LMFDB - Embedded newform 720.2.cf.a.11.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.21
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12365 + 0.858726i) q^{2} +(-1.61286 - 0.631411i) q^{3} +(0.525178 - 1.92982i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.35450 - 0.675522i) q^{6} +(-1.12628 + 1.95077i) q^{7} +(1.06707 + 2.61942i) q^{8} +(2.20264 + 2.03676i) q^{9} +O(q^{10})$	\(q+(-1.12365 + 0.858726i) q^{2} +(-1.61286 - 0.631411i) q^{3} +(0.525178 - 1.92982i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.35450 - 0.675522i) q^{6} +(-1.12628 + 1.95077i) q^{7} +(1.06707 + 2.61942i) q^{8} +(2.20264 + 2.03676i) q^{9} +(-1.30762 + 0.538644i) q^{10} +(1.28587 - 0.344548i) q^{11} +(-2.06554 + 2.78092i) q^{12} +(-3.50820 - 0.940019i) q^{13} +(-0.409637 - 3.15915i) q^{14} +(-1.39448 - 1.02734i) q^{15} +(-3.44838 - 2.02699i) q^{16} -6.51283i q^{17} +(-4.22401 - 0.397133i) q^{18} +(5.35979 + 5.35979i) q^{19} +(1.00676 - 1.72813i) q^{20} +(3.04827 - 2.43518i) q^{21} +(-1.14900 + 1.49136i) q^{22} +(-3.23731 + 1.86906i) q^{23} +(-0.0671023 - 4.89852i) q^{24} +(0.866025 + 0.500000i) q^{25} +(4.74921 - 1.95633i) q^{26} +(-2.26653 - 4.67577i) q^{27} +(3.17313 + 3.19801i) q^{28} +(1.22629 - 0.328583i) q^{29} +(2.44911 - 0.0431147i) q^{30} +(-7.37559 + 4.25830i) q^{31} +(5.61540 - 0.683584i) q^{32} +(-2.29148 - 0.256205i) q^{33} +(5.59274 + 7.31814i) q^{34} +(-1.59280 + 1.59280i) q^{35} +(5.08734 - 3.18103i) q^{36} +(2.77821 + 2.77821i) q^{37} +(-10.6251 - 1.41993i) q^{38} +(5.06470 + 3.73123i) q^{39} +(0.352753 + 2.80634i) q^{40} +(0.620748 + 1.07517i) q^{41} +(-1.33403 + 5.35392i) q^{42} +(2.74826 + 10.2567i) q^{43} +(0.0103964 - 2.66244i) q^{44} +(1.60044 + 2.53744i) q^{45} +(2.03259 - 4.88014i) q^{46} +(-4.42552 + 7.66523i) q^{47} +(4.28189 + 5.44660i) q^{48} +(0.962991 + 1.66795i) q^{49} +(-1.40247 + 0.181854i) q^{50} +(-4.11227 + 10.5043i) q^{51} +(-3.65649 + 6.27650i) q^{52} +(0.816936 - 0.816936i) q^{53} +(6.56199 + 3.30761i) q^{54} +1.33123 q^{55} +(-6.31171 - 0.868592i) q^{56} +(-5.26037 - 12.0288i) q^{57} +(-1.09576 + 1.42226i) q^{58} +(-2.90800 + 10.8528i) q^{59} +(-2.71492 + 2.15156i) q^{60} +(0.541672 + 2.02155i) q^{61} +(4.63087 - 11.1185i) q^{62} +(-6.45403 + 2.00290i) q^{63} +(-5.72273 + 5.59020i) q^{64} +(-3.14537 - 1.81598i) q^{65} +(2.79484 - 1.67987i) q^{66} +(0.171267 - 0.639176i) q^{67} +(-12.5686 - 3.42039i) q^{68} +(6.40148 - 0.970466i) q^{69} +(0.421970 - 3.15753i) q^{70} -13.2012i q^{71} +(-2.98475 + 7.94300i) q^{72} +14.2744i q^{73} +(-5.50745 - 0.736012i) q^{74} +(-1.08107 - 1.35325i) q^{75} +(13.1583 - 7.52857i) q^{76} +(-0.776115 + 2.89650i) q^{77} +(-8.89506 + 0.156591i) q^{78} +(-14.1761 - 8.18455i) q^{79} +(-2.80625 - 2.85043i) q^{80} +(0.703256 + 8.97248i) q^{81} +(-1.62078 - 0.675058i) q^{82} +(-0.780157 - 2.91159i) q^{83} +(-3.09857 - 7.16150i) q^{84} +(1.68564 - 6.29091i) q^{85} +(-11.8958 - 9.16489i) q^{86} +(-2.18530 - 0.244333i) q^{87} +(2.27463 + 3.00058i) q^{88} +0.500668 q^{89} +(-3.97730 - 1.47686i) q^{90} +(5.78497 - 5.78497i) q^{91} +(1.90678 + 7.22901i) q^{92} +(14.5845 - 2.21102i) q^{93} +(-1.60960 - 12.4133i) q^{94} +(3.78995 + 6.56438i) q^{95} +(-9.48848 - 2.44310i) q^{96} +(-5.12008 + 8.86824i) q^{97} +(-2.51438 - 1.04725i) q^{98} +(3.53407 + 1.86009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.12365	+	0.858726i	−0.794540	+	0.607211i
$2$	−1.12365	+	0.858726i	−0.794540	+	0.607211i
$3$	−1.61286	−	0.631411i	−0.931186	−	0.364545i
$3$	−1.61286	−	0.631411i	−0.931186	−	0.364545i
$4$	0.525178	−	1.92982i	0.262589	−	0.964908i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	2.35450	−	0.675522i	0.961221	−	0.275781i
$7$	−1.12628	+	1.95077i	−0.425693	+	0.737323i	−0.996485	−	0.0837724i	$-0.973303\pi$
$7$	−1.12628	+	1.95077i	−0.425693	+	0.737323i	0.570791	+	0.821095i	$0.306636\pi$
$8$	1.06707	+	2.61942i	0.377266	+	0.926105i
$9$	2.20264	+	2.03676i	0.734214	+	0.678918i
$10$	−1.30762	+	0.538644i	−0.413505	+	0.170334i
$11$	1.28587	−	0.344548i	0.387705	−	0.103885i	−0.0597008	−	0.998216i	$-0.519015\pi$
$11$	1.28587	−	0.344548i	0.387705	−	0.103885i	0.447406	+	0.894331i	$0.352348\pi$
$12$	−2.06554	+	2.78092i	−0.596271	+	0.802783i
$13$	−3.50820	−	0.940019i	−0.972999	−	0.260714i	−0.262906	−	0.964822i	$-0.584681\pi$
$13$	−3.50820	−	0.940019i	−0.972999	−	0.260714i	−0.710094	+	0.704107i	$0.751347\pi$
$14$	−0.409637	−	3.15915i	−0.109480	−	0.844319i
$15$	−1.39448	−	1.02734i	−0.360054	−	0.265257i
$16$	−3.44838	−	2.02699i	−0.862094	−	0.506748i
$17$		−	6.51283i		−	1.57959i	−0.613369	−	0.789796i	$-0.710186\pi$
$17$		−	6.51283i		−	1.57959i	0.613369	−	0.789796i	$-0.289814\pi$
$18$	−4.22401	−	0.397133i	−0.995609	−	0.0936052i
$19$	5.35979	+	5.35979i	1.22962	+	1.22962i	0.964107	+	0.265514i	$0.0855417\pi$
$19$	5.35979	+	5.35979i	1.22962	+	1.22962i	0.265514	+	0.964107i	$0.414458\pi$
$20$	1.00676	−	1.72813i	0.225117	−	0.386422i
$21$	3.04827	−	2.43518i	0.665187	−	0.531400i
$22$	−1.14900	+	1.49136i	−0.244967	+	0.317960i
$23$	−3.23731	+	1.86906i	−0.675026	+	0.389727i	−0.797978	−	0.602686i	$-0.794097\pi$
$23$	−3.23731	+	1.86906i	−0.675026	+	0.389727i	0.122952	+	0.992413i	$0.460764\pi$
$24$	−0.0671023	−	4.89852i	−0.0136972	−	0.999906i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	4.74921	−	1.95633i	0.931396	−	0.383668i
$27$	−2.26653	−	4.67577i	−0.436193	−	0.899853i
$28$	3.17313	+	3.19801i	0.599666	+	0.604368i
$29$	1.22629	−	0.328583i	0.227716	−	0.0610164i	−0.143157	−	0.989700i	$-0.545725\pi$
$29$	1.22629	−	0.328583i	0.227716	−	0.0610164i	0.370873	+	0.928684i	$0.379059\pi$
$30$	2.44911	−	0.0431147i	0.447144	−	0.00787164i
$31$	−7.37559	+	4.25830i	−1.32469	+	0.764813i	−0.984474	−	0.175532i	$-0.943835\pi$
$31$	−7.37559	+	4.25830i	−1.32469	+	0.764813i	−0.340221	+	0.940345i	$0.610502\pi$
$32$	5.61540	−	0.683584i	0.992672	−	0.120842i
$33$	−2.29148	−	0.256205i	−0.398896	−	0.0445995i
$34$	5.59274	+	7.31814i	0.959146	+	1.25505i
$35$	−1.59280	+	1.59280i	−0.269232	+	0.269232i
$36$	5.08734	−	3.18103i	0.847890	−	0.530172i
$37$	2.77821	+	2.77821i	0.456734	+	0.456734i	0.897582	−	0.440848i	$-0.145322\pi$
$37$	2.77821	+	2.77821i	0.456734	+	0.456734i	−0.440848	+	0.897582i	$0.645322\pi$
$38$	−10.6251	−	1.41993i	−1.72362	−	0.230344i
$39$	5.06470	+	3.73123i	0.811001	+	0.597476i
$40$	0.352753	+	2.80634i	0.0557751	+	0.443722i
$41$	0.620748	+	1.07517i	0.0969445	+	0.167913i	0.910418	−	0.413688i	$-0.135760\pi$
$41$	0.620748	+	1.07517i	0.0969445	+	0.167913i	−0.813474	+	0.581601i	$0.802426\pi$
$42$	−1.33403	+	5.35392i	−0.205846	+	0.826128i
$43$	2.74826	+	10.2567i	0.419106	+	1.56413i	0.776466	+	0.630160i	$0.217011\pi$
$43$	2.74826	+	10.2567i	0.419106	+	1.56413i	−0.357359	+	0.933967i	$0.616323\pi$
$44$	0.0103964	−	2.66244i	0.00156731	−	0.401379i
$45$	1.60044	+	2.53744i	0.238579	+	0.378259i
$46$	2.03259	−	4.88014i	0.299689	−	0.719537i
$47$	−4.42552	+	7.66523i	−0.645529	+	1.11809i	0.338650	+	0.940912i	$0.390030\pi$
$47$	−4.42552	+	7.66523i	−0.645529	+	1.11809i	−0.984179	+	0.177176i	$0.943304\pi$
$48$	4.28189	+	5.44660i	0.618037	+	0.786149i
$49$	0.962991	+	1.66795i	0.137570	+	0.238278i
$50$	−1.40247	+	0.181854i	−0.198340	+	0.0257180i
$51$	−4.11227	+	10.5043i	−0.575833	+	1.47089i
$52$	−3.65649	+	6.27650i	−0.507064	+	0.870394i
$53$	0.816936	−	0.816936i	0.112215	−	0.112215i	−0.648770	−	0.760985i	$-0.724716\pi$
$53$	0.816936	−	0.816936i	0.112215	−	0.112215i	0.760985	+	0.648770i	$0.224716\pi$
$54$	6.56199	+	3.30761i	0.892974	+	0.450108i
$55$	1.33123			0.179503
$56$	−6.31171	−	0.868592i	−0.843438	−	0.116070i
$57$	−5.26037	−	12.0288i	−0.696753	−	1.59326i
$58$	−1.09576	+	1.42226i	−0.143880	+	0.186752i
$59$	−2.90800	+	10.8528i	−0.378590	+	1.41292i	0.469439	+	0.882965i	$0.344456\pi$
$59$	−2.90800	+	10.8528i	−0.378590	+	1.41292i	−0.848028	+	0.529951i	$0.822210\pi$
$60$	−2.71492	+	2.15156i	−0.350494	+	0.277765i
$61$	0.541672	+	2.02155i	0.0693540	+	0.258833i	0.991894	−	0.127069i	$-0.0405570\pi$
$61$	0.541672	+	2.02155i	0.0693540	+	0.258833i	−0.922540	+	0.385902i	$0.873890\pi$
$62$	4.63087	−	11.1185i	0.588121	−	1.41204i
$63$	−6.45403	+	2.00290i	−0.813132	+	0.252341i
$64$	−5.72273	+	5.59020i	−0.715341	+	0.698775i
$65$	−3.14537	−	1.81598i	−0.390135	−	0.225244i
$66$	2.79484	−	1.67987i	0.344020	−	0.206778i
$67$	0.171267	−	0.639176i	0.0209236	−	0.0780878i	−0.954675	−	0.297651i	$-0.903797\pi$
$67$	0.171267	−	0.639176i	0.0209236	−	0.0780878i	0.975598	+	0.219564i	$0.0704634\pi$
$68$	−12.5686	−	3.42039i	−1.52416	−	0.414783i
$69$	6.40148	−	0.970466i	0.770648	−	0.116830i
$70$	0.421970	−	3.15753i	0.0504350	−	0.377397i
$71$		−	13.2012i		−	1.56669i	−0.621587	−	0.783345i	$-0.713512\pi$
$71$		−	13.2012i		−	1.56669i	0.621587	−	0.783345i	$-0.286488\pi$
$72$	−2.98475	+	7.94300i	−0.351756	+	0.936092i
$73$			14.2744i			1.67070i	0.549721	+	0.835348i	$0.314734\pi$
$73$			14.2744i			1.67070i	−0.549721	+	0.835348i	$0.685266\pi$
$74$	−5.50745	−	0.736012i	−0.640228	−	0.0855596i
$75$	−1.08107	−	1.35325i	−0.124832	−	0.156260i
$76$	13.1583	−	7.52857i	1.50936	−	0.863586i
$77$	−0.776115	+	2.89650i	−0.0884465	+	0.330087i
$78$	−8.89506	+	0.156591i	−1.00717	+	0.0177304i
$79$	−14.1761	−	8.18455i	−1.59493	−	0.920834i	−0.992443	−	0.122705i	$-0.960843\pi$
