LMFDB - Embedded newform 231.2.p.a.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(10,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 3]))

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

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

chi := DirichletCharacter("231.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.p (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	231.10
Dual form			231.2.p.a.208.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.567337 - 0.327552i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.785419 + 1.36039i) q^{4} +(-2.94602 + 1.70089i) q^{5} +0.655105 q^{6} +(-2.64073 - 0.162880i) q^{7} +2.33927i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.567337 - 0.327552i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.785419 + 1.36039i) q^{4} +(-2.94602 + 1.70089i) q^{5} +0.655105 q^{6} +(-2.64073 - 0.162880i) q^{7} +2.33927i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.11426 + 1.92995i) q^{10} +(1.82318 + 2.77056i) q^{11} +(-1.36039 + 0.785419i) q^{12} +5.44628 q^{13} +(-1.55154 + 0.772570i) q^{14} -3.40177 q^{15} +(-0.804604 - 1.39362i) q^{16} +(0.850644 - 1.47336i) q^{17} +(0.567337 + 0.327552i) q^{18} +(-3.12887 - 5.41937i) q^{19} -5.34364i q^{20} +(-2.20550 - 1.46142i) q^{21} +(1.94186 + 0.974655i) q^{22} +(3.09034 + 5.35263i) q^{23} +(-1.16964 + 2.02587i) q^{24} +(3.28603 - 5.69158i) q^{25} +(3.08987 - 1.78394i) q^{26} +1.00000i q^{27} +(2.29566 - 3.46449i) q^{28} +3.61505i q^{29} +(-1.92995 + 1.11426i) q^{30} +(5.63025 + 3.25063i) q^{31} +(-4.96470 - 2.86637i) q^{32} +(0.193641 + 3.31097i) q^{33} -1.11452i q^{34} +(8.05670 - 4.01174i) q^{35} -1.57084 q^{36} +(-0.0828974 - 0.143582i) q^{37} +(-3.55025 - 2.04974i) q^{38} +(4.71661 + 2.72314i) q^{39} +(-3.97884 - 6.89155i) q^{40} -1.35583 q^{41} +(-1.72996 - 0.106703i) q^{42} +3.12830i q^{43} +(-5.20099 + 0.304179i) q^{44} +(-2.94602 - 1.70089i) q^{45} +(3.50653 + 2.02450i) q^{46} +(-0.693427 + 0.400350i) q^{47} -1.60921i q^{48} +(6.94694 + 0.860244i) q^{49} -4.30539i q^{50} +(1.47336 - 0.850644i) q^{51} +(-4.27761 + 7.40904i) q^{52} +(-3.20074 + 5.54384i) q^{53} +(0.327552 + 0.567337i) q^{54} +(-10.0835 - 5.06111i) q^{55} +(0.381020 - 6.17739i) q^{56} -6.25775i q^{57} +(1.18412 + 2.05095i) q^{58} +(1.54520 + 0.892122i) q^{59} +(2.67182 - 4.62773i) q^{60} +(-1.78024 - 3.08347i) q^{61} +4.25900 q^{62} +(-1.17931 - 2.36838i) q^{63} -0.537130 q^{64} +(-16.0449 + 9.26350i) q^{65} +(1.19437 + 1.81501i) q^{66} +(4.44901 - 7.70591i) q^{67} +(1.33622 + 2.31441i) q^{68} +6.18068i q^{69} +(3.25681 - 4.91500i) q^{70} +3.59161 q^{71} +(-2.02587 + 1.16964i) q^{72} +(5.41218 - 9.37418i) q^{73} +(-0.0940615 - 0.0543064i) q^{74} +(5.69158 - 3.28603i) q^{75} +9.82991 q^{76} +(-4.36327 - 7.61327i) q^{77} +3.56788 q^{78} +(4.09831 - 2.36616i) q^{79} +(4.74076 + 2.73708i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.769213 + 0.444105i) q^{82} -14.2220 q^{83} +(3.72034 - 1.85250i) q^{84} +5.78740i q^{85} +(1.02468 + 1.77480i) q^{86} +(-1.80752 + 3.13072i) q^{87} +(-6.48110 + 4.26492i) q^{88} +(3.31004 - 1.91105i) q^{89} -2.22852 q^{90} +(-14.3822 - 0.887088i) q^{91} -9.70885 q^{92} +(3.25063 + 5.63025i) q^{93} +(-0.262271 + 0.454267i) q^{94} +(18.4355 + 10.6437i) q^{95} +(-2.86637 - 4.96470i) q^{96} -3.87321i q^{97} +(4.22303 - 1.78744i) q^{98} +(-1.48779 + 2.96420i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	$ 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.567337	−	0.327552i	0.401168	−	0.231614i	−0.285820	−	0.958283i	$-0.592266\pi$
$2$	0.567337	−	0.327552i	0.401168	−	0.231614i	0.686988	+	0.726669i	$0.258933\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.785419	+	1.36039i	−0.392710	+	0.680193i
$5$	−2.94602	+	1.70089i	−1.31750	+	0.760660i	−0.983326	−	0.181851i	$-0.941791\pi$
$5$	−2.94602	+	1.70089i	−1.31750	+	0.760660i	−0.334175	+	0.942511i	$0.608458\pi$
$6$	0.655105			0.267445
$7$	−2.64073	−	0.162880i	−0.998103	−	0.0615628i
$7$	−2.64073	−	0.162880i	−0.998103	−	0.0615628i
$8$			2.33927i			0.827058i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.11426	+	1.92995i	−0.352360	+	0.610305i
$11$	1.82318	+	2.77056i	0.549710	+	0.835356i
$11$	1.82318	+	2.77056i	0.549710	+	0.835356i
$12$	−1.36039	+	0.785419i	−0.392710	+	0.226731i
$13$	5.44628			1.51053			0.755263	−	0.655422i	$-0.227509\pi$
$13$	5.44628			1.51053			0.755263	+	0.655422i	$0.227509\pi$
$14$	−1.55154	+	0.772570i	−0.414666	+	0.206478i
$15$	−3.40177			−0.878334
$16$	−0.804604	−	1.39362i	−0.201151	−	0.348404i
$17$	0.850644	−	1.47336i	0.206311	−	0.357342i	−0.744238	−	0.667914i	$-0.767187\pi$
$17$	0.850644	−	1.47336i	0.206311	−	0.357342i	0.950550	+	0.310572i	$0.100521\pi$
$18$	0.567337	+	0.327552i	0.133723	+	0.0772048i
$19$	−3.12887	−	5.41937i	−0.717813	−	1.24329i	−0.961864	−	0.273526i	$-0.911810\pi$
$19$	−3.12887	−	5.41937i	−0.717813	−	1.24329i	0.244051	−	0.969762i	$-0.421523\pi$
$20$		−	5.34364i		−	1.19487i
$21$	−2.20550	−	1.46142i	−0.481280	−	0.318909i
$22$	1.94186	+	0.974655i	0.414006	+	0.207797i
$23$	3.09034	+	5.35263i	0.644381	+	1.11610i	0.984444	+	0.175698i	$0.0562181\pi$
$23$	3.09034	+	5.35263i	0.644381	+	1.11610i	−0.340063	+	0.940403i	$0.610449\pi$
$24$	−1.16964	+	2.02587i	−0.238751	+	0.413529i
$25$	3.28603	−	5.69158i	0.657207	−	1.13832i
$26$	3.08987	−	1.78394i	0.605974	−	0.349859i
$27$			1.00000i			0.192450i
$28$	2.29566	−	3.46449i	0.433839	−	0.654726i
$29$			3.61505i			0.671297i	0.941987	+	0.335649i	$0.108955\pi$
$29$			3.61505i			0.671297i	−0.941987	+	0.335649i	$0.891045\pi$
$30$	−1.92995	+	1.11426i	−0.352360	+	0.203435i
$31$	5.63025	+	3.25063i	1.01122	+	0.583830i	0.911550	−	0.411190i	$-0.134887\pi$
$31$	5.63025	+	3.25063i	1.01122	+	0.583830i	0.0996735	+	0.995020i	$0.468220\pi$
$32$	−4.96470	−	2.86637i	−0.877644	−	0.506708i
$33$	0.193641	+	3.31097i	0.0337086	+	0.576365i
$34$		−	1.11452i		−	0.191139i
$35$	8.05670	−	4.01174i	1.36183	−	0.678108i
$36$	−1.57084			−0.261806
$37$	−0.0828974	−	0.143582i	−0.0136282	−	0.0236048i	0.859131	−	0.511756i	$-0.171005\pi$
$37$	−0.0828974	−	0.143582i	−0.0136282	−	0.0236048i	−0.872759	+	0.488151i	$0.837671\pi$
$38$	−3.55025	−	2.04974i	−0.575927	−	0.332512i
$39$	4.71661	+	2.72314i	0.755263	+	0.436051i
$40$	−3.97884	−	6.89155i	−0.629110	−	1.08965i
$41$	−1.35583			−0.211745			−0.105873	−	0.994380i	$-0.533764\pi$
$41$	−1.35583			−0.211745			−0.105873	+	0.994380i	$0.533764\pi$
$42$	−1.72996	−	0.106703i	−0.266938	−	0.0164647i
$43$			3.12830i			0.477062i	0.971135	+	0.238531i	$0.0766658\pi$
$43$			3.12830i			0.477062i	−0.971135	+	0.238531i	$0.923334\pi$
$44$	−5.20099	+	0.304179i	−0.784079	+	0.0458567i
$45$	−2.94602	−	1.70089i	−0.439167	−	0.253553i
$46$	3.50653	+	2.02450i	0.517010	+	0.298496i
$47$	−0.693427	+	0.400350i	−0.101147	+	0.0583971i	−0.549720	−	0.835349i	$-0.685266\pi$
$47$	−0.693427	+	0.400350i	−0.101147	+	0.0583971i	0.448573	+	0.893746i	$0.351932\pi$
$48$		−	1.60921i		−	0.232269i
$49$	6.94694	+	0.860244i	0.992420	+	0.122892i
$50$		−	4.30539i		−	0.608874i
$51$	1.47336	−	0.850644i	0.206311	−	0.119114i
$52$	−4.27761	+	7.40904i	−0.593198	+	1.02745i
$53$	−3.20074	+	5.54384i	−0.439655	+	0.761505i	−0.997663	−	0.0683306i	$-0.978233\pi$
$53$	−3.20074	+	5.54384i	−0.439655	+	0.761505i	0.558007	+	0.829836i	$0.311566\pi$
$54$	0.327552	+	0.567337i	0.0445742	+	0.0772048i
$55$	−10.0835	−	5.06111i	−1.35967	−	0.682440i
$56$	0.381020	−	6.17739i	0.0509160	−	0.825489i
$57$		−	6.25775i		−	0.828859i
$58$	1.18412	+	2.05095i	0.155482	+	0.269303i
$59$	1.54520	+	0.892122i	0.201168	+	0.116144i	0.597200	−	0.802092i	$-0.296280\pi$
$59$	1.54520	+	0.892122i	0.201168	+	0.116144i	−0.396032	+	0.918237i	$0.629613\pi$
$60$	2.67182	−	4.62773i	0.344930	−	0.597437i
$61$	−1.78024	−	3.08347i	−0.227936	−	0.394798i	0.729260	−	0.684237i	$-0.239865\pi$
$61$	−1.78024	−	3.08347i	−0.227936	−	0.394798i	−0.957196	+	0.289439i	$0.906531\pi$
$62$	4.25900			0.540894
$63$	−1.17931	−	2.36838i	−0.148579	−	0.298388i
$64$	−0.537130			−0.0671412
$65$	−16.0449	+	9.26350i	−1.99012	+	1.14900i
$66$	1.19437	+	1.81501i	0.147017	+	0.223412i
$67$	4.44901	−	7.70591i	0.543533	−	0.941427i	−0.455165	−	0.890407i	$-0.650420\pi$
$67$	4.44901	−	7.70591i	0.543533	−	0.941427i	0.998698	−	0.0510195i	$-0.0162471\pi$
$68$	1.33622	+	2.31441i	0.162041	+	0.280663i
$69$			6.18068i			0.744067i
$70$	3.25681	−	4.91500i	0.389263	−	0.587455i
$71$	3.59161			0.426245			0.213123	−	0.977025i	$-0.431637\pi$
$71$	3.59161			0.426245			0.213123	+	0.977025i	$0.431637\pi$
$72$	−2.02587	+	1.16964i	−0.238751	+	0.137843i
$73$	5.41218	−	9.37418i	0.633448	−	1.09716i	−0.353394	−	0.935475i	$-0.614972\pi$
$73$	5.41218	−	9.37418i	0.633448	−	1.09716i	0.986842	−	0.161690i	$-0.0516943\pi$
$74$	−0.0940615	−	0.0543064i	−0.0109344	−	0.00631300i
$75$	5.69158	−	3.28603i	0.657207	−	0.379439i
$76$	9.82991			1.12757
