LMFDB - Embedded newform 616.2.bi.c.237.5

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			237.5
Character	$\chi$	$=$	616.237
Dual form			616.2.bi.c.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41337 - 0.0487330i) q^{2} +(-1.21258 - 0.880988i) q^{3} +(1.99525 + 0.137756i) q^{4} +(-1.22746 + 3.77772i) q^{5} +(1.67089 + 1.30426i) q^{6} +(2.64103 - 0.157973i) q^{7} +(-2.81332 - 0.291935i) q^{8} +(-0.232850 - 0.716639i) q^{9} +O(q^{10})$	\(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} +(2.64103 - 0.157973i) 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} +(-3.74046 + 0.0945698i) 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} +(5.29128 + 0.0486215i) 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} +(-2.64497 + 10.1710i) 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} +(4.61891 + 3.18063i) 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} +(6.95009 - 0.834424i) 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} +(-7.47619 - 0.326580i) 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} +(-0.728174 - 1.85588i) 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} +(4.23400 - 14.2465i) 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} +(2.48673 - 8.41523i) 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} +(-6.37324 - 4.72051i) 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} +(4.52818 - 1.77668i) 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} +(-9.86374 + 0.840654i) 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 $\left(\mathbb{Z}/616\mathbb{Z}\right)^\times$.

$n$	$57$	$309$	$353$	$463$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$-1$	$1$

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	$-0.442430\pi$
$3$	−1.21258	−	0.880988i	−0.700081	−	0.508639i	−0.879959	+	0.475050i	$0.842430\pi$
$4$	1.99525	+	0.137756i	0.997625	+	0.0688779i
$5$	−1.22746	+	3.77772i	−0.548935	+	1.68945i	0.162509	+	0.986707i	$0.448041\pi$
$5$	−1.22746	+	3.77772i	−0.548935	+	1.68945i	−0.711445	+	0.702742i	$0.751959\pi$
$6$	1.67089	+	1.30426i	0.682138	+	0.532461i
$7$	2.64103	−	0.157973i	0.998216	−	0.0597082i
$7$	2.64103	−	0.157973i	0.998216	−	0.0597082i
$8$	−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	$-0.517939\pi$
$13$	1.74853	−	0.568132i	0.484955	−	0.157572i	0.541282	+	0.840841i	$0.317939\pi$
$14$	−3.74046	+	0.0945698i	−0.999681	+	0.0252748i
$15$	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	$-0.995876\pi$
$17$	−0.755978	+	2.32666i	−0.183352	+	0.564298i	0.816564	+	0.577254i	$0.195876\pi$
$18$	0.294180	+	1.02423i	0.0693389	+	0.241412i
$19$	−2.44132	+	3.36019i	−0.560078	+	0.770881i	−0.991336	−	0.131347i	$-0.958070\pi$
$19$	−2.44132	+	3.36019i	−0.560078	+	0.770881i	0.431258	+	0.902228i	$0.358070\pi$
$20$	−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
$28$	5.29128	+	0.0486215i	0.999958	+	0.00918860i
$29$	−4.26464	+	3.09844i	−0.791923	+	0.575366i	−0.908534	−	0.417812i	$-0.862797\pi$
$29$	−4.26464	+	3.09844i	−0.791923	+	0.575366i	0.116610	+	0.993178i	$0.462797\pi$
$30$	−6.97807	+	4.71124i	−1.27402	+	0.860151i
$31$	6.19340	−	2.01236i	1.11237	−	0.361430i	0.305518	−	0.952186i	$-0.401170\pi$
$31$	6.19340	−	2.01236i	1.11237	−	0.361430i	0.806850	+	0.590756i	$0.201170\pi$
$32$	−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
$35$	−2.64497	+	10.1710i	−0.447082	+	1.71921i
$36$	−0.365873	−	1.46195i	−0.0609788	−	0.243658i
$37$	3.54074	+	4.87341i	0.582094	+	0.801184i	0.993923	−	0.110077i	$-0.0351098\pi$
$37$	3.54074	+	4.87341i	0.582094	+	0.801184i	−0.411829	+	0.911261i	$0.635110\pi$
$38$	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	$-0.137881\pi$
$41$	5.05152	+	3.67014i	0.788915	+	0.573180i	−0.118726	+	0.992927i	$0.537881\pi$
$42$	4.61891	+	3.18063i	0.712713	+	0.490782i
$43$	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	0.298301	+	0.954472i	$0.403580\pi$
$47$	−4.81017	+	6.62063i	−0.701636	+	0.965718i	−0.999937	+	0.0112467i	$0.996420\pi$
$48$	−4.31999	−	4.15709i	−0.623537	−	0.600024i
$49$	6.95009	−	0.834424i	0.992870	−	0.119203i
$50$	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	0.134196	−	0.990955i	$-0.457155\pi$
$53$	6.00777	−	1.95204i	0.825231	−	0.268134i	0.691035	+	0.722821i	$0.257155\pi$
$54$	2.71788	−	7.47757i	0.369857	−	1.01757i
$55$	10.3975	+	8.09004i	1.40200	+	1.09086i
$56$	−7.47619	−	0.326580i	−0.999047	−	0.0436411i
$57$	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	$-0.703339\pi$
$59$	−0.130351	+	0.0947053i	−0.0169702	+	0.0123296i	0.579268	+	0.815137i	$0.303339\pi$
$60$	10.0922	−	6.31868i	1.30290	−	0.815738i
$61$	−3.03197	−	0.985146i	−0.388204	−	0.126135i	0.108411	−	0.994106i	$-0.465424\pi$
$61$	−3.03197	−	0.985146i	−0.388204	−	0.126135i	−0.496615	+	0.867971i	$0.665424\pi$
$62$	−8.85166	+	2.54239i	−1.12416	+	0.322884i
$63$	−0.728174	−	1.85588i	−0.0917413	−	0.233819i
$64$	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	$0.143583\pi$
$67$			7.13660i			0.871874i	−0.899977	+	0.435937i	$0.856417\pi$
$68$	−1.82888	+	4.53813i	−0.221784	+	0.550329i
$69$	−5.25417	−	3.81738i	−0.632527	−	0.459558i
$70$	4.23400	−	14.2465i	0.506059	−	1.70278i
$71$	−3.77254	+	11.6107i	−0.447719	+	1.37794i	0.431756	+	0.901990i	$0.357894\pi$
$71$	−3.77254	+	11.6107i	−0.447719	+	1.37794i	−0.879475	+	0.475946i	$0.842106\pi$
$72$	0.445870	+	2.08411i	0.0525463	+	0.245615i
$73$	−9.15891	+	6.65433i	−1.07197	+	0.778831i	−0.976265	−	0.216579i	$-0.930510\pi$
