LMFDB - Embedded newform 669.2.i.b.4.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [720] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$20$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	669.4
Dual form			669.2.i.b.502.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.49775 - 0.529190i) q^{2} +(0.372856 - 0.927889i) q^{3} +(0.407155 - 0.328755i) q^{4} +(1.79333 + 2.91256i) q^{5} +(0.0674176 - 1.58706i) q^{6} +(-0.0506160 + 0.395268i) q^{7} +(-1.22987 + 1.99744i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(4.22727 + 3.41328i) q^{10} +(-0.214043 + 5.03873i) q^{11} +(-0.153237 - 0.500373i) q^{12} +(0.769396 + 1.91472i) q^{13} +(0.133362 + 0.618800i) q^{14} +(3.37119 - 0.578048i) q^{15} +(-1.00552 + 4.66564i) q^{16} +(0.176351 - 4.15143i) q^{17} +(-1.44748 - 0.654302i) q^{18} +(1.87240 - 0.487536i) q^{19} +(1.68768 + 0.596296i) q^{20} +(0.347892 + 0.194344i) q^{21} +(2.34586 + 7.66005i) q^{22} +(-4.51073 - 7.32589i) q^{23} +(1.39484 + 1.88594i) q^{24} +(-3.01593 + 5.98174i) q^{25} +(2.16562 + 2.46062i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.109338 + 0.177575i) q^{28} +(0.811534 - 3.76553i) q^{29} +(4.74331 - 2.64977i) q^{30} +(8.90974 - 0.758330i) q^{31} +(0.367093 + 2.86668i) q^{32} +(4.59557 + 2.07733i) q^{33} +(-1.93277 - 6.31114i) q^{34} +(-1.24201 + 0.561424i) q^{35} +(-0.521426 - 0.0443799i) q^{36} +(-0.214565 - 5.05103i) q^{37} +(2.54640 - 1.72107i) q^{38} +2.06352 q^{39} -8.02323 q^{40} +(-0.973745 + 0.658137i) q^{41} +(0.623902 + 0.106979i) q^{42} +(-3.55532 - 7.05156i) q^{43} +(1.56936 + 2.12191i) q^{44} +(0.720604 - 3.34362i) q^{45} +(-10.6328 - 8.58535i) q^{46} +(2.36046 + 0.614617i) q^{47} +(3.95428 + 2.67263i) q^{48} +(6.62046 + 1.72383i) q^{49} +(-1.35164 + 10.5552i) q^{50} +(-3.78631 - 1.71152i) q^{51} +(0.942735 + 0.526643i) q^{52} +(1.70710 - 1.93965i) q^{53} +(-1.14682 + 1.09914i) q^{54} +(-15.0594 + 8.41271i) q^{55} +(-0.727273 - 0.587232i) q^{56} +(0.245759 - 1.91916i) q^{57} +(-0.777204 - 6.06930i) q^{58} +(-1.00383 + 3.27783i) q^{59} +(1.18256 - 1.34365i) q^{60} +(2.81183 + 6.99752i) q^{61} +(12.9433 - 5.85074i) q^{62} +(0.310044 - 0.250343i) q^{63} +(-2.23060 - 4.42413i) q^{64} +(-4.19694 + 5.67463i) q^{65} +(7.98235 + 0.679398i) q^{66} +(5.75150 - 4.64401i) q^{67} +(-1.29300 - 1.74825i) q^{68} +(-8.47947 + 1.45395i) q^{69} +(-1.56313 + 1.49814i) q^{70} +(0.00464403 - 0.0151643i) q^{71} +(2.27002 - 0.591068i) q^{72} +(-4.71715 - 2.63516i) q^{73} +(-2.99432 - 7.45165i) q^{74} +(4.42588 + 5.02878i) q^{75} +(0.602079 - 0.814064i) q^{76} +(-1.98081 - 0.339645i) q^{77} +(3.09064 - 1.09199i) q^{78} +(12.3062 - 8.31751i) q^{79} +(-15.3922 + 5.43841i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-1.11015 + 1.50102i) q^{82} +(0.146775 - 0.291110i) q^{83} +(0.205537 - 0.0352429i) q^{84} +(12.4075 - 6.93126i) q^{85} +(-9.05662 - 8.68007i) q^{86} +(-3.19141 - 2.15702i) q^{87} +(-9.80132 - 6.62453i) q^{88} +(-1.39719 + 2.26918i) q^{89} +(-0.690121 - 5.38925i) q^{90} +(-0.795769 + 0.207202i) q^{91} +(-4.24499 - 1.49985i) q^{92} +(2.61841 - 8.55000i) q^{93} +(3.86065 - 0.328589i) q^{94} +(4.77782 + 4.57917i) q^{95} +(2.79683 + 0.728239i) q^{96} +(-6.00702 + 9.75602i) q^{97} +(10.8281 - 0.921603i) q^{98} +(3.64102 - 3.48964i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) $ 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

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 $

$2$	1.49775	−	0.529190i	1.05907	−	0.374194i	0.253897	−	0.967231i	$-0.418287\pi$
$2$	1.49775	−	0.529190i	1.05907	−	0.374194i	0.805175	+	0.593037i	$0.202071\pi$
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$3$	0.372856	−	0.927889i	0.215269	−	0.535717i
$4$	0.407155	−	0.328755i	0.203577	−	0.164377i
$5$	1.79333	+	2.91256i	0.802003	+	1.30254i	0.949593	+	0.313487i	$0.101497\pi$
$5$	1.79333	+	2.91256i	0.802003	+	1.30254i	−0.147590	+	0.989049i	$0.547152\pi$
$6$	0.0674176	−	1.58706i	0.0275231	−	0.647915i
$7$	−0.0506160	+	0.395268i	−0.0191311	+	0.149397i	−0.998649	−	0.0519585i	$-0.983454\pi$
$7$	−0.0506160	+	0.395268i	−0.0191311	+	0.149397i	0.979518	+	0.201356i	$0.0645347\pi$
$8$	−1.22987	+	1.99744i	−0.434826	+	0.706202i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	4.22727	+	3.41328i	1.33678	+	1.07937i
$11$	−0.214043	+	5.03873i	−0.0645363	+	1.51923i	0.616716	+	0.787186i	$0.288463\pi$
$11$	−0.214043	+	5.03873i	−0.0645363	+	1.51923i	−0.681253	+	0.732048i	$0.738564\pi$
$12$	−0.153237	−	0.500373i	−0.0442358	−	0.144445i
$13$	0.769396	+	1.91472i	0.213392	+	0.531046i	0.995783	−	0.0917413i	$-0.0292433\pi$
$13$	0.769396	+	1.91472i	0.213392	+	0.531046i	−0.782391	+	0.622788i	$0.786000\pi$
$14$	0.133362	+	0.618800i	0.0356424	+	0.165381i
$15$	3.37119	−	0.578048i	0.870436	−	0.149251i
$16$	−1.00552	+	4.66564i	−0.251381	+	1.16641i
$17$	0.176351	−	4.15143i	0.0427713	−	1.00687i	−0.841605	−	0.540094i	$-0.818389\pi$
$17$	0.176351	−	4.15143i	0.0427713	−	1.00687i	0.884376	−	0.466775i	$-0.154584\pi$
$18$	−1.44748	−	0.654302i	−0.341174	−	0.154221i
$19$	1.87240	−	0.487536i	0.429559	−	0.111848i	−0.0309142	−	0.999522i	$-0.509842\pi$
$19$	1.87240	−	0.487536i	0.429559	−	0.111848i	0.460473	+	0.887674i	$0.347680\pi$
$20$	1.68768	+	0.596296i	0.377377	+	0.133336i
$21$	0.347892	+	0.194344i	0.0759163	+	0.0424094i
$22$	2.34586	+	7.66005i	0.500140	+	1.63313i
$23$	−4.51073	−	7.32589i	−0.940552	−	1.52755i	−0.846769	−	0.531961i	$-0.821455\pi$
$23$	−4.51073	−	7.32589i	−0.940552	−	1.52755i	−0.0937836	−	0.995593i	$-0.529896\pi$
$24$	1.39484	+	1.88594i	0.284720	+	0.384967i
$25$	−3.01593	+	5.98174i	−0.603186	+	1.19635i
$26$	2.16562	+	2.46062i	0.424712	+	0.482567i
$27$	−0.911228	+	0.411901i	−0.175366	+	0.0792704i
$28$	0.109338	+	0.177575i	0.0206628	+	0.0335586i
$29$	0.811534	−	3.76553i	0.150698	−	0.699242i	−0.837547	−	0.546365i	$-0.816011\pi$
$29$	0.811534	−	3.76553i	0.150698	−	0.699242i	0.988245	−	0.152877i	$-0.0488537\pi$
$30$	4.74331	−	2.64977i	0.866006	−	0.483780i
$31$	8.90974	−	0.758330i	1.60024	−	0.136200i	0.749577	−	0.661917i	$-0.230257\pi$
$31$	8.90974	−	0.758330i	1.60024	−	0.136200i	0.850659	+	0.525717i	$0.176203\pi$
$32$	0.367093	+	2.86668i	0.0648935	+	0.506762i
$33$	4.59557	+	2.07733i	0.799987	+	0.361617i
$34$	−1.93277	−	6.31114i	−0.331467	−	1.08235i
$35$	−1.24201	+	0.561424i	−0.209938	+	0.0948981i
$36$	−0.521426	−	0.0443799i	−0.0869043	−	0.00739665i
$37$	−0.214565	−	5.05103i	−0.0352743	−	0.830384i	−0.926380	−	0.376589i	$-0.877097\pi$
$37$	−0.214565	−	5.05103i	−0.0352743	−	0.830384i	0.891106	−	0.453795i	$-0.149930\pi$
$38$	2.54640	−	1.72107i	0.413081	−	0.279194i
$39$	2.06352			0.330427
$40$	−8.02323			−1.26858
$41$	−0.973745	+	0.658137i	−0.152073	+	0.102784i	−0.633648	−	0.773621i	$-0.718443\pi$
$41$	−0.973745	+	0.658137i	−0.152073	+	0.102784i	0.481575	+	0.876405i	$0.340065\pi$
$42$	0.623902	+	0.106979i	0.0962702	+	0.0165072i
$43$	−3.55532	−	7.05156i	−0.542182	−	1.07535i	−0.983987	−	0.178242i	$-0.942959\pi$
$43$	−3.55532	−	7.05156i	−0.542182	−	1.07535i	0.441805	−	0.897111i	$-0.354338\pi$
$44$	1.56936	+	2.12191i	0.236589	+	0.319890i
$45$	0.720604	−	3.34362i	0.107421	−	0.498437i
$46$	−10.6328	−	8.58535i	−1.56771	−	1.26584i
$47$	2.36046	+	0.614617i	0.344309	+	0.0896511i	0.420113	−	0.907472i	$-0.361990\pi$
$47$	2.36046	+	0.614617i	0.344309	+	0.0896511i	−0.0758044	+	0.997123i	$0.524152\pi$
$48$	3.95428	+	2.67263i	0.570752	+	0.385761i
$49$	6.62046	+	1.72383i	0.945779	+	0.246262i
$50$	−1.35164	+	10.5552i	−0.191151	+	1.49273i
$51$	−3.78631	−	1.71152i	−0.530190	−	0.239661i
$52$	0.942735	+	0.526643i	0.130734	+	0.0730323i
$53$	1.70710	−	1.93965i	0.234489	−	0.266431i	−0.621513	−	0.783404i	$-0.713482\pi$
$53$	1.70710	−	1.93965i	0.234489	−	0.266431i	0.856002	+	0.516973i	$0.172941\pi$
$54$	−1.14682	+	1.09914i	−0.156063	+	0.149574i
$55$	−15.0594	+	8.41271i	−2.03061	+	1.13437i
$56$	−0.727273	−	0.587232i	−0.0971859	−	0.0784721i
$57$	0.245759	−	1.91916i	0.0325515	−	0.254200i
$58$	−0.777204	−	6.06930i	−0.102052	−	0.796938i
$59$	−1.00383	+	3.27783i	−0.130687	+	0.426738i	−0.997400	−	0.0720702i	$-0.977039\pi$
$59$	−1.00383	+	3.27783i	−0.130687	+	0.426738i	0.866713	+	0.498808i	$0.166229\pi$
$60$	1.18256	−	1.34365i	0.152668	−	0.173464i
$61$	2.81183	+	6.99752i	0.360018	+	0.895940i	0.992598	+	0.121445i	$0.0387528\pi$
$61$	2.81183	+	6.99752i	0.360018	+	0.895940i	−0.632580	+	0.774495i	$0.718004\pi$
$62$	12.9433	−	5.85074i	1.64380	−	0.743045i
$63$	0.310044	−	0.250343i	0.0390618	−	0.0315402i
$64$	−2.23060	−	4.42413i	−0.278825	−	0.553017i
$65$	−4.19694	+	5.67463i	−0.520566	+	0.703851i
$66$	7.98235	+	0.679398i	0.982559	+	0.0836281i
$67$	5.75150	−	4.64401i	0.702657	−	0.567356i	−0.209196	−	0.977874i	$-0.567085\pi$
$67$	5.75150	−	4.64401i	0.702657	−	0.567356i	0.911853	+	0.410518i	$0.134652\pi$
$68$	−1.29300	−	1.74825i	−0.156799	−	0.212007i
$69$	−8.47947	+	1.45395i	−1.02081	+	0.175035i
$70$	−1.56313	+	1.49814i	−0.186829	+	0.179062i
$71$	0.00464403	−	0.0151643i	0.000551144	−	0.00179968i	−0.955891	−	0.293722i	$-0.905106\pi$
$71$	0.00464403	−	0.0151643i	0.000551144	−	0.00179968i	0.956442	+	0.291923i	$0.0942950\pi$
