LMFDB - Embedded newform 570.2.bh.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	570.67
Dual form			570.2.bh.a.553.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23514 - 0.0643515i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.48134 - 0.664873i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})$	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23514 - 0.0643515i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.48134 - 0.664873i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.79401 + 1.33474i) q^{10} +(2.25231 + 3.90112i) q^{11} +(0.258819 + 0.965926i) q^{12} +(0.135835 + 1.55260i) q^{13} +(-2.41395 - 0.878606i) q^{14} +(-2.22103 - 0.258912i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-3.87323 + 5.53155i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.76072 - 3.98746i) q^{19} +(-0.703993 - 2.12236i) q^{20} +(2.52984 - 0.446080i) q^{21} +(0.392604 - 4.48749i) q^{22} +(2.78925 - 5.98157i) q^{23} +(0.342020 - 0.939693i) q^{24} +(4.99172 + 0.287669i) q^{25} +(0.779267 - 1.34973i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.47344 + 2.10430i) q^{28} +(-0.441532 + 2.50405i) q^{29} +(1.67085 + 1.48602i) q^{30} +(8.08774 + 4.66946i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.90374 + 4.08258i) q^{33} +(6.34553 - 2.30958i) q^{34} +(-5.58893 + 1.32641i) q^{35} +(0.173648 + 0.984808i) q^{36} +(4.41081 - 4.41081i) q^{37} +(-3.72941 + 2.25643i) q^{38} +1.55853i q^{39} +(-0.640656 + 2.14233i) q^{40} +(5.55375 + 6.61870i) q^{41} +(-2.32819 - 1.08565i) q^{42} +(-3.65323 + 1.70353i) q^{43} +(-2.89552 + 3.45074i) q^{44} +(-2.19001 - 0.451502i) q^{45} +(-5.71571 + 3.29997i) q^{46} +(7.58557 - 5.31147i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(-0.347189 + 0.200450i) q^{49} +(-3.92398 - 3.09878i) q^{50} +(-4.34060 + 5.17293i) q^{51} +(-1.41251 + 0.658665i) q^{52} +(1.89475 + 0.883538i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-4.78320 - 8.86450i) q^{55} -2.56887i q^{56} +(2.10155 - 3.81883i) q^{57} +(1.79795 - 1.79795i) q^{58} +(-1.04421 - 5.92203i) q^{59} +(-0.516339 - 2.17564i) q^{60} +(-5.99313 + 2.18132i) q^{61} +(-3.94680 - 8.46393i) q^{62} +(2.55910 - 0.223892i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.203699 - 3.47903i) q^{65} +(0.782220 - 4.43619i) q^{66} +(5.46194 + 7.80046i) q^{67} +(-6.52268 - 1.74775i) q^{68} +(3.29997 - 5.71571i) q^{69} +(5.33898 + 2.11915i) q^{70} +(-3.96123 + 10.8834i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.410204 + 4.68865i) q^{73} +(-6.14306 + 1.08319i) q^{74} +(4.94765 + 0.721631i) q^{75} +(4.34919 + 0.290746i) q^{76} +(8.18250 + 8.18250i) q^{77} +(0.893939 - 1.27668i) q^{78} +(-2.08713 + 1.75131i) q^{79} +(1.75358 - 1.38743i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.753035 - 8.60723i) q^{82} +(-3.31223 - 12.3614i) q^{83} +(1.28444 + 2.22471i) q^{84} +(9.01319 - 12.1145i) q^{85} +(3.96965 + 0.699957i) q^{86} +(-0.658094 + 2.45604i) q^{87} +(4.35114 - 1.16588i) q^{88} +(-7.51102 - 6.30249i) q^{89} +(1.53498 + 1.62599i) q^{90} +(1.36934 + 3.76222i) q^{91} +(6.57482 + 0.575222i) q^{92} +(7.64999 + 5.35658i) q^{93} -9.26027 q^{94} +(-4.19207 + 8.79924i) q^{95} +1.00000 q^{96} +(-14.3552 - 10.0516i) q^{97} +(0.399374 + 0.0349407i) q^{98} +(1.54067 + 4.23296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$2$	−0.819152	−	0.573576i	−0.579228	−	0.405580i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$3$	0.996195	+	0.0871557i	0.575153	+	0.0503194i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.23514	−	0.0643515i	−0.999586	−	0.0287788i
$5$	−2.23514	−	0.0643515i	−0.999586	−	0.0287788i
$6$	−0.766044	−	0.642788i	−0.312736	−	0.262417i
$7$	2.48134	−	0.664873i	0.937858	−	0.251298i	0.242656	−	0.970112i	$-0.421981\pi$
$7$	2.48134	−	0.664873i	0.937858	−	0.251298i	0.695202	+	0.718814i	$0.255315\pi$
$8$	0.258819	−	0.965926i	0.0915064	−	0.341506i
$9$	0.984808	+	0.173648i	0.328269	+	0.0578827i
$10$	1.79401	+	1.33474i	0.567316	+	0.422081i
$11$	2.25231	+	3.90112i	0.679098	+	1.17623i	0.975253	+	0.221092i	$0.0709622\pi$
$11$	2.25231	+	3.90112i	0.679098	+	1.17623i	−0.296155	+	0.955140i	$0.595704\pi$
$12$	0.258819	+	0.965926i	0.0747146	+	0.278839i
$13$	0.135835	+	1.55260i	0.0376739	+	0.430615i	0.991486	+	0.130212i	$0.0415657\pi$
$13$	0.135835	+	1.55260i	0.0376739	+	0.430615i	−0.953812	+	0.300403i	$0.902879\pi$
$14$	−2.41395	−	0.878606i	−0.645155	−	0.234817i
$15$	−2.22103	−	0.258912i	−0.573467	−	0.0668508i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−3.87323	+	5.53155i	−0.939397	+	1.34160i	0.000449500		1.00000i	$0.499857\pi$
$17$	−3.87323	+	5.53155i	−0.939397	+	1.34160i	−0.939846	+	0.341598i	$0.889032\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	1.76072	−	3.98746i	0.403938	−	0.914787i
$19$	1.76072	−	3.98746i	0.403938	−	0.914787i
$20$	−0.703993	−	2.12236i	−0.157418	−	0.474573i
$21$	2.52984	−	0.446080i	0.552057	−	0.0973426i
$22$	0.392604	−	4.48749i	0.0837035	−	0.956735i
$23$	2.78925	−	5.98157i	0.581599	−	1.24724i	−0.366840	−	0.930284i	$-0.619560\pi$
$23$	2.78925	−	5.98157i	0.581599	−	1.24724i	0.948439	−	0.316960i	$-0.102662\pi$
$24$	0.342020	−	0.939693i	0.0698146	−	0.191814i
$25$	4.99172	+	0.287669i	0.998344	+	0.0575338i
$26$	0.779267	−	1.34973i	0.152827	−	0.264704i
$27$	0.965926	+	0.258819i	0.185893	+	0.0498097i
$28$	1.47344	+	2.10430i	0.278455	+	0.397675i
$29$	−0.441532	+	2.50405i	−0.0819903	+	0.464990i	0.915975	+	0.401235i	$0.131419\pi$
$29$	−0.441532	+	2.50405i	−0.0819903	+	0.464990i	−0.997966	+	0.0637555i	$0.979692\pi$
$30$	1.67085	+	1.48602i	0.305055	+	0.271308i
$31$	8.08774	+	4.66946i	1.45260	+	0.838659i	0.998628	−	0.0523567i	$-0.0166733\pi$
$31$	8.08774	+	4.66946i	1.45260	+	0.838659i	0.453972	+	0.891016i	$0.350007\pi$
$32$	0.996195	−	0.0871557i	0.176104	−	0.0154071i
$33$	1.90374	+	4.08258i	0.331398	+	0.710686i
$34$	6.34553	−	2.30958i	1.08825	−	0.396091i
$35$	−5.58893	+	1.32641i	−0.944702	+	0.224204i
$36$	0.173648	+	0.984808i	0.0289414	+	0.164135i
$37$	4.41081	−	4.41081i	0.725132	−	0.725132i	−0.244513	−	0.969646i	$-0.578628\pi$
$37$	4.41081	−	4.41081i	0.725132	−	0.725132i	0.969646	+	0.244513i	$0.0786282\pi$
$38$	−3.72941	+	2.25643i	−0.604991	+	0.366041i
$39$			1.55853i			0.249565i
$40$	−0.640656	+	2.14233i	−0.101297	+	0.338731i
$41$	5.55375	+	6.61870i	0.867350	+	1.03367i	0.999101	+	0.0423851i	$0.0134956\pi$
$41$	5.55375	+	6.61870i	0.867350	+	1.03367i	−0.131751	+	0.991283i	$0.542060\pi$
$42$	−2.32819	−	1.08565i	−0.359247	−	0.167520i
$43$	−3.65323	+	1.70353i	−0.557112	+	0.259786i	−0.680718	−	0.732546i	$-0.738332\pi$
$43$	−3.65323	+	1.70353i	−0.557112	+	0.259786i	0.123606	+	0.992331i	$0.460554\pi$
$44$	−2.89552	+	3.45074i	−0.436516	+	0.520219i
$45$	−2.19001	−	0.451502i	−0.326467	−	0.0673060i
$46$	−5.71571	+	3.29997i	−0.842736	+	0.486554i
$47$	7.58557	−	5.31147i	1.10647	−	0.774758i	0.130236	−	0.991483i	$-0.458427\pi$
$47$	7.58557	−	5.31147i	1.10647	−	0.774758i	0.976233	+	0.216725i	$0.0695376\pi$
$48$	−0.819152	+	0.573576i	−0.118234	+	0.0827886i
$49$	−0.347189	+	0.200450i	−0.0495985	+	0.0286357i
$50$	−3.92398	−	3.09878i	−0.554934	−	0.438233i
$51$	−4.34060	+	5.17293i	−0.607806	+	0.724354i
$52$	−1.41251	+	0.658665i	−0.195880	+	0.0913404i
$53$	1.89475	+	0.883538i	0.260264	+	0.121363i	0.548371	−	0.836235i	$-0.315248\pi$
$53$	1.89475	+	0.883538i	0.260264	+	0.121363i	−0.288107	+	0.957598i	$0.593026\pi$
$54$	−0.642788	−	0.766044i	−0.0874723	−	0.104245i
$55$	−4.78320	−	8.86450i	−0.644966	−	1.19529i
$56$		−	2.56887i		−	0.343280i
$57$	2.10155	−	3.81883i	0.278358	−	0.505817i
$58$	1.79795	−	1.79795i	0.236082	−	0.236082i
$59$	−1.04421	−	5.92203i	−0.135945	−	0.770983i	−0.974197	−	0.225700i	$-0.927533\pi$
$59$	−1.04421	−	5.92203i	−0.135945	−	0.770983i	0.838252	−	0.545283i	$-0.183578\pi$
$60$	−0.516339	−	2.17564i	−0.0666590	−	0.280873i
$61$	−5.99313	+	2.18132i	−0.767342	+	0.279290i	−0.695884	−	0.718154i	$-0.744987\pi$
$61$	−5.99313	+	2.18132i	−0.767342	+	0.279290i	−0.0714577	+	0.997444i	$0.522765\pi$
$62$	−3.94680	−	8.46393i	−0.501244	−	1.07492i
$63$	2.55910	−	0.223892i	0.322416	−	0.0282077i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−0.203699	−	3.47903i	−0.0252657	−	0.431521i
$66$	0.782220	−	4.43619i	0.0962846	−	0.546057i
$67$	5.46194	+	7.80046i	0.667282	+	0.952977i	0.999951	+	0.00993366i	$0.00316204\pi$
$67$	5.46194	+	7.80046i	0.667282	+	0.952977i	−0.332669	+	0.943044i	$0.607949\pi$
$68$	−6.52268	−	1.74775i	−0.790991	−	0.211945i
$69$	3.29997	−	5.71571i	0.397269	−	0.688091i
$70$	5.33898	+	2.11915i	0.638130	+	0.253287i
$71$	−3.96123	+	10.8834i	−0.470112	+	1.29162i	0.447550	+	0.894259i	$0.352297\pi$
$71$	−3.96123	+	10.8834i	−0.470112	+	1.29162i	−0.917662	+	0.397362i	$0.869926\pi$
$72$	0.422618	−	0.906308i	0.0498060	−	0.106809i
$73$	−0.410204	+	4.68865i	−0.0480107	+	0.548765i	0.933657	+	0.358167i	$0.116598\pi$
$73$	−0.410204	+	4.68865i	−0.0480107	+	0.548765i	−0.981668	+	0.190598i	$0.938957\pi$
$74$	−6.14306	+	1.08319i	−0.714116	+	0.125918i
$75$	4.94765	+	0.721631i	0.571305	+	0.0833268i
$76$	4.34919	+	0.290746i	0.498886	+	0.0333509i
$77$	8.18250	+	8.18250i	0.932483	+	0.932483i
$78$	0.893939	−	1.27668i	0.101219	−	0.144555i
$79$	−2.08713	+	1.75131i	−0.234821	+	0.197038i	−0.752603	−	0.658474i	$-0.771202\pi$
$79$	−2.08713	+	1.75131i	−0.234821	+	0.197038i	0.517783	+	0.855512i	$0.326758\pi$