$79$	−14.1761	−	8.18455i	−1.59493	−	0.920834i	−0.602487	−	0.798128i	$-0.705824\pi$
$80$	−2.80625	−	2.85043i	−0.313749	−	0.318688i
$81$	0.703256	+	8.97248i	0.0781396	+	0.996942i
$82$	−1.62078	−	0.675058i	−0.178985	−	0.0745477i
$83$	−0.780157	−	2.91159i	−0.0856334	−	0.319588i	0.909800	−	0.415047i	$-0.136235\pi$
$83$	−0.780157	−	2.91159i	−0.0856334	−	0.319588i	−0.995433	+	0.0954588i	$0.969568\pi$
$84$	−3.09857	−	7.16150i	−0.338081	−	0.781384i
$85$	1.68564	−	6.29091i	0.182834	−	0.682345i
$86$	−11.8958	−	9.16489i	−1.28275	−	0.988276i
$87$	−2.18530	−	0.244333i	−0.234289	−	0.0261953i
$88$	2.27463	+	3.00058i	0.242476	+	0.319863i
$89$	0.500668			0.0530707			0.0265354	−	0.999648i	$-0.491553\pi$
$89$	0.500668			0.0530707			0.0265354	+	0.999648i	$0.491553\pi$
$90$	−3.97730	−	1.47686i	−0.419244	−	0.155674i
$91$	5.78497	−	5.78497i	0.606430	−	0.606430i
$92$	1.90678	+	7.22901i	0.198796	+	0.753676i
$93$	14.5845	−	2.21102i	1.51235	−	0.229272i
$94$	−1.60960	−	12.4133i	−0.166017	−	1.28034i
$95$	3.78995	+	6.56438i	0.388840	+	0.673491i
$96$	−9.48848	−	2.44310i	−0.968414	−	0.249348i
$97$	−5.12008	+	8.86824i	−0.519865	+	0.900433i	0.479868	+	0.877341i	$0.340685\pi$
$97$	−5.12008	+	8.86824i	−0.519865	+	0.900433i	−0.999733	+	0.0230926i	$0.992649\pi$
$98$	−2.51438	−	1.04725i	−0.253990	−	0.105788i
$99$	3.53407	+	1.86009i	0.355188	+	0.186946i
$100$	1.41972	−	1.40868i	0.141972	−	0.140868i
$101$	2.50724	+	9.35715i	0.249480	+	0.931071i	0.971079	+	0.238760i	$0.0767408\pi$
$101$	2.50724	+	9.35715i	0.249480	+	0.931071i	−0.721599	+	0.692311i	$0.756593\pi$
$102$	−4.39956	−	15.3344i	−0.435621	−	1.51834i
$103$	7.91409	+	13.7076i	0.779798	+	1.35065i	0.932058	+	0.362310i	$0.118012\pi$
$103$	7.91409	+	13.7076i	0.779798	+	1.35065i	−0.152259	+	0.988341i	$0.548655\pi$
$104$	−1.28118	−	10.1925i	−0.125630	−	0.999458i
$105$	3.57467	−	1.56325i	0.348852	−	0.152558i
$106$	−0.216425	+	1.61947i	−0.0210211	+	0.157297i
$107$	11.3444	+	11.3444i	1.09670	+	1.09670i	0.994794	+	0.101907i	$0.0324944\pi$
$107$	11.3444	+	11.3444i	1.09670	+	1.09670i	0.101907	+	0.994794i	$0.467506\pi$
$108$	−10.2137	+	1.91836i	−0.982815	+	0.184595i
$109$	−2.20589	+	2.20589i	−0.211286	+	0.211286i	−0.804814	−	0.593528i	$-0.797735\pi$
$109$	−2.20589	+	2.20589i	−0.211286	+	0.211286i	0.593528	+	0.804814i	$0.297735\pi$
$110$	−1.49584	+	1.14316i	−0.142623	+	0.108996i
$111$	−2.72667	−	6.23505i	−0.258804	−	0.591805i
$112$	7.83804	−	4.44404i	0.740625	−	0.419922i
$113$	2.38626	−	1.37771i	0.224480	−	0.129604i	−0.383543	−	0.923523i	$-0.625296\pi$
$113$	2.38626	−	1.37771i	0.224480	−	0.129604i	0.608023	+	0.793919i	$0.291963\pi$
$114$	16.2403	+	8.99898i	1.52104	+	0.842831i
$115$	−3.61075	+	0.967498i	−0.336704	+	0.0902197i
$116$	0.00991464	−	2.53908i	0.000920551	−	0.235747i
$117$	−5.81272	−	9.21587i	−0.537386	−	0.852007i
$118$	−6.05202	−	14.6919i	−0.557134	−	1.35250i
$119$	12.7050	+	7.33526i	1.16467	+	0.672422i
$120$	1.20301	−	4.74897i	0.109820	−	0.433520i
$121$	−7.99153	+	4.61391i	−0.726502	+	0.419446i
$122$	−2.34461	−	1.80636i	−0.212271	−	0.163541i
$123$	−0.322308	−	2.12604i	−0.0290615	−	0.191699i
$124$	4.34424	+	16.4699i	0.390124	+	1.47904i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	5.53213	−	7.79281i	0.492842	−	0.694238i
$127$		−	11.7657i		−	1.04403i	−0.852935	−	0.522017i	$-0.825180\pi$
$127$		−	11.7657i		−	1.04403i	0.852935	−	0.522017i	$-0.174820\pi$
$128$	1.62989	−	11.1957i	0.144063	−	0.989568i
$129$	2.04360	−	18.2779i	0.179929	−	1.60928i
$130$	5.09372	−	0.660486i	0.446749	−	0.0579284i
$131$	4.31538	+	1.15630i	0.377036	+	0.101027i	0.442360	−	0.896838i	$-0.354141\pi$
$131$	4.31538	+	1.15630i	0.377036	+	0.101027i	−0.0653239	+	0.997864i	$0.520808\pi$
$132$	−1.69786	+	4.28759i	−0.147780	+	0.373187i
$133$	−16.4924	+	4.41912i	−1.43007	+	0.383186i
$134$	0.356434	+	0.865281i	0.0307912	+	0.0747489i
$135$	−0.979116	−	5.10307i	−0.0842689	−	0.439202i
$136$	17.0598	−	6.94963i	1.46287	−	0.595926i
$137$	5.85154	−	10.1352i	0.499931	−	0.865906i	−0.500069	−	0.865985i	$-0.666692\pi$
$137$	5.85154	−	10.1352i	0.499931	−	0.865906i	1.00000		7.98350e-5i	$2.54123e-5\pi$
$138$	−6.35966	+	6.58759i	−0.541370	+	0.560773i
$139$	−4.16347	−	1.11560i	−0.353141	−	0.0946239i	0.0778875	−	0.996962i	$-0.475183\pi$
$139$	−4.16347	−	1.11560i	−0.353141	−	0.0946239i	−0.431029	+	0.902338i	$0.641849\pi$
$140$	2.23731	+	3.91031i	0.189087	+	0.330482i
$141$	11.9777	−	9.56863i	1.00870	−	0.805824i
$142$	11.3362	+	14.8335i	0.951312	+	1.24480i
$143$	−4.83498			−0.404321
$144$	−3.46705	−	11.4882i	−0.288921	−	0.957353i
$145$	1.26955			0.105430
$146$	−12.2578	−	16.0395i	−1.01447	−	1.32744i
$147$	−0.500010	−	3.29821i	−0.0412401	−	0.272032i
$148$	6.82048	−	3.90238i	0.560640	−	0.320773i
$149$	−5.10344	−	1.36746i	−0.418090	−	0.112027i	0.0436400	−	0.999047i	$-0.486105\pi$
$149$	−5.10344	−	1.36746i	−0.418090	−	0.112027i	−0.461730	+	0.887020i	$0.652771\pi$
$150$	2.37682	+	0.592231i	0.194066	+	0.0483554i
$151$	4.91754	−	8.51744i	0.400184	−	0.693139i	−0.593564	−	0.804787i	$-0.702280\pi$
$151$	4.91754	−	8.51744i	0.400184	−	0.693139i	0.993748	+	0.111648i	$0.0356128\pi$
$152$	−8.32029	+	19.7588i	−0.674865	+	1.60265i
$153$	13.2650	−	14.3454i	1.07241	−	1.15976i
$154$	−1.61522	−	3.92112i	−0.130158	−	0.315973i
$155$	−8.22640	+	2.20426i	−0.660760	+	0.177050i
$156$	9.86046	−	7.81438i	0.789469	−	0.625651i
$157$	17.0197	+	4.56043i	1.35832	+	0.363962i	0.863200	−	0.504861i	$-0.168456\pi$
$157$	17.0197	+	4.56043i	1.35832	+	0.363962i	0.495123	+	0.868823i	$0.335123\pi$
$158$	22.9572	−	2.97679i	1.82638	−	0.236820i
$159$	−1.83343	+	0.801782i	−0.145400	+	0.0635854i
$160$	5.60098	+	0.793081i	0.442797	+	0.0626986i
$161$		−	8.42035i		−	0.663616i
$162$	−8.49512	−	9.47802i	−0.667440	−	0.744664i
$163$	0.457096	+	0.457096i	0.0358025	+	0.0358025i	0.724781	−	0.688979i	$-0.241941\pi$
$163$	0.457096	+	0.457096i	0.0358025	+	0.0358025i	−0.688979	+	0.724781i	$0.741941\pi$
$164$	2.40088	−	0.633275i	0.187477	−	0.0494505i
$165$	−2.14709	−	0.840554i	−0.167151	−	0.0654371i
$166$	3.37688	+	2.60166i	0.262097	+	0.201928i
$167$	7.40530	−	4.27545i	0.573040	−	0.330845i	−0.185323	−	0.982678i	$-0.559333\pi$
$167$	7.40530	−	4.27545i	0.573040	−	0.330845i	0.758362	+	0.651833i	$0.226000\pi$
$168$	9.63147	+	5.38620i	0.743084	+	0.415554i
$169$	0.165496	+	0.0955490i	0.0127304	+	0.00734993i
$170$	3.50810	+	8.51628i	0.269059	+	0.653169i
$171$	0.889114	+	22.7223i	0.0679923	+	1.73762i
$172$	21.2368	+	0.0829259i	1.61929	+	0.00632304i
$173$	−24.9624	+	6.68865i	−1.89785	+	0.508529i	−0.900585	+	0.434679i	$0.856862\pi$
$173$	−24.9624	+	6.68865i	−1.89785	+	0.508529i	−0.997269	+	0.0738491i	$0.976472\pi$
$174$	2.66533	−	1.60203i	0.202058	−	0.121450i
$175$	−1.95077	+	1.12628i	−0.147465	+	0.0851387i
$176$	−5.13257	−	1.41832i	−0.386882	−	0.106910i
$177$	11.5428	−	15.6679i	0.867609	−	1.17767i
$178$	−0.562576	+	0.429937i	−0.0421668	+	0.0322251i
$179$	5.16019	−	5.16019i	0.385691	−	0.385691i	−0.487457	−	0.873147i	$-0.662075\pi$
$179$	5.16019	−	5.16019i	0.385691	−	0.385691i	0.873147	+	0.487457i	$0.162075\pi$
$180$	5.73731	−	1.75594i	0.427633	−	0.130880i
$181$	5.27937	+	5.27937i	0.392413	+	0.392413i	0.875547	−	0.483134i	$-0.160502\pi$
$181$	5.27937	+	5.27937i	0.392413	+	0.392413i	−0.483134	+	0.875547i	$0.660502\pi$
$182$	−1.53257	+	11.4680i	−0.113602	+	0.850064i
$183$	0.402785	−	3.60249i	0.0297747	−	0.266304i
$184$	−8.35030	−	6.48547i	−0.615592	−	0.478115i
$185$	1.96449	+	3.40259i	0.144432	+	0.250164i
$186$	−14.4893	+	15.0085i	−1.06240	+	1.10048i
$187$	−2.24398	−	8.37466i	−0.164096	−	0.612416i
$188$	12.4683	+	12.5660i	0.909344	+	0.916473i
$189$	11.6741	+	0.844752i	0.849167	+	0.0614466i
$190$	−9.89558	−	4.12154i	−0.717901	−	0.299008i
$191$	−3.68634	+	6.38493i	−0.266734	+	0.461997i	−0.968017	−	0.250886i	$-0.919278\pi$
$191$	−3.68634	+	6.38493i	−0.266734	+	0.461997i	0.701282	+	0.712884i	$0.252611\pi$
$192$	12.7597	−	5.40282i	0.920851	−	0.389915i
$193$	−4.78773	−	8.29260i	−0.344629	−	0.596914i	0.640658	−	0.767827i	$-0.278662\pi$
$193$	−4.78773	−	8.29260i	−0.344629	−	0.596914i	−0.985286	+	0.170912i	$0.945328\pi$
$194$	−1.86222	−	14.3615i	−0.133699	−	1.03110i
$195$	3.92641	+	4.91494i	0.281176	+	0.351966i
$196$	3.72458	−	0.982425i	0.266041	−	0.0701732i
$197$	6.33677	−	6.33677i	0.451476	−	0.451476i	−0.444368	−	0.895844i	$-0.646572\pi$
$197$	6.33677	−	6.33677i	0.451476	−	0.451476i	0.895844	+	0.444368i	$0.146572\pi$
$198$	−5.56837	+	0.944714i	−0.395727	+	0.0671379i
$199$	−3.94773			−0.279847			−0.139923	−	0.990162i	$-0.544686\pi$
$199$	−3.94773			−0.279847			−0.139923	+	0.990162i	$0.544686\pi$
$200$	−0.385602	+	2.80202i	−0.0272662	+	0.198133i
$201$	−0.679812	+	0.922763i	−0.0479502	+	0.0650867i
$202$	−10.8525	−	8.36112i	−0.763579	−	0.588287i
$203$	−0.740153	+	2.76229i	−0.0519485	+	0.193875i
$204$	18.1117	+	13.4525i	1.26807	+	0.941866i
$205$	0.321323	+	1.19919i	0.0224422	+	0.0837552i
$206$	−20.6637	−	8.60651i	−1.43971	−	0.599644i
$207$	−10.9375	−	2.47674i	−0.760206	−	0.172145i
$208$	10.1922	+	10.3526i	0.706701	+	0.717826i
$209$	8.73872	+	5.04530i	0.604470	+	0.348991i
$210$	−2.67427	+	4.82622i	−0.184542	+	0.333041i
$211$	−0.669011	+	2.49678i	−0.0460566	+	0.171886i	−0.985123	−	0.171850i	$-0.945026\pi$
