LMFDB - Embedded newform 720.2.cf.a.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35213 - 0.414413i) q^{2} +(0.970230 - 1.43480i) q^{3} +(1.65652 + 1.12068i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-1.90648 + 1.53796i) q^{6} +(-2.03154 + 3.51873i) q^{7} +(-1.77541 - 2.20180i) q^{8} +(-1.11731 - 2.78417i) q^{9} +O(q^{10})$	\(q+(-1.35213 - 0.414413i) q^{2} +(0.970230 - 1.43480i) q^{3} +(1.65652 + 1.12068i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-1.90648 + 1.53796i) q^{6} +(-2.03154 + 3.51873i) q^{7} +(-1.77541 - 2.20180i) q^{8} +(-1.11731 - 2.78417i) q^{9} +(-1.19880 - 0.750250i) q^{10} +(-5.55356 + 1.48807i) q^{11} +(3.21517 - 1.28946i) q^{12} +(2.41274 + 0.646492i) q^{13} +(4.20512 - 3.91590i) q^{14} +(1.30852 - 1.13480i) q^{15} +(1.48814 + 3.71288i) q^{16} +6.82037i q^{17} +(0.356948 + 4.22760i) q^{18} +(2.74559 + 2.74559i) q^{19} +(1.31002 + 1.51124i) q^{20} +(3.07762 + 6.32884i) q^{21} +(8.12583 + 0.289399i) q^{22} +(5.50714 - 3.17955i) q^{23} +(-4.88170 + 0.411113i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.99443 - 1.87401i) q^{26} +(-5.07878 - 1.09818i) q^{27} +(-7.30868 + 3.55215i) q^{28} +(-2.30986 + 0.618926i) q^{29} +(-2.23957 + 0.992126i) q^{30} +(-7.96865 + 4.60070i) q^{31} +(-0.473494 - 5.63700i) q^{32} +(-3.25314 + 9.41203i) q^{33} +(2.82645 - 9.22205i) q^{34} +(-2.87303 + 2.87303i) q^{35} +(1.26933 - 5.86420i) q^{36} +(4.82230 + 4.82230i) q^{37} +(-2.57459 - 4.85021i) q^{38} +(3.26850 - 2.83456i) q^{39} +(-1.14505 - 2.58628i) q^{40} +(-1.50602 - 2.60850i) q^{41} +(-1.53859 - 9.83284i) q^{42} +(1.88789 + 7.04570i) q^{43} +(-10.8673 - 3.75876i) q^{44} +(-0.358639 - 2.97849i) q^{45} +(-8.76403 + 2.01694i) q^{46} +(-0.945573 + 1.63778i) q^{47} +(6.77107 + 1.46716i) q^{48} +(-4.75433 - 8.23474i) q^{49} +(-0.963774 - 1.03496i) q^{50} +(9.78588 + 6.61733i) q^{51} +(3.27225 + 3.77485i) q^{52} +(5.91831 - 5.91831i) q^{53} +(6.41208 + 3.58959i) q^{54} -5.74947 q^{55} +(11.3544 - 1.77416i) q^{56} +(6.60323 - 1.27552i) q^{57} +(3.37973 + 0.120368i) q^{58} +(-1.48090 + 5.52680i) q^{59} +(3.43935 - 0.413377i) q^{60} +(-0.763827 - 2.85064i) q^{61} +(12.6813 - 2.91844i) q^{62} +(12.0666 + 1.72466i) q^{63} +(-1.69582 + 7.81820i) q^{64} +(2.16320 + 1.24893i) q^{65} +(8.29915 - 11.3782i) q^{66} +(-0.926685 + 3.45843i) q^{67} +(-7.64348 + 11.2981i) q^{68} +(0.781173 - 10.9865i) q^{69} +(5.07535 - 2.69410i) q^{70} -9.06339i q^{71} +(-4.14651 + 7.40314i) q^{72} +5.63553i q^{73} +(-4.52196 - 8.51881i) q^{74} +(1.55764 - 0.757459i) q^{75} +(1.47120 + 7.62507i) q^{76} +(6.04616 - 22.5646i) q^{77} +(-5.59412 + 2.47819i) q^{78} +(-1.90280 - 1.09858i) q^{79} +(0.476468 + 3.97152i) q^{80} +(-6.50325 + 6.22156i) q^{81} +(0.955339 + 4.15116i) q^{82} +(1.67299 + 6.24369i) q^{83} +(-1.99448 + 13.9329i) q^{84} +(-1.76524 + 6.58798i) q^{85} +(0.367156 - 10.3091i) q^{86} +(-1.35306 + 3.91470i) q^{87} +(13.1363 + 9.58587i) q^{88} -8.98343 q^{89} +(-0.749397 + 4.17593i) q^{90} +(-7.17642 + 7.17642i) q^{91} +(12.6860 + 0.904763i) q^{92} +(-1.13033 + 15.8972i) q^{93} +(1.95726 - 1.82264i) q^{94} +(1.94143 + 3.36265i) q^{95} +(-8.54738 - 4.78982i) q^{96} +(3.72934 - 6.45941i) q^{97} +(3.01589 + 13.1047i) q^{98} +(10.3481 + 13.7994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.35213	−	0.414413i	−0.956102	−	0.293034i
$2$	−1.35213	−	0.414413i	−0.956102	−	0.293034i
$3$	0.970230	−	1.43480i	0.560163	−	0.828383i
$3$	0.970230	−	1.43480i	0.560163	−	0.828383i
$4$	1.65652	+	1.12068i	0.828262	+	0.560342i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−1.90648	+	1.53796i	−0.778317	+	0.627871i
$7$	−2.03154	+	3.51873i	−0.767851	+	1.32996i	0.170875	+	0.985293i	$0.445340\pi$
$7$	−2.03154	+	3.51873i	−0.767851	+	1.32996i	−0.938726	+	0.344664i	$0.887993\pi$
$8$	−1.77541	−	2.20180i	−0.627703	−	0.778453i
$9$	−1.11731	−	2.78417i	−0.372436	−	0.928058i
$10$	−1.19880	−	0.750250i	−0.379094	−	0.237250i
$11$	−5.55356	+	1.48807i	−1.67446	+	0.448671i	−0.966308	−	0.257388i	$-0.917138\pi$
$11$	−5.55356	+	1.48807i	−1.67446	+	0.448671i	−0.708153	+	0.706059i	$0.750471\pi$
$12$	3.21517	−	1.28946i	0.928138	−	0.372235i
$13$	2.41274	+	0.646492i	0.669174	+	0.179305i	0.577383	−	0.816474i	$-0.304074\pi$
$13$	2.41274	+	0.646492i	0.669174	+	0.179305i	0.0917912	+	0.995778i	$0.470741\pi$
$14$	4.20512	−	3.91590i	1.12387	−	1.04657i
$15$	1.30852	−	1.13480i	0.337859	−	0.293003i
$16$	1.48814	+	3.71288i	0.372034	+	0.928219i
$17$			6.82037i			1.65418i	0.562067	+	0.827092i	$0.310006\pi$
$17$			6.82037i			1.65418i	−0.562067	+	0.827092i	$0.689994\pi$
$18$	0.356948	+	4.22760i	0.0841335	+	0.996454i
$19$	2.74559	+	2.74559i	0.629882	+	0.629882i	0.948038	−	0.318156i	$-0.103064\pi$
$19$	2.74559	+	2.74559i	0.629882	+	0.629882i	−0.318156	+	0.948038i	$0.603064\pi$
$20$	1.31002	+	1.51124i	0.292930	+	0.337923i
$21$	3.07762	+	6.32884i	0.671592	+	1.38107i
$22$	8.12583	+	0.289399i	1.73243	+	0.0617002i
$23$	5.50714	−	3.17955i	1.14832	−	0.662982i	0.199841	−	0.979828i	$-0.435957\pi$
$23$	5.50714	−	3.17955i	1.14832	−	0.662982i	0.948477	+	0.316847i	$0.102624\pi$
$24$	−4.88170	+	0.411113i	−0.996473	+	0.0839181i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.99443	−	1.87401i	−0.587256	−	0.367524i
$27$	−5.07878	−	1.09818i	−0.977412	−	0.211344i
$28$	−7.30868	+	3.55215i	−1.38121	+	0.671293i
$29$	−2.30986	+	0.618926i	−0.428931	+	0.114932i	−0.466824	−	0.884350i	$-0.654602\pi$
$29$	−2.30986	+	0.618926i	−0.428931	+	0.114932i	0.0378933	+	0.999282i	$0.487935\pi$
$30$	−2.23957	+	0.992126i	−0.408888	+	0.181137i
$31$	−7.96865	+	4.60070i	−1.43121	+	0.826311i	−0.997213	−	0.0746026i	$-0.976231\pi$
$31$	−7.96865	+	4.60070i	−1.43121	+	0.826311i	−0.433999	+	0.900913i	$0.642898\pi$
$32$	−0.473494	−	5.63700i	−0.0837027	−	0.996491i
$33$	−3.25314	+	9.41203i	−0.566300	+	1.63842i
$34$	2.82645	−	9.22205i	0.484733	−	1.58157i
$35$	−2.87303	+	2.87303i	−0.485631	+	0.485631i
$36$	1.26933	−	5.86420i	0.211555	−	0.977366i
$37$	4.82230	+	4.82230i	0.792781	+	0.792781i	0.981945	−	0.189164i	$-0.0605779\pi$
$37$	4.82230	+	4.82230i	0.792781	+	0.792781i	−0.189164	+	0.981945i	$0.560578\pi$
$38$	−2.57459	−	4.85021i	−0.417654	−	0.786808i
$39$	3.26850	−	2.83456i	0.523379	−	0.453892i
$40$	−1.14505	−	2.58628i	−0.181048	−	0.408927i
$41$	−1.50602	−	2.60850i	−0.235201	−	0.407380i	0.724130	−	0.689663i	$-0.242241\pi$
$41$	−1.50602	−	2.60850i	−0.235201	−	0.407380i	−0.959331	+	0.282284i	$0.908908\pi$
$42$	−1.53859	−	9.83284i	−0.237410	−	1.51724i
$43$	1.88789	+	7.04570i	0.287901	+	1.07446i	0.946694	+	0.322136i	$0.104401\pi$
$43$	1.88789	+	7.04570i	0.287901	+	1.07446i	−0.658793	+	0.752324i	$0.728933\pi$
$44$	−10.8673	−	3.75876i	−1.63830	−	0.566654i
$45$	−0.358639	−	2.97849i	−0.0534627	−	0.444006i
$46$	−8.76403	+	2.01694i	−1.29219	+	0.297381i
$47$	−0.945573	+	1.63778i	−0.137926	+	0.238895i	−0.926711	−	0.375774i	$-0.877377\pi$
$47$	−0.945573	+	1.63778i	−0.137926	+	0.238895i	0.788785	+	0.614669i	$0.210710\pi$
$48$	6.77107	+	1.46716i	0.977320	+	0.211767i
$49$	−4.75433	−	8.23474i	−0.679190	−	1.17639i
$50$	−0.963774	−	1.03496i	−0.136298	−	0.146365i
$51$	9.78588	+	6.61733i	1.37030	+	0.926612i
$52$	3.27225	+	3.77485i	0.453779	+	0.523477i
$53$	5.91831	−	5.91831i	0.812943	−	0.812943i	−0.172131	−	0.985074i	$-0.555065\pi$
$53$	5.91831	−	5.91831i	0.812943	−	0.812943i	0.985074	+	0.172131i	$0.0550654\pi$
$54$	6.41208	+	3.58959i	0.872574	+	0.488482i
$55$	−5.74947			−0.775258
$56$	11.3544	−	1.77416i	1.51729	−	0.237082i
$57$	6.60323	−	1.27552i	0.874619	−	0.168947i
$58$	3.37973	+	0.120368i	0.443781	+	0.0158052i
$59$	−1.48090	+	5.52680i	−0.192797	+	0.719528i	0.800029	+	0.599961i	$0.204817\pi$
$59$	−1.48090	+	5.52680i	−0.192797	+	0.719528i	−0.992826	+	0.119567i	$0.961849\pi$
$60$	3.43935	−	0.413377i	0.444018	−	0.0533667i
$61$	−0.763827	−	2.85064i	−0.0977980	−	0.364987i	0.899631	−	0.436651i	$-0.143836\pi$
$61$	−0.763827	−	2.85064i	−0.0977980	−	0.364987i	−0.997429	+	0.0716642i	$0.977169\pi$
$62$	12.6813	−	2.91844i	1.61052	−	0.370643i
$63$	12.0666	+	1.72466i	1.52025	+	0.217287i
$64$	−1.69582	+	7.81820i	−0.211978	+	0.977274i
$65$	2.16320	+	1.24893i	0.268312	+	0.154910i
$66$	8.29915	−	11.3782i	1.02155	−	1.40055i
$67$	−0.926685	+	3.45843i	−0.113213	+	0.422515i	−0.999147	−	0.0412956i	$-0.986851\pi$
$67$	−0.926685	+	3.45843i	−0.113213	+	0.422515i	0.885934	+	0.463810i	$0.153518\pi$
$68$	−7.64348	+	11.2981i	−0.926908	+	1.37010i
$69$	0.781173	−	10.9865i	0.0940422	−	1.32262i
$70$	5.07535	−	2.69410i	0.606620	−	0.322006i
$71$		−	9.06339i		−	1.07563i	−0.843064	−	0.537814i	$-0.819250\pi$
$71$		−	9.06339i		−	1.07563i	0.843064	−	0.537814i	$-0.180750\pi$
$72$	−4.14651	+	7.40314i	−0.488670	+	0.872468i
$73$			5.63553i			0.659589i	0.944053	+	0.329795i	$0.106979\pi$
$73$			5.63553i			0.659589i	−0.944053	+	0.329795i	$0.893021\pi$
$74$	−4.52196	−	8.51881i	−0.525667	−	0.990292i
$75$	1.55764	−	0.757459i	0.179861	−	0.0874638i
$76$	1.47120	+	7.62507i	0.168758	+	0.874656i
$77$	6.04616	−	22.5646i	0.689024	−	2.57147i
$78$	−5.59412	+	2.47819i	−0.633410	+	0.280599i
$79$	−1.90280	−	1.09858i	−0.214082	−	0.123600i	0.389125	−	0.921185i	$-0.372777\pi$
