LMFDB - Embedded newform 205.2.y.a.112.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.10
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.148419 + 0.107833i) q^{2} +(-1.27715 - 3.08332i) q^{3} +(-0.607634 - 1.87010i) q^{4} +(2.05032 + 0.892291i) q^{5} +(0.142929 - 0.595343i) q^{6} +(0.968740 - 1.58084i) q^{7} +(0.224857 - 0.692038i) q^{8} +(-5.75441 + 5.75441i) q^{9} +(0.208089 + 0.353526i) q^{10} +(-1.85533 + 2.17231i) q^{11} +(-4.99008 + 4.26193i) q^{12} +(0.525508 - 2.18890i) q^{13} +(0.314247 - 0.130165i) q^{14} +(0.132646 - 7.46138i) q^{15} +(-3.07361 + 2.23311i) q^{16} +(0.954191 + 0.814956i) q^{17} +(-1.47458 + 0.233551i) q^{18} +(3.95247 - 6.44984i) q^{19} +(0.422834 - 4.37650i) q^{20} +(-6.11146 - 0.967961i) q^{21} +(-0.509613 + 0.122347i) q^{22} +(0.431906 + 2.72695i) q^{23} +(-2.42095 + 0.190533i) q^{24} +(3.40763 + 3.65897i) q^{25} +(0.314031 - 0.268208i) q^{26} +(15.8420 + 6.56196i) q^{27} +(-3.54498 - 0.851073i) q^{28} +(-0.165884 + 2.10775i) q^{29} +(0.824271 - 1.09311i) q^{30} +(-2.78118 - 0.903661i) q^{31} -2.15229 q^{32} +(9.06744 + 2.94619i) q^{33} +(0.0537413 + 0.223849i) q^{34} +(3.39680 - 2.37683i) q^{35} +(14.2579 + 7.26477i) q^{36} +(0.468019 - 0.918539i) q^{37} +(1.28213 - 0.531075i) q^{38} +(-7.42022 + 1.17525i) q^{39} +(1.07853 - 1.21826i) q^{40} +(-2.47591 - 5.90507i) q^{41} +(-0.802682 - 0.802682i) q^{42} +(5.78823 - 7.96681i) q^{43} +(5.18980 + 2.14968i) q^{44} +(-16.9330 + 6.66378i) q^{45} +(-0.229952 + 0.451305i) q^{46} +(9.41330 - 5.76848i) q^{47} +(10.8109 + 6.62490i) q^{48} +(1.61733 + 3.17420i) q^{49} +(0.111201 + 0.910517i) q^{50} +(1.29412 - 3.98290i) q^{51} +(-4.41278 + 0.347293i) q^{52} +(0.796232 + 0.932268i) q^{53} +(1.64366 + 2.68221i) q^{54} +(-5.74234 + 2.79844i) q^{55} +(-0.876174 - 1.02587i) q^{56} +(-24.9348 - 3.94929i) q^{57} +(-0.251906 + 0.294944i) q^{58} +(-2.83878 + 3.90725i) q^{59} +(-14.0342 + 4.28572i) q^{60} +(-0.454226 + 2.86787i) q^{61} +(-0.315337 - 0.434024i) q^{62} +(3.52228 + 14.6713i) q^{63} +(5.82778 + 4.23413i) q^{64} +(3.03059 - 4.01904i) q^{65} +(1.02809 + 1.41504i) q^{66} +(-6.90832 - 0.543696i) q^{67} +(0.944254 - 2.27963i) q^{68} +(7.85643 - 4.81443i) q^{69} +(0.760452 + 0.0135191i) q^{70} +(6.09805 + 5.20822i) q^{71} +(2.68835 + 5.27619i) q^{72} -3.85098i q^{73} +(0.168512 - 0.0858611i) q^{74} +(6.92970 - 15.1799i) q^{75} +(-14.4635 - 3.47238i) q^{76} +(1.63674 + 5.03738i) q^{77} +(-1.22804 - 0.625715i) q^{78} +(-3.40565 + 8.22196i) q^{79} +(-8.29448 + 1.83604i) q^{80} -32.8126i q^{81} +(0.269288 - 1.14341i) q^{82} +(7.14872 - 7.14872i) q^{83} +(1.90334 + 12.0172i) q^{84} +(1.22922 + 2.52234i) q^{85} +(1.71817 - 0.558268i) q^{86} +(6.71074 - 2.18045i) q^{87} +(1.08614 + 1.77241i) q^{88} +(-3.62260 + 0.869708i) q^{89} +(-3.23176 - 0.836902i) q^{90} +(-2.95122 - 2.95122i) q^{91} +(4.83723 - 2.46469i) q^{92} +(0.765719 + 9.72938i) q^{93} +(2.01915 + 0.158910i) q^{94} +(13.8590 - 9.69749i) q^{95} +(2.74880 + 6.63619i) q^{96} +(-1.01295 + 12.8708i) q^{97} +(-0.102239 + 0.645515i) q^{98} +(-1.82404 - 23.1766i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.148419	+	0.107833i	0.104948	+	0.0762495i	0.639022	−	0.769189i	$-0.279339\pi$
$2$	0.148419	+	0.107833i	0.104948	+	0.0762495i	−0.534073	+	0.845438i	$0.679339\pi$
$3$	−1.27715	−	3.08332i	−0.737364	−	1.78015i	−0.616303	−	0.787509i	$-0.711370\pi$
$3$	−1.27715	−	3.08332i	−0.737364	−	1.78015i	−0.121061	−	0.992645i	$-0.538630\pi$
$4$	−0.607634	−	1.87010i	−0.303817	−	0.935052i
$5$	2.05032	+	0.892291i	0.916931	+	0.399045i
$5$	2.05032	+	0.892291i	0.916931	+	0.399045i
$6$	0.142929	−	0.595343i	0.0583506	−	0.243048i
$7$	0.968740	−	1.58084i	0.366149	−	0.597502i	−0.615514	−	0.788126i	$-0.711051\pi$
$7$	0.968740	−	1.58084i	0.366149	−	0.597502i	0.981663	+	0.190625i	$0.0610513\pi$
$8$	0.224857	−	0.692038i	0.0794988	−	0.244672i
$9$	−5.75441	+	5.75441i	−1.91814	+	1.91814i
$10$	0.208089	+	0.353526i	0.0658035	+	0.111795i
$11$	−1.85533	+	2.17231i	−0.559402	+	0.654975i	−0.965973	−	0.258644i	$-0.916724\pi$
$11$	−1.85533	+	2.17231i	−0.559402	+	0.654975i	0.406571	+	0.913619i	$0.366724\pi$
$12$	−4.99008	+	4.26193i	−1.44051	+	1.23031i
$13$	0.525508	−	2.18890i	0.145750	−	0.607091i	−0.850902	−	0.525325i	$-0.823944\pi$
$13$	0.525508	−	2.18890i	0.145750	−	0.607091i	0.996652	−	0.0817663i	$-0.0260561\pi$
$14$	0.314247	−	0.130165i	0.0839860	−	0.0347881i
$15$	0.132646	−	7.46138i	0.0342492	−	1.92652i
$16$	−3.07361	+	2.23311i	−0.768403	+	0.558278i
$17$	0.954191	+	0.814956i	0.231425	+	0.197656i	0.757597	−	0.652722i	$-0.226373\pi$
$17$	0.954191	+	0.814956i	0.231425	+	0.197656i	−0.526172	+	0.850378i	$0.676373\pi$
$18$	−1.47458	+	0.233551i	−0.347562	+	0.0550484i
$19$	3.95247	−	6.44984i	0.906758	−	1.47969i	0.0295618	−	0.999563i	$-0.490589\pi$
$19$	3.95247	−	6.44984i	0.906758	−	1.47969i	0.877196	−	0.480132i	$-0.159411\pi$
$20$	0.422834	−	4.37650i	0.0945485	−	0.978615i
$21$	−6.11146	−	0.967961i	−1.33363	−	0.211226i
$22$	−0.509613	+	0.122347i	−0.108650	+	0.0260845i
$23$	0.431906	+	2.72695i	0.0900586	+	0.568607i	0.990915	+	0.134490i	$0.0429397\pi$
$23$	0.431906	+	2.72695i	0.0900586	+	0.568607i	−0.900856	+	0.434117i	$0.857060\pi$
$24$	−2.42095	+	0.190533i	−0.494174	+	0.0388923i
$25$	3.40763	+	3.65897i	0.681526	+	0.731794i
$26$	0.314031	−	0.268208i	0.0615865	−	0.0525999i
$27$	15.8420	+	6.56196i	3.04879	+	1.26285i
$28$	−3.54498	−	0.851073i	−0.669937	−	0.160838i
$29$	−0.165884	+	2.10775i	−0.0308039	+	0.391400i	0.962118	+	0.272633i	$0.0878943\pi$
$29$	−0.165884	+	2.10775i	−0.0308039	+	0.391400i	−0.992922	+	0.118768i	$0.962106\pi$
$30$	0.824271	−	1.09311i	0.150491	−	0.199574i
$31$	−2.78118	−	0.903661i	−0.499515	−	0.162302i	0.0484136	−	0.998827i	$-0.484583\pi$
$31$	−2.78118	−	0.903661i	−0.499515	−	0.162302i	−0.547929	+	0.836525i	$0.684583\pi$
$32$	−2.15229			−0.380475
$33$	9.06744	+	2.94619i	1.57844	+	0.512866i
$34$	0.0537413	+	0.223849i	0.00921656	+	0.0383897i
$35$	3.39680	−	2.37683i	0.574164	−	0.401758i
$36$	14.2579	+	7.26477i	2.37632	+	1.21080i
$37$	0.468019	−	0.918539i	0.0769419	−	0.151007i	−0.849331	−	0.527861i	$-0.822994\pi$
$37$	0.468019	−	0.918539i	0.0769419	−	0.151007i	0.926273	+	0.376854i	$0.122994\pi$
$38$	1.28213	−	0.531075i	0.207989	−	0.0861518i
$39$	−7.42022	+	1.17525i	−1.18819	+	0.188190i
$40$	1.07853	−	1.21826i	0.170530	−	0.192624i
$41$	−2.47591	−	5.90507i	−0.386673	−	0.922217i
$41$	−2.47591	−	5.90507i	−0.386673	−	0.922217i
$42$	−0.802682	−	0.802682i	−0.123856	−	0.123856i
$43$	5.78823	−	7.96681i	0.882696	−	1.21493i	−0.0929705	−	0.995669i	$-0.529636\pi$
$43$	5.78823	−	7.96681i	0.882696	−	1.21493i	0.975667	−	0.219258i	$-0.0703638\pi$
$44$	5.18980	+	2.14968i	0.782391	+	0.324077i
$45$	−16.9330	+	6.66378i	−2.52422	+	0.993377i
$46$	−0.229952	+	0.451305i	−0.0339045	+	0.0665414i
$47$	9.41330	−	5.76848i	1.37307	−	0.841419i	0.376683	−	0.926342i	$-0.377065\pi$
$47$	9.41330	−	5.76848i	1.37307	−	0.841419i	0.996387	+	0.0849235i	$0.0270646\pi$
$48$	10.8109	+	6.62490i	1.56041	+	0.956223i
$49$	1.61733	+	3.17420i	0.231048	+	0.453457i
$50$	0.111201	+	0.910517i	0.0157262	+	0.128767i
$51$	1.29412	−	3.98290i	0.181213	−	0.557717i
$52$	−4.41278	+	0.347293i	−0.611943	+	0.0481609i
$53$	0.796232	+	0.932268i	0.109371	+	0.128057i	0.812391	−	0.583113i	$-0.198166\pi$
$53$	0.796232	+	0.932268i	0.109371	+	0.128057i	−0.703020	+	0.711170i	$0.748166\pi$
$54$	1.64366	+	2.68221i	0.223674	+	0.365003i
$55$	−5.74234	+	2.79844i	−0.774297	+	0.377341i
$56$	−0.876174	−	1.02587i	−0.117084	−	0.137087i
$57$	−24.9348	−	3.94929i	−3.30270	−	0.523096i
$58$	−0.251906	+	0.294944i	−0.0330769	+	0.0387280i
$59$	−2.83878	+	3.90725i	−0.369578	+	0.508680i	−0.952786	−	0.303642i	$-0.901797\pi$
$59$	−2.83878	+	3.90725i	−0.369578	+	0.508680i	0.583208	+	0.812323i	$0.301797\pi$
$60$	−14.0342	+	4.28572i	−1.81180	+	0.553285i
$61$	−0.454226	+	2.86787i	−0.0581576	+	0.367193i	0.941396	+	0.337304i	$0.109515\pi$
$61$	−0.454226	+	2.86787i	−0.0581576	+	0.367193i	−0.999553	+	0.0298884i	$0.990485\pi$
$62$	−0.315337	−	0.434024i	−0.0400478	−	0.0551211i
$63$	3.52228	+	14.6713i	0.443765	+	1.84841i
$64$	5.82778	+	4.23413i	0.728473	+	0.529267i
$65$	3.03059	−	4.01904i	0.375899	−	0.498500i
$66$	1.02809	+	1.41504i	0.126549	+	0.174180i
$67$	−6.90832	−	0.543696i	−0.843985	−	0.0664231i	−0.350909	−	0.936409i	$-0.614127\pi$
$67$	−6.90832	−	0.543696i	−0.843985	−	0.0664231i	−0.493076	+	0.869986i	$0.664127\pi$
$68$	0.944254	−	2.27963i	0.114508	−	0.276446i
$69$	7.85643	−	4.81443i	0.945803	−	0.579589i
$70$	0.760452	+	0.0135191i	0.0908914	+	0.00161584i
$71$	6.09805	+	5.20822i	0.723705	+	0.618102i	0.933053	−	0.359739i	$-0.117134\pi$
$71$	6.09805	+	5.20822i	0.723705	+	0.618102i	−0.209348	+	0.977841i	$0.567134\pi$
$72$	2.68835	+	5.27619i	0.316825	+	0.621805i
$73$		−	3.85098i		−	0.450723i	−0.974275	−	0.225362i	$-0.927644\pi$
$73$		−	3.85098i		−	0.450723i	0.974275	−	0.225362i	$-0.0723564\pi$
$74$	0.168512	−	0.0858611i	0.0195891	−	0.00998115i
$75$	6.92970	−	15.1799i	0.800172	−	1.75282i
$76$	−14.4635	−	3.47238i	−1.65908	−	0.398310i
$77$	1.63674	+	5.03738i	0.186524	+	0.574062i
$78$	−1.22804	−	0.625715i	−0.139048	−	0.0708483i
$79$	−3.40565	+	8.22196i	−0.383165	+	0.925043i	0.608185	+	0.793796i	$0.291898\pi$
$79$	−3.40565	+	8.22196i	−0.383165	+	0.925043i	−0.991350	+	0.131247i	$0.958102\pi$