$77$	−4.36327	−	7.61327i	−0.497241	−	0.867613i
$78$	3.56788			0.403983
$79$	4.09831	−	2.36616i	0.461096	−	0.266214i	−0.251409	−	0.967881i	$-0.580894\pi$
$79$	4.09831	−	2.36616i	0.461096	−	0.266214i	0.712505	+	0.701667i	$0.247561\pi$
$80$	4.74076	+	2.73708i	0.530034	+	0.306015i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.769213	+	0.444105i	−0.0849454	+	0.0490432i
$83$	−14.2220			−1.56107			−0.780533	−	0.625115i	$-0.785052\pi$
$83$	−14.2220			−1.56107			−0.780533	+	0.625115i	$0.785052\pi$
$84$	3.72034	−	1.85250i	0.405923	−	0.202125i
$85$			5.78740i			0.627731i
$86$	1.02468	+	1.77480i	0.110494	+	0.191382i
$87$	−1.80752	+	3.13072i	−0.193787	+	0.335649i
$88$	−6.48110	+	4.26492i	−0.690887	+	0.454642i
$89$	3.31004	−	1.91105i	0.350864	−	0.202571i	−0.314202	−	0.949356i	$-0.601737\pi$
$89$	3.31004	−	1.91105i	0.350864	−	0.202571i	0.665066	+	0.746785i	$0.268404\pi$
$90$	−2.22852			−0.234906
$91$	−14.3822	−	0.887088i	−1.50766	−	0.0929921i
$92$	−9.70885			−1.01222
$93$	3.25063	+	5.63025i	0.337074	+	0.583830i
$94$	−0.262271	+	0.454267i	−0.0270512	+	0.0468541i
$95$	18.4355	+	10.6437i	1.89144	+	1.09202i
$96$	−2.86637	−	4.96470i	−0.292548	−	0.506708i
$97$		−	3.87321i		−	0.393265i	−0.980477	−	0.196633i	$-0.936999\pi$
$97$		−	3.87321i		−	0.393265i	0.980477	−	0.196633i	$-0.0630006\pi$
$98$	4.22303	−	1.78744i	0.426591	−	0.180558i
$99$	−1.48779	+	2.96420i	−0.149528	+	0.297914i
$100$	5.16183	+	8.94055i	0.516183	+	0.894055i
$101$	6.55494	−	11.3535i	0.652241	−	1.12971i	−0.330337	−	0.943863i	$-0.607163\pi$
$101$	6.55494	−	11.3535i	0.652241	−	1.12971i	0.982578	−	0.185851i	$-0.0595041\pi$
$102$	0.557260	−	0.965203i	0.0551770	−	0.0955694i
$103$	−15.1805	+	8.76449i	−1.49578	+	0.863591i	−0.999988	−	0.00484868i	$-0.998457\pi$
$103$	−15.1805	+	8.76449i	−1.49578	+	0.863591i	−0.495795	+	0.868440i	$0.665123\pi$
$104$			12.7403i			1.24929i
$105$	8.98318	+	0.554080i	0.876668	+	0.0540727i
$106$			4.19364i			0.407322i
$107$	−1.93196	+	1.11542i	−0.186769	+	0.107831i	−0.590469	−	0.807060i	$-0.701057\pi$
$107$	−1.93196	+	1.11542i	−0.186769	+	0.107831i	0.403700	+	0.914891i	$0.367724\pi$
$108$	−1.36039	−	0.785419i	−0.130903	−	0.0755770i
$109$	8.41307	+	4.85729i	0.805826	+	0.465244i	0.845504	−	0.533969i	$-0.179300\pi$
$109$	8.41307	+	4.85729i	0.805826	+	0.465244i	−0.0396783	+	0.999213i	$0.512633\pi$
$110$	−7.37855	+	0.431533i	−0.703517	+	0.0411451i
$111$		−	0.165795i		−	0.0157365i
$112$	1.89775	+	3.81122i	0.179321	+	0.360126i
$113$	16.8216			1.58245			0.791224	−	0.611527i	$-0.209444\pi$
$113$	16.8216			1.58245			0.791224	+	0.611527i	$0.209444\pi$
$114$	−2.04974	−	3.55025i	−0.191976	−	0.332512i
$115$	−18.2084	−	10.5126i	−1.69795	−	0.980309i
$116$	−4.91786	−	2.83933i	−0.456611	−	0.263625i
$117$	2.72314	+	4.71661i	0.251754	+	0.436051i
$118$	1.16887			0.107603
$119$	−2.48630	+	3.75219i	−0.227919	+	0.343963i
$120$		−	7.95768i		−	0.726433i
$121$	−4.35202	+	10.1025i	−0.395638	+	0.918407i
$122$	−2.01999	−	1.16624i	−0.182882	−	0.105587i
$123$	−1.17418	−	0.677915i	−0.105873	−	0.0611256i
$124$	−8.84421	+	5.10621i	−0.794234	+	0.458551i
$125$			5.34783i			0.478324i
$126$	−1.44483	−	0.957386i	−0.128716	−	0.0852907i
$127$			17.7541i			1.57542i	0.616047	+	0.787709i	$0.288733\pi$
$127$			17.7541i			1.57542i	−0.616047	+	0.787709i	$0.711267\pi$
$128$	9.62467	−	5.55681i	0.850709	−	0.491157i
$129$	−1.56415	+	2.70919i	−0.137716	+	0.238531i
$130$	−6.06856	+	10.5111i	−0.532248	+	0.921881i
$131$	−4.03361	−	6.98642i	−0.352418	−	0.610407i	0.634254	−	0.773125i	$-0.281307\pi$
$131$	−4.03361	−	6.98642i	−0.352418	−	0.610407i	−0.986673	+	0.162718i	$0.947974\pi$
$132$	−4.65628	−	2.33707i	−0.405277	−	0.203416i
$133$	7.37982	+	14.8207i	0.639911	+	1.28512i
$134$		−	5.82913i		−	0.503560i
$135$	−1.70089	−	2.94602i	−0.146389	−	0.253553i
$136$	3.44659	+	1.98989i	0.295542	+	0.170631i
$137$	9.48525	−	16.4289i	0.810380	−	1.40362i	−0.102219	−	0.994762i	$-0.532594\pi$
$137$	9.48525	−	16.4289i	0.810380	−	1.40362i	0.912599	−	0.408857i	$-0.134072\pi$
$138$	2.02450	+	3.50653i	0.172337	+	0.298496i
$139$	13.8195			1.17216			0.586079	−	0.810254i	$-0.300671\pi$
$139$	13.8195			1.17216			0.586079	+	0.810254i	$0.300671\pi$
$140$	−0.870370	+	14.1111i	−0.0735597	+	1.19261i
$141$	−0.800701			−0.0674311
$142$	2.03765	−	1.17644i	0.170996	−	0.0987245i
$143$	9.92955	+	15.0892i	0.830351	+	1.26183i
$144$	0.804604	−	1.39362i	0.0670503	−	0.116135i
$145$	−6.14878	−	10.6500i	−0.510629	−	0.884435i
$146$		−	7.09109i		−	0.586863i
$147$	5.58610	+	4.21846i	0.460734	+	0.347933i
$148$	0.260437			0.0214078
$149$	−0.382898	+	0.221066i	−0.0313682	+	0.0181105i	−0.515602	−	0.856828i	$-0.672432\pi$
$149$	−0.382898	+	0.221066i	−0.0313682	+	0.0181105i	0.484234	+	0.874939i	$0.339098\pi$
$150$	2.15270	−	3.72858i	0.175767	−	0.304437i
$151$	−6.71688	−	3.87799i	−0.546612	−	0.315586i	0.201143	−	0.979562i	$-0.435535\pi$
$151$	−6.71688	−	3.87799i	−0.546612	−	0.315586i	−0.747754	+	0.663976i	$0.768868\pi$
$152$	12.6774	−	7.31929i	1.02827	−	0.593673i
$153$	1.70129			0.137541
$154$	−4.96919	−	2.89009i	−0.400429	−	0.232890i
$155$	−22.1158			−1.77638
$156$	−7.40904	+	4.27761i	−0.593198	+	0.342483i
$157$	−5.75481	−	3.32254i	−0.459284	−	0.265168i	0.252459	−	0.967608i	$-0.418761\pi$
$157$	−5.75481	−	3.32254i	−0.459284	−	0.265168i	−0.711743	+	0.702440i	$0.752094\pi$
$158$	1.55008	−	2.68482i	0.123318	−	0.213593i
$159$	−5.54384	+	3.20074i	−0.439655	+	0.253835i
$160$	19.5015			1.54173
$161$	−7.28893	−	14.6382i	−0.574448	−	1.15365i
$162$			0.655105i			0.0514699i
$163$	−10.7203	−	18.5682i	−0.839681	−	1.45437i	−0.890161	−	0.455645i	$-0.849408\pi$
$163$	−10.7203	−	18.5682i	−0.839681	−	1.45437i	0.0504802	−	0.998725i	$-0.483925\pi$
$164$	1.06490	−	1.84445i	0.0831543	−	0.144028i
$165$	−6.20205	−	9.42482i	−0.482829	−	0.733722i
$166$	−8.06866	+	4.65844i	−0.626250	+	0.361565i
$167$	8.45150			0.653997			0.326998	−	0.945025i	$-0.393963\pi$
$167$	8.45150			0.653997			0.326998	+	0.945025i	$0.393963\pi$
$168$	3.41867	−	5.15927i	0.263756	−	0.398046i
$169$	16.6619			1.28169
$170$	1.89567	+	3.28340i	0.145392	+	0.251826i
$171$	3.12887	−	5.41937i	0.239271	−	0.414430i
$172$	−4.25570	−	2.45703i	−0.324494	−	0.187347i
$173$	3.70427	+	6.41598i	0.281630	+	0.487798i	0.971786	−	0.235863i	$-0.0757915\pi$
$173$	3.70427	+	6.41598i	0.281630	+	0.487798i	−0.690156	+	0.723660i	$0.742458\pi$
$174$			2.36823i			0.179535i
$175$	−9.60458	+	14.4947i	−0.726038	+	1.09570i
$176$	2.39416	−	4.77002i	0.180466	−	0.359554i
$177$	0.892122	+	1.54520i	0.0670560	+	0.116144i
$178$	1.25194	−	2.16842i	0.0938368	−	0.162530i
$179$	−5.17860	+	8.96959i	−0.387067	+	0.670419i	−0.992054	−	0.125816i	$-0.959845\pi$
$179$	−5.17860	+	8.96959i	−0.387067	+	0.670419i	0.604987	+	0.796235i	$0.293178\pi$
$180$	4.62773	−	2.67182i	0.344930	−	0.199146i
$181$			22.3743i			1.66307i	0.555475	+	0.831533i	$0.312536\pi$
$181$			22.3743i			1.66307i	−0.555475	+	0.831533i	$0.687464\pi$
$182$	−8.45010	+	4.20763i	−0.626363	+	0.311890i
$183$		−	3.56048i		−	0.263198i
$184$	−12.5213	+	7.22915i	−0.923079	+	0.532940i
$185$	0.488435	+	0.281998i	0.0359105	+	0.0207329i
$186$	3.68840	+	2.12950i	0.270447	+	0.156143i
$187$	5.63291	−	0.329440i	0.411919	−	0.0240910i
$188$		−	1.25777i		−	0.0917324i
$189$	0.162880	−	2.64073i	0.0118478	−	0.192085i
$190$	13.9455			1.01171
$191$	−7.27156	−	12.5947i	−0.526152	−	0.911321i	−0.999536	−	0.0304651i	$-0.990301\pi$
$191$	−7.27156	−	12.5947i	−0.526152	−	0.911321i	0.473384	−	0.880856i	$-0.343032\pi$
$192$	−0.465168	−	0.268565i	−0.0335706	−	0.0193820i
$193$	−4.26046	−	2.45978i	−0.306674	−	0.177059i	0.338763	−	0.940872i	$-0.389992\pi$
$193$	−4.26046	−	2.45978i	−0.306674	−	0.177059i	−0.645437	+	0.763813i	$0.723325\pi$
$194$	−1.26868	−	2.19742i	−0.0910859	−	0.157765i
$195$	−18.5270			−1.32675
$196$	−6.62652	+	8.77487i	−0.473323	+	0.626776i
$197$			5.54286i			0.394912i	0.980312	+	0.197456i	$0.0632680\pi$
$197$			5.54286i			0.394912i	−0.980312	+	0.197456i	$0.936732\pi$
$198$	0.126855	+	2.16903i	0.00901521	+	0.154146i
$199$	−5.92436	−	3.42043i	−0.419967	−	0.242468i	0.275096	−	0.961417i	$-0.411290\pi$
$199$	−5.92436	−	3.42043i	−0.419967	−	0.242468i	−0.695063	+	0.718949i	$0.744624\pi$
$200$	13.3142	+	7.68693i	0.941453	+	0.543548i
$201$	7.70591	−	4.44901i	0.543533	−	0.313809i
$202$		−	8.58834i		−	0.604273i
$203$	0.588818	−	9.54637i	0.0413269	−	0.670024i
$204$			2.67245i			0.187109i
$205$	3.99431	−	2.30612i	0.278975	−	0.161066i
$206$	−5.74166	+	9.94484i	−0.400040	+	0.692890i
$207$	−3.09034	+	5.35263i	−0.214794	+	0.372033i
$208$	−4.38210	−	7.59001i	−0.303844	−	0.526273i
$209$	9.31019	−	18.5492i	0.643999	−	1.28308i
$210$	5.27798	−	2.62811i	0.364215	−	0.181357i
$211$			3.25560i			0.224125i	0.993701	+	0.112062i	$0.0357456\pi$
$211$			3.25560i			0.224125i	−0.993701	+	0.112062i	$0.964254\pi$
$212$	−5.02784	−	8.70848i	−0.345314	−	0.598101i
