LMFDB - Embedded newform 228.2.w.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(67,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.67"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.w (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	228.67
Dual form			228.2.w.a.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37612 - 0.326044i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(1.78739 + 0.897349i) q^{4} +(-1.25586 - 0.457097i) q^{5} +(1.26374 - 0.634786i) q^{6} +(-1.18216 - 0.682521i) q^{7} +(-2.16708 - 1.81762i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.57918 + 1.03849i) q^{10} +(-1.56682 + 0.904604i) q^{11} +(-1.94603 + 0.461503i) q^{12} +(3.73606 - 4.45246i) q^{13} +(1.40426 + 1.32467i) q^{14} +(1.25586 - 0.457097i) q^{15} +(2.38953 + 3.20783i) q^{16} +(-0.927369 - 5.25937i) q^{17} +(-0.560051 + 1.29859i) q^{18} +(-4.15334 - 1.32280i) q^{19} +(-1.83454 - 1.94396i) q^{20} +(1.34430 - 0.237037i) q^{21} +(2.45107 - 0.733988i) q^{22} +(-2.07944 - 5.71321i) q^{23} +(2.82843 - 0.000592445i) q^{24} +(-2.46197 - 2.06583i) q^{25} +(-6.59294 + 4.90898i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.50052 - 2.28074i) q^{28} +(0.589123 + 0.103878i) q^{29} +(-1.87725 + 0.219552i) q^{30} +(-0.450194 + 0.779760i) q^{31} +(-2.24238 - 5.19343i) q^{32} +(0.618786 - 1.70010i) q^{33} +(-0.438619 + 7.53987i) q^{34} +(1.17266 + 1.39752i) q^{35} +(1.19409 - 1.60441i) q^{36} +7.89511i q^{37} +(5.28418 + 3.17450i) q^{38} +5.81227i q^{39} +(1.89073 + 3.27326i) q^{40} +(-0.449691 - 0.535921i) q^{41} +(-1.92720 - 0.112112i) q^{42} +(2.55877 - 7.03016i) q^{43} +(-3.61227 + 0.210897i) q^{44} +(-0.668231 + 1.15741i) q^{45} +(0.998791 + 8.54003i) q^{46} +(6.84854 + 1.20758i) q^{47} +(-3.89244 - 0.921376i) q^{48} +(-2.56833 - 4.44848i) q^{49} +(2.71440 + 3.64554i) q^{50} +(4.09107 + 3.43281i) q^{51} +(10.6732 - 4.60574i) q^{52} +(3.67511 + 10.0973i) q^{53} +(-0.405696 - 1.35477i) q^{54} +(2.38121 - 0.419871i) q^{55} +(1.32127 + 3.62780i) q^{56} +(4.03192 - 1.65639i) q^{57} +(-0.776832 - 0.335028i) q^{58} +(1.38285 + 7.84254i) q^{59} +(2.65490 + 0.309937i) q^{60} +(-9.66972 + 3.51949i) q^{61} +(0.873756 - 0.926257i) q^{62} +(-0.877432 + 1.04568i) q^{63} +(1.39249 + 7.87788i) q^{64} +(-6.72719 + 3.88394i) q^{65} +(-1.40583 + 2.13778i) q^{66} +(0.147890 - 0.838725i) q^{67} +(3.06192 - 10.2327i) q^{68} +(5.26533 + 3.03994i) q^{69} +(-1.15806 - 2.30548i) q^{70} +(0.630487 + 0.229479i) q^{71} +(-2.16632 + 1.81853i) q^{72} +(-2.99543 + 2.51346i) q^{73} +(2.57415 - 10.8646i) q^{74} +3.21387 q^{75} +(-6.23662 - 6.09135i) q^{76} +2.46965 q^{77} +(1.89506 - 7.99836i) q^{78} +(2.83807 - 2.38143i) q^{79} +(-1.53464 - 5.12084i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.444093 + 0.884109i) q^{82} +(-8.34975 - 4.82073i) q^{83} +(2.61550 + 0.782632i) q^{84} +(-1.23939 + 7.02896i) q^{85} +(-5.81331 + 8.84005i) q^{86} +(-0.518066 + 0.299105i) q^{87} +(5.03966 + 0.887540i) q^{88} +(2.69672 - 3.21383i) q^{89} +(1.29693 - 1.37486i) q^{90} +(-7.45552 + 2.71359i) q^{91} +(1.40997 - 12.0777i) q^{92} +(-0.156351 - 0.886710i) q^{93} +(-9.03066 - 3.89470i) q^{94} +(4.61138 + 3.55973i) q^{95} +(5.05604 + 2.53703i) q^{96} +(7.53165 - 1.32803i) q^{97} +(2.08392 + 6.95901i) q^{98} +(0.618786 + 1.70010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$-1$

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 $

$2$	−1.37612	−	0.326044i	−0.973061	−	0.230548i
$2$	−1.37612	−	0.326044i	−0.973061	−	0.230548i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$3$	−0.766044	+	0.642788i	−0.442276	+	0.371114i
$4$	1.78739	+	0.897349i	0.893695	+	0.448674i
$5$	−1.25586	−	0.457097i	−0.561640	−	0.204420i	0.0455709	−	0.998961i	$-0.485489\pi$
$5$	−1.25586	−	0.457097i	−0.561640	−	0.204420i	−0.607210	+	0.794541i	$0.707712\pi$
$6$	1.26374	−	0.634786i	0.515921	−	0.259150i
$7$	−1.18216	−	0.682521i	−0.446815	−	0.257969i	0.259669	−	0.965698i	$-0.416387\pi$
$7$	−1.18216	−	0.682521i	−0.446815	−	0.257969i	−0.706484	+	0.707729i	$0.749720\pi$
$8$	−2.16708	−	1.81762i	−0.766179	−	0.642627i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	1.57918	+	1.03849i	0.499381	+	0.328398i
$11$	−1.56682	+	0.904604i	−0.472414	+	0.272748i	−0.717250	−	0.696816i	$-0.754599\pi$
$11$	−1.56682	+	0.904604i	−0.472414	+	0.272748i	0.244836	+	0.969565i	$0.421266\pi$
$12$	−1.94603	+	0.461503i	−0.561769	+	0.133225i
$13$	3.73606	−	4.45246i	1.03620	−	1.23489i	0.0646821	−	0.997906i	$-0.479397\pi$
$13$	3.73606	−	4.45246i	1.03620	−	1.23489i	0.971514	−	0.236984i	$-0.0761589\pi$
$14$	1.40426	+	1.32467i	0.375304	+	0.354032i
$15$	1.25586	−	0.457097i	0.324263	−	0.118022i
$16$	2.38953	+	3.20783i	0.597383	+	0.801956i
$17$	−0.927369	−	5.25937i	−0.224920	−	1.27559i	−0.862838	−	0.505481i	$-0.831315\pi$
$17$	−0.927369	−	5.25937i	−0.224920	−	1.27559i	0.637918	−	0.770104i	$-0.279796\pi$
$18$	−0.560051	+	1.29859i	−0.132005	+	0.306081i
$19$	−4.15334	−	1.32280i	−0.952841	−	0.303471i
$19$	−4.15334	−	1.32280i	−0.952841	−	0.303471i
$20$	−1.83454	−	1.94396i	−0.410217	−	0.434683i
$21$	1.34430	−	0.237037i	0.293351	−	0.0517257i
$22$	2.45107	−	0.733988i	0.522569	−	0.156487i
$23$	−2.07944	−	5.71321i	−0.433593	−	1.19129i	−0.943591	−	0.331112i	$-0.892576\pi$
$23$	−2.07944	−	5.71321i	−0.433593	−	1.19129i	0.509998	−	0.860175i	$-0.329646\pi$
$24$	2.82843		0.000592445i	0.577350		0.000120932i
$25$	−2.46197	−	2.06583i	−0.492393	−	0.413167i
$26$	−6.59294	+	4.90898i	−1.29298	+	0.962730i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−1.50052	−	2.28074i	−0.283572	−	0.431020i
$29$	0.589123	+	0.103878i	0.109397	+	0.0192897i	0.228079	−	0.973643i	$-0.426756\pi$
$29$	0.589123	+	0.103878i	0.109397	+	0.0192897i	−0.118681	+	0.992932i	$0.537867\pi$
$30$	−1.87725	+	0.219552i	−0.342737	+	0.0400845i
$31$	−0.450194	+	0.779760i	−0.0808573	+	0.140049i	−0.903618	−	0.428338i	$-0.859099\pi$
$31$	−0.450194	+	0.779760i	−0.0808573	+	0.140049i	0.822761	+	0.568387i	$0.192432\pi$
$32$	−2.24238	−	5.19343i	−0.396400	−	0.918078i
$33$	0.618786	−	1.70010i	0.107717	−	0.295949i
$34$	−0.438619	+	7.53987i	−0.0752226	+	1.29308i
$35$	1.17266	+	1.39752i	0.198215	+	0.236223i
$36$	1.19409	−	1.60441i	0.199016	−	0.267402i
$37$			7.89511i			1.29795i	0.760811	+	0.648974i	$0.224802\pi$
$37$			7.89511i			1.29795i	−0.760811	+	0.648974i	$0.775198\pi$
$38$	5.28418	+	3.17450i	0.857208	+	0.514971i
$39$			5.81227i			0.930708i
$40$	1.89073	+	3.27326i	0.298951	+	0.517547i
$41$	−0.449691	−	0.535921i	−0.0702300	−	0.0836968i	0.729786	−	0.683676i	$-0.239620\pi$
$41$	−0.449691	−	0.535921i	−0.0702300	−	0.0836968i	−0.800015	+	0.599979i	$0.795175\pi$
$42$	−1.92720	−	0.112112i	−0.297374	−	0.0172992i
$43$	2.55877	−	7.03016i	0.390209	−	1.07209i	−0.576697	−	0.816958i	$-0.695659\pi$
$43$	2.55877	−	7.03016i	0.390209	−	1.07209i	0.966906	−	0.255132i	$-0.0821189\pi$
$44$	−3.61227	+	0.210897i	−0.544570	+	0.0317939i
$45$	−0.668231	+	1.15741i	−0.0996141	+	0.172537i
$46$	0.998791	+	8.54003i	0.147264	+	1.25916i
$47$	6.84854	+	1.20758i	0.998962	+	0.176144i	0.649137	−	0.760671i	$-0.275130\pi$
$47$	6.84854	+	1.20758i	0.998962	+	0.176144i	0.349824	+	0.936815i	$0.386241\pi$
$48$	−3.89244	−	0.921376i	−0.561825	−	0.132989i
$49$	−2.56833	−	4.44848i	−0.366904	−	0.635497i
$50$	2.71440	+	3.64554i	0.383874	+	0.515557i
$51$	4.09107	+	3.43281i	0.572864	+	0.480690i
$52$	10.6732	−	4.60574i	1.48011	−	0.638701i
$53$	3.67511	+	10.0973i	0.504815	+	1.38697i	0.886522	+	0.462686i	$0.153114\pi$
$53$	3.67511	+	10.0973i	0.504815	+	1.38697i	−0.381707	+	0.924283i	$0.624664\pi$
$54$	−0.405696	−	1.35477i	−0.0552082	−	0.184361i
$55$	2.38121	−	0.419871i	0.321082	−	0.0566154i
$56$	1.32127	+	3.62780i	0.176563	+	0.484786i
$57$	4.03192	−	1.65639i	0.534041	−	0.219394i
$58$	−0.776832	−	0.335028i	−0.102003	−	0.0439914i
$59$	1.38285	+	7.84254i	0.180032	+	1.02101i	0.932174	+	0.362011i	$0.117910\pi$
$59$	1.38285	+	7.84254i	0.180032	+	1.02101i	−0.752142	+	0.659001i	$0.770979\pi$
$60$	2.65490	+	0.309937i	0.342746	+	0.0400127i
$61$	−9.66972	+	3.51949i	−1.23808	+	0.450624i	−0.876357	−	0.481661i	$-0.840034\pi$
$61$	−9.66972	+	3.51949i	−1.23808	+	0.450624i	−0.361723	+	0.932286i	$0.617811\pi$
$62$	0.873756	−	0.926257i	0.110967	−	0.117635i
$63$	−0.877432	+	1.04568i	−0.110546	+	0.131744i
$64$	1.39249	+	7.87788i	0.174061	+	0.984735i
$65$	−6.72719	+	3.88394i	−0.834405	+	0.481744i
$66$	−1.40583	+	2.13778i	−0.173046	+	0.263143i
$67$	0.147890	−	0.838725i	0.0180676	−	0.102467i	−0.974440	−	0.224646i	$-0.927877\pi$
$67$	0.147890	−	0.838725i	0.0180676	−	0.102467i	0.992508	+	0.122180i	$0.0389884\pi$
$68$	3.06192	−	10.2327i	0.371312	−	1.24090i
$69$	5.26533	+	3.03994i	0.633871	+	0.365965i
$70$	−1.15806	−	2.30548i	−0.138414	−	0.275558i
$71$	0.630487	+	0.229479i	0.0748251	+	0.0272341i	0.379162	−	0.925331i	$-0.376212\pi$
$71$	0.630487	+	0.229479i	0.0748251	+	0.0272341i	−0.304336	+	0.952565i	$0.598435\pi$
$72$	−2.16632	+	1.81853i	−0.255303	+	0.214316i
$73$	−2.99543	+	2.51346i	−0.350588	+	0.294178i	−0.801026	−	0.598629i	$-0.795712\pi$
$73$	−2.99543	+	2.51346i	−0.350588	+	0.294178i	0.450438	+	0.892808i	$0.351268\pi$
$74$	2.57415	−	10.8646i	0.299239	−	1.26298i
$75$	3.21387			0.371105
$76$	−6.23662	−	6.09135i	−0.715390	−	0.698726i
$77$	2.46965			0.281442
$78$	1.89506	−	7.99836i	0.214573	−	0.905636i
$79$	2.83807	−	2.38143i	0.319308	−	0.267932i	−0.469018	−	0.883188i	$-0.655392\pi$
$79$	2.83807	−	2.38143i	0.319308	−	0.267932i	0.788327	+	0.615257i	$0.210948\pi$
