LMFDB - Embedded newform 88.2.k.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(19,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("88.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.k (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.1
Character	$\chi$	$=$	88.51
Dual form			88.2.k.b.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37526 - 0.329627i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(1.78269 + 0.906646i) q^{4} +(-0.398383 - 0.548327i) q^{5} +(0.726027 - 1.18576i) q^{6} +(1.40393 + 4.32085i) q^{7} +(-2.15281 - 1.83450i) q^{8} +(1.64507 + 1.19522i) q^{9} +O(q^{10})$	\(q+(-1.37526 - 0.329627i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(1.78269 + 0.906646i) q^{4} +(-0.398383 - 0.548327i) q^{5} +(0.726027 - 1.18576i) q^{6} +(1.40393 + 4.32085i) q^{7} +(-2.15281 - 1.83450i) q^{8} +(1.64507 + 1.19522i) q^{9} +(0.367138 + 0.885411i) q^{10} +(3.31396 + 0.132807i) q^{11} +(-1.38934 + 1.39142i) q^{12} +(-1.90447 - 1.38368i) q^{13} +(-0.506504 - 6.40508i) q^{14} +(0.633734 - 0.205913i) q^{15} +(2.35598 + 3.23254i) q^{16} +(-2.07445 - 2.85523i) q^{17} +(-1.86843 - 2.18600i) q^{18} +(-4.38980 - 1.42633i) q^{19} +(-0.213056 - 1.33869i) q^{20} -4.46665 q^{21} +(-4.51379 - 1.27502i) q^{22} +1.11065i q^{23} +(2.36935 - 1.45560i) q^{24} +(1.40313 - 4.31839i) q^{25} +(2.16305 + 2.53068i) q^{26} +(-4.00349 + 2.90871i) q^{27} +(-1.41471 + 8.97562i) q^{28} +(-0.379398 - 1.16767i) q^{29} +(-0.939424 + 0.0742882i) q^{30} +(3.46109 - 4.76378i) q^{31} +(-2.17456 - 5.22219i) q^{32} +(-1.13099 + 3.05830i) q^{33} +(1.91175 + 4.61048i) q^{34} +(1.80994 - 2.49117i) q^{35} +(1.84902 + 3.62220i) q^{36} +(8.78677 - 2.85499i) q^{37} +(5.56697 + 3.40858i) q^{38} +(1.87237 - 1.36036i) q^{39} +(-0.148261 + 1.91128i) q^{40} +(1.88539 + 0.612601i) q^{41} +(6.14281 + 1.47233i) q^{42} +2.02637i q^{43} +(5.78737 + 3.24135i) q^{44} -1.37819i q^{45} +(0.366102 - 1.52744i) q^{46} +(-4.48649 - 1.45775i) q^{47} +(-3.73829 + 1.22084i) q^{48} +(-11.0356 + 8.01786i) q^{49} +(-3.35313 + 5.47641i) q^{50} +(3.29995 - 1.07222i) q^{51} +(-2.14058 - 4.19335i) q^{52} +(-4.70018 + 6.46924i) q^{53} +(6.46464 - 2.68058i) q^{54} +(-1.24741 - 1.87005i) q^{55} +(4.90420 - 11.8775i) q^{56} +(2.66732 - 3.67125i) q^{57} +(0.136877 + 1.73091i) q^{58} +(-0.400488 - 1.23257i) q^{59} +(1.31644 + 0.207494i) q^{60} +(6.73720 - 4.89486i) q^{61} +(-6.33017 + 5.41058i) q^{62} +(-2.85479 + 8.78613i) q^{63} +(1.26922 + 7.89868i) q^{64} +1.59551i q^{65} +(2.56351 - 3.83316i) q^{66} -0.483683 q^{67} +(-1.10941 - 6.97078i) q^{68} +(-1.03849 - 0.337427i) q^{69} +(-3.31030 + 2.82941i) q^{70} +(-8.68470 - 11.9535i) q^{71} +(-1.34892 - 5.59097i) q^{72} +(8.79393 - 2.85732i) q^{73} +(-13.0252 + 1.03001i) q^{74} +(3.61153 + 2.62393i) q^{75} +(-6.53249 - 6.52271i) q^{76} +(4.07874 + 14.5056i) q^{77} +(-3.02341 + 1.25367i) q^{78} +(-0.848366 - 0.616374i) q^{79} +(0.833907 - 2.57964i) q^{80} +(0.381661 + 1.17463i) q^{81} +(-2.39098 - 1.46396i) q^{82} +(-4.37741 - 6.02499i) q^{83} +(-7.96265 - 4.04967i) q^{84} +(-0.739176 + 2.27495i) q^{85} +(0.667946 - 2.78679i) q^{86} +1.20707 q^{87} +(-6.89072 - 6.36538i) q^{88} +2.47072 q^{89} +(-0.454289 + 1.89538i) q^{90} +(3.30493 - 10.1715i) q^{91} +(-1.00697 + 1.97996i) q^{92} +(3.40275 + 4.68349i) q^{93} +(5.68959 + 3.48365i) q^{94} +(0.966725 + 2.97527i) q^{95} +(5.54354 - 0.446729i) q^{96} +(-11.7932 - 8.56824i) q^{97} +(17.8198 - 7.38902i) q^{98} +(5.29298 + 4.17938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9	$ 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27} - 30 q^{28} + 30 q^{30} + 32 q^{33} - 14 q^{34} - 10 q^{35} + 16 q^{36} + 28 q^{38} + 30 q^{40} - 10 q^{41} + 64 q^{42} - 38 q^{44} + 40 q^{46} + 26 q^{48} - 18 q^{49} + 5 q^{50} + 60 q^{51} + 40 q^{52} + 76 q^{56} - 80 q^{57} - 56 q^{58} + 28 q^{59} + 34 q^{60} - 80 q^{62} + 55 q^{64} - 30 q^{66} - 28 q^{67} + 60 q^{68} - 44 q^{70} + 45 q^{72} - 10 q^{73} - 100 q^{74} + 4 q^{75} - 80 q^{78} - 76 q^{80} + 28 q^{81} + 13 q^{82} - 50 q^{84} - 39 q^{86} - 69 q^{88} + 20 q^{89} - 30 q^{90} + 78 q^{91} + 6 q^{92} - 30 q^{94} - 110 q^{96} - 52 q^{97} + 122 q^{99}+O(q^{100}) $ 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−1.37526	−	0.329627i	−0.972457	−	0.233081i
$2$	−1.37526	−	0.329627i	−0.972457	−	0.233081i
$3$	−0.303809	+	0.935028i	−0.175404	+	0.539839i	−0.999652	−	0.0263911i	$-0.991598\pi$
$3$	−0.303809	+	0.935028i	−0.175404	+	0.539839i	0.824248	+	0.566230i	$0.191598\pi$
$4$	1.78269	+	0.906646i	0.891346	+	0.453323i
$5$	−0.398383	−	0.548327i	−0.178162	−	0.245219i	0.710591	−	0.703605i	$-0.248428\pi$
$5$	−0.398383	−	0.548327i	−0.178162	−	0.245219i	−0.888753	+	0.458386i	$0.848428\pi$
$6$	0.726027	−	1.18576i	0.296399	−	0.484086i
$7$	1.40393	+	4.32085i	0.530636	+	1.63313i	0.752894	+	0.658142i	$0.228657\pi$
$7$	1.40393	+	4.32085i	0.530636	+	1.63313i	−0.222258	+	0.974988i	$0.571343\pi$
$8$	−2.15281	−	1.83450i	−0.761135	−	0.648594i
$9$	1.64507	+	1.19522i	0.548358	+	0.398405i
$10$	0.367138	+	0.885411i	0.116099	+	0.279992i
$11$	3.31396	+	0.132807i	0.999198	+	0.0400429i
$11$	3.31396	+	0.132807i	0.999198	+	0.0400429i
$12$	−1.38934	+	1.39142i	−0.401067	+	0.401668i
$13$	−1.90447	−	1.38368i	−0.528205	−	0.383763i	0.291481	−	0.956577i	$-0.405852\pi$
$13$	−1.90447	−	1.38368i	−0.528205	−	0.383763i	−0.819686	+	0.572813i	$0.805852\pi$
$14$	−0.506504	−	6.40508i	−0.135369	−	1.71183i
$15$	0.633734	−	0.205913i	0.163629	−	0.0531664i
$16$	2.35598	+	3.23254i	0.588996	+	0.808136i
$17$	−2.07445	−	2.85523i	−0.503127	−	0.692495i	0.479614	−	0.877479i	$-0.340777\pi$
$17$	−2.07445	−	2.85523i	−0.503127	−	0.692495i	−0.982741	+	0.184984i	$0.940777\pi$
$18$	−1.86843	−	2.18600i	−0.440394	−	0.515244i
$19$	−4.38980	−	1.42633i	−1.00709	−	0.327223i	−0.241394	−	0.970427i	$-0.577605\pi$
$19$	−4.38980	−	1.42633i	−1.00709	−	0.327223i	−0.765695	+	0.643204i	$0.777605\pi$
$20$	−0.213056	−	1.33869i	−0.0476407	−	0.299340i
$21$	−4.46665			−0.974702
$22$	−4.51379	−	1.27502i	−0.962344	−	0.271834i
$23$			1.11065i			0.231588i	0.993273	+	0.115794i	$0.0369412\pi$
$23$			1.11065i			0.231588i	−0.993273	+	0.115794i	$0.963059\pi$
$24$	2.36935	−	1.45560i	0.483642	−	0.297124i
$25$	1.40313	−	4.31839i	0.280626	−	0.863679i
$26$	2.16305	+	2.53068i	0.424209	+	0.496308i
$27$	−4.00349	+	2.90871i	−0.770473	+	0.559781i
$28$	−1.41471	+	8.97562i	−0.267355	+	1.69623i
$29$	−0.379398	−	1.16767i	−0.0704524	−	0.216830i	0.909631	−	0.415418i	$-0.136365\pi$
$29$	−0.379398	−	1.16767i	−0.0704524	−	0.216830i	−0.980083	+	0.198588i	$0.936365\pi$
$30$	−0.939424	+	0.0742882i	−0.171515	+	0.0135631i
$31$	3.46109	−	4.76378i	0.621630	−	0.855600i	−0.375841	−	0.926684i	$-0.622646\pi$
$31$	3.46109	−	4.76378i	0.621630	−	0.855600i	0.997470	+	0.0710846i	$0.0226460\pi$
$32$	−2.17456	−	5.22219i	−0.384412	−	0.923162i
$33$	−1.13099	+	3.05830i	−0.196880	+	0.532382i
$34$	1.91175	+	4.61048i	0.327862	+	0.790691i
$35$	1.80994	−	2.49117i	0.305936	−	0.421084i
$36$	1.84902	+	3.62220i	0.308170	+	0.603701i
$37$	8.78677	−	2.85499i	1.44454	−	0.469358i	0.521228	−	0.853418i	$-0.325474\pi$
$37$	8.78677	−	2.85499i	1.44454	−	0.469358i	0.923308	+	0.384059i	$0.125474\pi$
$38$	5.56697	+	3.40858i	0.903082	+	0.552944i
$39$	1.87237	−	1.36036i	0.299820	−	0.217832i
$40$	−0.148261	+	1.91128i	−0.0234422	+	0.302200i
$41$	1.88539	+	0.612601i	0.294449	+	0.0956722i	0.452516	−	0.891756i	$-0.350526\pi$
$41$	1.88539	+	0.612601i	0.294449	+	0.0956722i	−0.158068	+	0.987428i	$0.550526\pi$
$42$	6.14281	+	1.47233i	0.947856	+	0.227185i
$43$			2.02637i			0.309019i	0.987991	+	0.154509i	$0.0493797\pi$
$43$			2.02637i			0.309019i	−0.987991	+	0.154509i	$0.950620\pi$
$44$	5.78737	+	3.24135i	0.872479	+	0.488652i
$45$		−	1.37819i		−	0.205449i
$46$	0.366102	−	1.52744i	0.0539787	−	0.225209i
$47$	−4.48649	−	1.45775i	−0.654422	−	0.212634i	−0.0370589	−	0.999313i	$-0.511799\pi$
$47$	−4.48649	−	1.45775i	−0.654422	−	0.212634i	−0.617363	+	0.786679i	$0.711799\pi$
$48$	−3.73829	+	1.22084i	−0.539575	+	0.176212i
$49$	−11.0356	+	8.01786i	−1.57652	+	1.14541i
$50$	−3.35313	+	5.47641i	−0.474204	+	0.774482i
$51$	3.29995	−	1.07222i	0.462086	−	0.150141i
$52$	−2.14058	−	4.19335i	−0.296845	−	0.581513i
$53$	−4.70018	+	6.46924i	−0.645619	+	0.888619i	−0.998900	−	0.0468989i	$-0.985066\pi$
$53$	−4.70018	+	6.46924i	−0.645619	+	0.888619i	0.353280	+	0.935517i	$0.385066\pi$
$54$	6.46464	−	2.68058i	0.879727	−	0.364781i
$55$	−1.24741	−	1.87005i	−0.168200	−	0.252157i
$56$	4.90420	−	11.8775i	0.655352	−	1.58720i
$57$	2.66732	−	3.67125i	0.353295	−	0.486269i
$58$	0.136877	+	1.73091i	0.0179729	+	0.227279i
$59$	−0.400488	−	1.23257i	−0.0521391	−	0.160468i	0.921597	−	0.388149i	$-0.126885\pi$
$59$	−0.400488	−	1.23257i	−0.0521391	−	0.160468i	−0.973736	+	0.227682i	$0.926885\pi$
$60$	1.31644	+	0.207494i	0.169952	+	0.0267873i
$61$	6.73720	−	4.89486i	0.862610	−	0.626723i	−0.0659840	−	0.997821i	$-0.521019\pi$
$61$	6.73720	−	4.89486i	0.862610	−	0.626723i	0.928594	+	0.371098i	$0.121019\pi$
$62$	−6.33017	+	5.41058i	−0.803932	+	0.687144i
$63$	−2.85479	+	8.78613i	−0.359669	+	1.10695i
$64$	1.26922	+	7.89868i	0.158653	+	0.987334i
$65$			1.59551i			0.197898i
$66$	2.56351	−	3.83316i	0.315546	−	0.471830i
$67$	−0.483683			−0.0590913			−0.0295457	−	0.999563i	$-0.509406\pi$
$67$	−0.483683			−0.0590913			−0.0295457	+	0.999563i	$0.509406\pi$
$68$	−1.10941	−	6.97078i	−0.134536	−	0.845332i
$69$	−1.03849	−	0.337427i	−0.125020	−	0.0406214i
$70$	−3.31030	+	2.82941i	−0.395656	+	0.338179i
$71$	−8.68470	−	11.9535i	−1.03068	−	1.41862i	−0.904432	−	0.426618i	$-0.859705\pi$