$211$	−0.669011	+	2.49678i	−0.0460566	+	0.171886i	0.939067	+	0.343735i	$0.111692\pi$
$212$	−1.14750	−	2.00557i	−0.0788106	−	0.137743i
$213$	−8.33536	+	21.2916i	−0.571129	+	1.45888i
$214$	−22.4888	−	3.00539i	−1.53730	−	0.205444i
$215$			10.6185i			0.724174i
$216$	9.82928	−	10.9264i	0.668798	−	0.743444i
$217$		−	19.1841i		−	1.30230i
$218$	0.584392	−	4.37290i	0.0395800	−	0.296170i
$219$	9.01303	−	23.0227i	0.609044	−	1.55573i
$220$	0.699134	−	2.56903i	0.0471356	−	0.173204i
$221$	−6.12218	+	22.8483i	−0.411822	+	1.53694i
$222$	8.41803	+	4.66455i	0.564981	+	0.313064i
$223$	−12.8925	−	7.44349i	−0.863346	−	0.498453i	0.00178515	−	0.999998i	$-0.499432\pi$
$223$	−12.8925	−	7.44349i	−0.863346	−	0.498453i	−0.865131	+	0.501545i	$0.832765\pi$
$224$	−4.99099	+	11.7243i	−0.333475	+	0.783361i
$225$	0.889166	+	2.86520i	0.0592777	+	0.191013i
$226$	−1.49825	+	3.59720i	−0.0996618	+	0.239282i
$227$	−4.31803	−	16.1151i	−0.286598	−	1.06960i	−0.947664	−	0.319270i	$-0.896562\pi$
$227$	−4.31803	−	16.1151i	−0.286598	−	1.06960i	0.661066	−	0.750328i	$-0.270104\pi$
$228$	−25.9761	+	3.83427i	−1.72031	+	0.253931i
$229$	3.57090	−	13.3268i	0.235972	−	0.880658i	−0.741737	−	0.670691i	$-0.765998\pi$
$229$	3.57090	−	13.3268i	0.235972	−	0.880658i	0.977708	−	0.209967i	$-0.0673357\pi$
$230$	3.22641	−	4.18778i	0.212743	−	0.276134i
$231$	3.08065	−	4.18161i	0.202692	−	0.275129i
$232$	2.16923	+	2.86155i	0.142417	+	0.187870i
$233$	−9.01951			−0.590888			−0.295444	−	0.955360i	$-0.595467\pi$
$233$	−9.01951			−0.590888			−0.295444	+	0.955360i	$0.595467\pi$
$234$	14.4454	+	5.36388i	0.944323	+	0.350648i
$235$	−6.25863	+	6.25863i	−0.408268	+	0.408268i
$236$	19.4167	+	11.3116i	1.26392	+	0.736320i
$237$	17.6962	+	22.1514i	1.14949	+	1.43889i
$238$	−20.5750	+	2.66789i	−1.33368	+	0.172934i
$239$	−4.18216	−	7.24371i	−0.270521	−	0.468556i	0.698474	−	0.715635i	$-0.253863\pi$
$239$	−4.18216	−	7.24371i	−0.270521	−	0.468556i	−0.968995	+	0.247079i	$0.920529\pi$
$240$	2.72630	+	6.36924i	0.175982	+	0.411133i
$241$	4.08211	−	7.07042i	0.262952	−	0.455446i	−0.704073	−	0.710127i	$-0.748637\pi$
$241$	4.08211	−	7.07042i	0.262952	−	0.455446i	0.967025	+	0.254681i	$0.0819706\pi$
$242$	5.01759	−	12.0470i	0.322543	−	0.774408i
$243$	4.53107	−	14.9154i	0.290668	−	0.956824i
$244$	4.18569	+	0.0163444i	0.267961	+	0.00104634i
$245$	0.498481	+	1.86036i	0.0318468	+	0.118854i
$246$	2.18785	+	2.11215i	0.139492	+	0.134666i
$247$	−13.7649	−	23.8415i	−0.875841	−	1.51700i
$248$	−19.0245	−	14.7759i	−1.20806	−	0.938269i
$249$	−0.580121	+	5.18858i	−0.0367637	+	0.328813i
$250$	−1.40175	−	0.187329i	−0.0886546	−	0.0118477i
$251$	11.0408	+	11.0408i	0.696890	+	0.696890i	0.963738	−	0.266849i	$-0.0859823\pi$
$251$	11.0408	+	11.0408i	0.696890	+	0.696890i	−0.266849	+	0.963738i	$0.585982\pi$
$252$	0.475708	+	13.5070i	0.0299668	+	0.850859i
$253$	−3.51879	+	3.51879i	−0.221224	+	0.221224i
$254$	10.1035	+	13.2205i	0.633949	+	0.829527i
$255$	−6.69085	+	9.08202i	−0.418998	+	0.568738i
$256$	7.78261	+	13.9797i	0.486413	+	0.873729i
$257$	15.0885	−	8.71137i	0.941197	−	0.543400i	0.0508618	−	0.998706i	$-0.483803\pi$
$257$	15.0885	−	8.71137i	0.941197	−	0.543400i	0.890335	+	0.455305i	$0.150470\pi$
$258$	13.3994	+	22.2928i	0.834210	+	1.38789i
$259$	−8.54869	+	2.29061i	−0.531189	+	0.142332i
$260$	−5.15638	+	5.11626i	−0.319785	+	0.317297i
$261$	3.37032	+	1.77390i	0.208617	+	0.109802i
$262$	−5.84192	+	2.40645i	−0.360915	+	0.148671i
$263$	−3.85410	−	2.22516i	−0.237654	−	0.137209i	0.376444	−	0.926439i	$-0.377147\pi$
$263$	−3.85410	−	2.22516i	−0.237654	−	0.137209i	−0.614098	+	0.789230i	$0.710480\pi$
$264$	−1.77406	−	6.27575i	−0.109186	−	0.386246i
$265$	1.00054	−	0.577661i	0.0614626	−	0.0354854i
$266$	14.7368	−	19.1280i	0.903573	−	1.17281i
$267$	−0.807508	−	0.316127i	−0.0494187	−	0.0193467i
$268$	−1.14355	−	0.666194i	−0.0698532	−	0.0406943i
$269$	−6.08154	−	6.08154i	−0.370798	−	0.370798i	0.496970	−	0.867768i	$-0.334446\pi$
$269$	−6.08154	−	6.08154i	−0.370798	−	0.370798i	−0.867768	+	0.496970i	$0.834446\pi$
$270$	5.48233	+	4.89327i	0.333644	+	0.297795i
$271$			9.08528i			0.551891i	0.961173	+	0.275946i	$0.0889910\pi$
$271$			9.08528i			0.551891i	−0.961173	+	0.275946i	$0.911009\pi$
$272$	−13.2014	+	22.4587i	−0.800455	+	1.36176i
$273$	−12.9831	+	5.67767i	−0.785770	+	0.343628i
$274$	2.12825	+	16.4132i	0.128572	+	0.991561i
$275$	1.28587	+	0.344548i	0.0775410	+	0.0207770i
$276$	1.48910	−	12.8633i	0.0896330	−	0.774282i
$277$	−1.43140	+	0.383542i	−0.0860044	+	0.0230448i	−0.301565	−	0.953446i	$-0.597509\pi$
$277$	−1.43140	+	0.383542i	−0.0860044	+	0.0230448i	0.215560	+	0.976491i	$0.430842\pi$
$278$	5.63628	−	2.32174i	0.338042	−	0.139249i
$279$	−24.9189	−	5.64277i	−1.49185	−	0.337824i
$280$	−5.87184	−	2.47259i	−0.350909	−	0.147765i
$281$	6.34730	−	10.9939i	0.378648	−	0.655838i	−0.612217	−	0.790689i	$-0.709722\pi$
$281$	6.34730	−	10.9939i	0.378648	−	0.655838i	0.990866	+	0.134851i	$0.0430556\pi$
$282$	−5.24186	+	21.0373i	−0.312148	+	1.25275i
$283$	−0.280597	−	0.0751857i	−0.0166797	−	0.00446933i	0.250470	−	0.968124i	$-0.419415\pi$
$283$	−0.280597	−	0.0751857i	−0.0166797	−	0.00446933i	−0.267149	+	0.963655i	$0.586082\pi$
$284$	−25.4758	−	6.93296i	−1.51171	−	0.411395i
$285$	−1.96784	−	12.9804i	−0.116565	−	0.768895i
$286$	5.43282	−	4.15192i	0.321249	−	0.245508i
$287$	−2.79654			−0.165075
$288$	13.7610	+	9.93151i	0.810875	+	0.585220i
$289$	−25.4169			−1.49511
$290$	−1.42653	+	1.09019i	−0.0837686	+	0.0640184i
$291$	13.8575	−	11.0704i	0.812340	−	0.648956i
$292$	27.5470	+	7.49661i	1.61207	+	0.438706i
$293$	−1.64381	−	0.440458i	−0.0960325	−	0.0257318i	0.210483	−	0.977598i	$-0.432496\pi$
$293$	−1.64381	−	0.440458i	−0.0960325	−	0.0257318i	−0.306515	+	0.951866i	$0.599163\pi$
$294$	3.39410	+	3.27667i	0.197948	+	0.191099i
$295$	−5.61783	+	9.73036i	−0.327083	+	0.566524i
$296$	−4.31276	+	10.2418i	−0.250674	+	0.595294i
$297$	−4.52549	−	5.23152i	−0.262596	−	0.303564i
$298$	6.90876	−	2.84591i	0.400214	−	0.164859i
$299$	13.1141	−	3.51391i	0.758408	−	0.203215i
$300$	−3.17927	+	1.37558i	−0.183556	+	0.0794189i
$301$	−23.1037	−	6.19063i	−1.33168	−	0.356822i
$302$	1.78855	+	13.7934i	0.102920	+	0.793723i
$303$	1.86437	−	16.6749i	0.107105	−	0.957947i
$304$	−7.61833	−	29.3469i	−0.436941	−	1.68316i
$305$			2.09286i			0.119837i
$306$	−2.58646	+	27.5103i	−0.147858	+	1.57266i
$307$	6.24478	+	6.24478i	0.356408	+	0.356408i	0.862487	−	0.506079i	$-0.168906\pi$
$307$	6.24478	+	6.24478i	0.356408	+	0.356408i	−0.506079	+	0.862487i	$0.668906\pi$
$308$	5.18211	+	3.01894i	0.295278	+	0.172020i
$309$	−4.10920	−	27.1055i	−0.233764	−	1.54198i
$310$	7.35074	−	9.54104i	0.417494	−	0.541895i
$311$	−1.98783	+	1.14768i	−0.112720	+	0.0650787i	−0.555300	−	0.831650i	$-0.687397\pi$
$311$	−1.98783	+	1.14768i	−0.112720	+	0.0650787i	0.442580	+	0.896729i	$0.354063\pi$
$312$	−4.36929	+	17.2481i	−0.247363	+	0.976479i
$313$	25.2928	+	14.6028i	1.42964	+	0.825400i	0.997092	−	0.0762126i	$-0.0242828\pi$
$313$	25.2928	+	14.6028i	1.42964	+	0.825400i	0.432544	+	0.901613i	$0.357616\pi$
$314$	−23.0404	+	9.49098i	−1.30024	+	0.535607i
$315$	−6.75251	+	0.264223i	−0.380461	+	0.0148873i
$316$	−23.2396	+	23.0588i	−1.30733	+	1.29716i
$317$	22.9969	−	6.16200i	1.29163	−	0.346092i	0.453353	−	0.891331i	$-0.350228\pi$
$317$	22.9969	−	6.16200i	1.29163	−	0.346092i	0.838281	+	0.545238i	$0.183561\pi$
$318$	1.37162	−	2.47533i	0.0769165	−	0.138810i
$319$	1.46364	−	0.845032i	0.0819480	−	0.0473127i
$320$	−6.97458	+	3.91857i	−0.389891	+	0.219055i
$321$	−11.1339	−	25.4598i	−0.621435	−	1.42103i
$322$	7.23078	+	9.46152i	0.402955	+	0.527270i
$323$	34.9074	−	34.9074i	1.94230	−	1.94230i
$324$	17.6846	+	3.35499i	0.982476	+	0.186388i
$325$	−2.56818	−	2.56818i	−0.142457	−	0.142457i
$326$	−0.906137	−	0.121095i	−0.0501863	−	0.00670686i
$327$	4.95062	−	2.16497i	0.273770	−	0.119723i
$328$	−2.15393	+	2.77328i	−0.118931	+	0.153129i
$329$	−9.96875	−	17.2664i	−0.549595	−	0.951926i
$330$	3.13439	−	0.899277i	0.172542	−	0.0495036i
$331$	−5.23846	−	19.5502i	−0.287932	−	1.07458i	−0.946670	−	0.322204i	$-0.895576\pi$
$331$	−5.23846	−	19.5502i	−0.287932	−	1.07458i	0.658738	−	0.752372i	$-0.271090\pi$
$332$	−6.02855	−	0.0235404i	−0.330859	−	0.00129195i
$333$	0.460865	+	11.7779i	0.0252553	+	0.645426i
$334$	−4.64952	+	11.1632i	−0.254411	+	0.610826i
$335$	0.330862	−	0.573070i	0.0180769	−	0.0313101i
$336$	−15.4477	+	2.21860i	−0.842740	+	0.121035i
$337$	−11.8548	−	20.5331i	−0.645773	−	1.11851i	−0.984122	−	0.177491i	$-0.943202\pi$
$337$	−11.8548	−	20.5331i	−0.645773	−	1.11851i	0.338349	−	0.941021i	$-0.390131\pi$
$338$	−0.268010	+	0.0347520i	−0.0145778	+	0.00189026i
$339$	−4.71860	+	0.715341i	−0.256279	+	0.0388520i
$340$	−11.2550	−	6.55682i	−0.610390	−	0.355594i
$341$	−8.01687	+	8.01687i	−0.434138	+	0.434138i
$342$	−20.5113	−	24.7684i	−1.10912	−	1.33932i
$343$	−20.1063			−1.08564
$344$	−23.9339	+	18.1434i	−1.29043	+	0.978228i
$345$	6.43453	+	0.719428i	0.346424	+	0.0387327i
$346$	22.3053	−	28.9516i	1.19914	−	1.55645i
$347$	−5.23507	+	19.5375i	−0.281033	+	1.04883i	0.670656	+	0.741768i	$0.266013\pi$
$347$	−5.23507	+	19.5375i	−0.281033	+	1.04883i	−0.951690	+	0.307062i	$0.900654\pi$
$348$	−1.61919	+	4.08892i	−0.0867977	+	0.219189i