$80$	−1.53464	−	5.12084i	−0.171578	−	0.572527i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	0.444093	+	0.884109i	0.0490419	+	0.0976335i
$83$	−8.34975	−	4.82073i	−0.916504	−	0.529144i	−0.0339859	−	0.999422i	$-0.510820\pi$
$83$	−8.34975	−	4.82073i	−0.916504	−	0.529144i	−0.882518	+	0.470278i	$0.844153\pi$
$84$	2.61550	+	0.782632i	0.285375	+	0.0853921i
$85$	−1.23939	+	7.02896i	−0.134431	+	0.762397i
$86$	−5.81331	+	8.84005i	−0.626865	+	0.953247i
$87$	−0.518066	+	0.299105i	−0.0555425	+	0.0320675i
$88$	5.03966	+	0.887540i	0.537229	+	0.0946120i
$89$	2.69672	−	3.21383i	0.285852	−	0.340665i	−0.603941	−	0.797029i	$-0.706404\pi$
$89$	2.69672	−	3.21383i	0.285852	−	0.340665i	0.889793	+	0.456363i	$0.150848\pi$
$90$	1.29693	−	1.37486i	0.136709	−	0.144923i
$91$	−7.45552	+	2.71359i	−0.781551	+	0.284461i
$92$	1.40997	−	12.0777i	0.147000	−	1.25919i
$93$	−0.156351	−	0.886710i	−0.0162128	−	0.0919475i
$94$	−9.03066	−	3.89470i	−0.931441	−	0.401707i
$95$	4.61138	+	3.55973i	0.473117	+	0.365221i
$96$	5.05604	+	2.53703i	0.516029	+	0.258934i
$97$	7.53165	−	1.32803i	0.764723	−	0.134841i	0.222336	−	0.974970i	$-0.428632\pi$
$97$	7.53165	−	1.32803i	0.764723	−	0.134841i	0.542387	+	0.840129i	$0.317521\pi$
$98$	2.08392	+	6.95901i	0.210508	+	0.702966i
$99$	0.618786	+	1.70010i	0.0621903	+	0.170866i
$100$	−2.54672	−	5.90169i	−0.254672	−	0.590169i
$101$	0.403018	+	0.338172i	0.0401018	+	0.0336494i	0.662618	−	0.748957i	$-0.269445\pi$
$101$	0.403018	+	0.338172i	0.0401018	+	0.0336494i	−0.622517	+	0.782607i	$0.713890\pi$
$102$	−4.51053	−	6.05781i	−0.446609	−	0.599813i
$103$	−8.31062	−	14.3944i	−0.818870	−	1.41832i	−0.906515	−	0.422173i	$-0.861268\pi$
$103$	−8.31062	−	14.3944i	−0.818870	−	1.41832i	0.0876453	−	0.996152i	$-0.472066\pi$
$104$	−16.1892	+	2.85810i	−1.58749	+	0.280259i
$105$	−1.79661	−	0.316791i	−0.175331	−	0.0309157i
$106$	−1.76522	−	15.0933i	−0.171453	−	1.46599i
$107$	−2.53421	+	4.38938i	−0.244991	+	0.424337i	−0.962129	−	0.272594i	$-0.912118\pi$
$107$	−2.53421	+	4.38938i	−0.244991	+	0.424337i	0.717138	+	0.696931i	$0.245452\pi$
$108$	0.116568	+	1.99660i	0.0112168	+	0.192123i
$109$	−0.783126	+	2.15162i	−0.0750099	+	0.206088i	−0.971531	−	0.236914i	$-0.923864\pi$
$109$	−0.783126	+	2.15162i	−0.0750099	+	0.206088i	0.896521	+	0.443002i	$0.146086\pi$
$110$	−3.41371	−	0.198587i	−0.325485	−	0.0189345i
$111$	−5.07488	−	6.04800i	−0.481686	−	0.574051i
$112$	−0.635402	−	5.42307i	−0.0600398	−	0.512432i
$113$		−	11.5712i		−	1.08852i	−0.838915	−	0.544262i	$-0.816810\pi$
$113$		−	11.5712i		−	1.08852i	0.838915	−	0.544262i	$-0.183190\pi$
$114$	−6.08844	+	0.964802i	−0.570235	+	0.0903620i
$115$			8.12553i			0.757709i
$116$	0.959777	+	0.714319i	0.0891131	+	0.0663229i
$117$	−3.73606	−	4.45246i	−0.345399	−	0.411630i
$118$	0.654049	−	11.2431i	0.0602101	−	1.03501i
$119$	−2.49333	+	6.85038i	−0.228563	+	0.627973i
$120$	−3.55239	−	1.29212i	−0.324287	−	0.117954i
$121$	−3.86338	+	6.69157i	−0.351217	+	0.608325i
$122$	14.4542	−	1.69047i	1.30862	−	0.153048i
$123$	0.688967	+	0.121483i	0.0621220	+	0.0109538i
$124$	−1.50439	+	0.989754i	−0.135098	+	0.0888825i
$125$	5.48876	+	9.50682i	0.490930	+	0.850316i
$126$	1.54839	−	1.15290i	0.137941	−	0.102708i
$127$	−7.85651	−	6.59239i	−0.697153	−	0.584980i	0.223809	−	0.974633i	$-0.428151\pi$
$127$	−7.85651	−	6.59239i	−0.697153	−	0.584980i	−0.920962	+	0.389652i	$0.872595\pi$
$128$	0.652313	−	11.2949i	0.0576569	−	0.998336i
$129$	2.55877	+	7.03016i	0.225287	+	0.618971i
$130$	10.5237	−	3.15140i	0.922992	−	0.276396i
$131$	16.8151	−	2.96495i	1.46914	−	0.259049i	0.618910	−	0.785462i	$-0.287575\pi$
$131$	16.8151	−	2.96495i	1.46914	−	0.259049i	0.850229	+	0.526413i	$0.176464\pi$
$132$	2.63159	−	2.48348i	0.229051	−	0.216159i
$133$	4.00708	+	4.39850i	0.347458	+	0.381398i
$134$	−0.476975	+	1.10596i	−0.0412043	+	0.0955407i
$135$	−0.232074	−	1.31616i	−0.0199738	−	0.113277i
$136$	−7.54988	+	13.0831i	−0.647397	+	1.12187i
$137$	−1.40505	+	0.511397i	−0.120042	+	0.0436916i	−0.401343	−	0.915928i	$-0.631456\pi$
$137$	−1.40505	+	0.511397i	−0.120042	+	0.0436916i	0.281301	+	0.959620i	$0.409234\pi$
$138$	−6.25455	−	5.90003i	−0.532422	−	0.502244i
$139$	11.9953	−	14.2955i	1.01743	−	1.21253i	0.0404549	−	0.999181i	$-0.487119\pi$
$139$	11.9953	−	14.2955i	1.01743	−	1.21253i	0.976977	−	0.213346i	$-0.0684363\pi$
$140$	0.841934	+	3.55019i	0.0711564	+	0.300046i
$141$	−6.02250	+	3.47709i	−0.507186	+	0.292824i
$142$	−0.792804	−	0.521356i	−0.0665306	−	0.0437512i
$143$	−1.82602	+	10.3559i	−0.152699	+	0.866000i
$144$	3.57403	−	1.79619i	0.297836	−	0.149683i
$145$	−0.692376	−	0.399743i	−0.0574987	−	0.0331969i
$146$	4.94155	−	2.48217i	0.408966	−	0.205426i
$147$	4.82688	+	1.75684i	0.398114	+	0.144902i
$148$	−7.08467	+	14.1116i	−0.582356	+	1.15997i
$149$	9.83882	−	8.25575i	0.806028	−	0.676337i	−0.143629	−	0.989632i	$-0.545877\pi$
$149$	9.83882	−	8.25575i	0.806028	−	0.676337i	0.949656	+	0.313294i	$0.101433\pi$
$150$	−4.42265	−	1.04786i	−0.361108	−	0.0855576i
$151$	12.7827			1.04024			0.520122	−	0.854092i	$-0.325887\pi$
$151$	12.7827			1.04024			0.520122	+	0.854092i	$0.325887\pi$
$152$	6.59627	+	10.4158i	0.535028	+	0.844834i
$153$	−5.34051			−0.431754
$154$	−3.39852	−	0.805214i	−0.273861	−	0.0648860i
$155$	0.921809	−	0.773490i	0.0740415	−	0.0621282i
$156$	−5.21564	+	10.3888i	−0.417585	+	0.831770i
$157$	−13.2613	−	4.82672i	−1.05837	−	0.385214i	−0.246553	−	0.969129i	$-0.579298\pi$
$157$	−13.2613	−	4.82672i	−1.05837	−	0.385214i	−0.811815	+	0.583915i	$0.801520\pi$
$158$	−4.68197	+	2.35178i	−0.372478	+	0.187098i
$159$	−9.30571	−	5.37265i	−0.737991	−	0.426079i
$160$	0.442220	+	7.54723i	0.0349605	+	0.596661i
$161$	−1.44116	+	8.17320i	−0.113579	+	0.644139i
$162$	1.18161	+	0.777041i	0.0928362	+	0.0610501i
$163$	−15.4400	+	8.91427i	−1.20935	+	0.698219i	−0.962618	−	0.270864i	$-0.912691\pi$
$163$	−15.4400	+	8.91427i	−1.20935	+	0.698219i	−0.246734	+	0.969083i	$0.579357\pi$
$164$	−0.322866	−	1.36143i	−0.0252116	−	0.106310i
$165$	−1.55422	+	1.85225i	−0.120996	+	0.144197i
$166$	9.91845	+	9.35627i	0.769821	+	0.726187i
$167$	9.72858	−	3.54091i	0.752820	−	0.274004i	0.0630280	−	0.998012i	$-0.479924\pi$
$167$	9.72858	−	3.54091i	0.752820	−	0.274004i	0.689792	+	0.724008i	$0.257702\pi$
$168$	−3.34406	−	1.92976i	−0.258000	−	0.148884i
$169$	−3.60884	−	20.4668i	−0.277603	−	1.57437i
$170$	3.99730	−	9.26856i	0.306579	−	0.710866i
$171$	−2.02392	+	3.86054i	−0.154773	+	0.295223i
$172$	10.8820	−	10.2695i	0.829747	−	0.783045i
$173$	14.4030	−	2.53963i	1.09504	−	0.193085i	0.403182	−	0.915120i	$-0.367904\pi$
$173$	14.4030	−	2.53963i	1.09504	−	0.193085i	0.691856	+	0.722035i	$0.256793\pi$
$174$	0.810440	−	0.242692i	0.0614393	−	0.0183984i
$175$	1.50046	+	4.12249i	0.113424	+	0.311631i
$176$	−6.64578	−	2.86451i	−0.500944	−	0.215920i
$177$	−6.10041	−	5.11885i	−0.458535	−	0.384757i
$178$	−4.75885	+	3.54335i	−0.356691	+	0.265585i
$179$	−11.7089	−	20.2804i	−0.875164	−	1.51583i	−0.856588	−	0.516001i	$-0.827420\pi$
$179$	−11.7089	−	20.2804i	−0.875164	−	1.51583i	−0.0185761	−	0.999827i	$-0.505913\pi$
$180$	−2.23299	+	1.46911i	−0.166437	+	0.109501i
$181$	11.7776	+	2.07670i	0.875420	+	0.154360i	0.593264	−	0.805008i	$-0.297839\pi$
$181$	11.7776	+	2.07670i	0.875420	+	0.154360i	0.282156	+	0.959368i	$0.408950\pi$
$182$	11.1444	−	1.30338i	0.826079	−	0.0966132i
$183$	5.14515	−	8.91166i	0.380340	−	0.658769i
$184$	−5.87816	+	16.1606i	−0.433344	+	1.19138i
$185$	3.60883	−	9.91518i	0.265327	−	0.728979i
$186$	−0.0739495	+	1.27119i	−0.00542224	+	0.0932084i
$187$	6.21067	+	7.40159i	0.454169	+	0.541258i
$188$	11.1574	+	8.30395i	0.813736	+	0.605627i
$189$		−	1.36504i		−	0.0992922i
$190$	−5.18516	−	6.40212i	−0.376171	−	0.464459i
$191$			24.0981i			1.74368i	0.489792	+	0.871839i	$0.337073\pi$
$191$			24.0981i			1.74368i	−0.489792	+	0.871839i	$0.662927\pi$
$192$	−6.13051	−	5.13973i	−0.442431	−	0.370928i
$193$	−0.142369	−	0.169668i	−0.0102479	−	0.0122130i	0.760896	−	0.648874i	$-0.224760\pi$
$193$	−0.142369	−	0.169668i	−0.0102479	−	0.0122130i	−0.771144	+	0.636661i	$0.780315\pi$
$194$	−10.7974	−	0.628121i	−0.775209	−	0.0450965i
$195$	2.65677	−	7.29942i	0.190255	−	0.522723i
$196$	−0.598772	−	10.2559i	−0.0427695	−	0.732561i
$197$	−10.6034	+	18.3656i	−0.755458	+	1.30849i	0.189688	+	0.981844i	$0.439252\pi$
$197$	−10.6034	+	18.3656i	−0.755458	+	1.30849i	−0.945146	+	0.326648i	$0.894081\pi$
$198$	−0.297214	−	2.54129i	−0.0211221	−	0.180601i
$199$	9.96742	+	1.75752i	0.706572	+	0.124588i	0.515376	−	0.856964i	$-0.327652\pi$
$199$	9.96742	+	1.75752i	0.706572	+	0.124588i	0.191196	+	0.981552i	$0.438763\pi$
$200$	1.58037	+	8.95176i	0.111749	+	0.632985i
$201$	0.425832	+	0.737562i	0.0300359	+	0.0520236i
$202$	−0.444340	−	0.596765i	−0.0312637	−	0.0419883i
$203$	−0.625539	−	0.524890i	−0.0439042	−	0.0368400i
$204$	4.23190	+	9.80689i	0.296292	+	0.686620i
$205$	0.319783	+	0.878597i	0.0223346	+	0.0613638i
$206$	6.74317	+	22.5180i	0.469819	+	1.56891i
$207$	−5.98751	+	1.05576i	−0.416161	+	0.0733803i
$208$	23.2101	+	1.34533i	1.60933	+	0.0932820i
$209$	7.70414	−	1.68454i	0.532907	−	0.116522i
$210$	2.36906	+	1.02172i	0.163481	+	0.0705051i
$211$	4.68568	+	26.5738i	0.322576	+	1.82942i	0.526191	+	0.850367i	$0.323620\pi$
$211$	4.68568	+	26.5738i	0.322576	+	1.82942i	−0.203615	+	0.979051i	$0.565269\pi$
$212$	−2.49193	+	21.3457i	−0.171146	+	1.46603i
$213$	−0.630487	+	0.229479i	−0.0432003	+	0.0157236i
$214$	4.91850	−	5.21403i	0.336221	−	0.356424i