$72$	2.27002	−	0.591068i	0.267525	−	0.0696580i
$73$	−4.71715	−	2.63516i	−0.552100	−	0.308422i	0.186622	−	0.982432i	$-0.440246\pi$
$73$	−4.71715	−	2.63516i	−0.552100	−	0.308422i	−0.738722	+	0.674010i	$0.764570\pi$
$74$	−2.99432	−	7.45165i	−0.348083	−	0.866237i
$75$	4.42588	+	5.02878i	0.511057	+	0.580673i
$76$	0.602079	−	0.814064i	0.0690632	−	0.0933796i
$77$	−1.98081	−	0.339645i	−0.225735	−	0.0387061i
$78$	3.09064	−	1.09199i	0.349946	−	0.123644i
$79$	12.3062	−	8.31751i	1.38455	−	0.935793i	0.384632	−	0.923070i	$-0.374328\pi$
$79$	12.3062	−	8.31751i	1.38455	−	0.935793i	0.999919	−	0.0127234i	$-0.00405009\pi$
$80$	−15.3922	+	5.43841i	−1.72090	+	0.608033i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	−1.11015	+	1.50102i	−0.122596	+	0.165760i
$83$	0.146775	−	0.291110i	0.0161106	−	0.0319535i	−0.884728	−	0.466108i	$-0.845656\pi$
$83$	0.146775	−	0.291110i	0.0161106	−	0.0319535i	0.900838	+	0.434155i	$0.142953\pi$
$84$	0.205537	−	0.0352429i	0.0224260	−	0.00384532i
$85$	12.4075	−	6.93126i	1.34579	−	0.751801i
$86$	−9.05662	−	8.68007i	−0.976601	−	0.935996i
$87$	−3.19141	−	2.15702i	−0.342155	−	0.231256i
$88$	−9.80132	−	6.62453i	−1.04482	−	0.706178i
$89$	−1.39719	+	2.26918i	−0.148102	+	0.240533i	−0.917044	−	0.398785i	$-0.869432\pi$
$89$	−1.39719	+	2.26918i	−0.148102	+	0.240533i	0.768942	+	0.639318i	$0.220783\pi$
$90$	−0.690121	−	5.38925i	−0.0727451	−	0.568077i
$91$	−0.795769	+	0.207202i	−0.0834192	+	0.0217207i
$92$	−4.24499	−	1.49985i	−0.442570	−	0.156370i
$93$	2.61841	−	8.55000i	0.271516	−	0.886593i
$94$	3.86065	−	0.328589i	0.398195	−	0.0338914i
$95$	4.77782	+	4.57917i	0.490194	+	0.469813i
$96$	2.79683	+	0.728239i	0.285451	+	0.0743256i
$97$	−6.00702	+	9.75602i	−0.609920	+	0.990573i	0.387711	+	0.921781i	$0.373266\pi$
$97$	−6.00702	+	9.75602i	−0.609920	+	0.990573i	−0.997631	+	0.0687923i	$0.978085\pi$
$98$	10.8281	−	0.921603i	1.09380	−	0.0930960i
$99$	3.64102	−	3.48964i	0.365936	−	0.350722i
$100$	0.738574	+	3.42699i	0.0738574	+	0.342699i
$101$	4.01386	+	4.56063i	0.399394	+	0.453800i	0.915256	−	0.402872i	$-0.131988\pi$
$101$	4.01386	+	4.56063i	0.399394	+	0.453800i	−0.515863	+	0.856671i	$0.672528\pi$
$102$	−6.57669	−	0.559759i	−0.651189	−	0.0554244i
$103$	1.75833	−	4.37578i	0.173254	−	0.431159i	−0.815872	−	0.578233i	$-0.803742\pi$
$103$	1.75833	−	4.37578i	0.173254	−	0.431159i	0.989125	+	0.147074i	$0.0469857\pi$
$104$	−4.77079	−	0.818034i	−0.467814	−	0.0802148i
$105$	0.0578477	+	1.36178i	0.00564536	+	0.132896i
$106$	1.53038	−	3.80850i	0.148644	−	0.369914i
$107$	2.33333	+	4.62788i	0.225571	+	0.447394i	0.977237	−	0.212150i	$-0.0680467\pi$
$107$	2.33333	+	4.62788i	0.225571	+	0.447394i	−0.751666	+	0.659544i	$0.770749\pi$
$108$	−0.235597	+	0.467278i	−0.0226703	+	0.0449639i
$109$	2.46268	+	11.4269i	0.235882	+	1.09450i	0.927961	+	0.372676i	$0.121560\pi$
$109$	2.46268	+	11.4269i	0.235882	+	1.09450i	−0.692079	+	0.721822i	$0.743305\pi$
$110$	−18.1034	+	20.5695i	−1.72609	+	1.96122i
$111$	−4.76679	−	1.68422i	−0.452444	−	0.159859i
$112$	−1.79328	−	0.633607i	−0.169449	−	0.0598703i
$113$	−10.7096	+	12.1685i	−1.00748	+	1.14471i	−0.0180262	+	0.999838i	$0.505738\pi$
$113$	−10.7096	+	12.1685i	−1.00748	+	1.14471i	−0.989450	+	0.144877i	$0.953721\pi$
$114$	−0.647517	−	3.00449i	−0.0606456	−	0.281396i
$115$	13.2478	−	26.2755i	1.23537	−	2.45020i
$116$	−0.907516	−	1.79995i	−0.0842607	−	0.167121i
$117$	0.769396	−	1.91472i	0.0711307	−	0.177015i
$118$	0.231114	+	5.44061i	0.0212758	+	0.500848i
$119$	1.63200	+	0.279834i	0.149605	+	0.0256524i
$120$	−2.99151	+	7.44467i	−0.273087	+	0.679602i
$121$	−14.3826	−	1.22414i	−1.30751	−	0.111285i
$122$	7.91446	+	8.99257i	0.716541	+	0.814149i
$123$	0.247611	+	1.14892i	0.0223263	+	0.103594i
$124$	3.37834	−	3.23788i	0.303384	−	0.290770i
$125$	−5.79041	+	0.492836i	−0.517910	+	0.0440806i
$126$	0.331890	−	0.539024i	0.0295671	−	0.0480201i
$127$	−20.7062	−	5.39148i	−1.83738	−	0.478416i	−0.839491	−	0.543374i	$-0.817147\pi$
$127$	−20.7062	−	5.39148i	−1.83738	−	0.478416i	−0.997888	+	0.0649577i	$0.979309\pi$
$128$	−9.85514	−	9.44538i	−0.871079	−	0.834862i
$129$	−7.86869	+	0.669725i	−0.692800	+	0.0589660i
$130$	−3.28302	+	10.7202i	−0.287940	+	0.940222i
$131$	−17.0874	−	6.03735i	−1.49293	−	0.527486i	−0.542941	−	0.839771i	$-0.682689\pi$
$131$	−17.0874	−	6.03735i	−1.49293	−	0.527486i	−0.949989	+	0.312285i	$0.898906\pi$
$132$	2.55404	−	0.665021i	0.222301	−	0.0578826i
$133$	0.0979337	+	0.764778i	0.00849193	+	0.0663147i
$134$	6.15676	−	9.99922i	0.531863	−	0.863801i
$135$	−2.83382	−	1.91533i	−0.243897	−	0.164845i
$136$	8.07534	+	5.45798i	0.692455	+	0.468018i
$137$	−2.97403	−	2.85037i	−0.254088	−	0.243524i	0.554097	−	0.832452i	$-0.313064\pi$
$137$	−2.97403	−	2.85037i	−0.254088	−	0.243524i	−0.808185	+	0.588928i	$0.799550\pi$
$138$	−11.9307	+	6.66492i	−1.01561	+	0.567355i
$139$	7.42375	−	1.27293i	0.629674	−	0.107968i	0.154690	−	0.987963i	$-0.450562\pi$
$139$	7.42375	−	1.27293i	0.629674	−	0.107968i	0.474984	+	0.879995i	$0.342454\pi$
$140$	−0.321120	+	0.636904i	−0.0271396	+	0.0538282i
$141$	1.45041	−	1.96108i	0.122147	−	0.165153i
$142$	−0.00106921	−	0.0251700i	−8.97261e−5	−	0.00211222i
$143$	−9.81242	+	3.46695i	−0.820555	+	0.289921i
$144$	3.95428	−	2.67263i	0.329524	−	0.222719i
$145$	12.4227	−	4.38921i	1.03165	−	0.364504i
$146$	−8.45963	−	1.45055i	−0.700124	−	0.120048i
$147$	4.06801	−	5.50031i	0.335523	−	0.453658i
$148$	−1.74791	−	1.98601i	−0.143677	−	0.163249i
$149$	6.47774	+	16.1205i	0.530677	+	1.32064i	0.917224	+	0.398371i	$0.130424\pi$
$149$	6.47774	+	16.1205i	0.530677	+	1.32064i	−0.386547	+	0.922270i	$0.626332\pi$
$150$	9.29007	+	5.18974i	0.758531	+	0.423741i
$151$	−6.69303	+	1.74273i	−0.544671	+	0.141821i	−0.514130	−	0.857712i	$-0.671885\pi$
$151$	−6.69303	+	1.74273i	−0.544671	+	0.141821i	−0.0305410	+	0.999534i	$0.509723\pi$
$152$	−1.32900	+	4.33962i	−0.107796	+	0.351990i
$153$	−2.99985	+	2.87513i	−0.242524	+	0.232440i
$154$	−3.14651	+	0.539523i	−0.253553	+	0.0434760i
$155$	18.1868	+	24.5902i	1.46080	+	1.97513i
$156$	0.840171	−	0.678391i	0.0672675	−	0.0543147i
$157$	−8.22239	−	0.699829i	−0.656218	−	0.0558524i	−0.248033	−	0.968752i	$-0.579784\pi$
$157$	−8.22239	−	0.699829i	−0.656218	−	0.0558524i	−0.408185	+	0.912899i	$0.633838\pi$
$158$	14.0301	−	18.9699i	1.11617	−	1.50916i
$159$	−1.16327	−	2.30721i	−0.0922535	−	0.182974i
$160$	−7.69105	+	6.21009i	−0.608031	+	0.490951i
$161$	3.12400	−	1.41214i	0.246206	−	0.111292i
$162$	0.592280	+	1.47395i	0.0465339	+	0.115804i
$163$	−5.19737	+	5.90537i	−0.407090	+	0.462544i	−0.917703	−	0.397266i	$-0.869959\pi$
$163$	−5.19737	+	5.90537i	−0.407090	+	0.462544i	0.510613	+	0.859810i	$0.329418\pi$
$164$	−0.180099	+	0.588087i	−0.0140634	+	0.0459218i
$165$	2.19105	+	17.1102i	0.170573	+	1.33203i
$166$	0.0657797	−	0.513683i	0.00510549	−	0.0398695i
$167$	−19.7794	−	15.9708i	−1.53058	−	1.23586i	−0.878537	−	0.477675i	$-0.841480\pi$
$167$	−19.7794	−	15.9708i	−1.53058	−	1.23586i	−0.652043	−	0.758182i	$-0.726088\pi$
$168$	−0.816054	+	0.455875i	−0.0629599	+	0.0351715i
$169$	6.31126	−	6.04886i	0.485482	−	0.465297i
$170$	14.9155	−	16.9473i	1.14396	−	1.29980i
$171$	−1.68914	−	0.943610i	−0.129172	−	0.0721596i
$172$	−3.76580	−	1.70225i	−0.287140	−	0.129795i
$173$	−2.11728	+	16.5342i	−0.160974	+	1.25707i	0.686853	+	0.726796i	$0.258991\pi$
$173$	−2.11728	+	16.5342i	−0.160974	+	1.25707i	−0.847827	+	0.530272i	$0.822090\pi$
$174$	−5.92142	−	1.54182i	−0.448902	−	0.116885i
$175$	−2.21173	−	1.49487i	−0.167191	−	0.113002i
$176$	−23.2937	−	6.06521i	−1.75583	−	0.457182i
$177$	2.66718	+	2.15360i	0.200478	+	0.161874i
$178$	−0.891821	+	4.13806i	−0.0668448	+	0.310161i
$179$	−1.84886	−	2.49982i	−0.138190	−	0.186846i	0.729456	−	0.684028i	$-0.239773\pi$
$179$	−1.84886	−	2.49982i	−0.138190	−	0.186846i	−0.867646	+	0.497182i	$0.834368\pi$
$180$	−0.805831	−	1.59827i	−0.0600631	−	0.119128i
$181$	24.6246	+	4.22231i	1.83033	+	0.313842i	0.977912	−	0.209019i	$-0.0670271\pi$
$181$	24.6246	+	4.22231i	1.83033	+	0.313842i	0.852418	+	0.522861i	$0.175135\pi$
$182$	−1.08222	+	0.731451i	−0.0802193	+	0.0542188i
$183$	7.54133			0.557471
$184$	20.1807			1.48774
$185$	14.3266	−	9.68311i	1.05331	−	0.711916i
$186$	−0.602845	−	14.1914i	−0.0442027	−	1.04057i
$187$	20.8802	+	1.77717i	1.52691	+	0.129959i
$188$	1.16313	−	0.525769i	0.0848302	−	0.0383457i
$189$	−0.116689	−	0.381028i	−0.00848784	−	0.0277157i
$190$	9.57926	+	4.33010i	0.694952	+	0.314138i
$191$	0.256771	+	2.00517i	0.0185793	+	0.145089i	0.998534	−	0.0541333i	$-0.0172396\pi$
$191$	0.256771	+	2.00517i	0.0185793	+	0.145089i	−0.979954	+	0.199222i	$0.936159\pi$
$192$	−4.93680	+	0.420183i	−0.356283	+	0.0303241i
$193$	−6.11675	+	3.41702i	−0.440294	+	0.245963i	−0.692081	−	0.721820i	$-0.743306\pi$
$193$	−6.11675	+	3.41702i	−0.440294	+	0.245963i	0.251787	+	0.967783i	$0.418982\pi$
$194$	−3.83425	+	17.7910i	−0.275283	+	1.27732i
$195$	3.70057	+	6.01011i	0.265004	+	0.430393i
$196$	3.26227	−	1.47464i	0.233019	−	0.105331i
$197$	−3.09759	−	3.51954i	−0.220694	−	0.250757i	0.629781	−	0.776773i	$-0.283145\pi$