$73$	−9.15891	+	6.65433i	−1.07197	+	0.778831i	−0.0957037	+	0.995410i	$0.530510\pi$
$74$	−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
$77$	2.48673	−	8.41523i	0.283389	−	0.959005i
$78$	3.66259	+	1.33125i	0.414707	+	0.150734i
$79$	4.76686	−	1.54885i	0.536314	−	0.174259i	−0.0283223	−	0.999599i	$-0.509016\pi$
$79$	4.76686	−	1.54885i	0.536314	−	0.174259i	0.564636	+	0.825340i	$0.309016\pi$
$80$	−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	$-0.334169\pi$
$83$	3.55839	+	1.15619i	0.390584	+	0.126908i	−0.107140	+	0.994244i	$0.534169\pi$
$84$	−6.37324	−	4.72051i	−0.695378	−	0.515050i
$85$	−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
$91$	4.52818	−	1.77668i	0.474682	−	0.186246i
$92$	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	$-0.591662\pi$
$97$	0.490635	−	0.159417i	0.0498165	−	0.0161863i	0.333819	+	0.942637i	$0.391662\pi$
$98$	−9.86374	+	0.840654i	−0.996388	+	0.0849189i
$99$	−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	$-0.664103\pi$
$101$	−3.82373	+	1.24240i	−0.380475	+	0.123624i	0.112534	+	0.993648i	$0.464103\pi$
$102$	−4.29772	+	2.90161i	−0.425538	+	0.287302i
$103$	6.14760	+	8.46144i	0.605741	+	0.833731i	0.996219	−	0.0868817i	$-0.0276902\pi$
$103$	6.14760	+	8.46144i	0.605741	+	0.833731i	−0.390478	+	0.920612i	$0.627690\pi$
$104$	−5.08504	+	1.08788i	−0.498629	+	0.106675i
$105$	12.1678	−	10.0029i	1.18745	−	0.976184i
$106$	−8.58636	+	2.46619i	−0.833981	+	0.239538i
$107$	8.15776	+	5.92696i	0.788641	+	0.572981i	0.907560	−	0.419923i	$-0.137943\pi$
$107$	8.15776	+	5.92696i	0.788641	+	0.572981i	−0.118919	+	0.992904i	$0.537943\pi$
$108$	−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
$112$	10.5507	+	0.825917i	0.996950	+	0.0780418i
$113$	12.7320	+	9.25034i	1.19773	+	0.870199i	0.994059	−	0.108842i	$-0.0347141\pi$
$113$	12.7320	+	9.25034i	1.19773	+	0.870199i	0.203667	+	0.979040i	$0.434714\pi$
$114$	−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
$119$	−1.62901	+	6.26421i	−0.149331	+	0.574239i
$120$	−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
$126$	0.938739	+	2.65854i	0.0836295	+	0.236841i
$127$	7.50533	+	2.43863i	0.665990	+	0.216393i	0.622451	−	0.782658i	$-0.286137\pi$
$127$	7.50533	+	2.43863i	0.665990	+	0.216393i	0.0435388	+	0.999052i	$0.486137\pi$
$128$	−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	0.177066	+	0.984199i	$0.443339\pi$
$137$	−6.37533	+	19.6212i	−0.544681	+	1.67636i	−0.721747	+	0.692157i	$0.756661\pi$
$138$	7.24007	+	5.65143i	0.616316	+	0.481082i
$139$	−9.08070	−	12.4985i	−0.770215	−	1.06011i	−0.996295	−	0.0860010i	$-0.972591\pi$
$139$	−9.08070	−	12.4985i	−0.770215	−	1.06011i	0.226080	−	0.974109i	$-0.427409\pi$
$140$	−6.67849	+	19.9293i	−0.564436	+	1.68433i
$141$	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
$147$	−9.16263	−	5.11114i	−0.755721	−	0.421560i
$148$	6.39332	+	10.2114i	0.525528	+	0.839375i
$149$	5.90475	−	18.1730i	0.483736	−	1.48879i	−0.350067	−	0.936725i	$-0.613841\pi$
$149$	5.90475	−	18.1730i	0.483736	−	1.48879i	0.833803	−	0.552062i	$-0.186159\pi$
$150$	−6.30671	−	21.9576i	−0.514940	−	1.79283i
$151$	−8.39731	+	11.5579i	−0.683363	+	0.940569i	−0.999968	−	0.00798848i	$-0.997457\pi$
$151$	−8.39731	+	11.5579i	−0.683363	+	0.940569i	0.316605	+	0.948558i	$0.397457\pi$
$152$	7.84918	−	8.74059i	0.636653	−	0.708956i
$153$	1.84341			0.149031
$154$	−3.92478	+	11.7727i	−0.316268	+	0.948670i
$155$			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	$-0.192284\pi$
$157$	6.73048	+	4.88998i	0.537151	+	0.390263i	−0.285875	+	0.958267i	$0.592284\pi$
$158$	−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
$161$	11.4437	−	0.684507i	0.901894	−	0.0539467i
$162$	−7.23372	+	4.88384i	−0.568335	+	0.383711i
$163$	−1.95299	+	0.634564i	−0.152970	+	0.0497029i	−0.384501	−	0.923125i	$-0.625626\pi$
$163$	−1.95299	+	0.634564i	−0.152970	+	0.0497029i	0.231531	+	0.972827i	$0.425626\pi$
$164$	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	$-0.154149\pi$
$167$	−1.35211	−	4.16136i	−0.104629	−	0.322016i	−0.989643	+	0.143549i	$0.954149\pi$
$168$	8.77773	+	6.98243i	0.677217	+	0.538707i
$169$	−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	−0.125020	−	0.992154i	$-0.539900\pi$
$173$	11.2748	−	15.5184i	0.857208	−	1.17985i	0.982228	−	0.187691i	$-0.0601004\pi$
$174$	−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	0.0875177	−	0.996163i	$-0.472107\pi$
$179$	13.4845	−	18.5599i	1.00788	−	1.38723i	0.920363	−	0.391066i	$-0.127893\pi$
$180$	5.97193	+	0.412314i	0.445122	+	0.0307320i
$181$	1.34875	−	4.15103i	0.100252	−	0.308544i	−0.888335	−	0.459196i	$-0.848138\pi$
$181$	1.34875	−	4.15103i	0.100252	−	0.308544i	0.988587	+	0.150653i	$0.0481375\pi$
$182$	−6.48659	+	2.29044i	−0.480818	+	0.169778i
$183$	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
$189$	−3.74617	+	14.4055i	−0.272494	+	1.04785i
$190$	13.0554	+	19.3371i	0.947139	+	1.40286i
$191$	3.03759	−	2.20693i	0.219792	−	0.159688i	−0.472441	−	0.881362i	$-0.656627\pi$
$191$	3.03759	−	2.20693i	0.219792	−	0.159688i	0.692233	+	0.721674i	$0.256627\pi$
$192$	−8.04680	−	8.88953i	−0.580728	−	0.641547i
$193$	−10.9365	−	3.55347i	−0.787223	−	0.255784i	−0.112302	−	0.993674i	$-0.535822\pi$
$193$	−10.9365	−	3.55347i	−0.787223	−	0.255784i	−0.674921	+	0.737890i	$0.735822\pi$
$194$	−0.701220	+	0.201406i	−0.0503446	+	0.0144601i
$195$	6.43370	−	8.85523i	0.460727	−	0.634136i
$196$	13.9821	−	0.707469i	0.998722	−	0.0505335i
$197$	−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
$203$	−10.7736	+	8.85678i	−0.756156	+	0.621624i