$215$	−6.42694	+	7.65932i	−0.438313	+	0.522362i
$216$	0.490568	−	2.78556i	0.0333789	−	0.189533i
$217$	1.06441	−	0.614535i	0.0722565	−	0.0417173i
$218$	1.77920	−	2.70555i	0.120502	−	0.183243i
$219$	0.679008	−	3.85084i	0.0458831	−	0.260216i
$220$	4.63292	+	1.38630i	0.312351	+	0.0934643i
$221$	−26.8818	−	15.5202i	−1.80827	−	1.04400i
$222$	5.01171	+	9.97739i	0.336364	+	0.669639i
$223$	0.0346307	+	0.0126046i	0.00231905	+	0.000844064i	0.343179	−	0.939270i	$-0.388496\pi$
$223$	0.0346307	+	0.0126046i	0.00231905	+	0.000844064i	−0.340860	+	0.940114i	$0.610718\pi$
$224$	−0.893774	+	7.66995i	−0.0597178	+	0.512470i
$225$	−2.46197	+	2.06583i	−0.164131	+	0.137722i
$226$	−3.77271	+	15.9233i	−0.250957	+	1.05920i
$227$	−13.2865			−0.881859			−0.440929	−	0.897542i	$-0.645351\pi$
$227$	−13.2865			−0.881859			−0.440929	+	0.897542i	$0.645351\pi$
$228$	8.69297	+	0.657421i	0.575706	+	0.0435388i
$229$	28.8285			1.90504			0.952520	−	0.304477i	$-0.0984816\pi$
$229$	28.8285			1.90504			0.952520	+	0.304477i	$0.0984816\pi$
$230$	2.64928	−	11.1817i	0.174688	−	0.737297i
$231$	−1.89186	+	1.58746i	−0.124475	+	0.104447i
$232$	−1.08787	−	1.29592i	−0.0714219	−	0.0850811i
$233$	−14.3124	−	5.20928i	−0.937636	−	0.341272i	−0.172404	−	0.985026i	$-0.555153\pi$
$233$	−14.3124	−	5.20928i	−0.937636	−	0.341272i	−0.765232	+	0.643755i	$0.777376\pi$
$234$	3.68955	+	7.34522i	0.241193	+	0.480172i
$235$	−8.04885	−	4.64701i	−0.525049	−	0.303137i
$236$	−4.56580	+	15.2586i	−0.297208	+	0.993249i
$237$	−0.643339	+	3.64856i	−0.0417894	+	0.236999i
$238$	5.66464	−	8.61398i	0.367184	−	0.558361i
$239$	18.8499	−	10.8830i	1.21930	−	0.703964i	0.254533	−	0.967064i	$-0.418078\pi$
$239$	18.8499	−	10.8830i	1.21930	−	0.703964i	0.964768	+	0.263100i	$0.0847451\pi$
$240$	4.46721	+	2.93635i	0.288357	+	0.189540i
$241$	4.70691	−	5.60947i	0.303198	−	0.361338i	−0.592835	−	0.805324i	$-0.701992\pi$
$241$	4.70691	−	5.60947i	0.303198	−	0.361338i	0.896034	+	0.443986i	$0.146436\pi$
$242$	7.49821	−	7.94875i	0.482003	−	0.510965i
$243$	0.939693	−	0.342020i	0.0602813	−	0.0219406i
$244$	−20.4418	−	2.38641i	−1.30865	−	0.152774i
$245$	1.19209	+	6.76066i	0.0761596	+	0.431923i
$246$	−0.908489	−	0.391809i	−0.0579232	−	0.0249808i
$247$	−21.4068	+	13.5505i	−1.36208	+	0.862198i
$248$	2.39292	−	0.871519i	0.151950	−	0.0553415i
$249$	9.49498	−	1.67422i	0.601720	−	0.106099i
$250$	−4.45353	−	14.8721i	−0.281666	−	0.940592i
$251$	−10.3774	−	28.5117i	−0.655017	−	1.79964i	−0.598327	−	0.801252i	$-0.704167\pi$
$251$	−10.3774	−	28.5117i	−0.655017	−	1.79964i	−0.0566903	−	0.998392i	$-0.518055\pi$
$252$	−2.50666	+	1.08168i	−0.157905	+	0.0681395i
$253$	8.42631	+	7.07051i	0.529757	+	0.444519i
$254$	8.66206	+	11.6335i	0.543506	+	0.729949i
$255$	−3.56869	−	6.18116i	−0.223480	−	0.387079i
$256$	−4.58029	+	15.3304i	−0.286268	+	0.958150i
$257$	13.8423	+	2.44078i	0.863461	+	0.152251i	0.587803	−	0.809004i	$-0.299993\pi$
$257$	13.8423	+	2.44078i	0.863461	+	0.152251i	0.275658	+	0.961256i	$0.411104\pi$
$258$	−1.22902	−	10.5086i	−0.0765156	−	0.654236i
$259$	5.38858	−	9.33329i	0.334830	−	0.579943i
$260$	−15.5094	+	0.905490i	−0.961850	+	0.0561561i
$261$	0.204600	−	0.562134i	0.0126644	−	0.0347952i
$262$	−24.1062	−	1.40234i	−1.48928	−	0.0866366i
$263$	−10.9130	−	13.0056i	−0.672925	−	0.801961i	0.316254	−	0.948675i	$-0.397575\pi$
$263$	−10.9130	−	13.0056i	−0.672925	−	0.801961i	−0.989179	+	0.146713i	$0.953130\pi$
$264$	−4.43110	+	2.55954i	−0.272715	+	0.157529i
$265$		−	14.3607i		−	0.882171i
$266$	−4.08010	−	7.35933i	−0.250167	−	0.451230i
$267$			4.19536i			0.256752i
$268$	1.01697	−	1.36642i	0.0621210	−	0.0834674i
$269$	−2.93895	−	3.50250i	−0.179191	−	0.213551i	0.668971	−	0.743288i	$-0.266735\pi$
$269$	−2.93895	−	3.50250i	−0.179191	−	0.213551i	−0.848162	+	0.529737i	$0.822291\pi$
$270$	−0.109765	+	1.88685i	−0.00668006	+	0.114830i
$271$	−7.27616	+	19.9911i	−0.441995	+	1.21437i	0.496183	+	0.868218i	$0.334735\pi$
$271$	−7.27616	+	19.9911i	−0.441995	+	1.21437i	−0.938178	+	0.346153i	$0.887488\pi$
$272$	14.6552	−	15.5423i	0.888600	−	0.942389i
$273$	3.96700	−	6.87104i	0.240094	−	0.415854i
$274$	2.10025	−	0.245633i	0.126881	−	0.0148392i
$275$	5.72622	+	1.00969i	0.345304	+	0.0608864i
$276$	6.68331	+	10.1584i	0.402288	+	0.611463i
$277$	−2.28795	−	3.96285i	−0.137470	−	0.238104i	0.789069	−	0.614305i	$-0.210564\pi$
$277$	−2.28795	−	3.96285i	−0.137470	−	0.238104i	−0.926538	+	0.376201i	$0.877230\pi$
$278$	−21.1679	+	15.7612i	−1.26957	+	0.945297i
$279$	0.689738	+	0.578759i	0.0412935	+	0.0346494i
$280$	−0.00108081	−	5.15998i	−6.45910e−5	−	0.308368i
$281$	−6.42344	−	17.6482i	−0.383190	−	1.05281i	−0.970005	−	0.243085i	$-0.921841\pi$
$281$	−6.42344	−	17.6482i	−0.383190	−	1.05281i	0.586815	−	0.809721i	$-0.300382\pi$
$282$	9.42135	−	2.82128i	0.561033	−	0.168005i
$283$	24.9211	−	4.39427i	1.48141	−	0.261212i	0.626268	−	0.779608i	$-0.284582\pi$
$283$	24.9211	−	4.39427i	1.48141	−	0.261212i	0.855141	+	0.518396i	$0.173471\pi$
$284$	0.921005	+	0.975935i	0.0546516	+	0.0579111i
$285$	−5.82067	+	0.237222i	−0.344787	+	0.0140518i
$286$	5.88928	−	13.6555i	0.348240	−	0.807467i
$287$	0.165830	+	0.940469i	0.00978864	+	0.0555141i
$288$	−5.50392	+	1.30648i	−0.324321	+	0.0769852i
$289$	−10.8262	+	3.94042i	−0.636836	+	0.231789i
$290$	0.822455	+	0.775838i	0.0482962	+	0.0455588i
$291$	−4.91593	+	5.85858i	−0.288177	+	0.343436i
$292$	−7.60945	+	1.80459i	−0.445309	+	0.105606i
$293$	0.535807	−	0.309349i	0.0313022	−	0.0180723i	−0.484267	−	0.874920i	$-0.660914\pi$
$293$	0.535807	−	0.309349i	0.0313022	−	0.0180723i	0.515569	+	0.856848i	$0.327580\pi$
$294$	−6.06954	−	3.99139i	−0.353983	−	0.232783i
$295$	1.84813	−	10.4813i	0.107602	−	0.610242i
$296$	14.3503	−	17.1093i	0.834097	−	0.994460i
$297$	−1.56682	−	0.904604i	−0.0909162	−	0.0524905i
$298$	−16.2311	+	8.15298i	−0.940242	+	0.472290i
$299$	−33.2068	−	12.0863i	−1.92040	−	0.698967i
$300$	5.74444	+	2.88396i	0.331655	+	0.166506i
$301$	−7.82312	+	6.56437i	−0.450917	+	0.378364i
$302$	−17.5905	−	4.16773i	−1.01222	−	0.239826i
$303$	−0.526102			−0.0302238
$304$	−5.68121	−	16.4840i	−0.325840	−	0.945425i
$305$	13.7526			0.787472
$306$	7.34916	+	1.74124i	0.420123	+	0.0995401i
$307$	14.7710	−	12.3943i	0.843024	−	0.707381i	−0.115218	−	0.993340i	$-0.536757\pi$
$307$	14.7710	−	12.3943i	0.843024	−	0.707381i	0.958242	+	0.285959i	$0.0923122\pi$
$308$	4.41422	+	2.21613i	0.251524	+	0.126276i
$309$	15.6189	+	5.68480i	0.888526	+	0.323397i
$310$	−1.52071	+	0.763861i	−0.0863704	+	0.0433844i
$311$	7.47317	+	4.31464i	0.423765	+	0.244661i	0.696687	−	0.717375i	$-0.254657\pi$
$311$	7.47317	+	4.31464i	0.423765	+	0.244661i	−0.272922	+	0.962036i	$0.587990\pi$
$312$	10.5645	−	12.5957i	0.598098	−	0.713089i
$313$	5.84370	−	33.1413i	0.330305	−	1.87326i	−0.139109	−	0.990277i	$-0.544424\pi$
$313$	5.84370	−	33.1413i	0.330305	−	1.87326i	0.469414	−	0.882978i	$-0.344465\pi$
$314$	16.6754	+	10.9659i	0.941046	+	0.618841i
$315$	1.57991	−	0.912164i	0.0890181	−	0.0513946i
$316$	7.20972	−	1.70980i	0.405578	−	0.0961837i
$317$	−15.3580	+	18.3030i	−0.862592	+	1.02800i	0.136709	+	0.990611i	$0.456347\pi$
$317$	−15.3580	+	18.3030i	−0.862592	+	1.02800i	−0.999301	+	0.0373855i	$0.988097\pi$
$318$	11.0540	+	10.4275i	0.619878	+	0.584743i
$319$	−1.01702	+	0.370164i	−0.0569421	+	0.0207252i
$320$	1.85218	−	10.5300i	0.103540	−	0.588648i
$321$	−0.880122	−	4.99142i	−0.0491236	−	0.278594i
$322$	4.64802	−	10.7774i	0.259024	−	0.600601i
$323$	−3.10542	+	23.0707i	−0.172790	+	1.28369i
$324$	−1.37269	−	1.45456i	−0.0762604	−	0.0808086i
$325$	−18.3961	+	3.24373i	−1.02043	+	0.179930i
$326$	24.1536	−	7.23296i	1.33775	−	0.400596i
$327$	−0.783126	−	2.15162i	−0.0433070	−	0.118985i
$328$	0.000414471		1.97875i	2.28854e−5		0.109258i
$329$	−7.27187	−	6.10183i	−0.400911	−	0.336405i
$330$	2.74270	−	2.04217i	0.150981	−	0.112418i
$331$	11.1872	+	19.3767i	0.614902	+	1.06504i	0.990402	+	0.138219i	$0.0441379\pi$
$331$	11.1872	+	19.3767i	0.614902	+	1.06504i	−0.375499	+	0.926823i	$0.622529\pi$
$332$	−10.5984	−	16.1092i	−0.581662	−	0.884105i
$333$	7.77516	+	1.37097i	0.426076	+	0.0751288i
$334$	−14.5421	+	1.70076i	−0.795711	+	0.0930615i
$335$	−0.569108	+	0.985724i	−0.0310937	+	0.0538559i
$336$	3.97263	+	3.74589i	0.216725	+	0.204355i
$337$	−7.67933	+	21.0988i	−0.418320	+	1.14932i	0.534336	+	0.845272i	$0.320562\pi$
$337$	−7.67933	+	21.0988i	−0.418320	+	1.14932i	−0.952656	+	0.304051i	$0.901661\pi$
$338$	−1.70688	+	29.3413i	−0.0928421	+	1.59596i
$339$	7.43781	+	8.86404i	0.403966	+	0.481428i
$340$	−8.52271	+	11.4513i	−0.462209	+	0.621035i
$341$		−	1.62899i		−	0.0882148i
$342$	4.04386	−	4.65266i	0.218667	−	0.251587i
$343$			16.5671i			0.894537i
$344$	−18.3233	+	10.5841i	−0.987924	+	0.570654i
$345$	−5.22299	−	6.22451i	−0.281196	−	0.335117i
$346$	−20.6482	−	1.20117i	−1.11005	−	0.0645755i
$347$	6.73751	−	18.5112i	0.361689	−	0.993731i	−0.616744	−	0.787164i	$-0.711549\pi$
$347$	6.73751	−	18.5112i	0.361689	−	0.993731i	0.978432	−	0.206567i	$-0.0662293\pi$
$348$	−1.19439	+	0.0697325i	−0.0640259	+	0.00373806i
$349$	11.0085	−	19.0672i	0.589270	−	1.02064i	−0.405059	−	0.914291i	$-0.632749\pi$
$349$	11.0085	−	19.0672i	0.589270	−	1.02064i	0.994328	−	0.106354i	$-0.0339177\pi$
$350$	−0.720699	−	6.16225i	−0.0385230	−	0.329386i
$351$	5.72397	+	1.00929i	0.305523	+	0.0538719i
$352$	8.21141	+	6.10871i	0.437669	+	0.325595i
$353$	10.2460	+	17.7465i	0.545338	+	0.944553i	0.998586	+	0.0531686i	$0.0169321\pi$
$353$	10.2460	+	17.7465i	0.545338	+	0.944553i	−0.453247	+	0.891385i	$0.649735\pi$