$197$	−3.09759	−	3.51954i	−0.220694	−	0.250757i	−0.850475	+	0.526016i	$0.823685\pi$
$198$	3.60668	−	7.15341i	0.256315	−	0.508371i
$199$	−13.2205	−	17.8752i	−0.937173	−	1.26714i	−0.963561	−	0.267490i	$-0.913806\pi$
$199$	−13.2205	−	17.8752i	−0.937173	−	1.26714i	0.0263876	−	0.999652i	$-0.491600\pi$
$200$	−8.23896	−	13.3809i	−0.582582	−	0.946174i
$201$	−2.16464	−	7.06830i	−0.152682	−	0.498559i
$202$	8.42522	+	4.70661i	0.592796	+	0.331156i
$203$	1.44732	+	0.511370i	0.101582	+	0.0358911i
$204$	−2.10429	+	0.547913i	−0.147329	+	0.0383616i
$205$	−3.66311	−	1.65583i	−0.255843	−	0.115648i
$206$	0.317931	−	7.48434i	0.0221513	−	0.521459i
$207$	−1.81252	+	8.41012i	−0.125979	+	0.584544i
$208$	−9.70703	+	1.66444i	−0.673061	+	0.115408i
$209$	2.05579	+	9.53889i	0.142202	+	0.659819i
$210$	0.807282	+	2.00900i	0.0557078	+	0.138634i
$211$	−4.76831	−	15.5702i	−0.328264	−	1.07190i	−0.955975	−	0.293449i	$-0.905197\pi$
$211$	−4.76831	−	15.5702i	−0.328264	−	1.07190i	0.627711	−	0.778447i	$-0.283992\pi$
$212$	0.0573879	−	1.35096i	0.00394142	−	0.0927840i
$213$	−0.0123393	−	0.00996326i	−0.000845473	−	0.000682671i
$214$	5.94378	+	5.69665i	0.406308	+	0.389415i
$215$	14.1622	−	23.0009i	0.965854	−	1.56865i
$216$	0.297947	−	2.32671i	0.0202727	−	0.158313i
$217$	−0.151232	+	3.56012i	−0.0102663	+	0.241676i
$218$	9.73550	+	15.8115i	0.659371	+	1.07089i
$219$	−4.20395	+	3.39445i	−0.284077	+	0.229376i
$220$	−3.36581	+	8.37613i	−0.226923	+	0.564719i
$221$	8.08449	−	2.85643i	0.543821	−	0.192144i
$222$	−8.03076			−0.538989
$223$	13.1455	+	7.08486i	0.880289	+	0.474437i
$223$	13.1455	+	7.08486i	0.880289	+	0.474437i
$224$	−1.15169			−0.0769503
$225$	6.31637	−	2.23171i	0.421091	−	0.148781i
$226$	−9.60093	+	23.8928i	−0.638644	+	1.58933i
$227$	7.43602	−	6.00417i	0.493546	−	0.398511i	−0.349010	−	0.937119i	$-0.613482\pi$
$227$	7.43602	−	6.00417i	0.493546	−	0.398511i	0.842556	+	0.538608i	$0.181050\pi$
$228$	−0.530872	−	0.862192i	−0.0351579	−	0.0571000i
$229$	0.821924	−	19.3487i	0.0543143	−	1.27860i	−0.740628	−	0.671915i	$-0.765472\pi$
$229$	0.821924	−	19.3487i	0.0543143	−	1.27860i	0.794942	−	0.606685i	$-0.207501\pi$
$230$	5.93726	−	46.3649i	0.391491	−	3.05721i
$231$	−1.05371	+	1.71134i	−0.0693291	+	0.112598i
$232$	6.52334	+	6.25212i	0.428278	+	0.410472i
$233$	13.6661	+	11.0346i	0.895297	+	0.722902i	0.961471	−	0.274906i	$-0.0886467\pi$
$233$	13.6661	+	11.0346i	0.895297	+	0.722902i	−0.0661737	+	0.997808i	$0.521079\pi$
$234$	0.139117	−	3.27493i	0.00909438	−	0.214089i
$235$	2.44299	+	7.97720i	0.159363	+	0.520375i
$236$	0.668891	+	1.66460i	0.0435411	+	0.108356i
$237$	−3.12930	−	14.5200i	−0.203270	−	0.943175i
$238$	2.59242	−	0.444515i	0.168042	−	0.0288136i
$239$	2.67260	−	12.4009i	0.172876	−	0.802148i	−0.805052	−	0.593205i	$-0.797862\pi$
$239$	2.67260	−	12.4009i	0.172876	−	0.802148i	0.977928	−	0.208943i	$-0.0670024\pi$
$240$	−0.692840	+	16.3100i	−0.0447226	+	1.05281i
$241$	3.18156	+	1.43816i	0.204942	+	0.0926398i	0.511760	−	0.859129i	$-0.328994\pi$
$241$	3.18156	+	1.43816i	0.204942	+	0.0926398i	−0.306817	+	0.951768i	$0.599264\pi$
$242$	−22.1894	+	5.77767i	−1.42639	+	0.371403i
$243$	0.942877	+	0.333140i	0.0604856	+	0.0213709i
$244$	3.44532	+	1.92467i	0.220564	+	0.123214i
$245$	6.85192	+	22.3739i	0.437753	+	1.42941i
$246$	0.978856	+	1.58976i	0.0624096	+	0.101360i
$247$	2.37411	+	3.21001i	0.151061	+	0.204248i
$248$	−9.44313	+	18.7293i	−0.599639	+	1.18931i
$249$	−0.215392	−	0.244733i	−0.0136499	−	0.0155093i
$250$	−8.41181	+	3.80238i	−0.532009	+	0.240483i
$251$	5.23173	+	8.49686i	0.330224	+	0.536317i	0.973315	−	0.229472i	$-0.0736999\pi$
$251$	5.23173	+	8.49686i	0.330224	+	0.536317i	−0.643092	+	0.765789i	$0.722349\pi$
$252$	0.0439344	−	0.203857i	0.00276761	−	0.0128418i
$253$	37.8787	−	21.1603i	2.38141	−	1.33034i
$254$	−33.8659	+	2.88242i	−2.12494	+	0.180859i
$255$	−1.80521	−	14.0972i	−0.113047	−	0.882799i
$256$	−10.7294	−	4.84997i	−0.670584	−	0.303123i
$257$	−3.14126	−	10.2573i	−0.195946	−	0.639832i	−0.999033	−	0.0439698i	$-0.985999\pi$
$257$	−3.14126	−	10.2573i	−0.195946	−	0.639832i	0.803086	−	0.595863i	$-0.203190\pi$
$258$	−11.4310	+	5.16712i	−0.711660	+	0.321691i
$259$	2.00737	+	0.170852i	0.124732	+	0.0106162i
$260$	0.156758	+	3.69022i	0.00972174	+	0.228857i
$261$	−3.19141	+	2.15702i	−0.197543	+	0.133516i
$262$	−28.7876			−1.77850
$263$	−3.91875			−0.241640			−0.120820	−	0.992674i	$-0.538552\pi$
$263$	−3.91875			−0.241640			−0.120820	+	0.992674i	$0.538552\pi$
$264$	−9.80132	+	6.62453i	−0.603229	+	0.407712i
$265$	8.71074	+	1.49361i	0.535097	+	0.0917515i
$266$	0.551394	+	1.09362i	0.0338081	+	0.0670544i
$267$	1.58460	+	2.14252i	0.0969759	+	0.131120i
$268$	0.815010	−	3.78166i	0.0497847	−	0.231002i
$269$	0.915890	+	0.739530i	0.0558428	+	0.0450899i	0.655737	−	0.754990i	$-0.272358\pi$
$269$	0.915890	+	0.739530i	0.0558428	+	0.0450899i	−0.599894	+	0.800080i	$0.704791\pi$
$270$	−5.25794	−	1.36906i	−0.319988	−	0.0833185i
$271$	−17.1159	−	11.5683i	−1.03972	−	0.702726i	−0.0838352	−	0.996480i	$-0.526717\pi$
$271$	−17.1159	−	11.5683i	−1.03972	−	0.702726i	−0.955881	+	0.293754i	$0.905095\pi$
$272$	19.1918	+	4.99715i	1.16367	+	0.302997i
$273$	−0.104447	+	0.815642i	−0.00632142	+	0.0493649i
$274$	−5.96275	−	2.69533i	−0.360223	−	0.162831i
$275$	−29.4948	−	16.4768i	−1.77860	−	0.993588i
$276$	−2.97446	+	3.37965i	−0.179042	+	0.203431i
$277$	−12.6899	+	12.1623i	−0.762461	+	0.730759i	−0.968833	−	0.247714i	$-0.920321\pi$
$277$	−12.6899	+	12.1623i	−0.762461	+	0.730759i	0.206372	+	0.978474i	$0.433834\pi$
$278$	10.4453	−	5.83511i	0.626469	−	0.349967i
$279$	−6.95716	−	5.61751i	−0.416514	−	0.336312i
$280$	0.406104	−	3.17132i	0.0242694	−	0.189523i
$281$	1.87216	+	14.6200i	0.111684	+	0.872155i	0.946742	+	0.321993i	$0.104353\pi$
$281$	1.87216	+	14.6200i	0.111684	+	0.872155i	−0.835058	+	0.550162i	$0.814566\pi$
$282$	1.13457	−	3.70477i	0.0675628	−	0.220616i
$283$	16.8188	−	19.1098i	0.999772	−	1.13596i	0.00906399	−	0.999959i	$-0.497115\pi$
$283$	16.8188	−	19.1098i	0.999772	−	1.13596i	0.990708	−	0.136003i	$-0.0434257\pi$
$284$	−0.00309451	−	0.00770098i	−0.000183625	−	0.000456969i
$285$	6.03040	−	2.72591i	0.357210	−	0.161469i
$286$	−12.8619	+	10.3853i	−0.760541	+	0.614094i
$287$	−0.210853	−	0.418202i	−0.0124463	−	0.0246857i
$288$	1.71854	−	2.32362i	0.101266	−	0.136921i
$289$	−0.264506	−	0.0225128i	−0.0155592	−	0.00132428i
$290$	16.2834	−	13.1479i	0.956194	−	0.772073i
$291$	6.81275	+	9.21144i	0.399370	+	0.539984i
$292$	−2.78693	+	0.477867i	−0.163093	+	0.0279651i
$293$	−16.7023	+	16.0079i	−0.975761	+	0.935191i	−0.997914	−	0.0645632i	$-0.979435\pi$
$293$	−16.7023	+	16.0079i	−0.975761	+	0.935191i	0.0221524	+	0.999755i	$0.492948\pi$
$294$	3.18216	−	10.3909i	0.185588	−	0.606007i
$295$	−11.3471	+	2.95455i	−0.660652	+	0.172020i
$296$	10.3530	+	5.78354i	0.601757	+	0.336162i
$297$	−1.88042	−	4.67960i	−0.109113	−	0.271538i
$298$	18.2329	+	20.7166i	1.05620	+	1.20008i
$299$	10.5565	−	14.2733i	0.610496	−	0.825445i
$300$	3.45525	+	0.592463i	0.199489	+	0.0342058i
$301$	2.96721	−	1.04838i	0.171027	−	0.0604278i
$302$	−9.10228	+	6.15207i	−0.523777	+	0.354012i
$303$	5.72835	−	2.02396i	0.329085	−	0.116273i
$304$	0.391924	+	9.22620i	0.0224784	+	0.529159i
$305$	−15.3381	+	20.7385i	−0.878258	+	1.18748i
$306$	−2.97155	+	5.89373i	−0.169872	+	0.336922i
$307$	22.1235	−	3.79346i	1.26265	−	0.216504i	0.501548	−	0.865130i	$-0.332764\pi$
$307$	22.1235	−	3.79346i	1.26265	−	0.216504i	0.761107	+	0.648626i	$0.224656\pi$
$308$	−0.918157	+	0.512913i	−0.0523169	+	0.0292260i
$309$	−3.40463	−	3.26308i	−0.193683	−	0.185630i
$310$	40.2523	+	27.2058i	2.28617	+	1.54518i
$311$	−12.7644	−	8.62722i	−0.723802	−	0.489205i	0.141827	−	0.989891i	$-0.454702\pi$
$311$	−12.7644	−	8.62722i	−0.723802	−	0.489205i	−0.865628	+	0.500687i	$0.833081\pi$
$312$	−2.53786	+	4.12175i	−0.143678	+	0.233348i
$313$	−2.91176	−	22.7384i	−0.164582	−	1.28525i	−0.837871	−	0.545868i	$-0.816200\pi$
$313$	−2.91176	−	22.7384i	−0.164582	−	1.28525i	0.673288	−	0.739380i	$-0.264881\pi$
$314$	−12.6855	+	3.30304i	−0.715882	+	0.186401i
$315$	1.28515	+	0.454072i	0.0724099	+	0.0255841i
$316$	2.27609	−	7.43222i	0.128040	−	0.418095i
$317$	−24.4694	+	2.08265i	−1.37434	+	0.116973i	−0.748580	−	0.663044i	$-0.769264\pi$
$317$	−24.4694	+	2.08265i	−1.37434	+	0.116973i	−0.625757	+	0.780018i	$0.715210\pi$
$318$	−2.96325	−	2.84005i	−0.166171	−	0.159262i
$319$	18.7998	+	4.89509i	1.05259	+	0.274072i
$320$	8.88533	−	14.4307i	0.496705	−	0.806700i
$321$	5.16415	−	0.439534i	0.288235	−	0.0245324i
$322$	3.93170	−	3.76823i	0.219105	−	0.209995i
$323$	−1.69377	−	7.85913i	−0.0942440	−	0.437294i
$324$	0.345739	+	0.392835i	0.0192077	+	0.0218242i
$325$	−13.7738	−	1.17232i	−0.764031	−	0.0650287i
$326$	−4.65933	+	11.5952i	−0.258056	+	0.642198i
$327$	11.5211	+	1.97549i	0.637119	+	0.109245i
$328$	−0.117006	−	2.75442i	−0.00646060	−	0.152088i
$329$	−0.362416	+	0.901906i	−0.0199806	+	0.0497237i
$330$	12.3362	+	24.4674i	0.679086	+	1.34689i
$331$	1.24922	−	2.47768i	0.0686635	−	0.136186i	−0.855994	−	0.516986i	$-0.827054\pi$
$331$	1.24922	−	2.47768i	0.0686635	−	0.136186i	0.924657	+	0.380800i	$0.124351\pi$