$71$	−8.68470	−	11.9535i	−1.03068	−	1.41862i	−0.126253	−	0.991998i	$-0.540295\pi$
$72$	−1.34892	−	5.59097i	−0.158971	−	0.658902i
$73$	8.79393	−	2.85732i	1.02925	−	0.334424i	0.254758	−	0.967005i	$-0.418004\pi$
$73$	8.79393	−	2.85732i	1.02925	−	0.334424i	0.774495	+	0.632581i	$0.218004\pi$
$74$	−13.0252	+	1.03001i	−1.51415	+	0.119736i
$75$	3.61153	+	2.62393i	0.417024	+	0.302986i
$76$	−6.53249	−	6.52271i	−0.749327	−	0.748206i
$77$	4.07874	+	14.5056i	0.464815	+	1.65307i
$78$	−3.02341	+	1.25367i	−0.342334	+	0.141950i
$79$	−0.848366	−	0.616374i	−0.0954487	−	0.0693475i	0.539037	−	0.842282i	$-0.318788\pi$
$79$	−0.848366	−	0.616374i	−0.0954487	−	0.0693475i	−0.634486	+	0.772934i	$0.718788\pi$
$80$	0.833907	−	2.57964i	0.0932337	−	0.288413i
$81$	0.381661	+	1.17463i	0.0424067	+	0.130515i
$82$	−2.39098	−	1.46396i	−0.264039	−	0.161668i
$83$	−4.37741	−	6.02499i	−0.480483	−	0.661328i	0.498115	−	0.867111i	$-0.334026\pi$
$83$	−4.37741	−	6.02499i	−0.480483	−	0.661328i	−0.978598	+	0.205783i	$0.934026\pi$
$84$	−7.96265	−	4.04967i	−0.868797	−	0.441855i
$85$	−0.739176	+	2.27495i	−0.0801749	+	0.246753i
$86$	0.667946	−	2.78679i	0.0720265	−	0.300507i
$87$	1.20707			0.129411
$88$	−6.89072	−	6.36538i	−0.734553	−	0.678551i
$89$	2.47072			0.261895			0.130948	−	0.991389i	$-0.458198\pi$
$89$	2.47072			0.261895			0.130948	+	0.991389i	$0.458198\pi$
$90$	−0.454289	+	1.89538i	−0.0478863	+	0.199790i
$91$	3.30493	−	10.1715i	0.346451	−	1.06627i
$92$	−1.00697	+	1.97996i	−0.104984	+	0.206425i
$93$	3.40275	+	4.68349i	0.352849	+	0.485655i
$94$	5.68959	+	3.48365i	0.586836	+	0.359311i
$95$	0.966725	+	2.97527i	0.0991839	+	0.305257i
$96$	5.54354	−	0.446729i	0.565786	−	0.0455941i
$97$	−11.7932	−	8.56824i	−1.19741	−	0.869973i	−0.203387	−	0.979098i	$-0.565195\pi$
$97$	−11.7932	−	8.56824i	−1.19741	−	0.869973i	−0.994028	+	0.109126i	$0.965195\pi$
$98$	17.8198	−	7.38902i	1.80007	−	0.746404i
$99$	5.29298	+	4.17938i	0.531965	+	0.420044i
$100$	6.41661	−	6.42622i	0.641661	−	0.642622i
$101$	12.0780	+	8.77521i	1.20181	+	0.873166i	0.994462	−	0.105101i	$-0.0335166\pi$
$101$	12.0780	+	8.77521i	1.20181	+	0.873166i	0.207348	+	0.978267i	$0.433517\pi$
$102$	−4.89173	+	0.386831i	−0.484354	+	0.0383019i
$103$	−5.78997	+	1.88127i	−0.570502	+	0.185367i	−0.580041	−	0.814587i	$-0.696964\pi$
$103$	−5.78997	+	1.88127i	−0.570502	+	0.185367i	0.00953889	+	0.999955i	$0.496964\pi$
$104$	1.56161	+	6.47255i	0.153129	+	0.634686i
$105$	1.77944	+	2.44918i	0.173655	+	0.239016i
$106$	8.59641	−	7.34760i	0.834957	−	0.713662i
$107$	10.0872	+	3.27751i	0.975162	+	0.316849i	0.752898	−	0.658137i	$-0.228655\pi$
$107$	10.0872	+	3.27751i	0.975162	+	0.316849i	0.222264	+	0.974987i	$0.428655\pi$
$108$	−9.77417	+	1.55558i	−0.940520	+	0.149686i
$109$	−15.7342			−1.50706			−0.753530	−	0.657413i	$-0.771651\pi$
$109$	−15.7342			−1.50706			−0.753530	+	0.657413i	$0.771651\pi$
$110$	1.09909	+	2.98298i	0.104794	+	0.284416i
$111$			9.08325i			0.862144i
$112$	−10.6597	+	14.7181i	−1.00725	+	1.39073i
$113$	−4.68638	+	14.4232i	−0.440858	+	1.35682i	0.446105	+	0.894981i	$0.352811\pi$
$113$	−4.68638	+	14.4232i	−0.440858	+	1.35682i	−0.886963	+	0.461840i	$0.847189\pi$
$114$	−4.87841	+	4.16972i	−0.456905	+	0.390530i
$115$	0.609002	−	0.442466i	0.0567898	−	0.0412602i
$116$	0.382311	−	2.42557i	0.0354967	−	0.225209i
$117$	−1.47920	−	4.55251i	−0.136752	−	0.420879i
$118$	0.144486	+	1.82712i	0.0133010	+	0.168200i
$119$	9.42465	−	12.9719i	0.863957	−	1.18913i
$120$	−1.74206	−	0.719292i	−0.159027	−	0.0656621i
$121$	10.9647	+	0.880237i	0.996793	+	0.0800215i
$122$	−10.8789	+	4.51096i	−0.984928	+	0.408403i
$123$	−1.14560	+	1.57678i	−0.103295	+	0.142174i
$124$	10.4891	−	5.35437i	0.941950	−	0.480836i
$125$	−6.14986	+	1.99821i	−0.550061	+	0.178725i
$126$	6.82222	−	11.1422i	0.607772	−	0.992627i
$127$	4.99525	−	3.62926i	0.443257	−	0.322045i	−0.343671	−	0.939090i	$-0.611670\pi$
$127$	4.99525	−	3.62926i	0.443257	−	0.322045i	0.786928	+	0.617045i	$0.211670\pi$
$128$	0.858102	−	11.2811i	0.0758462	−	0.997120i
$129$	−1.89471	−	0.615629i	−0.166820	−	0.0542032i
$130$	0.525922	−	2.19424i	0.0461264	−	0.192448i
$131$			17.0297i			1.48789i	0.668242	+	0.743944i	$0.267047\pi$
$131$			17.0297i			1.48789i	−0.668242	+	0.743944i	$0.732953\pi$
$132$	−4.78901	+	4.42660i	−0.416829	+	0.385286i
$133$		−	20.9702i		−	1.81834i
$134$	0.665192	+	0.159435i	0.0574638	+	0.0137731i
$135$	3.18985	+	1.03644i	0.274538	+	0.0892030i
$136$	−0.772021	+	9.95235i	−0.0662002	+	0.853407i
$137$	4.87931	−	3.54503i	0.416868	−	0.302872i	−0.359508	−	0.933142i	$-0.617056\pi$
$137$	4.87931	−	3.54503i	0.416868	−	0.302872i	0.776376	+	0.630270i	$0.217056\pi$
$138$	1.31698	+	0.806366i	0.112108	+	0.0686424i
$139$	−13.6321	+	4.42932i	−1.15626	+	0.375690i	−0.823496	−	0.567322i	$-0.807980\pi$
$139$	−13.6321	+	4.42932i	−1.15626	+	0.375690i	−0.332759	+	0.943012i	$0.607980\pi$
$140$	5.48518	−	2.80001i	0.463582	−	0.236644i
$141$	2.72607	−	3.75211i	0.229577	−	0.315985i
$142$	8.00356	+	19.3019i	0.671644	+	1.61978i
$143$	−6.12758	−	4.83839i	−0.512414	−	0.404606i
$144$	0.0121805	+	8.13368i	0.00101504	+	0.677807i
$145$	−0.489118	+	0.673213i	−0.0406190	+	0.0559073i
$146$	−13.0358	+	1.03085i	−1.07885	+	0.0853139i
$147$	−4.14420	−	12.7545i	−0.341808	−	1.05198i
$148$	18.2526	+	2.87692i	1.50035	+	0.236481i
$149$	−6.77687	+	4.92369i	−0.555183	+	0.403364i	−0.829693	−	0.558220i	$-0.811484\pi$
$149$	−6.77687	+	4.92369i	−0.555183	+	0.403364i	0.274510	+	0.961584i	$0.411484\pi$
$150$	−4.10189	−	4.79905i	−0.334918	−	0.391841i
$151$	−4.67119	+	14.3764i	−0.380136	+	1.16994i	0.559812	+	0.828620i	$0.310873\pi$
$151$	−4.67119	+	14.3764i	−0.380136	+	1.16994i	−0.939948	+	0.341318i	$0.889127\pi$
$152$	6.83382	+	11.1237i	0.554296	+	0.902253i
$153$		−	7.17648i		−	0.580184i
$154$	−0.827894	−	21.2935i	−0.0667136	−	1.71588i
$155$	−3.99095			−0.320561
$156$	4.57123	−	0.727520i	0.365991	−	0.0582483i
$157$	11.3904	+	3.70098i	0.909057	+	0.295370i	0.725970	−	0.687726i	$-0.241391\pi$
$157$	11.3904	+	3.70098i	0.909057	+	0.295370i	0.183087	+	0.983097i	$0.441391\pi$
$158$	0.963553	+	1.12732i	0.0766561	+	0.0896848i
$159$	−4.62096	−	6.36021i	−0.366466	−	0.504398i
$160$	−1.99716	+	3.27280i	−0.157889	+	0.258738i
$161$	−4.79898	+	1.55928i	−0.378212	+	0.122889i
$162$	−0.137694	−	1.74123i	−0.0108182	−	0.136804i
$163$	0.263367	+	0.191347i	0.0206285	+	0.0149875i	0.598052	−	0.801457i	$-0.295942\pi$
$163$	0.263367	+	0.191347i	0.0206285	+	0.0149875i	−0.577423	+	0.816445i	$0.695942\pi$
$164$	2.80566	+	2.80146i	0.219085	+	0.218758i
$165$	2.12752	−	0.598222i	0.165627	−	0.0465716i
$166$	4.03409	+	9.72885i	0.313106	+	0.755105i
$167$	8.95740	+	6.50793i	0.693144	+	0.503599i	0.877692	−	0.479225i	$-0.159082\pi$
$167$	8.95740	+	6.50793i	0.693144	+	0.503599i	−0.184548	+	0.982823i	$0.559082\pi$
$168$	9.61586	+	8.19406i	0.741880	+	0.632185i
$169$	−2.30478	−	7.09339i	−0.177291	−	0.545645i
$170$	1.76645	−	2.88500i	0.135480	−	0.221269i
$171$	−5.51677	−	7.59318i	−0.421878	−	0.580665i
$172$	−1.83720	+	3.61240i	−0.140085	+	0.275443i
$173$	6.26024	−	19.2670i	0.475957	−	1.46485i	−0.368705	−	0.929546i	$-0.620199\pi$
$173$	6.26024	−	19.2670i	0.475957	−	1.46485i	0.844662	−	0.535299i	$-0.179801\pi$
$174$	−1.66003	−	0.397881i	−0.125847	−	0.0301633i
$175$	20.6290			1.55941
$176$	7.37834	+	11.0254i	0.556164	+	0.831073i
$177$	1.27416			0.0957720
$178$	−3.39788	−	0.814414i	−0.254682	−	0.0610429i
$179$	−2.93358	+	9.02862i	−0.219266	+	0.674831i	0.779557	+	0.626331i	$0.215444\pi$
$179$	−2.93358	+	9.02862i	−0.219266	+	0.674831i	−0.998823	+	0.0484999i	$0.984556\pi$
$180$	1.24953	−	2.45689i	0.0931347	−	0.183126i
$181$	−6.14986	−	8.46456i	−0.457116	−	0.629166i	0.516792	−	0.856111i	$-0.327126\pi$
$181$	−6.14986	−	8.46456i	−0.457116	−	0.629166i	−0.973908	+	0.226945i	$0.927126\pi$
$182$	−7.89795	+	12.8991i	−0.585435	+	0.956146i
$183$	2.53001	+	7.78657i	0.187024	+	0.575600i
$184$	2.03750	−	2.39103i	0.150206	−	0.176269i
$185$	−5.06597	−	3.68064i	−0.372458	−	0.270606i
$186$	−3.13588	−	7.56267i	−0.229934	−	0.554522i
$187$	−6.49544	−	9.73763i	−0.474994	−	0.712086i
$188$	−6.67637	−	6.66638i	−0.486924	−	0.486196i
$189$	−18.1887	−	13.2149i	−1.32304	−	0.961242i
$190$	−0.348771	−	4.41044i	−0.0253025	−	0.319967i
$191$	1.39594	−	0.453568i	0.101007	−	0.0328190i	−0.258078	−	0.966124i	$-0.583089\pi$
$191$	1.39594	−	0.453568i	0.101007	−	0.0328190i	0.359084	+	0.933305i	$0.383089\pi$
$192$	−7.77108	−	1.21293i	−0.560830	−	0.0875357i
$193$	−2.96615	−	4.08256i	−0.213508	−	0.293869i	0.688808	−	0.724944i	$-0.258134\pi$
$193$	−2.96615	−	4.08256i	−0.213508	−	0.293869i	−0.902316	+	0.431075i	$0.858134\pi$
$194$	13.3944	+	15.6709i	0.961660	+	1.12511i
$195$	−1.49184	−	0.484729i	−0.106833	−	0.0347122i
$196$	−26.9425	+	4.28796i	−1.92447	+	0.306283i
$197$	−15.3763			−1.09552			−0.547759	−	0.836636i	$-0.684519\pi$
$197$	−15.3763			−1.09552			−0.547759	+	0.836636i	$0.684519\pi$
$198$	−5.90160	−	7.49246i	−0.419409	−	0.532466i
$199$			12.6770i			0.898652i	0.893368	+	0.449326i	$0.148336\pi$
$199$			12.6770i			0.898652i	−0.893368	+	0.449326i	$0.851664\pi$
$200$	−10.9428	+	6.72266i	−0.773771	+	0.475364i
$201$	0.146947	−	0.452257i	0.0103649	−	0.0318998i
$202$	−13.7179	−	16.0495i	−0.965190	−	1.12924i
$203$	4.51267	−	3.27865i	0.316727	−	0.230116i
$204$	6.85493	+	1.08045i	0.479941	+	0.0756468i
$205$	−0.415203	−	1.27786i	−0.0289990	−	0.0892497i
$206$	8.58284	−	0.678718i	0.597995	−	0.0472885i
$207$	−1.32747	+	1.82711i	−0.0922657	+	0.126993i
$208$	−0.0141011	−	9.41621i	−0.000977734	−	0.652896i
$209$	−14.3582	−	5.30981i	−0.993179	−	0.367288i