$80$	1.75358	−	1.38743i	0.196056	−	0.155119i
$81$	0.939693	+	0.342020i	0.104410	+	0.0380022i
$82$	−0.753035	−	8.60723i	−0.0831588	−	0.950509i
$83$	−3.31223	−	12.3614i	−0.363564	−	1.35684i	−0.869356	−	0.494186i	$-0.835466\pi$
$83$	−3.31223	−	12.3614i	−0.363564	−	1.35684i	0.505792	−	0.862656i	$-0.331200\pi$
$84$	1.28444	+	2.22471i	0.140143	+	0.242736i
$85$	9.01319	−	12.1145i	0.977617	−	1.31401i
$86$	3.96965	+	0.699957i	0.428059	+	0.0754783i
$87$	−0.658094	+	2.45604i	−0.0705550	+	0.263315i
$88$	4.35114	−	1.16588i	0.463833	−	0.124284i
$89$	−7.51102	−	6.30249i	−0.796166	−	0.668063i	0.151097	−	0.988519i	$-0.451719\pi$
$89$	−7.51102	−	6.30249i	−0.796166	−	0.668063i	−0.947263	+	0.320456i	$0.896164\pi$
$90$	1.53498	+	1.62599i	0.161801	+	0.171394i
$91$	1.36934	+	3.76222i	0.143546	+	0.394388i
$92$	6.57482	+	0.575222i	0.685472	+	0.0599711i
$93$	7.64999	+	5.35658i	0.793267	+	0.555452i
$94$	−9.26027			−0.955124
$95$	−4.19207	+	8.79924i	−0.430097	+	0.902783i
$96$	1.00000			0.102062
$97$	−14.3552	−	10.0516i	−1.45755	−	1.02058i	−0.990673	−	0.136260i	$-0.956492\pi$
$97$	−14.3552	−	10.0516i	−1.45755	−	1.02058i	−0.466873	−	0.884324i	$-0.654620\pi$
$98$	0.399374	+	0.0349407i	0.0403429	+	0.00352954i
$99$	1.54067	+	4.23296i	0.154843	+	0.425429i
$100$	1.43695	+	4.78907i	0.143695	+	0.478907i
$101$	−2.41843	−	2.02930i	−0.240643	−	0.201923i	0.514488	−	0.857498i	$-0.327982\pi$
$101$	−2.41843	−	2.02930i	−0.240643	−	0.201923i	−0.755131	+	0.655574i	$0.772427\pi$
$102$	6.52268	−	1.74775i	0.645841	−	0.173053i
$103$	1.91941	−	7.16333i	0.189125	−	0.705824i	−0.804585	−	0.593838i	$-0.797612\pi$
$103$	1.91941	−	7.16333i	0.189125	−	0.705824i	0.993710	−	0.111986i	$-0.0357213\pi$
$104$	1.53486	+	0.270637i	0.150505	+	0.0265381i
$105$	−5.68327	+	0.834253i	−0.554630	+	0.0814147i
$106$	−1.04531	−	1.81054i	−0.101530	−	0.175855i
$107$	−4.44851	−	16.6021i	−0.430053	−	1.60498i	−0.752634	−	0.658439i	$-0.771217\pi$
$107$	−4.44851	−	16.6021i	−0.430053	−	1.60498i	0.322580	−	0.946542i	$-0.395450\pi$
$108$	0.0871557	+	0.996195i	0.00838657	+	0.0958589i
$109$	−7.67816	−	2.79462i	−0.735434	−	0.267676i	−0.0529711	−	0.998596i	$-0.516869\pi$
$109$	−7.67816	−	2.79462i	−0.735434	−	0.267676i	−0.682463	+	0.730920i	$0.739091\pi$
$110$	−1.16630	+	10.0049i	−0.111203	+	0.953930i
$111$	4.77845	−	4.00960i	0.453551	−	0.380574i
$112$	−1.47344	+	2.10430i	−0.139227	+	0.198837i
$113$	1.04406	+	1.04406i	0.0982166	+	0.0982166i	0.754508	−	0.656291i	$-0.227876\pi$
$113$	1.04406	+	1.04406i	0.0982166	+	0.0982166i	−0.656291	+	0.754508i	$0.727876\pi$
$114$	−3.91188	+	1.92280i	−0.366381	+	0.180087i
$115$	−6.61930	+	13.1902i	−0.617253	+	1.22999i
$116$	−2.50405	+	0.441532i	−0.232495	+	0.0409952i
$117$	−0.135835	+	1.55260i	−0.0125580	+	0.143538i
$118$	−2.54137	+	5.44998i	−0.233952	+	0.501712i
$119$	−5.93303	+	16.3009i	−0.543880	+	1.49430i
$120$	−0.824934	+	2.07834i	−0.0753058	+	0.189725i
$121$	−4.64583	+	8.04681i	−0.422348	+	0.731529i
$122$	6.16044	+	1.65069i	0.557740	+	0.149446i
$123$	4.95576	+	7.07756i	0.446846	+	0.638162i
$124$	−1.62169	+	9.19703i	−0.145632	+	0.825918i
$125$	−11.1387	−	0.964206i	−0.996274	−	0.0862412i
$126$	−2.22471	−	1.28444i	−0.198193	−	0.114427i
$127$	14.7109	−	1.28703i	1.30538	−	0.114206i	0.586846	−	0.809699i	$-0.300370\pi$
$127$	14.7109	−	1.28703i	1.30538	−	0.114206i	0.718533	+	0.695493i	$0.244814\pi$
$128$	0.422618	+	0.906308i	0.0373545	+	0.0801070i
$129$	−3.78780	+	1.37865i	−0.333497	+	0.121383i
$130$	−1.82863	+	2.96669i	−0.160381	+	0.260196i
$131$	−0.861039	−	4.88320i	−0.0752294	−	0.426647i	−0.999040	−	0.0437981i	$-0.986054\pi$
$131$	−0.861039	−	4.88320i	−0.0752294	−	0.426647i	0.923811	−	0.382849i	$-0.125057\pi$
$132$	−3.18525	+	3.18525i	−0.277241	+	0.277241i
$133$	1.71780	−	11.0649i	0.148952	−	0.959449i
$134$		−	9.52260i		−	0.822627i
$135$	−2.14233	−	0.640656i	−0.184382	−	0.0551389i
$136$	4.34060	+	5.17293i	0.372203	+	0.443575i
$137$	−14.4951	−	6.75916i	−1.23840	−	0.577474i	−0.310593	−	0.950543i	$-0.600528\pi$
$137$	−14.4951	−	6.75916i	−1.23840	−	0.577474i	−0.927804	+	0.373069i	$0.878305\pi$
$138$	−5.98157	+	2.78925i	−0.509185	+	0.237437i
$139$	−12.8277	+	15.2875i	−1.08803	+	1.29667i	−0.135987	+	0.990711i	$0.543421\pi$
$139$	−12.8277	+	15.2875i	−1.08803	+	1.29667i	−0.952046	+	0.305956i	$0.901024\pi$
$140$	−3.15794	−	4.79822i	−0.266895	−	0.405524i
$141$	8.01963	−	4.63013i	0.675374	−	0.389928i
$142$	9.48731	−	6.64309i	0.796157	−	0.557475i
$143$	−5.75095	+	4.02686i	−0.480919	+	0.336743i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	1.14802	−	5.56849i	0.0953383	−	0.462438i
$146$	3.02532	−	3.60544i	0.250377	−	0.298388i
$147$	−0.363338	+	0.169427i	−0.0299676	+	0.0139741i
$148$	5.65339	+	2.63622i	0.464706	+	0.216696i
$149$	−0.0884759	−	0.105441i	−0.00724823	−	0.00863810i	0.762408	−	0.647096i	$-0.224017\pi$
$149$	−0.0884759	−	0.105441i	−0.00724823	−	0.00863810i	−0.769656	+	0.638458i	$0.779572\pi$
$150$	−3.63897	−	3.42898i	−0.297120	−	0.279975i
$151$			11.7291i			0.954499i	0.878768	+	0.477250i	$0.158366\pi$
$151$			11.7291i			0.954499i	−0.878768	+	0.477250i	$0.841634\pi$
$152$	−3.39588	−	2.73276i	−0.275443	−	0.221656i
$153$	−4.77493	+	4.77493i	−0.386030	+	0.386030i
$154$	−2.00942	−	11.3960i	−0.161924	−	0.918316i
$155$	−17.7768	−	10.9574i	−1.42786	−	0.880116i
$156$	−1.46454	+	0.533050i	−0.117257	+	0.0426782i
$157$	−1.81253	−	3.88699i	−0.144656	−	0.310215i	0.820608	−	0.571491i	$-0.193635\pi$
$157$	−1.81253	−	3.88699i	−0.144656	−	0.310215i	−0.965264	+	0.261275i	$0.915857\pi$
$158$	2.71419	−	0.237461i	0.215929	−	0.0188914i
$159$	1.81054	+	1.04531i	0.143585	+	0.0828989i
$160$	−2.23225	+	0.130699i	−0.176474	+	0.0103327i
$161$	2.94410	−	16.6968i	0.232027	−	1.31589i
$162$	−0.573576	−	0.819152i	−0.0450644	−	0.0643587i
$163$	−23.4351	−	6.27942i	−1.83558	−	0.491842i	−0.837106	−	0.547041i	$-0.815754\pi$
$163$	−23.4351	−	6.27942i	−1.83558	−	0.491842i	−0.998475	+	0.0551991i	$0.982421\pi$
$164$	−4.32005	+	7.48255i	−0.337339	+	0.584289i
$165$	−3.99240	−	9.24765i	−0.310808	−	0.719929i
$166$	−4.37699	+	12.0257i	−0.339721	+	0.933375i
$167$	−5.45354	+	11.6952i	−0.422008	+	0.904998i	0.574259	+	0.818673i	$0.305290\pi$
$167$	−5.45354	+	11.6952i	−0.422008	+	0.904998i	−0.996267	+	0.0863249i	$0.972488\pi$
$168$	0.223892	−	2.55910i	0.0172736	−	0.197439i
$169$	10.4104	−	1.83563i	0.800798	−	0.141202i
$170$	−14.3318	+	4.75391i	−1.09920	+	0.364608i
$171$	2.42639	−	3.62114i	0.185551	−	0.276915i
$172$	−2.85027	−	2.85027i	−0.217331	−	0.217331i
$173$	3.06094	−	4.37148i	0.232719	−	0.332358i	−0.685759	−	0.727828i	$-0.740530\pi$
$173$	3.06094	−	4.37148i	0.232719	−	0.332358i	0.918479	+	0.395471i	$0.129419\pi$
$174$	1.94780	−	1.63440i	0.147663	−	0.123904i
$175$	12.5774	−	2.60505i	0.950763	−	0.196923i
$176$	−4.23296	−	1.54067i	−0.319072	−	0.116133i
$177$	−0.524102	−	5.99051i	−0.0393939	−	0.450274i
$178$	2.53770	+	9.47084i	0.190209	+	0.709870i
$179$	8.91726	+	15.4451i	0.666507	+	1.15442i	0.978874	+	0.204463i	$0.0655448\pi$
$179$	8.91726	+	15.4451i	0.666507	+	1.15442i	−0.312367	+	0.949962i	$0.601122\pi$
$180$	−0.324754	−	2.21236i	−0.0242058	−	0.164900i
$181$	−3.24122	−	0.571515i	−0.240918	−	0.0424804i	0.0518851	−	0.998653i	$-0.483477\pi$
$181$	−3.24122	−	0.571515i	−0.240918	−	0.0424804i	−0.292803	+	0.956173i	$0.594588\pi$
$182$	1.03623	−	3.86725i	0.0768103	−	0.286660i
$183$	−6.16044	+	1.65069i	−0.455393	+	0.122022i
$184$	−5.05584	−	4.24236i	−0.372722	−	0.312751i
$185$	−10.1426	+	9.57494i	−0.745701	+	0.703964i
$186$	−3.19410	−	8.77571i	−0.234203	−	0.643466i
$187$	−30.3030	−	2.65117i	−2.21597	−	0.193873i
$188$	7.58557	+	5.31147i	0.553234	+	0.387379i
$189$	2.56887			0.186858
$190$	8.48097	−	4.80344i	0.615275	−	0.348478i
$191$	−1.93441			−0.139969			−0.0699844	−	0.997548i	$-0.522295\pi$
$191$	−1.93441			−0.139969			−0.0699844	+	0.997548i	$0.522295\pi$
$192$	−0.819152	−	0.573576i	−0.0591172	−	0.0413943i
$193$	9.82207	+	0.859320i	0.707008	+	0.0618552i	0.434988	−	0.900436i	$-0.356753\pi$
$193$	9.82207	+	0.859320i	0.707008	+	0.0618552i	0.272020	+	0.962292i	$0.412308\pi$
$194$	5.99370	+	16.4676i	0.430323	+	1.18230i
$195$	0.100294	−	3.48355i	0.00718220	−	0.249462i
$196$	−0.307107	−	0.257693i	−0.0219362	−	0.0184067i
$197$	11.4820	−	3.07660i	0.818061	−	0.219199i	0.174562	−	0.984646i	$-0.444149\pi$
$197$	11.4820	−	3.07660i	0.818061	−	0.219199i	0.643499	+	0.765447i	$0.277482\pi$
$198$	1.16588	−	4.35114i	0.0828557	−	0.309222i
$199$	−5.69125	−	1.00352i	−0.403442	−	0.0711377i	−0.0317546	−	0.999496i	$-0.510109\pi$
$199$	−5.69125	−	1.00352i	−0.403442	−	0.0711377i	−0.371687	+	0.928358i	$0.621221\pi$
$200$	1.56982	−	4.74717i	0.111003	−	0.335676i
$201$	4.76130	+	8.24681i	0.335836	+	0.581685i
$202$	0.817101	+	3.04946i	0.0574911	+	0.214560i
$203$	0.569285	+	6.50696i	0.0399560	+	0.456699i
$204$	−6.34553	−	2.30958i	−0.444276	−	0.161703i
$205$	−11.9875	−	15.1511i	−0.837243	−	1.05820i
$206$	−5.68101	+	4.76693i	−0.395814	+	0.332128i
$207$	3.78557	−	5.40635i	0.263115	−	0.375767i
$208$	−1.10205	−	1.10205i	−0.0764135	−	0.0764135i
$209$	19.5213	−	2.11222i	1.35031	−	0.146105i
$210$	5.13397	+	2.57641i	0.354277	+	0.177789i
$211$	−8.01098	+	1.41255i	−0.551499	+	0.0972441i	−0.442451	−	0.896792i	$-0.645891\pi$
$211$	−8.01098	+	1.41255i	−0.551499	+	0.0972441i	−0.109047	+	0.994037i	$0.534780\pi$