$204$	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
$210$	−17.6851	+	13.5449i	−1.22038	+	0.934685i
$211$	1.60049	+	4.92579i	0.110182	+	0.339105i	0.990912	−	0.134514i	$-0.0429473\pi$
$211$	1.60049	+	4.92579i	0.110182	+	0.339105i	−0.880730	+	0.473619i	$0.842947\pi$
$212$	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
$217$	16.0391	−	6.29309i	1.08880	−	0.427203i
$218$	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	$-0.740028\pi$
$223$	3.28797	−	4.52551i	0.220179	−	0.303050i	0.904790	+	0.425858i	$0.140028\pi$
$224$	−14.8719	−	1.68150i	−0.993669	−	0.112350i
$225$	−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	−0.987807	−	0.155682i	$-0.950242\pi$
$227$	−12.5146	−	17.2248i	−0.830621	−	1.14325i	0.157186	−	0.987569i	$-0.449758\pi$
$228$	12.0780	−	3.02270i	0.799888	−	0.200183i
$229$	−2.55524	−	7.86421i	−0.168855	−	0.519682i	0.830445	−	0.557101i	$-0.188086\pi$
$229$	−2.55524	−	7.86421i	−0.168855	−	0.519682i	−0.999300	+	0.0374190i	$0.988086\pi$
$230$	8.31495	−	22.8765i	0.548271	−	1.50843i
$231$	−10.4291	+	8.01333i	−0.686183	+	0.527239i
$232$	12.9023	−	7.47191i	0.847080	−	0.490555i
$233$	−15.2958	+	4.96992i	−1.00206	+	0.325590i	−0.763690	−	0.645583i	$-0.776614\pi$
$233$	−15.2958	+	4.96992i	−1.00206	+	0.325590i	−0.238374	+	0.971173i	$0.576614\pi$
$234$	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
$238$	2.60768	−	8.77428i	0.169031	−	0.568752i
$239$	17.4600	−	24.0317i	1.12940	−	1.55448i	0.340182	−	0.940360i	$-0.389511\pi$
$239$	17.4600	−	24.0317i	1.12940	−	1.55448i	0.789213	−	0.614119i	$-0.210489\pi$
$240$	21.0069	−	11.2171i	1.35599	−	0.724060i
$241$	−9.43387			−0.607689			−0.303844	−	0.952722i	$-0.598270\pi$
$241$	−9.43387			−0.607689			−0.303844	+	0.952722i	$0.598270\pi$
$242$	11.6066	+	10.3579i	0.746103	+	0.665831i
$243$	7.62738			0.489297
$244$	−5.91383	−	2.38329i	−0.378594	−	0.152574i
$245$	−5.37871	+	27.2797i	−0.343633	+	1.74284i
$246$	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	0.995871	+	0.0907753i	$0.0289345\pi$
$251$	3.85857	+	11.8755i	0.243551	+	0.749573i	−0.752320	+	0.658797i	$0.771065\pi$
$252$	−1.19723	−	3.80326i	−0.0754184	−	0.239583i
$253$	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	0.994538	+	0.104373i	$0.0332836\pi$
$257$	12.6081	+	17.3536i	0.786474	+	1.08249i	−0.208065	+	0.978115i	$0.566716\pi$
$258$	12.7698	+	9.96784i	0.795016	+	0.620571i
$259$	10.1211	+	12.3115i	0.628893	+	0.764999i
$260$	−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	$9.02425e-5\pi$
$263$			0.00919536i			0.000567010i	−1.00000		0.000283505i	$0.999910\pi$
$264$	12.3925	−	6.64202i	0.762705	−	0.408788i
$265$			25.0918i			1.54137i
$266$	8.81391	−	12.7996i	0.540415	−	0.784791i
$267$	−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	0.424637	+	0.905364i	$0.360402\pi$
$269$	−7.39795	+	22.7685i	−0.451061	+	1.38822i	−0.875698	+	0.482859i	$0.839598\pi$
$270$	24.9121	+	19.4458i	1.51610	+	1.18343i
$271$	18.1023	−	13.1521i	1.09963	−	0.798931i	0.118634	−	0.992938i	$-0.462149\pi$
$271$	18.1023	−	13.1521i	1.09963	−	0.798931i	0.981000	+	0.194007i	$0.0621485\pi$
$272$	−4.27422	+	8.80277i	−0.259163	+	0.533746i
$273$	−7.05599	−	1.83491i	−0.427048	−	0.111054i
$274$	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	0.997536	+	0.0701629i	$0.0223519\pi$
$277$	3.85714	+	11.8711i	0.231753	+	0.713263i	−0.765782	+	0.643100i	$0.777648\pi$
$278$	12.2253	+	18.1076i	0.733227	+	1.08602i
$279$	−2.88427	−	3.96986i	−0.172677	−	0.237669i
$280$	10.4104	−	27.8421i	0.622142	−	1.66388i
$281$	−28.9929	−	9.42036i	−1.72957	−	0.561971i	−0.736183	−	0.676783i	$-0.763374\pi$
$281$	−28.9929	−	9.42036i	−1.72957	−	0.561971i	−0.993387	+	0.114811i	$0.963374\pi$
$282$	−16.6723	+	4.78865i	−0.992820	+	0.285160i
$283$	3.52902	−	4.85728i	0.209778	−	0.288735i	−0.691143	−	0.722718i	$-0.742892\pi$
$283$	3.52902	−	4.85728i	0.209778	−	0.288735i	0.900921	+	0.433983i	$0.142892\pi$
$284$	−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	$-0.240766\pi$
$293$	−2.57003	−	3.53734i	−0.150143	−	0.206654i	−0.877463	+	0.479645i	$0.840766\pi$
$294$	12.7011	+	7.67048i	0.740746	+	0.447351i
$295$	−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
$301$	20.1842	−	1.20732i	1.16340	−	0.0695885i
$302$	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	$0.945257\pi$
$308$	6.12090	−	16.4479i	0.348771	−	0.937208i
$309$		−	15.6761i		−	0.891782i
$310$	1.26058	−	36.5598i	0.0715961	−	2.07646i
$311$	12.6182	−	17.3675i	0.715513	−	0.984819i	−0.284148	−	0.958781i	$-0.591711\pi$
$311$	12.6182	−	17.3675i	0.715513	−	0.984819i	0.999661	−	0.0260390i	$-0.00828939\pi$
$312$	7.12441	+	3.16072i	0.403340	+	0.178941i
$313$	−17.0090	−	5.52657i	−0.961408	−	0.312380i	−0.214066	−	0.976819i	$-0.568671\pi$
$313$	−17.0090	−	5.52657i	−0.961408	−	0.312380i	−0.747343	+	0.664439i	$0.768671\pi$
$314$	−9.27438	−	7.23937i	−0.523384	−	0.408541i
$315$	7.90481	−	0.472826i	0.445385	−	0.0266407i
$316$	9.72445	−	2.43368i	0.547043	−	0.136905i
$317$	16.2265	−	5.27232i	0.911373	−	0.296123i	0.184450	−	0.982842i	$-0.440950\pi$
$317$	16.2265	−	5.27232i	0.911373	−	0.296123i	0.726923	+	0.686719i	$0.240950\pi$
$318$	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
$322$	−16.2077	+	0.409777i	−0.903217	+	0.0228360i
$323$	−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	$0.00535334\pi$
$331$			0.611925i			0.0336344i	−0.999859	+	0.0168172i	$0.994647\pi$
$332$	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
$336$	−12.0659	−	10.2966i	−0.658251	−	0.561723i
