LMFDB - Embedded newform 616.2.bi.c.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [616,2,Mod(13,616)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(616, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))

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

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

chi := DirichletCharacter("616.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 616 = 2^{3} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	616.bi (of order $10$, 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:	$4.91878476451$
Analytic rank:	$0$
Dimension:	$352$
Relative dimension:	$88$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	616.13
Dual form			616.2.bi.c.237.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41337 + 0.0487330i) q^{2} +(1.21258 - 0.880988i) q^{3} +(1.99525 - 0.137756i) q^{4} +(1.22746 + 3.77772i) q^{5} +(-1.67089 + 1.30426i) q^{6} +(-0.966365 - 2.46295i) q^{7} +(-2.81332 + 0.291935i) q^{8} +(-0.232850 + 0.716639i) q^{9} +O(q^{10})$	\(q+(-1.41337 + 0.0487330i) q^{2} +(1.21258 - 0.880988i) q^{3} +(1.99525 - 0.137756i) q^{4} +(1.22746 + 3.77772i) q^{5} +(-1.67089 + 1.30426i) q^{6} +(-0.966365 - 2.46295i) q^{7} +(-2.81332 + 0.291935i) q^{8} +(-0.232850 + 0.716639i) q^{9} +(-1.91895 - 5.27952i) q^{10} +(1.12813 + 3.11887i) q^{11} +(2.29803 - 1.92483i) q^{12} +(-1.74853 - 0.568132i) q^{13} +(1.48586 + 3.43398i) q^{14} +(4.81651 + 3.49940i) q^{15} +(3.96205 - 0.549715i) q^{16} +(0.755978 + 2.32666i) q^{17} +(0.294180 - 1.02423i) q^{18} +(2.44132 + 3.36019i) q^{19} +(2.96949 + 7.36841i) q^{20} +(-3.34162 - 2.13516i) q^{21} +(-1.74646 - 4.35314i) q^{22} +4.33306 q^{23} +(-3.15417 + 2.83250i) q^{24} +(-8.71946 + 6.33506i) q^{25} +(2.49901 + 0.717772i) q^{26} +(1.73849 + 5.35052i) q^{27} +(-2.26743 - 4.78109i) q^{28} +(-4.26464 - 3.09844i) q^{29} +(-6.97807 - 4.71124i) q^{30} +(-6.19340 - 2.01236i) q^{31} +(-5.57306 + 0.970035i) q^{32} +(4.11563 + 2.78799i) q^{33} +(-1.18187 - 3.25160i) q^{34} +(8.11818 - 6.67383i) q^{35} +(-0.365873 + 1.46195i) q^{36} +(3.54074 - 4.87341i) q^{37} +(-3.61425 - 4.63024i) q^{38} +(-2.62075 + 0.851532i) q^{39} +(-4.55608 - 10.2696i) q^{40} +(-5.05152 + 3.67014i) q^{41} +(4.82702 + 2.85494i) q^{42} +7.64254 q^{43} +(2.68055 + 6.06751i) q^{44} -2.99308 q^{45} +(-6.12424 + 0.211163i) q^{46} +(4.81017 + 6.62063i) q^{47} +(4.31999 - 4.15709i) q^{48} +(-5.13228 + 4.76022i) q^{49} +(12.0151 - 9.37873i) q^{50} +(2.96644 + 2.15525i) q^{51} +(-3.56702 - 0.892696i) q^{52} +(6.00777 + 1.95204i) q^{53} +(-2.71788 - 7.47757i) q^{54} +(-10.3975 + 8.09004i) q^{55} +(3.43772 + 6.64696i) q^{56} +(5.92058 + 1.92371i) q^{57} +(6.17852 + 4.17143i) q^{58} +(0.130351 + 0.0947053i) q^{59} +(10.0922 + 6.31868i) q^{60} +(3.03197 - 0.985146i) q^{61} +(8.85166 + 2.54239i) q^{62} +(1.99007 - 0.119036i) q^{63} +(7.82955 - 1.64261i) q^{64} -7.30283i q^{65} +(-5.95279 - 3.73991i) q^{66} -7.13660i q^{67} +(1.82888 + 4.53813i) q^{68} +(5.25417 - 3.81738i) q^{69} +(-11.1488 + 9.82823i) q^{70} +(-3.77254 - 11.6107i) q^{71} +(0.445870 - 2.08411i) q^{72} +(9.15891 + 6.65433i) q^{73} +(-4.76689 + 7.06050i) q^{74} +(-4.99190 + 15.3635i) q^{75} +(5.33394 + 6.36812i) q^{76} +(6.59143 - 5.79250i) q^{77} +(3.66259 - 1.33125i) q^{78} +(4.76686 + 1.54885i) q^{79} +(6.93991 + 14.2928i) q^{80} +(4.99297 + 3.62761i) q^{81} +(6.96083 - 5.43346i) q^{82} +(-3.55839 + 1.15619i) q^{83} +(-6.96151 - 3.79986i) q^{84} +(-7.86156 + 5.71175i) q^{85} +(-10.8018 + 0.372444i) q^{86} -7.90089 q^{87} +(-4.08430 - 8.44503i) q^{88} -6.31135i q^{89} +(4.23033 - 0.145862i) q^{90} +(0.290436 + 4.85557i) q^{91} +(8.64554 - 0.596905i) q^{92} +(-9.28284 + 3.01618i) q^{93} +(-7.12121 - 9.12301i) q^{94} +(-9.69726 + 13.3471i) q^{95} +(-5.90318 + 6.08604i) q^{96} +(-0.490635 - 0.159417i) q^{97} +(7.02185 - 6.97808i) q^{98} +(-2.49778 + 0.0822345i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	$ 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) $ 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41337	+	0.0487330i	−0.999406	+	0.0344594i
$2$	−1.41337	+	0.0487330i	−0.999406	+	0.0344594i
$3$	1.21258	−	0.880988i	0.700081	−	0.508639i	−0.179877	−	0.983689i	$-0.557570\pi$
$3$	1.21258	−	0.880988i	0.700081	−	0.508639i	0.879959	+	0.475050i	$0.157570\pi$
$4$	1.99525	−	0.137756i	0.997625	−	0.0688779i
$5$	1.22746	+	3.77772i	0.548935	+	1.68945i	0.711445	+	0.702742i	$0.248041\pi$
$5$	1.22746	+	3.77772i	0.548935	+	1.68945i	−0.162509	+	0.986707i	$0.551959\pi$
$6$	−1.67089	+	1.30426i	−0.682138	+	0.532461i
$7$	−0.966365	−	2.46295i	−0.365252	−	0.930909i
$7$	−0.966365	−	2.46295i	−0.365252	−	0.930909i
$8$	−2.81332	+	0.291935i	−0.994659	+	0.103215i
$9$	−0.232850	+	0.716639i	−0.0776167	+	0.238880i
$10$	−1.91895	−	5.27952i	−0.606827	−	1.66953i
$11$	1.12813	+	3.11887i	0.340144	+	0.940373i
$11$	1.12813	+	3.11887i	0.340144	+	0.940373i
$12$	2.29803	−	1.92483i	0.663385	−	0.555651i
$13$	−1.74853	−	0.568132i	−0.484955	−	0.157572i	0.0563271	−	0.998412i	$-0.482061\pi$
$13$	−1.74853	−	0.568132i	−0.484955	−	0.157572i	−0.541282	+	0.840841i	$0.682061\pi$
$14$	1.48586	+	3.43398i	0.397113	+	0.917770i
$15$	4.81651	+	3.49940i	1.24362	+	0.903542i
$16$	3.96205	−	0.549715i	0.990512	−	0.137429i
$17$	0.755978	+	2.32666i	0.183352	+	0.564298i	0.999916	−	0.0129559i	$-0.00412410\pi$
$17$	0.755978	+	2.32666i	0.183352	+	0.564298i	−0.816564	+	0.577254i	$0.804124\pi$
$18$	0.294180	−	1.02423i	0.0693389	−	0.241412i
$19$	2.44132	+	3.36019i	0.560078	+	0.770881i	0.991336	−	0.131347i	$-0.0419303\pi$
$19$	2.44132	+	3.36019i	0.560078	+	0.770881i	−0.431258	+	0.902228i	$0.641930\pi$
$20$	2.96949	+	7.36841i	0.663997	+	1.64763i
$21$	−3.34162	−	2.13516i	−0.729202	−	0.465931i
$22$	−1.74646	−	4.35314i	−0.372347	−	0.928094i
$23$	4.33306			0.903506			0.451753	−	0.892143i	$-0.350799\pi$
$23$	4.33306			0.903506			0.451753	+	0.892143i	$0.350799\pi$
$24$	−3.15417	+	2.83250i	−0.643843	+	0.578181i
$25$	−8.71946	+	6.33506i	−1.74389	+	1.26701i
$26$	2.49901	+	0.717772i	0.490097	+	0.140767i
$27$	1.73849	+	5.35052i	0.334573	+	1.02971i
$28$	−2.26743	−	4.78109i	−0.428503	−	0.903540i
$29$	−4.26464	−	3.09844i	−0.791923	−	0.575366i	0.116610	−	0.993178i	$-0.462797\pi$
$29$	−4.26464	−	3.09844i	−0.791923	−	0.575366i	−0.908534	+	0.417812i	$0.862797\pi$
$30$	−6.97807	−	4.71124i	−1.27402	−	0.860151i
$31$	−6.19340	−	2.01236i	−1.11237	−	0.361430i	−0.305518	−	0.952186i	$-0.598830\pi$
$31$	−6.19340	−	2.01236i	−1.11237	−	0.361430i	−0.806850	+	0.590756i	$0.798830\pi$
$32$	−5.57306	+	0.970035i	−0.985188	+	0.171480i
$33$	4.11563	+	2.78799i	0.716439	+	0.485327i
$34$	−1.18187	−	3.25160i	−0.202688	−	0.557645i
$35$	8.11818	−	6.67383i	1.37222	−	1.12808i
$36$	−0.365873	+	1.46195i	−0.0609788	+	0.243658i
$37$	3.54074	−	4.87341i	0.582094	−	0.801184i	−0.411829	−	0.911261i	$-0.635110\pi$
$37$	3.54074	−	4.87341i	0.582094	−	0.801184i	0.993923	+	0.110077i	$0.0351098\pi$
$38$	−3.61425	−	4.63024i	−0.586310	−	0.751123i
$39$	−2.62075	+	0.851532i	−0.419655	+	0.136354i
$40$	−4.55608	−	10.2696i	−0.720379	−	1.62377i
$41$	−5.05152	+	3.67014i	−0.788915	+	0.573180i	−0.907641	−	0.419747i	$-0.862119\pi$
$41$	−5.05152	+	3.67014i	−0.788915	+	0.573180i	0.118726	+	0.992927i	$0.462119\pi$
$42$	4.82702	+	2.85494i	0.744825	+	0.440526i
$43$	7.64254			1.16548			0.582738	−	0.812660i	$-0.301981\pi$
$43$	7.64254			1.16548			0.582738	+	0.812660i	$0.301981\pi$
$44$	2.68055	+	6.06751i	0.404107	+	0.914712i
$45$	−2.99308			−0.446181
$46$	−6.12424	+	0.211163i	−0.902969	+	0.0311343i
$47$	4.81017	+	6.62063i	0.701636	+	0.965718i	0.999937	+	0.0112467i	$0.00358001\pi$
$47$	4.81017	+	6.62063i	0.701636	+	0.965718i	−0.298301	+	0.954472i	$0.596420\pi$
$48$	4.31999	−	4.15709i	0.623537	−	0.600024i
$49$	−5.13228	+	4.76022i	−0.733183	+	0.680032i
$50$	12.0151	−	9.37873i	1.69920	−	1.32635i
$51$	2.96644	+	2.15525i	0.415385	+	0.301795i
$52$	−3.56702	−	0.892696i	−0.494657	−	0.123795i
$53$	6.00777	+	1.95204i	0.825231	+	0.268134i	0.691035	−	0.722821i	$-0.257155\pi$
$53$	6.00777	+	1.95204i	0.825231	+	0.268134i	0.134196	+	0.990955i	$0.457155\pi$
$54$	−2.71788	−	7.47757i	−0.369857	−	1.01757i
$55$	−10.3975	+	8.09004i	−1.40200	+	1.09086i
$56$	3.43772	+	6.64696i	0.459384	+	0.888238i
$57$	5.92058	+	1.92371i	0.784200	+	0.254802i
$58$	6.17852	+	4.17143i	0.811280	+	0.547735i
$59$	0.130351	+	0.0947053i	0.0169702	+	0.0123296i	0.596238	−	0.802808i	$-0.296661\pi$
$59$	0.130351	+	0.0947053i	0.0169702	+	0.0123296i	−0.579268	+	0.815137i	$0.696661\pi$
$60$	10.0922	+	6.31868i	1.30290	+	0.815738i
$61$	3.03197	−	0.985146i	0.388204	−	0.126135i	−0.108411	−	0.994106i	$-0.534576\pi$
$61$	3.03197	−	0.985146i	0.388204	−	0.126135i	0.496615	+	0.867971i	$0.334576\pi$
$62$	8.85166	+	2.54239i	1.12416	+	0.322884i
$63$	1.99007	−	0.119036i	0.250725	−	0.0149971i
$64$	7.82955	−	1.64261i	0.978693	−	0.205327i
$65$		−	7.30283i		−	0.905804i
$66$	−5.95279	−	3.73991i	−0.732738	−	0.460351i
$67$		−	7.13660i		−	0.871874i	−0.899977	−	0.435937i	$-0.856417\pi$
$67$		−	7.13660i		−	0.871874i	0.899977	−	0.435937i	$-0.143583\pi$
$68$	1.82888	+	4.53813i	0.221784	+	0.550329i
$69$	5.25417	−	3.81738i	0.632527	−	0.459558i
$70$	−11.1488	+	9.82823i	−1.33254	+	1.17470i
$71$	−3.77254	−	11.6107i	−0.447719	−	1.37794i	−0.879475	−	0.475946i	$-0.842106\pi$
$71$	−3.77254	−	11.6107i	−0.447719	−	1.37794i	0.431756	−	0.901990i	$-0.357894\pi$
