.583607i
$83$	2.76762	+	8.51786i	0.303786	+	0.934956i	0.980128	+	0.198368i	$0.0635642\pi$
$83$	2.76762	+	8.51786i	0.303786	+	0.934956i	−0.676342	+	0.736588i	$0.736436\pi$
$84$	−3.04683	−	3.29908i	−0.332436	−	0.359959i
$85$	1.56393	−	1.13626i	0.169632	−	0.123245i
$86$	0.303671	+	0.0986686i	0.0327457	+	0.0106397i
$87$	−4.60581	+	4.76057i	−0.493795	+	0.510387i
$88$	1.86775	−	5.53332i	0.199102	−	0.589854i
$89$	−9.27676			−0.983335			−0.491667	−	0.870783i	$-0.663612\pi$
$89$	−9.27676			−0.983335			−0.491667	+	0.870783i	$0.663612\pi$
$90$	0.419014	−	1.45106i	0.0441680	−	0.152955i
$91$	−10.2529	−	3.98154i	−1.07479	−	0.417379i
$92$	0.815790	−	1.12284i	0.0850520	−	0.117064i
$93$	9.03365	+	4.41643i	0.936746	+	0.457963i
$94$	5.88373	−	1.91174i	0.606861	−	0.197181i
$95$	−0.645736	+	0.888779i	−0.0662511	+	0.0911868i
$96$	1.23970	−	8.76164i	0.126526	−	0.894231i
$97$	2.36507	+	0.768458i	0.240137	+	0.0780251i	0.426613	−	0.904434i	$-0.359707\pi$
$97$	2.36507	+	0.768458i	0.240137	+	0.0780251i	−0.186476	+	0.982459i	$0.559707\pi$
$98$	−11.0005	−	5.00066i	−1.11122	−	0.505143i
$99$	−3.27896	−	9.39406i	−0.329548	−	0.944139i
$100$	4.81649			0.481649
$101$	−2.80127	+	8.62141i	−0.278736	+	0.857862i	0.709470	+	0.704735i	$0.248934\pi$
$101$	−2.80127	+	8.62141i	−0.278736	+	0.857862i	−0.988207	+	0.153127i	$0.951066\pi$
$102$	2.77652	−	19.6232i	0.274916	−	1.94299i
$103$	−0.0129190	+	0.0177815i	−0.00127295	+	0.00175206i	−0.809653	−	0.586909i	$-0.800345\pi$
$103$	−0.0129190	+	0.0177815i	−0.00127295	+	0.00175206i	0.808380	+	0.588661i	$0.200345\pi$
$104$	−2.26204	−	6.96183i	−0.221811	−	0.682664i
$105$	−0.156477	−	1.32728i	−0.0152705	−	0.129529i
$106$	4.44530	+	3.22970i	0.431766	+	0.313696i
$107$	−0.868130	−	1.19488i	−0.0839253	−	0.115513i	0.764990	−	0.644042i	$-0.222744\pi$
$107$	−0.868130	−	1.19488i	−0.0839253	−	0.115513i	−0.848915	+	0.528529i	$0.822744\pi$
$108$	−2.53369	−	4.41696i	−0.243804	−	0.425022i
$109$	1.62404			0.155555			0.0777773	−	0.996971i	$-0.475218\pi$
$109$	1.62404			0.155555			0.0777773	+	0.996971i	$0.475218\pi$
$110$	−1.36194	+	0.966024i	−0.129856	+	0.0921068i
$111$	9.09861	+	8.80283i	0.863602	+	0.835527i
$112$	−3.37385	−	12.7902i	−0.318799	−	1.20856i
$113$	4.64485	+	6.39309i	0.436951	+	0.601411i	0.969531	−	0.244968i	$-0.0787776\pi$
$113$	4.64485	+	6.39309i	0.436951	+	0.601411i	−0.532580	+	0.846379i	$0.678778\pi$
$114$	1.94545	+	11.0937i	0.182208	+	1.03902i
$115$	0.392830	−	0.127638i	0.0366316	−	0.0119023i
$116$	3.56430	−	1.15811i	0.330936	−	0.107528i
$117$	−10.3263	−	6.99324i	−0.954669	−	0.646525i
$118$	−3.06064	−	4.21262i	−0.281755	−	0.387803i
$119$	−4.47300	−	16.9570i	−0.410039	−	1.55445i
$120$	0.618473	−	0.639254i	0.0564586	−	0.0583556i
$121$	−3.63633	+	10.3816i	−0.330576	+	0.943779i
$122$	−25.3117			−2.29161
$123$	−15.1583	+	8.04169i	−1.36678	+	0.725095i
$124$	−3.34403	−	4.60266i	−0.300303	−	0.413331i
$125$	2.33937	+	1.69965i	0.209239	+	0.152021i
$126$	−10.8951	−	8.30875i	−0.970610	−	0.740202i
$127$	1.22972	+	3.78470i	0.109120	+	0.335838i	0.990675	−	0.136244i	$-0.0435030\pi$
$127$	1.22972	+	3.78470i	0.109120	+	0.335838i	−0.881555	+	0.472081i	$0.843503\pi$
$128$	7.20309	−	9.91420i	0.636669	−	0.876300i
$129$	0.317210	+	0.0448825i	0.0279288	+	0.00395169i
$130$	−0.646749	+	1.99049i	−0.0567237	+	0.174577i
$131$	8.45729			0.738917			0.369458	−	0.929247i	$-0.379543\pi$
$131$	8.45729			0.738917			0.369458	+	0.929247i	$0.379543\pi$
$132$	−0.852031	+	5.56463i	−0.0741598	+	0.484339i
$133$	5.39549	+	8.37951i	0.467848	+	0.726596i
$134$	23.8629	+	7.75352i	2.06144	+	0.669802i
$135$	0.162618	−	1.50667i	0.0139959	−	0.129673i
$136$	6.86036	−	9.44247i	0.588271	−	0.809685i
$137$	7.10428	−	2.30832i	0.606960	−	0.197213i	0.0106179	−	0.999944i	$-0.496620\pi$
$137$	7.10428	−	2.30832i	0.606960	−	0.197213i	0.596342	+	0.802730i	$0.296620\pi$
$138$	1.85988	−	3.80432i	0.158324	−	0.323845i
$139$	−7.14489	+	9.83410i	−0.606022	+	0.834118i	−0.996243	−	0.0866035i	$-0.972399\pi$
$139$	−7.14489	+	9.83410i	−0.606022	+	0.834118i	0.390221	+	0.920721i	$0.372399\pi$
$140$	−0.273726	+	0.704872i	−0.0231341	+	0.0595726i
$141$	5.48342	−	2.90903i	0.461787	−	0.244985i
$142$	1.65864			0.139190
$143$	4.11119	+	13.1606i	0.343795	+	1.10054i
$144$	−0.495508	−	14.9906i	−0.0412924	−	1.24922i
$145$	1.06075	+	0.344658i	0.0880903	+	0.0286223i
$146$	−6.92812	+	5.03358i	−0.573375	+	0.416582i
$147$	−11.7382	−	3.03553i	−0.968151	−	0.250366i
$148$	−2.21343	−	6.81223i	−0.181943	−	0.559962i
$149$	−12.4715	+	4.05225i	−1.02171	+	0.331973i	−0.771507	−	0.636221i	$-0.780497\pi$
$149$	−12.4715	+	4.05225i	−1.02171	+	0.331973i	−0.250201	+	0.968194i	$0.580497\pi$
$150$	14.4746	−	2.53836i	1.18185	−	0.207256i
$151$	6.65079	−	4.83208i	0.541233	−	0.393229i	−0.283310	−	0.959029i	$-0.591432\pi$
$151$	6.65079	−	4.83208i	0.541233	−	0.393229i	0.824543	+	0.565800i	$0.191432\pi$
$152$	−2.04969	+	6.30829i	−0.166252	+	0.511670i
$153$	−0.656938	−	19.8743i	−0.0531103	−	1.60674i
$154$	3.69672	+	14.6899i	0.297890	+	1.18374i
$155$		−	1.69313i		−	0.135995i
$156$	3.30687	+	6.23332i	0.264761	+	0.499065i
$157$	0.0463980	+	0.0638613i	0.00370296	+	0.00509669i	0.810864	−	0.585234i	$-0.198997\pi$
$157$	0.0463980	+	0.0638613i	0.00370296	+	0.00509669i	−0.807162	+	0.590331i	$0.798997\pi$
$158$	−13.0014	+	17.8949i	−1.03434	+	1.42364i
$159$	4.95291	+	2.42141i	0.392792	+	0.192031i
$160$	−1.41705	+	0.460428i	−0.112028	+	0.0364000i
$161$	0.210664	−	3.74119i	0.0166026	−	0.294847i
$162$	−9.94212	−	11.9387i	−0.781127	−	0.937990i
$163$	0.782213	−	2.40741i	0.0612677	−	0.188563i	−0.915738	−	0.401776i	$-0.868393\pi$
$163$	0.782213	−	2.40741i	0.0612677	−	0.188563i	0.977006	+	0.213214i	$0.0683930\pi$
$164$	9.70848			0.758105
$165$	−1.17855	+	1.19073i	−0.0917497	+	0.0926985i
$166$		−	15.4607i		−	1.19998i
$167$	−3.77212	+	11.6094i	−0.291895	+	0.898361i	0.692351	+	0.721561i	$0.256575\pi$
$167$	−3.77212	+	11.6094i	−0.291895	+	0.898361i	−0.984247	+	0.176801i	$0.943425\pi$
$168$	−3.37488	−	7.32952i	−0.260378	−	0.565485i
$169$	3.46424	+	2.51692i	0.266480	+	0.193609i
$170$	−3.17374	+	1.03121i	−0.243414	+	0.0790901i
$171$	3.84528	+	10.6264i	0.294056	+	0.812622i
$172$	−0.146643	−	0.106542i	−0.0111814	−	0.00812376i
$173$	10.2660	−	7.45865i	0.780506	−	0.567071i	−0.124625	−	0.992204i	$-0.539773\pi$
$173$	10.2660	−	7.45865i	0.780506	−	0.567071i	0.905131	+	0.425133i	$0.139773\pi$
$174$	10.1012	−	5.35882i	0.765768	−	0.406251i
$175$	10.9333	−	7.03986i	0.826480	−	0.532163i
$176$	−9.89852	+	13.3032i	−0.746129	+	1.00277i
$177$	−3.75484	−	3.63278i	−0.282231	−	0.273057i
$178$	15.2303	+	4.94862i	1.14156	+	0.370915i
$179$	7.65486	+	10.5360i	0.572151	+	0.787499i	0.992808	−	0.119721i	$-0.0382001\pi$
$179$	7.65486	+	10.5360i	0.572151	+	0.787499i	−0.420656	+	0.907220i	$0.638200\pi$
$180$	−0.480776	+	0.709921i	−0.0358349	+	0.0529144i
$181$	−2.27660	+	0.739711i	−0.169218	+	0.0549823i	−0.392401	−	0.919794i	$-0.628355\pi$
$181$	−2.27660	+	0.739711i	−0.169218	+	0.0549823i	0.223183	+	0.974777i	$0.428355\pi$
$182$	14.7089	+	12.0061i	1.09030	+	0.889952i
$183$	−25.0149	+	4.38677i	−1.84916	+	0.324279i
$184$	2.01756	−	1.46584i	0.148736	−	0.108063i
$185$	0.658725	−	2.02735i	0.0484304	−	0.149054i
$186$	−12.4752	−	12.0697i	−0.914730	−	0.884993i
$187$	−13.1233	+	17.6372i	−0.959672	+	1.28976i
$188$	−3.51198			−0.256138
$189$	−12.2073	−	6.32310i	−0.887951	−	0.459938i
$190$	1.53426	−	1.11471i	0.111307	−	0.0808693i
$191$	6.43628	−	8.85878i	0.465713	−	0.640999i	−0.509968	−	0.860193i	$-0.670343\pi$
$191$	6.43628	−	8.85878i	0.465713	−	0.640999i	0.975681	+	0.219194i	$0.0703429\pi$
$192$	0.897574	−	1.83595i	0.0647768	−	0.132499i
$193$	1.30868	+	4.02770i	0.0942007	+	0.289920i	0.987045	−	0.160446i	$-0.0512934\pi$
$193$	1.30868	+	4.02770i	0.0942007	+	0.289920i	−0.892844	+	0.450366i	$0.851293\pi$
$194$	−3.47297	−	2.52326i	−0.249345	−	0.181160i
$195$	−0.294194	+	2.07924i	−0.0210677	+	0.148897i
$196$	5.06194	+	4.62961i	0.361567	+	0.330686i
$197$		−	11.8118i		−	0.841554i	−0.907164	−	0.420777i	$-0.861758\pi$
$197$		−	11.8118i		−	0.841554i	0.907164	−	0.420777i	$-0.138242\pi$