$213$	3.11042	+	1.79580i	0.213123	+	0.123046i
$214$	−0.730714	+	1.26563i	−0.0499506	+	0.0865170i
$215$	−5.32089	−	9.21606i	−0.362882	−	0.628530i
$216$	−2.33927			−0.159167
$217$	−14.3385	−	9.50109i	−0.973363	−	0.644976i
$218$	6.36406			0.431029
$219$	9.37418	−	5.41218i	0.633448	−	0.365721i
$220$	14.8049	−	9.74242i	0.998144	−	0.656834i
$221$	4.63284	−	8.02431i	0.311639	−	0.539774i
$222$	−0.0543064	−	0.0940615i	−0.00364481	−	0.00631300i
$223$		−	3.60614i		−	0.241485i	−0.992684	−	0.120743i	$-0.961472\pi$
$223$		−	3.60614i		−	0.241485i	0.992684	−	0.120743i	$-0.0385275\pi$
$224$	12.6436	+	8.37797i	0.844785	+	0.559777i
$225$	6.57207			0.438138
$226$	9.54355	−	5.50997i	0.634827	−	0.366518i
$227$	−14.3516	+	24.8578i	−0.952552	+	1.64987i	−0.212677	+	0.977123i	$0.568218\pi$
$227$	−14.3516	+	24.8578i	−0.952552	+	1.64987i	−0.739874	+	0.672745i	$0.765115\pi$
$228$	8.51295	+	4.91496i	0.563784	+	0.325501i
$229$	21.0735	−	12.1668i	1.39257	−	0.804003i	0.398975	−	0.916962i	$-0.369366\pi$
$229$	21.0735	−	12.1668i	1.39257	−	0.804003i	0.993600	+	0.112958i	$0.0360327\pi$
$230$	−13.7738			−0.908215
$231$	0.0279345	−	8.77492i	0.00183795	−	0.577347i
$232$	−8.45658			−0.555201
$233$	17.5549	−	10.1353i	1.15006	−	0.663988i	0.201159	−	0.979559i	$-0.435529\pi$
$233$	17.5549	−	10.1353i	1.15006	−	0.663988i	0.948902	+	0.315570i	$0.102196\pi$
$234$	3.08987	+	1.78394i	0.201991	+	0.116620i
$235$	1.36190	−	2.35888i	0.0888406	−	0.153877i
$236$	−2.42726	+	1.40138i	−0.158001	+	0.0912220i
$237$	4.73232			0.307398
$238$	−0.181533	+	2.94315i	−0.0117670	+	0.190776i
$239$		−	26.4329i		−	1.70980i	−0.518791	−	0.854901i	$-0.673618\pi$
$239$		−	26.4329i		−	1.70980i	0.518791	−	0.854901i	$-0.326382\pi$
$240$	2.73708	+	4.74076i	0.176678	+	0.306015i
$241$	5.43039	−	9.40571i	0.349802	−	0.605875i	−0.636412	−	0.771349i	$-0.719582\pi$
$241$	5.43039	−	9.40571i	0.349802	−	0.605875i	0.986214	+	0.165474i	$0.0529155\pi$
$242$	0.840028	+	7.15702i	0.0539990	+	0.460071i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.59294			0.358051
$245$	−21.9290	+	9.28166i	−1.40099	+	0.592984i
$246$	−0.888211			−0.0566303
$247$	−17.0407	−	29.5154i	−1.08427	−	1.87802i
$248$	−7.60410	+	13.1707i	−0.482861	+	0.836340i
$249$	−12.3166	−	7.11099i	−0.780533	−	0.450641i
$250$	1.75169	+	3.03402i	0.110787	+	0.191888i
$251$			6.24229i			0.394010i	0.980403	+	0.197005i	$0.0631215\pi$
$251$			6.24229i			0.394010i	−0.980403	+	0.197005i	$0.936879\pi$
$252$	4.14816	+	0.255858i	0.261310	+	0.0161175i
$253$	−9.19553	+	18.3208i	−0.578118	+	1.15182i
$254$	5.81539	+	10.0725i	0.364890	+	0.632008i
$255$	−2.89370	+	5.01203i	−0.181210	+	0.313866i
$256$	4.17742	−	7.23550i	0.261089	−	0.452219i
$257$	3.44534	−	1.98917i	0.214915	−	0.124081i	−0.388679	−	0.921373i	$-0.627068\pi$
$257$	3.44534	−	1.98917i	0.214915	−	0.124081i	0.603593	+	0.797292i	$0.293735\pi$
$258$			2.04937i			0.127588i
$259$	0.195523	+	0.392665i	0.0121492	+	0.0243990i
$260$		−	29.1029i		−	1.80489i
$261$	−3.13072	+	1.80752i	−0.193787	+	0.111883i
$262$	−4.57684	−	2.64244i	−0.282758	−	0.163250i
$263$	−12.3806	−	7.14796i	−0.763423	−	0.440762i	0.0671006	−	0.997746i	$-0.478625\pi$
$263$	−12.3806	−	7.14796i	−0.763423	−	0.440762i	−0.830523	+	0.556984i	$0.811958\pi$
$264$	−7.74525	+	0.452980i	−0.476687	+	0.0278790i
$265$		−	21.7764i		−	1.33771i
$266$	9.04141	+	5.99108i	0.554364	+	0.367337i
$267$	3.82211			0.233909
$268$	6.98867	+	12.1047i	0.426901	+	0.739415i
$269$	10.5989	+	6.11930i	0.646229	+	0.373101i	0.787010	−	0.616940i	$-0.211628\pi$
$269$	10.5989	+	6.11930i	0.646229	+	0.373101i	−0.140781	+	0.990041i	$0.544961\pi$
$270$	−1.92995	−	1.11426i	−0.117453	−	0.0678116i
$271$	9.90486	+	17.1557i	0.601678	+	1.04214i	0.992567	+	0.121699i	$0.0388341\pi$
$271$	9.90486	+	17.1557i	0.601678	+	1.04214i	−0.390890	+	0.920438i	$0.627833\pi$
$272$	−2.73773			−0.165999
$273$	−12.0118	−	7.95932i	−0.726986	−	0.481720i
$274$		−	12.4277i		−	0.750783i
$275$	21.7599	−	1.27262i	1.31217	−	0.0767421i
$276$	−8.40811	−	4.85443i	−0.506109	−	0.292202i
$277$	−19.1566	−	11.0601i	−1.15101	−	0.664537i	−0.201878	−	0.979411i	$-0.564704\pi$
$277$	−19.1566	−	11.0601i	−1.15101	−	0.664537i	−0.949133	+	0.314874i	$0.898038\pi$
$278$	7.84034	−	4.52662i	0.470232	−	0.271489i
$279$			6.50125i			0.389220i
$280$	9.38455	+	18.8468i	0.560834	+	1.12631i
$281$		−	0.586866i		−	0.0350095i	−0.999847	−	0.0175047i	$-0.994428\pi$
$281$		−	0.586866i		−	0.0350095i	0.999847	−	0.0175047i	$-0.00557221\pi$
$282$	−0.454267	+	0.262271i	−0.0270512	+	0.0156180i
$283$	−3.09502	+	5.36073i	−0.183980	+	0.318662i	−0.943232	−	0.332134i	$-0.892231\pi$
$283$	−3.09502	+	5.36073i	−0.183980	+	0.318662i	0.759252	+	0.650796i	$0.225565\pi$
$284$	−2.82092	+	4.88597i	−0.167391	+	0.289929i
$285$	10.6437	+	18.4355i	0.630480	+	1.09202i
$286$	10.5759	+	5.30824i	0.625367	+	0.313883i
$287$	3.58039	+	0.220837i	0.211344	+	0.0130356i
$288$		−	5.73274i		−	0.337805i
$289$	7.05281	+	12.2158i	0.414871	+	0.718578i
$290$	−6.97687	−	4.02810i	−0.409696	−	0.236538i
$291$	1.93661	−	3.35430i	0.113526	−	0.196633i
$292$	8.50166	+	14.7253i	0.497522	+	0.861734i
$293$	−29.7672			−1.73902			−0.869509	−	0.493918i	$-0.835564\pi$
$293$	−29.7672			−1.73902			−0.869509	+	0.493918i	$0.835564\pi$
$294$	4.55097	+	0.563550i	0.265418	+	0.0328669i
$295$	−6.06960			−0.353386
$296$	0.335878	−	0.193920i	0.0195225	−	0.0112713i
$297$	−2.77056	+	1.82318i	−0.160764	+	0.105792i
$298$	−0.144821	+	0.250838i	−0.00838928	+	0.0145307i
$299$	16.8309	+	29.1519i	0.973353	+	1.68590i
$300$			10.3237i			0.596037i
$301$	0.509537	−	8.26102i	0.0293692	−	0.476157i
$302$	−5.08098			−0.292377
$303$	11.3535	−	6.55494i	0.652241	−	0.376571i
$304$	−5.03501	+	8.72090i	−0.288778	+	0.500178i
$305$	10.4893	+	6.05598i	0.600613	+	0.346764i
$306$	0.965203	−	0.557260i	0.0551770	−	0.0318565i
$307$	−20.6024			−1.17584			−0.587920	−	0.808919i	$-0.700053\pi$
$307$	−20.6024			−1.17584			−0.587920	+	0.808919i	$0.700053\pi$
$308$	13.7840	+	0.0438806i	0.785415	+	0.00250033i
$309$	−17.5290			−0.997189
$310$	−12.5471	+	7.24408i	−0.712628	+	0.411436i
$311$	−1.66087	−	0.958903i	−0.0941792	−	0.0543744i	0.452171	−	0.891931i	$-0.350650\pi$
$311$	−1.66087	−	0.958903i	−0.0941792	−	0.0543744i	−0.546350	+	0.837557i	$0.683983\pi$
$312$	−6.37016	+	11.0334i	−0.360639	+	0.624646i
$313$	16.2148	−	9.36162i	0.916514	−	0.529150i	0.0339929	−	0.999422i	$-0.489178\pi$
$313$	16.2148	−	9.36162i	0.916514	−	0.529150i	0.882521	+	0.470272i	$0.155844\pi$
$314$	−4.35322			−0.245667
$315$	7.50262	+	4.97144i	0.422725	+	0.280109i
$316$			7.43372i			0.418179i
$317$	−7.42370	−	12.8582i	−0.416956	−	0.722190i	0.578675	−	0.815558i	$-0.303570\pi$
$317$	−7.42370	−	12.8582i	−0.416956	−	0.722190i	−0.995632	+	0.0933684i	$0.970237\pi$
$318$	−2.09682	+	3.63180i	−0.117584	+	0.203661i
$319$	−10.0157	+	6.59089i	−0.560772	+	0.369019i
$320$	1.58240	−	0.913597i	0.0884587	−	0.0510717i
$321$	−2.23083			−0.124513
$322$	−8.93006	−	5.91730i	−0.497653	−	0.329758i
$323$	−10.6462			−0.592372
$324$	−0.785419	−	1.36039i	−0.0436344	−	0.0755770i
$325$	17.8967	−	30.9979i	0.992728	−	1.71945i
$326$	−12.1641	−	7.02294i	−0.673706	−	0.388965i
$327$	4.85729	+	8.41307i	0.268609	+	0.465244i
$328$		−	3.17166i		−	0.175125i
$329$	1.89636	−	0.944273i	0.104550	−	0.0520594i
$330$	−6.60578	−	3.31556i	−0.363636	−	0.182515i
$331$	15.7074	+	27.2060i	0.863357	+	1.49538i	0.868670	+	0.495392i	$0.164976\pi$
$331$	15.7074	+	27.2060i	0.863357	+	1.49538i	−0.00531285	+	0.999986i	$0.501691\pi$
$332$	11.1702	−	19.3474i	0.613045	−	1.06183i
$333$	0.0828974	−	0.143582i	0.00454275	−	0.00786827i
$334$	4.79485	−	2.76831i	0.262362	−	0.151475i
$335$			30.2691i			1.65378i
$336$	−0.262107	+	4.24949i	−0.0142991	+	0.231829i
$337$		−	15.8899i		−	0.865575i	−0.901496	−	0.432788i	$-0.857530\pi$
$337$		−	15.8899i		−	0.865575i	0.901496	−	0.432788i	$-0.142470\pi$
$338$	9.45293	−	5.45765i	0.514172	−	0.296857i
$339$	14.5680	+	8.41082i	0.791224	+	0.456813i
$340$	−7.87309	−	4.54553i	−0.426978	−	0.246516i
$341$	1.25891	+	21.5254i	0.0681739	+	1.16567i
$342$		−	4.09948i		−	0.221674i
$343$	−18.2049	−	3.40319i	−0.982972	−	0.183755i
$344$	−7.31795			−0.394558
$345$	−10.5126	−	18.2084i	−0.565982	−	0.980309i
$346$	4.20314	+	2.42668i	0.225962	+	0.130459i
$347$	−19.5389	−	11.2808i	−1.04890	−	0.605585i	−0.126561	−	0.991959i	$-0.540394\pi$
$347$	−19.5389	−	11.2808i	−1.04890	−	0.605585i	−0.922342	+	0.386374i	$0.873727\pi$
$348$	−2.83933	−	4.91786i	−0.152204	−	0.263625i
$349$	10.4473			0.559230			0.279615	−	0.960112i	$-0.409793\pi$
$349$	10.4473			0.559230			0.279615	+	0.960112i	$0.409793\pi$
$350$	−0.701261	+	11.3694i	−0.0374840	+	0.607720i
$351$			5.44628i			0.290701i
$352$	−1.11010	−	18.9809i	−0.0591683	−	1.01169i
$353$	−4.74745	−	2.74094i	−0.252681	−	0.145885i	0.368310	−	0.929703i	$-0.379936\pi$
$353$	−4.74745	−	2.74094i	−0.252681	−	0.145885i	−0.620991	+	0.783817i	$0.713270\pi$