$79$	−1.90280	−	1.09858i	−0.214082	−	0.123600i	−0.603207	+	0.797585i	$0.706111\pi$
$80$	0.476468	+	3.97152i	0.0532707	+	0.444030i
$81$	−6.50325	+	6.22156i	−0.722583	+	0.691284i
$82$	0.955339	+	4.15116i	0.105500	+	0.458418i
$83$	1.67299	+	6.24369i	0.183635	+	0.685334i	0.994919	+	0.100682i	$0.0321024\pi$
$83$	1.67299	+	6.24369i	0.183635	+	0.685334i	−0.811284	+	0.584652i	$0.801231\pi$
$84$	−1.99448	+	13.9329i	−0.217615	+	1.52020i
$85$	−1.76524	+	6.58798i	−0.191467	+	0.714566i
$86$	0.367156	−	10.3091i	0.0395914	−	1.11166i
$87$	−1.35306	+	3.91470i	−0.145064	+	0.419700i
$88$	13.1363	+	9.58587i	1.40033	+	1.02186i
$89$	−8.98343			−0.952241			−0.476121	−	0.879380i	$-0.657957\pi$
$89$	−8.98343			−0.952241			−0.476121	+	0.879380i	$0.657957\pi$
$90$	−0.749397	+	4.17593i	−0.0789934	+	0.440182i
$91$	−7.17642	+	7.17642i	−0.752293	+	0.752293i
$92$	12.6860	+	0.904763i	1.32260	+	0.0943281i
$93$	−1.13033	+	15.8972i	−0.117210	+	1.64846i
$94$	1.95726	−	1.82264i	0.201876	−	0.187991i
$95$	1.94143	+	3.36265i	0.199186	+	0.345000i
$96$	−8.54738	−	4.78982i	−0.872363	−	0.488859i
$97$	3.72934	−	6.45941i	0.378657	−	0.655854i	−0.612210	−	0.790695i	$-0.709719\pi$
$97$	3.72934	−	6.45941i	0.378657	−	0.655854i	0.990867	+	0.134841i	$0.0430525\pi$
$98$	3.01589	+	13.1047i	0.304651	+	1.32378i
$99$	10.3481	+	13.7994i	1.04002	+	1.38690i
$100$	0.874249	+	1.79880i	0.0874249	+	0.179880i
$101$	3.26075	+	12.1693i	0.324457	+	1.21089i	0.914857	+	0.403778i	$0.132303\pi$
$101$	3.26075	+	12.1693i	0.324457	+	1.21089i	−0.590401	+	0.807110i	$0.701030\pi$
$102$	−10.4895	−	13.0029i	−1.03861	−	1.28748i
$103$	−0.452860	−	0.784376i	−0.0446216	−	0.0772868i	0.842852	−	0.538145i	$-0.180875\pi$
$103$	−0.452860	−	0.784376i	−0.0446216	−	0.0772868i	−0.887474	+	0.460859i	$0.847542\pi$
$104$	−2.86017	−	6.46016i	−0.280462	−	0.633470i
$105$	1.33473	+	6.90974i	0.130256	+	0.674321i
$106$	−10.4550	+	5.54971i	−1.01548	+	0.539036i
$107$	−0.826463	−	0.826463i	−0.0798971	−	0.0798971i	0.666029	−	0.745926i	$-0.267993\pi$
$107$	−0.826463	−	0.826463i	−0.0798971	−	0.0798971i	−0.745926	+	0.666029i	$0.767993\pi$
$108$	−7.18241	−	7.51086i	−0.691128	−	0.722733i
$109$	8.67058	−	8.67058i	0.830491	−	0.830491i	−0.157093	−	0.987584i	$-0.550212\pi$
$109$	8.67058	−	8.67058i	0.830491	−	0.830491i	0.987584	+	0.157093i	$0.0502123\pi$
$110$	7.77404	+	2.38266i	0.741226	+	0.227177i
$111$	11.5978	−	2.24030i	1.10081	−	0.212640i
$112$	−16.0878	−	2.30650i	−1.52016	−	0.217944i
$113$	15.7643	−	9.10151i	1.48298	−	0.856198i	0.483166	−	0.875529i	$-0.339487\pi$
$113$	15.7643	−	9.10151i	1.48298	−	0.856198i	0.999813	+	0.0193302i	$0.00615337\pi$
$114$	−9.45704	−	1.01179i	−0.885733	−	0.0947631i
$115$	6.14241	−	1.64586i	0.572783	−	0.153477i
$116$	−4.51996	−	1.56336i	−0.419668	−	0.145154i
$117$	−0.895827	−	7.43982i	−0.0828192	−	0.687812i
$118$	4.29275	−	6.85926i	0.395180	−	0.631446i
$119$	−23.9991	−	13.8559i	−2.19999	−	1.27017i
$120$	−4.82176	−	0.866372i	−0.440165	−	0.0790886i
$121$	19.1014	−	11.0282i	1.73649	−	1.00256i
$122$	−0.148549	+	4.17098i	−0.0134490	+	0.377623i
$123$	−5.20387	−	0.370009i	−0.469217	−	0.0333626i
$124$	−18.3562	−	1.30916i	−1.64843	−	0.117566i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−15.6010	−	7.33254i	−1.38984	−	0.653234i
$127$		−	7.64862i		−	0.678706i	−0.940659	−	0.339353i	$-0.889792\pi$
$127$		−	7.64862i		−	0.678706i	0.940659	−	0.339353i	$-0.110208\pi$
$128$	5.53294	−	9.86846i	0.489048	−	0.872257i
$129$	11.9409	+	4.12721i	1.05134	+	0.363380i
$130$	−2.40737	−	2.58517i	−0.211140	−	0.226735i
$131$	−13.6421	−	3.65540i	−1.19192	−	0.319374i	−0.392275	−	0.919848i	$-0.628312\pi$
$131$	−13.6421	−	3.65540i	−1.19192	−	0.319374i	−0.799644	+	0.600474i	$0.794979\pi$
$132$	−15.9368	+	11.9455i	−1.38712	+	1.03972i
$133$	−15.2388	+	4.08322i	−1.32137	+	0.354060i
$134$	2.68622	−	4.29223i	0.232054	−	0.370792i
$135$	−4.62150	−	2.37524i	−0.397755	−	0.204428i
$136$	15.0171	−	12.1090i	1.28770	−	1.03834i
$137$	−6.59446	+	11.4219i	−0.563403	+	0.975842i	0.433793	+	0.901012i	$0.357175\pi$
$137$	−6.59446	+	11.4219i	−0.563403	+	0.975842i	−0.997196	+	0.0748301i	$0.976159\pi$
$138$	−5.60922	+	14.5315i	−0.477488	+	1.23701i
$139$	14.1021	+	3.77865i	1.19613	+	0.320501i	0.801305	−	0.598257i	$-0.204140\pi$
$139$	14.1021	+	3.77865i	1.19613	+	0.320501i	0.394822	+	0.918758i	$0.370806\pi$
$140$	−7.97901	+	1.53949i	−0.674349	+	0.130110i
$141$	1.43247	+	2.94573i	0.120635	+	0.248076i
$142$	−3.75599	+	12.2549i	−0.315196	+	1.02841i
$143$	−14.3613			−1.20095
$144$	8.67458	−	8.29166i	0.722882	−	0.690971i
$145$	−2.39135			−0.198591
$146$	2.33544	−	7.61998i	0.193282	−	0.630634i
$147$	−16.4280	−	1.16808i	−1.35496	−	0.0963412i
$148$	2.58398	+	13.3925i	0.212402	+	1.10086i
$149$	8.30118	+	2.22429i	0.680059	+	0.182221i	0.582282	−	0.812987i	$-0.302160\pi$
$149$	8.30118	+	2.22429i	0.680059	+	0.182221i	0.0977772	+	0.995208i	$0.468827\pi$
$150$	−2.42004	+	0.378676i	−0.197596	+	0.0309188i
$151$	5.41799	−	9.38424i	0.440910	−	0.763679i	−0.556847	−	0.830615i	$-0.687989\pi$
$151$	5.41799	−	9.38424i	0.440910	−	0.763679i	0.997757	+	0.0669362i	$0.0213224\pi$
$152$	1.17068	−	10.9198i	0.0949546	−	0.885712i
$153$	18.9891	−	7.62045i	1.53518	−	0.616077i
$154$	−17.5263	+	28.0047i	−1.41231	+	2.25668i
$155$	−8.88788	+	2.38150i	−0.713891	+	0.191287i
$156$	8.59099	−	1.03255i	0.687830	−	0.0826705i
$157$	−10.3394	−	2.77045i	−0.825178	−	0.221106i	−0.178569	−	0.983927i	$-0.557147\pi$
$157$	−10.3394	−	2.77045i	−0.825178	−	0.221106i	−0.646609	+	0.762822i	$0.723813\pi$
$158$	2.11757	+	2.27398i	0.168465	+	0.180908i
$159$	−2.74947	−	14.2337i	−0.218048	−	1.12881i
$160$	1.00160	−	5.56748i	0.0791837	−	0.440148i
$161$			25.8375i			2.03628i
$162$	11.3715	−	5.71733i	0.893433	−	0.449196i
$163$	−8.27835	−	8.27835i	−0.648410	−	0.648410i	0.304198	−	0.952609i	$-0.401611\pi$
$163$	−8.27835	−	8.27835i	−0.648410	−	0.648410i	−0.952609	+	0.304198i	$0.901611\pi$
$164$	0.428549	−	6.00882i	0.0334640	−	0.469210i
$165$	−5.57831	+	8.24934i	−0.434271	+	0.642211i
$166$	0.325363	−	9.13561i	0.0252530	−	0.709060i
$167$	−3.67079	+	2.11933i	−0.284054	+	0.163999i	−0.635257	−	0.772301i	$-0.719106\pi$
$167$	−3.67079	+	2.11933i	−0.284054	+	0.163999i	0.351203	+	0.936299i	$0.385773\pi$
$168$	8.47078	−	18.0126i	0.653535	−	1.38970i
$169$	−5.85496	−	3.38037i	−0.450382	−	0.260028i
$170$	5.11699	−	8.17627i	0.392455	−	0.627092i
$171$	4.57653	−	10.7119i	0.349976	−	0.819157i
$172$	−4.76867	+	13.7871i	−0.363608	+	1.05126i
$173$	−6.68858	+	1.79220i	−0.508523	+	0.136258i	−0.503953	−	0.863731i	$-0.668122\pi$
$173$	−6.68858	+	1.79220i	−0.508523	+	0.136258i	−0.00457050	+	0.999990i	$0.501455\pi$
$174$	3.45182	−	4.73246i	0.261682	−	0.358767i
$175$	−3.51873	+	2.03154i	−0.265991	+	0.153570i
$176$	−13.7895	−	18.4052i	−1.03942	−	1.38735i
$177$	6.49304	+	7.48706i	0.488047	+	0.562762i
$178$	12.1468	+	3.72285i	0.910440	+	0.279040i
$179$	−2.84365	+	2.84365i	−0.212544	+	0.212544i	−0.805347	−	0.592803i	$-0.798021\pi$
$179$	−2.84365	+	2.84365i	−0.212544	+	0.212544i	0.592803	+	0.805347i	$0.298021\pi$
$180$	2.74385	−	5.33585i	0.204514	−	0.397711i
$181$	−7.86191	−	7.86191i	−0.584371	−	0.584371i	0.351730	−	0.936101i	$-0.385593\pi$
$181$	−7.86191	−	7.86191i	−0.584371	−	0.584371i	−0.936101	+	0.351730i	$0.885593\pi$
$182$	12.6775	−	6.72946i	0.939717	−	0.498821i
$183$	−4.83119	−	1.66984i	−0.357132	−	0.123438i
$184$	−16.7782	−	6.48059i	−1.23690	−	0.477756i
$185$	3.40988	+	5.90609i	0.250699	+	0.434224i
$186$	8.11636	−	21.0267i	0.595120	−	1.54175i
$187$	−10.1492	−	37.8774i	−0.742184	−	2.76987i
$188$	−3.40180	+	1.65333i	−0.248102	+	0.120582i
$189$	14.1819	−	15.6399i	1.03158	−	1.13763i
$190$	−1.23154	−	5.35130i	−0.0893452	−	0.388224i
$191$	−2.31446	+	4.00876i	−0.167468	+	0.290063i	−0.937529	−	0.347907i	$-0.886892\pi$
$191$	−2.31446	+	4.00876i	−0.167468	+	0.290063i	0.770061	+	0.637970i	$0.220226\pi$
$192$	9.57222	+	10.0186i	0.690815	+	0.723031i
$193$	3.66930	+	6.35542i	0.264122	+	0.457473i	0.967333	−	0.253508i	$-0.0815845\pi$
$193$	3.66930	+	6.35542i	0.264122	+	0.457473i	−0.703211	+	0.710981i	$0.748251\pi$
$194$	−7.71943	+	7.18849i	−0.554223	+	0.516104i
$195$	3.89077	−	1.89202i	0.278624	−	0.135490i
$196$	1.35288	−	18.9691i	0.0966342	−	1.35494i
$197$	−15.4176	+	15.4176i	−1.09846	+	1.09846i	−0.103869	+	0.994591i	$0.533122\pi$
$197$	−15.4176	+	15.4176i	−1.09846	+	1.09846i	−0.994591	+	0.103869i	$0.966878\pi$
$198$	−8.27331	−	22.9471i	−0.587958	−	1.63078i
$199$	17.7977			1.26164			0.630821	−	0.775928i	$-0.282718\pi$
$199$	17.7977			1.26164			0.630821	+	0.775928i	$0.282718\pi$
$200$	−0.436653	−	2.79452i	−0.0308761	−	0.197602i
$201$	4.06307	+	4.68508i	0.286587	+	0.330460i
$202$	0.634148	−	17.8058i	0.0446185	−	1.25281i
$203$	2.51475	−	9.38517i	0.176501	−	0.658710i
$204$	8.79460	+	21.9286i	0.615745	+	1.53531i
$205$	−0.779573	−	2.90941i	−0.0544478	−	0.203202i
$206$	0.287270	+	1.24825i	0.0200151	+	0.0869697i
$207$	−15.0056	−	11.7803i	−1.04296	−	0.818787i
$208$	1.19015	+	9.92028i	0.0825218	+	0.687847i
$209$	−19.3334	−	11.1622i	−1.33732	−	0.772103i
$210$	1.05876	−	9.89601i	0.0730613	−	0.682889i
$211$	−3.33087	+	12.4310i	−0.229307	+	0.855784i	0.751326	+	0.659931i	$0.229414\pi$