$198$	0.372098	+	17.1720i	0.0264438	+	1.22036i
$199$			20.6500i			1.46384i	0.681390	+	0.731921i	$0.261376\pi$
$199$			20.6500i			1.46384i	−0.681390	+	0.731921i	$0.738624\pi$
$200$	8.23085	+	2.67437i	0.582009	+	0.189106i
$201$	24.9268	+	3.52693i	1.75820	+	0.248770i
$202$	9.19806	−	12.6600i	0.647173	−	0.890758i
$203$	6.39815	−	7.83851i	0.449062	−	0.550156i
$204$	−4.94142	+	10.1075i	−0.345968	+	0.707666i
$205$	2.33748	+	1.69828i	0.163257	+	0.118613i
$206$	0.0306955	−	0.0223016i	0.00213866	−	0.00155382i
$207$	1.17875	−	4.08205i	0.0819286	−	0.283722i
$208$			20.7842i			1.44112i
$209$	3.99562	−	11.8373i	0.276383	−	0.818802i
$210$	−0.451130	+	2.26256i	−0.0311309	+	0.156131i
$211$	−3.97810	+	12.2433i	−0.273864	+	0.842865i	0.715654	+	0.698455i	$0.246129\pi$
$211$	−3.97810	+	12.2433i	−0.273864	+	0.842865i	−0.989518	+	0.144411i	$0.953871\pi$
$212$	−1.83345	−	2.52352i	−0.125922	−	0.173316i
$213$	1.63919	−	0.287459i	0.112316	−	0.0196963i
$214$	0.787869	+	2.42481i	0.0538576	+	0.165757i
$215$	−0.0166695	−	0.0513036i	−0.00113685	−	0.00349887i
$216$	−1.87728	−	8.95493i	−0.127732	−	0.609306i
$217$	−14.3182	−	5.56024i	−0.971983	−	0.377454i
$218$	−2.66630	−	0.866332i	−0.180584	−	0.0586754i
$219$	−5.97452	+	6.17526i	−0.403720	+	0.417286i
$220$	0.904772	−	0.282639i	0.0609997	−	0.0190555i
$221$			27.5553i			1.85357i
$222$	−10.2420	−	19.3058i	−0.687399	−	1.29572i
$223$	4.58244	+	6.30719i	0.306863	+	0.422361i	0.934400	−	0.356226i	$-0.115937\pi$
$223$	4.58244	+	6.30719i	0.306863	+	0.422361i	−0.627537	+	0.778587i	$0.715937\pi$
$224$	−0.759926	+	13.4956i	−0.0507747	+	0.901710i
$225$	13.8650	−	5.01719i	0.924333	−	0.334480i
$226$	−4.21542	−	12.9737i	−0.280406	−	0.863000i
$227$	19.3161	+	14.0340i	1.28205	+	0.931467i	0.999613	−	0.0278180i	$-0.00885590\pi$
$227$	19.3161	+	14.0340i	1.28205	+	0.931467i	0.282441	+	0.959285i	$0.408856\pi$
$228$	0.895744	−	6.33073i	0.0593221	−	0.419263i
$229$	−6.56760	−	2.13394i	−0.433999	−	0.141015i	0.0838660	−	0.996477i	$-0.473273\pi$
$229$	−6.56760	−	2.13394i	−0.433999	−	0.141015i	−0.517865	+	0.855462i	$0.673273\pi$
$230$	−0.713024			−0.0470154
$231$	6.19927	+	13.8769i	0.407882	+	0.913035i
$232$	6.73404			0.442111
$233$	11.2429	+	3.65305i	0.736549	+	0.239319i	0.653184	−	0.757200i	$-0.273433\pi$
$233$	11.2429	+	3.65305i	0.736549	+	0.239319i	0.0833659	+	0.996519i	$0.473433\pi$
$234$	13.2229	+	16.9898i	0.864411	+	1.11066i
$235$	−0.845568	−	0.614341i	−0.0551588	−	0.0400752i
$236$	0.913445	+	2.81130i	0.0594602	+	0.183000i
$237$	−9.74759	+	19.9383i	−0.633174	+	1.29513i
$238$	−1.70199	+	30.2257i	−0.110323	+	1.95924i
$239$	−5.68907	−	7.83033i	−0.367995	−	0.506502i	0.584359	−	0.811495i	$-0.301346\pi$
$239$	−5.68907	−	7.83033i	−0.367995	−	0.506502i	−0.952355	+	0.304993i	$0.901346\pi$
$240$	−2.23098	+	1.18357i	−0.144009	+	0.0763990i
$241$			11.7340i			0.755853i	0.925836	+	0.377926i	$0.123363\pi$
$241$			11.7340i			0.755853i	−0.925836	+	0.377926i	$0.876637\pi$
$242$	11.5080	−	15.1044i	0.739762	−	0.970946i
$243$	−11.8946	−	10.0756i	−0.763041	−	0.646350i
$244$	13.6658	+	4.44027i	0.874861	+	0.284259i
$245$	0.408902	+	2.00013i	0.0261238	+	0.127783i
$246$	29.1762	−	5.11652i	1.86021	−	0.326217i
$247$	−4.83911	−	14.8933i	−0.307905	−	0.947635i
$248$	−3.15894	−	9.72223i	−0.200593	−	0.617362i
$249$	−2.67950	−	15.2794i	−0.169806	−	0.968295i
$250$	−2.93403	−	4.03835i	−0.185565	−	0.255408i
$251$	6.69655	−	20.6099i	0.422682	−	1.30088i	−0.482514	−	0.875888i	$-0.660276\pi$
$251$	6.69655	−	20.6099i	0.422682	−	1.30088i	0.905196	−	0.424994i	$-0.139724\pi$
$252$	4.42469	+	6.39714i	0.278729	+	0.402982i
$253$	−3.83133	+	2.71757i	−0.240873	+	0.170852i
$254$		−	6.86959i		−	0.431036i
$255$	−2.95780	+	1.56916i	−0.185225	+	0.0982644i
$256$	−15.2054	+	11.0474i	−0.950336	+	0.690459i
$257$	−24.5650	−	17.8475i	−1.53232	−	1.11330i	−0.954932	−	0.296826i	$-0.904072\pi$
$257$	−24.5650	−	17.8475i	−1.53232	−	1.11330i	−0.577389	−	0.816469i	$-0.695928\pi$
$258$	−0.496844	−	0.242900i	−0.0309321	−	0.0151223i
$259$	−14.9813	−	12.2284i	−0.930893	−	0.759837i
$260$	0.698358	−	0.961207i	0.0433103	−	0.0596116i
$261$	9.05400	−	7.04662i	0.560428	−	0.436175i
$262$	−13.8849	−	4.51148i	−0.857813	−	0.278720i
$263$			6.55382i			0.404126i	0.979373	+	0.202063i	$0.0647645\pi$
$263$			6.55382i			0.404126i	−0.979373	+	0.202063i	$0.935235\pi$
$264$	−4.54580	+	9.03626i	−0.279775	+	0.556143i
$265$		−	0.928299i		−	0.0570250i
$266$	−4.38816	−	16.6354i	−0.269055	−	1.01998i
$267$	15.9094	+	2.25104i	0.973637	+	0.137761i
$268$	−11.5234	−	8.37223i	−0.703903	−	0.511415i
$269$	1.54932	+	4.76830i	0.0944634	+	0.290728i	0.987113	−	0.160022i	$-0.0511565\pi$
$269$	1.54932	+	4.76830i	0.0944634	+	0.290728i	−0.892650	+	0.450750i	$0.851156\pi$
$270$	−1.07070	+	2.38685i	−0.0651608	+	0.145259i
$271$	6.39766	−	8.80562i	0.388630	−	0.534903i	−0.569215	−	0.822189i	$-0.692753\pi$
$271$	6.39766	−	8.80562i	0.388630	−	0.534903i	0.957845	+	0.287285i	$0.0927528\pi$
$272$	−26.8103	+	19.4788i	−1.62561	+	1.18108i
$273$	16.6172	+	9.31612i	1.00572	+	0.563837i
$274$	−12.8950			−0.779013
$275$	−15.4449	−	5.21335i	−0.931362	−	0.314377i
$276$	−1.67152	+	1.72768i	−0.100613	+	0.103994i
$277$	5.75701	−	17.7183i	0.345905	−	1.06459i	−0.615192	−	0.788377i	$-0.710922\pi$
$277$	5.75701	−	17.7183i	0.345905	−	1.06459i	0.961097	−	0.276210i	$-0.0890785\pi$
$278$	16.9762	−	12.3339i	1.01816	−	0.739740i
$279$	−14.4208	−	9.76609i	−0.863349	−	0.584680i
$280$	−0.859150	+	1.05256i	−0.0513440	+	0.0629027i
$281$	−24.6289	+	8.00243i	−1.46924	+	0.477385i	−0.930878	−	0.365330i	$-0.880956\pi$
$281$	−24.6289	+	8.00243i	−1.46924	+	0.477385i	−0.538361	+	0.842714i	$0.680956\pi$
$282$	−10.5543	+	1.85087i	−0.628500	+	0.110218i
$283$	−1.34508	−	1.85134i	−0.0799565	−	0.110051i	0.767165	−	0.641449i	$-0.221667\pi$
$283$	−1.34508	−	1.85134i	−0.0799565	−	0.110051i	−0.847122	+	0.531399i	$0.821667\pi$
$284$	−0.895498	−	0.290965i	−0.0531380	−	0.0172656i
$285$	1.32308	−	1.36754i	0.0783726	−	0.0810060i
$286$	0.270784	−	23.7997i	0.0160118	−	1.40731i
$287$	22.0380	−	14.1901i	1.30086	−	0.837614i
$288$	−4.25208	+	14.7251i	−0.250556	+	0.867686i
$289$	−21.7914	+	15.8324i	−1.28184	+	0.931315i
$290$	−1.55765	−	1.13170i	−0.0914682	−	0.0664556i
$291$	−3.86956	−	1.89178i	−0.226837	−	0.110898i
$292$	4.62349	−	1.50226i	0.270569	−	0.0879133i
$293$	−4.56156	−	3.31416i	−0.266489	−	0.193616i	0.446514	−	0.894777i	$-0.352665\pi$
$293$	−4.56156	−	3.31416i	−0.266489	−	0.193616i	−0.713003	+	0.701161i	$0.752665\pi$
$294$	17.6522	+	11.2453i	1.02949	+	0.655839i
$295$	−0.271845	+	0.836653i	−0.0158274	+	0.0487118i
$296$		−	12.8704i		−	0.748076i
$297$	3.34382	+	16.9062i	0.194028	+	0.980996i
$298$	22.6370			1.31133
$299$	−1.81940	+	5.59953i	−0.105219	+	0.323829i
$300$	−8.26013	−	1.16874i	−0.476899	−	0.0674770i
$301$	−0.488599	−	0.0275127i	−0.0281624	−	0.00158581i
$302$	−13.4967	+	4.38534i	−0.776647	+	0.252348i
$303$	6.89610	−	14.1057i	0.396170	−	0.810352i
$304$	11.0698	−	15.2363i	0.634896	−	0.873860i
$305$	2.51353	+	3.45958i	0.143925	+	0.198095i
$306$	−9.52328	+	32.9795i	−0.544410	+	1.88531i
$307$		−	32.3586i		−	1.84680i	−0.383839	−	0.923400i	$-0.625398\pi$
$307$		−	32.3586i		−	1.84680i	0.383839	−	0.923400i	$-0.374602\pi$
$308$	0.581094	−	8.57952i	0.0331109	−	0.488864i
$309$	0.0264705	−	0.0273599i	0.00150585	−	0.00155645i
$310$	−0.903188	+	2.77973i	−0.0512977	+	0.157878i
$311$	4.12215	−	2.99492i	0.233746	−	0.169826i	−0.464747	−	0.885444i	$-0.653855\pi$
$311$	4.12215	−	2.99492i	0.233746	−	0.169826i	0.698492	+	0.715617i	$0.253855\pi$
$312$	2.19001	+	12.4882i	0.123985	+	0.707006i
$313$	21.6694	−	7.04082i	1.22483	−	0.397970i	0.375989	−	0.926624i	$-0.377303\pi$
$313$	21.6694	−	7.04082i	1.22483	−	0.397970i	0.848838	+	0.528654i	$0.177303\pi$
$314$	−0.0421084	−	0.129596i	−0.00237631	−	0.00731354i
$315$	−0.0537165	+	2.31421i	−0.00302658	+	0.130391i
$316$	10.1586	−	7.38068i	0.571468	−	0.415196i
$317$	−3.52118	−	1.14410i	−0.197769	−	0.0642590i	0.208458	−	0.978031i	$-0.433156\pi$
$317$	−3.52118	−	1.14410i	−0.197769	−	0.0642590i	−0.406227	+	0.913772i	$0.633156\pi$