$80$	−8.29448	+	1.83604i	−0.927351	+	0.205275i
$81$		−	32.8126i		−	3.64584i
$82$	0.269288	−	1.14341i	0.0297379	−	0.126269i
$83$	7.14872	−	7.14872i	0.784674	−	0.784674i	−0.195942	−	0.980616i	$-0.562776\pi$
$83$	7.14872	−	7.14872i	0.784674	−	0.784674i	0.980616	+	0.195942i	$0.0627763\pi$
$84$	1.90334	+	12.0172i	0.207672	+	1.31119i
$85$	1.22922	+	2.52234i	0.133328	+	0.273586i
$86$	1.71817	−	0.558268i	0.185275	−	0.0601995i
$87$	6.71074	−	2.18045i	0.719466	−	0.233769i
$88$	1.08614	+	1.77241i	0.115782	+	0.188940i
$89$	−3.62260	+	0.869708i	−0.383994	+	0.0921889i	−0.420847	−	0.907132i	$-0.638267\pi$
$89$	−3.62260	+	0.869708i	−0.383994	+	0.0921889i	0.0368521	+	0.999321i	$0.488267\pi$
$90$	−3.23176	−	0.836902i	−0.340658	−	0.0882173i
$91$	−2.95122	−	2.95122i	−0.309372	−	0.309372i
$92$	4.83723	−	2.46469i	0.504316	−	0.256962i
$93$	0.765719	+	9.72938i	0.0794013	+	1.00889i
$94$	2.01915	+	0.158910i	0.208259	+	0.0163904i
$95$	13.8590	−	9.69749i	1.42190	−	0.994941i
$96$	2.74880	+	6.63619i	0.280548	+	0.677304i
$97$	−1.01295	+	12.8708i	−0.102850	+	1.30683i	0.701500	+	0.712670i	$0.252514\pi$
$97$	−1.01295	+	12.8708i	−0.102850	+	1.30683i	−0.804349	+	0.594157i	$0.797486\pi$
$98$	−0.102239	+	0.645515i	−0.0103277	+	0.0652068i
$99$	−1.82404	−	23.1766i	−0.183323	−	2.32934i
$100$	4.77206	−	8.59594i	0.477206	−	0.859594i
$101$	6.84037	+	4.19178i	0.680642	+	0.417098i	0.819395	−	0.573229i	$-0.194309\pi$
$101$	6.84037	+	4.19178i	0.680642	+	0.417098i	−0.138753	+	0.990327i	$0.544309\pi$
$102$	0.621560	−	0.451590i	0.0615437	−	0.0447141i
$103$	−10.6740	+	7.75512i	−1.05174	+	0.764135i	−0.972543	−	0.232724i	$-0.925236\pi$
$103$	−10.6740	+	7.75512i	−1.05174	+	0.764135i	−0.0791989	+	0.996859i	$0.525236\pi$
$104$	−1.39664	−	0.855859i	−0.136951	−	0.0839239i
$105$	−11.6668	−	7.43784i	−1.13856	−	0.725858i
$106$	0.0176470	+	0.224227i	0.00171403	+	0.0217788i
$107$	−0.806273	+	5.09061i	−0.0779454	+	0.492128i	0.917574	+	0.397566i	$0.130145\pi$
$107$	−0.806273	+	5.09061i	−0.0779454	+	0.492128i	−0.995519	+	0.0945618i	$0.969855\pi$
$108$	2.64543	−	33.6134i	0.254557	−	3.23445i
$109$	−1.96214	−	4.73702i	−0.187939	−	0.453724i	0.801624	−	0.597829i	$-0.203970\pi$
$109$	−1.96214	−	4.73702i	−0.187939	−	0.453724i	−0.989562	+	0.144105i	$0.953970\pi$
$110$	−1.15404	−	0.203872i	−0.110033	−	0.0194384i
$111$	−3.42988	−	0.269937i	−0.325550	−	0.0256213i
$112$	0.552659	+	7.02220i	0.0522214	+	0.663535i
$113$	−5.56888	+	2.83748i	−0.523876	+	0.266928i	−0.695867	−	0.718170i	$-0.744980\pi$
$113$	−5.56888	+	2.83748i	−0.523876	+	0.266928i	0.171991	+	0.985098i	$0.444980\pi$
$114$	−3.27495	−	3.27495i	−0.306727	−	0.306727i
$115$	−1.54768	+	5.97650i	−0.144322	+	0.557311i
$116$	4.04252	−	0.970522i	0.375338	−	0.0901107i
$117$	9.57183	+	15.6198i	0.884916	+	1.44405i
$118$	−0.842661	+	0.273797i	−0.0775732	+	0.0252051i
$119$	2.21268	−	0.718943i	0.202836	−	0.0659054i
$120$	−5.13373	−	1.76954i	−0.468643	−	0.161536i
$121$	0.444094	+	2.80390i	0.0403722	+	0.254900i
$122$	−0.376667	+	0.376667i	−0.0341018	+	0.0341018i
$123$	−15.0451	+	15.1757i	−1.35657	+	1.36835i
$124$			5.75019i			0.516383i
$125$	3.72187	+	10.5427i	0.332895	+	0.942964i
$126$	−1.05928	+	2.55733i	−0.0943682	+	0.227825i
$127$	−10.3175	−	5.25702i	−0.915528	−	0.466485i	−0.0682701	−	0.997667i	$-0.521748\pi$
$127$	−10.3175	−	5.25702i	−0.915528	−	0.466485i	−0.847258	+	0.531182i	$0.821748\pi$
$128$	1.73857	+	5.35075i	0.153669	+	0.472944i
$129$	−31.9567	−	7.67211i	−2.81363	−	0.675492i
$130$	0.883184	−	0.269705i	0.0774603	−	0.0236547i
$131$	2.05177	−	1.04543i	0.179264	−	0.0913395i	−0.362056	−	0.932157i	$-0.617925\pi$
$131$	2.05177	−	1.04543i	0.179264	−	0.0913395i	0.541320	+	0.840817i	$0.317925\pi$
$132$		−	18.7473i		−	1.63174i
$133$	−6.36726	−	12.4964i	−0.552111	−	1.08358i
$134$	−0.966700	−	0.825640i	−0.0835101	−	0.0713244i
$135$	26.6260	+	27.5898i	2.29160	+	2.37455i
$136$	0.778536	−	0.477088i	0.0667590	−	0.0409099i
$137$	4.89310	−	11.8130i	0.418045	−	1.00925i	−0.564868	−	0.825181i	$-0.691073\pi$
$137$	4.89310	−	11.8130i	0.418045	−	1.00925i	0.982913	−	0.184069i	$-0.0589271\pi$
$138$	1.68520	+	0.132628i	0.143454	+	0.0112901i
$139$	10.7537	+	14.8012i	0.912115	+	1.25542i	0.966439	+	0.256895i	$0.0826994\pi$
$139$	10.7537	+	14.8012i	0.912115	+	1.25542i	−0.0543248	+	0.998523i	$0.517301\pi$
$140$	−6.50893	−	4.90813i	−0.550105	−	0.414812i
$141$	−29.8083	−	21.6570i	−2.51031	−	1.82385i
$142$	0.343450	+	1.43057i	0.0288217	+	0.120051i
$143$	3.77997	+	5.20268i	0.316097	+	0.435070i
$144$	4.83660	−	30.5371i	0.403050	−	2.54476i
$145$	−2.22085	+	4.17356i	−0.184431	+	0.346595i
$146$	0.415263	−	0.571561i	0.0343674	−	0.0473027i
$147$	7.72148	−	9.04069i	0.636857	−	0.745663i
$148$	−2.00215	−	0.317109i	−0.164576	−	0.0260662i
$149$	11.8954	+	13.9277i	0.974507	+	1.14100i	0.989992	+	0.141121i	$0.0450705\pi$
$149$	11.8954	+	13.9277i	0.974507	+	1.14100i	−0.0154857	+	0.999880i	$0.504929\pi$
$150$	2.66539	−	1.50574i	0.217628	−	0.122943i
$151$	1.48738	+	2.42718i	0.121041	+	0.197521i	0.907422	−	0.420221i	$-0.138047\pi$
$151$	1.48738	+	2.42718i	0.121041	+	0.197521i	−0.786380	+	0.617742i	$0.788047\pi$
$152$	−3.57479	−	4.18555i	−0.289954	−	0.339493i
$153$	−10.1804	+	0.801214i	−0.823036	+	0.0647744i
$154$	−0.300271	+	0.924139i	−0.0241965	+	0.0744693i
$155$	−4.89599	−	4.33442i	−0.393255	−	0.348149i
$156$	6.70661	+	13.1625i	0.536958	+	1.05384i
$157$	10.9324	+	6.69937i	0.872499	+	0.534668i	0.885179	−	0.465251i	$-0.154036\pi$
$157$	10.9324	+	6.69937i	0.872499	+	0.534668i	−0.0126794	+	0.999920i	$0.504036\pi$
$158$	−1.39206	+	0.853057i	−0.110747	+	0.0678656i
$159$	1.85757	−	3.64568i	0.147315	−	0.289122i
$160$	−4.41289	−	1.92047i	−0.348869	−	0.151826i
$161$	4.72927	+	1.95893i	0.372719	+	0.154385i
$162$	3.53828	−	4.87002i	0.277993	−	0.382625i
$163$	−9.98879	−	9.98879i	−0.782382	−	0.782382i	0.197850	−	0.980232i	$-0.436604\pi$
$163$	−9.98879	−	9.98879i	−0.782382	−	0.782382i	−0.980232	+	0.197850i	$0.936604\pi$
$164$	−9.53865	+	8.21834i	−0.744843	+	0.641744i
$165$	15.9623	+	14.1314i	1.24266	+	1.10013i
$166$	1.83188	−	0.290141i	0.142181	−	0.0225193i
$167$	−18.7472	+	7.76534i	−1.45070	+	0.600900i	−0.962366	−	0.271756i	$-0.912396\pi$
$167$	−18.7472	+	7.76534i	−1.45070	+	0.600900i	−0.488335	+	0.872656i	$0.662396\pi$
$168$	−2.04407	+	4.01171i	−0.157703	+	0.309510i
$169$	7.06797	+	3.60131i	0.543690	+	0.277024i
$170$	−0.0895513	+	0.506914i	−0.00686827	+	0.0388786i
$171$	14.3709	+	59.8591i	1.09897	+	4.57754i
$172$	−18.4159	−	5.98368i	−1.40420	−	0.456252i
$173$	−2.96788			−0.225644			−0.112822	−	0.993615i	$-0.535989\pi$
$173$	−2.96788			−0.225644			−0.112822	+	0.993615i	$0.535989\pi$
$174$	1.23113	+	0.400018i	0.0933316	+	0.0303253i
$175$	9.08536	−	1.84233i	0.686788	−	0.139267i
$176$	0.851551	−	10.8200i	0.0641881	−	0.815587i
$177$	15.6728	+	3.76272i	1.17804	+	0.282823i
$178$	−0.631447	−	0.261554i	−0.0473290	−	0.0196043i
$179$	−2.76214	+	2.35909i	−0.206452	+	0.176327i	−0.746662	−	0.665204i	$-0.768345\pi$
$179$	−2.76214	+	2.35909i	−0.206452	+	0.176327i	0.540210	+	0.841530i	$0.318345\pi$
$180$	22.7510	+	27.6173i	1.69576	+	2.05847i
$181$	7.56309	−	0.595228i	0.562160	−	0.0442429i	0.205804	−	0.978593i	$-0.434019\pi$
$181$	7.56309	−	0.595228i	0.562160	−	0.0442429i	0.356356	+	0.934350i	$0.384019\pi$
$182$	−0.119779	−	0.756257i	−0.00887863	−	0.0560575i
$183$	9.42266	−	2.26218i	0.696543	−	0.167225i
$184$	1.98427	+	0.314277i	0.146282	+	0.0231688i
$185$	1.77919	−	1.46569i	0.130809	−	0.107760i
$186$	−0.935501	+	1.52660i	−0.0685943	+	0.111936i
$187$	−3.54067	+	0.560787i	−0.258919	+	0.0410088i
$188$	−16.5075	−	14.0987i	−1.20393	−	1.02826i
$189$	25.7202	−	18.6868i	1.87087	−	1.35926i
$190$	3.10265	+	0.0551581i	0.225090	+	0.00400159i
$191$	−17.5537	+	7.27097i	−1.27014	+	0.526109i	−0.913007	−	0.407945i	$-0.866246\pi$
$191$	−17.5537	+	7.27097i	−1.27014	+	0.526109i	−0.357132	+	0.934054i	$0.616246\pi$
$192$	5.61221	−	23.3765i	0.405026	−	1.68706i
$193$	10.1758	−	8.69093i	0.732468	−	0.625587i	−0.202926	−	0.979194i	$-0.565045\pi$
$193$	10.1758	−	8.69093i	0.732468	−	0.625587i	0.935394	+	0.353607i	$0.115045\pi$
$194$	−1.53823	+	1.80104i	−0.110439	+	0.129307i
$195$	−16.2625	−	4.21136i	−1.16458	−	0.301582i
$196$	4.95333	−	4.95333i	0.353809	−	0.353809i
$197$	−1.81439	+	5.58412i	−0.129270	+	0.397852i	−0.994655	−	0.103256i	$-0.967074\pi$
$197$	−1.81439	+	5.58412i	−0.129270	+	0.397852i	0.865385	+	0.501108i	$0.167074\pi$
$198$	2.22848	−	3.63656i	0.158372	−	0.258439i
$199$	4.49692	−	18.7310i	0.318778	−	1.32781i	−0.551058	−	0.834467i	$-0.685776\pi$
$199$	4.49692	−	18.7310i	0.318778	−	1.32781i	0.869836	−	0.493341i	$-0.164224\pi$
$200$	3.29837	−	1.53547i	0.233230	−	0.108574i
$201$	7.14658	+	21.9949i	0.504081	+	1.55140i
$202$	0.563231	+	1.35976i	0.0396288	+	0.0956723i
$203$	3.17133	+	2.30410i	0.222583	+	0.161716i
$204$	−8.23478			−0.576550
$205$	0.192625	−	14.3165i	0.0134535	−	0.999909i
$206$	−2.42049			−0.168643
$207$	−18.1773	−	13.2066i	−1.26341	−	0.917922i
$208$	3.27284	+	7.90134i	0.226931	+	0.547859i
$209$	6.67792	+	20.5525i	0.461921	+	1.42165i
$210$	−0.929529	−	2.36198i	−0.0641436	−	0.162992i
$211$	−3.16595	+	13.1871i	−0.217953	+	0.907838i	0.750943	+	0.660368i	$0.229599\pi$
$211$	−3.16595	+	13.1871i	−0.217953	+	0.907838i	−0.968895	+	0.247471i	$0.920401\pi$
