LMFDB - Embedded newform 960.2.cn.a.731.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			731.19
Character	$\chi$	$=$	960.731
Dual form			960.2.cn.a.851.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27383 - 0.614289i) q^{2} +(0.216308 - 1.71849i) q^{3} +(1.24530 + 1.56500i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(-1.33119 + 2.05619i) q^{6} +(2.39545 + 0.992229i) q^{7} +(-0.624939 - 2.75852i) q^{8} +(-2.90642 - 0.743447i) q^{9} +O(q^{10})$	\(q+(-1.27383 - 0.614289i) q^{2} +(0.216308 - 1.71849i) q^{3} +(1.24530 + 1.56500i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(-1.33119 + 2.05619i) q^{6} +(2.39545 + 0.992229i) q^{7} +(-0.624939 - 2.75852i) q^{8} +(-2.90642 - 0.743447i) q^{9} +(1.12951 + 0.850998i) q^{10} +(-1.60070 + 1.06955i) q^{11} +(2.95881 - 1.80151i) q^{12} +(0.531894 + 2.67401i) q^{13} +(-2.44189 - 2.73543i) q^{14} +(-0.547413 + 1.64327i) q^{15} +(-0.898462 + 3.89779i) q^{16} +(-2.20327 - 2.20327i) q^{17} +(3.24560 + 2.73241i) q^{18} +(-1.40473 - 7.06207i) q^{19} +(-0.916054 - 1.77788i) q^{20} +(2.22329 - 3.90194i) q^{21} +(2.69604 - 0.379140i) q^{22} +(-6.47784 + 2.68321i) q^{23} +(-4.87568 + 0.477261i) q^{24} +(0.923880 + 0.382683i) q^{25} +(0.965072 - 3.73298i) q^{26} +(-1.90629 + 4.83385i) q^{27} +(1.43021 + 4.98451i) q^{28} +(2.54515 - 3.80909i) q^{29} +(1.70675 - 1.75698i) q^{30} -9.85644 q^{31} +(3.53886 - 4.41322i) q^{32} +(1.49177 + 2.98214i) q^{33} +(1.45315 + 4.16003i) q^{34} +(-2.15585 - 1.44049i) q^{35} +(-2.45587 - 5.47437i) q^{36} +(-4.73655 - 0.942158i) q^{37} +(-2.54876 + 9.85881i) q^{38} +(4.71032 - 0.335645i) q^{39} +(0.0747698 + 2.82744i) q^{40} +(-4.81210 - 11.6174i) q^{41} +(-5.22902 + 3.60467i) q^{42} +(4.10956 - 2.74592i) q^{43} +(-3.66720 - 1.17318i) q^{44} +(2.70554 + 1.29618i) q^{45} +(9.89995 + 0.561305i) q^{46} +(-1.51125 + 1.51125i) q^{47} +(6.50397 + 2.38712i) q^{48} +(-0.196068 - 0.196068i) q^{49} +(-0.941790 - 1.05500i) q^{50} +(-4.26288 + 3.30971i) q^{51} +(-3.52247 + 4.16236i) q^{52} +(4.07045 + 6.09185i) q^{53} +(5.39767 - 4.98650i) q^{54} +(1.77860 - 0.736721i) q^{55} +(1.24008 - 7.22800i) q^{56} +(-12.4400 + 0.886438i) q^{57} +(-5.58198 + 3.28868i) q^{58} +(0.0928532 - 0.466804i) q^{59} +(-3.25341 + 1.18966i) q^{60} +(-4.35588 + 6.51903i) q^{61} +(12.5555 + 6.05470i) q^{62} +(-6.22453 - 4.66473i) q^{63} +(-7.21890 + 3.44782i) q^{64} -2.72640i q^{65} +(-0.0683740 - 4.71513i) q^{66} +(-7.43485 - 4.96781i) q^{67} +(0.704391 - 6.19184i) q^{68} +(3.20986 + 11.7125i) q^{69} +(1.86131 + 3.15926i) q^{70} +(2.52818 - 6.10357i) q^{71} +(-0.234479 + 8.48204i) q^{72} +(-1.24905 - 3.01547i) q^{73} +(5.45481 + 4.10976i) q^{74} +(0.857481 - 1.50490i) q^{75} +(9.30284 - 10.9928i) q^{76} +(-4.89565 + 0.973804i) q^{77} +(-6.20634 - 2.46594i) q^{78} +(2.90875 - 2.90875i) q^{79} +(1.64162 - 3.64761i) q^{80} +(7.89457 + 4.32154i) q^{81} +(-1.00665 + 17.7547i) q^{82} +(5.30261 - 1.05475i) q^{83} +(8.87520 - 1.37962i) q^{84} +(1.73109 + 2.59077i) q^{85} +(-6.92169 + 0.973387i) q^{86} +(-5.99535 - 5.19776i) q^{87} +(3.95073 + 3.74716i) q^{88} +(-5.90962 + 14.2671i) q^{89} +(-2.65017 - 3.31309i) q^{90} +(-1.37911 + 6.93324i) q^{91} +(-12.2661 - 6.79643i) q^{92} +(-2.13203 + 16.9382i) q^{93} +(2.85342 - 0.996735i) q^{94} +7.20042i q^{95} +(-6.81859 - 7.03611i) q^{96} +15.8093i q^{97} +(0.129316 + 0.370201i) q^{98} +(5.44747 - 1.91854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{9}{16}\right)$

Coefficient data

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

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

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

$2$	−1.27383	−	0.614289i	−0.900736	−	0.434368i
$2$	−1.27383	−	0.614289i	−0.900736	−	0.434368i
$3$	0.216308	−	1.71849i	0.124886	−	0.992171i
$3$	0.216308	−	1.71849i	0.124886	−	0.992171i
$4$	1.24530	+	1.56500i	0.622649	+	0.782501i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$5$	−0.980785	−	0.195090i	−0.438621	−	0.0872470i
$6$	−1.33119	+	2.05619i	−0.543456	+	0.839438i
$7$	2.39545	+	0.992229i	0.905396	+	0.375027i	0.786293	−	0.617854i	$-0.211998\pi$
$7$	2.39545	+	0.992229i	0.905396	+	0.375027i	0.119104	+	0.992882i	$0.461998\pi$
$8$	−0.624939	−	2.75852i	−0.220949	−	0.975285i
$9$	−2.90642	−	0.743447i	−0.968807	−	0.247816i
$10$	1.12951	+	0.850998i	0.357184	+	0.269109i
$11$	−1.60070	+	1.06955i	−0.482629	+	0.322483i	−0.772972	−	0.634440i	$-0.781231\pi$
$11$	−1.60070	+	1.06955i	−0.482629	+	0.322483i	0.290343	+	0.956923i	$0.406231\pi$
$12$	2.95881	−	1.80151i	0.854135	−	0.520052i
$13$	0.531894	+	2.67401i	0.147521	+	0.741638i	0.981743	+	0.190210i	$0.0609168\pi$
$13$	0.531894	+	2.67401i	0.147521	+	0.741638i	−0.834223	+	0.551428i	$0.814083\pi$
$14$	−2.44189	−	2.73543i	−0.652623	−	0.731076i
$15$	−0.547413	+	1.64327i	−0.141341	+	0.424291i
$16$	−0.898462	+	3.89779i	−0.224616	+	0.974447i
$17$	−2.20327	−	2.20327i	−0.534370	−	0.534370i	0.387499	−	0.921870i	$-0.373339\pi$
$17$	−2.20327	−	2.20327i	−0.534370	−	0.534370i	−0.921870	+	0.387499i	$0.873339\pi$
$18$	3.24560	+	2.73241i	0.764996	+	0.644035i
$19$	−1.40473	−	7.06207i	−0.322268	−	1.62015i	−0.714052	−	0.700093i	$-0.753142\pi$
$19$	−1.40473	−	7.06207i	−0.322268	−	1.62015i	0.391784	−	0.920057i	$-0.371858\pi$
$20$	−0.916054	−	1.77788i	−0.204836	−	0.397545i
$21$	2.22329	−	3.90194i	0.485162	−	0.851473i
$22$	2.69604	−	0.379140i	0.574797	−	0.0808330i
$23$	−6.47784	+	2.68321i	−1.35072	+	0.559488i	−0.936493	−	0.350685i	$-0.885949\pi$
$23$	−6.47784	+	2.68321i	−1.35072	+	0.559488i	−0.414229	+	0.910173i	$0.635949\pi$
$24$	−4.87568	+	0.477261i	−0.995243	+	0.0974205i
$25$	0.923880	+	0.382683i	0.184776	+	0.0765367i
$26$	0.965072	−	3.73298i	0.189266	−	0.732098i
$27$	−1.90629	+	4.83385i	−0.366866	+	0.930274i
$28$	1.43021	+	4.98451i	0.270285	+	0.941984i
$29$	2.54515	−	3.80909i	0.472623	−	0.707330i	−0.516193	−	0.856472i	$-0.672651\pi$
$29$	2.54515	−	3.80909i	0.472623	−	0.707330i	0.988816	+	0.149142i	$0.0476512\pi$
$30$	1.70675	−	1.75698i	0.311609	−	0.320780i
$31$	−9.85644			−1.77027			−0.885135	−	0.465335i	$-0.845934\pi$
$31$	−9.85644			−1.77027			−0.885135	+	0.465335i	$0.845934\pi$
$32$	3.53886	−	4.41322i	0.625588	−	0.780154i
$33$	1.49177	+	2.98214i	0.259684	+	0.519124i
$34$	1.45315	+	4.16003i	0.249213	+	0.713440i
$35$	−2.15585	−	1.44049i	−0.364405	−	0.243488i
$36$	−2.45587	−	5.47437i	−0.409311	−	0.912395i
$37$	−4.73655	−	0.942158i	−0.778684	−	0.154890i	−0.210282	−	0.977641i	$-0.567438\pi$
$37$	−4.73655	−	0.942158i	−0.778684	−	0.154890i	−0.568402	+	0.822751i	$0.692438\pi$
$38$	−2.54876	+	9.85881i	−0.413463	+	1.59931i
$39$	4.71032	−	0.335645i	0.754255	−	0.0537462i
$40$	0.0747698	+	2.82744i	0.0118221	+	0.447057i
$41$	−4.81210	−	11.6174i	−0.751524	−	1.81434i	−0.550680	−	0.834716i	$-0.685632\pi$
$41$	−4.81210	−	11.6174i	−0.751524	−	1.81434i	−0.200844	−	0.979623i	$-0.564368\pi$
$42$	−5.22902	+	3.60467i	−0.806855	+	0.556213i
$43$	4.10956	−	2.74592i	0.626703	−	0.418749i	−0.201256	−	0.979539i	$-0.564502\pi$
$43$	4.10956	−	2.74592i	0.626703	−	0.418749i	0.827959	+	0.560789i	$0.189502\pi$
$44$	−3.66720	−	1.17318i	−0.552852	−	0.176864i
$45$	2.70554	+	1.29618i	0.403318	+	0.193223i
$46$	9.89995	+	0.561305i	1.45967	+	0.0827599i
$47$	−1.51125	+	1.51125i	−0.220438	+	0.220438i	−0.808683	−	0.588245i	$-0.799819\pi$
$47$	−1.51125	+	1.51125i	−0.220438	+	0.220438i	0.588245	+	0.808683i	$0.299819\pi$
$48$	6.50397	+	2.38712i	0.938767	+	0.344551i
$49$	−0.196068	−	0.196068i	−0.0280097	−	0.0280097i
$50$	−0.941790	−	1.05500i	−0.133189	−	0.149200i
$51$	−4.26288	+	3.30971i	−0.596922	+	0.463452i
$52$	−3.52247	+	4.16236i	−0.488478	+	0.577216i
$53$	4.07045	+	6.09185i	0.559119	+	0.836780i	0.998094	−	0.0617191i	$-0.0196583\pi$
$53$	4.07045	+	6.09185i	0.559119	+	0.836780i	−0.438975	+	0.898499i	$0.644658\pi$
$54$	5.39767	−	4.98650i	0.734530	−	0.678576i
$55$	1.77860	−	0.736721i	0.239827	−	0.0993395i
$56$	1.24008	−	7.22800i	0.165712	−	0.965882i
$57$	−12.4400	+	0.886438i	−1.64771	+	0.117412i
$58$	−5.58198	+	3.28868i	−0.732950	+	0.431825i
$59$	0.0928532	−	0.466804i	0.0120885	−	0.0607727i	−0.974270	−	0.225383i	$-0.927637\pi$
$59$	0.0928532	−	0.466804i	0.0120885	−	0.0607727i	0.986359	+	0.164610i	$0.0526366\pi$
$60$	−3.25341	+	1.18966i	−0.420014	+	0.153585i
$61$	−4.35588	+	6.51903i	−0.557713	+	0.834676i	−0.998002	−	0.0631798i	$-0.979876\pi$
$61$	−4.35588	+	6.51903i	−0.557713	+	0.834676i	0.440289	+	0.897856i	$0.354876\pi$
$62$	12.5555	+	6.05470i	1.59455	+	0.768948i
$63$	−6.22453	−	4.66473i	−0.784217	−	0.587701i
$64$	−7.21890	+	3.44782i	−0.902363	+	0.430977i
$65$		−	2.72640i		−	0.338168i
$66$	−0.0683740	−	4.71513i	−0.00841626	−	0.580392i
$67$	−7.43485	−	4.96781i	−0.908311	−	0.606914i	0.0112176	−	0.999937i	$-0.496429\pi$
$67$	−7.43485	−	4.96781i	−0.908311	−	0.606914i	−0.919529	+	0.393023i	$0.871429\pi$
$68$	0.704391	−	6.19184i	0.0854200	−	0.750871i
$69$	3.20986	+	11.7125i	0.386422	+	1.41002i
$70$	1.86131	+	3.15926i	0.222470	+	0.377604i
$71$	2.52818	−	6.10357i	0.300040	−	0.724360i	−0.699909	−	0.714232i	$-0.746776\pi$
$71$	2.52818	−	6.10357i	0.300040	−	0.724360i	0.999949	−	0.0101281i	$-0.00322392\pi$
$72$	−0.234479	+	8.48204i	−0.0276336	+	0.999618i
$73$	−1.24905	−	3.01547i	−0.146190	−	0.352934i	0.833775	−	0.552105i	$-0.186175\pi$
$73$	−1.24905	−	3.01547i	−0.146190	−	0.352934i	−0.979965	+	0.199170i	$0.936175\pi$