$318$	−6.83985	−	6.61750i	−0.383560	−	0.371091i
$319$	−12.6831	−	0.144303i	−0.710115	−	0.00807940i
$320$	−0.344104			−0.0192360
$321$	1.19887	+	2.25983i	0.0669147	+	0.126132i
$322$	−2.34157	+	6.02979i	−0.130491	+	0.336027i
$323$	14.6762	−	20.2000i	0.816604	−	1.12396i
$324$	3.27341	+	8.18975i	0.181856	+	0.454986i
$325$	−19.4322	+	6.31391i	−1.07791	+	0.350233i
$326$	−2.56843	+	3.53514i	−0.142252	+	0.195793i
$327$	−2.78518	−	0.394078i	−0.154021	−	0.0217926i
$328$	16.5907	+	5.39066i	0.916070	+	0.297649i
$329$	−7.97212	+	5.13317i	−0.439517	+	0.283001i
$330$	2.57009	−	1.32622i	0.141479	−	0.0730062i
$331$	−1.34245			−0.0737880			−0.0368940	−	0.999319i	$-0.511746\pi$
$331$	−1.34245			−0.0737880			−0.0368940	+	0.999319i	$0.511746\pi$
$332$	−2.71218	+	8.34722i	−0.148850	+	0.458113i
$333$	−13.4678	−	17.3044i	−0.738031	−	0.948275i
$334$	12.3859	−	17.0477i	0.677726	−	0.932810i
$335$	−1.30992	−	4.03151i	−0.0715683	−	0.220265i
$336$	2.68247	+	22.7535i	0.146341	+	1.24130i
$337$	11.1267	+	8.08405i	0.606112	+	0.440366i	0.848043	−	0.529927i	$-0.177781\pi$
$337$	11.1267	+	8.08405i	0.606112	+	0.440366i	−0.241931	+	0.970294i	$0.577781\pi$
$338$	−4.34485	−	5.98018i	−0.236329	−	0.325279i
$339$	−6.41447	−	12.0910i	−0.348386	−	0.656695i
$340$	1.89439			0.102738
$341$	5.74130	+	18.3788i	0.310909	+	0.995268i
$342$	−0.644477	−	19.4974i	−0.0348493	−	1.05430i
$343$	18.2572	+	3.11048i	0.985795	+	0.167950i
$344$	−0.191439	−	0.263493i	−0.0103217	−	0.0142066i
$345$	−0.704663	+	0.123574i	−0.0379378	+	0.00665300i
$346$	−20.8331	+	6.76908i	−1.11999	+	0.363908i
$347$	−1.88458	+	0.612337i	−0.101170	+	0.0328720i	−0.359164	−	0.933274i	$-0.616938\pi$
$347$	−1.88458	+	0.612337i	−0.101170	+	0.0328720i	0.257995	+	0.966146i	$0.416938\pi$
$348$	−6.39368	+	1.12123i	−0.342737	+	0.0601045i
$349$	−8.14441	−	11.2098i	−0.435960	−	0.600048i	0.533348	−	0.845896i	$-0.320934\pi$
$349$	−8.14441	−	11.2098i	−0.435960	−	0.600048i	−0.969308	+	0.245848i	$0.920934\pi$
$350$	−21.7053	+	5.72552i	−1.16020	+	0.306042i
$351$	16.0124	+	14.4989i	0.854679	+	0.773894i
$352$	13.8207	−	9.80305i	0.736646	−	0.522504i
$353$	−4.82272			−0.256688			−0.128344	−	0.991730i	$-0.540966\pi$
$353$	−4.82272			−0.256688			−0.128344	+	0.991730i	$0.540966\pi$
$354$	4.22671	+	7.96718i	0.224647	+	0.423451i
$355$	−0.164708	−	0.226702i	−0.00874181	−	0.0120321i
$356$	−7.35471	−	5.34351i	−0.389799	−	0.283206i
$357$	3.55637	+	30.1662i	0.188223	+	1.59656i
$358$	−6.94715	−	21.3811i	−0.367168	−	1.13003i
$359$	1.66860	−	2.29663i	0.0880652	−	0.121211i	−0.762711	−	0.646739i	$-0.776132\pi$
$359$	1.66860	−	2.29663i	0.0880652	−	0.121211i	0.850776	+	0.525528i	$0.176132\pi$
$360$	−1.21578	+	0.946227i	−0.0640772	+	0.0498705i
$361$	1.48648	−	4.57491i	0.0782358	−	0.240785i
$362$	4.13224			0.217186
$363$	8.75532	−	16.9217i	0.459535	−	0.888160i
$364$	−5.83518	−	9.06238i	−0.305847	−	0.474998i
$365$	1.37597	+	0.447080i	0.0720215	+	0.0234012i
$366$	43.4088	+	6.14197i	2.26901	+	0.321046i
$367$	−6.17827	+	8.50366i	−0.322503	+	0.443887i	−0.939229	−	0.343290i	$-0.888459\pi$
$367$	−6.17827	+	8.50366i	−0.322503	+	0.443887i	0.616726	+	0.787178i	$0.288459\pi$
$368$	−6.73425	+	2.18809i	−0.351047	+	0.114062i
$369$	27.9473	−	10.1130i	1.45488	−	0.526464i
$370$	−2.16295	+	2.97704i	−0.112446	+	0.154769i
$371$	−7.85030	−	3.04854i	−0.407567	−	0.158272i
$372$	4.61806	+	8.70487i	0.239435	+	0.451326i
$373$	32.6008			1.68801			0.844003	−	0.536339i	$-0.180193\pi$
$373$	32.6008			1.68801			0.844003	+	0.536339i	$0.180193\pi$
$374$	30.9539	−	21.9556i	1.60059	−	1.13530i
$375$	−3.59952	−	3.48250i	−0.185878	−	0.179836i
$376$	−6.00160	−	1.95004i	−0.309509	−	0.100566i
$377$	−12.8621	+	9.34484i	−0.662430	+	0.481284i
$378$	16.6686	+	16.8930i	0.857339	+	0.868881i
$379$	6.94340	+	21.3696i	0.356659	+	1.09768i	0.955041	+	0.296472i	$0.0958103\pi$
$379$	6.94340	+	21.3696i	0.356659	+	1.09768i	−0.598383	+	0.801210i	$0.704190\pi$
$380$	−1.02389	+	0.332683i	−0.0525246	+	0.0170663i
$381$	−1.19057	−	6.78903i	−0.0609946	−	0.347813i
$382$	−15.2925	+	11.1107i	−0.782434	+	0.568472i
$383$	−10.3648	+	31.8995i	−0.529616	+	1.62999i	0.225387	+	0.974269i	$0.427635\pi$
$383$	−10.3648	+	31.8995i	−0.529616	+	1.62999i	−0.755003	+	0.655721i	$0.772365\pi$
$384$	−14.7588	+	15.2547i	−0.753156	+	0.778463i
$385$	1.64070	−	1.96401i	0.0836178	−	0.100095i
$386$		−	7.31066i		−	0.372103i
$387$	−0.533115	−	0.153944i	−0.0270998	−	0.00782543i
$388$	1.43241	+	1.97155i	0.0727198	+	0.100090i
$389$	10.7808	−	14.8385i	0.546607	−	0.752340i	−0.442940	−	0.896551i	$-0.646065\pi$
$389$	10.7808	−	14.8385i	0.546607	−	0.752340i	0.989547	+	0.144211i	$0.0460645\pi$
$390$	1.59215	−	3.25669i	0.0806218	−	0.164909i
$391$	−8.92818	+	2.90094i	−0.451517	+	0.146707i
$392$	6.07970	+	10.7221i	0.307071	+	0.541550i
$393$	−14.5040	−	2.05219i	−0.731630	−	0.103519i
$394$	−6.30091	+	19.3922i	−0.317435	+	0.976965i
$395$	3.73694			0.188026
$396$	2.81148	−	9.33643i	0.141282	−	0.469173i
$397$		−	30.2194i		−	1.51667i	−0.651867	−	0.758334i	$-0.726014\pi$
$397$		−	30.2194i		−	1.51667i	0.651867	−	0.758334i	$-0.273986\pi$
$398$	11.0156	−	33.9026i	0.552163	−	1.69938i
$399$	−7.21978	−	15.6798i	−0.361441	−	0.784974i
$400$	−19.8798	−	14.4435i	−0.993989	−	0.722175i
$401$	−18.1352	+	5.89247i	−0.905626	+	0.294256i	−0.724557	−	0.689214i	$-0.757956\pi$
$401$	−18.1352	+	5.89247i	−0.905626	+	0.294256i	−0.181069	+	0.983470i	$0.557956\pi$
$402$	−39.0427	−	19.0874i	−1.94727	−	0.951995i
$403$	19.5252	+	14.1859i	0.972619	+	0.706649i
$404$	−7.18689	+	5.22158i	−0.357561	+	0.259783i
$405$	−0.644482	+	2.54443i	−0.0320246	+	0.126434i
$406$	−14.6857	+	9.45598i	−0.728838	+	0.469292i
$407$	−0.275798	+	24.2404i	−0.0136708	+	1.20155i
$408$	−14.0565	+	14.5289i	−0.695903	+	0.719286i
$409$	13.6847	+	4.44642i	0.676664	+	0.219861i	0.627134	−	0.778911i	$-0.284228\pi$
$409$	13.6847	+	4.44642i	0.676664	+	0.219861i	0.0495296	+	0.998773i	$0.484228\pi$
$410$	−2.93166	−	4.03509i	−0.144785	−	0.199279i
$411$	−12.7438	+	2.23482i	−0.628603	+	0.110236i
$412$	−0.0204847	+	0.00665587i	−0.00100921	+	0.000327911i
$413$	6.18254	+	5.04647i	0.304223	+	0.248320i
$414$	−4.11277	+	6.07298i	−0.202132	+	0.298471i
$415$	−2.11316	+	1.53530i	−0.103731	+	0.0753649i
$416$	6.56310	−	20.1991i	0.321782	−	0.990344i
$417$	14.6396	−	15.1315i	0.716902	−	0.740990i
$418$	−12.8744	+	17.3026i	−0.629707	+	0.846300i
$419$	0.617734			0.0301783			0.0150891	−	0.999886i	$-0.495197\pi$
$419$	0.617734			0.0301783			0.0150891	+	0.999886i	$0.495197\pi$
$420$	0.640471	−	1.14241i	0.0312518	−	0.0557441i
$421$	−12.0609	+	8.76274i	−0.587811	+	0.427070i	−0.841532	−	0.540208i	$-0.818346\pi$
$421$	−12.0609	+	8.76274i	−0.587811	+	0.427070i	0.253720	+	0.967278i	$0.418346\pi$
$422$	13.0622	−	17.9786i	0.635860	−	0.875186i
$423$	−10.1098	+	3.65833i	−0.491554	+	0.177874i
$424$	−1.73197	−	5.33045i	−0.0841118	−	0.258869i
$425$	−26.3563	−	19.1490i	−1.27847	−	0.928862i
$426$	−2.84452	−	0.402475i	−0.137817	−	0.0195000i
$427$	37.5109	−	9.89478i	1.81528	−	0.478842i
$428$		−	1.44736i		−	0.0699610i
$429$	−3.85711	−	23.5676i	−0.186223	−	1.13785i
$430$			0.0931209i			0.00449069i
$431$	−27.7252	−	9.00845i	−1.33547	−	0.433922i	−0.447693	−	0.894187i	$-0.647754\pi$
$431$	−27.7252	−	9.00845i	−1.33547	−	0.433922i	−0.887781	+	0.460265i	$0.847754\pi$
$432$	−2.78774	+	25.8287i	−0.134125	+	1.24268i
$433$	−10.3687	+	14.2713i	−0.498288	+	0.685834i	−0.981890	−	0.189454i	$-0.939328\pi$
$433$	−10.3687	+	14.2713i	−0.498288	+	0.685834i	0.483602	+	0.875288i	$0.339328\pi$
$434$	20.5411	+	16.7666i	0.986005	+	0.804822i
$435$	−1.73552	−	0.848472i	−0.0832117	−	0.0406811i
$436$	1.28755	+	0.935463i	0.0616627	+	0.0448006i
$437$	4.31610	−	3.13583i	0.206467	−	0.150007i
$438$	13.1029	−	6.95129i	0.626082	−	0.332146i
$439$			2.08666i			0.0995910i	0.998759	+	0.0497955i	$0.0158570\pi$
$439$			2.08666i			0.0995910i	−0.998759	+	0.0497955i	$0.984143\pi$
$440$	1.70309	+	0.0193771i	0.0811918	+	0.000923767i
$441$	19.3941	+	8.05415i	0.923528	+	0.383531i
$442$	14.6992	−	45.2395i	0.699170	−	2.15182i
$443$	4.39515	+	6.04941i	0.208820	+	0.287416i	0.900561	−	0.434730i	$-0.143156\pi$