$212$	1.25962	−	2.05551i	0.0865111	−	0.141173i
$213$	8.27047	−	25.4539i	0.566684	−	1.74407i
$214$	−0.668602	+	0.668602i	−0.0457047	+	0.0457047i
$215$	18.9764	−	11.1697i	1.29418	−	0.761770i
$216$	8.10330	−	9.48774i	0.551360	−	0.645559i
$217$	−4.12279	+	3.52119i	−0.279873	+	0.239034i
$218$	0.219588	−	0.914649i	0.0148724	−	0.0619478i
$219$	−11.8738	+	4.91829i	−0.802357	+	0.332347i
$220$	8.72261	+	9.03836i	0.588078	+	0.609366i
$221$	2.28529	−	1.66036i	0.153725	−	0.111688i
$222$	−0.479953	−	0.409918i	−0.0322123	−	0.0275119i
$223$	−10.7131	+	1.69680i	−0.717405	+	0.113626i	−0.504456	−	0.863437i	$-0.668307\pi$
$223$	−10.7131	+	1.69680i	−0.717405	+	0.113626i	−0.212949	+	0.977063i	$0.568307\pi$
$224$	−2.08501	+	3.40243i	−0.139311	+	0.227334i
$225$	−40.6641	−	1.44629i	−2.71094	−	0.0964192i
$226$	−1.13250	−	0.179371i	−0.0753331	−	0.0119316i
$227$	12.8126	−	3.07603i	0.850401	−	0.204163i	0.215257	−	0.976557i	$-0.430941\pi$
$227$	12.8126	−	3.07603i	0.850401	−	0.204163i	0.635144	+	0.772394i	$0.280941\pi$
$228$	7.76565	+	49.0304i	0.514293	+	3.24712i
$229$	10.1614	−	0.799718i	0.671483	−	0.0528469i	0.261866	−	0.965104i	$-0.415662\pi$
$229$	10.1614	−	0.799718i	0.671483	−	0.0528469i	0.409617	+	0.912257i	$0.365662\pi$
$230$	−0.874171	+	0.720137i	−0.0576411	+	0.0474844i
$231$	13.4415	−	11.4801i	0.884383	−	0.755334i
$232$	1.42135	+	0.588741i	0.0933159	+	0.0386527i
$233$	13.9210	+	3.34214i	0.911997	+	0.218951i	0.662183	−	0.749343i	$-0.269630\pi$
$233$	13.9210	+	3.34214i	0.911997	+	0.218951i	0.249815	+	0.968294i	$0.419630\pi$
$234$	−0.263685	+	3.35044i	−0.0172377	+	0.219025i
$235$	24.4474	−	3.42782i	1.59478	−	0.223606i
$236$	9.03190	+	2.93464i	0.587926	+	0.191029i
$237$	29.7004			1.92925
$238$	0.405930	+	0.131895i	0.0263126	+	0.00854947i
$239$	−2.79372	−	11.6367i	−0.180710	−	0.752713i	−0.986937	−	0.161106i	$-0.948494\pi$
$239$	−2.79372	−	11.6367i	−0.180710	−	0.752713i	0.806227	−	0.591607i	$-0.201506\pi$
$240$	16.2544	+	23.2296i	1.04922	+	1.49947i
$241$	−3.40124	−	1.73302i	−0.219093	−	0.111634i	0.340999	−	0.940063i	$-0.389235\pi$
$241$	−3.40124	−	1.73302i	−0.219093	−	0.111634i	−0.560093	+	0.828430i	$0.689235\pi$
$242$	−0.236441	+	0.464041i	−0.0151990	+	0.0298297i
$243$	−53.6456	+	22.2208i	−3.44137	+	1.42546i
$244$	5.63921	−	0.893164i	0.361014	−	0.0571789i
$245$	0.483745	+	7.95126i	0.0309054	+	0.507987i
$246$	−3.86943	+	0.630012i	−0.246706	+	0.0401681i
$247$	−12.0410	−	12.0410i	−0.766150	−	0.766150i
$248$	−1.25073	+	1.72149i	−0.0794217	+	0.109315i
$249$	−31.1718	−	12.9118i	−1.97543	−	0.818250i
$250$	−0.584448	+	1.96608i	−0.0369638	+	0.124346i
$251$	−13.5694	+	26.6315i	−0.856493	+	1.68096i	−0.132470	+	0.991187i	$0.542291\pi$
$251$	−13.5694	+	26.6315i	−0.856493	+	1.68096i	−0.724023	+	0.689776i	$0.757709\pi$
$252$	25.2967	−	15.5018i	1.59354	−	0.976523i
$253$	−6.72509	−	4.12114i	−0.422803	−	0.259094i
$254$	−0.964434	−	1.89281i	−0.0605140	−	0.118765i
$255$	6.20727	−	7.01148i	0.388714	−	0.439076i
$256$	4.13308	−	12.7203i	0.258318	−	0.795020i
$257$	−1.22195	+	0.0961698i	−0.0762234	+	0.00599891i	−0.116513	−	0.993189i	$-0.537172\pi$
$257$	−1.22195	+	0.0961698i	−0.0762234	+	0.00599891i	0.0402901	+	0.999188i	$0.487172\pi$
$258$	−3.91568	−	4.58467i	−0.243780	−	0.285429i
$259$	−0.998675	−	1.62969i	−0.0620546	−	0.101264i
$260$	−9.35751	−	3.22542i	−0.580328	−	0.200032i
$261$	−11.1743	−	13.0834i	−0.691673	−	0.809845i
$262$	0.417254	+	0.0660866i	0.0257781	+	0.00408284i
$263$	3.00261	−	3.51560i	0.185149	−	0.216781i	−0.660067	−	0.751207i	$-0.729472\pi$
$263$	3.00261	−	3.51560i	0.185149	−	0.216781i	0.845216	+	0.534426i	$0.179472\pi$
$264$	4.07775	−	5.61254i	0.250968	−	0.345428i
$265$	0.800677	+	2.62192i	0.0491852	+	0.161063i
$266$	0.402505	−	2.54132i	0.0246792	−	0.155818i
$267$	7.30819	+	10.0589i	0.447254	+	0.615593i
$268$	3.18096	+	13.2496i	0.194308	+	0.809350i
$269$	−1.97887	−	1.43773i	−0.120654	−	0.0876601i	0.525822	−	0.850595i	$-0.323758\pi$
$269$	−1.97887	−	1.43773i	−0.120654	−	0.0876601i	−0.646476	+	0.762935i	$0.723758\pi$
$270$	0.976719	+	6.96602i	0.0594412	+	0.423938i
$271$	−0.0659788	−	0.0908120i	−0.00400793	−	0.00551644i	0.807008	−	0.590540i	$-0.201085\pi$
$271$	−0.0659788	−	0.0908120i	−0.00400793	−	0.00551644i	−0.811016	+	0.585024i	$0.801085\pi$
$272$	−4.75270	−	0.374046i	−0.288175	−	0.0226798i
$273$	−5.33039	+	12.8687i	−0.322610	+	0.778849i
$274$	2.00006	−	1.22564i	0.120828	−	0.0740435i
$275$	−14.2707	+	0.613847i	−0.860554	+	0.0370164i
$276$	−13.7773	−	11.7669i	−0.829297	−	0.708286i
$277$	8.73076	+	17.1351i	0.524580	+	1.02955i	0.989546	+	0.144218i	$0.0460667\pi$
$277$	8.73076	+	17.1351i	0.524580	+	1.02955i	−0.464966	+	0.885329i	$0.653933\pi$
$278$			3.35638i			0.201302i
$279$	21.2041	−	10.8040i	1.26946	−	0.646820i
$280$	−0.881064	−	2.88516i	−0.0526537	−	0.172421i
$281$	−26.9370	−	6.46701i	−1.60693	−	0.385789i	−0.671978	−	0.740571i	$-0.734555\pi$
$281$	−26.9370	−	6.46701i	−1.60693	−	0.385789i	−0.934949	+	0.354782i	$0.884555\pi$
$282$	−2.08879	−	6.42863i	−0.124386	−	0.382819i
$283$	−17.8085	−	9.07387i	−1.05860	−	0.539386i	−0.164099	−	0.986444i	$-0.552472\pi$
$283$	−17.8085	−	9.07387i	−1.05860	−	0.539386i	−0.894505	+	0.447058i	$0.852472\pi$
$284$	6.03454	−	14.5687i	0.358084	−	0.864492i
$285$	−47.6004	−	30.3464i	−2.81961	−	1.79757i
$286$			1.17978i			0.0697621i
$287$	−11.7335	−	1.80645i	−0.692606	−	0.106632i
$288$	12.3852	−	12.3852i	0.729803	−	0.729803i
$289$	−2.41306	−	15.2355i	−0.141945	−	0.896203i
$290$	−0.779664	+	0.379956i	−0.0457834	+	0.0223118i
$291$	40.9783	−	13.3147i	2.40219	−	0.780519i
$292$	−7.20174	+	2.33999i	−0.421450	+	0.136937i
$293$	2.85569	+	4.66007i	0.166831	+	0.272244i	0.925120	−	0.379675i	$-0.123964\pi$
$293$	2.85569	+	4.66007i	0.166831	+	0.272244i	−0.758289	+	0.651919i	$0.773964\pi$
$294$	2.12090	−	0.509183i	0.123693	−	0.0296962i
$295$	−9.30682	+	5.47809i	−0.541864	+	0.318947i
$296$	−0.530426	−	0.530426i	−0.0308304	−	0.0308304i
$297$	−43.6466	+	22.2391i	−2.53263	+	1.29044i
$298$	0.263639	+	3.34985i	0.0152722	+	0.194052i
$299$	6.19597	+	0.487634i	0.358322	+	0.0282006i
$300$	−32.5986	−	3.73545i	−1.88208	−	0.215666i
$301$	−6.98697	−	16.8680i	−0.402722	−	0.972258i
$302$	−0.0409745	+	0.520630i	−0.00235782	+	0.0299589i
$303$	4.18841	−	26.4446i	0.240618	−	1.51920i
$304$	2.25485	+	28.6506i	0.129325	+	1.64323i
$305$	−3.49028	+	5.47475i	−0.199853	+	0.313483i
$306$	−1.59737	−	0.978867i	−0.0913153	−	0.0559581i
$307$	3.80820	−	2.76682i	0.217346	−	0.157911i	−0.473785	−	0.880640i	$-0.657113\pi$
$307$	3.80820	−	2.76682i	0.217346	−	0.157911i	0.691131	+	0.722730i	$0.257113\pi$
$308$	8.42588	−	6.12176i	0.480109	−	0.348819i
$309$	37.5438	+	23.0069i	2.13579	+	1.30882i
$310$	−0.259266	−	1.17126i	−0.0147253	−	0.0665232i
$311$	1.27512	+	16.2019i	0.0723052	+	0.918725i	0.920930	+	0.389729i	$0.127431\pi$
$311$	1.27512	+	16.2019i	0.0723052	+	0.918725i	−0.848624	+	0.528996i	$0.822569\pi$
$312$	−0.855170	+	5.39933i	−0.0484145	+	0.305677i
$313$	0.302154	−	3.83922i	0.0170787	−	0.217006i	−0.982456	−	0.186496i	$-0.940287\pi$
$313$	0.302154	−	3.83922i	0.0170787	−	0.217006i	0.999534	−	0.0305099i	$-0.00971311\pi$
$314$	0.900164	+	2.17319i	0.0507992	+	0.122640i
$315$	−5.86931	+	33.2238i	−0.330698	+	1.87195i
$316$	17.4453	+	1.37298i	0.981375	+	0.0772359i
$317$	−1.42032	−	18.0469i	−0.0797733	−	1.01362i	−0.898368	−	0.439244i	$-0.855246\pi$
$317$	−1.42032	−	18.0469i	−0.0797733	−	1.01362i	0.818594	−	0.574372i	$-0.194754\pi$
$318$	0.668825	−	0.340783i	0.0375058	−	0.0191102i
$319$	−4.27092	−	4.27092i	−0.239126	−	0.239126i
$320$	8.17075	+	13.8814i	0.456759	+	0.775995i
$321$	16.7257	−	4.01549i	0.933537	−	0.224123i
$322$	0.490679	+	0.800715i	0.0273444	+	0.0446221i
$323$	9.02774	−	2.93329i	0.502317	−	0.163213i
$324$	−61.3629	+	19.9380i	−3.40905	+	1.10767i
$325$	9.79984	−	5.53614i	0.543597	−	0.307090i
$326$	−0.405409	−	2.55965i	−0.0224535	−	0.141766i
$327$	−12.0998	+	12.0998i	−0.669120	+	0.669120i
$328$	−4.64326	+	0.385632i	−0.256381	+	0.0212929i
$329$		−	20.4691i		−	1.12850i
$330$	0.845281	+	3.81864i	0.0465312	+	0.210209i
$331$	8.96470	−	21.6427i	0.492745	−	1.18959i	−0.460573	−	0.887622i	$-0.652356\pi$
$331$	8.96470	−	21.6427i	0.492745	−	1.18959i	0.953318	−	0.301969i	$-0.0976440\pi$
$332$	−17.7126	−	9.02505i	−0.972108	−	0.495314i
$333$	2.59248	+	7.97882i	0.142067	+	0.437237i
$334$	−3.61981	−	0.869039i	−0.198067	−	0.0475517i
$335$	−13.6791	−	7.27898i	−0.747371	−	0.397693i
$336$	20.9458	−	10.6724i	1.14269	−	0.582229i
$337$		−	6.30497i		−	0.343454i	−0.985145	−	0.171727i	$-0.945065\pi$
$337$		−	6.30497i		−	0.343454i	0.985145	−	0.171727i	$-0.0549347\pi$
$338$	0.660684	+	1.29667i	0.0359365	+	0.0705293i
$339$	15.8612	+	13.5467i	0.861461	+	0.735757i
$340$	3.97012	−	3.83142i	0.215310	−	0.207788i
$341$	7.12303	−	4.36500i	0.385733	−	0.236378i
$342$	−4.32187	+	10.4339i	−0.233700	+	0.564202i
$343$	19.5230	+	1.53650i	1.05415	+	0.0829630i
$344$	−4.21181	−	5.79706i	−0.227086	−	0.312557i
$345$	20.4041	−	2.86089i	1.09852	−	0.154025i
$346$	−0.440491	−	0.320036i	−0.0236810	−	0.0172052i
$347$	−5.10801	−	21.2764i	−0.274212	−	1.14218i	−0.924101	−	0.382148i	$-0.875185\pi$
$347$	−5.10801	−	21.2764i	−0.274212	−	1.14218i	0.649889	−	0.760029i	$-0.274815\pi$
$348$	−8.15534	−	11.2249i	−0.437172	−	0.601716i
$349$	0.174983	−	1.10480i	0.00936665	−	0.0591387i	−0.982562	−	0.185934i	$-0.940469\pi$