$72$	0.445870	−	2.08411i	0.0525463	−	0.245615i
$73$	9.15891	+	6.65433i	1.07197	+	0.778831i	0.976265	−	0.216579i	$-0.0694899\pi$
$73$	9.15891	+	6.65433i	1.07197	+	0.778831i	0.0957037	+	0.995410i	$0.469490\pi$
$74$	−4.76689	+	7.06050i	−0.554140	+	0.820767i
$75$	−4.99190	+	15.3635i	−0.576415	+	1.77402i
$76$	5.33394	+	6.36812i	0.611845	+	0.730474i
$77$	6.59143	−	5.79250i	0.751164	−	0.660116i
$78$	3.66259	−	1.33125i	0.414707	−	0.150734i
$79$	4.76686	+	1.54885i	0.536314	+	0.174259i	0.564636	−	0.825340i	$-0.309016\pi$
$79$	4.76686	+	1.54885i	0.536314	+	0.174259i	−0.0283223	+	0.999599i	$0.509016\pi$
$80$	6.93991	+	14.2928i	0.775906	+	1.59798i
$81$	4.99297	+	3.62761i	0.554775	+	0.403068i
$82$	6.96083	−	5.43346i	0.768695	−	0.600025i
$83$	−3.55839	+	1.15619i	−0.390584	+	0.126908i	−0.497724	−	0.867335i	$-0.665831\pi$
$83$	−3.55839	+	1.15619i	−0.390584	+	0.126908i	0.107140	+	0.994244i	$0.465831\pi$
$84$	−6.96151	−	3.79986i	−0.759563	−	0.414598i
$85$	−7.86156	+	5.71175i	−0.852705	+	0.619527i
$86$	−10.8018	+	0.372444i	−1.16478	+	0.0401616i
$87$	−7.90089			−0.847064
$88$	−4.08430	−	8.44503i	−0.435388	−	0.900243i
$89$		−	6.31135i		−	0.669001i	−0.942395	−	0.334501i	$-0.891432\pi$
$89$		−	6.31135i		−	0.669001i	0.942395	−	0.334501i	$-0.108568\pi$
$90$	4.23033	−	0.145862i	0.445916	−	0.0153752i
$91$	0.290436	+	4.85557i	0.0304460	+	0.509002i
$92$	8.64554	−	0.596905i	0.901360	−	0.0622316i
$93$	−9.28284	+	3.01618i	−0.962586	+	0.312763i
$94$	−7.12121	−	9.12301i	−0.734497	−	0.940967i
$95$	−9.69726	+	13.3471i	−0.994918	+	1.36939i
$96$	−5.90318	+	6.08604i	−0.602490	+	0.621154i
$97$	−0.490635	−	0.159417i	−0.0498165	−	0.0161863i	0.284003	−	0.958823i	$-0.408338\pi$
$97$	−0.490635	−	0.159417i	−0.0498165	−	0.0161863i	−0.333819	+	0.942637i	$0.608338\pi$
$98$	7.02185	−	6.97808i	0.709314	−	0.704893i
$99$	−2.49778	+	0.0822345i	−0.251037	+	0.00826487i
$100$	−16.5248	+	13.8412i	−1.65248	+	1.38412i
$101$	3.82373	+	1.24240i	0.380475	+	0.123624i	0.493009	−	0.870024i	$-0.335897\pi$
$101$	3.82373	+	1.24240i	0.380475	+	0.123624i	−0.112534	+	0.993648i	$0.535897\pi$
$102$	−4.29772	−	2.90161i	−0.425538	−	0.287302i
$103$	−6.14760	+	8.46144i	−0.605741	+	0.833731i	−0.996219	−	0.0868817i	$-0.972310\pi$
$103$	−6.14760	+	8.46144i	−0.605741	+	0.833731i	0.390478	+	0.920612i	$0.372310\pi$
$104$	5.08504	+	1.08788i	0.498629	+	0.106675i
$105$	3.96436	−	15.2446i	0.386881	−	1.48772i
$106$	−8.58636	−	2.46619i	−0.833981	−	0.239538i
$107$	8.15776	−	5.92696i	0.788641	−	0.572981i	−0.118919	−	0.992904i	$-0.537943\pi$
$107$	8.15776	−	5.92696i	0.788641	−	0.572981i	0.907560	+	0.419923i	$0.137943\pi$
$108$	4.20579	+	10.4361i	0.404702	+	1.00422i
$109$	−6.38273			−0.611355			−0.305677	−	0.952135i	$-0.598883\pi$
$109$	−6.38273			−0.611355			−0.305677	+	0.952135i	$0.598883\pi$
$110$	14.3013	−	11.9409i	1.36357	−	1.13852i
$111$		−	9.02874i		−	0.856970i
$112$	−5.18270	−	9.22711i	−0.489720	−	0.871880i
$113$	12.7320	−	9.25034i	1.19773	−	0.870199i	0.203667	−	0.979040i	$-0.434714\pi$
$113$	12.7320	−	9.25034i	1.19773	−	0.870199i	0.994059	+	0.108842i	$0.0347141\pi$
$114$	−8.46174	−	2.43040i	−0.792515	−	0.227628i
$115$	5.31865	+	16.3691i	0.495966	+	1.52643i
$116$	−8.93585	−	5.59469i	−0.829673	−	0.519454i
$117$	0.814291	−	1.12078i	0.0752812	−	0.103616i
$118$	−0.188849	−	0.127502i	−0.0173850	−	0.0117375i
$119$	4.99991	−	4.11034i	0.458341	−	0.376795i
$120$	−14.5720	−	8.43883i	−1.33024	−	0.770357i
$121$	−8.45464	+	7.03698i	−0.768604	+	0.639725i
$122$	−4.23730	+	1.54014i	−0.383627	+	0.139437i
$123$	−2.89200	+	8.90066i	−0.260763	+	0.802545i
$124$	−12.6346	−	3.16198i	−1.13462	−	0.283954i
$125$	−18.5672	−	13.4899i	−1.66070	−	1.20657i
$126$	−2.80691	+	0.265224i	−0.250059	+	0.0236280i
$127$	7.50533	−	2.43863i	0.665990	−	0.216393i	0.0435388	−	0.999052i	$-0.486137\pi$
$127$	7.50533	−	2.43863i	0.665990	−	0.216393i	0.622451	+	0.782658i	$0.286137\pi$
$128$	−10.9860	+	2.70318i	−0.971037	+	0.238930i
$129$	9.26716	−	6.73299i	0.815928	−	0.592806i
$130$	0.355888	+	10.3216i	0.0312135	+	0.905266i
$131$		−	9.63747i		−	0.842030i	−0.907054	−	0.421015i	$-0.861674\pi$
$131$		−	9.63747i		−	0.842030i	0.907054	−	0.421015i	$-0.138326\pi$
$132$	8.59577	+	4.99579i	0.748166	+	0.434828i
$133$	5.91679	−	9.26004i	0.513051	−	0.802947i
$134$	0.347788	+	10.0867i	0.0300443	+	0.871356i
$135$	−18.0789	+	13.1351i	−1.55598	+	1.13049i
$136$	−2.80604	−	6.32495i	−0.240616	−	0.542360i
$137$	−6.37533	−	19.6212i	−0.544681	−	1.67636i	−0.721747	−	0.692157i	$-0.756661\pi$
$137$	−6.37533	−	19.6212i	−0.544681	−	1.67636i	0.177066	−	0.984199i	$-0.443339\pi$
$138$	−7.24007	+	5.65143i	−0.616316	+	0.481082i
$139$	9.08070	−	12.4985i	0.770215	−	1.06011i	−0.226080	−	0.974109i	$-0.572591\pi$
$139$	9.08070	−	12.4985i	0.770215	−	1.06011i	0.996295	−	0.0860010i	$-0.0274088\pi$
$140$	15.2785	−	14.4343i	1.29126	−	1.21992i
$141$	11.6654	+	3.79032i	0.982404	+	0.319202i
$142$	5.89784	+	16.2264i	0.494936	+	1.36169i
$143$	−0.200644	−	6.09436i	−0.0167787	−	0.509636i
$144$	−0.528616	+	2.96736i	−0.0440513	+	0.247280i
$145$	6.47039	−	19.9138i	0.537337	−	1.65375i
$146$	−13.2692	−	8.95872i	−1.09817	−	0.741429i
$147$	−2.02958	+	10.2936i	−0.167397	+	0.849003i
$148$	6.39332	−	10.2114i	0.525528	−	0.839375i
$149$	5.90475	+	18.1730i	0.483736	+	1.48879i	0.833803	+	0.552062i	$0.186159\pi$
$149$	5.90475	+	18.1730i	0.483736	+	1.48879i	−0.350067	+	0.936725i	$0.613841\pi$
$150$	6.30671	−	21.9576i	0.514940	−	1.79283i
$151$	−8.39731	−	11.5579i	−0.683363	−	0.940569i	0.316605	−	0.948558i	$-0.397457\pi$
$151$	−8.39731	−	11.5579i	−0.683363	−	0.940569i	−0.999968	+	0.00798848i	$0.997457\pi$
$152$	−7.84918	−	8.74059i	−0.636653	−	0.708956i
$153$	−1.84341			−0.149031
$154$	−9.03387	+	8.50818i	−0.727970	+	0.685609i
$155$		−	25.8671i		−	2.07769i
$156$	−5.11174	+	2.06004i	−0.409267	+	0.164935i
$157$	−6.73048	+	4.88998i	−0.537151	+	0.390263i	−0.823026	−	0.568004i	$-0.807716\pi$
$157$	−6.73048	+	4.88998i	−0.537151	+	0.390263i	0.285875	+	0.958267i	$0.407716\pi$
$158$	−6.81284	−	1.95680i	−0.542000	−	0.155674i
$159$	9.00461	−	2.92578i	0.714112	−	0.232029i
$160$	−10.5052	−	19.8628i	−0.830510	−	1.57029i
$161$	−4.18732	−	10.6721i	−0.330007	−	0.841082i
$162$	−7.23372	−	4.88384i	−0.568335	−	0.383711i
$163$	−1.95299	−	0.634564i	−0.152970	−	0.0497029i	0.231531	−	0.972827i	$-0.425626\pi$
$163$	−1.95299	−	0.634564i	−0.152970	−	0.0497029i	−0.384501	+	0.923125i	$0.625626\pi$
$164$	−9.57346	+	8.01873i	−0.747562	+	0.626158i
$165$	−5.48051	+	18.9698i	−0.426657	+	1.47680i
$166$	4.97299	−	1.80754i	0.385979	−	0.140292i
$167$	1.35211	−	4.16136i	0.104629	−	0.322016i	−0.885014	−	0.465564i	$-0.845851\pi$
$167$	1.35211	−	4.16136i	0.104629	−	0.322016i	0.989643	+	0.143549i	$0.0458514\pi$
$168$	10.0244	+	5.03136i	0.773398	+	0.388178i
$169$	−7.78263	−	5.65441i	−0.598664	−	0.434955i
$170$	10.8330	−	8.45596i	0.830850	−	0.648543i
$171$	−2.97651	+	0.967126i	−0.227619	+	0.0739579i
$172$	15.2488	−	1.05280i	1.16271	−	0.0802756i
$173$	−11.2748	−	15.5184i	−0.857208	−	1.17985i	−0.982228	−	0.187691i	$-0.939900\pi$
$173$	−11.2748	−	15.5184i	−0.857208	−	1.17985i	0.125020	−	0.992154i	$-0.460100\pi$
$174$	11.1669	−	0.385034i	0.846561	−	0.0291893i
$175$	24.0291	+	15.3536i	1.81643	+	1.16063i
$176$	6.18419	+	11.7369i	0.466151	+	0.884705i
$177$	0.241494			0.0181518
$178$	0.307571	+	8.92029i	0.0230534	+	0.668604i
$179$	13.4845	+	18.5599i	1.00788	+	1.38723i	0.920363	+	0.391066i	$0.127893\pi$
$179$	13.4845	+	18.5599i	1.00788	+	1.38723i	0.0875177	+	0.996163i	$0.472107\pi$
$180$	−5.97193	+	0.412314i	−0.445122	+	0.0307320i
$181$	−1.34875	−	4.15103i	−0.100252	−	0.308544i	0.888335	−	0.459196i	$-0.151862\pi$
$181$	−1.34875	−	4.15103i	−0.100252	−	0.308544i	−0.988587	+	0.150653i	$0.951862\pi$
$182$	−0.647121	−	6.84859i	−0.0479678	−	0.507651i
$183$	2.80859	−	3.86569i	0.207617	−	0.285760i
$184$	−12.1903	+	1.26497i	−0.898680	+	0.0932550i
$185$	22.7565	+	7.39404i	1.67309	+	0.543621i
$186$	12.9731	−	4.71537i	0.951236	−	0.345747i
$187$	−6.40370	+	4.98257i	−0.468285	+	0.364362i
$188$	10.5095	+	12.5472i	0.766486	+	0.915098i
$189$	11.4981	−	9.45238i	0.836362	−	0.687559i
$190$	13.0554	−	19.3371i	0.947139	−	1.40286i
$191$	3.03759	+	2.20693i	0.219792	+	0.159688i	0.692233	−	0.721674i	$-0.256627\pi$
$191$	3.03759	+	2.20693i	0.219792	+	0.159688i	−0.472441	+	0.881362i	$0.656627\pi$
$192$	8.04680	−	8.88953i	0.580728	−	0.641547i
$193$	−10.9365	+	3.55347i	−0.787223	+	0.255784i	−0.674921	−	0.737890i	$-0.735822\pi$
$193$	−10.9365	+	3.55347i	−0.787223	+	0.255784i	−0.112302	+	0.993674i	$0.535822\pi$
$194$	0.701220	+	0.201406i	0.0503446	+	0.0144601i
$195$	−6.43370	−	8.85523i	−0.460727	−	0.634136i
$196$	−9.58443	+	10.2048i	−0.684602	+	0.728917i
$197$	−13.1303			−0.935495			−0.467747	−	0.883862i	$-0.654934\pi$
$197$	−13.1303			−0.935495			−0.467747	+	0.883862i	$0.654934\pi$
$198$	3.52630	−	0.237953i	0.250603	−	0.0169105i
$199$		−	20.7768i		−	1.47283i	−0.676530	−	0.736415i	$-0.736517\pi$
$199$		−	20.7768i		−	1.47283i	0.676530	−	0.736415i	$-0.263483\pi$
$200$	22.6812	−	20.3681i	1.60380	−	1.44024i
$201$	−6.28726	−	8.65367i	−0.443469	−	0.610383i
$202$	−5.46490	−	1.56964i	−0.384509	−	0.110439i
$203$	−3.51012	+	13.4978i	−0.246362	+	0.947362i
$204$	6.21570	+	3.89161i	0.435186	+	0.272467i
$205$	−20.0653	−	14.5783i	−1.40142	−	1.01819i
$206$	8.27650	−	12.2588i	0.576651	−	0.854109i
$207$	−1.00895	+	3.10524i	−0.0701271	+	0.215829i
$208$	−7.24007	−	1.28977i	−0.502009	−	0.0894297i
