LMFDB - Embedded newform 936.2.cj.a.373.107

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(133,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.133"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cj (of order $6$, degree $2$, 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:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$328$
Relative dimension:	$164$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.107
Character	$\chi$	$=$	936.373
Dual form			936.2.cj.a.133.108

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.586085 - 1.28705i) q^{2} +(1.39269 - 1.02977i) q^{3} +(-1.31301 - 1.50865i) q^{4} +(-0.951819 - 0.549533i) q^{5} +(-0.509136 - 2.39599i) q^{6} +(1.30283 - 2.25656i) q^{7} +(-2.71124 + 0.805715i) q^{8} +(0.879145 - 2.86829i) q^{9} +(-1.26512 + 0.902967i) q^{10} +0.788764i q^{11} +(-3.38217 - 0.748971i) q^{12} +(2.30976 + 2.76858i) q^{13} +(-2.14075 - 2.99934i) q^{14} +(-1.89148 + 0.214829i) q^{15} +(-0.552021 + 3.96173i) q^{16} +(-2.29757 - 3.97951i) q^{17} +(-3.17639 - 2.81257i) q^{18} +(2.63985 - 1.52412i) q^{19} +(0.420695 + 2.15750i) q^{20} +(-0.509314 - 4.48429i) q^{21} +(1.01518 + 0.462283i) q^{22} +(-4.29012 - 7.43071i) q^{23} +(-2.94620 + 3.91406i) q^{24} +(-1.89603 - 3.28402i) q^{25} +(4.91702 - 1.35016i) q^{26} +(-1.72931 - 4.89995i) q^{27} +(-5.11497 + 0.997380i) q^{28} +8.36190i q^{29} +(-0.832071 + 2.56034i) q^{30} +(-2.61428 + 4.52806i) q^{31} +(4.77542 + 3.03239i) q^{32} +(0.812246 + 1.09850i) q^{33} +(-6.46841 + 0.624762i) q^{34} +(-2.48011 + 1.43189i) q^{35} +(-5.48156 + 2.43977i) q^{36} +(-1.26850 - 0.732368i) q^{37} +(-0.414443 - 4.29089i) q^{38} +(6.06777 + 1.47723i) q^{39} +(3.02338 + 0.723021i) q^{40} +(3.13996 + 5.43858i) q^{41} +(-6.07002 - 1.97266i) q^{42} +(3.94666 + 2.27861i) q^{43} +(1.18996 - 1.03565i) q^{44} +(-2.41301 + 2.24698i) q^{45} +(-12.0781 + 1.16658i) q^{46} +(5.29828 + 9.17688i) q^{47} +(3.31088 + 6.08589i) q^{48} +(0.105288 + 0.182363i) q^{49} +(-5.33793 + 0.515573i) q^{50} +(-7.29777 - 3.17623i) q^{51} +(1.14407 - 7.11977i) q^{52} -0.616458i q^{53} +(-7.32001 - 0.646072i) q^{54} +(0.433452 - 0.750760i) q^{55} +(-1.71413 + 7.16779i) q^{56} +(2.10699 - 4.84106i) q^{57} +(10.7622 + 4.90078i) q^{58} -9.91768i q^{59} +(2.80762 + 2.57150i) q^{60} +(0.954069 + 0.550832i) q^{61} +(4.29566 + 6.01854i) q^{62} +(-5.32711 - 5.72073i) q^{63} +(6.70165 - 4.36897i) q^{64} +(-0.677048 - 3.90447i) q^{65} +(1.88987 - 0.401588i) q^{66} +(11.4089 - 6.58691i) q^{67} +(-2.98694 + 8.69135i) q^{68} +(-13.6267 - 5.93079i) q^{69} +(0.389364 + 4.03124i) q^{70} +(-7.67022 - 13.2852i) q^{71} +(-0.0725455 + 8.48497i) q^{72} -3.19793 q^{73} +(-1.68605 + 1.20339i) q^{74} +(-6.02235 - 2.62113i) q^{75} +(-5.76550 - 1.98142i) q^{76} +(1.77989 + 1.02762i) q^{77} +(5.45751 - 6.94375i) q^{78} +(7.48433 + 12.9632i) q^{79} +(2.70252 - 3.46749i) q^{80} +(-7.45421 - 5.04329i) q^{81} +(8.84002 - 0.853828i) q^{82} +(-1.72293 + 0.994734i) q^{83} +(-6.09647 + 6.65628i) q^{84} +5.05036i q^{85} +(5.24577 - 3.74410i) q^{86} +(8.61083 + 11.6455i) q^{87} +(-0.635519 - 2.13853i) q^{88} +(5.76546 - 9.98606i) q^{89} +(1.47775 + 4.42259i) q^{90} +(9.25668 - 1.60514i) q^{91} +(-5.57734 + 16.2288i) q^{92} +(1.02200 + 8.99826i) q^{93} +(14.9164 - 1.44072i) q^{94} -3.35021 q^{95} +(9.77332 - 0.694422i) q^{96} +(5.69622 - 9.86614i) q^{97} +(0.296419 - 0.0286301i) q^{98} +(2.26241 + 0.693438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 328 q - 2 q^{2} - 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} - 14 q^{15} - 2 q^{16} - 4 q^{17} - 12 q^{18} + 9 q^{20} + 14 q^{22} - 22 q^{23} + 18 q^{24} + 144 q^{25}+ \cdots + 39 q^{98}+O(q^{100}) $ 328 * q - 2 * q^2 - 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 - 14 * q^15 - 2 * q^16 - 4 * q^17 - 12 * q^18 + 9 * q^20 + 14 * q^22 - 22 * q^23 + 18 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 22 * q^33 - 22 * q^36 + 6 * q^38 + 2 * q^39 + 8 * q^40 + 2 * q^41 + 17 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 + 41 * q^48 - 138 * q^49 - 34 * q^50 + 24 * q^52 - 41 * q^54 - 14 * q^55 + 28 * q^56 - 20 * q^57 + 50 * q^58 - 41 * q^60 + 3 * q^62 + 26 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 + 32 * q^68 - 17 * q^70 - 4 * q^71 + 32 * q^72 - 16 * q^73 + 19 * q^74 + 9 * q^76 + 2 * q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 27 * q^84 + 36 * q^86 + 34 * q^87 - 10 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 + 3 * q^94 - 112 * q^95 - 113 * q^96 + 2 * q^97 + 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$1$

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 $

$2$	0.586085	−	1.28705i	0.414425	−	0.910083i
$2$	0.586085	−	1.28705i	0.414425	−	0.910083i
$3$	1.39269	−	1.02977i	0.804067	−	0.594538i
$3$	1.39269	−	1.02977i	0.804067	−	0.594538i
$4$	−1.31301	−	1.50865i	−0.656504	−	0.754323i
$5$	−0.951819	−	0.549533i	−0.425666	−	0.245759i	0.271832	−	0.962345i	$-0.412370\pi$
$5$	−0.951819	−	0.549533i	−0.425666	−	0.245759i	−0.697499	+	0.716586i	$0.745704\pi$
$6$	−0.509136	−	2.39599i	−0.207854	−	0.978160i
$7$	1.30283	−	2.25656i	0.492422	−	0.852900i	−0.507540	−	0.861628i	$-0.669445\pi$
$7$	1.30283	−	2.25656i	0.492422	−	0.852900i	0.999962	+	0.00872829i	$0.00277834\pi$
$8$	−2.71124	+	0.805715i	−0.958568	+	0.284863i
$9$	0.879145	−	2.86829i	0.293048	−	0.956098i
$10$	−1.26512	+	0.902967i	−0.400067	+	0.285543i
$11$			0.788764i			0.237821i	0.992905	+	0.118911i	$0.0379402\pi$
$11$			0.788764i			0.237821i	−0.992905	+	0.118911i	$0.962060\pi$
$12$	−3.38217	−	0.748971i	−0.976347	−	0.216209i
$13$	2.30976	+	2.76858i	0.640612	+	0.767865i
$13$	2.30976	+	2.76858i	0.640612	+	0.767865i
$14$	−2.14075	−	2.99934i	−0.572138	−	0.801608i
$15$	−1.89148	+	0.214829i	−0.488377	+	0.0554685i
$16$	−0.552021	+	3.96173i	−0.138005	+	0.990432i
$17$	−2.29757	−	3.97951i	−0.557243	−	0.965173i	−0.997725	−	0.0674115i	$-0.978526\pi$
$17$	−2.29757	−	3.97951i	−0.557243	−	0.965173i	0.440483	−	0.897761i	$-0.354807\pi$
$18$	−3.17639	−	2.81257i	−0.748682	−	0.662929i
$19$	2.63985	−	1.52412i	0.605624	−	0.349657i	−0.165627	−	0.986188i	$-0.552965\pi$
$19$	2.63985	−	1.52412i	0.605624	−	0.349657i	0.771251	+	0.636531i	$0.219631\pi$
$20$	0.420695	+	2.15750i	0.0940704	+	0.482431i
$21$	−0.509314	−	4.48429i	−0.111141	−	0.978553i
$22$	1.01518	+	0.462283i	0.216437	+	0.0985591i
$23$	−4.29012	−	7.43071i	−0.894552	−	1.54941i	−0.834358	−	0.551222i	$-0.814162\pi$
$23$	−4.29012	−	7.43071i	−0.894552	−	1.54941i	−0.0601935	−	0.998187i	$-0.519172\pi$
$24$	−2.94620	+	3.91406i	−0.601391	+	0.798955i
$25$	−1.89603	−	3.28402i	−0.379206	−	0.656803i
$26$	4.91702	−	1.35016i	0.964307	−	0.264788i
$27$	−1.72931	−	4.89995i	−0.332806	−	0.942995i
$28$	−5.11497	+	0.997380i	−0.966639	+	0.188487i
$29$			8.36190i			1.55277i	0.630262	+	0.776383i	$0.282947\pi$
$29$			8.36190i			1.55277i	−0.630262	+	0.776383i	$0.717053\pi$
$30$	−0.832071	+	2.56034i	−0.151915	+	0.467452i
$31$	−2.61428	+	4.52806i	−0.469538	+	0.813263i	−0.999393	−	0.0348246i	$-0.988913\pi$
$31$	−2.61428	+	4.52806i	−0.469538	+	0.813263i	0.529856	+	0.848088i	$0.322246\pi$
$32$	4.77542	+	3.03239i	0.844183	+	0.536056i
$33$	0.812246	+	1.09850i	0.141394	+	0.191224i
$34$	−6.46841	+	0.624762i	−1.10932	+	0.107146i
$35$	−2.48011	+	1.43189i	−0.419215	+	0.242034i
$36$	−5.48156	+	2.43977i	−0.913593	+	0.406629i
$37$	−1.26850	−	0.732368i	−0.208540	−	0.120401i	0.392093	−	0.919926i	$-0.371751\pi$
$37$	−1.26850	−	0.732368i	−0.208540	−	0.120401i	−0.600633	+	0.799525i	$0.705085\pi$
$38$	−0.414443	−	4.29089i	−0.0672315	−	0.696075i
$39$	6.06777	+	1.47723i	0.971620	+	0.236547i
$40$	3.02338	+	0.723021i	0.478038	+	0.114320i
$41$	3.13996	+	5.43858i	0.490380	+	0.849363i	0.999939	−	0.0110730i	$-0.00352472\pi$
$41$	3.13996	+	5.43858i	0.490380	+	0.849363i	−0.509559	+	0.860436i	$0.670191\pi$
$42$	−6.07002	−	1.97266i	−0.936624	−	0.304389i
$43$	3.94666	+	2.27861i	0.601860	+	0.347484i	0.769773	−	0.638318i	$-0.220369\pi$
$43$	3.94666	+	2.27861i	0.601860	+	0.347484i	−0.167913	+	0.985802i	$0.553703\pi$
$44$	1.18996	−	1.03565i	0.179394	−	0.156131i
$45$	−2.41301	+	2.24698i	−0.359710	+	0.334959i
$46$	−12.0781	+	1.16658i	−1.78082	+	0.172003i
$47$	5.29828	+	9.17688i	0.772833	+	1.33859i	0.936004	+	0.351988i	$0.114494\pi$
$47$	5.29828	+	9.17688i	0.772833	+	1.33859i	−0.163171	+	0.986598i	$0.552172\pi$
$48$	3.31088	+	6.08589i	0.477884	+	0.878423i
$49$	0.105288	+	0.182363i	0.0150411	+	0.0260519i
$50$	−5.33793	+	0.515573i	−0.754898	+	0.0729130i
$51$	−7.29777	−	3.17623i	−1.02189	−	0.444762i
$52$	1.14407	−	7.11977i	0.158654	−	0.987334i
$53$		−	0.616458i		−	0.0846770i	−0.999103	−	0.0423385i	$-0.986519\pi$
$53$		−	0.616458i		−	0.0846770i	0.999103	−	0.0423385i	$-0.0134808\pi$
$54$	−7.32001	−	0.646072i	−0.996128	−	0.0879193i
$55$	0.433452	−	0.750760i	0.0584466	−	0.101232i
$56$	−1.71413	+	7.16779i	−0.229060	+	0.957836i
$57$	2.10699	−	4.84106i	0.279078	−	0.641214i
$58$	10.7622	+	4.90078i	1.41315	+	0.643505i
$59$		−	9.91768i		−	1.29117i	−0.763688	−	0.645586i	$-0.776613\pi$
$59$		−	9.91768i		−	1.29117i	0.763688	−	0.645586i	$-0.223387\pi$
$60$	2.80762	+	2.57150i	0.362463	+	0.331979i
$61$	0.954069	+	0.550832i	0.122156	+	0.0705268i	0.559833	−	0.828606i	$-0.310865\pi$
$61$	0.954069	+	0.550832i	0.122156	+	0.0705268i	−0.437677	+	0.899132i	$0.644199\pi$
$62$	4.29566	+	6.01854i	0.545549	+	0.764355i