$349$	0.174983	−	1.10480i	0.00936665	−	0.0591387i	0.991929	+	0.126795i	$0.0404690\pi$
$350$	1.54711	+	0.706263i	0.0826964	+	0.0377514i
$351$	22.6885	−	31.2281i	1.21102	−	1.66683i
$352$	3.99320	−	4.67543i	0.212838	−	0.249201i
$353$	−10.9049	−	1.72717i	−0.580410	−	0.0919279i	−0.140676	−	0.990056i	$-0.544927\pi$
$353$	−10.9049	−	1.72717i	−0.580410	−	0.0919279i	−0.439734	+	0.898128i	$0.644927\pi$
$354$	1.92041	+	2.24851i	0.102069	+	0.119507i
$355$	7.85570	+	16.1198i	0.416937	+	0.855548i
$356$	3.82766	+	6.24617i	0.202865	+	0.331046i
$357$	−5.04266	−	5.90419i	−0.266886	−	0.312483i
$358$	−0.664343	+	0.0522849i	−0.0351116	+	0.00276334i
$359$	6.92987	−	21.3279i	0.365745	−	1.12565i	−0.583769	−	0.811920i	$-0.698423\pi$
$359$	6.92987	−	21.3279i	0.365745	−	1.12565i	0.949513	−	0.313726i	$-0.101577\pi$
$360$	0.804087	+	13.2167i	0.0423791	+	0.696580i
$361$	−17.3526	−	34.0564i	−0.913296	−	1.79244i
$362$	1.18669	+	0.727207i	0.0623713	+	0.0382212i
$363$	8.07814	−	4.95029i	0.423992	−	0.259823i
$364$	−3.72582	+	7.31234i	−0.195286	+	0.383271i
$365$	3.43620	−	7.89575i	0.179859	−	0.413282i
$366$	1.64244	+	0.680323i	0.0858519	+	0.0355610i
$367$	−2.89192	+	3.98039i	−0.150957	+	0.207775i	−0.877798	−	0.479032i	$-0.840988\pi$
$367$	−2.89192	+	3.98039i	−0.150957	+	0.207775i	0.726841	+	0.686806i	$0.240988\pi$
$368$	−7.41708	−	7.41708i	−0.386642	−	0.386642i
$369$	48.2276	+	19.7328i	2.51063	+	1.02725i
$370$	0.422117	−	0.0256811i	0.0219448	−	0.00133510i
$371$	2.24511	−	0.355590i	0.116560	−	0.0184613i
$372$	17.7297	−	7.34387i	0.919241	−	0.380762i
$373$	−8.51739	+	16.7163i	−0.441014	+	0.865538i	0.558341	+	0.829612i	$0.311438\pi$
$373$	−8.51739	+	16.7163i	−0.441014	+	0.865538i	−0.999354	+	0.0359264i	$0.988562\pi$
$374$	−0.585975	−	0.298569i	−0.0303001	−	0.0154387i
$375$	27.7530	−	24.9403i	1.43316	−	1.28791i
$376$	−1.87536	−	7.81144i	−0.0967143	−	0.402844i
$377$	4.52649	+	1.47074i	0.233126	+	0.0757472i
$378$	5.83243			0.299988
$379$	13.2900	+	4.31819i	0.682663	+	0.221811i	0.629761	−	0.776789i	$-0.283153\pi$
$379$	13.2900	+	4.31819i	0.682663	+	0.221811i	0.0529019	+	0.998600i	$0.483153\pi$
$380$	−26.5565	−	20.0252i	−1.36232	−	1.02727i
$381$	−3.03207	+	38.5261i	−0.155337	+	1.97375i
$382$	−3.38936	−	0.813712i	−0.173415	−	0.0416331i
$383$	5.56852	+	2.30656i	0.284538	+	0.117860i	0.520388	−	0.853930i	$-0.325787\pi$
$383$	5.56852	+	2.30656i	0.284538	+	0.117860i	−0.235850	+	0.971790i	$0.575787\pi$
$384$	14.2777	−	12.1943i	0.728604	−	0.622287i
$385$	−1.13896	+	11.7887i	−0.0580467	+	0.600807i
$386$	2.44745	−	0.192619i	0.124572	−	0.00980403i
$387$	12.5365	+	79.1521i	0.637264	+	4.02353i
$388$	24.6851	−	5.92638i	1.25320	−	0.300866i
$389$	−13.0247	−	2.06291i	−0.660379	−	0.104594i	−0.182756	−	0.983158i	$-0.558502\pi$
$389$	−13.0247	−	2.06291i	−0.660379	−	0.104594i	−0.477624	+	0.878565i	$0.658502\pi$
$390$	−1.95955	−	2.37868i	−0.0992255	−	0.120449i
$391$	−1.81022	+	2.95401i	−0.0915468	+	0.149391i
$392$	2.56033	−	0.405517i	0.129316	−	0.0204817i
$393$	−5.84381	−	4.99109i	−0.294781	−	0.251767i
$394$	−0.871444	+	0.633141i	−0.0439027	+	0.0318972i
$395$	−14.3191	+	13.8188i	−0.720470	+	0.695301i
$396$	−42.2344	+	17.4941i	−2.12236	+	0.879109i
$397$	−4.29066	+	17.8719i	−0.215342	+	0.896965i	0.755096	+	0.655614i	$0.227590\pi$
$397$	−4.29066	+	17.8719i	−0.215342	+	0.896965i	−0.970438	+	0.241350i	$0.922410\pi$
$398$	2.68725	−	2.29513i	0.134700	−	0.115045i
$399$	−30.3985	+	35.5921i	−1.52183	+	1.78183i
$400$	−18.6446	−	3.63663i	−0.932231	−	0.181832i
$401$	−10.1319	+	10.1319i	−0.505963	+	0.505963i	−0.913285	−	0.407321i	$-0.866463\pi$
$401$	−10.1319	+	10.1319i	−0.505963	+	0.505963i	0.407321	+	0.913285i	$0.366463\pi$
$402$	−1.31109	+	4.03511i	−0.0653911	+	0.201253i
$403$	−3.43955	+	5.61284i	−0.171336	+	0.279596i
$404$	3.68263	−	15.3393i	0.183218	−	0.763157i
$405$	29.2784	−	67.2763i	1.45485	−	3.34299i
$406$	0.222228	+	0.683947i	0.0110290	+	0.0339437i
$407$	1.12702	+	2.72087i	0.0558644	+	0.134868i
$408$	−2.46532	−	1.79116i	−0.122052	−	0.0886757i
$409$	−19.6489			−0.971578			−0.485789	−	0.874076i	$-0.661468\pi$
$409$	−19.6489			−0.971578			−0.485789	+	0.874076i	$0.661468\pi$
$410$	1.57238	−	2.10408i	0.0776545	−	0.103913i
$411$	−42.6724			−2.10487
$412$	20.9888	+	15.2492i	1.03404	+	0.751276i
$413$	3.42669	+	8.27277i	0.168617	+	0.407076i
$414$	−1.27376	−	3.92023i	−0.0626019	−	0.192669i
$415$	21.0359	−	8.27843i	1.03261	−	0.406372i
$416$	−1.13105	+	4.71114i	−0.0554541	+	0.230983i
$417$	31.9026	−	52.0603i	1.56228	−	2.54940i
$418$	−1.22511	+	3.77049i	−0.0599220	+	0.184421i
$419$	−12.6501	+	12.6501i	−0.618000	+	0.618000i	−0.945018	−	0.327018i	$-0.893956\pi$
$419$	−12.6501	+	12.6501i	−0.618000	+	0.618000i	0.327018	+	0.945018i	$0.393956\pi$
$420$	−6.82041	+	26.3375i	−0.332802	+	1.28514i
$421$	−8.37762	+	9.80893i	−0.408300	+	0.478058i	−0.926010	−	0.377498i	$-0.876785\pi$
$421$	−8.37762	+	9.80893i	−0.408300	+	0.478058i	0.517710	+	0.855556i	$0.326785\pi$
$422$	−1.89189	+	1.61583i	−0.0920960	+	0.0786574i
$423$	−20.9738	+	87.3621i	−1.01978	+	4.24769i
$424$	0.824203	−	0.341396i	0.0400268	−	0.0165797i
$425$	0.269634	+	6.26842i	0.0130792	+	0.304063i
$426$	3.97227	−	2.88602i	0.192457	−	0.139828i
$427$	4.09362	+	3.49628i	0.198104	+	0.169197i
$428$	10.0099	−	1.58541i	0.483846	−	0.0766337i
$429$	11.2139	−	18.2995i	0.541413	−	0.883506i
$430$	4.02094	+	0.388481i	0.193907	+	0.0187342i
$431$	2.82905	+	0.448078i	0.136271	+	0.0215832i	0.224197	−	0.974544i	$-0.428024\pi$
$431$	2.82905	+	0.448078i	0.136271	+	0.0215832i	−0.0879264	+	0.996127i	$0.528024\pi$
$432$	−63.3457	+	15.2080i	−3.04772	+	0.731693i
$433$	−0.896946	−	5.66310i	−0.0431045	−	0.272151i	0.956718	−	0.291018i	$-0.0939940\pi$
$433$	−0.896946	−	5.66310i	−0.0431045	−	0.272151i	−0.999822	+	0.0188672i	$0.993994\pi$
$434$	−0.991603	+	0.0780408i	−0.0475985	+	0.00374608i
$435$	15.7048	+	1.51731i	0.752986	+	0.0727494i
$436$	−7.66646	+	6.54777i	−0.367157	+	0.313581i
$437$	19.2955	+	7.99244i	0.923027	+	0.382330i
$438$	−2.29266	−	0.550418i	−0.109547	−	0.0263000i
$439$	2.59468	−	32.9685i	0.123837	−	1.57350i	−0.550345	−	0.834937i	$-0.685504\pi$
$439$	2.59468	−	32.9685i	0.123837	−	1.57350i	0.674183	−	0.738565i	$-0.264496\pi$
$440$	0.645419	+	4.60317i	0.0307691	+	0.219447i
$441$	−27.5724	−	8.95883i	−1.31297	−	0.426611i
$442$	0.518223			0.0246494
$443$	6.10519	+	1.98370i	0.290066	+	0.0942483i	0.450436	−	0.892809i	$-0.351269\pi$
$443$	6.10519	+	1.98370i	0.290066	+	0.0942483i	−0.160370	+	0.987057i	$0.551269\pi$
$444$	1.57930	+	6.57825i	0.0749502	+	0.312190i
$445$	−8.20352	−	1.44923i	−0.388884	−	0.0687001i
$446$	−1.77301	−	0.903394i	−0.0839544	−	0.0427769i
$447$	27.7513	−	54.4650i	1.31259	−	2.57611i
$448$	12.3391	−	5.11102i	0.582968	−	0.241473i
$449$	−2.58486	+	0.409402i	−0.121987	+	0.0193209i	−0.217129	−	0.976143i	$-0.569669\pi$
$449$	−2.58486	+	0.409402i	−0.121987	+	0.0193209i	0.0951423	+	0.995464i	$0.469669\pi$
$450$	−5.87939	−	4.59959i	−0.277157	−	0.216827i
$451$	17.4212	+	5.57738i	0.820335	+	0.262629i
$452$	8.69023	+	8.69023i	0.408754	+	0.408754i
$453$	5.58417	−	7.68595i	0.262367	−	0.361117i
$454$	2.23333	+	0.925077i	0.104816	+	0.0434160i
$455$	−3.41760	−	8.68429i	−0.160219	−	0.407126i
$456$	−8.33981	+	16.3678i	−0.390548	+	0.766493i
$457$	−20.0636	+	12.2950i	−0.938538	+	0.575137i	−0.905513	−	0.424318i	$-0.860514\pi$
$457$	−20.0636	+	12.2950i	−0.938538	+	0.575137i	−0.0330243	+	0.999455i	$0.510514\pi$
$458$	1.59438	+	0.977039i	0.0745006	+	0.0456540i
$459$	9.76856	+	19.1719i	0.455957	+	0.894866i
$460$	12.1171	−	0.737191i	0.564963	−	0.0343717i
$461$	−5.78923	+	17.8174i	−0.269631	+	0.829840i	0.720959	+	0.692978i	$0.243702\pi$
$461$	−5.78923	+	17.8174i	−0.269631	+	0.829840i	−0.990590	+	0.136862i	$0.956298\pi$
$462$	3.23291	−	0.254435i	0.150408	−	0.0118374i
$463$	−22.7233	−	26.6056i	−1.05604	−	1.23647i	−0.970745	−	0.240112i	$-0.922816\pi$
$463$	−22.7233	−	26.6056i	−1.05604	−	1.23647i	−0.0852979	−	0.996355i	$-0.527184\pi$
$464$	−4.19699	−	6.84886i	−0.194840	−	0.317950i
$465$	−7.11147	+	20.6316i	−0.329787	+	0.956767i
$466$	1.70576	+	1.99719i	0.0790177	+	0.0925179i
$467$	1.83068	+	0.289951i	0.0847137	+	0.0134173i	0.198647	−	0.980071i	$-0.436345\pi$
$467$	1.83068	+	0.289951i	0.0847137	+	0.0134173i	−0.113934	+	0.993488i	$0.536345\pi$
$468$	23.3945	−	27.3914i	1.08141	−	1.26617i
$469$	−7.55186	+	10.3942i	−0.348713	+	0.479962i
$470$	3.99811	+	2.12749i	0.184419	+	0.0981336i
$471$	6.69398	−	42.2641i	0.308442	−	1.94743i
$472$	2.06564	+	2.84311i	0.0950790	+	0.130865i
$473$	6.56731	+	27.3548i	0.301965	+	1.25778i
$474$	4.40812	+	3.20269i	0.202472	+	0.147104i
$475$	37.0683	−	7.51673i	1.70081	−	0.344891i
$476$	−2.68900	−	3.70109i	−0.123250	−	0.169639i
$477$	−9.94650	−	0.782806i	−0.455419	−	0.0358422i
$478$	0.840175	−	2.02836i	0.0384287	−	0.0927751i
$479$	−11.9396	+	7.31660i	−0.545534	+	0.334304i	−0.767808	−	0.640681i	$-0.778652\pi$
$479$	−11.9396	+	7.31660i	−0.545534	+	0.334304i	0.222273	+	0.974984i	$0.428652\pi$
$480$	−0.285494	+	16.0591i	−0.0130309	+	0.732992i
$481$	−1.76464	−	1.50714i	−0.0804607	−	0.0687199i
$482$	−0.317934	−	0.623980i	−0.0144815	−	0.0284215i
$483$		−	17.0837i		−	0.777335i
$484$	4.97374	−	2.53425i	0.226079	−	0.115193i
$485$	−13.5613	+	25.4853i	−0.615788	+	1.15723i
$486$	−10.3582	−	2.48678i	−0.469857	−	0.112803i