$210$	−1.63987	−	3.95482i	−0.113162	−	0.272908i
$211$	−1.12319	+	1.54593i	−0.0773233	+	0.106426i	−0.845927	−	0.533299i	$-0.820952\pi$
$211$	−1.12319	+	1.54593i	−0.0773233	+	0.106426i	0.768603	+	0.639726i	$0.220952\pi$
$212$	−14.2443	+	7.27127i	−0.978302	+	0.499393i
$213$	13.8153	−	4.48887i	0.946610	−	0.307572i
$214$	−12.7921	−	7.83244i	−0.874452	−	0.535414i
$215$	1.11111	−	0.807272i	0.0757774	−	0.0550555i
$216$	13.9548	+	1.08250i	0.949504	+	0.0736547i
$217$	25.4427	+	8.26684i	1.72716	+	0.561190i
$218$	21.6386	+	5.18640i	1.46555	+	0.351268i
$219$			9.09065i			0.614289i
$220$	−0.528271	−	4.46467i	−0.0356160	−	0.301008i
$221$			8.30806i			0.558861i
$222$	2.99408	−	12.4918i	0.200950	−	0.838398i
$223$	−9.95822	−	3.23562i	−0.666852	−	0.216673i	−0.0440220	−	0.999031i	$-0.514017\pi$
$223$	−9.95822	−	3.23562i	−0.666852	−	0.216673i	−0.622830	+	0.782357i	$0.714017\pi$
$224$	19.5114	−	16.7276i	1.30366	−	1.11766i
$225$	7.46967	−	5.42703i	0.497978	−	0.361802i
$226$	11.1993	−	18.2909i	0.744965	−	1.21669i
$227$	14.4585	−	4.69785i	0.959644	−	0.311807i	0.213016	−	0.977049i	$-0.431671\pi$
$227$	14.4585	−	4.69785i	0.959644	−	0.311807i	0.746628	+	0.665241i	$0.231671\pi$
$228$	8.08354	−	4.12640i	0.535346	−	0.273277i
$229$	−15.5186	+	21.3595i	−1.02550	+	1.41148i	−0.117220	+	0.993106i	$0.537398\pi$
$229$	−15.5186	+	21.3595i	−1.02550	+	1.41148i	−0.908277	+	0.418370i	$0.862602\pi$
$230$	−0.983387	+	0.407763i	−0.0648426	+	0.0268871i
$231$	−14.8023	−	0.593203i	−0.973920	−	0.0390299i
$232$	−1.32531	+	3.20978i	−0.0870109	+	0.210732i
$233$	−3.56834	+	4.91140i	−0.233770	+	0.321757i	−0.909745	−	0.415168i	$-0.863723\pi$
$233$	−3.56834	+	4.91140i	−0.233770	+	0.321757i	0.675975	+	0.736925i	$0.263723\pi$
$234$	0.533659	+	6.74847i	0.0348864	+	0.441161i
$235$	0.988018	+	3.04081i	0.0644512	+	0.198360i
$236$	0.403563	−	2.56040i	0.0262697	−	0.166668i
$237$	0.834068	−	0.605986i	0.0541786	−	0.0393630i
$238$	−17.2373	+	14.7332i	−1.11733	+	0.955010i
$239$	3.83978	−	11.8176i	0.248375	−	0.764418i	−0.746689	−	0.665174i	$-0.768357\pi$
$239$	3.83978	−	11.8176i	0.248375	−	0.764418i	0.995063	−	0.0992444i	$-0.0316425\pi$
$240$	2.15869	+	1.56344i	0.139343	+	0.100920i
$241$			8.63844i			0.556451i	0.960516	+	0.278225i	$0.0897462\pi$
$241$			8.63844i			0.556451i	−0.960516	+	0.278225i	$0.910254\pi$
$242$	−14.7892	−	4.82482i	−0.950687	−	0.310151i
$243$	−16.0600			−1.03025
$244$	16.4483	−	2.61777i	1.05299	−	0.167586i
$245$	8.79282	+	2.85696i	0.561753	+	0.182525i
$246$	2.09525	−	1.79087i	0.133588	−	0.114182i
$247$	6.38666	+	8.79048i	0.406373	+	0.559325i
$248$	−16.1902	+	3.90617i	−1.02808	+	0.248042i
$249$	6.96343	−	2.26255i	0.441289	−	0.143384i
$250$	9.11634	−	0.720906i	0.576568	−	0.0455941i
$251$	−0.223050	−	0.162055i	−0.0140788	−	0.0102288i	0.580724	−	0.814101i	$-0.302770\pi$
$251$	−0.223050	−	0.162055i	−0.0140788	−	0.0102288i	−0.594802	+	0.803872i	$0.702770\pi$
$252$	−13.0551	+	13.0747i	−0.822395	+	0.823627i
$253$	−0.147503	+	3.68067i	−0.00927343	+	0.231402i
$254$	−8.06608	+	3.34462i	−0.506111	+	0.209860i
$255$	−1.90257	−	1.38230i	−0.119144	−	0.0865630i
$256$	−4.89867	+	15.2316i	−0.306167	+	0.951978i
$257$	2.16006	+	6.64799i	0.134741	+	0.414690i	0.995550	−	0.0942387i	$-0.0300417\pi$
$257$	2.16006	+	6.64799i	0.134741	+	0.414690i	−0.860809	+	0.508929i	$0.830042\pi$
$258$	2.40280	+	1.47120i	0.149592	+	0.0915929i
$259$	24.6720	+	33.9581i	1.53305	+	2.11006i
$260$	−1.44656	+	2.84430i	−0.0897119	+	0.176396i
$261$	0.771477	−	2.37436i	0.0477532	−	0.146969i
$262$	5.61343	−	23.4202i	0.346799	−	1.44691i
$263$	11.5402			0.711602			0.355801	−	0.934562i	$-0.384208\pi$
$263$	11.5402			0.711602			0.355801	+	0.934562i	$0.384208\pi$
$264$	8.04527	−	4.50915i	0.495152	−	0.277519i
$265$	5.41973			0.332932
$266$	−6.91233	+	28.8395i	−0.423822	+	1.76826i
$267$	−0.750625	+	2.31019i	−0.0459375	+	0.141381i
$268$	−0.862259	−	0.438530i	−0.0526708	−	0.0267875i
$269$	11.3719	+	15.6521i	0.693356	+	0.954323i	0.999997	+	0.00249771i	$0.000795047\pi$
$269$	11.3719	+	15.6521i	0.693356	+	0.954323i	−0.306641	+	0.951825i	$0.599205\pi$
$270$	−4.04524	−	2.47684i	−0.246185	−	0.150736i
$271$	−1.38625	−	4.26643i	−0.0842086	−	0.259167i	0.900083	−	0.435719i	$-0.143506\pi$
$271$	−1.38625	−	4.26643i	−0.0842086	−	0.259167i	−0.984291	+	0.176551i	$0.943506\pi$
$272$	4.34229	−	13.4326i	0.263290	−	0.814472i
$273$	8.50659	+	6.18040i	0.514842	+	0.374055i
$274$	−7.87887	+	3.26699i	−0.475980	+	0.197366i
$275$	5.22344	−	14.1247i	0.314985	−	0.851749i
$276$	−1.54539	−	1.54307i	−0.0930214	−	0.0928822i
$277$	13.7180	+	9.96671i	0.824235	+	0.598842i	0.917922	−	0.396760i	$-0.129865\pi$
$277$	13.7180	+	9.96671i	0.824235	+	0.598842i	−0.0936874	+	0.995602i	$0.529865\pi$
$278$	20.2077	−	1.59799i	1.21198	−	0.0958411i
$279$	11.3875	−	3.70002i	0.681751	−	0.221514i
$280$	−8.46651	+	2.04269i	−0.505971	+	0.122074i
$281$	−4.32677	−	5.95529i	−0.258113	−	0.355263i	0.660219	−	0.751073i	$-0.270464\pi$
$281$	−4.32677	−	5.95529i	−0.258113	−	0.355263i	−0.918332	+	0.395811i	$0.870464\pi$
$282$	−4.98586	+	4.26156i	−0.296904	+	0.253772i
$283$	−1.17501	−	0.381784i	−0.0698470	−	0.0226947i	0.273885	−	0.961762i	$-0.411691\pi$
$283$	−1.17501	−	0.381784i	−0.0698470	−	0.0226947i	−0.343732	+	0.939068i	$0.611691\pi$
$284$	−4.64459	−	29.1833i	−0.275605	−	1.73171i
$285$	−3.07566			−0.182187
$286$	6.83217	+	8.67387i	0.403995	+	0.512897i
$287$			9.00655i			0.531640i
$288$	2.66433	−	11.1900i	0.156997	−	0.659375i
$289$	1.40428	−	4.32192i	0.0826046	−	0.254231i
$290$	0.894574	−	0.764618i	0.0525312	−	0.0448999i
$291$	11.5944	−	8.42383i	0.679676	−	0.493814i
$292$	18.2675	+	2.87926i	1.06902	+	0.168496i
$293$	0.464488	+	1.42955i	0.0271357	+	0.0835150i	0.963707	−	0.266961i	$-0.0860197\pi$
$293$	0.464488	+	1.42955i	0.0271357	+	0.0835150i	−0.936572	+	0.350476i	$0.886020\pi$
$294$	1.49512	+	18.9069i	0.0871974	+	1.10267i
$295$	−0.516307	+	0.710635i	−0.0300605	+	0.0413748i
$296$	−24.1538	−	9.97305i	−1.40391	−	0.579672i
$297$	−13.6537	+	9.10767i	−0.792270	+	0.528480i
$298$	10.9430	−	4.53752i	0.633908	−	0.262852i
$299$	1.53679	−	2.11521i	0.0888748	−	0.122326i
$300$	4.05928	+	7.95205i	0.234362	+	0.459112i
$301$	−8.75565	+	2.84488i	−0.504667	+	0.163976i
$302$	11.1630	−	18.2316i	0.642357	−	1.04911i
$303$	−11.8745	+	8.62732i	−0.682171	+	0.495626i
$304$	−5.73162	−	17.5506i	−0.328731	−	1.00660i
$305$	−5.36797	−	1.74416i	−0.307369	−	0.0998703i
$306$	−2.36556	+	9.86954i	−0.135230	+	0.564204i
$307$		−	28.1622i		−	1.60730i	−0.595100	−	0.803652i	$-0.702888\pi$
$307$		−	28.1622i		−	1.60730i	0.595100	−	0.803652i	$-0.297112\pi$
$308$	−5.88033	+	29.5570i	−0.335063	+	1.68417i
$309$		−	5.98533i		−	0.340493i
$310$	5.48860	+	1.31552i	0.311731	+	0.0747167i
$311$	−29.7223	−	9.65736i	−1.68540	−	0.547619i	−0.699451	−	0.714681i	$-0.746572\pi$
$311$	−29.7223	−	9.65736i	−1.68540	−	0.547619i	−0.985946	+	0.167062i	$0.946572\pi$
$312$	−6.52645	−	0.506268i	−0.369487	−	0.0286618i
$313$	−7.97204	+	5.79203i	−0.450606	+	0.327385i	−0.789835	−	0.613319i	$-0.789834\pi$
$313$	−7.97204	+	5.79203i	−0.450606	+	0.327385i	0.339229	+	0.940704i	$0.389834\pi$
$314$	−14.4449	−	8.84441i	−0.815173	−	0.499119i
$315$	5.95497	−	1.93489i	0.335525	−	0.109019i
$316$	−0.953543	−	1.86797i	−0.0536410	−	0.105082i
$317$	1.47669	−	2.03248i	0.0829389	−	0.114156i	−0.765532	−	0.643398i	$-0.777524\pi$
$317$	1.47669	−	2.03248i	0.0829389	−	0.114156i	0.848470	+	0.529243i	$0.177524\pi$
$318$	4.25854	+	10.2702i	0.238807	+	0.575921i
$319$	−1.10224	−	3.91999i	−0.0617134	−	0.219477i
$320$	3.82542	−	3.84265i	0.213848	−	0.214811i
$321$	−6.12913	+	8.43603i	−0.342095	+	0.470853i
$322$	7.11383	−	0.562551i	0.396439	−	0.0313497i
$323$	5.03390	+	15.4927i	0.280093	+	0.862039i
$324$	−0.384591	+	2.44004i	−0.0213662	+	0.135558i
$325$	−8.64749	+	6.28277i	−0.479676	+	0.348505i
$326$	−0.299126	−	0.349966i	−0.0165670	−	0.0193828i
$327$	4.78018	−	14.7119i	0.264345	−	0.813569i
$328$	−2.93508	−	4.77757i	−0.162063	−	0.263797i
$329$		−	21.4320i		−	1.18159i
$330$	−3.12308	+	0.121426i	−0.171920	+	0.00668429i
$331$	3.34398			0.183802			0.0919009	−	0.995768i	$-0.470706\pi$
$331$	3.34398			0.183802			0.0919009	+	0.995768i	$0.470706\pi$
$332$	−2.34104	−	14.7095i	−0.128481	−	0.807287i
$333$	17.8672	+	5.80541i	0.979118	+	0.318135i
$334$	−10.1736	−	11.9027i	−0.556674	−	0.651287i
$335$	0.192691	+	0.265217i	0.0105279	+	0.0144903i
$336$	−10.5233	−	14.4386i	−0.574096	−	0.787692i
$337$	−15.8356	+	5.14531i	−0.862622	+	0.280283i	−0.706723	−	0.707490i	$-0.749827\pi$
$337$	−15.8356	+	5.14531i	−0.862622	+	0.280283i	−0.155899	+	0.987773i	$0.549827\pi$
$338$	0.831509	+	10.5150i	0.0452281	+	0.571940i
$339$	−12.0623	−	8.76380i	−0.655136	−	0.475984i
$340$	−3.38030	+	3.38537i	−0.183322	+	0.183597i
$341$	12.1026	−	15.3273i	0.655392	−	0.830022i
$342$	5.08409	+	12.2611i	0.274916	+	0.663004i
$343$	−24.4085	−	17.7338i	−1.31794	−	0.957537i
$344$	3.71738	−	4.36240i	0.200428	−	0.235205i
$345$	0.228698	+	0.703859i	0.0123127	+	0.0378945i
$346$	−14.9604	+	24.4337i	−0.804276	+	1.31356i
$347$	−11.7164	−	16.1263i	−0.628972	−	0.865705i	0.368996	−	0.929431i	$-0.379702\pi$
$347$	−11.7164	−	16.1263i	−0.628972	−	0.865705i	−0.997967	+	0.0637258i	$0.979702\pi$
$348$	2.15183	+	1.09438i	0.115350	+	0.0586650i
$349$	0.0914787	−	0.281543i	0.00489674	−	0.0150706i	−0.948578	−	0.316543i	$-0.897478\pi$
$349$	0.0914787	−	0.281543i	0.00489674	−	0.0150706i	0.953475	+	0.301472i	$0.0974780\pi$
$350$	−28.3704	−	6.79989i	−1.51646	−	0.363469i
$351$	11.6493			0.621791
$352$	−6.51288	−	17.5950i	−0.347138	−	0.937814i
$353$	12.3132			0.655366			0.327683	−	0.944788i	$-0.393732\pi$