$211$	−3.33087	+	12.4310i	−0.229307	+	0.855784i	−0.980633	+	0.195854i	$0.937252\pi$
$212$	16.4364	−	3.17127i	1.12885	−	0.217804i
$213$	−13.0042	−	8.79358i	−0.891031	−	0.602526i
$214$	0.774990	+	1.45998i	0.0529772	+	0.0998024i
$215$			7.29425i			0.497464i
$216$	6.59897	+	13.1322i	0.449003	+	0.893530i
$217$		−	37.3861i		−	2.53793i
$218$	−15.3170	+	8.13056i	−1.03740	+	0.550671i
$219$	8.08586	+	5.46776i	0.546392	+	0.369477i
$220$	−9.52413	−	6.44333i	−0.642117	−	0.434409i
$221$	−4.40932	+	16.4558i	−0.296603	+	1.10694i
$222$	−16.6101	−	1.77709i	−1.11480	−	0.119271i
$223$	5.54654	+	3.20229i	0.371424	+	0.214442i	0.674080	−	0.738658i	$-0.264540\pi$
$223$	5.54654	+	3.20229i	0.371424	+	0.214442i	−0.302657	+	0.953100i	$0.597874\pi$
$224$	20.7970	+	9.78571i	1.38956	+	0.653835i
$225$	0.424470	−	2.96982i	0.0282980	−	0.197988i
$226$	−25.0872	+	5.77352i	−1.66877	+	0.384049i
$227$	−2.10175	−	7.84385i	−0.139498	−	0.520615i	−0.999939	−	0.0110638i	$-0.996478\pi$
$227$	−2.10175	−	7.84385i	−0.139498	−	0.520615i	0.860441	−	0.509551i	$-0.170188\pi$
$228$	12.3679	+	5.28720i	0.819082	+	0.350153i
$229$	−0.298338	+	1.11341i	−0.0197147	+	0.0735763i	−0.975082	−	0.221843i	$-0.928793\pi$
$229$	−0.298338	+	1.11341i	−0.0197147	+	0.0735763i	0.955368	+	0.295419i	$0.0954594\pi$
$230$	−8.98742	−	0.320085i	−0.592613	−	0.0211058i
$231$	−26.5095	−	30.5679i	−1.74420	−	2.01122i
$232$	5.46371	+	3.98700i	0.358710	+	0.261760i
$233$	21.8840			1.43367			0.716835	−	0.697243i	$-0.245590\pi$
$233$	21.8840			1.43367			0.716835	+	0.697243i	$0.245590\pi$
$234$	−1.87188	+	10.4309i	−0.122369	+	0.681887i
$235$	−1.33724	+	1.33724i	−0.0872321	+	0.0872321i
$236$	−8.64694	+	7.49565i	−0.562868	+	0.487925i
$237$	−3.42241	+	1.66426i	−0.222309	+	0.108106i
$238$	26.7079	+	28.6805i	1.73121	+	1.85908i
$239$	6.62827	+	11.4805i	0.428747	+	0.742612i	0.996762	−	0.0804063i	$-0.0256218\pi$
$239$	6.62827	+	11.4805i	0.428747	+	0.742612i	−0.568015	+	0.823018i	$0.692288\pi$
$240$	6.16063	+	3.16965i	0.397667	+	0.204600i
$241$	5.46027	−	9.45746i	0.351727	−	0.609208i	−0.634825	−	0.772656i	$-0.718928\pi$
$241$	5.46027	−	9.45746i	0.351727	−	0.609208i	0.986552	+	0.163447i	$0.0522613\pi$
$242$	−30.3978	+	6.99571i	−1.95405	+	0.449701i
$243$	2.61705	+	15.3672i	0.167884	+	0.985807i
$244$	1.92937	−	5.57816i	0.123515	−	0.357105i
$245$	−2.46102	−	9.18465i	−0.157229	−	0.586786i
$246$	6.88298	+	2.65685i	0.438843	+	0.169395i
$247$	4.84940	+	8.39940i	0.308560	+	0.534441i
$248$	24.2775	+	9.37721i	1.54162	+	0.595454i
$249$	10.5816	+	3.65741i	0.670584	+	0.231779i
$250$	−0.663067	−	1.24914i	−0.0419361	−	0.0790023i
$251$	3.64002	+	3.64002i	0.229756	+	0.229756i	0.812591	−	0.582835i	$-0.198056\pi$
$251$	3.64002	+	3.64002i	0.229756	+	0.229756i	−0.582835	+	0.812591i	$0.698056\pi$
$252$	18.0558	+	16.3798i	1.13741	+	1.03183i
$253$	−25.8528	+	25.8528i	−1.62535	+	1.62535i
$254$	−3.16969	+	10.3419i	−0.198884	+	0.648912i
$255$	7.73974	+	8.92462i	0.484681	+	0.558882i
$256$	−11.5709	+	11.0505i	−0.723181	+	0.690659i
$257$	3.38998	−	1.95721i	0.211461	−	0.122087i	−0.390529	−	0.920591i	$-0.627708\pi$
$257$	3.38998	−	1.95721i	0.211461	−	0.122087i	0.601990	+	0.798503i	$0.294375\pi$
$258$	−14.4353	−	10.5290i	−0.898701	−	0.655506i
$259$	−26.7651	+	7.17169i	−1.66310	+	0.445627i
$260$	2.18375	+	4.49314i	0.135430	+	0.278653i
$261$	4.30403	+	5.73953i	0.266413	+	0.355268i
$262$	16.9311	+	10.5961i	1.04601	+	0.654627i
$263$	−18.2570	−	10.5407i	−1.12578	−	0.649968i	−0.182908	−	0.983130i	$-0.558551\pi$
$263$	−18.2570	−	10.5407i	−1.12578	−	0.649968i	−0.942869	+	0.333162i	$0.891884\pi$
$264$	26.4990	−	9.54746i	1.63090	−	0.587606i
$265$	7.24842	−	4.18488i	0.445267	−	0.257075i
$266$	22.2970	+	0.794103i	1.36712	+	0.0486896i
$267$	−8.71599	+	12.8894i	−0.533410	+	0.788820i
$268$	−5.41088	+	4.69046i	−0.330522	+	0.286515i
$269$	−3.29039	−	3.29039i	−0.200619	−	0.200619i	0.599646	−	0.800265i	$-0.295308\pi$
$269$	−3.29039	−	3.29039i	−0.200619	−	0.200619i	−0.800265	+	0.599646i	$0.795308\pi$
$270$	5.26454	+	5.12685i	0.320390	+	0.312010i
$271$		−	18.4994i		−	1.12376i	−0.827220	−	0.561878i	$-0.810079\pi$
$271$		−	18.4994i		−	1.12376i	0.827220	−	0.561878i	$-0.189921\pi$
$272$	−25.3232	+	10.1497i	−1.53544	+	0.615413i
$273$	3.33395	+	17.2595i	0.201780	+	1.04459i
$274$	13.6500	−	12.7111i	0.824626	−	0.767908i
$275$	−5.55356	−	1.48807i	−0.334892	−	0.0897341i
$276$	13.6065	−	17.3240i	0.819013	−	1.04278i
$277$	17.0652	−	4.57260i	1.02535	−	0.274741i	0.293318	−	0.956015i	$-0.405240\pi$
$277$	17.0652	−	4.57260i	1.02535	−	0.274741i	0.732028	+	0.681274i	$0.238574\pi$
$278$	−17.5020	−	10.9533i	−1.04970	−	0.656938i
$279$	21.7126	+	17.0457i	1.29990	+	1.02050i
$280$	11.4267	+	1.22502i	0.682874	+	0.0732089i
$281$	−0.909610	+	1.57549i	−0.0542628	+	0.0939859i	−0.891881	−	0.452270i	$-0.850614\pi$
$281$	−0.909610	+	1.57549i	−0.0542628	+	0.0939859i	0.837618	+	0.546256i	$0.183948\pi$
$282$	−0.716132	−	4.57665i	−0.0426450	−	0.272536i
$283$	−21.9778	−	5.88892i	−1.30644	−	0.350060i	−0.462560	−	0.886588i	$-0.653069\pi$
$283$	−21.9778	−	5.88892i	−1.30644	−	0.350060i	−0.843882	+	0.536528i	$0.819736\pi$
$284$	10.1572	−	15.0137i	0.602719	−	0.890901i
$285$	6.70836	+	0.476983i	0.397369	+	0.0282540i
$286$	19.4184	+	5.95153i	1.14823	+	0.351921i
$287$	12.2382			0.722396
$288$	−15.1654	+	7.61655i	−0.893627	+	0.448810i
$289$	−29.5175			−1.73632
$290$	3.23342	+	0.991006i	0.189873	+	0.0581939i
$291$	−5.64965	−	11.6180i	−0.331188	−	0.681058i
$292$	−6.31565	+	9.33539i	−0.369595	+	0.546312i
$293$	6.66461	+	1.78578i	0.389351	+	0.104326i	0.448183	−	0.893942i	$-0.352071\pi$
$293$	6.66461	+	1.78578i	0.389351	+	0.104326i	−0.0588326	+	0.998268i	$0.518738\pi$
$294$	21.7288	+	8.38737i	1.26725	+	0.489162i
$295$	−2.86088	+	4.95519i	−0.166567	+	0.288502i
$296$	2.05616	−	19.1793i	0.119512	−	1.11477i
$297$	29.8395	−	1.45881i	1.73146	−	0.0846485i
$298$	−10.3025	−	6.44766i	−0.596809	−	0.373503i
$299$	15.3428	−	4.11110i	0.887300	−	0.237751i
$300$	3.42915	+	0.490878i	0.197982	+	0.0283408i
$301$	−28.6273	−	7.67066i	−1.65005	−	0.442129i
$302$	−11.2148	+	10.4434i	−0.645339	+	0.600953i
$303$	20.6242	+	7.12847i	1.18483	+	0.409520i
$304$	−6.10822	+	14.2799i	−0.350330	+	0.819006i
$305$		−	2.95120i		−	0.168985i
$306$	−28.8338	+	2.43452i	−1.64832	+	0.139172i
$307$	2.09392	+	2.09392i	0.119506	+	0.119506i	0.764331	−	0.644824i	$-0.223069\pi$
$307$	2.09392	+	2.09392i	0.119506	+	0.119506i	−0.644824	+	0.764331i	$0.723069\pi$
$308$	35.3034	−	30.6029i	2.01160	−	1.74376i
$309$	−1.56480	−	0.111262i	−0.0890184	−	0.00632945i
$310$	13.0045	+	0.463153i	0.738607	+	0.0263053i
$311$	15.4333	−	8.91041i	0.875141	−	0.505263i	0.00608783	−	0.999981i	$-0.498062\pi$
$311$	15.4333	−	8.91041i	0.875141	−	0.505263i	0.869053	+	0.494719i	$0.164729\pi$
$312$	−12.0441	−	2.16407i	−0.681860	−	0.122516i
$313$	8.06215	+	4.65469i	0.455700	+	0.263098i	0.710234	−	0.703965i	$-0.248589\pi$
$313$	8.06215	+	4.65469i	0.455700	+	0.263098i	−0.254535	+	0.967064i	$0.581922\pi$
$314$	12.8322	+	8.03081i	0.724162	+	0.453205i
$315$	11.2091	+	4.78897i	0.631561	+	0.269828i
$316$	−1.92087	−	3.95227i	−0.108058	−	0.222332i
$317$	18.9218	−	5.07008i	1.06275	−	0.284764i	0.315241	−	0.949012i	$-0.397915\pi$
$317$	18.9218	−	5.07008i	1.06275	−	0.284764i	0.747513	+	0.664248i	$0.231248\pi$
$318$	−2.18099	+	20.3853i	−0.122304	+	1.14315i
$319$	11.9070	−	6.87449i	0.666662	−	0.384898i
$320$	−3.66154	+	7.11289i	−0.204686	+	0.397622i
$321$	−1.98767	+	0.383950i	−0.110941	+	0.0214300i
$322$	10.7074	−	34.9358i	0.596701	−	1.94689i
$323$	−18.7260	+	18.7260i	−1.04194	+	1.04194i
$324$	−17.7452	+	3.01807i	−0.985843	+	0.167670i
$325$	1.76625	+	1.76625i	0.0979739	+	0.0979739i
$326$	7.76277	+	14.6241i	0.429940	+	0.809953i
$327$	−4.02810	−	20.8530i	−0.222754	−	1.15317i
$328$	−3.06959	+	7.94712i	−0.169490	+	0.438806i
$329$	−3.84194	−	6.65444i	−0.211813	−	0.366871i
$330$	10.9612	−	8.84248i	0.603397	−	0.486762i
$331$	4.51464	+	16.8488i	0.248147	+	0.926096i	0.971776	+	0.235907i	$0.0758061\pi$
$331$	4.51464	+	16.8488i	0.248147	+	0.926096i	−0.723629	+	0.690189i	$0.757527\pi$
$332$	−4.22585	+	12.2177i	−0.231924	+	0.670534i
$333$	8.03813	−	18.8141i	0.440487	−	1.03101i
$334$	5.84167	−	1.34439i	0.319642	−	0.0735619i
$335$	−1.79022	+	3.10075i	−0.0978100	+	0.169412i
$336$	−18.9183	+	20.8450i	−1.03208	+	1.13719i
$337$	12.5344	+	21.7103i	0.682795	+	1.18264i	0.974124	+	0.226013i	$0.0725691\pi$
$337$	12.5344	+	21.7103i	0.682795	+	1.18264i	−0.291329	+	0.956623i	$0.594098\pi$
$338$	6.51582	+	6.99708i	0.354414	+	0.380591i
$339$	2.23612	−	31.4492i	0.121449	−	1.70808i
$340$	−10.3072	+	8.93486i	−0.558986	+	0.484561i
$341$	37.4082	−	37.4082i	2.02577	−	2.02577i
$342$	−10.6272	+	12.5873i	−0.574654	+	0.680643i
$343$	10.1929			0.550363
$344$	12.1614	−	16.6658i	0.655700	−	0.898559i
$345$	3.59808	−	10.4100i	0.193714	−	0.560456i
$346$	9.78656	+	0.348546i	0.526129	+	0.0187380i
$347$	−9.15858	+	34.1803i	−0.491658	+	1.83489i	0.0563366	+	0.998412i	$0.482058\pi$
$347$	−9.15858	+	34.1803i	−0.491658	+	1.83489i	−0.547995	+	0.836482i	$0.684609\pi$
$348$	−6.62852	+	4.96843i	−0.355326	+	0.266336i
$349$	−1.93564	−	7.22390i	−0.103612	−	0.386687i	0.894572	−	0.446925i	$-0.147481\pi$