$487$	1.59434	+	4.90686i	0.0722462	+	0.222351i	0.980659	−	0.195723i	$-0.0627053\pi$
$487$	1.59434	+	4.90686i	0.0722462	+	0.222351i	−0.908413	+	0.418074i	$0.862705\pi$
$488$	1.88254	+	0.959200i	0.0852184	+	0.0434210i
$489$	−18.0414	+	43.5558i	−0.815861	+	1.96966i
$490$	−0.785611	+	1.23228i	−0.0354903	+	0.0556689i
$491$			35.1974i			1.58844i	0.607632	+	0.794219i	$0.292120\pi$
$491$			35.1974i			1.58844i	−0.607632	+	0.794219i	$0.707880\pi$
$492$	37.5220	+	18.9146i	1.69162	+	0.852737i
$493$	−1.87601	+	1.87601i	−0.0844913	+	0.0844913i
$494$	−0.488700	−	3.08553i	−0.0219877	−	0.138825i
$495$	16.9405	−	49.1471i	0.761417	−	2.20900i
$496$	10.5663	−	3.43318i	0.474439	−	0.154154i
$497$	14.1408	−	4.59462i	0.634301	−	0.206097i
$498$	−3.23418	−	5.27770i	−0.144927	−	0.236500i
$499$	−12.6747	+	3.04293i	−0.567399	+	0.136220i	−0.506988	−	0.861953i	$-0.669241\pi$
$499$	−12.6747	+	3.04293i	−0.567399	+	0.136220i	−0.0604110	+	0.998174i	$0.519241\pi$
$500$	17.4543	−	13.3664i	0.780581	−	0.597762i
$501$	47.8860	+	47.8860i	2.13939	+	2.13939i
$502$	−4.88571	+	2.48940i	−0.218060	+	0.111107i
$503$	−2.16742	−	27.5397i	−0.0966404	−	1.22793i	−0.833743	−	0.552152i	$-0.813807\pi$
$503$	−2.16742	−	27.5397i	−0.0966404	−	1.22793i	0.737103	−	0.675781i	$-0.236193\pi$
$504$	10.9451	+	0.861400i	0.487535	+	0.0383698i
$505$	10.2847	+	14.6981i	0.457661	+	0.654057i
$506$	−0.553739	−	1.33684i	−0.0246167	−	0.0594300i
$507$	2.07711	−	26.3922i	0.0922478	−	1.17212i
$508$	−3.56192	+	22.4891i	−0.158035	+	0.997792i
$509$	−1.79601	−	22.8205i	−0.0796069	−	1.01150i	−0.898908	−	0.438138i	$-0.855638\pi$
$509$	−1.79601	−	22.8205i	−0.0796069	−	1.01150i	0.819301	−	0.573364i	$-0.194362\pi$
$510$	1.67735	−	0.371292i	0.0742742	−	0.0164411i
$511$	−6.08779	−	3.73060i	−0.269308	−	0.165032i
$512$	11.0883	−	8.05616i	0.490040	−	0.356035i
$513$	104.938	−	76.2423i	4.63315	−	3.36618i
$514$	−0.191732	−	0.117493i	−0.00845693	−	0.00518241i
$515$	−28.8050	+	6.37616i	−1.26930	+	0.280967i
$516$	5.07029	+	64.4241i	0.223207	+	2.83611i
$517$	−4.93383	+	31.1510i	−0.216990	+	1.37002i
$518$	0.0275116	−	0.349568i	0.00120879	−	0.0153591i
$519$	3.79044	+	9.15092i	0.166382	+	0.401681i
$520$	−2.09988	−	3.00099i	−0.0920856	−	0.131602i
$521$	−16.6590	−	1.31109i	−0.729845	−	0.0574401i	−0.291909	−	0.956446i	$-0.594290\pi$
$521$	−16.6590	−	1.31109i	−0.729845	−	0.0574401i	−0.437936	+	0.899006i	$0.644290\pi$
$522$	−0.247658	−	3.14680i	−0.0108397	−	0.137732i
$523$	15.1340	−	7.71115i	0.661763	−	0.337185i	−0.0906443	−	0.995883i	$-0.528893\pi$
$523$	15.1340	−	7.71115i	0.661763	−	0.337185i	0.752407	+	0.658698i	$0.228893\pi$
$524$	−3.20178	−	3.20178i	−0.139871	−	0.139871i
$525$	−17.2839	−	25.6601i	−0.754330	−	1.11990i
$526$	0.824744	−	0.198003i	0.0359605	−	0.00863336i
$527$	−1.91733	−	3.12881i	−0.0835204	−	0.136293i
$528$	−34.4490	+	11.1932i	−1.49920	+	0.487120i
$529$	14.6246	−	4.75182i	0.635853	−	0.206601i
$530$	−0.163894	+	0.475483i	−0.00711908	+	0.0206537i
$531$	−6.14839	−	38.8194i	−0.266817	−	1.68462i
$532$	−19.5007	+	19.5007i	−0.845462	+	0.845462i
$533$	−14.2267	+	2.31636i	−0.616227	+	0.100333i
$534$			2.28100i			0.0987083i
$535$	−6.19543	+	9.71795i	−0.267852	+	0.420144i
$536$	−1.92964	+	4.65856i	−0.0833477	+	0.201219i
$537$	10.8015	+	5.50364i	0.466119	+	0.237499i
$538$	−0.138668	−	0.426775i	−0.00597838	−	0.0183996i
$539$	−9.89601	−	2.37582i	−0.426251	−	0.102334i
$540$	35.4169	−	66.5578i	1.52410	−	2.86419i
$541$	27.5347	−	14.0296i	1.18381	−	0.603180i	0.252565	−	0.967580i	$-0.418726\pi$
$541$	27.5347	−	14.0296i	1.18381	−	0.603180i	0.931243	+	0.364400i	$0.118726\pi$
$542$		−	0.0205930i		−	0.000884543i
$543$	−11.4945	−	22.5592i	−0.493276	−	0.968108i
$544$	−2.05370	−	1.75402i	−0.0880515	−	0.0752031i
$545$	0.203790	−	11.4632i	0.00872939	−	0.491030i
$546$	−2.17880	+	1.33517i	−0.0932442	+	0.0571401i
$547$	3.74900	−	9.05089i	0.160296	−	0.386988i	−0.823242	−	0.567691i	$-0.807837\pi$
$547$	3.74900	−	9.05089i	0.160296	−	0.386988i	0.983538	+	0.180702i	$0.0578370\pi$
$548$	−25.0647	−	1.97264i	−1.07071	−	0.0842668i
$549$	−13.8891	−	19.1167i	−0.592772	−	0.815880i
$550$	−2.18424	−	1.44774i	−0.0931362	−	0.0617319i
$551$	12.9390	+	9.40075i	0.551221	+	0.400486i
$552$	−1.56519	−	6.51950i	−0.0666191	−	0.277488i
$553$	9.69842	+	13.3487i	0.412419	+	0.567646i
$554$	−0.551913	+	3.48464i	−0.0234485	+	0.148048i
$555$	−6.79149	−	3.61391i	−0.288283	−	0.153402i
$556$	21.1454	−	29.1042i	0.896765	−	1.23429i
$557$	7.00390	−	8.20052i	0.296765	−	0.347467i	−0.591911	−	0.806004i	$-0.701626\pi$
$557$	7.00390	−	8.20052i	0.296765	−	0.347467i	0.888676	+	0.458537i	$0.151626\pi$
$558$	4.31213	+	0.682974i	0.182547	+	0.0289126i
$559$	−14.3968	−	16.8565i	−0.608919	−	0.712952i
$560$	−5.13272	+	14.8909i	−0.216897	+	0.629255i
$561$	6.25106	+	10.2008i	0.263920	+	0.430678i
$562$	−3.30062	−	3.86453i	−0.139228	−	0.163015i
$563$	−12.4680	+	0.981254i	−0.525464	+	0.0413549i	−0.338417	−	0.940996i	$-0.609892\pi$
$563$	−12.4680	+	0.981254i	−0.525464	+	0.0413549i	−0.187047	+	0.982351i	$0.559892\pi$
$564$	−22.3883	+	68.9040i	−0.942717	+	2.90138i
$565$	−13.9499	+	0.848693i	−0.586875	+	0.0357048i
$566$	−1.66466	−	3.26708i	−0.0699709	−	0.137326i
$567$	−51.8714	−	31.7869i	−2.17840	−	1.33492i
$568$	4.97547	−	3.04897i	0.208766	−	0.127932i
$569$	−9.73444	+	19.1049i	−0.408089	+	0.800920i	−0.999987	−	0.00509298i	$-0.998379\pi$
$569$	−9.73444	+	19.1049i	−0.408089	+	0.800920i	0.591898	+	0.806013i	$0.298379\pi$
$570$	−3.79248	−	9.63690i	−0.158850	−	0.403645i
$571$	−17.4980	−	7.24789i	−0.732267	−	0.303315i	−0.0147836	−	0.999891i	$-0.504706\pi$
$571$	−17.4980	−	7.24789i	−0.732267	−	0.303315i	−0.717483	+	0.696576i	$0.754706\pi$
$572$	7.43272	−	10.2303i	0.310778	−	0.427749i
$573$	44.8374	+	44.8374i	1.87311	+	1.87311i
$574$	−1.54668	−	1.53337i	−0.0645573	−	0.0640017i
$575$	−8.50603	+	10.8728i	−0.354726	+	0.453425i
$576$	−57.9004	+	9.17052i	−2.41252	+	0.382105i
$577$	24.5906	−	10.1858i	1.02372	−	0.424039i	0.193279	−	0.981144i	$-0.438088\pi$
$577$	24.5906	−	10.1858i	1.02372	−	0.424039i	0.830443	+	0.557104i	$0.188088\pi$
$578$	1.28474	−	2.52145i	0.0534382	−	0.104878i
$579$	−39.7929	−	20.2755i	−1.65374	−	0.842621i
$580$	9.15445	+	1.61722i	0.380118	+	0.0671514i
$581$	−4.37573	−	18.2262i	−0.181536	−	0.756152i
$582$	7.51774	+	2.44266i	0.311620	+	0.101252i
$583$	−3.50244			−0.145056
$584$	−2.66502	−	0.865919i	−0.110280	−	0.0358320i
$585$	5.68790	+	40.5665i	0.235166	+	1.67722i
$586$	−0.0786688	+	0.999582i	−0.00324978	+	0.0412924i
$587$	−38.4071	−	9.22073i	−1.58523	−	0.380580i	−0.657389	−	0.753552i	$-0.728339\pi$
$587$	−38.4071	−	9.22073i	−1.58523	−	0.380580i	−0.927843	+	0.372971i	$0.878339\pi$
$588$	−21.5989	−	8.94654i	−0.890722	−	0.368949i
$589$	−16.8210	+	14.3665i	−0.693097	+	0.591961i
$590$	−1.97203	−	0.190527i	−0.0811872	−	0.00784387i
$591$	19.5349	−	1.53743i	0.803558	−	0.0632414i
$592$	0.612690	+	3.86837i	0.0251814	+	0.158989i
$593$	−1.98862	+	0.477426i	−0.0816630	+	0.0196055i	−0.274071	−	0.961709i	$-0.588370\pi$
$593$	−1.98862	+	0.477426i	−0.0816630	+	0.0196055i	0.192408	+	0.981315i	$0.438370\pi$
$594$	−8.87611	−	1.40584i	−0.364191	−	0.0576822i
$595$	5.17821	+	0.500291i	0.212286	+	0.0205099i
$596$	18.8182	−	30.7085i	0.770824	−	1.25787i
$597$	−63.4970	+	10.0569i	−2.59876	+	0.411603i
$598$	0.867020	+	0.740505i	0.0354551	+	0.0302815i
$599$	−22.2776	+	16.1857i	−0.910240	+	0.661328i	−0.941076	−	0.338196i	$-0.890183\pi$
$599$	−22.2776	+	16.1857i	−0.910240	+	0.661328i	0.0308355	+	0.999524i	$0.490183\pi$
$600$	−8.94685	−	8.20891i	−0.365254	−	0.335127i
$601$	−21.8380	+	9.04559i	−0.890790	+	0.368977i	−0.780672	−	0.624941i	$-0.785123\pi$
$601$	−21.8380	+	9.04559i	−0.890790	+	0.368977i	−0.110118	+	0.993919i	$0.535123\pi$
$602$	0.781929	−	3.25697i	0.0318691	−	0.132744i
$603$	42.8819	−	36.6246i	1.74629	−	1.49147i
$604$	3.63531	−	4.25640i	0.147918	−	0.173190i
$605$	−1.59136	+	6.14516i	−0.0646980	+	0.249836i
$606$	3.47324	−	3.47324i	0.141091	−	0.141091i
$607$	−3.65242	+	11.2410i	−0.148247	+	0.456258i	−0.997414	−	0.0718665i	$-0.977104\pi$
$607$	−3.65242	+	11.2410i	−0.148247	+	0.456258i	0.849167	+	0.528124i	$0.177104\pi$
$608$	−8.50686	+	13.8819i	−0.344999	+	0.562986i
$609$	3.05402	−	12.7209i	0.123755	−	0.515477i
$610$	−1.10838	+	0.436191i	−0.0448772	+	0.0176609i
$611$	−7.67984	−	23.6361i	−0.310693	−	0.956215i
$612$	7.68430	+	18.5516i	0.310620	+	0.749902i
$613$	−5.52915	−	4.01716i	−0.223320	−	0.162252i	0.470500	−	0.882400i	$-0.344074\pi$
$613$	−5.52915	−	4.01716i	−0.223320	−	0.162252i	−0.693820	+	0.720148i	$0.744074\pi$
$614$	0.863566			0.0348507
$615$	−44.3884	+	17.6905i	−1.78991	+	0.713348i
$616$	3.85409			0.155286
$617$	26.9059	+	19.5483i	1.08319	+	0.786985i	0.978237	−	0.207492i	$-0.0665302\pi$
$617$	26.9059	+	19.5483i	1.08319	+	0.786985i	0.104955	+	0.994477i	$0.466530\pi$
$618$	3.09133	+	7.46314i	0.124352	+	0.300211i
$619$	7.17780	+	22.0910i	0.288500	+	0.887912i	0.985328	+	0.170673i	$0.0545942\pi$
$619$	7.17780	+	22.0910i	0.288500	+	0.887912i	−0.696828	+	0.717239i	$0.745406\pi$
$620$	−5.13085	+	11.7897i	−0.206060	+	0.473487i
$621$	−11.0519	+	46.0344i	−0.443496	+	1.84729i
$622$	−1.55785	+	2.54217i	−0.0624640	+	0.101932i
$623$	−2.13449	+	6.56927i	−0.0855163	+	0.263192i
$624$	20.1824	−	20.1824i	0.807944	−	0.807944i