$74$	5.45481	+	4.10976i	0.634109	+	0.477750i
$75$	0.857481	−	1.50490i	0.0990133	−	0.173771i
$76$	9.30284	−	10.9928i	1.06711	−	1.26096i
$77$	−4.89565	+	0.973804i	−0.557911	+	0.110975i
$78$	−6.20634	−	2.46594i	−0.702730	−	0.279213i
$79$	2.90875	−	2.90875i	0.327260	−	0.327260i	−0.524284	−	0.851544i	$-0.675667\pi$
$79$	2.90875	−	2.90875i	0.327260	−	0.327260i	0.851544	+	0.524284i	$0.175667\pi$
$80$	1.64162	−	3.64761i	0.183539	−	0.407816i
$81$	7.89457	+	4.32154i	0.877175	+	0.480171i
$82$	−1.00665	+	17.7547i	−0.111166	+	1.96068i
$83$	5.30261	−	1.05475i	0.582037	−	0.115774i	0.104714	−	0.994502i	$-0.466607\pi$
$83$	5.30261	−	1.05475i	0.582037	−	0.115774i	0.477323	+	0.878728i	$0.341607\pi$
$84$	8.87520	−	1.37962i	0.968364	−	0.150529i
$85$	1.73109	+	2.59077i	0.187764	+	0.281008i
$86$	−6.92169	+	0.973387i	−0.746385	+	0.104963i
$87$	−5.99535	−	5.19776i	−0.642769	−	0.557258i
$88$	3.95073	+	3.74716i	0.421149	+	0.399449i
$89$	−5.90962	+	14.2671i	−0.626418	+	1.51231i	0.217626	+	0.976032i	$0.430169\pi$
$89$	−5.90962	+	14.2671i	−0.626418	+	1.51231i	−0.844044	+	0.536274i	$0.819831\pi$
$90$	−2.65017	−	3.31309i	−0.279353	−	0.349231i
$91$	−1.37911	+	6.93324i	−0.144570	+	0.726801i
$92$	−12.2661	−	6.79643i	−1.27883	−	0.708577i
$93$	−2.13203	+	16.9382i	−0.221081	+	1.75641i
$94$	2.85342	−	0.996735i	0.294308	−	0.102805i
$95$			7.20042i			0.738748i
$96$	−6.81859	−	7.03611i	−0.695919	−	0.718120i
$97$			15.8093i			1.60519i	0.596523	+	0.802596i	$0.296549\pi$
$97$			15.8093i			1.60519i	−0.596523	+	0.802596i	$0.703451\pi$
$98$	0.129316	+	0.370201i	0.0130628	+	0.0373959i
$99$	5.44747	−	1.91854i	0.547491	−	0.192820i
$100$	0.551606	+	1.92243i	0.0551606	+	0.192243i
$101$	−0.963785	+	4.84528i	−0.0959002	+	0.482123i	0.902749	+	0.430167i	$0.141545\pi$
$101$	−0.963785	+	4.84528i	−0.0959002	+	0.482123i	−0.998649	+	0.0519557i	$0.983455\pi$
$102$	7.46331	−	1.59738i	0.738977	−	0.158164i
$103$	0.0495922	−	0.119726i	0.00488647	−	0.0117970i	−0.921417	−	0.388574i	$-0.872968\pi$
$103$	0.0495922	−	0.119726i	0.00488647	−	0.0117970i	0.926304	+	0.376777i	$0.122968\pi$
$104$	7.04393	−	3.13834i	0.690714	−	0.307739i
$105$	−2.94180	+	3.39322i	−0.287091	+	0.331144i
$106$	−1.44291	−	10.2604i	−0.140148	−	0.996581i
$107$	3.34974	+	5.01325i	0.323832	+	0.484649i	0.957291	−	0.289128i	$-0.0933653\pi$
$107$	3.34974	+	5.01325i	0.323832	+	0.484649i	−0.633458	+	0.773777i	$0.718365\pi$
$108$	−9.93888	+	3.03624i	−0.956369	+	0.292162i
$109$	19.7204	−	3.92263i	1.88887	−	0.375719i	0.891814	−	0.452402i	$-0.149433\pi$
$109$	19.7204	−	3.92263i	1.88887	−	0.375719i	0.997056	+	0.0766830i	$0.0244329\pi$
$110$	−2.71820	−	0.154116i	−0.259170	−	0.0146944i
$111$	−2.64364	+	7.93592i	−0.250924	+	0.753244i
$112$	−6.01973	+	8.44549i	−0.568811	+	0.798024i
$113$	−9.36118	+	9.36118i	−0.880626	+	0.880626i	−0.993598	−	0.112973i	$-0.963963\pi$
$113$	−9.36118	+	9.36118i	−0.880626	+	0.880626i	0.112973	+	0.993598i	$0.463963\pi$
$114$	16.3910	+	6.51255i	1.53515	+	0.609956i
$115$	6.87684	−	1.36789i	0.641268	−	0.127556i
$116$	9.13071	−	0.760286i	0.847765	−	0.0705908i
$117$	0.442078	−	8.16724i	0.0408701	−	0.755062i
$118$	−0.405032	+	0.537592i	−0.0372862	+	0.0494893i
$119$	−3.09168	−	7.46397i	−0.283413	−	0.684221i
$120$	4.87510	+	0.483107i	0.445034	+	0.0441014i
$121$	−2.79122	+	6.73861i	−0.253747	+	0.612601i
$122$	9.55322	−	5.62839i	0.864908	−	0.509570i
$123$	−21.0054	+	5.75661i	−1.89399	+	0.519056i
$124$	−12.2742	−	15.4254i	−1.10226	−	1.38524i
$125$	−0.831470	−	0.555570i	−0.0743689	−	0.0496917i
$126$	5.06352	+	9.76574i	0.451094	+	0.870001i
$127$		−	12.4626i		−	1.10587i	−0.833223	−	0.552937i	$-0.813507\pi$
$127$		−	12.4626i		−	1.10587i	0.833223	−	0.552937i	$-0.186493\pi$
$128$	11.3136	+	0.0425473i	0.999993	+	0.00376068i
$129$	−3.82991	−	7.65622i	−0.337205	−	0.674092i
$130$	−1.67480	+	3.47298i	−0.146889	+	0.304600i
$131$	−4.23080	+	6.33184i	−0.369646	+	0.553215i	−0.968934	−	0.247319i	$-0.920451\pi$
$131$	−4.23080	+	6.33184i	−0.369646	+	0.553215i	0.599288	+	0.800534i	$0.295451\pi$
$132$	−2.80935	+	6.04829i	−0.244523	+	0.526436i
$133$	3.64222	−	18.3107i	0.315821	−	1.58774i
$134$	6.41908	+	10.8953i	0.554524	+	0.941210i
$135$	2.81270	−	4.36907i	0.242078	−	0.376029i
$136$	−4.70085	+	7.45467i	−0.403095	+	0.639232i
$137$	−15.3260	+	6.34822i	−1.30938	+	0.542365i	−0.924705	−	0.380685i	$-0.875688\pi$
$137$	−15.3260	+	6.34822i	−1.30938	+	0.542365i	−0.384680	+	0.923050i	$0.625688\pi$
$138$	3.10604	−	16.8916i	0.264403	−	1.43790i
$139$	−4.70419	−	7.04031i	−0.399004	−	0.597151i	0.576510	−	0.817090i	$-0.304414\pi$
$139$	−4.70419	−	7.04031i	−0.399004	−	0.597151i	−0.975514	+	0.219939i	$0.929414\pi$
$140$	−0.430303	−	5.16776i	−0.0363673	−	0.436755i
$141$	2.27017	+	2.92396i	0.191183	+	0.246242i
$142$	−6.96983	+	6.22189i	−0.584895	+	0.522129i
$143$	−3.71140	−	3.71140i	−0.310363	−	0.310363i
$144$	5.50911	−	10.6607i	0.459092	−	0.888389i
$145$	−3.23937	+	3.23937i	−0.269015	+	0.269015i
$146$	−0.261291	+	4.60849i	−0.0216246	+	0.381401i
$147$	−0.379353	+	0.294530i	−0.0312885	+	0.0242925i
$148$	−4.42394	−	8.58597i	−0.363645	−	0.705763i
$149$	8.67532	−	5.79666i	0.710710	−	0.474881i	−0.146920	−	0.989148i	$-0.546936\pi$
$149$	8.67532	−	5.79666i	0.710710	−	0.474881i	0.857630	+	0.514267i	$0.171936\pi$
$150$	−2.01673	+	1.39025i	−0.164665	+	0.113514i
$151$	−5.59280	−	13.5022i	−0.455136	−	1.09879i	−0.970344	−	0.241730i	$-0.922285\pi$
$151$	−5.59280	−	13.5022i	−0.455136	−	1.09879i	0.515208	−	0.857065i	$-0.327715\pi$
$152$	−18.6030	+	8.28835i	−1.50890	+	0.672274i
$153$	4.76561	+	8.04163i	0.385277	+	0.650127i
$154$	6.83443	+	1.76688i	0.550734	+	0.142379i
$155$	9.66706	+	1.92290i	0.776477	+	0.154451i
$156$	6.39104	+	6.95368i	0.511693	+	0.556740i
$157$	−4.15308	−	2.77500i	−0.331452	−	0.221469i	0.378697	−	0.925521i	$-0.376372\pi$
$157$	−4.15308	−	2.77500i	−0.331452	−	0.221469i	−0.710149	+	0.704052i	$0.751372\pi$
$158$	−5.49208	+	1.91845i	−0.436926	+	0.152624i
$159$	11.3493	−	5.67731i	0.900055	−	0.450240i
$160$	−4.33184	+	3.63802i	−0.342462	+	0.287611i
$161$	−18.1797			−1.43276
$162$	−7.40169	−	10.3545i	−0.581532	−	0.813524i
$163$	8.22531	−	12.3100i	0.644256	−	0.964197i	−0.355310	−	0.934748i	$-0.615625\pi$
$163$	8.22531	−	12.3100i	0.644256	−	0.964197i	0.999566	−	0.0294488i	$-0.00937520\pi$
$164$	12.1888	−	21.9981i	0.951786	−	1.71777i
$165$	−0.881323	−	3.21587i	−0.0686109	−	0.250355i
$166$	−7.40256	−	1.91375i	−0.574550	−	0.148536i
$167$	−7.79422	−	3.22847i	−0.603135	−	0.249827i	0.0601553	−	0.998189i	$-0.480840\pi$
$167$	−7.79422	−	3.22847i	−0.603135	−	0.249827i	−0.663290	+	0.748362i	$0.730840\pi$
$168$	−12.1530	−	3.69453i	−0.937625	−	0.285039i
$169$	5.14300	−	2.13030i	0.395615	−	0.163869i
$170$	−0.613646	−	4.36359i	−0.0470645	−	0.334672i
$171$	−1.16753	+	21.5697i	−0.0892831	+	1.64948i
$172$	9.41501	+	3.01198i	0.717888	+	0.229661i
$173$	0.0374298	+	0.188172i	0.00284574	+	0.0143065i	0.982182	−	0.187932i	$-0.0601784\pi$
$173$	0.0374298	+	0.188172i	0.00284574	+	0.0143065i	−0.979336	+	0.202238i	$0.935178\pi$
$174$	4.44415	+	10.3040i	0.336910	+	0.781140i
$175$	1.83340	+	1.83340i	0.138592	+	0.138592i
$176$	−2.73073	−	7.20015i	−0.205836	−	0.542731i
$177$	−0.782114	−	0.260541i	−0.0587873	−	0.0195834i
$178$	16.2920	−	14.5437i	1.22113	−	1.09009i
$179$	−4.74114	−	23.8353i	−0.354369	−	1.78154i	−0.587639	−	0.809123i	$-0.699943\pi$
$179$	−4.74114	−	23.8353i	−0.354369	−	1.78154i	0.233270	−	0.972412i	$-0.425057\pi$
$180$	1.34068	+	5.84830i	0.0999286	+	0.435906i
$181$	2.70351	−	1.80643i	0.200950	−	0.134271i	−0.451024	−	0.892512i	$-0.648941\pi$
$181$	2.70351	−	1.80643i	0.200950	−	0.134271i	0.651974	+	0.758241i	$0.273941\pi$
$182$	6.01576	−	7.98461i	0.445918	−	0.591859i
$183$	10.2607	+	8.89565i	0.758491	+	0.657586i
$184$	11.4499	+	16.1924i	0.844101	+	1.19372i
$185$	4.46173	+	1.84811i	0.328033	+	0.135876i
$186$	13.1208	−	20.2668i	0.962064	−	1.48603i
$187$	5.88328	+	1.17026i	0.430228	+	0.0855777i
$188$	−4.24707	−	0.483151i	−0.309749	−	0.0352374i
$189$	−9.36271	+	9.68778i	−0.681037	+	0.704682i
$190$	4.42314	−	9.17213i	0.320888	−	0.665417i
$191$	−3.22232			−0.233159			−0.116580	−	0.993181i	$-0.537193\pi$
$191$	−3.22232			−0.233159			−0.116580	+	0.993181i	$0.537193\pi$
$192$	4.36354	+	13.1514i	0.314911	+	0.949121i
$193$	0.400502			0.0288287			0.0144144	−	0.999896i	$-0.495412\pi$
$193$	0.400502			0.0288287			0.0144144	+	0.999896i	$0.495412\pi$
$194$	9.71148	−	20.1384i	0.697244	−	1.44585i
$195$	−4.68529	−	0.589742i	−0.335521	−	0.0422323i
$196$	0.0626836	−	0.551011i	0.00447740	−	0.0393579i
$197$	21.6358	+	4.30363i	1.54149	+	0.306621i	0.891392	−	0.453233i	$-0.149729\pi$
$197$	21.6358	+	4.30363i	1.54149	+	0.306621i	0.650094	+	0.759854i	$0.274729\pi$
$198$	−8.11770	−	0.902420i	−0.576900	−	0.0641322i
$199$	−3.43415	−	1.42247i	−0.243440	−	0.100836i	0.257627	−	0.966244i	$-0.417059\pi$
$199$	−3.43415	−	1.42247i	−0.243440	−	0.100836i	−0.501068	+	0.865408i	$0.667059\pi$
$200$	0.478273	−	2.78770i	0.0338190	−	0.197120i
$201$	−10.1453	+	11.7021i	−0.715597	+	0.825405i
$202$	4.20410	−	5.58003i	0.295799	−	0.392609i
$203$	9.87629	−	6.59912i	0.693180	−	0.463168i
$204$	−10.4883	−	2.54983i	−0.734325	−	0.178524i
$205$	2.45319	+	12.3330i	0.171338	+	0.861375i
$206$	−0.136719	+	0.122047i	−0.00952564	+	0.00850343i
$207$	20.8222	−	2.98261i	1.44724	−	0.207305i