$63$	−5.32711	−	5.72073i	−0.671152	−	0.720744i
$64$	6.70165	−	4.36897i	0.837706	−	0.546122i
$65$	−0.677048	−	3.90447i	−0.0839775	−	0.484290i
$66$	1.88987	−	0.401588i	0.232627	−	0.0494321i
$67$	11.4089	−	6.58691i	1.39382	−	0.804720i	0.400080	−	0.916480i	$-0.368982\pi$
$67$	11.4089	−	6.58691i	1.39382	−	0.804720i	0.993735	+	0.111760i	$0.0356489\pi$
$68$	−2.98694	+	8.69135i	−0.362220	+	1.05398i
$69$	−13.6267	−	5.93079i	−1.64046	−	0.713984i
$70$	0.389364	+	4.03124i	0.0465379	+	0.481825i
$71$	−7.67022	−	13.2852i	−0.910288	−	1.57666i	−0.813658	−	0.581344i	$-0.802527\pi$
$71$	−7.67022	−	13.2852i	−0.910288	−	1.57666i	−0.0966302	−	0.995320i	$-0.530806\pi$
$72$	−0.0725455	+	8.48497i	−0.00854956	+	0.999963i
$73$	−3.19793			−0.374289			−0.187145	−	0.982332i	$-0.559923\pi$
$73$	−3.19793			−0.374289			−0.187145	+	0.982332i	$0.559923\pi$
$74$	−1.68605	+	1.20339i	−0.195999	+	0.139892i
$75$	−6.02235	−	2.62113i	−0.695401	−	0.302662i
$76$	−5.76550	−	1.98142i	−0.661349	−	0.227284i
$77$	1.77989	+	1.02762i	0.202838	+	0.117108i
$78$	5.45751	−	6.94375i	0.617941	−	0.786225i
$79$	7.48433	+	12.9632i	0.842053	+	1.45848i	0.888156	+	0.459542i	$0.151986\pi$
$79$	7.48433	+	12.9632i	0.842053	+	1.45848i	−0.0461034	+	0.998937i	$0.514680\pi$
$80$	2.70252	−	3.46749i	0.302151	−	0.387677i
$81$	−7.45421	−	5.04329i	−0.828245	−	0.560365i
$82$	8.84002	−	0.853828i	0.976217	−	0.0942895i
$83$	−1.72293	+	0.994734i	−0.189116	+	0.109186i	−0.591569	−	0.806255i	$-0.701491\pi$
$83$	−1.72293	+	0.994734i	−0.189116	+	0.109186i	0.402453	+	0.915441i	$0.368158\pi$
$84$	−6.09647	+	6.65628i	−0.665180	+	0.726260i
$85$			5.05036i			0.547789i
$86$	5.24577	−	3.74410i	0.565666	−	0.403737i
$87$	8.61083	+	11.6455i	0.923178	+	1.24853i
$88$	−0.635519	−	2.13853i	−0.0677466	−	0.227968i
$89$	5.76546	−	9.98606i	0.611137	−	1.05852i	−0.379912	−	0.925023i	$-0.624046\pi$
$89$	5.76546	−	9.98606i	0.611137	−	1.05852i	0.991049	−	0.133498i	$-0.0426210\pi$
$90$	1.47775	+	4.42259i	0.155768	+	0.466182i
$91$	9.25668	−	1.60514i	0.970363	−	0.168264i
$92$	−5.57734	+	16.2288i	−0.581478	+	1.69197i
$93$	1.02200	+	8.99826i	0.105976	+	0.933076i
$94$	14.9164	−	1.44072i	1.53851	−	0.148599i
$95$	−3.35021			−0.343725
$96$	9.77332	−	0.694422i	0.997485	−	0.0708741i
$97$	5.69622	−	9.86614i	0.578363	−	1.00175i	−0.417304	−	0.908767i	$-0.637025\pi$
$97$	5.69622	−	9.86614i	0.578363	−	1.00175i	0.995667	−	0.0929875i	$-0.0296417\pi$
$98$	0.296419	−	0.0286301i	0.0299428	−	0.00289208i
$99$	2.26241	+	0.693438i	0.227380	+	0.0696931i
$100$	−2.46492	+	7.17237i	−0.246492	+	0.717237i
$101$			13.2341i			1.31684i	0.752652	+	0.658419i	$0.228774\pi$
$101$			13.2341i			1.31684i	−0.752652	+	0.658419i	$0.771226\pi$
$102$	−8.36510	+	7.53107i	−0.828268	+	0.745688i
$103$	5.32038	−	9.21518i	0.524233	−	0.907998i	−0.475369	−	0.879787i	$-0.657685\pi$
$103$	5.32038	−	9.21518i	0.524233	−	0.907998i	0.999602	−	0.0282117i	$-0.00898125\pi$
$104$	−8.49299	−	5.64527i	−0.832807	−	0.553564i
$105$	−1.97949	+	4.54812i	−0.193179	+	0.443851i
$106$	−0.793414	−	0.361297i	−0.0770631	−	0.0350923i
$107$	2.41925	+	1.39675i	0.233877	+	0.135029i	0.612359	−	0.790579i	$-0.290221\pi$
$107$	2.41925	+	1.39675i	0.233877	+	0.135029i	−0.378482	+	0.925609i	$0.623554\pi$
$108$	−5.12168	+	9.04259i	−0.492834	+	0.870123i
$109$		−	16.2575i		−	1.55719i	−0.627529	−	0.778593i	$-0.715934\pi$
$109$		−	16.2575i		−	1.55719i	0.627529	−	0.778593i	$-0.284066\pi$
$110$	−0.712228	−	0.997885i	−0.0679083	−	0.0951446i
$111$	−2.52079	+	0.286305i	−0.239263	+	0.0271748i
$112$	8.22069	+	6.40711i	0.776782	+	0.605415i
$113$	−15.2559			−1.43516			−0.717579	−	0.696477i	$-0.754750\pi$
$113$	−15.2559			−1.43516			−0.717579	+	0.696477i	$0.754750\pi$
$114$	−4.99582	−	5.54908i	−0.467902	−	0.519719i
$115$			9.43024i			0.879375i
$116$	12.6151	−	10.9792i	1.17129	−	1.01940i
$117$	9.97170	−	4.19109i	0.921884	−	0.387466i
$118$	−12.7646	−	5.81261i	−1.17507	−	0.535094i
$119$	−11.9733			−1.09759
$120$	4.95516	−	2.10644i	0.452342	−	0.192291i
$121$	10.3779			0.943441
$122$	1.26812	−	0.905102i	0.114810	−	0.0819441i
$123$	9.97347	+	4.34078i	0.899277	+	0.391395i
$124$	10.2638	−	2.00136i	0.921716	−	0.179728i
$125$			9.66304i			0.864289i
$126$	−10.4850	+	3.50343i	−0.934080	+	0.312110i
$127$	−0.868706	+	1.50464i	−0.0770852	+	0.133516i	−0.901991	−	0.431755i	$-0.857895\pi$
$127$	−0.868706	+	1.50464i	−0.0770852	+	0.133516i	0.824906	+	0.565270i	$0.191228\pi$
$128$	−1.69536	−	11.1860i	−0.149850	−	0.988709i
$129$	7.84290	−	0.890775i	0.690529	−	0.0784284i
$130$	−5.42207	−	1.41696i	−0.475547	−	0.124275i
$131$	13.7390	+	7.93221i	1.20038	+	0.693041i	0.960640	−	0.277796i	$-0.0896039\pi$
$131$	13.7390	+	7.93221i	1.20038	+	0.693041i	0.239742	+	0.970837i	$0.422937\pi$
$132$	0.590761	−	2.66773i	0.0514192	−	0.232196i
$133$		−	7.94265i		−	0.688715i
$134$	−1.79113	−	18.5443i	−0.154730	−	1.60198i
$135$	−1.04669	+	5.61417i	−0.0900847	+	0.483191i
$136$	9.43562	+	8.93822i	0.809097	+	0.766446i
$137$	9.56255	−	16.5628i	0.816984	−	1.41506i	−0.0909110	−	0.995859i	$-0.528978\pi$
$137$	9.56255	−	16.5628i	0.816984	−	1.41506i	0.907895	−	0.419198i	$-0.137689\pi$
$138$	−15.6197	+	14.0623i	−1.32963	+	1.19707i
$139$			9.74981i			0.826968i	0.910511	+	0.413484i	$0.135688\pi$
$139$			9.74981i			0.826968i	−0.910511	+	0.413484i	$0.864312\pi$
$140$	5.41662	+	1.86152i	0.457788	+	0.157327i
$141$	16.8289	+	7.32450i	1.41725	+	0.616834i
$142$	−21.5942	+	2.08571i	−1.81214	+	0.175029i
$143$	−2.18375	+	1.82185i	−0.182615	+	0.152351i
$144$	10.8781	+	5.06629i	0.906507	+	0.422191i
$145$	4.59514	−	7.95901i	0.381605	−	0.660960i
$146$	−1.87426	+	4.11590i	−0.155115	+	0.340634i
$147$	0.334425	+	0.145553i	0.0275829	+	0.0120050i
$148$	0.560665	+	2.87532i	0.0460864	+	0.236350i
$149$			0.336190i			0.0275418i	0.999905	+	0.0137709i	$0.00438355\pi$
$149$			0.336190i			0.0275418i	−0.999905	+	0.0137709i	$0.995616\pi$
$150$	−6.90314	+	6.21488i	−0.563639	+	0.507443i
$151$	4.27767	+	7.40914i	0.348112	+	0.602947i	0.985914	−	0.167253i	$-0.0534897\pi$
$151$	4.27767	+	7.40914i	0.348112	+	0.602947i	−0.637802	+	0.770200i	$0.720156\pi$
$152$	−5.92927	+	6.25922i	−0.480927	+	0.507690i
$153$	−13.4343	+	3.09154i	−1.08610	+	0.249936i
$154$	2.36577	−	1.68854i	0.190639	−	0.136067i
$155$	4.97663	−	2.87326i	0.399733	−	0.230786i
$156$	−5.73840	−	11.0937i	−0.459440	−	0.888209i
$157$	−0.808781	−	0.466950i	−0.0645478	−	0.0372667i	0.467379	−	0.884057i	$-0.345198\pi$
$157$	−0.808781	−	0.466950i	−0.0645478	−	0.0372667i	−0.531927	+	0.846790i	$0.678532\pi$
$158$	21.0708	−	2.03516i	1.67630	−	0.161909i
$159$	−0.634810	−	0.858532i	−0.0503437	−	0.0680860i
$160$	−2.87893	−	5.51053i	−0.227600	−	0.435646i
$161$	−22.3571			−1.76199
$162$	−10.8598	+	6.63816i	−0.853225	+	0.521543i
$163$	2.43874	−	1.40800i	0.191017	−	0.110283i	−0.401442	−	0.915885i	$-0.631491\pi$
$163$	2.43874	−	1.40800i	0.191017	−	0.110283i	0.592458	+	0.805601i	$0.298157\pi$
$164$	4.08208	−	11.8780i	0.318757	−	0.927515i
$165$	−0.169449	−	1.49193i	−0.0131916	−	0.116146i
$166$	0.270491	+	2.80050i	0.0209942	+	0.217361i
$167$	2.19707	+	3.80544i	0.170014	+	0.294473i	0.938425	−	0.345484i	$-0.112285\pi$
$167$	2.19707	+	3.80544i	0.170014	+	0.294473i	−0.768410	+	0.639957i	$0.778952\pi$
$168$	4.99393	+	11.7476i	0.385290	+	0.906349i
$169$	−2.33003	+	12.7895i	−0.179233	+	0.983807i
$170$	6.50008	+	2.95994i	0.498533	+	0.227017i
$171$	−2.05081	−	8.91179i	−0.156829	−	0.681502i
$172$	−1.74439	−	8.94594i	−0.133008	−	0.682122i
$173$	−14.3018	−	8.25717i	−1.08735	−	0.627781i	−0.154479	−	0.987996i	$-0.549370\pi$
$173$	−14.3018	−	8.25717i	−1.08735	−	0.627781i	−0.932869	+	0.360215i	$0.882703\pi$
$174$	20.0350	−	4.25735i	1.51885	−	0.322748i
$175$	−9.88078			−0.746917
$176$	−3.12487	−	0.435414i	−0.235546	−	0.0328206i
$177$	−10.2129	−	13.8122i	−0.767651	−	1.03819i
$178$	−9.47354	−	13.2731i	−0.710072	−	0.994863i
$179$	14.7604	+	8.52195i	1.10325	+	0.636960i	0.937072	−	0.349136i	$-0.113525\pi$
$179$	14.7604	+	8.52195i	1.10325	+	0.636960i	0.166175	+	0.986096i	$0.446858\pi$
$180$	6.55819	+	0.690075i	0.488818	+	0.0514351i
$181$		−	3.54674i		−	0.263627i	−0.991275	−	0.131814i	$-0.957920\pi$
$181$		−	3.54674i		−	0.263627i	0.991275	−	0.131814i	$-0.0420800\pi$
$182$	3.35931	−	12.8546i	0.249008	−	0.952845i
$183$	1.89595	−	0.215337i	0.140153	−	0.0159181i
$184$	17.6186	+	16.6898i	1.29886	+	1.23039i
$185$	0.804921	+	1.39416i	0.0591789	+	0.102501i
$186$	12.1802	+	3.95839i	0.893097	+	0.290243i
$187$	3.13889	−	1.81224i	0.229539	−	0.132524i
$188$	6.88798	−	20.0425i	0.502358	−	1.46175i
$189$	−13.3100	−	2.48148i	−0.968162	−	0.180501i
$190$	−1.96351	+	4.31190i	−0.142448	+	0.312818i
$191$	1.22176	−	2.11615i	0.0884035	−	0.153119i	−0.818433	−	0.574602i	$-0.805157\pi$
$191$	1.22176	−	2.11615i	0.0884035	−	0.153119i	0.906836	+	0.421483i	$0.138490\pi$
$192$	4.83424	−	12.9858i	0.348881	−	0.937167i
$193$	−0.271183	−	0.469703i	−0.0195202	−	0.0338099i	0.856100	−	0.516810i	$-0.172881\pi$
$193$	−0.271183	−	0.469703i	−0.0195202	−	0.0338099i	−0.875620	+	0.483000i	$0.839547\pi$
$194$	−9.35977	−	13.1137i	−0.671992	−	0.941511i
$195$	−4.96362	−	4.74049i	−0.355453	−	0.339474i
$196$	0.136878	−	0.398286i	0.00977702	−	0.0284490i
$197$	−12.5387	−	7.23924i	−0.893348	−	0.515775i	−0.0183118	−	0.999832i	$-0.505829\pi$
$197$	−12.5387	−	7.23924i	−0.893348	−	0.515775i	−0.875036	+	0.484058i	$0.839162\pi$
$198$	2.21845	−	2.50542i	0.157659	−	0.178053i