$332$	−0.0359438	−	0.166780i	−0.00197267	−	0.00915322i
$333$	−3.34010	+	3.79509i	−0.183036	+	0.207969i
$334$	−38.0763	−	13.4532i	−2.08345	−	0.736128i
$335$	23.8403	+	8.42331i	1.30253	+	0.460214i
$336$	−1.25655	+	1.42772i	−0.0685507	+	0.0778887i
$337$	2.27240	+	10.5440i	0.123786	+	0.574367i	0.996312	+	0.0858008i	$0.0273449\pi$
$337$	2.27240	+	10.5440i	0.123786	+	0.574367i	−0.872527	+	0.488566i	$0.837520\pi$
$338$	6.25173	−	12.3996i	0.340049	−	0.674447i
$339$	7.29786	+	14.4744i	0.396365	+	0.786143i
$340$	2.77310	−	6.90113i	0.150393	−	0.374266i
$341$	1.91396	+	45.0561i	0.103647	+	2.43992i
$342$	−3.02927	−	0.519420i	−0.163804	−	0.0280870i
$343$	−2.05655	+	5.11792i	−0.111043	+	0.276341i
$344$	18.4577	+	1.57098i	0.995171	+	0.0847015i
$345$	−19.4412	−	22.0895i	−1.04668	−	1.18926i
$346$	5.57855	+	25.8845i	0.299905	+	1.39156i
$347$	10.2961	−	9.86801i	0.552724	−	0.529743i	−0.362874	−	0.931838i	$-0.618204\pi$
$347$	10.2961	−	9.86801i	0.552724	−	0.529743i	0.915598	+	0.402095i	$0.131718\pi$
$348$	−2.00853	+	0.170951i	−0.107668	+	0.00916393i
$349$	11.4319	−	18.5666i	0.611935	−	0.993846i	−0.385530	−	0.922695i	$-0.625981\pi$
$349$	11.4319	−	18.5666i	0.611935	−	0.993846i	0.997466	−	0.0711510i	$-0.0226672\pi$
$350$	−4.10371	−	1.06852i	−0.219352	−	0.0571149i
$351$	−1.48977	−	1.42783i	−0.0795180	−	0.0762118i
$352$	−14.5230	+	1.23609i	−0.774079	+	0.0658838i
$353$	6.40184	−	20.9042i	0.340736	−	1.11262i	−0.607305	−	0.794469i	$-0.707749\pi$
$353$	6.40184	−	20.9042i	0.340736	−	1.11262i	0.948040	−	0.318150i	$-0.103061\pi$
$354$	5.13445	+	1.81412i	0.272893	+	0.0964192i
$355$	0.0524953	−	0.0136687i	0.00278616	−	0.000725460i
$356$	0.177131	+	1.38324i	0.00938794	+	0.0733117i
$357$	0.868157	−	1.40998i	0.0459477	−	0.0746239i
$358$	−4.09202	−	2.76572i	−0.216270	−	0.146173i
$359$	−3.13275	−	2.11737i	−0.165340	−	0.111750i	0.474510	−	0.880250i	$-0.342625\pi$
$359$	−3.13275	−	2.11737i	−0.165340	−	0.111750i	−0.639850	+	0.768500i	$0.721004\pi$
$360$	5.79242	+	5.55159i	0.305287	+	0.292594i
$361$	−13.3191	+	7.44047i	−0.701003	+	0.391604i
$362$	39.1160	−	6.70711i	2.05589	−	0.352518i
$363$	−6.49851	+	12.8890i	−0.341084	+	0.676499i
$364$	−0.255883	+	0.345976i	−0.0134119	+	0.0181341i
$365$	−0.784370	−	18.4647i	−0.0410558	−	0.966485i
$366$	11.2951	−	3.99080i	0.590402	−	0.208602i
$367$	−29.8390	+	20.1677i	−1.55758	+	1.05274i	−0.587730	+	0.809057i	$0.699978\pi$
$367$	−29.8390	+	20.1677i	−1.55758	+	1.05274i	−0.969854	+	0.243686i	$0.921643\pi$
$368$	38.7156	−	13.6791i	2.01819	−	0.713073i
$369$	1.15839	+	0.198626i	0.0603034	+	0.0103401i
$370$	16.3336	−	22.0844i	0.849141	−	1.14811i
$371$	0.680273	+	0.772941i	0.0353180	+	0.0401291i
$372$	−1.74475	−	4.34199i	−0.0904613	−	0.225121i
$373$	−7.02584	−	3.92487i	−0.363784	−	0.203222i	0.295100	−	0.955466i	$-0.404647\pi$
$373$	−7.02584	−	3.92487i	−0.363784	−	0.203222i	−0.658884	+	0.752244i	$0.728971\pi$
$374$	32.2138	−	8.38783i	1.66574	−	0.433725i
$375$	−1.70169	+	5.55661i	−0.0878751	+	0.286942i
$376$	−4.13073	+	3.95899i	−0.213026	+	0.204169i
$377$	7.83431	−	1.34333i	0.403488	−	0.0691849i
$378$	−0.376407	−	0.508936i	−0.0193603	−	0.0261768i
$379$	29.3152	−	23.6703i	1.50582	−	1.21586i	0.594545	−	0.804063i	$-0.297332\pi$
$379$	29.3152	−	23.6703i	1.50582	−	1.21586i	0.911274	−	0.411801i	$-0.135100\pi$
$380$	3.45074	+	0.293701i	0.177019	+	0.0150665i
$381$	−12.7231	+	17.2028i	−0.651826	+	0.881327i
$382$	1.44569	+	2.86736i	0.0739682	+	0.146707i
$383$	−17.7407	+	14.3246i	−0.906507	+	0.731953i	−0.963862	−	0.266401i	$-0.914166\pi$
$383$	−17.7407	+	14.3246i	−0.906507	+	0.731953i	0.0573557	+	0.998354i	$0.481733\pi$
$384$	−12.4388	+	5.62270i	−0.634766	+	0.286932i
$385$	−2.56302	−	6.37833i	−0.130624	−	0.325070i
$386$	−7.35314	+	8.35479i	−0.374265	+	0.425248i
$387$	−2.31246	+	7.55099i	−0.117549	+	0.383838i
$388$	0.761549	+	5.94704i	0.0386618	+	0.301915i
$389$	−0.256523	+	2.00322i	−0.0130062	+	0.101568i	−0.997103	−	0.0760675i	$-0.975764\pi$
$389$	−0.256523	+	2.00322i	−0.0130062	+	0.101568i	0.984096	+	0.177635i	$0.0568446\pi$
$390$	8.72304	+	7.04337i	0.441709	+	0.356655i
$391$	−31.2084	+	17.4341i	−1.57828	+	0.881678i
$392$	−11.5856	+	11.1039i	−0.585160	+	0.560830i
$393$	−11.9731	+	13.6041i	−0.603964	+	0.686237i
$394$	−6.50193	−	3.63220i	−0.327563	−	0.182987i
$395$	46.2943	+	20.9263i	2.32932	+	1.05292i
$396$	0.335226	−	2.61783i	0.0168457	−	0.131551i
$397$	−24.0238	−	6.25532i	−1.20572	−	0.313945i	−0.405750	−	0.913984i	$-0.632990\pi$
$397$	−24.0238	−	6.25532i	−1.20572	−	0.313945i	−0.799971	+	0.600039i	$0.795152\pi$
$398$	−29.2604	−	19.7766i	−1.46669	−	0.991310i
$399$	0.746145	+	0.194281i	0.0373539	+	0.00972621i
$400$	−24.8761	−	20.0860i	−1.24380	−	1.00430i
$401$	−0.546488	+	2.53571i	−0.0272903	+	0.126627i	−0.989148	−	0.146923i	$-0.953063\pi$
$401$	−0.546488	+	2.53571i	−0.0272903	+	0.126627i	0.961858	+	0.273551i	$0.0881981\pi$
$402$	−6.98258	−	9.44107i	−0.348259	−	0.470878i
$403$	8.30710	+	16.4762i	0.413806	+	0.820736i
$404$	3.13359	+	0.537308i	0.155902	+	0.0267321i
$405$	−2.83382	+	1.91533i	−0.140814	+	0.0951735i
$406$	2.43834			0.121013
$407$	25.4967			1.26382
$408$	8.07534	−	5.45798i	0.399789	−	0.270210i
$409$	−0.660618	−	15.5515i	−0.0326655	−	0.768970i	−0.938488	−	0.345313i	$-0.887773\pi$
$409$	−0.660618	−	15.5515i	−0.0326655	−	0.768970i	0.905822	−	0.423658i	$-0.139254\pi$
$410$	−6.36269	−	0.541544i	−0.314231	−	0.0267450i
$411$	−3.75371	+	1.69679i	−0.185157	+	0.0836963i
$412$	−0.722644	−	2.35968i	−0.0356021	−	0.116253i
$413$	−1.24481	−	0.562691i	−0.0612532	−	0.0276882i
$414$	1.73585	+	13.5555i	0.0853121	+	0.666215i
$415$	1.11109	−	0.0945677i	0.0545413	−	0.00464214i
$416$	−5.20644	+	2.90849i	−0.255267	+	0.142600i
$417$	1.58685	−	7.36303i	0.0777086	−	0.360569i
$418$	8.12696	+	13.1990i	0.397502	+	0.645585i
$419$	27.9063	−	12.6144i	1.36331	−	0.616256i	0.408306	−	0.912845i	$-0.366119\pi$
$419$	27.9063	−	12.6144i	1.36331	−	0.616256i	0.955005	+	0.296589i	$0.0958492\pi$
$420$	0.471244	+	0.535437i	0.0229944	+	0.0261267i
$421$	5.86285	−	11.6283i	0.285738	−	0.566727i	−0.703902	−	0.710297i	$-0.748561\pi$
$421$	5.86285	−	11.6283i	0.285738	−	0.566727i	0.989640	+	0.143569i	$0.0458581\pi$
$422$	−15.3814	−	20.7970i	−0.748753	−	1.01238i
$423$	−1.27887	−	2.07702i	−0.0621810	−	0.100988i
$424$	1.77481	+	5.79536i	0.0861924	+	0.281448i
$425$	24.3009	+	13.5753i	1.17877	+	0.658499i
$426$	−0.0237537	−	0.00839270i	−0.00115087	−	0.000406628i
$427$	−2.90822	+	0.757241i	−0.140738	+	0.0366455i
$428$	2.47146	+	1.11717i	0.119463	+	0.0540005i
$429$	−0.441681	+	10.3975i	−0.0213245	+	0.501996i
$430$	9.03966	−	41.9442i	0.435931	−	2.02273i
$431$	−17.4919	+	2.99929i	−0.842557	+	0.144471i	−0.574064	−	0.818811i	$-0.694634\pi$
$431$	−17.4919	+	2.99929i	−0.842557	+	0.144471i	−0.268493	+	0.963282i	$0.586526\pi$
$432$	−1.00552	−	4.66564i	−0.0483783	−	0.224476i
$433$	4.46803	+	11.1191i	0.214720	+	0.534351i	0.995952	−	0.0898901i	$-0.0286516\pi$
$433$	4.46803	+	11.1191i	0.214720	+	0.534351i	−0.781232	+	0.624241i	$0.785408\pi$
$434$	1.65747	+	5.41221i	0.0795611	+	0.259794i
$435$	0.559175	−	13.1634i	0.0268104	−	0.631137i
$436$	4.75934	+	3.84290i	0.227931	+	0.184041i
$437$	−12.0175	−	11.5179i	−0.574877	−	0.550975i
$438$	−4.50018	+	7.30875i	−0.215027	+	0.349226i
$439$	−2.76504	+	21.5926i	−0.131968	+	1.03056i	0.781574	+	0.623813i	$0.214417\pi$
$439$	−2.76504	+	21.5926i	−0.131968	+	1.03056i	−0.913542	+	0.406745i	$0.866664\pi$
$440$	1.71731	−	40.4269i	0.0818697	−	1.92728i
$441$	−3.58689	−	5.82548i	−0.170804	−	0.277404i
$442$	10.5970	−	8.55647i	0.504047	−	0.406990i
$443$	−0.338988	+	0.843605i	−0.0161058	+	0.0400809i	−0.935725	−	0.352729i	$-0.885254\pi$
$443$	−0.338988	+	0.843605i	−0.0161058	+	0.0400809i	0.919620	+	0.392810i	$0.128497\pi$
$444$	−2.49452	+	0.881369i	−0.118385	+	0.0418279i
$445$	−9.11476			−0.432081
$446$	23.4380	+	3.65489i	1.10982	+	0.173064i
$447$	17.3733			0.821728
$448$	1.86162	−	0.657753i	0.0879533	−	0.0310759i
$449$	10.0028	−	24.8929i	0.472061	−	1.17477i	−0.482271	−	0.876022i	$-0.660188\pi$
$449$	10.0028	−	24.8929i	0.472061	−	1.17477i	0.954332	−	0.298747i	$-0.0965688\pi$
$450$	8.27937	−	6.68512i	0.390293	−	0.315140i
$451$	−3.10775	−	5.04731i	−0.146338	−	0.237668i
$452$	−0.360026	+	8.47529i	−0.0169342	+	0.398644i
$453$	−0.878480	+	6.86018i	−0.0412746	+	0.322319i
$454$	7.95999	−	12.9278i	0.373581	−	0.606734i
$455$	−2.03057	−	1.94614i	−0.0951944	−	0.0912365i
$456$	3.53117	+	2.85122i	0.165362	+	0.133520i
$457$	−0.0235872	+	0.555262i	−0.00110336	+	0.0259741i	−0.999566	−	0.0294506i	$-0.990624\pi$
$457$	−0.0235872	+	0.555262i	−0.00110336	+	0.0259741i	0.998463	+	0.0554247i	$0.0176513\pi$
$458$	−9.00812	−	29.4146i	−0.420922	−	1.37445i
$459$	1.54928	+	3.85554i	0.0723143	+	0.179961i
$460$	−3.24428	−	15.0535i	−0.151265	−	0.701873i
$461$	28.6206	−	4.90749i	1.33299	−	0.228565i	0.541994	−	0.840382i	$-0.317670\pi$
$461$	28.6206	−	4.90749i	1.33299	−	0.228565i	0.790999	+	0.611818i	$0.209561\pi$
$462$	−0.672579	+	3.12078i	−0.0312912	+	0.145192i
$463$	−1.30039	+	30.6122i	−0.0604342	+	1.42267i	0.671354	+	0.741137i	$0.265713\pi$
