LMFDB - Embedded newform 370.2.o.d.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			181.2
Character	$\chi$	$=$	370.181
Dual form			370.2.o.d.231.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{2} +(0.0797653 + 0.452371i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.459350 q^{6} +(-0.742184 + 0.622767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.62080 - 0.953893i) q^{9} +(0.500000 + 0.866025i) q^{10} +(3.09972 - 5.36887i) q^{11} +(0.0797653 - 0.452371i) q^{12} +(2.80643 + 1.02146i) q^{13} +(0.484426 + 0.839051i) q^{14} +(-0.351882 - 0.295264i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.72303 - 1.71904i) q^{17} +(-0.484304 - 2.74663i) q^{18} +(-0.768682 - 4.35941i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-0.340922 - 0.286068i) q^{21} +(-4.74904 - 3.98492i) q^{22} +(2.69101 + 4.66097i) q^{23} +(-0.431648 - 0.157107i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.49327 - 2.58642i) q^{26} +(1.32959 + 2.30291i) q^{27} +(0.910424 - 0.331367i) q^{28} +(-4.15705 + 7.20022i) q^{29} +(-0.351882 + 0.295264i) q^{30} -3.85619 q^{31} +(0.766044 - 0.642788i) q^{32} +(2.67597 + 0.973973i) q^{33} +(-0.872782 - 4.94979i) q^{34} +(0.168240 - 0.954134i) q^{35} -2.78900 q^{36} +(-4.50032 - 4.09232i) q^{37} -4.42666 q^{38} +(-0.238222 + 1.35103i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(-1.81302 - 0.659885i) q^{41} +(-0.340922 + 0.286068i) q^{42} +4.68859 q^{43} +(-4.74904 + 3.98492i) q^{44} +(-1.39450 + 2.41534i) q^{45} +(5.05745 - 1.84076i) q^{46} +(-1.41973 - 2.45905i) q^{47} +(-0.229675 + 0.397809i) q^{48} +(-1.05254 + 5.96924i) q^{49} +(-0.939693 - 0.342020i) q^{50} +(1.15438 + 1.99945i) q^{51} +(-2.28782 - 1.91971i) q^{52} +(5.31542 + 4.46017i) q^{53} +(2.49881 - 0.909491i) q^{54} +(1.07652 + 6.10525i) q^{55} +(-0.168240 - 0.954134i) q^{56} +(1.91076 - 0.695459i) q^{57} +(6.36897 + 5.34420i) q^{58} +(-5.13091 - 4.30535i) q^{59} +(0.229675 + 0.397809i) q^{60} +(-7.78715 - 2.83429i) q^{61} +(-0.669620 + 3.79760i) q^{62} +(-1.35106 + 2.34011i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.80643 + 1.02146i) q^{65} +(1.42385 - 2.46619i) q^{66} +(6.44497 - 5.40797i) q^{67} -5.02615 q^{68} +(-1.89384 + 1.58912i) q^{69} +(-0.910424 - 0.331367i) q^{70} +(-0.976855 - 5.54002i) q^{71} +(-0.484304 + 2.74663i) q^{72} -5.73486 q^{73} +(-4.81162 + 3.72133i) q^{74} +0.459350 q^{75} +(-0.768682 + 4.35941i) q^{76} +(1.04299 + 5.91509i) q^{77} +(1.28913 + 0.469206i) q^{78} +(1.77563 - 1.48993i) q^{79} -1.00000 q^{80} +(5.47377 - 4.59304i) q^{81} +(-0.964687 + 1.67089i) q^{82} +(-11.7125 + 4.26302i) q^{83} +(0.222521 + 0.385418i) q^{84} +(-2.51307 + 4.35277i) q^{85} +(0.814166 - 4.61736i) q^{86} +(-3.58876 - 1.30620i) q^{87} +(3.09972 + 5.36887i) q^{88} +(6.89692 + 5.78720i) q^{89} +(2.13650 + 1.79273i) q^{90} +(-2.71902 + 0.989642i) q^{91} +(-0.934579 - 5.30026i) q^{92} +(-0.307590 - 1.74443i) q^{93} +(-2.66823 + 0.971155i) q^{94} +(3.39102 + 2.84541i) q^{95} +(0.351882 + 0.295264i) q^{96} +(4.91001 + 8.50439i) q^{97} +(5.69578 + 2.07309i) q^{98} +(3.00241 - 17.0275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31}+ \cdots + 165 q^{99}+O(q^{100}) $ 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	0.0797653	+	0.452371i	0.0460525	+	0.261177i	0.999137	−	0.0415264i	$-0.0132221\pi$
$3$	0.0797653	+	0.452371i	0.0460525	+	0.261177i	−0.953085	+	0.302703i	$0.902111\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$5$	−0.766044	+	0.642788i	−0.342585	+	0.287463i
$6$	0.459350			0.187529
$7$	−0.742184	+	0.622767i	−0.280519	+	0.235384i	−0.772181	−	0.635403i	$-0.780834\pi$
$7$	−0.742184	+	0.622767i	−0.280519	+	0.235384i	0.491662	+	0.870786i	$0.336390\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	2.62080	−	0.953893i	0.873600	−	0.317964i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	3.09972	−	5.36887i	0.934599	−	1.61877i	0.159253	−	0.987238i	$-0.449091\pi$
$11$	3.09972	−	5.36887i	0.934599	−	1.61877i	0.775347	−	0.631536i	$-0.217575\pi$
$12$	0.0797653	−	0.452371i	0.0230262	−	0.130588i
$13$	2.80643	+	1.02146i	0.778364	+	0.283301i	0.700490	−	0.713662i	$-0.252965\pi$
$13$	2.80643	+	1.02146i	0.778364	+	0.283301i	0.0778737	+	0.996963i	$0.475187\pi$
$14$	0.484426	+	0.839051i	0.129468	+	0.224246i
$15$	−0.351882	−	0.295264i	−0.0908556	−	0.0762369i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	4.72303	−	1.71904i	1.14550	−	0.416929i	0.301606	−	0.953433i	$-0.402477\pi$
$17$	4.72303	−	1.71904i	1.14550	−	0.416929i	0.843898	+	0.536503i	$0.180255\pi$
$18$	−0.484304	−	2.74663i	−0.114152	−	0.647386i
$19$	−0.768682	−	4.35941i	−0.176348	−	1.00012i	−0.936577	−	0.350463i	$-0.886024\pi$
$19$	−0.768682	−	4.35941i	−0.176348	−	1.00012i	0.760229	−	0.649655i	$-0.225087\pi$
$20$	0.939693	−	0.342020i	0.210122	−	0.0764780i
$21$	−0.340922	−	0.286068i	−0.0743953	−	0.0624251i
$22$	−4.74904	−	3.98492i	−1.01250	−	0.849587i
$23$	2.69101	+	4.66097i	0.561115	+	0.971879i	0.997400	+	0.0720706i	$0.0229607\pi$
$23$	2.69101	+	4.66097i	0.561115	+	0.971879i	−0.436285	+	0.899809i	$0.643706\pi$
$24$	−0.431648	−	0.157107i	−0.0881097	−	0.0320693i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	1.49327	−	2.58642i	0.292855	−	0.507239i
$27$	1.32959	+	2.30291i	0.255879	+	0.443196i
$28$	0.910424	−	0.331367i	0.172054	−	0.0626225i
$29$	−4.15705	+	7.20022i	−0.771945	+	1.33705i	0.164551	+	0.986369i	$0.447383\pi$
$29$	−4.15705	+	7.20022i	−0.771945	+	1.33705i	−0.936496	+	0.350679i	$0.885951\pi$
$30$	−0.351882	+	0.295264i	−0.0642446	+	0.0539076i
$31$	−3.85619			−0.692592			−0.346296	−	0.938125i	$-0.612561\pi$
$31$	−3.85619			−0.692592			−0.346296	+	0.938125i	$0.612561\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	2.67597	+	0.973973i	0.465827	+	0.169547i
$34$	−0.872782	−	4.94979i	−0.149681	−	0.848882i
$35$	0.168240	−	0.954134i	0.0284377	−	0.161278i
$36$	−2.78900			−0.464833
$37$	−4.50032	−	4.09232i	−0.739848	−	0.672774i
$37$	−4.50032	−	4.09232i	−0.739848	−	0.672774i
$38$	−4.42666			−0.718100
$39$	−0.238222	+	1.35103i	−0.0381461	+	0.216337i
$40$	−0.173648	−	0.984808i	−0.0274562	−	0.155712i
$41$	−1.81302	−	0.659885i	−0.283146	−	0.103057i	0.196543	−	0.980495i	$-0.437028\pi$
$41$	−1.81302	−	0.659885i	−0.283146	−	0.103057i	−0.479689	+	0.877438i	$0.659251\pi$
$42$	−0.340922	+	0.286068i	−0.0526054	+	0.0441412i
$43$	4.68859			0.715004			0.357502	−	0.933912i	$-0.383629\pi$
$43$	4.68859			0.715004			0.357502	+	0.933912i	$0.383629\pi$
$44$	−4.74904	+	3.98492i	−0.715945	+	0.600749i
$45$	−1.39450	+	2.41534i	−0.207880	+	0.360058i
$46$	5.05745	−	1.84076i	0.745680	−	0.271405i
$47$	−1.41973	−	2.45905i	−0.207089	−	0.358689i	0.743707	−	0.668506i	$-0.233066\pi$
$47$	−1.41973	−	2.45905i	−0.207089	−	0.358689i	−0.950796	+	0.309816i	$0.899732\pi$
$48$	−0.229675	+	0.397809i	−0.0331507	+	0.0574187i
$49$	−1.05254	+	5.96924i	−0.150363	+	0.852748i
$50$	−0.939693	−	0.342020i	−0.132893	−	0.0483690i
$51$	1.15438	+	1.99945i	0.161646	+	0.279978i
$52$	−2.28782	−	1.91971i	−0.317264	−	0.266216i
$53$	5.31542	+	4.46017i	0.730130	+	0.612652i	0.930167	−	0.367137i	$-0.119662\pi$
$53$	5.31542	+	4.46017i	0.730130	+	0.612652i	−0.200037	+	0.979788i	$0.564106\pi$
$54$	2.49881	−	0.909491i	0.340045	−	0.123766i
$55$	1.07652	+	6.10525i	0.145158	+	0.823232i
$56$	−0.168240	−	0.954134i	−0.0224820	−	0.127502i
$57$	1.91076	−	0.695459i	0.253086	−	0.0921159i
$58$	6.36897	+	5.34420i	0.836287	+	0.701728i
$59$	−5.13091	−	4.30535i	−0.667988	−	0.560508i	0.244481	−	0.969654i	$-0.421382\pi$
$59$	−5.13091	−	4.30535i	−0.667988	−	0.560508i	−0.912469	+	0.409146i	$0.865827\pi$
$60$	0.229675	+	0.397809i	0.0296509	+	0.0513569i
$61$	−7.78715	−	2.83429i	−0.997042	−	0.362894i	−0.208599	−	0.978001i	$-0.566890\pi$
$61$	−7.78715	−	2.83429i	−0.997042	−	0.362894i	−0.788443	+	0.615108i	$0.789113\pi$
$62$	−0.669620	+	3.79760i	−0.0850418	+	0.482296i
$63$	−1.35106	+	2.34011i	−0.170218	+	0.294826i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.80643	+	1.02146i	−0.348095	+	0.126696i
$66$	1.42385	−	2.46619i	0.175264	−	0.303567i
$67$	6.44497	−	5.40797i	0.787379	−	0.660689i	−0.157717	−	0.987484i	$-0.550413\pi$
$67$	6.44497	−	5.40797i	0.787379	−	0.660689i	0.945095	+	0.326795i	$0.105969\pi$
$68$	−5.02615			−0.609510
$69$	−1.89384	+	1.58912i	−0.227991	+	0.191308i
$70$	−0.910424	−	0.331367i	−0.108816	−	0.0396060i
$71$	−0.976855	−	5.54002i	−0.115931	−	0.657479i	−0.986285	−	0.165052i	$-0.947221\pi$
$71$	−0.976855	−	5.54002i	−0.115931	−	0.657479i	0.870354	−	0.492427i	$-0.163890\pi$
$72$	−0.484304	+	2.74663i	−0.0570758	+	0.323693i
$73$	−5.73486			−0.671214			−0.335607	−	0.942002i	$-0.608941\pi$
$73$	−5.73486			−0.671214			−0.335607	+	0.942002i	$0.608941\pi$
$74$	−4.81162	+	3.72133i	−0.559340	+	0.432596i
$75$	0.459350			0.0530411
$76$	−0.768682	+	4.35941i	−0.0881739	+	0.500059i
$77$	1.04299	+	5.91509i	0.118860	+	0.674087i
$78$	1.28913	+	0.469206i	0.145966	+	0.0531272i
$79$	1.77563	−	1.48993i	0.199774	−	0.167631i	−0.537413	−	0.843320i	$-0.680598\pi$
$79$	1.77563	−	1.48993i	0.199774	−	0.167631i	0.737187	+	0.675689i	$0.236154\pi$
$80$	−1.00000			−0.111803
$81$	5.47377	−	4.59304i	0.608197	−	0.510338i
$82$	−0.964687	+	1.67089i	−0.106532	+	0.184519i