$354$	1.01227	+	0.584433i	0.0538015	+	0.0310623i
$355$	−10.5810	+	6.10892i	−0.561579	+	0.324228i
$356$			6.00391i			0.318207i
$357$	−4.02930	+	2.00634i	−0.213253	+	0.106187i
$358$			6.78504i			0.358601i
$359$	1.27308	−	0.735012i	0.0671905	−	0.0387924i	−0.466028	−	0.884770i	$-0.654316\pi$
$359$	1.27308	−	0.735012i	0.0671905	−	0.0387924i	0.533219	+	0.845977i	$0.320982\pi$
$360$	3.97884	−	6.89155i	0.209703	−	0.363217i
$361$	−10.0797	+	17.4586i	−0.530511	+	0.918873i
$362$	7.32874	+	12.6938i	0.385190	+	0.667169i
$363$	−8.82019	+	6.57299i	−0.462940	+	0.344993i
$364$	12.5028	−	18.8685i	0.655325	−	0.988981i
$365$			36.8220i			1.92735i
$366$	−1.16624	−	2.01999i	−0.0609605	−	0.105587i
$367$	9.56645	+	5.52319i	0.499364	+	0.288308i	0.728451	−	0.685098i	$-0.240241\pi$
$367$	9.56645	+	5.52319i	0.499364	+	0.288308i	−0.229087	+	0.973406i	$0.573574\pi$
$368$	4.97300	−	8.61349i	0.259236	−	0.449009i
$369$	−0.677915	−	1.17418i	−0.0352909	−	0.0611256i
$370$	0.369477			0.0192082
$371$	9.35528	−	14.1185i	0.485702	−	0.732995i
$372$	−10.2124			−0.529489
$373$	23.4635	−	13.5467i	1.21490	−	0.701421i	0.251074	−	0.967968i	$-0.419216\pi$
$373$	23.4635	−	13.5467i	1.21490	−	0.701421i	0.963822	+	0.266547i	$0.0858829\pi$
$374$	3.08785	−	2.03197i	0.159669	−	0.105071i
$375$	−2.67391	+	4.63135i	−0.138080	+	0.239162i
$376$	−0.936528	−	1.62211i	−0.0482978	−	0.0836542i
$377$			19.6885i			1.01401i
$378$	−0.772570	−	1.55154i	−0.0397367	−	0.0798025i
$379$	21.2542			1.09176			0.545878	−	0.837865i	$-0.316196\pi$
$379$	21.2542			1.09176			0.545878	+	0.837865i	$0.316196\pi$
$380$	−28.9591	+	16.7196i	−1.48557	+	0.857696i
$381$	−8.87704	+	15.3755i	−0.454784	+	0.787709i
$382$	−8.25085	−	4.76363i	−0.422150	−	0.243729i
$383$	−27.9692	+	16.1480i	−1.42916	+	0.825125i	−0.997054	−	0.0766981i	$-0.975562\pi$
$383$	−27.9692	+	16.1480i	−1.42916	+	0.825125i	−0.432105	+	0.901823i	$0.642229\pi$
$384$	11.1136			0.567139
$385$	25.8036	+	15.0074i	1.31507	+	0.764850i
$386$	−3.22282			−0.164037
$387$	−2.70919	+	1.56415i	−0.137716	+	0.0795103i
$388$	5.26906	+	3.04209i	0.267496	+	0.154439i
$389$	−16.1948	+	28.0503i	−0.821111	+	1.42221i	0.0837437	+	0.996487i	$0.473312\pi$
$389$	−16.1948	+	28.0503i	−0.821111	+	1.42221i	−0.904855	+	0.425719i	$0.860021\pi$
$390$	−10.5111	+	6.06856i	−0.532248	+	0.307294i
$391$	10.5151			0.531772
$392$	−2.01234	+	16.2508i	−0.101639	+	0.820789i
$393$		−	8.06723i		−	0.406938i
$394$	1.81557	+	3.14467i	0.0914673	+	0.158426i
$395$	−8.04915	+	13.9415i	−0.404997	+	0.701475i
$396$	−2.86392	−	4.35210i	−0.143918	−	0.218701i
$397$	−6.40381	+	3.69724i	−0.321398	+	0.185559i	−0.652016	−	0.758206i	$-0.726076\pi$
$397$	−6.40381	+	3.69724i	−0.321398	+	0.185559i	0.330617	+	0.943765i	$0.392743\pi$
$398$	−4.48148			−0.224636
$399$	−1.01926	+	16.5250i	−0.0510269	+	0.827287i
$400$	−10.5758			−0.528791
$401$	−4.13158	−	7.15611i	−0.206321	−	0.357359i	0.744232	−	0.667922i	$-0.232816\pi$
$401$	−4.13158	−	7.15611i	−0.206321	−	0.357359i	−0.950553	+	0.310563i	$0.899483\pi$
$402$	2.91457	−	5.04818i	0.145365	−	0.251780i
$403$	30.6639	+	17.7038i	1.52748	+	0.881890i
$404$	10.2967	+	17.8345i	0.512282	+	0.887299i
$405$		−	3.40177i		−	0.169036i
$406$	−2.79288	−	5.60888i	−0.138608	−	0.278364i
$407$	0.246667	−	0.491449i	0.0122268	−	0.0243602i
$408$	1.98989	+	3.44659i	0.0985141	+	0.170631i
$409$	−5.86344	+	10.1558i	−0.289928	+	0.502170i	−0.973792	−	0.227439i	$-0.926965\pi$
$409$	−5.86344	+	10.1558i	−0.289928	+	0.502170i	0.683864	+	0.729609i	$0.260298\pi$
$410$	1.51075	−	2.61669i	0.0746104	−	0.129229i
$411$	16.4289	−	9.48525i	0.810380	−	0.467873i
$412$		−	27.5352i		−	1.35656i
$413$	−3.93515	−	2.60754i	−0.193636	−	0.128309i
$414$			4.04899i			0.198997i
$415$	41.8983	−	24.1900i	2.05671	−	1.18744i
$416$	−27.0391	−	15.6111i	−1.32570	−	0.765395i
$417$	11.9681	+	6.90977i	0.586079	+	0.338373i
$418$	−0.793829	−	13.5732i	−0.0388274	−	0.663889i
$419$		−	12.8814i		−	0.629297i	−0.949208	−	0.314649i	$-0.898113\pi$
$419$		−	12.8814i		−	0.629297i	0.949208	−	0.314649i	$-0.101887\pi$
$420$	−7.80932	+	11.7854i	−0.381056	+	0.575069i
$421$	19.1569			0.933652			0.466826	−	0.884349i	$-0.345397\pi$
$421$	19.1569			0.933652			0.466826	+	0.884349i	$0.345397\pi$
$422$	1.06638	+	1.84702i	0.0519105	+	0.0899117i
$423$	−0.693427	−	0.400350i	−0.0337156	−	0.0194657i
$424$	−12.9686	−	7.48740i	−0.629809	−	0.363620i
$425$	−5.59049	−	9.68301i	−0.271179	−	0.469695i
$426$	2.35288			0.113997
$427$	4.19891	+	8.43258i	0.203199	+	0.408081i
$428$		−	3.50428i		−	0.169386i
$429$	1.05462	+	18.0324i	0.0509177	+	0.870614i
$430$	−6.03748	−	3.48574i	−0.291153	−	0.168097i
$431$	−9.29039	−	5.36381i	−0.447502	−	0.258366i	0.259272	−	0.965804i	$-0.416517\pi$
$431$	−9.29039	−	5.36381i	−0.447502	−	0.258366i	−0.706775	+	0.707439i	$0.749851\pi$
$432$	1.39362	−	0.804604i	0.0670503	−	0.0387115i
$433$		−	12.4585i		−	0.598716i	−0.954141	−	0.299358i	$-0.903228\pi$
$433$		−	12.4585i		−	0.598716i	0.954141	−	0.299358i	$-0.0967725\pi$
$434$	−11.2469	−	0.693705i	−0.539868	−	0.0332989i
$435$		−	12.2976i		−	0.589623i
$436$	−13.2156	+	7.63001i	−0.632911	+	0.365411i
$437$	19.3386	−	33.4954i	0.925090	−	1.60230i
$438$	3.54555	−	6.14106i	0.169413	−	0.293431i
$439$	−12.8343	−	22.2296i	−0.612547	−	1.06096i	−0.990810	−	0.135265i	$-0.956812\pi$
$439$	−12.8343	−	22.2296i	−0.612547	−	1.06096i	0.378262	−	0.925698i	$-0.376522\pi$
$440$	11.8393	−	23.5882i	0.564417	−	1.12452i
$441$	2.72848	+	6.44635i	0.129927	+	0.306969i
$442$		−	6.06999i		−	0.288720i
$443$	−11.1012	−	19.2279i	−0.527434	−	0.913543i	−0.999489	−	0.0319736i	$-0.989821\pi$
$443$	−11.1012	−	19.2279i	−0.527434	−	0.913543i	0.472054	−	0.881569i	$-0.343513\pi$
$444$	0.225545	+	0.130218i	0.0107039	+	0.00617989i
$445$	−6.50097	+	11.2600i	−0.308176	+	0.533776i
$446$	−1.18120	−	2.04590i	−0.0559314	−	0.0968761i
$447$	−0.442132			−0.0209121
$448$	1.41842	+	0.0874876i	0.0670139	+	0.00413340i
$449$	16.0399			0.756970			0.378485	−	0.925607i	$-0.376445\pi$
$449$	16.0399			0.756970			0.378485	+	0.925607i	$0.376445\pi$
$450$	3.72858	−	2.15270i	0.175767	−	0.101479i
$451$	−2.47193	−	3.75641i	−0.116398	−	0.176883i
$452$	−13.2120	+	22.8839i	−0.621442	+	1.07637i
$453$	−3.87799	−	6.71688i	−0.182204	−	0.315586i
$454$			18.8036i			0.882499i
$455$	43.8790	−	21.8491i	2.05708	−	1.02430i
$456$	14.6386			0.685514
$457$	−8.25042	+	4.76338i	−0.385939	+	0.222822i	−0.680399	−	0.732842i	$-0.738193\pi$
$457$	−8.25042	+	4.76338i	−0.385939	+	0.222822i	0.294460	+	0.955664i	$0.404860\pi$
$458$	7.97051	−	13.8053i	0.372438	−	0.645081i
$459$	1.47336	+	0.850644i	0.0687705	+	0.0397046i
$460$	28.6025	−	16.5137i	1.33360	−	0.769954i
$461$	4.16942			0.194189			0.0970947	−	0.995275i	$-0.469045\pi$
$461$	4.16942			0.194189			0.0970947	+	0.995275i	$0.469045\pi$
$462$	−2.85840	−	4.98749i	−0.132985	−	0.232039i
$463$	−5.00283			−0.232501			−0.116251	−	0.993220i	$-0.537088\pi$
$463$	−5.00283			−0.232501			−0.116251	+	0.993220i	$0.537088\pi$
$464$	5.03798	−	2.90868i	0.233882	−	0.135032i
$465$	−19.1528	−	11.0579i	−0.888192	−	0.512798i
$466$	6.63971	−	11.5003i	0.307579	−	0.532742i
$467$	12.6313	−	7.29269i	0.584508	−	0.337466i	−0.178415	−	0.983955i	$-0.557097\pi$
$467$	12.6313	−	7.29269i	0.584508	−	0.337466i	0.762923	+	0.646490i	$0.223764\pi$
$468$	−8.55522			−0.395465
$469$	−13.0038	+	19.6246i	−0.600459	+	0.906180i
$470$		−	1.78438i		−	0.0823071i
$471$	−3.32254	−	5.75481i	−0.153095	−	0.265168i
$472$	−2.08692	+	3.61465i	−0.0960581	+	0.166378i
$473$	−8.66716	+	5.70347i	−0.398516	+	0.262246i
$474$	2.68482	−	1.55008i	0.123318	−	0.0711977i
$475$	−41.1264			−1.88701
$476$	−3.15164	−	6.32937i	−0.144455	−	0.290106i
$477$	−6.40148			−0.293104
$478$	−8.65816	−	14.9964i	−0.396015	−	0.685918i
$479$	9.31647	−	16.1366i	0.425681	−	0.737300i	−0.570803	−	0.821087i	$-0.693368\pi$
$479$	9.31647	−	16.1366i	0.425681	−	0.737300i	0.996484	+	0.0837865i	$0.0267014\pi$
$480$	16.8888	+	9.75075i	0.770865	+	0.445059i
$481$	−0.451482	−	0.781990i	−0.0205858	−	0.0356557i
$482$		−	7.11494i		−	0.324077i
$483$	1.00671	−	16.3215i	0.0458068	−	0.742656i
$484$	−10.3251	−	13.8551i	−0.469323	−	0.629777i
$485$	6.58790	+	11.4106i	0.299141	+	0.518127i
$486$	−0.327552	+	0.567337i	−0.0148581	+	0.0257349i
$487$	17.6178	−	30.5149i	0.798338	−	1.38276i	−0.122361	−	0.992486i	$-0.539046\pi$
$487$	17.6178	−	30.5149i	0.798338	−	1.38276i	0.920698	−	0.390276i	$-0.127620\pi$
$488$	7.21307	−	4.16447i	0.326520	−	0.188517i
$489$		−	21.4407i		−	0.969580i
$490$	−9.40092	+	12.4487i	−0.424690	+	0.562377i
$491$			11.5566i			0.521543i	0.965401	+	0.260771i	$0.0839769\pi$
$491$			11.5566i			0.521543i	−0.965401	+	0.260771i	$0.916023\pi$
$492$	1.84445	−	1.06490i	0.0831543	−	0.0480092i
$493$	5.32626	+	3.07512i	0.239883	+	0.138496i
$494$	−19.3357	−	11.1635i	−0.869953	−	0.502267i
$495$	−0.658724	−	11.2632i	−0.0296074	−	0.506242i
$496$		−	10.4619i		−	0.469752i