$349$	2.36994	+	8.84475i	0.126860	+	0.473449i	0.999899	−	0.0142017i	$-0.00452069\pi$
$349$	2.36994	+	8.84475i	0.126860	+	0.473449i	−0.873039	+	0.487651i	$0.837854\pi$
$350$	1.22482	−	2.94072i	0.0654694	−	0.157188i
$351$	3.55610	+	18.5341i	0.189811	+	0.989278i
$352$	6.98516	−	2.81378i	0.372310	−	0.149975i
$353$	−17.7072	−	10.2233i	−0.942462	−	0.544131i	−0.0517306	−	0.998661i	$-0.516474\pi$
$353$	−17.7072	−	10.2233i	−0.942462	−	0.544131i	−0.890731	+	0.454531i	$0.849807\pi$
$354$	0.484422	+	27.5174i	0.0257468	+	1.46253i
$355$	3.41671	−	12.7513i	0.181340	−	0.676771i
$356$	0.262940	−	0.966197i	0.0139358	−	0.0512083i
$357$	−15.8599	−	19.8529i	−0.839395	−	1.05072i
$358$	−1.36705	+	10.2294i	−0.0722511	+	0.540642i
$359$			35.5767i			1.87767i	0.344371	+	0.938834i	$0.388092\pi$
$359$			35.5767i			1.87767i	−0.344371	+	0.938834i	$0.611908\pi$
$360$	−4.93885	+	6.89984i	−0.260300	+	0.363653i
$361$			38.4548i			2.02394i
$362$	−10.4657	−	1.39863i	−0.550065	−	0.0735103i
$363$	15.8025	−	2.39566i	0.829416	−	0.125740i
$364$	−8.12580	−	14.2021i	−0.425907	−	0.744391i
$365$	−3.69450	+	13.7880i	−0.193379	+	0.721699i
$366$	2.64097	+	4.39382i	0.138046	+	0.229669i
$367$	−30.3232	−	17.5071i	−1.58286	−	0.913862i	−0.994440	−	0.105304i	$-0.966418\pi$
$367$	−30.3232	−	17.5071i	−1.58286	−	0.913862i	−0.588416	−	0.808558i	$-0.700248\pi$
$368$	14.9521	+	0.116772i	0.779430	+	0.00608716i
$369$	−0.822567	+	3.63252i	−0.0428211	+	0.189101i
$370$	−5.12930	−	2.13637i	−0.266659	−	0.111064i
$371$	0.673558	+	2.51375i	0.0349694	+	0.130508i
$372$	3.39262	−	29.3066i	0.175899	−	1.51948i
$373$	−8.87635	+	33.1270i	−0.459600	+	1.71525i	0.214601	+	0.976702i	$0.431155\pi$
$373$	−8.87635	+	33.1270i	−0.459600	+	1.71525i	−0.674201	+	0.738548i	$0.735512\pi$
$374$	9.71299	+	7.48322i	0.502247	+	0.386948i
$375$	−0.693990	−	1.58694i	−0.0358375	−	0.0819492i
$376$	−24.8008	−	3.41298i	−1.27900	−	0.176011i
$377$	−4.61094			−0.237476
$378$	−13.8430	+	9.07566i	−0.712008	+	0.466802i
$379$	12.3138	−	12.3138i	0.632516	−	0.632516i	−0.316182	−	0.948698i	$-0.602401\pi$
$379$	12.3138	−	12.3138i	0.632516	−	0.632516i	0.948698	+	0.316182i	$0.102401\pi$
$380$	14.6584	−	3.86643i	0.751962	−	0.198344i
$381$	−7.42896	+	18.9764i	−0.380597	+	0.972189i
$382$	−1.34075	−	10.3400i	−0.0685988	−	0.529039i
$383$	12.0246	+	20.8272i	0.614427	+	1.06422i	0.990485	+	0.137622i	$0.0439459\pi$
$383$	12.0246	+	20.8272i	0.614427	+	1.06422i	−0.376058	+	0.926596i	$0.622721\pi$
$384$	−9.69787	+	17.0280i	−0.494892	+	0.868954i
$385$	−1.49934	+	2.59693i	−0.0764134	+	0.132352i
$386$	12.5008	+	5.20662i	0.636274	+	0.265010i
$387$	−14.8369	+	28.1893i	−0.754201	+	1.43294i
$388$	14.4251	+	14.5382i	0.732324	+	0.738066i
$389$	2.27037	+	8.47314i	0.115112	+	0.429605i	0.999295	−	0.0375356i	$-0.0119508\pi$
$389$	2.27037	+	8.47314i	0.115112	+	0.429605i	−0.884183	+	0.467141i	$0.845284\pi$
$390$	−8.63250	−	2.15096i	−0.437123	−	0.108918i
$391$	12.1729	+	21.0841i	0.615609	+	1.06627i
$392$	−3.34148	+	4.30229i	−0.168770	+	0.217299i
$393$	−6.23000	−	4.58973i	−0.314262	−	0.231521i
$394$	−1.67876	+	12.5619i	−0.0845746	+	0.632858i
$395$	−11.5747	−	11.5747i	−0.582386	−	0.582386i
$396$	5.44565	−	5.84324i	0.273654	−	0.293634i
$397$	15.5805	−	15.5805i	0.781961	−	0.781961i	−0.198201	−	0.980161i	$-0.563510\pi$
$397$	15.5805	−	15.5805i	0.781961	−	0.781961i	0.980161	+	0.198201i	$0.0635098\pi$
$398$	4.43586	−	3.39002i	0.222350	−	0.169926i
$399$	29.3902	+	3.28604i	1.47135	+	0.164508i
$400$	−1.97289	−	3.47962i	−0.0986443	−	0.173981i
$401$	15.2302	−	8.79314i	0.760558	−	0.439109i	−0.0689378	−	0.997621i	$-0.521961\pi$
$401$	15.2302	−	8.79314i	0.760558	−	0.439109i	0.829496	+	0.558512i	$0.188628\pi$
$402$	−0.0285300	−	1.62063i	−0.00142295	−	0.0808299i
$403$	29.8779	−	8.00576i	1.48833	−	0.398796i
$404$	19.3743	+	0.0756533i	0.963908	+	0.00376389i
$405$	−1.64296	+	8.84877i	−0.0816391	+	0.439699i
$406$	−1.54038	−	3.73943i	−0.0764476	−	0.185585i
$407$	4.52964	+	2.61519i	0.224526	+	0.129630i
$408$	−31.9032	+	0.437025i	−1.57944	+	0.0216360i
$409$	−19.9532	+	11.5200i	−0.986621	+	0.569626i	−0.904262	−	0.426977i	$-0.859579\pi$
$409$	−19.9532	+	11.5200i	−0.986621	+	0.569626i	−0.0823583	+	0.996603i	$0.526245\pi$
$410$	−1.39083	−	1.07154i	−0.0686883	−	0.0529198i
$411$	−15.8372	+	12.6519i	−0.781190	+	0.624072i
$412$	30.6095	−	8.07381i	1.50802	−	0.397768i
$413$	−17.8961	−	17.8961i	−0.880612	−	0.880612i
$414$	14.4167	−	6.60930i	0.708543	−	0.324830i
$415$		−	3.01430i		−	0.147966i
$416$	−20.3425	−	2.88044i	−0.997374	−	0.141225i
$417$	6.01070	+	4.42817i	0.294345	+	0.216848i
$418$	−14.1518	+	1.83502i	−0.692187	+	0.0897536i
$419$	−12.6234	−	3.38242i	−0.616691	−	0.165242i	−0.0630680	−	0.998009i	$-0.520089\pi$
$419$	−12.6234	−	3.38242i	−0.616691	−	0.165242i	−0.553623	+	0.832767i	$0.686755\pi$
$420$	−1.13945	−	7.71945i	−0.0555996	−	0.376670i
$421$	0.517214	−	0.138587i	0.0252075	−	0.00675432i	−0.246193	−	0.969221i	$-0.579180\pi$
$421$	0.517214	−	0.138587i	0.0252075	−	0.00675432i	0.271401	+	0.962466i	$0.412513\pi$
$422$	−1.39232	−	3.38001i	−0.0677771	−	0.164536i
$423$	−25.3600	+	7.87004i	−1.23305	+	0.382655i
$424$	3.01162	+	1.26817i	0.146257	+	0.0615879i
$425$	3.25641	−	5.64027i	0.157959	−	0.273593i
$426$	−8.91768	−	31.0821i	−0.432063	−	1.50593i
$427$	−4.55366	−	1.22015i	−0.220367	−	0.0590471i
$428$	27.8503	−	15.9347i	1.34620	−	0.770234i
$429$	7.79815	+	3.05286i	0.376498	+	0.147393i
$430$	−9.11837	−	11.9315i	−0.439727	−	0.575386i
$431$	18.5938			0.895633			0.447817	−	0.894125i	$-0.352202\pi$
$431$	18.5938			0.895633			0.447817	+	0.894125i	$0.352202\pi$
$432$	−1.66192	+	20.7181i	−0.0799594	+	0.996798i
$433$	29.6091			1.42292			0.711462	−	0.702724i	$-0.248033\pi$
$433$	29.6091			1.42292			0.711462	+	0.702724i	$0.248033\pi$
$434$	16.4739	+	21.5562i	0.790774	+	1.03473i
$435$	−2.04760	−	0.801606i	−0.0981751	−	0.0384341i
$436$	3.09848	+	5.41544i	0.148390	+	0.259353i
$437$	−27.3691	−	7.33354i	−1.30924	−	0.350811i
$438$	9.64269	+	33.6092i	0.460746	+	1.60591i
$439$	−4.34013	+	7.51732i	−0.207143	+	0.358782i	−0.950813	−	0.309764i	$-0.899750\pi$
$439$	−4.34013	+	7.51732i	−0.207143	+	0.358782i	0.743670	+	0.668546i	$0.233083\pi$
$440$	1.42052	+	3.48706i	0.0677204	+	0.166239i
$441$	−1.27608	+	5.63527i	−0.0607658	+	0.268346i
$442$	−12.7412	−	30.9308i	−0.606039	−	1.47123i
$443$	24.2373	−	6.49438i	1.15155	−	0.308557i	0.367964	−	0.929840i	$-0.380055\pi$
$443$	24.2373	−	6.49438i	1.15155	−	0.308557i	0.783586	+	0.621283i	$0.213388\pi$
$444$	−13.4645	+	1.98747i	−0.638996	+	0.0943209i
$445$	0.483608	+	0.129582i	0.0229252	+	0.00614280i
$446$	20.8786	−	2.70726i	0.988630	−	0.128192i
$447$	7.36771	+	5.42790i	0.348481	+	0.256731i
$448$	−4.45982	−	17.4599i	−0.210707	−	0.824901i
$449$			8.55510i			0.403740i	0.979412	+	0.201870i	$0.0647019\pi$
$449$			8.55510i			0.403740i	−0.979412	+	0.201870i	$0.935298\pi$
$450$	−3.45954	−	2.45593i	−0.163084	−	0.115774i
$451$	1.16865	+	1.16865i	0.0550295	+	0.0550295i
$452$	−1.40551	−	5.32858i	−0.0661097	−	0.250635i
$453$	−13.3093	+	10.6325i	−0.625326	+	0.499556i
$454$	18.6904	+	14.3997i	0.877185	+	0.675813i
$455$	7.08512	−	4.09059i	0.332155	−	0.191770i
$456$	25.8954	−	26.6147i	1.21266	−	1.24635i
$457$	27.0643	+	15.6256i	1.26601	+	0.730933i	0.974231	−	0.225552i	$-0.0724184\pi$
$457$	27.0643	+	15.6256i	1.26601	+	0.730933i	0.291782	+	0.956485i	$0.405752\pi$
$458$	7.43162	+	18.0411i	0.347257	+	0.843003i
$459$	−30.4525	+	14.7615i	−1.42140	+	0.689007i
$460$	−0.0291932	+	7.47620i	−0.00136114	+	0.348579i
$461$	16.7366	−	4.48455i	0.779499	−	0.208866i	0.152935	−	0.988236i	$-0.451127\pi$
$461$	16.7366	−	4.48455i	0.779499	−	0.208866i	0.626564	+	0.779370i	$0.284461\pi$
$462$	0.129287	+	7.34409i	0.00601499	+	0.341678i
$463$	19.4392	−	11.2232i	0.903416	−	0.521588i	0.0251093	−	0.999685i	$-0.492007\pi$
$463$	19.4392	−	11.2232i	0.903416	−	0.521588i	0.878307	+	0.478097i	$0.158673\pi$
$464$	−4.89474	−	1.35260i	−0.227233	−	0.0627929i
$465$	14.6598	+	1.63908i	0.679833	+	0.0760103i
$466$	10.1348	−	7.74529i	0.469484	−	0.358794i
$467$	−15.1564	+	15.1564i	−0.701356	+	0.701356i	−0.964701	−	0.263346i	$-0.915174\pi$
$467$	−15.1564	+	15.1564i	−0.701356	+	0.701356i	0.263346	+	0.964701i	$0.415174\pi$
$468$	−20.8376	+	6.37750i	−0.963220	+	0.294800i
$469$	1.05399	+	1.05399i	0.0486689	+	0.0486689i
$470$	1.65806	−	12.4070i	0.0764805	−	0.572291i
$471$	−24.5710	−	18.1018i	−1.13217	−	0.834086i
$472$	−31.5311	+	3.96341i	−1.45134	+	0.182431i
$473$	7.06783	+	12.2418i	0.324979	+	0.562881i
$474$	−38.9064	−	9.69428i	−1.78703	−	0.445273i
$475$	1.96182	+	7.32162i	0.0900145	+	0.335939i
$476$	20.8281	−	20.6661i	0.954654	−	0.947228i
$477$	3.46331	−	0.135518i	0.158574	−	0.00620495i
$478$	10.9196	+	4.54806i	0.499453	+	0.208024i
$479$	8.10868	−	14.0446i	0.370495	−	0.641716i	−0.619147	−	0.785275i	$-0.712521\pi$
$479$	8.10868	−	14.0446i	0.370495	−	0.641716i	0.989642	+	0.143559i	$0.0458547\pi$
$480$	−8.53285	−	4.81565i	−0.389469	−	0.219803i
$481$	−7.13494	−	12.3581i	−0.325325	−	0.563480i
$482$	1.48470	+	11.4501i	0.0676261	+	0.521538i
$483$	−5.31670	+	13.5808i	−0.241918	+	0.617950i
$484$	4.70702	+	17.8453i	0.213956	+	0.811150i
$485$	−7.24089	+	7.24089i	−0.328792	+	0.328792i
$486$	7.71693	+	20.6506i	0.350047	+	0.936732i