$208$	−10.9006	−	0.329287i	−0.755823	−	0.0228320i
$209$	9.80182	+	9.80182i	0.678006	+	0.678006i
$210$	5.83178	−	2.51528i	0.402431	−	0.173571i
$211$	−2.84531	−	14.3043i	−0.195879	−	0.984750i	−0.946177	−	0.323650i	$-0.895090\pi$
$211$	−2.84531	−	14.3043i	−0.195879	−	0.984750i	0.750298	−	0.661100i	$-0.229910\pi$
$212$	−4.46484	+	13.9564i	−0.306646	+	0.958532i
$213$	−9.94206	−	5.66491i	−0.681219	−	0.388153i
$214$	−1.18743	−	8.44375i	−0.0811712	−	0.577203i
$215$	−4.56630	+	1.89142i	−0.311419	+	0.128994i
$216$	14.5256	+	2.23768i	0.988341	+	0.152255i
$217$	−23.6107	−	9.77985i	−1.60280	−	0.663900i
$218$	−27.5301	−	7.11723i	−1.86457	−	0.482040i
$219$	−5.45224	+	1.49421i	−0.368428	+	0.100969i
$220$	3.36786	+	1.86608i	0.227061	+	0.125811i
$221$	4.71966	−	7.06347i	0.317479	−	0.475140i
$222$	8.24250	−	8.48507i	0.553201	−	0.569481i
$223$	25.9745			1.73938			0.869691	−	0.493597i	$-0.164318\pi$
$223$	25.9745			1.73938			0.869691	+	0.493597i	$0.164318\pi$
$224$	12.8561	−	7.06030i	0.858984	−	0.471736i
$225$	−2.40068	−	1.79909i	−0.160045	−	0.119940i
$226$	17.6750	−	6.17411i	1.17573	−	0.410695i
$227$	11.7308	+	7.83828i	0.778601	+	0.520245i	0.880213	−	0.474579i	$-0.157400\pi$
$227$	11.7308	+	7.83828i	0.778601	+	0.520245i	−0.101611	+	0.994824i	$0.532400\pi$
$228$	−16.8787	−	18.3647i	−1.11782	−	1.21623i
$229$	−2.74213	−	0.545443i	−0.181205	−	0.0360439i	0.103654	−	0.994613i	$-0.466947\pi$
$229$	−2.74213	−	0.545443i	−0.181205	−	0.0360439i	−0.284859	+	0.958570i	$0.591947\pi$
$230$	−9.60022	−	2.48190i	−0.633019	−	0.163652i
$231$	0.614506	+	8.62376i	0.0404316	+	0.567402i
$232$	−12.0980	−	4.64041i	−0.794275	−	0.304658i
$233$	2.15909	+	5.21249i	0.141446	+	0.341482i	0.978688	−	0.205351i	$-0.0658335\pi$
$233$	2.15909	+	5.21249i	0.141446	+	0.341482i	−0.837242	+	0.546832i	$0.815833\pi$
$234$	−5.58018	+	10.1321i	−0.364788	+	0.662359i
$235$	1.77704	−	1.18738i	0.115921	−	0.0774562i
$236$	0.846180	−	0.435995i	0.0550816	−	0.0283809i
$237$	−4.36948	−	5.62785i	−0.283828	−	0.365568i
$238$	−0.646753	+	11.4070i	−0.0419227	+	0.739408i
$239$	−1.16888	+	1.16888i	−0.0756087	+	0.0756087i	−0.743900	−	0.668291i	$-0.767026\pi$
$239$	−1.16888	+	1.16888i	−0.0756087	+	0.0756087i	0.668291	+	0.743900i	$0.267026\pi$
$240$	−5.91330	−	3.61012i	−0.381702	−	0.233032i
$241$	−10.3968	−	10.3968i	−0.669715	−	0.669715i	0.287935	−	0.957650i	$-0.407031\pi$
$241$	−10.3968	−	10.3968i	−0.669715	−	0.669715i	−0.957650	+	0.287935i	$0.907031\pi$
$242$	7.69500	−	6.86924i	0.494653	−	0.441571i
$243$	9.13419	−	12.6320i	0.585958	−	0.810341i
$244$	−15.6267	+	1.30118i	−1.00039	+	0.0832998i
$245$	0.154050	+	0.230552i	0.00984188	+	0.0147294i
$246$	30.2935	+	5.57040i	1.93145	+	0.355156i
$247$	18.1369	−	7.51255i	1.15402	−	0.478012i
$248$	6.15968	+	27.1892i	0.391140	+	1.72652i
$249$	−0.665588	−	9.34063i	−0.0421800	−	0.591938i
$250$	0.717873	+	1.21847i	0.0454022	+	0.0770625i
$251$	−1.17987	+	5.93161i	−0.0744728	+	0.374400i	−0.999991	−	0.00430371i	$-0.998630\pi$
$251$	−1.17987	+	5.93161i	−0.0744728	+	0.374400i	0.925518	+	0.378704i	$0.123630\pi$
$252$	−0.451087	−	15.5504i	−0.0284158	−	0.979582i
$253$	7.49924	−	11.2234i	0.471473	−	0.705610i
$254$	−7.65561	+	15.8752i	−0.480356	+	0.996100i
$255$	4.82666	−	2.41447i	0.302257	−	0.151200i
$256$	−14.3855	−	7.00403i	−0.899096	−	0.437752i
$257$			1.40044i			0.0873573i	0.999046	+	0.0436787i	$0.0139078\pi$
$257$			1.40044i			0.0873573i	−0.999046	+	0.0436787i	$0.986092\pi$
$258$	0.175540	+	12.1054i	0.0109287	+	0.753650i
$259$	−10.4113	−	6.95664i	−0.646929	−	0.432264i
$260$	4.26682	−	3.39518i	0.264617	−	0.210560i
$261$	−10.2291	+	9.17864i	−0.633168	+	0.568143i
$262$	9.27890	−	5.46677i	0.573252	−	0.337738i
$263$	5.54177	−	13.3790i	0.341720	−	0.824986i	−0.655822	−	0.754916i	$-0.727678\pi$
$263$	5.54177	−	13.3790i	0.341720	−	0.824986i	0.997542	−	0.0700699i	$-0.0223222\pi$
$264$	7.29404	−	5.97875i	0.448917	−	0.367967i
$265$	−2.80377	−	6.76890i	−0.172234	−	0.415810i
$266$	−15.8876	+	21.0874i	−0.974133	+	1.29295i
$267$	23.2395	+	13.2417i	1.42224	+	0.810379i
$268$	−1.48398	−	17.8220i	−0.0906485	−	1.08865i
$269$	24.0645	−	4.78673i	1.46724	−	0.291852i	0.604137	−	0.796881i	$-0.293518\pi$
$269$	24.0645	−	4.78673i	1.46724	−	0.291852i	0.863103	+	0.505028i	$0.168518\pi$
$270$	−6.26677	+	3.83765i	−0.381384	+	0.233552i
$271$	−16.1610	+	16.1610i	−0.981711	+	0.981711i	−0.999836	−	0.0181242i	$-0.994231\pi$
$271$	−16.1610	+	16.1610i	−0.981711	+	0.981711i	0.0181242	+	0.999836i	$0.494231\pi$
$272$	10.5674	−	6.60832i	0.640744	−	0.400688i
$273$	11.6164	+	3.86970i	0.703056	+	0.234205i
$274$	23.4223	+	1.32799i	1.41500	+	0.0802271i
$275$	−1.88815	+	0.375577i	−0.113860	+	0.0226482i
$276$	−14.3329	+	19.6090i	−0.862737	+	1.18032i
$277$	9.18422	+	13.7451i	0.551826	+	0.825866i	0.997597	−	0.0692809i	$-0.0220705\pi$
$277$	9.18422	+	13.7451i	0.551826	+	0.825866i	−0.445771	+	0.895147i	$0.647070\pi$
$278$	1.66756	+	11.8579i	0.100014	+	0.711190i
$279$	28.6470	+	7.32774i	1.71505	+	0.438701i
$280$	−2.62636	+	6.84719i	−0.156955	+	0.409198i
$281$	9.37696	−	22.6380i	0.559383	−	1.35047i	−0.350873	−	0.936423i	$-0.614115\pi$
$281$	9.37696	−	22.6380i	0.559383	−	1.35047i	0.910256	−	0.414046i	$-0.135885\pi$
$282$	−1.09566	−	5.11918i	−0.0652457	−	0.304843i
$283$	−5.49214	+	27.6108i	−0.326474	+	1.64129i	0.373865	+	0.927483i	$0.378032\pi$
$283$	−5.49214	+	27.6108i	−0.326474	+	1.64129i	−0.700339	+	0.713811i	$0.746968\pi$
$284$	12.7004	−	3.64416i	0.753632	−	0.216241i
$285$	12.3739	+	1.55751i	0.732964	+	0.0922589i
$286$	2.44783	+	7.00758i	0.144743	+	0.414367i
$287$		−	32.6038i		−	1.92454i
$288$	−13.5664	+	10.1957i	−0.799408	+	0.600788i
$289$		−	7.29124i		−	0.428896i
$290$	6.11631	−	2.13650i	0.359162	−	0.125460i
$291$	27.1682	+	3.41968i	1.59263	+	0.200465i
$292$	3.16378	−	5.70993i	0.185146	−	0.334148i
$293$	1.62767	−	8.18285i	0.0950895	−	0.478047i	−0.903669	−	0.428232i	$-0.859137\pi$
$293$	1.62767	−	8.18285i	0.0950895	−	0.478047i	0.998758	−	0.0498153i	$-0.0158633\pi$
$294$	0.664158	−	0.142150i	0.0387345	−	0.00829037i
$295$	−0.182138	+	0.439720i	−0.0106045	+	0.0256015i
$296$	0.361089	+	13.6547i	0.0209879	+	0.793662i
$297$	−2.11866	−	9.77642i	−0.122937	−	0.567285i
$298$	−14.6117	+	2.05483i	−0.846435	+	0.119033i
$299$	−10.6205	−	15.8946i	−0.614197	−	0.919211i
$300$	3.42299	−	0.532093i	0.197627	−	0.0307204i
$301$	12.5689	−	2.50010i	0.724457	−	0.144103i
$302$	−1.16997	+	20.6352i	−0.0673240	+	1.18742i
$303$	8.11809	+	2.70433i	0.466372	+	0.155360i
$304$	28.7886	+	0.869647i	1.65114	+	0.0498777i
$305$	5.54398	−	5.54398i	0.317447	−	0.317447i
$306$	−1.13070	−	13.1711i	−0.0646380	−	0.752945i
$307$	4.17144	−	0.829750i	0.238076	−	0.0473563i	−0.0746099	−	0.997213i	$-0.523771\pi$
$307$	4.17144	−	0.829750i	0.238076	−	0.0473563i	0.312686	+	0.949856i	$0.398771\pi$
$308$	−7.62055	−	6.44902i	−0.434221	−	0.367467i
$309$	−0.195021	−	0.111122i	−0.0110944	−	0.00632148i
$310$	−11.1330	−	8.38781i	−0.632312	−	0.476396i
$311$	−2.86122	−	6.90759i	−0.162245	−	0.391693i	0.821760	−	0.569833i	$-0.192992\pi$
$311$	−2.86122	−	6.90759i	−0.162245	−	0.391693i	−0.984005	+	0.178140i	$0.942992\pi$
$312$	−3.86955	−	12.7838i	−0.219070	−	0.723739i
$313$	8.27178	−	19.9698i	0.467549	−	1.12876i	−0.497681	−	0.867360i	$-0.665815\pi$
$313$	8.27178	−	19.9698i	0.467549	−	1.12876i	0.965230	−	0.261402i	$-0.0841850\pi$
$314$	3.58568	+	6.08608i	0.202352	+	0.343457i
$315$	5.19488	+	5.78944i	0.292698	+	0.326198i
$316$	8.17447	+	0.929937i	0.459850	+	0.0523131i
$317$	−21.7721	−	14.5476i	−1.22284	−	0.817076i	−0.234917	−	0.972016i	$-0.575482\pi$
$317$	−21.7721	−	14.5476i	−1.22284	−	0.817076i	−0.987924	+	0.154940i	$0.950482\pi$
$318$	−17.9446	+	0.260214i	−1.00628	+	0.0145921i
$319$			8.81939i			0.493791i
$320$	7.75283	−	1.97323i	0.433396	−	0.110307i
$321$	9.33980	−	4.67210i	0.521297	−	0.260771i
$322$	23.1579	+	11.1676i	1.29054	+	0.622346i
$323$	−12.4646	+	18.6546i	−0.693550	+	1.03797i
$324$	3.06788	+	17.7366i	0.170438	+	0.985368i
$325$	−0.531894	+	2.67401i	−0.0295042	+	0.148328i
$326$	−18.0396	+	10.6282i	−0.999120	+	0.588643i
$327$	−2.47532	−	34.7378i	−0.136886	−	1.92100i
$328$	−29.0397	+	20.5345i	−1.60345	+	1.13383i
$329$	−5.11963	+	2.12062i	−0.282255	+	0.116914i
$330$	−0.852816	+	4.63787i	−0.0469460	+	0.255306i
$331$	−19.3434	−	28.9494i	−1.06321	−	1.59121i	−0.773179	−	0.634187i	$-0.781335\pi$
$331$	−19.3434	−	28.9494i	−1.06321	−	1.59121i	−0.290030	−	0.957018i	$-0.593665\pi$
$332$	8.25402	+	6.98511i	0.452998	+	0.383357i
$333$	13.0660	+	6.25968i	0.716010	+	0.343028i
$334$	7.94532	+	8.90043i	0.434748	+	0.487010i
$335$	6.32282	+	6.32282i	0.345452	+	0.345452i
$336$	13.2114	+	12.1717i	0.720740	+	0.664019i
$337$	4.70563	−	4.70563i	0.256332	−	0.256332i	−0.567228	−	0.823561i	$-0.691984\pi$
$337$	4.70563	−	4.70563i	0.256332	−	0.256332i	0.823561	+	0.567228i	$0.191984\pi$
$338$	−7.85994	−	0.445641i	−0.427524	−	0.0242397i
$339$	14.0622	+	18.1120i	0.763754	+	0.983709i
$340$	−1.89882	+	5.93544i	−0.102978	+	0.321895i
$341$	15.7772	−	10.5420i	0.854384	−	0.570881i
$342$	14.7373	−	26.7590i	0.796900	−	1.44696i
$343$	−7.22073	−	17.4324i	−0.389883	−	0.941261i
$344$	−10.1429	−	9.62030i	−0.546870	−	0.518692i
$345$	−0.863187	−	12.1137i	−0.0464724	−	0.652178i
$346$	0.0679129	−	0.262693i	0.00365102	−	0.0141225i
$347$	−11.2706	−	2.24186i	−0.605037	−	0.120349i	−0.116940	−	0.993139i	$-0.537309\pi$
