LMFDB - Embedded newform 930.2.be.b.37.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.5
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.0920628 + 2.23417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.111124 - 0.414720i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.0920628 + 2.23417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.111124 - 0.414720i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.51470 - 1.64490i) q^{10} +(-0.538947 - 0.311161i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.24443 + 0.601394i) q^{13} +(-0.371828 + 0.214675i) q^{14} +(2.18187 + 0.489320i) q^{15} -1.00000 q^{16} +(0.390069 + 0.104519i) q^{17} +(0.258819 + 0.965926i) q^{18} +(5.81454 - 3.35703i) q^{19} +(-2.23417 + 0.0920628i) q^{20} +(-0.371828 - 0.214675i) q^{21} +(0.161069 + 0.601118i) q^{22} +(5.68456 + 5.68456i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.98305 + 0.411368i) q^{25} +(2.01230 + 1.16180i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.414720 + 0.111124i) q^{28} +5.87810 q^{29} +(-1.19681 - 1.88882i) q^{30} +(2.71903 - 4.85869i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.440049 + 0.440049i) q^{33} +(-0.201914 - 0.349726i) q^{34} +(0.936787 + 0.210090i) q^{35} +(0.500000 - 0.866025i) q^{36} +(4.50280 + 1.20652i) q^{37} +(-6.48528 - 1.73773i) q^{38} +2.32361i q^{39} +(1.64490 + 1.51470i) q^{40} +(-3.63969 + 6.30413i) q^{41} +(0.111124 + 0.414720i) q^{42} +(-3.08282 + 11.5052i) q^{43} +(0.311161 - 0.538947i) q^{44} +(1.03736 - 1.98088i) q^{45} -8.03918i q^{46} +(9.29991 + 9.29991i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(5.90253 + 3.40783i) q^{49} +(3.81443 + 3.23267i) q^{50} +(0.201914 - 0.349726i) q^{51} +(-0.601394 - 2.24443i) q^{52} +(3.22717 - 0.864719i) q^{53} +1.00000 q^{54} +(0.645571 - 1.23275i) q^{55} +(-0.214675 - 0.371828i) q^{56} +(-1.73773 - 6.48528i) q^{57} +(-4.15645 - 4.15645i) q^{58} +(7.08515 - 4.09061i) q^{59} +(-0.489320 + 2.18187i) q^{60} -7.02015i q^{61} +(-5.35826 + 1.51297i) q^{62} +(-0.303596 + 0.303596i) q^{63} -1.00000i q^{64} +(-1.55025 - 4.95908i) q^{65} +0.622323 q^{66} +(1.02781 - 0.275400i) q^{67} +(-0.104519 + 0.390069i) q^{68} +(6.96213 - 4.01959i) q^{69} +(-0.513852 - 0.810964i) q^{70} +(-3.18352 + 5.51401i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(0.248350 - 0.0665451i) q^{73} +(-2.33082 - 4.03710i) q^{74} +(-0.892357 + 4.91973i) q^{75} +(3.35703 + 5.81454i) q^{76} +(-0.188935 + 0.188935i) q^{77} +(1.64304 - 1.64304i) q^{78} +(-3.83972 - 6.65060i) q^{79} +(-0.0920628 - 2.23417i) q^{80} +(0.500000 + 0.866025i) q^{81} +(7.03135 - 1.88404i) q^{82} +(-8.60909 + 2.30680i) q^{83} +(0.214675 - 0.371828i) q^{84} +(-0.197602 + 0.881103i) q^{85} +(10.3153 - 5.95555i) q^{86} +(1.52137 - 5.67781i) q^{87} +(-0.601118 + 0.161069i) q^{88} +11.3454 q^{89} +(-2.13422 + 0.667172i) q^{90} +0.997641i q^{91} +(-5.68456 + 5.68456i) q^{92} +(-3.98940 - 3.88390i) q^{93} -13.1521i q^{94} +(8.03548 + 12.6816i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-7.54995 - 7.54995i) q^{97} +(-1.76402 - 6.58342i) q^{98} +(0.311161 + 0.538947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	0.0920628	+	2.23417i	0.0411717	+	0.999152i
$5$	0.0920628	+	2.23417i	0.0411717	+	0.999152i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.111124	−	0.414720i	0.0420009	−	0.156750i	−0.941740	−	0.336340i	$-0.890811\pi$
$7$	0.111124	−	0.414720i	0.0420009	−	0.156750i	0.983741	+	0.179591i	$0.0574774\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	1.51470	−	1.64490i	0.478990	−	0.520162i
$11$	−0.538947	−	0.311161i	−0.162499	−	0.0938187i	0.416545	−	0.909115i	$-0.363241\pi$
$11$	−0.538947	−	0.311161i	−0.162499	−	0.0938187i	−0.579044	+	0.815296i	$0.696574\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	−2.24443	+	0.601394i	−0.622494	+	0.166797i	−0.556261	−	0.831008i	$-0.687765\pi$
$13$	−2.24443	+	0.601394i	−0.622494	+	0.166797i	−0.0662326	+	0.997804i	$0.521098\pi$
$14$	−0.371828	+	0.214675i	−0.0993752	+	0.0573743i
$15$	2.18187	+	0.489320i	0.563357	+	0.126342i
$16$	−1.00000			−0.250000
$17$	0.390069	+	0.104519i	0.0946056	+	0.0253495i	0.305811	−	0.952092i	$-0.401072\pi$
$17$	0.390069	+	0.104519i	0.0946056	+	0.0253495i	−0.211206	+	0.977442i	$0.567739\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	5.81454	−	3.35703i	1.33395	−	0.770155i	0.348045	−	0.937478i	$-0.386845\pi$
$19$	5.81454	−	3.35703i	1.33395	−	0.770155i	0.985902	+	0.167323i	$0.0535121\pi$
$20$	−2.23417	+	0.0920628i	−0.499576	+	0.0205859i
$21$	−0.371828	−	0.214675i	−0.0811395	−	0.0468459i
$22$	0.161069	+	0.601118i	0.0343400	+	0.128159i
$23$	5.68456	+	5.68456i	1.18531	+	1.18531i	0.978349	+	0.206964i	$0.0663583\pi$
$23$	5.68456	+	5.68456i	1.18531	+	1.18531i	0.206964	+	0.978349i	$0.433642\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.98305	+	0.411368i	−0.996610	+	0.0822736i
$26$	2.01230	+	1.16180i	0.394645	+	0.227849i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	0.414720	+	0.111124i	0.0783748	+	0.0210005i
$29$	5.87810			1.09154			0.545768	−	0.837936i	$-0.316238\pi$
$29$	5.87810			1.09154			0.545768	+	0.837936i	$0.316238\pi$
$30$	−1.19681	−	1.88882i	−0.218507	−	0.344849i
$31$	2.71903	−	4.85869i	0.488351	−	0.872647i
$31$	2.71903	−	4.85869i	0.488351	−	0.872647i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.440049	+	0.440049i	−0.0766026	+	0.0766026i
$34$	−0.201914	−	0.349726i	−0.0346280	−	0.0599775i
$35$	0.936787	+	0.210090i	0.158346	+	0.0355116i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	4.50280	+	1.20652i	0.740256	+	0.198351i	0.609192	−	0.793023i	$-0.291494\pi$
$37$	4.50280	+	1.20652i	0.740256	+	0.198351i	0.131064	+	0.991374i	$0.458161\pi$
$38$	−6.48528	−	1.73773i	−1.05205	−	0.281896i
$39$			2.32361i			0.372075i
$40$	1.64490	+	1.51470i	0.260081	+	0.239495i
$41$	−3.63969	+	6.30413i	−0.568425	+	0.984540i	0.428297	+	0.903638i	$0.359114\pi$
$41$	−3.63969	+	6.30413i	−0.568425	+	0.984540i	−0.996722	+	0.0809024i	$0.974220\pi$
$42$	0.111124	+	0.414720i	0.0171468	+	0.0639927i
$43$	−3.08282	+	11.5052i	−0.470125	+	1.75453i	0.169187	+	0.985584i	$0.445886\pi$
$43$	−3.08282	+	11.5052i	−0.470125	+	1.75453i	−0.639312	+	0.768947i	$0.720781\pi$
$44$	0.311161	−	0.538947i	0.0469094	−	0.0812494i
$45$	1.03736	−	1.98088i	0.154640	−	0.295292i
$46$		−	8.03918i		−	1.18531i
$47$	9.29991	+	9.29991i	1.35653	+	1.35653i	0.878155	+	0.478376i	$0.158774\pi$
$47$	9.29991	+	9.29991i	1.35653	+	1.35653i	0.478376	+	0.878155i	$0.341226\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	5.90253	+	3.40783i	0.843219	+	0.486833i
$50$	3.81443	+	3.23267i	0.539442	+	0.457168i
$51$	0.201914	−	0.349726i	0.0282737	−	0.0489715i
$52$	−0.601394	−	2.24443i	−0.0833984	−	0.311247i
$53$	3.22717	−	0.864719i	0.443286	−	0.118778i	−0.0302699	−	0.999542i	$-0.509637\pi$
$53$	3.22717	−	0.864719i	0.443286	−	0.118778i	0.473556	+	0.880764i	$0.342970\pi$
$54$	1.00000			0.136083
$55$	0.645571	−	1.23275i	0.0870488	−	0.166224i
$56$	−0.214675	−	0.371828i	−0.0286872	−	0.0496876i
$57$	−1.73773	−	6.48528i	−0.230167	−	0.858996i
$58$	−4.15645	−	4.15645i	−0.545768	−	0.545768i
$59$	7.08515	−	4.09061i	0.922408	−	0.532553i	0.0380057	−	0.999278i	$-0.487900\pi$
$59$	7.08515	−	4.09061i	0.922408	−	0.532553i	0.884403	+	0.466725i	$0.154566\pi$
$60$	−0.489320	+	2.18187i	−0.0631710	+	0.281678i
$61$		−	7.02015i		−	0.898838i	−0.893321	−	0.449419i	$-0.851631\pi$
$61$		−	7.02015i		−	0.898838i	0.893321	−	0.449419i	$-0.148369\pi$
$62$	−5.35826	+	1.51297i	−0.680499	+	0.192148i
$63$	−0.303596	+	0.303596i	−0.0382495	+	0.0382495i
$64$		−	1.00000i		−	0.125000i
$65$	−1.55025	−	4.95908i	−0.192284	−	0.615099i
$66$	0.622323			0.0766026
$67$	1.02781	−	0.275400i	0.125566	−	0.0336454i	−0.195489	−	0.980706i	$-0.562629\pi$
$67$	1.02781	−	0.275400i	0.125566	−	0.0336454i	0.321055	+	0.947061i	$0.395963\pi$
$68$	−0.104519	+	0.390069i	−0.0126747	+	0.0473028i
$69$	6.96213	−	4.01959i	0.838143	−	0.483902i
$70$	−0.513852	−	0.810964i	−0.0614171	−	0.0969288i
$71$	−3.18352	+	5.51401i	−0.377814	+	0.654393i	−0.990744	−	0.135744i	$-0.956657\pi$
$71$	−3.18352	+	5.51401i	−0.377814	+	0.654393i	0.612930	+	0.790137i	$0.289991\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	0.248350	−	0.0665451i	0.0290671	−	0.00778851i	−0.244256	−	0.969711i	$-0.578544\pi$
$73$	0.248350	−	0.0665451i	0.0290671	−	0.00778851i	0.273323	+	0.961922i	$0.411877\pi$
$74$	−2.33082	−	4.03710i	−0.270953	−	0.469304i
$75$	−0.892357	+	4.91973i	−0.103040	+	0.568081i
$76$	3.35703	+	5.81454i	0.385078	+	0.666974i
$77$	−0.188935	+	0.188935i	−0.0215311	+	0.0215311i
$78$	1.64304	−	1.64304i	0.186038	−	0.186038i
$79$	−3.83972	−	6.65060i	−0.432003	−	0.748251i	0.565043	−	0.825061i	$-0.308860\pi$
$79$	−3.83972	−	6.65060i	−0.432003	−	0.748251i	−0.997046	+	0.0768108i	$0.975526\pi$
$80$	−0.0920628	−	2.23417i	−0.0102929	−	0.249788i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	7.03135	−	1.88404i	0.776482	−	0.208058i
$83$	−8.60909	+	2.30680i	−0.944970	+	0.253204i	−0.698227	−	0.715877i	$-0.746027\pi$