$337$	−0.173465	−	0.238754i	−0.00944923	−	0.0130058i	0.804266	−	0.594269i	$-0.202559\pi$
$337$	−0.173465	−	0.238754i	−0.00944923	−	0.0130058i	−0.813715	+	0.581263i	$0.802559\pi$
$338$	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
$343$	18.2236	−	3.30167i	0.983981	−	0.178273i
$344$	−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	−0.199923	−	0.979812i	$-0.564069\pi$
$347$	10.0169	−	30.8289i	0.537737	−	1.65498i	0.737660	−	0.675173i	$-0.235931\pi$
$348$	15.7642	+	1.08839i	0.845052	+	0.0583440i
$349$	−1.16837	+	1.60813i	−0.0625415	+	0.0860810i	−0.839142	−	0.543912i	$-0.816942\pi$
$349$	−1.16837	+	1.60813i	−0.0625415	+	0.0860810i	0.776601	+	0.629993i	$0.216942\pi$
$350$	33.2139	+	22.8714i	1.77536	+	1.22253i
$351$			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
$357$	7.49400	−	6.16069i	0.396624	−	0.326058i
$358$	−19.9631	+	25.5749i	−1.05509	+	1.35167i
$359$	8.65087	+	11.9069i	0.456575	+	0.628422i	0.973794	−	0.227431i	$-0.0730327\pi$
$359$	8.65087	+	11.9069i	0.456575	+	0.628422i	−0.517219	+	0.855853i	$0.673033\pi$
$360$	−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
$364$	9.27959	−	2.92113i	0.486383	−	0.153109i
$365$	−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	$-0.177830\pi$
$367$	1.56729	+	2.15719i	0.0818119	+	0.112604i	−0.766150	+	0.642662i	$0.777830\pi$
$368$	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
$371$	15.5583	−	6.10447i	0.807749	−	0.316929i
$372$	−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
$378$	5.99676	−	20.1778i	0.308440	−	1.03784i
$379$	21.9048	+	7.11729i	1.12517	+	0.365590i	0.811739	−	0.584020i	$-0.198521\pi$
$379$	21.9048	+	7.11729i	1.12517	+	0.365590i	0.313432	+	0.949610i	$0.398521\pi$
$380$	−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	$-0.345189\pi$
$383$	26.7169	−	8.68085i	1.36517	−	0.443571i	0.897766	+	0.440473i	$0.145189\pi$
$384$	10.9399	+	12.9564i	0.558276	+	0.661177i
$385$	28.7381	+	19.7235i	1.46463	+	1.00520i
$386$	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	0.942320	−	0.334715i	$-0.108640\pi$
$389$	6.56373	+	9.03420i	0.332794	+	0.458052i	−0.609525	+	0.792767i	$0.708640\pi$
$390$	−9.52477	+	12.2022i	−0.482305	+	0.617883i
$391$	−3.27570	+	10.0816i	−0.165659	+	0.509847i
$392$	−19.7964	+	0.318528i	−0.999871	+	0.0160881i
$393$	−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	$-0.823767\pi$
$397$	−33.8966			−1.70122			−0.850611	+	0.525796i	$0.823767\pi$
$398$	−1.01252	+	29.3654i	−0.0507529	+	1.47196i
$399$	15.3325	−	6.01588i	0.767587	−	0.301171i
$400$	−31.0644	−	29.8930i	−1.55322	−	1.49465i
$401$	7.85626	−	24.1791i	0.392323	−	1.20745i	−0.538704	−	0.842495i	$-0.681086\pi$
$401$	7.85626	−	24.1791i	0.392323	−	1.20745i	0.931027	−	0.364950i	$-0.118914\pi$
$402$	−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
$406$	15.6587	−	11.9929i	0.777128	−	0.595198i
$407$	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	0.834069	+	0.551661i	$0.186006\pi$
$409$	9.77921	+	30.0973i	0.483551	+	1.48822i	−0.350518	+	0.936556i	$0.613994\pi$
$410$	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
$413$	−0.329299	+	0.270711i	−0.0162038	+	0.0133208i
$414$	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	$-0.800628\pi$
$419$	−33.1677			−1.62035			−0.810175	+	0.586189i	$0.800628\pi$
$420$	25.6557	−	18.2821i	1.25187	−	0.892077i
$421$	−5.58059	+	7.68102i	−0.271981	+	0.374350i	−0.923057	−	0.384662i	$-0.874318\pi$
$421$	−5.58059	+	7.68102i	−0.271981	+	0.374350i	0.651076	+	0.759012i	$0.274318\pi$
$422$	−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
$427$	−8.16315	−	2.12283i	−0.395043	−	0.102731i
$428$	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	−0.954844	−	0.297108i	$-0.903978\pi$
$431$	−32.2347	+	10.4737i	−1.55269	+	0.504501i	−0.597849	+	0.801609i	$0.703978\pi$
$432$	−9.82924	+	20.2434i	−0.472910	+	0.973959i
$433$	−14.5545	−	20.0326i	−0.699446	−	0.962704i	−0.999960	−	0.00892696i	$-0.997158\pi$
$433$	−14.5545	−	20.0326i	−0.699446	−	0.962704i	0.300515	−	0.953777i	$-0.402842\pi$
$434$	−22.9759	+	8.11286i	−1.10288	+	0.389430i
$435$	−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	$-0.460440\pi$
$439$	5.19462			0.247926			0.123963	+	0.992287i	$0.460440\pi$
$440$	−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	−0.893158	−	0.449742i	$-0.851516\pi$
$443$	−3.98697	+	5.48760i	−0.189427	+	0.260724i	0.703732	+	0.710466i	$0.251516\pi$
$444$	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
$448$	20.9376	+	3.10133i	0.989207	+	0.146524i
$449$	−2.66893	−	8.21412i	−0.125955	−	0.387648i	0.868119	−	0.496356i	$-0.165329\pi$
$449$	−2.66893	−	8.21412i	−0.125955	−	0.387648i	−0.994074	+	0.108708i	$0.965329\pi$
$450$	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
$455$	1.15365	+	19.2870i	0.0540840	+	0.904188i
$456$	−17.2181	+	3.68360i	−0.806311	+	0.172500i
$457$	4.65798	+	1.51347i	0.217891	+	0.0707971i	0.415928	−	0.909397i	$-0.363457\pi$
$457$	4.65798	+	1.51347i	0.217891	+	0.0707971i	−0.198037	+	0.980194i	$0.563457\pi$
$458$	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	$0.625238\pi$
$462$	15.1307	−	10.8176i	0.703944	−	0.503280i
$463$	−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	−0.631879	−	0.775067i	$-0.717716\pi$
$467$	7.23714	−	22.2736i	0.334895	−	1.03070i	0.966774	−	0.255634i	$-0.0822840\pi$
$468$	−1.47032	−	2.34840i	−0.0679656	−	0.108555i
$469$	1.12739	+	18.8480i	0.0520581	+	0.870318i
$470$	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