$347$	−11.2706	−	2.24186i	−0.605037	−	0.120349i	−0.488097	+	0.872790i	$0.662309\pi$
$348$	0.668501	−	15.8555i	0.0358354	−	0.849944i
$349$	−0.0554294	−	0.0370368i	−0.00296707	−	0.00198253i	0.554086	−	0.832460i	$-0.313068\pi$
$349$	−0.0554294	−	0.0370368i	−0.00296707	−	0.00198253i	−0.557053	+	0.830477i	$0.688068\pi$
$350$	−1.20921	−	3.46168i	−0.0646349	−	0.185035i
$351$	−13.9397	−	2.52635i	−0.744047	−	0.134846i
$352$	−0.944479	+	10.8492i	−0.0503409	+	0.578266i
$353$	−1.56790			−0.0834510			−0.0417255	−	0.999129i	$-0.513286\pi$
$353$	−1.56790			−0.0834510			−0.0417255	+	0.999129i	$0.513286\pi$
$354$	0.836235	+	0.812329i	0.0444454	+	0.0431748i
$355$	−3.67035	+	5.49307i	−0.194802	+	0.291542i
$356$	−29.6872	+	8.51821i	−1.57342	+	0.451464i
$357$	−13.4955	+	3.69850i	−0.714258	+	0.195745i
$358$	−8.60235	+	33.2746i	−0.454648	+	1.75862i
$359$	−5.40946	−	2.24067i	−0.285500	−	0.118258i	0.235338	−	0.971914i	$-0.424380\pi$
$359$	−5.40946	−	2.24067i	−0.285500	−	0.118258i	−0.520838	+	0.853656i	$0.674380\pi$
$360$	1.88474	−	8.27332i	0.0993344	−	0.436042i
$361$	−30.3458	+	12.5697i	−1.59715	+	0.661561i
$362$	−4.55348	+	0.640350i	−0.239326	+	0.0336560i
$363$	10.9765	+	6.25430i	0.576115	+	0.328266i
$364$	−12.5679	+	6.47565i	−0.658738	+	0.339416i
$365$	0.636760	+	3.20121i	0.0333296	+	0.167559i
$366$	−7.60589	−	17.6346i	−0.397566	−	0.921775i
$367$	11.0947	+	11.0947i	0.579137	+	0.579137i	0.934666	−	0.355528i	$-0.115699\pi$
$367$	11.0947	+	11.0947i	0.579137	+	0.579137i	−0.355528	+	0.934666i	$0.615699\pi$
$368$	−4.63849	−	27.6600i	−0.241798	−	1.44188i
$369$	5.34905	+	37.3427i	0.278460	+	1.94398i
$370$	−4.54823	−	5.09497i	−0.236451	−	0.264875i
$371$	3.70605	+	18.6316i	0.192408	+	0.967303i
$372$	−29.1633	+	17.7565i	−1.51205	+	0.920632i
$373$	−26.6246	+	17.7900i	−1.37857	+	0.921130i	−0.999990	−	0.00443939i	$-0.998587\pi$
$373$	−26.6246	+	17.7900i	−1.37857	+	0.921130i	−0.378578	+	0.925569i	$0.623587\pi$
$374$	−6.77544	−	5.10474i	−0.350349	−	0.263960i
$375$	−1.13460	+	1.30870i	−0.0585903	+	0.0675809i
$376$	5.11326	+	3.22438i	0.263696	+	0.166285i
$377$	11.5393	+	4.77974i	0.594305	+	0.246169i
$378$	17.8776	−	6.58920i	0.919525	−	0.338912i
$379$	−3.06129	−	0.608928i	−0.157248	−	0.0312785i	0.115839	−	0.993268i	$-0.463044\pi$
$379$	−3.06129	−	0.608928i	−0.157248	−	0.0312785i	−0.273086	+	0.961990i	$0.588044\pi$
$380$	−11.2687	+	8.96668i	−0.578071	+	0.459981i
$381$	−21.4168	−	2.69575i	−1.09722	−	0.138108i
$382$	4.10470	+	1.97944i	0.210015	+	0.101277i
$383$	−1.89314			−0.0967347			−0.0483674	−	0.998830i	$-0.515402\pi$
$383$	−1.89314			−0.0967347			−0.0483674	+	0.998830i	$0.515402\pi$
$384$	2.52035	−	19.4332i	0.128616	−	0.991694i
$385$	4.99156			0.254393
$386$	−0.510172	−	0.246024i	−0.0259671	−	0.0125223i
$387$	−13.9856	+	4.92557i	−0.710927	+	0.250381i
$388$	−24.7416	+	19.6873i	−1.25606	+	0.999472i
$389$	−29.3121	−	5.83053i	−1.48618	−	0.295620i	−0.615762	−	0.787932i	$-0.711152\pi$
$389$	−29.3121	−	5.83053i	−1.48618	−	0.295620i	−0.870418	+	0.492313i	$0.836152\pi$
$390$	5.60601	+	3.62936i	0.283871	+	0.183780i
$391$	20.1842	+	8.36058i	1.02076	+	0.422813i
$392$	−0.418328	+	0.663389i	−0.0211288	+	0.0335062i
$393$	9.96605	+	8.64021i	0.502720	+	0.435841i
$394$	−24.9167	−	18.7727i	−1.25529	−	0.945756i
$395$	−3.42033	+	2.28539i	−0.172095	+	0.114991i
$396$	9.78624	+	6.13614i	0.491777	+	0.308353i
$397$	2.82278	+	14.1911i	0.141671	+	0.712230i	0.984686	+	0.174339i	$0.0557789\pi$
$397$	2.82278	+	14.1911i	0.141671	+	0.712230i	−0.843014	+	0.537891i	$0.819221\pi$
$398$	3.50072	+	3.92155i	0.175475	+	0.196569i
$399$	−30.6789	−	10.2199i	−1.53587	−	0.511633i
$400$	−2.32169	+	3.25726i	−0.116085	+	0.162863i
$401$	14.1999	+	14.1999i	0.709108	+	0.709108i	0.966348	−	0.257240i	$-0.0828131\pi$
$401$	14.1999	+	14.1999i	0.709108	+	0.709108i	−0.257240	+	0.966348i	$0.582813\pi$
$402$	20.1120	−	8.67439i	1.00309	−	0.432639i
$403$	−5.24259	−	26.3563i	−0.261152	−	1.31290i
$404$	−8.78307	+	4.52549i	−0.436974	+	0.225152i
$405$	−6.89979	−	5.77866i	−0.342853	−	0.287144i
$406$	−16.6345	+	2.33929i	−0.825557	+	0.116097i
$407$	8.58948	−	3.55788i	0.425765	−	0.176358i
$408$	11.7939	+	9.69088i	0.583887	+	0.479770i
$409$	−15.4902	−	6.41626i	−0.765943	−	0.317264i	−0.0347150	−	0.999397i	$-0.511052\pi$
$409$	−15.4902	−	6.41626i	−0.765943	−	0.317264i	−0.731228	+	0.682133i	$0.761052\pi$
$410$	4.45108	−	17.2172i	0.219823	−	0.850295i
$411$	7.59423	+	27.7107i	0.374596	+	1.36687i
$412$	0.249129	−	0.0714830i	0.0122737	−	0.00352171i
$413$	0.685602	−	1.02608i	0.0337363	−	0.0504899i
$414$	−28.3561	−	8.99147i	−1.39363	−	0.441907i
$415$	−5.40649			−0.265394
$416$	13.6833	+	7.11559i	0.670879	+	0.348870i
$417$	−13.1163	+	6.56122i	−0.642306	+	0.321304i
$418$	−6.46473	−	18.5070i	−0.316200	−	0.905208i
$419$	24.9703	+	16.6846i	1.21988	+	0.815095i	0.987514	−	0.157534i	$-0.0503543\pi$
$419$	24.9703	+	16.6846i	1.21988	+	0.815095i	0.232363	+	0.972629i	$0.425354\pi$
$420$	−8.97382	−	0.378355i	−0.437878	−	0.0184618i
$421$	0.147714	+	0.0293822i	0.00719916	+	0.00143200i	0.198689	−	0.980063i	$-0.436332\pi$
$421$	0.147714	+	0.0293822i	0.00719916	+	0.00143200i	−0.191489	+	0.981495i	$0.561332\pi$
$422$	−5.16254	+	19.9691i	−0.251308	+	0.972083i
$423$	5.51586	−	3.26879i	0.268190	−	0.158934i
$424$	14.2607	−	15.0355i	0.692563	−	0.730186i
$425$	−1.19240	−	2.87871i	−0.0578398	−	0.139638i
$426$	9.18463	+	13.3234i	0.444997	+	0.645523i
$427$	−16.9027	+	11.2940i	−0.817978	+	0.546555i
$428$	−3.67431	+	11.4853i	−0.177604	+	0.555165i
$429$	−7.18082	+	5.57521i	−0.346693	+	0.269174i
$430$	6.97859	+	0.395670i	0.336537	+	0.0190809i
$431$	−0.410422	+	0.410422i	−0.0197693	+	0.0197693i	−0.716922	−	0.697153i	$-0.754450\pi$
$431$	−0.410422	+	0.410422i	−0.0197693	+	0.0197693i	0.697153	+	0.716922i	$0.254450\pi$
$432$	−17.1286	−	11.7733i	−0.824099	−	0.566445i
$433$	15.3584	+	15.3584i	0.738076	+	0.738076i	0.972205	−	0.234130i	$-0.0752240\pi$
$433$	15.3584	+	15.3584i	0.738076	+	0.738076i	−0.234130	+	0.972205i	$0.575224\pi$
$434$	24.0684	+	26.9617i	1.15532	+	1.29420i
$435$	4.86612	+	6.26752i	0.233313	+	0.300505i
$436$	30.6967	+	25.9776i	1.47010	+	1.24410i
$437$	28.0486	+	41.9778i	1.34175	+	2.00807i
$438$	7.86312	+	1.44588i	0.375714	+	0.0690867i
$439$	−31.9968	+	13.2535i	−1.52712	+	0.632555i	−0.979003	−	0.203846i	$-0.934656\pi$
$439$	−31.9968	+	13.2535i	−1.52712	+	0.632555i	−0.548119	+	0.836400i	$0.684656\pi$
$440$	−3.14378	−	4.44591i	−0.149874	−	0.211950i
$441$	0.424091	+	0.715623i	0.0201948	+	0.0340773i
$442$	−10.3511	+	6.09844i	−0.492350	+	0.290073i
$443$	−1.53474	+	7.71565i	−0.0729176	+	0.366581i	−0.999965	−	0.00836263i	$-0.997338\pi$
$443$	−1.53474	+	7.71565i	−0.0729176	+	0.366581i	0.927047	+	0.374944i	$0.122338\pi$
$444$	−15.7119	+	5.74528i	−0.745652	+	0.272659i
$445$	8.57943	−	12.8400i	0.406704	−	0.608676i
$446$	−33.0872	−	15.9558i	−1.56672	−	0.755531i
$447$	−8.08497	−	16.1623i	−0.382406	−	0.764452i
$448$	−20.7136	+	1.09628i	−0.978624	+	0.0517944i
$449$			20.3580i			0.960755i	0.877062	+	0.480377i	$0.159500\pi$
$449$			20.3580i			0.960755i	−0.877062	+	0.480377i	$0.840500\pi$
$450$	1.95290	+	3.76646i	0.0920605	+	0.177552i
$451$	20.1282	+	13.4492i	0.947800	+	0.633300i
$452$	−26.3077	−	2.99280i	−1.23741	−	0.140769i
$453$	−24.4132	+	6.69054i	−1.14703	+	0.314349i
$454$	−10.1281	−	17.1908i	−0.475336	−	0.806802i
$455$	2.70521	−	6.53097i	0.126822	−	0.306176i
$456$	10.2195	+	33.7619i	0.478571	+	1.58105i
$457$	0.935652	+	2.25886i	0.0437680	+	0.105665i	0.944252	−	0.329225i	$-0.106787\pi$
$457$	0.935652	+	2.25886i	0.0437680	+	0.105665i	−0.900484	+	0.434890i	$0.856787\pi$
$458$	3.15795	+	2.37926i	0.147561	+	0.111176i
$459$	14.8503	−	6.45018i	0.693153	−	0.301069i
$460$	10.7045	+	9.05883i	0.499098	+	0.422370i
$461$	6.19061	−	1.23139i	0.288326	−	0.0573515i	−0.0488086	−	0.998808i	$-0.515542\pi$
$461$	6.19061	−	1.23139i	0.288326	−	0.0573515i	0.337134	+	0.941457i	$0.390542\pi$
$462$	4.51470	−	11.3627i	0.210043	−	0.528641i
$463$	19.3983	−	19.3983i	0.901514	−	0.901514i	−0.0940530	−	0.995567i	$-0.529982\pi$
$463$	19.3983	−	19.3983i	0.901514	−	0.901514i	0.995567	+	0.0940530i	$0.0299823\pi$
$464$	12.5603	+	13.3428i	0.583098	+	0.619424i
$465$	5.39554	−	16.1968i	0.250212	−	0.751109i
$466$	0.451663	−	7.96615i	0.0209229	−	0.369025i
$467$	−13.2389	+	2.63338i	−0.612623	+	0.121858i	−0.491643	−	0.870797i	$-0.663604\pi$
$467$	−13.2389	+	2.63338i	−0.612623	+	0.121858i	−0.120979	+	0.992655i	$0.538604\pi$
$468$	13.3323	−	9.47881i	0.616285	−	0.438158i
$469$	−12.8806	−	19.2772i	−0.594772	−	0.890139i
$470$	−2.99305	+	0.420908i	−0.138059	+	0.0194150i
$471$	−5.66716	+	6.53678i	−0.261129	+	0.301199i
$472$	−1.34572	+	0.0355867i	−0.0619417	+	0.00163801i
$473$	−3.64127	+	8.79080i	−0.167426	+	0.404201i
$474$	2.10886	+	9.85306i	0.0968630	+	0.452566i
$475$	1.40473	−	7.06207i	0.0644536	−	0.324030i
$476$	7.83106	−	14.1333i	0.358936	−	0.647801i
$477$	−7.30146	−	20.7317i	−0.334311	−	0.949237i
$478$	2.20699	−	0.770929i	0.100945	−	0.0352615i
$479$			8.27272i			0.377990i	0.981978	+	0.188995i	$0.0605230\pi$
$479$			8.27272i			0.377990i	−0.981978	+	0.188995i	$0.939477\pi$
$480$	5.31489	+	8.23115i	0.242591	+	0.375699i
$481$		−	13.1667i		−	0.600351i
$482$	6.85713	+	19.6304i	0.312334	+	0.894139i
$483$	−3.93242	+	31.2417i	−0.178931	+	1.42155i
$484$	−14.0218	+	4.02331i	−0.637356	+	0.182878i