$349$	−1.93564	−	7.22390i	−0.103612	−	0.386687i	−0.998184	+	0.0602378i	$0.980814\pi$
$350$	5.59969	−	1.28870i	0.299316	−	0.0688841i
$351$	−11.5438	−	5.93300i	−0.616163	−	0.316680i
$352$	11.0178	+	30.6008i	0.587253	+	1.63103i
$353$	6.47944	+	3.74091i	0.344866	+	0.199108i	0.662422	−	0.749131i	$-0.269529\pi$
$353$	6.47944	+	3.74091i	0.344866	+	0.199108i	−0.317556	+	0.948240i	$0.602862\pi$
$354$	−5.67671	−	12.8143i	−0.301714	−	0.681072i
$355$	2.34578	−	8.75457i	0.124501	−	0.464644i
$356$	−14.8813	−	10.0676i	−0.788705	−	0.533581i
$357$	−43.1651	+	20.9905i	−2.28454	+	1.11094i
$358$	5.02344	−	2.66654i	0.265497	−	0.140931i
$359$			6.85684i			0.361890i	0.983493	+	0.180945i	$0.0579156\pi$
$359$			6.85684i			0.361890i	−0.983493	+	0.180945i	$0.942084\pi$
$360$	−5.92129	+	6.07769i	−0.312079	+	0.320322i
$361$		−	3.92346i		−	0.206498i
$362$	7.37226	+	13.8884i	0.387478	+	0.729959i
$363$	2.70948	−	38.1066i	0.142211	−	2.00008i
$364$	−19.9304	+	3.84541i	−1.04464	+	0.201554i
$365$	−1.45858	+	5.44350i	−0.0763457	+	0.284926i
$366$	5.84041	+	4.25995i	0.305283	+	0.222671i
$367$	9.36227	+	5.40531i	0.488706	+	0.282155i	0.724038	−	0.689760i	$-0.242284\pi$
$367$	9.36227	+	5.40531i	0.488706	+	0.282155i	−0.235331	+	0.971915i	$0.575617\pi$
$368$	20.0006	+	15.7157i	1.04261	+	0.819238i
$369$	−5.57984	+	7.10752i	−0.290475	+	0.370003i
$370$	−2.16305	−	9.39891i	−0.112452	−	0.488626i
$371$	8.80167	+	32.8483i	0.456960	+	1.70540i
$372$	−19.6881	+	25.0673i	−1.02078	+	1.29968i
$373$	2.33112	−	8.69986i	0.120701	−	0.450462i	−0.878949	−	0.476916i	$-0.841755\pi$
$373$	2.33112	−	8.69986i	0.120701	−	0.450462i	0.999650	+	0.0264536i	$0.00842143\pi$
$374$	−1.97381	+	55.4212i	−0.102063	+	2.86576i
$375$	1.70061	−	0.328501i	0.0878193	−	0.0169637i
$376$	5.28484	−	0.825776i	0.272545	−	0.0425861i
$377$	−5.97324			−0.307637
$378$	−25.6572	+	15.2700i	−1.31967	+	0.785405i
$379$	−6.91319	+	6.91319i	−0.355106	+	0.355106i	−0.862005	−	0.506899i	$-0.830792\pi$
$379$	−6.91319	+	6.91319i	−0.355106	+	0.355106i	0.506899	+	0.862005i	$0.330792\pi$
$380$	−0.552447	+	7.74603i	−0.0283399	+	0.397363i
$381$	−10.9743	−	7.42092i	−0.562228	−	0.380185i
$382$	4.79073	−	4.46123i	0.245115	−	0.228256i
$383$	−0.464824	−	0.805098i	−0.0237514	−	0.0411386i	0.853905	−	0.520428i	$-0.174228\pi$
$383$	−0.464824	−	0.805098i	−0.0237514	−	0.0411386i	−0.877657	+	0.479290i	$0.840894\pi$
$384$	−8.79105	−	17.5133i	−0.448617	−	0.893724i
$385$	11.6803	−	20.2309i	0.595283	−	1.03106i
$386$	−2.32761	−	10.1140i	−0.118472	−	0.514788i
$387$	17.5071	−	13.1284i	0.889937	−	0.667356i
$388$	13.4167	−	6.52075i	0.681130	−	0.331041i
$389$	1.35620	+	5.06140i	0.0687620	+	0.256623i	0.991747	−	0.128214i	$-0.0409243\pi$
$389$	1.35620	+	5.06140i	0.0687620	+	0.256623i	−0.922985	+	0.384837i	$0.874258\pi$
$390$	−6.04491	+	0.945877i	−0.306096	+	0.0478964i
$391$	21.6857	+	37.5607i	1.09669	+	1.89953i
$392$	−9.69033	+	25.0881i	−0.489436	+	1.26714i
$393$	−18.4808	+	16.0272i	−0.932232	+	0.808464i
$394$	27.2359	−	14.4574i	1.37213	−	0.728353i
$395$	−1.55363	−	1.55363i	−0.0781717	−	0.0781717i
$396$	1.67704	+	34.4560i	0.0842742	+	1.73148i
$397$	4.96125	−	4.96125i	0.248998	−	0.248998i	−0.571561	−	0.820559i	$-0.693662\pi$
$397$	4.96125	−	4.96125i	0.248998	−	0.248998i	0.820559	+	0.571561i	$0.193662\pi$
$398$	−24.0648	−	7.37559i	−1.20626	−	0.369705i
$399$	−8.92652	+	25.8263i	−0.446885	+	1.29293i
$400$	−0.567673	+	3.95951i	−0.0283836	+	0.197976i
$401$	10.0893	−	5.82505i	0.503835	−	0.290889i	−0.226461	−	0.974020i	$-0.572716\pi$
$401$	10.0893	−	5.82505i	0.503835	−	0.290889i	0.730296	+	0.683131i	$0.239382\pi$
$402$	−3.55224	−	8.01864i	−0.177170	−	0.399934i
$403$	−22.2006	+	5.94864i	−1.10589	+	0.296323i
$404$	−8.23640	+	23.8130i	−0.409776	+	1.18474i
$405$	−7.89191	+	4.32640i	−0.392152	+	0.214980i
$406$	−7.28962	+	11.6479i	−0.361778	+	0.578073i
$407$	−33.9569	−	19.6050i	−1.68318	−	0.971784i
$408$	−2.80395	−	33.2950i	−0.138816	−	1.64835i
$409$	−5.87689	+	3.39303i	−0.290594	+	0.167774i	−0.638210	−	0.769863i	$-0.720325\pi$
$409$	−5.87689	+	3.39303i	−0.290594	+	0.167774i	0.347616	+	0.937637i	$0.386991\pi$
$410$	−0.151611	+	4.25697i	−0.00748753	+	0.210237i
$411$	9.99007	+	20.5437i	0.492774	+	1.01334i
$412$	0.128864	−	1.80685i	0.00634870	−	0.0890170i
$413$	−16.4388	−	16.4388i	−0.808901	−	0.808901i
$414$	15.4076	+	22.1470i	0.757243	+	1.08847i
$415$			6.46394i			0.317303i
$416$	2.50186	−	13.9067i	0.122664	−	0.681834i
$417$	19.1039	−	16.5676i	0.935523	−	0.811318i
$418$	21.5156	+	23.1048i	1.05236	+	1.13009i
$419$	−27.8237	−	7.45534i	−1.35928	−	0.364217i	−0.495727	−	0.868479i	$-0.665098\pi$
$419$	−27.8237	−	7.45534i	−1.35928	−	0.364217i	−0.863551	+	0.504261i	$0.831765\pi$
$420$	−5.53262	+	12.9419i	−0.269964	+	0.631502i
$421$	9.75995	−	2.61517i	0.475671	−	0.127456i	−0.0130152	−	0.999915i	$-0.504143\pi$
$421$	9.75995	−	2.61517i	0.475671	−	0.127456i	0.488686	+	0.872460i	$0.337476\pi$
$422$	9.65535	−	15.4280i	0.470015	−	0.751022i
$423$	5.61636	+	0.802736i	0.273077	+	0.0390303i
$424$	−23.5384	−	2.52348i	−1.14312	−	0.122551i
$425$	−3.41019	+	5.90662i	−0.165418	+	0.286513i
$426$	13.9392	+	17.2792i	0.675355	+	0.837179i
$427$	11.5824	+	3.10349i	0.560511	+	0.150189i
$428$	−0.442852	−	2.29526i	−0.0214060	−	0.110945i
$429$	−13.9338	+	20.6056i	−0.672730	+	0.994850i
$430$	3.02283	−	9.86279i	0.145774	−	0.475626i
$431$	23.1585			1.11551			0.557754	−	0.830006i	$-0.311663\pi$
$431$	23.1585			1.11551			0.557754	+	0.830006i	$0.311663\pi$
$432$	−3.48054	−	20.4911i	−0.167457	−	0.985879i
$433$	−0.601011			−0.0288828			−0.0144414	−	0.999896i	$-0.504597\pi$
$433$	−0.601011			−0.0288828			−0.0144414	+	0.999896i	$0.504597\pi$
$434$	−15.4933	+	50.5509i	−0.743702	+	2.42652i
$435$	−2.32016	+	3.43111i	−0.111243	+	0.164509i
$436$	24.0800	−	4.64604i	1.15322	−	0.222505i
$437$	23.8501	+	6.39061i	1.14090	+	0.305704i
$438$	−8.66725	−	10.7440i	−0.414137	−	0.513369i
$439$	14.5702	−	25.2364i	0.695399	−	1.20447i	−0.274647	−	0.961545i	$-0.588561\pi$
$439$	14.5702	−	25.2364i	0.695399	−	1.20447i	0.970046	−	0.242921i	$-0.0781056\pi$
$440$	10.2077	+	12.6592i	0.486632	+	0.603502i
$441$	−17.6149	+	22.4376i	−0.838804	+	1.06846i
$442$	12.7815	−	20.4231i	0.607953	−	0.971429i
$443$	10.4586	−	2.80238i	0.496903	−	0.133145i	−0.00165906	−	0.999999i	$-0.500528\pi$
$443$	10.4586	−	2.80238i	0.496903	−	0.133145i	0.498563	+	0.866854i	$0.333861\pi$
$444$	21.7227	+	9.28633i	1.03091	+	0.440710i
$445$	−8.67733	−	2.32508i	−0.411345	−	0.110219i
$446$	−6.17258	−	6.62848i	−0.292280	−	0.313868i
$447$	11.2455	−	9.75246i	0.531893	−	0.461276i
$448$	−24.0650	−	21.8501i	−1.13697	−	1.03232i
$449$			12.1952i			0.575528i	0.957701	+	0.287764i	$0.0929119\pi$
$449$			12.1952i			0.575528i	−0.957701	+	0.287764i	$0.907088\pi$
$450$	−1.80467	+	3.83968i	−0.0850731	+	0.181004i
$451$	12.2454	+	12.2454i	0.576614	+	0.576614i
$452$	36.3138	+	2.58990i	1.70806	+	0.121819i
$453$	−8.20782	−	16.8786i	−0.385637	−	0.793027i
$454$	−0.408748	+	11.4769i	−0.0191835	+	0.538638i
$455$	−8.78928	+	5.07449i	−0.412048	+	0.237896i
$456$	−14.5319	−	12.2744i	−0.680519	−	0.574802i
$457$	−19.2488	−	11.1133i	−0.900421	−	0.519859i	−0.0230846	−	0.999734i	$-0.507349\pi$
$457$	−19.2488	−	11.1133i	−0.900421	−	0.519859i	−0.877337	+	0.479875i	$0.840682\pi$
$458$	0.864805	−	1.38184i	0.0404097	−	0.0645693i
$459$	7.48997	−	34.6392i	0.349602	−	1.61682i
$460$	12.0195	+	4.15730i	0.560414	+	0.193835i
$461$	−10.7003	+	2.86713i	−0.498362	+	0.133536i	−0.499240	−	0.866464i	$-0.666387\pi$
$461$	−10.7003	+	2.86713i	−0.498362	+	0.133536i	0.000877858		1.00000i	$0.499721\pi$
$462$	23.1766	+	52.3177i	1.07827	+	2.43404i
$463$	33.2782	−	19.2132i	1.54657	−	0.892911i	0.548167	−	0.836369i	$-0.315326\pi$
$463$	33.2782	−	19.2132i	1.54657	−	0.892911i	0.998400	−	0.0565422i	$-0.0180075\pi$
$464$	−5.73539	−	7.65519i	−0.266259	−	0.355383i
$465$	−5.20631	+	15.0629i	−0.241437	+	0.698527i
$466$	−29.5901	−	9.06903i	−1.37073	−	0.420115i
$467$	17.0863	−	17.0863i	0.790660	−	0.790660i	−0.190941	−	0.981601i	$-0.561154\pi$
$467$	17.0863	−	17.0863i	0.790660	−	0.790660i	0.981601	+	0.190941i	$0.0611540\pi$
$468$	6.85372	−	13.3282i	0.316814	−	0.616095i
$469$	−10.2867	−	10.2867i	−0.474996	−	0.474996i
$470$	2.36230	−	1.25396i	0.108965	−	0.0578407i
$471$	−14.0067	+	12.1471i	−0.645394	+	0.559708i
$472$	14.7981	−	6.55170i	0.681138	−	0.301566i
$473$	−20.9690	−	36.3194i	−0.964157	−	1.66997i
$474$	5.31724	−	0.832015i	0.244229	−	0.0382157i
$475$	1.00496	+	3.75055i	0.0461105	+	0.172087i
$476$	−24.2270	−	49.8480i	−1.11044	−	2.28478i
$477$	−23.0902	−	9.86504i	−1.05723	−	0.451689i
$478$	−4.20463	−	18.2700i	−0.192315	−	0.835650i
$479$	−13.5995	+	23.5550i	−0.621376	+	1.07626i	0.367853	+	0.929884i	$0.380093\pi$
$479$	−13.5995	+	23.5550i	−0.621376	+	1.07626i	−0.989230	+	0.146372i	$0.953240\pi$
$480$	−7.01643	−	6.83883i	−0.320255	−	0.312149i
$481$	8.51738	+	14.7525i	0.388359	+	0.672658i
$482$	−11.3023	+	10.5249i	−0.514806	+	0.479397i
$483$	37.0717	+	25.0684i	1.68682	+	1.14065i
$484$	44.0010	+	3.13815i	2.00005	+	0.142643i
$485$	5.27409	−	5.27409i	0.239484	−	0.239484i
$486$	2.82978	−	21.8630i	0.128362	−	0.991727i
$487$	7.59971			0.344376			0.172188	−	0.985064i	$-0.444916\pi$