$83$	−11.7125	+	4.26302i	−1.28562	+	0.467927i	−0.892287	−	0.451469i	$-0.850900\pi$
$83$	−11.7125	+	4.26302i	−1.28562	+	0.467927i	−0.393332	+	0.919396i	$0.628678\pi$
$84$	0.222521	+	0.385418i	0.0242791	+	0.0420526i
$85$	−2.51307	+	4.35277i	−0.272581	+	0.472124i
$86$	0.814166	−	4.61736i	0.0877937	−	0.497903i
$87$	−3.58876	−	1.30620i	−0.384756	−	0.140040i
$88$	3.09972	+	5.36887i	0.330431	+	0.572323i
$89$	6.89692	+	5.78720i	0.731072	+	0.613442i	0.930424	−	0.366486i	$-0.119439\pi$
$89$	6.89692	+	5.78720i	0.731072	+	0.613442i	−0.199351	+	0.979928i	$0.563884\pi$
$90$	2.13650	+	1.79273i	0.225206	+	0.188971i
$91$	−2.71902	+	0.989642i	−0.285031	+	0.103743i
$92$	−0.934579	−	5.30026i	−0.0974366	−	0.552590i
$93$	−0.307590	−	1.74443i	−0.0318956	−	0.180889i
$94$	−2.66823	+	0.971155i	−0.275206	+	0.100167i
$95$	3.39102	+	2.84541i	0.347911	+	0.291932i
$96$	0.351882	+	0.295264i	0.0359138	+	0.0301353i
$97$	4.91001	+	8.50439i	0.498536	+	0.863490i	0.999999	−	0.00168934i	$-0.000537735\pi$
$97$	4.91001	+	8.50439i	0.498536	+	0.863490i	−0.501462	+	0.865179i	$0.667204\pi$
$98$	5.69578	+	2.07309i	0.575361	+	0.209414i
$99$	3.00241	−	17.0275i	0.301754	−	1.71133i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	8.95364	+	15.5082i	0.890921	+	1.54312i	0.838774	+	0.544480i	$0.183273\pi$
$101$	8.95364	+	15.5082i	0.890921	+	1.54312i	0.0521471	+	0.998639i	$0.483394\pi$
$102$	2.16953	−	0.789643i	0.214815	−	0.0781863i
$103$	−5.86763	+	10.1630i	−0.578155	+	1.00139i	0.417536	+	0.908660i	$0.362894\pi$
$103$	−5.86763	+	10.1630i	−0.578155	+	1.00139i	−0.995691	+	0.0927336i	$0.970440\pi$
$104$	−2.28782	+	1.91971i	−0.224340	+	0.188243i
$105$	0.445042			0.0434317
$106$	5.31542	−	4.46017i	0.516280	−	0.433210i
$107$	6.03193	+	2.19544i	0.583129	+	0.212242i	0.616705	−	0.787195i	$-0.288467\pi$
$107$	6.03193	+	2.19544i	0.583129	+	0.212242i	−0.0335758	+	0.999436i	$0.510690\pi$
$108$	−0.461761	−	2.61878i	−0.0444330	−	0.251992i
$109$	1.59932	−	9.07021i	0.153187	−	0.868768i	−0.807237	−	0.590227i	$-0.799038\pi$
$109$	1.59932	−	9.07021i	0.153187	−	0.868768i	0.960424	−	0.278541i	$-0.0898508\pi$
$110$	6.19943			0.591093
$111$	1.49228	−	2.36224i	0.141641	−	0.224214i
$112$	−0.968853			−0.0915480
$113$	−2.66380	+	15.1072i	−0.250589	+	1.42116i	0.556556	+	0.830810i	$0.312123\pi$
$113$	−2.66380	+	15.1072i	−0.250589	+	1.42116i	−0.807145	+	0.590353i	$0.798989\pi$
$114$	−0.353094	−	2.00250i	−0.0330703	−	0.187551i
$115$	−5.05745	−	1.84076i	−0.471609	−	0.171652i
$116$	6.36897	−	5.34420i	0.591344	−	0.496197i
$117$	8.32946			0.770059
$118$	−5.13091	+	4.30535i	−0.472339	+	0.396339i
$119$	−2.43480	+	4.21720i	−0.223198	+	0.386590i
$120$	0.431648	−	0.157107i	0.0394039	−	0.0143418i
$121$	−13.7165	−	23.7576i	−1.24695	−	2.15978i
$122$	−4.14345	+	7.17667i	−0.375131	+	0.649745i
$123$	0.153897	−	0.872793i	0.0138764	−	0.0786971i
$124$	3.62363	+	1.31889i	0.325412	+	0.118440i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	2.06995	+	1.73689i	0.184406	+	0.154735i
$127$	−8.79432	−	7.37931i	−0.780370	−	0.654808i	0.162972	−	0.986631i	$-0.447892\pi$
$127$	−8.79432	−	7.37931i	−0.780370	−	0.654808i	−0.943342	+	0.331823i	$0.892336\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	0.373987	+	2.12098i	0.0329277	+	0.186742i
$130$	0.518608	+	2.94117i	0.0454849	+	0.257958i
$131$	−18.1061	+	6.59009i	−1.58194	+	0.575779i	−0.975624	−	0.219447i	$-0.929575\pi$
$131$	−18.1061	+	6.59009i	−1.58194	+	0.575779i	−0.606314	+	0.795225i	$0.707353\pi$
$132$	−2.18147	−	1.83047i	−0.189873	−	0.159322i
$133$	3.28540	+	2.75678i	0.284880	+	0.239043i
$134$	−4.20666	−	7.28614i	−0.363400	−	0.629427i
$135$	−2.49881	−	0.909491i	−0.215063	−	0.0782766i
$136$	−0.872782	+	4.94979i	−0.0748404	+	0.424441i
$137$	−8.03242	+	13.9126i	−0.686256	+	1.18863i	0.286785	+	0.957995i	$0.407413\pi$
$137$	−8.03242	+	13.9126i	−0.686256	+	1.18863i	−0.973040	+	0.230634i	$0.925920\pi$
$138$	1.23612	+	2.14102i	0.105225	+	0.182255i
$139$	4.46705	−	1.62587i	0.378890	−	0.137905i	−0.145553	−	0.989351i	$-0.546496\pi$
$139$	4.46705	−	1.62587i	0.378890	−	0.137905i	0.524442	+	0.851446i	$0.324274\pi$
$140$	−0.484426	+	0.839051i	−0.0409415	+	0.0709128i
$141$	0.999158	−	0.838393i	0.0841443	−	0.0706054i
$142$	−5.62548			−0.472080
$143$	14.1832	−	11.9011i	1.18606	−	0.995222i
$144$	2.62080	+	0.953893i	0.218400	+	0.0794911i
$145$	−1.44373	−	8.18779i	−0.119895	−	0.679959i
$146$	−0.995847	+	5.64773i	−0.0824169	+	0.467409i
$147$	−2.78427			−0.229643
$148$	2.82926	+	5.38473i	0.232564	+	0.442622i
$149$	13.5653			1.11131			0.555656	−	0.831412i	$-0.312467\pi$
$149$	13.5653			1.11131			0.555656	+	0.831412i	$0.312467\pi$
$150$	0.0797653	−	0.452371i	0.00651281	−	0.0369360i
$151$	−1.51079	−	8.56813i	−0.122947	−	0.697264i	−0.982506	−	0.186229i	$-0.940373\pi$
$151$	−1.51079	−	8.56813i	−0.122947	−	0.697264i	0.859560	−	0.511035i	$-0.170738\pi$
$152$	4.15970	+	1.51401i	0.337397	+	0.122802i
$153$	10.7383	−	9.01054i	0.868144	−	0.728459i
$154$	6.00634			0.484004
$155$	2.95401	−	2.47871i	0.237272	−	0.199095i
$156$	0.685934	−	1.18807i	0.0549187	−	0.0951219i
$157$	9.24486	−	3.36485i	0.737820	−	0.268545i	0.0543490	−	0.998522i	$-0.482692\pi$
$157$	9.24486	−	3.36485i	0.737820	−	0.268545i	0.683471	+	0.729977i	$0.260469\pi$
$158$	−1.15896	−	2.00738i	−0.0922021	−	0.159699i
$159$	−1.59367	+	2.76031i	−0.126386	+	0.218907i
$160$	−0.173648	+	0.984808i	−0.0137281	+	0.0778559i
$161$	−4.89992	−	1.78343i	−0.386168	−	0.140554i
$162$	−3.57275	−	6.18819i	−0.280702	−	0.486190i
$163$	−13.4044	−	11.2476i	−1.04991	−	0.880981i	−0.0568282	−	0.998384i	$-0.518099\pi$
$163$	−13.4044	−	11.2476i	−1.04991	−	0.880981i	−0.993084	+	0.117403i	$0.962543\pi$
$164$	1.47799	+	1.24018i	0.115411	+	0.0968416i
$165$	−2.67597	+	0.973973i	−0.208324	+	0.0758237i
$166$	2.16439	+	12.2749i	0.167989	+	0.952715i
$167$	0.148241	+	0.840715i	0.0114712	+	0.0650565i	0.990006	−	0.141025i	$-0.0450399\pi$
$167$	0.148241	+	0.840715i	0.0114712	+	0.0650565i	−0.978535	+	0.206082i	$0.933929\pi$
$168$	0.418203	−	0.152213i	0.0322651	−	0.0117435i
$169$	−3.12589	−	2.62294i	−0.240453	−	0.201764i
$170$	3.85025	+	3.23075i	0.295301	+	0.247787i
$171$	−6.17298	−	10.6919i	−0.472059	−	0.817631i
$172$	−4.40584	−	1.60359i	−0.335942	−	0.122273i
$173$	−0.973376	+	5.52029i	−0.0740044	+	0.419700i	0.925188	+	0.379510i	$0.123907\pi$
$173$	−0.973376	+	5.52029i	−0.0740044	+	0.419700i	−0.999192	+	0.0401898i	$0.987204\pi$
$174$	−1.90954	+	3.30742i	−0.144762	+	0.250735i
$175$	0.484426	+	0.839051i	0.0366192	+	0.0634263i
$176$	5.82556	−	2.12033i	0.439118	−	0.159826i
$177$	1.53835	−	2.66449i	0.115629	−	0.200276i
$178$	6.89692	−	5.78720i	0.516946	−	0.433769i
$179$	11.6450			0.870385			0.435193	−	0.900337i	$-0.356680\pi$
$179$	11.6450			0.870385			0.435193	+	0.900337i	$0.356680\pi$
$180$	2.13650	−	1.79273i	0.159245	−	0.133622i
$181$	−17.6837	−	6.43635i	−1.31442	−	0.478410i	−0.412754	−	0.910842i	$-0.635433\pi$
$181$	−17.6837	−	6.43635i	−1.31442	−	0.478410i	−0.901666	+	0.432433i	$0.857655\pi$
$182$	0.502454	+	2.84956i	0.0372444	+	0.211224i
$183$	0.661007	−	3.74876i	0.0488631	−	0.277116i
$184$	−5.38202			−0.396768
$185$	6.07794	+	0.242150i	0.446859	+	0.0178032i
$186$	−1.77134			−0.129881
$187$	5.41075	−	30.6859i	0.395673	−	2.24397i
$188$	0.493068	+	2.79633i	0.0359607	+	0.203943i
$189$	−2.42098	−	0.881163i	−0.176100	−	0.0640952i
$190$	3.39102	−	2.84541i	0.246011	−	0.206427i
$191$	−14.1065			−1.02071			−0.510355	−	0.859964i	$-0.670486\pi$
$191$	−14.1065			−1.02071			−0.510355	+	0.859964i	$0.670486\pi$
$192$	0.351882	−	0.295264i	0.0253949	−	0.0213089i
$193$	−3.76366	+	6.51885i	−0.270914	+	0.469237i	−0.969096	−	0.246683i	$-0.920659\pi$
$193$	−3.76366	+	6.51885i	−0.270914	+	0.469237i	0.698182	+	0.715920i	$0.253993\pi$
$194$	9.22781	−	3.35865i	0.662518	−	0.241137i
$195$	−0.685934	−	1.18807i	−0.0491207	−	0.0850796i
$196$	3.03066	−	5.24926i	0.216476	−	0.374947i
$197$	2.91325	−	16.5219i	0.207561	−	1.17713i	−0.685798	−	0.727792i	$-0.740547\pi$
$197$	2.91325	−	16.5219i	0.207561	−	1.17713i	0.893359	−	0.449343i	$-0.148342\pi$
$198$	−16.2475	−	5.91360i	−1.15466	−	0.420261i
$199$	10.4842	+	18.1591i	0.743202	+	1.28726i	0.951030	+	0.309098i	$0.100027\pi$
$199$	10.4842	+	18.1591i	0.743202	+	1.28726i	−0.207828	+	0.978165i	$0.566640\pi$
$200$	0.766044	+	0.642788i	0.0541675	+	0.0454519i
$201$	2.96050	+	2.48415i	0.208817	+	0.175219i
$202$	16.8273	−	6.12465i	1.18397	−	0.430929i
$203$	−1.39876	−	7.93277i	−0.0981738	−	0.556771i
$204$	−0.400912	−	2.27369i	−0.0280695	−	0.159190i
$205$	1.81302	−	0.659885i	0.126627	−	0.0460884i
$206$	8.98974	+	7.54328i	0.626345	+	0.525566i
$207$	11.4987	+	9.64853i	0.799213	+	0.670619i
$208$	1.49327	+	2.58642i	0.103540	+	0.179336i
$209$	−25.7878	−	9.38599i	−1.78378	−	0.649243i
$210$	0.0772808	−	0.438281i	0.00533288	−	0.0302443i
$211$	4.97128	−	8.61050i	0.342237	−	0.592772i	−0.642611	−	0.766193i	$-0.722149\pi$
$211$	4.97128	−	8.61050i	0.342237	−	0.592772i	0.984848	+	0.173421i	$0.0554822\pi$
$212$	−3.46940	−	6.00917i	−0.238279	−	0.412712i
$213$	2.42823	−	0.883802i	0.166379	−	0.0605571i
$214$	3.20952	−	5.55906i	0.219399	−	0.380009i
$215$	−3.59167	+	3.01377i	−0.244950	+	0.205537i
$216$	−2.65917			−0.180934
$217$	2.86200	−	2.40150i	0.194285	−	0.163025i