$83$	−8.60909	+	2.30680i	−0.944970	+	0.253204i	−0.246743	+	0.969081i	$0.579360\pi$
$84$	0.214675	−	0.371828i	0.0234230	−	0.0405698i
$85$	−0.197602	+	0.881103i	−0.0214329	+	0.0955691i
$86$	10.3153	−	5.95555i	1.11233	−	0.642203i
$87$	1.52137	−	5.67781i	0.163107	−	0.608725i
$88$	−0.601118	+	0.161069i	−0.0640794	+	0.0171700i
$89$	11.3454			1.20261			0.601306	−	0.799019i	$-0.294647\pi$
$89$	11.3454			1.20261			0.601306	+	0.799019i	$0.294647\pi$
$90$	−2.13422	+	0.667172i	−0.224966	+	0.0703261i
$91$			0.997641i			0.104581i
$92$	−5.68456	+	5.68456i	−0.592656	+	0.592656i
$93$	−3.98940	−	3.88390i	−0.413682	−	0.402742i
$94$		−	13.1521i		−	1.35653i
$95$	8.03548	+	12.6816i	0.824423	+	1.30111i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−7.54995	−	7.54995i	−0.766581	−	0.766581i	0.210922	−	0.977503i	$-0.432353\pi$
$97$	−7.54995	−	7.54995i	−0.766581	−	0.766581i	−0.977503	+	0.210922i	$0.932353\pi$
$98$	−1.76402	−	6.58342i	−0.178193	−	0.665026i
$99$	0.311161	+	0.538947i	0.0312729	+	0.0541663i
$100$	−0.411368	−	4.98305i	−0.0411368	−	0.498305i
$101$	−3.15451			−0.313885			−0.156943	−	0.987608i	$-0.550164\pi$
$101$	−3.15451			−0.313885			−0.156943	+	0.987608i	$0.550164\pi$
$102$	−0.390069	+	0.104519i	−0.0386226	+	0.0103489i
$103$	−4.65809	−	17.3842i	−0.458975	−	1.71292i	−0.676131	−	0.736782i	$-0.736345\pi$
$103$	−4.65809	−	17.3842i	−0.458975	−	1.71292i	0.217156	−	0.976137i	$-0.430322\pi$
$104$	−1.16180	+	2.01230i	−0.113924	+	0.197323i
$105$	0.445389	−	0.850491i	0.0434656	−	0.0829995i
$106$	−2.89341	−	1.67051i	−0.281032	−	0.162254i
$107$	0.302116	−	1.12751i	0.0292067	−	0.109001i	−0.949784	−	0.312907i	$-0.898697\pi$
$107$	0.302116	−	1.12751i	0.0292067	−	0.109001i	0.978990	+	0.203906i	$0.0653638\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	16.6900i		−	1.59861i	−0.600926	−	0.799305i	$-0.705201\pi$
$109$		−	16.6900i		−	1.59861i	0.600926	−	0.799305i	$-0.294799\pi$
$110$	−1.32817	+	0.415196i	−0.126636	+	0.0395874i
$111$	2.33082	−	4.03710i	0.221232	−	0.383185i
$112$	−0.111124	+	0.414720i	−0.0105002	+	0.0391874i
$113$	−0.909270	−	3.39344i	−0.0855369	−	0.319228i	0.909878	−	0.414875i	$-0.136175\pi$
$113$	−0.909270	−	3.39344i	−0.0855369	−	0.319228i	−0.995415	+	0.0956470i	$0.969508\pi$
$114$	−3.35703	+	5.81454i	−0.314414	+	0.544582i
$115$	−12.1769	+	13.2236i	−1.13551	+	1.23311i
$116$			5.87810i			0.545768i
$117$	2.24443	+	0.601394i	0.207498	+	0.0555989i
$118$	−7.90246	−	2.11746i	−0.727480	−	0.194928i
$119$	0.0866920	−	0.150155i	0.00794704	−	0.0137647i
$120$	1.88882	−	1.19681i	0.172425	−	0.109254i
$121$	−5.30636	−	9.19088i	−0.482396	−	0.835535i
$122$	−4.96400	+	4.96400i	−0.449419	+	0.449419i
$123$	5.14730	+	5.14730i	0.464117	+	0.464117i
$124$	4.85869	+	2.71903i	0.436324	+	0.244176i
$125$	−1.37782	−	11.0951i	−0.123236	−	0.992377i
$126$	0.429350			0.0382495
$127$	−3.46861	−	0.929410i	−0.307789	−	0.0824718i	0.101619	−	0.994823i	$-0.467598\pi$
$127$	−3.46861	−	0.929410i	−0.307789	−	0.0824718i	−0.409407	+	0.912352i	$0.634265\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.3153	+	5.95555i	0.908212	+	0.524357i
$130$	−2.41041	+	4.60279i	−0.211407	+	0.403692i
$131$	6.93829	+	12.0175i	0.606201	+	1.04997i	0.991860	+	0.127330i	$0.0406407\pi$
$131$	6.93829	+	12.0175i	0.606201	+	1.04997i	−0.385659	+	0.922641i	$0.626026\pi$
$132$	−0.440049	−	0.440049i	−0.0383013	−	0.0383013i
$133$	−0.746093	−	2.78446i	−0.0646944	−	0.241443i
$134$	−0.921505	−	0.532031i	−0.0796059	−	0.0459605i
$135$	−1.64490	−	1.51470i	−0.141570	−	0.130365i
$136$	0.349726	−	0.201914i	0.0299888	−	0.0173140i
$137$	0.356781	+	1.33152i	0.0304818	+	0.113760i	0.979491	−	0.201490i	$-0.0645784\pi$
$137$	0.356781	+	1.33152i	0.0304818	+	0.113760i	−0.949009	+	0.315250i	$0.897912\pi$
$138$	−7.76525	−	2.08069i	−0.661022	−	0.177120i
$139$	14.7255			1.24900			0.624500	−	0.781025i	$-0.285303\pi$
$139$	14.7255			1.24900			0.624500	+	0.781025i	$0.285303\pi$
$140$	−0.210090	+	0.936787i	−0.0177558	+	0.0791729i
$141$	11.3900	−	6.57603i	0.959212	−	0.553802i
$142$	6.15008	−	1.64791i	0.516103	−	0.138289i
$143$	1.39676	+	0.374261i	0.116803	+	0.0312973i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.541154	+	13.1327i	0.0449404	+	1.09061i
$146$	−0.222664	−	0.128555i	−0.0184278	−	0.0106393i
$147$	4.81940	−	4.81940i	0.397497	−	0.397497i
$148$	−1.20652	+	4.50280i	−0.0991755	+	0.370128i
$149$	−18.9397	+	10.9348i	−1.55160	+	0.895817i	−0.553588	+	0.832790i	$0.686742\pi$
$149$	−18.9397	+	10.9348i	−1.55160	+	0.895817i	−0.998012	+	0.0630263i	$0.979925\pi$
$150$	4.10976	−	2.84778i	0.335561	−	0.232520i
$151$			21.6368i			1.76078i	0.474251	+	0.880390i	$0.342719\pi$
$151$			21.6368i			1.76078i	−0.474251	+	0.880390i	$0.657281\pi$
$152$	1.73773	−	6.48528i	0.140948	−	0.526026i
$153$	−0.285550	−	0.285550i	−0.0230854	−	0.0230854i
$154$	0.267194			0.0215311
$155$	11.1055	+	5.62747i	0.892013	+	0.452009i
$156$	−2.32361			−0.186038
$157$	11.0501	+	11.0501i	0.881898	+	0.881898i	0.993727	−	0.111830i	$-0.0356711\pi$
$157$	11.0501	+	11.0501i	0.881898	+	0.881898i	−0.111830	+	0.993727i	$0.535671\pi$
$158$	−1.98759	+	7.41778i	−0.158124	+	0.590127i
$159$		−	3.34102i		−	0.264960i
$160$	−1.51470	+	1.64490i	−0.119748	+	0.130040i
$161$	2.98919	−	1.72581i	0.235581	−	0.136013i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−12.2452	+	12.2452i	−0.959115	+	0.959115i	−0.999196	−	0.0400815i	$-0.987238\pi$
$163$	−12.2452	+	12.2452i	−0.959115	+	0.959115i	0.0400815	+	0.999196i	$0.487238\pi$
$164$	−6.30413	−	3.63969i	−0.492270	−	0.284212i
$165$	−1.02366	−	0.942632i	−0.0796916	−	0.0733838i
$166$	7.71870	+	4.45639i	0.599087	+	0.345883i
$167$	−15.8769	−	4.25421i	−1.22859	−	0.329201i	−0.414563	−	0.910021i	$-0.636065\pi$
$167$	−15.8769	−	4.25421i	−1.22859	−	0.329201i	−0.814032	+	0.580820i	$0.802732\pi$
$168$	−0.414720	+	0.111124i	−0.0319964	+	0.00857340i
$169$	−6.58252	+	3.80042i	−0.506348	+	0.292340i
$170$	0.762760	−	0.483308i	0.0585010	−	0.0370681i
$171$	−6.71406			−0.513437
$172$	−11.5052	−	3.08282i	−0.877266	−	0.235063i
$173$	3.27550	+	12.2243i	0.249031	+	0.929398i	0.971314	+	0.237800i	$0.0764262\pi$
$173$	3.27550	+	12.2243i	0.249031	+	0.929398i	−0.722283	+	0.691598i	$0.756907\pi$
$174$	−5.09059	+	2.93905i	−0.385916	+	0.222809i
$175$	−0.383133	+	2.11228i	−0.0289622	+	0.159674i
$176$	0.538947	+	0.311161i	0.0406247	+	0.0234547i
$177$	−2.11746	−	7.90246i	−0.159158	−	0.593985i
$178$	−8.02242	−	8.02242i	−0.601306	−	0.601306i
$179$	−1.89653	−	3.28489i	−0.141753	−	0.245524i	0.786404	−	0.617713i	$-0.211941\pi$
$179$	−1.89653	−	3.28489i	−0.141753	−	0.245524i	−0.928157	+	0.372189i	$0.878607\pi$
$180$	1.98088	+	1.03736i	0.147646	+	0.0773200i
$181$	1.42867	+	0.824843i	0.106192	+	0.0613101i	0.552156	−	0.833741i	$-0.313805\pi$
$181$	1.42867	+	0.824843i	0.106192	+	0.0613101i	−0.445963	+	0.895051i	$0.647139\pi$
$182$	0.705439	−	0.705439i	0.0522906	−	0.0522906i
$183$	−6.78094	−	1.81695i	−0.501262	−	0.134313i
$184$	8.03918			0.592656
$185$	−2.28104	+	10.1711i	−0.167705	+	0.747795i
$186$	0.0746010	+	5.56726i	0.00547001	+	0.408212i
$187$	−0.177704	−	0.177704i	−0.0129950	−	0.0129950i
$188$	−9.29991	+	9.29991i	−0.678266	+	0.678266i
$189$	0.214675	+	0.371828i	0.0156153	+	0.0270465i
$190$	3.28532	−	14.6492i	0.238343	−	1.06277i
$191$	6.20202	−	10.7422i	0.448762	−	0.777279i	−0.549544	−	0.835465i	$-0.685198\pi$
$191$	6.20202	−	10.7422i	0.448762	−	0.777279i	0.998306	+	0.0581862i	$0.0185317\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−0.0515685	−	0.0138177i	−0.00371198	−	0.000994623i	0.256963	−	0.966421i	$-0.417278\pi$
$193$	−0.0515685	−	0.0138177i	−0.00371198	−	0.000994623i	−0.260675	+	0.965427i	$0.583945\pi$
$194$			10.6772i			0.766581i
$195$	−5.19134	+	0.213918i	−0.371760	+	0.0153190i
$196$	−3.40783	+	5.90253i	−0.243416	+	0.421610i
$197$	2.05409	+	7.66596i	0.146348	+	0.546177i	0.999692	+	0.0248287i	$0.00790403\pi$
$197$	2.05409	+	7.66596i	0.146348	+	0.546177i	−0.853344	+	0.521348i	$0.825429\pi$
$198$	0.161069	−	0.601118i	0.0114467	−	0.0427196i
$199$	5.09349	−	8.82219i	0.361068	−	0.625388i	−0.627069	−	0.778964i	$-0.715746\pi$
$199$	5.09349	−	8.82219i	0.361068	−	0.625388i	0.988137	+	0.153576i	$0.0490789\pi$
$200$	−3.23267	+	3.81443i	−0.228584	+	0.269721i
$201$		−	1.06406i		−	0.0750532i
$202$	2.23057	+	2.23057i	0.156943	+	0.156943i
$203$	0.653198	−	2.43777i	0.0458455	−	0.171098i
$204$	0.349726	+	0.201914i	0.0244857	+	0.0141368i
$205$	−14.4196	−	7.55132i	−1.00711	−	0.527407i
$206$	−8.99874	+	15.5863i	−0.626972	+	1.08595i
$207$	−2.08069	−	7.76525i	−0.144618	−	0.539722i
$208$	2.24443	−	0.601394i	0.155623	−	0.0416992i
$209$	−4.17831			−0.289020
$210$	−0.916326	+	0.286450i	−0.0632325	+	0.0197670i
$211$	10.4795	+	18.1510i	0.721436	+	1.24956i	0.960424	+	0.278542i	$0.0898510\pi$
$211$	10.4795	+	18.1510i	0.721436	+	1.24956i	−0.238988	+	0.971023i	$0.576816\pi$
$212$	0.864719	+	3.22717i	0.0593891	+	0.221643i
$213$	4.50217	+	4.50217i	0.308484	+	0.308484i
$214$	−1.01090	+	0.583643i	−0.0691037	+	0.0398970i
$215$	−25.9885	−	5.82834i	−1.77240	−	0.397490i
$216$			1.00000i			0.0680414i