$212$	−0.182210	+	2.08267i	−0.0125143	+	0.143039i
$213$	−4.89471	+	10.4967i	−0.335380	+	0.719225i
$214$	−5.87854	+	16.1512i	−0.401849	+	1.10407i
$215$	8.27511	−	3.57254i	0.564358	−	0.243645i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	23.1730	+	6.20919i	1.57309	+	0.421507i
$218$	4.68665	+	6.69323i	0.317420	+	0.453323i
$219$	−0.817286	+	4.63506i	−0.0552271	+	0.313208i
$220$	6.69395	−	7.52657i	0.451306	−	0.507441i
$221$	−9.11443	−	5.26222i	−0.613103	−	0.353975i
$222$	−6.21409	+	0.543662i	−0.417062	+	0.0364882i
$223$	0.231252	+	0.495922i	0.0154858	+	0.0332094i	0.913899	−	0.405943i	$-0.133057\pi$
$223$	0.231252	+	0.495922i	0.0154858	+	0.0332094i	−0.898413	+	0.439152i	$0.855279\pi$
$224$	2.41395	−	0.878606i	0.161289	−	0.0587043i
$225$	4.86593	+	1.15010i	0.324395	+	0.0766734i
$226$	−0.256395	−	1.45409i	−0.0170551	−	0.0967245i
$227$	−6.29708	+	6.29708i	−0.417952	+	0.417952i	−0.884497	−	0.466546i	$-0.845498\pi$
$227$	−6.29708	+	6.29708i	−0.417952	+	0.417952i	0.466546	+	0.884497i	$0.345498\pi$
$228$	4.30730	+	0.668697i	0.285258	+	0.0442855i
$229$		−	2.49381i		−	0.164796i	−0.996600	−	0.0823978i	$-0.973742\pi$
$229$		−	2.49381i		−	0.164796i	0.996600	−	0.0823978i	$-0.0262578\pi$
$230$	12.9878	−	7.00808i	0.856389	−	0.462099i
$231$	7.43821	+	8.86452i	0.489399	+	0.583242i
$232$	2.30445	+	1.07458i	0.151295	+	0.0705498i
$233$	21.5402	−	10.0444i	1.41115	−	0.658029i	0.440328	−	0.897837i	$-0.354862\pi$
$233$	21.5402	−	10.0444i	1.41115	−	0.658029i	0.970820	+	0.239808i	$0.0770845\pi$
$234$	1.00181	−	1.19391i	0.0654902	−	0.0780481i
$235$	−17.2966	+	11.3837i	−1.12831	+	0.742594i
$236$	5.20775	−	3.00670i	0.338996	−	0.195719i
$237$	−2.23183	+	1.56274i	−0.144973	+	0.101511i
$238$	14.2098	−	9.94984i	0.921087	−	0.644952i
$239$	21.9676	−	12.6830i	1.42096	−	0.820394i	0.424583	−	0.905389i	$-0.360421\pi$
$239$	21.9676	−	12.6830i	1.42096	−	0.820394i	0.996381	+	0.0849947i	$0.0270873\pi$
$240$	1.86783	−	1.22931i	0.120568	−	0.0793517i
$241$	1.35230	−	1.61160i	0.0871090	−	0.103812i	−0.720729	−	0.693217i	$-0.756193\pi$
$241$	1.35230	−	1.61160i	0.0871090	−	0.103812i	0.807838	+	0.589404i	$0.200637\pi$
$242$	8.42110	−	3.92683i	0.541329	−	0.252426i
$243$	0.906308	+	0.422618i	0.0581397	+	0.0271110i
$244$	−4.09954	−	4.88565i	−0.262446	−	0.312771i
$245$	0.788916	−	0.425692i	0.0504020	−	0.0271964i
$246$		−	8.64010i		−	0.550873i
$247$	6.43012	+	2.19207i	0.409139	+	0.139478i
$248$	6.60361	−	6.60361i	0.419330	−	0.419330i
$249$	−2.22226	−	12.6031i	−0.140830	−	0.798686i
$250$	8.57123	+	7.17872i	0.542092	+	0.454022i
$251$	10.1340	−	3.68847i	0.639651	−	0.232814i	−0.00177557	−	0.999998i	$-0.500565\pi$
$251$	10.1340	−	3.68847i	0.639651	−	0.232814i	0.641426	+	0.767185i	$0.278343\pi$
$252$	1.08565	+	2.32819i	0.0683896	+	0.146662i
$253$	29.6171	−	2.59116i	1.86201	−	0.162905i
$254$	−12.7886	−	7.38353i	−0.802431	−	0.463284i
$255$	10.0347	−	11.2829i	0.628400	−	0.706562i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	9.01457	+	12.8741i	0.562314	+	0.803067i	0.995146	−	0.0984072i	$-0.0313748\pi$
$257$	9.01457	+	12.8741i	0.562314	+	0.803067i	−0.432833	+	0.901474i	$0.642486\pi$
$258$	3.89354	+	1.04327i	0.242401	+	0.0649512i
$259$	8.01209	−	13.8773i	0.497847	−	0.862296i
$260$	3.19955	−	1.38131i	0.198428	−	0.0856654i
$261$	−0.869647	+	2.38934i	−0.0538298	+	0.147896i
$262$	−2.09556	+	4.49395i	−0.129464	+	0.277637i
$263$	−1.46446	+	16.7388i	−0.0903023	+	1.03216i	0.806943	+	0.590629i	$0.201120\pi$
$263$	−1.46446	+	16.7388i	−0.0903023	+	1.03216i	−0.897246	+	0.441532i	$0.854435\pi$
$264$	4.43619	−	0.782220i	0.273029	−	0.0481423i
$265$	−4.17819	−	2.09676i	−0.256664	−	0.128803i
$266$	−7.75370	+	8.07855i	−0.475410	+	0.495328i
$267$	−6.93314	−	6.93314i	−0.424301	−	0.424301i
$268$	−5.46194	+	7.80046i	−0.333641	+	0.476489i
$269$	12.0943	−	10.1483i	0.737403	−	0.618755i	−0.194735	−	0.980856i	$-0.562385\pi$
$269$	12.0943	−	10.1483i	0.737403	−	0.618755i	0.932139	+	0.362101i	$0.117940\pi$
$270$	1.38743	+	1.75358i	0.0844360	+	0.106720i
$271$	−3.16446	−	1.15177i	−0.192227	−	0.0699649i	0.244113	−	0.969747i	$-0.421503\pi$
$271$	−3.16446	−	1.15177i	−0.192227	−	0.0699649i	−0.436340	+	0.899782i	$0.643725\pi$
$272$	−0.588543	−	6.72708i	−0.0356857	−	0.407889i
$273$	1.03623	+	3.86725i	0.0627153	+	0.234057i
$274$	7.99677	+	13.8508i	0.483102	+	0.836758i
$275$	10.1207	+	20.1212i	0.610300	+	1.21336i
$276$	6.49967	+	1.14607i	0.391234	+	0.0689851i
$277$	3.31797	−	12.3828i	0.199357	−	0.744012i	−0.791738	−	0.610861i	$-0.790824\pi$
$277$	3.31797	−	12.3828i	0.199357	−	0.744012i	0.991096	−	0.133152i	$-0.0425097\pi$
$278$	19.2764	−	5.16509i	1.15612	−	0.309782i
$279$	7.15402	+	6.00294i	0.428300	+	0.359387i
$280$	−0.165311	+	5.74179i	−0.00987920	+	0.343138i
$281$	0.823996	+	2.26391i	0.0491555	+	0.135054i	0.961841	−	0.273609i	$-0.0882175\pi$
$281$	0.823996	+	2.26391i	0.0491555	+	0.135054i	−0.912685	+	0.408663i	$0.865995\pi$
$282$	−9.22503	−	0.807085i	−0.549342	−	0.0480612i
$283$	−10.8826	−	7.62006i	−0.646902	−	0.452966i	0.203517	−	0.979071i	$-0.434763\pi$
$283$	−10.8826	−	7.62006i	−0.646902	−	0.452966i	−0.850419	+	0.526106i	$0.823652\pi$
$284$	−11.5819			−0.687257
$285$	−4.94302	+	8.40039i	−0.292799	+	0.497596i
$286$	7.02062			0.415138
$287$	18.1813	+	12.7307i	1.07321	+	0.751470i
$288$	0.996195	+	0.0871557i	0.0587013	+	0.00513570i
$289$	−9.78176	−	26.8752i	−0.575398	−	1.58089i
$290$	−4.13436	+	3.90296i	−0.242778	+	0.229190i
$291$	−13.4245	−	11.2645i	−0.786957	−	0.660336i
$292$	−4.54619	+	1.21815i	−0.266046	+	0.0712867i
$293$	−2.21047	+	8.24958i	−0.129137	+	0.481946i	−0.999953	−	0.00966270i	$-0.996924\pi$
$293$	−2.21047	+	8.24958i	−0.129137	+	0.481946i	0.870816	+	0.491609i	$0.163591\pi$
$294$	0.394809	+	0.0696155i	0.0230257	+	0.00406006i
$295$	1.95288	+	13.3038i	0.113701	+	0.774576i
$296$	−3.11891	−	5.40211i	−0.181283	−	0.313992i
$297$	1.16588	+	4.35114i	0.0676514	+	0.252478i
$298$	0.0119965	+	0.137120i	0.000694937	+	0.00794316i
$299$	9.66589	+	3.51810i	0.558993	+	0.203457i
$300$	1.01408	+	4.89608i	0.0585482	+	0.282676i
$301$	−7.93227	+	6.65596i	−0.457208	+	0.383643i
$302$	6.72753	−	9.60790i	0.387126	−	0.552873i
$303$	−2.23236	−	2.23236i	−0.128246	−	0.128246i
$304$	1.21430	+	4.18634i	0.0696448	+	0.240103i
$305$	13.5359	−	4.48990i	0.775062	−	0.257091i
$306$	6.65018	−	1.17261i	0.380166	−	0.0670335i
$307$	−1.27523	+	14.5760i	−0.0727814	+	0.831895i	0.868812	+	0.495143i	$0.164884\pi$
$307$	−1.27523	+	14.5760i	−0.0727814	+	0.831895i	−0.941593	+	0.336753i	$0.890671\pi$
$308$	−4.89046	+	10.4876i	−0.278660	+	0.597588i
$309$	2.53643	−	6.96879i	0.144292	−	0.396440i
$310$	8.27698	+	19.1721i	0.470101	+	1.08890i
$311$	13.0264	−	22.5623i	0.738657	−	1.27939i	−0.214443	−	0.976736i	$-0.568794\pi$
$311$	13.0264	−	22.5623i	0.738657	−	1.27939i	0.953100	−	0.302655i	$-0.0978729\pi$
$312$	1.50543	+	0.403379i	0.0852281	+	0.0228368i
$313$	−11.0741	−	15.8154i	−0.625944	−	0.893941i	0.373488	−	0.927635i	$-0.378162\pi$
$313$	−11.0741	−	15.8154i	−0.625944	−	0.893941i	−0.999432	+	0.0336942i	$0.989273\pi$
$314$	−0.744745	+	4.22366i	−0.0420284	+	0.238355i
$315$	−5.73435	+	0.335749i	−0.323094	+	0.0189173i
$316$	−2.35953	−	1.36228i	−0.132734	−	0.0766341i
$317$	−26.1015	+	2.28359i	−1.46601	+	0.128259i	−0.792026	−	0.610488i	$-0.790973\pi$
$317$	−26.1015	+	2.28359i	−1.46601	+	0.128259i	−0.673983	+	0.738747i	$0.735418\pi$
$318$	−0.883538	−	1.89475i	−0.0495464	−	0.106253i
$319$	−10.7631	+	3.91744i	−0.602616	+	0.219334i
$320$	1.90351	+	1.17330i	0.106410	+	0.0655895i
$321$	−2.98461	−	16.9266i	−0.166585	−	0.944750i
$322$	−11.9886	+	11.9886i	−0.668096	+	0.668096i
$323$	15.2372	+	25.1839i	0.847818	+	1.40127i
$324$			1.00000i			0.0555556i
$325$	0.231415	+	7.78924i	0.0128366	+	0.432069i
$326$	15.5952	+	18.5856i	0.863738	+	1.02936i
$327$	−7.40538	−	3.45318i	−0.409518	−	0.190961i
$328$	7.83059	−	3.65147i	0.432372	−	0.201618i
$329$	15.2909	−	18.2230i	0.843015	−	1.00467i
$330$	−2.03385	+	9.86518i	−0.111960	+	0.543060i
$331$	8.18197	−	4.72386i	0.449722	−	0.259647i	−0.257991	−	0.966147i	$-0.583060\pi$
$331$	8.18197	−	4.72386i	0.449722	−	0.259647i	0.707713	+	0.706500i	$0.249727\pi$
$332$	10.4831	−	7.34033i	0.575334	−	0.402853i
$333$	5.10973	−	3.57787i	0.280011	−	0.196066i
$334$	11.1753	−	6.45209i	0.611488	−	0.353043i
$335$	−11.7062	−	17.7866i	−0.639580	−	0.971786i
$336$	−1.65124	+	1.96787i	−0.0900825	+	0.107356i
$337$	18.2644	−	8.51683i	0.994926	−	0.463941i	0.144198	−	0.989549i	$-0.453940\pi$
$337$	18.2644	−	8.51683i	0.994926	−	0.463941i	0.850727	+	0.525607i	$0.176162\pi$
$338$	−9.58055	−	4.46748i	−0.521113	−	0.242999i
$339$	0.949089	+	1.13108i	0.0515474	+	0.0614318i
$340$	14.4666	+	4.32621i	0.784564	+	0.234621i
$341$			42.0683i			2.27813i
$342$	−4.06458	+	1.57454i	−0.219787	+	0.0851415i
$343$	−13.4435	+	13.4435i	−0.725880	+	0.725880i
$344$	0.699957	+	3.96965i	0.0377391	+	0.214029i
$345$	−7.74371	+	12.5631i	−0.416907	+	0.676373i
$346$	−5.01476	+	1.82522i	−0.269595	+	0.0981246i
$347$	−9.78544	−	20.9849i	−0.525310	−	1.12653i	−0.972673	−	0.232179i	$-0.925415\pi$
$347$	−9.78544	−	20.9849i	−0.525310	−	1.12653i	0.447363	−	0.894352i	$-0.352363\pi$
$348$	−2.53300	+	0.221609i	−0.135783	+	0.0118795i
$349$	−22.3692	−	12.9149i	−1.19740	−	0.691318i	−0.237423	−	0.971406i	$-0.576303\pi$