$354$	6.72590	+	9.03314i	0.357478	+	0.480106i
$355$	−0.686912	−	0.576388i	−0.0364575	−	0.0305915i
$356$	7.70402	−	3.32447i	0.408312	−	0.176196i
$357$	−2.49333	−	6.85038i	−0.131961	−	0.362560i
$358$	9.50050	+	31.7258i	0.502117	+	1.67676i
$359$	11.1171	−	1.96024i	0.586738	−	0.103458i	0.127605	−	0.991825i	$-0.459271\pi$
$359$	11.1171	−	1.96024i	0.586738	−	0.103458i	0.459133	+	0.888367i	$0.348160\pi$
$360$	3.55185	−	1.29361i	0.187199	−	0.0681792i
$361$	15.5004	+	10.9881i	0.815811	+	0.578319i
$362$	−15.5302	−	6.69779i	−0.816249	−	0.352028i
$363$	−1.34174	−	7.60938i	−0.0704230	−	0.399389i
$364$	−15.7610	−	1.83996i	−0.826099	−	0.0964402i
$365$	4.91074	−	1.78736i	0.257040	−	0.0935549i
$366$	−9.98592	+	10.5859i	−0.521972	+	0.553336i
$367$	4.93537	−	5.88174i	0.257624	−	0.307025i	−0.621693	−	0.783261i	$-0.713555\pi$
$367$	4.93537	−	5.88174i	0.257624	−	0.307025i	0.879317	+	0.476236i	$0.157999\pi$
$368$	13.3581	−	20.3224i	0.696340	−	1.05938i
$369$	−0.605867	+	0.349798i	−0.0315402	+	0.0182097i
$370$	−8.19896	+	12.4678i	−0.426244	+	0.648170i
$371$	2.54704	−	14.4450i	0.132236	−	0.749945i
$372$	0.516228	−	1.72520i	0.0267652	−	0.0894474i
$373$	10.6167	+	6.12955i	0.549711	+	0.317376i	0.749005	−	0.662564i	$-0.230532\pi$
$373$	10.6167	+	6.12955i	0.549711	+	0.317376i	−0.199294	+	0.979940i	$0.563865\pi$
$374$	−6.13336	−	12.2104i	−0.317149	−	0.631385i
$375$	−10.3155	−	3.75454i	−0.532690	−	0.193883i
$376$	−12.6464	−	15.0650i	−0.652189	−	0.776918i
$377$	2.66351	−	2.23495i	0.137178	−	0.115106i
$378$	−0.445064	+	1.87846i	−0.0228916	+	0.0966174i
$379$	−8.64524			−0.444076			−0.222038	−	0.975038i	$-0.571271\pi$
$379$	−8.64524			−0.444076			−0.222038	+	0.975038i	$0.571271\pi$
$380$	5.04801	+	10.5007i	0.258958	+	0.538672i
$381$	10.2559			0.525428
$382$	7.85705	−	33.1618i	0.402001	−	1.69671i
$383$	14.4544	−	12.1287i	0.738584	−	0.619745i	−0.193873	−	0.981027i	$-0.562105\pi$
$383$	14.4544	−	12.1287i	0.738584	−	0.619745i	0.932457	+	0.361281i	$0.117661\pi$
$384$	6.76051	+	9.07168i	0.344996	+	0.462937i
$385$	−3.10154	−	1.12887i	−0.158069	−	0.0575325i
$386$	0.140596	+	0.279902i	0.00715617	+	0.0142466i
$387$	−6.47903	−	3.74067i	−0.329348	−	0.190149i
$388$	14.6537	+	4.38480i	0.743929	+	0.222605i
$389$	0.467114	−	2.64914i	0.0236836	−	0.134317i	−0.970673	−	0.240402i	$-0.922721\pi$
$389$	0.467114	−	2.64914i	0.0236836	−	0.134317i	0.994357	+	0.106086i	$0.0338318\pi$
$390$	−6.03596	+	9.17863i	−0.305643	+	0.464778i
$391$	−28.1195	+	16.2348i	−1.42206	+	0.821030i
$392$	−2.51988	+	14.3085i	−0.127273	+	0.722687i
$393$	−10.9753	+	13.0798i	−0.553628	+	0.659788i
$394$	20.5794	−	21.8160i	1.03678	−	1.09907i
$395$	−4.65278	+	1.69347i	−0.234107	+	0.0852079i
$396$	−0.419571	+	3.59401i	−0.0210842	+	0.180606i
$397$	−0.105492	−	0.598277i	−0.00529451	−	0.0300267i	0.982046	−	0.188641i	$-0.0604084\pi$
$397$	−0.105492	−	0.598277i	−0.00529451	−	0.0300267i	−0.987341	+	0.158615i	$0.949297\pi$
$398$	−13.1433	−	5.66838i	−0.658814	−	0.284130i
$399$	−5.89690	−	0.793750i	−0.295214	−	0.0397372i
$400$	0.743895	−	12.8339i	0.0371947	−	0.641696i
$401$	−37.4771	+	6.60822i	−1.87152	+	0.329999i	−0.989877	−	0.141925i	$-0.954671\pi$
$401$	−37.4771	+	6.60822i	−1.87152	+	0.329999i	−0.881639	+	0.471924i	$0.843560\pi$
$402$	−0.345516	−	1.15381i	−0.0172328	−	0.0575469i
$403$	1.78990	+	4.91770i	0.0891611	+	0.244968i
$404$	0.416892	+	0.966093i	0.0207411	+	0.0480649i
$405$	1.02379	+	0.859062i	0.0508725	+	0.0426871i
$406$	0.689677	+	0.926262i	0.0342281	+	0.0459696i
$407$	−7.14195	−	12.3702i	−0.354013	−	0.613169i
$408$	−2.62611	−	14.8752i	−0.130012	−	0.736432i
$409$	−8.87907	−	1.56562i	−0.439042	−	0.0774149i	−0.0502417	−	0.998737i	$-0.515999\pi$
$409$	−8.87907	−	1.56562i	−0.439042	−	0.0774149i	−0.388800	+	0.921322i	$0.627110\pi$
$410$	−0.153597	−	1.31331i	−0.00758563	−	0.0648600i
$411$	0.747612	−	1.29490i	0.0368770	−	0.0638728i
$412$	−1.93751	−	33.1860i	−0.0954544	−	1.63496i
$413$	3.71795	−	10.2150i	0.182948	−	0.502646i
$414$	8.58373	+	0.499344i	0.421867	+	0.0245414i
$415$	8.28261	+	9.87083i	0.406577	+	0.484540i
$416$	−31.5012	−	9.41886i	−1.54447	−	0.461797i
$417$			18.6614i			0.913855i
$418$	−11.1510	−	0.193771i	−0.545415	−	0.00947765i
$419$			8.75167i			0.427547i	0.976883	+	0.213774i	$0.0685755\pi$
$419$			8.75167i			0.427547i	−0.976883	+	0.213774i	$0.931425\pi$
$420$	−2.92698	−	2.17842i	−0.142822	−	0.106296i
$421$	8.76572	+	10.4466i	0.427215	+	0.509135i	0.936117	−	0.351690i	$-0.114393\pi$
$421$	8.76572	+	10.4466i	0.427215	+	0.509135i	−0.508902	+	0.860825i	$0.669948\pi$
$422$	2.21619	−	38.0964i	0.107883	−	1.85450i
$423$	2.37847	−	6.53480i	0.115645	−	0.317733i
$424$	10.3888	−	28.5616i	0.504525	−	1.38707i
$425$	−8.58184	+	14.8642i	−0.416280	+	0.721019i
$426$	0.942444	−	0.110223i	0.0456616	−	0.00534030i
$427$	13.8333	+	2.43918i	0.669440	+	0.118040i
$428$	−8.46843	+	5.57147i	−0.409337	+	0.269307i
$429$	−5.25781	−	9.10679i	−0.253849	−	0.439680i
$430$	11.3415	−	8.44465i	0.546935	−	0.407237i
$431$	−2.79520	−	2.34545i	−0.134640	−	0.112977i	0.572981	−	0.819569i	$-0.305787\pi$
$431$	−2.79520	−	2.34545i	−0.134640	−	0.112977i	−0.707621	+	0.706592i	$0.750231\pi$
$432$	−1.58329	+	3.67331i	−0.0761762	+	0.176732i
$433$	4.79840	+	13.1835i	0.230596	+	0.633558i	0.999986	−	0.00522103i	$-0.00166191\pi$
$433$	4.79840	+	13.1835i	0.230596	+	0.633558i	−0.769390	+	0.638779i	$0.779440\pi$
$434$	−1.66511	+	0.498628i	−0.0799278	+	0.0239349i
$435$	0.787341	−	0.138829i	0.0377501	−	0.00665636i
$436$	−3.33051	+	3.14305i	−0.159502	+	0.150525i
$437$	1.07918	+	26.4796i	0.0516241	+	1.26669i
$438$	−2.18994	+	5.07782i	−0.104639	+	0.242628i
$439$	−0.314211	−	1.78198i	−0.0149965	−	0.0850492i	0.976391	−	0.216011i	$-0.0693046\pi$
$439$	−0.314211	−	1.78198i	−0.0149965	−	0.0850492i	−0.991387	+	0.130962i	$0.958194\pi$
$440$	−5.92344	−	3.41824i	−0.282389	−	0.162958i
$441$	−4.82688	+	1.75684i	−0.229851	+	0.0836591i
$442$	31.9323	+	30.1223i	1.51886	+	1.43277i
$443$	−7.88486	+	9.39682i	−0.374621	+	0.446456i	−0.920109	−	0.391663i	$-0.871900\pi$
$443$	−7.88486	+	9.39682i	−0.374621	+	0.446456i	0.545488	+	0.838119i	$0.316344\pi$
$444$	−3.64362	−	15.3641i	−0.172919	−	0.729147i
$445$	−4.85575	+	2.80347i	−0.230185	+	0.132897i
$446$	−0.0435463	−	0.0286365i	−0.00206198	−	0.00135598i
$447$	−2.23028	+	12.6485i	−0.105489	+	0.598256i
$448$	3.73068	−	10.2633i	0.176258	−	0.484897i
$449$	5.13353	+	2.96384i	0.242266	+	0.139872i	0.616218	−	0.787576i	$-0.288664\pi$
$449$	5.13353	+	2.96384i	0.242266	+	0.139872i	−0.373952	+	0.927448i	$0.621997\pi$
$450$	4.06150	−	2.04012i	0.191461	−	0.0961721i
$451$	1.18938	+	0.432900i	0.0560058	+	0.0203844i
$452$	10.3834	−	20.6822i	0.488393	−	0.972809i
$453$	−9.79214	+	8.21658i	−0.460075	+	0.386049i
$454$	18.2838	+	4.33200i	0.858102	+	0.203311i
$455$	10.6035			0.497099
$456$	−11.7482	−	3.73898i	−0.550160	−	0.175094i
$457$	−19.0703			−0.892069			−0.446034	−	0.895016i	$-0.647164\pi$
$457$	−19.0703			−0.892069			−0.446034	+	0.895016i	$0.647164\pi$
$458$	−39.6713	−	9.39935i	−1.85372	−	0.439203i
$459$	4.09107	−	3.43281i	0.190955	−	0.160230i
$460$	−7.29143	+	14.5235i	−0.339965	+	0.677161i
$461$	19.6569	+	7.15452i	0.915512	+	0.333219i	0.756451	−	0.654050i	$-0.226931\pi$
$461$	19.6569	+	7.15452i	0.915512	+	0.333219i	0.159060	+	0.987269i	$0.449154\pi$
$462$	3.12100	−	1.56770i	0.145202	−	0.0729359i
$463$	−8.52005	−	4.91905i	−0.395960	−	0.228608i	0.288779	−	0.957396i	$-0.406751\pi$
$463$	−8.52005	−	4.91905i	−0.395960	−	0.228608i	−0.684740	+	0.728788i	$0.740084\pi$
$464$	1.07450	+	2.13802i	0.0498826	+	0.0992552i
$465$	−0.208957	+	1.18505i	−0.00969016	+	0.0549556i
$466$	17.9971	+	11.8350i	0.833698	+	0.548248i
$467$	−3.88633	+	2.24377i	−0.179838	+	0.103829i	−0.587216	−	0.809430i	$-0.699776\pi$
$467$	−3.88633	+	2.24377i	−0.179838	+	0.103829i	0.407379	+	0.913259i	$0.366443\pi$
$468$	−2.68238	−	11.3108i	−0.123993	−	0.522843i
$469$	−0.747277	+	0.890570i	−0.0345060	+	0.0411227i
$470$	9.56102	+	9.01910i	0.441017	+	0.416020i
$471$	13.2613	−	4.82672i	0.611049	−	0.222404i
$472$	11.2580	−	19.5089i	0.518193	−	0.897971i
$473$	2.35038	+	13.3297i	0.108071	+	0.612899i
$474$	2.07490	−	4.81108i	0.0953033	−	0.220980i
$475$	7.49269	+	11.8368i	0.343788	+	0.543109i
$476$	−10.6037	+	10.0069i	−0.486022	+	0.458666i
$477$	10.5821	−	1.86590i	0.484519	−	0.0854338i
$478$	−29.4880	+	8.83038i	−1.34875	+	0.403892i
$479$	7.66192	+	21.0509i	0.350082	+	0.961842i	0.982343	+	0.187087i	$0.0599047\pi$
$479$	7.66192	+	21.0509i	0.350082	+	0.961842i	−0.632261	+	0.774755i	$0.717873\pi$
$480$	−5.19003	−	5.49726i	−0.236891	−	0.250914i
$481$	35.1526	+	29.4966i	1.60282	+	1.34493i
$482$	−8.30618	+	6.18463i	−0.378336	+	0.281702i
$483$	−4.14964	−	7.18739i	−0.188815	−	0.327038i
$484$	−12.9100	+	8.49365i	−0.586820	+	0.386075i
$485$	−10.0658	−	1.77487i	−0.457063	−	0.0805925i
$486$	−1.40464	+	0.164278i	−0.0637158	+	0.00745181i
$487$	16.6226	−	28.7912i	0.753242	−	1.30465i	−0.193001	−	0.981199i	$-0.561822\pi$
$487$	16.6226	−	28.7912i	0.753242	−	1.30465i	0.946243	−	0.323455i	$-0.104845\pi$
$488$	27.3522	+	9.94889i	1.23817	+	0.450365i
$489$	6.09772	−	16.7533i	0.275748	−	0.757612i
$490$	0.563823	−	9.69212i	0.0254709	−	0.437846i
$491$	−16.0502	−	19.1279i	−0.724335	−	0.863228i	0.270710	−	0.962661i	$-0.412742\pi$
$491$	−16.0502	−	19.1279i	−0.724335	−	0.863228i	−0.995044	+	0.0994326i	$0.968297\pi$
$492$	1.12244	+	0.835382i	0.0506035	+	0.0376619i