$463$	−1.30039	+	30.6122i	−0.0604342	+	1.42267i	−0.731788	+	0.681532i	$0.761314\pi$
$464$	16.7526	+	7.57266i	0.777721	+	0.351552i
$465$	29.5980	−	7.70673i	1.37258	−	0.357391i
$466$	26.3079	+	9.29518i	1.21869	+	0.430591i
$467$	−20.1101	−	11.2342i	−0.930585	−	0.519856i	−0.0526379	−	0.998614i	$-0.516763\pi$
$467$	−20.1101	−	11.2342i	−0.930585	−	0.519856i	−0.877947	+	0.478758i	$0.841087\pi$
$468$	−0.316208	−	1.03253i	−0.0146167	−	0.0477286i
$469$	1.54451	+	2.50844i	0.0713188	+	0.115829i
$470$	7.88046	+	10.6551i	0.363498	+	0.491482i
$471$	−3.71513	+	7.36853i	−0.171184	+	0.339524i
$472$	−5.31270	−	6.03640i	−0.244537	−	0.277848i
$473$	36.2919	−	16.4050i	1.66870	−	0.754302i
$474$	−12.3708	−	20.0914i	−0.568208	−	0.922828i
$475$	−2.73073	+	12.6706i	−0.125294	+	0.581368i
$476$	0.756473	−	0.422591i	0.0346729	−	0.0193694i
$477$	−2.57457	+	0.219128i	−0.117882	+	0.0100332i
$478$	−2.55954	−	19.9878i	−0.117071	−	0.914222i
$479$	29.9478	+	13.5373i	1.36835	+	0.618534i	0.956235	−	0.292598i	$-0.0945198\pi$
$479$	29.9478	+	13.5373i	1.36835	+	0.618534i	0.412115	+	0.911132i	$0.364790\pi$
$480$	2.89462	+	9.45192i	0.132121	+	0.431419i
$481$	9.50619	−	4.29707i	0.433445	−	0.195930i
$482$	5.52626	+	0.470354i	0.251714	+	0.0214240i
$483$	−0.145503	−	3.42525i	−0.00662062	−	0.155854i
$484$	−6.25839	+	4.22993i	−0.284472	+	0.192270i
$485$	−39.1875			−1.77941
$486$	1.58849			0.0720555
$487$	−15.7852	+	10.6689i	−0.715297	+	0.483456i	−0.862762	−	0.505611i	$-0.831267\pi$
$487$	−15.7852	+	10.6689i	−0.715297	+	0.483456i	0.147465	+	0.989067i	$0.452889\pi$
$488$	−17.4353	−	2.98959i	−0.789260	−	0.135332i
$489$	3.54165	+	7.02444i	0.160159	+	0.317656i
$490$	22.1025	+	29.8846i	0.998490	+	1.35005i
$491$	−7.91784	+	36.7389i	−0.357327	+	1.65800i	0.339380	+	0.940649i	$0.389783\pi$
$491$	−7.91784	+	36.7389i	−0.357327	+	1.65800i	−0.696708	+	0.717355i	$0.745352\pi$
$492$	0.478528	+	0.386384i	0.0215737	+	0.0174195i
$493$	−15.4892	−	4.03308i	−0.697600	−	0.181641i
$494$	5.25455	+	3.55145i	0.236413	+	0.159787i
$495$	16.6933	+	4.34661i	0.750309	+	0.195365i
$496$	−5.42085	+	42.3322i	−0.243403	+	1.90077i
$497$	0.00575891	+	0.00260319i	0.000258322	+	0.000116769i
$498$	−0.452114	−	0.252566i	−0.0202597	−	0.0113178i
$499$	−14.3625	+	16.3190i	−0.642955	+	0.730539i	−0.977288	−	0.211916i	$-0.932030\pi$
$499$	−14.3625	+	16.3190i	−0.642955	+	0.730539i	0.334333	+	0.942455i	$0.391489\pi$
$500$	−2.19557	+	2.10428i	−0.0981889	+	0.0941065i
$501$	−22.1940	+	12.3983i	−0.991556	+	0.553916i
$502$	12.3323	+	9.95764i	0.550418	+	0.444431i
$503$	−4.32312	+	33.7598i	−0.192758	+	1.50528i	0.549687	+	0.835371i	$0.314747\pi$
$503$	−4.32312	+	33.7598i	−0.192758	+	1.50528i	−0.742445	+	0.669907i	$0.766334\pi$
$504$	0.118731	+	0.927184i	0.00528868	+	0.0413000i
$505$	−6.08491	+	19.8693i	−0.270775	+	0.884173i
$506$	45.5351	−	51.7380i	2.02428	−	2.30003i
$507$	−3.25947	−	8.11151i	−0.144758	−	0.360245i
$508$	−10.2031	+	4.61209i	−0.452690	+	0.204629i
$509$	−28.7426	+	23.2080i	−1.27399	+	1.02868i	−0.276281	+	0.961077i	$0.589102\pi$
$509$	−28.7426	+	23.2080i	−1.27399	+	1.02868i	−0.997712	+	0.0676014i	$0.978465\pi$
$510$	−10.1639	−	20.1588i	−0.450063	−	0.892647i
$511$	1.28036	−	1.73116i	0.0566396	−	0.0765818i
$512$	8.56636	+	0.729105i	0.378583	+	0.0322222i
$513$	−1.50537	+	1.21550i	−0.0664638	+	0.0536658i
$514$	−10.1329	−	13.7006i	−0.446943	−	0.604307i
$515$	15.8980	−	2.72599i	0.700549	−	0.120121i
$516$	−2.98360	+	2.85955i	−0.131346	+	0.125885i
$517$	−3.60213	+	11.7622i	−0.158421	+	0.517300i
$518$	3.09696	−	0.806385i	0.136073	−	0.0354305i
$519$	14.5524	+	8.12947i	0.638780	+	0.356844i
$520$	−6.17304	−	15.3622i	−0.270706	−	0.673677i
$521$	−15.1509	−	17.2148i	−0.663774	−	0.754194i	0.317194	−	0.948361i	$-0.397259\pi$
$521$	−15.1509	−	17.2148i	−0.663774	−	0.754194i	−0.980969	+	0.194166i	$0.937800\pi$
$522$	−3.63848	+	4.91955i	−0.159252	+	0.215323i
$523$	−24.0842	−	4.12965i	−1.05313	−	0.180577i	−0.383703	−	0.923457i	$-0.625351\pi$
$523$	−24.0842	−	4.12965i	−1.05313	−	0.180577i	−0.669425	+	0.742880i	$0.733459\pi$
$524$	−8.94201	+	3.15941i	−0.390634	+	0.138020i
$525$	−2.21173	+	1.49487i	−0.0965280	+	0.0652415i
$526$	−5.86932	+	2.07376i	−0.255915	+	0.0904204i
$527$	−1.57692	−	37.1219i	−0.0686916	−	1.61705i
$528$	−14.3130	+	19.3525i	−0.622895	+	0.842210i
$529$	−22.9673	+	45.5529i	−0.998579	+	1.98056i
$530$	13.8370	−	2.37258i	0.601039	−	0.103058i
$531$	2.99278	−	1.67187i	0.129876	−	0.0725528i
$532$	0.291299	+	0.279187i	0.0126294	+	0.0121043i
$533$	−2.00934	−	1.35808i	−0.0870341	−	0.0588248i
$534$	3.50714	+	2.37041i	0.151769	+	0.102578i
$535$	−9.29452	+	15.0953i	−0.401837	+	0.652625i
$536$	2.20252	+	17.1998i	0.0951345	+	0.742919i
$537$	−3.00892	+	0.783461i	−0.129844	+	0.0338088i
$538$	1.76313	+	0.622954i	0.0760140	+	0.0268574i
$539$	−10.1030	+	32.9897i	−0.435166	+	1.42097i
$540$	−1.78348	+	0.151796i	−0.0767487	+	0.00653227i
$541$	24.8785	+	23.8441i	1.06961	+	1.02514i	0.999619	+	0.0275907i	$0.00878351\pi$
$541$	24.8785	+	23.8441i	1.06961	+	1.02514i	0.0699909	+	0.997548i	$0.477703\pi$
$542$	−31.7572	−	8.26894i	−1.36409	−	0.355182i
$543$	13.0993	−	21.2746i	0.562143	−	0.912978i
$544$	11.9656	−	1.01842i	0.513019	−	0.0436644i
$545$	−28.8651	+	27.6649i	−1.23644	+	1.18504i
$546$	0.275194	+	1.27690i	0.0117772	+	0.0546464i
$547$	9.50835	+	10.8036i	0.406548	+	0.461928i	0.917532	−	0.397662i	$-0.130178\pi$
$547$	9.50835	+	10.8036i	0.406548	+	0.461928i	−0.510984	+	0.859590i	$0.670719\pi$
$548$	−2.14796	−	0.182819i	−0.0917564	−	0.00780962i
$549$	2.81183	−	6.99752i	0.120006	−	0.298647i
$550$	−52.8954	−	9.06982i	−2.25547	−	0.386739i
$551$	−0.316313	−	7.44625i	−0.0134754	−	0.317221i
$552$	7.52449	−	18.7254i	0.320264	−	0.797006i
$553$	2.66476	+	5.28523i	0.113317	+	0.224751i
$554$	−12.5702	+	24.9314i	−0.534055	+	1.05924i
$555$	−3.64307	−	16.9039i	−0.154640	−	0.717532i
$556$	2.60413	−	2.95887i	0.110440	−	0.125484i
$557$	−32.3545	−	11.4316i	−1.37091	−	0.484372i	−0.456700	−	0.889621i	$-0.650969\pi$
$557$	−32.3545	−	11.4316i	−1.37091	−	0.484372i	−0.914206	+	0.405249i	$0.867185\pi$
$558$	−13.3928	−	4.73199i	−0.566964	−	0.200321i
$559$	10.7663	−	12.2329i	0.455365	−	0.517395i
$560$	−1.37054	−	6.35931i	−0.0579157	−	0.268730i
$561$	9.43432	−	18.7119i	0.398317	−	0.790015i
$562$	10.5408	+	20.9064i	0.444637	+	0.881884i
$563$	2.75507	−	6.85625i	0.116112	−	0.288957i	−0.858516	−	0.512787i	$-0.828613\pi$
$563$	2.75507	−	6.85625i	0.116112	−	0.288957i	0.974628	+	0.223831i	$0.0718562\pi$
$564$	−0.0541738	−	1.27529i	−0.00228113	−	0.0536996i
$565$	−54.6473	−	9.37022i	−2.29903	−	0.394208i
$566$	15.0777	−	37.5222i	0.633761	−	1.57718i
$567$	−0.397060	−	0.0337948i	−0.0166749	−	0.00141925i
$568$	0.0245783	+	0.0279264i	0.00103128	+	0.00117176i
$569$	−1.94691	−	9.03370i	−0.0816188	−	0.378712i	0.918231	−	0.396045i	$-0.129618\pi$
$569$	−1.94691	−	9.03370i	−0.0816188	−	0.378712i	−0.999850	+	0.0173328i	$0.994483\pi$
$570$	7.58954	−	7.27398i	0.317891	−	0.304674i
$571$	−41.9050	+	3.56664i	−1.75367	+	0.149259i	−0.917115	−	0.398622i	$-0.869488\pi$
$571$	−41.9050	+	3.56664i	−1.75367	+	0.149259i	−0.836556	+	0.547882i	$0.815434\pi$
$572$	−2.85540	+	4.63746i	−0.119390	+	0.193902i
$573$	1.95631	+	0.509383i	0.0817260	+	0.0212798i
$574$	−0.537115	−	0.514783i	−0.0224187	−	0.0214866i
$575$	57.4256	−	4.88764i	2.39481	−	0.203829i
$576$	−1.45083	+	4.73747i	−0.0604514	+	0.197395i
$577$	5.27100	+	1.86236i	0.219435	+	0.0775312i	0.440594	−	0.897706i	$-0.354768\pi$
$577$	5.27100	+	1.86236i	0.219435	+	0.0775312i	−0.221159	+	0.975238i	$0.570984\pi$
$578$	−0.408079	+	0.106255i	−0.0169738	+	0.00441964i
$579$	0.889947	+	6.94973i	0.0369850	+	0.288821i
$580$	3.61498	−	5.87110i	0.150104	−	0.243784i
$581$	0.107637	+	0.0727500i	0.00446554	+	0.00301818i
$582$	15.0784	+	10.1912i	0.625021	+	0.422440i
$583$	9.40797	+	9.01680i	0.389638	+	0.373438i
$584$	11.0651	−	6.18131i	0.457876	−	0.255785i
$585$	6.95650	−	1.19281i	0.287616	−	0.0493167i
$586$	−16.5448	+	32.8146i	−0.683459	+	1.35556i
$587$	13.8634	−	18.7445i	0.572202	−	0.773669i	−0.418718	−	0.908116i	$-0.637521\pi$
$587$	13.8634	−	18.7445i	0.572202	−	0.773669i	0.990921	+	0.134447i	$0.0429259\pi$
$588$	−0.151943	−	3.57685i	−0.00626602	−	0.147507i
$589$	16.3129	−	5.76372i	0.672162	−	0.237490i
$590$	−15.4316	+	10.4299i	−0.635309	+	0.429394i
$591$	−4.42070	+	1.56193i	−0.181843	+	0.0642493i
$592$	23.7820	+	4.07784i	0.977436	+	0.167598i
$593$	−27.0638	+	36.5927i	−1.11138	+	1.50268i	−0.269508	+	0.962998i	$0.586861\pi$
$593$	−27.0638	+	36.5927i	−1.11138	+	1.50268i	−0.841869	+	0.539682i	$0.818544\pi$
$594$	−5.29280	−	6.01379i	−0.217166	−	0.246749i
$595$	2.11168	+	5.25513i	0.0865706	+	0.215439i
$596$	7.93713	+	4.43394i	0.325117	+	0.181621i
$597$	−21.5156	+	5.60222i	−0.880573	+	0.229283i
$598$	8.25771	−	26.9642i	0.337683	−	1.10265i
$599$	−2.21445	+	2.12237i	−0.0904798	+	0.0867179i	−0.735819	−	0.677178i	$-0.763203\pi$
$599$	−2.21445	+	2.12237i	−0.0904798	+	0.0867179i	0.645339	+	0.763896i	$0.276716\pi$
$600$	−15.4880	+	2.65568i	−0.632293	+	0.108418i
$601$	−11.3877	−	15.3972i	−0.464513	−	0.628063i	0.507876	−	0.861430i	$-0.330431\pi$