$199$	10.3208	+	17.8762i	0.731625	+	1.26721i	0.956189	+	0.292752i	$0.0945709\pi$
$199$	10.3208	+	17.8762i	0.731625	+	1.26721i	−0.224564	+	0.974459i	$0.572096\pi$
$200$	7.78657	+	7.37610i	0.550593	+	0.521569i
$201$	9.10596	−	20.9220i	0.642285	−	1.47573i
$202$	17.0329	+	7.75628i	1.19843	+	0.545730i
$203$	18.8691	+	10.8941i	1.32435	+	0.764616i
$204$	4.79023	+	15.1802i	0.335383	+	1.06282i
$205$		−	6.90205i		−	0.482060i
$206$	−8.74221	−	12.2485i	−0.609099	−	0.853393i
$207$	−25.0851	+	5.77265i	−1.74353	+	0.401227i
$208$	−12.2434	+	7.62232i	−0.848925	+	0.528513i
$209$	1.20217	+	2.08222i	0.0831559	+	0.144030i
$210$	4.69351	+	5.21329i	0.323883	+	0.359751i
$211$	−11.5880	+	6.69032i	−0.797750	+	0.460581i	−0.842684	−	0.538409i	$-0.819026\pi$
$211$	−11.5880	+	6.69032i	−0.797750	+	0.460581i	0.0449341	+	0.998990i	$0.485692\pi$
$212$	−0.930016	+	0.809414i	−0.0638738	+	0.0555908i
$213$	−24.3629	−	10.6036i	−1.66932	−	0.726543i
$214$	3.21558	−	2.29508i	0.219812	−	0.156888i
$215$	−2.50434	−	4.33764i	−0.170794	−	0.295825i
$216$	8.63654	+	11.8916i	0.587642	+	0.809121i
$217$	6.81189	+	11.7985i	0.462421	+	0.800937i
$218$	−20.9243	−	9.52828i	−1.41717	−	0.645337i
$219$	−4.45371	+	3.29313i	−0.300954	+	0.222529i
$220$	−1.70176	+	0.331829i	−0.114732	+	0.0223719i
$221$	5.71074	−	15.5527i	0.384146	−	1.04619i
$222$	−1.10891	+	3.41219i	−0.0744252	+	0.229011i
$223$	13.2479			0.887142			0.443571	−	0.896239i	$-0.353711\pi$
$223$	13.2479			0.887142			0.443571	+	0.896239i	$0.353711\pi$
$224$	13.0643	−	6.82535i	0.872896	−	0.456038i
$225$	−11.0864	+	2.55124i	−0.739094	+	0.170082i
$226$	−8.94128	+	19.6352i	−0.594765	+	1.30611i
$227$	2.20634	+	1.27383i	0.146440	+	0.0845470i	0.571430	−	0.820651i	$-0.306389\pi$
$227$	2.20634	+	1.27383i	0.146440	+	0.0845470i	−0.424990	+	0.905198i	$0.639722\pi$
$228$	−10.0699	+	3.17765i	−0.666898	+	0.210445i
$229$	13.7300	+	7.92704i	0.907306	+	0.523834i	0.879563	−	0.475782i	$-0.157835\pi$
$229$	13.7300	+	7.92704i	0.907306	+	0.523834i	0.0277428	+	0.999615i	$0.491168\pi$
$230$	12.1372	+	5.52693i	0.800305	+	0.364435i
$231$	3.53705	−	0.401728i	0.232721	−	0.0264318i
$232$	−6.73731	−	22.6711i	−0.442326	−	1.48843i
$233$	−13.2878			−0.870510			−0.435255	−	0.900307i	$-0.643342\pi$
$233$	−13.2878			−0.870510			−0.435255	+	0.900307i	$0.643342\pi$
$234$	0.450121	−	15.2904i	0.0294253	−	0.999567i
$235$		−	11.6463i		−	0.759721i
$236$	−14.9623	+	13.0220i	−0.973960	+	0.847659i
$237$	23.7725	+	10.3466i	1.54419	+	0.672082i
$238$	−7.01740	+	15.4103i	−0.454870	+	0.998903i
$239$	2.19077	−	3.79453i	0.141709	−	0.245448i	−0.786431	−	0.617678i	$-0.788073\pi$
$239$	2.19077	−	3.79453i	0.141709	−	0.245448i	0.928140	+	0.372230i	$0.121407\pi$
$240$	0.193041	−	7.61210i	0.0124608	−	0.491359i
$241$	−0.631223	+	1.09331i	−0.0406606	+	0.0704263i	−0.885640	−	0.464373i	$-0.846280\pi$
$241$	−0.631223	+	1.09331i	−0.0406606	+	0.0704263i	0.844979	+	0.534800i	$0.179613\pi$
$242$	6.08231	−	13.3568i	0.390985	−	0.858610i
$243$	−15.5748	+	0.652411i	−0.999124	+	0.0418522i
$244$	−0.421690	−	2.16260i	−0.0269959	−	0.138446i
$245$		−	0.231436i		−	0.0147859i
$246$	11.4321	−	10.2923i	0.728885	−	0.656213i
$247$	10.3171	+	3.78828i	0.656459	+	0.241043i
$248$	3.43960	−	14.3830i	0.218415	−	0.913322i
$249$	−1.37515	+	3.15957i	−0.0871467	+	0.200230i
$250$	12.4368	+	5.66337i	0.786575	+	0.358183i
$251$	−11.5952	+	6.69447i	−0.731880	+	0.422551i	−0.819110	−	0.573637i	$-0.805532\pi$
$251$	−11.5952	+	6.69447i	−0.731880	+	0.422551i	0.0872293	+	0.996188i	$0.472199\pi$
$252$	−1.63602	+	15.5481i	−0.103060	+	0.979437i
$253$	5.86107	−	3.38389i	0.368482	−	0.212743i
$254$	1.42742	+	1.99992i	0.0895642	+	0.125486i
$255$	5.20071	+	7.03356i	0.325681	+	0.440459i
$256$	−15.3905	−	4.37391i	−0.961909	−	0.273369i
$257$	−8.21477	−	14.2284i	−0.512424	−	0.887544i	−0.999896	−	0.0144054i	$-0.995414\pi$
$257$	−8.21477	−	14.2284i	−0.512424	−	0.887544i	0.487473	−	0.873138i	$-0.337919\pi$
$258$	3.45013	−	10.6163i	0.214796	−	0.660942i
$259$	−3.30527	+	1.90830i	−0.205379	+	0.118576i
$260$	−5.00149	+	6.14803i	−0.310179	+	0.381284i
$261$	23.9844	+	7.35132i	1.48459	+	0.455035i
$262$	18.2614	−	13.0339i	1.12819	−	0.805234i
$263$	11.2390			0.693028			0.346514	−	0.938045i	$-0.387365\pi$
$263$	11.2390			0.693028			0.346514	+	0.938045i	$0.387365\pi$
$264$	−3.08727	−	2.32386i	−0.190008	−	0.143024i
$265$	−0.338764	+	0.586756i	−0.0208101	+	0.0360441i
$266$	−10.2226	−	4.65507i	−0.626788	−	0.285421i
$267$	−2.25389	−	19.8445i	−0.137936	−	1.21447i
$268$	−24.9173	−	8.56327i	−1.52206	−	0.523085i
$269$	−6.99000	+	4.03568i	−0.426188	+	0.246060i	−0.697721	−	0.716369i	$-0.745803\pi$
$269$	−6.99000	+	4.03568i	−0.426188	+	0.246060i	0.271533	+	0.962429i	$0.412469\pi$
$270$	6.61229	+	4.63753i	0.402411	+	0.282231i
$271$	0.0161082	−	0.0279003i	0.000978506	−	0.00169482i	−0.865536	−	0.500847i	$-0.833022\pi$
$271$	0.0161082	−	0.0279003i	0.000978506	−	0.00169482i	0.866514	+	0.499152i	$0.166355\pi$
$272$	17.0340	−	6.90557i	1.03284	−	0.418712i
$273$	11.2387	−	11.7677i	0.680198	−	0.712214i
$274$	−15.7127	−	22.0147i	−0.949242	−	1.32996i
$275$	2.59031	−	1.49552i	0.156202	−	0.0901831i
$276$	8.94451	+	28.3450i	0.538396	+	1.70617i
$277$	4.94990	+	2.85783i	0.297411	+	0.171710i	0.641279	−	0.767308i	$-0.278404\pi$
$277$	4.94990	+	2.85783i	0.297411	+	0.171710i	−0.343868	+	0.939018i	$0.611737\pi$
$278$	12.5485	+	5.71422i	0.752610	+	0.342716i
$279$	10.6895	+	11.4793i	0.639962	+	0.687249i
$280$	5.57047	−	5.88046i	0.332899	−	0.351425i
$281$	10.6750	+	18.4896i	0.636814	+	1.10299i	0.986128	+	0.165989i	$0.0530816\pi$
$281$	10.6750	+	18.4896i	0.636814	+	1.10299i	−0.349313	+	0.937006i	$0.613585\pi$
$282$	19.2902	−	17.3669i	1.14871	−	1.03418i
$283$	−18.3335	+	10.5848i	−1.08981	+	0.629203i	−0.933526	−	0.358509i	$-0.883285\pi$
$283$	−18.3335	+	10.5848i	−1.08981	+	0.629203i	−0.156285	+	0.987712i	$0.549952\pi$
$284$	−9.97161	+	29.0152i	−0.591706	+	1.72174i
$285$	−4.66579	+	3.44995i	−0.276378	+	0.204358i
$286$	1.06496	+	3.87837i	0.0629722	+	0.229333i
$287$	16.3633			0.965895
$288$	12.8961	−	11.0314i	0.759908	−	0.650031i
$289$	−2.05766	+	3.56398i	−0.121039	+	0.209646i
$290$	−7.55052	−	10.5788i	−0.443382	−	0.621211i
$291$	−2.22682	−	19.6062i	−0.130539	−	1.14934i
$292$	4.19891	+	4.82454i	0.245722	+	0.282335i
$293$			19.4085i			1.13386i	0.823767	+	0.566928i	$0.191868\pi$
$293$			19.4085i			1.13386i	−0.823767	+	0.566928i	$0.808132\pi$
$294$	0.383336	−	0.345116i	0.0223566	−	0.0201276i
$295$	−5.45009	+	9.43983i	−0.317316	+	0.549608i
$296$	4.02929	+	0.963577i	0.234197	+	0.0560068i
$297$	3.86490	−	1.36402i	0.224264	−	0.0791484i
$298$	0.432694	+	0.197036i	0.0250653	+	0.0114140i
$299$	10.6633	−	29.0407i	0.616676	−	1.67946i
$300$	3.95305	+	12.5272i	0.228229	+	0.723256i
$301$	10.2836	−	5.93726i	0.592739	−	0.342218i
$302$	12.0430	−	1.16320i	0.692998	−	0.0669344i
$303$	13.6280	+	18.4309i	0.782910	+	1.05883i
$304$	4.58089	+	11.2997i	0.262732	+	0.648083i
$305$	−0.605400	−	1.04858i	−0.0346651	−	0.0600418i
$306$	−3.89467	+	19.1025i	−0.222643	+	1.09202i
$307$			19.6660i			1.12240i	0.827682	+	0.561198i	$0.189659\pi$
$307$			19.6660i			1.12240i	−0.827682	+	0.561198i	$0.810341\pi$
$308$	−0.786698	−	4.03451i	−0.0448263	−	0.229887i
$309$	−2.07990	−	18.3126i	−0.118321	−	1.04177i
$310$	−0.781305	−	8.08916i	−0.0443751	−	0.459434i
$311$	−2.90685	+	5.03481i	−0.164832	+	0.285498i	−0.936596	−	0.350412i	$-0.886042\pi$
$311$	−2.90685	+	5.03481i	−0.164832	+	0.285498i	0.771763	+	0.635910i	$0.219375\pi$
$312$	−17.6414	+	0.883755i	−0.998748	+	0.0500328i
$313$	−10.8847	−	18.8528i	−0.615237	−	1.06562i	−0.990343	−	0.138640i	$-0.955727\pi$
$313$	−10.8847	−	18.8528i	−0.615237	−	1.06562i	0.375106	−	0.926982i	$-0.377606\pi$
$314$	−1.07500	+	0.767271i	−0.0606660	+	0.0432996i
$315$	1.92671	+	8.37252i	0.108558	+	0.471738i
$316$	9.72994	−	28.3120i	0.547352	−	1.59268i
$317$	−2.53961	+	1.46625i	−0.142639	+	0.0823526i	−0.569621	−	0.821907i	$-0.692910\pi$
$317$	−2.53961	+	1.46625i	−0.142639	+	0.0823526i	0.426982	+	0.904260i	$0.359577\pi$
$318$	−1.47703	+	0.313861i	−0.0828276	+	0.0176005i
$319$	−6.59556			−0.369281
$320$	−8.77965	+	0.475697i	−0.490797	+	0.0265923i
$321$	4.80758	−	0.546032i	0.268333	−	0.0304765i
$322$	−13.1032	+	28.7748i	−0.730212	+	1.60356i
$323$	−12.1305	−	7.00354i	−0.674959	−	0.389688i
$324$	2.17890	+	17.8676i	0.121050	+	0.992646i
$325$	4.71268	−	12.8346i	0.261413	−	0.711934i
$326$	−0.382869	−	3.96399i	−0.0212051	−	0.219545i
$327$	−16.7415	−	22.6416i	−0.925807	−	1.25208i
$328$	−12.8951	−	12.2154i	−0.712015	−	0.674481i
$329$	27.6109			1.52224
$330$	−2.01950	−	0.656308i	−0.111170	−	0.0361285i
$331$	16.1216	+	9.30783i	0.886125	+	0.511604i	0.872673	−	0.488305i	$-0.162385\pi$
$331$	16.1216	+	9.30783i	0.886125	+	0.511604i	0.0134519	+	0.999910i	$0.495718\pi$
$332$	3.76292	+	1.29320i	0.206517	+	0.0709734i
$333$	−3.21584	+	2.99457i	−0.176227	+	0.164101i
$334$	6.18546	−	0.597433i	0.338454	−	0.0326901i
$335$	−14.4789			−0.791067
$336$	18.0467	+	0.457660i	0.984528	+	0.0249674i
$337$	−10.8924	+	18.8662i	−0.593346	+	1.02771i	0.400432	+	0.916327i	$0.368860\pi$
$337$	−10.8924	+	18.8662i	−0.593346	+	1.02771i	−0.993778	+	0.111379i	$0.964473\pi$
$338$	15.0951	+	10.4946i	0.821068	+	0.570831i
$339$	−21.2467	+	15.7101i	−1.15396	+	0.853257i
$340$	7.61920	−	6.63116i	0.413209	−	0.359625i
$341$	−3.57157	−	2.06205i	−0.193411	−	0.111666i