$353$	12.3132			0.655366			0.327683	+	0.944788i	$0.393732\pi$
$354$	−1.75231	−	0.419998i	−0.0931341	−	0.0223227i
$355$	−3.09457	+	9.52412i	−0.164243	+	0.505488i
$356$	4.40453	+	2.24007i	0.233439	+	0.118723i
$357$	9.26581	+	12.7533i	0.490399	+	0.674976i
$358$	7.01051	−	11.4497i	0.370517	−	0.605137i
$359$	−3.65694	−	11.2549i	−0.193006	−	0.594011i	−0.999994	−	0.00344333i	$-0.998904\pi$
$359$	−3.65694	−	11.2549i	−0.193006	−	0.594011i	0.806988	−	0.590567i	$-0.201096\pi$
$360$	−2.52829	+	2.96699i	−0.133253	+	0.156374i
$361$	1.86460	+	1.35471i	0.0981371	+	0.0713008i
$362$	5.66753	+	13.6682i	0.297879	+	0.718382i
$363$	−4.15423	+	9.98490i	−0.218040	+	0.524071i
$364$	15.1136	−	15.1363i	0.792170	−	0.793358i
$365$	−5.07010	−	3.68365i	−0.265381	−	0.192811i
$366$	−0.912765	−	11.5425i	−0.0477110	−	0.603338i
$367$	−24.6571	+	8.01159i	−1.28709	+	0.418202i	−0.871073	−	0.491154i	$-0.836575\pi$
$367$	−24.6571	+	8.01159i	−1.28709	+	0.418202i	−0.416020	+	0.909356i	$0.636575\pi$
$368$	−3.59024	+	2.61669i	−0.187154	+	0.136404i
$369$	2.36942	+	3.26123i	0.123347	+	0.169773i
$370$	5.75380	+	6.73173i	0.299126	+	0.349966i
$371$	−34.5514	−	11.2264i	−1.79382	−	0.582847i
$372$	1.81980	+	11.4343i	0.0943520	+	0.592842i
$373$	15.3985			0.797305			0.398652	−	0.917102i	$-0.369478\pi$
$373$	15.3985			0.797305			0.398652	+	0.917102i	$0.369478\pi$
$374$	5.72316	+	15.5329i	0.295937	+	0.803186i
$375$		−	6.35737i		−	0.328293i
$376$	6.98434	+	11.3687i	0.360190	+	0.586297i
$377$	−0.893123	+	2.74875i	−0.0459982	+	0.141568i
$378$	20.6583	+	24.1694i	1.06255	+	1.24314i
$379$	6.68999	−	4.86056i	0.343642	−	0.249670i	−0.402555	−	0.915396i	$-0.631878\pi$
$379$	6.68999	−	4.86056i	0.343642	−	0.249670i	0.746197	+	0.665725i	$0.231878\pi$
$380$	−0.974148	+	6.18048i	−0.0499727	+	0.317052i
$381$	1.87586	+	5.77330i	0.0961032	+	0.295775i
$382$	−2.06929	+	0.163636i	−0.105874	+	0.00837236i
$383$	0.0941501	−	0.129586i	0.00481085	−	0.00662156i	−0.806605	−	0.591091i	$-0.798697\pi$
$383$	0.0941501	−	0.129586i	0.00481085	−	0.00662156i	0.811416	+	0.584470i	$0.198697\pi$
$384$	10.2875	+	4.22965i	0.524980	+	0.215844i
$385$	6.32892	−	8.01527i	0.322552	−	0.408496i
$386$	2.73352	+	6.59231i	0.139132	+	0.335540i
$387$	−2.42195	+	3.33353i	−0.123115	+	0.169453i
$388$	−13.2552	−	25.9668i	−0.672932	−	1.31826i
$389$	−14.1473	+	4.59673i	−0.717295	+	0.233063i	−0.644850	−	0.764309i	$-0.723080\pi$
$389$	−14.1473	+	4.59673i	−0.717295	+	0.233063i	−0.0724452	+	0.997372i	$0.523080\pi$
$390$	1.89190	+	1.15838i	0.0957999	+	0.0586569i
$391$	3.17117	−	2.30399i	0.160373	−	0.116518i
$392$	38.4665	+	2.98391i	1.94285	+	0.150710i
$393$	−15.9232	−	5.17376i	−0.803219	−	0.260982i
$394$	21.1465	+	5.06845i	1.06534	+	0.255345i
$395$			0.710735i			0.0357610i
$396$	5.64654	+	12.2494i	0.283749	+	0.615556i
$397$		−	14.1188i		−	0.708603i	−0.935131	−	0.354301i	$-0.884719\pi$
$397$		−	14.1188i		−	0.708603i	0.935131	−	0.354301i	$-0.115281\pi$
$398$	4.17869	−	17.4343i	0.209459	−	0.873901i
$399$	19.6077	+	6.37092i	0.981612	+	0.318945i
$400$	17.2652	−	5.63839i	0.863258	−	0.281919i
$401$	12.8915	−	9.36625i	0.643772	−	0.467728i	−0.217372	−	0.976089i	$-0.569748\pi$
$401$	12.8915	−	9.36625i	0.643772	−	0.467728i	0.861144	+	0.508361i	$0.169748\pi$
$402$	−0.351167	+	0.573535i	−0.0175146	+	0.0286053i
$403$	−13.1831	+	4.28344i	−0.656695	+	0.213373i
$404$	13.5754	+	26.5940i	0.675402	+	1.32310i
$405$	0.492035	−	0.677228i	0.0244494	−	0.0336517i
$406$	−7.28683	+	3.02150i	−0.361639	+	0.149955i
$407$	29.4982	−	8.29441i	1.46217	−	0.411138i
$408$	−9.07118	−	3.74547i	−0.449090	−	0.185429i
$409$	−11.8080	+	16.2524i	−0.583870	+	0.803629i	−0.994113	−	0.108348i	$-0.965444\pi$
$409$	−11.8080	+	16.2524i	−0.583870	+	0.803629i	0.410243	+	0.911976i	$0.365444\pi$
$410$	0.149795	+	1.89426i	0.00739784	+	0.0935507i
$411$	1.83232	+	5.63930i	0.0903817	+	0.278166i
$412$	−12.0274	−	1.89572i	−0.592547	−	0.0933954i
$413$	4.76352	−	3.46090i	0.234397	−	0.170300i
$414$	2.42789	−	2.07518i	0.119324	−	0.101990i
$415$	−1.55978	+	4.80051i	−0.0765665	+	0.235648i
$416$	−3.08444	+	12.9544i	−0.151227	+	0.635142i
$417$		−	14.0920i		−	0.690089i
$418$	17.9961	+	12.0352i	0.880216	+	0.588663i
$419$	13.8395			0.676103			0.338052	−	0.941128i	$-0.390232\pi$
$419$	13.8395			0.676103			0.338052	+	0.941128i	$0.390232\pi$
$420$	0.951643	+	5.97946i	0.0464354	+	0.291768i
$421$	−11.9971	−	3.89810i	−0.584704	−	0.189982i	0.00170305	−	0.999999i	$-0.499458\pi$
$421$	−11.9971	−	3.89810i	−0.584704	−	0.189982i	−0.586407	+	0.810017i	$0.699458\pi$
$422$	2.05426	−	1.75583i	0.0999997	−	0.0854726i
$423$	−5.63828	−	7.76043i	−0.274143	−	0.377325i
$424$	21.9864	−	5.30460i	1.06776	−	0.257614i
$425$	−15.2407	+	4.95201i	−0.739284	+	0.240208i
$426$	−20.4793	+	1.61947i	−0.992227	+	0.0784637i
$427$	30.6085	+	22.2384i	1.48125	+	1.07619i
$428$	15.0107	+	14.9883i	0.725572	+	0.724486i
$429$	6.38564	−	4.25951i	0.308302	−	0.205651i
$430$	−1.79417	+	0.743957i	−0.0865226	+	0.0358768i
$431$	12.6175	+	9.16714i	0.607763	+	0.441566i	0.848626	−	0.528993i	$-0.177430\pi$
$431$	12.6175	+	9.16714i	0.607763	+	0.441566i	−0.240863	+	0.970559i	$0.577430\pi$
$432$	−18.8347	−	6.08860i	−0.906185	−	0.292938i
$433$	0.235781	+	0.725659i	0.0113309	+	0.0348729i	0.956562	−	0.291529i	$-0.0941638\pi$
$433$	0.235781	+	0.725659i	0.0113309	+	0.0348729i	−0.945231	+	0.326402i	$0.894164\pi$
$434$	−32.2654	−	19.7557i	−1.54879	−	0.948302i
$435$	−0.480874	−	0.661867i	−0.0230562	−	0.0317341i
$436$	−28.0492	−	14.2653i	−1.34331	−	0.683186i
$437$	1.58416	−	4.87555i	0.0757808	−	0.233229i
$438$	2.99652	−	12.5020i	0.143179	−	0.597370i
$439$	1.62453			0.0775344			0.0387672	−	0.999248i	$-0.487657\pi$
$439$	1.62453			0.0775344			0.0387672	+	0.999248i	$0.487657\pi$
$440$	−0.745164	+	6.31423i	−0.0355243	+	0.301019i
$441$	−27.7375			−1.32083
$442$	2.73856	−	11.4258i	0.130260	−	0.543468i
$443$	10.2530	−	31.5554i	0.487134	−	1.49924i	−0.341732	−	0.939797i	$-0.611014\pi$
$443$	10.2530	−	31.5554i	0.487134	−	1.49924i	0.828866	−	0.559447i	$-0.188986\pi$
$444$	−8.23529	+	16.1926i	−0.390830	+	0.768468i
$445$	−0.984291	−	1.35476i	−0.0466599	−	0.0642218i
$446$	12.6286	+	7.73233i	0.597982	+	0.366136i
$447$	−2.54491	−	7.83242i	−0.120370	−	0.370461i
$448$	−32.3471	+	16.5733i	−1.52826	+	0.783016i
$449$	20.6014	+	14.9678i	0.972239	+	0.706373i	0.955961	−	0.293495i	$-0.0948183\pi$
$449$	20.6014	+	14.9678i	0.972239	+	0.706373i	0.0162782	+	0.999868i	$0.494818\pi$
$450$	−12.0616	+	5.00139i	−0.568592	+	0.235768i
$451$	6.16677	+	2.28053i	0.290382	+	0.107386i
$452$	−21.4311	+	21.4632i	−1.00804	+	1.00955i
$453$	−12.0232	−	8.73538i	−0.564900	−	0.410424i
$454$	−21.4328	+	1.69487i	−1.00589	+	0.0795442i
$455$	−6.89395	+	2.23998i	−0.323193	+	0.105012i
$456$	−12.4772	+	3.01033i	−0.584297	+	0.140971i
$457$	20.3313	+	27.9836i	0.951058	+	1.30902i	0.951056	+	0.309019i	$0.100001\pi$
$457$	20.3313	+	27.9836i	0.951058	+	1.30902i	1.63349e−6		1.00000i	$0.499999\pi$
$458$	28.3828	−	24.2596i	1.32624	−	1.13358i
$459$	16.6101	+	5.39694i	0.775291	+	0.251907i
$460$	1.48682	−	0.236631i	0.0693235	−	0.0110330i
$461$	11.5194			0.536510			0.268255	−	0.963348i	$-0.413553\pi$
$461$	11.5194			0.536510			0.268255	+	0.963348i	$0.413553\pi$
$462$	20.1615	+	5.69504i	0.937999	+	0.264957i
$463$		−	11.0442i		−	0.513267i	−0.966509	−	0.256634i	$-0.917387\pi$
$463$		−	11.0442i		−	0.513267i	0.966509	−	0.256634i	$-0.0826133\pi$
$464$	2.88068	−	3.97742i	0.133732	−	0.184647i
$465$	1.21249	−	3.73165i	0.0562277	−	0.173051i
$466$	6.52634	−	5.57825i	0.302327	−	0.258407i
$467$	−10.7423	+	7.80474i	−0.497095	+	0.361160i	−0.807906	−	0.589311i	$-0.799399\pi$
$467$	−10.7423	+	7.80474i	−0.497095	+	0.361160i	0.310812	+	0.950472i	$0.399399\pi$
$468$	1.49056	−	9.45683i	0.0689010	−	0.437142i
$469$	−0.679058	−	2.08993i	−0.0313560	−	0.0965038i
$470$	−0.356453	−	4.50758i	−0.0164419	−	0.207919i
$471$	−6.92104	+	9.52599i	−0.318905	+	0.438935i
$472$	−1.39898	+	3.38820i	−0.0643934	+	0.155954i
$473$	−0.269117	+	6.71532i	−0.0123740	+	0.308771i
$474$	−1.34681	+	0.558458i	−0.0618611	+	0.0256508i
$475$	−12.3189	+	16.9556i	−0.565231	+	0.777974i
$476$	28.5622	−	14.5801i	1.30915	−	0.668279i
$477$	−15.4643	+	5.02465i	−0.708061	+	0.230063i
$478$	−9.17610	+	14.9866i	−0.419705	+	0.685472i
$479$	−7.66139	+	5.56633i	−0.350058	+	0.254332i	−0.748893	−	0.662691i	$-0.769414\pi$
$479$	−7.66139	+	5.56633i	−0.350058	+	0.254332i	0.398835	+	0.917023i	$0.369414\pi$
$480$	−2.45341	−	2.86171i	−0.111982	−	0.130618i
$481$	−20.6845	−	6.72081i	−0.943133	−	0.306443i
$482$	2.84746	−	11.8801i	0.129698	−	0.541124i
$483$		−	4.96090i		−	0.225729i
$484$	18.7487	+	11.5103i	0.852212	+	0.523196i
$485$			9.87996i			0.448626i
$486$	22.0868	+	5.29382i	1.00188	+	0.240132i
$487$	26.0060	+	8.44986i	1.17844	+	0.382900i	0.831789	−	0.555092i	$-0.187317\pi$
$487$	26.0060	+	8.44986i	1.17844	+	0.382900i	0.346656	+	0.937992i	$0.387317\pi$
$488$	−23.4836	−	1.82166i	−1.06305	−	0.0824627i
$489$	−0.258928	+	0.188123i	−0.0117091	+	0.00850719i
$490$	−11.1507	−	6.82742i	−0.503738	−	0.308431i
$491$	−22.5899	+	7.33990i	−1.01947	+	0.331245i	−0.770618	−	0.637297i	$-0.780052\pi$
$491$	−22.5899	+	7.33990i	−1.01947	+	0.331245i	−0.248849	+	0.968542i	$0.580052\pi$
$492$	−3.47183	+	1.77226i	−0.156522	+	0.0798998i
$493$	−2.54692	+	3.50553i	−0.114707	+	0.157881i
$494$	−5.88575	−	14.1944i	−0.264812	−	0.638637i
$495$	0.183034	−	4.56728i	0.00822676	−	0.205284i
$496$	23.5534	−	0.0352720i	1.05758	−	0.00158376i
$497$	39.4565	−	54.3072i	1.76986	−	2.43601i
$498$	−10.3223	+	0.816274i	−0.462555	+	0.0365781i