$625$	−1.77609	+	24.9368i	−0.0710435	+	0.997473i
$626$	0.458841	−	0.537233i	0.0183390	−	0.0214722i
$627$	54.8412	−	46.8388i	2.19015	−	1.87056i
$628$	5.88564	−	24.5155i	0.234863	−	0.978273i
$629$	1.19515	−	0.495047i	0.0476537	−	0.0197388i
$630$	−4.45375	+	4.29816i	−0.177442	+	0.171243i
$631$	−1.10765	+	0.804757i	−0.0440950	+	0.0320369i	−0.609614	−	0.792698i	$-0.708676\pi$
$631$	−1.10765	+	0.804757i	−0.0440950	+	0.0320369i	0.565519	+	0.824735i	$0.308676\pi$
$632$	4.92412	+	4.20560i	0.195871	+	0.167290i
$633$	44.7035	−	7.08033i	1.77680	−	0.281418i
$634$	1.73525	−	2.83167i	0.0689156	−	0.112460i
$635$	−16.4633	−	19.9848i	−0.653328	−	0.793071i
$636$	−7.94653	−	1.25861i	−0.315100	−	0.0499070i
$637$	7.79791	−	1.87211i	0.308965	−	0.0741758i
$638$	−0.173341	−	1.09443i	−0.00686265	−	0.0433291i
$639$	−65.0609	+	5.12040i	−2.57377	+	0.202560i
$640$	−1.20982	+	12.5221i	−0.0478221	+	0.494978i
$641$	−14.4950	+	12.3799i	−0.572518	+	0.488976i	−0.887930	−	0.459978i	$-0.847857\pi$
$641$	−14.4950	+	12.3799i	−0.572518	+	0.488976i	0.315412	+	0.948955i	$0.397857\pi$
$642$	2.91542	+	1.20761i	0.115062	+	0.0476604i
$643$	−19.5562	−	4.69503i	−0.771222	−	0.185154i	−0.171307	−	0.985218i	$-0.554799\pi$
$643$	−19.5562	−	4.69503i	−0.771222	−	0.185154i	−0.599915	+	0.800064i	$0.704799\pi$
$644$	0.789735	−	10.0345i	0.0311199	−	0.395416i
$645$	−58.6756	−	44.2449i	−2.31035	−	1.74214i
$646$	1.65620	+	0.538131i	0.0651622	+	0.0211725i
$647$	−21.2152			−0.834054			−0.417027	−	0.908894i	$-0.636928\pi$
$647$	−21.2152			−0.834054			−0.417027	+	0.908894i	$0.636928\pi$
$648$	−22.7075	−	7.37813i	−0.892036	−	0.289840i
$649$	−3.22088	−	13.4159i	−0.126430	−	0.526621i
$650$	2.05147	+	0.235076i	0.0804651	+	0.00922043i
$651$	16.1224	+	8.21476i	0.631886	+	0.321962i
$652$	−12.6106	+	24.7496i	−0.493867	+	0.969269i
$653$	−33.5073	+	13.8792i	−1.31124	+	0.543134i	−0.925246	−	0.379367i	$-0.876142\pi$
$653$	−33.5073	+	13.8792i	−1.31124	+	0.543134i	−0.385995	+	0.922501i	$0.626142\pi$
$654$	−3.10060	+	0.491087i	−0.121243	+	0.0192030i
$655$	5.13961	−	0.312688i	0.200821	−	0.0122177i
$656$	20.7967	+	12.6209i	0.811974	+	0.492764i
$657$	22.1601	+	22.1601i	0.864549	+	0.864549i
$658$	2.20724	−	3.03801i	0.0860473	−	0.118434i
$659$	24.3659	+	10.0927i	0.949161	+	0.393155i	0.802915	−	0.596093i	$-0.203281\pi$
$659$	24.3659	+	10.0927i	0.949161	+	0.393155i	0.146245	+	0.989248i	$0.453281\pi$
$660$	16.7280	−	38.4379i	0.651138	−	1.49619i
$661$	20.7073	−	40.6404i	0.805422	−	1.58073i	−0.00864762	−	0.999963i	$-0.502753\pi$
$661$	20.7073	−	40.6404i	0.805422	−	1.58073i	0.814070	−	0.580767i	$-0.197247\pi$
$662$	3.66434	−	2.24551i	0.142418	−	0.0872741i
$663$	−8.03808	−	4.92574i	−0.312173	−	0.191300i
$664$	−3.33975	−	6.55462i	−0.129607	−	0.254369i
$665$	−1.90445	−	31.3032i	−0.0738514	−	1.21388i
$666$	−0.475607	+	1.46377i	−0.0184294	+	0.0567198i
$667$	−5.81938	+	0.457995i	−0.225327	+	0.0177336i
$668$	25.9134	+	30.3407i	1.00262	+	1.17392i
$669$	18.9141	+	30.8650i	0.731260	+	1.19331i
$670$	−1.24533	−	2.55540i	−0.0481114	−	0.0987239i
$671$	−5.38715	−	6.30754i	−0.207969	−	0.243500i
$672$	13.1536	+	2.08333i	0.507413	+	0.0803663i
$673$	−22.4037	+	26.2314i	−0.863599	+	1.01114i	0.136191	+	0.990683i	$0.456514\pi$
$673$	−22.4037	+	26.2314i	−0.863599	+	1.01114i	−0.999791	+	0.0204623i	$0.993486\pi$
$674$	0.679884	−	0.935780i	0.0261882	−	0.0360449i
$675$	29.9736	+	80.3260i	1.15369	+	3.09175i
$676$	2.44009	−	15.4061i	0.0938496	−	0.592543i
$677$	22.4886	+	30.9529i	0.864308	+	1.18962i	0.980525	+	0.196394i	$0.0629232\pi$
$677$	22.4886	+	30.9529i	0.864308	+	1.18962i	−0.116217	+	0.993224i	$0.537077\pi$
$678$	0.893322	+	3.72095i	0.0343078	+	0.142902i
$679$	19.3653	+	14.0697i	0.743173	+	0.539947i
$680$	2.02195	−	0.283502i	0.0775383	−	0.0108718i
$681$	−25.8480	−	35.5767i	−0.990497	−	1.36330i
$682$	1.52789	+	0.120247i	0.0585058	+	0.00460450i
$683$	3.46306	−	8.36058i	0.132510	−	0.319909i	−0.843672	−	0.536859i	$-0.819611\pi$
$683$	3.46306	−	8.36058i	0.132510	−	0.319909i	0.976183	+	0.216950i	$0.0696109\pi$
$684$	103.211	−	63.2475i	3.94635	−	2.41833i
$685$	20.5730	−	19.8543i	0.786055	−	0.758595i
$686$	2.73191	+	2.33328i	0.104305	+	0.0890849i
$687$	−15.4434	−	30.3094i	−0.589203	−	1.15638i
$688$			37.4126i			1.42634i
$689$	2.45907	−	1.25296i	0.0936829	−	0.0477338i
$690$	3.33686	+	1.77562i	0.127032	+	0.0675967i
$691$	16.5086	+	3.96337i	0.628018	+	0.150774i	0.534947	−	0.844886i	$-0.320332\pi$
$691$	16.5086	+	3.96337i	0.628018	+	0.150774i	0.0930712	+	0.995659i	$0.470332\pi$
$692$	1.80338	+	5.55025i	0.0685544	+	0.210989i
$693$	−38.4056	−	19.5686i	−1.45891	−	0.743351i
$694$	1.53617	−	3.70864i	0.0583122	−	0.140778i
$695$	8.84153	+	39.9425i	0.335378	+	1.51511i
$696$		−	5.13437i		−	0.194618i
$697$	2.44988	−	7.65232i	0.0927957	−	0.289852i
$698$	0.145105	−	0.145105i	0.00549231	−	0.00549231i
$699$	−7.47438	−	47.1914i	−0.282707	−	1.78494i
$700$	−8.96592	−	15.8711i	−0.338880	−	0.599871i
$701$	38.8191	−	12.6131i	1.46618	−	0.476390i	0.536228	−	0.844073i	$-0.319849\pi$
$701$	38.8191	−	12.6131i	1.46618	−	0.476390i	0.929951	+	0.367683i	$0.119849\pi$
$702$	6.73484	−	2.18828i	0.254190	−	0.0825914i
$703$	−4.07460	−	6.64914i	−0.153676	−	0.250777i
$704$	−20.0103	+	4.80404i	−0.754166	+	0.181059i
$705$	−41.7922	−	71.0014i	−1.57398	−	2.67407i
$706$	−1.43226	−	1.43226i	−0.0539036	−	0.0539036i
$707$	13.2531	−	6.75278i	0.498433	−	0.253964i
$708$	−2.48667	−	31.5962i	−0.0934549	−	1.18746i
$709$	−4.81736	−	0.379134i	−0.180920	−	0.0142387i	−0.0123244	−	0.999924i	$-0.503923\pi$
$709$	−4.81736	−	0.379134i	−0.180920	−	0.0142387i	−0.168595	+	0.985685i	$0.553923\pi$
$710$	−0.572305	+	3.23959i	−0.0214782	+	0.121580i
$711$	−27.7150	−	66.9100i	−1.03939	−	2.50932i
$712$	−0.212694	+	2.70253i	−0.00797104	+	0.101282i
$713$	1.26303	−	7.97443i	0.0473007	−	0.298645i
$714$	−0.111761	−	1.42006i	−0.00418256	−	0.0531445i
$715$	3.10784	+	14.0400i	0.116227	+	0.525066i
$716$	6.09011	+	3.73202i	0.227598	+	0.139472i
$717$	−32.3115	+	23.4757i	−1.20670	+	0.876716i
$718$	3.32838	−	2.41821i	0.124214	−	0.0902469i
$719$	31.8471	+	19.5159i	1.18770	+	0.727821i	0.968780	−	0.247922i	$-0.0797477\pi$
$719$	31.8471	+	19.5159i	1.18770	+	0.727821i	0.218917	+	0.975744i	$0.429748\pi$
$720$	37.1645	−	58.2951i	1.38504	−	2.17253i
$721$	1.91927	+	24.3866i	0.0714773	+	0.908205i
$722$	1.09694	−	6.92582i	0.0408240	−	0.257752i
$723$	−0.999547	+	12.7004i	−0.0371736	+	0.472335i
$724$	−5.70872	−	13.7821i	−0.212163	−	0.512207i
$725$	−8.27748	+	6.57549i	−0.307418	+	0.244207i
$726$	1.73276	+	0.136371i	0.0643087	+	0.00506120i
$727$	2.26062	+	28.7239i	0.0838416	+	1.06531i	0.884609	+	0.466333i	$0.154425\pi$
$727$	2.26062	+	28.7239i	0.0838416	+	1.06531i	−0.800767	+	0.598975i	$0.795575\pi$
$728$	−2.70595	+	1.37875i	−0.100289	+	0.0511000i
$729$	67.4213	+	67.4213i	2.49709	+	2.49709i
$730$	1.36142	−	0.801347i	0.0503885	−	0.0296592i
$731$	12.0157	−	2.88471i	0.444416	−	0.106695i
$732$	−9.95604	−	16.2468i	−0.367986	−	0.600498i
$733$	−23.8175	+	7.73877i	−0.879719	+	0.285838i	−0.713840	−	0.700308i	$-0.753046\pi$
$733$	−23.8175	+	7.73877i	−0.879719	+	0.285838i	−0.165878	+	0.986146i	$0.553046\pi$
$734$	−0.858435	+	0.278922i	−0.0316854	+	0.0102952i
$735$	23.8984	−	11.6465i	0.881507	−	0.429588i
$736$	−0.929587	−	5.86918i	−0.0342650	−	0.216341i
$737$	13.9982	−	13.9982i	0.515632	−	0.515632i
$738$	5.03007	+	8.12926i	0.185159	+	0.299242i
$739$		−	46.8639i		−	1.72392i	−0.506980	−	0.861958i	$-0.669238\pi$
$739$		−	46.8639i		−	1.72392i	0.506980	−	0.861958i	$-0.330762\pi$
$740$	−3.82209	−	2.43667i	−0.140503	−	0.0895739i
$741$	−21.7480	+	52.5043i	−0.798933	+	1.92880i
$742$	0.371562	+	0.189320i	0.0136405	+	0.00695017i
$743$	13.0040	+	40.0221i	0.477069	+	1.46827i	0.843147	+	0.537683i	$0.180700\pi$
$743$	13.0040	+	40.0221i	0.477069	+	1.46827i	−0.366078	+	0.930584i	$0.619300\pi$
$744$	6.90527	+	1.65781i	0.253160	+	0.0607783i
$745$	11.9618	+	39.1704i	0.438245	+	1.43509i
$746$	−3.06672	+	1.56257i	−0.112280	+	0.0572098i
$747$			82.2733i			3.01022i
$748$	3.20016	+	6.28067i	0.117009	+	0.229644i
$749$	7.26637	+	6.20607i	0.265508	+	0.226765i
$750$	6.80847	−	0.708938i	0.248610	−	0.0258868i
$751$	−11.0308	+	6.75971i	−0.402521	+	0.246665i	−0.708995	−	0.705214i	$-0.750851\pi$
$751$	−11.0308	+	6.75971i	−0.402521	+	0.246665i	0.306473	+	0.951879i	$0.400851\pi$
$752$	−16.0512	+	38.7510i	−0.585327	+	1.41310i
$753$	99.4434	+	7.82637i	3.62392	+	0.285209i
$754$	0.513224	+	0.706392i	0.0186905	+	0.0257253i
$755$	0.883852	+	6.30368i	0.0321667	+	0.229415i
$756$	−50.5747	−	36.7447i	−1.83938	−	1.33639i
$757$	1.46056	+	6.08365i	0.0530848	+	0.221114i	0.992607	−	0.121374i	$-0.0387302\pi$
$757$	1.46056	+	6.08365i	0.0530848	+	0.221114i	−0.939522	+	0.342489i	$0.888730\pi$
$758$	1.50685	+	2.07401i	0.0547314	+	0.0753313i
$759$	−4.11782	+	25.9989i	−0.149467	+	0.943700i
$760$	−3.59475	−	11.7715i	−0.130395	−	0.426996i
$761$	12.3318	−	16.9732i	0.447027	−	0.615280i	−0.524729	−	0.851270i	$-0.675833\pi$
$761$	12.3318	−	16.9732i	0.447027	−	0.615280i	0.971756	+	0.235990i	$0.0758332\pi$
$762$	−4.60440	+	5.39106i	−0.166800	+	0.195297i
$763$	−9.38927	−	1.48711i	−0.339914	−	0.0538372i
$764$	24.2637	+	28.4091i	0.877829	+	1.02781i
$765$	−21.5880	−	7.44113i	−0.780516	−	0.269035i
$766$	0.577754	+	0.942809i	0.0208751	+	0.0340651i
$767$	7.06076	+	8.26709i	0.254949	+	0.298507i