$218$	−8.65469	−	3.15005i	−0.586170	−	0.213348i
$219$	−0.457442	−	2.59428i	−0.0309111	−	0.175305i
$220$	1.07652	−	6.10525i	0.0725790	−	0.411616i
$221$	15.0108			1.00974
$222$	−2.06722	−	1.87981i	−0.138743	−	0.126164i
$223$	−20.1985			−1.35259			−0.676297	−	0.736629i	$-0.736416\pi$
$223$	−20.1985			−1.35259			−0.676297	+	0.736629i	$0.736416\pi$
$224$	−0.168240	+	0.954134i	−0.0112410	+	0.0637508i
$225$	−0.484304	−	2.74663i	−0.0322870	−	0.183108i
$226$	14.4151	+	5.24667i	0.958878	+	0.349003i
$227$	−7.45072	+	6.25190i	−0.494522	+	0.414953i	−0.855644	−	0.517566i	$-0.826838\pi$
$227$	−7.45072	+	6.25190i	−0.494522	+	0.414953i	0.361122	+	0.932519i	$0.382394\pi$
$228$	−2.03339			−0.134664
$229$	−0.367673	+	0.308514i	−0.0242965	+	0.0203872i	−0.654855	−	0.755755i	$-0.727270\pi$
$229$	−0.367673	+	0.308514i	−0.0242965	+	0.0203872i	0.630559	+	0.776142i	$0.282826\pi$
$230$	−2.69101	+	4.66097i	−0.177440	+	0.307335i
$231$	−2.59262	+	0.943637i	−0.170582	+	0.0620867i
$232$	−4.15705	−	7.20022i	−0.272924	−	0.472718i
$233$	−9.22873	+	15.9846i	−0.604594	+	1.04719i	0.387522	+	0.921861i	$0.373331\pi$
$233$	−9.22873	+	15.9846i	−0.604594	+	1.04719i	−0.992116	+	0.125327i	$0.960002\pi$
$234$	1.44640	−	8.20292i	0.0945538	−	0.536241i
$235$	2.66823	+	0.971155i	0.174056	+	0.0633511i
$236$	3.34896	+	5.80058i	0.217999	+	0.377585i
$237$	0.815637	+	0.684401i	0.0529813	+	0.0444566i
$238$	3.73033	+	3.13012i	0.241801	+	0.202895i
$239$	25.9258	−	9.43623i	1.67700	−	0.610379i	0.684108	−	0.729380i	$-0.260192\pi$
$239$	25.9258	−	9.43623i	1.67700	−	0.610379i	0.992894	+	0.119002i	$0.0379694\pi$
$240$	−0.0797653	−	0.452371i	−0.00514882	−	0.0292004i
$241$	4.29768	+	24.3734i	0.276838	+	1.57003i	0.733062	+	0.680161i	$0.238090\pi$
$241$	4.29768	+	24.3734i	0.276838	+	1.57003i	−0.456225	+	0.889865i	$0.650799\pi$
$242$	−25.7785	+	9.38262i	−1.65711	+	0.603138i
$243$	8.62551	+	7.23767i	0.553327	+	0.464296i
$244$	6.34814	+	5.32672i	0.406398	+	0.341008i
$245$	−3.03066	−	5.24926i	−0.193622	−	0.335363i
$246$	−0.832810	−	0.303118i	−0.0530980	−	0.0193261i
$247$	2.29570	−	13.0196i	0.146072	−	0.828416i
$248$	1.92809	−	3.33956i	0.122434	−	0.212062i
$249$	−2.86272	−	4.95838i	−0.181418	−	0.314224i
$250$	0.939693	−	0.342020i	0.0594314	−	0.0216313i
$251$	11.6609	−	20.1973i	0.736031	−	1.27484i	−0.218238	−	0.975896i	$-0.570031\pi$
$251$	11.6609	−	20.1973i	0.736031	−	1.27484i	0.954269	−	0.298948i	$-0.0966357\pi$
$252$	2.06995	−	1.73689i	0.130395	−	0.109414i
$253$	33.3655			2.09767
$254$	−8.79432	+	7.37931i	−0.551805	+	0.463019i
$255$	−2.16953	−	0.789643i	−0.135861	−	0.0494493i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.30196	+	24.3976i	−0.268349	+	1.52188i	0.490978	+	0.871172i	$0.336640\pi$
$257$	−4.30196	+	24.3976i	−0.268349	+	1.52188i	−0.759327	+	0.650710i	$0.774471\pi$
$258$	2.15370			0.134084
$259$	5.88863	+	0.234608i	0.365902	+	0.0145778i
$260$	2.98654			0.185217
$261$	−4.02656	+	22.8357i	−0.249238	+	1.41350i
$262$	3.34587	+	18.9754i	0.206709	+	1.17230i
$263$	−11.9561	−	4.35167i	−0.737245	−	0.268335i	−0.0540169	−	0.998540i	$-0.517202\pi$
$263$	−11.9561	−	4.35167i	−0.737245	−	0.268335i	−0.683229	+	0.730205i	$0.739425\pi$
$264$	−2.18147	+	1.83047i	−0.134260	+	0.112658i
$265$	−6.93879			−0.426247
$266$	3.28540	−	2.75678i	0.201441	−	0.169029i
$267$	−2.06783	+	3.58159i	−0.126549	+	0.219190i
$268$	−7.90593	+	2.87752i	−0.482931	+	0.175773i
$269$	−4.24586	−	7.35405i	−0.258875	−	0.448384i	0.707066	−	0.707148i	$-0.250018\pi$
$269$	−4.24586	−	7.35405i	−0.258875	−	0.448384i	−0.965941	+	0.258763i	$0.916685\pi$
$270$	−1.32959	+	2.30291i	−0.0809161	+	0.140151i
$271$	−1.96594	+	11.1494i	−0.119422	+	0.677277i	0.865043	+	0.501698i	$0.167291\pi$
$271$	−1.96594	+	11.1494i	−0.119422	+	0.677277i	−0.984465	+	0.175580i	$0.943820\pi$
$272$	4.72303	+	1.71904i	0.286376	+	0.104232i
$273$	−0.664569	−	1.15107i	−0.0402215	−	0.0696658i
$274$	12.3064	+	10.3263i	0.743455	+	0.623833i
$275$	−4.74904	−	3.98492i	−0.286378	−	0.240300i
$276$	2.32314	−	0.845553i	0.139836	−	0.0508963i
$277$	−1.17140	−	6.64336i	−0.0703828	−	0.399161i	−0.999564	−	0.0295356i	$-0.990597\pi$
$277$	−1.17140	−	6.64336i	−0.0703828	−	0.399161i	0.929181	−	0.369625i	$-0.120514\pi$
$278$	−0.825477	−	4.68151i	−0.0495088	−	0.280778i
$279$	−10.1063	+	3.67839i	−0.605048	+	0.220220i
$280$	0.742184	+	0.622767i	0.0443540	+	0.0372174i
$281$	13.4410	+	11.2784i	0.801825	+	0.672811i	0.948642	−	0.316353i	$-0.102458\pi$
$281$	13.4410	+	11.2784i	0.801825	+	0.672811i	−0.146817	+	0.989164i	$0.546903\pi$
$282$	−0.652154	−	1.12956i	−0.0388352	−	0.0672646i
$283$	−6.71030	−	2.44235i	−0.398886	−	0.145183i	0.134785	−	0.990875i	$-0.456966\pi$
$283$	−6.71030	−	2.44235i	−0.398886	−	0.145183i	−0.533671	+	0.845692i	$0.679188\pi$
$284$	−0.976855	+	5.54002i	−0.0579657	+	0.328740i
$285$	−1.01669	+	1.76097i	−0.0602237	+	0.104311i
$286$	−9.25743	−	16.0343i	−0.547403	−	0.948131i
$287$	1.75655	−	0.639331i	0.103686	−	0.0377385i
$288$	1.39450	−	2.41534i	0.0821716	−	0.142325i
$289$	6.32919	−	5.31082i	0.372305	−	0.312401i
$290$	−8.31410			−0.488221
$291$	−3.45549	+	2.89950i	−0.202565	+	0.169972i
$292$	5.38900	+	1.96144i	0.315367	+	0.114784i
$293$	−1.02145	−	5.79292i	−0.0596736	−	0.338426i	0.940325	−	0.340279i	$-0.110521\pi$
$293$	−1.02145	−	5.79292i	−0.0596736	−	0.338426i	−0.999998	+	0.00185263i	$0.999410\pi$
$294$	−0.483483	+	2.74197i	−0.0281973	+	0.159915i
$295$	6.69793			0.389968
$296$	5.79422	−	1.85123i	0.336782	−	0.107601i
$297$	16.4854			0.956578
$298$	2.35559	−	13.3592i	0.136456	−	0.773878i
$299$	2.79116	+	15.8294i	0.161417	+	0.915441i
$300$	−0.431648	−	0.157107i	−0.0249212	−	0.00907057i
$301$	−3.47980	+	2.91990i	−0.200572	+	0.168300i
$302$	−8.70030			−0.500646
$303$	−6.30126	+	5.28738i	−0.361998	+	0.303752i
$304$	2.21333	−	3.83360i	0.126943	−	0.219872i
$305$	7.78715	−	2.83429i	0.445891	−	0.162291i
$306$	−7.00896	−	12.1399i	−0.400676	−	0.693990i
$307$	−10.5838	+	18.3317i	−0.604050	+	1.04624i	0.388151	+	0.921596i	$0.373114\pi$
$307$	−10.5838	+	18.3317i	−0.604050	+	1.04624i	−0.992201	+	0.124649i	$0.960220\pi$
$308$	1.04299	−	5.91509i	0.0594298	−	0.337043i
$309$	−5.06550	−	1.84369i	−0.288166	−	0.104884i
$310$	−1.92809	−	3.33956i	−0.109508	−	0.189674i
$311$	−3.15694	−	2.64899i	−0.179014	−	0.150210i	0.548878	−	0.835903i	$-0.315055\pi$
$311$	−3.15694	−	2.64899i	−0.179014	−	0.150210i	−0.727892	+	0.685692i	$0.759500\pi$
$312$	−1.05091	−	0.881819i	−0.0594961	−	0.0499232i
$313$	23.2346	−	8.45672i	1.31330	−	0.478002i	0.411994	−	0.911186i	$-0.364832\pi$
$313$	23.2346	−	8.45672i	1.31330	−	0.478002i	0.901305	+	0.433184i	$0.142610\pi$
$314$	−1.70838	−	9.68871i	−0.0964095	−	0.546766i
$315$	−0.469220	−	2.66108i	−0.0264375	−	0.149935i
$316$	−2.17814	+	0.792777i	−0.122530	+	0.0445972i
$317$	5.39740	+	4.52896i	0.303148	+	0.254372i	0.781653	−	0.623713i	$-0.214377\pi$
$317$	5.39740	+	4.52896i	0.303148	+	0.254372i	−0.478505	+	0.878085i	$0.658821\pi$
$318$	2.44164	+	2.04878i	0.136920	+	0.114890i
$319$	25.7714	+	44.6373i	1.44292	+	2.49921i
$320$	0.939693	+	0.342020i	0.0525304	+	0.0191195i
$321$	−0.512017	+	2.90379i	−0.0285780	+	0.162074i
$322$	−2.60719	+	4.51579i	−0.145293	+	0.251655i
$323$	−11.1245	−	19.2683i	−0.618986	−	1.07211i
$324$	−6.71458	+	2.44391i	−0.373032	+	0.135773i
$325$	1.49327	−	2.58642i	0.0828318	−	0.143469i
$326$	−13.4044	+	11.2476i	−0.742400	+	0.622948i
$327$	4.23067			0.233957
$328$	1.47799	−	1.24018i	0.0816081	−	0.0684774i
$329$	2.58512	+	0.940906i	0.142522	+	0.0518738i
$330$	0.494499	+	2.80444i	0.0272213	+	0.154380i
$331$	−2.19979	+	12.4757i	−0.120912	+	0.685724i	0.862741	+	0.505646i	$0.168746\pi$
$331$	−2.19979	+	12.4757i	−0.120912	+	0.685724i	−0.983652	+	0.180078i	$0.942365\pi$
$332$	12.4642			0.684064
$333$	−15.6981	−	6.43233i	−0.860250	−	0.352490i
$334$	0.853684			0.0467115
$335$	−1.46096	+	8.28550i	−0.0798206	+	0.452685i
$336$	−0.0772808	−	0.438281i	−0.00421601	−	0.0239102i
$337$	−23.0250	−	8.38040i	−1.25425	−	0.456509i	−0.372414	−	0.928067i	$-0.621470\pi$
$337$	−23.0250	−	8.38040i	−1.25425	−	0.456509i	−0.881835	+	0.471557i	$0.843692\pi$
$338$	−3.12589	+	2.62294i	−0.170026	+	0.142669i
$339$	−7.04653			−0.382715
$340$	3.85025	−	3.23075i	0.208809	−	0.175212i
$341$	−11.9531	+	20.7033i	−0.647296	+	1.12115i
$342$	−11.6014	+	4.22257i	−0.627332	+	0.228330i
$343$	−6.32725	−	10.9591i	−0.341639	−	0.591737i
$344$	−2.34430	+	4.06044i	−0.126396	+	0.218924i
$345$	0.429298	−	2.43467i	0.0231127	−	0.131078i
$346$	5.26740	+	1.91718i	0.283177	+	0.103068i
$347$	15.9912	+	27.6975i	0.858451	+	1.48688i	0.873406	+	0.486993i	$0.161906\pi$
$347$	15.9912	+	27.6975i	0.858451	+	1.48688i	−0.0149551	+	0.999888i	$0.504761\pi$
$348$	2.92559	+	2.45486i	0.156828	+	0.131594i
$349$	−14.6001	−	12.2509i	−0.781525	−	0.655777i	0.162107	−	0.986773i	$-0.448171\pi$
$349$	−14.6001	−	12.2509i	−0.781525	−	0.655777i	−0.943632	+	0.330996i	$0.892615\pi$
$350$	0.910424	−	0.331367i	0.0486642	−	0.0177123i
$351$	1.37907	+	7.82108i	0.0736092	+	0.417459i
$352$	−1.07652	−	6.10525i	−0.0573787	−	0.325411i
$353$	0.610203	−	0.222096i	0.0324778	−	0.0118210i	−0.325730	−	0.945463i	$-0.605610\pi$
$353$	0.610203	−	0.222096i	0.0324778	−	0.0118210i	0.358208	+	0.933642i	$0.383388\pi$