$209$	−7.72586	+	11.4049i	−0.534409	+	0.788893i
$210$	−4.86020	+	21.7394i	−0.335386	+	1.50016i
$211$	1.60049	−	4.92579i	0.110182	−	0.339105i	−0.880730	−	0.473619i	$-0.842947\pi$
$211$	1.60049	−	4.92579i	0.110182	−	0.339105i	0.990912	+	0.134514i	$0.0429473\pi$
$212$	12.2559	+	3.06721i	0.841740	+	0.210657i
$213$	−14.8034	−	10.7553i	−1.01431	−	0.736940i
$214$	−11.2411	+	8.77457i	−0.768428	+	0.599817i
$215$	9.38089	+	28.8714i	0.639771	+	1.96901i
$216$	−6.45294	−	14.5452i	−0.439067	−	0.989676i
$217$	1.02874	+	17.1987i	0.0698355	+	1.16753i
$218$	9.02118	−	0.311050i	0.610992	−	0.0210669i
$219$	16.9683			1.14661
$220$	−19.6311	+	17.5740i	−1.32353	+	1.18484i
$221$		−	4.49774i		−	0.302551i
$222$	0.439997	+	12.7610i	0.0295307	+	0.856461i
$223$	−3.28797	−	4.52551i	−0.220179	−	0.303050i	0.684611	−	0.728909i	$-0.259972\pi$
$223$	−3.28797	−	4.52551i	−0.220179	−	0.303050i	−0.904790	+	0.425858i	$0.859972\pi$
$224$	7.77476	+	12.7888i	0.519473	+	0.854487i
$225$	−2.50962	−	7.72382i	−0.167308	−	0.514921i
$226$	−17.5443	+	13.6947i	−1.16703	+	0.910955i
$227$	12.5146	−	17.2248i	0.830621	−	1.14325i	−0.157186	−	0.987569i	$-0.550242\pi$
$227$	12.5146	−	17.2248i	0.830621	−	1.14325i	0.987807	−	0.155682i	$-0.0497577\pi$
$228$	12.0780	+	3.02270i	0.799888	+	0.200183i
$229$	2.55524	−	7.86421i	0.168855	−	0.519682i	−0.830445	−	0.557101i	$-0.811914\pi$
$229$	2.55524	−	7.86421i	0.168855	−	0.519682i	0.999300	+	0.0374190i	$0.0119136\pi$
$230$	−8.31495	−	22.8765i	−0.548271	−	1.50843i
$231$	2.88950	−	12.8308i	0.190115	−	0.844206i
$232$	12.9023	+	7.47191i	0.847080	+	0.490555i
$233$	−15.2958	−	4.96992i	−1.00206	−	0.325590i	−0.238374	−	0.971173i	$-0.576614\pi$
$233$	−15.2958	−	4.96992i	−1.00206	−	0.325590i	−0.763690	+	0.645583i	$0.776614\pi$
$234$	−1.09628	+	1.62376i	−0.0716660	+	0.106148i
$235$	−19.1066	+	26.2980i	−1.24638	+	1.71549i
$236$	0.273128	+	0.171004i	0.0177791	+	0.0111314i
$237$	7.14470	−	2.32145i	0.464098	−	0.150795i
$238$	−6.86643	+	6.05311i	−0.445085	+	0.392365i
$239$	17.4600	+	24.0317i	1.12940	+	1.55448i	0.789213	+	0.614119i	$0.210489\pi$
$239$	17.4600	+	24.0317i	1.12940	+	1.55448i	0.340182	+	0.940360i	$0.389511\pi$
$240$	21.0069	+	11.2171i	1.35599	+	0.724060i
$241$	9.43387			0.607689			0.303844	−	0.952722i	$-0.401730\pi$
$241$	9.43387			0.607689			0.303844	+	0.952722i	$0.401730\pi$
$242$	11.6066	−	10.3579i	0.746103	−	0.665831i
$243$	−7.62738			−0.489297
$244$	5.91383	−	2.38329i	0.378594	−	0.152574i
$245$	−24.2825	−	13.5454i	−1.55135	−	0.865381i
$246$	3.65372	−	12.7209i	0.232953	−	0.811055i
$247$	−2.35970	−	7.26240i	−0.150144	−	0.462095i
$248$	18.0115	+	3.85334i	1.14373	+	0.244687i
$249$	−3.29623	+	4.53687i	−0.208890	+	0.287512i
$250$	26.8998	+	18.1614i	1.70129	+	1.14863i
$251$	−3.85857	+	11.8755i	−0.243551	+	0.749573i	0.752320	+	0.658797i	$0.228935\pi$
$251$	−3.85857	+	11.8755i	−0.243551	+	0.749573i	−0.995871	+	0.0907753i	$0.971065\pi$
$252$	3.95428	−	0.511649i	0.249096	−	0.0322309i
$253$	4.88826	+	13.5142i	0.307322	+	0.849633i
$254$	−10.4890	+	3.81245i	−0.658138	+	0.239214i
$255$	−4.50075	+	13.8519i	−0.281848	+	0.867438i
$256$	15.3956	−	4.35599i	0.962227	−	0.272249i
$257$	−12.6081	+	17.3536i	−0.786474	+	1.08249i	0.208065	+	0.978115i	$0.433284\pi$
$257$	−12.6081	+	17.3536i	−0.786474	+	1.08249i	−0.994538	+	0.104373i	$0.966716\pi$
$258$	−12.7698	+	9.96784i	−0.795016	+	0.620571i
$259$	−15.4246	−	4.01119i	−0.958440	−	0.249243i
$260$	−1.00601	−	14.5710i	−0.0623899	−	0.903653i
$261$	3.21348	−	2.33473i	0.198910	−	0.144516i
$262$	0.469663	+	13.6213i	0.0290159	+	0.841530i
$263$		−	0.00919536i		−	0.000567010i	−1.00000		0.000283505i	$-0.999910\pi$
$263$		−	0.00919536i		−	0.000567010i	1.00000		0.000283505i	$-9.02425e-5\pi$
$264$	−12.3925	−	6.64202i	−0.762705	−	0.408788i
$265$			25.0918i			1.54137i
$266$	−7.91137	+	13.3762i	−0.485077	+	0.820150i
$267$	−5.56022	−	7.65299i	−0.340280	−	0.468355i
$268$	−0.983108	−	14.2393i	−0.0600529	−	0.869803i
$269$	7.39795	+	22.7685i	0.451061	+	1.38822i	0.875698	+	0.482859i	$0.160402\pi$
$269$	7.39795	+	22.7685i	0.451061	+	1.38822i	−0.424637	+	0.905364i	$0.639598\pi$
$270$	24.9121	−	19.4458i	1.51610	−	1.18343i
$271$	−18.1023	−	13.1521i	−1.09963	−	0.798931i	−0.118634	−	0.992938i	$-0.537851\pi$
$271$	−18.1023	−	13.1521i	−1.09963	−	0.798931i	−0.981000	+	0.194007i	$0.937851\pi$
$272$	4.27422	+	8.80277i	0.259163	+	0.533746i
$273$	4.62988	+	5.63188i	0.280213	+	0.340857i
$274$	9.96692	+	27.4215i	0.602124	+	1.65659i
$275$	−29.5949	−	20.0480i	−1.78464	−	1.20894i
$276$	9.95751	−	8.34041i	0.599372	−	0.502034i
$277$	3.85714	−	11.8711i	0.231753	−	0.713263i	−0.765782	−	0.643100i	$-0.777648\pi$
$277$	3.85714	−	11.8711i	0.231753	−	0.713263i	0.997536	−	0.0701629i	$-0.0223519\pi$
$278$	−12.2253	+	18.1076i	−0.733227	+	1.08602i
$279$	2.88427	−	3.96986i	0.172677	−	0.237669i
$280$	−20.8907	+	21.1456i	−1.24846	+	1.26369i
$281$	−28.9929	+	9.42036i	−1.72957	+	0.561971i	−0.993387	−	0.114811i	$-0.963374\pi$
$281$	−28.9929	+	9.42036i	−1.72957	+	0.561971i	−0.736183	+	0.676783i	$0.763374\pi$
$282$	−16.6723	−	4.78865i	−0.992820	−	0.285160i
$283$	−3.52902	−	4.85728i	−0.209778	−	0.288735i	0.691143	−	0.722718i	$-0.257108\pi$
$283$	−3.52902	−	4.85728i	−0.209778	−	0.288735i	−0.900921	+	0.433983i	$0.857108\pi$
$284$	−9.12661	−	22.6466i	−0.541565	−	1.34383i
$285$			24.7276i			1.46474i
$286$	0.580582	+	8.60383i	0.0343305	+	0.508755i
$287$	13.9210	+	8.89496i	0.821731	+	0.525053i
$288$	0.602523	−	4.21974i	0.0355040	−	0.248651i
$289$	8.91143	−	6.47454i	0.524202	−	0.380855i
$290$	−8.17462	+	28.4610i	−0.480030	+	1.67129i
$291$	−0.735377	+	0.238939i	−0.0431086	+	0.0140068i
$292$	19.1910	+	12.0154i	1.12307	+	0.703146i
$293$	2.57003	−	3.53734i	0.150143	−	0.206654i	−0.727320	−	0.686298i	$-0.759234\pi$
$293$	2.57003	−	3.53734i	0.150143	−	0.206654i	0.877463	+	0.479645i	$0.159234\pi$
$294$	2.36691	−	14.6476i	0.138041	−	0.854267i
$295$	−0.197771	+	0.608675i	−0.0115146	+	0.0354384i
$296$	−8.53852	+	14.7441i	−0.496292	+	0.856986i
$297$	−14.7263	+	11.4582i	−0.854508	+	0.664873i
$298$	−9.23125	−	25.3974i	−0.534752	−	1.47123i
$299$	−7.57649	−	2.46175i	−0.438160	−	0.142367i
$300$	−7.84367	+	31.3416i	−0.452855	+	1.80951i
$301$	−7.38548	−	18.8232i	−0.425692	−	1.08495i
$302$	12.4318	+	15.9264i	0.715369	+	0.916462i
$303$	5.73111	−	1.86215i	0.329243	−	0.106978i
$304$	11.5198	+	11.9712i	0.660705	+	0.686596i
$305$	7.44322	+	10.2447i	0.426198	+	0.586611i
$306$	2.60542	−	0.0898347i	0.148942	−	0.00513551i
$307$			5.99703i			0.342268i	0.985248	+	0.171134i	$0.0547432\pi$
$307$			5.99703i			0.342268i	−0.985248	+	0.171134i	$0.945257\pi$
$308$	12.3536	−	12.4655i	0.703912	−	0.710287i
$309$			15.6761i			0.891782i
$310$	1.26058	+	36.5598i	0.0715961	+	2.07646i
$311$	−12.6182	−	17.3675i	−0.715513	−	0.984819i	−0.999661	−	0.0260390i	$-0.991711\pi$
$311$	−12.6182	−	17.3675i	−0.715513	−	0.984819i	0.284148	−	0.958781i	$-0.408289\pi$
$312$	7.12441	−	3.16072i	0.403340	−	0.178941i
$313$	17.0090	−	5.52657i	0.961408	−	0.312380i	0.214066	−	0.976819i	$-0.431329\pi$
$313$	17.0090	−	5.52657i	0.961408	−	0.312380i	0.747343	+	0.664439i	$0.231329\pi$
$314$	9.27438	−	7.23937i	0.523384	−	0.408541i
$315$	2.89240	+	7.37181i	0.162968	+	0.415354i
$316$	9.72445	+	2.43368i	0.547043	+	0.136905i
$317$	16.2265	+	5.27232i	0.911373	+	0.296123i	0.726923	−	0.686719i	$-0.240950\pi$
$317$	16.2265	+	5.27232i	0.911373	+	0.296123i	0.184450	+	0.982842i	$0.440950\pi$
$318$	−12.5843	+	4.57404i	−0.705692	+	0.256499i
$319$	4.85255	−	16.7963i	0.271691	−	0.940411i
$320$	15.8158	+	27.5616i	0.884128	+	1.54074i
$321$	4.67033	−	14.3738i	0.260672	−	0.802267i
$322$	6.43833	+	14.8796i	0.358794	+	0.829210i
$323$	−5.97245	+	8.22037i	−0.332316	+	0.457394i
$324$	10.4620	+	6.55017i	0.581220	+	0.363899i
$325$	18.8454	−	6.12324i	1.04535	−	0.339656i
$326$	2.79123	+	0.801702i	0.154592	+	0.0444021i
$327$	−7.73955	+	5.62311i	−0.427998	+	0.310959i
$328$	13.1401	−	11.8000i	0.725541	−	0.651546i
$329$	11.6579	−	18.2452i	0.642722	−	1.00589i
$330$	6.82155	−	27.0786i	0.375514	−	1.49063i
$331$		−	0.611925i		−	0.0336344i	−0.999859	−	0.0168172i	$-0.994647\pi$
$331$		−	0.611925i		−	0.0336344i	0.999859	−	0.0168172i	$-0.00535334\pi$
$332$	−6.94061	+	2.79708i	−0.380915	+	0.153510i
$333$	2.66801	+	3.67221i	0.146206	+	0.201236i
$334$	−1.70824	+	5.94745i	−0.0934706	+	0.325430i
$335$	26.9601	−	8.75986i	1.47299	−	0.478602i
$336$	−14.4134	−	6.62267i	−0.786315	−	0.361297i
$337$	−0.173465	+	0.238754i	−0.00944923	+	0.0130058i	−0.813715	−	0.581263i	$-0.802559\pi$
$337$	−0.173465	+	0.238754i	−0.00944923	+	0.0130058i	0.804266	+	0.594269i	$0.202559\pi$
$338$	11.2753	+	7.61253i	0.613297	+	0.414067i
$339$	7.28908	−	22.4335i	0.395889	−	1.21842i
$340$	−14.8989	+	12.4794i	−0.808009	+	0.676788i
$341$	−0.710695	−	21.5866i	−0.0384863	−	1.16898i
$342$	4.15979	−	1.51196i	0.224935	−	0.0817577i
$343$	16.6839	+	8.04045i	0.900844	+	0.434143i
$344$	−21.5009	+	2.23112i	−1.15925	+	0.120294i
$345$	20.8703	+	15.1631i	1.12362	+	0.816355i
$346$	16.6918	+	21.3839i	0.897355	+	1.14961i
$347$	10.0169	+	30.8289i	0.537737	+	1.65498i	0.737660	+	0.675173i	$0.235931\pi$
$347$	10.0169	+	30.8289i	0.537737	+	1.65498i	−0.199923	+	0.979812i	$0.564069\pi$
$348$	−15.7642	+	1.08839i	−0.845052	+	0.0583440i
$349$	1.16837	+	1.60813i	0.0625415	+	0.0860810i	0.839142	−	0.543912i	$-0.183058\pi$
$349$	1.16837	+	1.60813i	0.0625415	+	0.0860810i	−0.776601	+	0.629993i	$0.783058\pi$