$443$	4.39515	+	6.04941i	0.208820	+	0.287416i	−0.691741	+	0.722146i	$0.743156\pi$
$444$	2.14295	+	12.2199i	0.101700	+	0.579929i
$445$	−0.836044	−	2.57308i	−0.0396323	−	0.121976i
$446$	−4.15878	−	12.7994i	−0.196924	−	0.606070i
$447$	22.3716	−	3.92322i	1.05814	−	0.185562i
$448$	−1.13004	+	2.90996i	−0.0533892	+	0.137483i
$449$	33.8137	+	10.9867i	1.59577	+	0.518496i	0.966056	−	0.258332i	$-0.0831730\pi$
$449$	33.8137	+	10.9867i	1.59577	+	0.518496i	0.629712	+	0.776829i	$0.283173\pi$
$450$	−25.4395	+	0.840892i	−1.19923	+	0.0396400i
$451$	−31.1319	−	10.5084i	−1.46594	−	0.494822i
$452$			7.74399i			0.364247i
$453$	−12.5784	+	6.67303i	−0.590985	+	0.313526i
$454$	−24.2262	−	33.3446i	−1.13699	−	1.56494i
$455$	0.180339	−	3.20265i	0.00845443	−	0.150143i
$456$	5.04588	−	10.3212i	0.236295	−	0.483333i
$457$	12.0844	+	37.1918i	0.565282	+	1.73976i	0.667111	+	0.744959i	$0.267531\pi$
$457$	12.0844	+	37.1918i	0.565282	+	1.73976i	−0.101828	+	0.994802i	$0.532469\pi$
$458$	9.64415	+	7.00689i	0.450642	+	0.327410i
$459$	−3.69594	+	34.2433i	−0.172512	+	1.59834i
$460$	0.384961	+	0.125081i	0.0179489	+	0.00583195i
$461$	−19.8679			−0.925342			−0.462671	−	0.886530i	$-0.653109\pi$
$461$	−19.8679			−0.925342			−0.462671	+	0.886530i	$0.653109\pi$
$462$	−2.77522	−	26.0897i	−0.129115	−	1.21380i
$463$	5.42537			0.252138			0.126069	−	0.992021i	$-0.459764\pi$
$463$	5.42537			0.252138			0.126069	+	0.992021i	$0.459764\pi$
$464$	−18.1843	−	5.90844i	−0.844186	−	0.274293i
$465$	−0.410844	+	2.90367i	−0.0190524	+	0.134654i
$466$	−16.5096	−	11.9949i	−0.764793	−	0.555655i
$467$	−1.46291	−	4.50239i	−0.0676956	−	0.208346i	0.911486	−	0.411330i	$-0.134936\pi$
$467$	−1.46291	−	4.50239i	−0.0676956	−	0.208346i	−0.979182	+	0.202985i	$0.934936\pi$
$468$	−4.15864	−	11.4924i	−0.192233	−	0.531236i
$469$	−38.3948	−	2.16199i	−1.77291	−	0.0998312i
$470$	1.06051	+	1.45967i	0.0489178	+	0.0673295i
$471$	−0.0640749	−	0.120779i	−0.00295242	−	0.00556519i
$472$			5.31139i			0.244477i
$473$	0.354914	+	0.500371i	0.0163190	+	0.0230071i
$474$	26.6393	−	27.5344i	1.22358	−	1.26470i
$475$	17.6080	+	5.72120i	0.807912	+	0.262507i
$476$	6.22120	−	16.0202i	0.285148	−	0.734286i
$477$	−7.90653	−	5.35449i	−0.362015	−	0.245165i
$478$	5.16310	+	15.8904i	0.236155	+	0.726810i
$479$	−7.26581	−	22.3619i	−0.331983	−	1.02174i	−0.968189	−	0.250220i	$-0.919497\pi$
$479$	−7.26581	−	22.3619i	−0.331983	−	1.02174i	0.636206	−	0.771519i	$-0.280503\pi$
$480$	2.54192	−	0.445767i	0.116022	−	0.0203464i
$481$	17.8603	+	24.5825i	0.814358	+	1.12087i
$482$	6.25942	−	19.2645i	0.285109	−	0.877474i
$483$	−1.26909	+	6.36491i	−0.0577458	+	0.289613i
$484$	−8.86282	+	6.13605i	−0.402855	+	0.278912i
$485$			0.725251i			0.0329319i
$486$	14.1535	+	22.8869i	0.642014	+	1.03817i
$487$	−7.40415	+	5.37943i	−0.335514	+	0.243765i	−0.742767	−	0.669550i	$-0.766487\pi$
$487$	−7.40415	+	5.37943i	−0.335514	+	0.243765i	0.407253	+	0.913316i	$0.366487\pi$
$488$	20.8878	+	15.1759i	0.945547	+	0.686980i
$489$	−1.92564	+	3.93882i	−0.0870803	+	0.178120i
$490$	0.395631	−	3.50187i	0.0178728	−	0.158198i
$491$	20.9523	−	28.8384i	0.945565	−	1.30146i	−0.00790451	−	0.999969i	$-0.502516\pi$
$491$	20.9523	−	28.8384i	0.945565	−	1.30146i	0.953469	−	0.301490i	$-0.0974839\pi$
$492$	−16.6497	−	2.35580i	−0.750629	−	0.106207i
$493$	−24.1085	−	7.83333i	−1.08579	−	0.352795i
$494$			27.0327i			1.21626i
$495$	2.31011	−	1.75609i	0.103832	−	0.0789306i
$496$			29.0252i			1.30327i
$497$	−2.45804	+	0.648391i	−0.110258	+	0.0290843i
$498$	−3.75160	+	26.5147i	−0.168113	+	1.18815i
$499$	22.4856	+	16.3368i	1.00659	+	0.731334i	0.963492	−	0.267737i	$-0.0862759\pi$
$499$	22.4856	+	16.3368i	1.00659	+	0.731334i	0.0431023	+	0.999071i	$0.486276\pi$
$500$	0.875658	+	2.69500i	0.0391606	+	0.120524i
$501$	9.28612	−	18.9944i	0.414873	−	0.848608i
$502$	−21.9884	+	30.2644i	−0.981389	+	1.35077i
$503$	−0.882970	+	0.641515i	−0.0393697	+	0.0286038i	−0.607296	−	0.794476i	$-0.707746\pi$
$503$	−0.882970	+	0.641515i	−0.0393697	+	0.0286038i	0.567926	+	0.823079i	$0.307746\pi$
$504$	4.00928	+	13.3888i	0.178588	+	0.596386i
$505$	−2.64376			−0.117646
$506$	7.73982	−	2.41782i	0.344077	−	0.107485i
$507$	−5.33033	−	5.15705i	−0.236728	−	0.229033i
$508$	−1.20509	+	3.70888i	−0.0534671	+	0.164555i
$509$	21.6455	−	15.7264i	0.959420	−	0.697059i	0.00640378	−	0.999979i	$-0.497962\pi$
$509$	21.6455	−	15.7264i	0.959420	−	0.697059i	0.953016	+	0.302920i	$0.0979616\pi$
$510$	5.69308	−	0.998374i	0.252094	−	0.0442088i
$511$	8.29948	−	10.1679i	0.367147	−	0.449800i
$512$	7.54717	−	2.45222i	0.333541	−	0.108374i
$513$	−4.01600	−	19.1570i	−0.177311	−	0.845804i
$514$	30.8094	+	42.4055i	1.35894	+	1.87042i
$515$	−0.00609632	−	0.00198081i	−0.000268636	−	8.72851e-5i
$516$	0.225635	+	0.218300i	0.00993302	+	0.00961011i
$517$	11.2618	+	3.80136i	0.495292	+	0.167184i
$518$	18.0727	+	28.0679i	0.794068	+	1.23323i
$519$	−19.4157	+	10.3003i	−0.852253	+	0.452133i
$520$	1.72713	−	1.25483i	0.0757397	−	0.0550281i
$521$	−6.10061	−	4.43235i	−0.267273	−	0.194185i	0.446074	−	0.894996i	$-0.352822\pi$
$521$	−6.10061	−	4.43235i	−0.267273	−	0.194185i	−0.713347	+	0.700811i	$0.752822\pi$
$522$	−18.6235	+	6.73913i	−0.815130	+	0.294964i
$523$	24.1624	−	7.85085i	1.05655	−	0.343294i	0.271314	−	0.962491i	$-0.412542\pi$
$523$	24.1624	−	7.85085i	1.05655	−	0.343294i	0.785236	+	0.619197i	$0.212542\pi$
$524$	6.70503	+	4.87149i	0.292910	+	0.212812i
$525$	−20.4585	+	9.42013i	−0.892883	+	0.411128i
$526$	3.49609	−	10.7599i	0.152437	−	0.469152i
$527$			38.4812i			1.67627i
$528$	20.2037	−	20.4127i	0.879254	−	0.888347i
$529$	20.9942			0.912790
$530$	−0.495195	+	1.52405i	−0.0215099	+	0.0662006i
$531$	5.55794	+	7.14123i	0.241194	+	0.309903i
$532$	−0.549085	+	9.75122i	−0.0238059	+	0.422769i
$533$	−39.1691	+	12.7268i	−1.69660	+	0.551259i
$534$	−24.9187	−	12.1824i	−1.07834	−	0.527185i
$535$	0.253183	−	0.348477i	0.0109461	−	0.0150660i
$536$	−15.0435	−	20.7056i	−0.649780	−	0.894346i
$537$	−10.5713	−	19.9264i	−0.456183	−	0.859889i
$538$		−	8.65492i		−	0.373140i
$539$	−11.2209	−	20.3246i	−0.483319	−	0.875445i
$540$	0.996781	−	1.10083i	0.0428946	−	0.0473722i
$541$	−7.50023	+	23.0833i	−0.322460	+	0.992430i	0.650114	+	0.759837i	$0.274721\pi$
$541$	−7.50023	+	23.0833i	−0.322460	+	0.992430i	−0.972574	+	0.232594i	$0.925279\pi$
$542$	−15.2008	+	11.0440i	−0.652929	+	0.474381i
$543$	4.08379	−	0.716158i	0.175252	−	0.0307333i
$544$	32.2065	−	10.4645i	1.38084	−	0.448663i
$545$	0.146362	+	0.450457i	0.00626947	+	0.0192954i
$546$	−22.3121	−	24.1593i	−0.954868	−	1.03392i
$547$	−18.8845	+	13.7204i	−0.807441	+	0.586640i	−0.913088	−	0.407763i	$-0.866309\pi$
$547$	−18.8845	+	13.7204i	−0.807441	+	0.586640i	0.105647	+	0.994404i	$0.466309\pi$
$548$	6.96197	+	2.26208i	0.297401	+	0.0966313i
$549$	43.9643	−	1.45322i	1.87635	−	0.0620220i
$550$	22.5759	+	16.7981i	0.962640	+	0.716273i
$551$	14.4059			0.613714
$552$	−3.81574	+	2.02430i	−0.162409	+	0.0861601i
$553$	12.2721	−	31.6020i	0.521864	−	1.34385i
$554$	−18.9034	+	26.0183i	−0.803127	+	1.10541i
$555$	−1.62164	+	3.31700i	−0.0688346	+	0.140799i
$556$	−11.3291	+	3.68105i	−0.480461	+	0.156111i
$557$	−18.0748	+	24.8778i	−0.765853	+	1.05411i	0.230852	+	0.972989i	$0.425849\pi$
$557$	−18.0748	+	24.8778i	−0.765853	+	1.05411i	−0.996705	+	0.0811172i	$0.974151\pi$
$558$	18.4659	+	23.7263i	0.781724	+	1.00442i
$559$	0.731299	+	0.237613i	0.0309306	+	0.0100500i
$560$	3.24353	−	2.08848i	0.137064	−	0.0882544i
$561$	26.7858	−	27.0628i	1.13090	−	1.14259i
$562$	44.7039			1.88572
$563$	−6.90933	+	21.2647i	−0.291193	+	0.896201i	0.693280	+	0.720668i	$0.256165\pi$
$563$	−6.90933	+	21.2647i	−0.291193	+	0.896201i	−0.984474	+	0.175533i	$0.943835\pi$
$564$	6.02294	+	0.852195i	0.253612	+	0.0358839i
$565$	−1.35463	+	1.86449i	−0.0569899	+	0.0784399i
$566$	1.22072	+	3.75699i	0.0513107	+	0.157918i
$567$	19.4008	+	13.8061i	0.814759	+	0.579800i
$568$	−1.36875	−	0.994455i	−0.0574314	−	0.0417264i
$569$	5.32077	+	7.32341i	0.223058	+	0.307013i	0.905849	−	0.423601i	$-0.139234\pi$
$569$	5.32077	+	7.32341i	0.223058	+	0.307013i	−0.682791	+	0.730614i	$0.739234\pi$