$354$	−2.35688	−	1.97766i	−0.125267	−	0.105111i
$355$	4.30937	+	3.61599i	0.228718	+	0.191917i
$356$	−4.50165	−	7.79708i	−0.238587	−	0.413244i
$357$	−2.10195	−	0.765047i	−0.111247	−	0.0404906i
$358$	2.02213	−	11.4680i	0.106873	−	0.606105i
$359$	−2.33634	+	4.04665i	−0.123307	+	0.213574i	−0.921070	−	0.389397i	$-0.872683\pi$
$359$	−2.33634	+	4.04665i	−0.123307	+	0.213574i	0.797763	+	0.602971i	$0.206017\pi$
$360$	−1.39450	−	2.41534i	−0.0734965	−	0.127300i
$361$	−0.559454	+	0.203624i	−0.0294449	+	0.0107171i
$362$	−9.40931	+	16.2974i	−0.494542	+	0.856573i
$363$	9.65317	−	8.09997i	0.506660	−	0.425138i
$364$	2.89352			0.151662
$365$	4.39315	−	3.68629i	0.229948	−	0.192949i
$366$	−3.57702	−	1.30193i	−0.186974	−	0.0680530i
$367$	0.152232	+	0.863352i	0.00794646	+	0.0450666i	0.988523	−	0.151069i	$-0.0482717\pi$
$367$	0.152232	+	0.863352i	0.00794646	+	0.0450666i	−0.980577	+	0.196136i	$0.937161\pi$
$368$	−0.934579	+	5.30026i	−0.0487183	+	0.276295i
$369$	−5.38102			−0.280125
$370$	1.29389	−	5.94355i	0.0672664	−	0.308991i
$371$	−6.72267			−0.349024
$372$	−0.307590	+	1.74443i	−0.0159478	+	0.0904444i
$373$	0.0394266	+	0.223599i	0.00204143	+	0.0115775i	0.985811	−	0.167856i	$-0.0536845\pi$
$373$	0.0394266	+	0.223599i	0.00204143	+	0.0115775i	−0.983770	+	0.179434i	$0.942573\pi$
$374$	−29.2801	−	10.6571i	−1.51404	−	0.551065i
$375$	−0.351882	+	0.295264i	−0.0181711	+	0.0152474i
$376$	2.83947			0.146434
$377$	−19.0212	+	15.9607i	−0.979642	+	0.822017i
$378$	−1.28817	+	2.23118i	−0.0662566	+	0.114760i
$379$	−20.9448	+	7.62330i	−1.07586	+	0.391582i	−0.818367	−	0.574697i	$-0.805120\pi$
$379$	−20.9448	+	7.62330i	−1.07586	+	0.391582i	−0.257497	+	0.966279i	$0.582898\pi$
$380$	−2.21333	−	3.83360i	−0.113542	−	0.196660i
$381$	2.63671	−	4.56691i	0.135083	−	0.233970i
$382$	−2.44957	+	13.8922i	−0.125331	+	0.710786i
$383$	10.3999	+	3.78525i	0.531409	+	0.193417i	0.593767	−	0.804637i	$-0.297640\pi$
$383$	10.3999	+	3.78525i	0.531409	+	0.193417i	−0.0623583	+	0.998054i	$0.519862\pi$
$384$	−0.229675	−	0.397809i	−0.0117205	−	0.0203006i
$385$	−4.60112	−	3.86080i	−0.234495	−	0.196765i
$386$	5.76626	+	4.83847i	0.293495	+	0.246271i
$387$	12.2879	−	4.47242i	0.624627	−	0.227346i
$388$	−1.70523	−	9.67084i	−0.0865699	−	0.490962i
$389$	−3.57160	−	20.2556i	−0.181087	−	1.02700i	−0.930880	−	0.365325i	$-0.880958\pi$
$389$	−3.57160	−	20.2556i	−0.181087	−	1.02700i	0.749793	−	0.661673i	$-0.230153\pi$
$390$	−1.28913	+	0.469206i	−0.0652778	+	0.0237592i
$391$	20.7222	+	17.3880i	1.04796	+	0.879347i
$392$	−4.64324	−	3.89614i	−0.234519	−	0.196785i
$393$	−4.42540	−	7.66502i	−0.223232	−	0.386649i
$394$	−15.7650	−	5.73799i	−0.794229	−	0.289076i
$395$	−0.402503	+	2.28271i	−0.0202521	+	0.114856i
$396$	−8.64510	+	14.9738i	−0.434433	+	0.752459i
$397$	−8.52289	−	14.7621i	−0.427752	−	0.740888i	0.568921	−	0.822392i	$-0.307361\pi$
$397$	−8.52289	−	14.7621i	−0.427752	−	0.740888i	−0.996673	+	0.0815042i	$0.974028\pi$
$398$	19.7038	−	7.17158i	0.987660	−	0.359479i
$399$	−0.985027	+	1.70612i	−0.0493130	+	0.0854126i
$400$	0.766044	−	0.642788i	0.0383022	−	0.0321394i
$401$	−0.653975			−0.0326579			−0.0163290	−	0.999867i	$-0.505198\pi$
$401$	−0.653975			−0.0326579			−0.0163290	+	0.999867i	$0.505198\pi$
$402$	2.96050	−	2.48415i	0.147656	−	0.123898i
$403$	−10.8221	−	3.93893i	−0.539088	−	0.196212i
$404$	−3.10957	−	17.6352i	−0.154707	−	0.877386i
$405$	−1.24080	+	7.03695i	−0.0616560	+	0.349669i
$406$	−8.05514			−0.399770
$407$	−35.9208	+	11.4766i	−1.78053	+	0.568873i
$408$	−2.30876			−0.114301
$409$	−1.25252	+	7.10342i	−0.0619333	+	0.351241i	0.938055	+	0.346485i	$0.112625\pi$
$409$	−1.25252	+	7.10342i	−0.0619333	+	0.351241i	−0.999989	+	0.00475598i	$0.998486\pi$
$410$	−0.335032	−	1.90006i	−0.0165461	−	0.0938374i
$411$	−6.93435	−	2.52390i	−0.342046	−	0.124495i
$412$	8.98974	−	7.54328i	0.442892	−	0.371631i
$413$	6.48931			0.319318
$414$	11.4987	−	9.64853i	0.565129	−	0.474200i
$415$	6.23212	−	10.7943i	0.305923	−	0.529873i
$416$	2.80643	−	1.02146i	0.137597	−	0.0500811i
$417$	1.09181	+	1.89107i	0.0534663	+	0.0926063i
$418$	−13.7214	+	23.7662i	−0.671136	+	1.16244i
$419$	0.724675	−	4.10984i	0.0354027	−	0.200779i	−0.961976	−	0.273133i	$-0.911940\pi$
$419$	0.724675	−	4.10984i	0.0354027	−	0.200779i	0.997379	+	0.0723542i	$0.0230512\pi$
$420$	−0.418203	−	0.152213i	−0.0204062	−	0.00742726i
$421$	10.1443	+	17.5704i	0.494402	+	0.856330i	0.999979	−	0.00645167i	$-0.00205364\pi$
$421$	10.1443	+	17.5704i	0.494402	+	0.856330i	−0.505577	+	0.862782i	$0.668720\pi$
$422$	−7.61644	−	6.39095i	−0.370762	−	0.311107i
$423$	−6.06651	−	5.09041i	−0.294964	−	0.247504i
$424$	−6.52033	+	2.37321i	−0.316655	+	0.115253i
$425$	−0.872782	−	4.94979i	−0.0423361	−	0.240100i
$426$	−0.448718	−	2.54481i	−0.0217405	−	0.123296i
$427$	7.54460	−	2.74601i	0.365109	−	0.132889i
$428$	−4.91728	−	4.12608i	−0.237686	−	0.199442i
$429$	6.51505	+	5.46678i	0.314550	+	0.263939i
$430$	2.34430	+	4.06044i	0.113052	+	0.195812i
$431$	16.8399	+	6.12923i	0.811151	+	0.295235i	0.714099	−	0.700045i	$-0.246837\pi$
$431$	16.8399	+	6.12923i	0.811151	+	0.295235i	0.0970518	+	0.995279i	$0.469059\pi$
$432$	−0.461761	+	2.61878i	−0.0222165	+	0.125996i
$433$	13.4362	−	23.2722i	0.645704	−	1.11839i	−0.338434	−	0.940990i	$-0.609897\pi$
$433$	13.4362	−	23.2722i	0.645704	−	1.11839i	0.984138	−	0.177402i	$-0.0567694\pi$
$434$	−1.86804	−	3.23554i	−0.0896687	−	0.155311i
$435$	3.58876	−	1.30620i	0.172068	−	0.0626276i
$436$	−4.60507	+	7.97621i	−0.220543	+	0.381991i
$437$	18.2506	−	15.3140i	0.873043	−	0.732570i
$438$	−2.63430			−0.125872
$439$	−5.52408	+	4.63526i	−0.263650	+	0.221229i	−0.765024	−	0.644002i	$-0.777273\pi$
$439$	−5.52408	+	4.63526i	−0.263650	+	0.221229i	0.501373	+	0.865231i	$0.332828\pi$
$440$	−5.82556	−	2.12033i	−0.277723	−	0.101083i
$441$	2.93553	+	16.6482i	0.139787	+	0.792771i
$442$	2.60660	−	14.7828i	0.123983	−	0.703144i
$443$	5.69596			0.270623			0.135312	−	0.990803i	$-0.456796\pi$
$443$	5.69596			0.270623			0.135312	+	0.990803i	$0.456796\pi$
$444$	−2.21022	+	1.70939i	−0.104892	+	0.0811241i
$445$	−9.00329			−0.426797
$446$	−3.50744	+	19.8917i	−0.166082	+	0.941898i
$447$	1.08204	+	6.13655i	0.0511787	+	0.290249i
$448$	0.910424	+	0.331367i	0.0430135	+	0.0156556i
$449$	−1.38412	+	1.16142i	−0.0653207	+	0.0548106i	−0.674863	−	0.737943i	$-0.735797\pi$
$449$	−1.38412	+	1.16142i	−0.0653207	+	0.0548106i	0.609543	+	0.792753i	$0.291353\pi$
$450$	−2.78900			−0.131475
$451$	−9.16267	+	7.68840i	−0.431453	+	0.362032i
$452$	7.67011	−	13.2850i	0.360772	−	0.624875i
$453$	3.75547	−	1.36688i	0.176447	−	0.0642215i
$454$	4.86311	+	8.42316i	0.228237	+	0.395319i
$455$	1.44676	−	2.50586i	0.0678252	−	0.117477i
$456$	−0.353094	+	2.00250i	−0.0165351	+	0.0937754i
$457$	1.11598	+	0.406182i	0.0522031	+	0.0190004i	0.367990	−	0.929830i	$-0.380046\pi$
$457$	1.11598	+	0.406182i	0.0522031	+	0.0190004i	−0.315787	+	0.948830i	$0.602268\pi$
$458$	0.239981	+	0.415660i	0.0112136	+	0.0194225i
$459$	10.2385	+	8.59112i	0.477892	+	0.400999i
$460$	4.12287	+	3.45950i	0.192230	+	0.161300i
$461$	26.3469	−	9.58948i	1.22710	−	0.446627i	0.354494	−	0.935058i	$-0.384653\pi$
$461$	26.3469	−	9.58948i	1.22710	−	0.446627i	0.872602	+	0.488432i	$0.162431\pi$
$462$	0.479097	+	2.71709i	0.0222896	+	0.126411i
$463$	5.53376	+	31.3835i	0.257176	+	1.45852i	0.790426	+	0.612558i	$0.209859\pi$
$463$	5.53376	+	31.3835i	0.257176	+	1.45852i	−0.533250	+	0.845958i	$0.679029\pi$
$464$	−7.81270	+	2.84359i	−0.362696	+	0.132010i
$465$	1.35692	+	1.13859i	0.0629259	+	0.0528011i
$466$	14.1392	+	11.8642i	0.654987	+	0.549599i
$467$	11.3663	+	19.6870i	0.525970	+	0.911006i	0.999542	+	0.0302513i	$0.00963075\pi$
$467$	11.3663	+	19.6870i	0.525970	+	0.911006i	−0.473573	+	0.880755i	$0.657036\pi$
$468$	−7.82713	−	2.84884i	−0.361809	−	0.131688i
$469$	−1.41545	+	8.02743i	−0.0653595	+	0.370672i
$470$	1.41973	−	2.45905i	0.0654874	−	0.113428i
$471$	2.25958	+	3.91371i	0.104116	+	0.180334i
$472$	6.29399	−	2.29083i	0.289705	−	0.105444i
$473$	14.5333	−	25.1724i	0.668242	−	1.15743i
$474$	0.815637	−	0.684401i	0.0374634	−	0.0314356i
$475$	−4.42666			−0.203109
$476$	3.73033	−	3.13012i	0.170979	−	0.143469i
$477$	18.1852	+	6.61887i	0.832643	+	0.303057i
$478$	−4.79090	−	27.1705i	−0.219131	−	1.24275i
$479$	3.21074	−	18.2090i	0.146702	−	0.831991i	−0.819282	−	0.573391i	$-0.805628\pi$
$479$	3.21074	−	18.2090i	0.146702	−	0.831991i	0.965984	−	0.258600i	$-0.0832612\pi$
$480$	−0.459350			−0.0209664
$481$	−8.44971	−	16.0817i	−0.385274	−	0.733263i
$482$	24.7494			1.12730
$483$	0.415927	−	2.35884i	0.0189253	−	0.107331i
$484$	4.76368	+	27.0162i	0.216531	+	1.22801i
$485$	−9.22781	−	3.35865i	−0.419013	−	0.152508i
$486$	8.62551	−	7.23767i	0.391261	−	0.328307i
$487$	22.7287			1.02994			0.514968	−	0.857210i	$-0.327804\pi$
$487$	22.7287			1.02994			0.514968	+	0.857210i	$0.327804\pi$
$488$	6.34814	−	5.32672i	0.287367	−	0.241129i
$489$	4.01889	−	6.96093i	0.181741	−	0.314784i
$490$	−5.69578	+	2.07309i	−0.257309	+	0.0936529i
$491$	−21.1739	−	36.6743i	−0.955566	−	1.65509i	−0.733067	−	0.680156i	$-0.761912\pi$
$491$	−21.1739	−	36.6743i	−0.955566	−	1.65509i	−0.222499	−	0.974933i	$-0.571422\pi$
$492$	−0.443129	+	0.767521i	−0.0199778	+	0.0346025i
$493$	−7.25640	+	41.1531i	−0.326812	+	1.85344i