$485$	3.08424	−	15.5055i	0.140048	−	0.704070i
$486$	−19.3951	+	10.4800i	−0.879780	+	0.475382i
$487$	−9.23789	+	22.3022i	−0.418609	+	1.01061i	0.564143	+	0.825677i	$0.309207\pi$
$487$	−9.23789	+	22.3022i	−0.418609	+	1.01061i	−0.982751	+	0.184933i	$0.940793\pi$
$488$	20.7051	+	7.94179i	0.937274	+	0.359508i
$489$	−19.3755	−	16.7979i	−0.876190	−	0.759626i
$490$	−0.0546083	−	0.388316i	−0.00246695	−	0.0175423i
$491$	−16.7659	−	25.0920i	−0.756635	−	1.13238i	−0.987225	−	0.159333i	$-0.949065\pi$
$491$	−16.7659	−	25.0920i	−0.756635	−	1.13238i	0.230590	−	0.973051i	$-0.425935\pi$
$492$	−35.1671	−	25.7047i	−1.58545	−	1.15886i
$493$	−14.0001	+	2.78479i	−0.630532	+	0.125421i
$494$	−27.7182	−	1.57156i	−1.24710	−	0.0707079i
$495$	−5.71708	+	0.818926i	−0.256964	+	0.0368080i
$496$	8.85564	−	38.4184i	0.397630	−	1.72503i
$497$	12.1123	−	12.1123i	0.543310	−	0.543310i
$498$	−4.89000	+	12.3073i	−0.219126	+	0.551502i
$499$	8.35793	−	1.66250i	0.374152	−	0.0744236i	−0.00443229	−	0.999990i	$-0.501411\pi$
$499$	8.35793	−	1.66250i	0.374152	−	0.0744236i	0.378585	+	0.925567i	$0.376411\pi$
$500$	−0.165960	−	1.99310i	−0.00742194	−	0.0891343i
$501$	−7.23405	+	12.6960i	−0.323194	+	0.567213i
$502$	5.14668	−	6.83110i	0.229708	−	0.304887i
$503$	−9.58490	−	23.1400i	−0.427370	−	1.03176i	−0.980118	−	0.198414i	$-0.936421\pi$
$503$	−9.58490	−	23.1400i	−0.427370	−	1.03176i	0.552749	−	0.833348i	$-0.313579\pi$
$504$	−8.97781	+	20.0857i	−0.399904	+	0.894687i
$505$	1.89053	−	4.56415i	0.0841276	−	0.203102i
$506$	−16.4472	+	9.69004i	−0.731167	+	0.430775i
$507$	−2.54843	−	9.29900i	−0.113180	−	0.412983i
$508$	19.5039	−	15.5196i	0.865347	−	0.688572i
$509$	12.3416	+	8.24642i	0.547034	+	0.365516i	0.798167	−	0.602436i	$-0.205803\pi$
$509$	12.3416	+	8.24642i	0.547034	+	0.365516i	−0.251133	+	0.967953i	$0.580803\pi$
$510$	−7.63153	+	0.110665i	−0.337930	+	0.00490032i
$511$		−	8.46277i		−	0.374371i
$512$	14.0223	+	17.7588i	0.619702	+	0.784837i
$513$	36.8148	+	6.67208i	1.62541	+	0.294580i
$514$	0.860277	−	1.78393i	0.0379452	−	0.0786859i
$515$	−0.0719967	+	0.107751i	−0.00317256	+	0.00474807i
$516$	7.21261	−	15.5281i	0.317517	−	0.683586i
$517$	0.802695	−	4.03542i	0.0353025	−	0.177478i
$518$	8.98893	+	15.2572i	0.394951	+	0.670361i
$519$	0.331469	−	0.0236196i	0.0145499	−	0.00103678i
$520$	−7.52084	+	1.70383i	−0.329811	+	0.0747181i
$521$	−5.74889	+	2.38127i	−0.251863	+	0.104325i	−0.505043	−	0.863094i	$-0.668524\pi$
$521$	−5.74889	+	2.38127i	−0.251863	+	0.104325i	0.253180	+	0.967419i	$0.418524\pi$
$522$	18.6685	−	5.40840i	0.817100	−	0.236719i
$523$	0.573019	+	0.857583i	0.0250564	+	0.0374995i	0.843786	−	0.536679i	$-0.180321\pi$
$523$	0.573019	+	0.857583i	0.0250564	+	0.0374995i	−0.818730	+	0.574179i	$0.805321\pi$
$524$	−15.1779	+	1.26382i	−0.663051	+	0.0552103i
$525$	3.54726	−	2.75410i	0.154815	−	0.120199i
$526$	−15.2779	+	13.6384i	−0.666147	+	0.594662i
$527$	21.7164	+	21.7164i	0.945980	+	0.945980i
$528$	−12.9641	+	3.13528i	−0.564188	+	0.136446i
$529$	18.4993	−	18.4993i	0.804318	−	0.804318i
$530$	−0.586525	+	10.3448i	−0.0254770	+	0.449348i
$531$	−0.616915	+	1.28770i	−0.0267718	+	0.0558814i
$532$	33.1919	−	17.1022i	1.43905	−	0.741474i
$533$	28.5057	−	19.0469i	1.23472	−	0.825012i
$534$	−21.4691	−	31.1435i	−0.929057	−	1.34771i
$535$	−2.30734	−	5.57042i	−0.0997552	−	0.240830i
$536$	−9.05748	+	23.6138i	−0.391224	+	1.01996i
$537$	−41.9863	+	2.99183i	−1.81184	+	0.129107i
$538$	−33.5946	−	8.68507i	−1.44837	−	0.374440i
$539$	0.523552	+	0.104141i	0.0225510	+	0.00448567i
$540$	10.3402	−	1.03892i	0.444973	−	0.0447078i
$541$	24.2354	+	16.1936i	1.04196	+	0.696216i	0.953969	−	0.299905i	$-0.0969551\pi$
$541$	24.2354	+	16.1936i	1.04196	+	0.696216i	0.0879916	+	0.996121i	$0.471955\pi$
$542$	30.5139	−	10.6589i	1.31069	−	0.457839i
$543$	−2.51953	−	5.03669i	−0.108124	−	0.216145i
$544$	−17.5205	+	1.92644i	−0.751187	+	0.0825956i
$545$	−20.1067			−0.861277
$546$	−12.4202	−	12.0652i	−0.531537	−	0.516341i
$547$	9.77458	−	14.6287i	0.417931	−	0.625478i	−0.561447	−	0.827512i	$-0.689755\pi$
$547$	9.77458	−	14.6287i	0.417931	−	0.625478i	0.979378	+	0.202035i	$0.0647553\pi$
$548$	−29.0204	−	16.0797i	−1.23969	−	0.686892i
$549$	17.5066	−	15.7087i	0.747162	−	0.670430i
$550$	2.63591	+	0.681449i	0.112395	+	0.0290571i
$551$	−30.4753	−	12.6233i	−1.29829	−	0.537770i
$552$	30.3033	−	16.1741i	1.28979	−	0.688414i
$553$	9.85393	−	4.08163i	0.419032	−	0.173569i
$554$	−3.25566	−	23.1508i	−0.138320	−	0.983582i
$555$	4.14107	−	7.26768i	0.175779	−	0.308496i
$556$	5.15998	−	16.1293i	0.218832	−	0.684037i
$557$	6.47929	+	32.5736i	0.274536	+	1.38019i	0.834198	+	0.551466i	$0.185931\pi$
$557$	6.47929	+	32.5736i	0.274536	+	1.38019i	−0.559661	+	0.828721i	$0.689069\pi$
$558$	−31.9901	−	26.9318i	−1.35425	−	1.14012i
$559$	9.52849	+	9.52849i	0.403012	+	0.403012i
$560$	7.55169	−	7.10883i	0.319117	−	0.300403i
$561$	3.28368	−	9.85722i	0.138637	−	0.416172i
$562$	−25.8509	+	23.0768i	−1.09046	+	0.973438i
$563$	−5.01641	−	25.2192i	−0.211416	−	1.06286i	−0.930039	−	0.367462i	$-0.880227\pi$
$563$	−5.01641	−	25.2192i	−0.211416	−	1.06286i	0.718622	−	0.695401i	$-0.244773\pi$
$564$	−1.74897	+	7.19403i	−0.0736447	+	0.302923i
$565$	11.0076	−	7.35503i	0.463092	−	0.309428i
$566$	23.9571	−	31.7978i	1.00699	−	1.33656i
$567$	14.6231	+	18.1853i	0.614114	+	0.763710i
$568$	−18.4168	−	3.15969i	−0.772751	−	0.132578i
$569$	25.6175	+	10.6111i	1.07394	+	0.444840i	0.848379	−	0.529389i	$-0.177579\pi$
$569$	25.6175	+	10.6111i	1.07394	+	0.444840i	0.225560	+	0.974229i	$0.427579\pi$
$570$	−14.8055	−	9.58513i	−0.620133	−	0.401477i
$571$	−24.2687	−	4.82735i	−1.01561	−	0.202018i	−0.340902	−	0.940099i	$-0.610732\pi$
$571$	−24.2687	−	4.82735i	−1.01561	−	0.202018i	−0.674713	+	0.738081i	$0.735732\pi$
$572$	1.18655	−	10.4302i	0.0496120	−	0.436107i
$573$	−0.697014	+	5.53753i	−0.0291182	+	0.231334i
$574$	−20.0281	+	41.5317i	−0.835957	+	1.73350i
$575$	−7.01156			−0.292402
$576$	23.5444	−	4.65394i	0.981018	−	0.193914i
$577$	−4.94251			−0.205759			−0.102880	−	0.994694i	$-0.532806\pi$
$577$	−4.94251			−0.205759			−0.102880	+	0.994694i	$0.532806\pi$
$578$	−4.47893	+	9.28782i	−0.186299	+	0.386322i
$579$	0.0866317	−	0.688258i	0.00360029	−	0.0286030i
$580$	−9.10359	−	1.03564i	−0.378006	−	0.0430024i
$581$	13.7487	+	2.73479i	0.570392	+	0.113458i
$582$	−32.5070	−	21.0452i	−1.34746	−	0.872352i
$583$	−13.0311	−	5.39767i	−0.539694	−	0.223549i
$584$	−7.53767	+	5.33002i	−0.311911	+	0.220558i
$585$	−2.02693	+	7.92407i	−0.0838034	+	0.327620i
$586$	−7.10001	+	9.42372i	−0.293299	+	0.389290i
$587$	−2.53137	+	1.69141i	−0.104481	+	0.0698118i	−0.606713	−	0.794921i	$-0.707512\pi$
$587$	−2.53137	+	1.69141i	−0.104481	+	0.0698118i	0.502232	+	0.864733i	$0.332512\pi$
$588$	−0.933348	−	0.226909i	−0.0384906	−	0.00935758i
$589$	13.8457	+	69.6069i	0.570501	+	2.86810i
$590$	0.502128	−	0.448244i	0.0206723	−	0.0184539i
$591$	12.0757	−	36.2500i	0.496729	−	1.49113i
$592$	7.92794	−	17.6156i	0.325836	−	0.723996i
$593$	14.0672	+	14.0672i	0.577669	+	0.577669i	0.934261	−	0.356591i	$-0.116061\pi$
$593$	14.0672	+	14.0672i	0.577669	+	0.577669i	−0.356591	+	0.934261i	$0.616061\pi$
$594$	−3.30672	+	13.7550i	−0.135677	+	0.564374i
$595$	1.57612	+	7.92370i	0.0646147	+	0.324840i
$596$	19.8752	+	6.35831i	0.814118	+	0.260447i
$597$	−3.18734	+	5.59386i	−0.130449	+	0.228941i
$598$	3.76479	+	26.7711i	0.153954	+	1.09475i
$599$	−2.27826	+	0.943685i	−0.0930871	+	0.0385579i	−0.428741	−	0.903427i	$-0.641043\pi$
$599$	−2.27826	+	0.943685i	−0.0930871	+	0.0385579i	0.335654	+	0.941985i	$0.391043\pi$
$600$	−4.68718	−	1.42491i	−0.191353	−	0.0581717i
$601$	18.1960	+	7.53704i	0.742231	+	0.307442i	0.721567	−	0.692344i	$-0.243422\pi$
$601$	18.1960	+	7.53704i	0.742231	+	0.307442i	0.0206638	+	0.999786i	$0.493422\pi$
$602$	−17.5464	−	4.53620i	−0.715138	−	0.184882i
$603$	17.9155	+	19.9660i	0.729575	+	0.813076i
$604$	14.1663	−	25.5670i	0.576418	−	1.04031i
$605$	4.05223	−	6.06458i	0.164746	−	0.246560i
$606$	−8.67985	−	8.43171i	−0.352595	−	0.342515i
$607$	7.76496			0.315170			0.157585	−	0.987505i	$-0.449629\pi$
$607$	7.76496			0.315170			0.157585	+	0.987505i	$0.449629\pi$
$608$	−36.1376	−	18.7923i	−1.46557	−	0.762127i
$609$	−9.20421	−	18.3998i	−0.372974	−	0.745596i
$610$	−10.4677	+	3.65650i	−0.423825	+	0.148047i
$611$	−4.84493	−	3.23728i	−0.196005	−	0.130966i
$612$	−6.65056	+	17.4724i	−0.268833	+	0.706281i
$613$	21.6711	+	4.31065i	0.875288	+	0.174106i	0.612235	−	0.790676i	$-0.290271\pi$
$613$	21.6711	+	4.31065i	0.875288	+	0.174106i	0.263053	+	0.964781i	$0.415271\pi$
$614$	−5.82342	−	1.50550i	−0.235014	−	0.0607572i
$615$	21.7248	−	1.54805i	0.876029	−	0.0624235i
$616$	5.74574	+	12.8962i	0.231503	+	0.519602i
$617$	−1.64541	−	3.97236i	−0.0662415	−	0.159921i	0.887292	−	0.461208i	$-0.152584\pi$
$617$	−1.64541	−	3.97236i	−0.0662415	−	0.159921i	−0.953534	+	0.301287i	$0.902584\pi$
$618$	0.180164	+	0.261350i	0.00724725	+	0.0105130i
$619$	5.43660	−	3.63262i	0.218515	−	0.146007i	−0.441495	−	0.897264i	$-0.645552\pi$
$619$	5.43660	−	3.63262i	0.218515	−	0.146007i	0.660011	+	0.751256i	$0.270552\pi$
$620$	9.02904	+	17.5235i	0.362615	+	0.703762i
$621$	−0.621582	−	36.4278i	−0.0249432	−	1.46180i
$622$	−0.598543	+	10.5567i	−0.0239994	+	0.423286i
$623$	−28.3124	+	28.3124i	−1.13431	+	1.13431i
$624$	−2.92377	+	18.6614i	−0.117045	+	0.747054i