$570$	−2.90170	+	1.53939i	−0.121539	+	0.0644781i
$571$	−12.2205			−0.511412			−0.255706	−	0.966755i	$-0.582308\pi$
$571$	−12.2205			−0.511412			−0.255706	+	0.966755i	$0.582308\pi$
$572$	−4.32123	+	12.8019i	−0.180680	+	0.535275i
$573$	−13.1876	+	13.6307i	−0.550921	+	0.569433i
$574$	−43.7509	+	11.5408i	−1.82613	+	0.481704i
$575$	−4.09153	−	5.63150i	−0.170628	−	0.234850i
$576$	−1.98481	+	2.93081i	−0.0827005	+	0.122117i
$577$	27.2415	−	8.85129i	1.13408	−	0.368484i	0.318953	−	0.947771i	$-0.396669\pi$
$577$	27.2415	−	8.85129i	1.13408	−	0.368484i	0.815124	+	0.579287i	$0.196669\pi$
$578$	44.2220	−	14.3686i	1.83939	−	0.597656i
$579$	−1.26701	−	7.22493i	−0.0526551	−	0.300258i
$580$	0.642446	+	0.884250i	0.0266761	+	0.0367165i
$581$	6.04386	+	22.9122i	0.250742	+	0.950556i
$582$	5.34376	+	5.17005i	0.221506	+	0.214305i
$583$	3.14781	+	10.0766i	0.130369	+	0.417331i
$584$	8.73518			0.361464
$585$	1.00907	−	3.49444i	0.0417198	−	0.144477i
$586$	5.72110	+	7.87442i	0.236337	+	0.325289i
$587$	25.4996	+	18.5266i	1.05248	+	0.764673i	0.972683	−	0.232138i	$-0.0745721\pi$
$587$	25.4996	+	18.5266i	1.05248	+	0.764673i	0.0797991	+	0.996811i	$0.474572\pi$
$588$	−7.55768	−	9.16793i	−0.311673	−	0.378079i
$589$	−6.75784	−	20.7985i	−0.278452	−	0.856987i
$590$	0.892613	−	1.22858i	0.0367483	−	0.0505797i
$591$	−2.86617	+	20.2568i	−0.117898	+	0.833254i
$592$	−11.2925	+	34.7547i	−0.464118	+	1.42841i
$593$	29.3976			1.20721			0.603606	−	0.797282i	$-0.293730\pi$
$593$	29.3976			1.20721			0.603606	+	0.797282i	$0.293730\pi$
$594$	3.52871	−	29.5398i	0.144785	−	1.21203i
$595$	4.30023	−	2.76888i	0.176292	−	0.113513i
$596$	−12.2217	−	3.97107i	−0.500620	−	0.162661i
$597$	5.01080	−	35.4142i	0.205078	−	1.44941i
$598$	5.97407	−	8.22260i	0.244298	−	0.336247i
$599$	35.8903	−	11.6615i	1.46644	−	0.476474i	0.536408	−	0.843959i	$-0.319781\pi$
$599$	35.8903	−	11.6615i	1.46644	−	0.476474i	0.930030	+	0.367485i	$0.119781\pi$
$600$	−13.4667	−	6.58370i	−0.549776	−	0.268778i
$601$	3.45676	−	4.75782i	0.141004	−	0.194076i	−0.732674	−	0.680580i	$-0.761728\pi$
$601$	3.45676	−	4.75782i	0.141004	−	0.194076i	0.873678	+	0.486504i	$0.161728\pi$
$602$	0.787490	+	0.305809i	0.0320957	+	0.0124639i
$603$	−41.8929	−	12.0972i	−1.70601	−	0.492634i
$604$	8.05614			0.327800
$605$	−3.20723	−	0.0729907i	−0.130393	−	0.00296749i
$606$	−18.8464	+	19.4796i	−0.765582	+	0.791307i
$607$	−30.6055	−	9.94432i	−1.24224	−	0.403628i	−0.387105	−	0.922036i	$-0.626525\pi$
$607$	−30.6055	−	9.94432i	−1.24224	−	0.403628i	−0.855133	+	0.518408i	$0.826525\pi$
$608$	−15.5694	+	11.3118i	−0.631424	+	0.458756i
$609$	−12.8747	+	11.8903i	−0.521708	+	0.481818i
$610$	−2.28115	−	7.02066i	−0.0923611	−	0.284258i
$611$	14.1692	−	4.60385i	0.573224	−	0.186252i
$612$	10.9270	−	16.1350i	0.441698	−	0.652218i
$613$	32.4782	−	23.5968i	1.31178	−	0.953067i	0.311788	−	0.950152i	$-0.399072\pi$
$613$	32.4782	−	23.5968i	1.31178	−	0.953067i	0.999996	−	0.00291491i	$-0.000927846\pi$
$614$	−17.2615	+	53.1253i	−0.696615	+	2.14396i
$615$	−3.59661	−	3.47969i	−0.145029	−	0.140315i
$616$	5.75683	−	14.3388i	0.231949	−	0.577727i
$617$		−	7.04393i		−	0.283578i	−0.989897	−	0.141789i	$-0.954715\pi$
$617$		−	7.04393i		−	0.283578i	0.989897	−	0.141789i	$-0.0452854\pi$
$618$	−0.0580534	+	0.0307981i	−0.00233525	+	0.00123888i
$619$	−6.96166	−	9.58190i	−0.279813	−	0.385129i	0.645859	−	0.763457i	$-0.276499\pi$
$619$	−6.96166	−	9.58190i	−0.279813	−	0.385129i	−0.925672	+	0.378327i	$0.876499\pi$
$620$	0.975260	−	1.34233i	0.0391674	−	0.0539093i
$621$	−3.01204	+	6.71456i	−0.120869	+	0.269446i
$622$	−8.36524	+	2.71803i	−0.335416	+	0.108983i
$623$	−24.5052	−	1.37987i	−0.981779	−	0.0552834i
$624$	5.04335	−	35.6442i	0.201896	−	1.42691i
$625$	7.33341	−	22.5699i	0.293336	−	0.902796i
$626$	−39.3320			−1.57202
$627$	−9.72472	+	19.3310i	−0.388368	+	0.772007i
$628$			0.0773556i			0.00308683i
$629$	−14.9714	+	46.0772i	−0.596949	+	1.83722i
$630$	1.32269	−	3.77075i	0.0526973	−	0.150230i
$631$	−20.6695	−	15.0173i	−0.822840	−	0.597828i	0.0946848	−	0.995507i	$-0.469816\pi$
$631$	−20.6695	−	15.0173i	−0.822840	−	0.597828i	−0.917524	+	0.397679i	$0.869816\pi$
$632$	21.4581	−	6.97217i	0.853559	−	0.277338i
$633$	9.79320	−	20.0316i	0.389245	−	0.796186i
$634$	5.17065	+	3.75670i	0.205353	+	0.149197i
$635$	−0.938929	+	0.682172i	−0.0372603	+	0.0270712i
$636$	2.53196	+	4.77265i	0.100399	+	0.189248i
$637$	−26.4914	−	12.0426i	−1.04963	−	0.477144i
$638$	20.7457	+	7.00260i	0.821329	+	0.277236i
$639$	−2.88092	+	0.0952275i	−0.113967	+	0.00376714i
$640$	3.39904	+	1.10442i	0.134359	+	0.0436559i
$641$	2.41510	+	3.32410i	0.0953906	+	0.131294i	0.854044	−	0.520200i	$-0.174143\pi$
$641$	2.41510	+	3.32410i	0.0953906	+	0.131294i	−0.758654	+	0.651494i	$0.774143\pi$
$642$	−0.762783	−	4.34966i	−0.0301046	−	0.171667i
$643$	18.6347	−	6.05477i	0.734880	−	0.238777i	0.0824174	−	0.996598i	$-0.473736\pi$
$643$	18.6347	−	6.05477i	0.734880	−	0.238777i	0.652463	+	0.757821i	$0.273736\pi$
$644$	2.32198	−	2.84471i	0.0914989	−	0.112097i
$645$	0.0161388	+	0.0920289i	0.000635463	+	0.00362364i
$646$	−34.8705	+	25.3349i	−1.37196	+	0.996787i
$647$	5.08848	−	15.6607i	0.200049	−	0.615687i	−0.799832	−	0.600224i	$-0.795078\pi$
$647$	5.08848	−	15.6607i	0.200049	−	0.615687i	0.999880	−	0.0154624i	$-0.00492203\pi$
$648$	1.04653	+	15.8130i	0.0411114	+	0.621192i
$649$	0.113817	−	10.0036i	0.00446771	−	0.392676i
$650$	35.2713			1.38346
$651$	23.2061	+	13.0100i	0.909517	+	0.509902i
$652$	2.00684	−	1.45805i	0.0785938	−	0.0571018i
$653$	−12.9006	+	17.7562i	−0.504841	+	0.694854i	−0.983039	−	0.183398i	$-0.941290\pi$
$653$	−12.9006	+	17.7562i	−0.504841	+	0.694854i	0.478198	+	0.878252i	$0.341290\pi$
$654$	4.36240	+	2.13272i	0.170583	+	0.0833959i
$655$	0.762191	+	2.34578i	0.0297813	+	0.0916573i
$656$	−40.0712	−	29.1134i	−1.56452	−	1.13669i
$657$	11.7446	−	9.14065i	0.458199	−	0.356611i
$658$	15.8266	−	4.17482i	0.616986	−	0.162751i
$659$		−	25.3124i		−	0.986032i	−0.870020	−	0.493016i	$-0.835894\pi$
$659$		−	25.3124i		−	0.986032i	0.870020	−	0.493016i	$-0.164106\pi$
$660$	−1.62024	+	0.265172i	−0.0630677	+	0.0103218i
$661$			19.9228i			0.774905i	0.921890	+	0.387453i	$0.126645\pi$
$661$			19.9228i			0.774905i	−0.921890	+	0.387453i	$0.873355\pi$
$662$	2.20400	+	0.716123i	0.0856609	+	0.0278329i
$663$	6.68640	−	47.2566i	0.259678	−	1.83529i
$664$	−9.26963	+	12.7586i	−0.359731	+	0.495128i
$665$	−1.83796	+	2.25172i	−0.0712729	+	0.0873179i
$666$	12.8801	+	35.5941i	0.499094	+	1.37924i
$667$	−4.38189	−	3.18363i	−0.169667	−	0.123271i
$668$	−9.67770	+	7.03126i	−0.374442	+	0.272048i
$669$	−6.32829	−	11.9286i	−0.244666	−	0.461186i
$670$			7.31757i			0.282702i
$671$	−39.0155	−	29.0303i	−1.50617	−	1.12070i
$672$	4.57799	−	22.9601i	0.176600	−	0.885703i
$673$	2.28991	−	7.04761i	0.0882695	−	0.271666i	−0.897172	−	0.441682i	$-0.854382\pi$
$673$	2.28991	−	7.04761i	0.0882695	−	0.271666i	0.985441	+	0.170016i	$0.0543820\pi$
$674$	−13.9552	−	19.2076i	−0.537533	−	0.739850i
$675$	−24.9955	+	5.23995i	−0.962076	+	0.201686i
$676$	1.29672	+	3.99088i	0.0498737	+	0.153495i
$677$	−12.2942	−	37.8377i	−0.472505	−	1.45422i	−0.849293	−	0.527922i	$-0.822971\pi$
$677$	−12.2942	−	37.8377i	−0.472505	−	1.45422i	0.376787	−	0.926300i	$-0.377029\pi$
$678$	4.08120	+	23.2724i	0.156738	+	0.893773i
$679$	6.13319	+	2.38173i	0.235370	+	0.0914023i
$680$	3.23731	+	1.05187i	0.124145	+	0.0403372i
$681$	−29.7211	−	28.7549i	−1.13892	−	1.10189i
$682$	0.378150	−	33.2364i	0.0144801	−	1.27269i
$683$		−	16.0658i		−	0.614741i	−0.951590	−	0.307371i	$-0.900551\pi$
$683$		−	16.0658i		−	0.614741i	0.951590	−	0.307371i	$-0.0994491\pi$
$684$	−3.07235	+	10.6397i	−0.117474	+	0.406817i
$685$	1.28051	+	1.76247i	0.0489258	+	0.0673406i
$686$	−28.3148	−	14.8459i	−1.08107	−	0.566818i
$687$	10.7454	+	5.25330i	0.409964	+	0.200426i
$688$	0.285765	+	0.879493i	0.0108947	+	0.0335304i
$689$	10.7051	+	7.77775i	0.407834	+	0.296309i
$690$	1.22281	+	0.173018i	0.0465517	+	0.00658667i
$691$	−33.6302	−	10.9271i	−1.27935	−	0.415687i	−0.411000	−	0.911635i	$-0.634821\pi$
$691$	−33.6302	−	10.9271i	−1.27935	−	0.415687i	−0.868352	+	0.495948i	$0.834821\pi$