$494$	−12.4231	−	4.52165i	−0.558943	−	0.203439i
$495$	8.64510	+	14.9738i	0.388568	+	0.673020i
$496$	−2.95401	−	2.47871i	−0.132639	−	0.111297i
$497$	4.17514	+	3.50336i	0.187281	+	0.157147i
$498$	−5.38016	+	1.95822i	−0.241091	+	0.0877498i
$499$	−1.46178	−	8.29019i	−0.0654385	−	0.371120i	−0.999887	−	0.0150222i	$-0.995218\pi$
$499$	−1.46178	−	8.29019i	−0.0654385	−	0.371120i	0.934449	−	0.356098i	$-0.115893\pi$
$500$	−0.173648	−	0.984808i	−0.00776578	−	0.0440419i
$501$	−0.368491	+	0.134120i	−0.0164629	+	0.00599202i
$502$	−17.8656	−	14.9910i	−0.797380	−	0.669081i
$503$	−30.2388	−	25.3733i	−1.34828	−	1.13134i	−0.979415	−	0.201858i	$-0.935302\pi$
$503$	−30.2388	−	25.3733i	−1.34828	−	1.13134i	−0.368865	−	0.929483i	$-0.620254\pi$
$504$	−1.35106	−	2.34011i	−0.0601812	−	0.104237i
$505$	−16.8273	−	6.12465i	−0.748807	−	0.272543i
$506$	5.79386	−	32.8586i	0.257568	−	1.46074i
$507$	0.937203	−	1.62328i	0.0416227	−	0.0720926i
$508$	5.74008	+	9.94212i	0.254675	+	0.441110i
$509$	−12.5134	+	4.55452i	−0.554648	+	0.201875i	−0.604111	−	0.796901i	$-0.706471\pi$
$509$	−12.5134	+	4.55452i	−0.554648	+	0.201875i	0.0494622	+	0.998776i	$0.484249\pi$
$510$	−1.15438	+	1.99945i	−0.0511168	+	0.0885369i
$511$	4.25632	−	3.57148i	0.188289	−	0.157993i
$512$	1.00000			0.0441942
$513$	9.01732	−	7.56643i	0.398124	−	0.334066i
$514$	23.2799	+	8.47321i	1.02683	+	0.373737i
$515$	−2.03781	−	11.5570i	−0.0897965	−	0.509261i
$516$	0.373987	−	2.12098i	0.0164639	−	0.0933711i
$517$	−17.6031			−0.774182
$518$	1.25359	−	5.75843i	0.0550797	−	0.253011i
$519$	−2.57486			−0.113024
$520$	0.518608	−	2.94117i	0.0227424	−	0.128979i
$521$	−1.15349	−	6.54176i	−0.0505352	−	0.286600i	0.949059	−	0.315100i	$-0.102038\pi$
$521$	−1.15349	−	6.54176i	−0.0505352	−	0.286600i	−0.999594	+	0.0285002i	$0.990927\pi$
$522$	21.7896	+	7.93077i	0.953705	+	0.347120i
$523$	21.3508	−	17.9155i	0.933606	−	0.783389i	−0.0428550	−	0.999081i	$-0.513645\pi$
$523$	21.3508	−	17.9155i	0.933606	−	0.783389i	0.976461	+	0.215693i	$0.0692009\pi$
$524$	19.2681			0.841732
$525$	−0.340922	+	0.286068i	−0.0148791	+	0.0124850i
$526$	−6.36171	+	11.0188i	−0.277384	+	0.480443i
$527$	−18.2129	+	6.62896i	−0.793367	+	0.288762i
$528$	1.42385	+	2.46619i	0.0619653	+	0.107327i
$529$	−2.98309	+	5.16686i	−0.129700	+	0.224646i
$530$	−1.20491	+	6.83338i	−0.0523379	+	0.296823i
$531$	−17.5539	−	6.38911i	−0.761776	−	0.277264i
$532$	−2.14439	−	3.71420i	−0.0929712	−	0.161031i
$533$	−4.41407	−	3.70384i	−0.191195	−	0.160431i
$534$	3.16810	+	2.65835i	0.137097	+	0.115038i
$535$	−6.03193	+	2.19544i	−0.260783	+	0.0949173i
$536$	1.46096	+	8.28550i	0.0631037	+	0.357879i
$537$	0.928863	+	5.26785i	0.0400834	+	0.227324i
$538$	−7.97961	+	2.90434i	−0.344025	+	0.125215i
$539$	28.7855	+	24.1539i	1.23988	+	1.04038i
$540$	2.03705	+	1.70928i	0.0876605	+	0.0735559i
$541$	−10.2728	−	17.7930i	−0.441661	−	0.764980i	0.556151	−	0.831081i	$-0.312277\pi$
$541$	−10.2728	−	17.7930i	−0.441661	−	0.764980i	−0.997813	+	0.0661008i	$0.978944\pi$
$542$	10.6386	+	3.87214i	0.456968	+	0.166323i
$543$	1.50107	−	8.51300i	0.0644172	−	0.365328i
$544$	2.51307	−	4.35277i	0.107747	−	0.186624i
$545$	4.60507	+	7.97621i	0.197259	+	0.341663i
$546$	−1.24898	+	0.454592i	−0.0534515	+	0.0194547i
$547$	14.6998	−	25.4607i	0.628517	−	1.08862i	−0.359333	−	0.933209i	$-0.616996\pi$
$547$	14.6998	−	25.4607i	0.628517	−	1.08862i	0.987850	−	0.155413i	$-0.0496709\pi$
$548$	12.3064	−	10.3263i	0.525702	−	0.441117i
$549$	−23.1122			−0.986403
$550$	−4.74904	+	3.98492i	−0.202500	+	0.169917i
$551$	34.5842	+	12.5876i	1.47334	+	0.536251i
$552$	−0.429298	−	2.43467i	−0.0182722	−	0.103627i
$553$	−0.389967	+	2.21161i	−0.0165831	+	0.0940473i
$554$	−6.74584			−0.286603
$555$	0.375267	+	2.76880i	0.0159292	+	0.117529i
$556$	−4.75373			−0.201603
$557$	−4.48910	+	25.4590i	−0.190209	+	1.07873i	0.728868	+	0.684654i	$0.240047\pi$
$557$	−4.48910	+	25.4590i	−0.190209	+	1.07873i	−0.919077	+	0.394077i	$0.871064\pi$
$558$	1.86757	+	10.5915i	0.0790605	+	0.448374i
$559$	13.1582	+	4.78920i	0.556533	+	0.202562i
$560$	0.742184	−	0.622767i	0.0313630	−	0.0263167i
$561$	14.3130			0.604295
$562$	13.4410	−	11.2784i	0.566976	−	0.475749i
$563$	−2.52255	+	4.36919i	−0.106313	+	0.184139i	−0.914274	−	0.405097i	$-0.867238\pi$
$563$	−2.52255	+	4.36919i	−0.106313	+	0.184139i	0.807961	+	0.589236i	$0.200571\pi$
$564$	−1.22565	+	0.446100i	−0.0516091	+	0.0187842i
$565$	−7.67011	−	13.2850i	−0.322684	−	0.558905i
$566$	−3.57048	+	6.18425i	−0.150078	+	0.259943i
$567$	−1.20216	+	6.81777i	−0.0504858	+	0.286319i
$568$	5.28622	+	1.92403i	0.221805	+	0.0807304i
$569$	−18.7817	−	32.5308i	−0.787369	−	1.36376i	−0.927574	−	0.373640i	$-0.878110\pi$
$569$	−18.7817	−	32.5308i	−0.787369	−	1.36376i	0.140205	−	0.990122i	$-0.455224\pi$
$570$	1.55767	+	1.30704i	0.0652434	+	0.0547457i
$571$	15.1977	+	12.7524i	0.636004	+	0.533671i	0.902788	−	0.430086i	$-0.141517\pi$
$571$	15.1977	+	12.7524i	0.636004	+	0.533671i	−0.266784	+	0.963756i	$0.585961\pi$
$572$	−17.3983	+	6.33246i	−0.727459	+	0.264773i
$573$	−1.12521	−	6.38137i	−0.0470062	−	0.266586i
$574$	−0.324597	−	1.84088i	−0.0135484	−	0.0768369i
$575$	5.05745	−	1.84076i	0.210910	−	0.0767650i
$576$	−2.13650	−	1.79273i	−0.0890207	−	0.0746972i
$577$	−3.97300	−	3.33374i	−0.165398	−	0.138786i	0.556332	−	0.830960i	$-0.312208\pi$
$577$	−3.97300	−	3.33374i	−0.165398	−	0.138786i	−0.721730	+	0.692175i	$0.756653\pi$
$578$	−4.13109	−	7.15525i	−0.171831	−	0.297619i
$579$	−3.24915	−	1.18259i	−0.135030	−	0.0491469i
$580$	−1.44373	+	8.18779i	−0.0599476	+	0.339980i
$581$	6.03800	−	10.4581i	0.250499	−	0.433876i
$582$	2.25541	+	3.90649i	0.0934899	+	0.161929i
$583$	40.4224	−	14.7125i	1.67412	−	0.609331i
$584$	2.86743	−	4.96653i	0.118655	−	0.205516i
$585$	−6.38074	+	5.35407i	−0.263811	+	0.221364i
$586$	−5.88229			−0.242995
$587$	22.9835	−	19.2854i	0.948631	−	0.795996i	−0.0304357	−	0.999537i	$-0.509689\pi$
$587$	22.9835	−	19.2854i	0.948631	−	0.795996i	0.979066	+	0.203541i	$0.0652450\pi$
$588$	2.61636	+	0.952276i	0.107897	+	0.0392712i
$589$	2.96418	+	16.8107i	0.122137	+	0.692673i
$590$	1.16308	−	6.59617i	0.0478834	−	0.271560i
$591$	7.70640			0.316999
$592$	−0.816952	−	6.02765i	−0.0335765	−	0.247735i
$593$	9.38044			0.385209			0.192604	−	0.981277i	$-0.438307\pi$
$593$	9.38044			0.385209			0.192604	+	0.981277i	$0.438307\pi$
$594$	2.86265	−	16.2349i	0.117456	−	0.666127i
$595$	−0.845597	−	4.79562i	−0.0346661	−	0.196601i
$596$	−12.7472	−	4.63960i	−0.522146	−	0.190045i
$597$	−7.37838	+	6.19119i	−0.301977	+	0.253389i
$598$	16.0736			0.657300
$599$	15.2838	−	12.8246i	0.624480	−	0.524001i	−0.274728	−	0.961522i	$-0.588588\pi$
$599$	15.2838	−	12.8246i	0.624480	−	0.524001i	0.899208	+	0.437521i	$0.144144\pi$
$600$	−0.229675	+	0.397809i	−0.00937644	+	0.0162405i
$601$	38.1356	−	13.8802i	1.55558	−	0.566187i	0.585866	−	0.810408i	$-0.300755\pi$
$601$	38.1356	−	13.8802i	1.55558	−	0.566187i	0.969719	+	0.244222i	$0.0785325\pi$
$602$	2.27128	+	3.93397i	0.0925704	+	0.160337i
$603$	11.7324	−	20.3210i	0.477778	−	0.827537i
$604$	−1.51079	+	8.56813i	−0.0614733	+	0.348632i
$605$	25.7785	+	9.38262i	1.04805	+	0.381458i
$606$	4.11285	+	7.12367i	0.167073	+	0.289379i
$607$	−10.7466	−	9.01749i	−0.436192	−	0.366009i	0.398090	−	0.917346i	$-0.369673\pi$
$607$	−10.7466	−	9.01749i	−0.436192	−	0.366009i	−0.834282	+	0.551338i	$0.814118\pi$
$608$	−3.39102	−	2.84541i	−0.137524	−	0.115396i
$609$	3.47698	−	1.26552i	0.140894	−	0.0512814i
$610$	−1.43901	−	8.16101i	−0.0582637	−	0.330430i
$611$	−1.47257	−	8.35135i	−0.0595738	−	0.337860i
$612$	−13.1725	+	4.79441i	−0.532468	+	0.193803i
$613$	−16.8888	−	14.1714i	−0.682131	−	0.572376i	0.234497	−	0.972117i	$-0.424656\pi$
$613$	−16.8888	−	14.1714i	−0.682131	−	0.572376i	−0.916628	+	0.399741i	$0.869100\pi$
$614$	16.2153	+	13.6063i	0.654397	+	0.549105i
$615$	0.443129	+	0.767521i	0.0178687	+	0.0309495i
$616$	−5.64411	−	2.05429i	−0.227408	−	0.0827696i
$617$	3.19325	−	18.1098i	0.128555	−	0.729074i	−0.850577	−	0.525851i	$-0.823747\pi$
$617$	3.19325	−	18.1098i	0.128555	−	0.729074i	0.979132	−	0.203223i	$-0.0651418\pi$
$618$	−2.69530	+	4.66839i	−0.108421	+	0.187790i
$619$	−12.5096	−	21.6672i	−0.502803	−	0.870880i	−0.999995	−	0.00323919i	$-0.998969\pi$
$619$	−12.5096	−	21.6672i	−0.502803	−	0.870880i	0.497192	−	0.867640i	$-0.334364\pi$
$620$	−3.62363	+	1.31889i	−0.145529	+	0.0529680i
$621$	−7.15587	+	12.3943i	−0.287155	+	0.497367i
$622$	−3.15694	+	2.64899i	−0.126582	+	0.106215i
$623$	−8.72287			−0.349474
$624$	−1.05091	+	0.881819i	−0.0420701	+	0.0353010i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−4.29359	−	24.3502i	−0.171606	−	0.973228i
$627$	2.18898	−	12.4143i	0.0874195	−	0.495781i
$628$	−9.83818			−0.392586
$629$	−28.2901	−	11.5919i	−1.12800	−	0.462201i
$630$	−2.70213			−0.107655
$631$	−7.01038	+	39.7579i	−0.279079	+	1.58274i	0.446621	+	0.894723i	$0.352627\pi$
$631$	−7.01038	+	39.7579i	−0.279079	+	1.58274i	−0.725700	+	0.688012i	$0.758484\pi$
$632$	0.402503	+	2.28271i	0.0160107	+	0.0908014i
$633$	4.29168	+	1.56204i	0.170579	+	0.0620857i
$634$	5.39740	−	4.52896i	0.214358	−	0.179868i
$635$	11.4802			0.455577
$636$	2.44164	−	2.04878i	0.0968173	−	0.0812393i
$637$	−9.05120	+	15.6771i	−0.358622	+	0.621151i