$342$	−12.6719	−	2.58357i	−0.685217	−	0.139704i
$343$	18.7883			1.01447
$344$	−12.5363	−	2.99796i	−0.675910	−	0.161639i
$345$	9.71099	+	13.1334i	0.522822	+	0.707077i
$346$	−19.0095	+	13.5678i	−1.02196	+	0.729410i
$347$			32.9290i			1.76772i	0.467752	+	0.883860i	$0.345064\pi$
$347$			32.9290i			1.76772i	−0.467752	+	0.883860i	$0.654936\pi$
$348$	6.26282	−	28.2813i	0.335722	−	1.51604i
$349$		−	19.6760i		−	1.05323i	−0.850103	−	0.526616i	$-0.823460\pi$
$349$		−	19.6760i		−	1.05323i	0.850103	−	0.526616i	$-0.176540\pi$
$350$	−5.79098	+	12.7171i	−0.309541	+	0.679756i
$351$	9.57158	−	16.1054i	0.510893	−	0.859644i
$352$	−2.39184	+	3.76668i	−0.127485	+	0.200765i
$353$	12.8291			0.682823			0.341412	−	0.939914i	$-0.389095\pi$
$353$	12.8291			0.682823			0.341412	+	0.939914i	$0.389095\pi$
$354$	−23.7627	+	5.04945i	−1.26297	+	0.268375i
$355$			16.8602i			0.894844i
$356$	−22.6355	+	4.41375i	−1.19968	+	0.233928i
$357$	−16.6751	+	12.3298i	−0.882540	+	0.652562i
$358$	19.6191	−	14.0029i	1.03690	−	0.740075i
$359$	−2.53795			−0.133948			−0.0669738	−	0.997755i	$-0.521334\pi$
$359$	−2.53795			−0.133948			−0.0669738	+	0.997755i	$0.521334\pi$
$360$	4.73182	−	8.03629i	0.249389	−	0.423550i
$361$	−4.85412	+	8.40758i	−0.255480	+	0.442504i
$362$	−4.56484	−	2.07869i	−0.239923	−	0.109254i
$363$	14.4531	−	10.6868i	0.758590	−	0.560912i
$364$	−14.5757	−	11.8575i	−0.763973	−	0.621501i
$365$	3.04385	+	1.75737i	0.159322	+	0.0919848i
$366$	0.834038	−	2.56639i	0.0435959	−	0.134147i
$367$	32.0628			1.67367			0.836833	−	0.547459i	$-0.184405\pi$
$367$	32.0628			1.67367			0.836833	+	0.547459i	$0.184405\pi$
$368$	31.8067	−	12.8944i	1.65804	−	0.672166i
$369$	18.3599	−	4.22504i	0.955779	−	0.219947i
$370$	2.26611	−	0.218876i	0.117810	−	0.0113788i
$371$	−1.39107	−	0.803137i	−0.0722210	−	0.0416968i
$372$	12.2333	−	13.3566i	0.634267	−	0.692509i
$373$		−	8.26211i		−	0.427796i	−0.976856	−	0.213898i	$-0.931384\pi$
$373$		−	8.26211i		−	0.427796i	0.976856	−	0.213898i	$-0.0686160\pi$
$374$	−0.492790	−	5.10205i	−0.0254815	−	0.263821i
$375$	9.95072	+	13.4576i	0.513853	+	0.694946i
$376$	−21.7589	−	20.6118i	−1.12213	−	1.06297i
$377$	−23.1505	+	19.3140i	−1.19231	+	0.994720i
$378$	−10.9946	+	15.6763i	−0.565502	+	0.806304i
$379$	2.16207	+	1.24827i	0.111058	+	0.0641193i	0.554500	−	0.832184i	$-0.312910\pi$
$379$	2.16207	+	1.24827i	0.111058	+	0.0641193i	−0.443442	+	0.896303i	$0.646243\pi$
$380$	4.39886	+	5.05428i	0.225657	+	0.259279i
$381$	0.339603	+	2.99006i	0.0173984	+	0.153186i
$382$	−2.00754	−	2.81271i	−0.102715	−	0.143911i
$383$	−7.99104			−0.408323			−0.204161	−	0.978937i	$-0.565447\pi$
$383$	−7.99104			−0.408323			−0.204161	+	0.978937i	$0.565447\pi$
$384$	−13.8801	−	13.8327i	−0.708315	−	0.705897i
$385$	−1.12942	−	1.95622i	−0.0575608	−	0.0996982i
$386$	−0.763468	+	0.0737408i	−0.0388595	+	0.00375331i
$387$	10.0054	−	9.31696i	0.508603	−	0.473608i
$388$	−22.3637	+	4.36075i	−1.13534	+	0.221383i
$389$	−14.3211	+	8.26828i	−0.726107	+	0.419218i	−0.816996	−	0.576643i	$-0.804362\pi$
$389$	−14.3211	+	8.26828i	−0.726107	+	0.419218i	0.0908891	+	0.995861i	$0.471029\pi$
$390$	−9.01037	+	3.61011i	−0.456258	+	0.182805i
$391$	−19.7137	+	34.1451i	−0.996965	+	1.72679i
$392$	−0.432393	−	0.409599i	−0.0218391	−	0.0206879i
$393$	27.3025	−	3.10094i	1.37723	−	0.156422i
$394$	−16.6661	+	11.8952i	−0.839624	+	0.599271i
$395$		−	16.4515i		−	0.827767i
$396$	−1.92441	−	4.32366i	−0.0967050	−	0.217272i
$397$	−11.8706	+	6.85348i	−0.595767	+	0.343966i	−0.767375	−	0.641199i	$-0.778437\pi$
$397$	−11.8706	+	6.85348i	−0.595767	+	0.343966i	0.171608	+	0.985165i	$0.445104\pi$
$398$	29.0565	−	2.80647i	1.45647	−	0.140676i
$399$	−8.17911	−	11.0616i	−0.409468	−	0.553773i
$400$	14.0570	−	5.69870i	0.702851	−	0.284935i
$401$	0.492492	+	0.853021i	0.0245939	+	0.0425978i	0.878060	−	0.478550i	$-0.158837\pi$
$401$	0.492492	+	0.853021i	0.0245939	+	0.0425978i	−0.853467	+	0.521148i	$0.825504\pi$
$402$	−21.5909	−	23.9819i	−1.07685	−	1.19611i
$403$	−18.5746	+	3.22090i	−0.925268	+	0.160444i
$404$	19.9655	−	17.3764i	0.993320	−	0.864509i
$405$	4.32360	+	8.89663i	0.214842	+	0.442077i
$406$	25.0802	−	17.9007i	1.24471	−	0.888396i
$407$	0.577666	−	1.00055i	0.0286338	−	0.0495952i
$408$	22.3452	+	2.73160i	1.10625	+	0.135234i
$409$	−19.3894			−0.958743			−0.479371	−	0.877612i	$-0.659135\pi$
$409$	−19.3894			−0.958743			−0.479371	+	0.877612i	$0.659135\pi$
$410$	−8.88330	−	4.04519i	−0.438715	−	0.199778i
$411$	−3.73829	−	32.9140i	−0.184396	−	1.62353i
$412$	−20.8881	+	4.07303i	−1.02908	+	0.200664i
$413$	−22.3799	−	12.9210i	−1.10124	−	0.635801i
$414$	−7.27229	+	35.6691i	−0.357413	+	1.75304i
$415$	2.18656			0.107334
$416$	2.63466	+	20.2252i	0.129175	+	0.991622i
$417$	10.0401	+	13.5784i	0.491664	+	0.664938i
$418$	3.38450	−	0.326898i	0.165541	−	0.0159891i
$419$	7.05646	−	4.07405i	0.344731	−	0.199030i	−0.317631	−	0.948214i	$-0.602887\pi$
$419$	7.05646	−	4.07405i	0.344731	−	0.199030i	0.662362	+	0.749184i	$0.269554\pi$
$420$	9.46058	−	2.98536i	0.461629	−	0.145671i
$421$	−17.9654	+	10.3723i	−0.875582	+	0.505517i	−0.869199	−	0.494462i	$-0.835365\pi$
$421$	−17.9654	+	10.3723i	−0.875582	+	0.505517i	−0.00638266	+	0.999980i	$0.502032\pi$
$422$	1.81925	+	18.8354i	0.0885598	+	0.916895i
$423$	30.9799	−	7.12920i	1.50630	−	0.346634i
$424$	0.496689	+	1.67137i	0.0241214	+	0.0811687i
$425$	−8.71251	+	15.0905i	−0.422619	+	0.731998i
$426$	−27.9261	+	25.1418i	−1.35302	+	1.21812i
$427$	2.48597	−	1.43528i	0.120305	−	0.0694579i
$428$	−1.06929	−	5.48373i	−0.0516858	−	0.265066i
$429$	−1.16519	+	4.78604i	−0.0562558	+	0.231072i
$430$	−7.05053	+	0.680987i	−0.340007	+	0.0328401i
$431$	−11.6930	+	20.2528i	−0.563231	+	0.975545i	0.433981	+	0.900922i	$0.357109\pi$
$431$	−11.6930	+	20.2528i	−0.563231	+	0.975545i	−0.997212	+	0.0746227i	$0.976225\pi$
$432$	20.3669	−	4.14619i	0.979901	−	0.199484i
$433$	−5.73141	−	9.92709i	−0.275434	−	0.477066i	0.694811	−	0.719193i	$-0.255488\pi$
$433$	−5.73141	−	9.92709i	−0.275434	−	0.477066i	−0.970245	+	0.242127i	$0.922155\pi$
$434$	19.1777	−	1.85231i	0.920559	−	0.0889137i
$435$	−1.79638	−	15.8163i	−0.0861296	−	0.758335i
$436$	−24.5268	+	21.3462i	−1.17462	+	1.02230i
$437$	−22.6506	−	13.0773i	−1.08352	−	0.625573i
$438$	1.62818	+	7.66221i	0.0777975	+	0.366115i
$439$	−25.9513			−1.23859			−0.619293	−	0.785160i	$-0.712581\pi$
$439$	−25.9513			−1.23859			−0.619293	+	0.785160i	$0.712581\pi$
$440$	−0.570293	+	2.38473i	−0.0271876	+	0.113688i
$441$	0.615635	−	0.141672i	0.0293159	−	0.00674627i
$442$	−16.6702	−	16.4652i	−0.792919	−	0.783171i
$443$	−11.8732	+	6.85501i	−0.564114	+	0.325691i	−0.754795	−	0.655961i	$-0.772264\pi$
$443$	−11.8732	+	6.85501i	−0.564114	+	0.325691i	0.190681	+	0.981652i	$0.438930\pi$
$444$	3.74175	+	3.42706i	0.177576	+	0.162641i
$445$	−10.9753	+	6.33661i	−0.520281	+	0.300384i
$446$	7.76438	−	17.0507i	0.367654	−	0.807374i
$447$	0.346199	+	0.468207i	0.0163746	+	0.0221454i
$448$	−1.12778	−	20.8147i	−0.0532825	−	0.983402i
$449$	9.12459	+	15.8042i	0.430616	+	0.745849i	0.996926	−	0.0783434i	$-0.0249631\pi$
$449$	9.12459	+	15.8042i	0.430616	+	0.745849i	−0.566311	+	0.824192i	$0.691630\pi$
$450$	−3.21400	+	15.7640i	−0.151510	+	0.743123i
$451$	−4.28975	+	2.47669i	−0.201997	+	0.116623i
$452$	20.0312	+	23.0158i	0.942187	+	1.08257i
$453$	13.5872	+	5.91358i	0.638380	+	0.277844i
$454$	2.93259	−	2.09310i	0.137633	−	0.0982340i
$455$	−9.69275	−	3.55905i	−0.454403	−	0.166851i
$456$	−1.81204	+	14.8229i	−0.0848565	+	0.694147i
$457$	−37.1593			−1.73824			−0.869119	−	0.494603i	$-0.835314\pi$
$457$	−37.1593			−1.73824			−0.869119	+	0.494603i	$0.835314\pi$
$458$	18.2495	−	13.0254i	0.852743	−	0.608635i
$459$	−15.5262	+	18.1398i	−0.724699	+	0.846693i
$460$	14.2269	−	12.3820i	0.663332	−	0.577313i
$461$	23.0438	+	13.3044i	1.07326	+	0.619645i	0.929070	−	0.369905i	$-0.120610\pi$
$461$	23.0438	+	13.3044i	1.07326	+	0.619645i	0.144188	+	0.989550i	$0.453943\pi$
$462$	1.55597	−	4.78781i	0.0723901	−	0.222749i
$463$	13.3735	−	23.1637i	0.621521	−	1.07651i	−0.367681	−	0.929952i	$-0.619848\pi$
$463$	13.3735	−	23.1637i	0.621521	−	1.07651i	0.989203	−	0.146554i	$-0.0468183\pi$
$464$	−33.1275	−	4.61594i	−1.53791	−	0.214290i
$465$	3.97208	−	9.12634i	0.184201	−	0.423224i
$466$	−7.78776	+	17.1021i	−0.360761	+	0.792237i
$467$			0.685279i			0.0317109i	0.999874	+	0.0158555i	$0.00504716\pi$
$467$			0.685279i			0.0317109i	−0.999874	+	0.0158555i	$0.994953\pi$
$468$	−19.4158	−	9.54083i	−0.897495	−	0.441025i
$469$		−	34.3264i		−	1.58505i
$470$	−14.9894	−	6.82573i	−0.691410	−	0.314847i
$471$	−1.60723	+	0.182545i	−0.0740572	+	0.00841121i
$472$	7.99082	+	26.8892i	0.367808	+	1.23768i
$473$	−1.79728	+	3.11298i	−0.0826391	+	0.143135i
$474$	27.2493	−	24.5325i	1.25160	−	1.12681i
$475$	−10.0105	−	5.77955i	−0.459312	−	0.265184i
$476$	15.7211	+	18.0635i	0.720575	+	0.827940i
$477$	−1.76818	−	0.541956i	−0.0809595	−	0.0248144i
$478$	−3.59978	−	5.04356i	−0.164650	−	0.230687i
$479$	−5.88298			−0.268800			−0.134400	−	0.990927i	$-0.542911\pi$
$479$	−5.88298			−0.268800			−0.134400	+	0.990927i	$0.542911\pi$
$480$	−9.68404	−	4.70980i	−0.442014	−	0.214972i
$481$	−0.902309	−	5.20353i	−0.0411418	−	0.237261i
$482$	1.03720	+	1.45319i	0.0472430	+	0.0661910i
$483$	−31.1364	+	23.0227i	−1.41676	+	1.04757i
$484$	−13.6262	−	15.6565i	−0.619373	−	0.711659i
$485$	−10.8435	+	6.26052i	−0.492379	+	0.284275i