$350$	−34.7104	−	20.5294i	−1.85535	−	1.09734i
$351$		−	10.3433i		−	0.552082i
$352$	−9.31255	−	16.2873i	−0.496361	−	0.868116i
$353$		−	35.7880i		−	1.90480i	−0.304846	−	0.952402i	$-0.598605\pi$
$353$		−	35.7880i		−	1.90480i	0.304846	−	0.952402i	$-0.401395\pi$
$354$	−0.341322	+	0.0117687i	−0.0181410	+	0.000625501i
$355$	39.2314	−	28.5033i	2.08218	−	1.51280i
$356$	−0.869425	−	12.5927i	−0.0460794	−	0.667413i
$357$	2.44161	−	9.38897i	0.129224	−	0.496917i
$358$	−19.9631	−	25.5749i	−1.05509	−	1.35167i
$359$	8.65087	−	11.9069i	0.456575	−	0.628422i	−0.517219	−	0.855853i	$-0.673033\pi$
$359$	8.65087	−	11.9069i	0.456575	−	0.628422i	0.973794	+	0.227431i	$0.0730327\pi$
$360$	8.42048	−	0.873783i	0.443798	−	0.0460524i
$361$	0.540482	−	1.66343i	0.0284464	−	0.0875491i
$362$	2.10858	+	5.80123i	0.110825	+	0.304906i
$363$	−4.05240	+	15.9813i	−0.212696	+	0.838801i
$364$	1.24838	+	9.64808i	0.0654327	+	0.505697i
$365$	−13.8961	+	42.7677i	−0.727354	+	2.23856i
$366$	−3.78120	+	5.60054i	−0.197647	+	0.292745i
$367$	−1.56729	+	2.15719i	−0.0818119	+	0.112604i	−0.847961	−	0.530058i	$-0.822170\pi$
$367$	−1.56729	+	2.15719i	−0.0818119	+	0.112604i	0.766150	+	0.642662i	$0.222170\pi$
$368$	17.1678	−	2.38195i	0.894933	−	0.124168i
$369$	−1.45392	−	4.47471i	−0.0756881	−	0.232944i
$370$	−32.5238	−	9.34155i	−1.69083	−	0.485644i
$371$	−0.997908	−	16.6833i	−0.0518088	−	0.866151i
$372$	−18.1061	+	7.29679i	−0.938757	+	0.378321i
$373$	18.1838			0.941522			0.470761	−	0.882261i	$-0.343979\pi$
$373$	18.1838			0.941522			0.470761	+	0.882261i	$0.343979\pi$
$374$	8.80801	−	7.35431i	0.455451	−	0.380282i
$375$	−34.3986			−1.77634
$376$	−15.4653	−	17.2217i	−0.797564	−	0.888142i
$377$	5.69653	+	7.84060i	0.293386	+	0.403811i
$378$	−15.7904	+	13.9201i	−0.812172	+	0.715972i
$379$	21.9048	−	7.11729i	1.12517	−	0.365590i	0.313432	−	0.949610i	$-0.398521\pi$
$379$	21.9048	−	7.11729i	1.12517	−	0.365590i	0.811739	+	0.584020i	$0.198521\pi$
$380$	−17.5098	+	27.9667i	−0.898235	+	1.43466i
$381$	6.95238	−	9.56913i	0.356181	−	0.490241i
$382$	−4.40079	−	2.97119i	−0.225164	−	0.152019i
$383$	−26.7169	−	8.68085i	−1.36517	−	0.443571i	−0.467405	−	0.884044i	$-0.654811\pi$
$383$	−26.7169	−	8.68085i	−1.36517	−	0.443571i	−0.897766	+	0.440473i	$0.854811\pi$
$384$	−10.9399	+	12.9564i	−0.558276	+	0.661177i
$385$	29.9731	+	17.7906i	1.52757	+	0.906692i
$386$	15.2841	−	5.55535i	0.777942	−	0.282760i
$387$	−1.77957	+	5.47694i	−0.0904604	+	0.278408i
$388$	−1.00090	−	0.250489i	−0.0508130	−	0.0127167i
$389$	6.56373	−	9.03420i	0.332794	−	0.458052i	−0.609525	−	0.792767i	$-0.708640\pi$
$389$	6.56373	−	9.03420i	0.332794	−	0.458052i	0.942320	+	0.334715i	$0.108640\pi$
$390$	9.52477	+	12.2022i	0.482305	+	0.617883i
$391$	3.27570	+	10.0816i	0.165659	+	0.509847i
$392$	13.0491	−	14.8903i	0.659078	−	0.752075i
$393$	−8.49050	−	11.6862i	−0.428289	−	0.589489i
$394$	18.5580	−	0.639879i	0.934939	−	0.0322366i
$395$			19.9090i			1.00173i
$396$	−4.97238	+	0.508163i	−0.249871	+	0.0255361i
$397$	33.8966			1.70122			0.850611	−	0.525796i	$-0.176233\pi$
$397$	33.8966			1.70122			0.850611	+	0.525796i	$0.176233\pi$
$398$	1.01252	+	29.3654i	0.0507529	+	1.47196i
$399$	−0.983425	−	16.4411i	−0.0492328	−	0.823086i
$400$	−31.0644	+	29.8930i	−1.55322	+	1.49465i
$401$	7.85626	+	24.1791i	0.392323	+	1.20745i	0.931027	+	0.364950i	$0.118914\pi$
$401$	7.85626	+	24.1791i	0.392323	+	1.20745i	−0.538704	+	0.842495i	$0.681086\pi$
$402$	9.30796	+	11.9245i	0.464239	+	0.594738i
$403$	9.68608	+	7.03735i	0.482498	+	0.350555i
$404$	7.80044	+	1.95217i	0.388086	+	0.0971239i
$405$	−7.57544	+	23.3148i	−0.376427	+	1.15852i
$406$	4.30332	−	19.2485i	0.213570	−	0.955289i
$407$	19.1939	+	5.54525i	0.951408	+	0.274868i
$408$	−8.97475	−	5.19739i	−0.444316	−	0.257309i
$409$	−9.77921	+	30.0973i	−0.483551	+	1.48822i	0.350518	+	0.936556i	$0.386006\pi$
$409$	−9.77921	+	30.0973i	−0.483551	+	1.48822i	−0.834069	+	0.551661i	$0.813994\pi$
$410$	29.0702	+	19.6267i	1.43568	+	0.969296i
$411$	−25.0167	−	18.1757i	−1.23398	−	0.896539i
$412$	−11.1004	+	17.7296i	−0.546877	+	0.873473i
$413$	0.107288	−	0.412567i	0.00527932	−	0.0203011i
$414$	1.27470	−	4.43803i	0.0626481	−	0.218117i
$415$	−8.73554	−	12.0234i	−0.428811	−	0.590207i
$416$	10.2958	+	1.47010i	0.504792	+	0.0720776i
$417$		−	23.1554i		−	1.13392i
$418$	10.3637	−	16.4959i	0.506907	−	0.806840i
$419$	33.1677			1.62035			0.810175	−	0.586189i	$-0.199372\pi$
$419$	33.1677			1.62035			0.810175	+	0.586189i	$0.199372\pi$
$420$	5.80985	−	30.9628i	0.283492	−	1.51083i
$421$	−5.58059	−	7.68102i	−0.271981	−	0.374350i	0.651076	−	0.759012i	$-0.274318\pi$
$421$	−5.58059	−	7.68102i	−0.271981	−	0.374350i	−0.923057	+	0.384662i	$0.874318\pi$
$422$	−2.02204	+	7.03998i	−0.0984312	+	0.342701i
$423$	−5.86465	+	1.90554i	−0.285149	+	0.0926505i
$424$	−17.4717	−	3.73785i	−0.848499	−	0.181526i
$425$	−21.3313	−	15.4981i	−1.03472	−	0.751767i
$426$	21.4469	+	14.4798i	1.03910	+	0.701550i
$427$	−5.35636	−	6.51559i	−0.259212	−	0.315311i
$428$	15.4603	−	12.9496i	0.747302	−	0.625940i
$429$	−5.61236	−	7.21311i	−0.270967	−	0.348252i
$430$	−14.6657	−	40.3489i	−0.707242	−	1.94580i
$431$	−32.2347	−	10.4737i	−1.55269	−	0.504501i	−0.597849	−	0.801609i	$-0.703978\pi$
$431$	−32.2347	−	10.4737i	−1.55269	−	0.504501i	−0.954844	+	0.297108i	$0.903978\pi$
$432$	9.82924	+	20.2434i	0.472910	+	0.973959i
$433$	14.5545	−	20.0326i	0.699446	−	0.962704i	−0.300515	−	0.953777i	$-0.597158\pi$
$433$	14.5545	−	20.0326i	0.699446	−	0.962704i	0.999960	−	0.00892696i	$-0.00284158\pi$
$434$	−2.29214	−	24.2581i	−0.110026	−	1.16443i
$435$	−9.69800	−	29.8474i	−0.464983	−	1.43107i
$436$	−12.7351	+	0.879258i	−0.609903	+	0.0421088i
$437$	10.5784	+	14.5599i	0.506034	+	0.696496i
$438$	−23.9825	+	0.826914i	−1.14593	+	0.0395115i
$439$	−5.19462			−0.247926			−0.123963	−	0.992287i	$-0.539560\pi$
$439$	−5.19462			−0.247926			−0.123963	+	0.992287i	$0.539560\pi$
$440$	26.8897	−	25.7953i	1.28191	−	1.22974i
$441$	−2.21631	−	4.78641i	−0.105539	−	0.227924i
$442$	0.219188	+	6.35698i	0.0104257	+	0.302371i
$443$	−3.98697	−	5.48760i	−0.189427	−	0.260724i	0.703732	−	0.710466i	$-0.251516\pi$
$443$	−3.98697	−	5.48760i	−0.189427	−	0.260724i	−0.893158	+	0.449742i	$0.851516\pi$
$444$	−1.24376	−	18.0146i	−0.0590263	−	0.854935i
$445$	23.8425	−	7.74691i	1.13024	−	0.367239i
$446$	4.86768	+	6.23600i	0.230491	+	0.295283i
$447$	23.1701	+	16.8341i	1.09591	+	0.796225i
$448$	−11.6119	−	17.6964i	−0.548610	−	0.836079i
$449$	−2.66893	+	8.21412i	−0.125955	+	0.387648i	−0.994074	−	0.108708i	$-0.965329\pi$
$449$	−2.66893	+	8.21412i	−0.125955	+	0.387648i	0.868119	+	0.496356i	$0.165329\pi$
$450$	3.92344	+	10.7943i	0.184953	+	0.508850i
$451$	−17.1455	−	11.6146i	−0.807348	−	0.546911i
$452$	24.1292	−	20.2106i	1.13494	−	0.950629i
$453$	−20.3648	−	6.61691i	−0.956820	−	0.310890i
$454$	−16.8483	+	24.9550i	−0.790732	+	1.17120i
$455$	−17.9865	+	7.05719i	−0.843221	+	0.330846i
$456$	−17.2181	−	3.68360i	−0.806311	−	0.172500i
$457$	4.65798	−	1.51347i	0.217891	−	0.0707971i	−0.198037	−	0.980194i	$-0.563457\pi$
$457$	4.65798	−	1.51347i	0.217891	−	0.0707971i	0.415928	+	0.909397i	$0.363457\pi$
$458$	−3.22826	+	11.2396i	−0.150847	+	0.525192i
$459$	−11.1346	+	8.08976i	−0.519719	+	0.377598i
$460$	12.8670	+	31.9278i	0.599925	+	1.48864i
$461$			39.6608i			1.84719i	0.383374	+	0.923593i	$0.374762\pi$
$461$			39.6608i			1.84719i	−0.383374	+	0.923593i	$0.625238\pi$
$462$	−3.45865	+	18.2756i	−0.160911	+	0.850256i
$463$	−7.15799			−0.332660			−0.166330	−	0.986070i	$-0.553192\pi$
$463$	−7.15799			−0.332660			−0.166330	+	0.986070i	$0.553192\pi$
$464$	−18.6000	−	9.93183i	−0.863481	−	0.461074i
$465$	−22.7886	−	31.3658i	−1.05679	−	1.45455i
$466$	21.8609	+	6.27894i	1.01269	+	0.290866i
$467$	−7.23714	−	22.2736i	−0.334895	−	1.03070i	−0.966774	−	0.255634i	$-0.917716\pi$
$467$	−7.23714	−	22.2736i	−0.334895	−	1.03070i	0.631879	−	0.775067i	$-0.282284\pi$
$468$	1.47032	−	2.34840i	0.0679656	−	0.108555i
$469$	−17.5771	+	6.89656i	−0.811635	+	0.318453i
$470$	25.7232	−	38.1001i	1.18652	−	1.75743i
$471$	−3.85321	+	11.8590i	−0.177546	+	0.546432i
$472$	−0.394366	−	0.228382i	−0.0181522	−	0.0105122i
$473$	8.62179	+	23.8360i	0.396430	+	1.09598i
$474$	−9.98500	+	3.62927i	−0.458626	+	0.166698i
$475$	−42.5740	−	13.8331i	−1.95343	−	0.634708i
$476$	9.40985	−	8.88993i	0.431300	−	0.407469i
$477$	−2.79782	+	3.85087i	−0.128103	+	0.176319i
$478$	−25.8487	−	33.1148i	−1.18229	−	1.51464i
$479$	8.26005	+	25.4218i	0.377411	+	1.16155i	0.941837	+	0.336069i	$0.109098\pi$
$479$	8.26005	+	25.4218i	0.377411	+	1.16155i	−0.564426	+	0.825484i	$0.690902\pi$
$480$	−30.2373	−	14.8302i	−1.38014	−	0.676903i
$481$	−8.95984	+	6.50971i	−0.408534	+	0.296817i
$482$	−13.3336	+	0.459741i	−0.607328	+	0.0209406i
$483$	−14.4795	−	9.25179i	−0.658838	−	0.420971i
$484$	−15.8997	+	15.2052i	−0.722715	+	0.691146i
$485$		−	2.04916i		−	0.0930476i
$486$	10.7803	−	0.371705i	0.489006	−	0.0168609i
$487$	8.62207	−	6.26430i	0.390703	−	0.283862i	−0.375040	−	0.927008i	$-0.622371\pi$
$487$	8.62207	−	6.26430i	0.390703	−	0.283862i	0.765744	+	0.643146i	$0.222371\pi$
$488$	−8.24230	+	3.65667i	−0.373112	+	0.165530i
$489$	−2.92719	+	0.951102i	−0.132372	+	0.0430103i
$490$	34.9803	+	17.9613i	1.58025	+	0.811409i
$491$	18.5379	+	13.4685i	0.836602	+	0.607827i	0.921419	−	0.388570i	$-0.127031\pi$
$491$	18.5379	+	13.4685i	0.836602	+	0.607827i	−0.0848175	+	0.996397i	$0.527031\pi$