$476$	−4.11322	+	12.2743i	−0.188529	+	0.562590i
$477$	−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	0.564426	+	0.825484i	$0.309098\pi$
$479$	−8.26005	+	25.4218i	−0.377411	+	1.16155i	−0.941837	+	0.336069i	$0.890902\pi$
$480$	−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	0.765744	−	0.643146i	$-0.222371\pi$
$487$	8.62207	+	6.26430i	0.390703	+	0.283862i	−0.375040	+	0.927008i	$0.622371\pi$
$488$	8.24230	+	3.65667i	0.373112	+	0.165530i
$489$	2.92719	+	0.951102i	0.132372	+	0.0430103i
$490$	8.93155	−	38.2943i	0.403486	−	1.72996i
$491$	18.5379	−	13.4685i	0.836602	−	0.607827i	−0.0848175	−	0.996397i	$-0.527031\pi$
$491$	18.5379	−	13.4685i	0.836602	−	0.607827i	0.921419	+	0.388570i	$0.127031\pi$
$492$	−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
$497$	−8.12923	+	31.2602i	−0.364646	+	1.40221i
$498$	4.43771	+	6.57293i	0.198858	+	0.294540i
$499$	0.970146	+	1.33529i	0.0434297	+	0.0597758i	0.830180	−	0.557496i	$-0.188238\pi$
$499$	0.970146	+	1.33529i	0.0434297	+	0.0597758i	−0.786750	+	0.617272i	$0.788238\pi$
$500$	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	−0.998870	−	0.0475228i	$-0.984867\pi$
$503$	−30.3387	−	22.0423i	−1.35273	−	0.982819i	−0.353865	−	0.935297i	$-0.615133\pi$
$504$	1.50679	+	5.43377i	0.0671178	+	0.242039i
$505$		−	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	$-0.114748\pi$
$509$	20.0659	+	14.5787i	0.889406	+	0.646191i	−0.0463172	+	0.998927i	$0.514748\pi$
$510$	−5.68619	−	19.7972i	−0.251789	−	0.876635i
$511$	−23.1377	+	19.0212i	−1.02355	+	0.841447i
$512$	−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
$518$	−13.7049	−	17.8940i	−0.602158	−	0.786216i
$519$	−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	$-0.258754\pi$
$521$	−4.92477	−	6.77836i	−0.215758	−	0.296965i	−0.903153	+	0.429318i	$0.858754\pi$
$522$	−4.42807	−	3.45645i	−0.193812	−	0.151285i
$523$	−8.17698	−	2.65686i	−0.357554	−	0.116176i	0.124731	−	0.992191i	$-0.460193\pi$
$523$	−8.17698	−	2.65686i	−0.357554	−	0.116176i	−0.482285	+	0.876014i	$0.660193\pi$
$524$	1.32762	−	19.2292i	0.0579973	−	0.840030i
$525$	15.6108	+	39.7868i	0.681310	+	1.73644i
$526$	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
$532$	−13.0811	+	17.6610i	−0.567138	+	0.765702i
$533$	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
$539$	5.23816	−	22.6177i	0.225623	−	0.974215i
$540$	−34.2624	−	28.6982i	−1.47442	−	1.23498i
$541$	−3.51281	−	10.8113i	−0.151027	−	0.464814i	0.846709	−	0.532056i	$-0.178580\pi$
$541$	−3.51281	−	10.8113i	−0.151027	−	0.464814i	−0.997737	+	0.0672413i	$0.978580\pi$
$542$	−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
$546$	9.88333	+	2.93728i	0.422967	+	0.125704i
$547$	−0.531438	−	0.386112i	−0.0227227	−	0.0165090i	0.576366	−	0.817192i	$-0.304470\pi$
$547$	−0.531438	−	0.386112i	−0.0227227	−	0.0165090i	−0.599089	+	0.800683i	$0.704470\pi$
$548$	−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
$553$	12.3448	−	4.84359i	0.524952	−	0.205970i
$554$	−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	−0.574173	−	0.818734i	$-0.694676\pi$
$557$	0.638638	−	0.463998i	0.0270600	−	0.0196602i	0.601233	+	0.799074i	$0.294676\pi$
$558$	3.88309	+	5.75145i	0.164384	+	0.243478i
$559$	13.3632	−	4.34197i	0.565204	−	0.183646i
$560$	−16.0706	+	38.8440i	−0.679109	+	1.64146i
$561$	−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	$-0.705815\pi$
$563$	−14.7285	+	4.78559i	−0.620734	+	0.201689i	−0.0182679	+	0.999833i	$0.505815\pi$
$564$	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
$567$	12.6135	−	10.3694i	0.529719	−	0.435473i
$568$	14.0029	−	31.5633i	0.587551	−	1.32437i
$569$	1.24663	−	1.71584i	0.0522616	−	0.0719319i	−0.782086	−	0.623170i	$-0.785844\pi$
$569$	1.24663	−	1.71584i	0.0522616	−	0.0719319i	0.834348	+	0.551238i	$0.185844\pi$
$570$	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
$574$	−19.2421	−	13.2503i	−0.803150	−	0.553057i
$575$	−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	$-0.141956\pi$
$577$	33.1140	+	10.7594i	1.37855	+	0.447919i	0.476359	+	0.879251i	$0.341956\pi$
$578$	−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
$581$	9.58047	+	2.49141i	0.397465	+	0.103361i
$582$	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	−0.384976	+	0.922927i	$0.625790\pi$
$587$	−33.4758	+	24.3216i	−1.38170	+	1.00386i	−0.996719	+	0.0809340i	$0.974210\pi$
$588$	−17.5777	−	11.4602i	−0.724890	−	0.472611i
$589$	−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	$-0.645226\pi$
$593$	−21.4575			−0.881152			−0.440576	+	0.897715i	$0.645226\pi$
$594$	−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	−0.322827	−	0.946458i	$-0.604633\pi$
$599$	12.1065	−	37.2601i	0.494659	−	1.52241i	0.817487	−	0.575947i	$-0.195367\pi$
$600$	−9.55867	−	44.6797i	−0.390231	−	1.82404i
$601$	−15.7762	+	11.4621i	−0.643525	+	0.467548i	−0.861060	−	0.508504i	$-0.830199\pi$
$601$	−15.7762	+	11.4621i	−0.643525	+	0.467548i	0.217534	+	0.976053i	$0.430199\pi$
$602$	−28.5866	+	0.722753i	−1.16510	+	0.0294572i
$603$	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	$-0.129063\pi$
$607$	−1.38834	−	4.27288i	−0.0563512	−	0.173431i	−0.975271	+	0.221014i	$0.929063\pi$
$608$	16.8652	−	16.3584i	0.683972	−	0.663421i
$609$	20.8665	−	1.24813i	0.845553	−	0.0505767i
$610$	−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	−0.955829	−	0.293924i	$-0.905039\pi$
$613$	−37.8992	−	27.5354i	−1.53073	−	1.11214i	−0.574905	−	0.818220i	$-0.694961\pi$
$614$	0.292253	−	8.47604i	0.0117944	−	0.342065i
$615$	37.1740			1.49900