$487$	7.59971			0.344376			0.172188	+	0.985064i	$0.444916\pi$
$488$	−4.92043	+	6.74286i	−0.222737	+	0.305235i
$489$	−19.9097	+	3.84588i	−0.900347	+	0.173917i
$490$	−0.478618	+	13.4387i	−0.0216218	+	0.607101i
$491$	−8.32111	+	31.0548i	−0.375527	+	1.40148i	0.477047	+	0.878878i	$0.341707\pi$
$491$	−8.32111	+	31.0548i	−0.375527	+	1.40148i	−0.852574	+	0.522607i	$0.824960\pi$
$492$	−8.20566	−	6.44482i	−0.369940	−	0.290555i
$493$	−4.22131	−	15.7541i	−0.190118	−	0.709531i
$494$	−3.07620	−	13.3668i	−0.138405	−	0.601399i
$495$	6.42392	+	16.0075i	0.288734	+	0.719485i
$496$	−28.9403	−	22.7401i	−1.29946	−	1.02106i
$497$	31.8917	+	18.4127i	1.43054	+	0.825921i
$498$	−12.7921	−	9.33047i	−0.573228	−	0.418108i
$499$	3.05211	−	11.3906i	0.136631	−	0.509915i	−0.863355	−	0.504598i	$-0.831641\pi$
$499$	3.05211	−	11.3906i	0.136631	−	0.509915i	0.999986	−	0.00531714i	$-0.00169251\pi$
$500$	0.378896	+	1.96378i	0.0169447	+	0.0878230i
$501$	−0.520692	+	7.32309i	−0.0232628	+	0.327172i
$502$	−3.41332	−	6.43027i	−0.152344	−	0.286997i
$503$		−	34.0171i		−	1.51675i	−0.651821	−	0.758373i	$-0.725995\pi$
$503$		−	34.0171i		−	1.51675i	0.651821	−	0.758373i	$-0.274005\pi$
$504$	−17.6259	−	29.6302i	−0.785119	−	1.31984i
$505$			12.5986i			0.560629i
$506$	45.6702	−	24.2427i	2.03029	−	1.07772i
$507$	−10.5308	+	5.12098i	−0.467690	+	0.227431i
$508$	8.57168	−	12.6701i	0.380307	−	0.562146i
$509$	−10.4865	+	39.1362i	−0.464806	+	1.73468i	0.192724	+	0.981253i	$0.438268\pi$
$509$	−10.4865	+	39.1362i	−0.464806	+	1.73468i	−0.657530	+	0.753428i	$0.728399\pi$
$510$	−6.76667	−	15.2747i	−0.299633	−	0.676376i
$511$	−19.8299	−	11.4488i	−0.877225	−	0.506466i
$512$	20.2249	−	10.1467i	0.893821	−	0.448423i
$513$	−10.9291	−	16.9594i	−0.482532	−	0.748776i
$514$	−5.39480	+	1.24155i	−0.237954	+	0.0547624i
$515$	−0.234417	−	0.874857i	−0.0103297	−	0.0385508i
$516$	15.1550	+	20.2187i	0.667163	+	0.890081i
$517$	2.81416	−	10.5026i	0.123767	−	0.461904i
$518$	39.1620	+	1.39475i	1.72068	+	0.0612816i
$519$	−3.91801	+	11.3356i	−0.171982	+	0.497579i
$520$	−1.09070	−	6.98030i	−0.0478302	−	0.306106i
$521$	−30.8271			−1.35056			−0.675279	−	0.737562i	$-0.735977\pi$
$521$	−30.8271			−1.35056			−0.675279	+	0.737562i	$0.735977\pi$
$522$	−3.44107	−	9.54426i	−0.150612	−	0.417741i
$523$	23.5484	−	23.5484i	1.02970	−	1.02970i	0.0301559	−	0.999545i	$-0.490400\pi$
$523$	23.5484	−	23.5484i	1.02970	−	1.02970i	0.999545	−	0.0301559i	$-0.00960038\pi$
$524$	−18.5020	−	21.3438i	−0.808262	−	0.932407i
$525$	−0.499123	+	7.01975i	−0.0217835	+	0.306367i
$526$	20.3177	+	21.8184i	0.885895	+	0.951327i
$527$	−31.3785	−	54.3492i	−1.36687	−	2.36749i
$528$	−39.7868	+	1.92787i	−1.73150	+	0.0838999i
$529$	8.71905	−	15.1018i	0.379089	−	0.656602i
$530$	−11.5351	+	2.65467i	−0.501052	+	0.115311i
$531$	17.0422	−	2.05205i	0.739568	−	0.0890512i
$532$	−29.8194	−	10.3139i	−1.29284	−	0.447165i
$533$	−1.94726	−	7.26727i	−0.0843452	−	0.314780i
$534$	17.1267	−	13.8162i	0.741146	−	0.597885i
$535$	−0.584397	−	1.01221i	−0.0252657	−	0.0437615i
$536$	9.26002	−	4.09977i	0.399972	−	0.177083i
$537$	1.32108	+	6.83907i	0.0570087	+	0.295127i
$538$	3.08546	+	5.81262i	0.133024	+	0.250600i
$539$	38.6573	+	38.6573i	1.66509	+	1.66509i
$540$	−4.99372	−	9.11388i	−0.214896	−	0.392199i
$541$	9.69243	−	9.69243i	0.416710	−	0.416710i	−0.467358	−	0.884068i	$-0.654794\pi$
$541$	9.69243	−	9.69243i	0.416710	−	0.416710i	0.884068	+	0.467358i	$0.154794\pi$
$542$	−7.66638	+	25.0136i	−0.329299	+	1.07443i
$543$	−18.9081	+	3.65242i	−0.811426	+	0.156740i
$544$	38.4465	−	3.22941i	1.64838	−	0.138460i
$545$	10.6192	−	6.13102i	0.454879	−	0.262624i
$546$	2.64462	−	24.7188i	0.113179	−	1.05787i
$547$	5.30082	−	1.42035i	0.226647	−	0.0607298i	−0.143708	−	0.989620i	$-0.545903\pi$
$547$	5.30082	−	1.42035i	0.226647	−	0.0607298i	0.370355	+	0.928890i	$0.379236\pi$
$548$	−23.7243	+	11.5304i	−1.01345	+	0.492555i
$549$	−7.08325	+	5.31167i	−0.302306	+	0.226697i
$550$	6.89247	+	4.31354i	0.293896	+	0.183930i
$551$	−8.04126	−	4.64263i	−0.342569	−	0.197782i
$552$	−25.5770	+	17.7857i	−1.08863	+	0.757008i
$553$	7.73125	−	4.46364i	0.328766	−	0.189813i
$554$	−24.9693	−	0.889276i	−1.06084	−	0.0377817i
$555$	11.7824	+	0.837763i	0.500136	+	0.0355610i
$556$	19.1258	+	22.0634i	0.811115	+	0.935698i
$557$	27.2943	+	27.2943i	1.15650	+	1.15650i	0.985224	+	0.171273i	$0.0547879\pi$
$557$	27.2943	+	27.2943i	1.15650	+	1.15650i	0.171273	+	0.985224i	$0.445212\pi$
$558$	−22.2943	−	32.0460i	−0.943794	−	1.35662i
$559$			18.2200i			0.770622i
$560$	−14.9427	−	6.39175i	−0.631444	−	0.270101i
$561$	−64.1935	−	22.1877i	−2.71025	−	0.936764i
$562$	1.88282	−	1.75332i	0.0794218	−	0.0739592i
$563$	25.2719	+	6.77157i	1.06508	+	0.285388i	0.748471	−	0.663168i	$-0.230788\pi$
$563$	25.2719	+	6.77157i	1.06508	+	0.285388i	0.316611	+	0.948556i	$0.397455\pi$
$564$	−0.928321	+	6.48502i	−0.0390894	+	0.273068i
$565$	17.5828	−	4.71129i	0.739713	−	0.198205i
$566$	27.2764	+	17.0705i	1.14651	+	0.717526i
$567$	−8.68038	−	35.5226i	−0.364542	−	1.49181i
$568$	−19.9558	+	16.0913i	−0.837325	+	0.675174i
$569$	17.1621	−	29.7256i	0.719471	−	1.24616i	−0.241739	−	0.970341i	$-0.577718\pi$
$569$	17.1621	−	29.7256i	0.719471	−	1.24616i	0.961210	−	0.275819i	$-0.0889489\pi$
$570$	−8.87292	−	3.42498i	−0.371646	−	0.143457i
$571$	30.0224	+	8.04449i	1.25640	+	0.336651i	0.824806	−	0.565417i	$-0.191285\pi$
$571$	30.0224	+	8.04449i	1.25640	+	0.336651i	0.431594	+	0.902068i	$0.357951\pi$
$572$	−23.7899	−	16.0945i	−0.994705	−	0.672945i
$573$	3.50621	+	7.21020i	0.146474	+	0.301210i
$574$	−16.5476	−	5.07166i	−0.690684	−	0.211687i
$575$	6.35910			0.265193
$576$	23.6620	−	4.01386i	0.985915	−	0.167244i
$577$	−27.4483			−1.14269			−0.571344	−	0.820711i	$-0.693578\pi$
$577$	−27.4483			−1.14269			−0.571344	+	0.820711i	$0.693578\pi$
$578$	39.9116	+	12.2324i	1.66010	+	0.508803i
$579$	12.6788	+	0.901499i	0.526914	+	0.0374650i
$580$	−3.96132	−	2.67994i	−0.164485	−	0.111279i
$581$	−25.3686	−	6.79751i	−1.05247	−	0.282008i
$582$	2.82443	+	18.0503i	0.117076	+	0.748211i
$583$	−24.0608	+	41.6746i	−0.996498	+	1.72598i
$584$	12.4083	−	10.0054i	0.513459	−	0.414026i
$585$	1.06026	−	7.41817i	0.0438366	−	0.306704i
$586$	−8.27139	−	5.17651i	−0.341688	−	0.213840i
$587$	29.1190	−	7.80242i	1.20187	−	0.322040i	0.398303	−	0.917254i	$-0.369599\pi$
$587$	29.1190	−	7.80242i	1.20187	−	0.322040i	0.803568	+	0.595214i	$0.202933\pi$
$588$	−25.9043	−	20.3455i	−1.06828	−	0.839035i
$589$	−34.5103	−	9.24701i	−1.42197	−	0.381016i
$590$	5.92179	−	5.51449i	0.243796	−	0.227028i
$591$	7.16258	+	37.0799i	0.294629	+	1.52526i
$592$	−10.7284	+	25.0808i	−0.440933	+	1.03082i
$593$			2.30054i			0.0944719i	0.998884	+	0.0472359i	$0.0150413\pi$
$593$			2.30054i			0.0944719i	−0.998884	+	0.0472359i	$0.984959\pi$
$594$	−40.9515	−	10.3934i	−1.68026	−	0.426446i
$595$	−19.5952	−	19.5952i	−0.803324	−	0.803324i
$596$	11.2584	+	12.9876i	0.461161	+	0.531992i
$597$	17.2678	−	25.5361i	0.706725	−	1.04512i
$598$	−22.4493	−	0.799525i	−0.918018	−	0.0326950i
$599$	35.6581	−	20.5872i	1.45695	−	0.841172i	0.458092	−	0.888905i	$-0.348533\pi$
$599$	35.6581	−	20.5872i	1.45695	−	0.841172i	0.998860	+	0.0477328i	$0.0151996\pi$
$600$	−4.43323	−	2.08482i	−0.180986	−	0.0851122i
$601$	33.4767	+	19.3278i	1.36554	+	0.788397i	0.990355	−	0.138551i	$-0.0442446\pi$
$601$	33.4767	+	19.3278i	1.36554	+	0.788397i	0.375189	+	0.926948i	$0.377578\pi$
$602$	35.5291	+	22.2353i	1.44806	+	0.906242i
$603$	10.6643	−	1.28408i	0.434283	−	0.0522919i
$604$	19.4918	−	9.47336i	0.793110	−	0.385465i
$605$	21.3048	−	5.70861i	0.866165	−	0.232088i
$606$	−24.9325	−	18.1856i	−1.01281	−	0.738738i
$607$	26.0267	−	15.0265i	1.05639	−	0.609907i	0.131958	−	0.991255i	$-0.457873\pi$
$607$	26.0267	−	15.0265i	1.05639	−	0.609907i	0.924431	+	0.381348i	$0.124540\pi$
$608$	14.1769	−	16.7769i	0.574949	−	0.680394i
$609$	−11.0260	−	12.7139i	−0.446795	−	0.515195i
$610$	−1.22302	+	3.99041i	−0.0495185	+	0.161567i
$611$	−3.34024	+	3.34024i	−0.135131	+	0.135131i
$612$	39.9960	+	8.65732i	1.61674	+	0.349951i
$613$	−8.95042	−	8.95042i	−0.361504	−	0.361504i	0.502862	−	0.864367i	$-0.332280\pi$
$613$	−8.95042	−	8.95042i	−0.361504	−	0.361504i	−0.864367	+	0.502862i	$0.832280\pi$
$614$	−1.96351	−	3.69901i	−0.0792408	−	0.149280i
$615$	−4.93078	−	1.70426i	−0.198828	−	0.0687225i
$616$	−60.4171	+	26.7490i	−2.43427	+	1.07775i
$617$	5.19227	+	8.99328i	0.209033	+	0.362056i	0.951410	−	0.307926i	$-0.0996351\pi$
$617$	5.19227	+	8.99328i	0.209033	+	0.362056i	−0.742377	+	0.669982i	$0.766302\pi$
$618$	2.06971	+	0.798915i	0.0832559	+	0.0321371i
$619$	−4.42058	−	16.4978i	−0.177678	−	0.663103i	−0.996080	−	0.0884572i	$-0.971806\pi$
$619$	−4.42058	−	16.4978i	−0.177678	−	0.663103i	0.818402	−	0.574646i	$-0.194860\pi$
$620$	−17.3919	−	6.01549i	−0.698475	−	0.241588i
$621$	−31.4612	+	10.1004i	−1.26250	+	0.405316i
$622$	−24.5604	+	5.65229i	−0.984784	+	0.226636i
$623$	18.2502	−	31.6103i	0.731179	−	1.26644i
$624$	15.3883	+	7.91733i	0.616026	+	0.316947i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−8.97213	−	9.63481i	−0.358598	−	0.385085i
$627$	−34.7734	+	16.9098i	−1.38872	+	0.675311i
$628$	−14.0227	−	16.1766i	−0.559568	−	0.645515i