$499$	−1.99682	−	6.14559i	−0.0893901	−	0.275114i	0.896361	−	0.443325i	$-0.146201\pi$
$499$	−1.99682	−	6.14559i	−0.0893901	−	0.275114i	−0.985751	+	0.168210i	$0.946201\pi$
$500$	−12.7750	−	2.01355i	−0.571315	−	0.0900489i
$501$	−8.80643	+	6.39825i	−0.393442	+	0.285853i
$502$	0.253334	+	0.296392i	0.0113069	+	0.0132286i
$503$	−11.1405	+	34.2869i	−0.496730	+	1.52878i	0.317513	+	0.948254i	$0.397152\pi$
$503$	−11.1405	+	34.2869i	−0.496730	+	1.52878i	−0.814243	+	0.580524i	$0.802848\pi$
$504$	22.2640	−	13.6778i	0.991716	−	0.609257i
$505$		−	10.1186i		−	0.450272i
$506$	1.41610	−	5.01327i	0.0629535	−	0.222867i
$507$	7.33273			0.325658
$508$	12.1955	−	1.94093i	0.541086	−	0.0861149i
$509$	−35.4254	−	11.5104i	−1.57021	−	0.510191i	−0.610695	−	0.791866i	$-0.709110\pi$
$509$	−35.4254	−	11.5104i	−1.57021	−	0.510191i	−0.959510	+	0.281675i	$0.909110\pi$
$510$	2.16089	+	2.52816i	0.0956860	+	0.111949i
$511$	24.6921	+	33.9858i	1.09232	+	1.50344i
$512$	11.7577	−	19.3328i	0.519623	−	0.854396i
$513$	21.7233	−	7.05834i	0.959109	−	0.311633i
$514$	−0.779297	−	9.85474i	−0.0343733	−	0.434674i
$515$	3.33818	+	2.42533i	0.147098	+	0.106873i
$516$	−2.81953	−	2.81531i	−0.124123	−	0.123937i
$517$	−14.6745	−	5.42677i	−0.645382	−	0.238669i
$518$	−22.7370	−	54.8339i	−0.999006	−	2.40926i
$519$	16.1133	+	11.7070i	0.707295	+	0.513880i
$520$	2.92696	−	3.43483i	0.128356	−	0.150627i
$521$	6.23908	+	19.2019i	0.273339	+	0.841251i	0.989654	+	0.143474i	$0.0458273\pi$
$521$	6.23908	+	19.2019i	0.273339	+	0.841251i	−0.716315	+	0.697777i	$0.754173\pi$
$522$	−1.84364	+	3.01107i	−0.0806937	+	0.131791i
$523$	−0.813147	−	1.11920i	−0.0355564	−	0.0489392i	0.790869	−	0.611986i	$-0.209629\pi$
$523$	−0.813147	−	1.11920i	−0.0355564	−	0.0489392i	−0.826425	+	0.563047i	$0.809629\pi$
$524$	−15.4399	+	30.3586i	−0.674494	+	1.32622i
$525$	−6.26729	+	19.2887i	−0.273527	+	0.841829i
$526$	−15.8709	−	3.80397i	−0.692003	−	0.165861i
$527$	−20.7815			−0.905257
$528$	−12.5507	+	3.54933i	−0.546199	+	0.154465i
$529$	21.7664			0.946367
$530$	−7.45355	−	1.78649i	−0.323762	−	0.0776001i
$531$	0.814361	−	2.50635i	0.0353403	−	0.108766i
$532$	19.0125	−	37.3833i	0.824297	−	1.62077i
$533$	−2.74303	−	3.77546i	−0.118814	−	0.163533i
$534$	1.79381	−	2.92969i	0.0776256	−	0.126780i
$535$	−2.22140	−	6.83677i	−0.0960395	−	0.295579i
$536$	1.04128	+	0.887317i	0.0449765	+	0.0383263i
$537$	−7.55076	−	5.48595i	−0.325839	−	0.236736i
$538$	−10.4800	−	25.2742i	−0.451824	−	1.08965i
$539$	−37.6366	+	25.1053i	−1.62112	+	1.08136i
$540$	4.74683	+	4.73973i	0.204271	+	0.203965i
$541$	20.6634	+	15.0128i	0.888389	+	0.645452i	0.935457	−	0.353440i	$-0.114988\pi$
$541$	20.6634	+	15.0128i	0.888389	+	0.645452i	−0.0470688	+	0.998892i	$0.514988\pi$
$542$	0.500124	+	6.32441i	0.0214822	+	0.271657i
$543$	9.78298	−	3.17868i	0.419828	−	0.136410i
$544$	−10.3995	+	17.0420i	−0.445877	+	0.730671i
$545$	6.26823	+	8.62748i	0.268501	+	0.369560i
$546$	−9.66157	−	11.3037i	−0.413477	−	0.483752i
$547$	3.13486	+	1.01858i	0.134037	+	0.0435512i	0.375267	−	0.926917i	$-0.377551\pi$
$547$	3.13486	+	1.01858i	0.134037	+	0.0435512i	−0.241230	+	0.970468i	$0.577551\pi$
$548$	11.9124	−	1.89588i	0.508873	−	0.0809881i
$549$	16.9336			0.722709
$550$	−11.8395	+	17.7033i	−0.504837	+	0.754872i
$551$			5.66697i			0.241421i
$552$	1.61667	+	2.63153i	0.0688102	+	0.112005i
$553$	1.47222	−	4.53101i	0.0626050	−	0.192678i
$554$	−15.5806	−	18.2287i	−0.661954	−	0.774462i
$555$	4.98059	−	3.61861i	0.211414	−	0.153602i
$556$	−28.3176	−	4.46333i	−1.20093	−	0.189287i
$557$	−10.8949	−	33.5309i	−0.461630	−	1.42075i	−0.863172	−	0.504911i	$-0.831525\pi$
$557$	−10.8949	−	33.5309i	−0.461630	−	1.42075i	0.401542	−	0.915841i	$-0.368475\pi$
$558$	−16.8804	+	1.33488i	−0.714605	+	0.0565098i
$559$	2.80384	−	3.85916i	0.118590	−	0.163225i
$560$	12.3170	−	0.0184451i	0.520488	−	0.000779448i
$561$	11.0783	−	3.11504i	0.467727	−	0.131517i
$562$	3.98742	+	9.61630i	0.168199	+	0.405639i
$563$	21.2821	−	29.2923i	0.896934	−	1.23452i	−0.0745021	−	0.997221i	$-0.523737\pi$
$563$	21.2821	−	29.2923i	0.896934	−	1.23452i	0.971436	−	0.237303i	$-0.0762633\pi$
$564$	8.26159	−	4.21728i	0.347876	−	0.177580i
$565$	9.77561	−	3.17629i	0.411263	−	0.133627i
$566$	1.49010	+	0.912367i	0.0626336	+	0.0383496i
$567$	−4.53958	+	3.29820i	−0.190645	+	0.138511i
$568$	−3.23208	+	41.6657i	−0.135615	+	1.74825i
$569$	−31.6218	−	10.2745i	−1.32565	−	0.430731i	−0.441221	−	0.897398i	$-0.645455\pi$
$569$	−31.6218	−	10.2745i	−1.32565	−	0.430731i	−0.884433	+	0.466667i	$0.845455\pi$
$570$	4.22984	+	1.01382i	0.177169	+	0.0424643i
$571$		−	3.91193i		−	0.163709i	−0.996644	−	0.0818547i	$-0.973916\pi$
$571$		−	3.91193i		−	0.163709i	0.996644	−	0.0818547i	$-0.0260843\pi$
$572$	−6.53689	−	14.1809i	−0.273321	−	0.592934i
$573$			1.44304i			0.0602839i
$574$	2.96880	−	12.3864i	0.123915	−	0.516997i
$575$	4.79625	+	1.55839i	0.200017	+	0.0649896i
$576$	−7.35266	+	14.5109i	−0.306361	+	0.604621i
$577$	7.41867	−	5.38998i	0.308843	−	0.224388i	−0.422557	−	0.906337i	$-0.638867\pi$
$577$	7.41867	−	5.38998i	0.308843	−	0.224388i	0.731400	+	0.681949i	$0.238867\pi$
$578$	−3.35587	+	5.48089i	−0.139586	+	0.227975i
$579$	4.71845	−	1.53312i	0.196092	−	0.0637142i
$580$	−1.48231	+	0.756675i	−0.0615497	+	0.0314192i
$581$	19.8875	−	27.3728i	0.825073	−	1.13562i
$582$	−18.7221	+	7.76315i	−0.776055	+	0.321793i
$583$	−16.4354	+	20.8146i	−0.680684	+	0.862053i
$584$	−24.1735	−	9.98118i	−1.00031	−	0.413024i
$585$	−1.90698	+	2.62473i	−0.0788437	+	0.108519i
$586$	−0.167576	−	2.11911i	−0.00692249	−	0.0875396i
$587$	6.32965	+	19.4807i	0.261253	+	0.804053i	0.992533	+	0.121976i	$0.0389231\pi$
$587$	6.32965	+	19.4807i	0.261253	+	0.804053i	−0.731280	+	0.682077i	$0.761077\pi$
$588$	4.17602	−	26.4947i	0.172216	−	1.09262i
$589$	−21.9882	+	15.9754i	−0.906009	+	0.658254i
$590$	0.944301	−	0.807121i	0.0388763	−	0.0332287i
$591$	4.67146	−	14.3773i	0.192158	−	0.591402i
$592$	29.9304	+	21.6773i	1.23013	+	0.890931i
$593$			28.8970i			1.18666i	0.804961	+	0.593328i	$0.202186\pi$
$593$			28.8970i			1.18666i	−0.804961	+	0.593328i	$0.797814\pi$
$594$	21.7796	−	8.02479i	0.893628	−	0.329261i
$595$	−10.8675			−0.445523
$596$	−16.5451	+	2.63319i	−0.677715	+	0.107860i
$597$	−11.8534	−	3.85140i	−0.485127	−	0.157627i
$598$	−2.81072	+	2.40240i	−0.114939	+	0.0982414i
$599$	21.8408	+	30.0612i	0.892389	+	1.22827i	0.972833	+	0.231509i	$0.0743664\pi$
$599$	21.8408	+	30.0612i	0.892389	+	1.22827i	−0.0804433	+	0.996759i	$0.525634\pi$
$600$	−2.96136	−	12.2742i	−0.120897	−	0.501092i
$601$	−2.38032	+	0.773413i	−0.0970953	+	0.0315482i	−0.357162	−	0.934043i	$-0.616256\pi$
$601$	−2.38032	+	0.773413i	−0.0970953	+	0.0315482i	0.260066	+	0.965591i	$0.416256\pi$
$602$	12.9791	−	1.02636i	0.528987	−	0.0418315i
$603$	−0.795695	−	0.578106i	−0.0324032	−	0.0235423i
$604$	−21.3616	+	21.3937i	−0.869193	+	0.870496i
$605$	−3.88550	−	6.36293i	−0.157968	−	0.258690i
$606$	19.1743	−	7.95068i	0.778904	−	0.322974i
$607$	−25.7355	−	18.6979i	−1.04457	−	0.758925i	−0.0733985	−	0.997303i	$-0.523384\pi$
$607$	−25.7355	−	18.6979i	−1.04457	−	0.758925i	−0.971173	+	0.238377i	$0.923384\pi$
$608$	2.09732	+	26.0260i	0.0850576	+	1.05549i
$609$	1.69464	+	5.21555i	0.0686701	+	0.211345i
$610$	6.80745	+	4.16810i	0.275625	+	0.168762i
$611$	6.52733	+	8.98410i	0.264067	+	0.363458i
$612$	6.50653	−	12.7934i	0.263011	−	0.517144i
$613$	−0.969682	+	2.98437i	−0.0391651	+	0.120538i	−0.968728	−	0.248127i	$-0.920185\pi$
$613$	−0.969682	+	2.98437i	−0.0391651	+	0.120538i	0.929562	+	0.368665i	$0.120185\pi$
$614$	−9.28302	+	38.7304i	−0.374632	+	1.56303i
$615$	1.32098			0.0532670
$616$	17.8298	−	38.7103i	0.718382	−	1.55968i
$617$	−23.5622			−0.948577			−0.474289	−	0.880369i	$-0.657295\pi$
$617$	−23.5622			−0.948577			−0.474289	+	0.880369i	$0.657295\pi$
$618$	−1.97292	+	8.23140i	−0.0793627	+	0.331115i
$619$	9.71231	−	29.8914i	0.390371	−	1.20144i	−0.542138	−	0.840289i	$-0.682385\pi$
$619$	9.71231	−	29.8914i	0.390371	−	1.20144i	0.932509	−	0.361148i	$-0.117615\pi$
$620$	−7.11463	−	3.61838i	−0.285730	−	0.145318i
$621$	−3.23057	−	4.44650i	−0.129638	−	0.178432i
$622$	37.6926	+	23.0787i	1.51134	+	0.925370i
$623$	3.46871	+	10.6756i	0.138971	+	0.427709i
$624$	8.80870	+	2.84754i	0.352630	+	0.113993i
$625$	−14.8216	−	10.7685i	−0.592862	−	0.430739i
$626$	12.8729	−	5.33776i	0.514503	−	0.213340i
$627$	9.32698	−	11.8122i	0.372484	−	0.471732i
$628$	16.9502	+	16.9248i	0.676386	+	0.675374i
$629$	−26.3793	−	19.1657i	−1.05181	−	0.764187i
$630$	−8.82744	+	0.698060i	−0.351693	+	0.0278114i
$631$	12.5873	−	4.08986i	0.501092	−	0.162815i	−0.0475553	−	0.998869i	$-0.515143\pi$
$631$	12.5873	−	4.08986i	0.501092	−	0.162815i	0.548647	+	0.836054i	$0.315143\pi$
$632$	0.695637	+	2.88327i	0.0276710	+	0.114690i
$633$	−1.10426	−	1.51988i	−0.0438903	−	0.0604098i
$634$	−2.70079	+	2.30844i	−0.107262	+	0.0916799i
$635$	−3.98005	−	1.29320i	−0.157943	−	0.0513189i
$636$	−2.47129	−	15.5279i	−0.0979932	−	0.615720i
$637$	32.1112			1.27229
$638$	0.223730	+	5.75435i	0.00885756	+	0.227817i
$639$		−	30.0444i		−	1.18854i
$640$	−6.52760	+	4.02369i	−0.258026	+	0.159050i
$641$	1.84448	−	5.67673i	0.0728527	−	0.224217i	−0.907999	−	0.418971i	$-0.862391\pi$
$641$	1.84448	−	5.67673i	0.0728527	−	0.224217i	0.980852	+	0.194754i	$0.0623908\pi$
$642$	11.2099	−	9.58143i	0.442420	−	0.378149i
$643$	−16.6320	+	12.0839i	−0.655903	+	0.476542i	−0.865277	−	0.501294i	$-0.832858\pi$
$643$	−16.6320	+	12.0839i	−0.655903	+	0.476542i	0.209374	+	0.977836i	$0.432858\pi$
$644$	−9.96882	−	1.57126i	−0.392827	−	0.0619161i
$645$	0.417255	+	1.28418i	0.0164294	+	0.0505645i