$616$	−9.45268	+	22.9488i	−0.380859	+	0.924633i
$617$	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	$-0.302598\pi$
$619$	−0.328517	−	0.238682i	−0.0132042	−	0.00959343i	−0.594368	+	0.804193i	$0.702598\pi$
$620$	−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
$623$	−0.997023	−	16.6685i	−0.0399449	−	0.667808i
$624$	−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
$630$	−11.1955	+	0.283054i	−0.446039	+	0.0112772i
$631$	13.9226	−	10.1153i	0.554248	−	0.402685i	−0.275101	−	0.961415i	$-0.588711\pi$
$631$	13.9226	−	10.1153i	0.554248	−	0.402685i	0.829349	+	0.558730i	$0.188711\pi$
$632$	−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	0.143646	−	0.989629i	$-0.454117\pi$
$641$	−19.0684	−	13.8540i	−0.753158	−	0.547202i	−0.896804	+	0.442428i	$0.854117\pi$
$642$	5.90044	+	20.5431i	0.232872	+	0.810773i
$643$	1.40484	−	4.32367i	0.0554016	−	0.170509i	−0.919527	−	0.393027i	$-0.871428\pi$
$643$	1.40484	−	4.32367i	0.0554016	−	0.170509i	0.974928	+	0.222519i	$0.0714278\pi$
$644$	22.9274	+	0.210680i	0.903468	+	0.00830195i
$645$	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	$-0.752080\pi$
$647$	−22.2464	+	7.22829i	−0.874596	+	0.284174i	−0.162885	+	0.986645i	$0.552080\pi$
$648$	−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
$651$	−24.9927	−	6.49938i	−0.979543	−	0.254731i
$652$	−3.98412	+	0.997079i	−0.156030	+	0.0390486i
$653$	−4.31189	−	5.93481i	−0.168737	−	0.232247i	0.716271	−	0.697822i	$-0.245847\pi$
$653$	−4.31189	−	5.93481i	−0.168737	−	0.232247i	−0.885008	+	0.465575i	$0.845847\pi$
$654$	−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
$658$	17.3662	−	25.2191i	0.677003	−	0.983144i
$659$	−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	$-0.392851\pi$
$661$	16.9838			0.660593			0.330296	+	0.943877i	$0.392851\pi$
$662$	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
$665$	−27.7193	−	33.7183i	−1.07491	−	1.30754i
$666$	−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
$672$	16.5519	+	15.1409i	0.638503	+	0.584072i
$673$	−19.8317	+	6.44371i	−0.764456	+	0.248387i	−0.665190	−	0.746674i	$-0.731649\pi$
$673$	−19.8317	+	6.44371i	−0.764456	+	0.248387i	−0.0992660	+	0.995061i	$0.531649\pi$
$674$	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	$-0.192024\pi$
$677$	30.0845	+	9.77503i	1.15624	+	0.375685i	0.332749	+	0.943015i	$0.392024\pi$
$678$	9.20894	+	32.0621i	0.353667	+	1.23134i
$679$	1.27060	−	0.498533i	0.0487611	−	0.0191319i
$680$	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	$-0.960466\pi$
$683$		−	6.47508i		−	0.247762i	0.992297	−	0.123881i	$-0.0395341\pi$
$684$	5.80565	+	2.33969i	0.221985	+	0.0894602i
$685$	−66.2982	−	48.1684i	−2.53312	−	1.84042i
$686$	−25.9176	+	3.77840i	−0.989540	+	0.144260i
$687$	−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	$-0.141613\pi$
$691$	−2.11781	−	6.51796i	−0.0805654	−	0.247955i	−0.983224	+	0.182403i	$0.941613\pi$
$692$	24.6338	−	29.4100i	0.936437	−	1.11800i
$693$	−6.60972	+	0.177399i	−0.251082	+	0.00673884i
$694$	−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
$700$	−45.8291	−	33.9445i	−1.73218	−	1.28298i
$701$	−27.7901	−	20.1907i	−1.04962	−	0.762592i	−0.0774783	−	0.996994i	$-0.524687\pi$
$701$	−27.7901	−	20.1907i	−1.04962	−	0.762592i	−0.972140	+	0.234402i	$0.924687\pi$
$702$	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
$707$	−9.90232	+	3.88527i	−0.372415	+	0.146121i
$708$	0.481842	+	0.0332673i	0.0181087	+	0.00125026i
$709$	28.1087	+	9.13307i	1.05564	+	0.343000i	0.784881	−	0.619647i	$-0.212724\pi$
$709$	28.1087	+	9.13307i	1.05564	+	0.343000i	0.270763	+	0.962646i	$0.412724\pi$
$710$	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
$714$	−10.8920	+	8.34216i	−0.407625	+	0.312197i
$715$	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	$-0.0100209\pi$
$719$	17.7163	+	24.3843i	0.660705	+	0.909382i	−0.338800	+	0.940859i	$0.610021\pi$
$720$	11.8587	+	1.64534i	0.441948	+	0.0613181i
$721$	17.5727	+	21.3758i	0.654441	+	0.796075i
$722$	−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	$0.953364\pi$
$728$	−13.2579	+	3.67643i	−0.491370	+	0.136257i
$729$	−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	$-0.0868937\pi$
$733$	11.0729	+	15.2405i	0.408985	+	0.562920i	−0.553985	+	0.832526i	$0.686894\pi$
$734$	−2.11004	−	3.12530i	−0.0778831	−	0.115357i
$735$	30.5552	−	28.3402i	1.12705	−	1.04534i
$736$	−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	0.938088	−	0.346396i	$-0.112595\pi$
$739$	−0.664596	−	2.04542i	−0.0244476	−	0.0752419i	−0.962536	+	0.271154i	$0.912595\pi$
$740$	−46.4235	+	11.6181i	−1.70656	+	0.427090i
$741$	9.25940	−	6.72735i	0.340153	−	0.247135i
$742$	−22.2872	+	7.86970i	−0.818190	+	0.288906i
$743$	29.2447	+	9.50217i	1.07288	+	0.348601i	0.791610	−	0.611027i	$-0.209243\pi$
$743$	29.2447	+	9.50217i	1.07288	+	0.348601i	0.281274	+	0.959628i	$0.409243\pi$
$744$	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	0.740784	−	0.671743i	$-0.234454\pi$
$751$	9.06629	+	6.58705i	0.330834	+	0.240365i	−0.409951	+	0.912108i	$0.634454\pi$
$752$	−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
$756$	−9.45899	+	28.2266i	−0.344020	+	1.02659i
$757$	24.9464	−	8.10558i	0.906692	−	0.294602i	0.181696	−	0.983355i	$-0.441841\pi$
$757$	24.9464	−	8.10558i	0.906692	−	0.294602i	0.724996	+	0.688753i	$0.241841\pi$
$758$	−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	−0.999181	−	0.0404518i	$-0.987120\pi$
$761$	−5.92010	−	18.2202i	−0.214604	−	0.660482i	0.784578	−	0.620030i	$-0.212880\pi$