$692$	12.4352			0.472716
$693$	−7.26427	−	25.3028i	−0.275947	−	0.961173i
$694$	3.42069			0.129848
$695$	−3.37158	−	1.09549i	−0.127891	−	0.0415544i
$696$	−11.5487	−	1.63404i	−0.437751	−	0.0619380i
$697$	−53.1258	−	38.5982i	−2.01228	−	1.46201i
$698$	7.39144	+	22.7485i	0.279770	+	0.861044i
$699$	−18.3949	−	8.99301i	−0.695758	−	0.340147i
$700$	12.7231	+	0.716428i	0.480887	+	0.0270784i
$701$	24.5800	+	33.8314i	0.928372	+	1.27779i	0.960491	+	0.278311i	$0.0897744\pi$
$701$	24.5800	+	33.8314i	0.928372	+	1.27779i	−0.0321190	+	0.999484i	$0.510226\pi$
$702$	−18.5543	−	32.3456i	−0.700288	−	1.22080i
$703$		−	27.5332i		−	1.03844i
$704$	3.73522	−	1.16683i	0.140776	−	0.0439767i
$705$	1.30105	+	1.25876i	0.0490004	+	0.0474075i
$706$	7.91779	+	2.57265i	0.297990	+	0.0968228i
$707$	−8.68212	+	22.3573i	−0.326525	+	0.840835i
$708$	−0.884360	−	5.04294i	−0.0332363	−	0.189525i
$709$	−7.03960	−	21.6657i	−0.264378	−	0.813671i	−0.991836	−	0.127519i	$-0.959298\pi$
$709$	−7.03960	−	21.6657i	−0.264378	−	0.813671i	0.727458	−	0.686152i	$-0.240702\pi$
$710$	0.149481	+	0.460054i	0.00560991	+	0.0172655i
$711$	21.5549	−	31.8284i	0.808373	−	1.19366i
$712$	−9.60141	−	13.2152i	−0.359828	−	0.495261i
$713$	−2.54080	+	7.81978i	−0.0951537	+	0.292853i
$714$	10.2532	−	51.4231i	0.383717	−	1.92446i
$715$	−3.27981	+	2.32638i	−0.122658	+	0.0870015i
$716$			12.7623i			0.476951i
$717$	7.85652	+	14.8092i	0.293407	+	0.553062i
$718$	−3.96457	+	2.88043i	−0.147957	+	0.107497i
$719$	−5.61172	−	4.07716i	−0.209282	−	0.152052i	0.478207	−	0.878247i	$-0.341287\pi$
$719$	−5.61172	−	4.07716i	−0.209282	−	0.152052i	−0.687489	+	0.726195i	$0.741287\pi$
$720$	4.11326	−	1.48843i	0.153292	−	0.0554704i
$721$	−0.0367714	+	0.0450494i	−0.00136944	+	0.00167773i
$722$	−4.88091	+	6.71800i	−0.181649	+	0.250018i
$723$	2.84729	−	20.1234i	0.105892	−	0.748399i
$724$	−2.23099	−	0.724893i	−0.0829141	−	0.0269404i
$725$		−	18.7964i		−	0.698080i
$726$	−23.4010	+	23.1111i	−0.868492	+	0.857733i
$727$		−	16.4986i		−	0.611900i	−0.952048	−	0.305950i	$-0.901026\pi$
$727$		−	16.4986i		−	0.611900i	0.952048	−	0.305950i	$-0.0989740\pi$
$728$	−4.93978	−	18.7266i	−0.183081	−	0.694054i
$729$	17.9540	+	20.1656i	0.664964	+	0.746875i
$730$	−2.02053	−	1.46800i	−0.0747833	−	0.0543332i
$731$	0.378862	+	1.16602i	0.0140127	+	0.0431268i
$732$	−22.3589	−	10.9310i	−0.826409	−	0.404020i
$733$	−15.3403	+	21.1141i	−0.566608	+	0.779868i	−0.992148	−	0.125071i	$-0.960084\pi$
$733$	−15.3403	+	21.1141i	−0.566608	+	0.779868i	0.425540	+	0.904940i	$0.360084\pi$
$734$	14.6795	−	10.6653i	0.541831	−	0.393663i
$735$	−0.215917	−	3.52937i	−0.00796422	−	0.130183i
$736$	7.23564			0.266709
$737$	27.8896	+	39.3198i	1.02733	+	1.44836i
$738$	−51.2778	+	1.69497i	−1.88756	+	0.0623926i
$739$	5.74743	−	17.6888i	0.211423	−	0.650692i	−0.787966	−	0.615719i	$-0.788866\pi$
$739$	5.74743	−	17.6888i	0.211423	−	0.650692i	0.999388	−	0.0349728i	$-0.0111345\pi$
$740$	1.69002	−	1.22787i	0.0621263	−	0.0451374i
$741$	4.68503	+	26.7157i	0.172109	+	0.981426i
$742$	11.2622	+	9.19268i	0.413447	+	0.337474i
$743$	33.7612	−	10.9697i	1.23858	−	0.402439i	0.384764	−	0.923015i	$-0.374283\pi$
$743$	33.7612	−	10.9697i	1.23858	−	0.402439i	0.853815	+	0.520576i	$0.174283\pi$
$744$	3.05836	+	17.4399i	0.112125	+	0.639376i
$745$	−2.24793	−	3.09401i	−0.0823577	−	0.113356i
$746$	−53.5230	−	17.3907i	−1.95962	−	0.636718i
$747$	0.887646	+	26.8539i	0.0324773	+	0.982534i
$748$	−20.5635	+	6.42378i	−0.751876	+	0.234877i
$749$	−2.11549	−	3.28548i	−0.0772984	−	0.120049i
$750$	4.05186	+	7.63760i	0.147953	+	0.278886i
$751$	12.4609	−	9.05335i	0.454704	−	0.330362i	−0.336746	−	0.941595i	$-0.609327\pi$
$751$	12.4609	−	9.05335i	0.454704	−	0.330362i	0.791450	+	0.611234i	$0.209327\pi$
$752$	14.4955	+	10.5316i	0.528597	+	0.384048i
$753$	−16.4854	+	33.7203i	−0.600762	+	1.22884i
$754$	26.1015	−	8.48089i	0.950560	−	0.308856i
$755$	1.93965	+	1.40924i	0.0705911	+	0.0512874i
$756$	−6.03591	−	12.0446i	−0.219524	−	0.438056i
$757$	−0.706647	+	2.17483i	−0.0256835	+	0.0790457i	−0.963077	−	0.269227i	$-0.913232\pi$
$757$	−0.706647	+	2.17483i	−0.0256835	+	0.0790457i	0.937393	+	0.348273i	$0.113232\pi$
$758$		−	38.7879i		−	1.40884i
$759$	7.23003	−	3.73086i	0.262434	−	0.135422i
$760$	−1.93444			−0.0701696
$761$	14.7250	−	45.3188i	0.533779	−	1.64280i	−0.212493	−	0.977163i	$-0.568158\pi$
$761$	14.7250	−	45.3188i	0.533779	−	1.64280i	0.746272	−	0.665641i	$-0.231842\pi$
$762$	−1.66693	+	11.7811i	−0.0603864	+	0.426785i
$763$	4.29001	+	0.241567i	0.155309	+	0.00874533i
$764$	10.2055	−	3.31597i	0.369222	−	0.119967i
$765$	5.45330	−	1.97334i	0.197165	−	0.0713461i
$766$	34.0332	−	46.8427i	1.22967	−	1.69249i
$767$	−7.37063	−	10.1448i	−0.266138	−	0.366308i
$768$	28.7574	−	15.2562i	1.03769	−	0.550512i
$769$			36.8282i			1.32806i	0.747707	+	0.664029i	$0.231155\pi$
$769$			36.8282i			1.32806i	−0.747707	+	0.664029i	$0.768845\pi$
$770$	−3.74134	+	2.34924i	−0.134829	+	0.0846606i
$771$	37.7974	+	36.5687i	1.36124	+	1.31699i
$772$	−1.28246	+	3.94701i	−0.0461568	+	0.142056i
$773$	−39.1840	+	28.4689i	−1.40935	+	1.02395i	−0.415935	+	0.909394i	$0.636546\pi$
$773$	−39.1840	+	28.4689i	−1.40935	+	1.02395i	−0.993416	+	0.114559i	$0.963454\pi$
$774$	0.793131	+	0.537127i	0.0285085	+	0.0193066i
$775$	−27.1372	+	8.81741i	−0.974797	+	0.316731i
$776$	1.35313	+	4.16451i	0.0485746	+	0.149497i
$777$	22.7252	+	24.6066i	0.815262	+	0.882758i
$778$	−25.6150	+	18.6104i	−0.918343	+	0.667215i
$779$	35.4921	+	11.5321i	1.27164	+	0.413180i
$780$	−1.43090	+	1.47898i	−0.0512345	+	0.0529561i
$781$	2.55663	+	1.90231i	0.0914833	+	0.0680701i
$782$	16.2055			0.579507
$783$	−17.2372	+	9.88775i	−0.616008	+	0.353359i
$784$	−7.00977	−	34.2880i	−0.250349	−	1.22457i
$785$	−0.0135316	+	0.0186247i	−0.000482964	+	0.000664742i
$786$	22.7175	+	11.1063i	0.810306	+	0.396148i
$787$	24.8093	−	8.06104i	0.884357	−	0.287345i	0.168592	−	0.985686i	$-0.446078\pi$
$787$	24.8093	−	8.06104i	0.884357	−	0.287345i	0.715765	+	0.698341i	$0.246078\pi$
$788$	6.80370	−	9.36449i	0.242372	−	0.333596i
$789$	1.59031	−	11.2396i	0.0566164	−	0.400140i
$790$	−6.13519	−	1.99345i	−0.218280	−	0.0709236i
$791$	11.3187	+	17.5787i	0.402448	+	0.625025i
$792$	9.98859	−	14.3939i	0.354929	−	0.511463i
$793$	−60.9555			−2.16459
$794$	−16.1203	+	49.6132i	−0.572089	+	1.76071i
$795$	−0.225255	+	1.59200i	−0.00798897	+	0.0564626i
$796$	−11.8946	+	16.3716i	−0.421594	+	0.580275i
$797$	15.8083	+	48.6529i	0.559958	+	1.72337i	0.682477	+	0.730907i	$0.260903\pi$
$797$	15.8083	+	48.6529i	0.559958	+	1.72337i	−0.122519	+	0.992466i	$0.539097\pi$
$798$	3.48892	+	29.5940i	0.123506	+	1.04762i
$799$	19.2179	+	13.9626i	0.679882	+	0.493963i
$800$	14.7593	+	20.3145i	0.521821	+	0.718225i
$801$	−26.7378	−	7.72092i	−0.944735	−	0.272805i
$802$	32.9170			1.16234
$803$	−16.4521	−	0.187185i	−0.580581	−	0.00660562i
$804$	17.7307	+	17.1543i	0.625313	+	0.604985i
$805$	1.05667	−	0.278733i	0.0372428	−	0.00982406i
$806$	−24.4885	−	33.7055i	−0.862570	−	1.18723i
$807$	−1.49998	−	8.55344i	−0.0528019	−	0.301095i
$808$	−15.1809	+	4.93258i	−0.534063	+	0.173527i
$809$	−28.5660	+	9.28166i	−1.00433	+	0.326326i	−0.764594	−	0.644513i	$-0.777060\pi$
$809$	−28.5660	+	9.28166i	−1.00433	+	0.326326i	−0.239734	+	0.970839i	$0.577060\pi$
$810$	2.41540	−	3.83357i	0.0848684	−	0.134698i
$811$	28.0340	+	38.5855i	0.984408	+	1.35492i	0.934421	+	0.356171i	$0.115918\pi$
$811$	28.0340	+	38.5855i	0.984408	+	1.35492i	0.0499867	+	0.998750i	$0.484082\pi$
$812$	9.58759	−	2.52905i	0.336458	−	0.0887524i
$813$	−13.1085	+	13.5490i	−0.459735	+	0.475183i
$814$	13.3837	−	39.6500i	0.469097	−	1.38973i
$815$	0.738233			0.0258592
$816$	50.7054	−	26.8999i	1.77504	−	0.941686i
$817$	−0.409539	−	0.563682i	−0.0143280	−	0.0197207i
$818$	−20.0952	−	14.6000i	−0.702611	−	0.510477i
$819$	−26.2375	−	20.0091i	−0.916811	−	0.699174i
$820$	0.874951	+	2.69282i	0.0305546	+	0.0940375i
$821$	−19.3707	+	26.6615i	−0.676044	+	0.930494i	−0.999878	−	0.0156194i	$-0.995028\pi$
$821$	−19.3707	+	26.6615i	−0.676044	+	0.930494i	0.323834	+	0.946114i	$0.395028\pi$