$487$	6.33207			0.286934			0.143467	−	0.989655i	$-0.454175\pi$
$487$	6.33207			0.286934			0.143467	+	0.989655i	$0.454175\pi$
$488$	−4.71729	+	3.57600i	−0.213541	+	0.161878i
$489$	−0.448617	−	1.02585i	−0.0202872	−	0.0463905i
$490$	−2.15765	−	1.66233i	−0.0974729	−	0.0750964i
$491$	−1.61524	+	6.02814i	−0.0728945	+	0.272046i	−0.992748	−	0.120217i	$-0.961641\pi$
$491$	−1.61524	+	6.02814i	−0.0728945	+	0.272046i	0.919853	+	0.392263i	$0.128308\pi$
$492$	−4.27214	−	0.494554i	−0.192603	−	0.0222962i
$493$	−2.14001	−	7.98661i	−0.0963810	−	0.359699i
$494$	35.9403	+	14.9692i	1.61703	+	0.673498i
$495$	2.93223	+	2.71139i	0.131794	+	0.121868i
$496$	34.0654	+	0.266042i	1.52958	+	0.0119457i
$497$	25.7525	+	14.8682i	1.15516	+	0.666930i
$498$	−3.80372	−	6.32832i	−0.170449	−	0.283579i
$499$	8.46066	−	31.5756i	0.378751	−	1.41352i	−0.469035	−	0.883180i	$-0.655398\pi$
$499$	8.46066	−	31.5756i	0.378751	−	1.41352i	0.847786	−	0.530339i	$-0.177935\pi$
$500$	1.73594	−	0.993229i	0.0776337	−	0.0444186i
$501$	−14.6433	+	2.21993i	−0.654214	+	0.0991790i
$502$	−21.8870	−	2.92497i	−0.976867	−	0.130548i
$503$			1.26286i			0.0563083i	0.999604	+	0.0281541i	$0.00896292\pi$
$503$			1.26286i			0.0563083i	−0.999604	+	0.0281541i	$0.991037\pi$
$504$	−12.1333	−	14.7686i	−0.540461	−	0.657846i
$505$			9.68723i			0.431076i
$506$	0.932208	−	6.97556i	0.0414417	−	0.310101i
$507$	−0.206591	−	0.258603i	−0.00917503	−	0.0114850i
$508$	−22.7056	−	6.17906i	−1.00740	−	0.274151i
$509$	−0.297891	+	1.11174i	−0.0132038	+	0.0492771i	−0.972213	−	0.234096i	$-0.924787\pi$
$509$	−0.297891	+	1.11174i	−0.0132038	+	0.0492771i	0.959010	+	0.283373i	$0.0914536\pi$
$510$	−0.280799	−	15.9506i	−0.0124340	−	0.706306i
$511$	−27.8462	−	16.0770i	−1.23184	−	0.711204i
$512$	−20.7496	−	9.02512i	−0.917013	−	0.398858i
$513$	12.9131	−	37.2093i	0.570126	−	1.64283i
$514$	−9.47355	+	22.7455i	−0.417860	+	1.00326i
$515$	4.09663	+	15.2888i	0.180519	+	0.673707i
$516$	−34.1996	−	13.5429i	−1.50556	−	0.596192i
$517$	−3.04961	+	11.3813i	−0.134122	+	0.500549i
$518$	7.63872	−	9.91483i	0.335626	−	0.435633i
$519$	44.4841	+	4.97365i	1.95264	+	0.218319i
$520$	1.40049	−	10.1768i	0.0614156	−	0.446283i
$521$	−20.0191			−0.877051			−0.438526	−	0.898719i	$-0.644499\pi$
$521$	−20.0191			−0.877051			−0.438526	+	0.898719i	$0.644499\pi$
$522$	−5.31035	+	0.900939i	−0.232428	+	0.0394330i
$523$	22.9633	−	22.9633i	1.00412	−	1.00412i	0.00412437	−	0.999991i	$-0.498687\pi$
$523$	22.9633	−	22.9633i	1.00412	−	1.00412i	0.999991	−	0.00412437i	$-0.00131283\pi$
$524$	4.49779	−	7.72062i	0.196487	−	0.337277i
$525$	3.85747	−	0.584793i	0.168354	−	0.0255225i
$526$	6.24146	−	0.809310i	0.272141	−	0.0352876i
$527$	27.7336	+	48.0359i	1.20809	+	2.09248i
$528$	7.38258	+	5.52831i	0.321285	+	0.240589i
$529$	−4.51320	+	7.81710i	−0.196226	+	0.339874i
$530$	−0.628202	+	1.50828i	−0.0272873	+	0.0655154i
$531$	−28.5098	+	17.9820i	−1.23722	+	0.780351i
$532$	−0.133342	+	34.1480i	−0.00578111	+	1.48051i
$533$	−1.16703	−	4.35541i	−0.0505497	−	0.188654i
$534$	1.17882	−	0.338212i	0.0510127	−	0.0146359i
$535$	8.02167	+	13.8939i	0.346807	+	0.600688i
$536$	1.85702	−	0.233425i	0.0802112	−	0.0100824i
$537$	−11.5809	+	5.06447i	−0.499751	+	0.218548i
$538$	12.0559	+	1.61114i	0.519767	+	0.0694613i
$539$	1.81297	+	1.81297i	0.0780902	+	0.0780902i
$540$	−10.3622	−	0.790506i	−0.445918	−	0.0340180i
$541$	1.87477	−	1.87477i	0.0806025	−	0.0806025i	−0.665656	−	0.746259i	$-0.731848\pi$
$541$	1.87477	−	1.87477i	0.0806025	−	0.0806025i	0.746259	+	0.665656i	$0.231848\pi$
$542$	−7.80177	−	10.2087i	−0.335115	−	0.438500i
$543$	−5.18144	−	11.8483i	−0.222357	−	0.508461i
$544$	−4.45206	−	36.5721i	−0.190881	−	1.56802i
$545$	−2.70165	+	1.55980i	−0.115726	+	0.0668145i
$546$	9.71285	−	17.5286i	0.415671	−	0.750155i
$547$	26.2349	−	7.02961i	1.12172	−	0.300565i	0.350142	−	0.936697i	$-0.386133\pi$
$547$	26.2349	−	7.02961i	1.12172	−	0.300565i	0.771580	+	0.636132i	$0.219467\pi$
$548$	−16.4859	−	16.6152i	−0.704243	−	0.709764i
$549$	−2.92429	+	5.55600i	−0.124806	+	0.237124i
$550$	−1.74074	+	0.717061i	−0.0742255	+	0.0305756i
$551$	8.33380	+	4.81152i	0.355032	+	0.204978i
$552$	9.37287	+	15.7326i	0.398936	+	0.669625i
$553$	31.9324	−	18.4362i	1.35790	−	0.783986i
$554$	1.27903	−	1.66015i	0.0543409	−	0.0705329i
$555$	−1.02001	−	6.72831i	−0.0432971	−	0.285601i
$556$	−4.33946	+	7.44885i	−0.184034	+	0.315901i
$557$	−14.2580	−	14.2580i	−0.604129	−	0.604129i	0.337277	−	0.941406i	$-0.390494\pi$
$557$	−14.2580	−	14.2580i	−0.604129	−	0.604129i	−0.941406	+	0.337277i	$0.890494\pi$
$558$	32.8457	−	15.0580i	1.39047	−	0.637457i
$559$		−	38.5658i		−	1.63116i
$560$	8.72116	−	2.26398i	0.368536	−	0.0956706i
$561$	−1.66862	+	14.9240i	−0.0704490	+	0.630093i
$562$	2.30857	+	17.8038i	0.0973810	+	0.751010i
$563$	−33.1644	−	8.88638i	−1.39771	−	0.374516i	−0.520190	−	0.854050i	$-0.674139\pi$
$563$	−33.1644	−	8.88638i	−1.39771	−	0.374516i	−0.877523	+	0.479534i	$0.840806\pi$
$564$	−12.1753	−	28.1399i	−0.512672	−	1.18490i
$565$	2.66153	−	0.713154i	0.111971	−	0.0300026i
$566$	0.379856	−	0.156474i	0.0159666	−	0.00657707i
$567$	−18.2953	−	8.73363i	−0.768332	−	0.366778i
$568$	34.5794	−	14.0865i	1.45092	−	0.591058i
$569$	−9.36949	+	16.2284i	−0.392789	+	0.680331i	−0.992816	−	0.119649i	$-0.961823\pi$
$569$	−9.36949	+	16.2284i	−0.392789	+	0.680331i	0.600027	+	0.799980i	$0.295157\pi$
$570$	13.3578	+	12.8956i	0.559497	+	0.540139i
$571$	40.6514	+	10.8925i	1.70121	+	0.455838i	0.973243	−	0.229776i	$-0.0737995\pi$
$571$	40.6514	+	10.8925i	1.70121	+	0.455838i	0.727965	+	0.685614i	$0.240466\pi$
$572$	−2.53922	+	9.33061i	−0.106170	+	0.390133i
$573$	9.97707	−	7.97041i	0.416798	−	0.332969i
$574$	3.14233	−	2.40146i	0.131158	−	0.100235i
$575$	−3.73813			−0.155891
$576$	−23.9910	+	0.657404i	−0.999625	+	0.0273918i
$577$	15.9796			0.665238			0.332619	−	0.943061i	$-0.392068\pi$
$577$	15.9796			0.665238			0.332619	+	0.943061i	$0.392068\pi$
$578$	28.5597	−	21.8262i	1.18793	−	0.907849i
$579$	2.48591	+	16.3978i	0.103311	+	0.681471i
$580$	0.666738	−	2.44999i	0.0276848	−	0.101730i
$581$	6.55852	+	1.75735i	0.272093	+	0.0729071i
$582$	−6.06454	+	24.3390i	−0.251383	+	1.00888i
$583$	0.769001	−	1.33195i	0.0318488	−	0.0551637i
$584$	−37.3907	+	15.2318i	−1.54724	+	0.630296i
$585$	−3.22941	−	10.4063i	−0.133520	−	0.430247i
$586$	2.22530	−	0.916664i	0.0919264	−	0.0378671i
$587$	−17.3688	+	4.65395i	−0.716886	+	0.192089i	−0.598782	−	0.800912i	$-0.704348\pi$
$587$	−17.3688	+	4.65395i	−0.716886	+	0.192089i	−0.118104	+	0.993001i	$0.537682\pi$
$588$	−6.62754	−	0.767221i	−0.273315	−	0.0316397i
$589$	−62.3553	−	16.7080i	−2.56930	−	0.688443i
$590$	−2.04325	−	15.7577i	−0.0841193	−	0.648734i
$591$	−14.2214	+	6.21923i	−0.584992	+	0.255825i
$592$	−3.94890	−	15.2117i	−0.162299	−	0.625197i
$593$		−	25.1607i		−	1.03323i	−0.856219	−	0.516613i	$-0.827192\pi$
$593$		−	25.1607i		−	1.03323i	0.856219	−	0.516613i	$-0.172808\pi$
$594$	9.57751	+	1.99224i	0.392970	+	0.0817424i
$595$	10.3736	+	10.3736i	0.425277	+	0.425277i
$596$	−5.31916	+	9.13054i	−0.217881	+	0.374002i
$597$	6.36713	+	2.49264i	0.260589	+	0.102017i
$598$	−11.7182	+	15.2098i	−0.479191	+	0.621976i
$599$	6.80833	−	3.93079i	0.278181	−	0.160608i	−0.354419	−	0.935087i	$-0.615321\pi$
$599$	6.80833	−	3.93079i	0.278181	−	0.160608i	0.632600	+	0.774479i	$0.281988\pi$
$600$	2.39115	−	4.27579i	0.0976182	−	0.174559i
$601$	−18.6640	−	10.7757i	−0.761319	−	0.439548i	0.0684498	−	0.997655i	$-0.478195\pi$
$601$	−18.6640	−	10.7757i	−0.761319	−	0.439548i	−0.829769	+	0.558107i	$0.811528\pi$
$602$	31.2766	−	12.8837i	1.27474	−	0.525100i
$603$	1.67908	−	1.05905i	0.0683776	−	0.0431277i
$604$	−13.8545	−	13.9631i	−0.563732	−	0.568151i
$605$	−8.91339	+	2.38834i	−0.362381	+	0.0970996i
$606$	12.2243	+	20.3377i	0.496576	+	0.826163i
$607$	−25.3515	+	14.6367i	−1.02899	+	0.594085i	−0.916694	−	0.399590i	$-0.869153\pi$
$607$	−25.3515	+	14.6367i	−1.02899	+	0.594085i	−0.112292	+	0.993675i	$0.535819\pi$
$608$	33.7613	+	26.4335i	1.36920	+	1.07202i
$609$	2.93790	−	3.98785i	0.119050	−	0.161596i
$610$	−1.79720	−	2.35164i	−0.0727663	−	0.0952152i
$611$	22.7311	−	22.7311i	0.919601	−	0.919601i
$612$	−20.7175	−	33.1330i	−0.837456	−	1.33932i
$613$	20.9761	+	20.9761i	0.847216	+	0.847216i	0.989785	−	0.142569i	$-0.0455363\pi$
$613$	20.9761	+	20.9761i	0.847216	+	0.847216i	−0.142569	+	0.989785i	$0.545536\pi$
$614$	−12.3795	−	1.65439i	−0.499596	−	0.0667656i
$615$	0.238934	−	2.13702i	0.00963476	−	0.0861729i
$616$	−8.41532	+	1.05779i	−0.339063	+	0.0426196i
$617$	4.48199	+	7.76304i	0.180438	+	0.312528i	0.942030	−	0.335529i	$-0.108915\pi$
$617$	4.48199	+	7.76304i	0.180438	+	0.312528i	−0.761592	+	0.648057i	$0.775582\pi$
$618$	27.8935	+	26.9284i	1.12204	+	1.08322i
$619$	−4.80450	−	17.9307i	−0.193109	−	0.720694i	−0.992748	−	0.120213i	$-0.961642\pi$
$619$	−4.80450	−	17.9307i	−0.193109	−	0.720694i	0.799639	−	0.600481i	$-0.205024\pi$
$620$	−0.0665111	+	17.0331i	−0.00267115	+	0.684064i
$621$	16.0768	+	10.9007i	0.645138	+	0.437429i
$622$	1.24809	−	2.99659i	0.0500438	−	0.120152i
$623$	−0.563892	+	0.976690i	−0.0225919	+	0.0391302i
$624$	−9.90181	−	23.1328i	−0.396390	−	0.926054i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−40.9601	+	5.31117i	−1.63710	+	0.212277i
$627$	−10.9087	−	13.6551i	−0.435651	−	0.545332i