$217$	−1.71285	−	1.66755i	−0.116276	−	0.113201i
$218$	−11.8016	+	11.8016i	−0.799305	+	0.799305i
$219$		−	0.257110i		−	0.0173739i
$220$	1.23275	+	0.645571i	0.0831118	+	0.0435244i
$221$	−0.938340			−0.0631196
$222$	−4.50280	+	1.20652i	−0.302208	+	0.0809765i
$223$	2.69782	−	10.0684i	0.180660	−	0.674231i	−0.814858	−	0.579660i	$-0.803185\pi$
$223$	2.69782	−	10.0684i	0.180660	−	0.674231i	0.995518	−	0.0945712i	$-0.0301480\pi$
$224$	0.371828	−	0.214675i	0.0248438	−	0.0143436i
$225$	4.52113	+	2.13527i	0.301409	+	0.142351i
$226$	−1.75657	+	3.04248i	−0.116846	+	0.202382i
$227$	−13.0096	+	3.48592i	−0.863481	+	0.231369i	−0.663267	−	0.748383i	$-0.730830\pi$
$227$	−13.0096	+	3.48592i	−0.863481	+	0.231369i	−0.200214	+	0.979752i	$0.564164\pi$
$228$	6.48528	−	1.73773i	0.429498	−	0.115084i
$229$	−12.3171	−	21.3339i	−0.813938	−	1.40978i	−0.910088	−	0.414415i	$-0.863986\pi$
$229$	−12.3171	−	21.3339i	−0.813938	−	1.40978i	0.0961502	−	0.995367i	$-0.469347\pi$
$230$	17.9609	−	0.740109i	1.18431	−	0.0488014i
$231$	0.133597	+	0.231397i	0.00879005	+	0.0152248i
$232$	4.15645	−	4.15645i	0.272884	−	0.272884i
$233$	−2.64240	+	2.64240i	−0.173110	+	0.173110i	−0.788344	−	0.615234i	$-0.789061\pi$
$233$	−2.64240	+	2.64240i	−0.173110	+	0.173110i	0.615234	+	0.788344i	$0.289061\pi$
$234$	−1.16180	−	2.01230i	−0.0759495	−	0.131548i
$235$	−19.9214	+	21.6338i	−1.29953	+	1.41123i
$236$	4.09061	+	7.08515i	0.266276	+	0.461204i
$237$	−7.41778	+	1.98759i	−0.481836	+	0.129108i
$238$	−0.167476	+	0.0448751i	−0.0108559	+	0.00290882i
$239$	11.5455	−	19.9973i	0.746813	−	1.29352i	−0.202530	−	0.979276i	$-0.564916\pi$
$239$	11.5455	−	19.9973i	0.746813	−	1.29352i	0.949343	−	0.314242i	$-0.101750\pi$
$240$	−2.18187	−	0.489320i	−0.140839	−	0.0315855i
$241$	10.1189	−	5.84217i	0.651818	−	0.376327i	−0.137335	−	0.990525i	$-0.543854\pi$
$241$	10.1189	−	5.84217i	0.651818	−	0.376327i	0.789152	+	0.614198i	$0.210520\pi$
$242$	−2.74677	+	10.2511i	−0.176569	+	0.658965i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	7.02015			0.449419
$245$	−7.07027	+	13.5010i	−0.451703	+	0.862548i
$246$		−	7.27939i		−	0.464117i
$247$	−11.0315	+	11.0315i	−0.701915	+	0.701915i
$248$	−1.51297	−	5.35826i	−0.0960739	−	0.340250i
$249$			8.91278i			0.564825i
$250$	−6.87117	+	8.81970i	−0.434571	+	0.557807i
$251$	−1.95811	+	1.13051i	−0.123595	+	0.0713574i	−0.560523	−	0.828139i	$-0.689400\pi$
$251$	−1.95811	+	1.13051i	−0.123595	+	0.0713574i	0.436928	+	0.899496i	$0.356066\pi$
$252$	−0.303596	−	0.303596i	−0.0191248	−	0.0191248i
$253$	−1.29486	−	4.83249i	−0.0814073	−	0.303816i
$254$	1.79548	+	3.10987i	0.112659	+	0.195130i
$255$	0.799937	+	0.418915i	0.0500940	+	0.0262335i
$256$	1.00000			0.0625000
$257$	−1.66093	+	0.445044i	−0.103606	+	0.0277611i	−0.310249	−	0.950655i	$-0.600413\pi$
$257$	−1.66093	+	0.445044i	−0.103606	+	0.0277611i	0.206644	+	0.978416i	$0.433746\pi$
$258$	−3.08282	−	11.5052i	−0.191928	−	0.716284i
$259$	1.00074	−	1.73333i	0.0621829	−	0.107704i
$260$	4.95908	−	1.55025i	0.307549	−	0.0961422i
$261$	−5.09059	−	2.93905i	−0.315099	−	0.181923i
$262$	3.59152	−	13.4037i	0.221885	−	0.828086i
$263$	−18.3869	−	18.3869i	−1.13379	−	1.13379i	−0.989542	−	0.144245i	$-0.953925\pi$
$263$	−18.3869	−	18.3869i	−1.13379	−	1.13379i	−0.144245	−	0.989542i	$-0.546075\pi$
$264$			0.622323i			0.0383013i
$265$	2.22903	+	7.13045i	0.136928	+	0.438020i
$266$	−1.44134	+	2.49647i	−0.0883742	+	0.153069i
$267$	2.93641	−	10.9588i	0.179705	−	0.670670i
$268$	0.275400	+	1.02781i	0.0168227	+	0.0627832i
$269$	4.35187	−	7.53765i	0.265338	−	0.459579i	−0.702314	−	0.711867i	$-0.747850\pi$
$269$	4.35187	−	7.53765i	0.265338	−	0.459579i	0.967652	+	0.252288i	$0.0811831\pi$
$270$	0.0920628	+	2.23417i	0.00560276	+	0.135967i
$271$			29.3226i			1.78122i	0.454767	+	0.890610i	$0.349722\pi$
$271$			29.3226i			1.78122i	−0.454767	+	0.890610i	$0.650278\pi$
$272$	−0.390069	−	0.104519i	−0.0236514	−	0.00633737i
$273$	0.963647	+	0.258209i	0.0583226	+	0.0156275i
$274$	0.689247	−	1.19381i	0.0416389	−	0.0721208i
$275$	2.81360	+	1.32883i	0.169667	+	0.0801313i
$276$	4.01959	+	6.96213i	0.241951	+	0.419071i
$277$	13.7063	−	13.7063i	0.823530	−	0.823530i	−0.163083	−	0.986612i	$-0.552144\pi$
$277$	13.7063	−	13.7063i	0.823530	−	0.823530i	0.986612	+	0.163083i	$0.0521438\pi$
$278$	−10.4125	−	10.4125i	−0.624500	−	0.624500i
$279$	−4.78409	+	2.84824i	−0.286416	+	0.170520i
$280$	0.810964	−	0.513852i	0.0484644	−	0.0307086i
$281$	−15.1123			−0.901525			−0.450763	−	0.892644i	$-0.648848\pi$
$281$	−15.1123			−0.901525			−0.450763	+	0.892644i	$0.648848\pi$
$282$	−12.7039	−	3.40400i	−0.756507	−	0.202705i
$283$	2.86229	−	2.86229i	0.170145	−	0.170145i	−0.616898	−	0.787043i	$-0.711611\pi$
$283$	2.86229	−	2.86229i	0.170145	−	0.170145i	0.787043	+	0.616898i	$0.211611\pi$
$284$	−5.51401	−	3.18352i	−0.327196	−	0.188907i
$285$	14.3293	−	4.47943i	0.848792	−	0.265339i
$286$	−0.723017	−	1.25230i	−0.0427529	−	0.0740502i
$287$	2.20999	+	2.20999i	0.130452	+	0.130452i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−14.5812	−	8.41846i	−0.857718	−	0.495204i
$290$	8.90356	−	9.66887i	0.522835	−	0.567776i
$291$	−9.24676	+	5.33862i	−0.542055	+	0.312955i
$292$	0.0665451	+	0.248350i	0.00389426	+	0.0145336i
$293$	1.51845	+	0.406868i	0.0887090	+	0.0237695i	0.302901	−	0.953022i	$-0.402045\pi$
$293$	1.51845	+	0.406868i	0.0887090	+	0.0237695i	−0.214192	+	0.976792i	$0.568712\pi$
$294$	−6.81566			−0.397497
$295$	9.79141	+	15.4529i	0.570078	+	0.899700i
$296$	4.03710	−	2.33082i	0.234652	−	0.135476i
$297$	0.601118	−	0.161069i	0.0348804	−	0.00934617i
$298$	21.1245	+	5.66029i	1.22371	+	0.327892i
$299$	−16.1773	−	9.33995i	−0.935556	−	0.540143i
$300$	−4.91973	−	0.892357i	−0.284040	−	0.0515202i
$301$	4.42888	+	2.55701i	0.255276	+	0.147384i
$302$	15.2995	−	15.2995i	0.880390	−	0.880390i
$303$	−0.816447	+	3.04702i	−0.0469036	+	0.175047i
$304$	−5.81454	+	3.35703i	−0.333487	+	0.192539i
$305$	15.6842	−	0.646294i	0.898076	−	0.0370067i
$306$			0.403829i			0.0230854i
$307$	−6.62413	+	24.7216i	−0.378059	+	1.41094i	0.470764	+	0.882259i	$0.343978\pi$
$307$	−6.62413	+	24.7216i	−0.378059	+	1.41094i	−0.848823	+	0.528677i	$0.822688\pi$
$308$	−0.188935	−	0.188935i	−0.0107656	−	0.0107656i
$309$	−17.9975			−1.02384
$310$	−3.87354	−	11.8320i	−0.220002	−	0.672011i
$311$	−23.0367			−1.30629			−0.653147	−	0.757231i	$-0.726552\pi$
$311$	−23.0367			−1.30629			−0.653147	+	0.757231i	$0.726552\pi$
$312$	1.64304	+	1.64304i	0.0930188	+	0.0930188i
$313$	−0.892007	+	3.32902i	−0.0504192	+	0.188167i	−0.986543	−	0.163505i	$-0.947720\pi$
$313$	−0.892007	+	3.32902i	−0.0504192	+	0.188167i	0.936123	+	0.351672i	$0.114387\pi$
$314$		−	15.6273i		−	0.881898i
$315$	−0.706236	−	0.650336i	−0.0397919	−	0.0366423i
$316$	6.65060	−	3.83972i	0.374125	−	0.216001i
$317$	8.81439	−	32.8958i	0.495066	−	1.84761i	−0.0345968	−	0.999401i	$-0.511015\pi$
$317$	8.81439	−	32.8958i	0.495066	−	1.84761i	0.529662	−	0.848209i	$-0.322319\pi$
$318$	−2.36246	+	2.36246i	−0.132480	+	0.132480i
$319$	−3.16799	−	1.82904i	−0.177373	−	0.102407i
$320$	2.23417	−	0.0920628i	0.124894	−	0.00514647i
$321$	−1.01090	−	0.583643i	−0.0564229	−	0.0325758i
$322$	−3.33401	−	0.893346i	−0.185797	−	0.0497842i
$323$	2.61894	−	0.701744i	0.145722	−	0.0390461i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	10.9367	−	3.92006i	0.606660	−	0.217446i
$326$	17.3173			0.959115
$327$	−16.1213	−	4.31968i	−0.891509	−	0.238879i
$328$	1.88404	+	7.03135i	0.104029	+	0.388241i
$329$	4.89030	−	2.82342i	0.269611	−	0.155660i
$330$	0.0572928	+	1.39038i	0.00315386	+	0.0765377i
$331$	−9.09855	−	5.25305i	−0.500102	−	0.288734i	0.228654	−	0.973508i	$-0.426568\pi$
$331$	−9.09855	−	5.25305i	−0.500102	−	0.288734i	−0.728756	+	0.684774i	$0.759901\pi$
$332$	−2.30680	−	8.60909i	−0.126602	−	0.472485i
$333$	−3.29628	−	3.29628i	−0.180635	−	0.180635i
$334$	8.21851	+	14.2349i	0.449697	+	0.778898i
$335$	0.709913	+	2.27094i	0.0387867	+	0.124075i
$336$	0.371828	+	0.214675i	0.0202849	+	0.0117115i
$337$	5.35337	−	5.35337i	0.291617	−	0.291617i	−0.546102	−	0.837719i	$-0.683889\pi$
$337$	5.35337	−	5.35337i	0.291617	−	0.291617i	0.837719	+	0.546102i	$0.183889\pi$
$338$	7.34185	+	1.96724i	0.399344	+	0.107004i
$339$	−3.51315			−0.190808
$340$	−0.881103	−	0.197602i	−0.0477845	−	0.0107165i
$341$	−2.97725	+	1.77252i	−0.161227	+	0.0959876i
$342$	4.74755	+	4.74755i	0.256718	+	0.256718i
$343$	4.19438	−	4.19438i	0.226475	−	0.226475i
$344$	5.95555	+	10.3153i	0.321102	+	0.556164i
$345$	9.62141	+	15.1846i	0.517999	+	0.817509i
$346$	6.32777	−	10.9600i	0.340183	−	0.589214i
$347$	15.8682	+	4.25187i	0.851850	+	0.228253i	0.658223	−	0.752823i	$-0.271308\pi$
$347$	15.8682	+	4.25187i	0.851850	+	0.228253i	0.193627	+	0.981075i	$0.437975\pi$
$348$	5.67781	+	1.52137i	0.304363	+	0.0815537i
$349$			15.6634i			0.838442i	0.907884	+	0.419221i	$0.137697\pi$
$349$			15.6634i			0.838442i	−0.907884	+	0.419221i	$0.862303\pi$
$350$	1.76453	−	1.22269i	0.0943179	−	0.0653558i
$351$	1.16180	−	2.01230i	0.0620125	−	0.107409i
$352$	−0.161069	−	0.601118i	−0.00858501	−	0.0320397i