$493$		−	3.19475i		−	0.143884i
$494$	33.8763	−	11.6675i	1.52417	−	0.524946i
$495$		−	2.41794i		−	0.108678i
$496$	−3.57709	+	0.419114i	−0.160616	+	0.0188188i
$497$	−0.588714	−	0.701602i	−0.0264074	−	0.0314711i
$498$	−13.6121	−	0.791859i	−0.609971	−	0.0354841i
$499$	−1.81073	+	4.97495i	−0.0810595	+	0.222709i	−0.973601	−	0.228256i	$-0.926698\pi$
$499$	−1.81073	+	4.97495i	−0.0810595	+	0.222709i	0.892542	+	0.450965i	$0.148920\pi$
$500$	1.27963	+	21.9177i	0.0572270	+	0.980191i
$501$	−5.17647	+	8.96590i	−0.231267	+	0.400567i
$502$	4.98446	+	42.6189i	0.222467	+	1.90218i
$503$	36.9767	+	6.52000i	1.64871	+	0.290712i	0.919357	−	0.393424i	$-0.128710\pi$
$503$	36.9767	+	6.52000i	1.64871	+	0.290712i	0.729354	+	0.684136i	$0.239821\pi$
$504$	3.80213	−	0.671239i	0.169360	−	0.0298993i
$505$	−0.351558	−	0.608916i	−0.0156441	−	0.0270964i
$506$	−9.29028	−	12.4772i	−0.413003	−	0.554679i
$507$	15.9203	+	13.3587i	0.707046	+	0.593282i
$508$	−8.12697	−	18.8332i	−0.360576	−	0.835589i
$509$	−5.95327	−	16.3565i	−0.263874	−	0.724988i	−0.998897	−	0.0469459i	$-0.985051\pi$
$509$	−5.95327	−	16.3565i	−0.263874	−	0.724988i	0.735024	−	0.678042i	$-0.237171\pi$
$510$	2.89561	+	9.66954i	0.128220	+	0.428175i
$511$	5.25657	−	0.926874i	0.232537	−	0.0410025i
$512$	11.3014	−	19.6030i	0.499456	−	0.866339i
$513$	−0.931091	−	4.25829i	−0.0411087	−	0.188008i
$514$	−18.2529	−	7.87200i	−0.805099	−	0.347219i
$515$	3.85736	+	21.8762i	0.169976	+	0.963981i
$516$	−1.73499	+	14.8618i	−0.0763785	+	0.654252i
$517$	−11.8228	+	4.30315i	−0.519967	+	0.189252i
$518$	−10.4584	+	11.0868i	−0.459515	+	0.487125i
$519$	−9.40088	+	11.2035i	−0.412653	+	0.491780i
$520$	21.6379	+	3.81067i	0.948885	+	0.167109i
$521$	−20.0104	+	11.5530i	−0.876671	+	0.506146i	−0.869559	−	0.493828i	$-0.835597\pi$
$521$	−20.0104	+	11.5530i	−0.876671	+	0.506146i	−0.00711171	+	0.999975i	$0.502264\pi$
$522$	−0.464834	+	0.706853i	−0.0203452	+	0.0309381i
$523$	−3.96812	+	22.5043i	−0.173514	+	0.984046i	0.766331	+	0.642446i	$0.222080\pi$
$523$	−3.96812	+	22.5043i	−0.173514	+	0.984046i	−0.939845	+	0.341601i	$0.889031\pi$
$524$	32.7157	+	9.78945i	1.42919	+	0.427654i
$525$	−3.79931	−	2.19353i	−0.165815	−	0.0957336i
$526$	10.7772	+	21.4554i	0.469907	+	0.935499i
$527$	4.51854	+	1.64462i	0.196831	+	0.0716406i
$528$	6.93223	−	2.07748i	0.301687	−	0.0904109i
$529$	−10.6977	+	8.97645i	−0.465118	+	0.390281i
$530$	−4.68222	+	19.7620i	−0.203383	+	0.858406i
$531$	7.96352			0.345587
$532$	3.21522	+	11.4576i	0.139397	+	0.496749i
$533$	−4.06624			−0.176128
$534$	1.36787	−	5.77330i	0.0591936	−	0.249835i
$535$	5.18900	−	4.35408i	0.224340	−	0.188243i
$536$	−1.84498	+	1.54878i	−0.0796908	+	0.0668970i
$537$	22.0055	+	8.00936i	0.949609	+	0.345629i
$538$	2.90236	+	5.77807i	0.125130	+	0.249110i
$539$	8.04822	+	4.64664i	0.346662	+	0.200145i
$540$	0.766246	−	2.56074i	0.0329740	−	0.110197i
$541$	4.71561	−	26.7436i	0.202740	−	1.14980i	−0.698217	−	0.715886i	$-0.746023\pi$
$541$	4.71561	−	26.7436i	0.202740	−	1.14980i	0.900957	−	0.433909i	$-0.142866\pi$
$542$	16.5308	−	25.1377i	0.710059	−	1.07976i
$543$	−10.3570	+	5.97963i	−0.444462	+	0.256610i
$544$	−25.2347	+	16.6097i	−1.08193	+	0.712137i
$545$	1.96700	−	2.34418i	0.0842571	−	0.100414i
$546$	−7.69931	+	8.16194i	−0.329500	+	0.349299i
$547$	20.4989	−	7.46099i	0.876469	−	0.319009i	0.135685	−	0.990752i	$-0.456676\pi$
$547$	20.4989	−	7.46099i	0.876469	−	0.319009i	0.740784	+	0.671743i	$0.234454\pi$
$548$	−2.97028	−	0.346755i	−0.126884	−	0.0148126i
$549$	1.78689	+	10.1340i	0.0762627	+	0.432507i
$550$	−7.55074	−	3.25645i	−0.321965	−	0.138855i
$551$	−2.30941	−	1.21073i	−0.0983844	−	0.0515789i
$552$	−5.88493	−	16.1582i	−0.250479	−	0.687738i
$553$	−4.98044	+	0.878185i	−0.211790	+	0.0373442i
$554$	1.85642	+	6.19931i	0.0788719	+	0.263383i
$555$	3.60883	+	9.91518i	0.153186	+	0.420876i
$556$	34.2684	−	14.7876i	1.45330	−	0.627135i
$557$	−25.3187	−	21.2449i	−1.07279	−	0.900176i	−0.0774855	−	0.996993i	$-0.524689\pi$
$557$	−25.3187	−	21.2449i	−1.07279	−	0.900176i	−0.995302	+	0.0968178i	$0.969134\pi$
$558$	−0.760459	−	1.02132i	−0.0321928	−	0.0432361i
$559$	−21.7418	−	37.6579i	−0.919580	−	1.59276i
$560$	−1.68089	+	7.10108i	−0.0710307	+	0.300076i
$561$	−9.51530	−	1.67780i	−0.401736	−	0.0708370i
$562$	3.08529	+	26.3804i	0.130145	+	1.11279i
$563$	−6.93499	+	12.0118i	−0.292275	+	0.506235i	−0.974347	−	0.225049i	$-0.927746\pi$
$563$	−6.93499	+	12.0118i	−0.292275	+	0.506235i	0.682072	+	0.731285i	$0.261079\pi$
$564$	−13.8847	+	0.810639i	−0.584653	+	0.0341340i
$565$	−5.28915	+	14.5318i	−0.222516	+	0.611359i
$566$	−35.7271	−	2.07836i	−1.50172	−	0.0873602i
$567$	0.877432	+	1.04568i	0.0368487	+	0.0439146i
$568$	−0.949212	−	1.64329i	−0.0398280	−	0.0689508i
$569$			3.92803i			0.164672i	0.996605	+	0.0823358i	$0.0262380\pi$
$569$			3.92803i			0.164672i	−0.996605	+	0.0823358i	$0.973762\pi$
$570$	8.08727	+	1.57135i	0.338738	+	0.0658166i
$571$		−	10.5601i		−	0.441928i	−0.975282	−	0.220964i	$-0.929080\pi$
$571$		−	10.5601i		−	0.441928i	0.975282	−	0.220964i	$-0.0709203\pi$
$572$	−12.5566	+	16.8714i	−0.525019	+	0.705428i
$573$	−15.4900	−	18.4602i	−0.647103	−	0.771187i
$574$	0.0784329	−	1.34826i	0.00327373	−	0.0562754i
$575$	−6.68304	+	18.3615i	−0.278702	+	0.765728i
$576$	8.00000	−	0.00335137i	0.333333	−	0.000139641i
$577$	8.16413	−	14.1407i	0.339877	−	0.588685i	−0.644532	−	0.764577i	$-0.722948\pi$
$577$	8.16413	−	14.1407i	0.339877	−	0.588685i	0.984409	+	0.175893i	$0.0562811\pi$
$578$	16.1829	−	1.89265i	0.673119	−	0.0787239i
$579$	0.218121	+	0.0384607i	0.00906481	+	0.00159837i
$580$	−0.878837	−	1.33580i	−0.0364917	−	0.0554661i
$581$	6.58050	+	11.3978i	0.273005	+	0.472859i
$582$	8.67505	−	6.45928i	0.359592	−	0.267746i
$583$	−14.8923	−	12.4961i	−0.616776	−	0.517536i
$584$	11.0599	−	0.00231661i	0.457660	−	9.58619e-5i
$585$	2.65677	+	7.29942i	0.109844	+	0.301794i
$586$	−0.838194	+	0.251003i	−0.0346255	+	0.0103688i
$587$	−29.6611	+	5.23004i	−1.22424	+	0.215867i	−0.748151	−	0.663529i	$-0.769058\pi$
$587$	−29.6611	+	5.23004i	−1.22424	+	0.215867i	−0.476092	+	0.879396i	$0.657947\pi$
$588$	7.05102	+	7.47156i	0.290779	+	0.308122i
$589$	2.90127	−	2.64309i	0.119545	−	0.108907i
$590$	−5.96059	+	13.8209i	−0.245394	+	0.568996i
$591$	−3.68251	−	20.8846i	−0.151478	−	0.859076i
$592$	−25.3261	+	18.8656i	−1.04090	+	0.775371i
$593$	40.3277	−	14.6781i	1.65606	−	0.602756i	0.666323	−	0.745663i	$-0.267867\pi$
$593$	40.3277	−	14.6781i	1.65606	−	0.602756i	0.989736	+	0.142907i	$0.0456449\pi$
$594$	1.86119	+	1.75569i	0.0763654	+	0.0720370i
$595$	6.26258	−	7.46345i	0.256741	−	0.305972i
$596$	24.9941	−	5.92740i	1.02380	−	0.242796i
$597$	−8.76520	+	5.06059i	−0.358736	+	0.207116i
$598$	41.7557	+	27.4590i	1.70752	+	1.12288i
$599$	3.44329	−	19.5279i	0.140689	−	0.797887i	−0.830039	−	0.557705i	$-0.811682\pi$
$599$	3.44329	−	19.5279i	0.140689	−	0.797887i	0.970728	−	0.240182i	$-0.0772070\pi$
$600$	−6.96471	−	5.84160i	−0.284333	−	0.238482i
$601$	23.4312	+	13.5280i	0.955778	+	0.551819i	0.894871	−	0.446325i	$-0.147267\pi$
$601$	23.4312	+	13.5280i	0.955778	+	0.551819i	0.0609068	+	0.998143i	$0.480601\pi$
$602$	12.9058	−	6.48266i	0.526001	−	0.264213i
$603$	−0.800302	−	0.291286i	−0.0325908	−	0.0118621i
$604$	22.8477	+	11.4706i	0.929661	+	0.466731i
$605$	7.91058	−	6.63777i	0.321611	−	0.269864i
$606$	0.723978	+	0.171532i	0.0294096	+	0.00696803i
$607$	−5.36045			−0.217574			−0.108787	−	0.994065i	$-0.534697\pi$
$607$	−5.36045			−0.217574			−0.108787	+	0.994065i	$0.534697\pi$
$608$	2.44349	+	24.5363i	0.0990964	+	0.995078i
$609$	0.816583			0.0330896
$610$	−18.9252	−	4.48395i	−0.766258	−	0.181550i
$611$	30.9632	−	25.9812i	1.25264	−	1.05109i
$612$	−9.54557	−	4.79230i	−0.385857	−	0.193717i
$613$	−13.2066	−	4.80681i	−0.533410	−	0.194145i	0.0612502	−	0.998122i	$-0.480491\pi$
$613$	−13.2066	−	4.80681i	−0.533410	−	0.194145i	−0.594660	+	0.803977i	$0.702713\pi$
$614$	−24.3677	+	12.2400i	−0.983399	+	0.493967i
$615$	−0.809719	−	0.467491i	−0.0326510	−	0.0188511i
$616$	−5.35193	−	4.48889i	−0.215635	−	0.180863i
$617$	4.11256	−	23.3235i	0.165565	−	0.938967i	−0.782914	−	0.622129i	$-0.786268\pi$
$617$	4.11256	−	23.3235i	0.165565	−	0.938967i	0.948480	−	0.316838i	$-0.102621\pi$
$618$	−19.6399	−	12.9154i	−0.790032	−	0.519533i
$619$	−17.2160	+	9.93966i	−0.691969	+	0.399509i	−0.804349	−	0.594157i	$-0.797486\pi$
$619$	−17.2160	+	9.93966i	−0.691969	+	0.399509i	0.112380	+	0.993665i	$0.464153\pi$
$620$	2.34172	−	0.555344i	0.0940459	−	0.0223031i
$621$	3.90807	−	4.65745i	0.156825	−	0.186897i
$622$	−8.87719	−	8.37403i	−0.355943	−	0.335768i
$623$	−5.38147	+	1.95869i	−0.215604	+	0.0784734i
$624$	−18.6448	+	13.8886i	−0.746388	+	0.555989i
$625$	0.242809	+	1.37704i	0.00971235	+	0.0550815i
$626$	−18.8471	+	43.7009i	−0.753282	+	1.74664i
$627$	−4.81892	+	6.24256i	−0.192449	+	0.249304i
$628$	−19.3719	−	20.5273i	−0.773022	−	0.819127i
$629$	41.5233	−	7.32168i	1.65564	−	0.291935i
$630$	−2.47155	+	0.740122i	−0.0984690	+	0.0294872i
$631$	−0.440226	−	1.20951i	−0.0175251	−	0.0481499i	0.930622	−	0.365983i	$-0.119267\pi$
$631$	−0.440226	−	1.20951i	−0.0175251	−	0.0481499i	−0.948147	+	0.317833i	$0.897045\pi$
$632$	−10.4789	+	0.00219491i	−0.416827	+	8.73090e-5i
$633$	−20.6708	−	17.3448i	−0.821589	−	0.689395i
$634$	27.1020	−	20.1796i	1.07636	−	0.801435i
$635$	6.85334	+	11.8703i	0.271967	+	0.471060i
$636$	−11.8118	−	17.9535i	−0.468368	−	0.711903i
$637$	−29.4021	−	5.18438i	−1.16495	−	0.205413i
$638$	1.52023	−	0.177796i	0.0601863	−	0.00703903i