$628$	17.7392	−	30.4499i	0.707870	−	1.21508i
$629$	18.0940	−	18.0940i	0.721454	−	0.721454i
$630$	7.36056	−	6.09545i	0.293252	−	0.242849i
$631$	−2.97364			−0.118379			−0.0591894	−	0.998247i	$-0.518852\pi$
$631$	−2.97364			−0.118379			−0.0591894	+	0.998247i	$0.518852\pi$
$632$	6.31196	−	45.8665i	0.251076	−	1.82447i
$633$	2.65552	−	3.60455i	0.105547	−	0.143268i
$634$	−20.5490	+	26.6720i	−0.816104	+	1.05928i
$635$	3.04518	−	11.3648i	0.120844	−	0.450996i
$636$	0.584417	+	3.95925i	0.0231736	+	0.156995i
$637$	−1.81046	−	6.75673i	−0.0717330	−	0.267711i
$638$	−0.918965	+	2.20638i	−0.0363822	+	0.0873516i
$639$	26.8875	−	29.0774i	1.06365	−	1.15029i
$640$	4.47201	−	10.3924i	0.176772	−	0.410794i
$641$	11.2139	+	6.47435i	0.442922	+	0.255721i	0.704836	−	0.709370i	$-0.251020\pi$
$641$	11.2139	+	6.47435i	0.442922	+	0.255721i	−0.261914	+	0.965091i	$0.584354\pi$
$642$	34.3737	+	19.0469i	1.35662	+	0.751722i
$643$	−4.75080	+	17.7302i	−0.187353	+	0.699213i	0.806761	+	0.590878i	$0.201218\pi$
$643$	−4.75080	+	17.7302i	−0.187353	+	0.699213i	−0.994114	+	0.108335i	$0.965448\pi$
$644$	−16.2497	−	4.42218i	−0.640329	−	0.174258i
$645$	6.70462	−	17.1261i	0.263994	−	0.674341i
$646$	−9.24778	+	69.1996i	−0.363849	+	2.72262i
$647$			0.796109i			0.0312983i	0.999878	+	0.0156491i	$0.00498148\pi$
$647$			0.796109i			0.0312983i	−0.999878	+	0.0156491i	$0.995019\pi$
$648$	−22.7523	+	11.4164i	−0.893794	+	0.448477i
$649$			14.9573i			0.587124i
$650$	5.09110	+	0.680371i	0.199689	+	0.0266863i
$651$	−12.1131	+	30.9413i	−0.474748	+	1.21269i
$652$	1.12217	−	0.642055i	0.0439475	−	0.0251448i
$653$	3.73162	−	13.9266i	0.146030	−	0.544990i	−0.853678	−	0.520802i	$-0.825633\pi$
$653$	3.73162	−	13.9266i	0.146030	−	0.544990i	0.999707	−	0.0241886i	$-0.00770022\pi$
$654$	−3.70364	+	6.68389i	−0.144824	+	0.261361i
$655$	3.86906	+	2.23380i	0.151177	+	0.0872819i
$656$	0.0387820	−	4.96583i	0.00151418	−	0.193883i
$657$	−29.0735	+	31.4415i	−1.13427	+	1.22665i
$658$	26.0285	+	10.8409i	1.01470	+	0.422624i
$659$	−7.40333	−	27.6296i	−0.288393	−	1.07630i	−0.946324	−	0.323219i	$-0.895235\pi$
$659$	−7.40333	−	27.6296i	−0.288393	−	1.07630i	0.657931	−	0.753078i	$-0.271432\pi$
$660$	−2.74972	+	3.70205i	−0.107033	+	0.144102i
$661$	2.63399	−	9.83018i	0.102450	−	0.382350i	−0.895593	−	0.444874i	$-0.853248\pi$
$661$	2.63399	−	9.83018i	0.102450	−	0.382350i	0.998043	+	0.0625244i	$0.0199151\pi$
$662$	22.6745	+	17.4692i	0.881269	+	0.678959i
$663$	24.3009	−	32.9855i	0.943768	−	1.28105i
$664$	6.79419	−	5.15042i	0.263666	−	0.199875i
$665$	−17.0742			−0.662107
$666$	−10.6319	−	12.8385i	−0.411976	−	0.497482i
$667$	−3.35574	+	3.35574i	−0.129935	+	0.129935i
$668$	−4.36174	−	16.5362i	−0.168761	−	0.639806i
$669$	16.0939	+	20.1458i	0.622227	+	0.778881i
$670$	0.120337	+	0.928049i	0.00464903	+	0.0358537i
$671$	1.39304	+	2.41282i	0.0537778	+	0.0931459i
$672$	15.4526	−	15.7583i	0.596097	−	0.607888i
$673$	−19.6129	+	33.9705i	−0.756022	+	1.30947i	0.188843	+	0.982007i	$0.439526\pi$
$673$	−19.6129	+	33.9705i	−0.756022	+	1.30947i	−0.944865	+	0.327461i	$0.893807\pi$
$674$	30.9530	+	12.8920i	1.19227	+	0.496582i
$675$	0.375019	−	5.18260i	0.0144345	−	0.199478i
$676$	0.271307	−	0.269196i	0.0104349	−	0.0103537i
$677$	3.28608	+	12.2638i	0.126294	+	0.471336i	0.999882	−	0.0153294i	$-0.00487971\pi$
$677$	3.28608	+	12.2638i	0.126294	+	0.471336i	−0.873588	+	0.486666i	$0.838213\pi$
$678$	4.68777	−	4.85578i	0.180033	−	0.186485i
$679$	−11.5333	−	19.9762i	−0.442607	−	0.766617i
$680$	18.2772	−	2.29742i	0.700900	−	0.0881019i
$681$	−3.21087	+	28.7179i	−0.123041	+	1.10047i
$682$	2.12386	−	15.8925i	0.0813267	−	0.608554i
$683$	−3.07528	−	3.07528i	−0.117672	−	0.117672i	0.645818	−	0.763491i	$-0.276516\pi$
$683$	−3.07528	−	3.07528i	−0.117672	−	0.117672i	−0.763491	+	0.645818i	$0.776516\pi$
$684$	44.3168	+	10.2174i	1.69449	+	0.390673i
$685$	8.27533	−	8.27533i	0.316184	−	0.316184i
$686$	22.5924	−	17.2658i	0.862583	−	0.659212i
$687$	−14.1740	+	19.2395i	−0.540773	+	0.734034i
$688$	11.3131	−	40.9396i	0.431309	−	1.56081i
$689$	−3.63391	+	2.09804i	−0.138441	+	0.0799289i
$690$	−7.84795	+	4.71712i	−0.298766	+	0.179578i
$691$	31.3003	−	8.38688i	1.19072	−	0.319052i	0.391549	−	0.920157i	$-0.371939\pi$
$691$	31.3003	−	8.38688i	1.19072	−	0.319052i	0.799170	+	0.601105i	$0.205273\pi$
$692$	−0.201823	+	51.6855i	−0.00767215	+	1.96479i
$693$	−7.60897	+	4.79920i	−0.289041	+	0.182306i
$694$	−10.8950	−	26.4488i	−0.413569	−	1.00398i
$695$	−3.73287	−	2.15517i	−0.141596	−	0.0817503i
$696$	−1.69186	−	5.98495i	−0.0641297	−	0.226859i
$697$	7.00237	−	4.04282i	0.265234	−	0.153133i
$698$	−10.2582	−	7.90327i	−0.388279	−	0.299143i
$699$	14.5472	+	5.69501i	0.550226	+	0.215405i
$700$	1.14901	+	4.35613i	0.0434285	+	0.164646i
$701$	4.27389	+	4.27389i	0.161423	+	0.161423i	0.783197	−	0.621774i	$-0.213588\pi$
$701$	4.27389	+	4.27389i	0.161423	+	0.161423i	−0.621774	+	0.783197i	$0.713588\pi$
$702$	−19.9116	−	17.7721i	−0.751513	−	0.670766i
$703$			29.7812i			1.12322i
$704$	−5.43260	+	9.16004i	−0.204749	+	0.345232i
$705$	14.0461	−	6.14254i	0.529006	−	0.231341i
$706$	28.6758	−	3.71829i	1.07923	−	0.139940i
$707$	−21.0775	−	5.64770i	−0.792702	−	0.212404i
$708$	−24.1742	−	30.5039i	−0.908522	−	1.14641i
$709$	−14.7301	+	3.94692i	−0.553201	+	0.148230i	−0.524581	−	0.851361i	$-0.675778\pi$
$709$	−14.7301	+	3.94692i	−0.553201	+	0.148230i	−0.0286202	+	0.999590i	$0.509111\pi$
$710$	7.11073	+	17.2621i	0.266861	+	0.647834i
$711$	−14.5548	−	46.9008i	−0.545849	−	1.75892i
$712$	0.534247	+	1.31146i	0.0200218	+	0.0491491i
$713$	15.9181	−	27.5709i	0.596136	−	1.03254i
$714$	34.8691	+	8.68833i	1.30495	+	0.325153i
$715$	−4.67023	−	1.25138i	−0.174657	−	0.0467991i
$716$	−7.24820	−	12.6682i	−0.270878	−	0.473434i
$717$	2.17148	+	14.3238i	0.0810955	+	0.534930i
$718$	−30.5507	−	39.9758i	−1.14014	−	1.49188i
$719$	2.16854			0.0808728			0.0404364	−	0.999182i	$-0.487125\pi$
$719$	2.16854			0.0808728			0.0404364	+	0.999182i	$0.487125\pi$
$720$	−0.375539	−	11.9941i	−0.0139955	−	0.446995i
$721$	−35.6539			−1.32782
$722$	−33.0222	−	43.2097i	−1.22896	−	1.60810i
$723$	−11.0482	+	8.82612i	−0.410888	+	0.328247i
$724$	12.9608	−	7.41561i	0.481685	−	0.275599i
$725$	1.22629	+	0.328583i	0.0455432	+	0.0122033i
$726$	−15.6993	+	16.2619i	−0.582654	+	0.603536i
$727$	5.63186	−	9.75468i	0.208874	−	0.361781i	−0.742486	−	0.669862i	$-0.766353\pi$
$727$	5.63186	−	9.75468i	0.208874	−	0.361781i	0.951360	+	0.308081i	$0.0996867\pi$
$728$	21.3262	+	8.98032i	0.790403	+	0.332833i
$729$	−16.7257	+	21.1955i	−0.619471	+	0.785019i
$730$	−7.68884	−	18.6655i	−0.284577	−	0.690841i
$731$	66.7999	−	17.8990i	2.47068	−	0.662017i
$732$	−6.74062	−	2.66925i	−0.249140	−	0.0986583i
$733$	12.2290	+	3.27676i	0.451690	+	0.121030i	0.477490	−	0.878637i	$-0.341547\pi$
$733$	12.2290	+	3.27676i	0.451690	+	0.121030i	−0.0257999	+	0.999667i	$0.508213\pi$
$734$	49.1064	−	6.36747i	1.81255	−	0.235028i
$735$	0.370668	−	3.31524i	0.0136723	−	0.122285i
$736$	−16.9011	+	12.7085i	−0.622984	+	0.468442i
$737$		−	0.880908i		−	0.0324487i
$738$	−2.19506	−	4.78804i	−0.0808014	−	0.176250i
$739$	−23.8322	−	23.8322i	−0.876681	−	0.876681i	0.116509	−	0.993190i	$-0.462830\pi$
$739$	−23.8322	−	23.8322i	−0.876681	−	0.876681i	−0.993190	+	0.116509i	$0.962830\pi$
$740$	7.59809	−	2.00413i	0.279311	−	0.0736735i
$741$	7.14710	+	47.1444i	0.262555	+	1.73189i
$742$	−2.91547	−	2.24618i	−0.107030	−	0.0824597i
$743$	20.6142	−	11.9016i	0.756262	−	0.436628i	−0.0716899	−	0.997427i	$-0.522839\pi$
$743$	20.6142	−	11.9016i	0.756262	−	0.436628i	0.827952	+	0.560799i	$0.189506\pi$
$744$	21.3543	+	35.8437i	0.782886	+	1.31409i
$745$	−4.57562	−	2.64174i	−0.167638	−	0.0967857i
$746$	−18.4731	−	44.8455i	−0.676349	−	1.64191i
$747$	4.21178	−	8.00217i	0.154101	−	0.292784i
$748$	−17.3400	−	0.0677098i	−0.634015	−	0.00247571i
$749$	−34.9072	+	9.35335i	−1.27548	+	0.341764i
$750$	2.14255	+	1.18722i	0.0782348	+	0.0433510i
$751$	23.4926	−	13.5634i	0.857256	−	0.494937i	−0.00583665	−	0.999983i	$-0.501858\pi$
$751$	23.4926	−	13.5634i	0.857256	−	0.494937i	0.863092	+	0.505046i	$0.168525\pi$
$752$	30.7982	−	17.4621i	1.12310	−	0.636777i
$753$	−10.8360	−	24.7786i	−0.394886	−	0.902982i
$754$	5.18108	−	3.95954i	0.188684	−	0.144198i
$755$	6.95446	−	6.95446i	0.253099	−	0.253099i
$756$	7.76120	−	22.0852i	0.282272	−	0.803232i
$757$	15.0227	+	15.0227i	0.546009	+	0.546009i	0.925284	−	0.379275i	$-0.123827\pi$
$757$	15.0227	+	15.0227i	0.546009	+	0.546009i	−0.379275	+	0.925284i	$0.623827\pi$
$758$	−3.26221	+	24.4105i	−0.118489	+	0.886631i
$759$	7.89711	−	3.45351i	0.286647	−	0.125355i
$760$	−13.1507	+	16.9321i	−0.477028	+	0.614192i
$761$	−16.3418	−	28.3048i	−0.592390	−	1.02605i	−0.993910	−	0.110199i	$-0.964851\pi$
$761$	−16.3418	−	28.3048i	−0.592390	−	1.02605i	0.401520	−	0.915850i	$-0.368482\pi$
$762$	−7.94796	−	27.7022i	−0.287924	−	1.00355i
$763$	−1.81874	−	6.78764i	−0.0658429	−	0.245729i
$764$	10.3858	+	10.4672i	0.375743	+	0.378689i
$765$	16.5259	−	10.4234i	0.597495	−	0.376858i
$766$	−31.3962	−	13.0766i	−1.13439	−	0.472477i
$767$	20.4037	−	35.3402i	0.736735	−	1.27606i
$768$	−3.72535	−	27.4613i	−0.134427	−	0.990923i
$769$	19.3617	+	33.5355i	0.698202	+	1.20932i	0.969089	+	0.246710i	$0.0793495\pi$