$353$	4.25013	−	15.8617i	0.226211	−	0.844232i	−0.755704	−	0.654913i	$-0.772705\pi$
$353$	4.25013	−	15.8617i	0.226211	−	0.844232i	0.981916	−	0.189319i	$-0.0606281\pi$
$354$	−4.09061	+	7.08515i	−0.217414	+	0.376572i
$355$	−12.6123	−	6.60489i	−0.669393	−	0.350551i
$356$			11.3454i			0.601306i
$357$	−0.122601	−	0.122601i	−0.00648873	−	0.00648873i
$358$	−0.981716	+	3.66381i	−0.0518853	+	0.193639i
$359$	10.8405	+	6.25879i	0.572142	+	0.330326i	0.758004	−	0.652249i	$-0.226175\pi$
$359$	10.8405	+	6.25879i	0.572142	+	0.330326i	−0.185862	+	0.982576i	$0.559508\pi$
$360$	−0.667172	−	2.13422i	−0.0351631	−	0.112483i
$361$	13.0393	−	22.5847i	0.686278	−	1.18867i
$362$	−0.426970	−	1.59348i	−0.0224411	−	0.0837512i
$363$	−10.2511	+	2.74677i	−0.538043	+	0.144168i
$364$	−0.997641			−0.0522906
$365$	0.171537	+	0.548729i	0.00897865	+	0.0287218i
$366$	3.51008	+	6.07963i	0.183475	+	0.317787i
$367$	2.02339	+	7.55141i	0.105620	+	0.394180i	0.998415	−	0.0562838i	$-0.0179252\pi$
$367$	2.02339	+	7.55141i	0.105620	+	0.394180i	−0.892794	+	0.450464i	$0.851259\pi$
$368$	−5.68456	−	5.68456i	−0.296328	−	0.296328i
$369$	6.30413	−	3.63969i	0.328180	−	0.189475i
$370$	8.80500	−	5.57912i	0.457750	−	0.290045i
$371$		−	1.43447i		−	0.0744737i
$372$	3.88390	−	3.98940i	0.201371	−	0.206841i
$373$	−22.0521	+	22.0521i	−1.14181	+	1.14181i	−0.153696	+	0.988118i	$0.549118\pi$
$373$	−22.0521	+	22.0521i	−1.14181	+	1.14181i	−0.988118	+	0.153696i	$0.950882\pi$
$374$			0.251312i			0.0129950i
$375$	−11.0737	−	1.54076i	−0.571842	−	0.0795643i
$376$	13.1521			0.678266
$377$	−13.1930	+	3.53506i	−0.679475	+	0.182065i
$378$	0.111124	−	0.414720i	0.00571560	−	0.0213309i
$379$	21.6895	−	12.5224i	1.11411	−	0.643233i	0.174221	−	0.984707i	$-0.444259\pi$
$379$	21.6895	−	12.5224i	1.11411	−	0.643233i	0.939891	+	0.341474i	$0.110926\pi$
$380$	−12.6816	+	8.03548i	−0.650554	+	0.412211i
$381$	−1.79548	+	3.10987i	−0.0919853	+	0.159323i
$382$	−11.9814	+	3.21040i	−0.613020	+	0.164258i
$383$	−3.14359	+	0.842324i	−0.160630	+	0.0430407i	−0.338238	−	0.941061i	$-0.609831\pi$
$383$	−3.14359	+	0.842324i	−0.160630	+	0.0430407i	0.177608	+	0.984101i	$0.443164\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−0.439507	−	0.404719i	−0.0223993	−	0.0206264i
$386$	0.0266938	+	0.0462351i	0.00135868	+	0.00235330i
$387$	8.42241	−	8.42241i	0.428135	−	0.428135i
$388$	7.54995	−	7.54995i	0.383290	−	0.383290i
$389$	9.45710	+	16.3802i	0.479494	+	0.830508i	0.999723	−	0.0235188i	$-0.00748694\pi$
$389$	9.45710	+	16.3802i	0.479494	+	0.830508i	−0.520230	+	0.854026i	$0.674154\pi$
$390$	3.82209	+	3.51957i	0.193539	+	0.178220i
$391$	1.62323	+	2.81151i	0.0820901	+	0.142184i
$392$	6.58342	−	1.76402i	0.332513	−	0.0890966i
$393$	13.4037	−	3.59152i	0.676130	−	0.181168i
$394$	3.96819	−	6.87311i	0.199915	−	0.346262i
$395$	14.5051	−	9.19088i	0.729830	−	0.462443i
$396$	−0.538947	+	0.311161i	−0.0270831	+	0.0156365i
$397$	−0.214547	+	0.800699i	−0.0107678	+	0.0401860i	−0.971101	−	0.238670i	$-0.923289\pi$
$397$	−0.214547	+	0.800699i	−0.0107678	+	0.0401860i	0.960333	+	0.278856i	$0.0899552\pi$
$398$	−9.83987	+	2.63659i	−0.493228	+	0.132160i
$399$	−2.88268			−0.144315
$400$	4.98305	−	0.411368i	0.249152	−	0.0205684i
$401$		−	22.6116i		−	1.12917i	−0.825374	−	0.564586i	$-0.809036\pi$
$401$		−	22.6116i		−	1.12917i	0.825374	−	0.564586i	$-0.190964\pi$
$402$	−0.752406	+	0.752406i	−0.0375266	+	0.0375266i
$403$	−3.18068	+	12.5402i	−0.158441	+	0.624673i
$404$		−	3.15451i		−	0.156943i
$405$	−1.88882	+	1.19681i	−0.0938561	+	0.0594702i
$406$	−2.18564	+	1.26188i	−0.108472	+	0.0626261i
$407$	−2.05135	−	2.05135i	−0.101682	−	0.101682i
$408$	−0.104519	−	0.390069i	−0.00517444	−	0.0193113i
$409$	−1.33399	−	2.31054i	−0.0659616	−	0.114249i	0.831159	−	0.556036i	$-0.187678\pi$
$409$	−1.33399	−	2.31054i	−0.0659616	−	0.114249i	−0.897120	+	0.441787i	$0.854345\pi$
$410$	4.85660	+	15.5358i	0.239851	+	0.767258i
$411$	1.37849			0.0679961
$412$	17.3842	−	4.65809i	0.856459	−	0.229488i
$413$	−0.909131	−	3.39292i	−0.0447354	−	0.166955i
$414$	−4.01959	+	6.96213i	−0.197552	+	0.342170i
$415$	−5.94636	−	19.0218i	−0.291895	−	0.933744i
$416$	−2.01230	−	1.16180i	−0.0986613	−	0.0569621i
$417$	3.81124	−	14.2237i	0.186637	−	0.696539i
$418$	2.95451	+	2.95451i	0.144510	+	0.144510i
$419$			31.7777i			1.55244i	0.630461	+	0.776221i	$0.282866\pi$
$419$			31.7777i			1.55244i	−0.630461	+	0.776221i	$0.717134\pi$
$420$	0.850491	+	0.445389i	0.0414997	+	0.0217328i
$421$	9.64079	−	16.6983i	0.469863	−	0.813827i	−0.529543	−	0.848283i	$-0.677637\pi$
$421$	9.64079	−	16.6983i	0.469863	−	0.813827i	0.999406	+	0.0344560i	$0.0109698\pi$
$422$	5.42457	−	20.2448i	0.264064	−	0.985500i
$423$	−3.40400	−	12.7039i	−0.165508	−	0.617685i
$424$	1.67051	−	2.89341i	0.0811271	−	0.140516i
$425$	−1.98673	−	0.360360i	−0.0963705	−	0.0174800i
$426$		−	6.36703i		−	0.308484i
$427$	−2.91140	−	0.780107i	−0.140892	−	0.0377520i
$428$	1.12751	+	0.302116i	0.0545004	+	0.0146033i
$429$	0.723017	−	1.25230i	0.0349076	−	0.0604617i
$430$	14.2554	+	22.4979i	0.687455	+	1.08494i
$431$	−7.10718	−	12.3100i	−0.342341	−	0.592952i	0.642526	−	0.766264i	$-0.277886\pi$
$431$	−7.10718	−	12.3100i	−0.342341	−	0.592952i	−0.984867	+	0.173312i	$0.944553\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	1.60451	+	1.60451i	0.0771076	+	0.0771076i	0.744609	−	0.667501i	$-0.232636\pi$
$433$	1.60451	+	1.60451i	0.0771076	+	0.0771076i	−0.667501	+	0.744609i	$0.732636\pi$
$434$	0.0320300	+	2.39031i	0.00153749	+	0.114738i
$435$	12.8253	+	2.87628i	0.614925	+	0.137907i
$436$	16.6900			0.799305
$437$	52.1363	+	13.9699i	2.49402	+	0.668270i
$438$	−0.181804	+	0.181804i	−0.00868695	+	0.00868695i
$439$	0.903462	+	0.521614i	0.0431199	+	0.0248953i	0.521405	−	0.853309i	$-0.325408\pi$
$439$	0.903462	+	0.521614i	0.0431199	+	0.0248953i	−0.478285	+	0.878205i	$0.658741\pi$
$440$	−0.415196	−	1.32817i	−0.0197937	−	0.0633181i
$441$	−3.40783	−	5.90253i	−0.162278	−	0.281073i
$442$	0.663507	+	0.663507i	0.0315598	+	0.0315598i
$443$	1.17298	+	4.37762i	0.0557299	+	0.207987i	0.988176	−	0.153321i	$-0.0489969\pi$
$443$	1.17298	+	4.37762i	0.0557299	+	0.207987i	−0.932446	+	0.361308i	$0.882330\pi$
$444$	4.03710	+	2.33082i	0.191592	+	0.110616i
$445$	1.04449	+	25.3476i	0.0495136	+	1.20159i
$446$	−9.02710	+	5.21180i	−0.427445	+	0.246786i
$447$	5.66029	+	21.1245i	0.267722	+	0.999154i
$448$	−0.414720	−	0.111124i	−0.0195937	−	0.00525011i
$449$	18.9231			0.893036			0.446518	−	0.894775i	$-0.352664\pi$
$449$	18.9231			0.893036			0.446518	+	0.894775i	$0.352664\pi$
$450$	−1.68706	−	4.70679i	−0.0795287	−	0.221880i
$451$	3.92321	−	2.26506i	0.184737	−	0.106658i
$452$	3.39344	−	0.909270i	0.159614	−	0.0427684i
$453$	20.8996	+	5.60002i	0.981947	+	0.263112i
$454$	11.6641	+	6.73429i	0.547425	+	0.316056i
$455$	−2.22890	+	0.0918456i	−0.104493	+	0.00430579i
$456$	−5.81454	−	3.35703i	−0.272291	−	0.157207i
$457$	−1.64407	+	1.64407i	−0.0769063	+	0.0769063i	−0.744514	−	0.667607i	$-0.767319\pi$
$457$	−1.64407	+	1.64407i	−0.0769063	+	0.0769063i	0.667607	+	0.744514i	$0.267319\pi$
$458$	−6.37581	+	23.7948i	−0.297922	+	1.11186i
$459$	−0.349726	+	0.201914i	−0.0163238	+	0.00942456i
$460$	−13.2236	−	12.1769i	−0.616554	−	0.567753i
$461$		−	6.49151i		−	0.302340i	−0.988508	−	0.151170i	$-0.951696\pi$
$461$		−	6.49151i		−	0.302340i	0.988508	−	0.151170i	$-0.0483041\pi$
$462$	0.0691550	−	0.258090i	0.00321738	−	0.0120074i
$463$	6.98870	+	6.98870i	0.324792	+	0.324792i	0.850602	−	0.525810i	$-0.176238\pi$
$463$	6.98870	+	6.98870i	0.324792	+	0.324792i	−0.525810	+	0.850602i	$0.676238\pi$
$464$	−5.87810			−0.272884
$465$	8.31002	−	9.27057i	0.385368	−	0.429912i
$466$	3.73692			0.173110
$467$	−21.6041	−	21.6041i	−0.999721	−	0.999721i	0.000279334	−	1.00000i	$-0.499911\pi$
$467$	−21.6041	−	21.6041i	−0.999721	−	0.999721i	−1.00000		0.000279334i	$0.999911\pi$
$468$	−0.601394	+	2.24443i	−0.0277995	+	0.103749i
$469$		−	0.456855i		−	0.0210956i
$470$	29.3840	−	1.21081i	1.35538	−	0.0558507i
$471$	13.5336	−	7.81364i	0.623596	−	0.360033i
$472$	2.11746	−	7.90246i	0.0974639	−	0.363740i
$473$	5.24146	−	5.24146i	0.241003	−	0.241003i
$474$	6.65060	+	3.83972i	0.305472	+	0.176364i
$475$	−27.5932	+	19.1202i	−1.26606	+	0.877293i
$476$	0.150155	+	0.0866920i	0.00688234	+	0.00397352i
$477$	−3.22717	−	0.864719i	−0.147762	−	0.0395927i
$478$	−22.3041	+	5.97637i	−1.02017	+	0.273353i
$479$	−17.3936	+	10.0422i	−0.794733	+	0.458839i	−0.841626	−	0.540060i	$-0.818401\pi$
$479$	−17.3936	+	10.0422i	−0.794733	+	0.458839i	0.0468930	+	0.998900i	$0.485068\pi$
$480$	1.19681	+	1.88882i	0.0546269	+	0.0862124i
$481$	−10.8318			−0.493889
$482$	−11.2862	−	3.02413i	−0.514072	−	0.137745i
$483$	−0.893346	−	3.33401i	−0.0406486	−	0.151703i
$484$	9.19088	−	5.30636i	0.417767	−	0.241198i
$485$	16.1728	−	17.5629i	0.734369	−	0.797492i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−1.77575	−	6.62720i	−0.0804670	−	0.300307i	0.913950	−	0.405826i	$-0.133016\pi$
$487$	−1.77575	−	6.62720i	−0.0804670	−	0.300307i	−0.994417	+	0.105519i	$0.966350\pi$
$488$	−4.96400	−	4.96400i	−0.224710	−	0.224710i