$601$	−11.3877	−	15.3972i	−0.464513	−	0.628063i	−0.972389	+	0.233367i	$0.925026\pi$
$602$	3.88936	−	3.14044i	0.158519	−	0.127995i
$603$	−7.36570	−	0.626913i	−0.299954	−	0.0255299i
$604$	−2.15217	+	2.90993i	−0.0875705	+	0.118403i
$605$	−22.2274	−	44.0855i	−0.903673	−	1.79233i
$606$	7.50861	−	6.06278i	0.305016	−	0.246283i
$607$	43.3425	−	19.5921i	1.75922	−	0.795217i	0.772044	−	0.635569i	$-0.219234\pi$
$607$	43.3425	−	19.5921i	1.75922	−	0.795217i	0.987174	−	0.159648i	$-0.0510360\pi$
$608$	2.08496	+	5.18862i	0.0845562	+	0.210426i
$609$	1.01414	−	1.15228i	0.0410949	−	0.0466928i
$610$	−11.9981	+	39.1780i	−0.485790	+	1.58627i
$611$	0.639315	+	4.99250i	0.0258639	+	0.201975i
$612$	−0.276194	+	2.15684i	−0.0111645	+	0.0871850i
$613$	−34.4262	−	27.7972i	−1.39046	−	1.12272i	−0.977251	−	0.212084i	$-0.931975\pi$
$613$	−34.4262	−	27.7972i	−1.39046	−	1.12272i	−0.413211	−	0.910635i	$-0.635593\pi$
$614$	31.1281	−	17.3892i	1.25623	−	0.701771i
$615$	−2.90224	+	2.78157i	−0.117030	+	0.112164i
$616$	3.11457	−	3.53884i	0.125490	−	0.142584i
$617$	0.591788	+	0.330592i	0.0238245	+	0.0133091i	0.499562	−	0.866278i	$-0.333494\pi$
$617$	0.591788	+	0.330592i	0.0238245	+	0.0133091i	−0.475737	+	0.879587i	$0.657819\pi$
$618$	−6.82610	−	3.08559i	−0.274586	−	0.124121i
$619$	1.91681	−	14.9686i	0.0770430	−	0.601640i	−0.906663	−	0.421855i	$-0.861379\pi$
$619$	1.91681	−	14.9686i	0.0770430	−	0.601640i	0.983706	−	0.179784i	$-0.0575399\pi$
$620$	15.4890	+	4.03302i	0.622052	+	0.161970i
$621$	7.12785	+	4.81759i	0.286031	+	0.193323i
$622$	−23.6833	−	6.16666i	−0.949616	−	0.247261i
$623$	−0.826215	−	0.667122i	−0.0331016	−	0.0267277i
$624$	−2.07491	+	9.62764i	−0.0830631	+	0.385414i
$625$	8.09779	+	10.9489i	0.323912	+	0.437957i
$626$	−16.3940	−	32.5156i	−0.655237	−	1.29959i
$627$	9.61755	+	1.64909i	0.384088	+	0.0658585i
$628$	−3.57786	+	2.41821i	−0.142772	+	0.0964971i
$629$	−21.0068			−0.837597
$630$	2.16513			0.0862608
$631$	−1.93097	+	1.30511i	−0.0768706	+	0.0519555i	−0.597807	−	0.801640i	$-0.703961\pi$
$631$	−1.93097	+	1.30511i	−0.0768706	+	0.0519555i	0.520937	+	0.853595i	$0.325583\pi$
$632$	1.47872	+	34.8103i	0.0588205	+	1.38468i
$633$	−16.2253	−	1.38098i	−0.644898	−	0.0548889i
$634$	−35.5470	+	16.0683i	−1.41175	+	0.638152i
$635$	−21.4301	−	69.9767i	−0.850429	−	2.77694i
$636$	−1.23214	−	0.556962i	−0.0488575	−	0.0220850i
$637$	1.79310	+	14.0026i	0.0710453	+	0.554803i
$638$	30.7479	−	2.61703i	1.21732	−	0.103609i
$639$	−0.0138456	+	0.00773460i	−0.000547723	+	0.000305976i
$640$	9.83668	−	45.6424i	0.388829	−	1.80417i
$641$	22.5905	+	36.6893i	0.892272	+	1.44914i	0.893460	+	0.449142i	$0.148270\pi$
$641$	22.5905	+	36.6893i	0.892272	+	1.44914i	−0.00118823	+	0.999999i	$0.500378\pi$
$642$	7.50203	−	3.39113i	0.296082	−	0.133837i
$643$	−15.9768	−	18.1532i	−0.630064	−	0.715892i	0.344804	−	0.938675i	$-0.387945\pi$
$643$	−15.9768	−	18.1532i	−0.630064	−	0.715892i	−0.974868	+	0.222783i	$0.928486\pi$
$644$	0.807706	−	1.60199i	0.0318281	−	0.0631272i
$645$	−16.0618	−	21.7170i	−0.632433	−	0.855105i
$646$	−6.69583	−	10.8747i	−0.263444	−	0.427860i
$647$	−3.37330	−	11.0150i	−0.132618	−	0.433043i	0.865020	−	0.501738i	$-0.167306\pi$
$647$	−3.37330	−	11.0150i	−0.132618	−	0.433043i	−0.997638	+	0.0686945i	$0.978117\pi$
$648$	−2.04784	−	1.14399i	−0.0804467	−	0.0449402i
$649$	−16.3013	−	5.75960i	−0.639880	−	0.226084i
$650$	−21.2501	+	5.53310i	−0.833498	+	0.217026i
$651$	3.24700	+	1.46774i	0.127260	+	0.0575252i
$652$	−0.174721	+	4.11306i	−0.00684259	+	0.161080i
$653$	−0.543815	+	2.52331i	−0.0212811	+	0.0987448i	−0.986948	−	0.161038i	$-0.948516\pi$
$653$	−0.543815	+	2.52331i	−0.0212811	+	0.0987448i	0.965667	+	0.259783i	$0.0836510\pi$
$654$	18.3012	−	3.13806i	0.715634	−	0.122708i
$655$	−13.0592	−	60.5949i	−0.510265	−	2.36764i
$656$	−2.09151	−	5.20492i	−0.0816597	−	0.203218i
$657$	1.58221	+	5.16645i	0.0617277	+	0.201562i
$658$	−0.0655297	+	1.54262i	−0.00255461	+	0.0601376i
$659$	21.7615	+	17.5712i	0.847707	+	0.684476i	0.950668	−	0.310210i	$-0.100399\pi$
$659$	21.7615	+	17.5712i	0.847707	+	0.684476i	−0.102961	+	0.994685i	$0.532832\pi$
$660$	6.51716	+	6.24619i	0.253680	+	0.243133i
$661$	−2.13151	+	3.46178i	−0.0829060	+	0.134648i	−0.890317	−	0.455342i	$-0.849517\pi$
$661$	−2.13151	+	3.46178i	−0.0829060	+	0.134648i	0.807411	+	0.589990i	$0.200868\pi$
$662$	0.559862	−	4.37204i	0.0217596	−	0.169924i
$663$	0.363902	−	8.56655i	0.0141328	−	0.332697i
$664$	0.400961	+	0.651202i	0.0155603	+	0.0252715i
$665$	−2.05183	+	1.65674i	−0.0795667	+	0.0642456i
$666$	−2.99432	+	7.45165i	−0.116028	+	0.288746i
$667$	−31.2465	+	11.0401i	−1.20987	+	0.427474i
$668$	−13.3038			−0.514738
$669$	11.4754	−	9.55595i	0.443663	−	0.369455i
$670$	40.1644			1.55169
$671$	−35.8605	+	12.6703i	−1.38438	+	0.489132i
$672$	−0.429414	+	1.06864i	−0.0165650	+	0.0412236i
$673$	21.5362	−	17.3893i	0.830159	−	0.670307i	−0.116270	−	0.993218i	$-0.537094\pi$
$673$	21.5362	−	17.3893i	0.830159	−	0.670307i	0.946429	+	0.322911i	$0.104661\pi$
$674$	8.98327	+	14.5898i	0.346023	+	0.561977i
$675$	0.284315	−	6.69300i	0.0109433	−	0.257614i
$676$	0.581073	−	4.53768i	0.0223489	−	0.174526i
$677$	−4.64884	+	7.55019i	−0.178669	+	0.290177i	−0.928412	−	0.371552i	$-0.878826\pi$
$677$	−4.64884	+	7.55019i	−0.178669	+	0.290177i	0.749743	+	0.661729i	$0.230177\pi$
$678$	18.5901	+	17.8172i	0.713950	+	0.684265i
$679$	−3.55219	−	2.86819i	−0.136320	−	0.110071i
$680$	−1.41490	+	33.3079i	−0.0542590	+	1.27730i
$681$	−2.79863	−	9.13850i	−0.107244	−	0.350188i
$682$	26.7099	+	66.4701i	1.02277	+	2.54527i
$683$	−7.50056	−	34.8027i	−0.287001	−	1.33169i	−0.859227	−	0.511594i	$-0.829055\pi$
$683$	−7.50056	−	34.8027i	−0.287001	−	1.33169i	0.572226	−	0.820096i	$-0.306080\pi$
$684$	−0.997957	+	0.171117i	−0.0381579	+	0.00654282i
$685$	2.96846	−	13.7737i	0.113419	−	0.526265i
$686$	−0.371852	+	8.75369i	−0.0141974	+	0.334217i
$687$	−17.6470	−	7.97695i	−0.673275	−	0.304340i
$688$	36.4750	−	9.49736i	1.39060	−	0.362084i
$689$	5.02731	+	1.77626i	0.191525	+	0.0676702i
$690$	−40.8077	−	22.7966i	−1.55352	−	0.867851i
$691$	−7.37902	−	24.0950i	−0.280711	−	0.916619i	−0.979526	−	0.201316i	$-0.935478\pi$
$691$	−7.37902	−	24.0950i	−0.280711	−	0.916619i	0.698815	−	0.715302i	$-0.253711\pi$
$692$	4.57362	+	7.42803i	0.173863	+	0.282371i
$693$	1.19505	+	1.61581i	0.0453961	+	0.0613795i
$694$	10.1990	−	20.2285i	0.387148	−	0.767862i
$695$	17.0207	+	19.3393i	0.645633	+	0.733581i
$696$	8.23354	−	3.72180i	0.312092	−	0.141074i
$697$	2.56049	+	4.15849i	0.0969854	+	0.157514i
$698$	7.29692	−	33.8578i	0.276193	−	1.28154i
$699$	15.3344	−	8.56631i	0.580001	−	0.324008i
$700$	−1.39196	+	0.118474i	−0.0526113	+	0.00447788i
$701$	−2.87030	−	22.4146i	−0.108410	−	0.846588i	−0.951249	−	0.308423i	$-0.900199\pi$
$701$	−2.87030	−	22.4146i	−0.108410	−	0.846588i	0.842840	−	0.538165i	$-0.180882\pi$
$702$	−2.98690	−	1.35016i	−0.112733	−	0.0509587i
$703$	−2.86431	−	9.35296i	−0.108030	−	0.352754i
$704$	22.7695	−	10.2924i	0.858156	−	0.387911i
$705$	8.31284	+	0.707527i	0.313080	+	0.0266470i
$706$	−1.47392	−	34.6972i	−0.0554716	−	1.30584i
$707$	−2.00583	+	1.35571i	−0.0754372	+	0.0509866i
$708$	1.79396			0.0674212
$709$	51.0441			1.91700			0.958501	−	0.285089i	$-0.0920231\pi$
$709$	51.0441			1.91700			0.958501	+	0.285089i	$0.0920231\pi$
$710$	0.0713917	−	0.0482524i	0.00267928	−	0.00181088i
$711$	−14.6397	−	2.51023i	−0.549032	−	0.0941410i
$712$	−2.81419	−	5.58162i	−0.105466	−	0.209180i
$713$	−45.7449	−	61.8511i	−1.71316	−	2.31634i
$714$	0.554140	−	2.57122i	0.0207382	−	0.0962255i
$715$	−27.6946	−	22.3618i	−1.03572	−	0.836285i
$716$	−1.57460	−	0.409994i	−0.0588456	−	0.0153222i
$717$	−10.5102	−	7.10363i	−0.392509	−	0.265290i
$718$	−5.81258	−	1.51348i	−0.216923	−	0.0564825i
$719$	−1.38422	+	10.8096i	−0.0516227	+	0.403129i	0.945393	+	0.325932i	$0.105678\pi$
$719$	−1.38422	+	10.8096i	−0.0516227	+	0.403129i	−0.997016	+	0.0771968i	$0.975403\pi$
$720$	14.8755	+	6.72417i	0.554378	+	0.250595i
$721$	1.64061	+	0.916497i	0.0610994	+	0.0341321i
$722$	−16.0113	+	18.1923i	−0.595877	+	0.677048i
$723$	2.52072	−	2.41591i	0.0937464	−	0.0898487i
$724$	11.4141	−	6.37631i	0.424202	−	0.236974i
$725$	20.0769	+	16.2110i	0.745637	+	0.602060i
$726$	−2.91243	+	22.7436i	−0.108090	+	0.844093i
$727$	6.49469	+	50.7180i	0.240875	+	1.88103i	0.435560	+	0.900160i	$0.356550\pi$
$727$	6.49469	+	50.7180i	0.240875	+	1.88103i	−0.194685	+	0.980866i	$0.562368\pi$
$728$	0.564821	−	1.84433i	0.0209336	−	0.0683555i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	−10.9461	−	27.2405i	−0.405134	−	1.00822i
$731$	−29.9010	+	13.5161i	−1.10593	+	0.499912i
$732$	3.07049	−	2.47925i	0.113489	−	0.0916356i
$733$	3.16528	+	6.27795i	0.116912	+	0.231881i	0.943823	−	0.330452i	$-0.107201\pi$
$733$	3.16528	+	6.27795i	0.116912	+	0.231881i	−0.826911	+	0.562333i	$0.809904\pi$
$734$	−34.0190	+	45.9967i	−1.25566	+	1.69777i
$735$	23.3152	+	1.98442i	0.859996	+	0.0731964i
$736$	19.3451	−	15.6201i	0.713071	−	0.575765i
$737$	22.1688	+	29.9742i	0.816600	+	1.10412i
$738$	1.84010	−	0.315516i	0.0677349	−	0.0116143i