$486$	−8.28847	+	20.4280i	−0.375973	+	0.926631i
$487$	4.30239	+	7.45196i	0.194960	+	0.337681i	0.946887	−	0.321565i	$-0.104209\pi$
$487$	4.30239	+	7.45196i	0.194960	+	0.337681i	−0.751927	+	0.659246i	$0.770876\pi$
$488$	−3.03052	−	0.724730i	−0.137185	−	0.0328070i
$489$	1.94647	−	4.47225i	0.0880224	−	0.202242i
$490$	−0.297870	−	0.135641i	−0.0134564	−	0.00612764i
$491$	22.3735	−	12.9174i	1.00970	−	0.582953i	0.0985986	−	0.995127i	$-0.468564\pi$
$491$	22.3735	−	12.9174i	1.00970	−	0.582953i	0.911105	+	0.412175i	$0.135231\pi$
$492$	−6.54654	−	20.7459i	−0.295141	−	0.935298i
$493$	33.2762	−	19.2120i	1.49869	−	0.865267i
$494$	10.9224	−	11.0583i	0.491422	−	0.497538i
$495$	−1.77233	−	1.90329i	−0.0796605	−	0.0855467i
$496$	−16.4958	−	12.8566i	−0.740683	−	0.577279i
$497$	−39.9719			−1.79298
$498$	3.26058	+	3.62167i	0.146110	+	0.162291i
$499$	−20.7450	−	11.9771i	−0.928675	−	0.536171i	−0.0422825	−	0.999106i	$-0.513463\pi$
$499$	−20.7450	−	11.9771i	−0.928675	−	0.536171i	−0.886392	+	0.462935i	$0.846796\pi$
$500$	14.5781	−	12.6877i	0.651953	−	0.567409i
$501$	6.97855	+	3.03730i	0.311779	+	0.135696i
$502$	1.82038	+	18.8471i	0.0812475	+	0.841188i
$503$	−7.08931	−	12.2791i	−0.316097	−	0.547496i	0.663573	−	0.748111i	$-0.269039\pi$
$503$	−7.08931	−	12.2791i	−0.316097	−	0.547496i	−0.979670	+	0.200616i	$0.935706\pi$
$504$	19.0523	+	11.2181i	0.848659	+	0.499696i
$505$	7.27254	−	12.5964i	0.323624	−	0.560533i
$506$	−0.920157	−	9.52676i	−0.0409060	−	0.423516i
$507$	9.92524	+	20.2111i	0.440795	+	0.897608i
$508$	3.41059	−	0.665039i	0.151321	−	0.0295063i
$509$	−27.9042	+	16.1105i	−1.23683	+	0.714086i	−0.968446	−	0.249225i	$-0.919824\pi$
$509$	−27.9042	+	16.1105i	−1.23683	+	0.714086i	−0.268388	+	0.963311i	$0.586491\pi$
$510$	12.1006	−	2.57132i	0.535825	−	0.113860i
$511$	−4.16635	+	7.21632i	−0.184308	+	0.319231i
$512$	−14.6496	+	17.2450i	−0.647428	+	0.762127i
$513$	−12.0332	−	10.2995i	−0.531280	−	0.454732i
$514$	−23.1273	+	2.23378i	−1.02010	+	0.0985280i
$515$	−10.1281	+	5.84745i	−0.446297	+	0.257669i
$516$	−11.6417	−	10.6626i	−0.512495	−	0.469393i
$517$	−7.23840	+	4.17909i	−0.318344	+	0.183796i
$518$	0.518910	+	5.37248i	0.0227996	+	0.236053i
$519$	−28.4210	+	3.22797i	−1.24754	+	0.141692i
$520$	4.98153	+	10.0404i	0.218455	+	0.440303i
$521$	5.44426			0.238517			0.119259	−	0.992863i	$-0.461948\pi$
$521$	5.44426			0.238517			0.119259	+	0.992863i	$0.461948\pi$
$522$	23.5184	−	26.5606i	1.02937	−	1.16253i
$523$	1.14504	+	0.661092i	0.0500693	+	0.0289075i	0.524826	−	0.851210i	$-0.324130\pi$
$523$	1.14504	+	0.661092i	0.0500693	+	0.0289075i	−0.474756	+	0.880117i	$0.657464\pi$
$524$	−6.07252	−	31.1423i	−0.265279	−	1.36046i
$525$	−13.7608	+	10.1749i	−0.600571	+	0.444071i
$526$	6.58703	−	14.4652i	0.287208	−	0.630713i
$527$	24.0259			1.04659
$528$	−4.80033	+	2.61150i	−0.208908	+	0.113651i
$529$	−25.3103	+	43.8386i	−1.10045	+	1.90603i
$530$	0.556641	+	0.779896i	0.0241790	+	0.0338765i
$531$	−28.4468	−	8.71908i	−1.23449	−	0.378376i
$532$	−11.9826	+	10.4288i	−0.519513	+	0.452144i
$533$	−7.80455	+	21.2550i	−0.338053	+	0.920657i
$534$	−26.8619	−	8.72972i	−1.16243	−	0.377772i
$535$	−1.53512	−	2.65891i	−0.0663691	−	0.114955i
$536$	−25.6250	+	27.0510i	−1.10683	+	1.16843i
$537$	29.3323	−	3.33148i	1.26578	−	0.143764i
$538$	1.09739	+	11.3617i	0.0473120	+	0.489840i
$539$	−0.143842	+	0.0830470i	−0.00619570	+	0.00357709i
$540$	9.84411	−	5.79237i	0.423623	−	0.249264i
$541$			8.27239i			0.355658i	0.984061	+	0.177829i	$0.0569073\pi$
$541$			8.27239i			0.355658i	−0.984061	+	0.177829i	$0.943093\pi$
$542$	−0.0264683	−	0.0370841i	−0.00113691	−	0.00159290i
$543$	−3.65233	−	4.93949i	−0.156736	−	0.211974i
$544$	1.09556	−	25.9709i	0.0469717	−	1.11350i
$545$	−8.93403	+	15.4742i	−0.382692	+	0.662842i
$546$	−8.55881	−	21.3617i	−0.366283	−	0.914196i
$547$	−20.7704	+	11.9918i	−0.888079	+	0.512733i	−0.873314	−	0.487158i	$-0.838033\pi$
$547$	−20.7704	+	11.9918i	−0.888079	+	0.512733i	−0.0147652	+	0.999891i	$0.504700\pi$
$548$	−37.5431	+	7.32062i	−1.60376	+	0.312721i
$549$	2.41871	−	2.25229i	0.103228	−	0.0961253i
$550$	−0.406666	−	4.21037i	−0.0173403	−	0.179531i
$551$	12.7445	+	22.0742i	0.542935	+	0.940391i
$552$	41.7238	+	5.10056i	1.77588	+	0.217094i
$553$	39.0031			1.65858
$554$	6.57924	−	4.69585i	0.279525	−	0.199508i
$555$	2.55667	+	1.11275i	0.108525	+	0.0472335i
$556$	14.7090	−	12.8016i	0.623800	−	0.542908i
$557$	5.54287	+	3.20018i	0.234859	+	0.135596i	0.612812	−	0.790229i	$-0.290038\pi$
$557$	5.54287	+	3.20018i	0.234859	+	0.135596i	−0.377953	+	0.925825i	$0.623372\pi$
$558$	21.0394	−	7.03004i	0.890670	−	0.297605i
$559$	2.80734	+	16.1897i	0.118738	+	0.684750i
$560$	−4.30369	−	10.6159i	−0.181864	−	0.448606i
$561$	2.50530	−	5.75622i	0.105774	−	0.243028i
$562$	30.0535	−	2.90276i	1.26773	−	0.122446i
$563$		−	29.0696i		−	1.22514i	−0.790418	−	0.612568i	$-0.790137\pi$
$563$		−	29.0696i		−	1.22514i	0.790418	−	0.612568i	$-0.209863\pi$
$564$	−11.0464	−	35.0060i	−0.465139	−	1.47402i
$565$	14.5209	+	8.38364i	0.610898	+	0.352702i
$566$	2.87826	+	29.7998i	0.120982	+	1.25258i
$567$	−21.0920	+	10.2503i	−0.885782	+	0.430474i
$568$	31.4999	+	29.8394i	1.32171	+	1.25203i
$569$	18.1706			0.761750			0.380875	−	0.924627i	$-0.375623\pi$
$569$	18.1706			0.761750			0.380875	+	0.924627i	$0.375623\pi$
$570$	1.70572	+	8.02709i	0.0714446	+	0.336218i
$571$	27.0813	+	15.6354i	1.13332	+	0.654320i	0.944767	−	0.327744i	$-0.106288\pi$
$571$	27.0813	+	15.6354i	1.13332	+	0.654320i	0.188549	+	0.982064i	$0.439622\pi$
$572$	5.61582	+	0.902399i	0.234809	+	0.0377312i
$573$	−0.477623	−	4.20527i	−0.0199530	−	0.175677i
$574$	9.59029	−	21.0604i	0.400291	−	0.879045i
$575$	−16.2684	+	28.1776i	−0.678438	+	1.17509i
$576$	−6.63978	−	23.0632i	−0.276658	−	0.960969i
$577$	3.07397			0.127971			0.0639854	−	0.997951i	$-0.479619\pi$
$577$	3.07397			0.127971			0.0639854	+	0.997951i	$0.479619\pi$
$578$	3.38106	+	4.73711i	0.140633	+	0.197038i
$579$	−0.861359	−	0.374892i	−0.0357968	−	0.0155800i
$580$	−18.0408	+	3.51781i	−0.749102	+	0.146069i
$581$			5.18386i			0.215063i
$582$	−26.5393	−	8.62488i	−1.10009	−	0.357513i
$583$	0.486240			0.0201380
$584$	8.67035	−	2.57662i	0.358782	−	0.106621i
$585$	−11.7944	−	1.49062i	−0.487638	−	0.0616297i
$586$	24.9798	+	11.3750i	1.03190	+	0.469898i
$587$			27.9800i			1.15486i	0.816442	+	0.577428i	$0.195944\pi$
$587$			27.9800i			1.15486i	−0.816442	+	0.577428i	$0.804056\pi$
$588$	−0.219515	−	0.695641i	−0.00905265	−	0.0286877i
$589$			15.9379i			0.656709i
$590$	8.95534	+	12.5471i	0.368686	+	0.516556i
$591$	−24.9173	+	2.83004i	−1.02496	+	0.116412i
$592$	3.60168	−	4.62116i	0.148028	−	0.189929i
$593$	15.1241			0.621070			0.310535	−	0.950562i	$-0.399492\pi$
$593$	15.1241			0.621070			0.310535	+	0.950562i	$0.399492\pi$
$594$	0.509598	−	5.77376i	0.0209091	−	0.236900i
$595$	11.3964	+	6.57974i	0.467209	+	0.269743i
$596$	0.507192	−	0.441420i	0.0207754	−	0.0180813i
$597$	32.7821	+	14.2678i	1.34168	+	0.583944i
$598$	−31.1272	−	30.7446i	−1.27289	−	1.25724i
$599$	18.8449	−	32.6403i	0.769982	−	1.33365i	−0.167590	−	0.985857i	$-0.553599\pi$
$599$	18.8449	−	32.6403i	0.769982	−	1.33365i	0.937572	−	0.347791i	$-0.113068\pi$
$600$	18.4399	+	2.25420i	0.752807	+	0.0920275i
$601$	28.7680			1.17347			0.586736	−	0.809778i	$-0.300413\pi$
$601$	28.7680			1.17347			0.586736	+	0.809778i	$0.300413\pi$
$602$	−1.61448	−	16.7153i	−0.0658011	−	0.681265i
$603$	−8.86315	−	38.5148i	−0.360935	−	1.56845i
$604$	5.56115	−	16.1817i	0.226280	−	0.658426i
$605$	−9.87783	−	5.70297i	−0.401591	−	0.231859i
$606$	31.7087	−	6.73794i	1.28808	−	0.273710i
$607$	−7.78631			−0.316036			−0.158018	−	0.987436i	$-0.550510\pi$
$607$	−7.78631			−0.316036			−0.158018	+	0.987436i	$0.550510\pi$
$608$	17.2281	+	0.726752i	0.698693	+	0.0294737i
$609$	37.4972	−	4.25883i	1.51946	−	0.172576i
$610$	−1.70440	+	0.164622i	−0.0690091	+	0.00666536i
$611$	−13.1692	+	35.8651i	−0.532767	+	1.45095i
$612$	22.3034	+	16.2084i	0.901560	+	0.655184i
$613$	−21.5412	−	12.4368i	−0.870040	−	0.502318i	−0.00267850	−	0.999996i	$-0.500853\pi$
$613$	−21.5412	−	12.4368i	−0.870040	−	0.502318i	−0.867362	+	0.497679i	$0.834186\pi$
$614$	25.3111	+	11.5259i	1.02147	+	0.465149i
$615$	−7.10753	−	9.61238i	−0.286603	−	0.387609i
$616$	−5.65369	−	1.35204i	−0.227794	−	0.0544754i
$617$	22.5767			0.908902			0.454451	−	0.890772i	$-0.349835\pi$
$617$	22.5767			0.908902			0.454451	+	0.890772i	$0.349835\pi$
$618$	−24.7883	−	8.05582i	−0.997131	−	0.324053i
$619$	−21.7039	+	12.5308i	−0.872355	+	0.503655i	−0.868130	−	0.496337i	$-0.834678\pi$
$619$	−21.7039	+	12.5308i	−0.872355	+	0.503655i	−0.00422503	+	0.999991i	$0.501345\pi$
$620$	−10.8691	−	3.73536i	−0.436513	−	0.150016i
$621$	−28.9911	+	33.8714i	−1.16337	+	1.35921i
$622$	4.77640	+	6.69209i	0.191516	+	0.268328i
$623$	−15.0228	−	26.0202i	−0.601875	−	1.04248i
$624$	−9.20193	+	23.2234i	−0.368372	+	0.929679i
$625$	−4.16998	+	7.22261i	−0.166799	+	0.288905i
$626$	−30.6438	+	2.95979i	−1.22477	+	0.118297i
$627$	3.81846	+	1.66192i	0.152494	+	0.0663706i
$628$	0.357474	+	1.83327i	0.0142648	+	0.0731555i
$629$			6.73067i			0.268369i
$630$	11.9051	+	2.42723i	0.474310	+	0.0967033i
$631$	−20.2917	−	35.1462i	−0.807798	−	1.39915i	−0.914386	−	0.404844i	$-0.867326\pi$
$631$	−20.2917	−	35.1462i	−0.807798	−	1.39915i	0.106588	−	0.994303i	$-0.466008\pi$
$632$	−30.7365	−	29.1162i	−1.22263	−	1.15818i
$633$	−9.24891	+	21.2505i	−0.367611	+	0.844631i