$822$	22.1144	+	3.12900i	0.771330	+	0.109137i
$823$	−10.3641	+	31.8973i	−0.361269	+	1.11187i	0.591016	+	0.806660i	$0.298727\pi$
$823$	−10.3641	+	31.8973i	−0.361269	+	1.11187i	−0.952285	+	0.305211i	$0.901273\pi$
$824$	−0.0387018			−0.00134824
$825$	25.2225	+	12.6885i	0.878134	+	0.441756i
$826$	−7.45829	−	11.5832i	−0.259507	−	0.403030i
$827$	22.0469	+	7.16348i	0.766647	+	0.249099i	0.666129	−	0.745837i	$-0.267950\pi$
$827$	22.0469	+	7.16348i	0.766647	+	0.249099i	0.100518	+	0.994935i	$0.467950\pi$
$828$	3.28582	−	2.55732i	0.114190	−	0.0888730i
$829$	8.20350	−	11.2911i	0.284919	−	0.392158i	−0.642436	−	0.766339i	$-0.722076\pi$
$829$	8.20350	−	11.2911i	0.284919	−	0.392158i	0.927356	+	0.374181i	$0.122076\pi$
$830$	4.28831	−	1.39336i	0.148849	−	0.0483641i
$831$	−14.1725	+	28.9893i	−0.491638	+	1.00563i
$832$	2.88307	−	3.96820i	0.0999524	−	0.137573i
$833$	−9.29345	−	45.4585i	−0.321999	−	1.57504i
$834$	−32.1065	+	17.0330i	−1.11176	+	0.589804i
$835$	−3.56003			−0.123200
$836$	9.98616	−	7.08320i	0.345379	−	0.244978i
$837$	22.3614	+	20.2478i	0.772923	+	0.699866i
$838$	−1.01418	−	0.329526i	−0.0350342	−	0.0113833i
$839$	37.2312	−	27.0500i	1.28536	−	0.933870i	0.285661	−	0.958331i	$-0.407787\pi$
$839$	37.2312	−	27.0500i	1.28536	−	0.933870i	0.999701	+	0.0244602i	$0.00778671\pi$
$840$	1.72882	−	1.59664i	0.0596501	−	0.0550892i
$841$	4.44196	+	13.6709i	0.153171	+	0.471412i
$842$	24.4756	−	7.95261i	0.843485	−	0.274065i
$843$	44.1797	−	7.74762i	1.52163	−	0.266842i
$844$	−10.2062	+	7.41521i	−0.351311	+	0.255242i
$845$	−0.385908	+	1.18770i	−0.0132756	+	0.0408582i
$846$	18.5494	−	0.613144i	0.637743	−	0.0210803i
$847$	−11.1498	+	26.8827i	−0.383112	+	0.923702i
$848$			15.9138i			0.546481i
$849$	1.85753	+	3.50138i	0.0637503	+	0.120167i
$850$	33.0561	+	45.4978i	1.13381	+	1.56056i
$851$	−6.08469	+	8.37485i	−0.208580	+	0.287086i
$852$	1.46515	+	0.716291i	0.0501951	+	0.0245397i
$853$	−39.7291	+	12.9088i	−1.36030	+	0.441988i	−0.896143	−	0.443765i	$-0.853642\pi$
$853$	−39.7291	+	12.9088i	−1.36030	+	0.441988i	−0.464156	+	0.885753i	$0.653642\pi$
$854$	−66.8626	−	3.76499i	−2.28799	−	0.128835i
$855$	−2.60088	+	2.02424i	−0.0889483	+	0.0692274i
$856$	0.803652	−	2.47339i	0.0274683	−	0.0845386i
$857$	32.0368			1.09436			0.547178	−	0.837017i	$-0.315702\pi$
$857$	32.0368			1.09436			0.547178	+	0.837017i	$0.315702\pi$
$858$	−6.23946	+	40.7500i	−0.213012	+	1.39118i
$859$		−	41.6968i		−	1.42268i	−0.702850	−	0.711338i	$-0.748090\pi$
$859$		−	41.6968i		−	1.42268i	0.702850	−	0.711338i	$-0.251910\pi$
$860$	0.0163356	−	0.0502758i	0.000557040	−	0.00171439i
$861$	−41.2378	+	18.9879i	−1.40538	+	0.647107i
$862$	40.7128	+	29.5796i	1.38668	+	1.00749i
$863$	−44.2742	+	14.3856i	−1.50711	+	0.489690i	−0.942083	−	0.335381i	$-0.891135\pi$
$863$	−44.2742	+	14.3856i	−1.50711	+	0.489690i	−0.565029	+	0.825071i	$0.691135\pi$
$864$	10.8653	−	24.2214i	0.369645	−	0.824027i
$865$	2.99399	+	2.17526i	0.101799	+	0.0739610i
$866$	24.6359	−	17.8990i	0.837163	−	0.608234i
$867$	41.2133	−	21.8642i	1.39968	−	0.742549i
$868$	−8.14886	−	12.6557i	−0.276590	−	0.429561i
$869$	−40.5642	+	12.6717i	−1.37605	+	0.429859i
$870$	2.39671	+	2.31879i	0.0812560	+	0.0786145i
$871$	57.4665	+	18.6720i	1.94718	+	0.632676i
$872$	1.68087	+	2.31352i	0.0569215	+	0.0783458i
$873$	6.17712	+	4.18330i	0.209064	+	0.141583i
$874$	−8.75883	+	2.84592i	−0.296272	+	0.0962645i
$875$	5.92678	+	4.83771i	0.200362	+	0.163544i
$876$	−8.29368	+	1.45443i	−0.280217	+	0.0491406i
$877$	25.6573	−	18.6411i	0.866384	−	0.629465i	−0.0632303	−	0.997999i	$-0.520140\pi$
$877$	25.6573	−	18.6411i	0.866384	−	0.629465i	0.929614	+	0.368534i	$0.120140\pi$
$878$	1.11312	−	3.42582i	0.0375659	−	0.115616i
$879$	7.01873	+	6.79057i	0.236736	+	0.229040i
$880$	−4.58196	−	1.54662i	−0.154458	−	0.0521365i
$881$	16.4390			0.553844			0.276922	−	0.960892i	$-0.410686\pi$
$881$	16.4390			0.553844			0.276922	+	0.960892i	$0.410686\pi$
$882$	−27.5442	−	23.5687i	−0.927461	−	0.793599i
$883$	15.1013	−	10.9717i	0.508198	−	0.369228i	−0.303941	−	0.952691i	$-0.598303\pi$
$883$	15.1013	−	10.9717i	0.508198	−	0.369228i	0.812140	+	0.583463i	$0.198303\pi$
$884$	−15.8722	+	21.8462i	−0.533839	+	0.734766i
$885$	0.669222	−	1.36887i	0.0224957	−	0.0460140i
$886$	−3.98881	−	12.2763i	−0.134007	−	0.412430i
$887$	14.9163	+	10.8373i	0.500840	+	0.363881i	0.809338	−	0.587344i	$-0.199826\pi$
$887$	14.9163	+	10.8373i	0.500840	+	0.363881i	−0.308498	+	0.951225i	$0.599826\pi$
$888$	−3.12304	+	22.0723i	−0.104802	+	0.740698i
$889$	2.68544	+	10.1804i	0.0900668	+	0.341441i
$890$			4.67038i			0.156552i
$891$	−1.63220	−	29.8050i	−0.0546807	−	0.998504i
$892$			7.63994i			0.255804i
$893$	−12.8391	−	4.17166i	−0.429643	−	0.139599i
$894$	−38.8218	−	5.49295i	−1.29840	−	0.183712i
$895$	−2.23248	+	3.07275i	−0.0746236	+	0.102711i
$896$	20.5021	−	25.1176i	0.684928	−	0.839120i
$897$	4.47896	−	9.16155i	0.149548	−	0.305895i
$898$	−49.6535	−	36.0754i	−1.65696	−	1.20385i
$899$	−17.9619	+	13.0501i	−0.599064	+	0.435246i
$900$	13.8823	+	4.00869i	0.462742	+	0.133623i
$901$			21.0982i			0.702884i
$902$	45.5058	+	33.8595i	1.51518	+	1.12740i
$903$	0.831256	+	0.165744i	0.0276625	+	0.00551560i
$904$	−4.29987	+	13.2336i	−0.143012	+	0.440144i
$905$	−0.410345	−	0.564791i	−0.0136403	−	0.0187743i
$906$	24.2105	−	4.24571i	0.804341	−	0.141054i
$907$	−6.04724	−	18.6115i	−0.200795	−	0.617985i	−0.999860	−	0.0167393i	$-0.994671\pi$
$907$	−6.04724	−	18.6115i	−0.200795	−	0.617985i	0.799065	−	0.601245i	$-0.205329\pi$
$908$	7.23029	+	22.2525i	0.239946	+	0.738476i
$909$	−15.2494	+	22.5175i	−0.505790	+	0.746858i
$910$	−2.00451	+	5.16181i	−0.0664487	+	0.171112i
$911$	−7.26979	−	2.36210i	−0.240859	−	0.0782598i	0.186100	−	0.982531i	$-0.440415\pi$
$911$	−7.26979	−	2.36210i	−0.240859	−	0.0782598i	−0.426959	+	0.904271i	$0.640415\pi$
$912$	−22.6815	+	23.4436i	−0.751059	+	0.776295i
$913$	17.7321	−	23.8311i	0.586846	−	0.788696i
$914$		−	67.5067i		−	2.23292i
$915$	−3.47115	−	6.54299i	−0.114753	−	0.216305i
$916$	−3.97769	−	5.47482i	−0.131427	−	0.180893i
$917$	22.3405	+	1.25798i	0.737748	+	0.0415421i
$918$	24.3347	−	54.2480i	0.803166	−	1.79045i
$919$	8.39208	+	25.8282i	0.276829	+	0.851993i	0.988730	+	0.149712i	$0.0478347\pi$
$919$	8.39208	+	25.8282i	0.276829	+	0.851993i	−0.711900	+	0.702280i	$0.752165\pi$
$920$	0.588404	+	0.427501i	0.0193991	+	0.0140943i
$921$	−7.85191	+	55.4939i	−0.258729	+	1.82859i
$922$	32.6186	+	10.5984i	1.07424	+	0.349040i
$923$	3.99433			0.131475
$924$	−3.07841	+	14.5726i	−0.101272	+	0.479404i
$925$	−35.9245			−1.18119
$926$	−8.90720	−	2.89413i	−0.292709	−	0.0951069i
$927$	−0.0520350	+	0.0404982i	−0.00170905	+	0.00133014i
$928$	15.8067	+	11.4843i	0.518882	+	0.376990i
$929$	7.70342	+	23.7087i	0.252741	+	0.777857i	0.994266	+	0.106932i	$0.0341027\pi$
$929$	7.70342	+	23.7087i	0.252741	+	0.777857i	−0.741525	+	0.670925i	$0.765897\pi$
$930$	2.22345	−	4.54799i	0.0729098	−	0.149134i
$931$	13.0061	+	22.9376i	0.426259	+	0.751749i
$932$	6.80932	+	9.37223i	0.223047	+	0.306998i
$933$	−7.79609	+	4.13594i	−0.255233	+	0.135405i
$934$			8.17226i			0.267405i
$935$	−6.07470	−	2.05048i	−0.198664	−	0.0670580i
$936$	−0.725493	−	21.9483i	−0.0237135	−	0.717403i
$937$	−5.85098	−	1.90110i	−0.191143	−	0.0621062i	0.211881	−	0.977295i	$-0.432041\pi$
$937$	−5.85098	−	1.90110i	−0.191143	−	0.0621062i	−0.403024	+	0.915189i	$0.632041\pi$
$938$	61.8821	+	24.0309i	2.02052	+	0.784637i
$939$	−38.8708	+	6.81663i	−1.26850	+	0.222452i
$940$	−0.316508	−	0.974113i	−0.0103234	−	0.0317720i
$941$	5.97477	+	18.3884i	0.194772	+	0.599446i	0.999979	+	0.00645267i	$0.00205396\pi$
$941$	5.97477	+	18.3884i	0.194772	+	0.599446i	−0.805207	+	0.592993i	$0.797946\pi$
$942$	0.0407676	+	0.232471i	0.00132828	+	0.00757432i
$943$	−8.24720	−	11.3513i	−0.268566	−	0.369649i
$944$	4.66022	−	14.3427i	0.151677	−	0.466814i
$945$	0.653674	−	3.95577i	0.0212640	−	0.128681i
$946$	−0.315767	−	1.01082i	−0.0102665	−	0.0328646i
$947$		−	24.0057i		−	0.780081i	−0.920798	−	0.390040i	$-0.872461\pi$
$947$		−	24.0057i		−	0.780081i	0.920798	−	0.390040i	$-0.127539\pi$
$948$	−19.2127	+	10.1926i	−0.623999	+	0.331041i