$768$	−44.4993	+	3.50217i	−1.60573	+	0.126374i
$769$	−3.78948	+	11.6628i	−0.136652	+	0.420573i	−0.995843	−	0.0910823i	$-0.970967\pi$
$769$	−3.78948	+	11.6628i	−0.136652	+	0.420573i	0.859191	+	0.511655i	$0.170967\pi$
$770$	−1.44025	+	1.62685i	−0.0519031	+	0.0586277i
$771$	1.85714	+	3.64485i	0.0668833	+	0.131266i
$772$	−22.4361	−	13.7489i	−0.807492	−	0.494832i
$773$	42.8838	−	26.2792i	1.54242	−	0.945198i	0.548377	−	0.836231i	$-0.315246\pi$
$773$	42.8838	−	26.2792i	1.54242	−	0.945198i	0.994045	−	0.108967i	$-0.0347542\pi$
$774$	−6.67456	+	13.0996i	−0.239912	+	0.470854i
$775$	−6.17078	−	13.2556i	−0.221661	−	0.476155i
$776$	8.67928	+	3.59507i	0.311568	+	0.129056i
$777$	−3.74939	+	5.16059i	−0.134509	+	0.185135i
$778$	−1.71067	−	1.71067i	−0.0613305	−	0.0613305i
$779$	−47.8727	−	7.37034i	−1.71522	−	0.264070i
$780$	2.00595	+	32.9715i	0.0718245	+	1.18057i
$781$	−22.6277	+	3.58388i	−0.809683	+	0.128241i
$782$	−0.587212	+	0.243231i	−0.0209986	+	0.00869793i
$783$	−16.4589	+	32.3025i	−0.588194	+	1.15440i
$784$	−12.0594	−	6.14457i	−0.430693	−	0.219449i
$785$	16.4371	+	23.4907i	0.586665	+	0.838420i
$786$	−0.329131	−	1.37093i	−0.0117397	−	0.0488994i
$787$	2.81969	+	0.916172i	0.100511	+	0.0326580i	0.358841	−	0.933399i	$-0.383172\pi$
$787$	2.81969	+	0.916172i	0.100511	+	0.0326580i	−0.258330	+	0.966057i	$0.583172\pi$
$788$	11.5454			0.411287
$789$	−14.6745	−	4.76804i	−0.522426	−	0.169747i
$790$	−3.61535	+	0.506915i	−0.128628	+	0.0180352i
$791$	−0.909185	+	11.5523i	−0.0323269	+	0.410752i
$792$	−16.4493	−	3.94912i	−0.584499	−	0.140326i
$793$	6.03877	+	2.50134i	0.214443	+	0.0888252i
$794$	−2.56400	+	2.18986i	−0.0909929	+	0.0777153i
$795$	7.06163	−	5.81733i	0.250450	−	0.206319i
$796$	−37.7615	+	2.97189i	−1.33842	+	0.105336i
$797$	−8.33754	−	52.6412i	−0.295331	−	1.86465i	−0.473706	−	0.880683i	$-0.657084\pi$
$797$	−8.33754	−	52.6412i	−0.295331	−	1.86465i	0.178375	−	0.983963i	$-0.442916\pi$
$798$	−8.34974	+	2.00460i	−0.295578	+	0.0709619i
$799$	13.6831	+	2.16720i	0.484075	+	0.0766699i
$800$	−7.33421	−	7.87516i	−0.259304	−	0.278429i
$801$	15.8412	−	25.8506i	0.559723	−	0.913385i
$802$	−2.59633	+	0.411218i	−0.0916795	+	0.0145206i
$803$	8.36551	+	7.14482i	0.295213	+	0.252135i
$804$	36.7903	−	26.7297i	1.29749	−	0.942684i
$805$	7.94859	+	8.23632i	0.280151	+	0.290292i
$806$	−1.11575	+	0.462157i	−0.0393005	+	0.0162788i
$807$	−1.90567	+	7.93768i	−0.0670827	+	0.279420i
$808$	4.43897	−	3.79124i	0.156163	−	0.133375i
$809$	9.75001	−	11.4158i	0.342792	−	0.401358i	−0.562051	−	0.827102i	$-0.689988\pi$
$809$	9.75001	−	11.4158i	0.342792	−	0.401358i	0.904843	+	0.425744i	$0.139988\pi$
$810$	11.6001	−	6.82793i	0.407585	−	0.239909i
$811$	−22.4902	+	22.4902i	−0.789737	+	0.789737i	−0.981451	−	0.191714i	$-0.938595\pi$
$811$	−22.4902	+	22.4902i	−0.789737	+	0.789737i	0.191714	+	0.981451i	$0.438595\pi$
$812$	2.38191	−	7.33076i	0.0835886	−	0.257259i
$813$	−0.195737	+	0.319414i	−0.00686481	+	0.0112023i
$814$	−0.126128	+	0.525360i	−0.00442078	+	0.0184139i
$815$	−11.5673	−	29.3931i	−0.405185	−	1.02960i
$816$	4.91662	+	15.1318i	0.172116	+	0.529719i
$817$	−28.5069	−	68.8217i	−0.997329	−	2.40777i
$818$	−2.91629	−	2.11881i	−0.101966	−	0.0740823i
$819$	33.9650			1.18683
$820$	−26.8904	+	8.33897i	−0.939055	+	0.291210i
$821$	24.7809			0.864859			0.432430	−	0.901668i	$-0.357656\pi$
$821$	24.7809			0.864859			0.432430	+	0.901668i	$0.357656\pi$
$822$	−6.33341	−	4.60149i	−0.220903	−	0.160496i
$823$	−10.1986	−	24.6216i	−0.355501	−	0.858256i	−0.995921	−	0.0902307i	$-0.971240\pi$
$823$	−10.1986	−	24.6216i	−0.355501	−	0.858256i	0.640420	−	0.768025i	$-0.278760\pi$
$824$	2.96672	+	9.13061i	0.103350	+	0.318080i
$825$	20.1185	+	43.2170i	0.700436	+	1.50462i
$826$	−0.383490	+	1.59735i	−0.0133433	+	0.0555789i
$827$	−6.33304	+	10.3346i	−0.220221	+	0.359368i	−0.943603	−	0.331080i	$-0.892587\pi$
$827$	−6.33304	+	10.3346i	−0.220221	+	0.359368i	0.723381	+	0.690449i	$0.242587\pi$
$828$	−13.6526	+	42.0183i	−0.474459	+	1.46024i
$829$	20.5884	−	20.5884i	0.715066	−	0.715066i	−0.252524	−	0.967591i	$-0.581261\pi$
$829$	20.5884	−	20.5884i	0.715066	−	0.715066i	0.967591	+	0.252524i	$0.0812608\pi$
$830$	4.01483	+	1.03969i	0.139357	+	0.0360880i
$831$	41.6824	−	48.8038i	1.44595	−	1.69298i
$832$	12.3306	−	10.5314i	0.427488	−	0.365109i
$833$	−1.04359	+	4.34685i	−0.0361581	+	0.150609i
$834$	10.3488	−	4.28661i	0.358349	−	0.148433i
$835$	−45.3667	−	0.806517i	−1.56998	−	0.0279107i
$836$	34.3776	−	24.9768i	1.18898	−	0.863841i
$837$	−38.1296	−	32.5658i	−1.31795	−	1.12564i
$838$	−3.24163	+	0.513423i	−0.111980	+	0.0177359i
$839$	25.1372	−	41.0202i	0.867833	−	1.41617i	−0.0410654	−	0.999156i	$-0.513075\pi$
$839$	25.1372	−	41.0202i	0.867833	−	1.41617i	0.908898	−	0.417018i	$-0.136925\pi$
$840$	−7.77061	+	6.40139i	−0.268112	+	0.220869i
$841$	24.2279	+	3.83731i	0.835443	+	0.132321i
$842$	−2.30113	+	0.552452i	−0.0793021	+	0.0190388i
$843$	14.4628	+	91.3147i	0.498126	+	3.14505i
$844$	26.5850	−	2.09229i	0.915094	−	0.0720195i
$845$	11.2782	+	13.6905i	0.387982	+	0.470969i
$846$	−12.5334	+	10.7046i	−0.430909	+	0.368031i
$847$	4.86273	+	2.01421i	0.167085	+	0.0692091i
$848$	−4.52917	−	1.08736i	−0.155532	−	0.0373400i
$849$	−5.23350	+	66.4979i	−0.179613	+	2.28220i
$850$	−0.635924	+	0.959431i	−0.0218120	+	0.0329082i
$851$	2.70695	+	0.879540i	0.0927929	+	0.0301502i
$852$	−52.6269			−1.80297
$853$	−2.45827	−	0.798740i	−0.0841695	−	0.0273483i	0.266630	−	0.963799i	$-0.414090\pi$
$853$	−2.45827	−	0.798740i	−0.0841695	−	0.0273483i	−0.350799	+	0.936451i	$0.614090\pi$
$854$	0.230558	+	0.960342i	0.00788953	+	0.0328622i
$855$	−23.9468	+	135.553i	−0.818964	+	4.63583i
$856$	3.34160	+	1.70263i	0.114213	+	0.0581947i
$857$	−7.35143	+	14.4280i	−0.251120	+	0.492851i	−0.981812	−	0.189857i	$-0.939198\pi$
$857$	−7.35143	+	14.4280i	−0.251120	+	0.492851i	0.730692	+	0.682707i	$0.239198\pi$
$858$	3.63765	−	1.50676i	0.124187	−	0.0514401i
$859$	−12.6999	+	2.01147i	−0.433315	+	0.0686304i	−0.369282	−	0.929317i	$-0.620396\pi$
$859$	−12.6999	+	2.01147i	−0.433315	+	0.0686304i	−0.0640331	+	0.997948i	$0.520396\pi$
$860$	−32.4193	−	28.7008i	−1.10549	−	0.978690i
$861$	9.41558	+	38.4852i	0.320882	+	1.31157i
$862$	0.371569	+	0.371569i	0.0126557	+	0.0126557i
$863$	−31.8714	+	43.8672i	−1.08491	+	1.49326i	−0.230922	+	0.972972i	$0.574174\pi$
$863$	−31.8714	+	43.8672i	−1.08491	+	1.49326i	−0.853993	+	0.520285i	$0.825826\pi$
$864$	−34.0965	−	14.1232i	−1.15999	−	0.480483i
$865$	−6.08511	−	2.64822i	−0.206900	−	0.0900420i
$866$	0.477545	−	0.937234i	0.0162276	−	0.0318485i
$867$	−43.8939	+	26.8982i	−1.49072	+	0.913511i
$868$	9.09014	+	5.57045i	0.308539	+	0.189073i
$869$	−11.5420	−	22.6525i	−0.391537	−	0.768434i
$870$	2.16728	+	1.91869i	0.0734775	+	0.0650497i
$871$	−4.82047	+	14.8359i	−0.163335	+	0.502695i
$872$	−3.71939	+	0.292723i	−0.125955	+	0.00991284i
$873$	−68.2347	−	79.8925i	−2.30939	−	2.70395i
$874$	2.00197	+	3.26692i	0.0677177	+	0.110505i
$875$	20.2718	+	4.32941i	0.685312	+	0.146361i
$876$	16.4126	+	19.2167i	0.554531	+	0.649273i
$877$	37.0147	+	5.86256i	1.24990	+	0.197965i	0.746087	−	0.665849i	$-0.231930\pi$
$877$	37.0147	+	5.86256i	1.24990	+	0.197965i	0.503812	+	0.863813i	$0.331930\pi$
$878$	3.94020	−	4.61338i	0.132975	−	0.155694i
$879$	10.7213	−	14.7566i	0.361621	−	0.497728i
$880$	11.4005	−	21.4246i	0.384312	−	0.722223i
$881$	2.20882	−	13.9459i	0.0744171	−	0.469851i	−0.922134	−	0.386870i	$-0.873556\pi$
$881$	2.20882	−	13.9459i	0.0744171	−	0.469851i	0.996551	−	0.0829805i	$-0.0264439\pi$
$882$	−3.12623	−	4.30288i	−0.105266	−	0.144886i
$883$	0.0104319	+	0.0434522i	0.000351063	+	0.00146228i	0.972545	−	0.232714i	$-0.0747607\pi$
$883$	0.0104319	+	0.0434522i	0.000351063	+	0.00146228i	−0.972194	+	0.234176i	$0.924761\pi$
$884$	−4.49366	−	3.26484i	−0.151138	−	0.109808i
$885$	28.7769	+	21.6995i	0.967325	+	0.729421i
$886$	0.692221	+	0.952760i	0.0232556	+	0.0320086i
$887$	58.6379	+	4.61491i	1.96887	+	0.154953i	0.996812	−	0.0797884i	$-0.0254245\pi$
$887$	58.6379	+	4.61491i	1.96887	+	0.154953i	0.972058	+	0.234742i	$0.0754245\pi$
$888$	−0.958038	+	2.31291i	−0.0321497	+	0.0776161i
$889$	−18.3055	+	11.2176i	−0.613945	+	0.376226i
$890$	−1.06129	−	1.09970i	−0.0355744	−	0.0368622i
$891$	71.2790	+	60.8780i	2.38794	+	2.03949i
$892$	9.68285	+	19.0037i	0.324206	+	0.636290i
$893$		−	83.5140i		−	2.79469i
$894$	9.99195	−	5.09116i	0.334181	−	0.170274i
$895$	−7.76827	+	2.37226i	−0.259664	+	0.0792958i
$896$	10.1429	+	2.43510i	0.338851	+	0.0813509i
$897$	−6.40967	−	19.7269i	−0.214013	−	0.658663i
$898$	−0.427791	−	0.217970i	−0.0142756	−	0.00727376i
$899$	2.36605	−	5.71215i	0.0789121	−	0.190511i
$900$	22.0042	+	76.9249i	0.733472	+	2.56416i
$901$			1.53846i			0.0512534i
$902$	1.98423	+	2.70638i	0.0660675	+	0.0901125i
$903$	−43.0861	+	43.0861i	−1.43382	+	1.43382i
$904$	0.711447	+	4.49190i	0.0236624	+	0.149398i
$905$	16.0379	+	5.52807i	0.533117	+	0.183759i
$906$	1.65760	−	0.538586i	0.0550700	−	0.0178933i
$907$	29.4036	−	9.55380i	0.976329	−	0.317229i	0.222961	−	0.974827i	$-0.428428\pi$
$907$	29.4036	−	9.55380i	0.976329	−	0.317229i	0.753368	+	0.657599i	$0.228428\pi$
$908$	−13.5379	−	22.0918i	−0.449269	−	0.733141i
$909$	−63.4835	+	15.2410i	−2.10561	+	0.505513i
$910$	0.429215	−	1.65745i	0.0142284	−	0.0549438i