$646$	−1.81611	−	22.9659i	−0.0714537	−	0.903581i
$647$	−20.0669	+	27.6197i	−0.788911	+	1.08584i	0.205332	+	0.978692i	$0.434173\pi$
$647$	−20.0669	+	27.6197i	−0.788911	+	1.08584i	−0.994243	+	0.107150i	$0.965827\pi$
$648$	1.33322	−	3.22892i	0.0523736	−	0.126844i
$649$	−1.16351	−	4.13790i	−0.0456717	−	0.162427i
$650$	13.9635	−	5.79001i	0.547695	−	0.227103i
$651$	−15.4594	+	21.2781i	−0.605903	+	0.833955i
$652$	0.296018	+	0.579894i	0.0115930	+	0.0227104i
$653$	21.8273	−	7.09213i	0.854169	−	0.277536i	0.150978	−	0.988537i	$-0.451758\pi$
$653$	21.8273	−	7.09213i	0.854169	−	0.277536i	0.703191	+	0.711001i	$0.251758\pi$
$654$	−11.4234	+	18.6570i	−0.446692	+	0.729548i
$655$	9.33782	−	6.78433i	0.364859	−	0.265086i
$656$	2.46170	+	7.53789i	0.0961131	+	0.294305i
$657$	17.8818	+	5.81015i	0.697635	+	0.226675i
$658$	−7.06457	+	29.4747i	−0.275406	+	1.14904i
$659$		−	11.3191i		−	0.440930i	−0.975395	−	0.220465i	$-0.929242\pi$
$659$		−	11.3191i		−	0.440930i	0.975395	−	0.220465i	$-0.0707575\pi$
$660$	4.33508	+	0.862459i	0.168743	+	0.0335712i
$661$			29.7411i			1.15680i	0.815755	+	0.578398i	$0.196322\pi$
$661$			29.7411i			1.15680i	−0.815755	+	0.578398i	$0.803678\pi$
$662$	−4.59885	−	1.10227i	−0.178739	−	0.0428408i
$663$	−7.76827	−	2.52406i	−0.301695	−	0.0980265i
$664$	−1.62909	+	21.0010i	−0.0632208	+	0.814998i
$665$	−11.4985	+	8.35416i	−0.445893	+	0.323960i
$666$	−22.6585	−	13.8735i	−0.877999	−	0.537586i
$667$	1.29687	−	0.421380i	0.0502152	−	0.0163159i
$668$	10.0679	+	19.7228i	0.389538	+	0.763099i
$669$	6.05079	−	8.32820i	0.233937	−	0.321987i
$670$	−0.177579	−	0.428259i	−0.00686046	−	0.0165451i
$671$	22.9769	−	15.3266i	0.887014	−	0.591679i
$672$	9.71300	+	23.3257i	0.374687	+	0.899807i
$673$	−14.6339	+	20.1418i	−0.564095	+	0.776410i	−0.991840	−	0.127489i	$-0.959308\pi$
$673$	−14.6339	+	20.1418i	−0.564095	+	0.776410i	0.427745	+	0.903899i	$0.359308\pi$
$674$	23.4742	−	1.85630i	0.904192	−	0.0715021i
$675$	6.94352	+	21.3700i	0.267256	+	0.822530i
$676$	2.32248	−	14.7350i	0.0893261	−	0.566729i
$677$	31.1545	−	22.6351i	1.19736	−	0.869936i	0.203341	−	0.979108i	$-0.434820\pi$
$677$	31.1545	−	22.6351i	1.19736	−	0.869936i	0.994023	+	0.109172i	$0.0348199\pi$
$678$	13.7001	+	16.0286i	0.526149	+	0.615574i
$679$	20.4653	−	62.9858i	0.785387	−	2.41717i
$680$	5.76470	−	3.54153i	0.221066	−	0.135811i
$681$			14.9463i			0.572745i
$682$	−21.6965	+	17.0898i	−0.830803	+	0.654401i
$683$	32.8926			1.25860			0.629299	−	0.777163i	$-0.283342\pi$
$683$	32.8926			1.25860			0.629299	+	0.777163i	$0.283342\pi$
$684$	−2.95037	−	18.5381i	−0.112810	−	0.708821i
$685$	−3.88767	−	1.26318i	−0.148540	−	0.0482637i
$686$	27.7226	+	32.4344i	1.05845	+	1.23835i
$687$	−15.2570	−	20.9995i	−0.582093	−	0.801182i
$688$	−6.55033	+	4.77410i	−0.249729	+	0.182011i
$689$	17.9027	−	5.81694i	0.682038	−	0.221608i
$690$	−0.0825085	−	1.04338i	−0.00314105	−	0.0397206i
$691$	−35.0702	−	25.4800i	−1.33413	−	0.969303i	−0.999638	−	0.0269051i	$-0.991435\pi$
$691$	−35.0702	−	25.4800i	−1.33413	−	0.969303i	−0.334493	−	0.942398i	$-0.608565\pi$
$692$	28.6285	−	28.6714i	1.08829	−	1.08992i
$693$	−10.6275	+	28.7378i	−0.403706	+	1.09166i
$694$	10.7975	+	26.0399i	0.409868	+	0.988463i
$695$	7.85950	+	5.71026i	0.298128	+	0.216602i
$696$	−2.59859	−	2.21436i	−0.0984992	−	0.0839351i
$697$	−2.16203	−	6.65404i	−0.0818926	−	0.252040i
$698$	−0.218611	+	0.357041i	−0.00827456	+	0.0135142i
$699$	−3.50820	−	4.82863i	−0.132692	−	0.182636i
$700$	36.7753	+	18.7033i	1.38997	+	0.706917i
$701$	0.458220	−	1.41026i	0.0173067	−	0.0532647i	−0.942030	−	0.335528i	$-0.891085\pi$
$701$	0.458220	−	1.41026i	0.0173067	−	0.0532647i	0.959337	+	0.282263i	$0.0910852\pi$
$702$	−16.0208	−	3.83990i	−0.604665	−	0.144928i
$703$	−42.6443			−1.60836
$704$	3.15715	+	26.3445i	0.118990	+	0.992895i
$705$	−3.14341			−0.118388
$706$	−16.9339	−	4.05876i	−0.637316	−	0.152754i
$707$	−20.9597	+	64.5072i	−0.788270	+	2.42604i
$708$	2.27144	+	1.15522i	0.0853660	+	0.0434157i
$709$	4.74019	+	6.52432i	0.178022	+	0.245026i	0.888698	−	0.458494i	$-0.151611\pi$
$709$	4.74019	+	6.52432i	0.178022	+	0.245026i	−0.710676	+	0.703519i	$0.751611\pi$
$710$	7.39526	−	12.0781i	0.277539	−	0.453283i
$711$	−0.658925	−	2.02796i	−0.0247116	−	0.0760545i
$712$	−5.31899	−	4.53253i	−0.199338	−	0.169864i
$713$	5.29091	+	3.84407i	0.198146	+	0.143962i
$714$	−8.53909	−	20.5934i	−0.319568	−	0.770688i
$715$	−0.211895	+	5.28745i	−0.00792441	+	0.197740i
$716$	−13.4154	+	13.4355i	−0.501358	+	0.502109i
$717$	9.88324	+	7.18060i	0.369096	+	0.268164i
$718$	1.31933	+	16.6839i	0.0492371	+	0.622636i
$719$	8.47135	−	2.75251i	0.315928	−	0.102651i	−0.146761	−	0.989172i	$-0.546885\pi$
$719$	8.47135	−	2.75251i	0.315928	−	0.102651i	0.462689	+	0.886521i	$0.346885\pi$
$720$	4.45507	−	3.24700i	0.166031	−	0.121009i
$721$	−16.2574	−	22.3764i	−0.605458	−	0.833342i
$722$	−2.11777	−	2.47771i	−0.0788153	−	0.0922109i
$723$	−8.07718	−	2.62443i	−0.300393	−	0.0976037i
$724$	−3.28895	−	20.6655i	−0.122233	−	0.768026i
$725$	−5.57479			−0.207043
$726$	9.00444	−	12.3625i	0.334186	−	0.458816i
$727$		−	34.2174i		−	1.26905i	−0.772901	−	0.634527i	$-0.781195\pi$
$727$		−	34.2174i		−	1.26905i	0.772901	−	0.634527i	$-0.218805\pi$
$728$	−25.7746	+	15.8345i	−0.955269	+	0.586866i
$729$	3.73420	−	11.4927i	0.138304	−	0.425655i
$730$	5.75849	+	6.73722i	0.213131	+	0.249356i
$731$	5.78575	−	4.20360i	0.213994	−	0.155476i
$732$	−2.54944	+	16.1749i	−0.0942299	+	0.597841i
$733$	10.4338	+	32.1121i	0.385383	+	1.18609i	0.936202	+	0.351462i	$0.114315\pi$
$733$	10.4338	+	32.1121i	0.385383	+	1.18609i	−0.550820	+	0.834624i	$0.685685\pi$
$734$	36.5509	−	2.89039i	1.34912	−	0.106686i
$735$	−5.34268	+	7.35356i	−0.197068	+	0.271240i
$736$	5.80005	−	2.41519i	0.213793	−	0.0890251i
$737$	−1.60291	−	0.0642366i	−0.0590439	−	0.00236619i
$738$	−2.18359	−	5.26606i	−0.0803789	−	0.193847i
$739$	17.0290	−	23.4384i	0.626421	−	0.862195i	−0.371379	−	0.928481i	$-0.621115\pi$
$739$	17.0290	−	23.4384i	0.626421	−	0.862195i	0.997801	+	0.0662863i	$0.0211151\pi$
$740$	−5.69403	−	11.1545i	−0.209317	−	0.410048i
$741$	−10.1597	+	3.30108i	−0.373225	+	0.121268i
$742$	43.8167	+	26.8283i	1.60856	+	0.984899i
$743$	−7.72726	+	5.61419i	−0.283486	+	0.205964i	−0.720436	−	0.693521i	$-0.756058\pi$
$743$	−7.72726	+	5.61419i	−0.283486	+	0.205964i	0.436951	+	0.899486i	$0.356058\pi$
$744$	1.26636	−	16.3250i	0.0464270	−	0.598505i
$745$	5.39958	+	1.75443i	0.197825	+	0.0642774i
$746$	−21.1770	−	5.07576i	−0.775345	−	0.185837i
$747$		−	15.1435i		−	0.554072i
$748$	−2.75079	−	23.2483i	−0.100579	−	0.850041i
$749$			48.1865i			1.76070i
$750$	−2.09556	+	8.74305i	−0.0765190	+	0.319251i
$751$	7.57353	+	2.46079i	0.276362	+	0.0897955i	0.443919	−	0.896067i	$-0.353588\pi$
$751$	7.57353	+	2.46079i	0.276362	+	0.0897955i	−0.167557	+	0.985862i	$0.553588\pi$
$752$	−5.85786	−	17.9372i	−0.213614	−	0.654103i
$753$	0.219291	−	0.159324i	0.00799140	−	0.00580609i
$754$	2.13434	−	3.48586i	0.0777281	−	0.126947i
$755$	9.74392	−	3.16599i	0.354617	−	0.115222i
$756$	−20.4437	−	40.0488i	−0.743530	−	1.45656i
$757$	8.25126	−	11.3569i	0.299897	−	0.412773i	−0.632300	−	0.774724i	$-0.717889\pi$
$757$	8.25126	−	11.3569i	0.299897	−	0.412773i	0.932197	+	0.361950i	$0.117889\pi$
$758$	−10.8027	+	4.47935i	−0.392371	+	0.162697i
$759$	−3.39672	−	1.25614i	−0.123293	−	0.0455950i
$760$	3.37696	−	8.17867i	0.122495	−	0.296672i
$761$	−17.6554	+	24.3006i	−0.640008	+	0.880895i	−0.998616	−	0.0525928i	$-0.983251\pi$
$761$	−17.6554	+	24.3006i	−0.640008	+	0.880895i	0.358608	+	0.933488i	$0.383251\pi$
$762$	−0.676764	−	8.55814i	−0.0245166	−	0.310029i
$763$	−22.0897	−	67.9851i	−0.799700	−	2.46122i
$764$	2.89976	+	0.457051i	0.104910	+	0.0165355i
$765$	−3.93506	+	2.85899i	−0.142272	+	0.103367i
$766$	−0.172196	+	0.147181i	−0.00622170	+	0.00531787i
$767$	−0.942770	+	2.90155i	−0.0340414	+	0.104769i
$768$	−12.7537	−	9.20791i	−0.460211	−	0.332262i
$769$		−	9.64819i		−	0.347923i	−0.984752	−	0.173961i	$-0.944343\pi$
$769$		−	9.64819i		−	0.347923i	0.984752	−	0.173961i	$-0.0556568\pi$
$770$	−11.3460	+	8.93692i	−0.408881	+	0.322064i
$771$	−6.87230			−0.247500
$772$	−1.58630	−	9.96720i	−0.0570922	−	0.358727i
$773$	26.9139	+	8.74484i	0.968024	+	0.314530i	0.750018	−	0.661417i	$-0.230045\pi$
$773$	26.9139	+	8.74484i	0.968024	+	0.314530i	0.218006	+	0.975947i	$0.430045\pi$
$774$	4.42964	−	3.78614i	0.159220	−	0.136090i
$775$	−15.7155	−	21.6305i	−0.564518	−	0.776992i
$776$	9.67007	+	40.0804i	0.347135	+	1.43880i
$777$	−39.2474	+	12.7522i	−1.40799	+	0.457484i
$778$	20.9714	−	1.65839i	0.751862	−	0.0594560i
$779$	−7.40272	−	5.37839i	−0.265230	−	0.192701i
$780$	−2.22002	−	2.21670i	−0.0794894	−	0.0793705i
$781$	−27.1933	−	40.7668i	−0.973053	−	1.45875i
$782$	−5.12066	+	2.12329i	−0.183114	+	0.0759287i
$783$	4.91532	+	3.57119i	0.175659	+	0.127624i
$784$	−51.9179	−	16.7832i	−1.85421	−	0.599401i
$785$	−2.50841	−	7.72010i	−0.0895291	−	0.275542i
$786$	20.1932	+	12.3640i	0.720266	+	0.441009i
$787$	8.29975	+	11.4236i	0.295854	+	0.407208i	0.930905	−	0.365262i	$-0.119021\pi$
$787$	8.29975	+	11.4236i	0.295854	+	0.407208i	−0.635051	+	0.772471i	$0.719021\pi$
$788$	−27.4112	−	13.9409i	−0.976485	−	0.496623i
$789$	−3.50603	+	10.7905i	−0.124818	+	0.384150i
$790$	0.234277	−	0.977447i	0.00833522	−	0.0347760i
$791$	−68.8999			−2.44980
$792$	−3.72774	−	18.7074i	−0.132459	−	0.664739i
$793$	−19.6037			−0.696148
$794$	−4.65394	+	19.4171i	−0.165162	+	0.689086i
$795$	−1.64656	+	5.06760i	−0.0583976	+	0.179729i
$796$	−11.4936	+	22.5993i	−0.407380	+	0.801010i
$797$	−19.7252	−	27.1494i	−0.698703	−	0.961683i	−0.999967	−	0.00814175i	$-0.997408\pi$