$638$	48.4343	−	17.6286i	1.91753	−	0.697925i
$639$	−7.84473	−	13.5875i	−0.310333	−	0.537512i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	0.0663347	−	0.376203i	0.00262006	−	0.0148591i	−0.983470	−	0.181073i	$-0.942043\pi$
$641$	0.0663347	−	0.376203i	0.00262006	−	0.0148591i	0.986090	+	0.166214i	$0.0531541\pi$
$642$	2.77077	+	1.00848i	0.109353	+	0.0398014i
$643$	15.5785	+	26.9828i	0.614357	+	1.06410i	0.990497	+	0.137535i	$0.0439179\pi$
$643$	15.5785	+	26.9828i	0.614357	+	1.06410i	−0.376140	+	0.926563i	$0.622749\pi$
$644$	3.99445	+	3.35174i	0.157404	+	0.132077i
$645$	−1.64983	−	1.38437i	−0.0649621	−	0.0545097i
$646$	−20.9073	+	7.60963i	−0.822586	+	0.299397i
$647$	4.85840	+	27.5533i	0.191003	+	1.08323i	0.917996	+	0.396589i	$0.129806\pi$
$647$	4.85840	+	27.5533i	0.191003	+	1.08323i	−0.726993	+	0.686645i	$0.759083\pi$
$648$	1.24080	+	7.03695i	0.0487434	+	0.276437i
$649$	−39.0192	+	14.2018i	−1.53164	+	0.557470i
$650$	−2.28782	−	1.91971i	−0.0897358	−	0.0752973i
$651$	1.31466	+	1.10313i	0.0515256	+	0.0432351i
$652$	8.74909	+	15.1539i	0.342641	+	0.593471i
$653$	−30.7883	−	11.2060i	−1.20484	−	0.438525i	−0.339928	−	0.940451i	$-0.610403\pi$
$653$	−30.7883	−	11.2060i	−1.20484	−	0.438525i	−0.864911	+	0.501926i	$0.832625\pi$
$654$	0.734648	−	4.16640i	0.0287270	−	0.162919i
$655$	9.63406	−	16.6867i	0.376434	−	0.652003i
$656$	−0.964687	−	1.67089i	−0.0376647	−	0.0652372i
$657$	−15.0299	+	5.47044i	−0.586373	+	0.213422i
$658$	1.37551	−	2.38246i	0.0536231	−	0.0928779i
$659$	9.00862	−	7.55913i	0.350926	−	0.294462i	−0.450236	−	0.892910i	$-0.648660\pi$
$659$	9.00862	−	7.55913i	0.350926	−	0.294462i	0.801162	+	0.598448i	$0.204216\pi$
$660$	2.84771			0.110847
$661$	−3.52734	+	2.95979i	−0.137198	+	0.115123i	−0.708804	−	0.705405i	$-0.750765\pi$
$661$	−3.52734	+	2.95979i	−0.137198	+	0.115123i	0.571606	+	0.820528i	$0.306320\pi$
$662$	11.9041	+	4.33275i	0.462667	+	0.168397i
$663$	1.19734	+	6.79046i	0.0465009	+	0.263719i
$664$	2.16439	−	12.2749i	0.0839947	−	0.476357i
$665$	−4.28879			−0.166312
$666$	−9.06056	+	14.3426i	−0.351089	+	0.555766i
$667$	−44.7467			−1.73260
$668$	0.148241	−	0.840715i	0.00573560	−	0.0325282i
$669$	−1.61114	−	9.13723i	−0.0622903	−	0.353266i
$670$	7.90593	+	2.87752i	0.305433	+	0.111168i
$671$	−39.3549	+	33.0226i	−1.51928	+	1.27483i
$672$	−0.445042			−0.0171679
$673$	−4.79938	+	4.02716i	−0.185002	+	0.155235i	−0.730585	−	0.682821i	$-0.760753\pi$
$673$	−4.79938	+	4.02716i	−0.185002	+	0.155235i	0.545583	+	0.838057i	$0.316308\pi$
$674$	−12.2513	+	21.2199i	−0.471903	+	0.817361i
$675$	2.49881	−	0.909491i	0.0961791	−	0.0350063i
$676$	2.04028	+	3.53387i	0.0784724	+	0.135918i
$677$	25.3282	−	43.8697i	0.973440	−	1.68605i	0.288451	−	0.957495i	$-0.406860\pi$
$677$	25.3282	−	43.8697i	0.973440	−	1.68605i	0.684989	−	0.728553i	$-0.259807\pi$
$678$	−1.22362	+	6.93948i	−0.0469927	+	0.266509i
$679$	−8.94039	−	3.25403i	−0.343101	−	0.124878i
$680$	−2.51307	−	4.35277i	−0.0963720	−	0.166921i
$681$	−3.42249	−	2.87181i	−0.131150	−	0.110048i
$682$	18.3132	+	15.3666i	0.701248	+	0.588417i
$683$	−28.6996	+	10.4458i	−1.09816	+	0.399697i	−0.826637	−	0.562735i	$-0.809749\pi$
$683$	−28.6996	+	10.4458i	−1.09816	+	0.399697i	−0.271521	+	0.962432i	$0.587527\pi$
$684$	2.14385	+	12.1584i	0.0819723	+	0.464888i
$685$	−2.78963	−	15.8208i	−0.106586	−	0.604481i
$686$	−11.8913	+	4.32809i	−0.454014	+	0.165247i
$687$	−0.168890	−	0.141716i	−0.00644357	−	0.00540679i
$688$	3.59167	+	3.01377i	0.136931	+	0.114899i
$689$	10.3615	+	17.9466i	0.394742	+	0.683713i
$690$	−2.32314	−	0.845553i	−0.0884403	−	0.0321897i
$691$	2.17891	−	12.3572i	0.0828897	−	0.470091i	−0.914902	−	0.403675i	$-0.867733\pi$
$691$	2.17891	−	12.3572i	0.0828897	−	0.470091i	0.997792	−	0.0664158i	$-0.0211564\pi$
$692$	2.80272	−	4.85446i	0.106544	−	0.184539i
$693$	8.37583	+	14.5074i	0.318172	+	0.551089i
$694$	30.0536	−	10.9386i	1.14082	−	0.415224i
$695$	−2.37687	+	4.11685i	−0.0901596	+	0.156161i
$696$	2.92559	−	2.45486i	0.110894	−	0.0930512i
$697$	−9.69732			−0.367312
$698$	−14.6001	+	12.2509i	−0.552622	+	0.463705i
$699$	−7.96711	−	2.89979i	−0.301344	−	0.109680i
$700$	−0.168240	−	0.954134i	−0.00635886	−	0.0360629i
$701$	5.00357	−	28.3767i	0.188982	−	1.07177i	−0.731749	−	0.681574i	$-0.761296\pi$
$701$	5.00357	−	28.3767i	0.188982	−	1.07177i	0.920731	−	0.390197i	$-0.127593\pi$
$702$	7.94174			0.299742
$703$	−14.3808	+	22.7645i	−0.542382	+	0.858578i
$704$	−6.19943			−0.233650
$705$	−0.226491	+	1.28449i	−0.00853014	+	0.0483768i
$706$	−0.112761	−	0.639500i	−0.00424382	−	0.0240679i
$707$	−16.3032	−	5.93389i	−0.613146	−	0.223167i
$708$	−2.35688	+	1.97766i	−0.0885771	+	0.0743250i
$709$	−10.7788			−0.404808			−0.202404	−	0.979302i	$-0.564875\pi$
$709$	−10.7788			−0.404808			−0.202404	+	0.979302i	$0.564875\pi$
$710$	4.30937	−	3.61599i	0.161728	−	0.135706i
$711$	3.23234	−	5.59858i	0.121222	−	0.209963i
$712$	−8.46033	+	3.07931i	−0.317064	+	0.115402i
$713$	−10.3770	−	17.9736i	−0.388623	−	0.673116i
$714$	−1.11842	+	1.93717i	−0.0418560	+	0.0724967i
$715$	−3.21507	+	18.2336i	−0.120237	+	0.681897i
$716$	−10.9427	−	3.98281i	−0.408947	−	0.148845i
$717$	6.33666	+	10.9754i	0.236647	+	0.409884i
$718$	3.57947	+	3.00354i	0.133585	+	0.112091i
$719$	16.1782	+	13.5751i	0.603345	+	0.506266i	0.892519	−	0.451010i	$-0.148936\pi$
$719$	16.1782	+	13.5751i	0.603345	+	0.506266i	−0.289174	+	0.957276i	$0.593381\pi$
$720$	−2.62080	+	0.953893i	−0.0976715	+	0.0355495i
$721$	−1.97434	−	11.1970i	−0.0735281	−	0.416999i
$722$	0.103383	+	0.586313i	0.00384751	+	0.0218203i
$723$	−10.6830	+	3.88829i	−0.397305	+	0.144607i
$724$	14.4159	+	12.0964i	0.535763	+	0.449558i
$725$	6.36897	+	5.34420i	0.236538	+	0.198479i
$726$	−6.30066	−	10.9131i	−0.233839	−	0.405022i
$727$	−41.3321	−	15.0436i	−1.53292	−	0.557938i	−0.568587	−	0.822623i	$-0.692510\pi$
$727$	−41.3321	−	15.0436i	−1.53292	−	0.557938i	−0.964335	+	0.264686i	$0.914732\pi$
$728$	0.502454	−	2.84956i	0.0186222	−	0.105612i
$729$	8.13216	−	14.0853i	0.301191	−	0.521678i
$730$	−2.86743	−	4.96653i	−0.106128	−	0.183820i
$731$	22.1444	−	8.05990i	0.819040	−	0.298106i
$732$	−1.90329	+	3.29660i	−0.0703478	+	0.121846i
$733$	21.7610	−	18.2597i	0.803761	−	0.674436i	−0.145349	−	0.989380i	$-0.546430\pi$
$733$	21.7610	−	18.2597i	0.803761	−	0.674436i	0.949110	+	0.314945i	$0.101986\pi$
$734$	0.876671			0.0323585
$735$	2.13287	−	1.78969i	0.0786722	−	0.0660138i
$736$	5.05745	+	1.84076i	0.186420	+	0.0678513i
$737$	−9.05710	−	51.3654i	−0.333623	−	1.89207i
$738$	−0.934404	+	5.29927i	−0.0343959	+	0.195069i
$739$	49.5330			1.82210			0.911050	−	0.412295i	$-0.135273\pi$
$739$	49.5330			1.82210			0.911050	+	0.412295i	$0.135273\pi$
$740$	−5.62858	−	2.30632i	−0.206911	−	0.0847822i
$741$	6.07280			0.223090
$742$	−1.16738	+	6.62054i	−0.0428558	+	0.243048i
$743$	3.73057	+	21.1571i	0.136861	+	0.776180i	0.973545	+	0.228494i	$0.0733801\pi$
$743$	3.73057	+	21.1571i	0.136861	+	0.776180i	−0.836684	+	0.547686i	$0.815509\pi$
$744$	1.66451	+	0.605834i	0.0610240	+	0.0222109i
$745$	−10.3916	+	8.71960i	−0.380719	+	0.319461i
$746$	0.227048			0.00831284
$747$	−26.6298	+	22.3450i	−0.974333	+	0.817562i
$748$	−15.5796	+	26.9847i	−0.569648	+	0.986659i
$749$	−5.84406	+	2.12706i	−0.213537	+	0.0777212i
$750$	0.229675	+	0.397809i	0.00838654	+	0.0145259i
$751$	−15.4300	+	26.7256i	−0.563050	+	0.975231i	0.434178	+	0.900827i	$0.357039\pi$
$751$	−15.4300	+	26.7256i	−0.563050	+	0.975231i	−0.997228	+	0.0744039i	$0.976295\pi$
$752$	0.493068	−	2.79633i	0.0179803	−	0.101972i
$753$	10.0668	+	3.66402i	0.366855	+	0.133524i
$754$	12.4152	+	21.5038i	0.452135	+	0.783121i
$755$	6.66482	+	5.59245i	0.242558	+	0.203530i
$756$	1.97360	+	1.65605i	0.0717791	+	0.0602298i
$757$	15.8168	−	5.75684i	0.574871	−	0.209236i	−0.0381916	−	0.999270i	$-0.512160\pi$
$757$	15.8168	−	5.75684i	0.574871	−	0.209236i	0.613062	+	0.790035i	$0.289938\pi$
$758$	3.87045	+	21.9504i	0.140581	+	0.797275i
$759$	2.66141	+	15.0936i	0.0966029	+	0.547862i
$760$	−4.15970	+	1.51401i	−0.150888	+	0.0549189i
$761$	19.4089	+	16.2860i	0.703573	+	0.590368i	0.922788	−	0.385309i	$-0.125905\pi$
$761$	19.4089	+	16.2860i	0.703573	+	0.590368i	−0.219214	+	0.975677i	$0.570349\pi$
$762$	−4.03967	−	3.38968i	−0.146342	−	0.122795i
$763$	4.46163	+	7.72777i	0.161522	+	0.279764i
$764$	13.2558	+	4.82471i	0.479577	+	0.174552i
$765$	−2.43419	+	13.8050i	−0.0880082	+	0.499119i
$766$	5.53366	−	9.58458i	0.199939	−	0.346305i
$767$	−10.0018	−	17.3237i	−0.361145	−	0.625521i
$768$	−0.431648	+	0.157107i	−0.0155757	+	0.00566911i
$769$	−8.28078	+	14.3427i	−0.298612	+	0.517212i	−0.975819	−	0.218581i	$-0.929857\pi$
$769$	−8.28078	+	14.3427i	−0.298612	+	0.517212i	0.677206	+	0.735793i	$0.263190\pi$
$770$	−4.60112	+	3.86080i	−0.165813	+	0.139134i
$771$	−11.3799			−0.409838
$772$	5.76626	−	4.83847i	0.207532	−	0.174140i
$773$	−3.85875	−	1.40447i	−0.138790	−	0.0505153i	0.271691	−	0.962384i	$-0.412417\pi$
$773$	−3.85875	−	1.40447i	−0.138790	−	0.0505153i	−0.410481	+	0.911869i	$0.634639\pi$
$774$	−2.27071	−	12.8778i	−0.0816189	−	0.462884i
$775$	−0.669620	+	3.79760i	−0.0240535	+	0.136414i
$776$	−9.82003			−0.352518
$777$	0.363578	+	2.68256i	0.0130433	+	0.0962363i
$778$	−20.5680			−0.737400