$489$	8.65864	+	14.9972i	0.391557	+	0.678197i
$490$	14.5461	−	4.54722i	0.657126	−	0.205422i
$491$	−19.9433	−	11.5143i	−0.900029	−	0.519632i	−0.0228192	−	0.999740i	$-0.507264\pi$
$491$	−19.9433	−	11.5143i	−0.900029	−	0.519632i	−0.877210	+	0.480108i	$0.840598\pi$
$492$	−5.14730	+	5.14730i	−0.232058	+	0.232058i
$493$	2.29286	+	0.614371i	0.103265	+	0.0276699i
$494$	15.6008			0.701915
$495$	−1.17545	+	0.744805i	−0.0528328	+	0.0334765i
$496$	−2.71903	+	4.85869i	−0.122088	+	0.218162i
$497$	1.93301	+	1.93301i	0.0867072	+	0.0867072i
$498$	6.30229	−	6.30229i	0.282412	−	0.282412i
$499$	−11.5375	−	19.9836i	−0.516491	−	0.894589i	−0.999817	−	0.0191482i	$-0.993905\pi$
$499$	−11.5375	−	19.9836i	−0.516491	−	0.894589i	0.483326	−	0.875441i	$-0.339429\pi$
$500$	11.0951	−	1.37782i	0.496189	−	0.0616180i
$501$	−8.21851	+	14.2349i	−0.367176	+	0.635968i
$502$	2.18399	+	0.585197i	0.0974761	+	0.0261186i
$503$	17.9911	+	4.82070i	0.802183	+	0.214944i	0.636542	−	0.771242i	$-0.280364\pi$
$503$	17.9911	+	4.82070i	0.802183	+	0.214944i	0.165641	+	0.986186i	$0.447031\pi$
$504$			0.429350i			0.0191248i
$505$	−0.290413	−	7.04771i	−0.0129232	−	0.313619i
$506$	−2.50148	+	4.33270i	−0.111204	+	0.192612i
$507$	1.96724	+	7.34185i	0.0873683	+	0.326063i
$508$	0.929410	−	3.46861i	0.0412359	−	0.153894i
$509$	0.160598	−	0.278164i	0.00711837	−	0.0123294i	−0.862444	−	0.506152i	$-0.831067\pi$
$509$	0.160598	−	0.278164i	0.00711837	−	0.0123294i	0.869563	+	0.493823i	$0.164401\pi$
$510$	−0.269423	−	0.861859i	−0.0119303	−	0.0381637i
$511$		−	0.110390i		−	0.00488338i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−1.73773	+	6.48528i	−0.0767225	+	0.286332i
$514$	1.48915	+	0.859760i	0.0656835	+	0.0379224i
$515$	38.4105	−	12.0074i	1.69257	−	0.529110i
$516$	−5.95555	+	10.3153i	−0.262178	+	0.454106i
$517$	−2.11839	−	7.90594i	−0.0931666	−	0.347703i
$518$	−1.93328	+	0.518020i	−0.0849434	+	0.0227605i
$519$	12.6555			0.555517
$520$	−4.60279	−	2.41041i	−0.201846	−	0.105704i
$521$	−15.1003	−	26.1545i	−0.661556	−	1.14585i	−0.980207	−	0.197977i	$-0.936563\pi$
$521$	−15.1003	−	26.1545i	−0.661556	−	1.14585i	0.318651	−	0.947872i	$-0.396770\pi$
$522$	1.52137	+	5.67781i	0.0665883	+	0.248511i
$523$	−13.4673	−	13.4673i	−0.588882	−	0.588882i	0.348447	−	0.937329i	$-0.386709\pi$
$523$	−13.4673	−	13.4673i	−0.588882	−	0.588882i	−0.937329	+	0.348447i	$0.886709\pi$
$524$	−12.0175	+	6.93829i	−0.524986	+	0.303101i
$525$	1.94115	+	0.916778i	0.0847186	+	0.0400115i
$526$			26.0031i			1.13379i
$527$	1.56843	−	1.61104i	0.0683219	−	0.0701778i
$528$	0.440049	−	0.440049i	0.0191507	−	0.0191507i
$529$			41.6284i			1.80993i
$530$	3.46583	−	6.61816i	0.150546	−	0.287474i
$531$	−8.18123			−0.355035
$532$	2.78446	−	0.746093i	0.120721	−	0.0323472i
$533$	4.37778	−	16.3381i	0.189623	−	0.707682i
$534$	−9.82542	+	5.67271i	−0.425187	+	0.245482i
$535$	2.54687	+	0.571177i	0.110111	+	0.0246941i
$536$	0.532031	−	0.921505i	0.0229802	−	0.0398030i
$537$	−3.66381	+	0.981716i	−0.158105	+	0.0423642i
$538$	−8.40716	+	2.25269i	−0.362458	+	0.0971204i
$539$	−2.12077	−	3.67328i	−0.0913480	−	0.158219i
$540$	1.51470	−	1.64490i	0.0651823	−	0.0707851i
$541$	−4.88972	−	8.46925i	−0.210226	−	0.364121i	0.741559	−	0.670887i	$-0.234087\pi$
$541$	−4.88972	−	8.46925i	−0.210226	−	0.364121i	−0.951785	+	0.306766i	$0.900753\pi$
$542$	20.7342	−	20.7342i	0.890610	−	0.890610i
$543$	1.16650	−	1.16650i	0.0500595	−	0.0500595i
$544$	0.201914	+	0.349726i	0.00865701	+	0.0149944i
$545$	37.2883	−	1.53652i	1.59725	−	0.0658175i
$546$	−0.498821	−	0.863983i	−0.0213476	−	0.0369750i
$547$	1.65839	−	0.444364i	0.0709075	−	0.0189996i	−0.223191	−	0.974775i	$-0.571647\pi$
$547$	1.65839	−	0.444364i	0.0709075	−	0.0189996i	0.294098	+	0.955775i	$0.404981\pi$
$548$	−1.33152	+	0.356781i	−0.0568799	+	0.0152409i
$549$	−3.51008	+	6.07963i	−0.149806	+	0.259472i
$550$	−1.04990	−	2.92914i	−0.0447677	−	0.124899i
$551$	34.1785	−	19.7330i	1.45605	−	0.840652i
$552$	2.08069	−	7.76525i	0.0885602	−	0.330511i
$553$	−3.18482	+	0.853371i	−0.135432	+	0.0362890i
$554$	−19.3836			−0.823530
$555$	9.23416	+	4.83579i	0.391968	+	0.205268i
$556$			14.7255i			0.624500i
$557$	3.73382	−	3.73382i	0.158207	−	0.158207i	−0.623565	−	0.781772i	$-0.714316\pi$
$557$	3.73382	−	3.73382i	0.158207	−	0.158207i	0.781772	+	0.623565i	$0.214316\pi$
$558$	5.39687	+	1.36886i	0.228468	+	0.0579483i
$559$		−	27.6767i		−	1.17060i
$560$	−0.936787	−	0.210090i	−0.0395865	−	0.00887791i
$561$	−0.217643	+	0.125656i	−0.00918888	+	0.00530520i
$562$	10.6860	+	10.6860i	0.450763	+	0.450763i
$563$	4.72825	+	17.6461i	0.199272	+	0.743692i	0.991120	+	0.132974i	$0.0424526\pi$
$563$	4.72825	+	17.6461i	0.199272	+	0.743692i	−0.791848	+	0.610719i	$0.790881\pi$
$564$	6.57603	+	11.3900i	0.276901	+	0.479606i
$565$	7.49782	−	2.34387i	0.315436	−	0.0986075i
$566$	−4.04789			−0.170145
$567$	0.414720	−	0.111124i	0.0174166	−	0.00466677i
$568$	1.64791	+	6.15008i	0.0691447	+	0.258052i
$569$	3.35483	−	5.81074i	0.140642	−	0.243599i	−0.787097	−	0.616830i	$-0.788417\pi$
$569$	3.35483	−	5.81074i	0.140642	−	0.243599i	0.927739	+	0.373231i	$0.121750\pi$
$570$	−13.2997	−	6.96488i	−0.557065	−	0.291727i
$571$	18.8944	+	10.9087i	0.790706	+	0.456514i	0.840211	−	0.542260i	$-0.182431\pi$
$571$	18.8944	+	10.9087i	0.790706	+	0.456514i	−0.0495053	+	0.998774i	$0.515764\pi$
$572$	−0.374261	+	1.39676i	−0.0156487	+	0.0584016i
$573$	−8.77097	−	8.77097i	−0.366413	−	0.366413i
$574$		−	3.12540i		−	0.130452i
$575$	−30.6649	−	25.9880i	−1.27881	−	1.08377i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−4.27182	+	15.9427i	−0.177838	+	0.663702i	0.818212	+	0.574916i	$0.194965\pi$
$577$	−4.27182	+	15.9427i	−0.177838	+	0.663702i	−0.996051	+	0.0887856i	$0.971701\pi$
$578$	4.35772	+	16.2632i	0.181257	+	0.676461i
$579$	−0.0266938	+	0.0462351i	−0.00110936	+	0.00192146i
$580$	−13.1327	+	0.541154i	−0.545305	+	0.0224702i
$581$			3.82670i			0.158758i
$582$	10.3134	+	2.76347i	0.427505	+	0.114550i
$583$	−2.00834	−	0.538134i	−0.0831771	−	0.0222872i
$584$	0.128555	−	0.222664i	0.00531965	−	0.00921391i
$585$	−1.13699	+	5.06982i	−0.0470087	+	0.209611i
$586$	−0.786009	−	1.36141i	−0.0324698	−	0.0562393i
$587$	8.09190	−	8.09190i	0.333989	−	0.333989i	−0.520110	−	0.854099i	$-0.674109\pi$
$587$	8.09190	−	8.09190i	0.333989	−	0.333989i	0.854099	+	0.520110i	$0.174109\pi$
$588$	4.81940	+	4.81940i	0.198749	+	0.198749i
$589$	−0.500875	−	37.3789i	−0.0206382	−	1.54017i
$590$	4.00324	−	17.8504i	0.164811	−	0.734889i
$591$	7.93638			0.326459
$592$	−4.50280	−	1.20652i	−0.185064	−	0.0495878i
$593$	−1.70250	+	1.70250i	−0.0699133	+	0.0699133i	−0.741199	−	0.671286i	$-0.765742\pi$
$593$	−1.70250	+	1.70250i	−0.0699133	+	0.0699133i	0.671286	+	0.741199i	$0.265742\pi$
$594$	−0.538947	−	0.311161i	−0.0221133	−	0.0127671i
$595$	0.343453	+	0.179861i	0.0140802	+	0.00737359i
$596$	−10.9348	−	18.9397i	−0.447908	−	0.775800i
$597$	−7.20329	−	7.20329i	−0.294811	−	0.294811i
$598$	4.83472	+	18.0434i	0.197706	+	0.737850i
$599$	−19.4275	−	11.2165i	−0.793785	−	0.458292i	0.0475086	−	0.998871i	$-0.484872\pi$
$599$	−19.4275	−	11.2165i	−0.793785	−	0.458292i	−0.841293	+	0.540579i	$0.818205\pi$
$600$	2.84778	+	4.10976i	0.116260	+	0.167780i
$601$	−18.6026	+	10.7402i	−0.758815	+	0.438102i	−0.828870	−	0.559441i	$-0.811016\pi$
$601$	−18.6026	+	10.7402i	−0.758815	+	0.438102i	0.0700549	+	0.997543i	$0.477683\pi$
$602$	−1.32361	−	4.93977i	−0.0539462	−	0.201330i
$603$	−1.02781	−	0.275400i	−0.0418555	−	0.0112151i
$604$	−21.6368			−0.880390
$605$	20.0455	−	12.7015i	0.814965	−	0.516387i
$606$	2.73188	−	1.57725i	0.110975	−	0.0640716i
$607$	−14.8612	+	3.98205i	−0.603199	+	0.161627i	−0.547478	−	0.836820i	$-0.684412\pi$
$607$	−14.8612	+	3.98205i	−0.603199	+	0.161627i	−0.0557203	+	0.998446i	$0.517746\pi$
$608$	6.48528	+	1.73773i	0.263013	+	0.0704741i
$609$	−2.18564	−	1.26188i	−0.0885667	−	0.0511340i
$610$	−11.5474	−	10.6334i	−0.467541	−	0.430535i
$611$	−26.4659	−	15.2801i	−1.07070	−	0.618167i
$612$	0.285550	−	0.285550i	0.0115427	−	0.0115427i
$613$	11.8033	−	44.0506i	0.476732	−	1.77919i	−0.137980	−	0.990435i	$-0.544061\pi$
$613$	11.8033	−	44.0506i	0.476732	−	1.77919i	0.614711	−	0.788752i	$-0.289272\pi$
$614$	22.1648	−	12.7968i	0.894497	−	0.516438i
$615$	−11.0261	+	11.9738i	−0.444615	+	0.482832i
$616$			0.267194i			0.0107656i
$617$	−2.74081	+	10.2289i	−0.110341	+	0.411798i	−0.998896	−	0.0469715i	$-0.985043\pi$
$617$	−2.74081	+	10.2289i	−0.110341	+	0.411798i	0.888555	+	0.458770i	$0.151710\pi$
$618$	12.7261	+	12.7261i	0.511920	+	0.511920i
$619$	20.7399			0.833608			0.416804	−	0.908996i	$-0.363150\pi$
$619$	20.7399			0.833608			0.416804	+	0.908996i	$0.363150\pi$
$620$	−5.62747	+	11.1055i	−0.226005	+	0.446007i
$621$	−8.03918			−0.322601
$622$	16.2894	+	16.2894i	0.653147	+	0.653147i
$623$	1.26075	−	4.70517i	0.0505108	−	0.188509i
$624$		−	2.32361i		−	0.0930188i
$625$	24.6616	−	4.09973i	0.986462	−	0.163989i
$626$	2.98471	−	1.72323i	0.119293	−	0.0688739i
$627$	−1.08143	+	4.03594i	−0.0431880	+	0.161180i
$628$	−11.0501	+	11.0501i	−0.440949	+	0.440949i
$629$	1.63030	+	0.941253i	0.0650043	+	0.0375302i