$625$	0.707107	+	0.707107i	0.0282843	+	0.0282843i
$626$	−22.8041	+	20.3570i	−0.911436	+	0.813628i
$627$	18.9645	−	14.7241i	0.757371	−	0.588025i
$628$	−0.828947	−	9.95529i	−0.0330786	−	0.397259i
$629$	8.36005	+	12.5117i	0.333337	+	0.498874i
$630$	−3.06102	−	10.5659i	−0.121954	−	0.420957i
$631$	−21.1217	+	8.74888i	−0.840840	+	0.348287i	−0.761185	−	0.648535i	$-0.775382\pi$
$631$	−21.1217	+	8.74888i	−0.840840	+	0.348287i	−0.0796552	+	0.996822i	$0.525382\pi$
$632$	−9.84165	−	6.20607i	−0.391480	−	0.246864i
$633$	−25.1973	+	1.79549i	−1.00150	+	0.0713644i
$634$	18.7975	+	31.9056i	0.746545	+	1.26713i
$635$	−2.43133	+	12.2231i	−0.0964842	+	0.485059i
$636$	23.0182	+	10.6917i	0.912732	+	0.423953i
$637$	0.420001	−	0.628577i	0.0166411	−	0.0249051i
$638$	5.41765	−	11.2344i	0.214487	−	0.444775i
$639$	−11.8856	+	15.8600i	−0.470189	+	0.627411i
$640$	−11.0879	−	2.24891i	−0.438289	−	0.0888959i
$641$		−	32.3622i		−	1.27823i	−0.769112	−	0.639115i	$-0.779301\pi$
$641$		−	32.3622i		−	1.27823i	0.769112	−	0.639115i	$-0.220699\pi$
$642$	−14.7674	+	0.214141i	−0.582821	+	0.00845148i
$643$	9.71560	+	6.49176i	0.383146	+	0.256010i	0.732196	−	0.681094i	$-0.238496\pi$
$643$	9.71560	+	6.49176i	0.383146	+	0.256010i	−0.349050	+	0.937104i	$0.613496\pi$
$644$	−22.6392	−	28.4513i	−0.892109	−	1.12114i
$645$	2.26267	+	8.25628i	0.0890925	+	0.325091i
$646$	27.3372	−	16.1060i	1.07557	−	0.633681i
$647$	7.92622	−	19.1356i	0.311612	−	0.752297i	−0.688034	−	0.725678i	$-0.741526\pi$
$647$	7.92622	−	19.1356i	0.311612	−	0.752297i	0.999646	−	0.0266187i	$-0.00847400\pi$
$648$	6.98744	−	24.4781i	0.274493	−	0.961589i
$649$	0.350642	+	0.846525i	0.0137639	+	0.0332290i
$650$	2.32016	−	3.07951i	0.0910042	−	0.120788i
$651$	−21.9138	+	38.4592i	−0.858868	+	1.50734i
$652$	29.5082	−	2.45706i	1.15563	−	0.0962259i
$653$	−30.7481	+	6.11619i	−1.20327	+	0.239345i	−0.755708	−	0.654909i	$-0.772707\pi$
$653$	−30.7481	+	6.11619i	−1.20327	+	0.239345i	−0.447560	+	0.894254i	$0.647707\pi$
$654$	−18.1859	+	45.7707i	−0.711124	+	1.78978i
$655$	5.38478	−	5.38478i	0.210401	−	0.210401i
$656$	49.6058	−	8.31873i	1.93678	−	0.324792i
$657$	1.38842	+	9.69284i	0.0541675	+	0.378154i
$658$	7.82423	+	0.443616i	0.305020	+	0.0172940i
$659$	20.5970	−	4.09699i	0.802344	−	0.159596i	0.223148	−	0.974785i	$-0.428367\pi$
$659$	20.5970	−	4.09699i	0.802344	−	0.159596i	0.579196	+	0.815188i	$0.303367\pi$
$660$	3.93533	−	5.38399i	0.153183	−	0.209572i
$661$	−4.07240	−	6.09477i	−0.158398	−	0.237059i	0.743779	−	0.668426i	$-0.233032\pi$
$661$	−4.07240	−	6.09477i	−0.158398	−	0.237059i	−0.902177	+	0.431367i	$0.858032\pi$
$662$	6.85693	+	48.7592i	0.266502	+	1.89508i
$663$	−11.1176	−	9.63857i	−0.431772	−	0.374331i
$664$	−6.22337	−	13.9682i	−0.241514	−	0.542072i
$665$	−7.14447	+	17.2483i	−0.277051	+	0.668860i
$666$	−12.7986	−	16.0001i	−0.495936	−	0.619990i
$667$	−6.26650	+	31.5038i	−0.242640	+	1.21983i
$668$	−4.65357	−	16.2184i	−0.180052	−	0.627508i
$669$	5.61850	−	44.6370i	0.217224	−	1.72576i
$670$	−4.17017	−	11.9382i	−0.161108	−	0.461215i
$671$		−	15.0939i		−	0.582692i
$672$	−9.35218	−	23.6203i	−0.360768	−	0.911172i
$673$		−	31.7247i		−	1.22290i	−0.791284	−	0.611449i	$-0.790587\pi$
$673$		−	31.7247i		−	1.22290i	0.791284	−	0.611449i	$-0.209413\pi$
$674$	−8.88480	+	3.10357i	−0.342230	+	0.119545i
$675$	−3.61101	+	3.73639i	−0.138988	+	0.143814i
$676$	9.73849	+	5.39594i	0.374557	+	0.207536i
$677$	7.59975	−	38.2065i	0.292082	−	1.46840i	−0.504261	−	0.863552i	$-0.668235\pi$
$677$	7.59975	−	38.2065i	0.292082	−	1.46840i	0.796343	−	0.604845i	$-0.206765\pi$
$678$	−6.78689	−	31.7099i	−0.260649	−	1.21781i
$679$	−15.6865	+	37.8705i	−0.601991	+	1.45334i
$680$	6.06486	−	6.39434i	0.232577	−	0.245212i
$681$	16.0075	−	18.4638i	0.613408	−	0.707535i
$682$	−26.5734	+	3.73697i	−1.01755	+	0.143096i
$683$	22.9347	+	34.3242i	0.877572	+	1.31338i	0.948786	+	0.315919i	$0.102313\pi$
$683$	22.9347	+	34.3242i	0.877572	+	1.31338i	−0.0712141	+	0.997461i	$0.522687\pi$
$684$	−35.2105	+	25.0335i	−1.34631	+	0.957181i
$685$	16.2699	−	3.23629i	0.621643	−	0.123652i
$686$	−1.51052	+	26.6416i	−0.0576718	+	1.01718i
$687$	−1.53048	+	4.59434i	−0.0583916	+	0.175285i
$688$	7.01074	+	18.4853i	0.267282	+	0.704747i
$689$	−14.1246	+	14.1246i	−0.538106	+	0.538106i
$690$	−6.34173	+	15.9610i	−0.241426	+	0.607626i
$691$	−24.3922	+	4.85191i	−0.927923	+	0.184575i	−0.635843	−	0.771819i	$-0.719347\pi$
$691$	−24.3922	+	4.85191i	−0.927923	+	0.184575i	−0.292080	+	0.956394i	$0.594347\pi$
$692$	−0.247879	+	0.292909i	−0.00942294	+	0.0111347i
$693$	14.9528	+	0.809366i	0.568009	+	0.0307453i
$694$	12.9797	+	9.77915i	0.492702	+	0.371211i
$695$	3.24030	+	7.82277i	0.122912	+	0.296735i
$696$	−10.5914	+	19.7866i	−0.401466	+	0.750009i
$697$	−14.9940	+	36.1987i	−0.567937	+	1.37112i
$698$	0.0478565	+	0.0812283i	0.00181140	+	0.00307454i
$699$	9.42465	−	2.58286i	0.356473	−	0.0976929i
$700$	−0.586144	+	5.15241i	−0.0221542	+	0.194743i
$701$	−11.7793	−	7.87067i	−0.444897	−	0.297271i	0.312870	−	0.949796i	$-0.398710\pi$
$701$	−11.7793	−	7.87067i	−0.444897	−	0.297271i	−0.757767	+	0.652525i	$0.773710\pi$
$702$	16.2050	+	11.7812i	0.611616	+	0.444651i
$703$			34.7733i			1.31150i
$704$	7.86767	−	13.2399i	0.296524	−	0.498998i
$705$	−1.65612	−	3.31067i	−0.0623729	−	0.124687i
$706$	1.99725	+	0.963145i	0.0751673	+	0.0362484i
$707$	−7.11633	+	10.6503i	−0.267637	+	0.400547i
$708$	−0.566219	−	1.54846i	−0.0212798	−	0.0581947i
$709$	3.93900	−	19.8027i	0.147932	−	0.743706i	−0.833594	−	0.552378i	$-0.813721\pi$
$709$	3.93900	−	19.8027i	0.147932	−	0.743706i	0.981526	−	0.191328i	$-0.0612795\pi$
$710$	8.04974	−	4.74259i	0.302101	−	0.177986i
$711$	−10.6166	+	6.29156i	−0.398152	+	0.235952i
$712$	43.0492	+	7.38576i	1.61334	+	0.276793i
$713$	63.8485	−	26.4469i	2.39114	−	0.990444i
$714$	19.4630	+	3.57887i	0.728383	+	0.133936i
$715$	2.91603	+	4.36415i	0.109053	+	0.163210i
$716$	31.3982	−	37.1020i	1.17341	−	1.38657i
$717$	1.75587	+	2.26155i	0.0655743	+	0.0844592i
$718$	5.51433	+	6.17721i	0.205793	+	0.230531i
$719$	23.3536	+	23.3536i	0.870941	+	0.870941i	0.992575	−	0.121634i	$-0.0388134\pi$
$719$	23.3536	+	23.3536i	0.870941	+	0.870941i	−0.121634	+	0.992575i	$0.538813\pi$
$720$	−7.48305	+	9.38105i	−0.278877	+	0.349611i
$721$	0.237592	−	0.237592i	0.00884838	−	0.00884838i
$722$	46.3769	+	2.62947i	1.72597	+	0.0978586i
$723$	−20.1157	+	15.6179i	−0.748109	+	0.580834i
$724$	6.19373	+	1.98145i	0.230188	+	0.0736401i
$725$	3.80909	−	2.54515i	0.141466	−	0.0945246i
$726$	−10.1402	−	14.7097i	−0.376339	−	0.545927i
$727$	−4.55894	−	11.0063i	−0.169082	−	0.408199i	0.816512	−	0.577328i	$-0.195905\pi$
$727$	−4.55894	−	11.0063i	−0.169082	−	0.408199i	−0.985594	+	0.169129i	$0.945905\pi$
$728$	19.9874	−	0.528553i	0.740781	−	0.0195895i
$729$	−19.7321	−	18.4294i	−0.730819	−	0.682571i
$730$	1.15534	−	4.46896i	0.0427611	−	0.165404i
$731$	−15.1045	−	3.00446i	−0.558659	−	0.111124i
$732$	−1.14410	+	27.1357i	−0.0422871	+	1.00297i
$733$	−4.42496	−	2.95666i	−0.163439	−	0.109207i	0.471161	−	0.882047i	$-0.343835\pi$
$733$	−4.42496	−	2.95666i	−0.163439	−	0.109207i	−0.634600	+	0.772841i	$0.718835\pi$
$734$	−7.31742	−	20.9481i	−0.270091	−	0.773208i
$735$	0.429523	−	0.214863i	0.0158432	−	0.00792534i
$736$	−11.0826	+	38.0836i	−0.408509	+	1.40378i
$737$	17.2143			0.634097
$738$	16.1254	−	50.8542i	0.593585	−	1.87197i
$739$	21.0446	−	31.4955i	0.774140	−	1.15858i	−0.209389	−	0.977832i	$-0.567148\pi$
$739$	21.0446	−	31.4955i	0.774140	−	1.15858i	0.983529	−	0.180750i	$-0.0578524\pi$
$740$	2.66389	+	9.28407i	0.0979267	+	0.341289i
$741$	−8.98709	−	32.7931i	−0.330149	−	1.20469i
$742$	6.72428	−	26.0101i	0.246856	−	0.954860i
$743$	−1.97253	−	0.817050i	−0.0723653	−	0.0299747i	0.346207	−	0.938158i	$-0.387469\pi$
$743$	−1.97253	−	0.817050i	−0.0723653	−	0.0299747i	−0.418572	+	0.908183i	$0.637469\pi$
$744$	48.0568	−	4.70410i	1.76185	−	0.172461i
$745$	−9.63950	+	3.99281i	−0.353164	+	0.146285i
$746$	44.8434	−	6.30627i	1.64183	−	0.230889i
$747$	−16.1958	−	0.876646i	−0.592572	−	0.0320748i
$748$	5.49499	+	10.6647i	0.200917	+	0.389939i
$749$	3.04987	+	15.3327i	0.111440	+	0.560245i
$750$	2.24920	−	0.970093i	0.0821293	−	0.0354228i
$751$	−1.47880	−	1.47880i	−0.0539621	−	0.0539621i	0.679611	−	0.733573i	$-0.262149\pi$
$751$	−1.47880	−	1.47880i	−0.0539621	−	0.0539621i	−0.733573	+	0.679611i	$0.762149\pi$
$752$	−4.53273	−	7.24833i	−0.165292	−	0.264320i
$753$	9.93821	+	3.31065i	0.362168	+	0.120647i
$754$	−11.7630	−	13.1771i	−0.428384	−	0.479880i
$755$	2.85119	+	14.3339i	0.103765	+	0.521663i
$756$	−26.8208	−	2.58848i	−0.975462	−	0.0941423i
$757$	2.43849	−	1.62935i	0.0886284	−	0.0592196i	−0.510466	−	0.859898i	$-0.670527\pi$
$757$	2.43849	−	1.62935i	0.0886284	−	0.0592196i	0.599095	+	0.800678i	$0.295527\pi$
$758$	3.52551	+	2.65619i	0.128052	+	0.0964771i
$759$	−17.6652	−	15.3151i	−0.641205	−	0.555903i
$760$	19.8625	−	4.49983i	0.720490	−	0.163226i
$761$	−21.5630	−	8.93167i	−0.781657	−	0.323773i	−0.0440730	−	0.999028i	$-0.514033\pi$
$761$	−21.5630	−	8.93167i	−0.781657	−	0.323773i	−0.737584	+	0.675255i	$0.764033\pi$
$762$	25.6255	+	16.5900i	0.928312	+	0.600994i
$763$	51.1314	+	10.1707i	1.85108	+	0.368203i
$764$	−4.01275	−	5.04294i	−0.145176	−	0.182447i
$765$	−3.10519	−	8.81684i	−0.112269	−	0.318773i
$766$	2.41154	+	1.16293i	0.0871324	+	0.0420184i
$767$	1.29763			0.0468547
$768$	−15.1481	+	23.2064i	−0.546609	+	0.837388i