$949$	−16.6843	+	12.1218i	−0.541594	+	0.393491i
$950$	−25.8564	−	18.7858i	−0.838892	−	0.609491i
$951$	5.76109	+	2.81652i	0.186816	+	0.0913320i
$952$	19.5266	−	23.9225i	0.632861	−	0.775332i
$953$	4.13898	−	5.69682i	0.134075	−	0.184538i	−0.736701	−	0.676219i	$-0.763617\pi$
$953$	4.13898	−	5.69682i	0.134075	−	0.184538i	0.870775	+	0.491681i	$0.163617\pi$
$954$	10.1244	+	13.0085i	0.327789	+	0.421167i
$955$	3.03720	+	0.986845i	0.0982814	+	0.0319335i
$956$		−	9.48493i		−	0.306765i
$957$	21.7160	+	3.32506i	0.701980	+	0.107484i
$958$			40.5889i			1.31137i
$959$	19.1098	−	5.04086i	0.617087	−	0.162778i
$960$	0.590127	+	0.0834979i	0.0190463	+	0.00269488i
$961$	2.18748	+	1.58930i	0.0705640	+	0.0512677i
$962$	−16.2090	−	49.8863i	−0.522600	−	1.60840i
$963$	−1.50768	−	4.16646i	−0.0485842	−	0.134262i
$964$	−6.75890	+	9.30283i	−0.217690	+	0.299624i
$965$	−0.999214	+	0.725971i	−0.0321658	+	0.0233698i
$966$	5.47888	−	9.77272i	0.176280	−	0.314432i
$967$	−0.252415			−0.00811711			−0.00405855	−	0.999992i	$-0.501292\pi$
$967$	−0.252415			−0.00811711			−0.00405855	+	0.999992i	$0.501292\pi$
$968$	−18.5526	+	5.56475i	−0.596305	+	0.178858i
$969$	−30.0708	+	31.0812i	−0.966013	+	0.998472i
$970$	0.386880	−	1.19069i	0.0124220	−	0.0382309i
$971$	7.90022	−	5.73985i	0.253530	−	0.184200i	−0.453760	−	0.891124i	$-0.649918\pi$
$971$	7.90022	−	5.73985i	0.253530	−	0.184200i	0.707290	+	0.706924i	$0.249918\pi$
$972$	−3.62653	−	14.8395i	−0.116321	−	0.475976i
$973$	−20.3365	+	24.9147i	−0.651958	+	0.798728i
$974$	15.0255	−	4.88209i	0.481449	−	0.156432i
$975$	34.8578	−	6.11287i	1.11634	−	0.195769i
$976$	−43.0893	−	59.3073i	−1.37926	−	1.89838i
$977$	49.8917	+	16.2108i	1.59618	+	0.518630i	0.966159	−	0.257949i	$-0.0830467\pi$
$977$	49.8917	+	16.2108i	1.59618	+	0.518630i	0.630020	+	0.776579i	$0.283047\pi$
$978$	5.26259	−	5.43941i	0.168279	−	0.173933i
$979$	17.8003	+	25.0956i	0.568902	+	0.802059i
$980$	−0.827911	+	1.82125i	−0.0264467	+	0.0581778i
$981$	4.68087	+	1.35166i	0.149449	+	0.0431553i
$982$	−49.7825	+	36.1691i	−1.58862	+	1.15420i
$983$	−31.0608	−	22.5670i	−0.990685	−	0.719775i	−0.0306142	−	0.999531i	$-0.509746\pi$
$983$	−31.0608	−	22.5670i	−0.990685	−	0.719775i	−0.960071	+	0.279756i	$0.909746\pi$
$984$	−27.1445	−	13.2706i	−0.865336	−	0.423052i
$985$	3.27621	−	1.06450i	0.104389	−	0.0339179i
$986$	35.4020	+	25.7210i	1.12743	+	0.819125i
$987$	14.9175	−	6.86877i	0.474830	−	0.218635i
$988$	4.74217	−	14.5949i	0.150869	−	0.464326i
$989$			0.261962i			0.00832992i
$990$	−4.72944	+	1.65079i	−0.150311	+	0.0524656i
$991$	−7.09006			−0.225223			−0.112612	−	0.993639i	$-0.535922\pi$
$991$	−7.09006			−0.225223			−0.112612	+	0.993639i	$0.535922\pi$
$992$	9.16540	−	28.2082i	0.291002	−	0.895611i
$993$	2.30227	+	0.325751i	0.0730603	+	0.0103374i
$994$	4.38141	+	0.246714i	0.138970	+	0.00782530i
$995$	−5.72766	+	1.86103i	−0.181579	+	0.0589986i
$996$	6.67678	−	13.6571i	0.211562	−	0.432742i
$997$	−14.1223	+	19.4376i	−0.447257	+	0.615596i	−0.971805	−	0.235784i	$-0.924234\pi$
$997$	−14.1223	+	19.4376i	−0.447257	+	0.615596i	0.524549	+	0.851380i	$0.324234\pi$
$998$	−28.2015	−	38.8160i	−0.892702	−	1.22870i
$999$	18.8979	+	32.9445i	0.597903	+	1.04232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.u.a.20.5	✓	112
3.2	odd	2	inner	231.2.u.a.20.24	yes	112
7.6	odd	2	inner	231.2.u.a.20.6	yes	112
11.5	even	5	inner	231.2.u.a.104.23	yes	112
21.20	even	2	inner	231.2.u.a.20.23	yes	112
33.5	odd	10	inner	231.2.u.a.104.6	yes	112
77.27	odd	10	inner	231.2.u.a.104.24	yes	112
231.104	even	10	inner	231.2.u.a.104.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.u.a.20.5	✓	112	1.1	even	1	trivial
231.2.u.a.20.6	yes	112	7.6	odd	2	inner
231.2.u.a.20.23	yes	112	21.20	even	2	inner
231.2.u.a.20.24	yes	112	3.2	odd	2	inner
231.2.u.a.104.5	yes	112	231.104	even	10	inner
231.2.u.a.104.6	yes	112	33.5	odd	10	inner
231.2.u.a.104.23	yes	112	11.5	even	5	inner
231.2.u.a.104.24	yes	112	77.27	odd	10	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64177 - 0.533443i) q^{2} +(-1.71497 - 0.242653i) q^{3} +(0.792810 + 0.576010i) q^{4} +(0.0901224 + 0.277368i) q^{5} +(2.68614 + 1.31322i) q^{6} +(2.64157 + 0.148745i) q^{7} +(1.03500 + 1.42455i) q^{8} +(2.88224 + 0.832286i) q^{9} +O(q^{10})\)	\(q+(-1.64177 - 0.533443i) q^{2} +(-1.71497 - 0.242653i) q^{3} +(0.792810 + 0.576010i) q^{4} +(0.0901224 + 0.277368i) q^{5} +(2.68614 + 1.31322i) q^{6} +(2.64157 + 0.148745i) q^{7} +(1.03500 + 1.42455i) q^{8} +(2.88224 + 0.832286i) q^{9} -0.503450i q^{10} +(-1.91881 - 2.70521i) q^{11} +(-1.21987 - 1.18022i) q^{12} +(-3.95370 - 1.28464i) q^{13} +(-4.25750 - 1.65333i) q^{14} +(-0.0872528 - 0.497546i) q^{15} +(-1.54496 - 4.75490i) q^{16} +(-2.04829 - 6.30398i) q^{17} +(-4.28799 - 2.90393i) q^{18} +(2.21414 + 3.04750i) q^{19} +(-0.0883170 + 0.271812i) q^{20} +(-4.49411 - 0.896078i) q^{21} +(1.70717 + 5.46491i) q^{22} -1.41628i q^{23} +(-1.42931 - 2.69420i) q^{24} +(3.97627 - 2.88893i) q^{25} +(5.80578 + 4.21815i) q^{26} +(-4.74099 - 2.12673i) q^{27} +(2.00858 + 1.63950i) q^{28} +(2.24789 - 3.09395i) q^{29} +(-0.122164 + 0.863401i) q^{30} +(-5.52136 - 1.79400i) q^{31} +5.10892i q^{32} +(2.63427 + 5.10496i) q^{33} +11.4423i q^{34} +(0.196807 + 0.746092i) q^{35} +(1.80566 + 2.32004i) q^{36} +(-5.91329 - 4.29626i) q^{37} +(-2.00944 - 6.18441i) q^{38} +(6.46875 + 3.16249i) q^{39} +(-0.301848 + 0.415459i) q^{40} +(8.01488 - 5.82315i) q^{41} +(6.90029 + 3.86851i) q^{42} -0.184966 q^{43} +(0.0369769 - 3.24997i) q^{44} +(0.0289045 + 0.874449i) q^{45} +(-0.755503 + 2.32520i) q^{46} +(-2.89934 + 2.10649i) q^{47} +(1.49577 + 8.52940i) q^{48} +(6.95575 + 0.785839i) q^{49} +(-8.06920 + 2.62184i) q^{50} +(1.98307 + 11.3082i) q^{51} +(-2.39457 - 3.29585i) q^{52} +(-3.02722 - 0.983603i) q^{53} +(6.64913 + 6.02065i) q^{54} +(0.577412 - 0.776017i) q^{55} +(2.52212 + 3.91699i) q^{56} +(-3.05769 - 5.76363i) q^{57} +(-5.34096 + 3.88043i) q^{58} +(2.44032 + 1.77299i) q^{59} +(0.217417 - 0.444718i) q^{60} +(13.9451 - 4.53104i) q^{61} +(8.10781 + 5.89067i) q^{62} +(7.48983 + 2.62726i) q^{63} +(-0.364604 + 1.12214i) q^{64} -1.21241i q^{65} +(-1.60166 - 9.78640i) q^{66} -14.5349 q^{67} +(2.00725 - 6.17769i) q^{68} +(-0.343664 + 2.42887i) q^{69} +(0.0748856 - 1.32990i) q^{70} +(-0.913804 + 0.296913i) q^{71} +(1.79747 + 4.96730i) q^{72} +(2.91589 - 4.01338i) q^{73} +(7.41645 + 10.2079i) q^{74} +(-7.52020 + 3.98957i) q^{75} +3.69145i q^{76} +(-4.66628 - 7.43141i) q^{77} +(-8.93319 - 8.64279i) q^{78} +(3.95957 - 12.1863i) q^{79} +(1.17962 - 0.857046i) q^{80} +(7.61460 + 4.79769i) q^{81} +(-16.2649 + 5.28479i) q^{82} +(2.76762 + 8.51786i) q^{83} +(-3.04683 - 3.29908i) q^{84} +(1.56393 - 1.13626i) q^{85} +(0.303671 + 0.0986686i) q^{86} +(-4.60581 + 4.76057i) q^{87} +(1.86775 - 5.53332i) q^{88} -9.27676 q^{89} +(0.419014 - 1.45106i) q^{90} +(-10.2529 - 3.98154i) q^{91} +(0.815790 - 1.12284i) q^{92} +(9.03365 + 4.41643i) q^{93} +(5.88373 - 1.91174i) q^{94} +(-0.645736 + 0.888779i) q^{95} +(1.23970 - 8.76164i) q^{96} +(2.36507 + 0.768458i) q^{97} +(-11.0005 - 5.00066i) q^{98} +(-3.27896 - 9.39406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9}+O(q^{10}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9	\( 112 q + 12 q^{4} - 2 q^{7} - 12 q^{9} - 60 q^{16} + 2 q^{18} - 80 q^{22} - 36 q^{25} + 8 q^{28} + 24 q^{30} - 34 q^{36} + 4 q^{37} - 66 q^{39} - 30 q^{42} + 36 q^{46} + 26 q^{49} + 38 q^{51} - 86 q^{57} - 116 q^{58} + 88 q^{60} + 44 q^{63} - 32 q^{64} + 110 q^{70} + 86 q^{72} - 52 q^{78} - 156 q^{79} + 68 q^{81} - 30 q^{84} + 8 q^{85} - 112 q^{88} + 42 q^{91} + 56 q^{93} + 70 q^{99}+O(q^{100}) \) 112 * q + 12 * q^4 - 2 * q^7 - 12 * q^9 - 60 * q^16 + 2 * q^18 - 80 * q^22 - 36 * q^25 + 8 * q^28 + 24 * q^30 - 34 * q^36 + 4 * q^37 - 66 * q^39 - 30 * q^42 + 36 * q^46 + 26 * q^49 + 38 * q^51 - 86 * q^57 - 116 * q^58 + 88 * q^60 + 44 * q^63 - 32 * q^64 + 110 * q^70 + 86 * q^72 - 52 * q^78 - 156 * q^79 + 68 * q^81 - 30 * q^84 + 8 * q^85 - 112 * q^88 + 42 * q^91 + 56 * q^93 + 70 * q^99

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