$630$	0.0395271	+	0.959242i	0.00157480	+	0.0382171i
$631$	34.2678	+	19.7845i	1.36418	+	0.787609i	0.990177	−	0.139819i	$-0.0446520\pi$
$631$	34.2678	+	19.7845i	1.36418	+	0.787609i	0.374002	+	0.927428i	$0.377985\pi$
$632$	−7.41778	−	1.98759i	−0.295063	−	0.0790620i
$633$	20.2448	−	5.42457i	0.804658	−	0.215607i
$634$	−29.4935	+	17.0281i	−1.17134	+	0.676272i
$635$	1.75713	−	7.83503i	0.0697297	−	0.310924i
$636$	3.34102			0.132480
$637$	−15.2973	−	4.09890i	−0.606101	−	0.162404i
$638$	0.946780	+	3.53343i	0.0374834	+	0.139890i
$639$	5.51401	−	3.18352i	0.218131	−	0.125938i
$640$	−1.64490	−	1.51470i	−0.0650202	−	0.0598738i
$641$	−32.7048	−	18.8821i	−1.29176	−	0.745799i	−0.312796	−	0.949820i	$-0.601266\pi$
$641$	−32.7048	−	18.8821i	−1.29176	−	0.745799i	−0.978966	+	0.204021i	$0.934599\pi$
$642$	0.302116	+	1.12751i	0.0119236	+	0.0444994i
$643$	20.6592	+	20.6592i	0.814720	+	0.814720i	0.985337	−	0.170617i	$-0.0545762\pi$
$643$	20.6592	+	20.6592i	0.814720	+	0.814720i	−0.170617	+	0.985337i	$0.554576\pi$
$644$	1.72581	+	2.98919i	0.0680065	+	0.117791i
$645$	−12.3561	+	23.5945i	−0.486519	+	0.929031i
$646$	−2.34808	−	1.35567i	−0.0923840	−	0.0533379i
$647$	−0.580039	+	0.580039i	−0.0228037	+	0.0228037i	−0.718417	−	0.695613i	$-0.755133\pi$
$647$	−0.580039	+	0.580039i	−0.0228037	+	0.0228037i	0.695613	+	0.718417i	$0.255133\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−5.09137			−0.199854
$650$	−10.5053	−	4.96153i	−0.412053	−	0.194607i
$651$	−2.05405	+	1.22289i	−0.0805046	+	0.0479289i
$652$	−12.2452	−	12.2452i	−0.479557	−	0.479557i
$653$	−16.8240	+	16.8240i	−0.658374	+	0.658374i	−0.954995	−	0.296621i	$-0.904140\pi$
$653$	−16.8240	+	16.8240i	−0.658374	+	0.658374i	0.296621	+	0.954995i	$0.404140\pi$
$654$	8.34499	+	14.4539i	0.326315	+	0.565194i
$655$	−26.2103	+	16.6077i	−1.02412	+	0.648916i
$656$	3.63969	−	6.30413i	0.142106	−	0.246135i
$657$	−0.248350	−	0.0665451i	−0.00968904	−	0.00259617i
$658$	−5.45443	−	1.46151i	−0.212636	−	0.0569755i
$659$			34.8422i			1.35726i	0.734481	+	0.678629i	$0.237426\pi$
$659$			34.8422i			1.35726i	−0.734481	+	0.678629i	$0.762574\pi$
$660$	0.942632	−	1.02366i	0.0366919	−	0.0398458i
$661$	15.1683	−	26.2722i	0.589978	−	1.02187i	−0.404257	−	0.914646i	$-0.632470\pi$
$661$	15.1683	−	26.2722i	0.589978	−	1.02187i	0.994235	−	0.107226i	$-0.0341969\pi$
$662$	2.71918	+	10.1481i	0.105684	+	0.394418i
$663$	−0.242860	+	0.906367i	−0.00943191	+	0.0352004i
$664$	−4.45639	+	7.71870i	−0.172942	+	0.299543i
$665$	6.15226	−	1.92324i	0.238575	−	0.0745802i
$666$			4.66164i			0.180635i
$667$	33.4144	+	33.4144i	1.29381	+	1.29381i
$668$	4.25421	−	15.8769i	0.164601	−	0.614297i
$669$	−9.02710	−	5.21180i	−0.349008	−	0.201500i
$670$	1.10381	−	2.10778i	0.0426440	−	0.0814307i
$671$	−2.18440	+	3.78349i	−0.0843278	+	0.146060i
$672$	−0.111124	−	0.414720i	−0.00428670	−	0.0159982i
$673$	−20.4249	+	5.47284i	−0.787323	+	0.210962i	−0.630011	−	0.776586i	$-0.716950\pi$
$673$	−20.4249	+	5.47284i	−0.787323	+	0.210962i	−0.157312	+	0.987549i	$0.550283\pi$
$674$	−7.57081			−0.291617
$675$	3.23267	−	3.81443i	0.124425	−	0.146817i
$676$	−3.80042	−	6.58252i	−0.146170	−	0.253174i
$677$	6.21585	+	23.1979i	0.238895	+	0.891567i	0.976354	+	0.216176i	$0.0693585\pi$
$677$	6.21585	+	23.1979i	0.238895	+	0.891567i	−0.737460	+	0.675391i	$0.763975\pi$
$678$	2.48417	+	2.48417i	0.0954040	+	0.0954040i
$679$	−3.97010	+	2.29214i	−0.152358	+	0.0879641i
$680$	0.483308	+	0.762760i	0.0185340	+	0.0292505i
$681$			13.4686i			0.516117i
$682$	3.35860	+	0.851870i	0.128607	+	0.0326198i
$683$	11.4417	−	11.4417i	0.437806	−	0.437806i	−0.453467	−	0.891273i	$-0.649813\pi$
$683$	11.4417	−	11.4417i	0.437806	−	0.437806i	0.891273	+	0.453467i	$0.149813\pi$
$684$		−	6.71406i		−	0.256718i
$685$	−2.94201	+	0.919693i	−0.112408	+	0.0351397i
$686$	−5.93175			−0.226475
$687$	−23.7948	+	6.37581i	−0.907830	+	0.243252i
$688$	3.08282	−	11.5052i	0.117531	−	0.438633i
$689$	−6.72314	+	3.88161i	−0.256131	+	0.147877i
$690$	3.93374	−	17.5405i	0.149755	−	0.667754i
$691$	−2.81874	+	4.88220i	−0.107230	+	0.185728i	−0.914647	−	0.404253i	$-0.867531\pi$
$691$	−2.81874	+	4.88220i	−0.107230	+	0.185728i	0.807417	+	0.589981i	$0.200865\pi$
$692$	−12.2243	+	3.27550i	−0.464699	+	0.124516i
$693$	0.258090	−	0.0691550i	0.00980402	−	0.00262698i
$694$	−8.21399	−	14.2270i	−0.311799	−	0.540051i
$695$	1.35567	+	32.8993i	0.0514235	+	1.24794i
$696$	−2.93905	−	5.09059i	−0.111404	−	0.192958i
$697$	−2.07863	+	2.07863i	−0.0787337	+	0.0787337i
$698$	11.0757	−	11.0757i	0.419221	−	0.419221i
$699$	1.86846	+	3.23627i	0.0706717	+	0.122407i
$700$	−2.11228	−	0.383133i	−0.0798368	−	0.0144811i
$701$	−10.6816	−	18.5011i	−0.403440	−	0.698778i	0.590699	−	0.806892i	$-0.298852\pi$
$701$	−10.6816	−	18.5011i	−0.403440	−	0.698778i	−0.994138	+	0.108114i	$0.965519\pi$
$702$	−2.24443	+	0.601394i	−0.0847107	+	0.0226982i
$703$	30.2321	−	8.10066i	1.14022	−	0.305522i
$704$	−0.311161	+	0.538947i	−0.0117273	+	0.0203123i
$705$	15.7406	+	24.8418i	0.592824	+	0.935598i
$706$	−14.2212	+	8.21061i	−0.535222	+	0.309010i
$707$	−0.350541	+	1.30824i	−0.0131835	+	0.0492014i
$708$	7.90246	−	2.11746i	0.296993	−	0.0795789i
$709$	−20.4045			−0.766307			−0.383154	−	0.923685i	$-0.625162\pi$
$709$	−20.4045			−0.766307			−0.383154	+	0.923685i	$0.625162\pi$
$710$	4.24791	+	13.5886i	0.159421	+	0.509972i
$711$			7.67945i			0.288002i
$712$	8.02242	−	8.02242i	0.300653	−	0.300653i
$713$	43.0760	−	12.1631i	1.61321	−	0.455510i
$714$			0.173384i			0.00648873i
$715$	−0.707574	+	3.15506i	−0.0264618	+	0.117993i
$716$	3.28489	−	1.89653i	0.122762	−	0.0708767i
$717$	−16.3277	−	16.3277i	−0.609770	−	0.609770i
$718$	−3.23979	−	12.0911i	−0.120908	−	0.451234i
$719$	17.7509	+	30.7455i	0.661998	+	1.14661i	0.980090	+	0.198555i	$0.0636248\pi$
$719$	17.7509	+	30.7455i	0.661998	+	1.14661i	−0.318091	+	0.948060i	$0.603042\pi$
$720$	−1.03736	+	1.98088i	−0.0386600	+	0.0738231i
$721$	−7.72722			−0.287777
$722$	−25.1899	+	6.74963i	−0.937473	+	0.251195i
$723$	−3.02413	−	11.2862i	−0.112469	−	0.419738i
$724$	−0.824843	+	1.42867i	−0.0306551	+	0.0530961i
$725$	−29.2909	+	2.41806i	−1.08784	+	0.0898047i
$726$	9.19088	+	5.30636i	0.341106	+	0.196937i
$727$	−7.29885	+	27.2397i	−0.270699	+	1.01026i	0.687969	+	0.725740i	$0.258502\pi$
$727$	−7.29885	+	27.2397i	−0.270699	+	1.01026i	−0.958669	+	0.284524i	$0.908164\pi$
$728$	0.705439	+	0.705439i	0.0261453	+	0.0261453i
$729$		−	1.00000i		−	0.0370370i
$730$	0.266715	−	0.509305i	0.00987158	−	0.0188502i
$731$	−2.40502	+	4.16562i	−0.0889530	+	0.154071i
$732$	1.81695	−	6.78094i	0.0671564	−	0.250631i
$733$	−5.67625	−	21.1841i	−0.209657	−	0.782451i	−0.987979	−	0.154586i	$-0.950596\pi$
$733$	−5.67625	−	21.1841i	−0.209657	−	0.782451i	0.778322	−	0.627865i	$-0.216071\pi$
$734$	3.90890	−	6.77041i	0.144280	−	0.249900i
$735$	11.2111	+	10.3237i	0.413526	+	0.380795i
$736$			8.03918i			0.296328i
$737$	−0.639627	−	0.171387i	−0.0235610	−	0.00631314i
$738$	−7.03135	−	1.88404i	−0.258827	−	0.0693526i
$739$	14.3159	−	24.7959i	0.526620	−	0.912132i	−0.472899	−	0.881116i	$-0.656793\pi$
$739$	14.3159	−	24.7959i	0.526620	−	0.912132i	0.999519	−	0.0310154i	$-0.00987409\pi$
$740$	−10.1711	−	2.28104i	−0.373897	−	0.0838526i
$741$	7.80042	+	13.5107i	0.286556	+	0.496329i
$742$	−1.01432	+	1.01432i	−0.0372369	+	0.0372369i
$743$	−27.7759	−	27.7759i	−1.01900	−	1.01900i	−0.999816	−	0.0191842i	$-0.993893\pi$
$743$	−27.7759	−	27.7759i	−1.01900	−	1.01900i	−0.0191842	−	0.999816i	$-0.506107\pi$
$744$	−5.56726	+	0.0746010i	−0.204106	+	0.00273501i
$745$	−26.1739	−	41.3078i	−0.958939	−	1.51340i
$746$	31.1864			1.14181
$747$	8.60909	+	2.30680i	0.314990	+	0.0844013i
$748$	0.177704	−	0.177704i	0.00649752	−	0.00649752i
$749$	−0.434030	−	0.250587i	−0.0158591	−	0.00915626i
$750$	6.74079	+	8.91974i	0.246139	+	0.325703i
$751$	−25.0733	−	43.4282i	−0.914937	−	1.58472i	−0.806993	−	0.590561i	$-0.798907\pi$
$751$	−25.0733	−	43.4282i	−0.914937	−	1.58472i	−0.107944	−	0.994157i	$-0.534427\pi$
$752$	−9.29991	−	9.29991i	−0.339133	−	0.339133i
$753$	0.585197	+	2.18399i	0.0213258	+	0.0795889i
$754$	11.8285	+	6.82920i	0.430770	+	0.248705i
$755$	−48.3404	+	1.99195i	−1.75929	+	0.0724943i
$756$	−0.371828	+	0.214675i	−0.0135233	+	0.00780765i
$757$	−9.83500	−	36.7047i	−0.357459	−	1.33406i	−0.877361	−	0.479830i	$-0.840698\pi$
$757$	−9.83500	−	36.7047i	−0.357459	−	1.33406i	0.519902	−	0.854226i	$-0.325968\pi$
$758$	−24.1914	−	6.48208i	−0.878673	−	0.235440i
$759$	−5.00297			−0.181596
$760$	14.6492	+	3.28532i	0.531383	+	0.119171i
$761$	−23.1409	+	13.3604i	−0.838858	+	0.484315i	−0.856876	−	0.515523i	$-0.827598\pi$
$761$	−23.1409	+	13.3604i	−0.838858	+	0.484315i	0.0180177	+	0.999838i	$0.494264\pi$
$762$	3.46861	−	0.929410i	0.125654	−	0.0336690i
$763$	−6.92167	−	1.85466i	−0.250581	−	0.0671430i
$764$	10.7422	+	6.20202i	0.388639	+	0.224381i
$765$	0.611680	−	0.664257i	0.0221153	−	0.0240163i
$766$	2.81847	+	1.62724i	0.101835	+	0.0587947i
$767$	−13.4421	+	13.4421i	−0.485365	+	0.485365i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−24.8223	+	14.3311i	−0.895114	+	0.516794i	−0.875612	−	0.483015i	$-0.839541\pi$