$497$	−9.48447	−	0.585000i	−0.425437	−	0.0262408i
$498$	−9.31689			−0.417500
$499$	11.4300	+	19.7973i	0.511677	+	0.886251i	0.999908	+	0.0135365i	$0.00430892\pi$
$499$	11.4300	+	19.7973i	0.511677	+	0.886251i	−0.488231	+	0.872714i	$0.662358\pi$
$500$	−7.27511	−	4.20028i	−0.325353	−	0.187842i
$501$	7.31921	+	4.22575i	0.326998	+	0.188793i
$502$	2.04467	+	3.54148i	0.0912583	+	0.158064i
$503$	29.7190			1.32510			0.662551	−	0.749016i	$-0.269474\pi$
$503$	29.7190			1.32510			0.662551	+	0.749016i	$0.269474\pi$
$504$	5.54029	−	2.75872i	0.246784	−	0.122883i
$505$			44.5968i			1.98453i
$506$	0.784053	+	13.4061i	0.0348554	+	0.595973i
$507$	14.4296	+	8.33096i	0.640843	+	0.369991i
$508$	−24.1524	−	13.9444i	−1.07159	−	0.618682i
$509$	27.3833	−	15.8097i	1.21374	−	0.700754i	0.250170	−	0.968202i	$-0.419514\pi$
$509$	27.3833	−	15.8097i	1.21374	−	0.700754i	0.963572	+	0.267448i	$0.0861802\pi$
$510$			3.79135i			0.167884i
$511$	−15.8190	+	23.8732i	−0.699791	+	1.05609i
$512$			16.7539i			0.740426i
$513$	5.41937	−	3.12887i	0.239271	−	0.138143i
$514$	1.30311	−	2.25706i	0.0574779	−	0.0995547i
$515$	29.8148	−	51.6408i	1.31380	−	2.27556i
$516$	−2.45703	−	4.25570i	−0.108165	−	0.187347i
$517$	−2.37344	−	1.19127i	−0.104384	−	0.0523920i
$518$	0.239546	+	0.158730i	0.0105250	+	0.00697418i
$519$			7.40854i			0.325199i
$520$	−21.6699	−	37.5333i	−0.950286	−	1.64594i
$521$	−7.32135	−	4.22698i	−0.320754	−	0.185188i	0.330975	−	0.943640i	$-0.392623\pi$
$521$	−7.32135	−	4.22698i	−0.320754	−	0.185188i	−0.651729	+	0.758452i	$0.725956\pi$
$522$	−1.18412	+	2.05095i	−0.0518274	+	0.0897676i
$523$	2.62992	+	4.55515i	0.114998	+	0.199183i	0.917779	−	0.397091i	$-0.129980\pi$
$523$	2.62992	+	4.55515i	0.114998	+	0.199183i	−0.802781	+	0.596274i	$0.796647\pi$
$524$	12.6723			0.553592
$525$	−15.5652	+	7.75050i	−0.679320	+	0.338259i
$526$	−9.36533			−0.408348
$527$	9.57867	−	5.53025i	0.417254	−	0.240901i
$528$	4.45841	−	2.93388i	0.194027	−	0.127681i
$529$	−7.60042	+	13.1643i	−0.330453	+	0.572362i
$530$	−7.13290	−	12.3546i	−0.309834	−	0.536647i
$531$			1.78424i			0.0774296i
$532$	−25.9582	−	1.60109i	−1.12543	−	0.0694162i
$533$	−7.38423			−0.319846
$534$	2.16842	−	1.25194i	0.0938368	−	0.0541767i
$535$	3.79439	−	6.57208i	0.164046	−	0.284136i
$536$	18.0262	+	10.4074i	0.778614	+	0.449533i
$537$	−8.96959	+	5.17860i	−0.387067	+	0.223473i
$538$	8.01757			0.345662
$539$	10.2822	+	20.8153i	0.442885	+	0.896579i
$540$	5.34364			0.229954
$541$	1.78326	−	1.02957i	0.0766684	−	0.0442645i	−0.461176	−	0.887309i	$-0.652572\pi$
$541$	1.78326	−	1.02957i	0.0766684	−	0.0442645i	0.537844	+	0.843044i	$0.319239\pi$
$542$	11.2388	+	6.48872i	0.482748	+	0.278714i
$543$	−11.1871	+	19.3767i	−0.480086	+	0.831533i
$544$	−8.44638	+	4.87652i	−0.362136	+	0.209079i
$545$	−33.0468			−1.41557
$546$	−9.42182	−	0.581135i	−0.403217	−	0.0248703i
$547$		−	23.9876i		−	1.02564i	−0.858497	−	0.512818i	$-0.828601\pi$
$547$		−	23.9876i		−	1.02564i	0.858497	−	0.512818i	$-0.171399\pi$
$548$	14.8998	+	25.8072i	0.636488	+	1.10243i
$549$	1.78024	−	3.08347i	0.0759788	−	0.131599i
$550$	11.9284	−	7.84951i	0.508627	−	0.334704i
$551$	19.5913	−	11.3110i	0.834616	−	0.481866i
$552$	−14.4583			−0.615386
$553$	−11.2080	+	5.58087i	−0.476611	+	0.237323i
$554$	−14.4910			−0.615665
$555$	0.281998	+	0.488435i	0.0119702	+	0.0207329i
$556$	−10.8541	+	18.7999i	−0.460318	+	0.797293i
$557$	−22.1182	−	12.7699i	−0.937177	−	0.541080i	−0.0481030	−	0.998842i	$-0.515318\pi$
$557$	−22.1182	−	12.7699i	−0.937177	−	0.541080i	−0.889074	+	0.457763i	$0.848651\pi$
$558$	2.12950	+	3.68840i	0.0901490	+	0.156143i
$559$			17.0376i			0.720614i
$560$	−12.0733	−	8.00008i	−0.510189	−	0.338065i
$561$	5.04296	+	2.53115i	0.212914	+	0.106865i
$562$	−0.192229	−	0.332951i	−0.00810870	−	0.0140447i
$563$	−15.9242	+	27.5815i	−0.671124	+	1.16242i	0.306462	+	0.951883i	$0.400855\pi$
$563$	−15.9242	+	27.5815i	−0.671124	+	1.16242i	−0.977586	+	0.210538i	$0.932479\pi$
$564$	0.628885	−	1.08926i	0.0264809	−	0.0458662i
$565$	−49.5570	+	28.6117i	−2.08488	+	1.20370i
$566$			4.05512i			0.170450i
$567$	1.46142	−	2.20550i	0.0613741	−	0.0926224i
$568$			8.40174i			0.352529i
$569$	6.15126	−	3.55143i	0.257874	−	0.148884i	−0.365490	−	0.930815i	$-0.619099\pi$
$569$	6.15126	−	3.55143i	0.257874	−	0.148884i	0.623364	+	0.781931i	$0.285765\pi$
$570$	12.0772	+	6.97275i	0.505857	+	0.292056i
$571$	37.7741	+	21.8089i	1.58080	+	0.912675i	0.994743	+	0.102404i	$0.0326534\pi$
$571$	37.7741	+	21.8089i	1.58080	+	0.912675i	0.586056	+	0.810271i	$0.300680\pi$
$572$	−28.3260	+	1.65664i	−1.18437	+	0.0692678i
$573$		−	14.5431i		−	0.607547i
$574$	2.10362	−	1.04747i	0.0878035	−	0.0437207i
$575$	40.6199			1.69397
$576$	−0.268565	−	0.465168i	−0.0111902	−	0.0193820i
$577$	4.00447	+	2.31198i	0.166708	+	0.0962489i	0.581033	−	0.813880i	$-0.302649\pi$
$577$	4.00447	+	2.31198i	0.166708	+	0.0962489i	−0.414325	+	0.910129i	$0.635982\pi$
$578$	8.00264	+	4.62033i	0.332866	+	0.192180i
$579$	−2.45978	−	4.26046i	−0.102225	−	0.177059i
$580$	19.3175			0.802115
$581$	37.5565	+	2.31647i	1.55810	+	0.0961035i
$582$		−	2.53736i		−	0.105177i
$583$	−21.1951	+	1.23959i	−0.877811	+	0.0513386i
$584$	21.9287	+	12.6606i	0.907418	+	0.523898i
$585$	−16.0449	−	9.26350i	−0.663373	−	0.382999i
$586$	−16.8880	+	9.75031i	−0.697638	+	0.402781i
$587$		−	0.806781i		−	0.0332994i	−0.999861	−	0.0166497i	$-0.994700\pi$
$587$		−	0.806781i		−	0.0332994i	0.999861	−	0.0166497i	$-0.00530001\pi$
$588$	−10.1262	+	4.28600i	−0.417596	+	0.176751i
$589$		−	40.6832i		−	1.67632i
$590$	−3.44351	+	1.98811i	−0.141767	+	0.0818492i
$591$	−2.77143	+	4.80025i	−0.114001	+	0.197456i
$592$	−0.133399	+	0.231054i	−0.00548267	+	0.00949626i
$593$	12.5441	+	21.7269i	0.515123	+	0.892218i	0.999846	+	0.0175510i	$0.00558693\pi$
$593$	12.5441	+	21.7269i	0.515123	+	0.892218i	−0.484723	+	0.874667i	$0.661080\pi$
$594$	−0.974655	+	1.94186i	−0.0399906	+	0.0796756i
$595$	0.942650	−	15.2830i	0.0386449	−	0.626540i
$596$		−	0.694518i		−	0.0284486i
$597$	−3.42043	−	5.92436i	−0.139989	−	0.242468i
$598$	19.0975	+	11.0260i	0.780956	+	0.450885i
$599$	−4.04701	+	7.00962i	−0.165356	+	0.286405i	−0.936782	−	0.349914i	$-0.886211\pi$
$599$	−4.04701	+	7.00962i	−0.165356	+	0.286405i	0.771426	+	0.636320i	$0.219544\pi$
$600$	7.68693	+	13.3142i	0.313818	+	0.543548i
$601$	−14.0494			−0.573087			−0.286544	−	0.958067i	$-0.592506\pi$
$601$	−14.0494			−0.573087			−0.286544	+	0.958067i	$0.592506\pi$
$602$	−2.41683	−	4.85368i	−0.0985028	−	0.197821i
$603$	8.89802			0.362355
$604$	10.5511	−	6.09169i	0.429319	−	0.247868i
$605$	−4.36203	−	37.1644i	−0.177342	−	1.51095i
$606$	4.29417	−	7.43772i	0.174439	−	0.302137i
$607$	−1.19074	−	2.06242i	−0.0483307	−	0.0837112i	0.840848	−	0.541271i	$-0.182057\pi$
$607$	−1.19074	−	2.06242i	−0.0483307	−	0.0837112i	−0.889179	+	0.457560i	$0.848723\pi$
$608$			35.8741i			1.45489i
$609$	5.28312	−	7.97299i	0.214083	−	0.323082i
$610$	7.93460			0.321262
$611$	−3.77659	+	2.18042i	−0.152785	+	0.0882103i
$612$	−1.33622	+	2.31441i	−0.0540136	+	0.0935543i
$613$	15.1345	+	8.73793i	0.611278	+	0.352922i	0.773465	−	0.633838i	$-0.218522\pi$
$613$	15.1345	+	8.73793i	0.611278	+	0.352922i	−0.162187	+	0.986760i	$0.551855\pi$
$614$	−11.6885	+	6.74835i	−0.471709	+	0.272341i
$615$	4.61223			0.185983
$616$	17.8095	−	10.2069i	0.717566	−	0.411247i
$617$	−30.1286			−1.21293			−0.606465	−	0.795110i	$-0.707413\pi$
$617$	−30.1286			−1.21293			−0.606465	+	0.795110i	$0.707413\pi$
$618$	−9.94484	+	5.74166i	−0.400040	+	0.230963i
$619$	−23.5404	−	13.5911i	−0.946170	−	0.546272i	−0.0542811	−	0.998526i	$-0.517287\pi$
$619$	−23.5404	−	13.5911i	−0.946170	−	0.546272i	−0.891889	+	0.452254i	$0.850620\pi$
$620$	17.3702	−	30.0860i	0.697603	−	1.20828i
$621$	−5.35263	+	3.09034i	−0.214794	+	0.124011i
$622$	−1.25636			−0.0503756
$623$	−9.05221	+	4.50744i	−0.362669	+	0.180587i
$624$		−	8.76419i		−	0.350849i
$625$	7.33412	+	12.7031i	0.293365	+	0.508123i
$626$	6.13284	−	10.6224i	0.245117	−	0.424556i
$627$	17.3375	−	11.4090i	0.692392	−	0.455632i
$628$	9.03987	−	5.21917i	0.360730	−	0.208268i
$629$	−0.282064			−0.0112466
$630$	5.88492	+	0.362980i	0.234461	+	0.0144615i
$631$	−12.4342			−0.494996			−0.247498	−	0.968888i	$-0.579608\pi$
$631$	−12.4342			−0.494996			−0.247498	+	0.968888i	$0.579608\pi$
$632$	5.53510	+	9.58707i	0.220174	+	0.381353i
$633$	−1.62780	+	2.81943i	−0.0646992	+	0.112062i
$634$	−8.42348	−	4.86330i	−0.334539	−	0.193146i
$635$	−30.1977	−	52.3039i	−1.19836	−	2.07562i
$636$		−	10.0557i		−	0.398734i
$637$	37.8350	+	4.68513i	1.49908	+	0.185631i
$638$	−3.52342	+	7.01992i	−0.139494	+	0.277921i
$639$	1.79580	+	3.11042i	0.0710409	+	0.123046i
$640$	−18.9030	+	32.7410i	−0.747207	+	1.29420i
$641$	−1.13596	+	1.96755i	−0.0448679	+	0.0777135i	−0.887587	−	0.460640i	$-0.847620\pi$
$641$	−1.13596	+	1.96755i	−0.0448679	+	0.0777135i	0.842719	+	0.538353i	$0.180953\pi$