$634$	0.398706	+	4.12796i	0.0158346	+	0.163942i
$635$	1.65370	−	0.954765i	0.0656251	−	0.0378887i
$636$	−0.461709	+	2.08496i	−0.0183080	+	0.0826741i
$637$	−0.261698	+	0.712712i	−0.0103689	+	0.0282387i
$638$	−3.86556	+	8.48883i	−0.153039	+	0.336076i
$639$	−44.8491	+	10.3208i	−1.77420	+	0.408285i
$640$	−4.53337	+	11.5787i	−0.179197	+	0.457687i
$641$	−6.50750	+	11.2713i	−0.257031	+	0.445191i	−0.965445	−	0.260606i	$-0.916078\pi$
$641$	−6.50750	+	11.2713i	−0.257031	+	0.445191i	0.708414	+	0.705797i	$0.249411\pi$
$642$	2.11488	−	6.50763i	0.0834677	−	0.256836i
$643$			7.18080i			0.283183i	0.989925	+	0.141592i	$0.0452219\pi$
$643$			7.18080i			0.283183i	−0.989925	+	0.141592i	$0.954778\pi$
$644$	29.3551	+	33.7290i	1.15675	+	1.32911i
$645$	−7.95453	−	3.46207i	−0.313209	−	0.136319i
$646$	−16.1234	+	11.5079i	−0.634368	+	0.452773i
$647$	6.83502	−	11.8386i	0.268713	−	0.465424i	−0.699817	−	0.714322i	$-0.746735\pi$
$647$	6.83502	−	11.8386i	0.268713	−	0.465424i	0.968530	+	0.248898i	$0.0800685\pi$
$648$	24.2736	+	7.66760i	0.953557	+	0.301212i
$649$	7.82271			0.307068
$650$	−13.7567	−	13.5876i	−0.539584	−	0.532951i
$651$	21.6366	+	9.41697i	0.848006	+	0.369080i
$652$	−5.32626	−	1.83047i	−0.208592	−	0.0716866i
$653$	−29.8718	+	17.2465i	−1.16897	+	0.674907i	−0.953438	−	0.301590i	$-0.902483\pi$
$653$	−29.8718	+	17.2465i	−1.16897	+	0.674907i	−0.215535	+	0.976496i	$0.569149\pi$
$654$	−38.9529	+	8.27729i	−1.52318	+	0.323667i
$655$	−8.71802	−	15.1001i	−0.340641	−	0.590008i
$656$	−23.2795	+	9.43747i	−0.908911	+	0.368471i
$657$	−2.81144	+	9.17260i	−0.109685	+	0.357857i
$658$	16.1824	−	35.5367i	0.630854	−	1.38537i
$659$	−22.0993	−	12.7590i	−0.860865	−	0.497021i	0.00343653	−	0.999994i	$-0.498906\pi$
$659$	−22.0993	−	12.7590i	−0.860865	−	0.497021i	−0.864302	+	0.502973i	$0.832239\pi$
$660$	−2.02830	+	2.21455i	−0.0789516	+	0.0862013i
$661$	42.1629	−	24.3428i	1.63995	−	0.946824i	0.659097	−	0.752058i	$-0.270939\pi$
$661$	42.1629	−	24.3428i	1.63995	−	0.946824i	0.980850	−	0.194766i	$-0.0623947\pi$
$662$	21.4283	−	15.2942i	0.832835	−	0.594426i
$663$	−8.06246	−	27.5408i	−0.313120	−	1.06960i
$664$	3.86981	−	4.08515i	0.150178	−	0.158535i
$665$	−4.36475	+	7.55996i	−0.169258	+	0.293163i
$666$	1.96941	+	5.89403i	0.0763131	+	0.228389i
$667$	62.1348	−	35.8735i	2.40587	−	1.38903i
$668$	2.85628	−	8.31116i	0.110513	−	0.321569i
$669$	18.4501	−	13.6423i	0.713322	−	0.527440i
$670$	−8.48587	+	18.6351i	−0.327838	+	0.719937i
$671$	−0.434476	+	0.752535i	−0.0167728	+	0.0290513i
$672$	11.1659	−	22.9588i	0.430735	−	0.885655i
$673$	−37.5126			−1.44601			−0.723003	−	0.690845i	$-0.757239\pi$
$673$	−37.5126			−1.44601			−0.723003	+	0.690845i	$0.757239\pi$
$674$	17.8979	+	25.0763i	0.689401	+	0.965901i
$675$	−12.8127	+	14.9695i	−0.493160	+	0.576177i
$676$	22.3541	−	13.2775i	0.859775	−	0.510673i
$677$	−20.2093	+	11.6678i	−0.776705	+	0.448431i	−0.835261	−	0.549853i	$-0.814684\pi$
$677$	−20.2093	+	11.6678i	−0.776705	+	0.448431i	0.0585564	+	0.998284i	$0.481350\pi$
$678$	7.76735	+	36.5531i	0.298303	+	1.40381i
$679$	−14.8424	−	25.7077i	−0.569598	−	0.986572i
$680$	−4.06915	−	13.6927i	−0.156045	−	0.525093i
$681$	4.38449	−	0.497978i	0.168014	−	0.0190826i
$682$	−4.74721	+	3.38826i	−0.181780	+	0.129743i
$683$	31.0730	−	17.9400i	1.18897	−	0.686455i	0.230901	−	0.972977i	$-0.425833\pi$
$683$	31.0730	−	17.9400i	1.18897	−	0.686455i	0.958074	+	0.286522i	$0.0924993\pi$
$684$	−10.7520	+	14.7952i	−0.411113	+	0.565708i
$685$	−18.2036	+	10.5099i	−0.695525	+	0.401561i
$686$	11.0115	−	24.1815i	0.420422	−	0.923253i
$687$	27.2847	−	3.09892i	1.04097	−	0.118231i
$688$	−11.2059	+	14.3778i	−0.427219	+	0.548147i
$689$	1.70671	−	1.42387i	0.0650205	−	0.0542451i
$690$	22.5948	−	4.80128i	0.860169	−	0.182782i
$691$		−	17.7395i		−	0.674843i	−0.941354	−	0.337421i	$-0.890445\pi$
$691$		−	17.7395i		−	0.674843i	0.941354	−	0.337421i	$-0.109555\pi$
$692$	6.32129	+	32.4181i	0.240299	+	1.23235i
$693$	4.51231	−	4.20183i	0.171408	−	0.159614i
$694$	42.3813	+	19.2992i	1.60877	+	0.732587i
$695$	5.35784	−	9.28005i	0.203234	−	0.352012i
$696$	−32.7290	−	24.6358i	−1.24059	−	0.933819i
$697$	14.4286	−	24.9910i	0.546521	−	0.946603i
$698$	−25.3241	−	11.5318i	−0.958530	−	0.436486i
$699$	−18.5057	+	13.6834i	−0.699949	+	0.517552i
$700$	12.9735	+	14.9066i	0.490354	+	0.563416i
$701$		−	17.3881i		−	0.656739i	−0.944549	−	0.328370i	$-0.893501\pi$
$701$		−	17.3881i		−	0.656739i	0.944549	−	0.328370i	$-0.106499\pi$
$702$	−15.1188	−	21.7583i	−0.570621	−	0.821214i
$703$	−4.46487			−0.168396
$704$	3.44609	+	5.28602i	0.129879	+	0.199224i
$705$	−11.9930	−	16.2196i	−0.451683	−	0.610867i
$706$	7.51894	−	16.5117i	0.282979	−	0.621426i
$707$	29.8634	+	17.2417i	1.12313	+	0.648440i
$708$	−7.42805	+	33.5432i	−0.279163	+	1.26063i
$709$	−10.5606	−	6.09719i	−0.396613	−	0.228985i	0.288408	−	0.957508i	$-0.406874\pi$
$709$	−10.5606	−	6.09719i	−0.396613	−	0.228985i	−0.685022	+	0.728523i	$0.740207\pi$
$710$	21.6999	+	9.88149i	0.814383	+	0.370846i
$711$	43.7622	−	10.0707i	1.64121	−	0.377680i
$712$	−7.58562	+	31.7199i	−0.284283	+	1.18875i
$713$	44.8622			1.68010
$714$	6.09606	+	28.6880i	0.228139	+	1.07362i
$715$	3.07971	−	0.534031i	0.115174	−	0.0199716i
$716$	−6.52399	−	33.4577i	−0.243813	−	1.25037i
$717$	−0.856439	−	7.54058i	−0.0319843	−	0.281608i
$718$	−1.48745	+	3.26647i	−0.0555112	+	0.121904i
$719$	−1.17357	−	2.03268i	−0.0437667	−	0.0758062i	0.843312	−	0.537424i	$-0.180602\pi$
$719$	−1.17357	−	2.03268i	−0.0437667	−	0.0758062i	−0.887079	+	0.461618i	$0.847269\pi$
$720$	−7.56987	−	10.8001i	−0.282113	−	0.402494i
$721$	−13.8631	−	24.0115i	−0.516288	−	0.894237i
$722$	7.97607	+	11.1751i	0.296839	+	0.415893i
$723$	0.246764	+	2.17265i	0.00917725	+	0.0808018i
$724$	−5.35077	+	4.65690i	−0.198860	+	0.173072i
$725$	27.4606	−	15.8544i	1.01986	−	0.588817i
$726$	−5.28374	−	24.8653i	−0.196098	−	0.922836i
$727$	−12.2627	−	21.2395i	−0.454797	−	0.787731i	0.543880	−	0.839163i	$-0.316955\pi$
$727$	−12.2627	−	21.2395i	−0.454797	−	0.787731i	−0.998676	+	0.0514321i	$0.983621\pi$
$728$	−23.8038	+	11.8102i	−0.882227	+	0.437714i
$729$	−21.0190	+	16.9471i	−0.778480	+	0.627669i
$730$	4.04578	−	2.88763i	0.149741	−	0.106876i
$731$		−	20.9410i		−	0.774532i
$732$	−2.81426	−	2.57757i	−0.104018	−	0.0952699i
$733$	10.9501	+	6.32202i	0.404450	+	0.233509i	0.688402	−	0.725329i	$-0.258312\pi$
$733$	10.9501	+	6.32202i	0.404450	+	0.233509i	−0.283953	+	0.958838i	$0.591646\pi$
$734$	18.7915	−	41.2665i	0.693609	−	1.52318i
$735$	−0.238326	−	0.322317i	−0.00879078	−	0.0118889i
$736$	2.04567	−	48.4940i	0.0754046	−	1.78751i
$737$	5.19552	+	8.99891i	0.191379	+	0.331479i
$738$	5.32263	−	26.1064i	0.195929	−	0.960990i
$739$	7.63333	+	4.40710i	0.280797	+	0.162118i	0.633784	−	0.773510i	$-0.281501\pi$
$739$	7.63333	+	4.40710i	0.280797	+	0.162118i	−0.352987	+	0.935628i	$0.614834\pi$
$740$	1.04643	−	3.04489i	0.0384676	−	0.111932i
$741$	18.2695	−	5.34832i	0.671146	−	0.196475i
$742$	−1.84897	+	1.31968i	−0.0678778	+	0.0484469i
$743$	−1.07683	−	1.86513i	−0.0395052	−	0.0684250i	0.845597	−	0.533822i	$-0.179245\pi$
$743$	−1.07683	−	1.86513i	−0.0395052	−	0.0684250i	−0.885102	+	0.465397i	$0.845911\pi$
$744$	−10.0209	−	23.5730i	−0.367385	−	0.864229i
$745$	0.184747	−	0.319992i	0.00676862	−	0.0117236i
$746$	−10.6338	−	4.84230i	−0.389330	−	0.177289i
$747$	1.33848	+	5.81638i	0.0489726	+	0.212810i
$748$	−6.85542	−	2.35599i	−0.250659	−	0.0861435i
$749$	6.30371	−	3.63945i	0.230333	−	0.132983i
$750$	23.1526	−	4.91981i	0.845413	−	0.179646i
$751$	−11.2543	−	19.4930i	−0.410676	−	0.711311i	0.584288	−	0.811546i	$-0.301374\pi$
$751$	−11.2543	−	19.4930i	−0.410676	−	0.711311i	−0.994964	+	0.100235i	$0.968040\pi$
$752$	−39.2811	+	15.9245i	−1.43243	+	0.580706i
$753$	−9.25465	+	21.2637i	−0.337258	+	0.774891i
$754$	11.2899	+	41.1156i	0.411153	+	1.49734i
$755$		−	9.40287i		−	0.342206i
$756$	13.7325	+	23.3383i	0.499446	+	0.848806i
$757$	1.95836	+	1.13066i	0.0711777	+	0.0410945i	0.535166	−	0.844747i	$-0.320249\pi$
$757$	1.95836	+	1.13066i	0.0711777	+	0.0410945i	−0.463989	+	0.885841i	$0.653582\pi$
$758$	2.87375	−	2.05110i	0.104379	−	0.0744994i
$759$	4.67800	−	10.7483i	0.169801	−	0.390137i
$760$	9.08324	−	2.69932i	0.329484	−	0.0979146i
$761$	−21.1837			−0.767908			−0.383954	−	0.923352i	$-0.625438\pi$
$761$	−21.1837			−0.767908			−0.383954	+	0.923352i	$0.625438\pi$
$762$	4.04740	+	1.31535i	0.146622	+	0.0476499i
$763$	−36.6860	−	21.1807i	−1.32812	−	0.766793i
$764$	−4.79670	+	0.935320i	−0.173539	+	0.0338387i
$765$	14.4859	+	4.44000i	0.523739	+	0.160528i
$766$	−4.68343	+	10.2849i	−0.169219	+	0.371608i
$767$	27.4579	−	22.9074i	0.991446	−	0.827140i
$768$	−25.9383	+	9.75726i	−0.935968	+	0.352085i
$769$	14.7304	+	25.5138i	0.531191	+	0.920051i	0.999337	+	0.0363994i	$0.0115888\pi$
$769$	14.7304	+	25.5138i	0.531191	+	0.920051i	−0.468146	+	0.883651i	$0.655078\pi$
$770$	−3.17970	+	0.307116i	−0.114588	+	0.0110677i
$771$	−26.0926	−	11.3564i	−0.939702	−	0.408989i
$772$	−0.352549	+	1.02584i	−0.0126885	+	0.0369209i
$773$	9.18611	−	5.30360i	0.330401	−	0.190757i	−0.325618	−	0.945501i	$-0.605572\pi$
$773$	9.18611	−	5.30360i	0.330401	−	0.190757i	0.656019	+	0.754744i	$0.272239\pi$
$774$	−6.12740	−	18.3380i	−0.220245	−	0.659146i
$775$	19.8270			0.712205
$776$	−7.49452	+	31.3390i	−0.269037	+	1.12500i
$777$	−2.63809	+	6.06133i	−0.0946409	+	0.217449i