$762$	9.35998	+	13.8636i	0.339076	+	0.502224i
$763$	−16.8570	+	1.00830i	−0.610264	+	0.0365029i
$764$	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	$-0.529135\pi$
$769$	−5.06939			−0.182807			−0.0914035	+	0.995814i	$0.529135\pi$
$770$	−39.6564	−	29.2772i	−1.42912	−	1.05508i
$771$		−	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	$-0.0639587\pi$
$773$	30.3848	+	22.0759i	1.09287	+	0.794014i	0.112985	+	0.993597i	$0.463959\pi$
$774$	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
$777$	−1.42630	−	23.8452i	−0.0511682	−	0.855441i
$778$	−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
$784$	27.9953	+	0.514540i	0.999831	+	0.0183764i
$785$	−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	$-0.432570\pi$
$787$	−5.45054	−	1.77099i	−0.194291	−	0.0631288i	−0.404546	+	0.914518i	$0.632570\pi$
$788$	−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	$-0.846549\pi$
$797$	2.91613	−	8.97494i	0.103295	−	0.317909i	0.989326	+	0.145716i	$0.0465486\pi$
$798$	−21.9638	+	7.75549i	−0.777510	+	0.274541i
$799$	−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
$805$	−11.4608	+	44.0715i	−0.403941	+	1.55332i
$806$	−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	0.198066	−	0.980189i	$-0.436534\pi$
$809$	−6.19588	−	2.01316i	−0.217835	−	0.0707790i	−0.415902	+	0.909410i	$0.636534\pi$
$810$	−9.57073	−	33.3217i	−0.336281	−	1.17081i
$811$	8.95432	−	12.3246i	0.314429	−	0.432774i	−0.622327	−	0.782757i	$-0.713813\pi$
$811$	8.95432	−	12.3246i	0.314429	−	0.432774i	0.936756	+	0.349983i	$0.113813\pi$
$812$	−22.7160	+	16.1874i	−0.797177	+	0.568065i
$813$	−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
$819$	−2.32762	−	2.83137i	−0.0813336	−	0.0989360i
$820$	−42.0436	+	26.3232i	−1.46822	+	0.919248i
$821$	1.39594	−	1.01421i	0.0487186	−	0.0353961i	−0.563159	−	0.826348i	$-0.690414\pi$
$821$	1.39594	−	1.01421i	0.0487186	−	0.0353961i	0.611878	+	0.790952i	$0.290414\pi$
$822$	−36.2436	+	24.4699i	−1.26414	+	0.853485i
$823$	−3.28766	−	10.1184i	−0.114601	−	0.352705i	0.877263	−	0.480010i	$-0.159367\pi$
$823$	−3.28766	−	10.1184i	−0.114601	−	0.352705i	−0.991864	+	0.127306i	$0.959367\pi$
$824$	−14.8250	−	25.5994i	−0.516452	−	0.891799i
$825$	53.5481	+	1.76296i	1.86431	+	0.0613785i
$826$	0.478615	−	0.366569i	0.0166532	−	0.0127546i
$827$	14.6133	+	44.9750i	0.508153	+	1.56393i	0.795405	+	0.606078i	$0.207258\pi$
$827$	14.6133	+	44.9750i	0.508153	+	1.56393i	−0.287252	+	0.957855i	$0.592742\pi$
$828$	−1.58535	−	6.33472i	−0.0550947	−	0.220147i
$829$	−15.9603	+	11.5958i	−0.554323	+	0.402739i	−0.829377	−	0.558690i	$-0.811304\pi$
$829$	−15.9603	+	11.5958i	−0.554323	+	0.402739i	0.275054	+	0.961429i	$0.411304\pi$
$830$	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
$833$	−3.31269	+	16.8013i	−0.114778	+	0.582131i
$834$	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	$-0.648175\pi$
$839$	15.6326	−	21.5164i	0.539696	−	0.742828i	0.988569	+	0.150768i	$0.0481745\pi$
$840$	−37.1520	+	24.5892i	−1.28187	+	0.848408i
$841$	−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
$847$	−23.4406	−	17.2493i	−0.805429	−	0.592692i
$848$	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	$-0.460117\pi$
$853$	−10.4297	−	3.38881i	−0.357106	−	0.116031i	−0.482075	+	0.876130i	$0.660117\pi$
$854$	11.4341	+	3.39817i	0.391268	+	0.116283i
$855$	−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	$-0.666436\pi$
$857$	−29.2379			−0.998747			−0.499373	+	0.866387i	$0.666436\pi$
$858$	8.28387	−	9.92132i	0.282807	−	0.338708i
$859$	−7.60160			−0.259363			−0.129682	−	0.991556i	$-0.541396\pi$
$859$	−7.60160			−0.259363			−0.129682	+	0.991556i	$0.541396\pi$
$860$	−22.6944	+	56.3134i	−0.773873	+	1.92027i
$861$	−9.04393	−	23.0501i	−0.308216	−	0.785544i
$862$	46.0702	−	13.2324i	1.56916	−	0.450696i
$863$	−8.50663	+	26.1807i	−0.289569	+	0.891201i	0.695423	+	0.718601i	$0.255217\pi$
$863$	−8.50663	+	26.1807i	−0.289569	+	0.891201i	−0.984992	+	0.172601i	$0.944783\pi$
$864$	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
$868$	32.8689	−	10.3468i	1.11564	−	0.351194i
$869$	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
$875$	46.9056	−	38.5603i	1.58570	−	1.30358i
$876$	33.8559	+	2.33748i	1.14389	+	0.0789760i
$877$	7.68045	+	5.58018i	0.259351	+	0.188429i	0.709861	−	0.704342i	$-0.248758\pi$
$877$	7.68045	+	5.58018i	0.259351	+	0.188429i	−0.450510	+	0.892771i	$0.648758\pi$
$878$	−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	$-0.0639014\pi$
$882$	2.89922	+	6.87299i	0.0976217	+	0.231426i
$883$	−31.6354	+	43.5424i	−1.06462	+	1.46532i	−0.189206	+	0.981937i	$0.560591\pi$
$883$	−31.6354	+	43.5424i	−1.06462	+	1.46532i	−0.875410	+	0.483381i	$0.839409\pi$
$884$	−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	$-0.661426\pi$
$887$	5.82550	−	4.23247i	0.195601	−	0.142112i	0.681275	+	0.732028i	$0.261426\pi$
$888$	−2.63580	+	25.4007i	−0.0884518	+	0.852393i
$889$	20.2070	+	5.25485i	0.677722	+	0.176242i
$890$	−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
$896$	−29.4415	−	5.40370i	−0.983570	−	0.180525i
$897$	−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	−0.151671	−	0.988431i	$-0.548465\pi$
$907$	−25.7604	−	8.37006i	−0.855360	−	0.277923i	−0.703689	+	0.710508i	$0.748465\pi$
$908$	−22.5969	−	36.0918i	−0.749903	−	1.19775i
$909$	1.78071	+	2.45094i	0.0590624	+	0.0812925i
$910$	−0.690626	−	27.3159i	−0.0228940	−	0.905515i
$911$	5.73175	+	17.6405i	0.189901	+	0.584456i	0.999998	−	0.00183978i	$-0.000585622\pi$