$639$	0.335475	−	0.581060i	0.0132712	−	0.0229864i
$640$	−5.98208	+	13.8867i	−0.236462	+	0.548919i
$641$	1.62727	−	4.47089i	0.0642733	−	0.176590i	−0.903399	−	0.428802i	$-0.858936\pi$
$641$	1.62727	−	4.47089i	0.0642733	−	0.176590i	0.967672	+	0.252212i	$0.0811581\pi$
$642$	−0.416272	+	7.15573i	−0.0164290	+	0.282414i
$643$	−13.4534	−	16.0331i	−0.530550	−	0.632285i	0.432492	−	0.901638i	$-0.357635\pi$
$643$	−13.4534	−	16.0331i	−0.530550	−	0.632285i	−0.963041	+	0.269353i	$0.913190\pi$
$644$	−9.91012	+	13.3155i	−0.390514	+	0.524704i
$645$		−	9.99854i		−	0.393692i
$646$	11.7955	−	30.7354i	0.464086	−	1.20927i
$647$			33.1116i			1.30175i	0.759184	+	0.650875i	$0.225598\pi$
$647$			33.1116i			1.30175i	−0.759184	+	0.650875i	$0.774402\pi$
$648$	1.41473	+	2.44919i	0.0555757	+	0.0962134i
$649$	−9.26107	−	11.0369i	−0.363529	−	0.433237i
$650$	26.3727	+	1.53419i	1.03442	+	0.0601759i
$651$	−0.420366	+	1.15495i	−0.0164755	+	0.0452659i
$652$	−35.5964	+	2.07824i	−1.39406	+	0.0813903i
$653$	8.60908	−	14.9114i	0.336899	−	0.583527i	−0.646949	−	0.762534i	$-0.723955\pi$
$653$	8.60908	−	14.9114i	0.336899	−	0.583527i	0.983848	+	0.179007i	$0.0572885\pi$
$654$	0.376149	+	3.21622i	0.0147086	+	0.125764i
$655$	−22.4727	−	3.96254i	−0.878081	−	0.154829i
$656$	0.644591	−	2.72313i	0.0251670	−	0.106320i
$657$	1.95513	+	3.38638i	0.0762767	+	0.132115i
$658$	8.01748	+	10.7678i	0.312554	+	0.419772i
$659$	0.609150	+	0.511137i	0.0237291	+	0.0199111i	0.654575	−	0.755997i	$-0.272848\pi$
$659$	0.609150	+	0.511137i	0.0237291	+	0.0199111i	−0.630846	+	0.775908i	$0.717292\pi$
$660$	−4.44012	+	1.91601i	−0.172831	+	0.0745808i
$661$	−15.1036	−	41.4969i	−0.587463	−	1.61404i	−0.775125	−	0.631808i	$-0.782313\pi$
$661$	−15.1036	−	41.4969i	−0.587463	−	1.61404i	0.187662	−	0.982234i	$-0.439909\pi$
$662$	−9.07717	−	30.3122i	−0.352794	−	1.17812i
$663$	30.5689	−	5.39012i	1.18720	−	0.209335i
$664$	9.33231	+	25.6236i	0.362164	+	0.994389i
$665$	−3.02180	−	7.35554i	−0.117180	−	0.285236i
$666$	−10.2525	−	4.42166i	−0.397278	−	0.171336i
$667$	−0.631567	−	3.58179i	−0.0244544	−	0.138688i
$668$	20.5662	+	2.40093i	0.795730	+	0.0928949i
$669$	−0.0346307	+	0.0126046i	−0.00133890	+	0.000487320i
$670$	1.10455	−	1.17092i	0.0426724	−	0.0452365i
$671$	11.9670	−	14.2617i	0.461980	−	0.550566i
$672$	−4.24548	−	6.45003i	−0.163773	−	0.248815i
$673$	12.4476	−	7.18661i	0.479819	−	0.277024i	−0.240522	−	0.970644i	$-0.577319\pi$
$673$	12.4476	−	7.18661i	0.479819	−	0.277024i	0.720341	+	0.693620i	$0.243985\pi$
$674$	17.4468	−	26.5306i	0.672025	−	1.02192i
$675$	0.558082	−	3.16504i	0.0214806	−	0.121823i
$676$	11.9154	−	39.8205i	0.458285	−	1.53156i
$677$	−15.3724	−	8.87525i	−0.590809	−	0.341104i	0.174609	−	0.984638i	$-0.444134\pi$
$677$	−15.3724	−	8.87525i	−0.590809	−	0.341104i	−0.765417	+	0.643534i	$0.777467\pi$
$678$	−7.34522	−	14.6230i	−0.282092	−	0.561593i
$679$	−9.81003	−	3.57056i	−0.376474	−	0.137025i
$680$	15.4619	−	12.9796i	0.592936	−	0.497744i
$681$	10.1781	−	8.54042i	0.390025	−	0.327270i
$682$	−0.531123	+	2.24168i	−0.0203377	+	0.0858384i
$683$	−16.5441			−0.633042			−0.316521	−	0.948585i	$-0.602515\pi$
$683$	−16.5441			−0.633042			−0.316521	+	0.948585i	$0.602515\pi$
$684$	−7.08179	+	5.08412i	−0.270779	+	0.194396i
$685$	1.99831			0.0763515
$686$	5.40159	−	22.7982i	0.206234	−	0.870439i
$687$	−22.0839	+	18.5306i	−0.842553	+	0.706986i
$688$	28.6658	−	8.59070i	1.09287	−	0.327517i
$689$	58.6882	+	21.3608i	2.23584	+	0.813780i
$690$	5.15797	+	10.2686i	0.196361	+	0.390918i
$691$	−19.6705	−	11.3568i	−0.748302	−	0.432032i	0.0767783	−	0.997048i	$-0.475537\pi$
$691$	−19.6705	−	11.3568i	−0.748302	−	0.432032i	−0.825080	+	0.565016i	$0.808870\pi$
$692$	28.0227	+	8.38518i	1.06526	+	0.318757i
$693$	0.428850	−	2.43213i	0.0162907	−	0.0923889i
$694$	−15.3071	+	23.2768i	−0.581048	+	0.883575i
$695$	−21.5989	+	12.4702i	−0.819295	+	0.473020i
$696$	1.66635	+	0.293463i	0.0631629	+	0.0111237i
$697$	−2.40158	+	2.86209i	−0.0909663	+	0.108409i
$698$	−21.3657	+	22.6495i	−0.808703	+	0.857295i
$699$	14.3124	−	5.20928i	0.541344	−	0.197033i
$700$	−1.01740	+	8.71494i	−0.0384540	+	0.329394i
$701$	−5.86111	−	33.2400i	−0.221371	−	1.25546i	−0.869503	−	0.493928i	$-0.835560\pi$
$701$	−5.86111	−	33.2400i	−0.221371	−	1.25546i	0.648132	−	0.761528i	$-0.275551\pi$
$702$	−7.54777	−	3.25517i	−0.284872	−	0.122858i
$703$	10.4436	−	32.7910i	0.393889	−	1.23674i
$704$	−9.30814	−	11.0836i	−0.350814	−	0.417728i
$705$	9.15281	−	1.61389i	0.344715	−	0.0607825i
$706$	−8.31349	−	27.7619i	−0.312882	−	1.04483i
$707$	−0.245622	−	0.674842i	−0.00923758	−	0.0253800i
$708$	−6.31042	−	14.6236i	−0.237160	−	0.549588i
$709$	−2.99281	−	2.51127i	−0.112397	−	0.0943126i	0.584857	−	0.811137i	$-0.301151\pi$
$709$	−2.99281	−	2.51127i	−0.112397	−	0.0943126i	−0.697254	+	0.716824i	$0.745595\pi$
$710$	0.757343	+	1.01714i	0.0284226	+	0.0381726i
$711$	−1.85242	−	3.20849i	−0.0694712	−	0.120328i
$712$	−11.6856	+	2.06300i	−0.437935	+	0.0773143i
$713$	5.39109	+	0.950594i	0.201898	+	0.0356000i
$714$	1.19759	+	10.2398i	0.0448187	+	0.383217i
$715$	7.02686	−	12.1709i	0.262790	−	0.455165i
$716$	−2.72978	−	46.7560i	−0.102017	−	1.74735i
$717$	−7.44442	+	20.4534i	−0.278017	+	0.763845i
$718$	−15.9375	−	0.927140i	−0.594784	−	0.0346005i
$719$	−10.7238	−	12.7801i	−0.399930	−	0.476619i	0.528068	−	0.849202i	$-0.322917\pi$
$719$	−10.7238	−	12.7801i	−0.399930	−	0.476619i	−0.927999	+	0.372583i	$0.878472\pi$
$720$	−5.30953	+	0.622098i	−0.197875	+	0.0231842i
$721$			22.6887i			0.844972i
$722$	−17.7478	−	20.1747i	−0.660503	−	0.750823i
$723$			7.32264i			0.272332i
$724$	19.1876	+	14.2805i	0.713101	+	0.530729i
$725$	−1.23580	−	1.47277i	−0.0458966	−	0.0546975i
$726$	−0.634604	+	10.9089i	−0.0235524	+	0.404865i
$727$	−5.04395	+	13.8581i	−0.187070	+	0.513970i	−0.997405	−	0.0719967i	$-0.977063\pi$
$727$	−5.04395	+	13.8581i	−0.187070	+	0.513970i	0.810335	+	0.585967i	$0.199285\pi$
$728$	21.0890	+	7.67077i	0.781610	+	0.284298i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−7.34051	+	0.858502i	−0.271685	+	0.0317746i
$731$	−39.3472	−	6.93797i	−1.45531	−	0.256610i
$732$	17.1933	−	11.3116i	0.635481	−	0.418090i
$733$	−21.8482	−	37.8423i	−0.806983	−	1.39774i	−0.914944	−	0.403581i	$-0.867765\pi$
$733$	−21.8482	−	37.8423i	−0.806983	−	1.39774i	0.107961	−	0.994155i	$-0.465568\pi$
$734$	−8.70935	+	6.48482i	−0.321468	+	0.239359i
$735$	−5.25886	−	4.41271i	−0.193976	−	0.162765i
$736$	−25.0083	+	23.6106i	−0.921818	+	0.870299i
$737$	0.526997	+	1.44791i	0.0194122	+	0.0533346i
$738$	0.947793	−	0.283823i	0.0348887	−	0.0104477i
$739$	−40.8384	+	7.20091i	−1.50227	+	0.264890i	−0.863436	−	0.504458i	$-0.831692\pi$
$739$	−40.8384	+	7.20091i	−1.50227	+	0.264890i	−0.638829	+	0.769348i	$0.720581\pi$
$740$	15.3478	−	14.4839i	0.564195	−	0.532440i
$741$	7.68847	−	24.1403i	0.282443	−	0.886817i
$742$	−8.21471	+	19.0475i	−0.301572	+	0.699256i
$743$	8.77287	+	49.7534i	0.321845	+	1.82528i	0.530975	+	0.847387i	$0.321826\pi$
$743$	8.77287	+	49.7534i	0.321845	+	1.82528i	−0.209130	+	0.977888i	$0.567063\pi$
$744$	−1.27288	+	2.20576i	−0.0466661	+	0.0808671i
$745$	−16.1299	+	5.87080i	−0.590954	+	0.215090i
$746$	−12.6113	−	11.8965i	−0.461732	−	0.435561i
$747$	−6.19741	+	7.38579i	−0.226751	+	0.270232i
$748$	4.45909	+	18.8027i	0.163040	+	0.687494i
$749$	5.99169	−	3.45930i	0.218932	−	0.126400i
$750$	12.9712	+	8.52998i	0.473641	+	0.311471i
$751$	3.78440	−	21.4624i	0.138095	−	0.783174i	−0.834560	−	0.550917i	$-0.814278\pi$
$751$	3.78440	−	21.4624i	0.138095	−	0.783174i	0.972655	−	0.232256i	$-0.0746109\pi$
$752$	12.4911	+	24.8545i	0.455503	+	0.906349i
$753$	26.2765	+	15.1708i	0.957571	+	0.552854i
$754$	−4.39399	+	2.20713i	−0.160020	+	0.0803789i
$755$	−16.0534	−	5.84295i	−0.584242	−	0.212647i
$756$	1.22492	−	2.43986i	0.0445499	−	0.0887370i
$757$	0.0722766	−	0.0606473i	0.00262694	−	0.00220426i	−0.641473	−	0.767145i	$-0.721676\pi$
$757$	0.0722766	−	0.0606473i	0.00262694	−	0.00220426i	0.644100	+	0.764941i	$0.277232\pi$
$758$	11.8969	+	2.81873i	0.432113	+	0.102381i
$759$	−10.9998			−0.399266
$760$	−3.52298	−	16.0960i	−0.127792	−	0.583863i
$761$	−3.56523			−0.129240			−0.0646198	−	0.997910i	$-0.520583\pi$
$761$	−3.56523			−0.129240			−0.0646198	+	0.997910i	$0.520583\pi$
$762$	−14.1134	−	3.34389i	−0.511273	−	0.121136i
$763$	2.39431	−	2.00906i	0.0866798	−	0.0727330i
$764$	−21.6244	+	43.0727i	−0.782344	+	1.55832i
$765$	6.70695	+	2.44113i	0.242490	+	0.0882593i
$766$	−23.8454	+	11.9777i	−0.861568	+	0.432771i
$767$	40.0850	+	23.1431i	1.44738	+	0.835648i
$768$	−6.34548	−	14.6879i	−0.228973	−	0.530005i
$769$	3.64181	−	20.6537i	0.131327	−	0.744793i	−0.846020	−	0.533151i	$-0.821008\pi$
$769$	3.64181	−	20.6537i	0.131327	−	0.744793i	0.977347	−	0.211642i	$-0.0678811\pi$
$770$	3.90002	+	2.56469i	0.140547	+	0.0924251i
$771$	−12.1727	+	7.02793i	−0.438391	+	0.253105i
$772$	−0.102217	−	0.431018i	−0.00367886	−	0.0155127i
$773$	14.7529	−	17.5818i	0.530625	−	0.632375i	−0.432433	−	0.901666i	$-0.642345\pi$
$773$	14.7529	−	17.5818i	0.530625	−	0.632375i	0.963059	+	0.269291i	$0.0867894\pi$
$774$	7.69628	+	7.26005i	0.276637	+	0.260957i
$775$	2.71922	−	0.989714i	0.0976772	−	0.0355516i
$776$	−18.7356	−	10.8117i	−0.672567	−	0.388119i
$777$	1.87143	+	10.6134i	0.0671373	+	0.380755i
$778$	−1.50654	+	3.49322i	−0.0540120	+	0.125238i
$779$	1.15880	+	2.82071i	0.0415184	+	0.101062i
$780$	11.2988	−	10.6629i	0.404563	−	0.381792i
$781$	−1.19545	+	0.210790i	−0.0427765	+	0.00754265i