$769$	−24.8223	+	14.3311i	−0.895114	+	0.516794i	−0.0195023	+	0.999810i	$0.506208\pi$
$770$	0.0245986	+	0.596958i	0.000886474	+	0.0215129i
$771$			1.71952i			0.0619270i
$772$	0.0138177	−	0.0515685i	0.000497312	−	0.00185599i
$773$	18.3838	+	18.3838i	0.661220	+	0.661220i	0.955668	−	0.294448i	$-0.0951357\pi$
$773$	18.3838	+	18.3838i	0.661220	+	0.661220i	−0.294448	+	0.955668i	$0.595136\pi$
$774$	−11.9111			−0.428135
$775$	−11.5503	+	25.3296i	−0.414900	+	0.909867i
$776$	−10.6772			−0.383290
$777$	−1.41526	−	1.41526i	−0.0507721	−	0.0507721i
$778$	4.89535	−	18.2697i	0.175507	−	0.655001i
$779$			48.8742i			1.75110i
$780$	−0.213918	−	5.19134i	−0.00765949	−	0.185880i
$781$	3.43150	−	1.98118i	0.122789	−	0.0708920i
$782$	0.840244	−	3.13583i	0.0300471	−	0.112137i
$783$	−4.15645	+	4.15645i	−0.148539	+	0.148539i
$784$	−5.90253	−	3.40783i	−0.210805	−	0.121708i
$785$	−23.6706	+	25.7052i	−0.844841	+	0.917459i
$786$	−12.0175	−	6.93829i	−0.428649	−	0.247481i
$787$	−14.2959	−	3.83056i	−0.509592	−	0.136545i	−0.00514395	−	0.999987i	$-0.501637\pi$
$787$	−14.2959	−	3.83056i	−0.509592	−	0.136545i	−0.504448	+	0.863442i	$0.668304\pi$
$788$	−7.66596	+	2.05409i	−0.273088	+	0.0731738i
$789$	−22.5193	+	13.0015i	−0.801708	+	0.462867i
$790$	−16.7556	−	3.75771i	−0.596137	−	0.133693i
$791$	−1.50837			−0.0536315
$792$	0.601118	+	0.161069i	0.0213598	+	0.00572334i
$793$	4.22188	+	15.7563i	0.149923	+	0.559521i
$794$	0.717887	−	0.414473i	0.0254769	−	0.0147091i
$795$	7.46441	−	0.307583i	0.264735	−	0.0109089i
$796$	8.82219	+	5.09349i	0.312694	+	0.180534i
$797$	−1.11960	−	4.17840i	−0.0396582	−	0.148006i	0.943258	−	0.332062i	$-0.107744\pi$
$797$	−1.11960	−	4.17840i	−0.0396582	−	0.148006i	−0.982916	+	0.184055i	$0.941078\pi$
$798$	2.03836	+	2.03836i	0.0721573	+	0.0721573i
$799$	2.65559	+	4.59962i	0.0939481	+	0.162723i
$800$	−3.81443	−	3.23267i	−0.134860	−	0.114292i
$801$	−9.82542	−	5.67271i	−0.347164	−	0.200435i
$802$	−15.9888	+	15.9888i	−0.564586	+	0.564586i
$803$	−0.154554	−	0.0414125i	−0.00545408	−	0.00146142i
$804$	1.06406			0.0375266
$805$	4.13095	+	6.51949i	0.145597	+	0.229782i
$806$	11.1164	−	6.61819i	0.391557	−	0.233116i
$807$	−6.15447	−	6.15447i	−0.216648	−	0.216648i
$808$	−2.23057	+	2.23057i	−0.0784713	+	0.0784713i
$809$	−2.24134	−	3.88211i	−0.0788012	−	0.136488i	0.823932	−	0.566689i	$-0.191776\pi$
$809$	−2.24134	−	3.88211i	−0.0788012	−	0.136488i	−0.902733	+	0.430201i	$0.858443\pi$
$810$	2.18187	+	0.489320i	0.0766632	+	0.0171930i
$811$	−8.65543	+	14.9916i	−0.303933	+	0.526428i	−0.977023	−	0.213133i	$-0.931633\pi$
$811$	−8.65543	+	14.9916i	−0.303933	+	0.526428i	0.673090	+	0.739561i	$0.264967\pi$
$812$	2.43777	+	0.653198i	0.0855489	+	0.0229228i
$813$	28.3234	+	7.58924i	0.993347	+	0.266166i
$814$			2.90105i			0.101682i
$815$	−28.4851	−	26.2305i	−0.997790	−	0.918813i
$816$	−0.201914	+	0.349726i	−0.00706842	+	0.0122429i
$817$	20.6982	+	77.2468i	0.724139	+	2.70252i
$818$	−0.690525	+	2.57707i	−0.0241436	+	0.0901052i
$819$	0.498821	−	0.863983i	0.0174302	−	0.0301900i
$820$	7.55132	−	14.4196i	0.263704	−	0.503554i
$821$		−	11.9243i		−	0.416162i	−0.978112	−	0.208081i	$-0.933278\pi$
$821$		−	11.9243i		−	0.416162i	0.978112	−	0.208081i	$-0.0667218\pi$
$822$	−0.974743	−	0.974743i	−0.0339981	−	0.0339981i
$823$	−12.9138	+	48.1951i	−0.450148	+	1.67998i	0.251826	+	0.967773i	$0.418969\pi$
$823$	−12.9138	+	48.1951i	−0.450148	+	1.67998i	−0.701974	+	0.712203i	$0.747698\pi$
$824$	−15.5863	−	8.99874i	−0.542973	−	0.313486i
$825$	2.01176	−	2.37381i	0.0700406	−	0.0826453i
$826$	−1.75631	+	3.04201i	−0.0611097	+	0.105845i
$827$	2.17508	+	8.11752i	0.0756351	+	0.282274i	0.993377	−	0.114904i	$-0.0366561\pi$
$827$	2.17508	+	8.11752i	0.0756351	+	0.282274i	−0.917741	+	0.397178i	$0.869989\pi$
$828$	7.76525	−	2.08069i	0.269861	−	0.0723091i
$829$	49.1321			1.70643			0.853215	−	0.521560i	$-0.174650\pi$
$829$	49.1321			1.70643			0.853215	+	0.521560i	$0.174650\pi$
$830$	−9.24574	+	17.6552i	−0.320924	+	0.612820i
$831$	−9.69179	−	16.7867i	−0.336205	−	0.582323i
$832$	0.601394	+	2.24443i	0.0208496	+	0.0778117i
$833$	1.94621	+	1.94621i	0.0674323	+	0.0674323i
$834$	−12.7527	+	7.36275i	−0.441588	+	0.254951i
$835$	8.04297	−	35.8635i	0.278339	−	1.24111i
$836$		−	4.17831i		−	0.144510i
$837$	1.51297	+	5.35826i	0.0522960	+	0.185208i
$838$	22.4702	−	22.4702i	0.776221	−	0.776221i
$839$		−	55.3213i		−	1.90990i	−0.296760	−	0.954952i	$-0.595906\pi$
$839$		−	55.3213i		−	1.90990i	0.296760	−	0.954952i	$-0.404094\pi$
$840$	−0.286450	−	0.916326i	−0.00988348	−	0.0316163i
$841$	5.55210			0.191452
$842$	−18.6246	+	4.99044i	−0.641845	+	0.171982i
$843$	−3.91136	+	14.5974i	−0.134714	+	0.502760i
$844$	−18.1510	+	10.4795i	−0.624782	+	0.360718i
$845$	−9.09680	−	14.3566i	−0.312940	−	0.493883i
$846$	−6.57603	+	11.3900i	−0.226089	+	0.391597i
$847$	−4.40131	+	1.17933i	−0.151231	+	0.0405221i
$848$	−3.22717	+	0.864719i	−0.110822	+	0.0296946i
$849$	−2.02394	−	3.50558i	−0.0694616	−	0.120311i
$850$	1.15002	+	1.65964i	0.0394452	+	0.0569252i
$851$	18.7379	+	32.4550i	0.642327	+	1.11254i
$852$	−4.50217	+	4.50217i	−0.154242	+	0.154242i
$853$	−18.9739	+	18.9739i	−0.649653	+	0.649653i	−0.952909	−	0.303256i	$-0.901926\pi$
$853$	−18.9739	+	18.9739i	−0.649653	+	0.649653i	0.303256	+	0.952909i	$0.401926\pi$
$854$	1.50705	+	2.61029i	0.0515702	+	0.0893222i
$855$	−0.618115	−	15.0004i	−0.0211391	−	0.513001i
$856$	−0.583643	−	1.01090i	−0.0199485	−	0.0345518i
$857$	−26.2901	+	7.04441i	−0.898052	+	0.240632i	−0.678180	−	0.734896i	$-0.737231\pi$
$857$	−26.2901	+	7.04441i	−0.898052	+	0.240632i	−0.219873	+	0.975529i	$0.570564\pi$
$858$	−1.39676	+	0.374261i	−0.0476847	+	0.0127771i
$859$	15.5994	−	27.0190i	0.532246	−	0.921878i	−0.467045	−	0.884234i	$-0.654681\pi$
$859$	15.5994	−	27.0190i	0.532246	−	0.921878i	0.999291	−	0.0376440i	$-0.0119853\pi$
$860$	5.82834	−	25.9885i	0.198745	−	0.886200i
$861$	2.70668	−	1.56270i	0.0922434	−	0.0532568i
$862$	−3.67895	+	13.7300i	−0.125306	+	0.467647i
$863$	37.2851	−	9.99051i	1.26920	−	0.340081i	0.439475	−	0.898255i	$-0.355164\pi$
$863$	37.2851	−	9.99051i	1.26920	−	0.340081i	0.829724	+	0.558174i	$0.188498\pi$
$864$	−1.00000			−0.0340207
$865$	−27.0097	+	8.44343i	−0.918357	+	0.287085i
$866$		−	2.26911i		−	0.0771076i
$867$	−11.9055	+	11.9055i	−0.404332	+	0.404332i
$868$	1.66755	−	1.71285i	0.0566004	−	0.0581379i
$869$			4.77910i			0.162120i
$870$	−7.03500	−	11.1027i	−0.238509	−	0.376416i
$871$	−2.14122	+	1.23623i	−0.0725524	+	0.0418881i
$872$	−11.8016	−	11.8016i	−0.399652	−	0.399652i
$873$	2.76347	+	10.3134i	0.0935294	+	0.349056i
$874$	−26.9878	−	46.7442i	−0.912874	−	1.58114i
$875$	−4.75448	−	0.661523i	−0.160731	−	0.0223636i
$876$	0.257110			0.00868695
$877$	7.44417	−	1.99466i	0.251372	−	0.0673548i	−0.130933	−	0.991391i	$-0.541797\pi$
$877$	7.44417	−	1.99466i	0.251372	−	0.0673548i	0.382305	+	0.924036i	$0.375131\pi$
$878$	−0.270007	−	1.00768i	−0.00911231	−	0.0340076i
$879$	0.786009	−	1.36141i	0.0265114	−	0.0459192i
$880$	−0.645571	+	1.23275i	−0.0217622	+	0.0415559i
$881$	19.4579	+	11.2340i	0.655554	+	0.378484i	0.790581	−	0.612358i	$-0.209779\pi$
$881$	19.4579	+	11.2340i	0.655554	+	0.378484i	−0.135027	+	0.990842i	$0.543112\pi$
$882$	−1.76402	+	6.58342i	−0.0593977	+	0.221675i
$883$	38.6810	+	38.6810i	1.30172	+	1.30172i	0.927232	+	0.374487i	$0.122181\pi$
$883$	38.6810	+	38.6810i	1.30172	+	1.30172i	0.374487	+	0.927232i	$0.377819\pi$
$884$		−	0.938340i		−	0.0315598i
$885$	17.4605	−	5.45829i	0.586929	−	0.183478i
$886$	2.26602	−	3.92487i	0.0761285	−	0.131858i
$887$	5.00667	−	18.6852i	0.168108	−	0.627386i	−0.829516	−	0.558483i	$-0.811384\pi$
$887$	5.00667	−	18.6852i	0.168108	−	0.627386i	0.997623	−	0.0689028i	$-0.0219498\pi$
$888$	−1.20652	−	4.50280i	−0.0404882	−	0.151104i
$889$	−0.770890	+	1.33522i	−0.0258548	+	0.0447819i
$890$	17.1849	−	18.6620i	0.576039	−	0.625553i
$891$		−	0.622323i		−	0.0208486i
$892$	10.0684	+	2.69782i	0.337116	+	0.0903299i
$893$	85.2948	+	22.8547i	2.85428	+	0.764802i
$894$	10.9348	−	18.9397i	0.365716	−	0.633438i
$895$	7.16440	−	4.53959i	0.239480	−	0.151742i
$896$	0.214675	+	0.371828i	0.00717179	+	0.0124219i
$897$	−13.2087	+	13.2087i	−0.441025	+	0.441025i
$898$	−13.3806	−	13.3806i	−0.446518	−	0.446518i
$899$	15.9827	−	28.5599i	0.533053	−	0.952526i
$900$	−2.13527	+	4.52113i	−0.0711756	+	0.150704i
$901$	1.34920			0.0449483
$902$	−4.37577	−	1.17248i	−0.145697	−	0.0390394i
$903$	3.61616	−	3.61616i	0.120338	−	0.120338i
$904$	−3.04248	−	1.75657i	−0.101191	−	0.0584228i
$905$	−1.71131	+	3.26783i	−0.0568860	+	0.108626i
$906$	−10.8184	−	18.7380i	−0.359418	−	0.622529i
$907$	29.5802	+	29.5802i	0.982193	+	0.982193i	0.999844	−	0.0176510i	$-0.00561877\pi$
$907$	29.5802	+	29.5802i	0.982193	+	0.982193i	−0.0176510	+	0.999844i	$0.505619\pi$
$908$	−3.48592	−	13.0096i	−0.115684	−	0.431740i
$909$	2.73188	+	1.57725i	0.0906109	+	0.0523142i
$910$	1.64102	+	1.51113i	0.0543992	+	0.0500934i
$911$	−42.0959	+	24.3041i	−1.39470	+	0.805230i	−0.993831	−	0.110906i	$-0.964625\pi$