$911$	5.73175	+	17.6405i	0.189901	+	0.584456i	−0.810097	+	0.586296i	$0.800586\pi$
$912$	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
$917$	−1.52246	−	25.4529i	−0.0502761	−	0.840527i
$918$	15.3431	+	11.9765i	0.506398	+	0.395283i
$919$	−4.45024	−	1.44597i	−0.146800	−	0.0476982i	0.234695	−	0.972069i	$-0.424591\pi$
$919$	−4.45024	−	1.44597i	−0.146800	−	0.0476982i	−0.381495	+	0.924371i	$0.624591\pi$
$920$	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
$924$	−21.9125	+	14.5519i	−0.720868	+	0.478724i
$925$		−	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	$-0.191975\pi$
$929$	35.2487	+	11.4530i	1.15647	+	0.375761i	0.332895	+	0.942964i	$0.391975\pi$
$930$	−33.7373	+	43.2210i	−1.10629	+	1.41727i
$931$	−14.1636	+	25.3907i	−0.464193	+	0.832148i
$932$	−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	−0.851485	−	0.524379i	$-0.824298\pi$
$937$	−14.4127	−	44.3576i	−0.470841	−	1.44910i	0.380644	−	0.924722i	$-0.375702\pi$
$938$	−0.674906	−	26.6942i	−0.0220365	−	0.871595i
$939$	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	$-0.334049\pi$
$941$	12.0031	+	3.90005i	0.391290	+	0.127138i	−0.106763	+	0.994285i	$0.534049\pi$
$942$	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	$0.0252233\pi$
$947$			4.87194i			0.158317i	−0.996862	+	0.0791583i	$0.974777\pi$
$948$	−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
$952$	6.41168	−	17.1477i	0.207804	−	0.555759i
$953$	9.29076	+	12.7876i	0.300957	+	0.414232i	0.932535	−	0.361081i	$-0.117592\pi$
$953$	9.29076	+	12.7876i	0.300957	+	0.414232i	−0.631577	+	0.775313i	$0.717592\pi$
$954$	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
$959$	−13.7378	+	52.8274i	−0.443617	+	1.70589i
$960$	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
$966$	20.0140	+	13.7819i	0.643941	+	0.443424i
$967$		−	48.4826i		−	1.55910i	−0.626343	−	0.779548i	$-0.715449\pi$
$967$		−	48.4826i		−	1.55910i	0.626343	−	0.779548i	$-0.284551\pi$
$968$	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	$-0.500142\pi$
$971$	−29.6540	−	21.5449i	−0.951642	−	0.691409i	−0.951195	+	0.308591i	$0.900142\pi$
$972$	15.2185	+	1.05072i	0.488135	+	0.0337017i
$973$	−25.9568	−	31.5744i	−0.832138	−	1.01223i
$974$	−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	−0.981319	−	0.192387i	$-0.938377\pi$
$977$	−9.39265	−	28.9076i	−0.300498	−	0.924837i	0.680821	−	0.732449i	$-0.261623\pi$
$978$	−4.09086	−	1.48691i	−0.130811	−	0.0475462i
$979$	−19.6842	−	7.12003i	−0.629111	−	0.227557i
$980$	−14.4898	+	53.6889i	−0.462860	+	1.71503i
$981$	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	$-0.376332\pi$
$983$	−19.3893	−	26.6870i	−0.618421	−	0.851184i	−0.997237	+	0.0742882i	$0.976332\pi$
$984$	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
$987$	30.2099	−	11.8532i	0.961592	−	0.377290i
$988$	−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
$994$	13.0130	−	43.7861i	0.412749	−	1.38881i
$995$	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	$-0.316293\pi$
$997$	−13.2615	−	18.2529i	−0.419997	−	0.578076i	−0.965621	+	0.259954i	$0.916293\pi$
$998$	−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.237.5	yes	352
7.6	odd	2	inner	616.2.bi.c.237.6	yes	352
8.5	even	2	inner	616.2.bi.c.237.22	yes	352
11.2	odd	10	inner	616.2.bi.c.13.21	yes	352
56.13	odd	2	inner	616.2.bi.c.237.21	yes	352
77.13	even	10	inner	616.2.bi.c.13.22	yes	352
88.13	odd	10	inner	616.2.bi.c.13.6	yes	352
616.13	even	10	inner	616.2.bi.c.13.5	✓	352

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
616.2.bi.c.13.5	✓	352	616.13	even	10	inner
616.2.bi.c.13.6	yes	352	88.13	odd	10	inner
616.2.bi.c.13.21	yes	352	11.2	odd	10	inner
616.2.bi.c.13.22	yes	352	77.13	even	10	inner
616.2.bi.c.237.5	yes	352	1.1	even	1	trivial
616.2.bi.c.237.6	yes	352	7.6	odd	2	inner
616.2.bi.c.237.21	yes	352	56.13	odd	2	inner
616.2.bi.c.237.22	yes	352	8.5	even	2	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)

\(f(q)\)	\(=\)	\(q+(-1.41337 - 0.0487330i) q^{2} +(-1.21258 - 0.880988i) q^{3} +(1.99525 + 0.137756i) q^{4} +(-1.22746 + 3.77772i) q^{5} +(1.67089 + 1.30426i) q^{6} +(2.64103 - 0.157973i) q^{7} +(-2.81332 - 0.291935i) q^{8} +(-0.232850 - 0.716639i) q^{9} +O(q^{10})\)	\(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} +(2.64103 - 0.157973i) 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} +(-3.74046 + 0.0945698i) 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} +(5.29128 + 0.0486215i) 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} +(-2.64497 + 10.1710i) 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} +(4.61891 + 3.18063i) 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} +(6.95009 - 0.834424i) 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} +(-7.47619 - 0.326580i) 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} +(-0.728174 - 1.85588i) 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} +(4.23400 - 14.2465i) 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} +(2.48673 - 8.41523i) 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} +(-6.37324 - 4.72051i) 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} +(4.52818 - 1.77668i) 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} +(-9.86374 + 0.840654i) 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

Varieties

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Representations

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Database

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