$778$	2.24833	+	23.2779i	0.0806066	+	0.834553i
$779$	16.5781	+	9.57136i	0.593971	+	0.342929i
$780$	−0.634446	+	13.7127i	−0.0227168	+	0.490992i
$781$	10.4789	−	6.04999i	0.374964	−	0.216486i
$782$	32.3927	+	45.3845i	1.15836	+	1.62295i
$783$	40.9728	−	14.4603i	1.46425	−	0.516770i
$784$	−0.780595	+	0.316452i	−0.0278784	+	0.0113019i
$785$	0.513209	+	0.888903i	0.0183172	+	0.0317263i
$786$	12.0105	−	36.9571i	0.428400	−	1.31822i
$787$		−	38.8791i		−	1.38589i	−0.720990	−	0.692946i	$-0.756312\pi$
$787$		−	38.8791i		−	1.38589i	0.720990	−	0.692946i	$-0.243688\pi$
$788$	5.54201	+	28.4217i	0.197426	+	1.01248i
$789$	15.6524	−	11.5736i	0.557241	−	0.412032i
$790$	−21.1740	−	9.64200i	−0.753337	−	0.343047i
$791$	−19.8758	+	34.4260i	−0.706703	+	1.22405i
$792$	−6.69264	−	0.0572212i	−0.237813	−	0.00203327i
$793$	0.678649	+	3.91370i	0.0240995	+	0.138980i
$794$	1.86362	+	19.2948i	0.0661373	+	0.684746i
$795$	0.132433	+	1.16602i	0.00469691	+	0.0413543i
$796$	13.4175	−	39.0421i	0.475571	−	1.38381i
$797$		−	14.9209i		−	0.528524i	−0.964451	−	0.264262i	$-0.914872\pi$
$797$		−	14.9209i		−	0.528524i	0.964451	−	0.264262i	$-0.0851283\pi$
$798$	−19.0305	+	4.04389i	−0.673674	+	0.143152i
$799$	24.3463	−	42.1691i	0.861311	−	1.49183i
$800$	0.904090	−	21.4320i	0.0319644	−	0.757737i
$801$	−23.5743	−	25.3162i	−0.832956	−	0.894504i
$802$	1.38653	−	0.133920i	0.0489599	−	0.00472887i
$803$		−	2.52241i		−	0.0890140i
$804$	−43.5201	+	13.7331i	−1.53484	+	0.484330i
$805$	21.2799	+	12.2860i	0.750019	+	0.433024i
$806$	−6.74084	+	25.7942i	−0.237436	+	0.908563i
$807$	−5.57905	+	12.8185i	−0.196392	+	0.451234i
$808$	−10.6629	−	35.8807i	−0.375119	−	1.26228i
$809$	2.40609	−	4.16747i	0.0845936	−	0.146520i	−0.820624	−	0.571468i	$-0.806374\pi$
$809$	2.40609	−	4.16747i	0.0845936	−	0.146520i	0.905218	+	0.424948i	$0.139707\pi$
$810$	13.9844	−	0.350519i	0.491363	−	0.0123160i
$811$			13.3466i			0.468663i	0.972157	+	0.234332i	$0.0752901\pi$
$811$			13.3466i			0.468663i	−0.972157	+	0.234332i	$0.924710\pi$
$812$	−8.33999	−	42.7709i	−0.292676	−	1.50096i
$813$	−0.00629719	−	0.0554441i	−0.000220852	−	0.00194451i
$814$	−0.949194	−	1.32989i	−0.0332692	−	0.0466127i
$815$	−3.09498			−0.108412
$816$	16.6119	−	27.1584i	0.581532	−	0.950736i
$817$	13.8915			0.486001
$818$	−11.3638	+	24.9551i	−0.397327	+	0.872536i
$819$	3.53395	−	27.9620i	0.123486	−	0.977072i
$820$	−10.4127	+	9.06245i	−0.363629	+	0.316474i
$821$			26.4155i			0.921908i	0.887424	+	0.460954i	$0.152493\pi$
$821$			26.4155i			0.921908i	−0.887424	+	0.460954i	$0.847507\pi$
$822$	−44.5530	−	14.4791i	−1.55397	−	0.505015i
$823$	−31.9529			−1.11381			−0.556904	−	0.830577i	$-0.688011\pi$
$823$	−31.9529			−1.11381			−0.556904	+	0.830577i	$0.688011\pi$
$824$	−7.00003	+	29.2713i	−0.243858	+	1.01971i
$825$	2.06745	−	4.75022i	0.0719794	−	0.165381i
$826$	−29.7465	+	21.2312i	−1.03501	+	0.738729i
$827$			15.6038i			0.542596i	0.962495	+	0.271298i	$0.0874529\pi$
$827$			15.6038i			0.542596i	−0.962495	+	0.271298i	$0.912547\pi$
$828$	41.6458	+	30.2649i	1.44729	+	1.05178i
$829$	−32.0602	−	18.5100i	−1.11350	−	0.642878i	−0.173764	−	0.984787i	$-0.555593\pi$
$829$	−32.0602	−	18.5100i	−1.11350	−	0.642878i	−0.939733	+	0.341909i	$0.888926\pi$
$830$	1.28151	−	2.81421i	0.0444818	−	0.0976827i
$831$	9.83657	−	1.11721i	0.341227	−	0.0387556i
$832$	27.5750	+	8.46274i	0.955992	+	0.293393i
$833$	0.483811	−	0.837986i	0.0167631	−	0.0290345i
$834$	23.3605	−	4.96398i	0.808907	−	0.171889i
$835$		−	4.82945i		−	0.167130i
$836$	1.56287	−	4.54762i	0.0540531	−	0.157283i
$837$	26.7081	+	4.97939i	0.923168	+	0.172113i
$838$	−1.10783	−	11.4698i	−0.0382693	−	0.396217i
$839$	−3.66975	+	6.35619i	−0.126694	+	0.219440i	−0.922394	−	0.386251i	$-0.873770\pi$
$839$	−3.66975	+	6.35619i	−0.126694	+	0.219440i	0.795700	+	0.605691i	$0.207103\pi$
$840$	1.70239	−	13.9259i	0.0587380	−	0.480491i
$841$	−40.9213			−1.41108
$842$	2.82048	+	29.2015i	0.0972001	+	1.00635i
$843$	33.9069	+	14.7574i	1.16781	+	0.508271i
$844$	25.3084	+	8.69770i	0.871152	+	0.299387i
$845$	9.24601	−	10.8928i	0.318072	−	0.374725i
$846$	8.98124	−	44.0511i	0.308781	−	1.51451i
$847$	13.5205	−	23.4183i	0.464571	−	0.804661i
$848$	2.44224	+	0.340297i	0.0838668	+	0.0116859i
$849$	−14.6328	+	33.6206i	−0.502197	+	1.15386i
$850$	14.3160	+	20.0578i	0.491035	+	0.687977i
$851$			12.5678i			0.430818i
$852$	15.9917	+	50.6776i	0.547867	+	1.73618i
$853$	−6.92791	+	3.99983i	−0.237207	+	0.136952i	−0.613892	−	0.789390i	$-0.710397\pi$
$853$	−6.92791	+	3.99983i	−0.237207	+	0.136952i	0.376685	+	0.926341i	$0.377064\pi$
$854$	−0.390284	−	4.04077i	−0.0133553	−	0.138272i
$855$	−2.94532	+	9.60940i	−0.100728	+	0.328634i
$856$	−7.68454	−	1.83771i	−0.262652	−	0.0628115i
$857$	27.0704	+	46.8874i	0.924709	+	1.60164i	0.792029	+	0.610484i	$0.209025\pi$
$857$	27.0704	+	46.8874i	0.924709	+	1.60164i	0.132680	+	0.991159i	$0.457642\pi$
$858$	5.47698	+	4.30468i	0.186981	+	0.146959i
$859$	45.2361	+	26.1171i	1.54344	+	0.891103i	0.998618	+	0.0525490i	$0.0167346\pi$
$859$	45.2361	+	26.1171i	1.54344	+	0.891103i	0.544818	+	0.838554i	$0.316599\pi$
$860$	−3.25574	+	9.47351i	−0.111020	+	0.323044i
$861$	22.7889	−	16.8505i	0.776645	−	0.574262i
$862$	19.2134	+	26.9194i	0.654410	+	0.916877i
$863$	−7.34392			−0.249990			−0.124995	−	0.992157i	$-0.539891\pi$
$863$	−7.34392			−0.249990			−0.124995	+	0.992157i	$0.539891\pi$
$864$	6.60036	−	28.6432i	0.224549	−	0.974463i
$865$	9.07517	+	15.7187i	0.308565	+	0.534450i
$866$	−16.1358	+	1.55850i	−0.548316	+	0.0529600i
$867$	0.804401	+	7.08242i	0.0273189	+	0.240531i
$868$	8.85575	−	25.7683i	0.300584	−	0.874634i
$869$	−10.2249	+	5.90337i	−0.346857	+	0.200258i
$870$	−21.4093	−	6.95769i	−0.725842	−	0.235888i
$871$	44.5881	+	16.3721i	1.51081	+	0.554749i
$872$	13.0989	+	44.0780i	0.443585	+	1.49267i
$873$	−23.2912	−	25.0122i	−0.788287	−	0.846534i
$874$	−30.1064	+	21.4880i	−1.01836	+	0.726844i
$875$	21.8053	+	12.5893i	0.737152	+	0.425595i
$876$	10.8159	+	2.39516i	0.365436	+	0.0809248i
$877$		−	20.7555i		−	0.700864i	−0.936588	−	0.350432i	$-0.886035\pi$
$877$		−	20.7555i		−	0.700864i	0.936588	−	0.350432i	$-0.113965\pi$
$878$	−15.2097	+	33.4006i	−0.513301	+	1.12722i
$879$	19.9863	+	27.0299i	0.674121	+	0.911697i
$880$	2.73503	+	2.13165i	0.0921979	+	0.0718580i
$881$	−15.6869	+	27.1706i	−0.528506	+	0.915400i	0.470941	+	0.882165i	$0.343914\pi$
$881$	−15.6869	+	27.1706i	−0.528506	+	0.915400i	−0.999448	+	0.0332353i	$0.989419\pi$
$882$	0.178476	−	0.875386i	0.00600958	−	0.0294758i
$883$		−	22.3215i		−	0.751180i	−0.926786	−	0.375590i	$-0.877440\pi$
$883$		−	22.3215i		−	0.751180i	0.926786	−	0.375590i	$-0.122560\pi$
$884$	−30.9618	+	11.8053i	−1.04136	+	0.397057i
$885$	2.13060	+	18.7591i	0.0716194	+	0.630579i
$886$	1.86403	+	19.2991i	0.0626234	+	0.648365i
$887$	−10.9654	−	18.9927i	−0.368183	−	0.637712i	0.621098	−	0.783733i	$-0.286687\pi$
$887$	−10.9654	−	18.9927i	−0.368183	−	0.637712i	−0.989282	+	0.146021i	$0.953353\pi$
$888$	6.60379	−	2.80728i	0.221609	−	0.0942062i
$889$	2.26355	+	3.92058i	0.0759169	+	0.131492i
$890$	1.72307	+	17.8396i	0.0577574	+	0.597986i
$891$	3.97796	−	5.87961i	0.133267	−	0.196974i
$892$	−17.3945	−	19.9863i	−0.582412	−	0.669192i
$893$	27.9733	+	16.1504i	0.936092	+	0.540453i
$894$	0.805509	−	0.171167i	0.0269403	−	0.00572467i
$895$	−9.36618	−	16.2227i	−0.313077	−	0.542265i
$896$	−27.4506	−	10.7477i	−0.917059	−	0.359055i
$897$	−15.0546	−	51.4253i	−0.502657	−	1.71704i
$898$	25.6887	−	2.48118i	0.857242	−	0.0827981i
$899$	−37.8631	−	21.8603i	−1.26281	−	0.729082i
$900$	18.4054	+	13.3757i	0.613515	+	0.445855i
$901$	−2.45320	+	1.41636i	−0.0817279	+	0.0471856i
$902$	0.673468	+	6.97269i	0.0224240	+	0.232165i
$903$	8.20785	−	18.8585i	0.273140	−	0.627572i
$904$	41.3625	−	12.2919i	1.37570	−	0.408824i
$905$	−1.94905	+	3.37585i	−0.0647886	+	0.112217i
$906$	15.5743	−	14.0215i	0.517422	−	0.465834i
$907$			49.3975i			1.64022i	0.572207	+	0.820109i	$0.306087\pi$
$907$			49.3975i			1.64022i	−0.572207	+	0.820109i	$0.693913\pi$
$908$	−0.975182	−	5.00113i	−0.0323625	−	0.165968i
$909$	37.9591	+	11.6346i	1.25902	+	0.385897i
$910$	−10.2615	+	10.3892i	−0.340164	+	0.344398i
$911$	20.4751	+	35.4639i	0.678370	+	1.17497i	0.975472	+	0.220126i	$0.0706467\pi$
$911$	20.4751	+	35.4639i	0.678370	+	1.17497i	−0.297101	+	0.954846i	$0.596020\pi$
$912$	18.0159	+	11.0197i	0.596565	+	0.364898i
$913$	−0.784611	−	1.35899i	−0.0259668	−	0.0449759i
$914$	−21.7785	+	47.8260i	−0.720369	+	1.58194i
$915$	−1.92293	−	0.836924i	−0.0635702	−	0.0276679i
$916$	−6.06856	−	31.1220i	−0.200511	−	1.02830i
$917$	35.7991	−	20.6686i	1.18219	−	0.682537i
$918$	14.2472	+	30.6145i	0.470228	+	1.01043i
$919$	4.33945	+	7.51614i	0.143145	+	0.247935i	0.928679	−	0.370883i	$-0.120945\pi$
$919$	4.33945	+	7.51614i	0.143145	+	0.247935i	−0.785534	+	0.618818i	$0.787612\pi$
$920$	−7.59809	−	25.5677i	−0.250502	−	0.842941i
$921$	20.2514	+	27.3885i	0.667308	+	0.902482i
$922$	30.6290	−	21.8611i	1.00871	−	0.719957i
$923$	19.0648	−	51.9212i	0.627524	−	1.70901i
$924$	−5.25024	−	4.80868i	−0.172720	−	0.158194i
$925$			5.55436i			0.182626i
$926$	−21.9748	−	30.7883i	−0.722137	−	1.01177i
$927$	−21.7544	−	23.3619i	−0.714509	−	0.767305i
$928$	−25.3565	+	39.9315i	−0.832369	+	1.31082i
$929$	20.0144	−	34.6659i	0.656650	−	1.13735i	−0.324828	−	0.945773i	$-0.605306\pi$
$929$	20.0144	−	34.6659i	0.656650	−	1.13735i	0.981477	−	0.191578i	$-0.0613604\pi$