$492$	−4.54415	+	18.1574i	−0.204866	+	0.818600i
$493$	3.98505	−	12.2647i	0.179478	−	0.552375i
$494$	3.68905	+	10.1495i	0.165978	+	0.456647i
$495$	−3.37658	−	9.33500i	−0.151766	−	0.419577i
$496$	−25.6448	−	4.56846i	−1.15148	−	0.205130i
$497$	−24.9510	+	20.5118i	−1.11920	+	0.920079i
$498$	4.43771	−	6.57293i	0.198858	−	0.294540i
$499$	0.970146	−	1.33529i	0.0434297	−	0.0597758i	−0.786750	−	0.617272i	$-0.788238\pi$
$499$	0.970146	−	1.33529i	0.0434297	−	0.0597758i	0.830180	+	0.557496i	$0.188238\pi$
$500$	−38.9046	−	24.3579i	−1.73987	−	1.08932i
$501$	−2.02657	−	6.23715i	−0.0905407	−	0.278655i
$502$	4.87488	−	16.9725i	0.217576	−	0.757520i
$503$	30.3387	−	22.0423i	1.35273	−	0.982819i	0.353865	−	0.935297i	$-0.384867\pi$
$503$	30.3387	−	22.0423i	1.35273	−	0.982819i	0.998870	−	0.0475228i	$-0.0151327\pi$
$504$	−5.56394	+	0.915855i	−0.247838	+	0.0407954i
$505$			15.9700i			0.710655i
$506$	−7.56753	−	18.8624i	−0.336418	−	0.838538i
$507$	−14.4185			−0.640348
$508$	14.6391	−	5.89958i	0.649504	−	0.261751i
$509$	−20.0659	+	14.5787i	−0.889406	+	0.646191i	−0.935723	−	0.352736i	$-0.885252\pi$
$509$	−20.0659	+	14.5787i	−0.889406	+	0.646191i	0.0463172	+	0.998927i	$0.485252\pi$
$510$	5.68619	−	19.7972i	0.251789	−	0.876635i
$511$	7.53847	−	28.9885i	0.333482	−	1.28237i
$512$	−21.5475	+	6.90692i	−0.952274	+	0.305246i
$513$	−13.7346	+	18.9040i	−0.606396	+	0.834633i
$514$	16.9743	−	25.1416i	0.748705	−	1.10895i
$515$	−39.5109	−	12.8379i	−1.74106	−	0.565704i
$516$	17.5628	−	14.7106i	0.773159	−	0.647598i
$517$	−15.2224	+	22.4712i	−0.669479	+	0.988283i
$518$	21.9963	+	4.91762i	0.966460	+	0.216068i
$519$	−27.3431	−	8.88432i	−1.20023	−	0.389978i
$520$	2.13195	+	20.5452i	0.0934922	+	0.900966i
$521$	4.92477	−	6.77836i	0.215758	−	0.296965i	−0.687395	−	0.726283i	$-0.741246\pi$
$521$	4.92477	−	6.77836i	0.215758	−	0.296965i	0.903153	+	0.429318i	$0.141246\pi$
$522$	−4.42807	+	3.45645i	−0.193812	+	0.151285i
$523$	8.17698	−	2.65686i	0.357554	−	0.116176i	−0.124731	−	0.992191i	$-0.539807\pi$
$523$	8.17698	−	2.65686i	0.357554	−	0.116176i	0.482285	+	0.876014i	$0.339807\pi$
$524$	−1.32762	−	19.2292i	−0.0579973	−	0.840030i
$525$	42.6635	−	2.55192i	1.86199	−	0.111375i
$526$	0.000448118		0.0129965i	1.95389e−5		0.000566674i
$527$		−	15.9313i		−	0.693977i
$528$	17.8389	+	8.78373i	0.776339	+	0.382263i
$529$	−4.22458			−0.183677
$530$	−1.22280	−	35.4640i	−0.0531149	−	1.54046i
$531$	−0.0982216	+	0.0713622i	−0.00426245	+	0.00309685i
$532$	10.5299	−	19.2912i	0.456527	−	0.836378i
$533$	10.9179	−	3.54743i	0.472905	−	0.153656i
$534$	8.23163	+	10.5456i	0.356217	+	0.456351i
$535$	32.4037	+	23.5427i	1.40094	+	1.01784i
$536$	2.08342	+	20.0775i	0.0899901	+	0.867217i
$537$	32.7020	+	10.6255i	1.41120	+	0.458526i
$538$	−11.5656	−	31.8199i	−0.498630	−	1.37185i
$539$	−20.6364	−	10.6367i	−0.888872	−	0.458156i
$540$	−34.2624	+	28.6982i	−1.47442	+	1.23498i
$541$	−3.51281	+	10.8113i	−0.151027	+	0.464814i	−0.997737	−	0.0672413i	$-0.978580\pi$
$541$	−3.51281	+	10.8113i	−0.151027	+	0.464814i	0.846709	+	0.532056i	$0.178580\pi$
$542$	26.2262	+	17.7066i	1.12651	+	0.760564i
$543$	−5.29247	−	3.84520i	−0.227122	−	0.165014i
$544$	−6.47006	−	12.2333i	−0.277401	−	0.524499i
$545$	−7.83453	−	24.1122i	−0.335594	−	1.03285i
$546$	−6.81821	−	7.73433i	−0.291792	−	0.330999i
$547$	−0.531438	+	0.386112i	−0.0227227	+	0.0165090i	−0.599089	−	0.800683i	$-0.704470\pi$
$547$	−0.531438	+	0.386112i	−0.0227227	+	0.0165090i	0.576366	+	0.817192i	$0.304470\pi$
$548$	−15.4233	−	38.2710i	−0.658851	−	1.63486i
$549$			2.40222i			0.102524i
$550$	42.8056	+	26.8931i	1.82524	+	1.14673i
$551$		−	21.8943i		−	0.932729i
$552$	−13.6672	+	12.2734i	−0.581716	+	0.522390i
$553$	−0.791789	−	13.2373i	−0.0336703	−	0.562908i
$554$	−4.87307	+	16.9662i	−0.207037	+	0.720825i
$555$	34.1081	−	11.0824i	1.44781	−	0.470421i
$556$	16.3965	−	26.1886i	0.695367	−	1.11064i
$557$	0.638638	+	0.463998i	0.0270600	+	0.0196602i	0.601233	−	0.799074i	$-0.294676\pi$
$557$	0.638638	+	0.463998i	0.0270600	+	0.0196602i	−0.574173	+	0.818734i	$0.694676\pi$
$558$	−3.88309	+	5.75145i	−0.164384	+	0.243478i
$559$	−13.3632	−	4.34197i	−0.565204	−	0.183646i
$560$	28.4959	−	30.9047i	1.20417	−	1.30596i
$561$	−3.37539	+	11.6833i	−0.142509	+	0.493271i
$562$	40.5187	−	14.7274i	1.70918	−	0.621238i
$563$	14.7285	+	4.78559i	0.620734	+	0.201689i	0.602466	−	0.798144i	$-0.294185\pi$
$563$	14.7285	+	4.78559i	0.620734	+	0.201689i	0.0182679	+	0.999833i	$0.494185\pi$
$564$	23.7975	+	5.95566i	1.00206	+	0.250778i
$565$	50.5732	+	36.7436i	2.12763	+	1.54581i
$566$	5.22453	+	6.69317i	0.219603	+	0.281335i
$567$	4.10959	−	15.8031i	0.172587	−	0.663666i
$568$	14.0029	+	31.5633i	0.587551	+	1.32437i
$569$	1.24663	+	1.71584i	0.0522616	+	0.0719319i	0.834348	−	0.551238i	$-0.185844\pi$
$569$	1.24663	+	1.71584i	0.0522616	+	0.0719319i	−0.782086	+	0.623170i	$0.785844\pi$
$570$	−1.20505	−	34.9493i	−0.0504740	−	1.46387i
$571$	−7.95604			−0.332950			−0.166475	−	0.986046i	$-0.553238\pi$
$571$	−7.95604			−0.332950			−0.166475	+	0.986046i	$0.553238\pi$
$572$	−1.23987	−	12.1321i	−0.0518416	−	0.507270i
$573$	5.62759			0.235096
$574$	−20.1091	−	11.8935i	−0.839336	−	0.496425i
$575$	−37.7819	+	27.4502i	−1.57562	+	1.14475i
$576$	−0.645950	+	5.99344i	−0.0269146	+	0.249727i
$577$	−33.1140	+	10.7594i	−1.37855	+	0.447919i	−0.902193	−	0.431332i	$-0.858044\pi$
$577$	−33.1140	+	10.7594i	−1.37855	+	0.447919i	−0.476359	+	0.879251i	$0.658044\pi$
$578$	−12.2797	+	9.58522i	−0.510767	+	0.398693i
$579$	−10.1307	+	13.9437i	−0.421018	+	0.579482i
$580$	10.1668	−	40.6244i	0.422154	−	1.68684i
$581$	6.28635	+	7.64685i	0.260802	+	0.317245i
$582$	1.02772	−	0.373547i	0.0426003	−	0.0154840i
$583$	0.689393	+	20.9396i	0.0285518	+	0.867229i
$584$	−27.7096	−	16.0470i	−1.14663	−	0.664028i
$585$	5.23349	+	1.70046i	0.216378	+	0.0703055i
$586$	−3.46002	+	5.12483i	−0.142932	+	0.211705i
$587$	33.4758	+	24.3216i	1.38170	+	1.00386i	0.996719	+	0.0809340i	$0.0257903\pi$
$587$	33.4758	+	24.3216i	1.38170	+	1.00386i	0.384976	+	0.922927i	$0.374210\pi$
$588$	−2.63151	+	20.8179i	−0.108522	+	0.858516i
$589$	−8.35819	−	25.7239i	−0.344393	−	1.05993i
$590$	0.249861	−	0.869923i	0.0102866	−	0.0358142i
$591$	−15.9215	+	11.5676i	−0.654922	+	0.475829i
$592$	11.3496	−	21.2551i	0.466466	−	0.873579i
$593$	21.4575			0.881152			0.440576	−	0.897715i	$-0.354774\pi$
$593$	21.4575			0.881152			0.440576	+	0.897715i	$0.354774\pi$
$594$	20.2554	−	16.9124i	0.831089	−	0.693924i
$595$	21.6649	+	13.8430i	0.888175	+	0.567508i
$596$	14.2849	+	35.4462i	0.585132	+	1.45193i
$597$	−18.3041	−	25.1935i	−0.749139	−	1.03110i
$598$	10.8284	+	3.11015i	0.442806	+	0.127184i
$599$	12.1065	+	37.2601i	0.494659	+	1.52241i	0.817487	+	0.575947i	$0.195367\pi$
$599$	12.1065	+	37.2601i	0.494659	+	1.52241i	−0.322827	+	0.946458i	$0.604633\pi$
$600$	9.55867	−	44.6797i	0.390231	−	1.82404i
$601$	15.7762	+	11.4621i	0.643525	+	0.467548i	0.861060	−	0.508504i	$-0.169801\pi$
$601$	15.7762	+	11.4621i	0.643525	+	0.467548i	−0.217534	+	0.976053i	$0.569801\pi$
$602$	11.3558	+	26.2443i	0.462826	+	1.06964i
$603$	5.11436	+	1.66176i	0.208273	+	0.0676720i
$604$	−18.3469	−	21.9041i	−0.746525	−	0.891267i
$605$	−36.9615	−	23.3017i	−1.50270	−	0.947349i
$606$	−8.00945	+	2.91121i	−0.325361	+	0.118260i
$607$	1.38834	−	4.27288i	0.0563512	−	0.173431i	−0.918919	−	0.394445i	$-0.870937\pi$
$607$	1.38834	−	4.27288i	0.0563512	−	0.173431i	0.975271	+	0.221014i	$0.0709367\pi$
$608$	−16.8652	−	16.3584i	−0.683972	−	0.663421i
$609$	7.63514	+	19.4595i	0.309392	+	0.788540i
$610$	−11.0193	−	14.1169i	−0.446159	−	0.571576i
$611$	−4.64934	−	14.3092i	−0.188092	−	0.578888i
$612$	−3.67806	+	0.253940i	−0.148677	+	0.0102649i
$613$	−37.8992	+	27.5354i	−1.53073	+	1.11214i	−0.574905	+	0.818220i	$0.694961\pi$
$613$	−37.8992	+	27.5354i	−1.53073	+	1.11214i	−0.955829	+	0.293924i	$0.905039\pi$
$614$	−0.292253	−	8.47604i	−0.0117944	−	0.342065i
$615$	−37.1740			−1.49900
$616$	−16.8528	+	18.2204i	−0.679018	+	0.734122i
$617$	12.8290			0.516475			0.258237	−	0.966081i	$-0.416858\pi$
$617$	12.8290			0.516475			0.258237	+	0.966081i	$0.416858\pi$
$618$	−0.763943	−	22.1562i	−0.0307303	−	0.891253i
$619$	0.328517	−	0.238682i	0.0132042	−	0.00959343i	−0.581164	−	0.813787i	$-0.697402\pi$
$619$	0.328517	−	0.238682i	0.0132042	−	0.00959343i	0.594368	+	0.804193i	$0.297402\pi$
$620$	−3.56334	−	51.6112i	−0.143107	−	2.07276i
$621$	7.53299	+	23.1841i	0.302288	+	0.930348i
$622$	18.6806	+	23.9318i	0.749025	+	0.959578i
$623$	−15.5446	+	6.09906i	−0.622779	+	0.244354i
$624$	−9.91542	+	4.81447i	−0.396934	+	0.192733i
$625$	11.5179	−	35.4484i	0.460716	−	1.41794i
$626$	−23.7708	+	8.64002i	−0.950073	+	0.345325i
$627$	0.679388	+	20.6357i	0.0271322	+	0.824110i
$628$	−12.7554	+	10.6839i	−0.508995	+	0.426334i
$629$	14.0155	+	4.55392i	0.558835	+	0.181576i
$630$	−4.44730	−	10.2782i	−0.177185	−	0.409492i
$631$	13.9226	+	10.1153i	0.554248	+	0.402685i	0.829349	−	0.558730i	$-0.188711\pi$
$631$	13.9226	+	10.1153i	0.554248	+	0.402685i	−0.275101	+	0.961415i	$0.588711\pi$
$632$	−13.8629	−	2.96579i	−0.551436	−	0.117973i
$633$	−2.39885	−	7.38291i	−0.0953458	−	0.293444i
$634$	−23.1911	−	6.66099i	−0.921036	−	0.264542i
$635$	18.4249	+	25.3597i	0.731171	+	1.00637i
$636$	17.5634	−	7.07809i	0.696434	−	0.280665i
$637$	11.6784	−	5.40759i	0.462714	−	0.214256i
$638$	−6.03993	+	23.9759i	−0.239123	+	0.949215i
$639$	9.19911			0.363911
$640$	−23.6968	−	38.1841i	−0.936696	−	1.50936i