$911$	−14.2044	−	14.2044i	−0.470613	−	0.470613i	0.431500	−	0.902113i	$-0.357984\pi$
$911$	−14.2044	−	14.2044i	−0.470613	−	0.470613i	−0.902113	+	0.431500i	$0.857984\pi$
$912$	85.4591	−	43.5436i	2.82983	−	1.44187i
$913$	2.26601	+	28.7924i	0.0749940	+	0.952890i
$914$	−4.30364	−	0.338704i	−0.142352	−	0.0112033i
$915$	21.3380	+	3.76956i	0.705413	+	0.124618i
$916$	−7.66995	−	18.5169i	−0.253422	−	0.611816i
$917$	0.334976	−	4.25627i	0.0110619	−	0.140554i
$918$	−0.617517	+	3.89885i	−0.0203811	+	0.128681i
$919$	−3.45172	−	43.8583i	−0.113862	−	1.44675i	−0.742913	−	0.669388i	$-0.766556\pi$
$919$	−3.45172	−	43.8583i	−0.113862	−	1.44675i	0.629051	−	0.777364i	$-0.283444\pi$
$920$	3.78796	+	2.41491i	0.124885	+	0.0796173i
$921$	−13.3946	−	8.20825i	−0.441368	−	0.270471i
$922$	−2.78054	+	2.02018i	−0.0915722	+	0.0665311i
$923$	14.6048	−	10.6110i	0.480724	−	0.349266i
$924$	−29.6364	−	18.1612i	−0.974967	−	0.597461i
$925$	4.95574	−	1.41758i	0.162944	−	0.0466096i
$926$	−0.503621	−	6.39912i	−0.0165500	−	0.210288i
$927$	16.7965	−	106.049i	0.551669	−	3.48310i
$928$	0.357030	−	4.53650i	0.0117201	−	0.148918i
$929$	2.09979	+	5.06933i	0.0688918	+	0.166319i	0.954575	−	0.297970i	$-0.0963096\pi$
$929$	2.09979	+	5.06933i	0.0688918	+	0.166319i	−0.885683	+	0.464290i	$0.846310\pi$
$930$	−3.28025	+	2.29528i	−0.107564	+	0.0752651i
$931$	26.8655	+	2.11436i	0.880482	+	0.0692954i
$932$	−2.20873	−	28.0646i	−0.0723494	−	0.919286i
$933$	48.3270	−	24.6239i	1.58216	−	0.806149i
$934$	0.240442	+	0.240442i	0.00786750	+	0.00786750i
$935$	−7.75989	−	2.00952i	−0.253776	−	0.0657182i
$936$	12.9618	−	3.11185i	0.423669	−	0.101714i
$937$	−15.0617	−	24.5785i	−0.492044	−	0.802944i	0.506185	−	0.862425i	$-0.331055\pi$
$937$	−15.0617	−	24.5785i	−0.492044	−	0.802944i	−0.998229	+	0.0594814i	$0.981055\pi$
$938$	−2.24169	+	0.728368i	−0.0731936	+	0.0237821i
$939$	−12.2234	+	3.97164i	−0.398897	+	0.129610i
$940$	−21.2655	−	43.6364i	−0.693603	−	1.42326i
$941$	−6.04913	−	38.1927i	−0.197196	−	1.24505i	−0.865405	−	0.501073i	$-0.832939\pi$
$941$	−6.04913	−	38.1927i	−0.197196	−	1.24505i	0.668209	−	0.743973i	$-0.267061\pi$
$942$	5.55099	−	5.55099i	0.180861	−	0.180861i
$943$	15.0334	−	9.30212i	0.489556	−	0.302919i
$944$		−	18.3487i		−	0.597199i
$945$	69.4087	−	15.3640i	2.25786	−	0.499793i
$946$	−1.97504	+	4.76816i	−0.0642140	+	0.155026i
$947$	−1.12033	−	0.570835i	−0.0364057	−	0.0185496i	0.435693	−	0.900095i	$-0.356503\pi$
$947$	−1.12033	−	0.570835i	−0.0364057	−	0.0185496i	−0.472099	+	0.881546i	$0.656503\pi$
$948$	−18.0470	−	55.5429i	−0.586139	−	1.80395i
$949$	−8.42940	−	2.02372i	−0.273630	−	0.0656928i
$950$	6.31221	+	2.88156i	0.204795	+	0.0934901i
$951$	−53.8304	+	27.4280i	−1.74557	+	0.889413i
$952$		−	1.69292i		−	0.0548677i
$953$	12.7572	+	25.0375i	0.413247	+	0.811043i	0.999999	+	0.00127668i	$0.000406380\pi$
$953$	12.7572	+	25.0375i	0.413247	+	0.811043i	−0.586752	+	0.809767i	$0.699594\pi$
$954$	−1.39184	−	1.18874i	−0.0450625	−	0.0384870i
$955$	−42.4785	−	0.755171i	−1.37457	−	0.0244368i
$956$	−20.0642	+	12.2954i	−0.648923	+	0.397661i
$957$	−7.71399	+	18.6232i	−0.249358	+	0.602003i
$958$	−2.56104	−	0.201558i	−0.0827434	−	0.00651205i
$959$	−13.9343	−	19.1789i	−0.449962	−	0.619320i
$960$	32.3655	−	42.9217i	1.04459	−	1.38529i
$961$	−18.1612	−	13.1949i	−0.585844	−	0.425640i
$962$	−0.0993869	−	0.413976i	−0.00320436	−	0.0133471i
$963$	−24.6538	−	33.9331i	−0.794458	−	1.09348i
$964$	−1.17422	+	7.41372i	−0.0378190	+	0.238780i
$965$	28.6184	−	8.73944i	0.921260	−	0.281333i
$966$	1.84219	−	2.53555i	0.0592714	−	0.0815801i
$967$	11.8255	−	13.8459i	0.380284	−	0.445255i	−0.536944	−	0.843618i	$-0.680421\pi$
$967$	11.8255	−	13.8459i	0.380284	−	0.445255i	0.917228	+	0.398363i	$0.130421\pi$
$968$	2.04026	+	0.323146i	0.0655765	+	0.0103863i
$969$	−20.5741	−	24.0891i	−0.660934	−	0.773855i
$970$	−4.76093	+	2.32016i	−0.152864	+	0.0744958i
$971$	−12.2667	−	20.0174i	−0.393657	−	0.642390i	0.593000	−	0.805202i	$-0.297943\pi$
$971$	−12.2667	−	20.0174i	−0.393657	−	0.642390i	−0.986657	+	0.162813i	$0.947943\pi$
$972$	74.1520	+	86.8209i	2.37843	+	2.78478i
$973$	33.8158	−	2.66136i	1.08408	−	0.0853193i
$974$	−0.292491	+	0.900195i	−0.00937202	+	0.0288441i
$975$	−29.5856	−	23.1455i	−0.947496	−	0.741250i
$976$	−5.00815	−	9.82905i	−0.160307	−	0.314620i
$977$	33.4280	+	20.4847i	1.06946	+	0.655363i	0.941704	−	0.336443i	$-0.109224\pi$
$977$	33.4280	+	20.4847i	1.06946	+	0.655363i	0.127752	+	0.991806i	$0.459224\pi$
$978$	−7.37445	+	4.51907i	−0.235809	+	0.144504i
$979$	4.83182	−	9.48298i	0.154426	−	0.303077i
$980$	14.5757	−	5.73610i	0.465605	−	0.183233i
$981$	38.5497	+	15.9678i	1.23080	+	0.509813i
$982$	−3.79545	+	5.22398i	−0.121118	+	0.166704i
$983$	−15.4431	−	15.4431i	−0.492558	−	0.492558i	0.416553	−	0.909111i	$-0.363238\pi$
$983$	−15.4431	−	15.4431i	−0.492558	−	0.492558i	−0.909111	+	0.416553i	$0.863238\pi$
$984$	7.11917	+	13.8241i	0.226951	+	0.440697i
$985$	−8.70275	+	9.83028i	−0.277293	+	0.313219i
$986$	−0.480733	+	0.0761406i	−0.0153096	+	0.00242481i
$987$	−63.1127	+	26.1421i	−2.00890	+	0.832113i
$988$	−15.2014	+	29.8344i	−0.483621	+	0.949159i
$989$	24.2250	+	12.3433i	0.770311	+	0.392493i
$990$	7.81398	−	5.46765i	0.248344	−	0.173773i
$991$	7.87150	+	32.7872i	0.250046	+	1.04152i	0.946189	+	0.323615i	$0.104898\pi$
$991$	7.87150	+	32.7872i	0.250046	+	1.04152i	−0.696142	+	0.717904i	$0.745102\pi$
$992$	5.98591	+	1.94494i	0.190053	+	0.0617519i
$993$	−78.1806			−2.48099
$994$	2.59422	+	0.842913i	0.0822837	+	0.0267356i
$995$	25.9337	−	34.3921i	0.822153	−	1.09030i
$996$	−5.20534	+	66.1401i	−0.164937	+	2.09573i
$997$	−22.8270	−	5.48029i	−0.722940	−	0.173563i	−0.144754	−	0.989468i	$-0.546239\pi$
$997$	−22.8270	−	5.48029i	−0.722940	−	0.173563i	−0.578186	+	0.815905i	$0.696239\pi$
$998$	−2.20931	−	0.915124i	−0.0699343	−	0.0289678i
$999$	13.4418	−	11.4804i	0.425279	−	0.363222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.10	yes	304
5.3	odd	4		205.2.bb.a.153.10	yes	304
41.26	odd	40		205.2.bb.a.67.10	yes	304
205.108	even	40	inner	205.2.y.a.108.10	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.10	✓	304	205.108	even	40	inner
205.2.y.a.112.10	yes	304	1.1	even	1	trivial
205.2.bb.a.67.10	yes	304	41.26	odd	40
205.2.bb.a.153.10	yes	304	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.148419 + 0.107833i) q^{2} +(-1.27715 - 3.08332i) q^{3} +(-0.607634 - 1.87010i) q^{4} +(2.05032 + 0.892291i) q^{5} +(0.142929 - 0.595343i) q^{6} +(0.968740 - 1.58084i) q^{7} +(0.224857 - 0.692038i) q^{8} +(-5.75441 + 5.75441i) q^{9} +(0.208089 + 0.353526i) q^{10} +(-1.85533 + 2.17231i) q^{11} +(-4.99008 + 4.26193i) q^{12} +(0.525508 - 2.18890i) q^{13} +(0.314247 - 0.130165i) q^{14} +(0.132646 - 7.46138i) q^{15} +(-3.07361 + 2.23311i) q^{16} +(0.954191 + 0.814956i) q^{17} +(-1.47458 + 0.233551i) q^{18} +(3.95247 - 6.44984i) q^{19} +(0.422834 - 4.37650i) q^{20} +(-6.11146 - 0.967961i) q^{21} +(-0.509613 + 0.122347i) q^{22} +(0.431906 + 2.72695i) q^{23} +(-2.42095 + 0.190533i) q^{24} +(3.40763 + 3.65897i) q^{25} +(0.314031 - 0.268208i) q^{26} +(15.8420 + 6.56196i) q^{27} +(-3.54498 - 0.851073i) q^{28} +(-0.165884 + 2.10775i) q^{29} +(0.824271 - 1.09311i) q^{30} +(-2.78118 - 0.903661i) q^{31} -2.15229 q^{32} +(9.06744 + 2.94619i) q^{33} +(0.0537413 + 0.223849i) q^{34} +(3.39680 - 2.37683i) q^{35} +(14.2579 + 7.26477i) q^{36} +(0.468019 - 0.918539i) q^{37} +(1.28213 - 0.531075i) q^{38} +(-7.42022 + 1.17525i) q^{39} +(1.07853 - 1.21826i) q^{40} +(-2.47591 - 5.90507i) q^{41} +(-0.802682 - 0.802682i) q^{42} +(5.78823 - 7.96681i) q^{43} +(5.18980 + 2.14968i) q^{44} +(-16.9330 + 6.66378i) q^{45} +(-0.229952 + 0.451305i) q^{46} +(9.41330 - 5.76848i) q^{47} +(10.8109 + 6.62490i) q^{48} +(1.61733 + 3.17420i) q^{49} +(0.111201 + 0.910517i) q^{50} +(1.29412 - 3.98290i) q^{51} +(-4.41278 + 0.347293i) q^{52} +(0.796232 + 0.932268i) q^{53} +(1.64366 + 2.68221i) q^{54} +(-5.74234 + 2.79844i) q^{55} +(-0.876174 - 1.02587i) q^{56} +(-24.9348 - 3.94929i) q^{57} +(-0.251906 + 0.294944i) q^{58} +(-2.83878 + 3.90725i) q^{59} +(-14.0342 + 4.28572i) q^{60} +(-0.454226 + 2.86787i) q^{61} +(-0.315337 - 0.434024i) q^{62} +(3.52228 + 14.6713i) q^{63} +(5.82778 + 4.23413i) q^{64} +(3.03059 - 4.01904i) q^{65} +(1.02809 + 1.41504i) q^{66} +(-6.90832 - 0.543696i) q^{67} +(0.944254 - 2.27963i) q^{68} +(7.85643 - 4.81443i) q^{69} +(0.760452 + 0.0135191i) q^{70} +(6.09805 + 5.20822i) q^{71} +(2.68835 + 5.27619i) q^{72} -3.85098i q^{73} +(0.168512 - 0.0858611i) q^{74} +(6.92970 - 15.1799i) q^{75} +(-14.4635 - 3.47238i) q^{76} +(1.63674 + 5.03738i) q^{77} +(-1.22804 - 0.625715i) q^{78} +(-3.40565 + 8.22196i) q^{79} +(-8.29448 + 1.83604i) q^{80} -32.8126i q^{81} +(0.269288 - 1.14341i) q^{82} +(7.14872 - 7.14872i) q^{83} +(1.90334 + 12.0172i) q^{84} +(1.22922 + 2.52234i) q^{85} +(1.71817 - 0.558268i) q^{86} +(6.71074 - 2.18045i) q^{87} +(1.08614 + 1.77241i) q^{88} +(-3.62260 + 0.869708i) q^{89} +(-3.23176 - 0.836902i) q^{90} +(-2.95122 - 2.95122i) q^{91} +(4.83723 - 2.46469i) q^{92} +(0.765719 + 9.72938i) q^{93} +(2.01915 + 0.158910i) q^{94} +(13.8590 - 9.69749i) q^{95} +(2.74880 + 6.63619i) q^{96} +(-1.01295 + 12.8708i) q^{97} +(-0.102239 + 0.645515i) q^{98} +(-1.82404 - 23.1766i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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