$782$	43.9890	−	13.1728i	1.57304	−	0.471058i
$783$	0.204600	+	0.562134i	0.00731181	+	0.0200890i
$784$	8.13284	−	18.8685i	0.290458	−	0.673876i
$785$	14.4481	+	12.1234i	0.515676	+	0.432703i
$786$	19.3678	−	14.4209i	0.690827	−	0.514376i
$787$	−19.7759	−	34.2528i	−0.704933	−	1.22098i	−0.966716	−	0.255853i	$-0.917644\pi$
$787$	−19.7759	−	34.2528i	−0.704933	−	1.22098i	0.261782	−	0.965127i	$-0.415690\pi$
$788$	−35.4327	+	23.3115i	−1.26224	+	0.830439i
$789$	16.7197	+	2.94814i	0.595237	+	0.104956i
$790$	6.95491	−	0.813405i	0.247445	−	0.0289396i
$791$	−7.89757	+	13.6790i	−0.280805	+	0.486369i
$792$	1.74918	−	4.80898i	0.0621545	−	0.170880i
$793$	−20.4562	+	56.2030i	−0.726422	+	1.99583i
$794$	−0.0498949	+	0.857694i	−0.00177070	+	0.0304384i
$795$	9.23088	+	11.0009i	0.327386	+	0.390163i
$796$	16.2386	+	12.0856i	0.575560	+	0.428364i
$797$		−	13.4187i		−	0.475316i	−0.971349	−	0.237658i	$-0.923620\pi$
$797$		−	13.4187i		−	0.475316i	0.971349	−	0.237658i	$-0.0763798\pi$
$798$	7.85602	+	3.01494i	0.278100	+	0.106728i
$799$		−	37.1389i		−	1.31388i
$800$	−5.20811	+	17.4184i	−0.184135	+	0.615835i
$801$	−2.69672	−	3.21383i	−0.0952840	−	0.113555i
$802$	53.7274	+	3.12550i	1.89718	+	0.110365i
$803$	2.41961	−	6.64782i	0.0853861	−	0.234596i
$804$	0.0992771	+	1.70043i	0.00350123	+	0.0599696i
$805$	5.54584	−	9.60568i	0.195465	−	0.338556i
$806$	−0.859718	−	7.35091i	−0.0302823	−	0.258925i
$807$	4.50273	+	0.793952i	0.158504	+	0.0279484i
$808$	−0.258703	−	1.46538i	−0.00910113	−	0.0515519i
$809$	−4.70080	−	8.14202i	−0.165271	−	0.286258i	0.771480	−	0.636253i	$-0.219517\pi$
$809$	−4.70080	−	8.14202i	−0.165271	−	0.286258i	−0.936752	+	0.349995i	$0.886183\pi$
$810$	−1.12876	−	1.51597i	−0.0396606	−	0.0532657i
$811$	19.1736	+	16.0885i	0.673275	+	0.564945i	0.914033	−	0.405640i	$-0.132951\pi$
$811$	19.1736	+	16.0885i	0.673275	+	0.564945i	−0.240758	+	0.970585i	$0.577396\pi$
$812$	−0.647074	−	1.49951i	−0.0227078	−	0.0526225i
$813$	−7.27616	−	19.9911i	−0.255186	−	0.701118i
$814$	5.79492	+	19.3514i	0.203112	+	0.678268i
$815$	23.4652	−	4.13754i	0.821949	−	0.144932i
$816$	−1.23614	+	21.3262i	−0.0432734	+	0.746567i
$817$	−19.9269	+	25.8139i	−0.697155	+	0.903114i
$818$	11.7082	+	5.04944i	0.409366	+	0.176550i
$819$	1.37772	+	7.81346i	0.0481416	+	0.273024i
$820$	−0.216830	+	1.85735i	−0.00757205	+	0.0648616i
$821$	24.7423	−	9.00545i	0.863511	−	0.314292i	0.127975	−	0.991777i	$-0.459152\pi$
$821$	24.7423	−	9.00545i	0.863511	−	0.314292i	0.735537	+	0.677485i	$0.236930\pi$
$822$	−1.45100	+	1.53818i	−0.0506093	+	0.0536502i
$823$	−5.76680	+	6.87260i	−0.201018	+	0.239564i	−0.857131	−	0.515099i	$-0.827755\pi$
$823$	−5.76680	+	6.87260i	−0.201018	+	0.239564i	0.656113	+	0.754663i	$0.272200\pi$
$824$	−8.15385	+	46.2995i	−0.284053	+	1.61292i
$825$	−5.03555	+	2.90728i	−0.175315	+	0.101218i
$826$	−8.44685	+	12.8448i	−0.293904	+	0.446927i
$827$	−1.44344	+	8.18615i	−0.0501933	+	0.284660i	−0.999565	−	0.0294949i	$-0.990610\pi$
$827$	−1.44344	+	8.18615i	−0.0501933	+	0.284660i	0.949372	+	0.314155i	$0.101721\pi$
$828$	−11.6494	−	3.48583i	−0.404845	−	0.121141i
$829$	−20.1777	−	11.6496i	−0.700801	−	0.404608i	0.106845	−	0.994276i	$-0.465925\pi$
$829$	−20.1777	−	11.6496i	−0.700801	−	0.404608i	−0.807646	+	0.589668i	$0.799259\pi$
$830$	−8.17951	−	16.2839i	−0.283915	−	0.565222i
$831$	4.29994	+	1.56505i	0.149163	+	0.0542910i
$832$	40.2783	+	23.2322i	1.39640	+	0.805432i
$833$	−21.0144	+	17.6332i	−0.728106	+	0.610954i
$834$	6.08445	−	25.6803i	0.210687	−	0.889236i
$835$	−13.8363			−0.478825
$836$	15.2819	+	3.90238i	0.528537	+	0.134967i
$837$	−0.900389			−0.0311220
$838$	2.85343	−	12.0433i	0.0985701	−	0.416030i
$839$	0.765232	−	0.642106i	0.0264188	−	0.0221680i	−0.629483	−	0.777015i	$-0.716733\pi$
$839$	0.765232	−	0.642106i	0.0264188	−	0.0221680i	0.655901	+	0.754847i	$0.272289\pi$
$840$	3.31760	+	3.95208i	0.114468	+	0.136360i
$841$	−26.9148	−	9.79619i	−0.928097	−	0.337800i
$842$	−8.65660	−	17.2337i	−0.298326	−	0.593913i
$843$	16.2647	+	9.39043i	0.560186	+	0.323424i
$844$	−15.4708	+	51.7025i	−0.532529	+	1.77967i
$845$	−4.82309	+	27.3531i	−0.165919	+	0.940975i
$846$	−5.40368	+	8.21715i	−0.185782	+	0.282512i
$847$	9.13428	−	5.27368i	0.313858	−	0.181206i
$848$	−23.6085	+	35.9169i	−0.810721	+	1.23339i
$849$	−16.2661	+	19.3852i	−0.558252	+	0.665299i
$850$	16.6560	−	17.6568i	0.571296	−	0.605623i
$851$	45.1064	−	16.4174i	1.54623	−	0.562781i
$852$	−1.33285	−	0.155599i	−0.0456627	−	0.00533074i
$853$	4.28670	+	24.3111i	0.146774	+	0.832396i	0.965926	+	0.258820i	$0.0833335\pi$
$853$	4.28670	+	24.3111i	0.146774	+	0.832396i	−0.819152	+	0.573577i	$0.805555\pi$
$854$	−18.2409	−	7.86686i	−0.624192	−	0.269198i
$855$	4.30641	−	3.92318i	0.147276	−	0.134170i
$856$	13.4701	−	4.90590i	0.460398	−	0.167680i
$857$	−28.8784	+	5.09204i	−0.986467	+	0.173941i	−0.643533	−	0.765419i	$-0.722532\pi$
$857$	−28.8784	+	5.09204i	−0.986467	+	0.173941i	−0.342934	+	0.939359i	$0.611421\pi$
$858$	4.26614	+	14.2463i	0.145644	+	0.486360i
$859$	7.42637	+	20.4038i	0.253385	+	0.696168i	0.999538	+	0.0303943i	$0.00967631\pi$
$859$	7.42637	+	20.4038i	0.253385	+	0.696168i	−0.746153	+	0.665774i	$0.768101\pi$
$860$	−18.3605	+	7.92300i	−0.626089	+	0.270172i
$861$	−0.731555	−	0.613847i	−0.0249313	−	0.0209199i
$862$	3.08180	+	4.13898i	0.104967	+	0.140974i
$863$	13.3261	+	23.0815i	0.453626	+	0.785703i	0.998608	−	0.0527447i	$-0.0167969\pi$
$863$	13.3261	+	23.0815i	0.453626	+	0.785703i	−0.544982	+	0.838448i	$0.683464\pi$
$864$	3.37645	−	4.53867i	0.114869	−	0.154409i
$865$	−19.2490	−	3.39413i	−0.654487	−	0.115404i
$866$	−2.30475	−	19.7065i	−0.0783188	−	0.669654i
$867$	5.76051	−	9.97749i	0.195637	−	0.338853i
$868$	2.45396	−	0.143271i	0.0832928	−	0.00486292i
$869$	−2.29250	+	6.29860i	−0.0777679	+	0.213666i
$870$	−1.12874	−	0.0656623i	−0.0382677	−	0.00222616i
$871$	−3.18186	−	3.79200i	−0.107813	−	0.128487i
$872$	5.60794	−	3.23931i	0.189909	−	0.109697i
$873$		−	7.64783i		−	0.258840i
$874$	7.14843	−	36.7908i	0.241799	−	1.24447i
$875$		−	14.9848i		−	0.506578i
$876$	4.66920	−	6.27366i	0.157758	−	0.211967i
$877$	34.9016	+	41.5942i	1.17854	+	1.40454i	0.895286	+	0.445492i	$0.146971\pi$
$877$	34.9016	+	41.5942i	1.17854	+	1.40454i	0.283259	+	0.959044i	$0.408584\pi$
$878$	−0.148613	+	2.55466i	−0.00501544	+	0.0862155i
$879$	−0.211607	+	0.581385i	−0.00713732	+	0.0196096i
$880$	7.03684	+	6.63520i	0.237212	+	0.223673i
$881$	−16.7722	+	29.0502i	−0.565068	+	0.978727i	0.431975	+	0.901886i	$0.357817\pi$
$881$	−16.7722	+	29.0502i	−0.565068	+	0.978727i	−0.997043	+	0.0768413i	$0.975517\pi$
$882$	7.21516	−	0.843841i	0.242947	−	0.0284136i
$883$	36.0797	+	6.36182i	1.21418	+	0.214092i	0.743818	−	0.668383i	$-0.233013\pi$
$883$	36.0797	+	6.36182i	1.21418	+	0.214092i	0.470360	+	0.882475i	$0.344124\pi$
$884$	−34.1213	−	51.8631i	−1.14762	−	1.74435i
$885$	5.32147	+	9.21706i	0.178879	+	0.309828i
$886$	13.9143	−	10.3603i	0.467459	−	0.348061i
$887$	20.9279	+	17.5606i	0.702690	+	0.589627i	0.922538	−	0.385907i	$-0.126112\pi$
$887$	20.9279	+	17.5606i	0.702690	+	0.589627i	−0.219848	+	0.975534i	$0.570556\pi$
$888$	0.00467741	+	22.3307i	0.000156964	+	0.749371i
$889$	4.78821	+	13.1555i	0.160592	+	0.441222i
$890$	7.59613	−	2.27471i	0.254623	−	0.0762485i
$891$	1.78172	−	0.314166i	0.0596900	−	0.0105250i
$892$	0.0505880	+	0.0536051i	0.00169381	+	0.00179483i
$893$	−26.8469	−	14.0747i	−0.898397	−	0.470993i
$894$	7.19311	−	16.6787i	0.240573	−	0.557819i
$895$	5.43467	+	30.8215i	0.181661	+	1.03025i
$896$	−8.48014	+	12.9072i	−0.283302	+	0.431198i
$897$	33.2068	−	12.0863i	1.10874	−	0.403549i
$898$	−6.09798	−	5.75235i	−0.203492	−	0.191958i
$899$	−0.346220	+	0.412609i	−0.0115471	+	0.0137613i
$900$	−6.25427	+	1.48321i	−0.208476	+	0.0494404i
$901$	49.6972	−	28.6927i	1.65565	−	0.955892i
$902$	−1.49558	−	0.983511i	−0.0497975	−	0.0327473i
$903$	1.77336	−	10.0572i	0.0590136	−	0.334683i
$904$	−21.0320	+	25.0757i	−0.699516	+	0.834005i
$905$	−13.8418	−	7.99155i	−0.460116	−	0.265648i
$906$	16.1541	−	8.11430i	0.536683	−	0.269579i
$907$	23.1259	+	8.41712i	0.767882	+	0.279486i	0.696110	−	0.717935i	$-0.254913\pi$
$907$	23.1259	+	8.41712i	0.767882	+	0.279486i	0.0717715	+	0.997421i	$0.477135\pi$
$908$	−23.7482	−	11.9227i	−0.788113	−	0.395667i
$909$	0.403018	−	0.338172i	0.0133673	−	0.0112165i
$910$	−14.5916	−	3.45721i	−0.483708	−	0.114605i
$911$	12.3194			0.408160			0.204080	−	0.978954i	$-0.434580\pi$
$911$	12.3194			0.408160			0.204080	+	0.978954i	$0.434580\pi$
$912$	14.9478	+	8.97570i	0.494971	+	0.297215i
$913$	17.4434			0.577293
$914$	26.2429	+	6.21774i	0.868037	+	0.205665i
$915$	−10.5351	+	8.84000i	−0.348280	+	0.292241i
$916$	51.5278	+	25.8692i	1.70252	+	0.854742i
$917$	−21.9018	−	7.97159i	−0.723260	−	0.263245i
$918$	−6.74903	+	3.39008i	−0.222751	+	0.111889i
$919$	17.7965	+	10.2748i	0.587054	+	0.338936i	0.763932	−	0.645297i	$-0.223266\pi$
$919$	17.7965	+	10.2748i	0.587054	+	0.338936i	−0.176878	+	0.984233i	$0.556600\pi$
$920$	14.7692	−	17.6087i	0.486925	−	0.580541i
$921$	−3.34831	+	18.9892i	−0.110330	+	0.625715i
$922$	−24.7174	−	16.2544i	−0.814026	−	0.535312i
$923$	3.37728	−	1.94987i	0.111165	−	0.0641809i
$924$	−4.80600	+	1.13975i	−0.158106	+	0.0374950i
$925$	16.3100	−	19.4375i	0.536269	−	0.639101i
$926$	10.1208	+	9.54710i	0.332589	+	0.313737i
$927$	−15.6189	+	5.68480i	−0.512991	+	0.186713i
$928$	−0.781552	−	3.29250i	−0.0256557	−	0.108082i
$929$	8.88754	+	50.4037i	0.291591	+	1.65369i	0.680745	+	0.732521i	$0.261656\pi$