$641$	−19.0684	+	13.8540i	−0.753158	+	0.547202i	−0.896804	−	0.442428i	$-0.854117\pi$
$641$	−19.0684	+	13.8540i	−0.753158	+	0.547202i	0.143646	+	0.989629i	$0.454117\pi$
$642$	−5.90044	+	20.5431i	−0.232872	+	0.810773i
$643$	−1.40484	−	4.32367i	−0.0554016	−	0.170509i	0.919527	−	0.393027i	$-0.128572\pi$
$643$	−1.40484	−	4.32367i	−0.0554016	−	0.170509i	−0.974928	+	0.222519i	$0.928572\pi$
$644$	−9.82490	−	20.7167i	−0.387155	−	0.816354i
$645$	36.8104	+	26.7443i	1.44941	+	1.05306i
$646$	8.04070	−	11.9095i	0.316357	−	0.468573i
$647$	22.2464	+	7.22829i	0.874596	+	0.284174i	0.711712	−	0.702472i	$-0.247920\pi$
$647$	22.2464	+	7.22829i	0.874596	+	0.284174i	0.162885	+	0.986645i	$0.447920\pi$
$648$	−15.1059	−	8.74800i	−0.593414	−	0.343654i
$649$	−0.148320	+	0.513386i	−0.00582208	+	0.0201522i
$650$	−26.3372	+	9.57282i	−1.03303	+	0.375477i
$651$	16.3993	+	19.9485i	0.642740	+	0.781842i
$652$	−3.98412	−	0.997079i	−0.156030	−	0.0390486i
$653$	−4.31189	+	5.93481i	−0.168737	+	0.232247i	−0.885008	−	0.465575i	$-0.845847\pi$
$653$	−4.31189	+	5.93481i	−0.168737	+	0.232247i	0.716271	+	0.697822i	$0.245847\pi$
$654$	10.6648	−	8.32473i	0.417028	−	0.325523i
$655$	36.4077	−	11.8296i	1.42257	−	0.462220i
$656$	−17.9968	+	17.3182i	−0.702658	+	0.676161i
$657$	−6.90140	+	5.01416i	−0.269249	+	0.195621i
$658$	−15.5879	+	26.3554i	−0.607678	+	1.02744i
$659$	−28.2973			−1.10231			−0.551154	−	0.834404i	$-0.685812\pi$
$659$	−28.2973			−1.10231			−0.551154	+	0.834404i	$0.685812\pi$
$660$	−8.32177	+	38.6046i	−0.323925	+	1.50268i
$661$	−16.9838			−0.660593			−0.330296	−	0.943877i	$-0.607149\pi$
$661$	−16.9838			−0.660593			−0.330296	+	0.943877i	$0.607149\pi$
$662$	0.0298209	+	0.864879i	0.00115902	+	0.0336145i
$663$	−3.96245	−	5.45385i	−0.153889	−	0.211810i
$664$	9.67336	−	4.29156i	0.375399	−	0.166545i
$665$	42.2445	+	10.9857i	1.63817	+	0.426007i
$666$	−3.94986	−	5.06018i	−0.153054	−	0.196078i
$667$	−18.4789	−	13.4257i	−0.715507	−	0.519847i
$668$	2.12454	−	8.48921i	0.0822009	−	0.328457i
$669$	−7.97384	−	2.59086i	−0.308286	−	0.100168i
$670$	−37.6778	+	13.6948i	−1.45562	+	0.529076i
$671$	6.49300	+	8.34493i	0.250659	+	0.322152i
$672$	20.6943	+	8.65791i	0.798299	+	0.333986i
$673$	−19.8317	−	6.44371i	−0.764456	−	0.248387i	−0.0992660	−	0.995061i	$-0.531649\pi$
$673$	−19.8317	−	6.44371i	−0.764456	−	0.248387i	−0.665190	+	0.746674i	$0.731649\pi$
$674$	0.233536	−	0.345902i	0.00899545	−	0.0133236i
$675$	−49.0546	−	35.6402i	−1.88811	−	1.37179i
$676$	−16.3072	−	10.2099i	−0.627201	−	0.392687i
$677$	−30.0845	+	9.77503i	−1.15624	+	0.375685i	−0.823490	−	0.567330i	$-0.807976\pi$
$677$	−30.0845	+	9.77503i	−1.15624	+	0.375685i	−0.332749	+	0.943015i	$0.607976\pi$
$678$	−9.20894	+	32.0621i	−0.353667	+	1.23134i
$679$	0.0814959	+	1.36247i	0.00312752	+	0.0522867i
$680$	20.4496	−	18.3641i	0.784207	−	0.704230i
$681$		−	31.9116i		−	1.22285i
$682$	2.05646	+	30.4753i	0.0787458	+	1.16696i
$683$			6.47508i			0.247762i	0.992297	+	0.123881i	$0.0395341\pi$
$683$			6.47508i			0.247762i	−0.992297	+	0.123881i	$0.960466\pi$
$684$	−5.80565	+	2.33969i	−0.221985	+	0.0894602i
$685$	66.2982	−	48.1684i	2.53312	−	1.84042i
$686$	−23.9724	−	10.5511i	−0.915269	−	0.402843i
$687$	−3.82986	−	11.7871i	−0.146118	−	0.449706i
$688$	30.2801	−	4.20122i	1.15442	−	0.160170i
$689$	−9.39576	−	6.82642i	−0.357950	−	0.260066i
$690$	−30.2364	−	20.4141i	−1.15108	−	0.777151i
$691$	2.11781	−	6.51796i	0.0805654	−	0.247955i	−0.902658	−	0.430358i	$-0.858387\pi$
$691$	2.11781	−	6.51796i	0.0805654	−	0.247955i	0.983224	+	0.182403i	$0.0583875\pi$
$692$	−24.6338	−	29.4100i	−0.936437	−	1.11800i
$693$	2.61631	+	6.07246i	0.0993854	+	0.230674i
$694$	−15.6601	−	43.0847i	−0.594448	−	1.63547i
$695$	58.3621	+	18.9630i	2.21380	+	0.719307i
$696$	22.2277	−	2.30655i	0.842540	−	0.0874294i
$697$	−12.3580	−	8.97863i	−0.468094	−	0.340090i
$698$	−1.72971	−	2.21594i	−0.0654706	−	0.0838747i
$699$	−22.9258	+	7.44905i	−0.867134	+	0.281749i
$700$	50.0592	+	27.3242i	1.89206	+	1.03276i
$701$	−27.7901	+	20.1907i	−1.04962	+	0.762592i	−0.972140	−	0.234402i	$-0.924687\pi$
$701$	−27.7901	+	20.1907i	−1.04962	+	0.762592i	−0.0774783	+	0.996994i	$0.524687\pi$
$702$	0.504058	+	14.6189i	0.0190244	+	0.551754i
$703$	25.0197			0.943636
$704$	13.9558	+	22.5662i	0.525981	+	0.850496i
$705$			48.7211i			1.83494i
$706$	1.74406	+	50.5818i	0.0656384	+	1.90367i
$707$	−0.635132	−	10.6183i	−0.0238866	−	0.399341i
$708$	0.481842	−	0.0332673i	0.0181087	−	0.00125026i
$709$	28.1087	−	9.13307i	1.05564	−	0.343000i	0.270763	−	0.962646i	$-0.412724\pi$
$709$	28.1087	−	9.13307i	1.05564	−	0.343000i	0.784881	+	0.619647i	$0.212724\pi$
$710$	−54.0595	+	42.1976i	−2.02882	+	1.58365i
$711$	−2.21993	+	3.05547i	−0.0832538	+	0.114589i
$712$	1.84250	+	17.7558i	0.0690507	+	0.665428i
$713$	−26.8364	−	8.71968i	−1.00503	−	0.326554i
$714$	−2.99335	+	13.3891i	−0.112023	+	0.501075i
$715$	22.7765	−	8.23854i	0.851794	−	0.308104i
$716$	29.4617	+	35.1740i	1.10104	+	1.31451i
$717$	42.3432	+	13.7581i	1.58134	+	0.513807i
$718$	−11.6467	+	17.2505i	−0.434649	+	0.643782i
$719$	−17.7163	+	24.3843i	−0.660705	+	0.909382i	−0.999504	−	0.0314764i	$-0.989979\pi$
$719$	−17.7163	+	24.3843i	−0.660705	+	0.909382i	0.338800	+	0.940859i	$0.389979\pi$
$720$	−11.8587	+	1.64534i	−0.441948	+	0.0613181i
$721$	26.7810	+	6.96441i	0.997375	+	0.259368i
$722$	−0.682840	+	2.37739i	−0.0254127	+	0.0884774i
$723$	11.4393	−	8.31113i	0.425432	−	0.309094i
$724$	−3.26292	−	8.09654i	−0.121266	−	0.300906i
$725$	56.8141			2.11002
$726$	4.94874	−	22.7850i	0.183665	−	0.845633i
$727$			7.87256i			0.291977i	0.989286	+	0.145989i	$0.0466363\pi$
$727$			7.87256i			0.291977i	−0.989286	+	0.145989i	$0.953364\pi$
$728$	−2.23460	−	13.5755i	−0.0828198	−	0.503141i
$729$	−24.2277	+	17.6025i	−0.897322	+	0.651943i
$730$	17.5561	−	61.1240i	0.649782	−	2.26230i
$731$	5.77759	+	17.7816i	0.213692	+	0.657677i
$732$	5.07132	−	8.09993i	0.187441	−	0.299382i
$733$	−11.0729	+	15.2405i	−0.408985	+	0.562920i	−0.962971	−	0.269607i	$-0.913106\pi$
$733$	−11.0729	+	15.2405i	−0.408985	+	0.562920i	0.553985	+	0.832526i	$0.313106\pi$
$734$	2.11004	−	3.12530i	0.0778831	−	0.115357i
$735$	−41.3776	+	4.96778i	−1.52624	+	0.183239i
$736$	−24.1484	+	4.20322i	−0.890123	+	0.154933i
$737$	22.2581	−	8.05102i	0.819887	−	0.296563i
$738$	2.27300	+	6.25358i	0.0836703	+	0.230197i
$739$	−0.664596	+	2.04542i	−0.0244476	+	0.0752419i	−0.962536	−	0.271154i	$-0.912595\pi$
$739$	−0.664596	+	2.04542i	−0.0244476	+	0.0752419i	0.938088	+	0.346396i	$0.112595\pi$
$740$	46.4235	+	11.6181i	1.70656	+	0.427090i
$741$	−9.25940	−	6.72735i	−0.340153	−	0.247135i
$742$	2.22344	+	23.5310i	0.0816251	+	0.863851i
$743$	29.2447	−	9.50217i	1.07288	−	0.348601i	0.281274	−	0.959628i	$-0.409243\pi$
$743$	29.2447	−	9.50217i	1.07288	−	0.348601i	0.791610	+	0.611027i	$0.209243\pi$
$744$	25.2351	−	11.1955i	0.925163	−	0.410446i
$745$	−61.4046	+	44.6131i	−2.24969	+	1.63450i
$746$	−25.7005	+	0.886151i	−0.940962	+	0.0324443i
$747$		−	2.81930i		−	0.103153i
$748$	−12.0906	+	10.8236i	−0.442077	+	0.395751i
$749$	−22.4812	−	14.3646i	−0.821446	−	0.524870i
$750$	48.6181	−	1.67635i	1.77528	−	0.0612115i
$751$	9.06629	−	6.58705i	0.330834	−	0.240365i	−0.409951	−	0.912108i	$-0.634454\pi$
$751$	9.06629	−	6.58705i	0.330834	−	0.240365i	0.740784	+	0.671743i	$0.234454\pi$
$752$	22.6976	+	23.5870i	0.827696	+	0.860131i
$753$	5.78333	+	17.7993i	0.210756	+	0.648641i
$754$	−8.43342	−	10.8041i	−0.307127	−	0.393462i
$755$	33.3552	−	45.9095i	1.21392	−	1.67082i
$756$	21.6394	−	20.4438i	0.787018	−	0.743533i
$757$	24.9464	+	8.10558i	0.906692	+	0.294602i	0.724996	−	0.688753i	$-0.241841\pi$
$757$	24.9464	+	8.10558i	0.906692	+	0.294602i	0.181696	+	0.983355i	$0.441841\pi$
$758$	−30.6128	+	11.1269i	−1.11191	+	0.404146i
$759$	17.8333	+	12.0805i	0.647307	+	0.438496i
$760$	23.3850	−	40.3807i	0.848264	−	1.46476i
$761$	5.92010	−	18.2202i	0.214604	−	0.660482i	−0.784578	−	0.620030i	$-0.787120\pi$
$761$	5.92010	−	18.2202i	0.214604	−	0.660482i	0.999181	−	0.0404518i	$-0.0128797\pi$
$762$	−9.35998	+	13.8636i	−0.339076	+	0.502224i
$763$	6.16805	+	15.7204i	0.223298	+	0.569116i
$764$	6.36476	+	3.98494i	0.230269	+	0.144170i
$765$	−2.26270	−	6.96388i	−0.0818081	−	0.251779i
$766$	38.1840	+	10.9673i	1.37964	+	0.396264i
$767$	−0.174117	−	0.239652i	−0.00628700	−	0.00865332i
$768$	14.8308	−	18.8453i	0.535160	−	0.680023i
$769$	5.06939			0.182807			0.0914035	−	0.995814i	$-0.470865\pi$
$769$	5.06939			0.182807			0.0914035	+	0.995814i	$0.470865\pi$
$770$	−43.2302	−	23.6840i	−1.55791	−	0.853514i
$771$			32.1502i			1.15786i
$772$	−21.3315	+	8.59662i	−0.767736	+	0.309399i
$773$	−30.3848	+	22.0759i	−1.09287	+	0.794014i	−0.979881	−	0.199583i	$-0.936041\pi$
$773$	−30.3848	+	22.0759i	−1.09287	+	0.794014i	−0.112985	+	0.993597i	$0.536041\pi$
$774$	2.24828	−	7.82768i	0.0808129	−	0.281360i
$775$	66.7515	−	21.6889i	2.39779	−	0.779088i
$776$	1.42685	+	0.305258i	0.0512211	+	0.0109581i
$777$	−22.2374	+	8.72505i	−0.797761	+	0.313010i
$778$	−8.83674	+	13.0886i	−0.316813	+	0.469248i
$779$	−24.6648	−	8.01408i	−0.883708	−	0.287134i
$780$	−14.0567	−	16.7821i	−0.503311	−	0.600896i
$781$	31.9563	−	24.8644i	1.14349	−	0.889720i
$782$	−5.12109	−	14.0894i	−0.183130	−	0.503836i
$783$	9.16425	−	28.2047i	0.327504	−	1.00795i
$784$	−17.7176	+	21.6815i	−0.632770	+	0.774340i
$785$	−26.7344	−	19.4237i	−0.954191	−	0.693260i
$786$	12.5697	+	16.1032i	0.448348	+	0.574381i