$797$	−19.7252	−	27.1494i	−0.698703	−	0.961683i	0.301263	−	0.953541i	$-0.402592\pi$
$798$	−24.8657	−	15.2249i	−0.880236	−	0.538956i
$799$	5.14477	+	15.8340i	0.182009	+	0.560166i
$800$	−25.6027	+	2.06320i	−0.905191	+	0.0729453i
$801$	4.06451	+	2.95304i	0.143612	+	0.104340i
$802$	−20.8166	+	8.63165i	−0.735060	+	0.304794i
$803$	29.5223	−	8.30117i	1.04182	−	0.292942i
$804$	0.672000	−	0.673007i	0.0236996	−	0.0237351i
$805$	2.76683	+	2.01022i	0.0975179	+	0.0708509i
$806$	19.5421	−	1.54536i	0.688342	−	0.0544330i
$807$	−18.0900	+	5.87780i	−0.636798	+	0.206908i
$808$	−9.90366	−	41.0486i	−0.348410	−	1.44408i
$809$	−19.0271	−	26.1886i	−0.668959	−	0.920743i	0.330778	−	0.943709i	$-0.392689\pi$
$809$	−19.0271	−	26.1886i	−0.668959	−	0.920743i	−0.999736	+	0.0229661i	$0.992689\pi$
$810$	−0.899909	+	0.769178i	−0.0316196	+	0.0270262i
$811$	48.3019	+	15.6943i	1.69611	+	0.551100i	0.987926	−	0.154927i	$-0.0495143\pi$
$811$	48.3019	+	15.6943i	1.69611	+	0.551100i	0.708185	+	0.706027i	$0.249514\pi$
$812$	11.0173	−	1.75342i	0.386631	−	0.0615331i
$813$	4.41039			0.154679
$814$	−43.3018	+	1.68358i	−1.51773	+	0.0590096i
$815$		−	0.220641i		−	0.00772872i
$816$	11.2406	+	8.14111i	0.393501	+	0.284996i
$817$	2.89028	−	8.89536i	0.101118	−	0.311209i
$818$	21.5964	−	18.4590i	0.755100	−	0.645405i
$819$	17.5940	−	12.7828i	0.614785	−	0.446667i
$820$	0.418391	−	2.65448i	0.0146108	−	0.0926983i
$821$	6.41880	+	19.7550i	0.224018	+	0.689455i	0.998390	+	0.0567249i	$0.0180658\pi$
$821$	6.41880	+	19.7550i	0.224018	+	0.689455i	−0.774372	+	0.632730i	$0.781934\pi$
$822$	−0.661056	−	8.35950i	−0.0230570	−	0.291571i
$823$	25.5250	−	35.1322i	0.889746	−	1.22463i	−0.0838787	−	0.996476i	$-0.526731\pi$
$823$	25.5250	−	35.1322i	0.889746	−	1.22463i	0.973625	−	0.228155i	$-0.0732692\pi$
$824$	15.9159	+	6.57166i	0.554458	+	0.228935i
$825$	11.6200	+	9.17526i	0.404557	+	0.319442i
$826$	−7.69189	+	3.18946i	−0.267635	+	0.110975i
$827$	−4.54817	+	6.26002i	−0.158155	+	0.217682i	−0.880740	−	0.473600i	$-0.842954\pi$
$827$	−4.54817	+	6.26002i	−0.158155	+	0.217682i	0.722584	+	0.691283i	$0.242954\pi$
$828$	−4.02302	+	2.05363i	−0.139810	+	0.0713684i
$829$	42.6182	−	13.8475i	1.48019	−	0.480944i	0.546022	−	0.837771i	$-0.316141\pi$
$829$	42.6182	−	13.8475i	1.48019	−	0.480944i	0.934170	+	0.356827i	$0.116141\pi$
$830$	3.72748	−	6.08781i	0.129383	−	0.211311i
$831$	−13.4868	+	9.79874i	−0.467852	+	0.339914i
$832$	8.51203	−	16.7990i	0.295102	−	0.582400i
$833$	45.7857	+	14.8767i	1.58638	+	0.515446i
$834$	−4.64511	+	19.3802i	−0.160847	+	0.671082i
$835$		−	7.50423i		−	0.259695i
$836$	−20.7822	−	22.4836i	−0.718766	−	0.777611i
$837$			29.1391i			1.00719i
$838$	−19.0329	−	4.56186i	−0.657481	−	0.157587i
$839$	39.1351	+	12.7158i	1.35109	+	0.438997i	0.893060	−	0.449937i	$-0.148554\pi$
$839$	39.1351	+	12.7158i	1.35109	+	0.438997i	0.458035	+	0.888934i	$0.348554\pi$
$840$	0.662231	−	8.53701i	0.0228491	−	0.294555i
$841$	22.2420	−	16.1598i	0.766965	−	0.557233i
$842$	15.2143	+	9.31548i	0.524318	+	0.321033i
$843$	6.88287	−	2.23638i	0.237059	−	0.0770250i
$844$	−3.40391	+	1.73759i	−0.117167	+	0.0598103i
$845$	−2.97131	+	4.08966i	−0.102216	+	0.140689i
$846$	5.19607	+	12.5312i	0.178645	+	0.430830i
$847$	11.5903	+	48.6128i	0.398249	+	1.67035i
$848$	−31.9857	+	0.0478996i	−1.09839	+	0.00164488i
$849$	0.713957	−	0.982677i	0.0245029	−	0.0337254i
$850$	22.5923	−	1.78656i	0.774910	−	0.0612786i
$851$	3.17091	+	9.75907i	0.108698	+	0.334537i
$852$	28.6983	+	4.52334i	0.983187	+	0.154967i
$853$	13.8750	−	10.0808i	0.475071	−	0.345159i	−0.324343	−	0.945939i	$-0.605143\pi$
$853$	13.8750	−	10.0808i	0.475071	−	0.345159i	0.799414	+	0.600780i	$0.205143\pi$
$854$	−34.7644	−	40.6730i	−1.18961	−	1.39180i
$855$	−1.96576	+	6.04999i	−0.0672276	+	0.206905i
$856$	−15.7032	−	25.5608i	−0.536723	−	0.873649i
$857$			55.4066i			1.89265i	0.323210	+	0.946327i	$0.395238\pi$
$857$			55.4066i			1.89265i	−0.323210	+	0.946327i	$0.604762\pi$
$858$	−10.1860	+	3.75307i	−0.347744	+	0.128128i
$859$	4.87871			0.166459			0.0832297	−	0.996530i	$-0.473476\pi$
$859$	4.87871			0.166459			0.0832297	+	0.996530i	$0.473476\pi$
$860$	2.71268	−	0.431729i	0.0925018	−	0.0147219i
$861$	−8.42138	−	2.73627i	−0.287000	−	0.0932519i
$862$	−14.3306	−	16.7663i	−0.488103	−	0.571062i
$863$	0.0613516	+	0.0844432i	0.00208843	+	0.00287448i	0.810060	−	0.586347i	$-0.199435\pi$
$863$	0.0613516	+	0.0844432i	0.00208843	+	0.00287448i	−0.807972	+	0.589222i	$0.799435\pi$
$864$	23.8957	+	14.5818i	0.812948	+	0.496084i
$865$	−13.0586	+	4.24300i	−0.444006	+	0.144266i
$866$	−0.0850640	−	1.07569i	−0.00289059	−	0.0365535i
$867$	3.61449	+	2.62608i	0.122754	+	0.0891863i
$868$	37.8614	+	37.8048i	1.28510	+	1.28318i
$869$	−2.72960	−	2.15531i	−0.0925952	−	0.0731139i
$870$	0.443159	+	1.06875i	0.0150245	+	0.0362340i
$871$	0.921160	+	0.669262i	0.0312123	+	0.0226771i
$872$	33.8728	+	28.8643i	1.14708	+	0.977470i
$873$	−9.15974	−	28.1908i	−0.310010	−	0.954113i
$874$	−3.78575	+	6.18298i	−0.128055	+	0.209143i
$875$	−17.2680	−	23.7673i	−0.583764	−	0.803482i
$876$	−8.24201	+	16.2058i	−0.278472	+	0.547545i
$877$	−12.2636	+	37.7435i	−0.414113	+	1.27451i	0.498929	+	0.866643i	$0.333727\pi$
$877$	−12.2636	+	37.7435i	−0.414113	+	1.27451i	−0.913042	+	0.407866i	$0.866273\pi$
$878$	−2.23415	−	0.535488i	−0.0753989	−	0.0180718i
$879$	−1.47778			−0.0498443
$880$	3.10613	−	8.43809i	0.104708	−	0.284448i
$881$	45.8159			1.54358			0.771789	−	0.635879i	$-0.219362\pi$
$881$	45.8159			1.54358			0.771789	+	0.635879i	$0.219362\pi$
$882$	38.1464	+	9.14303i	1.28446	+	0.307862i
$883$	−15.4974	+	47.6960i	−0.521528	+	1.60510i	0.249552	+	0.968361i	$0.419717\pi$
$883$	−15.4974	+	47.6960i	−0.521528	+	1.60510i	−0.771081	+	0.636738i	$0.780283\pi$
$884$	−7.53248	+	14.8107i	−0.253345	+	0.498138i
$885$	−0.507605	−	0.698658i	−0.0170630	−	0.0234851i
$886$	−24.5021	+	40.0174i	−0.823163	+	1.34441i
$887$	−1.87115	−	5.75880i	−0.0628270	−	0.193362i	0.914716	−	0.404097i	$-0.132414\pi$
$887$	−1.87115	−	5.75880i	−0.0628270	−	0.193362i	−0.977543	+	0.210735i	$0.932414\pi$
$888$	16.6632	−	19.5545i	0.559181	−	0.656208i
$889$	22.6945	+	16.4885i	0.761149	+	0.553007i
$890$	0.907093	+	2.18760i	0.0304058	+	0.0733285i
$891$	1.10881	+	3.94337i	0.0371466	+	0.132108i
$892$	−14.8189	−	14.7967i	−0.496173	−	0.495430i
$893$	17.6156	+	12.7985i	0.589482	+	0.428284i
$894$	0.918140	+	11.6105i	0.0307072	+	0.388313i
$895$	6.11932	−	1.98829i	0.204546	−	0.0664612i
$896$	49.9488	−	12.1302i	1.66867	−	0.405241i
$897$	1.51089	+	2.07956i	0.0504471	+	0.0694345i
$898$	−23.3985	−	27.3754i	−0.780819	−	0.913528i
$899$	−6.87563	−	2.23403i	−0.229315	−	0.0745090i
$900$	18.2365	−	2.90238i	0.607884	−	0.0967460i
$901$	28.2214			0.940192
$902$	−7.72920	−	5.16906i	−0.257354	−	0.172111i
$903$		−	9.05108i		−	0.301201i
$904$	36.5483	−	22.4533i	1.21558	−	0.746786i
$905$	−2.19135	+	6.74428i	−0.0728429	+	0.224187i
$906$	13.6557	+	15.9766i	0.453679	+	0.530788i
$907$	−48.4559	+	35.2053i	−1.60895	+	1.16897i	−0.742290	+	0.670079i	$0.766260\pi$
$907$	−48.4559	+	35.2053i	−1.60895	+	1.16897i	−0.866663	+	0.498894i	$0.833740\pi$
$908$	30.0344	+	4.73392i	0.996725	+	0.157101i
$909$	9.38100	+	28.8717i	0.311148	+	0.957615i
$910$	10.2193	−	0.808130i	0.338768	−	0.0267892i
$911$	−26.1407	+	35.9795i	−0.866079	+	1.19206i	0.114007	+	0.993480i	$0.463631\pi$
$911$	−26.1407	+	35.9795i	−0.866079	+	1.19206i	−0.980086	+	0.198575i	$0.936369\pi$
$912$	18.1517	−	0.0271827i	0.601061	−	0.000900109i
$913$	−13.7064	−	20.5479i	−0.453616	−	0.680038i
$914$	−18.7367	−	45.1866i	−0.619755	−	1.49464i
$915$	3.26167	−	4.48931i	0.107828	−	0.148412i
$916$	−47.0304	+	24.0076i	−1.55393	+	0.793232i
$917$	−73.5827	+	23.9085i	−2.42991	+	0.789527i
$918$	−21.0642	−	12.8973i	−0.695223	−	0.425675i
$919$	6.54928	−	4.75833i	0.216041	−	0.156963i	−0.474502	−	0.880255i	$-0.657372\pi$
$919$	6.54928	−	4.75833i	0.216041	−	0.156963i	0.690543	+	0.723292i	$0.257372\pi$
$920$	−2.12277	−	0.164667i	−0.0699858	−	0.00542891i
$921$	26.3325	+	8.55594i	0.867684	+	0.281928i
$922$	−15.8421	−	3.79709i	−0.521733	−	0.125051i
$923$			34.7819i			1.14486i
$924$	−25.8501	−	14.4780i	−0.850407	−	0.476290i
$925$		−	41.9507i		−	1.37933i
$926$	−3.64046	+	15.1887i	−0.119633	+	0.499130i
$927$	−11.7735	−	3.82543i	−0.386691	−	0.125644i
$928$	−5.27275	+	4.52045i	−0.173087	+	0.148391i
$929$	−3.99231	+	2.90059i	−0.130984	+	0.0951651i	−0.651348	−	0.758779i	$-0.725796\pi$
$929$	−3.99231	+	2.90059i	−0.130984	+	0.0951651i	0.520364	+	0.853944i	$0.325796\pi$
$930$	−2.89754	+	4.73232i	−0.0950139	+	0.155179i
$931$	59.8804	−	19.4563i	1.96250	−	0.637655i
$932$	−10.8142	+	5.52030i	−0.354230	+	0.180823i
$933$	18.0598	−	24.8572i	0.591251	−	0.813788i
$934$	17.3461	−	7.19261i	0.567583	−	0.235350i
$935$	−2.75173	+	7.44094i	−0.0899913	+	0.243345i
$936$	−5.16713	+	12.5143i	−0.168893	+	0.409042i
$937$	−1.64936	+	2.27015i	−0.0538822	+	0.0741625i	−0.835108	−	0.550086i	$-0.814595\pi$
$937$	−1.64936	+	2.27015i	−0.0538822	+	0.0741625i	0.781226	+	0.624249i	$0.214595\pi$
$938$	0.244987	+	3.09803i	0.00799912	+	0.101154i
$939$	−2.99373	−	9.21375i	−0.0976966	−	0.300679i
$940$	−0.995604	+	6.31661i	−0.0324730	+	0.206025i
$941$	25.4946	−	18.5229i	0.831102	−	0.603831i	−0.0887691	−	0.996052i	$-0.528293\pi$
$941$	25.4946	−	18.5229i	0.831102	−	0.603831i	0.919871	+	0.392222i	$0.128293\pi$
$942$	12.6583	−	10.8194i	0.412429	−	0.352514i
$943$	−0.680388	+	2.09402i	−0.0221565	+	0.0681907i
$944$	3.04081	−	4.19852i	0.0989699	−	0.136650i
$945$			15.2380i			0.495691i
$946$	2.58366	−	9.14662i	0.0840019	−	0.297382i
$947$	−35.0634			−1.13941			−0.569703	−	0.821850i	$-0.692942\pi$