$739$	−23.1112	+	22.1503i	−0.850159	+	0.814811i	−0.984365	−	0.176142i	$-0.943638\pi$
$739$	−23.1112	+	22.1503i	−0.850159	+	0.814811i	0.134206	+	0.990953i	$0.457152\pi$
$740$	2.64979	−	8.65247i	0.0974081	−	0.318071i
$741$	3.86374	−	1.00604i	0.141938	−	0.0369578i
$742$	1.42792	+	0.797681i	0.0524204	+	0.0292838i
$743$	−10.8999	−	27.1254i	−0.399878	−	0.995136i	−0.983140	−	0.182852i	$-0.941467\pi$
$743$	−10.8999	−	27.1254i	−0.399878	−	0.995136i	0.583262	−	0.812284i	$-0.301776\pi$
$744$	13.8578	+	15.7455i	0.508052	+	0.577259i
$745$	−35.3351	+	47.7762i	−1.29458	+	1.75038i
$746$	−12.6000	−	2.16048i	−0.461318	−	0.0791009i
$747$	−0.307395	+	0.108610i	−0.0112470	+	0.00397382i
$748$	9.08572	−	6.14087i	0.332207	−	0.224533i
$749$	−1.94735	+	0.688044i	−0.0711547	+	0.0251406i
$750$	0.391787	+	9.22297i	0.0143060	+	0.336775i
$751$	−5.66867	+	7.66455i	−0.206853	+	0.279683i	−0.895169	−	0.445728i	$-0.852945\pi$
$751$	−5.66867	+	7.66455i	−0.206853	+	0.279683i	0.688316	+	0.725411i	$0.258350\pi$
$752$	−5.24109	+	10.3951i	−0.191123	+	0.379069i
$753$	9.83483	−	1.68635i	0.358401	−	0.0614540i
$754$	11.0230	−	6.15782i	0.401434	−	0.224255i
$755$	−17.0786	−	16.3685i	−0.621555	−	0.595712i
$756$	−0.172775	−	0.116776i	−0.00628377	−	0.00424708i
$757$	−23.5795	−	15.9370i	−0.857013	−	0.579240i	0.0507557	−	0.998711i	$-0.483837\pi$
$757$	−23.5795	−	15.9370i	−0.857013	−	0.579240i	−0.907768	+	0.419472i	$0.862215\pi$
$758$	31.3808	−	50.9657i	1.13980	−	1.85116i
$759$	−5.51110	−	43.0370i	−0.200040	−	1.56214i
$760$	−15.0227	+	3.91162i	−0.544932	+	0.141889i
$761$	−13.9295	−	4.92160i	−0.504944	−	0.178408i	0.0685030	−	0.997651i	$-0.478178\pi$
$761$	−13.9295	−	4.92160i	−0.504944	−	0.178408i	−0.573447	+	0.819243i	$0.694394\pi$
$762$	−9.95257	+	32.4986i	−0.360544	+	1.17730i
$763$	−4.64133	+	0.395036i	−0.168028	+	0.0143013i
$764$	0.763753	+	0.731998i	0.0276316	+	0.0264828i
$765$	−13.7537	−	3.58119i	−0.497266	−	0.129478i
$766$	−18.9907	+	30.8429i	−0.686164	+	1.11440i
$767$	−7.04846	+	0.599912i	−0.254505	+	0.0216616i
$768$	−8.50074	+	8.14730i	−0.306744	+	0.293990i
$769$	−9.04527	−	41.9702i	−0.326181	−	1.51348i	−0.781925	−	0.623373i	$-0.785762\pi$
$769$	−9.04527	−	41.9702i	−0.326181	−	1.51348i	0.455744	−	0.890111i	$-0.349373\pi$
$770$	−7.21413	−	8.19684i	−0.259979	−	0.295394i
$771$	−10.6889	−	0.909757i	−0.384950	−	0.0327641i
$772$	−1.36710	+	3.40217i	−0.0492031	+	0.122447i
$773$	−13.4307	−	2.30293i	−0.483070	−	0.0828307i	−0.0776874	−	0.996978i	$-0.524754\pi$
$773$	−13.4307	−	2.30293i	−0.483070	−	0.0828307i	−0.405383	+	0.914147i	$0.632862\pi$
$774$	0.532406	+	12.5333i	0.0191369	+	0.450499i
$775$	−22.3350	+	55.5828i	−0.802297	+	1.99659i
$776$	−12.0992	−	23.9973i	−0.434336	−	0.861454i
$777$	0.906992	−	1.79891i	0.0325382	−	0.0645356i
$778$	0.675879	+	3.13609i	0.0242314	+	0.112434i
$779$	−1.50238	+	1.70703i	−0.0538283	+	0.0611608i
$780$	3.48256	+	1.23047i	0.124696	+	0.0440578i
$781$	0.0754150	+	0.0266458i	0.00269856	+	0.000953462i
$782$	−37.5166	+	42.6271i	−1.34159	+	1.52434i
$783$	0.811534	+	3.76553i	0.0290019	+	0.134569i
$784$	−14.6998	+	29.1553i	−0.524993	+	1.04126i
$785$	−12.7072	−	25.2032i	−0.453539	−	0.899541i
$786$	−10.7336	+	26.7117i	−0.382856	+	0.952774i
$787$	−0.474242	−	11.1640i	−0.0169049	−	0.397955i	−0.987537	−	0.157386i	$-0.949693\pi$
$787$	−0.474242	−	11.1640i	−0.0169049	−	0.397955i	0.970632	−	0.240568i	$-0.0773338\pi$
$788$	−2.41826	−	0.414653i	−0.0861470	−	0.0147714i
$789$	−1.46113	+	3.63616i	−0.0520176	+	0.129451i
$790$	80.4115	+	6.84403i	2.86091	+	0.243499i
$791$	−4.26773	−	4.84909i	−0.151743	−	0.172414i
$792$	2.49235	+	11.5645i	0.0885617	+	0.410928i
$793$	−11.2348	+	10.7677i	−0.398961	+	0.382373i
$794$	−39.2920	+	3.34425i	−1.39442	+	0.118683i
$795$	4.63376	−	7.52570i	0.164342	−	0.266909i
$796$	−11.2593	−	2.93170i	−0.399077	−	0.103911i
$797$	26.3658	+	25.2696i	0.933925	+	0.895095i	0.994675	−	0.103058i	$-0.0328628\pi$
$797$	26.3658	+	25.2696i	0.933925	+	0.895095i	−0.0607500	+	0.998153i	$0.519349\pi$
$798$	1.22035	−	0.103867i	0.0432000	−	0.00367686i
$799$	2.96781	−	9.69091i	0.104993	−	0.342840i
$800$	−18.2549	−	6.44985i	−0.645407	−	0.228037i
$801$	2.57885	−	0.671480i	0.0911191	−	0.0237256i
$802$	0.523370	+	4.08707i	0.0184808	+	0.144320i
$803$	14.2875	−	23.2044i	0.504195	−	0.818865i
$804$	−3.20508	−	2.16626i	−0.113034	−	0.0763980i
$805$	9.71531	+	6.56641i	0.342420	+	0.231435i
$806$	21.1610	+	20.2812i	0.745365	+	0.714375i
$807$	1.02770	−	0.574106i	0.0361767	−	0.0202095i
$808$	−14.0461	+	2.40845i	−0.494141	+	0.0847290i
$809$	−7.00714	+	13.8978i	−0.246358	+	0.488622i	−0.982032	−	0.188714i	$-0.939568\pi$
$809$	−7.00714	+	13.8978i	−0.246358	+	0.488622i	0.735674	+	0.677336i	$0.236865\pi$
$810$	−3.23080	+	4.36832i	−0.113519	+	0.153487i
$811$	0.977511	+	23.0114i	0.0343251	+	0.808039i	0.930928	+	0.365203i	$0.119000\pi$
$811$	0.977511	+	23.0114i	0.0343251	+	0.808039i	−0.896603	+	0.442836i	$0.853973\pi$
$812$	0.757397	−	0.267605i	0.0265794	−	0.00939111i
$813$	−17.1159	+	11.5683i	−0.600280	+	0.405719i
$814$	38.1878	−	13.4926i	1.33848	−	0.472915i
$815$	−26.5203	−	4.54737i	−0.928967	−	0.159287i
$816$	11.7926	−	15.9446i	0.412823	−	0.558173i
$817$	−10.0949	−	11.4700i	−0.353176	−	0.401286i
$818$	−9.21913	−	22.9427i	−0.322339	−	0.802172i
$819$	0.717881	+	0.401033i	0.0250848	+	0.0140132i
$820$	−2.03581	+	0.530085i	−0.0710937	+	0.0185114i
$821$	0.710588	−	2.32031i	0.0247997	−	0.0809795i	−0.942909	−	0.333050i	$-0.891922\pi$
$821$	0.710588	−	2.32031i	0.0247997	−	0.0809795i	0.967709	+	0.252070i	$0.0811114\pi$
$822$	−4.72422	+	4.52780i	−0.164776	+	0.157925i
$823$	33.7217	−	5.78217i	1.17547	−	0.201554i	0.452067	−	0.891984i	$-0.350687\pi$
$823$	33.7217	−	5.78217i	1.17547	−	0.201554i	0.723399	+	0.690430i	$0.242579\pi$
$824$	6.57784	+	8.89382i	0.229150	+	0.309831i
$825$	−26.2860	+	21.2244i	−0.915160	+	0.738940i
$826$	−2.16219	−	0.184030i	−0.0752323	−	0.00640322i
$827$	−28.5206	+	38.5624i	−0.991759	+	1.34095i	−0.0521714	+	0.998638i	$0.516614\pi$
$827$	−28.5206	+	38.5624i	−0.991759	+	1.34095i	−0.939588	+	0.342309i	$0.888791\pi$
$828$	2.02689	+	4.02010i	0.0704393	+	0.139708i
$829$	−16.2955	+	13.1577i	−0.565967	+	0.456986i	−0.868177	−	0.496255i	$-0.834708\pi$
$829$	−16.2955	+	13.1577i	−0.565967	+	0.456986i	0.302210	+	0.953241i	$0.402276\pi$
$830$	1.61410	−	0.729617i	0.0560261	−	0.0253254i
$831$	6.55373	+	16.3096i	0.227346	+	0.565773i
$832$	6.75474	−	7.67488i	0.234178	−	0.266078i
$833$	8.32389	−	27.1804i	0.288406	−	0.941743i
$834$	−1.51973	−	11.8678i	−0.0526238	−	0.410947i
$835$	11.0447	−	86.2497i	0.382218	−	2.98479i
$836$	3.97298	+	3.20796i	0.137408	+	0.110950i
$837$	−7.80645	+	4.36094i	−0.269830	+	0.150736i
$838$	35.1213	−	33.6611i	1.21325	−	1.16280i
$839$	6.02174	−	6.84202i	0.207893	−	0.236213i	−0.637376	−	0.770553i	$-0.719980\pi$
$839$	6.02174	−	6.84202i	0.207893	−	0.236213i	0.845270	+	0.534340i	$0.179440\pi$
$840$	−2.79122	−	1.55927i	−0.0963062	−	0.0537999i
$841$	12.9050	+	5.83342i	0.444999	+	0.201152i
$842$	2.62754	−	20.5189i	0.0905511	−	0.707127i
$843$	14.2638	+	3.71400i	0.491270	+	0.127917i
$844$	−7.06021	−	4.77187i	−0.243022	−	0.164255i
$845$	28.9358	+	7.53431i	0.995423	+	0.259188i
$846$	−3.01458	−	2.43410i	−0.103643	−	0.0836862i
$847$	1.21185	−	5.62302i	0.0416398	−	0.193209i
$848$	7.33317	+	9.91510i	0.251822	+	0.340486i
$849$	−11.4608	−	22.7312i	−0.393334	−	0.780132i
$850$	43.5807	+	7.47266i	1.49481	+	0.256310i
$851$	−36.0354	+	24.3557i	−1.23528	+	0.834903i
$852$	−0.00829946			−0.000284335
$853$	5.63296			0.192869			0.0964344	−	0.995339i	$-0.469256\pi$
$853$	5.63296			0.192869			0.0964344	+	0.995339i	$0.469256\pi$
$854$	−3.95507	+	2.67316i	−0.135340	+	0.0914737i
$855$	−0.280871	−	6.61192i	−0.00960558	−	0.226123i
$856$	−12.1136	−	1.03102i	−0.414034	−	0.0352395i
$857$	−9.62328	+	4.35000i	−0.328725	+	0.148593i	−0.569508	−	0.821986i	$-0.692866\pi$
$857$	−9.62328	+	4.35000i	−0.328725	+	0.148593i	0.240783	+	0.970579i	$0.422596\pi$
$858$	4.84073	+	15.8066i	0.165260	+	0.539630i
$859$	26.3340	+	11.9037i	0.898503	+	0.406149i	0.807614	−	0.589712i	$-0.200759\pi$
$859$	26.3340	+	11.9037i	0.898503	+	0.406149i	0.0908896	+	0.995861i	$0.471029\pi$
$860$	−1.79544	−	14.0208i	−0.0612238	−	0.478106i
$861$	−0.466663	+	0.0397189i	−0.0159038	+	0.00135362i
$862$	−24.6114	+	13.7488i	−0.838268	+	0.468285i
$863$	1.98585	−	9.21439i	0.0675992	−	0.313662i	−0.931093	−	0.364781i	$-0.881144\pi$
$863$	1.98585	−	9.21439i	0.0675992	−	0.313662i	0.998693	+	0.0511196i	$0.0162790\pi$
$864$	−1.51529	−	2.46100i	−0.0515514	−	0.0837248i
$865$	−51.9537	+	23.4845i	−1.76648	+	0.798498i
$866$	12.5761	+	14.2893i	0.427355	+	0.485569i
$867$	−0.119512	+	0.237038i	−0.00405885	+	0.00805024i
$868$	1.10883	+	1.49924i	0.0376361	+	0.0508874i
$869$	39.2757	+	63.7877i	1.33234	+	2.16385i
$870$	−6.12845	−	20.0115i	−0.207774	−	0.678453i
$871$	13.3171	+	7.43939i	0.451234	+	0.252074i
$872$	−25.8533	−	9.13457i	−0.875505	−	0.309335i
$873$	11.0874	−	2.88693i	0.375251	−	0.0977077i
$874$	−24.0945	−	10.8914i	−0.815008	−	0.368407i
$875$	0.0982851	−	2.31371i	0.00332264	−	0.0782176i