$787$	5.45054	−	1.77099i	0.194291	−	0.0631288i	−0.210255	−	0.977646i	$-0.567430\pi$
$787$	5.45054	−	1.77099i	0.194291	−	0.0631288i	0.404546	+	0.914518i	$0.367430\pi$
$788$	−26.1982	+	1.80878i	−0.933273	+	0.0644349i
$789$	−0.00810101	−	0.0111501i	−0.000288403	−	0.000396953i
$790$	−0.970227	−	28.1389i	−0.0345191	−	1.00114i
$791$	−35.0869	−	22.4191i	−1.24755	−	0.797132i
$792$	7.00306	−	0.960543i	0.248843	−	0.0341314i
$793$	−5.86119			−0.208137
$794$	−47.9086	+	1.65188i	−1.70021	+	0.0586231i
$795$	22.1055	+	30.4257i	0.784003	+	1.07909i
$796$	−2.86213	−	41.4550i	−0.101445	−	1.46933i
$797$	−2.91613	−	8.97494i	−0.103295	−	0.317909i	0.886032	−	0.463625i	$-0.153451\pi$
$797$	−2.91613	−	8.97494i	−0.103295	−	0.317909i	−0.989326	+	0.145716i	$0.953451\pi$
$798$	2.19117	+	23.1895i	0.0775667	+	0.820900i
$799$	−11.7676	+	16.1967i	−0.416307	+	0.572998i
$800$	42.4489	−	43.7638i	1.50079	−	1.54729i
$801$	4.52296	+	1.46960i	0.159811	+	0.0519257i
$802$	−12.2821	−	33.7912i	−0.433698	−	1.19321i
$803$	−10.4215	+	36.0724i	−0.367768	+	1.27297i
$804$	−13.7367	−	16.4001i	−0.484458	−	0.578388i
$805$	35.1766	−	28.9181i	1.23981	−	1.01923i
$806$	−14.0330	−	9.47437i	−0.494291	−	0.333720i
$807$	29.0294	+	21.0911i	1.02188	+	0.742442i
$808$	−11.1201	−	2.37900i	−0.391203	−	0.0836930i
$809$	−6.19588	+	2.01316i	−0.217835	+	0.0707790i	−0.415902	−	0.909410i	$-0.636534\pi$
$809$	−6.19588	+	2.01316i	−0.217835	+	0.0707790i	0.198066	+	0.980189i	$0.436534\pi$
$810$	9.57073	−	33.3217i	0.336281	−	1.17081i
$811$	−8.95432	−	12.3246i	−0.314429	−	0.432774i	0.622327	−	0.782757i	$-0.286187\pi$
$811$	−8.95432	−	12.3246i	−0.314429	−	0.432774i	−0.936756	+	0.349983i	$0.886187\pi$
$812$	−5.14416	+	27.4151i	−0.180525	+	0.962081i
$813$	−33.5372			−1.17620
$814$	−27.3984	−	6.90213i	−0.960315	−	0.241920i
$815$		−	8.15675i		−	0.285718i
$816$	12.9380	+	6.90849i	0.452919	+	0.241846i
$817$	18.6579	+	25.6804i	0.652758	+	0.898444i
$818$	12.3549	−	43.0153i	0.431981	−	1.50400i
$819$	−3.54732	−	0.922483i	−0.123953	−	0.0322342i
$820$	−42.0436	−	26.3232i	−1.46822	−	0.919248i
$821$	1.39594	+	1.01421i	0.0487186	+	0.0353961i	0.611878	−	0.790952i	$-0.290414\pi$
$821$	1.39594	+	1.01421i	0.0487186	+	0.0353961i	−0.563159	+	0.826348i	$0.690414\pi$
$822$	36.2436	+	24.4699i	1.26414	+	0.853485i
$823$	−3.28766	+	10.1184i	−0.114601	+	0.352705i	−0.991864	−	0.127306i	$-0.959367\pi$
$823$	−3.28766	+	10.1184i	−0.114601	+	0.352705i	0.877263	+	0.480010i	$0.159367\pi$
$824$	14.8250	−	25.5994i	0.516452	−	0.891799i
$825$	−53.5481	+	1.76296i	−1.86431	+	0.0613785i
$826$	−0.131533	+	0.588340i	−0.00457662	+	0.0204710i
$827$	14.6133	−	44.9750i	0.508153	−	1.56393i	−0.287252	−	0.957855i	$-0.592742\pi$
$827$	14.6133	−	44.9750i	0.508153	−	1.56393i	0.795405	−	0.606078i	$-0.207258\pi$
$828$	−1.58535	+	6.33472i	−0.0550947	+	0.220147i
$829$	15.9603	+	11.5958i	0.554323	+	0.402739i	0.829377	−	0.558690i	$-0.188696\pi$
$829$	15.9603	+	11.5958i	0.554323	+	0.402739i	−0.275054	+	0.961429i	$0.588696\pi$
$830$	12.9325	+	16.5679i	0.448894	+	0.575080i
$831$	−5.78118	−	17.7927i	−0.200547	−	0.617220i
$832$	−14.6234	−	1.57606i	−0.506976	−	0.0546400i
$833$	−14.9553	−	8.34245i	−0.518171	−	0.289049i
$834$	1.12843	+	32.7272i	0.0390744	+	1.13325i
$835$	17.3801			0.601464
$836$	−13.8439	+	23.8199i	−0.478802	+	0.823829i
$837$		−	36.6364i		−	1.26634i
$838$	−46.8784	+	1.61636i	−1.61939	+	0.0558363i
$839$	−15.6326	−	21.5164i	−0.539696	−	0.742828i	0.448873	−	0.893595i	$-0.351825\pi$
$839$	−15.6326	−	21.5164i	−0.539696	−	0.742828i	−0.988569	+	0.150768i	$0.951825\pi$
$840$	−6.70259	+	44.0451i	−0.231261	+	1.51970i
$841$	−0.374692	−	1.15318i	−0.0129204	−	0.0397650i
$842$	8.26178	+	10.5842i	0.284720	+	0.364755i
$843$	−26.8569	+	36.9653i	−0.924999	+	1.27315i
$844$	2.51481	−	10.0487i	0.0865635	−	0.345889i
$845$	11.8080	−	36.3412i	0.406206	−	1.25017i
$846$	8.19608	−	2.97904i	0.281787	−	0.102422i
$847$	25.5020	+	14.0231i	0.876260	+	0.481839i
$848$	24.8761	+	4.43153i	0.854250	+	0.152179i
$849$	−8.55841	−	2.78080i	−0.293724	−	0.0954366i
$850$	30.9043	+	20.8650i	1.06001	+	0.715664i
$851$	15.3423	−	21.1168i	0.525926	−	0.723875i
$852$	−31.0181	−	19.4202i	−1.06266	−	0.665326i
$853$	10.4297	−	3.38881i	0.357106	−	0.116031i	−0.124969	−	0.992161i	$-0.539883\pi$
$853$	10.4297	−	3.38881i	0.357106	−	0.116031i	0.482075	+	0.876130i	$0.339883\pi$
$854$	7.88806	+	8.94793i	0.269924	+	0.306192i
$855$	−7.30707	−	10.0573i	−0.249896	−	0.343953i
$856$	−21.2201	+	19.0560i	−0.725289	+	0.651320i
$857$	29.2379			0.998747			0.499373	−	0.866387i	$-0.333564\pi$
$857$	29.2379			0.998747			0.499373	+	0.866387i	$0.333564\pi$
$858$	8.28387	+	9.92132i	0.282807	+	0.338708i
$859$	7.60160			0.259363			0.129682	−	0.991556i	$-0.458604\pi$
$859$	7.60160			0.259363			0.129682	+	0.991556i	$0.458604\pi$
$860$	22.6944	+	56.3134i	0.773873	+	1.92027i
$861$	24.7166	−	1.47842i	0.842341	−	0.0503846i
$862$	46.0702	+	13.2324i	1.56916	+	0.450696i
$863$	−8.50663	−	26.1807i	−0.289569	−	0.891201i	−0.984992	−	0.172601i	$-0.944783\pi$
$863$	−8.50663	−	26.1807i	−0.289569	−	0.891201i	0.695423	−	0.718601i	$-0.255217\pi$
$864$	−14.8789	−	28.1324i	−0.506191	−	0.957084i
$865$	44.7850	−	61.6413i	1.52274	−	2.09587i
$866$	−19.5947	+	29.0228i	−0.665856	+	0.986235i
$867$	5.10180	−	15.7017i	0.173266	−	0.533259i
$868$	4.42182	+	34.1741i	0.150086	+	1.15994i
$869$	0.546999	+	16.6145i	0.0185557	+	0.563609i
$870$	15.1614	+	41.7129i	0.514021	+	1.41420i
$871$	−4.05453	+	12.4786i	−0.137383	+	0.422820i
$872$	17.9567	−	1.86334i	0.608090	−	0.0631007i
$873$	0.228489	−	0.314488i	0.00773317	−	0.0106438i
$874$	−15.6608	−	20.0631i	−0.529734	−	0.678644i
$875$	−15.2822	+	58.7664i	−0.516634	+	1.98667i
$876$	33.8559	−	2.33748i	1.14389	−	0.0789760i
$877$	7.68045	−	5.58018i	0.259351	−	0.188429i	−0.450510	−	0.892771i	$-0.648758\pi$
$877$	7.68045	−	5.58018i	0.259351	−	0.188429i	0.709861	+	0.704342i	$0.248758\pi$
$878$	7.34195	−	0.253150i	0.247779	−	0.00854338i
$879$		−	6.55346i		−	0.221043i
$880$	−36.7481	+	37.7688i	−1.23878	+	1.27318i
$881$		−	11.8374i		−	0.398813i	−0.979917	−	0.199406i	$-0.936099\pi$
$881$		−	11.8374i		−	0.398813i	0.979917	−	0.199406i	$-0.0639014\pi$
$882$	3.36573	+	6.65697i	0.113330	+	0.224152i
$883$	−31.6354	−	43.5424i	−1.06462	−	1.46532i	−0.875410	−	0.483381i	$-0.839409\pi$
$883$	−31.6354	−	43.5424i	−1.06462	−	1.46532i	−0.189206	−	0.981937i	$-0.560591\pi$
$884$	−0.619590	−	8.97411i	−0.0208391	−	0.301832i
$885$	0.296424	+	0.912299i	0.00996418	+	0.0306666i
$886$	5.90251	+	7.56173i	0.198299	+	0.254041i
$887$	−5.82550	−	4.23247i	−0.195601	−	0.142112i	0.485674	−	0.874140i	$-0.338574\pi$
$887$	−5.82550	−	4.23247i	−0.195601	−	0.142112i	−0.681275	+	0.732028i	$0.738574\pi$
$888$	2.63580	+	25.4007i	0.0884518	+	0.852393i
$889$	−13.2591	−	16.1287i	−0.444696	−	0.540938i
$890$	−33.3209	+	12.1112i	−1.11692	+	0.405968i
$891$	−5.68129	+	19.6648i	−0.190330	+	0.658797i
$892$	−7.18374	−	8.57658i	−0.240530	−	0.287165i
$893$	−10.5034	+	32.3262i	−0.351484	+	1.08176i
$894$	−33.5684	−	22.6637i	−1.12270	−	0.757988i
$895$	−53.5623	+	73.7222i	−1.79039	+	2.46426i
$896$	17.2743	+	24.4458i	0.577095	+	0.816677i
$897$	−11.3559	+	3.68974i	−0.379161	+	0.123197i
$898$	3.37189	−	11.7397i	0.112522	−	0.391758i
$899$	20.1775	+	27.7719i	0.672956	+	0.926244i
$900$	−6.07132	−	15.0652i	−0.202377	−	0.502174i
$901$			15.4538i			0.514839i
$902$	24.7990	+	15.5802i	0.825715	+	0.518765i
$903$	−25.5385	−	16.3181i	−0.849868	−	0.543031i
$904$	−33.1187	+	29.7411i	−1.10151	+	0.989174i
$905$	14.0259	−	10.1904i	0.466237	−	0.338741i
$906$	29.1055	+	8.35973i	0.966965	+	0.277734i
$907$	−25.7604	+	8.37006i	−0.855360	+	0.277923i	−0.703689	−	0.710508i	$-0.748465\pi$
$907$	−25.7604	+	8.37006i	−0.855360	+	0.277923i	−0.151671	+	0.988431i	$0.548465\pi$
$908$	22.5969	−	36.0918i	0.749903	−	1.19775i
$909$	−1.78071	+	2.45094i	−0.0590624	+	0.0812925i
$910$	25.0778	−	10.8510i	0.831319	−	0.359707i
$911$	5.73175	−	17.6405i	0.189901	−	0.584456i	−0.810097	−	0.586296i	$-0.800586\pi$
$911$	5.73175	−	17.6405i	0.189901	−	0.584456i	0.999998	+	0.00183978i	$0.000585622\pi$
$912$	24.5151	+	4.36721i	0.811777	+	0.144613i
$913$	−7.62034	−	9.79381i	−0.252196	−	0.324128i
$914$	−6.50971	+	2.36609i	−0.215322	+	0.0782635i
$915$	18.0509	+	5.86511i	0.596746	+	0.193894i
$916$	4.01500	−	16.0431i	0.132659	−	0.530078i
$917$	−23.7366	+	9.31331i	−0.783853	+	0.307553i
$918$	15.3431	−	11.9765i	0.506398	−	0.395283i
$919$	−4.45024	+	1.44597i	−0.146800	+	0.0476982i	−0.381495	−	0.924371i	$-0.624591\pi$
$919$	−4.45024	+	1.44597i	−0.146800	+	0.0476982i	0.234695	+	0.972069i	$0.424591\pi$
$920$	−19.7418	−	44.4989i	−0.650867	−	1.46708i
$921$	5.28331	+	7.27185i	0.174091	+	0.239616i
$922$	−1.93279	−	56.0555i	−0.0636530	−	1.84609i
$923$			22.4450i			0.738785i
$924$	3.99775	−	25.9987i	0.131516	−	0.855296i
$925$			64.9243i			2.13470i
$926$	10.1169	−	0.348830i	0.332462	−	0.0114633i
$927$	−4.63233	−	6.37585i	−0.152146	−	0.209410i
$928$	26.7727	+	13.1310i	0.878857	+	0.431045i
$929$	−35.2487	+	11.4530i	−1.15647	+	0.375761i	−0.823578	−	0.567203i	$-0.808025\pi$
$929$	−35.2487	+	11.4530i	−1.15647	+	0.375761i	−0.332895	+	0.942964i	$0.608025\pi$
$930$	33.7373	+	43.2210i	1.10629	+	1.41727i
$931$	−28.5248	−	5.62420i	−0.934863	−	0.184326i
$932$	−31.2037	−	7.80914i	−1.02211	−	0.255797i
$933$	−30.6011	−	9.94290i	−1.00183	−	0.325516i
$934$	11.3142	+	31.1283i	0.370213	+	1.01855i
$935$	−26.6831	−	18.0755i	−0.872629	−	0.591133i