$930$	−9.41809	−	10.4611i	−0.308831	−	0.343033i
$931$	0.555887	+	0.320942i	0.0182185	+	0.0105184i
$932$	17.4469	+	20.0465i	0.571494	+	0.656646i
$933$	1.13637	+	10.0053i	0.0372032	+	0.327558i
$934$	0.881990	+	0.401632i	0.0288596	+	0.0131418i
$935$	−3.98354			−0.130276
$936$	−23.6589	+	19.3974i	−0.773314	+	0.634023i
$937$	−32.2151			−1.05242			−0.526211	−	0.850354i	$-0.676388\pi$
$937$	−32.2151			−1.05242			−0.526211	+	0.850354i	$0.676388\pi$
$938$	−44.1799	−	20.1182i	−1.44253	−	0.656883i
$939$	−34.5729	−	15.0473i	−1.12825	−	0.491050i
$940$	−17.5701	+	15.2917i	−0.573075	+	0.498760i
$941$	6.40001	+	3.69505i	0.208634	+	0.120455i	0.600677	−	0.799492i	$-0.294898\pi$
$941$	6.40001	+	3.69505i	0.208634	+	0.120455i	−0.392042	+	0.919947i	$0.628231\pi$
$942$	−0.707029	+	2.17557i	−0.0230362	+	0.0708840i
$943$	26.9416	−	46.6643i	0.877340	−	1.51960i
$944$	39.2911	+	5.47476i	1.27882	+	0.178188i
$945$	11.3051	+	9.67621i	0.367754	+	0.314767i
$946$	2.95321	+	4.13767i	0.0960173	+	0.134527i
$947$		−	38.8618i		−	1.26284i	−0.775441	−	0.631420i	$-0.782473\pi$
$947$		−	38.8618i		−	1.26284i	0.775441	−	0.631420i	$-0.217527\pi$
$948$	−15.6042	−	49.4494i	−0.506799	−	1.60604i
$949$	−7.38644	−	8.85371i	−0.239774	−	0.287404i
$950$	−13.3056	+	9.49669i	−0.431690	+	0.308113i
$951$	−2.02698	+	4.65724i	−0.0657294	+	0.151021i
$952$	32.4626	−	9.64710i	1.05212	−	0.312664i
$953$	3.74946	+	6.49426i	0.121457	+	0.210370i	0.920342	−	0.391114i	$-0.127910\pi$
$953$	3.74946	+	6.49426i	0.121457	+	0.210370i	−0.798885	+	0.601483i	$0.794577\pi$
$954$	−1.73383	+	1.95811i	−0.0561348	+	0.0633962i
$955$	−2.32579	+	1.34279i	−0.0752607	+	0.0434518i
$956$	−8.60111	+	1.67715i	−0.278180	+	0.0542429i
$957$	−9.18554	+	6.79192i	−0.296926	+	0.219551i
$958$	−3.44793	+	7.57170i	−0.111397	+	0.244630i
$959$	−24.9167	−	43.1570i	−0.804602	−	1.39361i
$960$	−11.7374	+	9.70352i	−0.378824	+	0.313180i
$961$	1.83113	+	3.17161i	0.0590687	+	0.102310i
$962$	−7.22605	−	1.88839i	−0.232977	−	0.0608842i
$963$	6.13316	−	5.71116i	0.197638	−	0.184039i
$964$	2.47822	−	0.483233i	0.0798180	−	0.0155639i
$965$			0.596096i			0.0191890i
$966$	11.3828	+	53.5675i	0.366236	+	1.72351i
$967$	−5.44937	+	9.43859i	−0.175240	+	0.303525i	−0.940244	−	0.340501i	$-0.889403\pi$
$967$	−5.44937	+	9.43859i	−0.175240	+	0.303525i	0.765004	+	0.644025i	$0.222737\pi$
$968$	−28.1368	+	8.36159i	−0.904353	+	0.268752i
$969$	−24.1060	+	2.73789i	−0.774397	+	0.0879538i
$970$	1.70238	+	17.6254i	0.0546600	+	0.565917i
$971$	16.5511	−	9.55578i	0.531150	−	0.306659i	−0.210335	−	0.977629i	$-0.567455\pi$
$971$	16.5511	−	9.55578i	0.531150	−	0.306659i	0.741485	+	0.670970i	$0.234122\pi$
$972$	21.4341	+	22.6402i	0.687499	+	0.726186i
$973$	22.0010	+	12.7023i	0.705321	+	0.407217i
$974$	12.1126	−	1.16992i	0.388114	−	0.0374866i
$975$	−6.65339	−	22.7275i	−0.213079	−	0.727863i
$976$	−2.70891	+	3.47569i	−0.0867101	+	0.111254i
$977$	4.71046	+	8.15876i	0.150701	+	0.261022i	0.931485	−	0.363779i	$-0.118514\pi$
$977$	4.71046	+	8.15876i	0.150701	+	0.261022i	−0.780784	+	0.624801i	$0.785180\pi$
$978$	−4.61522	−	5.12633i	−0.147578	−	0.163922i
$979$	7.87665	+	4.54758i	0.251739	+	0.145341i
$980$	−0.349155	+	0.303877i	−0.0111533	+	0.00970700i
$981$	−46.6313	−	14.2927i	−1.48882	−	0.456331i
$982$	−3.51253	−	36.3666i	−0.112089	−	1.16050i
$983$	−3.08894	−	5.35021i	−0.0985220	−	0.170645i	0.812551	−	0.582890i	$-0.198078\pi$
$983$	−3.08894	−	5.35021i	−0.0985220	−	0.170645i	−0.911073	+	0.412245i	$0.864745\pi$
$984$	−30.5379	−	3.73313i	−0.973513	−	0.119008i
$985$	7.95640	+	13.7809i	0.253512	+	0.439096i
$986$	−5.22419	−	54.0882i	−0.166372	−	1.72252i
$987$	38.4533	−	28.4329i	1.22398	−	0.905030i
$988$	−7.83121	−	20.5388i	−0.249144	−	0.653427i
$989$		−	39.1020i		−	1.24337i
$990$	−3.48838	+	1.16559i	−0.110868	+	0.0370450i
$991$	−25.9079	+	44.8738i	−0.822992	+	1.42546i	0.0804529	+	0.996758i	$0.474363\pi$
$991$	−25.9079	+	44.8738i	−0.822992	+	1.42546i	−0.903445	+	0.428705i	$0.858970\pi$
$992$	−26.2151	+	13.6959i	−0.832330	+	0.434844i
$993$	32.0373	−	3.63871i	1.01667	−	0.115471i
$994$	−23.4269	+	51.4459i	−0.743057	+	1.63176i
$995$		−	22.6865i		−	0.719212i
$996$	6.57226	−	2.07393i	0.208250	−	0.0657150i
$997$	26.7969	+	15.4712i	0.848667	+	0.489978i	0.860201	−	0.509955i	$-0.170338\pi$
$997$	26.7969	+	15.4712i	0.848667	+	0.489978i	−0.0115340	+	0.999933i	$0.503671\pi$
$998$	−27.5736	+	19.6803i	−0.872826	+	0.622969i
$999$	−1.39494	+	7.48207i	−0.0441338	+	0.236722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cj.a.373.107	yes	328
8.5	even	2	inner	936.2.cj.a.373.108	yes	328
9.7	even	3		936.2.db.a.61.4	yes	328
13.3	even	3		936.2.db.a.445.114	yes	328
72.61	even	6		936.2.db.a.61.114	yes	328
104.29	even	6		936.2.db.a.445.4	yes	328
117.16	even	3	inner	936.2.cj.a.133.107	✓	328
936.133	even	6	inner	936.2.cj.a.133.108	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cj.a.133.107	✓	328	117.16	even	3	inner
936.2.cj.a.133.108	yes	328	936.133	even	6	inner
936.2.cj.a.373.107	yes	328	1.1	even	1	trivial
936.2.cj.a.373.108	yes	328	8.5	even	2	inner
936.2.db.a.61.4	yes	328	9.7	even	3
936.2.db.a.61.114	yes	328	72.61	even	6
936.2.db.a.445.4	yes	328	104.29	even	6
936.2.db.a.445.114	yes	328	13.3	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.586085 - 1.28705i) q^{2} +(1.39269 - 1.02977i) q^{3} +(-1.31301 - 1.50865i) q^{4} +(-0.951819 - 0.549533i) q^{5} +(-0.509136 - 2.39599i) q^{6} +(1.30283 - 2.25656i) q^{7} +(-2.71124 + 0.805715i) q^{8} +(0.879145 - 2.86829i) q^{9} +(-1.26512 + 0.902967i) q^{10} +0.788764i q^{11} +(-3.38217 - 0.748971i) q^{12} +(2.30976 + 2.76858i) q^{13} +(-2.14075 - 2.99934i) q^{14} +(-1.89148 + 0.214829i) q^{15} +(-0.552021 + 3.96173i) q^{16} +(-2.29757 - 3.97951i) q^{17} +(-3.17639 - 2.81257i) q^{18} +(2.63985 - 1.52412i) q^{19} +(0.420695 + 2.15750i) q^{20} +(-0.509314 - 4.48429i) q^{21} +(1.01518 + 0.462283i) q^{22} +(-4.29012 - 7.43071i) q^{23} +(-2.94620 + 3.91406i) q^{24} +(-1.89603 - 3.28402i) q^{25} +(4.91702 - 1.35016i) q^{26} +(-1.72931 - 4.89995i) q^{27} +(-5.11497 + 0.997380i) q^{28} +8.36190i q^{29} +(-0.832071 + 2.56034i) q^{30} +(-2.61428 + 4.52806i) q^{31} +(4.77542 + 3.03239i) q^{32} +(0.812246 + 1.09850i) q^{33} +(-6.46841 + 0.624762i) q^{34} +(-2.48011 + 1.43189i) q^{35} +(-5.48156 + 2.43977i) q^{36} +(-1.26850 - 0.732368i) q^{37} +(-0.414443 - 4.29089i) q^{38} +(6.06777 + 1.47723i) q^{39} +(3.02338 + 0.723021i) q^{40} +(3.13996 + 5.43858i) q^{41} +(-6.07002 - 1.97266i) q^{42} +(3.94666 + 2.27861i) q^{43} +(1.18996 - 1.03565i) q^{44} +(-2.41301 + 2.24698i) q^{45} +(-12.0781 + 1.16658i) q^{46} +(5.29828 + 9.17688i) q^{47} +(3.31088 + 6.08589i) q^{48} +(0.105288 + 0.182363i) q^{49} +(-5.33793 + 0.515573i) q^{50} +(-7.29777 - 3.17623i) q^{51} +(1.14407 - 7.11977i) q^{52} -0.616458i q^{53} +(-7.32001 - 0.646072i) q^{54} +(0.433452 - 0.750760i) q^{55} +(-1.71413 + 7.16779i) q^{56} +(2.10699 - 4.84106i) q^{57} +(10.7622 + 4.90078i) q^{58} -9.91768i q^{59} +(2.80762 + 2.57150i) q^{60} +(0.954069 + 0.550832i) q^{61} +(4.29566 + 6.01854i) q^{62} +(-5.32711 - 5.72073i) q^{63} +(6.70165 - 4.36897i) q^{64} +(-0.677048 - 3.90447i) q^{65} +(1.88987 - 0.401588i) q^{66} +(11.4089 - 6.58691i) q^{67} +(-2.98694 + 8.69135i) q^{68} +(-13.6267 - 5.93079i) q^{69} +(0.389364 + 4.03124i) q^{70} +(-7.67022 - 13.2852i) q^{71} +(-0.0725455 + 8.48497i) q^{72} -3.19793 q^{73} +(-1.68605 + 1.20339i) q^{74} +(-6.02235 - 2.62113i) q^{75} +(-5.76550 - 1.98142i) q^{76} +(1.77989 + 1.02762i) q^{77} +(5.45751 - 6.94375i) q^{78} +(7.48433 + 12.9632i) q^{79} +(2.70252 - 3.46749i) q^{80} +(-7.45421 - 5.04329i) q^{81} +(8.84002 - 0.853828i) q^{82} +(-1.72293 + 0.994734i) q^{83} +(-6.09647 + 6.65628i) q^{84} +5.05036i q^{85} +(5.24577 - 3.74410i) q^{86} +(8.61083 + 11.6455i) q^{87} +(-0.635519 - 2.13853i) q^{88} +(5.76546 - 9.98606i) q^{89} +(1.47775 + 4.42259i) q^{90} +(9.25668 - 1.60514i) q^{91} +(-5.57734 + 16.2288i) q^{92} +(1.02200 + 8.99826i) q^{93} +(14.9164 - 1.44072i) q^{94} -3.35021 q^{95} +(9.77332 - 0.694422i) q^{96} +(5.69622 - 9.86614i) q^{97} +(0.296419 - 0.0286301i) q^{98} +(2.26241 + 0.693438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 328 q - 2 q^{2} - 2 q^{4} + 4 q^{6} + 2 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} - 14 q^{15} - 2 q^{16} - 4 q^{17} - 12 q^{18} + 9 q^{20} + 14 q^{22} - 22 q^{23} + 18 q^{24} + 144 q^{25}+ \cdots + 39 q^{98}+O(q^{100}) \) 328 * q - 2 * q^2 - 2 * q^4 + 4 * q^6 + 2 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 - 14 * q^15 - 2 * q^16 - 4 * q^17 - 12 * q^18 + 9 * q^20 + 14 * q^22 - 22 * q^23 + 18 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 2 * q^30 - 4 * q^31 - 2 * q^32 + 22 * q^33 - 22 * q^36 + 6 * q^38 + 2 * q^39 + 8 * q^40 + 2 * q^41 + 17 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 + 41 * q^48 - 138 * q^49 - 34 * q^50 + 24 * q^52 - 41 * q^54 - 14 * q^55 + 28 * q^56 - 20 * q^57 + 50 * q^58 - 41 * q^60 + 3 * q^62 + 26 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 + 32 * q^68 - 17 * q^70 - 4 * q^71 + 32 * q^72 - 16 * q^73 + 19 * q^74 + 9 * q^76 + 2 * q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 27 * q^84 + 36 * q^86 + 34 * q^87 - 10 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 + 3 * q^94 - 112 * q^95 - 113 * q^96 + 2 * q^97 + 39 * q^98

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