$779$	−1.48308	+	8.41094i	−0.0531367	+	0.301353i
$780$	0.238222	+	1.35103i	0.00852973	+	0.0483745i
$781$	−32.7716	−	11.9279i	−1.17266	−	0.426813i
$782$	20.7222	−	17.3880i	0.741023	−	0.621792i
$783$	−22.1087			−0.790099
$784$	−4.64324	+	3.89614i	−0.165830	+	0.139148i
$785$	−4.91909	+	8.52011i	−0.175570	+	0.304096i
$786$	−8.31704	+	3.02715i	−0.296659	+	0.107975i
$787$	5.91310	+	10.2418i	0.210779	+	0.365080i	0.951959	−	0.306227i	$-0.0990666\pi$
$787$	5.91310	+	10.2418i	0.210779	+	0.365080i	−0.741179	+	0.671307i	$0.765733\pi$
$788$	−8.38838	+	14.5291i	−0.298824	+	0.517578i
$789$	1.01489	−	5.75571i	0.0361309	−	0.204909i
$790$	2.17814	+	0.792777i	0.0774946	+	0.0282057i
$791$	−7.43121	−	12.8712i	−0.264223	−	0.457648i
$792$	13.2451	+	11.1139i	0.470643	+	0.394916i
$793$	−18.9590	−	15.9085i	−0.673253	−	0.564927i
$794$	−16.0178	+	5.83000i	−0.568450	+	0.206899i
$795$	−0.553475	−	3.13891i	−0.0196297	−	0.111326i
$796$	−3.64111	−	20.6498i	−0.129056	−	0.731911i
$797$	−23.1952	+	8.44235i	−0.821615	+	0.299043i	−0.718413	−	0.695617i	$-0.755131\pi$
$797$	−23.1952	+	8.44235i	−0.821615	+	0.299043i	−0.103202	+	0.994660i	$0.532909\pi$
$798$	1.50915	+	1.26633i	0.0534233	+	0.0448274i
$799$	−10.9327	−	9.17360i	−0.386770	−	0.324538i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	23.5958	+	8.58818i	0.833718	+	0.303448i
$802$	−0.113562	+	0.644040i	−0.00401000	+	0.0227418i
$803$	−17.7764	+	30.7897i	−0.627316	+	1.08654i
$804$	−1.93233	−	3.34689i	−0.0681479	−	0.118036i
$805$	4.89992	−	1.78343i	0.172700	−	0.0628575i
$806$	−5.75833	+	9.97373i	−0.202829	+	0.351309i
$807$	2.98809	−	2.50730i	0.105186	−	0.0882613i
$808$	−17.9073			−0.629976
$809$	35.5488	−	29.8290i	1.24983	−	1.04873i	0.253140	−	0.967430i	$-0.418537\pi$
$809$	35.5488	−	29.8290i	1.24983	−	1.04873i	0.996690	−	0.0813019i	$-0.0259078\pi$
$810$	6.71458	+	2.44391i	0.235926	+	0.0858701i
$811$	2.51952	+	14.2889i	0.0884723	+	0.501751i	0.996553	+	0.0829566i	$0.0264363\pi$
$811$	2.51952	+	14.2889i	0.0884723	+	0.501751i	−0.908081	+	0.418795i	$0.862453\pi$
$812$	−1.39876	+	7.93277i	−0.0490869	+	0.278386i
$813$	−5.20048			−0.182389
$814$	5.06464	+	37.3680i	0.177515	+	1.30975i
$815$	17.4982			0.612935
$816$	−0.400912	+	2.27369i	−0.0140347	+	0.0795949i
$817$	−3.60404	−	20.4395i	−0.126089	−	0.715088i
$818$	6.77800	+	2.46699i	0.236987	+	0.0862563i
$819$	−6.18199	+	5.18731i	−0.216016	+	0.181259i
$820$	−1.92937			−0.0673767
$821$	25.3331	−	21.2570i	0.884132	−	0.741875i	−0.0828925	−	0.996558i	$-0.526416\pi$
$821$	25.3331	−	21.2570i	0.884132	−	0.741875i	0.967024	+	0.254684i	$0.0819714\pi$
$822$	−3.68969	+	6.39073i	−0.128693	+	0.222902i
$823$	−2.78969	+	1.01537i	−0.0972426	+	0.0353934i	−0.390183	−	0.920737i	$-0.627588\pi$
$823$	−2.78969	+	1.01537i	−0.0972426	+	0.0353934i	0.292941	+	0.956131i	$0.405366\pi$
$824$	−5.86763	−	10.1630i	−0.204409	−	0.354046i
$825$	1.42385	−	2.46619i	0.0495722	−	0.0858616i
$826$	1.12686	−	6.39072i	0.0392084	−	0.222362i
$827$	−47.7156	−	17.3671i	−1.65923	−	0.603912i	−0.668992	−	0.743270i	$-0.733274\pi$
$827$	−47.7156	−	17.3671i	−1.65923	−	0.603912i	−0.990242	+	0.139358i	$0.955496\pi$
$828$	−7.50523	−	12.9994i	−0.260825	−	0.451762i
$829$	−33.4124	−	28.0363i	−1.16046	−	0.973742i	−0.160549	−	0.987028i	$-0.551326\pi$
$829$	−33.4124	−	28.0363i	−1.16046	−	0.973742i	−0.999912	+	0.0132858i	$0.995771\pi$
$830$	−9.54815	−	8.01185i	−0.331421	−	0.278095i
$831$	2.91183	−	1.05982i	0.101010	−	0.0367647i
$832$	−0.518608	−	2.94117i	−0.0179795	−	0.101967i
$833$	5.29021	+	30.0023i	0.183295	+	1.03952i
$834$	2.05194	−	0.746844i	0.0710527	−	0.0258611i
$835$	−0.653960	−	0.548738i	−0.0226312	−	0.0189898i
$836$	21.0224	+	17.6399i	0.727075	+	0.610088i
$837$	−5.12714	−	8.88046i	−0.177220	−	0.306954i
$838$	−3.92156	−	1.42733i	−0.135468	−	0.0493064i
$839$	−7.02029	+	39.8140i	−0.242367	+	1.37453i	0.584161	+	0.811638i	$0.301424\pi$
$839$	−7.02029	+	39.8140i	−0.242367	+	1.37453i	−0.826528	+	0.562895i	$0.809687\pi$
$840$	−0.222521	+	0.385418i	−0.00767771	+	0.0132982i
$841$	−20.0622	−	34.7487i	−0.691798	−	1.19823i
$842$	19.0650	−	6.93910i	0.657024	−	0.239137i
$843$	−4.02988	+	6.97996i	−0.138796	+	0.240403i
$844$	−7.61644	+	6.39095i	−0.262169	+	0.219986i
$845$	4.08057			0.140376
$846$	−6.06651	+	5.09041i	−0.208571	+	0.175012i
$847$	24.9756	+	9.09038i	0.858172	+	0.312349i
$848$	1.20491	+	6.83338i	0.0413767	+	0.234659i
$849$	0.569600	−	3.23036i	0.0195486	−	0.110866i
$850$	−5.02615			−0.172395
$851$	6.96377	−	31.9884i	0.238715	−	1.09655i
$852$	−2.58406			−0.0885286
$853$	−4.71753	+	26.7545i	−0.161525	+	0.916055i	0.791050	+	0.611752i	$0.209535\pi$
$853$	−4.71753	+	26.7545i	−0.161525	+	0.916055i	−0.952575	+	0.304304i	$0.901576\pi$
$854$	−1.39419	−	7.90682i	−0.0477081	−	0.270566i
$855$	11.6014	+	4.22257i	0.396760	+	0.144409i
$856$	−4.91728	+	4.12608i	−0.168069	+	0.141027i
$857$	10.1012			0.345049			0.172524	−	0.985005i	$-0.444808\pi$
$857$	10.1012			0.345049			0.172524	+	0.985005i	$0.444808\pi$
$858$	6.51505	−	5.46678i	0.222420	−	0.186633i
$859$	−13.5848	+	23.5295i	−0.463506	+	0.802817i	−0.999133	−	0.0416384i	$-0.986742\pi$
$859$	−13.5848	+	23.5295i	−0.463506	+	0.802817i	0.535626	+	0.844455i	$0.320076\pi$
$860$	4.40584	−	1.60359i	0.150238	−	0.0546821i
$861$	0.429327	+	0.743615i	0.0146314	+	0.0253423i
$862$	8.96034	−	15.5198i	0.305190	−	0.528605i
$863$	−6.03967	+	34.2526i	−0.205593	+	1.16597i	0.690912	+	0.722939i	$0.257209\pi$
$863$	−6.03967	+	34.2526i	−0.205593	+	1.16597i	−0.896504	+	0.443035i	$0.853902\pi$
$864$	2.49881	+	0.909491i	0.0850111	+	0.0309415i
$865$	−2.80272	−	4.85446i	−0.0952955	−	0.165057i
$866$	−20.5855	−	17.2733i	−0.699524	−	0.586970i
$867$	2.90731	+	2.43952i	0.0987375	+	0.0828506i
$868$	−3.51077	+	1.27781i	−0.119163	+	0.0433718i
$869$	−2.49529	−	14.1515i	−0.0846470	−	0.480057i
$870$	−0.663176	−	3.76106i	−0.0224838	−	0.127512i
$871$	23.6114	−	8.59384i	0.800041	−	0.291191i
$872$	7.05537	+	5.92016i	0.238925	+	0.200482i
$873$	20.9804	+	17.6047i	0.710081	+	0.595828i
$874$	−11.9122	−	20.6325i	−0.402936	−	0.697906i
$875$	−0.910424	−	0.331367i	−0.0307779	−	0.0112023i
$876$	−0.457442	+	2.59428i	−0.0154555	+	0.0876527i
$877$	−21.5894	+	37.3939i	−0.729021	+	1.26270i	0.228277	+	0.973596i	$0.426691\pi$
$877$	−21.5894	+	37.3939i	−0.729021	+	1.26270i	−0.957297	+	0.289105i	$0.906642\pi$
$878$	3.60559	+	6.24506i	0.121683	+	0.210761i
$879$	2.53907	−	0.924148i	0.0856409	−	0.0311707i
$880$	−3.09972	+	5.36887i	−0.104491	+	0.180984i
$881$	−8.97821	+	7.53361i	−0.302483	+	0.253814i	−0.781377	−	0.624059i	$-0.785482\pi$
$881$	−8.97821	+	7.53361i	−0.302483	+	0.253814i	0.478894	+	0.877873i	$0.341038\pi$
$882$	16.9050			0.569222
$883$	−18.6231	+	15.6266i	−0.626716	+	0.525877i	−0.899906	−	0.436083i	$-0.856365\pi$
$883$	−18.6231	+	15.6266i	−0.626716	+	0.525877i	0.273191	+	0.961960i	$0.411921\pi$
$884$	−14.1055	−	5.13400i	−0.474421	−	0.172675i
$885$	0.534262	+	3.02995i	0.0179590	+	0.101851i
$886$	0.989094	−	5.60943i	0.0332292	−	0.188452i
$887$	57.0905			1.91691			0.958456	−	0.285241i	$-0.0920735\pi$
$887$	57.0905			1.91691			0.958456	+	0.285241i	$0.0920735\pi$
$888$	1.29962	+	2.47347i	0.0436124	+	0.0830043i
$889$	11.1226			0.373040
$890$	−1.56341	+	8.86651i	−0.0524055	+	0.297206i
$891$	−7.69228	−	43.6251i	−0.257701	−	1.46149i
$892$	18.9804	+	6.90831i	0.635511	+	0.231307i
$893$	−9.62869	+	8.07943i	−0.322212	+	0.270368i
$894$	6.23121			0.208403
$895$	−8.92056	+	7.48524i	−0.298181	+	0.250204i
$896$	0.484426	−	0.839051i	0.0161836	−	0.0280307i
$897$	−6.93815	+	2.52528i	−0.231658	+	0.0843166i
$898$	0.903421	+	1.56477i	0.0301475	+	0.0522171i
$899$	16.0304	−	27.7654i	0.534643	−	0.926028i
$900$	−0.484304	+	2.74663i	−0.0161435	+	0.0915542i
$901$	32.7722	+	11.9281i	1.09180	+	0.397382i
$902$	5.98051	+	10.3585i	0.199129	+	0.344902i
$903$	−1.59845	−	1.34126i	−0.0531929	−	0.0446342i
$904$	−11.7513	−	9.86051i	−0.390842	−	0.327956i
$905$	17.6837	−	6.43635i	0.587827	−	0.213951i
$906$	−0.693982	−	3.93577i	−0.0230560	−	0.130757i
$907$	−2.77586	−	15.7427i	−0.0921708	−	0.522726i	−0.995578	−	0.0939421i	$-0.970053\pi$
$907$	−2.77586	−	15.7427i	−0.0921708	−	0.522726i	0.903407	−	0.428784i	$-0.141058\pi$
$908$	9.13967	−	3.32657i	0.303310	−	0.110396i
$909$	38.2588	+	32.1030i	1.26897	+	1.06479i
$910$	−2.21656	−	1.85992i	−0.0734784	−	0.0616557i
$911$	16.5006	+	28.5798i	0.546688	+	0.946892i	0.998499	+	0.0547779i	$0.0174451\pi$
$911$	16.5006	+	28.5798i	0.546688	+	0.946892i	−0.451810	+	0.892114i	$0.649222\pi$
$912$	1.91076	+	0.695459i	0.0632716	+	0.0230290i
$913$	−13.4180	+	76.0972i	−0.444071	+	2.51845i
$914$	0.593798	−	1.02849i	0.0196411	−	0.0340194i
$915$	1.90329	+	3.29660i	0.0629210	+	0.108982i
$916$	0.451017	−	0.164157i	0.0149020	−	0.00542389i
$917$	9.33399	−	16.1669i	0.308235	−	0.533880i
$918$	10.2385	−	8.59112i	0.337921	−	0.283549i
$919$	5.35043			0.176495			0.0882473	−	0.996099i	$-0.471873\pi$
$919$	5.35043			0.176495			0.0882473	+	0.996099i	$0.471873\pi$
$920$	4.12287	−	3.45950i	0.135927	−	0.114056i
$921$	−9.13695	−	3.32558i	−0.301073	−	0.109581i
$922$	−4.86871	−	27.6118i	−0.160342	−	0.909346i
$923$	2.91742	−	16.5455i	0.0960280	−	0.544602i
$924$	2.75901			0.0907648
$925$	−4.81162	+	3.72133i	−0.158205	+	0.122356i
$926$	31.8677			1.04724