$629$	−32.8899	+	32.8899i	−1.31141	+	1.31141i
$630$	−13.1716	−	11.1205i	−0.524768	−	0.443052i
$631$	39.7996			1.58440			0.792199	−	0.610263i	$-0.208936\pi$
$631$	39.7996			1.58440			0.792199	+	0.610263i	$0.208936\pi$
$632$	0.959401	+	6.14003i	0.0381629	+	0.244237i
$633$	14.6043	+	16.8401i	0.580468	+	0.669332i
$634$	−27.6859	−	0.986026i	−1.09955	−	0.0391601i
$635$	1.97961	−	7.38800i	0.0785584	−	0.293184i
$636$	11.3969	−	26.6598i	0.451917	−	1.05713i
$637$	−6.14727	−	22.9419i	−0.243564	−	0.908992i
$638$	−18.9487	+	4.36081i	−0.750185	+	0.172646i
$639$	−25.2341	+	10.1266i	−0.998244	+	0.400602i
$640$	7.89856	−	8.10017i	0.312218	−	0.320187i
$641$	−6.75802	−	3.90174i	−0.266926	−	0.154110i	0.360564	−	0.932734i	$-0.382584\pi$
$641$	−6.75802	−	3.90174i	−0.266926	−	0.154110i	−0.627490	+	0.778625i	$0.715918\pi$
$642$	2.84670	+	0.304564i	0.112350	+	0.0120202i
$643$	−7.66887	+	28.6206i	−0.302431	+	1.12869i	0.632703	+	0.774394i	$0.281945\pi$
$643$	−7.66887	+	28.6206i	−0.302431	+	1.12869i	−0.935134	+	0.354293i	$0.884721\pi$
$644$	−28.9557	+	42.8005i	−1.14101	+	1.68658i
$645$	10.4658	+	7.07710i	0.412090	+	0.278661i
$646$	33.0803	−	17.5597i	1.30153	−	0.690877i
$647$		−	9.11617i		−	0.358393i	−0.983813	−	0.179197i	$-0.942650\pi$
$647$		−	9.11617i		−	0.358393i	0.983813	−	0.179197i	$-0.0573499\pi$
$648$	25.2446	+	3.27301i	0.991700	+	0.128576i
$649$		−	32.8971i		−	1.29132i
$650$	−1.65624	−	3.12016i	−0.0649633	−	0.122383i
$651$	−53.6416	−	36.2731i	−2.10238	−	1.42166i
$652$	−4.43587	−	22.9907i	−0.173722	−	0.900385i
$653$	4.25997	−	15.8984i	0.166706	−	0.622154i	−0.831111	−	0.556107i	$-0.812295\pi$
$653$	4.25997	−	15.8984i	0.166706	−	0.622154i	0.997817	−	0.0660471i	$-0.0210387\pi$
$654$	−3.19524	+	29.8653i	−0.124944	+	1.16783i
$655$	−12.2312	−	7.06169i	−0.477913	−	0.275923i
$656$	7.44388	−	9.47348i	0.290635	−	0.369877i
$657$	15.6903	−	6.29662i	0.612137	−	0.245655i
$658$	2.43713	+	10.5898i	0.0950091	+	0.412835i
$659$	−3.00609	−	11.2189i	−0.117101	−	0.437026i	0.882335	−	0.470622i	$-0.155971\pi$
$659$	−3.00609	−	11.2189i	−0.117101	−	0.437026i	−0.999435	+	0.0335966i	$0.989304\pi$
$660$	−18.4855	+	7.41371i	−0.719547	+	0.288578i
$661$	−9.02130	+	33.6680i	−0.350888	+	1.30953i	0.534693	+	0.845046i	$0.320427\pi$
$661$	−9.02130	+	33.6680i	−0.350888	+	1.30953i	−0.885581	+	0.464485i	$0.846239\pi$
$662$	0.878004	−	24.6528i	0.0341246	−	0.958158i
$663$	19.3327	+	22.2924i	0.750821	+	0.865765i
$664$	10.7771	−	14.7687i	0.418232	−	0.573137i
$665$	−15.7764			−0.611781
$666$	−18.6654	+	22.1081i	−0.723271	+	0.856670i
$667$	−10.7528	+	10.7528i	−0.416352	+	0.416352i
$668$	−8.45585	−	0.603071i	−0.327167	−	0.0233335i
$669$	9.97607	−	4.85121i	0.385697	−	0.187559i
$670$	3.70560	−	3.45073i	0.143160	−	0.133313i
$671$	8.48392	+	14.6946i	0.327518	+	0.567278i
$672$	34.2185	−	20.3452i	1.32001	−	0.784834i
$673$	−9.81601	+	17.0018i	−0.378379	+	0.655372i	−0.990827	−	0.135139i	$-0.956852\pi$
$673$	−9.81601	+	17.0018i	−0.378379	+	0.655372i	0.612447	+	0.790511i	$0.290185\pi$
$674$	−7.95119	−	34.5496i	−0.306269	−	1.33080i
$675$	−3.84927	−	3.49044i	−0.148158	−	0.134347i
$676$	−5.91056	−	12.1612i	−0.227329	−	0.467739i
$677$	9.41293	+	35.1295i	0.361768	+	1.35014i	0.871749	+	0.489952i	$0.162986\pi$
$677$	9.41293	+	35.1295i	0.361768	+	1.35014i	−0.509981	+	0.860186i	$0.670348\pi$
$678$	−16.0565	+	41.5968i	−0.616646	+	1.59751i
$679$	15.1526	+	26.2451i	0.581505	+	1.00720i
$680$	17.6394	−	7.80967i	0.676441	−	0.299487i
$681$	−13.2935	−	4.59474i	−0.509410	−	0.176071i
$682$	−66.0833	+	35.0784i	−2.53046	+	1.34322i
$683$	−21.2677	−	21.2677i	−0.813787	−	0.813787i	0.171412	−	0.985199i	$-0.445167\pi$
$683$	−21.2677	−	21.2677i	−0.813787	−	0.813787i	−0.985199	+	0.171412i	$0.945167\pi$
$684$	19.5858	−	12.6156i	0.748880	−	0.482370i
$685$	−9.32598	+	9.32598i	−0.356327	+	0.356327i
$686$	−13.7821	−	4.22406i	−0.526203	−	0.161275i
$687$	1.30807	+	1.50832i	0.0499059	+	0.0575460i
$688$	−23.3504	+	17.4945i	−0.890225	+	0.666971i
$689$	18.1055	−	10.4532i	0.689764	−	0.398236i
$690$	−9.17912	+	12.5846i	−0.349443	+	0.479088i
$691$	−28.0758	+	7.52289i	−1.06805	+	0.286184i	−0.749693	−	0.661786i	$-0.769799\pi$
$691$	−28.0758	+	7.52289i	−1.06805	+	0.286184i	−0.318361	+	0.947970i	$0.603132\pi$
$692$	−13.0883	−	4.52696i	−0.497542	−	0.172089i
$693$	−69.5791	+	8.37801i	−2.64309	+	0.318254i
$694$	26.5484	−	42.4208i	1.00776	−	1.61027i
$695$	12.6436	+	7.29980i	0.479600	+	0.276897i
$696$	11.0216	−	3.97103i	0.417773	−	0.150521i
$697$	17.7910	−	10.2716i	0.673881	−	0.389065i
$698$	−0.376442	+	10.5698i	−0.0142485	+	0.400074i
$699$	21.2325	−	31.3992i	0.803088	−	1.18763i
$700$	−8.10558	−	0.578090i	−0.306362	−	0.0218498i
$701$	9.79768	+	9.79768i	0.370053	+	0.370053i	0.867497	−	0.497443i	$-0.165728\pi$
$701$	9.79768	+	9.79768i	0.370053	+	0.370053i	−0.497443	+	0.867497i	$0.665728\pi$
$702$	13.1501	+	12.8061i	0.496317	+	0.483336i
$703$			26.4801i			0.998717i
$704$	−2.21618	−	45.9423i	−0.0835256	−	1.73152i
$705$	0.621244	+	3.21611i	0.0233974	+	0.121126i
$706$	−7.21078	−	7.74337i	−0.271381	−	0.291426i
$707$	−49.4448	−	13.2487i	−1.85956	−	0.498268i
$708$	2.36524	+	19.6791i	0.0888913	+	0.739587i
$709$	15.8294	−	4.24148i	0.594486	−	0.159292i	0.0509836	−	0.998699i	$-0.483764\pi$
$709$	15.8294	−	4.24148i	0.594486	−	0.159292i	0.543503	+	0.839407i	$0.317098\pi$
$710$	−6.79981	+	10.8652i	−0.255192	+	0.407764i
$711$	−0.932633	+	6.52519i	−0.0349765	+	0.244714i
$712$	15.9493	+	19.7797i	0.597725	+	0.741275i
$713$	−29.2563	+	50.6734i	−1.09566	+	1.89773i
$714$	67.0636	−	10.4938i	2.50979	−	0.392720i
$715$	−13.8720	−	3.71699i	−0.518783	−	0.139007i
$716$	−7.89740	+	1.52374i	−0.295140	+	0.0569449i
$717$	22.9032	+	1.62848i	0.855335	+	0.0608167i
$718$	2.84157	−	9.27135i	0.106046	−	0.346004i
$719$	−8.31490			−0.310093			−0.155047	−	0.987907i	$-0.549553\pi$
$719$	−8.31490			−0.310093			−0.155047	+	0.987907i	$0.549553\pi$
$720$	10.5250	−	5.76398i	0.392245	−	0.214811i
$721$	3.68001			0.137051
$722$	−1.62593	+	5.30503i	−0.0605110	+	0.197433i
$723$	−8.27186	−	17.0103i	−0.307634	−	0.632620i
$724$	−4.21273	−	21.8342i	−0.156565	−	0.811460i
$725$	−2.30986	−	0.618926i	−0.0857862	−	0.0229863i
$726$	−19.4555	+	50.4023i	−0.722060	+	1.87060i
$727$	−11.1086	+	19.2406i	−0.411994	+	0.713594i	−0.995108	−	0.0987964i	$-0.968501\pi$
$727$	−11.1086	+	19.2406i	−0.411994	+	0.713594i	0.583114	+	0.812390i	$0.301834\pi$
$728$	28.5421	+	3.05992i	1.05784	+	0.113408i
$729$	24.5880	+	11.1548i	0.910667	+	0.413140i
$730$	4.22806	−	6.75588i	0.156487	−	0.250046i
$731$	−48.0543	+	12.8761i	−1.77735	+	0.476241i
$732$	−6.13162	−	8.18036i	−0.226631	−	0.302355i
$733$	2.10088	+	0.562928i	0.0775977	+	0.0207922i	0.297409	−	0.954750i	$-0.403878\pi$
$733$	2.10088	+	0.562928i	0.0775977	+	0.0207922i	−0.219811	+	0.975542i	$0.570544\pi$
$734$	−10.4190	−	11.1885i	−0.384572	−	0.412977i
$735$	−15.5659	−	5.38015i	−0.574157	−	0.198450i
$736$	−20.5307	−	29.5383i	−0.756772	−	1.08879i
$737$		−	20.5856i		−	0.758280i
$738$	10.4901	−	7.29795i	0.386147	−	0.268641i
$739$	23.9730	+	23.9730i	0.881861	+	0.881861i	0.993724	−	0.111862i	$-0.0356816\pi$
$739$	23.9730	+	23.9730i	0.881861	+	0.881861i	−0.111862	+	0.993724i	$0.535682\pi$
$740$	−0.970306	+	13.6050i	−0.0356692	+	0.500128i
$741$	16.7565	+	1.19143i	0.615565	+	0.0437684i
$742$	1.71174	−	48.0627i	0.0628401	−	1.76444i
$743$	8.12156	−	4.68898i	0.297951	−	0.172022i	−0.343571	−	0.939127i	$-0.611637\pi$
$743$	8.12156	−	4.68898i	0.297951	−	0.172022i	0.641522	+	0.767105i	$0.278303\pi$
$744$	37.0092	−	25.7353i	1.35682	−	0.943501i
$745$	7.44263	+	4.29701i	0.272677	+	0.157430i
$746$	−6.75732	+	10.7973i	−0.247403	+	0.395318i
$747$	15.5143	−	11.6340i	0.567638	−	0.425667i
$748$	25.6361	−	74.1188i	0.937350	−	2.71005i
$749$	4.58710	−	1.22911i	0.167609	−	0.0449106i
$750$	−2.43559	−	0.260580i	−0.0889352	−	0.00951503i
$751$	19.6398	−	11.3391i	0.716667	−	0.413768i	−0.0968574	−	0.995298i	$-0.530879\pi$
$751$	19.6398	−	11.3391i	0.716667	−	0.413768i	0.813525	+	0.581530i	$0.197546\pi$
$752$	−7.48802	−	1.07355i	−0.273060	−	0.0391484i
$753$	8.75437	−	1.69105i	0.319027	−	0.0616253i
$754$	8.07660	+	2.47539i	0.294133	+	0.0901483i
$755$	7.66220	−	7.66220i	0.278856	−	0.278856i
$756$	41.0201	−	10.0144i	1.49189	−	0.364219i
$757$	26.8564	+	26.8564i	0.976114	+	0.976114i	0.999721	−	0.0236073i	$-0.00751513\pi$
$757$	26.8564	+	26.8564i	0.976114	+	0.976114i	−0.0236073	+	0.999721i	$0.507515\pi$
$758$	12.2125	−	6.48262i	0.443576	−	0.235460i
$759$	12.0105	+	62.1769i	0.435953	+	2.25688i
$760$	3.95704	−	10.2447i	0.143537	−	0.371615i
$761$	9.81438	+	16.9990i	0.355771	+	0.616214i	0.987250	−	0.159180i	$-0.0508850\pi$
$761$	9.81438	+	16.9990i	0.355771	+	0.616214i	−0.631479	+	0.775393i	$0.717552\pi$
$762$	11.7633	+	14.5819i	0.426140	+	0.528248i
$763$	12.8948	+	48.1241i	0.466824	+	1.74221i
$764$	−8.32650	+	4.04683i	−0.301242	+	0.146409i
$765$	20.3144	−	2.44605i	0.734468	−	0.0884371i
$766$	0.294860	+	1.28123i	0.0106537	+	0.0462927i
$767$	−7.14606	+	12.3773i	−0.258029	+	0.446920i
$768$	4.62890	+	27.3235i	0.167031	+	0.985952i
$769$	−22.7718	−	39.4420i	−0.821173	−	1.42231i	−0.904809	−	0.425817i	$-0.859987\pi$