$349$	−22.3692	−	12.9149i	−1.19740	−	0.691318i	−0.959974	+	0.280089i	$0.909636\pi$
$350$	−11.7970	−	5.08017i	−0.630577	−	0.271547i
$351$	−0.270637	+	1.53486i	−0.0144455	+	0.0819246i
$352$	2.58375	+	3.68997i	0.137714	+	0.196676i
$353$	−32.8652	−	8.80622i	−1.74924	−	0.468708i	−0.764777	−	0.644295i	$-0.777151\pi$
$353$	−32.8652	−	8.80622i	−1.74924	−	0.468708i	−0.984464	+	0.175588i	$0.943817\pi$
$354$	−3.00670	+	5.20775i	−0.159804	+	0.276789i
$355$	9.55428	−	24.0710i	0.507088	−	1.27756i
$356$	3.35349	−	9.21363i	0.177734	−	0.488321i
$357$	−7.33116	+	15.7217i	−0.388006	+	0.832082i
$358$	1.55438	−	17.7667i	0.0821516	−	0.938997i
$359$	−11.8265	+	2.08533i	−0.624179	+	0.110060i	−0.476787	−	0.879019i	$-0.658199\pi$
$359$	−11.8265	+	2.08533i	−0.624179	+	0.110060i	−0.147391	+	0.989078i	$0.547088\pi$
$360$	−1.00293	+	1.99853i	−0.0528593	+	0.105332i
$361$	−12.7997	−	14.0416i	−0.673669	−	0.739033i
$362$	2.32725	+	2.32725i	0.122317	+	0.122317i
$363$	−5.32948	+	7.61128i	−0.279725	+	0.399489i
$364$	−3.06699	+	2.57351i	−0.160754	+	0.134889i
$365$	1.21859	−	10.4534i	0.0637837	−	0.547156i
$366$	5.99313	+	2.18132i	0.313266	+	0.114020i
$367$	−1.80464	−	20.6271i	−0.0942014	−	1.07673i	−0.885294	−	0.465031i	$-0.846043\pi$
$367$	−1.80464	−	20.6271i	−0.0942014	−	1.07673i	0.791093	−	0.611696i	$-0.209512\pi$
$368$	1.70819	+	6.37505i	0.0890455	+	0.332322i
$369$	4.32005	+	7.48255i	0.224893	+	0.389526i
$370$	13.8003	−	2.02576i	0.717444	−	0.105314i
$371$	5.28897	+	0.932588i	0.274590	+	0.0484175i
$372$	−2.41709	+	9.02070i	−0.125320	+	0.467701i
$373$	14.7634	−	3.95585i	0.764422	−	0.204826i	0.144516	−	0.989502i	$-0.453837\pi$
$373$	14.7634	−	3.95585i	0.764422	−	0.204826i	0.619906	+	0.784676i	$0.287171\pi$
$374$	23.3021	+	19.5528i	1.20492	+	1.01105i
$375$	−11.0123	−	1.93134i	−0.568671	−	0.0997338i
$376$	−3.16720	−	8.70180i	−0.163336	−	0.448761i
$377$	−3.94777	−	0.345385i	−0.203321	−	0.0177883i
$378$	−2.10430	−	1.47344i	−0.108233	−	0.0757858i
$379$	−3.39424			−0.174351			−0.0871753	−	0.996193i	$-0.527784\pi$
$379$	−3.39424			−0.174351			−0.0871753	+	0.996193i	$0.527784\pi$
$380$	−9.70235	−	0.929736i	−0.497720	−	0.0476945i
$381$	14.7671			0.756539
$382$	1.58457	+	1.10953i	0.0810739	+	0.0567685i
$383$	14.0753	+	1.23143i	0.719214	+	0.0629230i	0.440886	−	0.897563i	$-0.354664\pi$
$383$	14.0753	+	1.23143i	0.719214	+	0.0629230i	0.278328	+	0.960486i	$0.410220\pi$
$384$	0.342020	+	0.939693i	0.0174536	+	0.0479535i
$385$	−17.7625	−	18.8156i	−0.905261	−	0.958932i
$386$	−7.55288	−	6.33762i	−0.384432	−	0.322576i
$387$	−3.89354	+	1.04327i	−0.197920	+	0.0530325i
$388$	4.53565	−	16.9273i	0.230263	−	0.859353i
$389$	38.1128	+	6.72031i	1.93240	+	0.340733i	0.999796	−	0.0201808i	$-0.00642419\pi$
$389$	38.1128	+	6.72031i	1.93240	+	0.340733i	0.932599	+	0.360914i	$0.117535\pi$
$390$	−2.08024	+	2.79603i	−0.105337	+	0.141582i
$391$	22.2839	+	38.5969i	1.12695	+	1.95193i
$392$	0.103760	+	0.387239i	0.00524069	+	0.0195585i
$393$	−0.432164	−	4.93966i	−0.0217998	−	0.249173i
$394$	−11.1702	−	4.06562i	−0.562746	−	0.204823i
$395$	4.77773	−	3.78012i	0.240394	−	0.190198i
$396$	−3.45074	+	2.89552i	−0.173406	+	0.145505i
$397$	−5.68884	+	8.12450i	−0.285514	+	0.407757i	−0.936132	−	0.351649i	$-0.885621\pi$
$397$	−5.68884	+	8.12450i	−0.285514	+	0.407757i	0.650618	+	0.759406i	$0.274510\pi$
$398$	4.08640	+	4.08640i	0.204833	+	0.204833i
$399$	2.67563	−	10.8731i	0.133949	−	0.544335i
$400$	−4.00879	+	2.98825i	−0.200439	+	0.149412i
$401$	−9.11936	+	1.60799i	−0.455399	+	0.0802991i	−0.396642	−	0.917973i	$-0.629825\pi$
$401$	−9.11936	+	1.60799i	−0.455399	+	0.0802991i	−0.0587566	+	0.998272i	$0.518714\pi$
$402$	0.829949	−	9.48636i	0.0413941	−	0.473137i
$403$	−6.15122	+	13.1913i	−0.306414	+	0.657107i
$404$	1.07977	−	2.96664i	0.0537206	−	0.147596i
$405$	−2.07834	−	0.824934i	−0.103273	−	0.0409913i
$406$	3.26591	−	5.65672i	0.162084	−	0.280738i
$407$	27.1416	+	7.27257i	1.34536	+	0.360488i
$408$	3.87323	+	5.53155i	0.191754	+	0.273852i
$409$	−1.40766	+	7.98324i	−0.0696043	+	0.394746i	0.930024	+	0.367498i	$0.119785\pi$
$409$	−1.40766	+	7.98324i	−0.0696043	+	0.394746i	−0.999629	+	0.0272480i	$0.991326\pi$
$410$	1.12925	+	19.2868i	0.0557698	+	0.952509i
$411$	−13.8508	−	7.99677i	−0.683210	−	0.394451i
$412$	7.38781	−	0.646349i	0.363971	−	0.0318433i
$413$	−6.52845	−	14.0003i	−0.321244	−	0.688910i
$414$	−6.20191	+	2.25731i	−0.304807	+	0.110941i
$415$	6.60783	+	27.8427i	0.324366	+	1.36674i
$416$	0.270637	+	1.53486i	0.0132691	+	0.0752526i
$417$	−14.1113	+	14.1113i	−0.691033	+	0.691033i
$418$	−17.2024	−	9.46671i	−0.841397	−	0.463032i
$419$			0.785793i			0.0383885i	0.999816	+	0.0191942i	$0.00611009\pi$
$419$			0.785793i			0.0383885i	−0.999816	+	0.0191942i	$0.993890\pi$
$420$	−2.72773	−	5.05519i	−0.133100	−	0.246668i
$421$	−18.2986	−	21.8075i	−0.891821	−	1.06283i	−0.997655	−	0.0684470i	$-0.978196\pi$
$421$	−18.2986	−	21.8075i	−0.891821	−	1.06283i	0.105834	−	0.994384i	$-0.466249\pi$
$422$	7.37242	+	3.43782i	0.358884	+	0.167350i
$423$	8.39265	−	3.91356i	0.408065	−	0.190284i
$424$	1.34383	−	1.60152i	0.0652622	−	0.0777765i
$425$	−20.9253	+	26.4977i	−1.01503	+	1.28533i
$426$	10.0302	−	5.79093i	0.485964	−	0.280572i
$427$	−13.4207	+	9.39727i	−0.649473	+	0.454766i
$428$	14.0793	−	9.85847i	0.680551	−	0.476527i
$429$	−6.08003	+	3.51031i	−0.293547	+	0.169479i
$430$	−8.82769	−	1.81996i	−0.425709	−	0.0877660i
$431$	17.9617	−	21.4060i	0.865187	−	1.03109i	−0.134009	−	0.990980i	$-0.542785\pi$
$431$	17.9617	−	21.4060i	0.865187	−	1.03109i	0.999195	−	0.0401092i	$-0.0127706\pi$
$432$	−0.906308	+	0.422618i	−0.0436048	+	0.0203332i
$433$	8.29323	+	3.86719i	0.398547	+	0.185846i	0.611550	−	0.791206i	$-0.290546\pi$
$433$	8.29323	+	3.86719i	0.398547	+	0.185846i	−0.213003	+	0.977052i	$0.568324\pi$
$434$	−15.4208	−	18.3778i	−0.740221	−	0.882161i
$435$	1.62898	−	5.44725i	0.0781037	−	0.261175i
$436$		−	8.17093i		−	0.391316i
$437$	−18.9402	−	21.6539i	−0.906032	−	1.03585i
$438$	3.32804	−	3.32804i	0.159020	−	0.159020i
$439$	1.16560	+	6.61042i	0.0556308	+	0.315498i	0.999907	−	0.0136569i	$-0.00434726\pi$
$439$	1.16560	+	6.61042i	0.0556308	+	0.315498i	−0.944276	+	0.329155i	$0.893236\pi$
$440$	−9.80043	+	2.32591i	−0.467217	+	0.110884i
$441$	−0.376722	+	0.137116i	−0.0179392	+	0.00652932i
$442$	4.44782	+	9.53838i	0.211561	+	0.453694i
$443$	−18.3739	+	1.60751i	−0.872972	+	0.0763752i	−0.514830	−	0.857292i	$-0.672145\pi$
$443$	−18.3739	+	1.60751i	−0.872972	+	0.0763752i	−0.358142	+	0.933667i	$0.616590\pi$
$444$	5.40211	+	3.11891i	0.256373	+	0.148017i
$445$	16.3826	+	14.5703i	0.776610	+	0.690699i
$446$	0.0950184	−	0.538876i	0.00449925	−	0.0255165i
$447$	−0.0789494	−	0.112751i	−0.00373418	−	0.00533296i
$448$	−2.48134	−	0.664873i	−0.117232	−	0.0314123i
$449$	−4.67819	+	8.10286i	−0.220777	+	0.382397i	−0.955044	−	0.296463i	$-0.904193\pi$
$449$	−4.67819	+	8.10286i	−0.220777	+	0.382397i	0.734267	+	0.678861i	$0.237526\pi$
$450$	−3.32626	−	3.73309i	−0.156802	−	0.175980i
$451$	−13.3116	+	36.5733i	−0.626818	+	1.72217i
$452$	−0.624004	+	1.33818i	−0.0293507	+	0.0629428i
$453$	−1.02226	+	11.6845i	−0.0480298	+	0.548983i
$454$	8.77012	−	1.54641i	0.411602	−	0.0725766i
$455$	−2.81856	−	8.49722i	−0.132136	−	0.398356i
$456$	−3.14479	−	3.01833i	−0.147268	−	0.141346i
$457$	25.2171	+	25.2171i	1.17961	+	1.17961i	0.979844	+	0.199763i	$0.0640173\pi$
$457$	25.2171	+	25.2171i	1.17961	+	1.17961i	0.199763	+	0.979844i	$0.435983\pi$
$458$	−1.43039	+	2.04281i	−0.0668377	+	0.0954542i
$459$	−5.17293	+	4.34060i	−0.241451	+	0.202602i
$460$	−14.6586	−	1.70880i	−0.683463	−	0.0796733i
$461$	−12.1510	−	4.42261i	−0.565929	−	0.205981i	0.0431808	−	0.999067i	$-0.486251\pi$
$461$	−12.1510	−	4.42261i	−0.565929	−	0.205981i	−0.609110	+	0.793086i	$0.708473\pi$
$462$	−1.00855	−	11.5278i	−0.0469220	−	0.536321i
$463$	−6.55916	−	24.4791i	−0.304830	−	1.13764i	−0.933091	−	0.359639i	$-0.882900\pi$
$463$	−6.55916	−	24.4791i	−0.304830	−	1.13764i	0.628261	−	0.778002i	$-0.283767\pi$
$464$	−1.27134	−	2.20202i	−0.0590204	−	0.102226i
$465$	−16.7541	−	12.4650i	−0.776953	−	0.578051i
$466$	−23.4059	−	4.12710i	−1.08426	−	0.191184i
$467$	2.11372	−	7.88852i	0.0978114	−	0.365037i	−0.899619	−	0.436675i	$-0.856156\pi$
$467$	2.11372	−	7.88852i	0.0978114	−	0.365037i	0.997431	+	0.0716380i	$0.0228226\pi$
$468$	−1.50543	+	0.403379i	−0.0695885	+	0.0186462i
$469$	18.7392	+	15.7241i	0.865297	+	0.726071i
$470$	20.6980	+	0.595912i	0.954728	+	0.0274874i
$471$	−1.46686	−	4.03017i	−0.0675894	−	0.185700i
$472$	−5.99051	−	0.524102i	−0.275735	−	0.0241237i
$473$	−14.8739	−	10.4148i	−0.683902	−	0.478873i
$474$	2.72456			0.125143
$475$	9.93610	−	19.3978i	0.455900	−	0.890031i
$476$	−17.3470			−0.795099
$477$	1.71254	+	1.19914i	0.0784120	+	0.0549047i
$478$	−25.2694	−	2.21079i	−1.15580	−	0.101119i
$479$	3.34309	+	9.18507i	0.152750	+	0.419677i	0.992339	−	0.123545i	$-0.0394264\pi$
$479$	3.34309	+	9.18507i	0.152750	+	0.419677i	−0.839589	+	0.543222i	$0.817204\pi$
$480$	−2.23514	−	0.0643515i	−0.102020	−	0.00293723i
$481$	7.44738	+	6.24910i	0.339571	+	0.284934i
$482$	−2.03211	+	0.544503i	−0.0925602	+	0.0248014i
$483$	4.38812	−	16.3767i	0.199666	−	0.745165i
$484$	−9.15050	−	1.61348i	−0.415932	−	0.0733400i
$485$	31.4390	+	23.3905i	1.42757	+	1.06211i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.18098	−	8.13954i	−0.0988297	−	0.368838i	0.898742	−	0.438477i	$-0.144482\pi$