$769$	−18.4376			−0.664877			−0.332438	−	0.943125i	$-0.607871\pi$
$769$	−18.4376			−0.664877			−0.332438	+	0.943125i	$0.607871\pi$
$770$	−6.35841	−	3.06626i	−0.229141	−	0.110500i
$771$	2.40665	+	0.302927i	0.0866734	+	0.0109097i
$772$	0.498744	+	0.626786i	0.0179502	+	0.0225585i
$773$	10.1347	+	2.01592i	0.364520	+	0.0725075i	0.373952	−	0.927448i	$-0.378002\pi$
$773$	10.1347	+	2.01592i	0.364520	+	0.0725075i	−0.00943225	+	0.999956i	$0.503002\pi$
$774$	20.8410	+	2.31683i	0.749114	+	0.0832768i
$775$	−9.10617	−	3.77190i	−0.327103	−	0.135491i
$776$	43.6104	−	9.87986i	1.56552	−	0.354666i
$777$	−14.2070	+	16.3870i	−0.509672	+	0.587881i
$778$	33.7570	+	25.4332i	1.21025	+	0.911824i
$779$	−75.2835	+	50.3028i	−2.69731	+	1.80228i
$780$	−4.91164	−	8.06690i	−0.175865	−	0.288841i
$781$	2.48123	+	12.4740i	0.0887855	+	0.446355i
$782$	−20.5755	−	23.0489i	−0.735779	−	0.824228i
$783$	13.5608	+	19.5641i	0.484622	+	0.699164i
$784$	0.940393	−	0.588073i	0.0335855	−	0.0210026i
$785$	3.53191	+	3.53191i	0.126059	+	0.126059i
$786$	−7.38749	−	17.1282i	−0.263503	−	0.610943i
$787$	5.01080	+	25.1910i	0.178616	+	0.897962i	0.961292	+	0.275533i	$0.0888542\pi$
$787$	5.01080	+	25.1910i	0.178616	+	0.897962i	−0.782676	+	0.622429i	$0.786146\pi$
$788$	20.2078	+	39.2194i	0.719874	+	1.39713i
$789$	−21.7930	−	12.4175i	−0.775851	−	0.442074i
$790$	5.76082	−	0.810136i	0.204961	−	0.0288233i
$791$	−31.7127	+	13.1358i	−1.12757	+	0.467056i
$792$	−8.69667	−	13.8280i	−0.309023	−	0.491356i
$793$	−19.7488	−	8.18024i	−0.701302	−	0.290489i
$794$	5.12167	−	19.8111i	0.181761	−	0.703069i
$795$	−12.2388	+	3.35409i	−0.434065	+	0.118957i
$796$	−2.05037	−	7.14585i	−0.0726735	−	0.253278i
$797$	−28.1316	+	42.1020i	−0.996474	+	1.49133i	−0.130370	+	0.991465i	$0.541616\pi$
$797$	−28.1316	+	42.1020i	−0.996474	+	1.49133i	−0.866104	+	0.499863i	$0.833384\pi$
$798$	32.8018	+	31.8641i	1.16117	+	1.12798i
$799$	6.65937			0.235592
$800$	4.95834	−	2.72302i	0.175304	−	0.0962732i
$801$	27.7826	−	37.0726i	0.981651	−	1.30990i
$802$	−9.36544	−	26.8111i	−0.330705	−	0.946732i
$803$	5.22457	+	3.49094i	0.184371	+	0.123193i
$804$	−30.9479	−	1.30483i	−1.09145	−	0.0460177i
$805$	17.8304	+	3.54669i	0.628439	+	0.125004i
$806$	−9.51218	+	36.7939i	−0.335052	+	1.29601i
$807$	−3.02060	−	42.3901i	−0.106330	−	1.49220i
$808$	13.9681	−	0.369378i	0.491397	−	0.0129947i
$809$	14.6874	+	35.4586i	0.516383	+	1.24666i	0.940111	+	0.340869i	$0.110721\pi$
$809$	14.6874	+	35.4586i	0.516383	+	1.24666i	−0.423728	+	0.905790i	$0.639279\pi$
$810$	5.23941	+	11.5995i	0.184094	+	0.407565i
$811$	−13.8523	+	9.25581i	−0.486420	+	0.325016i	−0.774482	−	0.632596i	$-0.781989\pi$
$811$	−13.8523	+	9.25581i	−0.486420	+	0.325016i	0.288062	+	0.957612i	$0.406989\pi$
$812$	22.6266	+	7.23853i	0.794037	+	0.254023i
$813$	24.2768	+	31.2683i	0.851424	+	1.09663i
$814$	−13.1271	−	0.744279i	−0.460106	−	0.0260869i
$815$	−10.4688	+	10.4688i	−0.366707	+	0.366707i
$816$	−9.07051	−	19.5894i	−0.317531	−	0.685768i
$817$	−25.1647	−	25.1647i	−0.880403	−	0.880403i
$818$	15.7905	+	17.6887i	0.552103	+	0.618472i
$819$	9.16276	−	19.1256i	0.320173	−	0.668303i
$820$	−16.2462	+	19.1975i	−0.567343	+	0.670407i
$821$	6.27937	+	9.39774i	0.219152	+	0.327984i	0.924713	−	0.380665i	$-0.124305\pi$
$821$	6.27937	+	9.39774i	0.219152	+	0.327984i	−0.705561	+	0.708649i	$0.749305\pi$
$822$	7.34859	−	39.9638i	0.256311	−	1.39390i
$823$	38.8483	−	16.0915i	1.35417	−	0.560914i	0.416717	−	0.909036i	$-0.363181\pi$
$823$	38.8483	−	16.0915i	1.35417	−	0.560914i	0.937449	+	0.348122i	$0.113181\pi$
$824$	−0.361260	−	0.0619797i	−0.0125851	−	0.00215917i
$825$	0.237003	+	3.32602i	0.00825139	+	0.115797i
$826$	−1.50365	+	0.885892i	−0.0523187	+	0.0308241i
$827$	6.64043	−	33.3837i	0.230910	−	1.16086i	−0.675138	−	0.737691i	$-0.735916\pi$
$827$	6.64043	−	33.3837i	0.230910	−	1.16086i	0.906049	−	0.423173i	$-0.139084\pi$
$828$	30.5976	+	28.8725i	1.06334	+	1.00339i
$829$	−11.2113	+	16.7790i	−0.389386	+	0.582757i	−0.973436	−	0.228961i	$-0.926467\pi$
$829$	−11.2113	+	16.7790i	−0.389386	+	0.582757i	0.584050	+	0.811718i	$0.301467\pi$
$830$	6.88696	+	3.32115i	0.239050	+	0.115279i
$831$	25.6075	−	12.8098i	0.888316	−	0.444367i
$832$	−13.0592	−	17.4696i	−0.452746	−	0.605648i
$833$			0.863981i			0.0299352i
$834$	20.7384	−	0.300727i	0.718112	−	0.0104133i
$835$	7.01461	+	4.68701i	0.242751	+	0.162201i
$836$	−3.13367	+	27.5461i	−0.108380	+	0.952700i
$837$	18.7892	−	47.6445i	0.649451	−	1.64684i
$838$	−21.5588	−	36.5923i	−0.744735	−	1.26406i
$839$	8.06483	−	19.4702i	0.278429	−	0.672187i	−0.721364	−	0.692557i	$-0.756484\pi$
$839$	8.06483	−	19.4702i	0.278429	−	0.672187i	0.999793	+	0.0203696i	$0.00648428\pi$
$840$	11.1987	+	5.99448i	0.386393	+	0.206829i
$841$	3.06645	+	7.40307i	0.105740	+	0.255278i
$842$	−0.170114	−	0.128167i	−0.00586252	−	0.00441694i
$843$	−36.8749	−	21.0110i	−1.27004	−	0.723657i
$844$	18.8430	−	22.2661i	0.648604	−	0.766429i
$845$	−5.45978	+	1.08602i	−0.187822	+	0.0373601i
$846$	−9.03427	+	0.775565i	−0.310605	+	0.0266645i
$847$	−13.3725	+	13.3725i	−0.459484	+	0.459484i
$848$	−27.4019	+	10.3924i	−0.940985	+	0.356878i
$849$	46.2610	+	15.4106i	1.58767	+	0.528892i
$850$	−0.249440	+	4.39947i	−0.00855571	+	0.150900i
$851$	33.2106	−	6.60600i	1.13844	−	0.226451i
$852$	−3.51525	−	22.6138i	−0.120430	−	0.774737i
$853$	−17.0573	−	25.5281i	−0.584031	−	0.874064i	0.415335	−	0.909669i	$-0.363664\pi$
$853$	−17.0573	−	25.5281i	−0.584031	−	0.874064i	−0.999366	+	0.0356044i	$0.988664\pi$
$854$	28.4690	−	4.00355i	0.974188	−	0.136999i
$855$	5.35313	−	20.9275i	0.183073	−	0.715704i
$856$	11.7358	−	12.3733i	0.401120	−	0.422911i
$857$	−6.86641	+	16.5770i	−0.234552	+	0.566259i	−0.996703	−	0.0811412i	$-0.974144\pi$
$857$	−6.86641	+	16.5770i	−0.234552	+	0.566259i	0.762151	+	0.647400i	$0.224144\pi$
$858$	12.5719	−	2.69078i	0.429199	−	0.0918618i
$859$	7.96995	−	40.0677i	0.271931	−	1.36709i	−0.567387	−	0.823451i	$-0.692046\pi$
$859$	7.96995	−	40.0677i	0.271931	−	1.36709i	0.839319	−	0.543640i	$-0.182954\pi$
$860$	−8.64650	−	4.79089i	−0.294843	−	0.163368i
$861$	−56.0293	−	7.05246i	−1.90947	−	0.240347i
$862$	0.774926	−	0.270691i	0.0263941	−	0.00921977i
$863$		−	46.9617i		−	1.59859i	−0.600936	−	0.799297i	$-0.705206\pi$
$863$		−	46.9617i		−	1.59859i	0.600936	−	0.799297i	$-0.294794\pi$
$864$	14.5867	+	25.5192i	0.496250	+	0.868180i
$865$		−	0.191859i		−	0.00652340i
$866$	−10.1295	−	28.9985i	−0.344215	−	0.985408i
$867$	−12.5299	−	1.57715i	−0.425539	−	0.0535630i
$868$	−14.0968	−	49.1296i	−0.478478	−	1.66757i
$869$	−1.54497	+	7.76711i	−0.0524096	+	0.263481i
$870$	−2.34855	−	10.9730i	−0.0796234	−	0.372019i
$871$	9.32942	−	22.5232i	0.316116	−	0.763170i
$872$	−23.1447	−	51.9477i	−0.783778	−	1.75917i
$873$	11.7534	−	45.9485i	0.397792	−	1.55512i
$874$	−9.94281	−	70.7026i	−0.336320	−	2.39155i
$875$	−1.44049	−	2.15585i	−0.0486976	−	0.0728811i
$876$	−9.12811	−	6.67203i	−0.308410	−	0.225427i
$877$	34.4962	−	6.86172i	1.16485	−	0.231704i	0.425460	−	0.904977i	$-0.360112\pi$
$877$	34.4962	−	6.86172i	1.16485	−	0.231704i	0.739394	+	0.673273i	$0.235112\pi$
$878$	48.9000	+	2.77252i	1.65029	+	0.0935680i
$879$	−13.7101	−	4.56715i	−0.462429	−	0.154046i
$880$	1.27358	+	7.59454i	0.0429323	+	0.256012i
$881$	28.3026	−	28.3026i	0.953540	−	0.953540i	−0.0454279	−	0.998968i	$-0.514465\pi$
$881$	28.3026	−	28.3026i	0.953540	−	0.953540i	0.998968	+	0.0454279i	$0.0144651\pi$
$882$	−0.100621	−	1.17210i	−0.00338809	−	0.0394666i
$883$	−54.6269	+	10.8660i	−1.83834	+	0.365669i	−0.987228	−	0.159315i	$-0.949071\pi$
$883$	−54.6269	+	10.8660i	−1.83834	+	0.365669i	−0.851112	+	0.524984i	$0.824071\pi$
$884$	16.9317	−	1.40985i	0.569475	−	0.0474185i
$885$	0.716257	+	0.408118i	0.0240767	+	0.0137187i
$886$	6.69463	−	8.88567i	0.224911	−	0.298520i
$887$	−15.7290	−	37.9731i	−0.528128	−	1.27501i	−0.932748	−	0.360528i	$-0.882596\pi$
$887$	−15.7290	−	37.9731i	−0.528128	−	1.27501i	0.404621	−	0.914485i	$-0.367404\pi$
$888$	23.5435	+	2.33309i	0.790069	+	0.0782933i
$889$	12.3657	−	29.8535i	0.414733	−	1.00125i
$890$	−18.8162	+	11.0858i	−0.630722	+	0.371597i
$891$	−17.2590	+	1.52618i	−0.578197	+	0.0511289i
$892$	32.3460	+	40.6502i	1.08303	+	1.36107i
$893$	12.7955	+	8.54965i	0.428183	+	0.286103i
$894$	0.370567	+	25.5546i	0.0123936	+	0.854674i
$895$			24.3023i			0.812336i
$896$	27.0591	+	11.3276i	0.903980	+	0.378430i
$897$	−29.6121	+	14.8130i	−0.988719	+	0.494592i
$898$	12.5057	−	25.9327i	0.417321	−	0.865386i
$899$	−25.0862	+	37.5441i	−0.836670	+	1.25217i
$900$	−0.173975	−	5.99748i	−0.00579918	−	0.199916i
$901$	4.45370	−	22.3902i	0.148374	−	0.745927i
$902$	−17.3783	−	29.4966i	−0.578632	−	0.982130i
$903$	−1.57766	−	22.1403i	−0.0525011	−	0.736782i
$904$	31.6732	+	19.9729i	1.05343	+	0.664287i
$905$	−3.00397	+	1.24429i	−0.0998555	+	0.0413615i
$906$	35.2083	+	6.47413i	1.16972	+	0.215089i
$907$	18.5249	+	27.7245i	0.615111	+	0.920578i	0.999997	−	0.00238566i	$-0.000759380\pi$
$907$	18.5249	+	27.7245i	0.615111	+	0.920578i	−0.384886	+	0.922964i	$0.625759\pi$
$908$	2.34145	+	28.1197i	0.0777036	+	0.933186i
$909$	6.40337	−	13.3659i	0.212386	−	0.443319i
$910$	−7.45789	+	6.65757i	−0.247227	+	0.220696i
$911$	24.1853	+	24.1853i	0.801294	+	0.801294i	0.983298	−	0.182004i	$-0.0582583\pi$
$911$	24.1853	+	24.1853i	0.801294	+	0.801294i	−0.182004	+	0.983298i	$0.558258\pi$
$912$	7.72168	−	49.2848i	0.255690	−	1.63198i