$769$	−22.7718	−	39.4420i	−0.821173	−	1.42231i	0.0836360	−	0.996496i	$-0.473347\pi$
$770$	−24.1772	+	22.5143i	−0.871287	+	0.811360i
$771$	0.480860	−	6.76289i	0.0173177	−	0.243560i
$772$	−1.04413	+	14.6400i	−0.0375789	+	0.526906i
$773$	2.79790	−	2.79790i	0.100633	−	0.100633i	−0.654998	−	0.755631i	$-0.727330\pi$
$773$	2.79790	−	2.79790i	0.100633	−	0.100633i	0.755631	+	0.654998i	$0.227330\pi$
$774$	−29.1125	+	10.4962i	−1.04643	+	0.377278i
$775$	−9.20141			−0.330524
$776$	−20.8434	+	3.25686i	−0.748236	+	0.116915i
$777$	−15.6784	+	45.3608i	−0.562458	+	1.62731i
$778$	0.263753	−	7.40571i	0.00945599	−	0.265508i
$779$	3.02697	−	11.2968i	0.108452	−	0.404750i
$780$	8.56550	+	1.22614i	0.306694	+	0.0439029i
$781$	13.4870	+	50.3341i	0.482602	+	1.80110i
$782$	−13.7563	−	59.7739i	−0.491923	−	2.13751i
$783$	12.4110	−	0.606754i	0.443532	−	0.0216836i
$784$	23.4995	−	29.9066i	0.839266	−	1.06809i
$785$	−9.27009	−	5.35209i	−0.330864	−	0.191024i
$786$	31.6303	−	14.0122i	1.12822	−	0.499798i
$787$	11.8721	−	44.3073i	0.423195	−	1.57939i	−0.344637	−	0.938736i	$-0.611998\pi$
$787$	11.8721	−	44.3073i	0.423195	−	1.57939i	0.767833	−	0.640650i	$-0.221335\pi$
$788$	−42.8179	+	8.26138i	−1.52533	+	0.294299i
$789$	−32.8373	+	15.9683i	−1.16904	+	0.568487i
$790$	1.45687	+	2.74456i	0.0518331	+	0.0976471i
$791$			73.9604i			2.62973i
$792$	12.0115	−	47.2841i	0.426809	−	1.68017i
$793$		−	7.37167i		−	0.261776i
$794$	−8.76428	+	4.65226i	−0.311033	+	0.165103i
$795$	1.02817	−	14.4603i	0.0364654	−	0.512855i
$796$	29.4822	+	19.9455i	1.04497	+	0.706951i
$797$	−4.04083	+	15.0806i	−0.143134	+	0.534182i	0.856698	+	0.515819i	$0.172512\pi$
$797$	−4.04083	+	15.0806i	−0.143134	+	0.534182i	−0.999831	+	0.0183633i	$0.994154\pi$
$798$	22.7726	−	31.2213i	0.806141	−	1.10522i
$799$	−11.1703	−	6.44916i	−0.395176	−	0.228155i
$800$	2.40844	−	5.11853i	0.0851513	−	0.180968i
$801$	10.0372	+	25.0114i	0.354649	+	0.883735i
$802$	−16.0560	+	3.69510i	−0.566958	+	0.130479i
$803$	−8.38608	−	31.2973i	−0.295938	−	1.10446i
$804$	1.48007	+	12.3144i	0.0521980	+	0.434294i
$805$	−6.68725	+	24.9571i	−0.235695	+	0.879624i
$806$	32.4834	+	1.15689i	1.14418	+	0.0407496i
$807$	−7.91349	+	1.52862i	−0.278568	+	0.0538100i
$808$	21.0051	−	28.7850i	0.738957	−	1.01265i
$809$	−1.83099			−0.0643740			−0.0321870	−	0.999482i	$-0.510247\pi$
$809$	−1.83099			−0.0643740			−0.0321870	+	0.999482i	$0.510247\pi$
$810$	12.4638	−	2.57935i	0.437934	−	0.0906290i
$811$	−18.7171	+	18.7171i	−0.657247	+	0.657247i	−0.954728	−	0.297481i	$-0.903854\pi$
$811$	−18.7171	+	18.7171i	−0.657247	+	0.657247i	0.297481	+	0.954728i	$0.403854\pi$
$812$	14.6836	−	12.7285i	0.515292	−	0.446684i
$813$	−26.5429	−	17.9486i	−0.930900	−	0.629486i
$814$	37.7896	+	40.5807i	1.32452	+	1.42235i
$815$	−5.85368	−	10.1389i	−0.205045	−	0.355149i
$816$	−10.0066	+	46.1813i	−0.350301	+	1.61667i
$817$	−14.1612	+	24.5280i	−0.495439	+	0.858126i
$818$	9.35245	−	2.15236i	0.327001	−	0.0752554i
$819$	27.9987	+	11.9621i	0.978352	+	0.417991i
$820$	1.96914	−	5.69315i	0.0687654	−	0.198814i
$821$	−13.1045	−	48.9068i	−0.457352	−	1.70686i	−0.681081	−	0.732208i	$-0.738490\pi$
$821$	−13.1045	−	48.9068i	−0.457352	−	1.70686i	0.223729	−	0.974651i	$-0.428177\pi$
$822$	−4.99433	−	31.9178i	−0.174197	−	1.11326i
$823$	−9.84581	−	17.0534i	−0.343203	−	0.594445i	0.641822	−	0.766853i	$-0.278179\pi$
$823$	−9.84581	−	17.0534i	−0.343203	−	0.594445i	−0.985026	+	0.172408i	$0.944845\pi$
$824$	−0.923024	+	2.38970i	−0.0321551	+	0.0832490i
$825$	−7.52332	+	6.52448i	−0.261928	+	0.227153i
$826$	15.4150	+	29.0399i	0.536356	+	1.01043i
$827$	8.70036	+	8.70036i	0.302541	+	0.302541i	0.842007	−	0.539466i	$-0.181374\pi$
$827$	8.70036	+	8.70036i	0.302541	+	0.302541i	−0.539466	+	0.842007i	$0.681374\pi$
$828$	−11.6551	−	36.3308i	−0.405043	−	1.26258i
$829$	−6.17374	+	6.17374i	−0.214423	+	0.214423i	−0.806143	−	0.591720i	$-0.798449\pi$
$829$	−6.17374	+	6.17374i	−0.214423	+	0.214423i	0.591720	+	0.806143i	$0.298449\pi$
$830$	2.67874	−	8.74011i	0.0929806	−	0.303374i
$831$	9.99637	−	28.9216i	0.346770	−	1.00328i
$832$	−9.14598	+	17.7669i	−0.317080	+	0.615958i
$833$	56.1640	−	32.4263i	1.94597	−	1.12350i
$834$	−32.6968	+	14.4846i	−1.13220	+	0.501562i
$835$	−4.09423	+	1.09705i	−0.141687	+	0.0379649i
$836$	−19.5170	−	40.1571i	−0.675011	−	1.38886i
$837$	45.5234	−	14.6150i	1.57352	−	0.505168i
$838$	34.5318	+	21.6111i	1.19288	+	0.746544i
$839$	1.32309	+	0.763888i	0.0456782	+	0.0263723i	0.522665	−	0.852538i	$-0.324938\pi$
$839$	1.32309	+	0.763888i	0.0456782	+	0.0263723i	−0.476987	+	0.878910i	$0.658271\pi$
$840$	12.8441	−	15.2064i	0.443165	−	0.524672i
$841$	−20.1623	+	11.6407i	−0.695253	+	0.401404i
$842$	−14.2805	−	0.508597i	−0.492139	−	0.0175274i
$843$	1.37798	+	2.83370i	0.0474603	+	0.0975977i
$844$	−19.4489	+	16.8594i	−0.669458	+	0.580323i
$845$	−4.78056	−	4.78056i	−0.164456	−	0.164456i
$846$	−7.26140	−	3.41290i	−0.249652	−	0.117338i
$847$			89.6170i			3.07928i
$848$	30.7812	+	13.1667i	1.05703	+	0.452146i
$849$	−29.7729	+	25.8201i	−1.02180	+	0.886143i
$850$	7.05880	−	6.57330i	0.242115	−	0.225462i
$851$	41.8898	+	11.2243i	1.43596	+	0.384765i
$852$	−11.6869	−	29.1403i	−0.400386	−	0.998331i
$853$	11.8228	−	3.16792i	0.404806	−	0.108467i	−0.0506702	−	0.998715i	$-0.516136\pi$
$853$	11.8228	−	3.16792i	0.404806	−	0.108467i	0.455476	+	0.890248i	$0.349469\pi$
$854$	−14.3748	−	8.99623i	−0.491896	−	0.307845i
$855$	7.19303	−	9.16238i	0.245996	−	0.313347i
$856$	−0.352391	+	3.28701i	−0.0120445	+	0.112348i
$857$	−18.0467	+	31.2579i	−0.616465	+	1.06775i	0.373661	+	0.927566i	$0.378103\pi$
$857$	−18.0467	+	31.2579i	−0.616465	+	1.06775i	−0.990126	+	0.140183i	$0.955231\pi$
$858$	27.3796	−	22.0872i	0.934724	−	0.754045i
$859$	−44.0474	−	11.8025i	−1.50288	−	0.402695i	−0.588815	−	0.808268i	$-0.700405\pi$
$859$	−44.0474	−	11.8025i	−1.50288	−	0.402695i	−0.914063	+	0.405573i	$0.867072\pi$
$860$	−8.17454	+	12.0831i	−0.278750	+	0.412030i
$861$	11.8738	−	17.5593i	0.404659	−	0.598421i
$862$	−31.3134	−	9.59721i	−1.06654	−	0.326882i
$863$	9.56786			0.325694			0.162847	−	0.986651i	$-0.447932\pi$
$863$	9.56786			0.325694			0.162847	+	0.986651i	$0.447932\pi$
$864$	−3.78565	+	29.1491i	−0.128790	+	0.991672i
$865$	−6.92453			−0.235441
$866$	0.812647	+	0.249067i	0.0276149	+	0.00846364i
$867$	−28.6388	+	42.3517i	−0.972623	+	1.43834i
$868$	41.8980	−	61.9309i	1.42211	−	2.10207i
$869$	12.2021	+	3.26954i	0.413928	+	0.110912i
$870$	4.55906	−	3.67781i	0.154567	−	0.124689i
$871$	−4.47170	+	7.74521i	−0.151518	+	0.262436i
$872$	−34.4847	−	3.69701i	−1.16780	−	0.125196i
$873$	−22.1510	−	3.16599i	−0.749696	−	0.107153i
$874$	−29.6001	−	18.5247i	−1.00124	−	0.626609i
$875$	−3.92464	+	1.05160i	−0.132677	+	0.0355507i
$876$	7.26679	+	18.1192i	0.245522	+	0.612190i
$877$	−22.1933	−	5.94668i	−0.749415	−	0.200805i	−0.136156	−	0.990687i	$-0.543475\pi$
$877$	−22.1933	−	5.94668i	−0.749415	−	0.200805i	−0.613259	+	0.789882i	$0.710142\pi$
$878$	−30.1592	+	28.0848i	−1.01782	+	0.947816i
$879$	9.02844	−	7.82978i	0.304522	−	0.264092i
$880$	−8.55600	−	21.3471i	−0.288423	−	0.719609i
$881$			46.6020i			1.57006i	0.619457	+	0.785030i	$0.287353\pi$
$881$			46.6020i			1.57006i	−0.619457	+	0.785030i	$0.712647\pi$
$882$	33.1161	−	23.0388i	1.11508	−	0.775755i
$883$	29.7047	+	29.7047i	0.999641	+	0.999641i	1.00000		0.000358619i	$-0.000114152\pi$
$883$	29.7047	+	29.7047i	0.999641	+	0.999641i	−0.000358619		1.00000i	$0.500114\pi$
$884$	−25.7459	+	22.3180i	−0.865927	+	0.750634i
$885$	4.33400	+	8.91247i	0.145686	+	0.299589i
$886$	−15.3028	−	0.545004i	−0.514106	−	0.0183098i
$887$	−4.15164	+	2.39695i	−0.139399	+	0.0804818i	−0.568077	−	0.822975i	$-0.692313\pi$
$887$	−4.15164	+	2.39695i	−0.139399	+	0.0804818i	0.428679	+	0.903457i	$0.358979\pi$
$888$	−25.5235	−	21.5585i	−0.856513	−	0.723456i
$889$	26.9135	+	15.5385i	0.902649	+	0.521145i
$890$	10.7693	+	6.73982i	0.360989	+	0.225919i
$891$	26.8581	−	44.2291i	0.899779	−	1.48173i
$892$	5.59921	+	11.5206i	0.187475	+	0.385738i
$893$	−7.09283	+	1.90052i	−0.237353	+	0.0635984i
$894$	−19.2469	+	8.52634i	−0.643713	+	0.285164i
$895$	−3.48275	+	2.01076i	−0.116415	+	0.0672124i
$896$	23.4841	+	39.5171i	0.784549	+	1.32018i
$897$	8.98748	−	26.0027i	0.300083	−	0.868203i
$898$	5.05386	−	16.4896i	0.168650	−	0.550264i
$899$	15.5590	−	15.5590i	0.518922	−	0.518922i
$900$	4.03137	−	4.44388i	0.134379	−	0.148129i
$901$	40.3651	+	40.3651i	1.34476	+	1.34476i
$902$	−11.4828	−	21.6321i	−0.382334	−	0.720269i
$903$	−38.7809	+	33.6322i	−1.29055	+	1.11921i
$904$	−48.0278	−	18.5508i	−1.59738	−	0.616991i
$905$	−5.55921	−	9.62884i	−0.184794	−	0.320073i
$906$	4.10333	+	26.2236i	0.136324	+	0.871219i
$907$	14.6009	+	54.4912i	0.484814	+	1.80935i	0.580898	+	0.813976i	$0.302701\pi$
$907$	14.6009	+	54.4912i	0.484814	+	1.80935i	−0.0960847	+	0.995373i	$0.530632\pi$
$908$	5.30887	−	15.3489i	0.176181	−	0.509372i
$909$	30.2381	−	22.6753i	1.00294	−	0.752093i
$910$	13.9872	−	3.21899i	0.463671	−	0.106709i
$911$	22.3507	−	38.7125i	0.740511	−	1.28260i	−0.211752	−	0.977323i	$-0.567917\pi$
$911$	22.3507	−	38.7125i	0.740511	−	1.28260i	0.952263	−	0.305279i	$-0.0987496\pi$
$912$	14.5624	+	22.6188i	0.482208	+	0.748984i
$913$	−18.5821	−	32.1852i	−0.614979	−	1.06517i