$947$	−35.0634			−1.13941			−0.569703	+	0.821850i	$0.692942\pi$
$948$	2.03630	−	0.324082i	0.0661360	−	0.0105257i
$949$	−20.7014	−	6.72629i	−0.671996	−	0.218345i
$950$	22.5308	−	19.2577i	0.730995	−	0.624802i
$951$	1.45180	+	1.99823i	0.0470778	+	0.0647970i
$952$	−44.0865	+	10.6366i	−1.42885	+	0.344735i
$953$	23.1273	−	7.51452i	0.749167	−	0.243419i	0.0905443	−	0.995892i	$-0.471139\pi$
$953$	23.1273	−	7.51452i	0.749167	−	0.243419i	0.658623	+	0.752473i	$0.271139\pi$
$954$	22.9237	−	1.81277i	0.742182	−	0.0586906i
$955$	−0.804822	−	0.584738i	−0.0260434	−	0.0189217i
$956$	17.5595	−	17.5859i	0.567916	−	0.568767i
$957$	4.00017	+	0.160307i	0.129307	+	0.00518199i
$958$	12.3712	−	5.12976i	0.399696	−	0.165735i
$959$	22.1678	+	16.1058i	0.715835	+	0.520084i
$960$	2.43078	+	4.74431i	0.0784532	+	0.153122i
$961$	−1.13493	−	3.49294i	−0.0366105	−	0.112676i
$962$	26.2313	+	16.0611i	0.845731	+	0.517829i
$963$	12.6768	+	17.4481i	0.408503	+	0.562257i
$964$	−7.83201	+	15.3997i	−0.252252	+	0.495990i
$965$	−1.05691	+	3.25284i	−0.0340232	+	0.104713i
$966$	−1.63525	+	6.82254i	−0.0526132	+	0.219512i
$967$	11.0350			0.354861			0.177431	−	0.984133i	$-0.443221\pi$
$967$	11.0350			0.354861			0.177431	+	0.984133i	$0.443221\pi$
$968$	−21.9902	−	22.0098i	−0.706793	−	0.707421i
$969$	−16.0155			−0.514491
$970$	3.25670	−	13.5875i	0.104566	−	0.436269i
$971$	4.23253	−	13.0264i	0.135828	−	0.418037i	−0.859890	−	0.510480i	$-0.829468\pi$
$971$	4.23253	−	13.0264i	0.135828	−	0.418037i	0.995718	+	0.0924434i	$0.0294677\pi$
$972$	−28.6301	−	14.5608i	−0.918311	−	0.467037i
$973$	−38.2769	−	52.6837i	−1.22710	−	1.68896i
$974$	−32.9798	−	20.1931i	−1.05674	−	0.647027i
$975$	−3.24738	−	9.99440i	−0.103999	−	0.320077i
$976$	31.6956	+	10.2461i	1.01455	+	0.327969i
$977$	1.23456	+	0.896963i	0.0394972	+	0.0286964i	0.607359	−	0.794428i	$-0.292229\pi$
$977$	1.23456	+	0.896963i	0.0394972	+	0.0286964i	−0.567862	+	0.823124i	$0.692229\pi$
$978$	0.418105	−	0.173368i	0.0133695	−	0.00554370i
$979$	8.18786	+	0.328129i	0.261685	+	0.0104870i
$980$	13.0846	+	13.0651i	0.417974	+	0.417348i
$981$	−25.8839	−	18.8057i	−0.826409	−	0.600421i
$982$	33.4865	−	2.64806i	1.06860	−	0.0845029i
$983$	39.0389	−	12.6845i	1.24515	−	0.404572i	0.388967	−	0.921252i	$-0.372832\pi$
$983$	39.0389	−	12.6845i	1.24515	−	0.404572i	0.856179	+	0.516679i	$0.172832\pi$
$984$	5.35886	−	1.29292i	0.170834	−	0.0412167i
$985$	6.12566	+	8.43125i	0.195180	+	0.268642i
$986$	4.65819	−	3.98149i	0.148347	−	0.126796i
$987$	20.0396	+	6.51125i	0.637866	+	0.207255i
$988$	3.41559	+	21.4612i	0.108664	+	0.682770i
$989$	−2.25060			−0.0715649
$990$	−1.75722	+	6.22088i	−0.0558481	+	0.197712i
$991$		−	0.742581i		−	0.0235889i	−0.999930	−	0.0117944i	$-0.996246\pi$
$991$		−	0.742581i		−	0.0235889i	0.999930	−	0.0117944i	$-0.00375437\pi$
$992$	−32.4037	−	7.71532i	−1.02882	−	0.244962i
$993$	−1.01593	+	3.12672i	−0.0322396	+	0.0992233i
$994$	−72.1641	+	61.6807i	−2.28891	+	1.95639i
$995$	6.95117	−	5.05032i	0.220367	−	0.160106i
$996$	14.4650	+	2.27993i	0.458341	+	0.0722423i
$997$	−5.30363	−	16.3229i	−0.167967	−	0.516951i	0.831275	−	0.555861i	$-0.187611\pi$
$997$	−5.30363	−	16.3229i	−0.167967	−	0.516951i	−0.999243	+	0.0389103i	$0.987611\pi$
$998$	0.720405	+	9.11000i	0.0228040	+	0.288372i
$999$	−26.8734	+	36.9881i	−0.850238	+	1.17025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.k.b.51.1	yes	32
3.2	odd	2		792.2.bp.b.667.8		32
4.3	odd	2		352.2.s.b.271.5		32
8.3	odd	2	inner	88.2.k.b.51.6	yes	32
8.5	even	2		352.2.s.b.271.6		32
11.2	odd	10		968.2.k.e.699.3		32
11.3	even	5		968.2.k.h.723.3		32
11.4	even	5		968.2.k.e.475.5		32
11.5	even	5		968.2.g.e.483.25		32
11.6	odd	10		968.2.g.e.483.8		32
11.7	odd	10		968.2.k.i.475.4		32
11.8	odd	10	inner	88.2.k.b.19.6	yes	32
11.9	even	5		968.2.k.i.699.6		32
11.10	odd	2		968.2.k.h.403.8		32
24.11	even	2		792.2.bp.b.667.3		32
33.8	even	10		792.2.bp.b.19.3		32
44.19	even	10		352.2.s.b.239.6		32
44.27	odd	10		3872.2.g.d.1935.22		32
44.39	even	10		3872.2.g.d.1935.21		32
88.3	odd	10		968.2.k.h.723.8		32
88.5	even	10		3872.2.g.d.1935.24		32
88.19	even	10	inner	88.2.k.b.19.1	✓	32
88.27	odd	10		968.2.g.e.483.7		32
88.35	even	10		968.2.k.e.699.5		32
88.43	even	2		968.2.k.h.403.3		32
88.51	even	10		968.2.k.i.475.6		32
88.59	odd	10		968.2.k.e.475.3		32
88.61	odd	10		3872.2.g.d.1935.23		32
88.75	odd	10		968.2.k.i.699.4		32
88.83	even	10		968.2.g.e.483.26		32
88.85	odd	10		352.2.s.b.239.5		32
264.107	odd	10		792.2.bp.b.19.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.b.19.1	✓	32	88.19	even	10	inner
88.2.k.b.19.6	yes	32	11.8	odd	10	inner
88.2.k.b.51.1	yes	32	1.1	even	1	trivial
88.2.k.b.51.6	yes	32	8.3	odd	2	inner
352.2.s.b.239.5		32	88.85	odd	10
352.2.s.b.239.6		32	44.19	even	10
352.2.s.b.271.5		32	4.3	odd	2
352.2.s.b.271.6		32	8.5	even	2
792.2.bp.b.19.3		32	33.8	even	10
792.2.bp.b.19.8		32	264.107	odd	10
792.2.bp.b.667.3		32	24.11	even	2
792.2.bp.b.667.8		32	3.2	odd	2
968.2.g.e.483.7		32	88.27	odd	10
968.2.g.e.483.8		32	11.6	odd	10
968.2.g.e.483.25		32	11.5	even	5
968.2.g.e.483.26		32	88.83	even	10
968.2.k.e.475.3		32	88.59	odd	10
968.2.k.e.475.5		32	11.4	even	5
968.2.k.e.699.3		32	11.2	odd	10
968.2.k.e.699.5		32	88.35	even	10
968.2.k.h.403.3		32	88.43	even	2
968.2.k.h.403.8		32	11.10	odd	2
968.2.k.h.723.3		32	11.3	even	5
968.2.k.h.723.8		32	88.3	odd	10
968.2.k.i.475.4		32	11.7	odd	10
968.2.k.i.475.6		32	88.51	even	10
968.2.k.i.699.4		32	88.75	odd	10
968.2.k.i.699.6		32	11.9	even	5
3872.2.g.d.1935.21		32	44.39	even	10
3872.2.g.d.1935.22		32	44.27	odd	10
3872.2.g.d.1935.23		32	88.61	odd	10
3872.2.g.d.1935.24		32	88.5	even	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37526 - 0.329627i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(1.78269 + 0.906646i) q^{4} +(-0.398383 - 0.548327i) q^{5} +(0.726027 - 1.18576i) q^{6} +(1.40393 + 4.32085i) q^{7} +(-2.15281 - 1.83450i) q^{8} +(1.64507 + 1.19522i) q^{9} +O(q^{10})\)	\(q+(-1.37526 - 0.329627i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(1.78269 + 0.906646i) q^{4} +(-0.398383 - 0.548327i) q^{5} +(0.726027 - 1.18576i) q^{6} +(1.40393 + 4.32085i) q^{7} +(-2.15281 - 1.83450i) q^{8} +(1.64507 + 1.19522i) q^{9} +(0.367138 + 0.885411i) q^{10} +(3.31396 + 0.132807i) q^{11} +(-1.38934 + 1.39142i) q^{12} +(-1.90447 - 1.38368i) q^{13} +(-0.506504 - 6.40508i) q^{14} +(0.633734 - 0.205913i) q^{15} +(2.35598 + 3.23254i) q^{16} +(-2.07445 - 2.85523i) q^{17} +(-1.86843 - 2.18600i) q^{18} +(-4.38980 - 1.42633i) q^{19} +(-0.213056 - 1.33869i) q^{20} -4.46665 q^{21} +(-4.51379 - 1.27502i) q^{22} +1.11065i q^{23} +(2.36935 - 1.45560i) q^{24} +(1.40313 - 4.31839i) q^{25} +(2.16305 + 2.53068i) q^{26} +(-4.00349 + 2.90871i) q^{27} +(-1.41471 + 8.97562i) q^{28} +(-0.379398 - 1.16767i) q^{29} +(-0.939424 + 0.0742882i) q^{30} +(3.46109 - 4.76378i) q^{31} +(-2.17456 - 5.22219i) q^{32} +(-1.13099 + 3.05830i) q^{33} +(1.91175 + 4.61048i) q^{34} +(1.80994 - 2.49117i) q^{35} +(1.84902 + 3.62220i) q^{36} +(8.78677 - 2.85499i) q^{37} +(5.56697 + 3.40858i) q^{38} +(1.87237 - 1.36036i) q^{39} +(-0.148261 + 1.91128i) q^{40} +(1.88539 + 0.612601i) q^{41} +(6.14281 + 1.47233i) q^{42} +2.02637i q^{43} +(5.78737 + 3.24135i) q^{44} -1.37819i q^{45} +(0.366102 - 1.52744i) q^{46} +(-4.48649 - 1.45775i) q^{47} +(-3.73829 + 1.22084i) q^{48} +(-11.0356 + 8.01786i) q^{49} +(-3.35313 + 5.47641i) q^{50} +(3.29995 - 1.07222i) q^{51} +(-2.14058 - 4.19335i) q^{52} +(-4.70018 + 6.46924i) q^{53} +(6.46464 - 2.68058i) q^{54} +(-1.24741 - 1.87005i) q^{55} +(4.90420 - 11.8775i) q^{56} +(2.66732 - 3.67125i) q^{57} +(0.136877 + 1.73091i) q^{58} +(-0.400488 - 1.23257i) q^{59} +(1.31644 + 0.207494i) q^{60} +(6.73720 - 4.89486i) q^{61} +(-6.33017 + 5.41058i) q^{62} +(-2.85479 + 8.78613i) q^{63} +(1.26922 + 7.89868i) q^{64} +1.59551i q^{65} +(2.56351 - 3.83316i) q^{66} -0.483683 q^{67} +(-1.10941 - 6.97078i) q^{68} +(-1.03849 - 0.337427i) q^{69} +(-3.31030 + 2.82941i) q^{70} +(-8.68470 - 11.9535i) q^{71} +(-1.34892 - 5.59097i) q^{72} +(8.79393 - 2.85732i) q^{73} +(-13.0252 + 1.03001i) q^{74} +(3.61153 + 2.62393i) q^{75} +(-6.53249 - 6.52271i) q^{76} +(4.07874 + 14.5056i) q^{77} +(-3.02341 + 1.25367i) q^{78} +(-0.848366 - 0.616374i) q^{79} +(0.833907 - 2.57964i) q^{80} +(0.381661 + 1.17463i) q^{81} +(-2.39098 - 1.46396i) q^{82} +(-4.37741 - 6.02499i) q^{83} +(-7.96265 - 4.04967i) q^{84} +(-0.739176 + 2.27495i) q^{85} +(0.667946 - 2.78679i) q^{86} +1.20707 q^{87} +(-6.89072 - 6.36538i) q^{88} +2.47072 q^{89} +(-0.454289 + 1.89538i) q^{90} +(3.30493 - 10.1715i) q^{91} +(-1.00697 + 1.97996i) q^{92} +(3.40275 + 4.68349i) q^{93} +(5.68959 + 3.48365i) q^{94} +(0.966725 + 2.97527i) q^{95} +(5.54354 - 0.446729i) q^{96} +(-11.7932 - 8.56824i) q^{97} +(17.8198 - 7.38902i) q^{98} +(5.29298 + 4.17938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9	\( 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27} - 30 q^{28} + 30 q^{30} + 32 q^{33} - 14 q^{34} - 10 q^{35} + 16 q^{36} + 28 q^{38} + 30 q^{40} - 10 q^{41} + 64 q^{42} - 38 q^{44} + 40 q^{46} + 26 q^{48} - 18 q^{49} + 5 q^{50} + 60 q^{51} + 40 q^{52} + 76 q^{56} - 80 q^{57} - 56 q^{58} + 28 q^{59} + 34 q^{60} - 80 q^{62} + 55 q^{64} - 30 q^{66} - 28 q^{67} + 60 q^{68} - 44 q^{70} + 45 q^{72} - 10 q^{73} - 100 q^{74} + 4 q^{75} - 80 q^{78} - 76 q^{80} + 28 q^{81} + 13 q^{82} - 50 q^{84} - 39 q^{86} - 69 q^{88} + 20 q^{89} - 30 q^{90} + 78 q^{91} + 6 q^{92} - 30 q^{94} - 110 q^{96} - 52 q^{97} + 122 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more