$487$	−2.18098	−	8.13954i	−0.0988297	−	0.368838i	−0.997572	+	0.0696392i	$0.977815\pi$
$488$	0.555858	+	6.35349i	0.0251625	+	0.287609i
$489$	−22.7987	−	8.29803i	−1.03099	−	0.375250i
$490$	−0.890409	−	0.103798i	−0.0402246	−	0.00468910i
$491$	23.5968	−	19.8000i	1.06491	−	0.893564i	0.0703262	−	0.997524i	$-0.477596\pi$
$491$	23.5968	−	19.8000i	1.06491	−	0.893564i	0.994581	+	0.103960i	$0.0331515\pi$
$492$	−4.95576	+	7.07756i	−0.223423	+	0.319081i
$493$	−12.1411	−	12.1411i	−0.546808	−	0.546808i
$494$	−4.00993	−	5.48380i	−0.180415	−	0.246728i
$495$	−3.17123	−	9.56042i	−0.142536	−	0.429709i
$496$	−9.19703	+	1.62169i	−0.412959	+	0.0728158i
$497$	−2.59309	+	29.6391i	−0.116316	+	1.32950i
$498$	−5.40845	+	11.5985i	−0.242358	+	0.519739i
$499$	2.95734	−	8.12523i	0.132389	−	0.363735i	−0.855731	−	0.517421i	$-0.826892\pi$
$499$	2.95734	−	8.12523i	0.132389	−	0.363735i	0.988120	+	0.153686i	$0.0491144\pi$
$500$	−2.90360	−	10.7967i	−0.129853	−	0.482844i
$501$	−6.45209	+	11.1753i	−0.288258	+	0.499278i
$502$	−10.4169	−	2.79120i	−0.464928	−	0.124577i
$503$	−13.8339	−	19.7568i	−0.616822	−	0.880914i	0.382246	−	0.924060i	$-0.375151\pi$
$503$	−13.8339	−	19.7568i	−0.616822	−	0.880914i	−0.999069	+	0.0431468i	$0.986262\pi$
$504$	0.446080	−	2.52984i	0.0198700	−	0.112688i
$505$	5.27495	+	4.69141i	0.234732	+	0.208765i
$506$	−25.7471	−	14.8651i	−1.14460	−	0.660835i
$507$	10.5307	−	0.921321i	0.467687	−	0.0409173i
$508$	6.24083	+	13.3835i	0.276892	+	0.593797i
$509$	3.20411	−	1.16620i	0.142020	−	0.0516909i	−0.270032	−	0.962851i	$-0.587034\pi$
$509$	3.20411	−	1.16620i	0.142020	−	0.0516909i	0.412052	+	0.911160i	$0.364812\pi$
$510$	−14.6916	+	3.48672i	−0.650554	+	0.154394i
$511$	2.09950	+	11.9069i	0.0928765	+	0.526729i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.73276	−	3.39588i	0.120654	−	0.149932i
$514$		−	15.7164i		−	0.693222i
$515$	−4.75112	+	15.8875i	−0.209359	+	0.700089i
$516$	−2.59101	−	3.08784i	−0.114063	−	0.135935i
$517$	37.8058	+	17.6291i	1.66270	+	0.775328i
$518$	−14.5228	+	6.77211i	−0.638097	+	0.297549i
$519$	3.43030	−	4.08807i	0.150573	−	0.179446i
$520$	−3.41321	−	0.703682i	−0.149679	−	0.0308585i
$521$	7.18425	−	4.14783i	0.314748	−	0.181720i	−0.334301	−	0.942466i	$-0.608500\pi$
$521$	7.18425	−	4.14783i	0.314748	−	0.181720i	0.649049	+	0.760747i	$0.275167\pi$
$522$	2.08284	−	1.45842i	0.0911634	−	0.0638333i
$523$	−8.27206	+	5.79216i	−0.361712	+	0.253273i	−0.740278	−	0.672301i	$-0.765306\pi$
$523$	−8.27206	+	5.79216i	−0.361712	+	0.253273i	0.378566	+	0.925574i	$0.376417\pi$
$524$	4.29421	−	2.47926i	0.187593	−	0.108307i
$525$	12.7566	−	1.49895i	0.556743	−	0.0654194i
$526$	10.8006	−	12.8717i	0.470929	−	0.561231i
$527$	−57.1550	+	26.6518i	−2.48971	+	1.16097i
$528$	−4.08258	−	1.90374i	−0.177671	−	0.0828495i
$529$	−13.2152	−	15.7492i	−0.574572	−	0.684748i
$530$	2.21992	+	4.11408i	0.0964270	+	0.178704i
$531$		−	6.01339i		−	0.260959i
$532$	10.9851	−	2.17022i	0.476266	−	0.0940909i
$533$	−9.52183	+	9.52183i	−0.412436	+	0.412436i
$534$	1.70261	+	9.65598i	0.0736791	+	0.417855i
$535$	8.87468	+	37.3942i	0.383686	+	1.61669i
$536$	8.94832	−	3.25692i	0.386508	−	0.140678i
$537$	7.53719	+	16.1636i	0.325254	+	0.697509i
$538$	−15.7279	+	1.37602i	−0.678079	+	0.0593242i
$539$	−1.56396	−	0.902951i	−0.0673644	−	0.0388929i
$540$	−0.130699	−	2.23225i	−0.00562438	−	0.0960605i
$541$	1.66156	−	9.42320i	0.0714362	−	0.405135i	−0.928031	−	0.372502i	$-0.878500\pi$
$541$	1.66156	−	9.42320i	0.0714362	−	0.405135i	0.999467	−	0.0326325i	$-0.0103891\pi$
$542$	1.93154	+	2.75853i	0.0829669	+	0.118489i
$543$	−3.17908	−	0.851832i	−0.136427	−	0.0365556i
$544$	−3.37639	+	5.84807i	−0.144761	+	0.250734i
$545$	16.9819	+	6.74048i	0.727426	+	0.288730i
$546$	1.36934	−	3.76222i	0.0586022	−	0.161008i
$547$	−0.209319	+	0.448887i	−0.00894984	+	0.0191930i	−0.910732	−	0.412998i	$-0.864482\pi$
$547$	−0.209319	+	0.448887i	−0.00894984	+	0.0191930i	0.901782	+	0.432191i	$0.142259\pi$
$548$	1.39393	−	15.9327i	0.0595457	−	0.680610i
$549$	−6.28086	+	1.10749i	−0.268061	+	0.0472663i
$550$	3.25068	−	22.2873i	0.138609	−	0.950334i
$551$	9.20739	+	6.16953i	0.392248	+	0.262831i
$552$	−4.66686	−	4.66686i	−0.198635	−	0.198635i
$553$	−4.01448	+	5.73327i	−0.170713	+	0.243804i
$554$	−9.82042	+	8.24031i	−0.417230	+	0.350097i
$555$	−10.9385	+	8.65452i	−0.464315	+	0.367364i
$556$	−18.7529	−	6.82548i	−0.795299	−	0.289465i
$557$	0.450180	+	5.14558i	0.0190747	+	0.218025i	0.999750	+	0.0223803i	$0.00712446\pi$
$557$	0.450180	+	5.14558i	0.0190747	+	0.218025i	−0.980675	+	0.195645i	$0.937320\pi$
$558$	−2.41709	−	9.02070i	−0.102324	−	0.381877i
$559$	−3.14114	−	5.44062i	−0.132856	−	0.230114i
$560$	3.42877	−	4.60858i	0.144892	−	0.194748i
$561$	−29.9566	−	5.28216i	−1.26477	−	0.223013i
$562$	0.623548	−	2.32711i	0.0263028	−	0.0981633i
$563$	−5.97701	+	1.60154i	−0.251901	+	0.0674967i	−0.382560	−	0.923931i	$-0.624957\pi$
$563$	−5.97701	+	1.60154i	−0.251901	+	0.0674967i	0.130659	+	0.991427i	$0.458291\pi$
$564$	7.09378	+	5.95238i	0.298702	+	0.250641i
$565$	−2.26643	−	2.40080i	−0.0953494	−	0.101003i
$566$	4.54380	+	12.4840i	0.190990	+	0.524741i
$567$	2.55910	+	0.223892i	0.107472	+	0.00940258i
$568$	9.48731	+	6.64309i	0.398079	+	0.278738i
$569$	18.4662			0.774144			0.387072	−	0.922050i	$-0.373487\pi$
$569$	18.4662			0.774144			0.387072	+	0.922050i	$0.373487\pi$
$570$	8.86735	−	4.04600i	0.371412	−	0.169468i
$571$	0.648115			0.0271228			0.0135614	−	0.999908i	$-0.495683\pi$
$571$	0.648115			0.0271228			0.0135614	+	0.999908i	$0.495683\pi$
$572$	−5.75095	−	4.02686i	−0.240459	−	0.168372i
$573$	−1.92705	−	0.168595i	−0.0805035	−	0.00704315i
$574$	−7.59125	−	20.8568i	−0.316852	−	0.870545i
$575$	15.6439	−	29.0559i	0.652395	−	1.21172i
$576$	−0.766044	−	0.642788i	−0.0319185	−	0.0267828i
$577$	−1.95155	+	0.522915i	−0.0812439	+	0.0217692i	−0.299212	−	0.954187i	$-0.596724\pi$
$577$	−1.95155	+	0.522915i	−0.0812439	+	0.0217692i	0.217968	+	0.975956i	$0.430057\pi$
$578$	−7.40221	+	27.6254i	−0.307891	+	1.14907i
$579$	9.70980	+	1.71210i	0.403525	+	0.0711524i
$580$	5.62532	−	0.825746i	0.233579	−	0.0342872i
$581$	−16.4375	−	28.4706i	−0.681944	−	1.18116i
$582$	4.53565	+	16.9273i	0.188009	+	0.701659i
$583$	0.820790	+	9.38167i	0.0339936	+	0.388549i
$584$	4.42272	+	1.60974i	0.183014	+	0.0666115i
$585$	0.403523	−	3.46155i	0.0166836	−	0.143117i
$586$	6.54248	−	5.48979i	0.270267	−	0.226781i
$587$	−25.2681	+	36.0866i	−1.04293	+	1.48945i	−0.180302	+	0.983611i	$0.557708\pi$
$587$	−25.2681	+	36.0866i	−1.04293	+	1.48945i	−0.862625	+	0.505844i	$0.831181\pi$
$588$	−0.283479	−	0.283479i	−0.0116905	−	0.0116905i
$589$	32.8595	−	24.0279i	1.35395	−	0.990053i
$590$	6.03103	−	12.0179i	0.248294	−	0.494771i
$591$	11.7065	−	2.06417i	0.481540	−	0.0849086i
$592$	−0.543662	+	6.21409i	−0.0223444	+	0.255397i
$593$	−5.10449	+	10.9466i	−0.209616	+	0.449524i	−0.982804	−	0.184654i	$-0.940884\pi$
$593$	−5.10449	+	10.9466i	−0.209616	+	0.449524i	0.773187	+	0.634178i	$0.218661\pi$
$594$	1.54067	−	4.23296i	0.0632146	−	0.173681i
$595$	14.3101	−	36.0529i	0.586658	−	1.47803i
$596$	0.0688220	−	0.119203i	0.00281906	−	0.00488275i
$597$	−5.58213	−	1.49573i	−0.228461	−	0.0612160i
$598$	−5.89994	−	8.42598i	−0.241266	−	0.344564i
$599$	−4.55226	+	25.8171i	−0.186000	+	1.05486i	0.738663	+	0.674074i	$0.235457\pi$
$599$	−4.55226	+	25.8171i	−0.186000	+	1.05486i	−0.924664	+	0.380785i	$0.875654\pi$
$600$	1.97759	−	4.59229i	0.0807347	−	0.187480i
$601$	−22.0010	−	12.7023i	−0.897438	−	0.518136i	−0.0210697	−	0.999778i	$-0.506707\pi$
$601$	−22.0010	−	12.7023i	−0.897438	−	0.518136i	−0.876368	+	0.481642i	$0.840041\pi$
$602$	10.3154	−	0.902484i	0.420426	−	0.0367825i
$603$	4.02442	+	8.63041i	0.163887	+	0.351457i
$604$	−11.0217	+	4.01158i	−0.448468	+	0.163229i
$605$	10.9019	−	17.6868i	0.443226	−	0.719071i
$606$	0.548214	+	3.10907i	0.0222697	+	0.126298i
$607$	−1.72531	+	1.72531i	−0.0700284	+	0.0700284i	−0.741254	−	0.671225i	$-0.765768\pi$
$607$	−1.72531	+	1.72531i	−0.0700284	+	0.0700284i	0.671225	+	0.741254i	$0.265768\pi$
$608$	1.40649	−	4.12575i	0.0570408	−	0.167321i
$609$			6.53181i			0.264682i
$610$	−13.6632	−	4.08595i	−0.553208	−	0.165435i
$611$	9.27700	+	11.0559i	0.375307	+	0.447274i
$612$	−6.12009	−	2.85385i	−0.247390	−	0.115360i
$613$	−14.0916	+	6.57101i	−0.569154	+	0.265401i	−0.685821	−	0.727770i	$-0.740557\pi$
$613$	−14.0916	+	6.57101i	−0.569154	+	0.265401i	0.116667	+	0.993171i	$0.462779\pi$
$614$	9.40505	−	11.2085i	0.379557	−	0.452338i
$615$	−10.6214	−	16.1383i	−0.428295	−	0.650757i
$616$	10.0215	−	5.78590i	0.403777	−	0.233121i
$617$	21.3040	−	14.9172i	0.857667	−	0.600545i	−0.0598650	−	0.998206i	$-0.519067\pi$
$617$	21.3040	−	14.9172i	0.857667	−	0.600545i	0.917532	+	0.397661i	$0.130178\pi$
$618$	−6.07485	+	4.25366i	−0.244366	+	0.171107i
$619$	16.0295	−	9.25462i	0.644279	−	0.371974i	−0.141982	−	0.989869i	$-0.545348\pi$
$619$	16.0295	−	9.25462i	0.644279	−	0.371974i	0.786261	+	0.617895i	$0.212014\pi$
$620$	4.21654	−	20.4523i	0.169340	−	0.821385i
$621$	4.24236	−	5.05584i	0.170240	−	0.202884i
$622$	−23.6118	+	11.0104i	−0.946746	+	0.441475i
$623$	−22.8277	−	10.6447i	−0.914574	−	0.426473i
$624$	−1.00181	−	1.19391i	−0.0401044	−	0.0477945i
$625$	24.8345	+	2.87193i	0.993380	+	0.114877i
$626$			19.3071i			0.771666i
$627$	19.6311	−	0.402790i	0.783990	−	0.0160859i