$642$	−1.26563	+	0.730714i	−0.0499506	+	0.0288390i
$643$			39.5610i			1.56013i	0.625695	+	0.780067i	$0.284815\pi$
$643$			39.5610i			1.56013i	−0.625695	+	0.780067i	$0.715185\pi$
$644$	25.6385	+	1.58138i	1.01030	+	0.0623149i
$645$		−	10.6418i		−	0.419020i
$646$	−6.04000	+	3.48720i	−0.237641	+	0.137202i
$647$	−19.4689	−	11.2404i	−0.765403	−	0.441905i	0.0658295	−	0.997831i	$-0.479031\pi$
$647$	−19.4689	−	11.2404i	−0.765403	−	0.441905i	−0.831232	+	0.555925i	$0.812364\pi$
$648$	−2.02587	−	1.16964i	−0.0795837	−	0.0459476i
$649$	0.345504	+	5.90758i	0.0135622	+	0.231893i
$650$		−	23.4484i		−	0.919720i
$651$	−7.66698	−	15.3975i	−0.300493	−	0.603474i
$652$	33.6798			1.31900
$653$	4.58426	+	7.94017i	0.179396	+	0.310723i	0.941674	−	0.336527i	$-0.109252\pi$
$653$	4.58426	+	7.94017i	0.179396	+	0.310723i	−0.762278	+	0.647250i	$0.775919\pi$
$654$	5.51144	+	3.18203i	0.215514	+	0.124427i
$655$	23.7662	+	13.7214i	0.928624	+	0.536141i
$656$	1.09091	+	1.88951i	0.0425928	+	0.0737728i
$657$	10.8244			0.422299
$658$	0.766579	−	1.15688i	0.0298844	−	0.0450999i
$659$		−	31.8271i		−	1.23981i	−0.784677	−	0.619905i	$-0.787171\pi$
$659$		−	31.8271i		−	1.23981i	0.784677	−	0.619905i	$-0.212829\pi$
$660$	17.6926	−	1.03475i	0.688684	−	0.0402775i
$661$	19.6900	+	11.3681i	0.765854	+	0.442166i	0.831394	−	0.555684i	$-0.187544\pi$
$661$	19.6900	+	11.3681i	0.765854	+	0.442166i	−0.0655395	+	0.997850i	$0.520877\pi$
$662$	17.8228	+	10.2900i	0.692702	+	0.399932i
$663$	8.02431	−	4.63284i	0.311639	−	0.179925i
$664$		−	33.2691i		−	1.29109i
$665$	−46.9495	−	31.1100i	−1.82062	−	1.20639i
$666$		−	0.108613i		−	0.00420866i
$667$	−19.3500	+	11.1717i	−0.749235	+	0.432571i
$668$	−6.63797	+	11.4973i	−0.256831	+	0.444844i
$669$	1.80307	−	3.12301i	0.0697107	−	0.120743i
$670$	9.91470	+	17.1728i	0.383038	+	0.663442i
$671$	5.29723	−	10.5540i	0.204497	−	0.407432i
$672$	6.76067	+	13.5773i	0.260799	+	0.523757i
$673$			26.2927i			1.01351i	0.862090	+	0.506755i	$0.169155\pi$
$673$			26.2927i			1.01351i	−0.862090	+	0.506755i	$0.830845\pi$
$674$	−5.20476	−	9.01490i	−0.200480	−	0.347241i
$675$	5.69158	+	3.28603i	0.219069	+	0.126480i
$676$	−13.0866	+	22.6666i	−0.503330	+	0.871794i
$677$	9.93790	+	17.2129i	0.381944	+	0.661547i	0.991340	−	0.131319i	$-0.0419213\pi$
$677$	9.93790	+	17.2129i	0.381944	+	0.661547i	−0.609396	+	0.792866i	$0.708588\pi$
$678$	11.0199			0.423218
$679$	−0.630868	+	10.2281i	−0.0242105	+	0.392519i
$680$	−13.5383			−0.519170
$681$	−24.8578	+	14.3516i	−0.952552	+	0.549956i
$682$	7.76493	+	11.7998i	0.297335	+	0.451839i
$683$	−8.04944	+	13.9420i	−0.308003	+	0.533478i	−0.977925	−	0.208954i	$-0.932994\pi$
$683$	−8.04944	+	13.9420i	−0.308003	+	0.533478i	0.669922	+	0.742431i	$0.266327\pi$
$684$	4.91496	+	8.51295i	0.187928	+	0.325501i
$685$			64.5334i			2.46569i
$686$	−11.4430	+	4.03230i	−0.436897	+	0.153954i
$687$	24.3336			0.928383
$688$	4.35965	−	2.51705i	0.166210	−	0.0959615i
$689$	−17.4321	+	30.1933i	−0.664110	+	1.15027i
$690$	−11.9284	−	6.88688i	−0.454108	−	0.262179i
$691$	−16.5519	+	9.55627i	−0.629666	+	0.363538i	−0.780623	−	0.625003i	$-0.785098\pi$
$691$	−16.5519	+	9.55627i	−0.629666	+	0.363538i	0.150957	+	0.988540i	$0.451765\pi$
$692$	−11.6376			−0.442396
$693$	4.41165	−	7.58534i	0.167585	−	0.288143i
$694$	−14.7802			−0.561049
$695$	−40.7127	+	23.5055i	−1.54432	+	0.891614i
$696$	−7.32361	−	4.22829i	−0.277601	−	0.160273i
$697$	−1.15333	+	1.99762i	−0.0436854	+	0.0756654i
$698$	5.92713	−	3.42203i	0.224345	−	0.129526i
$699$	20.2707			0.766708
$700$	−12.1748	−	24.4504i	−0.460163	−	0.924137i
$701$			25.3053i			0.955768i	0.878423	+	0.477884i	$0.158596\pi$
$701$			25.3053i			0.955768i	−0.878423	+	0.477884i	$0.841404\pi$
$702$	1.78394	+	3.08987i	0.0673305	+	0.116620i
$703$	−0.518751	+	0.898503i	−0.0195651	+	0.0338877i
$704$	−0.979286	−	1.48815i	−0.0369082	−	0.0560868i
$705$	2.35888	−	1.36190i	0.0888406	−	0.0512922i
$706$	−3.59120			−0.135157
$707$	−19.1591	+	28.9138i	−0.720552	+	1.08742i
$708$	−2.80276			−0.105334
$709$	−13.1540	−	22.7833i	−0.494007	−	0.855646i	0.505969	−	0.862552i	$-0.331135\pi$
$709$	−13.1540	−	22.7833i	−0.494007	−	0.855646i	−0.999976	+	0.00690606i	$0.997802\pi$
$710$	−4.00198	+	6.93163i	−0.150192	+	0.260139i
$711$	4.09831	+	2.36616i	0.153699	+	0.0887380i
$712$	4.47047	+	7.74309i	0.167538	+	0.290184i
$713$			40.1822i			1.50484i
$714$	−1.62879	+	2.45808i	−0.0609559	+	0.0919913i
$715$	−54.9178	−	27.5642i	−2.05381	−	1.03084i
$716$	−8.13474	−	14.0898i	−0.304009	−	0.526560i
$717$	13.2165	−	22.8916i	0.493577	−	0.854901i
$718$	0.481510	−	0.833999i	0.0179698	−	0.0311246i
$719$	−17.6374	+	10.1830i	−0.657764	+	0.379760i	−0.791424	−	0.611267i	$-0.790660\pi$
$719$	−17.6374	+	10.1830i	−0.657764	+	0.379760i	0.133661	+	0.991027i	$0.457327\pi$
$720$			5.47416i			0.204010i
$721$	41.5153	−	20.6721i	1.54611	−	0.769868i
$722$			13.2065i			0.491496i
$723$	9.40571	−	5.43039i	0.349802	−	0.201958i
$724$	−30.4376	−	17.5732i	−1.13121	−	0.653102i
$725$	20.5753	+	11.8792i	0.764148	+	0.441181i
$726$	−2.85103	+	6.61818i	−0.105811	+	0.245624i
$727$		−	26.5000i		−	0.982832i	−0.870925	−	0.491416i	$-0.836479\pi$
$727$		−	26.5000i		−	0.982832i	0.870925	−	0.491416i	$-0.163521\pi$
$728$	2.07514	−	33.6438i	0.0769098	−	1.24692i
$729$	−1.00000			−0.0370370
$730$	12.0611	+	20.8905i	0.446403	+	0.773193i
$731$	4.60911	+	2.66107i	0.170474	+	0.0984233i
$732$	4.84363	+	2.79647i	0.179026	+	0.103361i
$733$	−23.0702	−	39.9588i	−0.852118	−	1.47591i	−0.879293	−	0.476280i	$-0.841985\pi$
$733$	−23.0702	−	39.9588i	−0.852118	−	1.47591i	0.0271758	−	0.999631i	$-0.491349\pi$
$734$	7.23653			0.267105
$735$	−23.6319	−	2.92636i	−0.871677	−	0.107940i
$736$		−	35.4323i		−	1.30605i
$737$	29.4610	−	1.72302i	1.08521	−	0.0634684i
$738$	−0.769213	−	0.444105i	−0.0283151	−	0.0163477i
$739$	23.2649	+	13.4320i	0.855812	+	0.494103i	0.862608	−	0.505874i	$-0.168830\pi$
$739$	23.2649	+	13.4320i	0.855812	+	0.494103i	−0.00679576	+	0.999977i	$0.502163\pi$
$740$	−0.767253	+	0.442973i	−0.0282048	+	0.0162840i
$741$		−	34.0814i		−	1.25201i
$742$	0.683059	−	11.0743i	0.0250759	−	0.406549i
$743$			6.53576i			0.239774i	0.992788	+	0.119887i	$0.0382532\pi$
$743$			6.53576i			0.239774i	−0.992788	+	0.119887i	$0.961747\pi$
$744$	−13.1707	+	7.60410i	−0.482861	+	0.278780i
$745$	0.752017	−	1.30253i	0.0275518	−	0.0477211i
$746$	8.87449	−	15.3711i	0.324918	−	0.562775i
$747$	−7.11099	−	12.3166i	−0.260178	−	0.450641i
$748$	−3.97603	+	7.92167i	−0.145378	+	0.289645i
$749$	5.28346	−	2.63084i	0.193054	−	0.0961288i
$750$			3.50339i			0.127926i
$751$	17.0749	+	29.5746i	0.623072	+	1.07919i	0.988910	+	0.148513i	$0.0474488\pi$
$751$	17.0749	+	29.5746i	0.623072	+	1.07919i	−0.365839	+	0.930678i	$0.619218\pi$
$752$	1.11587	+	0.644247i	0.0406915	+	0.0234933i
$753$	−3.12114	+	5.40598i	−0.113741	+	0.197005i
$754$	6.44902	+	11.1700i	0.234860	+	0.406789i
$755$	26.3841			0.960216
$756$	3.46449	+	2.29566i	0.126002	+	0.0834924i
$757$	−7.47251			−0.271593			−0.135796	−	0.990737i	$-0.543359\pi$
$757$	−7.47251			−0.271593			−0.135796	+	0.990737i	$0.543359\pi$
$758$	12.0583	−	6.96186i	0.437977	−	0.252866i
$759$	−17.1240	+	11.2685i	−0.621560	+	0.409021i
$760$	−24.8986	+	43.1256i	−0.903166	+	1.56433i
$761$	−3.21009	−	5.56004i	−0.116366	−	0.201551i	0.801959	−	0.597379i	$-0.203791\pi$
$761$	−3.21009	−	5.56004i	−0.116366	−	0.201551i	−0.918325	+	0.395828i	$0.870458\pi$
$762$			11.6308i			0.421338i
$763$	−21.4255	−	14.1971i	−0.775656	−	0.513970i
$764$	22.8449			0.826499
$765$	−5.01203	+	2.89370i	−0.181210	+	0.104622i
$766$	−10.5786	+	18.3227i	−0.382222	+	0.662028i
$767$	8.41559	+	4.85874i	0.303869	+	0.175439i
$768$	7.23550	−	4.17742i	0.261089	−	0.150740i
$769$	10.3850			0.374492			0.187246	−	0.982313i	$-0.440044\pi$
$769$	10.3850			0.374492			0.187246	+	0.982313i	$0.440044\pi$
$770$	19.5551	+	0.0622525i	0.704716	+	0.00224342i
$771$	3.97834			0.143276
$772$	6.69249	−	3.86391i	0.240868	−	0.139065i
$773$	−31.1288	−	17.9722i	−1.11963	−	0.646417i	−0.178321	−	0.983972i	$-0.557067\pi$
$773$	−31.1288	−	17.9722i	−1.11963	−	0.646417i	−0.941306	+	0.337556i	$0.890400\pi$
$774$	−1.02468	+	1.77480i	−0.0368315	+	0.0637940i
$775$	37.0024	−	21.3633i	1.32917	−	0.767394i
$776$	9.06050			0.325253
$777$	−0.0270046	+	0.437820i	−0.000968785	+	0.0157067i
$778$			21.2186i			0.760725i
$779$	4.24222	+	7.34775i	0.151993	+	0.263260i
$780$	14.5515	−	25.2039i	0.521026	−	0.902443i
$781$	6.54815	+	9.95076i	0.234311	+	0.356066i
$782$	5.96562	−	3.44425i	0.213330	−	0.123166i
$783$	−3.61505			−0.129191
$784$	−4.39069	−	10.3735i	−0.156810	−	0.370483i
$785$	22.6051			0.806810
$786$	−2.64244	−	4.57684i	−0.0942526	−	0.163250i
$787$	−14.6749	+	25.4176i	−0.523102	+	0.906039i	0.476537	+	0.879155i	$0.341892\pi$
$787$	−14.6749	+	25.4176i	−0.523102	+	0.906039i	−0.999639	+	0.0268846i	$0.991441\pi$
$788$	−7.54042	−	4.35346i	−0.268616	−	0.155086i