$913$	−7.35977	+	7.35977i	−0.243573	+	0.243573i
$914$	0.195731	−	3.45218i	0.00647419	−	0.114188i
$915$	−8.32807	−	10.7265i	−0.275317	−	0.354607i
$916$	−2.56115	−	4.97067i	−0.0846227	−	0.164236i
$917$	−16.4173	+	10.9697i	−0.542147	+	0.362251i
$918$	−22.8791	−	0.905922i	−0.755122	−	0.0298999i
$919$	−1.03385	−	2.49594i	−0.0341036	−	0.0823334i	0.905910	−	0.423470i	$-0.139188\pi$
$919$	−1.03385	−	2.49594i	−0.0341036	−	0.0823334i	−0.940014	+	0.341137i	$0.889188\pi$
$920$	−8.07095	−	18.1151i	−0.266091	−	0.597236i
$921$	−0.523603	−	7.34806i	−0.0172533	−	0.242127i
$922$	−8.64223	−	2.23424i	−0.284617	−	0.0735808i
$923$	17.6657	+	3.51394i	0.581475	+	0.115663i
$924$	−12.7310	+	11.7009i	−0.418818	+	0.384930i
$925$	−4.01545	−	2.68304i	−0.132027	−	0.0882178i
$926$	−36.6263	+	12.7940i	−1.20361	+	0.420437i
$927$	−0.233146	+	0.311106i	−0.00765752	+	0.0102181i
$928$	−7.80341	−	24.7121i	−0.256159	−	0.811216i
$929$	−27.9790			−0.917961			−0.458980	−	0.888446i	$-0.651785\pi$
$929$	−27.9790			−0.917961			−0.458980	+	0.888446i	$0.651785\pi$
$930$	−16.8225	+	17.3176i	−0.551633	+	0.567867i
$931$	−1.10922	+	1.66007i	−0.0363533	+	0.0544066i
$932$	−5.46886	+	9.87009i	−0.179138	+	0.323305i
$933$	−12.4895	+	3.42281i	−0.408889	+	0.112058i
$934$	18.4818	+	4.77802i	0.604742	+	0.156341i
$935$	−5.54193	−	2.29554i	−0.181240	−	0.0750722i
$936$	−22.8058	+	3.88455i	−0.745431	+	0.126970i
$937$	−51.8674	+	21.4842i	−1.69444	+	0.701858i	−0.999846	−	0.0175484i	$-0.994414\pi$
$937$	−51.8674	+	21.4842i	−1.69444	+	0.701858i	−0.694589	+	0.719407i	$0.744414\pi$
$938$	4.56598	+	32.4684i	0.149085	+	1.06013i
$939$	−32.5287	−	18.5346i	−1.06154	−	0.604854i
$940$	4.07120	+	1.30243i	0.132788	+	0.0424806i
$941$	−9.02162	−	45.3547i	−0.294096	−	1.47852i	−0.791589	−	0.611054i	$-0.790746\pi$
$941$	−9.02162	−	45.3547i	−0.294096	−	1.47852i	0.497493	−	0.867468i	$-0.334254\pi$
$942$	11.2345	−	4.84549i	0.366039	−	0.157875i
$943$	62.3440	+	62.3440i	2.03020	+	2.03020i
$944$	1.73608	+	0.781328i	0.0565046	+	0.0254301i
$945$	11.0728	−	7.67505i	0.360198	−	0.249670i
$946$	10.0385	−	8.96122i	0.326378	−	0.291354i
$947$	2.29535	+	11.5395i	0.0745890	+	0.374984i	0.999992	−	0.00400042i	$-0.00127338\pi$
$947$	2.29535	+	11.5395i	0.0745890	+	0.374984i	−0.925403	+	0.378984i	$0.876273\pi$
$948$	3.36629	−	13.8466i	0.109332	−	0.449716i
$949$	7.39905	−	4.94389i	0.240183	−	0.160485i
$950$	−6.12754	+	8.13298i	−0.198804	+	0.263869i
$951$	−29.7094	+	34.2683i	−0.963394	+	1.11123i
$952$	−18.6574	+	13.1930i	−0.604690	+	0.427587i
$953$	−11.1181	−	4.60525i	−0.360150	−	0.149179i	0.195269	−	0.980750i	$-0.437442\pi$
$953$	−11.1181	−	4.60525i	−0.360150	−	0.149179i	−0.555419	+	0.831571i	$0.687442\pi$
$954$	−3.43438	+	30.8939i	−0.111192	+	1.00023i
$955$	3.16041	+	0.628644i	0.102268	+	0.0203424i
$956$	−3.28491	−	0.373695i	−0.106242	−	0.0120862i
$957$	15.1560	+	1.90771i	0.489925	+	0.0616673i
$958$	5.08184	−	10.5381i	0.164187	−	0.340469i
$959$	−43.0115			−1.38891
$960$	−1.71398	−	13.7500i	−0.0553185	−	0.443779i
$961$	66.1495			2.13385
$962$	−8.08817	+	16.7722i	−0.260773	+	0.540757i
$963$	−6.00869	−	17.0610i	−0.193627	−	0.549782i
$964$	3.32388	−	29.2181i	0.107055	−	0.941050i
$965$	−0.392806	−	0.0781340i	−0.0126449	−	0.00251522i
$966$	24.2007	−	37.3810i	0.778643	−	1.20271i
$967$	−42.4621	−	17.5884i	−1.36549	−	0.565604i	−0.424926	−	0.905228i	$-0.639700\pi$
$967$	−42.4621	−	17.5884i	−1.36549	−	0.565604i	−0.940561	+	0.339624i	$0.889700\pi$
$968$	20.3329	+	3.48843i	0.653526	+	0.112122i
$969$	29.3616	+	25.4555i	0.943230	+	0.817748i
$970$	−13.4537	+	17.8568i	−0.431972	+	0.573349i
$971$	8.16307	−	5.45439i	0.261965	−	0.175040i	−0.417651	−	0.908608i	$-0.637146\pi$
$971$	8.16307	−	5.45439i	0.261965	−	0.175040i	0.679616	+	0.733568i	$0.262146\pi$
$972$	31.1438	−	1.43555i	0.998939	−	0.0460454i
$973$	−4.28305	−	21.5324i	−0.137308	−	0.690296i
$974$	25.4675	−	22.7346i	0.816032	−	0.728463i
$975$	4.48021	+	1.49247i	0.143482	+	0.0477972i
$976$	−21.4962	−	22.8354i	−0.688077	−	0.730943i
$977$	3.40070	+	3.40070i	0.108798	+	0.108798i	0.759410	−	0.650612i	$-0.225488\pi$
$977$	3.40070	+	3.40070i	0.108798	+	0.108798i	−0.650612	+	0.759410i	$0.725488\pi$
$978$	14.3624	+	33.2998i	0.459259	+	1.06481i
$979$	−5.79988	−	29.1580i	−0.185365	−	0.931892i
$980$	−0.168976	+	0.528194i	−0.00539774	+	0.0168725i
$981$	−60.2320	−	3.26025i	−1.92306	−	0.104092i
$982$	5.94326	+	42.2621i	0.189657	+	1.34864i
$983$	−16.0436	+	6.64546i	−0.511710	+	0.211957i	−0.623571	−	0.781767i	$-0.714319\pi$
$983$	−16.0436	+	6.64546i	−0.511710	+	0.211957i	0.111861	+	0.993724i	$0.464319\pi$
$984$	29.0068	+	54.3463i	0.924703	+	1.73250i
$985$	−20.3805	−	8.44187i	−0.649376	−	0.268980i
$986$	19.5444	+	5.05274i	0.622422	+	0.160912i
$987$	2.53685	+	9.25675i	0.0807489	+	0.294646i
$988$	34.3430	+	19.0289i	1.09260	+	0.605390i
$989$	−19.2532	+	28.8145i	−0.612216	+	0.916247i
$990$	7.78566	+	2.46876i	0.247445	+	0.0784625i
$991$	16.9699			0.539068			0.269534	−	0.962991i	$-0.413130\pi$
$991$	16.9699			0.539068			0.269534	+	0.962991i	$0.413130\pi$
$992$	−34.8806	+	43.4986i	−1.10746	+	1.38108i
$993$	−53.9335	+	26.9795i	−1.71153	+	0.856167i
$994$	−22.8695	+	7.98858i	−0.725375	+	0.253382i
$995$	3.09065	+	2.06511i	0.0979802	+	0.0654683i
$996$	13.7893	−	12.6735i	0.436929	−	0.401576i
$997$	29.8869	+	5.94488i	0.946529	+	0.188276i	0.644139	−	0.764908i	$-0.277216\pi$
$997$	29.8869	+	5.94488i	0.946529	+	0.188276i	0.302390	+	0.953184i	$0.402216\pi$
$998$	−11.6679	−	3.01644i	−0.369340	−	0.0954838i
$999$	13.5835	−	21.0997i	0.429762	−	0.667565i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.731.19	✓	1024
3.2	odd	2	inner	960.2.cn.a.731.110	yes	1024
64.19	odd	16	inner	960.2.cn.a.851.110	yes	1024
192.83	even	16	inner	960.2.cn.a.851.19	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.731.19	✓	1024	1.1	even	1	trivial
960.2.cn.a.731.110	yes	1024	3.2	odd	2	inner
960.2.cn.a.851.19	yes	1024	192.83	even	16	inner
960.2.cn.a.851.110	yes	1024	64.19	odd	16	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27383 - 0.614289i) q^{2} +(0.216308 - 1.71849i) q^{3} +(1.24530 + 1.56500i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(-1.33119 + 2.05619i) q^{6} +(2.39545 + 0.992229i) q^{7} +(-0.624939 - 2.75852i) q^{8} +(-2.90642 - 0.743447i) q^{9} +O(q^{10})\)	\(q+(-1.27383 - 0.614289i) q^{2} +(0.216308 - 1.71849i) q^{3} +(1.24530 + 1.56500i) q^{4} +(-0.980785 - 0.195090i) q^{5} +(-1.33119 + 2.05619i) q^{6} +(2.39545 + 0.992229i) q^{7} +(-0.624939 - 2.75852i) q^{8} +(-2.90642 - 0.743447i) q^{9} +(1.12951 + 0.850998i) q^{10} +(-1.60070 + 1.06955i) q^{11} +(2.95881 - 1.80151i) q^{12} +(0.531894 + 2.67401i) q^{13} +(-2.44189 - 2.73543i) q^{14} +(-0.547413 + 1.64327i) q^{15} +(-0.898462 + 3.89779i) q^{16} +(-2.20327 - 2.20327i) q^{17} +(3.24560 + 2.73241i) q^{18} +(-1.40473 - 7.06207i) q^{19} +(-0.916054 - 1.77788i) q^{20} +(2.22329 - 3.90194i) q^{21} +(2.69604 - 0.379140i) q^{22} +(-6.47784 + 2.68321i) q^{23} +(-4.87568 + 0.477261i) q^{24} +(0.923880 + 0.382683i) q^{25} +(0.965072 - 3.73298i) q^{26} +(-1.90629 + 4.83385i) q^{27} +(1.43021 + 4.98451i) q^{28} +(2.54515 - 3.80909i) q^{29} +(1.70675 - 1.75698i) q^{30} -9.85644 q^{31} +(3.53886 - 4.41322i) q^{32} +(1.49177 + 2.98214i) q^{33} +(1.45315 + 4.16003i) q^{34} +(-2.15585 - 1.44049i) q^{35} +(-2.45587 - 5.47437i) q^{36} +(-4.73655 - 0.942158i) q^{37} +(-2.54876 + 9.85881i) q^{38} +(4.71032 - 0.335645i) q^{39} +(0.0747698 + 2.82744i) q^{40} +(-4.81210 - 11.6174i) q^{41} +(-5.22902 + 3.60467i) q^{42} +(4.10956 - 2.74592i) q^{43} +(-3.66720 - 1.17318i) q^{44} +(2.70554 + 1.29618i) q^{45} +(9.89995 + 0.561305i) q^{46} +(-1.51125 + 1.51125i) q^{47} +(6.50397 + 2.38712i) q^{48} +(-0.196068 - 0.196068i) q^{49} +(-0.941790 - 1.05500i) q^{50} +(-4.26288 + 3.30971i) q^{51} +(-3.52247 + 4.16236i) q^{52} +(4.07045 + 6.09185i) q^{53} +(5.39767 - 4.98650i) q^{54} +(1.77860 - 0.736721i) q^{55} +(1.24008 - 7.22800i) q^{56} +(-12.4400 + 0.886438i) q^{57} +(-5.58198 + 3.28868i) q^{58} +(0.0928532 - 0.466804i) q^{59} +(-3.25341 + 1.18966i) q^{60} +(-4.35588 + 6.51903i) q^{61} +(12.5555 + 6.05470i) q^{62} +(-6.22453 - 4.66473i) q^{63} +(-7.21890 + 3.44782i) q^{64} -2.72640i q^{65} +(-0.0683740 - 4.71513i) q^{66} +(-7.43485 - 4.96781i) q^{67} +(0.704391 - 6.19184i) q^{68} +(3.20986 + 11.7125i) q^{69} +(1.86131 + 3.15926i) q^{70} +(2.52818 - 6.10357i) q^{71} +(-0.234479 + 8.48204i) q^{72} +(-1.24905 - 3.01547i) q^{73} +(5.45481 + 4.10976i) q^{74} +(0.857481 - 1.50490i) q^{75} +(9.30284 - 10.9928i) q^{76} +(-4.89565 + 0.973804i) q^{77} +(-6.20634 - 2.46594i) q^{78} +(2.90875 - 2.90875i) q^{79} +(1.64162 - 3.64761i) q^{80} +(7.89457 + 4.32154i) q^{81} +(-1.00665 + 17.7547i) q^{82} +(5.30261 - 1.05475i) q^{83} +(8.87520 - 1.37962i) q^{84} +(1.73109 + 2.59077i) q^{85} +(-6.92169 + 0.973387i) q^{86} +(-5.99535 - 5.19776i) q^{87} +(3.95073 + 3.74716i) q^{88} +(-5.90962 + 14.2671i) q^{89} +(-2.65017 - 3.31309i) q^{90} +(-1.37911 + 6.93324i) q^{91} +(-12.2661 - 6.79643i) q^{92} +(-2.13203 + 16.9382i) q^{93} +(2.85342 - 0.996735i) q^{94} +7.20042i q^{95} +(-6.81859 - 7.03611i) q^{96} +15.8093i q^{97} +(0.129316 + 0.370201i) q^{98} +(5.44747 - 1.91854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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