$929$	8.88754	+	50.4037i	0.291591	+	1.65369i	−0.389154	+	0.921173i	$0.627233\pi$
$930$	0.673929	−	1.56264i	0.0220990	−	0.0512411i
$931$	4.78270	+	21.8734i	0.156747	+	0.716872i
$932$	−20.9073	−	22.1542i	−0.684841	−	0.725686i
$933$	−8.49818	+	1.49846i	−0.278218	+	0.0490573i
$934$	6.07961	−	1.82058i	0.198931	−	0.0595711i
$935$	−4.41652	−	12.1343i	−0.144435	−	0.396833i
$936$	0.00344345	+	16.4396i	0.000112553	+	0.537345i
$937$	6.61304	+	5.54900i	0.216039	+	0.181278i	0.744384	−	0.667751i	$-0.232743\pi$
$937$	6.61304	+	5.54900i	0.216039	+	0.181278i	−0.528346	+	0.849029i	$0.677188\pi$
$938$	1.31870	−	0.981883i	0.0430572	−	0.0320596i
$939$	16.8263	+	29.1439i	0.549104	+	0.951077i
$940$	−10.2165	−	15.5286i	−0.333224	−	0.506488i
$941$	−26.3412	−	4.64466i	−0.858697	−	0.151412i	−0.273072	−	0.961994i	$-0.588040\pi$
$941$	−26.3412	−	4.64466i	−0.858697	−	0.151412i	−0.585625	+	0.810582i	$0.699151\pi$
$942$	−19.8228	+	2.31836i	−0.645862	+	0.0755362i
$943$	−2.12673	+	3.68360i	−0.0692557	+	0.119954i
$944$	−21.8531	+	23.1759i	−0.711259	+	0.754312i
$945$	−0.623957	+	1.71431i	−0.0202973	+	0.0557664i
$946$	1.11166	−	19.1095i	0.0361433	−	0.621304i
$947$	14.3653	+	17.1199i	0.466809	+	0.556322i	0.947163	−	0.320753i	$-0.103936\pi$
$947$	14.3653	+	17.1199i	0.466809	+	0.556322i	−0.480354	+	0.877075i	$0.659492\pi$
$948$	−4.42393	+	5.94410i	−0.143683	+	0.193055i
$949$			22.7274i			0.737764i
$950$	−6.45149	−	18.7317i	−0.209314	−	0.607738i
$951$		−	23.8928i		−	0.774778i
$952$	17.8547	−	10.3134i	0.578673	−	0.334259i
$953$	20.5766	+	24.5223i	0.666542	+	0.794354i	0.988309	−	0.152465i	$-0.0487211\pi$
$953$	20.5766	+	24.5223i	0.666542	+	0.794354i	−0.321767	+	0.946819i	$0.604277\pi$
$954$	−15.1705	−	0.882519i	−0.491164	−	0.0285726i
$955$	11.0152	−	30.2640i	0.356443	−	0.979319i
$956$	43.4581	−	2.53723i	1.40553	−	0.0820600i
$957$	0.541144	−	0.937289i	0.0174927	−	0.0302983i
$958$	−3.68015	−	31.4667i	−0.118900	−	1.01664i
$959$	2.01004	+	0.354424i	0.0649074	+	0.0114449i
$960$	5.34973	+	9.25705i	0.172662	+	0.298770i
$961$	15.0946	+	26.1447i	0.486924	+	0.843377i
$962$	−38.7569	−	52.0520i	−1.24957	−	1.67822i
$963$	3.88263	+	3.25792i	0.125116	+	0.104985i
$964$	13.4467	−	5.80258i	0.433090	−	0.186889i
$965$	0.101241	+	0.278157i	0.00325905	+	0.00895418i
$966$	3.36698	+	11.2437i	0.108331	+	0.361759i
$967$	−0.553021	+	0.0975125i	−0.0177840	+	0.00313579i	−0.182533	−	0.983200i	$-0.558430\pi$
$967$	−0.553021	+	0.0975125i	−0.0177840	+	0.00313579i	0.164749	+	0.986336i	$0.447319\pi$
$968$	20.5350	−	7.47901i	0.660021	−	0.240385i
$969$	−12.4507	−	19.6693i	−0.399973	−	0.631868i
$970$	13.2730	+	5.72430i	0.426170	+	0.183796i
$971$	−10.5773	−	59.9870i	−0.339443	−	1.92508i	−0.377970	−	0.925818i	$-0.623378\pi$
$971$	−10.5773	−	59.9870i	−0.339443	−	1.92508i	0.0385275	−	0.999258i	$-0.487733\pi$
$972$	1.98651	+	0.231908i	0.0637173	+	0.00743847i
$973$	−23.9374	+	8.71250i	−0.767398	+	0.279310i
$974$	−32.2618	+	34.2003i	−1.03374	+	1.09585i
$975$	12.0072	−	14.3096i	0.384538	−	0.458274i
$976$	−34.3960	−	22.6088i	−1.10099	−	0.723691i
$977$	−43.4749	+	25.1002i	−1.39089	+	0.803028i	−0.993413	−	0.114586i	$-0.963446\pi$
$977$	−43.4749	+	25.1002i	−1.39089	+	0.803028i	−0.397472	+	0.917614i	$0.630112\pi$
$978$	−13.8535	+	21.0664i	−0.442986	+	0.673630i
$979$	−1.31804	+	7.47496i	−0.0421247	+	0.238901i
$980$	−3.93595	+	13.1537i	−0.125729	+	0.420178i
$981$	1.98295	+	1.14485i	0.0633106	+	0.0365524i
$982$	15.8504	+	31.5552i	0.505806	+	1.00697i
$983$	−49.1688	−	17.8960i	−1.56824	−	0.570793i	−0.595636	−	0.803255i	$-0.703100\pi$
$983$	−49.1688	−	17.8960i	−1.56824	−	0.570793i	−0.972606	+	0.232462i	$0.925322\pi$
$984$	−1.27224	−	1.51555i	−0.0405574	−	0.0483139i
$985$	21.7112	−	18.2179i	0.691777	−	0.580470i
$986$	−1.04163	+	4.39635i	−0.0331722	+	0.140008i
$987$	9.49276			0.302158
$988$	−50.4219	+	5.01068i	−1.60413	+	0.159411i
$989$	−45.4856			−1.44636
$990$	−0.788355	+	3.32737i	−0.0250556	+	0.105751i
$991$	−41.7459	+	35.0290i	−1.32610	+	1.11273i	−0.341132	+	0.940015i	$0.610810\pi$
$991$	−41.7459	+	35.0290i	−1.32610	+	1.11273i	−0.984971	+	0.172718i	$0.944745\pi$
$992$	5.05914	+	0.589538i	0.160628	+	0.0187178i
$993$	−21.0250	−	7.65247i	−0.667208	−	0.242844i
$994$	0.581385	+	1.15743i	0.0184404	+	0.0367115i
$995$	−11.7144	−	6.76329i	−0.371370	−	0.214411i
$996$	18.4736	+	5.52782i	0.585359	+	0.175156i
$997$	−4.37523	+	24.8131i	−0.138565	+	0.785840i	0.833746	+	0.552148i	$0.186192\pi$
$997$	−4.37523	+	24.8131i	−0.138565	+	0.785840i	−0.972311	+	0.233692i	$0.924919\pi$
$998$	4.11383	−	6.25573i	0.130221	−	0.198022i
$999$	−6.83736	+	3.94755i	−0.216325	+	0.124895i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.w.a.67.1	✓	60
3.2	odd	2		684.2.cf.c.523.10		60
4.3	odd	2		228.2.w.b.67.2	yes	60
12.11	even	2		684.2.cf.b.523.9		60
19.2	odd	18		228.2.w.b.211.2	yes	60
57.2	even	18		684.2.cf.b.667.9		60
76.59	even	18	inner	228.2.w.a.211.1	yes	60
228.59	odd	18		684.2.cf.c.667.10		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.1	✓	60	1.1	even	1	trivial
228.2.w.a.211.1	yes	60	76.59	even	18	inner
228.2.w.b.67.2	yes	60	4.3	odd	2
228.2.w.b.211.2	yes	60	19.2	odd	18
684.2.cf.b.523.9		60	12.11	even	2
684.2.cf.b.667.9		60	57.2	even	18
684.2.cf.c.523.10		60	3.2	odd	2
684.2.cf.c.667.10		60	228.59	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.w (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37612 - 0.326044i) q^{2} +(-0.766044 + 0.642788i) q^{3} +(1.78739 + 0.897349i) q^{4} +(-1.25586 - 0.457097i) q^{5} +(1.26374 - 0.634786i) q^{6} +(-1.18216 - 0.682521i) q^{7} +(-2.16708 - 1.81762i) q^{8} +(0.173648 - 0.984808i) q^{9} +(1.57918 + 1.03849i) q^{10} +(-1.56682 + 0.904604i) q^{11} +(-1.94603 + 0.461503i) q^{12} +(3.73606 - 4.45246i) q^{13} +(1.40426 + 1.32467i) q^{14} +(1.25586 - 0.457097i) q^{15} +(2.38953 + 3.20783i) q^{16} +(-0.927369 - 5.25937i) q^{17} +(-0.560051 + 1.29859i) q^{18} +(-4.15334 - 1.32280i) q^{19} +(-1.83454 - 1.94396i) q^{20} +(1.34430 - 0.237037i) q^{21} +(2.45107 - 0.733988i) q^{22} +(-2.07944 - 5.71321i) q^{23} +(2.82843 - 0.000592445i) q^{24} +(-2.46197 - 2.06583i) q^{25} +(-6.59294 + 4.90898i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-1.50052 - 2.28074i) q^{28} +(0.589123 + 0.103878i) q^{29} +(-1.87725 + 0.219552i) q^{30} +(-0.450194 + 0.779760i) q^{31} +(-2.24238 - 5.19343i) q^{32} +(0.618786 - 1.70010i) q^{33} +(-0.438619 + 7.53987i) q^{34} +(1.17266 + 1.39752i) q^{35} +(1.19409 - 1.60441i) q^{36} +7.89511i q^{37} +(5.28418 + 3.17450i) q^{38} +5.81227i q^{39} +(1.89073 + 3.27326i) q^{40} +(-0.449691 - 0.535921i) q^{41} +(-1.92720 - 0.112112i) q^{42} +(2.55877 - 7.03016i) q^{43} +(-3.61227 + 0.210897i) q^{44} +(-0.668231 + 1.15741i) q^{45} +(0.998791 + 8.54003i) q^{46} +(6.84854 + 1.20758i) q^{47} +(-3.89244 - 0.921376i) q^{48} +(-2.56833 - 4.44848i) q^{49} +(2.71440 + 3.64554i) q^{50} +(4.09107 + 3.43281i) q^{51} +(10.6732 - 4.60574i) q^{52} +(3.67511 + 10.0973i) q^{53} +(-0.405696 - 1.35477i) q^{54} +(2.38121 - 0.419871i) q^{55} +(1.32127 + 3.62780i) q^{56} +(4.03192 - 1.65639i) q^{57} +(-0.776832 - 0.335028i) q^{58} +(1.38285 + 7.84254i) q^{59} +(2.65490 + 0.309937i) q^{60} +(-9.66972 + 3.51949i) q^{61} +(0.873756 - 0.926257i) q^{62} +(-0.877432 + 1.04568i) q^{63} +(1.39249 + 7.87788i) q^{64} +(-6.72719 + 3.88394i) q^{65} +(-1.40583 + 2.13778i) q^{66} +(0.147890 - 0.838725i) q^{67} +(3.06192 - 10.2327i) q^{68} +(5.26533 + 3.03994i) q^{69} +(-1.15806 - 2.30548i) q^{70} +(0.630487 + 0.229479i) q^{71} +(-2.16632 + 1.81853i) q^{72} +(-2.99543 + 2.51346i) q^{73} +(2.57415 - 10.8646i) q^{74} +3.21387 q^{75} +(-6.23662 - 6.09135i) q^{76} +2.46965 q^{77} +(1.89506 - 7.99836i) q^{78} +(2.83807 - 2.38143i) q^{79} +(-1.53464 - 5.12084i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(0.444093 + 0.884109i) q^{82} +(-8.34975 - 4.82073i) q^{83} +(2.61550 + 0.782632i) q^{84} +(-1.23939 + 7.02896i) q^{85} +(-5.81331 + 8.84005i) q^{86} +(-0.518066 + 0.299105i) q^{87} +(5.03966 + 0.887540i) q^{88} +(2.69672 - 3.21383i) q^{89} +(1.29693 - 1.37486i) q^{90} +(-7.45552 + 2.71359i) q^{91} +(1.40997 - 12.0777i) q^{92} +(-0.156351 - 0.886710i) q^{93} +(-9.03066 - 3.89470i) q^{94} +(4.61138 + 3.55973i) q^{95} +(5.05604 + 2.53703i) q^{96} +(7.53165 - 1.32803i) q^{97} +(2.08392 + 6.95901i) q^{98} +(0.618786 + 1.70010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{6} + 3 q^{8} - 6 q^{10} - 6 q^{13} - 9 q^{14} - 27 q^{16} - 18 q^{19} + 30 q^{20} - 6 q^{21} + 12 q^{22} + 18 q^{24} + 30 q^{27} - 18 q^{28} + 12 q^{31} - 63 q^{32} - 39 q^{34}+ \cdots + 117 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^6 + 3 * q^8 - 6 * q^10 - 6 * q^13 - 9 * q^14 - 27 * q^16 - 18 * q^19 + 30 * q^20 - 6 * q^21 + 12 * q^22 + 18 * q^24 + 30 * q^27 - 18 * q^28 + 12 * q^31 - 63 * q^32 - 39 * q^34 - 3 * q^36 - 48 * q^38 + 33 * q^40 - 12 * q^41 - 9 * q^42 + 18 * q^43 - 9 * q^44 - 69 * q^46 + 6 * q^48 + 30 * q^49 - 27 * q^50 - 3 * q^52 + 12 * q^53 + 3 * q^54 - 42 * q^56 - 36 * q^58 - 3 * q^60 + 27 * q^62 + 12 * q^63 + 21 * q^64 - 36 * q^65 + 24 * q^66 - 42 * q^67 + 93 * q^68 - 72 * q^69 + 132 * q^70 - 24 * q^71 + 18 * q^72 + 18 * q^73 + 27 * q^74 - 60 * q^75 + 66 * q^76 - 72 * q^77 - 33 * q^78 - 12 * q^79 + 6 * q^80 - 9 * q^82 + 69 * q^84 - 60 * q^85 + 123 * q^86 + 36 * q^88 - 12 * q^89 + 15 * q^90 + 84 * q^91 - 99 * q^92 - 12 * q^93 + 24 * q^95 + 12 * q^97 + 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more