$769$	19.3617	+	33.5355i	0.698202	+	1.20932i	−0.270887	+	0.962611i	$0.587317\pi$
$770$	−0.545322	−	4.20556i	−0.0196520	−	0.151558i
$771$	−29.8362	+	4.52317i	−1.07452	+	0.162898i
$772$	−18.5176	+	4.88436i	−0.666463	+	0.175792i
$773$	−31.7887	+	31.7887i	−1.14336	+	1.14336i	−0.155531	+	0.987831i	$0.549709\pi$
$773$	−31.7887	+	31.7887i	−1.14336	+	1.14336i	−0.987831	+	0.155531i	$0.950291\pi$
$774$	−7.53544	−	44.4157i	−0.270856	−	1.59649i
$775$	−8.51660			−0.305925
$776$	−28.6931	−	3.94863i	−1.03002	−	0.141748i
$777$	15.2342	+	1.70329i	0.546522	+	0.0611052i
$778$	−9.82721	−	7.57121i	−0.352323	−	0.271441i
$779$	−2.43559	+	9.08975i	−0.0872641	+	0.325674i
$780$	11.5470	−	4.99603i	0.413448	−	0.178887i
$781$	−4.54844	−	16.9750i	−0.162756	−	0.607414i
$782$	−31.7835	−	13.2379i	−1.13658	−	0.473387i
$783$	−4.31580	−	4.98911i	−0.154234	−	0.178296i
$784$	0.0601640	−	7.70369i	0.00214871	−	0.275132i
$785$	15.2595	+	8.81007i	0.544634	+	0.314445i
$786$	10.9417	−	0.192620i	0.390276	−	0.00687051i
$787$	0.0944598	−	0.352529i	0.00336713	−	0.0125663i	−0.964222	−	0.265097i	$-0.914596\pi$
$787$	0.0944598	−	0.352529i	0.00336713	−	0.0125663i	0.967589	+	0.252530i	$0.0812628\pi$
$788$	−8.90087	−	15.5567i	−0.317080	−	0.554186i
$789$	4.81113	+	6.02240i	0.171281	+	0.214403i
$790$	22.9454	+	3.06641i	0.816361	+	0.109098i
$791$			6.20673i			0.220686i
$792$	−1.10126	+	11.2421i	−0.0391316	+	0.399470i
$793$		−	7.60118i		−	0.269926i
$794$	−4.12763	+	30.8863i	−0.146484	+	1.09611i
$795$	−1.97847	+	0.299936i	−0.0701691	+	0.0106376i
$796$	−2.07326	+	7.61838i	−0.0734847	+	0.270026i
$797$	5.74881	−	21.4549i	0.203633	−	0.759970i	−0.786228	−	0.617936i	$-0.787969\pi$
$797$	5.74881	−	21.4549i	0.203633	−	0.759970i	0.989862	−	0.142034i	$-0.0453642\pi$
$798$	−35.8461	+	21.5458i	−1.26894	+	0.762712i
$799$	49.9223	+	28.8227i	1.76612	+	1.01967i
$800$	5.20487	+	2.21570i	0.184020	+	0.0783368i
$801$	1.10279	+	1.01974i	0.0389652	+	0.0360307i
$802$	−9.56247	+	22.9590i	−0.337663	+	0.810709i
$803$	4.91823	+	18.3551i	0.173561	+	0.647737i
$804$	1.42374	+	1.79653i	0.0502114	+	0.0633586i
$805$	2.17935	−	8.13343i	0.0768119	−	0.286666i
$806$	−26.6976	+	34.6526i	−0.940381	+	1.22059i
$807$	5.96873	+	13.6486i	0.210109	+	0.480455i
$808$	−21.8349	+	16.5522i	−0.768149	+	0.582305i
$809$	−50.7945			−1.78584			−0.892920	−	0.450216i	$-0.851347\pi$
$809$	−50.7945			−1.78584			−0.892920	+	0.450216i	$0.851347\pi$
$810$	−5.75256	−	11.3538i	−0.202125	−	0.398931i
$811$	−31.8528	+	31.8528i	−1.11850	+	1.11850i	−0.126542	+	0.991961i	$0.540388\pi$
$811$	−31.8528	+	31.8528i	−1.11850	+	1.11850i	−0.991961	+	0.126542i	$0.959612\pi$
$812$	4.94199	+	2.87905i	0.173430	+	0.101035i
$813$	5.73654	−	14.6533i	0.201189	−	0.513913i
$814$	−7.33547	+	0.951166i	−0.257108	+	0.0333384i
$815$	0.323216	+	0.559826i	0.0113218	+	0.0196099i
$816$	35.4727	−	27.8872i	1.24179	−	0.976247i
$817$	−40.2435	+	69.7037i	−1.40794	+	2.43863i
$818$	12.5279	−	30.0787i	0.438027	−	1.05168i
$819$	24.5248	−	0.959646i	0.856966	−	0.0335327i
$820$	2.48297	+	0.00969556i	0.0867092	+	0.000338584i
$821$	−2.09432	−	7.81610i	−0.0730922	−	0.272784i	0.919702	−	0.392618i	$-0.128430\pi$
$821$	−2.09432	−	7.81610i	−0.0730922	−	0.272784i	−0.992794	+	0.119834i	$0.961764\pi$
$822$	6.93092	−	27.8161i	0.241744	−	0.970198i
$823$	18.4486	+	31.9540i	0.643079	+	1.11385i	0.984742	+	0.174023i	$0.0556767\pi$
$823$	18.4486	+	31.9540i	0.643079	+	1.11385i	−0.341663	+	0.939823i	$0.610990\pi$
$824$	−27.4611	+	35.3573i	−0.956653	+	1.23173i
$825$	−1.85638	−	1.36762i	−0.0646309	−	0.0476145i
$826$	35.4769	+	4.74111i	1.23440	+	0.164964i
$827$	−26.6653	−	26.6653i	−0.927242	−	0.927242i	0.0702845	−	0.997527i	$-0.477609\pi$
$827$	−26.6653	−	26.6653i	−0.927242	−	0.927242i	−0.997527	+	0.0702845i	$0.977609\pi$
$828$	−10.5238	+	19.8066i	−0.365726	+	0.688326i
$829$	17.4014	−	17.4014i	0.604377	−	0.604377i	−0.337094	−	0.941471i	$-0.609444\pi$
$829$	17.4014	−	17.4014i	0.604377	−	0.604377i	0.941471	+	0.337094i	$0.109444\pi$
$830$	2.58846	+	3.38701i	0.0898466	+	0.117565i
$831$	2.55082	+	0.285200i	0.0884869	+	0.00989349i
$832$	25.3314	−	14.2321i	0.878208	−	0.493408i
$833$	10.8631	−	6.27179i	0.376383	−	0.217305i
$834$	−10.5565	+	0.185839i	−0.365542	+	0.00643509i
$835$	8.25954	−	2.21314i	0.285833	−	0.0765888i
$836$	14.3259	−	14.2144i	0.495471	−	0.491616i
$837$	36.6278	+	24.8351i	1.26604	+	0.858425i
$838$	17.0888	−	7.03936i	0.590323	−	0.243170i
$839$	17.8086	+	10.2818i	0.614821	+	0.354967i	0.774850	−	0.632145i	$-0.217825\pi$
$839$	17.8086	+	10.2818i	0.614821	+	0.354967i	−0.160029	+	0.987112i	$0.551159\pi$
$840$	7.90924	+	7.69548i	0.272895	+	0.265519i
$841$	−23.7189	+	13.6941i	−0.817894	+	0.472211i
$842$	−0.462159	+	0.599869i	−0.0159271	+	0.0206728i
$843$	−17.1790	+	13.7238i	−0.591675	+	0.472673i
$844$	4.46698	+	2.60232i	0.153760	+	0.0895757i
$845$	0.135127	+	0.135127i	0.00464850	+	0.00464850i
$846$	21.7376	−	30.6205i	0.747353	−	1.05275i
$847$		−	20.7862i		−	0.714222i
$848$	−4.47302	+	1.16118i	−0.153604	+	0.0398751i
$849$	0.405091	+	0.298436i	0.0139027	+	0.0102423i
$850$	1.18438	+	9.13406i	0.0406240	+	0.313296i
$851$	−14.1866	−	3.80128i	−0.486309	−	0.130306i
$852$	36.7114	+	27.2676i	1.25771	+	0.934172i
$853$	27.2705	−	7.30712i	0.933725	−	0.250191i	0.240283	−	0.970703i	$-0.422760\pi$
$853$	27.2705	−	7.30712i	0.933725	−	0.250191i	0.693442	+	0.720512i	$0.256093\pi$
$854$	6.16449	−	2.53933i	0.210944	−	0.0868939i
$855$	−5.02214	+	22.1782i	−0.171754	+	0.758477i
$856$	−17.6104	+	41.8209i	−0.601913	+	1.42941i
$857$	27.9195	−	48.3581i	0.953713	−	1.65188i	0.216428	−	0.976299i	$-0.430559\pi$
$857$	27.9195	−	48.3581i	0.953713	−	1.65188i	0.737285	−	0.675581i	$-0.236107\pi$
$858$	−11.3840	+	3.26613i	−0.388642	+	0.111504i
$859$	1.38364	+	0.370745i	0.0472091	+	0.0126497i	0.282346	−	0.959313i	$-0.408887\pi$
$859$	1.38364	+	0.370745i	0.0472091	+	0.0126497i	−0.235137	+	0.971962i	$0.575554\pi$
$860$	20.4917	+	5.57659i	0.698761	+	0.190160i
$861$	4.51043	+	1.76577i	0.153715	+	0.0601771i
$862$	−20.8929	+	15.9670i	−0.711617	+	0.543839i
$863$	−51.9380			−1.76799			−0.883995	−	0.467496i	$-0.845156\pi$
$863$	−51.9380			−1.76799			−0.883995	+	0.467496i	$0.845156\pi$
$864$	−15.9237	−	24.7070i	−0.541736	−	0.840549i
$865$	−25.8430			−0.878687
$866$	−33.2703	+	25.4262i	−1.13057	+	0.864016i
$867$	40.9939	+	16.0485i	1.39223	+	0.545036i
$868$	−37.0218	−	10.0751i	−1.25660	−	0.341970i
$869$	−21.0486	−	5.63994i	−0.714024	−	0.191322i
$870$	2.98915	−	0.857608i	0.101342	−	0.0290756i
$871$	−1.20168	+	2.08136i	−0.0407172	+	0.0705243i
$872$	−8.13199	−	3.42432i	−0.275384	−	0.115962i
$873$	−29.3401	+	9.10520i	−0.993013	+	0.308164i
$874$	37.0508	−	15.2623i	1.25326	−	0.516254i
$875$	−2.17580	+	0.583005i	−0.0735556	+	0.0197092i
$876$	−39.6961	−	29.4845i	−1.34121	−	0.996188i
$877$	−16.4166	−	4.39882i	−0.554349	−	0.148537i	−0.0292403	−	0.999572i	$-0.509309\pi$
$877$	−16.4166	−	4.39882i	−0.554349	−	0.148537i	−0.525109	+	0.851035i	$0.675975\pi$
$878$	−1.57854	−	12.1738i	−0.0532731	−	0.410847i
$879$	2.37313	+	1.74832i	0.0800437	+	0.0589693i
$880$	−4.59059	−	2.69840i	−0.154749	−	0.0909630i
$881$			56.8279i			1.91458i	0.289129	+	0.957290i	$0.406634\pi$
$881$			56.8279i			1.91458i	−0.289129	+	0.957290i	$0.593366\pi$
$882$	−3.40529	−	7.42788i	−0.114662	−	0.250110i
$883$	−26.4966	−	26.4966i	−0.891680	−	0.891680i	0.103001	−	0.994681i	$-0.467156\pi$
$883$	−26.4966	−	26.4966i	−0.891680	−	0.891680i	−0.994681	+	0.103001i	$0.967156\pi$
$884$	40.8778	+	23.8141i	1.37487	+	0.800955i
$885$	15.2046	−	12.1466i	0.511098	−	0.408302i
$886$	−21.6574	+	28.1106i	−0.727594	+	0.944396i
$887$	−20.1164	+	11.6142i	−0.675443	+	0.389967i	−0.798136	−	0.602478i	$-0.794180\pi$
$887$	−20.1164	+	11.6142i	−0.675443	+	0.389967i	0.122693	+	0.992445i	$0.460847\pi$
$888$	13.4227	−	13.7955i	0.450436	−	0.462948i
$889$	22.9521	+	13.2514i	0.769789	+	0.444438i
$890$	−0.654682	+	0.269682i	−0.0219450	+	0.00903976i
$891$	3.99575	+	11.2952i	0.133863	+	0.378402i
$892$	−21.1354	+	20.9710i	−0.707666	+	0.702161i
$893$	−64.8039	+	17.3642i	−2.16858	+	0.581070i
$894$	−12.9398	+	0.227795i	−0.432772	+	0.00761862i
$895$	6.31991	−	3.64880i	0.211251	−	0.121966i
$896$	20.0045	+	15.7890i	0.668304	+	0.527474i
$897$	−23.3699	−	2.61293i	−0.780299	−	0.0872432i
$898$	−7.34649	−	9.61294i	−0.245156	−	0.320788i
$899$	−7.64540	+	7.64540i	−0.254988	+	0.254988i
$900$	5.99628	−	0.211185i	0.199876	−	0.00703952i
$901$	−5.32056	−	5.32056i	−0.177254	−	0.177254i
$902$	−2.31670	−	0.309602i	−0.0771377	−	0.0103086i
$903$	33.3543	+	24.5726i	1.10996	+	0.817724i
$904$	6.15510	+	4.78051i	0.204715	+	0.158997i
$905$	3.73308	+	6.46589i	0.124092	+	0.214933i
$906$	5.82464	−	23.3762i	0.193511	−	0.776623i
$907$	−1.72310	−	6.43070i	−0.0572146	−	0.213528i	0.931400	−	0.363997i	$-0.118588\pi$
$907$	−1.72310	−	6.43070i	−0.0572146	−	0.213528i	−0.988615	+	0.150469i	$0.951922\pi$
$908$	−33.3669	−	0.130292i	−1.10732	−	0.00432389i
$909$	−13.5357	+	25.7171i	−0.448950	+	0.852981i
$910$	−4.44849	+	10.6806i	−0.147466	+	0.354058i
$911$	−1.17196	+	2.02989i	−0.0388288	+	0.0672534i	−0.884787	−	0.465996i	$-0.845696\pi$
$911$	−1.17196	+	2.02989i	−0.0388288	+	0.0672534i	0.845958	+	0.533250i	$0.179029\pi$
$912$	−6.24261	+	52.1427i	−0.206713	+	1.72662i