$628$	3.03265	−	3.03265i	0.121016	−	0.121016i
$629$	7.31452	+	41.4827i	0.291649	+	1.65402i
$630$	4.88988	+	3.01406i	0.194818	+	0.120083i
$631$	43.7978	−	15.9411i	1.74356	−	0.634605i	0.744121	−	0.668045i	$-0.232868\pi$
$631$	43.7978	−	15.9411i	1.74356	−	0.634605i	0.999441	+	0.0334399i	$0.0106462\pi$
$632$	1.15145	+	2.46929i	0.0458021	+	0.0982229i
$633$	−8.10361	+	0.708974i	−0.322090	+	0.0281792i
$634$	22.6909	+	13.1006i	0.901172	+	0.520292i
$635$	−32.9637	+	1.93004i	−1.30812	+	0.0765912i
$636$	−0.363034	+	2.05887i	−0.0143952	+	0.0816394i
$637$	−0.358380	−	0.511819i	−0.0141995	−	0.0202790i
$638$	11.0635	+	2.96447i	0.438010	+	0.117364i
$639$	−5.79093	+	10.0302i	−0.229086	+	0.396788i
$640$	−0.886290	−	2.05292i	−0.0350337	−	0.0811489i
$641$	9.35622	−	25.7060i	0.369549	−	1.01533i	−0.605985	−	0.795476i	$-0.707221\pi$
$641$	9.35622	−	25.7060i	0.369549	−	1.01533i	0.975534	−	0.219850i	$-0.0705569\pi$
$642$	−7.26384	+	15.5774i	−0.286681	+	0.614789i
$643$	0.227321	−	2.59830i	0.00896468	−	0.102467i	−0.990394	−	0.138274i	$-0.955845\pi$
$643$	0.227321	−	2.59830i	0.00896468	−	0.102467i	0.999359	+	0.0358070i	$0.0114002\pi$
$644$	16.6968	−	2.94410i	0.657946	−	0.116014i
$645$	8.55498	−	2.83772i	0.336852	−	0.111735i
$646$	1.96334	−	29.3691i	0.0772467	−	1.15551i
$647$	−3.07665	−	3.07665i	−0.120956	−	0.120956i	0.644038	−	0.764994i	$-0.277258\pi$
$647$	−3.07665	−	3.07665i	−0.120956	−	0.120956i	−0.764994	+	0.644038i	$0.777258\pi$
$648$	0.573576	−	0.819152i	0.0225322	−	0.0321793i
$649$	20.7507	−	17.4119i	0.814535	−	0.683476i
$650$	4.27816	−	6.51330i	0.167803	−	0.255473i
$651$	22.5437	+	8.20522i	0.883556	+	0.321588i
$652$	−2.11456	−	24.1695i	−0.0828125	−	0.946551i
$653$	3.92697	+	14.6557i	0.153674	+	0.573520i	0.999215	+	0.0396098i	$0.0126115\pi$
$653$	3.92697	+	14.6557i	0.153674	+	0.573520i	−0.845541	+	0.533911i	$0.820722\pi$
$654$	4.08546	+	7.07623i	0.159754	+	0.276703i
$655$	1.61030	+	10.9700i	0.0629198	+	0.428635i
$656$	−8.50884	−	1.50034i	−0.332214	−	0.0585784i
$657$	−1.21815	+	4.54619i	−0.0475245	+	0.177364i
$658$	−22.9779	+	6.15690i	−0.895770	+	0.240021i
$659$	−27.5315	−	23.1017i	−1.07247	−	0.899913i	−0.0772002	−	0.997016i	$-0.524598\pi$
$659$	−27.5315	−	23.1017i	−1.07247	−	0.899913i	−0.995274	+	0.0971026i	$0.969042\pi$
$660$	7.32447	−	6.91451i	0.285104	−	0.269147i
$661$	10.5814	+	29.0720i	0.411567	+	1.13077i	0.956358	+	0.292199i	$0.0943869\pi$
$661$	10.5814	+	29.0720i	0.411567	+	1.13077i	−0.544791	+	0.838572i	$0.683391\pi$
$662$	−9.41178	−	0.823424i	−0.365799	−	0.0320033i
$663$	−8.62111	−	6.03657i	−0.334816	−	0.234441i
$664$	−12.7975			−0.496638
$665$	−4.55156	+	24.6211i	−0.176502	+	0.954765i
$666$	−6.23782			−0.241711
$667$	13.7466	+	9.62548i	0.532271	+	0.372700i
$668$	−12.8551	−	1.12467i	−0.497378	−	0.0435149i
$669$	0.187150	+	0.514190i	0.00723563	+	0.0198797i
$670$	−0.612793	+	21.2844i	−0.0236743	+	0.822287i
$671$	−22.0080	−	18.4669i	−0.849610	−	0.712907i
$672$	2.48134	−	0.664873i	0.0957197	−	0.0256480i
$673$	−9.81114	+	36.6157i	−0.378192	+	1.41143i	0.470434	+	0.882435i	$0.344097\pi$
$673$	−9.81114	+	36.6157i	−0.378192	+	1.41143i	−0.848625	+	0.528995i	$0.822569\pi$
$674$	−19.8464	−	3.49945i	−0.764454	−	0.134794i
$675$	4.74717	+	1.56982i	0.182719	+	0.0604224i
$676$	5.28548	+	9.15473i	0.203288	+	0.352105i
$677$	−2.37100	−	8.84868i	−0.0911248	−	0.340082i	0.905279	−	0.424818i	$-0.139662\pi$
$677$	−2.37100	−	8.84868i	−0.0911248	−	0.340082i	−0.996403	+	0.0847358i	$0.972995\pi$
$678$	−0.128687	−	1.47090i	−0.00494220	−	0.0564896i
$679$	−42.3031	−	15.3971i	−1.62344	−	0.590885i
$680$	−9.36897	−	11.8415i	−0.359284	−	0.454103i
$681$	−6.82194	+	5.72429i	−0.261417	+	0.219355i
$682$	24.1294	−	34.4604i	0.923962	−	1.31956i
$683$	23.8820	+	23.8820i	0.913818	+	0.913818i	0.996570	−	0.0827523i	$-0.0263710\pi$
$683$	23.8820	+	23.8820i	0.913818	+	0.913818i	−0.0827523	+	0.996570i	$0.526371\pi$
$684$	4.23263	+	1.04156i	0.161839	+	0.0398250i
$685$	31.9636	+	16.0405i	1.22126	+	0.612874i
$686$	18.7231	−	3.30139i	0.714852	−	0.126048i
$687$	0.217350	−	2.48432i	0.00829241	−	0.0947827i
$688$	1.70353	−	3.65323i	0.0649464	−	0.139278i
$689$	−1.11441	+	3.06182i	−0.0424557	+	0.116646i
$690$	13.5492	−	5.84945i	0.515807	−	0.222685i
$691$	−14.3449	+	24.8461i	−0.545705	+	0.945189i	0.452857	+	0.891583i	$0.350405\pi$
$691$	−14.3449	+	24.8461i	−0.545705	+	0.945189i	−0.998562	+	0.0536055i	$0.982929\pi$
$692$	5.15475	+	1.38121i	0.195954	+	0.0525058i
$693$	6.63732	+	9.47907i	0.252131	+	0.360080i
$694$	−4.02071	+	22.8026i	−0.152624	+	0.865573i
$695$	29.6555	−	33.3442i	1.12490	−	1.26482i
$696$	2.20202	+	1.27134i	0.0834675	+	0.0481900i
$697$	−58.1227	+	5.08507i	−2.20155	+	0.192611i
$698$	10.9161	+	23.4097i	0.413182	+	0.886071i
$699$	22.3337	−	8.12880i	0.844738	−	0.307459i
$700$	6.74968	+	10.9279i	0.255114	+	0.413036i
$701$	−0.582352	−	3.30268i	−0.0219951	−	0.124741i	0.971833	−	0.235670i	$-0.0757284\pi$
$701$	−0.582352	−	3.30268i	−0.0219951	−	0.124741i	−0.993828	+	0.110929i	$0.964617\pi$
$702$	1.10205	−	1.10205i	0.0415942	−	0.0415942i
$703$	−9.82172	−	25.3541i	−0.370433	−	0.956250i
$704$		−	4.50463i		−	0.169775i
$705$	−18.2230	+	9.83293i	−0.686316	+	0.370330i
$706$	21.8706	+	26.0644i	0.823111	+	0.980945i
$707$	−7.35018	−	3.42744i	−0.276432	−	0.128902i
$708$	5.44998	−	2.54137i	0.204823	−	0.0955105i
$709$	−16.1553	+	19.2531i	−0.606723	+	0.723065i	−0.978727	−	0.205167i	$-0.934226\pi$
$709$	−16.1553	+	19.2531i	−0.606723	+	0.723065i	0.372004	+	0.928231i	$0.378671\pi$
$710$	−21.6330	+	14.2377i	−0.811871	+	0.534332i
$711$	−2.35953	+	1.36228i	−0.0884895	+	0.0510894i
$712$	−8.03173	+	5.62388i	−0.301002	+	0.210764i
$713$	50.4894	−	35.3531i	1.89084	−	1.32398i
$714$	15.0229	−	8.67350i	0.562220	−	0.324598i
$715$	13.1133	−	8.63052i	0.490411	−	0.322763i
$716$	−11.4638	+	13.6620i	−0.428423	+	0.510574i
$717$	22.9894	−	10.7201i	0.858554	−	0.400350i
$718$	10.8838	+	5.07520i	0.406180	+	0.189405i
$719$	−22.1274	−	26.3704i	−0.825211	−	0.983449i	0.174788	−	0.984606i	$-0.444076\pi$
$719$	−22.1274	−	26.3704i	−0.825211	−	0.983449i	−0.999999	+	0.00115758i	$0.999632\pi$
$720$	1.96787	−	1.06184i	0.0733380	−	0.0395725i
$721$		−	19.0508i		−	0.709490i
$722$	2.43096	+	18.8438i	0.0904708	+	0.701295i
$723$	1.48761	−	1.48761i	0.0553248	−	0.0553248i
$724$	−0.571515	−	3.24122i	−0.0212402	−	0.120459i
$725$	−2.92434	+	12.3725i	−0.108607	+	0.459503i
$726$	8.73130	−	3.17794i	0.324049	−	0.117944i
$727$	−9.48542	−	20.3416i	−0.351795	−	0.754426i	0.648180	−	0.761487i	$-0.275530\pi$
$727$	−9.48542	−	20.3416i	−0.351795	−	0.754426i	−0.999975	+	0.00706049i	$0.997753\pi$
$728$	3.98844	−	0.348943i	0.147821	−	0.0129327i
$729$	0.866025	+	0.500000i	0.0320750	+	0.0185185i
$730$	−6.99403	+	7.86398i	−0.258861	+	0.291059i
$731$	4.72665	−	26.8062i	0.174821	−	0.991462i
$732$	−3.65813	−	5.22435i	−0.135208	−	0.193098i
$733$	13.3404	+	3.57454i	0.492738	+	0.132029i	0.496628	−	0.867964i	$-0.334571\pi$
$733$	13.3404	+	3.57454i	0.492738	+	0.132029i	−0.00388964	+	0.999992i	$0.501238\pi$
$734$	−10.3530	+	17.9318i	−0.382135	+	0.661876i
$735$	0.823016	−	0.355313i	0.0303574	−	0.0131059i
$736$	2.25731	−	6.20191i	0.0832056	−	0.228605i
$737$	−18.1285	+	38.8768i	−0.667773	+	1.43204i
$738$	0.753035	−	8.60723i	0.0277196	−	0.316836i
$739$	−44.8792	+	7.91341i	−1.65091	+	0.291099i	−0.920158	−	0.391547i	$-0.871940\pi$
$739$	−44.8792	+	7.91341i	−1.65091	+	0.291099i	−0.730749	+	0.682647i	$0.760829\pi$
$740$	−12.4665	−	6.25613i	−0.458277	−	0.229980i
$741$	6.21460	+	2.74415i	0.228299	+	0.100809i
$742$	−3.79756	−	3.79756i	−0.139413	−	0.139413i
$743$	25.4705	−	36.3757i	0.934423	−	1.33449i	−0.00796338	−	0.999968i	$-0.502535\pi$
$743$	25.4705	−	36.3757i	0.934423	−	1.33449i	0.942386	−	0.334526i	$-0.108576\pi$
$744$	7.15402	−	6.00294i	0.262279	−	0.220078i
$745$	0.190971	+	0.241370i	0.00699663	+	0.00884312i
$746$	−14.3625	−	5.22752i	−0.525848	−	0.191393i
$747$	−1.11537	−	12.7488i	−0.0408094	−	0.466453i
$748$	−7.87295	−	29.3822i	−0.287863	−	1.07432i
$749$	−22.0765	−	38.2376i	−0.806658	−	1.39717i
$750$	7.91295	+	7.89843i	0.288940	+	0.288410i
$751$	27.0520	+	4.77001i	0.987143	+	0.174060i	0.643836	−	0.765163i	$-0.277342\pi$
$751$	27.0520	+	4.77001i	0.987143	+	0.174060i	0.343307	+	0.939223i	$0.388453\pi$
$752$	−2.39673	+	8.94473i	−0.0873999	+	0.326181i
$753$	10.4169	−	2.79120i	0.379612	−	0.101717i
$754$	3.03572	+	2.54727i	0.110554	+	0.0927662i
$755$	0.754784	−	26.2162i	0.0274694	−	0.954104i
$756$	0.878606	+	2.41395i	0.0319546	+	0.0877945i
$757$	−4.10781	−	0.359387i	−0.149301	−	0.0130621i	0.0122603	−	0.999925i	$-0.496097\pi$
$757$	−4.10781	−	0.359387i	−0.149301	−	0.0130621i	−0.161561	+	0.986863i	$0.551653\pi$
$758$	2.78040	+	1.94686i	0.100989	+	0.0707130i
$759$	29.7302			1.07914
$760$	7.41442	+	6.32663i	0.268949	+	0.229491i
$761$	−39.1676			−1.41983			−0.709913	−	0.704290i	$-0.751266\pi$
$761$	−39.1676			−1.41983			−0.709913	+	0.704290i	$0.751266\pi$
$762$	−12.0965	−	8.47004i	−0.438209	−	0.306837i
$763$	−20.9102	−	1.82940i	−0.757000	−	0.0662289i
$764$	−0.661606	−	1.81775i	−0.0239361	−	0.0657638i
$765$	10.9799	−	10.3654i	0.396980	−	0.374761i
$766$	−10.8235	−	9.08198i	−0.391068	−	0.328145i
$767$	9.05273	−	2.42567i	0.326875	−	0.0875860i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	4.11387	+	0.725387i	0.148350	+	0.0261581i	0.247330	−	0.968931i	$-0.420447\pi$