$914$	21.4214	+	23.0036i	0.708558	+	0.760892i
$915$	−4.23439	−	2.86334i	−0.139984	−	0.0946592i
$916$	−1.74198	+	1.51005i	−0.0575568	+	0.0498934i
$917$	40.5770	−	40.5770i	1.33997	−	1.33997i
$918$	−24.4824	+	43.7328i	−0.808039	+	1.44340i
$919$	12.9901			0.428503			0.214252	−	0.976779i	$-0.431269\pi$
$919$	12.9901			0.428503			0.214252	+	0.976779i	$0.431269\pi$
$920$	−14.5292	−	10.6023i	−0.479012	−	0.349547i
$921$	5.03595	−	0.972775i	0.165940	−	0.0320540i
$922$	15.6564	+	0.557598i	0.515615	+	0.0183635i
$923$	5.85941	−	21.8676i	0.192865	−	0.719782i
$924$	−9.65672	−	80.3452i	−0.317683	−	2.64316i
$925$	1.76508	+	6.58738i	0.0580356	+	0.216592i
$926$	−52.9587	+	12.1878i	−1.74033	+	0.400516i
$927$	−1.67786	+	2.13723i	−0.0551080	+	0.0701958i
$928$	4.58260	+	12.7277i	0.150431	+	0.417806i
$929$	−38.7126	−	22.3507i	−1.27012	−	0.733304i	−0.295109	−	0.955464i	$-0.595356\pi$
$929$	−38.7126	−	22.3507i	−1.27012	−	0.733304i	−0.975010	+	0.222160i	$0.928689\pi$
$930$	13.2819	−	18.2095i	0.435531	−	0.597114i
$931$	9.55578	−	35.6627i	0.313178	−	1.16880i
$932$	36.2514	+	24.5251i	1.18745	+	0.803345i
$933$	2.18917	−	30.7888i	0.0716702	−	1.00798i
$934$	−30.1837	+	16.0222i	−0.987642	+	0.524261i
$935$		−	39.2135i		−	1.28242i
$936$	−14.7905	+	15.1812i	−0.483443	+	0.496212i
$937$		−	36.5421i		−	1.19378i	−0.802324	−	0.596889i	$-0.796403\pi$
$937$		−	36.5421i		−	1.19378i	0.802324	−	0.596889i	$-0.203597\pi$
$938$	9.64604	+	18.1719i	0.314954	+	0.593335i
$939$	14.5007	−	7.05147i	0.473212	−	0.230116i
$940$	−3.71380	+	0.716548i	−0.121131	+	0.0233712i
$941$	7.08695	−	26.4489i	0.231028	−	0.862208i	−0.748871	−	0.662715i	$-0.769404\pi$
$941$	7.08695	−	26.4489i	0.231028	−	0.862208i	0.979899	−	0.199493i	$-0.0639294\pi$
$942$	23.9728	−	10.6199i	0.781076	−	0.346015i
$943$	−16.5877	−	9.57692i	−0.540170	−	0.311868i
$944$	−22.7241	+	2.72624i	−0.739606	+	0.0887314i
$945$	17.7466	−	11.4364i	0.577297	−	0.372027i
$946$	13.3016	+	57.7985i	0.432474	+	1.87919i
$947$	4.62784	+	17.2713i	0.150384	+	0.561242i	0.999456	+	0.0329654i	$0.0104951\pi$
$947$	4.62784	+	17.2713i	0.150384	+	0.561242i	−0.849072	+	0.528277i	$0.822838\pi$
$948$	−7.53441	−	1.07854i	−0.244706	−	0.0350294i
$949$	−3.64333	+	13.5971i	−0.118267	+	0.441380i
$950$	0.195443	−	5.48770i	0.00634102	−	0.178045i
$951$	11.0839	−	32.0681i	0.359421	−	1.03988i
$952$	12.1004	+	77.4410i	0.392177	+	2.50988i
$953$	−12.6782			−0.410688			−0.205344	−	0.978690i	$-0.565831\pi$
$953$	−12.6782			−0.410688			−0.205344	+	0.978690i	$0.565831\pi$
$954$	27.1328	+	22.9077i	0.878456	+	0.741665i
$955$	−3.27314	+	3.27314i	−0.105916	+	0.105916i
$956$	−1.88612	+	26.4459i	−0.0610016	+	0.855322i
$957$	1.68897	−	23.7540i	0.0545967	−	0.767857i
$958$	28.1498	−	26.2137i	0.909479	−	0.846925i
$959$	−26.7939	−	46.4083i	−0.865219	−	1.49860i
$960$	6.65304	+	12.1547i	0.214726	+	0.392292i
$961$	26.8329	−	46.4760i	0.865579	−	1.49923i
$962$	−5.40298	−	23.4771i	−0.174199	−	0.756932i
$963$	−1.37760	+	3.22443i	−0.0443926	+	0.103906i
$964$	19.6439	−	9.54727i	0.632687	−	0.307497i
$965$	1.89937	+	7.08855i	0.0611429	+	0.228188i
$966$	−39.7372	−	49.2588i	−1.27852	−	1.58487i
$967$	8.76279	+	15.1776i	0.281792	+	0.488078i	0.971826	−	0.235699i	$-0.0757378\pi$
$967$	8.76279	+	15.1776i	0.281792	+	0.488078i	−0.690034	+	0.723777i	$0.742404\pi$
$968$	−58.1947	−	22.4778i	−1.87045	−	0.722464i
$969$	8.69953	+	45.0365i	0.279469	+	1.44678i
$970$	−9.31692	+	4.94561i	−0.299148	+	0.158794i
$971$	27.0084	+	27.0084i	0.866742	+	0.866742i	0.992110	−	0.125369i	$-0.0400114\pi$
$971$	27.0084	+	27.0084i	0.866742	+	0.866742i	−0.125369	+	0.992110i	$0.540011\pi$
$972$	−12.8866	+	28.3890i	−0.413337	+	0.910578i
$973$	−41.9451	+	41.9451i	−1.34470	+	1.34470i
$974$	−10.2758	−	3.14942i	−0.329258	−	0.100914i
$975$	4.24788	−	0.820548i	0.136041	−	0.0262786i
$976$	9.44740	−	7.07814i	0.302404	−	0.226566i
$977$	−26.0944	+	15.0656i	−0.834833	+	0.481991i	−0.855505	−	0.517795i	$-0.826753\pi$
$977$	−26.0944	+	15.0656i	−0.834833	+	0.481991i	0.0206713	+	0.999786i	$0.493420\pi$
$978$	28.5143	+	3.05070i	0.911787	+	0.0975507i
$979$	49.8900	−	13.3680i	1.59449	−	0.427243i
$980$	6.21635	−	17.9726i	0.198574	−	0.574114i
$981$	−33.8281	−	14.4527i	−1.08005	−	0.461439i
$982$	24.1208	−	38.5418i	0.769725	−	1.22992i
$983$	43.8679	+	25.3271i	1.39917	+	0.807810i	0.994305	−	0.106568i	$-0.0339861\pi$
$983$	43.8679	+	25.3271i	1.39917	+	0.807810i	0.404862	+	0.914378i	$0.367319\pi$
$984$	8.42432	+	12.1148i	0.268558	+	0.386205i
$985$	−18.8827	+	10.9019i	−0.601652	+	0.347364i
$986$	−0.820958	+	23.0510i	−0.0261446	+	0.734095i
$987$	−13.2754	−	0.943915i	−0.422560	−	0.0300451i
$988$	−1.37993	+	19.3484i	−0.0439015	+	0.615556i
$989$	32.7990	+	32.7990i	1.04295	+	1.04295i
$990$	−2.05226	−	24.3064i	−0.0652252	−	0.772510i
$991$		−	49.1106i		−	1.56005i	−0.625749	−	0.780024i	$-0.715207\pi$
$991$		−	49.1106i		−	1.56005i	0.625749	−	0.780024i	$-0.284793\pi$
$992$	29.7073	+	42.7409i	0.943207	+	1.35703i
$993$	28.5550	+	9.86966i	0.906165	+	0.313204i
$994$	−35.4913	−	38.1127i	−1.12572	−	1.20886i
$995$	17.1912	+	4.60637i	0.544998	+	0.146032i
$996$	13.4299	+	17.9172i	0.425544	+	0.567730i
$997$	−17.2125	+	4.61207i	−0.545125	+	0.146066i	−0.520864	−	0.853640i	$-0.674390\pi$
$997$	−17.2125	+	4.61207i	−0.545125	+	0.146066i	−0.0242611	+	0.999706i	$0.507723\pi$
$998$	−8.84729	+	14.1368i	−0.280056	+	0.447493i
$999$	−19.1957	−	29.7871i	−0.607324	−	0.942423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.13	✓	384
9.5	odd	6	inner	720.2.cf.a.491.22	yes	384
16.3	odd	4	inner	720.2.cf.a.371.22	yes	384
144.131	even	12	inner	720.2.cf.a.131.13	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.13	✓	384	1.1	even	1	trivial
720.2.cf.a.131.13	yes	384	144.131	even	12	inner
720.2.cf.a.371.22	yes	384	16.3	odd	4	inner
720.2.cf.a.491.22	yes	384	9.5	odd	6	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35213 - 0.414413i) q^{2} +(0.970230 - 1.43480i) q^{3} +(1.65652 + 1.12068i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-1.90648 + 1.53796i) q^{6} +(-2.03154 + 3.51873i) q^{7} +(-1.77541 - 2.20180i) q^{8} +(-1.11731 - 2.78417i) q^{9} +O(q^{10})\)	\(q+(-1.35213 - 0.414413i) q^{2} +(0.970230 - 1.43480i) q^{3} +(1.65652 + 1.12068i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-1.90648 + 1.53796i) q^{6} +(-2.03154 + 3.51873i) q^{7} +(-1.77541 - 2.20180i) q^{8} +(-1.11731 - 2.78417i) q^{9} +(-1.19880 - 0.750250i) q^{10} +(-5.55356 + 1.48807i) q^{11} +(3.21517 - 1.28946i) q^{12} +(2.41274 + 0.646492i) q^{13} +(4.20512 - 3.91590i) q^{14} +(1.30852 - 1.13480i) q^{15} +(1.48814 + 3.71288i) q^{16} +6.82037i q^{17} +(0.356948 + 4.22760i) q^{18} +(2.74559 + 2.74559i) q^{19} +(1.31002 + 1.51124i) q^{20} +(3.07762 + 6.32884i) q^{21} +(8.12583 + 0.289399i) q^{22} +(5.50714 - 3.17955i) q^{23} +(-4.88170 + 0.411113i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.99443 - 1.87401i) q^{26} +(-5.07878 - 1.09818i) q^{27} +(-7.30868 + 3.55215i) q^{28} +(-2.30986 + 0.618926i) q^{29} +(-2.23957 + 0.992126i) q^{30} +(-7.96865 + 4.60070i) q^{31} +(-0.473494 - 5.63700i) q^{32} +(-3.25314 + 9.41203i) q^{33} +(2.82645 - 9.22205i) q^{34} +(-2.87303 + 2.87303i) q^{35} +(1.26933 - 5.86420i) q^{36} +(4.82230 + 4.82230i) q^{37} +(-2.57459 - 4.85021i) q^{38} +(3.26850 - 2.83456i) q^{39} +(-1.14505 - 2.58628i) q^{40} +(-1.50602 - 2.60850i) q^{41} +(-1.53859 - 9.83284i) q^{42} +(1.88789 + 7.04570i) q^{43} +(-10.8673 - 3.75876i) q^{44} +(-0.358639 - 2.97849i) q^{45} +(-8.76403 + 2.01694i) q^{46} +(-0.945573 + 1.63778i) q^{47} +(6.77107 + 1.46716i) q^{48} +(-4.75433 - 8.23474i) q^{49} +(-0.963774 - 1.03496i) q^{50} +(9.78588 + 6.61733i) q^{51} +(3.27225 + 3.77485i) q^{52} +(5.91831 - 5.91831i) q^{53} +(6.41208 + 3.58959i) q^{54} -5.74947 q^{55} +(11.3544 - 1.77416i) q^{56} +(6.60323 - 1.27552i) q^{57} +(3.37973 + 0.120368i) q^{58} +(-1.48090 + 5.52680i) q^{59} +(3.43935 - 0.413377i) q^{60} +(-0.763827 - 2.85064i) q^{61} +(12.6813 - 2.91844i) q^{62} +(12.0666 + 1.72466i) q^{63} +(-1.69582 + 7.81820i) q^{64} +(2.16320 + 1.24893i) q^{65} +(8.29915 - 11.3782i) q^{66} +(-0.926685 + 3.45843i) q^{67} +(-7.64348 + 11.2981i) q^{68} +(0.781173 - 10.9865i) q^{69} +(5.07535 - 2.69410i) q^{70} -9.06339i q^{71} +(-4.14651 + 7.40314i) q^{72} +5.63553i q^{73} +(-4.52196 - 8.51881i) q^{74} +(1.55764 - 0.757459i) q^{75} +(1.47120 + 7.62507i) q^{76} +(6.04616 - 22.5646i) q^{77} +(-5.59412 + 2.47819i) q^{78} +(-1.90280 - 1.09858i) q^{79} +(0.476468 + 3.97152i) q^{80} +(-6.50325 + 6.22156i) q^{81} +(0.955339 + 4.15116i) q^{82} +(1.67299 + 6.24369i) q^{83} +(-1.99448 + 13.9329i) q^{84} +(-1.76524 + 6.58798i) q^{85} +(0.367156 - 10.3091i) q^{86} +(-1.35306 + 3.91470i) q^{87} +(13.1363 + 9.58587i) q^{88} -8.98343 q^{89} +(-0.749397 + 4.17593i) q^{90} +(-7.17642 + 7.17642i) q^{91} +(12.6860 + 0.904763i) q^{92} +(-1.13033 + 15.8972i) q^{93} +(1.95726 - 1.82264i) q^{94} +(1.94143 + 3.36265i) q^{95} +(-8.54738 - 4.78982i) q^{96} +(3.72934 - 6.45941i) q^{97} +(3.01589 + 13.1047i) q^{98} +(10.3481 + 13.7994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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