$789$	−7.14796	−	12.3806i	−0.254474	−	0.440762i
$790$			10.5461i			0.375212i
$791$	−44.4215	−	2.73991i	−1.57945	−	0.0974198i
$792$	−6.93408	−	3.48033i	−0.246392	−	0.123668i
$793$	−9.69568	−	16.7934i	−0.344304	−	0.596352i
$794$	−2.42208	+	4.19517i	−0.0859565	+	0.148881i
$795$	10.8882	−	18.8589i	0.386164	−	0.668856i
$796$	9.30620	−	5.37294i	0.329850	−	0.190439i
$797$			10.7401i			0.380433i	0.981742	+	0.190217i	$0.0609191\pi$
$797$			10.7401i			0.380433i	−0.981742	+	0.190217i	$0.939081\pi$
$798$	4.83455	+	9.70913i	0.171141	+	0.343700i
$799$			1.36222i			0.0481919i
$800$	−32.6284	+	18.8380i	−1.15359	+	0.666024i
$801$	3.31004	+	1.91105i	0.116955	+	0.0675237i
$802$	−4.68800	−	2.70662i	−0.165539	−	0.0955740i
$803$	35.8391	−	2.09604i	1.26473	−	0.0739678i
$804$			13.9773i			0.492943i
$805$	46.3713	+	30.7269i	1.63437	+	1.08298i
$806$	23.1957			0.817034
$807$	6.11930	+	10.5989i	0.215410	+	0.373101i
$808$	26.5589	+	15.3338i	0.934338	+	0.539440i
$809$	−22.4957	−	12.9879i	−0.790907	−	0.456630i	0.0493747	−	0.998780i	$-0.484277\pi$
$809$	−22.4957	−	12.9879i	−0.790907	−	0.456630i	−0.840282	+	0.542150i	$0.817610\pi$
$810$	−1.11426	−	1.92995i	−0.0391511	−	0.0678116i
$811$	−39.4934			−1.38680			−0.693400	−	0.720553i	$-0.743888\pi$
$811$	−39.4934			−1.38680			−0.693400	+	0.720553i	$0.743888\pi$
$812$	12.5243	+	8.29892i	0.439516	+	0.291235i
$813$			19.8097i			0.694757i
$814$	−0.0210319	−	0.359614i	−0.000737169	−	0.0126045i
$815$	63.1647	+	36.4682i	2.21256	+	1.27742i
$816$	−2.37094	−	1.36886i	−0.0829995	−	0.0479198i
$817$	16.9534	−	9.78807i	0.593126	−	0.342441i
$818$			7.68233i			0.268606i
$819$	−6.42284	−	12.8989i	−0.224432	−	0.450723i
$820$			7.24507i			0.253009i
$821$	−21.0077	+	12.1288i	−0.733175	+	0.423299i	−0.819583	−	0.572961i	$-0.805795\pi$
$821$	−21.0077	+	12.1288i	−0.733175	+	0.423299i	0.0864074	+	0.996260i	$0.472461\pi$
$822$	6.21383	−	10.7627i	0.216732	−	0.375391i
$823$	15.4700	−	26.7947i	0.539249	−	0.934006i	−0.459696	−	0.888076i	$-0.652042\pi$
$823$	15.4700	−	26.7947i	0.539249	−	0.934006i	0.998945	−	0.0459298i	$-0.0146251\pi$
$824$	−20.5025	−	35.5114i	−0.714239	−	1.23710i
$825$	19.4809	+	9.77783i	0.678239	+	0.340420i
$826$	−3.08666	−	0.190385i	−0.107399	−	0.00662433i
$827$		−	55.1334i		−	1.91718i	−0.284796	−	0.958588i	$-0.591926\pi$
$827$		−	55.1334i		−	1.91718i	0.284796	−	0.958588i	$-0.408074\pi$
$828$	−4.85443	−	8.40811i	−0.168703	−	0.292202i
$829$	−8.53165	−	4.92575i	−0.296317	−	0.171078i	0.344470	−	0.938797i	$-0.388058\pi$
$829$	−8.53165	−	4.92575i	−0.296317	−	0.171078i	−0.640787	+	0.767719i	$0.721392\pi$
$830$	15.8470	−	27.4478i	0.550057	−	0.952726i
$831$	−11.0601	−	19.1566i	−0.383670	−	0.664537i
$832$	−2.92536			−0.101419
$833$	7.17682	−	9.50357i	0.248662	−	0.329279i
$834$	9.05324			0.313488
$835$	−24.8983	+	14.3750i	−0.861641	+	0.497469i
$836$	17.9217	+	27.2344i	0.619835	+	0.941920i
$837$	−3.25063	+	5.63025i	−0.112358	+	0.194610i
$838$	−4.21933	−	7.30810i	−0.145754	−	0.252454i
$839$		−	43.5757i		−	1.50440i	−0.658934	−	0.752200i	$-0.728993\pi$
$839$		−	43.5757i		−	1.50440i	0.658934	−	0.752200i	$-0.271007\pi$
$840$	−1.29614	+	21.0141i	−0.0447212	+	0.725055i
$841$	15.9314			0.549360
$842$	10.8684	−	6.27490i	0.374551	−	0.216247i
$843$	0.293433	−	0.508241i	0.0101064	−	0.0175047i
$844$	−4.42887	−	2.55701i	−0.152448	−	0.0880159i
$845$	−49.0864	+	28.3401i	−1.68862	+	0.974927i
$846$	−0.524543			−0.0180341
$847$	13.1380	−	25.9691i	0.451427	−	0.892308i
$848$	10.3013			0.353748
$849$	−5.36073	+	3.09502i	−0.183980	+	0.106221i
$850$	−6.34338	−	3.66235i	−0.217576	−	0.125618i
$851$	0.512362	−	0.887438i	0.0175636	−	0.0304210i
$852$	−4.88597	+	2.82092i	−0.167391	+	0.0966430i
$853$	−31.3797			−1.07442			−0.537210	−	0.843449i	$-0.680522\pi$
$853$	−31.3797			−1.07442			−0.537210	+	0.843449i	$0.680522\pi$
$854$	5.14431	+	3.40875i	0.176035	+	0.116645i
$855$			21.2875i			0.728016i
$856$	−2.60926	−	4.51937i	−0.0891827	−	0.154469i
$857$	−1.95409	+	3.38458i	−0.0667504	+	0.115615i	−0.897469	−	0.441077i	$-0.854596\pi$
$857$	−1.95409	+	3.38458i	−0.0667504	+	0.115615i	0.830719	+	0.556692i	$0.187930\pi$
$858$	6.50489	+	9.88503i	0.222073	+	0.337469i
$859$	−11.0511	+	6.38033i	−0.377057	+	0.217694i	−0.676537	−	0.736409i	$-0.736520\pi$
$859$	−11.0511	+	6.38033i	−0.377057	+	0.217694i	0.299480	+	0.954103i	$0.403187\pi$
$860$	16.7165			0.570029
$861$	2.99029	+	1.98144i	0.101909	+	0.0675274i
$862$	−7.02771			−0.239365
$863$	−6.75076	−	11.6927i	−0.229798	−	0.398023i	0.727950	−	0.685630i	$-0.240473\pi$
$863$	−6.75076	−	11.6927i	−0.229798	−	0.398023i	−0.957748	+	0.287608i	$0.907140\pi$
$864$	2.86637	−	4.96470i	0.0975160	−	0.168903i
$865$	−21.8257	−	12.6011i	−0.742097	−	0.428450i
$866$	−4.08080	−	7.06815i	−0.138671	−	0.240186i
$867$			14.1056i			0.479052i
$868$	24.1869	−	12.0436i	0.820957	−	0.408786i
$869$	14.0276	+	7.04068i	0.475853	+	0.238839i
$870$	−4.02810	−	6.97687i	−0.136565	−	0.236538i
$871$	24.2305	−	41.9685i	0.821020	−	1.42205i
$872$	−11.3625	+	19.6805i	−0.384783	+	0.666464i
$873$	3.35430	−	1.93661i	0.113526	−	0.0655442i
$874$		−	25.3376i		−	0.857057i
$875$	0.871053	−	14.1222i	0.0294470	−	0.477417i
$876$			17.0033i			0.574489i
$877$	−24.5548	+	14.1767i	−0.829157	+	0.478714i	−0.853564	−	0.520988i	$-0.825564\pi$
$877$	−24.5548	+	14.1767i	−0.829157	+	0.478714i	0.0244067	+	0.999702i	$0.492230\pi$
$878$	−14.5627	−	8.40780i	−0.491469	−	0.283750i
$879$	−25.7791	−	14.8836i	−0.869509	−	0.502011i
$880$	1.06002	+	18.1248i	0.0357334	+	0.610986i
$881$		−	57.2184i		−	1.92774i	−0.266380	−	0.963868i	$-0.585828\pi$
$881$		−	57.2184i		−	1.92774i	0.266380	−	0.963868i	$-0.414172\pi$
$882$	3.65948	+	2.76353i	0.123221	+	0.0930530i
$883$	8.06965			0.271565			0.135783	−	0.990739i	$-0.456645\pi$
$883$	8.06965			0.271565			0.135783	+	0.990739i	$0.456645\pi$
$884$	7.27744	+	12.6049i	0.244767	+	0.423949i
$885$	−5.25643	−	3.03480i	−0.176693	−	0.102014i
$886$	−12.5963	−	7.27245i	−0.423179	−	0.244323i
$887$	2.39858	+	4.15446i	0.0805364	+	0.139493i	0.903480	−	0.428629i	$-0.141003\pi$
$887$	2.39858	+	4.15446i	0.0805364	+	0.139493i	−0.822944	+	0.568122i	$0.807670\pi$
$888$	0.387839			0.0130150
$889$	2.89178	−	46.8838i	0.0969871	−	1.57243i
$890$			8.51763i			0.285512i
$891$	−3.31097	+	0.193641i	−0.110922	+	0.00648723i
$892$	4.90574	+	2.83233i	0.164256	+	0.0948335i
$893$	4.33929	+	2.50529i	0.145209	+	0.0838364i
$894$	−0.250838	+	0.144821i	−0.00838928	+	0.00484355i
$895$		−	35.2328i		−	1.17770i
$896$	−26.3213	+	13.1064i	−0.879332	+	0.437853i
$897$			33.6617i			1.12393i
$898$	9.10004	−	5.25391i	0.303672	−	0.175325i
$899$	−11.7512	+	20.3536i	−0.391923	+	0.678831i
$900$	−5.16183	+	8.94055i	−0.172061	+	0.298018i
$901$	5.44538	+	9.43167i	0.181412	+	0.314214i
$902$	−2.63284	−	1.32147i	−0.0876639	−	0.0440000i
$903$	4.57178	−	6.89948i	0.152139	−	0.229600i
$904$			39.3504i			1.30878i
$905$	−38.0561	−	65.9151i	−1.26503	−	2.19109i
$906$	−4.40026	−	2.54049i	−0.146189	−	0.0844021i
$907$	−4.97473	+	8.61649i	−0.165183	+	0.286106i	−0.936720	−	0.350079i	$-0.886155\pi$
$907$	−4.97473	+	8.61649i	−0.165183	+	0.286106i	0.771537	+	0.636184i	$0.219488\pi$
$908$	−22.5441	−	39.0475i	−0.748152	−	1.29584i
$909$	13.1099			0.434827
$910$	17.7375	−	26.7684i	0.587992	−	0.887365i
$911$	20.3216			0.673286			0.336643	−	0.941632i	$-0.390708\pi$
$911$	20.3216			0.673286			0.336643	+	0.941632i	$0.390708\pi$
$912$	−8.72090	+	5.03501i	−0.288778	+	0.166726i
$913$	−25.9293	−	39.4029i	−0.858134	−	1.30405i
$914$	−3.12051	+	5.40489i	−0.103217	+	0.178778i
$915$	6.05598	+	10.4893i	0.200204	+	0.346764i
$916$			38.2241i			1.26296i
$917$	9.51375	+	19.1063i	0.314172	+	0.630945i
$918$	1.11452			0.0367847
$919$	−40.0916	+	23.1469i	−1.32250	+	0.763546i	−0.984127	−	0.177465i	$-0.943210\pi$
$919$	−40.0916	+	23.1469i	−1.32250	+	0.763546i	−0.338374	+	0.941012i	$0.609877\pi$
$920$	24.5919	−	42.5945i	0.810772	−	1.40430i
$921$	−17.8422	−	10.3012i	−0.587920	−	0.339436i
$922$	2.36547	−	1.36570i	0.0779026	−	0.0449771i
$923$	19.5609			0.643854
$924$	11.9153	+	6.92999i	0.391986	+	0.227980i
$925$	−1.08961			−0.0358263
$926$	−2.83829	+	1.63869i	−0.0932721	+	0.0538506i
$927$	−15.1805	−	8.76449i	−0.498594	−	0.287864i
$928$	10.3621	−	17.9476i	0.340151	−	0.589160i
$929$	−9.26074	+	5.34669i	−0.303835	+	0.175419i	−0.644164	−	0.764887i	$-0.722795\pi$
$929$	−9.26074	+	5.34669i	−0.303835	+	0.175419i	0.340329	+	0.940306i	$0.389461\pi$
$930$	−14.4882			−0.475086
$931$	−17.0741	−	40.3396i	−0.559582	−	1.32208i
$932$			31.8420i			1.04302i
$933$	−0.958903	−	1.66087i	−0.0313931	−	0.0543744i
$934$	4.77748	−	8.27483i	0.156324	−	0.270761i
$935$	−16.0343	+	10.5515i	−0.524379	+	0.345070i
$936$	−11.0334	+	6.37016i	−0.360639	+	0.208215i
$937$	23.9939			0.783847			0.391923	−	0.919998i	$-0.371810\pi$
$937$	23.9939			0.783847			0.391923	+	0.919998i	$0.371810\pi$
$938$	−0.949448	+	15.3932i	−0.0310006	+	0.502605i