$913$	−2.00636	−	3.47512i	−0.0664010	−	0.115010i
$914$	−43.8289	+	5.68315i	−1.44973	+	0.187982i
$915$	1.32145	−	3.37549i	0.0436859	−	0.111590i
$916$	−23.8429	−	13.8901i	−0.787790	−	0.458942i
$917$	−7.11600	+	7.11600i	−0.234991	+	0.234991i
$918$	21.5419	−	42.7371i	0.710988	−	1.41053i
$919$	2.08643			0.0688249			0.0344125	−	0.999408i	$-0.489044\pi$
$919$	2.08643			0.0688249			0.0344125	+	0.999408i	$0.489044\pi$
$920$	−6.38720	−	8.42570i	−0.210580	−	0.277787i
$921$	−6.12894	−	14.0150i	−0.201955	−	0.461809i
$922$	−14.9550	+	19.4112i	−0.492518	+	0.639274i
$923$	−12.4093	+	46.3123i	−0.408459	+	1.52439i
$924$	−6.45184	−	8.14117i	−0.212250	−	0.267825i
$925$	1.01689	+	3.79510i	0.0334353	+	0.124782i
$926$	−12.2052	+	29.3039i	−0.401087	+	0.962987i
$927$	−10.4871	+	46.3120i	−0.344443	+	1.52109i
$928$	6.66149	−	2.68340i	0.218674	−	0.0880868i
$929$	46.8485	+	27.0480i	1.53705	+	0.887415i	0.999010	+	0.0444956i	$0.0141681\pi$
$929$	46.8485	+	27.0480i	1.53705	+	0.887415i	0.538039	+	0.842920i	$0.319165\pi$
$930$	−17.8800	+	10.7470i	−0.586310	+	0.352409i
$931$	−3.77843	+	14.1013i	−0.123833	+	0.462151i
$932$	−4.73684	+	17.4060i	−0.155160	+	0.570152i
$933$	3.93075	−	0.595903i	0.128687	−	0.0195090i
$934$	4.01529	−	30.0457i	0.131384	−	0.983126i
$935$		−	8.67009i		−	0.283542i
$936$	17.9377	−	25.0599i	0.586311	−	0.819109i
$937$		−	23.9571i		−	0.782644i	−0.920254	−	0.391322i	$-0.872018\pi$
$937$		−	23.9571i		−	0.782644i	0.920254	−	0.391322i	$-0.127982\pi$
$938$	−2.08941	−	0.279227i	−0.0682217	−	0.00911709i
$939$	−31.5734	−	39.5225i	−1.03036	−	1.28977i
$940$	8.79112	+	15.3649i	0.286735	+	0.501148i
$941$	−11.5006	+	42.9209i	−0.374909	+	1.39918i	0.478568	+	0.878050i	$0.341156\pi$
$941$	−11.5006	+	42.9209i	−0.374909	+	1.39918i	−0.853477	+	0.521130i	$0.825511\pi$
$942$	43.1536	−	0.759687i	1.40602	−	0.0247520i
$943$	−4.01911	−	2.32043i	−0.130880	−	0.0755637i
$944$	32.0264	−	31.5301i	1.04237	−	1.02622i
$945$	11.0577	+	3.83745i	0.359707	+	0.124832i
$946$	−18.4542	−	7.68621i	−0.599997	−	0.249900i
$947$	−6.96557	−	25.9959i	−0.226351	−	0.844753i	−0.981859	−	0.189613i	$-0.939277\pi$
$947$	−6.96557	−	25.9959i	−0.226351	−	0.844753i	0.755508	−	0.655139i	$-0.227390\pi$
$948$	52.0419	−	22.5169i	1.69024	−	0.731316i
$949$	13.4182	−	50.0776i	0.435575	−	1.62559i
$950$	−8.49166	−	6.54226i	−0.275506	−	0.212259i
$951$	−40.9815	−	4.58204i	−1.32892	−	0.148583i
$952$	−5.65699	+	41.1071i	−0.183344	+	1.33229i
$953$	−16.3547			−0.529782			−0.264891	−	0.964278i	$-0.585336\pi$
$953$	−16.3547			−0.529782			−0.264891	+	0.964278i	$0.585336\pi$
$954$	−3.77518	+	3.12631i	−0.122226	+	0.101218i
$955$	−5.21327	+	5.21327i	−0.168698	+	0.168698i
$956$	−16.1754	+	4.26656i	−0.523150	+	0.137990i
$957$	−2.89421	+	0.438762i	−0.0935564	+	0.0141832i
$958$	2.94919	+	22.7444i	0.0952841	+	0.734838i
$959$	13.1809	+	22.8300i	0.425635	+	0.737221i
$960$	13.7233	−	1.91628i	0.442916	−	0.0618476i
$961$	20.7662	−	35.9681i	0.669878	−	1.16026i
$962$	18.6294	+	7.75919i	0.600635	+	0.250166i
$963$	1.88187	+	48.0932i	0.0606424	+	1.54978i
$964$	−11.5008	−	11.5910i	−0.370415	−	0.373319i
$965$	−2.47831	−	9.24919i	−0.0797797	−	0.297742i
$966$	−5.68813	−	19.8257i	−0.183013	−	0.637882i
$967$	0.862193	+	1.49336i	0.0277262	+	0.0480233i	0.879556	−	0.475796i	$-0.157840\pi$
$967$	0.862193	+	1.49336i	0.0277262	+	0.0480233i	−0.851829	+	0.523819i	$0.824507\pi$
$968$	−20.6133	−	16.0098i	−0.662536	−	0.514575i
$969$	−78.3417	+	34.2599i	−2.51670	+	1.10059i
$970$	1.91828	−	14.3542i	0.0615923	−	0.460884i
$971$	−35.5355	−	35.5355i	−1.14039	−	1.14039i	−0.988379	−	0.152010i	$-0.951425\pi$
$971$	−35.5355	−	35.5355i	−1.14039	−	1.14039i	−0.152010	−	0.988379i	$-0.548575\pi$
$972$	−26.4044	−	16.5774i	−0.846921	−	0.531719i
$973$	6.86551	−	6.86551i	0.220098	−	0.220098i
$974$	−7.11503	+	5.43752i	−0.227980	+	0.174229i
$975$	2.52054	+	5.76369i	0.0807219	+	0.184586i
$976$	2.22977	−	8.06903i	0.0713733	−	0.258283i
$977$	29.8812	−	17.2519i	0.955985	−	0.551938i	0.0610502	−	0.998135i	$-0.480555\pi$
$977$	29.8812	−	17.2519i	0.955985	−	0.551938i	0.894935	+	0.446196i	$0.147222\pi$
$978$	1.38501	+	0.767455i	0.0442878	+	0.0245405i
$979$	0.643795	−	0.172504i	0.0205758	−	0.00551326i
$980$	3.85193	+	0.0150411i	0.123046	+	0.000480471i
$981$	−9.35164	+	0.365926i	−0.298575	+	0.0116831i
$982$	−3.36156	−	8.16056i	−0.107272	−	0.260414i
$983$	−15.5219	−	8.96156i	−0.495071	−	0.285830i	0.231605	−	0.972810i	$-0.425602\pi$
$983$	−15.5219	−	8.96156i	−0.495071	−	0.285830i	−0.726676	+	0.686980i	$0.758936\pi$
$984$	5.22507	−	3.11289i	0.166569	−	0.0992354i
$985$	7.76093	−	4.48077i	0.247284	−	0.142769i
$986$	9.26293	+	7.13647i	0.294992	+	0.227272i
$987$	5.17603	+	34.1426i	0.164755	+	1.08677i
$988$	−53.2388	+	14.0427i	−1.69375	+	0.446758i
$989$	−28.0673	−	28.0673i	−0.892490	−	0.892490i
$990$	−5.62314	−	0.528677i	−0.178715	−	0.0168024i
$991$		−	19.0237i		−	0.604307i	−0.953259	−	0.302154i	$-0.902294\pi$
$991$		−	19.0237i		−	0.604307i	0.953259	−	0.302154i	$-0.0977056\pi$
$992$	−38.5060	+	28.9539i	−1.22257	+	0.919287i
$993$	−3.89530	+	34.8394i	−0.123614	+	1.10559i
$994$	−41.7045	+	5.40768i	−1.32279	+	0.171521i
$995$	−3.81321	−	1.02175i	−0.120887	−	0.0323915i
$996$	9.70834	+	3.84446i	0.307621	+	0.121816i
$997$	−3.79246	+	1.01619i	−0.120109	+	0.0321830i	−0.318373	−	0.947966i	$-0.603136\pi$
$997$	−3.79246	+	1.01619i	−0.120109	+	0.0321830i	0.198264	+	0.980149i	$0.436470\pi$
$998$	17.6080	+	42.7453i	0.557371	+	1.35308i
$999$	6.69339	−	19.2871i	0.211770	−	0.610218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.21	✓	384
9.5	odd	6	inner	720.2.cf.a.491.54	yes	384
16.3	odd	4	inner	720.2.cf.a.371.54	yes	384
144.131	even	12	inner	720.2.cf.a.131.21	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.21	✓	384	1.1	even	1	trivial
720.2.cf.a.131.21	yes	384	144.131	even	12	inner
720.2.cf.a.371.54	yes	384	16.3	odd	4	inner
720.2.cf.a.491.54	yes	384	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12365 + 0.858726i) q^{2} +(-1.61286 - 0.631411i) q^{3} +(0.525178 - 1.92982i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.35450 - 0.675522i) q^{6} +(-1.12628 + 1.95077i) q^{7} +(1.06707 + 2.61942i) q^{8} +(2.20264 + 2.03676i) q^{9} +O(q^{10})\)	\(q+(-1.12365 + 0.858726i) q^{2} +(-1.61286 - 0.631411i) q^{3} +(0.525178 - 1.92982i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.35450 - 0.675522i) q^{6} +(-1.12628 + 1.95077i) q^{7} +(1.06707 + 2.61942i) q^{8} +(2.20264 + 2.03676i) q^{9} +(-1.30762 + 0.538644i) q^{10} +(1.28587 - 0.344548i) q^{11} +(-2.06554 + 2.78092i) q^{12} +(-3.50820 - 0.940019i) q^{13} +(-0.409637 - 3.15915i) q^{14} +(-1.39448 - 1.02734i) q^{15} +(-3.44838 - 2.02699i) q^{16} -6.51283i q^{17} +(-4.22401 - 0.397133i) q^{18} +(5.35979 + 5.35979i) q^{19} +(1.00676 - 1.72813i) q^{20} +(3.04827 - 2.43518i) q^{21} +(-1.14900 + 1.49136i) q^{22} +(-3.23731 + 1.86906i) q^{23} +(-0.0671023 - 4.89852i) q^{24} +(0.866025 + 0.500000i) q^{25} +(4.74921 - 1.95633i) q^{26} +(-2.26653 - 4.67577i) q^{27} +(3.17313 + 3.19801i) q^{28} +(1.22629 - 0.328583i) q^{29} +(2.44911 - 0.0431147i) q^{30} +(-7.37559 + 4.25830i) q^{31} +(5.61540 - 0.683584i) q^{32} +(-2.29148 - 0.256205i) q^{33} +(5.59274 + 7.31814i) q^{34} +(-1.59280 + 1.59280i) q^{35} +(5.08734 - 3.18103i) q^{36} +(2.77821 + 2.77821i) q^{37} +(-10.6251 - 1.41993i) q^{38} +(5.06470 + 3.73123i) q^{39} +(0.352753 + 2.80634i) q^{40} +(0.620748 + 1.07517i) q^{41} +(-1.33403 + 5.35392i) q^{42} +(2.74826 + 10.2567i) q^{43} +(0.0103964 - 2.66244i) q^{44} +(1.60044 + 2.53744i) q^{45} +(2.03259 - 4.88014i) q^{46} +(-4.42552 + 7.66523i) q^{47} +(4.28189 + 5.44660i) q^{48} +(0.962991 + 1.66795i) q^{49} +(-1.40247 + 0.181854i) q^{50} +(-4.11227 + 10.5043i) q^{51} +(-3.65649 + 6.27650i) q^{52} +(0.816936 - 0.816936i) q^{53} +(6.56199 + 3.30761i) q^{54} +1.33123 q^{55} +(-6.31171 - 0.868592i) q^{56} +(-5.26037 - 12.0288i) q^{57} +(-1.09576 + 1.42226i) q^{58} +(-2.90800 + 10.8528i) q^{59} +(-2.71492 + 2.15156i) q^{60} +(0.541672 + 2.02155i) q^{61} +(4.63087 - 11.1185i) q^{62} +(-6.45403 + 2.00290i) q^{63} +(-5.72273 + 5.59020i) q^{64} +(-3.14537 - 1.81598i) q^{65} +(2.79484 - 1.67987i) q^{66} +(0.171267 - 0.639176i) q^{67} +(-12.5686 - 3.42039i) q^{68} +(6.40148 - 0.970466i) q^{69} +(0.421970 - 3.15753i) q^{70} -13.2012i q^{71} +(-2.98475 + 7.94300i) q^{72} +14.2744i q^{73} +(-5.50745 - 0.736012i) q^{74} +(-1.08107 - 1.35325i) q^{75} +(13.1583 - 7.52857i) q^{76} +(-0.776115 + 2.89650i) q^{77} +(-8.89506 + 0.156591i) q^{78} +(-14.1761 - 8.18455i) q^{79} +(-2.80625 - 2.85043i) q^{80} +(0.703256 + 8.97248i) q^{81} +(-1.62078 - 0.675058i) q^{82} +(-0.780157 - 2.91159i) q^{83} +(-3.09857 - 7.16150i) q^{84} +(1.68564 - 6.29091i) q^{85} +(-11.8958 - 9.16489i) q^{86} +(-2.18530 - 0.244333i) q^{87} +(2.27463 + 3.00058i) q^{88} +0.500668 q^{89} +(-3.97730 - 1.47686i) q^{90} +(5.78497 - 5.78497i) q^{91} +(1.90678 + 7.22901i) q^{92} +(14.5845 - 2.21102i) q^{93} +(-1.60960 - 12.4133i) q^{94} +(3.78995 + 6.56438i) q^{95} +(-9.48848 - 2.44310i) q^{96} +(-5.12008 + 8.86824i) q^{97} +(-2.51438 - 1.04725i) q^{98} +(3.53407 + 1.86009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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