$769$	4.11387	+	0.725387i	0.148350	+	0.0261581i	−0.0989799	+	0.995089i	$0.531558\pi$
$770$	3.75800	+	25.6010i	0.135429	+	0.922596i
$771$	7.85821	+	13.6108i	0.283007	+	0.490182i
$772$	2.55185	+	9.52363i	0.0918431	+	0.342763i
$773$	0.142300	+	1.62649i	0.00511817	+	0.0585009i	0.998324	−	0.0578677i	$-0.0184302\pi$
$773$	0.142300	+	1.62649i	0.00511817	+	0.0585009i	−0.993206	+	0.116369i	$0.962875\pi$
$774$	3.78780	+	1.37865i	0.136150	+	0.0495544i
$775$	39.0284	+	25.6352i	1.40194	+	0.920844i
$776$	−13.4245	+	11.2645i	−0.481911	+	0.404371i
$777$	9.19109	−	13.1262i	0.329728	−	0.470901i
$778$	−27.3656	−	27.3656i	−0.981103	−	0.981103i
$779$	36.1705	−	10.4917i	1.29594	−	0.375903i
$780$	3.30777	−	1.09720i	0.118437	−	0.0392860i
$781$	−51.3794	+	9.05957i	−1.83850	+	0.324177i
$782$	3.88435	−	44.3983i	0.138904	−	1.58768i
$783$	−1.07458	+	2.30445i	−0.0384024	+	0.0823543i
$784$	0.137116	−	0.376722i	0.00489699	−	0.0134544i
$785$	3.80113	+	8.80461i	0.135668	+	0.314250i
$786$	−2.47926	+	4.29421i	−0.0884324	+	0.153169i
$787$	36.7126	+	9.83711i	1.30866	+	0.350655i	0.844719	−	0.535210i	$-0.179767\pi$
$787$	36.7126	+	9.83711i	1.30866	+	0.350655i	0.463943	+	0.885865i	$0.346434\pi$
$788$	6.81815	+	9.73732i	0.242886	+	0.346878i
$789$	−2.91777	+	16.5475i	−0.103875	+	0.589107i
$790$	−6.08188	+	0.356096i	−0.216383	+	0.0126693i
$791$	3.28483	+	1.89649i	0.116795	+	0.0674316i
$792$	4.48749	−	0.392604i	0.159456	−	0.0139506i
$793$	−4.20081	−	9.00866i	−0.149175	−	0.319907i
$794$	9.32004	−	3.39222i	0.330756	−	0.120385i
$795$	−3.97954	−	2.45294i	−0.141140	−	0.0869967i
$796$	−1.00352	−	5.69125i	−0.0355688	−	0.201721i
$797$	−33.6786	+	33.6786i	−1.19296	+	1.19296i	−0.216725	+	0.976233i	$0.569538\pi$
$797$	−33.6786	+	33.6786i	−1.19296	+	1.19296i	−0.976233	+	0.216725i	$0.930462\pi$
$798$	−8.42829	+	7.37203i	−0.298358	+	0.260967i
$799$			62.5325i			2.21224i
$800$	4.99779	−	0.148482i	0.176699	−	0.00524964i
$801$	−6.30249	−	7.51102i	−0.222688	−	0.265389i
$802$	8.39245	+	3.91346i	0.296348	+	0.138189i
$803$	−19.2149	+	8.96006i	−0.678079	+	0.316194i
$804$	−6.12101	+	7.29473i	−0.215871	+	0.257265i
$805$	−7.65494	+	37.1303i	−0.269801	+	1.30867i
$806$	12.6050	−	7.27751i	0.443993	−	0.256339i
$807$	12.9328	−	9.05563i	0.455255	−	0.318773i
$808$	−2.58609	+	1.81080i	−0.0909785	+	0.0637038i
$809$	−24.4504	+	14.1165i	−0.859631	+	0.496308i	−0.863889	−	0.503683i	$-0.831978\pi$
$809$	−24.4504	+	14.1165i	−0.859631	+	0.496308i	0.00425766	+	0.999991i	$0.498645\pi$
$810$	1.22931	+	1.86783i	0.0431936	+	0.0656289i
$811$	−36.4091	+	43.3907i	−1.27850	+	1.52365i	−0.558978	+	0.829183i	$0.688806\pi$
$811$	−36.4091	+	43.3907i	−1.27850	+	1.52365i	−0.719520	+	0.694472i	$0.755638\pi$
$812$	−5.91983	+	2.76046i	−0.207745	+	0.0968733i
$813$	−3.05203	−	1.42319i	−0.107039	−	0.0499133i
$814$	−18.0617	−	21.5251i	−0.633063	−	0.754456i
$815$	51.9767	+	15.5435i	1.82067	+	0.544465i
$816$		−	6.75277i		−	0.236394i
$817$	0.360430	+	17.5665i	0.0126099	+	0.614576i
$818$	5.73209	−	5.73209i	0.200418	−	0.200418i
$819$	0.695231	+	3.94285i	0.0242933	+	0.137774i
$820$	10.1374	−	16.4466i	0.354015	−	0.574339i
$821$	17.4118	−	6.33737i	0.607675	−	0.221176i	−0.0198107	−	0.999804i	$-0.506306\pi$
$821$	17.4118	−	6.33737i	0.607675	−	0.221176i	0.627486	+	0.778628i	$0.284084\pi$
$822$	6.75916	+	14.4951i	0.235753	+	0.505573i
$823$	39.5814	−	3.46292i	1.37972	−	0.120710i	0.626984	−	0.779032i	$-0.284289\pi$
$823$	39.5814	−	3.46292i	1.37972	−	0.120710i	0.752736	+	0.658323i	$0.228734\pi$
$824$	−6.42247	−	3.70801i	−0.223737	−	0.129175i
$825$	8.32849	+	20.9267i	0.289961	+	0.728575i
$826$	−2.68245	+	15.2129i	−0.0933345	+	0.529326i
$827$	0.604195	+	0.862880i	0.0210099	+	0.0300053i	0.829520	−	0.558478i	$-0.188614\pi$
$827$	0.604195	+	0.862880i	0.0210099	+	0.0300053i	−0.808510	+	0.588483i	$0.799725\pi$
$828$	6.37505	+	1.70819i	0.221548	+	0.0593637i
$829$	18.4819	−	32.0115i	0.641902	−	1.11181i	−0.343106	−	0.939297i	$-0.611479\pi$
$829$	18.4819	−	32.0115i	0.641902	−	1.11181i	0.985008	−	0.172509i	$-0.0551875\pi$
$830$	10.5571	−	26.5975i	0.366441	−	0.923211i
$831$	4.38458	−	12.0465i	0.152099	−	0.417889i
$832$	0.658665	−	1.41251i	0.0228351	−	0.0489701i
$833$	0.235947	−	2.69688i	0.00817507	−	0.0934414i
$834$	19.6532	−	3.46539i	0.680535	−	0.119997i
$835$	12.9420	−	25.7894i	0.447878	−	0.892479i
$836$	8.66151	+	17.6216i	0.299564	+	0.609455i
$837$	6.60361	+	6.60361i	0.228254	+	0.228254i
$838$	0.450712	−	0.643684i	0.0155696	−	0.0222357i
$839$	−7.85737	+	6.59312i	−0.271267	+	0.227620i	−0.768265	−	0.640132i	$-0.778880\pi$
$839$	−7.85737	+	6.59312i	−0.271267	+	0.227620i	0.496999	+	0.867751i	$0.334435\pi$
$840$	−0.665112	+	5.70553i	−0.0229485	+	0.196860i
$841$	21.1758	+	7.70735i	0.730199	+	0.265771i
$842$	2.48112	+	28.3593i	0.0855049	+	0.977326i
$843$	0.623548	+	2.32711i	0.0214761	+	0.0801500i
$844$	−4.06728	−	7.04474i	−0.140002	−	0.242490i
$845$	−23.3868	+	3.43297i	−0.804530	+	0.118098i
$846$	−9.11958	−	1.60803i	−0.313538	−	0.0552852i
$847$	−6.17777	+	23.0558i	−0.212271	+	0.792205i
$848$	−2.01939	+	0.541095i	−0.0693463	+	0.0185813i
$849$	−10.1770	−	8.53954i	−0.349275	−	0.293076i
$850$	32.3395	−	9.70338i	1.10924	−	0.332823i
$851$	−14.0807	−	38.6864i	−0.482680	−	1.32615i
$852$	−11.5378	−	1.00943i	−0.395278	−	0.0345824i
$853$	−2.38734	−	1.67163i	−0.0817408	−	0.0572355i	0.531992	−	0.846750i	$-0.321444\pi$
$853$	−2.38734	−	1.67163i	−0.0817408	−	0.0572355i	−0.613732	+	0.789514i	$0.710333\pi$
$854$	16.3836			0.560637
$855$	−5.65635	+	7.93761i	−0.193443	+	0.271461i
$856$	−17.1877			−0.587464
$857$	28.8928	+	20.2309i	0.986958	+	0.691076i	0.951293	−	0.308288i	$-0.0997561\pi$
$857$	28.8928	+	20.2309i	0.986958	+	0.691076i	0.0356653	+	0.999364i	$0.488645\pi$
$858$	6.99390	+	0.611887i	0.238768	+	0.0208895i
$859$	5.26622	+	14.4688i	0.179681	+	0.493670i	0.996535	−	0.0831750i	$-0.0265060\pi$
$859$	5.26622	+	14.4688i	0.179681	+	0.493670i	−0.816854	+	0.576845i	$0.804284\pi$
$860$	6.18734	+	6.55418i	0.210986	+	0.223496i
$861$	17.0026	+	14.2669i	0.579447	+	0.486214i
$862$	−26.9914	+	7.23231i	−0.919329	+	0.246334i
$863$	−8.11843	+	30.2984i	−0.276355	+	1.03137i	0.678574	+	0.734532i	$0.262598\pi$
$863$	−8.11843	+	30.2984i	−0.276355	+	1.03137i	−0.954928	+	0.296837i	$0.904068\pi$
$864$	0.984808	+	0.173648i	0.0335038	+	0.00590763i
$865$	−7.12296	+	9.57390i	−0.242188	+	0.325523i
$866$	−4.57528	−	7.92462i	−0.155474	−	0.269290i
$867$	−7.40221	−	27.6254i	−0.251392	−	0.938209i
$868$	2.09091	+	23.8992i	0.0709700	+	0.811191i
$869$	−11.5329	−	4.19765i	−0.391228	−	0.142396i
$870$	−4.45880	+	3.52778i	−0.151167	+	0.119603i
$871$	−11.3691	+	9.53981i	−0.385227	+	0.323244i
$872$	−4.68665	+	6.69323i	−0.158710	+	0.226661i
$873$	−12.3916	−	12.3916i	−0.419393	−	0.419393i
$874$	3.09471	+	28.6015i	0.104680	+	0.967460i
$875$	−28.2799	+	5.01329i	−0.956036	+	0.169480i
$876$	−4.63506	+	0.817286i	−0.156604	+	0.0276135i
$877$	2.12173	−	24.2515i	0.0716458	−	0.818916i	−0.872334	−	0.488911i	$-0.837394\pi$
$877$	2.12173	−	24.2515i	0.0716458	−	0.818916i	0.943979	−	0.330005i	$-0.107050\pi$
$878$	2.83678	−	6.08350i	0.0957367	−	0.205308i
$879$	−2.92106	+	8.02554i	−0.0985248	+	0.270695i
$880$	9.36213	+	3.71602i	0.315597	+	0.125267i
$881$	6.82125	−	11.8148i	0.229814	−	0.398049i	−0.727939	−	0.685642i	$-0.759522\pi$
$881$	6.82125	−	11.8148i	0.229814	−	0.398049i	0.957753	+	0.287593i	$0.0928550\pi$
$882$	0.387239	+	0.103760i	0.0130390	+	0.00349380i
$883$	−13.6213	−	19.4532i	−0.458393	−	0.654653i	0.521715	−	0.853120i	$-0.325293\pi$
$883$	−13.6213	−	19.4532i	−0.458393	−	0.654653i	−0.980108	+	0.198467i	$0.936404\pi$
$884$	1.82755	−	10.3645i	0.0614671	−	0.348597i
$885$	0.785943	+	13.4234i	0.0264192	+	0.451221i
$886$	15.9731	+	9.22206i	0.536626	+	0.309821i
$887$	−26.6824	+	2.33441i	−0.895908	+	0.0783818i	−0.525801	−	0.850607i	$-0.676234\pi$
$887$	−26.6824	+	2.33441i	−0.895908	+	0.0783818i	−0.370107	+	0.928989i	$0.620679\pi$
$888$	−2.63622	−	5.65339i	−0.0884657	−	0.189715i
$889$	35.6469	−	12.9744i	1.19556	−	0.435148i
$890$	−5.06267	−	21.3320i	−0.169701	−	0.715050i
$891$	0.782220	+	4.43619i	0.0262054	+	0.148618i
$892$	−0.386921	+	0.386921i	−0.0129551	+	0.0129551i
$893$	−7.82320	−	39.5992i	−0.261794	−	1.32514i
$894$			0.137644i			0.00460350i
$895$	−18.9374	−	35.0959i	−0.633008	−	1.17313i
$896$	1.65124	+	1.96787i	0.0551640	+	0.0657419i
$897$	9.32249	+	4.34715i	0.311269	+	0.145147i
$898$	8.47975	−	3.95417i	0.282973	−	0.131952i
$899$	−15.2635	+	18.1904i	−0.509068	+	0.606683i
$900$	0.583504	+	4.96584i	0.0194501	+	0.165528i
$901$	−12.2262	+	7.05878i	−0.407312	+	0.235162i
$902$	31.8818	−	22.3238i	1.06155	−	0.743303i
$903$	−8.48219	+	5.93929i	−0.282270	+	0.197647i
$904$	1.27870	−	0.738260i	0.0425291	−	0.0245542i
$905$	7.20782	+	1.48599i	0.239596	+	0.0493961i
$906$	7.53931	−	8.98500i	0.250477	−	0.298507i
$907$	−8.90163	+	4.15090i	−0.295574	+	0.137828i	−0.564748	−	0.825263i	$-0.691027\pi$
$907$	−8.90163	+	4.15090i	−0.295574	+	0.137828i	0.269175	+	0.963091i	$0.413249\pi$
$908$	−8.07104	−	3.76359i	−0.267847	−	0.124899i
$909$	−2.02930	−	2.41843i	−0.0673078	−	0.0802143i
$910$	−2.56498	+	8.57718i	−0.0850282	+	0.284331i
$911$			35.7988i			1.18607i	0.805178	+	0.593034i	$0.202070\pi$
$911$			35.7988i			1.18607i	−0.805178	+	0.593034i	$0.797930\pi$
$912$	0.844814	+	4.27625i	0.0279746	+	0.141601i