$939$	18.7232			0.611010
$940$	2.13933	+	3.70542i	0.0697771	+	0.120858i
$941$	−9.78274	+	16.9442i	−0.318908	+	0.552365i	−0.980261	−	0.197710i	$-0.936650\pi$
$941$	−9.78274	+	16.9442i	−0.318908	+	0.552365i	0.661352	+	0.750075i	$0.269983\pi$
$942$	−3.77000	−	2.17661i	−0.122833	−	0.0709178i
$943$	−4.18998	−	7.25726i	−0.136445	−	0.236329i
$944$		−	2.87122i		−	0.0934503i
$945$	4.01174	+	8.05670i	0.130502	+	0.262084i
$946$	−3.04902	+	6.07474i	−0.0991321	+	0.197507i
$947$	21.2110	+	36.7386i	0.689266	+	1.19384i	0.972076	+	0.234668i	$0.0754001\pi$
$947$	21.2110	+	36.7386i	0.689266	+	1.19384i	−0.282810	+	0.959176i	$0.591267\pi$
$948$	−3.71686	+	6.43779i	−0.120718	+	0.209090i
$949$	29.4762	−	51.0543i	0.956839	−	1.65729i
$950$	−23.3325	+	13.4710i	−0.757007	+	0.437058i
$951$		−	14.8474i		−	0.481460i
$952$	−8.77740	−	5.81614i	−0.284477	−	0.188502i
$953$			34.7916i			1.12701i	0.826112	+	0.563505i	$0.190548\pi$
$953$			34.7916i			1.12701i	−0.826112	+	0.563505i	$0.809452\pi$
$954$	−3.63180	+	2.09682i	−0.117584	+	0.0678870i
$955$	42.8444	+	24.7362i	1.38641	+	0.800445i
$956$	35.9589	+	20.7609i	1.16300	+	0.671456i
$957$	−11.9693	+	0.700022i	−0.386912	+	0.0226285i
$958$		−	12.2065i		−	0.394375i
$959$	−27.7240	+	41.8395i	−0.895253	+	1.35107i
$960$	1.82719			0.0589725
$961$	5.63316	+	9.75691i	0.181715	+	0.314739i
$962$	−0.512285	−	0.295768i	−0.0165167	−	0.00953594i
$963$	−1.93196	−	1.11542i	−0.0622565	−	0.0359438i
$964$	8.53026	+	14.7748i	0.274741	+	0.475866i
$965$	16.7352			0.538725
$966$	−4.77501	−	9.58956i	−0.153634	−	0.308539i
$967$			5.49837i			0.176816i	0.996084	+	0.0884079i	$0.0281779\pi$
$967$			5.49837i			0.176816i	−0.996084	+	0.0884079i	$0.971822\pi$
$968$	−23.6324	−	10.1805i	−0.759575	−	0.327215i
$969$	−9.21990	−	5.32311i	−0.296186	−	0.171003i
$970$	7.47512	+	4.31576i	0.240012	+	0.138571i
$971$	−17.6281	+	10.1776i	−0.565712	+	0.326614i	−0.755435	−	0.655224i	$-0.772574\pi$
$971$	−17.6281	+	10.1776i	−0.565712	+	0.326614i	0.189723	+	0.981838i	$0.439241\pi$
$972$		−	1.57084i		−	0.0503847i
$973$	−36.4937	−	2.25092i	−1.16993	−	0.0721613i
$974$		−	23.0830i		−	0.739626i
$975$	30.9979	−	17.8967i	0.992728	−	0.573152i
$976$	−2.86478	+	4.96194i	−0.0916993	+	0.158828i
$977$	23.3802	−	40.4957i	0.748000	−	1.29557i	−0.200780	−	0.979636i	$-0.564348\pi$
$977$	23.3802	−	40.4957i	0.748000	−	1.29557i	0.948780	−	0.315937i	$-0.102319\pi$
$978$	−7.02294	−	12.1641i	−0.224569	−	0.388965i
$979$	11.3295	+	5.68647i	0.362092	+	0.181740i
$980$	4.59683	−	37.1219i	0.146840	−	1.18582i
$981$			9.71458i			0.310163i
$982$	3.78540	+	6.55650i	0.120797	+	0.209226i
$983$	−17.7782	−	10.2643i	−0.567037	−	0.327379i	0.188928	−	0.981991i	$-0.439499\pi$
$983$	−17.7782	−	10.2643i	−0.567037	−	0.327379i	−0.755965	+	0.654612i	$0.772832\pi$
$984$	1.58583	−	2.74674i	0.0505544	−	0.0875627i
$985$	−9.42777	−	16.3294i	−0.300394	−	0.520297i
$986$	4.02904			0.128311
$987$	2.11444	+	0.130418i	0.0673032	+	0.00415125i
$988$	53.5364			1.70322
$989$	−16.7447	+	9.66753i	−0.532449	+	0.307410i
$990$	−4.06299	−	6.17424i	−0.129130	−	0.196230i
$991$	18.3624	−	31.8047i	0.583302	−	1.01031i	−0.411783	−	0.911282i	$-0.635094\pi$
$991$	18.3624	−	31.8047i	0.583302	−	1.01031i	0.995085	−	0.0990270i	$-0.0315730\pi$
$992$	−18.6350	−	32.2768i	−0.591662	−	1.02479i
$993$			31.4148i			0.996919i
$994$	−5.57251	+	2.77477i	−0.176749	+	0.0880103i
$995$	23.2711			0.737742
$996$	19.3474	−	11.1702i	0.613045	−	0.353942i
$997$	−0.661990	+	1.14660i	−0.0209654	+	0.0363132i	−0.876318	−	0.481734i	$-0.840007\pi$
$997$	−0.661990	+	1.14660i	−0.0209654	+	0.0363132i	0.855352	+	0.518047i	$0.173341\pi$
$998$	12.9693	+	7.48785i	0.410537	+	0.237024i
$999$	0.143582	−	0.0828974i	0.00454275	−	0.00262276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.p.a.10.11	yes	32
3.2	odd	2		693.2.bg.b.10.6		32
7.3	odd	6		1617.2.c.a.538.22		32
7.4	even	3		1617.2.c.a.538.21		32
7.5	odd	6	inner	231.2.p.a.208.6	yes	32
11.10	odd	2	inner	231.2.p.a.10.6	✓	32
21.5	even	6		693.2.bg.b.208.11		32
33.32	even	2		693.2.bg.b.10.11		32
77.10	even	6		1617.2.c.a.538.12		32
77.32	odd	6		1617.2.c.a.538.11		32
77.54	even	6	inner	231.2.p.a.208.11	yes	32
231.131	odd	6		693.2.bg.b.208.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.6	✓	32	11.10	odd	2	inner
231.2.p.a.10.11	yes	32	1.1	even	1	trivial
231.2.p.a.208.6	yes	32	7.5	odd	6	inner
231.2.p.a.208.11	yes	32	77.54	even	6	inner
693.2.bg.b.10.6		32	3.2	odd	2
693.2.bg.b.10.11		32	33.32	even	2
693.2.bg.b.208.6		32	231.131	odd	6
693.2.bg.b.208.11		32	21.5	even	6
1617.2.c.a.538.11		32	77.32	odd	6
1617.2.c.a.538.12		32	77.10	even	6
1617.2.c.a.538.21		32	7.4	even	3
1617.2.c.a.538.22		32	7.3	odd	6

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567337 - 0.327552i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.785419 + 1.36039i) q^{4} +(-2.94602 + 1.70089i) q^{5} +0.655105 q^{6} +(-2.64073 - 0.162880i) q^{7} +2.33927i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.567337 - 0.327552i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.785419 + 1.36039i) q^{4} +(-2.94602 + 1.70089i) q^{5} +0.655105 q^{6} +(-2.64073 - 0.162880i) q^{7} +2.33927i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.11426 + 1.92995i) q^{10} +(1.82318 + 2.77056i) q^{11} +(-1.36039 + 0.785419i) q^{12} +5.44628 q^{13} +(-1.55154 + 0.772570i) q^{14} -3.40177 q^{15} +(-0.804604 - 1.39362i) q^{16} +(0.850644 - 1.47336i) q^{17} +(0.567337 + 0.327552i) q^{18} +(-3.12887 - 5.41937i) q^{19} -5.34364i q^{20} +(-2.20550 - 1.46142i) q^{21} +(1.94186 + 0.974655i) q^{22} +(3.09034 + 5.35263i) q^{23} +(-1.16964 + 2.02587i) q^{24} +(3.28603 - 5.69158i) q^{25} +(3.08987 - 1.78394i) q^{26} +1.00000i q^{27} +(2.29566 - 3.46449i) q^{28} +3.61505i q^{29} +(-1.92995 + 1.11426i) q^{30} +(5.63025 + 3.25063i) q^{31} +(-4.96470 - 2.86637i) q^{32} +(0.193641 + 3.31097i) q^{33} -1.11452i q^{34} +(8.05670 - 4.01174i) q^{35} -1.57084 q^{36} +(-0.0828974 - 0.143582i) q^{37} +(-3.55025 - 2.04974i) q^{38} +(4.71661 + 2.72314i) q^{39} +(-3.97884 - 6.89155i) q^{40} -1.35583 q^{41} +(-1.72996 - 0.106703i) q^{42} +3.12830i q^{43} +(-5.20099 + 0.304179i) q^{44} +(-2.94602 - 1.70089i) q^{45} +(3.50653 + 2.02450i) q^{46} +(-0.693427 + 0.400350i) q^{47} -1.60921i q^{48} +(6.94694 + 0.860244i) q^{49} -4.30539i q^{50} +(1.47336 - 0.850644i) q^{51} +(-4.27761 + 7.40904i) q^{52} +(-3.20074 + 5.54384i) q^{53} +(0.327552 + 0.567337i) q^{54} +(-10.0835 - 5.06111i) q^{55} +(0.381020 - 6.17739i) q^{56} -6.25775i q^{57} +(1.18412 + 2.05095i) q^{58} +(1.54520 + 0.892122i) q^{59} +(2.67182 - 4.62773i) q^{60} +(-1.78024 - 3.08347i) q^{61} +4.25900 q^{62} +(-1.17931 - 2.36838i) q^{63} -0.537130 q^{64} +(-16.0449 + 9.26350i) q^{65} +(1.19437 + 1.81501i) q^{66} +(4.44901 - 7.70591i) q^{67} +(1.33622 + 2.31441i) q^{68} +6.18068i q^{69} +(3.25681 - 4.91500i) q^{70} +3.59161 q^{71} +(-2.02587 + 1.16964i) q^{72} +(5.41218 - 9.37418i) q^{73} +(-0.0940615 - 0.0543064i) q^{74} +(5.69158 - 3.28603i) q^{75} +9.82991 q^{76} +(-4.36327 - 7.61327i) q^{77} +3.56788 q^{78} +(4.09831 - 2.36616i) q^{79} +(4.74076 + 2.73708i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.769213 + 0.444105i) q^{82} -14.2220 q^{83} +(3.72034 - 1.85250i) q^{84} +5.78740i q^{85} +(1.02468 + 1.77480i) q^{86} +(-1.80752 + 3.13072i) q^{87} +(-6.48110 + 4.26492i) q^{88} +(3.31004 - 1.91105i) q^{89} -2.22852 q^{90} +(-14.3822 - 0.887088i) q^{91} -9.70885 q^{92} +(3.25063 + 5.63025i) q^{93} +(-0.262271 + 0.454267i) q^{94} +(18.4355 + 10.6437i) q^{95} +(-2.86637 - 4.96470i) q^{96} -3.87321i q^{97} +(4.22303 - 1.78744i) q^{98} +(-1.48779 + 2.96420i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9}+O(q^{10}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9	\( 32 q + 12 q^{4} - 12 q^{5} + 16 q^{9} + 2 q^{11} - 32 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{22} + 24 q^{23} - 24 q^{26} - 12 q^{31} - 18 q^{33} + 24 q^{36} - 32 q^{37} + 24 q^{38} - 24 q^{42} - 28 q^{44} - 12 q^{45} + 24 q^{47} - 36 q^{49} + 36 q^{53} - 56 q^{56} + 12 q^{58} - 48 q^{59} + 8 q^{64} - 36 q^{66} + 20 q^{67} + 24 q^{70} + 72 q^{71} + 24 q^{75} - 48 q^{78} + 72 q^{80} - 16 q^{81} - 48 q^{82} + 64 q^{86} + 24 q^{88} + 60 q^{89} - 28 q^{91} - 16 q^{92} + 16 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 - 12 * q^5 + 16 * q^9 + 2 * q^11 - 32 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^22 + 24 * q^23 - 24 * q^26 - 12 * q^31 - 18 * q^33 + 24 * q^36 - 32 * q^37 + 24 * q^38 - 24 * q^42 - 28 * q^44 - 12 * q^45 + 24 * q^47 - 36 * q^49 + 36 * q^53 - 56 * q^56 + 12 * q^58 - 48 * q^59 + 8 * q^64 - 36 * q^66 + 20 * q^67 + 24 * q^70 + 72 * q^71 + 24 * q^75 - 48 * q^78 + 72 * q^80 - 16 * q^81 - 48 * q^82 + 64 * q^86 + 24 * q^88 + 60 * q^89 - 28 * q^91 - 16 * q^92 + 16 * q^93 + 4 * q^99

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