$927$	−5.68344	+	32.2324i	−0.186669	+	1.05865i
$928$	1.44373	+	8.18779i	0.0473927	+	0.268777i
$929$	−16.8841	−	6.14529i	−0.553948	−	0.201620i	0.0498519	−	0.998757i	$-0.484125\pi$
$929$	−16.8841	−	6.14529i	−0.553948	−	0.201620i	−0.603800	+	0.797136i	$0.706347\pi$
$930$	1.35692	−	1.13859i	0.0444953	−	0.0373360i
$931$	26.8314			0.879365
$932$	14.1392	−	11.8642i	0.463146	−	0.388626i
$933$	0.946513	−	1.63941i	0.0309874	−	0.0536718i
$934$	21.3617	−	7.77501i	0.698975	−	0.254406i
$935$	15.5796	+	26.9847i	0.509508	+	0.882495i
$936$	−4.16473	+	7.21352i	−0.136128	+	0.235781i
$937$	1.30173	−	7.38246i	0.0425255	−	0.241174i	−0.956134	−	0.292929i	$-0.905370\pi$
$937$	1.30173	−	7.38246i	0.0425255	−	0.241174i	0.998660	+	0.0517543i	$0.0164813\pi$
$938$	7.65968	+	2.78790i	0.250097	+	0.0910280i
$939$	5.67889	+	9.83613i	0.185324	+	0.320990i
$940$	−2.17516	−	1.82517i	−0.0709458	−	0.0595306i
$941$	−25.9826	−	21.8020i	−0.847009	−	0.710725i	0.112120	−	0.993695i	$-0.464236\pi$
$941$	−25.9826	−	21.8020i	−0.847009	−	0.710725i	−0.959129	+	0.282970i	$0.908680\pi$
$942$	4.24663	−	1.54565i	0.138363	−	0.0503598i
$943$	−1.80315	−	10.2262i	−0.0587187	−	0.333010i
$944$	−1.16308	−	6.59617i	−0.0378551	−	0.214687i
$945$	2.42098	−	0.881163i	0.0787544	−	0.0286642i
$946$	−22.2663	−	18.6837i	−0.723940	−	0.607458i
$947$	−15.7012	−	13.1748i	−0.510219	−	0.428125i	0.350987	−	0.936380i	$-0.385846\pi$
$947$	−15.7012	−	13.1748i	−0.510219	−	0.428125i	−0.861206	+	0.508255i	$0.830291\pi$
$948$	−0.532369	−	0.922090i	−0.0172905	−	0.0299481i
$949$	−16.0945	−	5.85791i	−0.522449	−	0.190156i
$950$	−0.768682	+	4.35941i	−0.0249393	+	0.141438i
$951$	−1.61824	+	2.80288i	−0.0524752	+	0.0908897i
$952$	−2.43480	−	4.21720i	−0.0789123	−	0.136680i
$953$	27.5538	−	10.0288i	0.892556	−	0.324864i	0.145290	−	0.989389i	$-0.453588\pi$
$953$	27.5538	−	10.0288i	0.892556	−	0.324864i	0.747266	+	0.664525i	$0.231366\pi$
$954$	9.67614	−	16.7596i	0.313277	−	0.542611i
$955$	10.8062	−	9.06748i	0.349681	−	0.293417i
$956$	−27.5897			−0.892314
$957$	−18.1370	+	15.2187i	−0.586285	+	0.491951i
$958$	−17.3748	−	6.32392i	−0.561355	−	0.204317i
$959$	−2.70274	−	15.3280i	−0.0872760	−	0.494967i
$960$	−0.0797653	+	0.452371i	−0.00257441	+	0.0146002i
$961$	−16.1298			−0.520317
$962$	−17.3047	+	5.52878i	−0.557925	+	0.178255i
$963$	17.9027			0.576907
$964$	4.29768	−	24.3734i	0.138419	−	0.785013i
$965$	−1.30710	−	7.41296i	−0.0420772	−	0.238632i
$966$	−2.25078	−	0.819216i	−0.0724176	−	0.0263579i
$967$	−31.5781	+	26.4972i	−1.01548	+	0.852091i	−0.989053	−	0.147559i	$-0.952858\pi$
$967$	−31.5781	+	26.4972i	−1.01548	+	0.852091i	−0.0264295	+	0.999651i	$0.508414\pi$
$968$	27.4330			0.881728
$969$	7.82906	−	6.56936i	0.251506	−	0.211038i
$970$	−4.91001	+	8.50439i	−0.157651	+	0.273060i
$971$	−28.9945	+	10.5531i	−0.930477	+	0.338666i	−0.762398	−	0.647108i	$-0.775978\pi$
$971$	−28.9945	+	10.5531i	−0.930477	+	0.338666i	−0.168078	+	0.985774i	$0.553756\pi$
$972$	−5.62990	−	9.75128i	−0.180579	−	0.312772i
$973$	−2.30283	+	3.98862i	−0.0738254	+	0.127869i
$974$	3.94680	−	22.3834i	0.126463	−	0.717210i
$975$	1.28913	+	0.469206i	0.0412853	+	0.0150266i
$976$	−4.14345	−	7.17667i	−0.132629	−	0.229720i
$977$	24.1302	+	20.2476i	0.771993	+	0.647779i	0.941219	−	0.337798i	$-0.109682\pi$
$977$	24.1302	+	20.2476i	0.771993	+	0.647779i	−0.169225	+	0.985577i	$0.554127\pi$
$978$	−6.15730	−	5.16659i	−0.196889	−	0.165209i
$979$	52.4492	−	19.0900i	1.67628	−	0.610118i
$980$	1.05254	+	5.96924i	0.0336221	+	0.190680i
$981$	−4.46051	−	25.2968i	−0.142413	−	0.807664i
$982$	−39.7940	+	14.4838i	−1.26988	+	0.462197i
$983$	−5.00196	−	4.19714i	−0.159538	−	0.133868i	0.559524	−	0.828814i	$-0.310984\pi$
$983$	−5.00196	−	4.19714i	−0.159538	−	0.133868i	−0.719062	+	0.694946i	$0.755428\pi$
$984$	0.678913	+	0.569675i	0.0216429	+	0.0181606i
$985$	8.38838	+	14.5291i	0.267276	+	0.462935i
$986$	39.2678	+	14.2923i	1.25054	+	0.455160i
$987$	−0.219436	+	1.24448i	−0.00698473	+	0.0396124i
$988$	−6.61021	+	11.4492i	−0.210299	+	0.364248i
$989$	12.6171	+	21.8534i	0.401199	+	0.694897i
$990$	16.2475	−	5.91360i	0.516379	−	0.187946i
$991$	−4.53557	+	7.85584i	−0.144077	+	0.249549i	−0.929028	−	0.370009i	$-0.879355\pi$
$991$	−4.53557	+	7.85584i	−0.144077	+	0.249549i	0.784951	+	0.619558i	$0.212688\pi$
$992$	−2.95401	+	2.47871i	−0.0937899	+	0.0786991i
$993$	−5.81909			−0.184663
$994$	4.17514	−	3.50336i	0.132428	−	0.111120i
$995$	−19.7038	−	7.17158i	−0.624651	−	0.227354i
$996$	0.994212	+	5.63846i	0.0315028	+	0.178661i
$997$	1.90019	−	10.7765i	0.0601796	−	0.341295i	−0.939820	−	0.341669i	$-0.889008\pi$
$997$	1.90019	−	10.7765i	0.0601796	−	0.341295i	1.00000		0.000373625i	$0.000118929\pi$
$998$	−8.41808			−0.266470
$999$	3.44069	−	15.8049i	0.108859	−	0.500046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.d.181.2	✓	24
37.9	even	9	inner	370.2.o.d.231.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.d.181.2	✓	24	1.1	even	1	trivial
370.2.o.d.231.2	yes	24	37.9	even	9	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(0.0797653 + 0.452371i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{5} +0.459350 q^{6} +(-0.742184 + 0.622767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.62080 - 0.953893i) q^{9} +(0.500000 + 0.866025i) q^{10} +(3.09972 - 5.36887i) q^{11} +(0.0797653 - 0.452371i) q^{12} +(2.80643 + 1.02146i) q^{13} +(0.484426 + 0.839051i) q^{14} +(-0.351882 - 0.295264i) q^{15} +(0.766044 + 0.642788i) q^{16} +(4.72303 - 1.71904i) q^{17} +(-0.484304 - 2.74663i) q^{18} +(-0.768682 - 4.35941i) q^{19} +(0.939693 - 0.342020i) q^{20} +(-0.340922 - 0.286068i) q^{21} +(-4.74904 - 3.98492i) q^{22} +(2.69101 + 4.66097i) q^{23} +(-0.431648 - 0.157107i) q^{24} +(0.173648 - 0.984808i) q^{25} +(1.49327 - 2.58642i) q^{26} +(1.32959 + 2.30291i) q^{27} +(0.910424 - 0.331367i) q^{28} +(-4.15705 + 7.20022i) q^{29} +(-0.351882 + 0.295264i) q^{30} -3.85619 q^{31} +(0.766044 - 0.642788i) q^{32} +(2.67597 + 0.973973i) q^{33} +(-0.872782 - 4.94979i) q^{34} +(0.168240 - 0.954134i) q^{35} -2.78900 q^{36} +(-4.50032 - 4.09232i) q^{37} -4.42666 q^{38} +(-0.238222 + 1.35103i) q^{39} +(-0.173648 - 0.984808i) q^{40} +(-1.81302 - 0.659885i) q^{41} +(-0.340922 + 0.286068i) q^{42} +4.68859 q^{43} +(-4.74904 + 3.98492i) q^{44} +(-1.39450 + 2.41534i) q^{45} +(5.05745 - 1.84076i) q^{46} +(-1.41973 - 2.45905i) q^{47} +(-0.229675 + 0.397809i) q^{48} +(-1.05254 + 5.96924i) q^{49} +(-0.939693 - 0.342020i) q^{50} +(1.15438 + 1.99945i) q^{51} +(-2.28782 - 1.91971i) q^{52} +(5.31542 + 4.46017i) q^{53} +(2.49881 - 0.909491i) q^{54} +(1.07652 + 6.10525i) q^{55} +(-0.168240 - 0.954134i) q^{56} +(1.91076 - 0.695459i) q^{57} +(6.36897 + 5.34420i) q^{58} +(-5.13091 - 4.30535i) q^{59} +(0.229675 + 0.397809i) q^{60} +(-7.78715 - 2.83429i) q^{61} +(-0.669620 + 3.79760i) q^{62} +(-1.35106 + 2.34011i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.80643 + 1.02146i) q^{65} +(1.42385 - 2.46619i) q^{66} +(6.44497 - 5.40797i) q^{67} -5.02615 q^{68} +(-1.89384 + 1.58912i) q^{69} +(-0.910424 - 0.331367i) q^{70} +(-0.976855 - 5.54002i) q^{71} +(-0.484304 + 2.74663i) q^{72} -5.73486 q^{73} +(-4.81162 + 3.72133i) q^{74} +0.459350 q^{75} +(-0.768682 + 4.35941i) q^{76} +(1.04299 + 5.91509i) q^{77} +(1.28913 + 0.469206i) q^{78} +(1.77563 - 1.48993i) q^{79} -1.00000 q^{80} +(5.47377 - 4.59304i) q^{81} +(-0.964687 + 1.67089i) q^{82} +(-11.7125 + 4.26302i) q^{83} +(0.222521 + 0.385418i) q^{84} +(-2.51307 + 4.35277i) q^{85} +(0.814166 - 4.61736i) q^{86} +(-3.58876 - 1.30620i) q^{87} +(3.09972 + 5.36887i) q^{88} +(6.89692 + 5.78720i) q^{89} +(2.13650 + 1.79273i) q^{90} +(-2.71902 + 0.989642i) q^{91} +(-0.934579 - 5.30026i) q^{92} +(-0.307590 - 1.74443i) q^{93} +(-2.66823 + 0.971155i) q^{94} +(3.39102 + 2.84541i) q^{95} +(0.351882 + 0.295264i) q^{96} +(4.91001 + 8.50439i) q^{97} +(5.69578 + 2.07309i) q^{98} +(3.00241 - 17.0275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{6} - 9 q^{7} - 12 q^{8} + 12 q^{9} + 12 q^{10} - 3 q^{11} - 3 q^{14} + 6 q^{17} - 6 q^{18} - 18 q^{19} + 18 q^{21} + 3 q^{22} + 15 q^{23} - 6 q^{26} - 12 q^{27} + 9 q^{28} - 18 q^{29} - 6 q^{31}+ \cdots + 165 q^{99}+O(q^{100}) \) 24 * q + 6 * q^6 - 9 * q^7 - 12 * q^8 + 12 * q^9 + 12 * q^10 - 3 * q^11 - 3 * q^14 + 6 * q^17 - 6 * q^18 - 18 * q^19 + 18 * q^21 + 3 * q^22 + 15 * q^23 - 6 * q^26 - 12 * q^27 + 9 * q^28 - 18 * q^29 - 6 * q^31 - 45 * q^33 - 3 * q^34 + 30 * q^36 - 18 * q^37 - 24 * q^38 + 12 * q^39 + 3 * q^41 + 18 * q^42 + 3 * q^44 + 15 * q^45 + 9 * q^46 - 36 * q^47 - 3 * q^48 - 15 * q^49 + 54 * q^51 - 9 * q^52 - 6 * q^53 + 45 * q^54 - 3 * q^55 + 3 * q^57 - 15 * q^58 - 9 * q^59 + 3 * q^60 - 24 * q^61 + 81 * q^62 - 45 * q^63 - 12 * q^64 - 3 * q^66 + 12 * q^67 + 12 * q^68 + 60 * q^69 - 9 * q^70 + 42 * q^71 - 6 * q^72 - 42 * q^73 + 12 * q^74 + 6 * q^75 - 18 * q^76 + 9 * q^77 + 30 * q^78 - 6 * q^79 - 24 * q^80 - 66 * q^81 - 24 * q^82 - 3 * q^83 - 42 * q^84 + 6 * q^85 - 18 * q^86 - 84 * q^87 - 3 * q^88 + 27 * q^89 + 6 * q^90 + 153 * q^91 - 9 * q^92 - 54 * q^93 - 21 * q^94 - 9 * q^95 - 9 * q^97 - 24 * q^98 + 165 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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