$913$	40.7632	−	40.7632i	1.34906	−	1.34906i
$914$	−6.19271	−	35.1206i	−0.204837	−	1.16169i
$915$	13.8757	−	3.29308i	0.458716	−	0.108866i
$916$	2.34341	−	0.852933i	0.0774286	−	0.0281817i
$917$	−5.38324	−	11.5444i	−0.177770	−	0.381229i
$918$	6.72708	−	0.588543i	0.222027	−	0.0194248i
$919$	28.8925	+	16.6811i	0.953075	+	0.550258i	0.894035	−	0.447997i	$-0.147863\pi$
$919$	28.8925	+	16.6811i	0.953075	+	0.550258i	0.0590405	+	0.998256i	$0.481196\pi$
$920$	11.0275	+	9.80762i	0.363567	+	0.323348i
$921$	−2.54076	+	14.4094i	−0.0837209	+	0.474805i
$922$	7.41682	+	10.5923i	0.244260	+	0.348839i
$923$	−17.4357	−	4.67188i	−0.573902	−	0.153777i
$924$	−5.78590	+	10.0215i	−0.190342	+	0.329682i
$925$	23.2864	−	20.7487i	0.765651	−	0.682212i
$926$	−8.66770	+	23.8143i	−0.284838	+	0.782587i
$927$	3.13415	−	6.72120i	0.102939	−	0.220753i
$928$	−0.221609	+	2.53300i	−0.00727467	+	0.0831499i
$929$	−25.8410	+	4.55646i	−0.847815	+	0.149493i	−0.580645	−	0.814157i	$-0.697200\pi$
$929$	−25.8410	+	4.55646i	−0.847815	+	0.149493i	−0.267170	+	0.963649i	$0.586088\pi$
$930$	6.57453	+	19.8205i	0.215587	+	0.649940i
$931$	0.187982	+	1.73734i	0.00616085	+	0.0569390i
$932$	16.8058	+	16.8058i	0.550493	+	0.550493i
$933$	14.9432	−	21.3411i	0.489219	−	0.698677i
$934$	−6.25613	+	5.24951i	−0.204707	+	0.171769i
$935$	67.5608	+	7.87577i	2.20948	+	0.257565i
$936$	1.46454	+	0.533050i	0.0478701	+	0.0174233i
$937$	−3.25516	−	37.2067i	−0.106342	−	1.21549i	−0.842506	−	0.538687i	$-0.818921\pi$
$937$	−3.25516	−	37.2067i	−0.106342	−	1.21549i	0.736164	−	0.676803i	$-0.236635\pi$
$938$	−6.33132	−	23.6288i	−0.206725	−	0.771508i
$939$	−9.65353	−	16.7204i	−0.315031	−	0.545650i
$940$	−16.6130	−	12.3600i	−0.541857	−	0.403140i
$941$	38.5288	+	6.79367i	1.25600	+	0.221467i	0.761762	−	0.647857i	$-0.224335\pi$
$941$	38.5288	+	6.79367i	1.25600	+	0.221467i	0.494242	+	0.869325i	$0.335446\pi$
$942$	−1.11003	+	4.14268i	−0.0361667	+	0.134976i
$943$	55.0811	−	14.7589i	1.79369	−	0.480617i
$944$	4.60652	+	3.86533i	0.149930	+	0.125806i
$945$	−5.74179	−	0.165311i	−0.186781	−	0.00537755i
$946$	6.21028	+	17.0626i	0.201914	+	0.554753i
$947$	−16.0309	−	1.40252i	−0.520934	−	0.0455758i	−0.176343	−	0.984329i	$-0.556427\pi$
$947$	−16.0309	−	1.40252i	−0.520934	−	0.0455758i	−0.344591	+	0.938753i	$0.611982\pi$
$948$	−2.23183	−	1.56274i	−0.0724863	−	0.0507555i
$949$	−7.33534			−0.238115
$950$	−19.2653	+	10.1906i	−0.625049	+	0.330627i
$951$	−26.2012			−0.849634
$952$	14.2098	+	9.94984i	0.460543	+	0.322476i
$953$	−59.7475	−	5.22723i	−1.93541	−	0.169327i	−0.947012	−	0.321198i	$-0.895915\pi$
$953$	−59.7475	−	5.22723i	−1.93541	−	0.169327i	−0.988400	+	0.151871i	$0.951470\pi$
$954$	−0.715038	−	1.96455i	−0.0231502	−	0.0636046i
$955$	4.32368	+	0.124482i	0.139911	+	0.00402814i
$956$	19.4315	+	16.3049i	0.628458	+	0.527339i
$957$	−11.0635	+	2.96447i	−0.357633	+	0.0958276i
$958$	2.52984	−	9.44149i	0.0817354	−	0.305041i
$959$	−40.4611	−	7.13439i	−1.30656	−	0.230382i
$960$	1.79401	+	1.33474i	0.0579014	+	0.0430785i
$961$	28.1077	+	48.6839i	0.906699	+	1.57045i
$962$	−2.51620	−	9.39060i	−0.0811257	−	0.302765i
$963$	−1.49801	−	17.1223i	−0.0482726	−	0.551759i
$964$	1.97692	+	0.719541i	0.0636724	+	0.0231749i
$965$	−21.8984	−	2.55277i	−0.704935	−	0.0821764i
$966$	−12.9878	+	10.8981i	−0.417876	+	0.350640i
$967$	4.28119	−	6.11417i	0.137674	−	0.196618i	−0.744395	−	0.667740i	$-0.767262\pi$
$967$	4.28119	−	6.11417i	0.137674	−	0.196618i	0.882068	+	0.471122i	$0.156151\pi$
$968$	6.57020	+	6.57020i	0.211174	+	0.211174i
$969$	12.9842	+	26.4161i	0.417114	+	0.848606i
$970$	−12.3371	−	37.1931i	−0.396119	−	1.19420i
$971$	40.2770	−	7.10192i	1.29255	−	0.227912i	0.515249	−	0.857040i	$-0.327699\pi$
$971$	40.2770	−	7.10192i	1.29255	−	0.227912i	0.777301	+	0.629129i	$0.216588\pi$
$972$	−0.0871557	+	0.996195i	−0.00279552	+	0.0319530i
$973$	−21.6657	+	46.4622i	−0.694570	+	1.48951i
$974$	−2.88209	+	7.91848i	−0.0923481	+	0.253724i
$975$	−0.448343	+	7.77977i	−0.0143585	+	0.249152i
$976$	3.18888	−	5.52330i	0.102074	−	0.176797i
$977$	−7.92642	−	2.12388i	−0.253589	−	0.0679489i	0.129785	−	0.991542i	$-0.458571\pi$
$977$	−7.92642	−	2.12388i	−0.253589	−	0.0679489i	−0.383374	+	0.923593i	$0.625238\pi$
$978$	13.9160	+	19.8741i	0.444985	+	0.635505i
$979$	7.66962	−	43.4966i	0.245122	−	1.39016i
$980$	0.669845	+	0.595744i	0.0213974	+	0.0190303i
$981$	−7.07623	−	4.08546i	−0.225927	−	0.130439i
$982$	−30.6862	+	2.68469i	−0.979236	+	0.0856720i
$983$	−0.112630	−	0.241536i	−0.00359234	−	0.00770380i	0.904503	−	0.426466i	$-0.140242\pi$
$983$	−0.112630	−	0.241536i	−0.00359234	−	0.00770380i	−0.908096	+	0.418763i	$0.862464\pi$
$984$	8.11904	−	2.95509i	0.258826	−	0.0942048i
$985$	−25.8620	+	6.13775i	−0.824030	+	0.195565i
$986$	2.98156	+	16.9093i	0.0949523	+	0.538501i
$987$	16.8210	−	16.8210i	0.535417	−	0.535417i
$988$	0.139360	+	6.79207i	0.00443362	+	0.216084i
$989$			26.6036i			0.845946i
$990$	−2.88592	+	9.65038i	−0.0917204	+	0.306709i
$991$	−21.9049	−	26.1053i	−0.695832	−	0.829261i	0.296216	−	0.955121i	$-0.404275\pi$
$991$	−21.9049	−	26.1053i	−0.695832	−	0.829261i	−0.992048	+	0.125860i	$0.959831\pi$
$992$	8.46393	+	3.94680i	0.268730	+	0.125311i
$993$	8.56255	−	3.99278i	0.271724	−	0.126707i
$994$	19.1244	−	22.7916i	0.606590	−	0.722906i
$995$	12.6562	+	2.60925i	0.401227	+	0.0827188i
$996$	11.0829	−	6.39874i	0.351176	−	0.202752i
$997$	29.3503	−	20.5513i	0.929532	−	0.650865i	−0.00755113	−	0.999971i	$-0.502404\pi$
$997$	29.3503	−	20.5513i	0.929532	−	0.650865i	0.937083	+	0.349106i	$0.113515\pi$
$998$	−7.08295	+	4.95954i	−0.224207	+	0.156991i
$999$	5.40211	−	3.11891i	0.170915	−	0.0986780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.67.1	✓	120
5.3	odd	4	inner	570.2.bh.a.523.2	yes	120
19.2	odd	18	inner	570.2.bh.a.97.2	yes	120
95.78	even	36	inner	570.2.bh.a.553.1	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.67.1	✓	120	1.1	even	1	trivial
570.2.bh.a.97.2	yes	120	19.2	odd	18	inner
570.2.bh.a.523.2	yes	120	5.3	odd	4	inner
570.2.bh.a.553.1	yes	120	95.78	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23514 - 0.0643515i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.48134 - 0.664873i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +O(q^{10})\)	\(q+(-0.819152 - 0.573576i) q^{2} +(0.996195 + 0.0871557i) q^{3} +(0.342020 + 0.939693i) q^{4} +(-2.23514 - 0.0643515i) q^{5} +(-0.766044 - 0.642788i) q^{6} +(2.48134 - 0.664873i) q^{7} +(0.258819 - 0.965926i) q^{8} +(0.984808 + 0.173648i) q^{9} +(1.79401 + 1.33474i) q^{10} +(2.25231 + 3.90112i) q^{11} +(0.258819 + 0.965926i) q^{12} +(0.135835 + 1.55260i) q^{13} +(-2.41395 - 0.878606i) q^{14} +(-2.22103 - 0.258912i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(-3.87323 + 5.53155i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(1.76072 - 3.98746i) q^{19} +(-0.703993 - 2.12236i) q^{20} +(2.52984 - 0.446080i) q^{21} +(0.392604 - 4.48749i) q^{22} +(2.78925 - 5.98157i) q^{23} +(0.342020 - 0.939693i) q^{24} +(4.99172 + 0.287669i) q^{25} +(0.779267 - 1.34973i) q^{26} +(0.965926 + 0.258819i) q^{27} +(1.47344 + 2.10430i) q^{28} +(-0.441532 + 2.50405i) q^{29} +(1.67085 + 1.48602i) q^{30} +(8.08774 + 4.66946i) q^{31} +(0.996195 - 0.0871557i) q^{32} +(1.90374 + 4.08258i) q^{33} +(6.34553 - 2.30958i) q^{34} +(-5.58893 + 1.32641i) q^{35} +(0.173648 + 0.984808i) q^{36} +(4.41081 - 4.41081i) q^{37} +(-3.72941 + 2.25643i) q^{38} +1.55853i q^{39} +(-0.640656 + 2.14233i) q^{40} +(5.55375 + 6.61870i) q^{41} +(-2.32819 - 1.08565i) q^{42} +(-3.65323 + 1.70353i) q^{43} +(-2.89552 + 3.45074i) q^{44} +(-2.19001 - 0.451502i) q^{45} +(-5.71571 + 3.29997i) q^{46} +(7.58557 - 5.31147i) q^{47} +(-0.819152 + 0.573576i) q^{48} +(-0.347189 + 0.200450i) q^{49} +(-3.92398 - 3.09878i) q^{50} +(-4.34060 + 5.17293i) q^{51} +(-1.41251 + 0.658665i) q^{52} +(1.89475 + 0.883538i) q^{53} +(-0.642788 - 0.766044i) q^{54} +(-4.78320 - 8.86450i) q^{55} -2.56887i q^{56} +(2.10155 - 3.81883i) q^{57} +(1.79795 - 1.79795i) q^{58} +(-1.04421 - 5.92203i) q^{59} +(-0.516339 - 2.17564i) q^{60} +(-5.99313 + 2.18132i) q^{61} +(-3.94680 - 8.46393i) q^{62} +(2.55910 - 0.223892i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.203699 - 3.47903i) q^{65} +(0.782220 - 4.43619i) q^{66} +(5.46194 + 7.80046i) q^{67} +(-6.52268 - 1.74775i) q^{68} +(3.29997 - 5.71571i) q^{69} +(5.33898 + 2.11915i) q^{70} +(-3.96123 + 10.8834i) q^{71} +(0.422618 - 0.906308i) q^{72} +(-0.410204 + 4.68865i) q^{73} +(-6.14306 + 1.08319i) q^{74} +(4.94765 + 0.721631i) q^{75} +(4.34919 + 0.290746i) q^{76} +(8.18250 + 8.18250i) q^{77} +(0.893939 - 1.27668i) q^{78} +(-2.08713 + 1.75131i) q^{79} +(1.75358 - 1.38743i) q^{80} +(0.939693 + 0.342020i) q^{81} +(-0.753035 - 8.60723i) q^{82} +(-3.31223 - 12.3614i) q^{83} +(1.28444 + 2.22471i) q^{84} +(9.01319 - 12.1145i) q^{85} +(3.96965 + 0.699957i) q^{86} +(-0.658094 + 2.45604i) q^{87} +(4.35114 - 1.16588i) q^{88} +(-7.51102 - 6.30249i) q^{89} +(1.53498 + 1.62599i) q^{90} +(1.36934 + 3.76222i) q^{91} +(6.57482 + 0.575222i) q^{92} +(7.64999 + 5.35658i) q^{93} -9.26027 q^{94} +(-4.19207 + 8.79924i) q^{95} +1.00000 q^{96} +(-14.3552 - 10.0516i) q^{97} +(0.399374 + 0.0349407i) q^{98} +(1.54067 + 4.23296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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