$936$	−1.96367	+	3.39082i	−0.0641845	+	0.110832i
$937$	14.4127	−	44.3576i	0.470841	−	1.44910i	−0.380644	−	0.924722i	$-0.624298\pi$
$937$	14.4127	−	44.3576i	0.470841	−	1.44910i	0.851485	−	0.524379i	$-0.175702\pi$
$938$	24.5069	−	10.6040i	0.800179	−	0.346233i
$939$	15.7559	−	21.6862i	0.514175	−	0.707701i
$940$	−34.4998	+	55.1032i	−1.12526	+	1.79727i
$941$	−12.0031	+	3.90005i	−0.391290	+	0.127138i	−0.498053	−	0.867147i	$-0.665951\pi$
$941$	−12.0031	+	3.90005i	−0.391290	+	0.127138i	0.106763	+	0.994285i	$0.465951\pi$
$942$	4.86810	−	16.9489i	0.158611	−	0.552225i
$943$	−21.8885	+	15.9030i	−0.712789	+	0.517872i
$944$	0.568516	+	0.303571i	0.0185036	+	0.00988040i
$945$	49.8219	+	31.8342i	1.62071	+	1.03557i
$946$	−13.3474	−	33.2691i	−0.433962	−	1.08167i
$947$		−	4.87194i		−	0.158317i	−0.996862	−	0.0791583i	$-0.974777\pi$
$947$		−	4.87194i		−	0.158317i	0.996862	−	0.0791583i	$-0.0252233\pi$
$948$	13.9357	−	5.61611i	0.452610	−	0.182403i
$949$	−12.2341	−	16.8388i	−0.397135	−	0.546610i
$950$	60.8471	+	17.4766i	1.97414	+	0.567017i
$951$	24.3208	−	7.90230i	0.788655	−	0.256250i
$952$	−12.8664	+	13.0234i	−0.417002	+	0.422090i
$953$	9.29076	−	12.7876i	0.300957	−	0.414232i	−0.631577	−	0.775313i	$-0.717592\pi$
$953$	9.29076	−	12.7876i	0.300957	−	0.414232i	0.932535	+	0.361081i	$0.117592\pi$
$954$	3.76670	−	5.57906i	0.121951	−	0.180629i
$955$	−4.60868	+	14.1841i	−0.149134	+	0.458986i
$956$	38.1476	+	45.5440i	1.23378	+	1.47300i
$957$	−8.91324	−	24.6418i	−0.288124	−	0.796556i
$958$	−12.9134	−	35.5280i	−0.417214	−	1.14786i
$959$	−42.1653	+	34.6634i	−1.36159	+	1.11934i
$960$	43.4593	+	19.4871i	1.40264	+	0.628942i
$961$	9.22915	+	6.70537i	0.297714	+	0.216302i
$962$	12.3464	−	9.63729i	0.398063	−	0.310719i
$963$	2.34795	+	7.22626i	0.0756618	+	0.232863i
$964$	18.8229	−	1.29957i	0.606246	−	0.0418563i
$965$	−26.8481	−	36.9532i	−0.864269	−	1.18956i
$966$	20.9158	+	12.3706i	0.672953	+	0.398018i
$967$			48.4826i			1.55910i	0.626343	+	0.779548i	$0.284551\pi$
$967$			48.4826i			1.55910i	−0.626343	+	0.779548i	$0.715449\pi$
$968$	21.7313	−	22.2655i	0.698470	−	0.715640i
$969$			15.2295i			0.489241i
$970$	0.0998618	+	2.89623i	0.00320637	+	0.0929924i
$971$	29.6540	−	21.5449i	0.951642	−	0.691409i	0.000447478	−	1.00000i	$-0.499858\pi$
$971$	29.6540	−	21.5449i	0.951642	−	0.691409i	0.951195	+	0.308591i	$0.0998576\pi$
$972$	−15.2185	+	1.05072i	−0.488135	+	0.0337017i
$973$	−39.5585	−	10.2872i	−1.26819	−	0.329793i
$974$	−11.8809	+	9.27397i	−0.380689	+	0.297157i
$975$	17.4570	−	24.0275i	0.559071	−	0.769495i
$976$	11.4713	−	5.56991i	0.367186	−	0.178289i
$977$	−9.39265	+	28.9076i	−0.300498	+	0.924837i	0.680821	+	0.732449i	$0.261623\pi$
$977$	−9.39265	+	28.9076i	−0.300498	+	0.924837i	−0.981319	+	0.192387i	$0.938377\pi$
$978$	4.09086	−	1.48691i	0.130811	−	0.0475462i
$979$	19.6842	−	7.12003i	0.629111	−	0.227557i
$980$	−50.3155	−	23.6813i	−1.60727	−	0.756472i
$981$	1.48622	−	4.57411i	0.0474513	−	0.146040i
$982$	−26.8573	−	18.1327i	−0.857050	−	0.578637i
$983$	19.3893	−	26.6870i	0.618421	−	0.851184i	−0.378815	−	0.925472i	$-0.623668\pi$
$983$	19.3893	−	26.6870i	0.618421	−	0.851184i	0.997237	+	0.0742882i	$0.0236685\pi$
$984$	5.53771	−	25.8847i	0.176536	−	0.825174i
$985$	−16.1169	−	49.6026i	−0.513526	−	1.58047i
$986$	−5.03467	+	17.5288i	−0.160337	+	0.558232i
$987$	−1.93766	−	32.3942i	−0.0616762	−	1.03112i
$988$	−5.70862	−	14.1652i	−0.181615	−	0.450656i
$989$	33.1156			1.05301
$990$	5.22729	+	13.0293i	0.166134	+	0.414098i
$991$	−45.7990			−1.45485			−0.727426	−	0.686186i	$-0.759284\pi$
$991$	−45.7990			−1.45485			−0.727426	+	0.686186i	$0.759284\pi$
$992$	36.4683	+	5.20719i	1.15787	+	0.165328i
$993$	−0.539099	−	0.742006i	−0.0171078	−	0.0235468i
$994$	34.2654	−	30.2067i	1.08683	−	0.958099i
$995$	78.4891	−	25.5027i	2.48827	−	0.808488i
$996$	−5.95182	+	9.50627i	−0.188591	+	0.301218i
$997$	13.2615	−	18.2529i	0.419997	−	0.578076i	−0.545624	−	0.838030i	$-0.683707\pi$
$997$	13.2615	−	18.2529i	0.419997	−	0.578076i	0.965621	+	0.259954i	$0.0837074\pi$
$998$	−1.30611	+	1.93454i	−0.0413441	+	0.0612369i
$999$	32.2309	+	10.4724i	1.01974	+	0.331333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	616.2.bi.c.13.6	yes	352
7.6	odd	2	inner	616.2.bi.c.13.5	✓	352
8.5	even	2	inner	616.2.bi.c.13.21	yes	352
11.6	odd	10	inner	616.2.bi.c.237.22	yes	352
56.13	odd	2	inner	616.2.bi.c.13.22	yes	352
77.6	even	10	inner	616.2.bi.c.237.21	yes	352
88.61	odd	10	inner	616.2.bi.c.237.5	yes	352
616.237	even	10	inner	616.2.bi.c.237.6	yes	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.5	✓	352	7.6	odd	2	inner
616.2.bi.c.13.6	yes	352	1.1	even	1	trivial
616.2.bi.c.13.21	yes	352	8.5	even	2	inner
616.2.bi.c.13.22	yes	352	56.13	odd	2	inner
616.2.bi.c.237.5	yes	352	88.61	odd	10	inner
616.2.bi.c.237.6	yes	352	616.237	even	10	inner
616.2.bi.c.237.21	yes	352	77.6	even	10	inner
616.2.bi.c.237.22	yes	352	11.6	odd	10	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:	\( N \)	\(=\)	\( 616 = 2^{3} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	616.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41337 + 0.0487330i) q^{2} +(1.21258 - 0.880988i) q^{3} +(1.99525 - 0.137756i) q^{4} +(1.22746 + 3.77772i) q^{5} +(-1.67089 + 1.30426i) q^{6} +(-0.966365 - 2.46295i) q^{7} +(-2.81332 + 0.291935i) q^{8} +(-0.232850 + 0.716639i) q^{9} +O(q^{10})\)	\(q+(-1.41337 + 0.0487330i) q^{2} +(1.21258 - 0.880988i) q^{3} +(1.99525 - 0.137756i) q^{4} +(1.22746 + 3.77772i) q^{5} +(-1.67089 + 1.30426i) q^{6} +(-0.966365 - 2.46295i) q^{7} +(-2.81332 + 0.291935i) q^{8} +(-0.232850 + 0.716639i) q^{9} +(-1.91895 - 5.27952i) q^{10} +(1.12813 + 3.11887i) q^{11} +(2.29803 - 1.92483i) q^{12} +(-1.74853 - 0.568132i) q^{13} +(1.48586 + 3.43398i) q^{14} +(4.81651 + 3.49940i) q^{15} +(3.96205 - 0.549715i) q^{16} +(0.755978 + 2.32666i) q^{17} +(0.294180 - 1.02423i) q^{18} +(2.44132 + 3.36019i) q^{19} +(2.96949 + 7.36841i) q^{20} +(-3.34162 - 2.13516i) q^{21} +(-1.74646 - 4.35314i) q^{22} +4.33306 q^{23} +(-3.15417 + 2.83250i) q^{24} +(-8.71946 + 6.33506i) q^{25} +(2.49901 + 0.717772i) q^{26} +(1.73849 + 5.35052i) q^{27} +(-2.26743 - 4.78109i) q^{28} +(-4.26464 - 3.09844i) q^{29} +(-6.97807 - 4.71124i) q^{30} +(-6.19340 - 2.01236i) q^{31} +(-5.57306 + 0.970035i) q^{32} +(4.11563 + 2.78799i) q^{33} +(-1.18187 - 3.25160i) q^{34} +(8.11818 - 6.67383i) q^{35} +(-0.365873 + 1.46195i) q^{36} +(3.54074 - 4.87341i) q^{37} +(-3.61425 - 4.63024i) q^{38} +(-2.62075 + 0.851532i) q^{39} +(-4.55608 - 10.2696i) q^{40} +(-5.05152 + 3.67014i) q^{41} +(4.82702 + 2.85494i) q^{42} +7.64254 q^{43} +(2.68055 + 6.06751i) q^{44} -2.99308 q^{45} +(-6.12424 + 0.211163i) q^{46} +(4.81017 + 6.62063i) q^{47} +(4.31999 - 4.15709i) q^{48} +(-5.13228 + 4.76022i) q^{49} +(12.0151 - 9.37873i) q^{50} +(2.96644 + 2.15525i) q^{51} +(-3.56702 - 0.892696i) q^{52} +(6.00777 + 1.95204i) q^{53} +(-2.71788 - 7.47757i) q^{54} +(-10.3975 + 8.09004i) q^{55} +(3.43772 + 6.64696i) q^{56} +(5.92058 + 1.92371i) q^{57} +(6.17852 + 4.17143i) q^{58} +(0.130351 + 0.0947053i) q^{59} +(10.0922 + 6.31868i) q^{60} +(3.03197 - 0.985146i) q^{61} +(8.85166 + 2.54239i) q^{62} +(1.99007 - 0.119036i) q^{63} +(7.82955 - 1.64261i) q^{64} -7.30283i q^{65} +(-5.95279 - 3.73991i) q^{66} -7.13660i q^{67} +(1.82888 + 4.53813i) q^{68} +(5.25417 - 3.81738i) q^{69} +(-11.1488 + 9.82823i) q^{70} +(-3.77254 - 11.6107i) q^{71} +(0.445870 - 2.08411i) q^{72} +(9.15891 + 6.65433i) q^{73} +(-4.76689 + 7.06050i) q^{74} +(-4.99190 + 15.3635i) q^{75} +(5.33394 + 6.36812i) q^{76} +(6.59143 - 5.79250i) q^{77} +(3.66259 - 1.33125i) q^{78} +(4.76686 + 1.54885i) q^{79} +(6.93991 + 14.2928i) q^{80} +(4.99297 + 3.62761i) q^{81} +(6.96083 - 5.43346i) q^{82} +(-3.55839 + 1.15619i) q^{83} +(-6.96151 - 3.79986i) q^{84} +(-7.86156 + 5.71175i) q^{85} +(-10.8018 + 0.372444i) q^{86} -7.90089 q^{87} +(-4.08430 - 8.44503i) q^{88} -6.31135i q^{89} +(4.23033 - 0.145862i) q^{90} +(0.290436 + 4.85557i) q^{91} +(8.64554 - 0.596905i) q^{92} +(-9.28284 + 3.01618i) q^{93} +(-7.12121 - 9.12301i) q^{94} +(-9.69726 + 13.3471i) q^{95} +(-5.90318 + 6.08604i) q^{96} +(-0.490635 - 0.159417i) q^{97} +(7.02185 - 6.97808i) q^{98} +(-2.49778 + 0.0822345i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9}+O(q^{10}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9	\( 352 q - 10 q^{2} - 10 q^{4} - 10 q^{7} - 10 q^{8} - 108 q^{9} + 10 q^{14} + 12 q^{15} + 14 q^{16} - 20 q^{18} + 54 q^{22} - 72 q^{23} - 108 q^{25} + 30 q^{28} + 20 q^{30} - 20 q^{39} - 26 q^{42} + 26 q^{44} - 50 q^{46} - 34 q^{49} + 40 q^{50} + 44 q^{56} - 20 q^{57} + 78 q^{58} + 88 q^{60} + 20 q^{63} - 34 q^{64} - 72 q^{70} - 152 q^{71} + 90 q^{72} - 150 q^{74} + 116 q^{78} - 200 q^{79} - 12 q^{81} - 50 q^{84} + 50 q^{86} - 38 q^{88} + 16 q^{92} - 20 q^{95}+O(q^{100}) \) 352 * q - 10 * q^2 - 10 * q^4 - 10 * q^7 - 10 * q^8 - 108 * q^9 + 10 * q^14 + 12 * q^15 + 14 * q^16 - 20 * q^18 + 54 * q^22 - 72 * q^23 - 108 * q^25 + 30 * q^28 + 20 * q^30 - 20 * q^39 - 26 * q^42 + 26 * q^44 - 50 * q^46 - 34 * q^49 + 40 * q^50 + 44 * q^56 - 20 * q^57 + 78 * q^58 + 88 * q^60 + 20 * q^63 - 34 * q^64 - 72 * q^70 - 152 * q^71 + 90 * q^72 - 150 * q^74 + 116 * q^78 - 200 * q^79 - 12 * q^81 - 50 * q^84 + 50 * q^86 - 38 * q^88 + 16 * q^92 - 20 * q^95

Introduction

L-functions

Modular forms

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