$911$	−42.0959	+	24.3041i	−1.39470	+	0.805230i	−0.400868	+	0.916136i	$0.631291\pi$
$912$	1.73773	+	6.48528i	0.0575418	+	0.214749i
$913$	5.35763	+	1.43557i	0.177312	+	0.0475105i
$914$	2.32506			0.0769063
$915$	3.43510	−	15.3171i	0.113561	−	0.506367i
$916$	21.3339	−	12.3171i	0.704891	−	0.406969i
$917$	5.75490	−	1.54202i	0.190044	−	0.0509220i
$918$	0.390069	+	0.104519i	0.0128742	+	0.00344963i
$919$	2.14410	+	1.23790i	0.0707274	+	0.0408345i	0.534947	−	0.844886i	$-0.320332\pi$
$919$	2.14410	+	1.23790i	0.0707274	+	0.0408345i	−0.464219	+	0.885720i	$0.653665\pi$
$920$	0.740109	+	17.9609i	0.0244007	+	0.592154i
$921$	22.1648	+	12.7968i	0.730354	+	0.421670i
$922$	−4.59019	+	4.59019i	−0.151170	+	0.151170i
$923$	3.82910	−	14.2904i	0.126036	−	0.470374i
$924$	−0.231397	+	0.133597i	−0.00761240	+	0.00439502i
$925$	−22.9340	−	4.15985i	−0.754066	−	0.136775i
$926$		−	9.88351i		−	0.324792i
$927$	−4.65809	+	17.3842i	−0.152992	+	0.570973i
$928$	4.15645	+	4.15645i	0.136442	+	0.136442i
$929$	−23.9348			−0.785274			−0.392637	−	0.919693i	$-0.628437\pi$
$929$	−23.9348			−0.785274			−0.392637	+	0.919693i	$0.628437\pi$
$930$	−12.4314	+	0.679209i	−0.407640	+	0.0222722i
$931$	45.7607			1.49975
$932$	−2.64240	−	2.64240i	−0.0865548	−	0.0865548i
$933$	−5.96235	+	22.2518i	−0.195199	+	0.728491i
$934$			30.5529i			0.999721i
$935$	0.380662	−	0.413382i	0.0124490	−	0.0135190i
$936$	2.01230	−	1.16180i	0.0657742	−	0.0379748i
$937$	11.0356	−	41.1854i	0.360517	−	1.34547i	−0.512881	−	0.858460i	$-0.671422\pi$
$937$	11.0356	−	41.1854i	0.360517	−	1.34547i	0.873398	−	0.487007i	$-0.161912\pi$
$938$	−0.323045	+	0.323045i	−0.0105478	+	0.0105478i
$939$	2.98471	+	1.72323i	0.0974025	+	0.0562353i
$940$	−21.6338	−	19.9214i	−0.705616	−	0.649765i
$941$	−31.4257	−	18.1436i	−1.02445	−	0.591466i	−0.109059	−	0.994035i	$-0.534784\pi$
$941$	−31.4257	−	18.1436i	−1.02445	−	0.591466i	−0.915389	+	0.402570i	$0.868117\pi$
$942$	−15.0948	−	4.04464i	−0.491815	−	0.131781i
$943$	−56.5263	+	15.1462i	−1.84075	+	0.493227i
$944$	−7.08515	+	4.09061i	−0.230602	+	0.133138i
$945$	−0.810964	+	0.513852i	−0.0263807	+	0.0167156i
$946$	−7.41254			−0.241003
$947$	23.8694	+	6.39578i	0.775650	+	0.207835i	0.624866	−	0.780732i	$-0.285154\pi$
$947$	23.8694	+	6.39578i	0.775650	+	0.207835i	0.150784	+	0.988567i	$0.451820\pi$
$948$	−1.98759	−	7.41778i	−0.0645538	−	0.240918i
$949$	−0.517384	+	0.298712i	−0.0167950	+	0.00969660i
$950$	33.0313	+	5.99133i	1.07168	+	0.194385i
$951$	−29.4935	−	17.0281i	−0.956393	−	0.552174i
$952$	−0.0448751	−	0.167476i	−0.00145441	−	0.00542793i
$953$	−20.1250	−	20.1250i	−0.651913	−	0.651913i	0.301541	−	0.953453i	$-0.402499\pi$
$953$	−20.1250	−	20.1250i	−0.651913	−	0.651913i	−0.953453	+	0.301541i	$0.902499\pi$
$954$	1.67051	+	2.89341i	0.0540847	+	0.0936775i
$955$	24.5709	+	12.8674i	0.795096	+	0.416380i
$956$	19.9973	+	11.5455i	0.646759	+	0.373407i
$957$	−2.58665	+	2.58665i	−0.0836146	+	0.0836146i
$958$	19.4000	+	5.19822i	0.626786	+	0.167947i
$959$	0.591857			0.0191120
$960$	0.489320	−	2.18187i	0.0157927	−	0.0704196i
$961$	−16.2138	−	26.4218i	−0.523026	−	0.852317i
$962$	7.65926	+	7.65926i	0.246945	+	0.246945i
$963$	−0.825396	+	0.825396i	−0.0265980	+	0.0265980i
$964$	5.84217	+	10.1189i	0.188164	+	0.325909i
$965$	0.0261237	−	0.116485i	0.000840951	−	0.00374979i
$966$	−1.72581	+	2.98919i	−0.0555271	+	0.0961757i
$967$	−11.8927	−	3.18665i	−0.382445	−	0.102476i	0.0624741	−	0.998047i	$-0.480101\pi$
$967$	−11.8927	−	3.18665i	−0.382445	−	0.102476i	−0.444919	+	0.895571i	$0.646768\pi$
$968$	−10.2511	−	2.74677i	−0.329483	−	0.0882846i
$969$		−	2.71133i		−	0.0871005i
$970$	−23.8548	+	0.982976i	−0.765931	+	0.0315615i
$971$	−11.2662	+	19.5137i	−0.361550	+	0.626223i	−0.988216	−	0.153065i	$-0.951086\pi$
$971$	−11.2662	+	19.5137i	−0.361550	+	0.626223i	0.626666	+	0.779288i	$0.284419\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	1.63636	−	6.10696i	0.0524591	−	0.195780i
$974$	−3.43049	+	5.94178i	−0.109920	+	0.190387i
$975$	−0.955858	−	11.5787i	−0.0306120	−	0.370814i
$976$			7.02015i			0.224710i
$977$	26.0449	+	26.0449i	0.833251	+	0.833251i	0.987960	−	0.154709i	$-0.0494439\pi$
$977$	26.0449	+	26.0449i	0.833251	+	0.833251i	−0.154709	+	0.987960i	$0.549444\pi$
$978$	4.48204	−	16.7272i	0.143320	−	0.534877i
$979$	−6.11458	−	3.53026i	−0.195423	−	0.112827i
$980$	−13.5010	−	7.07027i	−0.431274	−	0.225852i
$981$	−8.34499	+	14.4539i	−0.266435	+	0.461479i
$982$	5.96023	+	22.2439i	0.190198	+	0.709830i
$983$	20.2950	−	5.43802i	0.647308	−	0.173446i	0.0797968	−	0.996811i	$-0.474573\pi$
$983$	20.2950	−	5.43802i	0.647308	−	0.173446i	0.567512	+	0.823365i	$0.307906\pi$
$984$	7.27939			0.232058
$985$	−16.9380	+	5.29493i	−0.539688	+	0.168711i
$986$	−1.18687	−	2.05573i	−0.0377978	−	0.0654677i
$987$	−1.46151	−	5.45443i	−0.0465203	−	0.173616i
$988$	−11.0315	−	11.0315i	−0.350957	−	0.350957i
$989$	−82.9266	+	47.8777i	−2.63691	+	1.52242i
$990$	1.35783	+	0.304515i	0.0431546	+	0.00967813i
$991$		−	37.9887i		−	1.20675i	−0.797457	−	0.603376i	$-0.793822\pi$
$991$		−	37.9887i		−	1.20675i	0.797457	−	0.603376i	$-0.206178\pi$
$992$	5.35826	−	1.51297i	0.170125	−	0.0480369i
$993$	−7.42894	+	7.42894i	−0.235750	+	0.235750i
$994$		−	2.73369i		−	0.0867072i
$995$	20.1792	+	10.5675i	0.639724	+	0.335014i
$996$	−8.91278			−0.282412
$997$	−9.04848	+	2.42453i	−0.286568	+	0.0767858i	−0.399240	−	0.916847i	$-0.630726\pi$
$997$	−9.04848	+	2.42453i	−0.286568	+	0.0767858i	0.112671	+	0.993632i	$0.464059\pi$
$998$	−5.97227	+	22.2888i	−0.189049	+	0.705540i
$999$	−4.03710	+	2.33082i	−0.127728	+	0.0737439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.5	yes	64
5.3	odd	4		930.2.be.a.223.2	✓	64
31.26	odd	6		930.2.be.a.367.2	yes	64
155.88	even	12	inner	930.2.be.b.553.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.2	✓	64	5.3	odd	4
930.2.be.a.367.2	yes	64	31.26	odd	6
930.2.be.b.37.5	yes	64	1.1	even	1	trivial
930.2.be.b.553.5	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.0920628 + 2.23417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.111124 - 0.414720i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(0.0920628 + 2.23417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.111124 - 0.414720i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.51470 - 1.64490i) q^{10} +(-0.538947 - 0.311161i) q^{11} +(0.965926 + 0.258819i) q^{12} +(-2.24443 + 0.601394i) q^{13} +(-0.371828 + 0.214675i) q^{14} +(2.18187 + 0.489320i) q^{15} -1.00000 q^{16} +(0.390069 + 0.104519i) q^{17} +(0.258819 + 0.965926i) q^{18} +(5.81454 - 3.35703i) q^{19} +(-2.23417 + 0.0920628i) q^{20} +(-0.371828 - 0.214675i) q^{21} +(0.161069 + 0.601118i) q^{22} +(5.68456 + 5.68456i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.98305 + 0.411368i) q^{25} +(2.01230 + 1.16180i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(0.414720 + 0.111124i) q^{28} +5.87810 q^{29} +(-1.19681 - 1.88882i) q^{30} +(2.71903 - 4.85869i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.440049 + 0.440049i) q^{33} +(-0.201914 - 0.349726i) q^{34} +(0.936787 + 0.210090i) q^{35} +(0.500000 - 0.866025i) q^{36} +(4.50280 + 1.20652i) q^{37} +(-6.48528 - 1.73773i) q^{38} +2.32361i q^{39} +(1.64490 + 1.51470i) q^{40} +(-3.63969 + 6.30413i) q^{41} +(0.111124 + 0.414720i) q^{42} +(-3.08282 + 11.5052i) q^{43} +(0.311161 - 0.538947i) q^{44} +(1.03736 - 1.98088i) q^{45} -8.03918i q^{46} +(9.29991 + 9.29991i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(5.90253 + 3.40783i) q^{49} +(3.81443 + 3.23267i) q^{50} +(0.201914 - 0.349726i) q^{51} +(-0.601394 - 2.24443i) q^{52} +(3.22717 - 0.864719i) q^{53} +1.00000 q^{54} +(0.645571 - 1.23275i) q^{55} +(-0.214675 - 0.371828i) q^{56} +(-1.73773 - 6.48528i) q^{57} +(-4.15645 - 4.15645i) q^{58} +(7.08515 - 4.09061i) q^{59} +(-0.489320 + 2.18187i) q^{60} -7.02015i q^{61} +(-5.35826 + 1.51297i) q^{62} +(-0.303596 + 0.303596i) q^{63} -1.00000i q^{64} +(-1.55025 - 4.95908i) q^{65} +0.622323 q^{66} +(1.02781 - 0.275400i) q^{67} +(-0.104519 + 0.390069i) q^{68} +(6.96213 - 4.01959i) q^{69} +(-0.513852 - 0.810964i) q^{70} +(-3.18352 + 5.51401i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(0.248350 - 0.0665451i) q^{73} +(-2.33082 - 4.03710i) q^{74} +(-0.892357 + 4.91973i) q^{75} +(3.35703 + 5.81454i) q^{76} +(-0.188935 + 0.188935i) q^{77} +(1.64304 - 1.64304i) q^{78} +(-3.83972 - 6.65060i) q^{79} +(-0.0920628 - 2.23417i) q^{80} +(0.500000 + 0.866025i) q^{81} +(7.03135 - 1.88404i) q^{82} +(-8.60909 + 2.30680i) q^{83} +(0.214675 - 0.371828i) q^{84} +(-0.197602 + 0.881103i) q^{85} +(10.3153 - 5.95555i) q^{86} +(1.52137 - 5.67781i) q^{87} +(-0.601118 + 0.161069i) q^{88} +11.3454 q^{89} +(-2.13422 + 0.667172i) q^{90} +0.997641i q^{91} +(-5.68456 + 5.68456i) q^{92} +(-3.98940 - 3.88390i) q^{93} -13.1521i q^{94} +(8.03548 + 12.6816i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-7.54995 - 7.54995i) q^{97} +(-1.76402 - 6.58342i) q^{98} +(0.311161 + 0.538947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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