$876$	−0.595717	+	2.76414i	−0.0201274	+	0.0933915i
$877$	8.38699	−	1.43809i	0.283209	−	0.0485610i	−0.0256433	−	0.999671i	$-0.508163\pi$
$877$	8.38699	−	1.43809i	0.283209	−	0.0485610i	0.308852	+	0.951110i	$0.400055\pi$
$878$	7.28524	+	33.8036i	0.245865	+	1.14082i
$879$	8.62598	+	21.4666i	0.290947	+	0.724049i
$880$	−24.1081	−	78.7211i	−0.812683	−	2.65369i
$881$	−0.113120	+	2.66293i	−0.00381111	+	0.0897164i	0.996186	+	0.0872566i	$0.0278100\pi$
$881$	−0.113120	+	2.66293i	−0.00381111	+	0.0897164i	−0.999997	+	0.00245982i	$0.999217\pi$
$882$	−8.45507	−	6.82699i	−0.284697	−	0.229877i
$883$	34.0889	+	32.6716i	1.14718	+	1.09949i	0.993784	+	0.111322i	$0.0355084\pi$
$883$	34.0889	+	32.6716i	1.14718	+	1.09949i	0.153399	+	0.988164i	$0.450978\pi$
$884$	2.35257	−	3.82082i	0.0791256	−	0.128508i
$885$	−1.48934	+	11.6304i	−0.0500635	+	0.390953i
$886$	−0.0612937	+	1.44290i	−0.00205920	+	0.0484752i
$887$	−5.57503	−	9.05442i	−0.187191	−	0.304018i	0.744256	−	0.667895i	$-0.232804\pi$
$887$	−5.57503	−	9.05442i	−0.187191	−	0.304018i	−0.931447	+	0.363877i	$0.881453\pi$
$888$	9.22667	−	7.45002i	0.309627	−	0.250006i
$889$	3.17914	−	7.91160i	0.106625	−	0.265347i
$890$	−13.6517	+	4.82344i	−0.457605	+	0.161682i
$891$	−5.04327			−0.168956
$892$	7.68144	−	1.43702i	0.257194	−	0.0481149i
$893$	4.71939			0.157928
$894$	26.0209	−	9.19377i	0.870270	−	0.307486i
$895$	3.96526	−	9.86792i	0.132544	−	0.329848i
$896$	4.23228	−	3.41733i	0.141391	−	0.114165i
$897$	−9.30797	−	15.1171i	−0.310784	−	0.504745i
$898$	1.80864	−	42.5769i	0.0603552	−	1.42081i
$899$	4.37504	−	34.1653i	0.145916	−	1.13948i
$900$	1.83805	−	2.98519i	0.0612684	−	0.0995063i
$901$	−7.75126	−	7.42898i	−0.258232	−	0.247495i
$902$	−7.32563	−	5.91503i	−0.243917	−	0.196949i
$903$	0.133561	−	3.14414i	0.00444465	−	0.104630i
$904$	−11.1344	−	36.3575i	−0.370323	−	1.20923i
$905$	31.8623	+	79.2925i	1.05914	+	2.63577i
$906$	2.31459	+	10.7397i	0.0768972	+	0.356804i
$907$	27.5540	−	4.72462i	0.914917	−	0.156878i	0.307764	−	0.951463i	$-0.400419\pi$
$907$	27.5540	−	4.72462i	0.914917	−	0.156878i	0.607154	+	0.794585i	$0.292311\pi$
$908$	1.05371	−	4.88925i	0.0349688	−	0.162256i
$909$	0.257847	−	6.06992i	0.00855224	−	0.201326i
$910$	−4.07117	−	1.84028i	−0.134958	−	0.0610048i
$911$	−23.6232	+	6.15101i	−0.782673	+	0.203792i	−0.621793	−	0.783182i	$-0.713595\pi$
$911$	−23.6232	+	6.15101i	−0.782673	+	0.203792i	−0.160880	+	0.986974i	$0.551433\pi$
$912$	8.70702	+	3.07639i	0.288318	+	0.101869i
$913$	1.43541	+	0.801867i	0.0475051	+	0.0265379i
$914$	0.258511	+	0.844128i	0.00855080	+	0.0279213i
$915$	13.5241	+	21.9646i	0.447093	+	0.726126i
$916$	−6.02633	−	8.14814i	−0.199116	−	0.269222i
$917$	3.25126	−	6.44850i	0.107366	−	0.212948i
$918$	4.36076	+	4.95479i	0.143927	+	0.163532i
$919$	45.2910	−	20.4728i	1.49401	−	0.675335i	0.511117	−	0.859511i	$-0.329232\pi$
$919$	45.2910	−	20.4728i	1.49401	−	0.675335i	0.982893	+	0.184175i	$0.0589615\pi$
$920$	36.1906	+	58.7773i	1.19317	+	1.93783i
$921$	4.72899	−	21.9426i	0.155825	−	0.723032i
$922$	40.2696	−	22.4959i	1.32621	−	0.740864i
$923$	0.0326085	−	0.00277539i	0.00107332	−	9.13531e-5i
$924$	0.133586	+	1.04319i	0.00439465	+	0.0343185i
$925$	30.8610	+	13.9501i	1.01470	+	0.458676i
$926$	14.2520	+	46.5377i	0.468350	+	1.52932i
$927$	−4.29721	+	1.94246i	−0.141139	+	0.0637989i
$928$	11.0925	+	0.944110i	0.364129	+	0.0309919i
$929$	0.600520	+	14.1367i	0.0197024	+	0.463810i	0.981663	+	0.190623i	$0.0610509\pi$
$929$	0.600520	+	14.1367i	0.0197024	+	0.463810i	−0.961961	+	0.273187i	$0.911922\pi$
$930$	40.2523	−	27.2058i	1.31992	−	0.892113i
$931$	13.2366			0.433812
$932$	9.19191			0.301091
$933$	−12.7644	+	8.62722i	−0.417887	+	0.282442i
$934$	−36.0650	−	6.18397i	−1.18008	−	0.202346i
$935$	32.2690	+	64.0018i	1.05531	+	2.09308i
$936$	2.87827	+	3.89168i	0.0940792	+	0.127204i
$937$	4.77762	−	22.1682i	0.156078	−	0.724205i	−0.829979	−	0.557795i	$-0.811647\pi$
$937$	4.77762	−	22.1682i	0.156078	−	0.724205i	0.986057	−	0.166410i	$-0.0532174\pi$
$938$	3.64074	+	2.93969i	0.118874	+	0.0959843i
$939$	−22.1843	−	5.77635i	−0.723959	−	0.188504i
$940$	3.61722	+	2.44481i	0.117981	+	0.0797410i
$941$	−36.3752	−	9.47136i	−1.18580	−	0.308757i	−0.393750	−	0.919218i	$-0.628822\pi$
$941$	−36.3752	−	9.47136i	−1.18580	−	0.308757i	−0.792047	+	0.610460i	$0.790984\pi$
$942$	−1.66500	+	13.0023i	−0.0542488	+	0.423637i
$943$	9.21374	+	4.16487i	0.300041	+	0.135627i
$944$	−14.2838	−	7.97943i	−0.464899	−	0.259708i
$945$	0.900505	−	1.02317i	0.0292934	−	0.0332838i
$946$	45.6750	−	43.7760i	1.48502	−	1.42328i
$947$	51.1531	−	28.5758i	1.66225	−	0.928590i	0.681873	−	0.731471i	$-0.261166\pi$
$947$	51.1531	−	28.5758i	1.66225	−	0.928590i	0.980380	−	0.197119i	$-0.0631585\pi$
$948$	−6.04762	−	4.88311i	−0.196418	−	0.158596i
$949$	1.41622	−	11.0595i	0.0459725	−	0.359006i
$950$	2.61521	+	20.4225i	0.0848486	+	0.662595i
$951$	−7.19110	+	23.4814i	−0.233187	+	0.761437i
$952$	−2.56611	+	2.91566i	−0.0831679	+	0.0944971i
$953$	17.9113	+	44.5739i	0.580203	+	1.44389i	0.873002	+	0.487717i	$0.162170\pi$
$953$	17.9113	+	44.5739i	0.580203	+	1.44389i	−0.292799	+	0.956174i	$0.594587\pi$
$954$	−3.74012	+	1.69064i	−0.121091	+	0.0547365i
$955$	−5.37968	+	4.34379i	−0.174082	+	0.140562i
$956$	−2.98869	−	5.92772i	−0.0966612	−	0.191716i
$957$	11.5517	−	15.6190i	0.373414	−	0.504889i
$958$	52.0183	+	4.42741i	1.68063	+	0.143043i
$959$	1.27719	−	1.03126i	0.0412427	−	0.0333012i
$960$	−10.0771	−	13.6252i	−0.325238	−	0.439751i
$961$	48.2543	−	8.27403i	1.55659	−	0.266904i
$962$	11.9640	−	11.4665i	0.385734	−	0.369696i
$963$	1.51765	−	4.95564i	0.0489055	−	0.159693i
$964$	1.76819	−	0.460401i	0.0569495	−	0.0148285i
$965$	−20.9217	−	11.6875i	−0.673492	−	0.376235i
$966$	−2.03054	−	5.05319i	−0.0653315	−	0.162584i
$967$	39.3676	+	44.7303i	1.26598	+	1.43843i	0.848020	+	0.529964i	$0.177795\pi$
$967$	39.3676	+	44.7303i	1.26598	+	1.43843i	0.417958	+	0.908466i	$0.362746\pi$
$968$	20.1339	−	27.2229i	0.647129	−	0.874976i
$969$	−7.92394	−	1.35870i	−0.254554	−	0.0436476i
$970$	−58.6933	+	20.7377i	−1.88453	+	0.665846i
$971$	−6.50656	+	4.39767i	−0.208805	+	0.141128i	−0.659914	−	0.751341i	$-0.729407\pi$
$971$	−6.50656	+	4.39767i	−0.208805	+	0.141128i	0.451108	+	0.892469i	$0.351029\pi$
$972$	0.493418	−	0.174336i	0.0158264	−	0.00559182i
$973$	0.127387	+	2.99880i	0.00408385	+	0.0961370i
$974$	−17.9965	+	24.3329i	−0.576645	+	0.779675i
$975$	−6.22342	+	12.3434i	−0.199309	+	0.395306i
$976$	−35.4753	+	6.08285i	−1.13554	+	0.194707i
$977$	42.5883	−	23.7913i	1.36252	−	0.761150i	0.376286	−	0.926504i	$-0.377201\pi$
$977$	42.5883	−	23.7913i	1.36252	−	0.761150i	0.986234	+	0.165354i	$0.0528766\pi$
$978$	9.02179	+	8.64668i	0.288485	+	0.276490i
$979$	−11.1347	−	7.52578i	−0.355868	−	0.240525i
$980$	10.1453	+	6.85703i	0.324080	+	0.219040i
$981$	6.12876	−	9.95375i	0.195676	−	0.317799i
$982$	7.58290	+	59.2159i	0.241980	+	1.88966i
$983$	−15.2756	+	3.97745i	−0.487215	+	0.126861i	−0.487471	−	0.873139i	$-0.662081\pi$
$983$	−15.2756	+	3.97745i	−0.487215	+	0.126861i	0.000256433		1.00000i	$0.499918\pi$
$984$	−2.59942	−	0.918435i	−0.0828666	−	0.0292786i
$985$	4.69586	−	15.3336i	0.149623	−	0.488569i
$986$	−25.3333	+	2.15618i	−0.806778	+	0.0686669i
$987$	0.701739	+	0.672563i	0.0223366	+	0.0214079i
$988$	2.02194	+	0.526472i	0.0643264	+	0.0167493i
$989$	−35.6219	+	57.8536i	−1.13271	+	1.83964i
$990$	27.3027	−	2.32380i	0.867737	−	0.0738553i
$991$	34.5630	−	33.1259i	1.09793	−	1.05228i	0.0995698	−	0.995031i	$-0.468253\pi$
$991$	34.5630	−	33.1259i	1.09793	−	1.05228i	0.998360	−	0.0572498i	$-0.0182331\pi$
$992$	5.44459	+	25.2630i	0.172866	+	0.802101i
$993$	−1.83324	−	2.08296i	−0.0581760	−	0.0661008i
$994$	0.0100030		0.000851382i	0.000317276		2.70042e-5i
$995$	28.3540	−	70.5616i	0.898881	−	2.23695i
$996$	−0.168155	−	0.0288330i	−0.00532819	−	0.000913610i
$997$	−0.624276	−	14.6959i	−0.0197710	−	0.465425i	−0.981505	−	0.191439i	$-0.938685\pi$
$997$	−0.624276	−	14.6959i	−0.0197710	−	0.465425i	0.961734	−	0.273986i	$-0.0883423\pi$
$998$	−12.8757	+	32.0424i	−0.407573	+	1.01428i
$999$	2.27604	+	4.51426i	0.0720108	+	0.142825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.b.4.15	✓	720
223.56	even	37	inner	669.2.i.b.502.15	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.b.4.15	✓	720	1.1	even	1	trivial
669.2.i.b.502.15	yes	720	223.56	even	37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49775 - 0.529190i) q^{2} +(0.372856 - 0.927889i) q^{3} +(0.407155 - 0.328755i) q^{4} +(1.79333 + 2.91256i) q^{5} +(0.0674176 - 1.58706i) q^{6} +(-0.0506160 + 0.395268i) q^{7} +(-1.22987 + 1.99744i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(4.22727 + 3.41328i) q^{10} +(-0.214043 + 5.03873i) q^{11} +(-0.153237 - 0.500373i) q^{12} +(0.769396 + 1.91472i) q^{13} +(0.133362 + 0.618800i) q^{14} +(3.37119 - 0.578048i) q^{15} +(-1.00552 + 4.66564i) q^{16} +(0.176351 - 4.15143i) q^{17} +(-1.44748 - 0.654302i) q^{18} +(1.87240 - 0.487536i) q^{19} +(1.68768 + 0.596296i) q^{20} +(0.347892 + 0.194344i) q^{21} +(2.34586 + 7.66005i) q^{22} +(-4.51073 - 7.32589i) q^{23} +(1.39484 + 1.88594i) q^{24} +(-3.01593 + 5.98174i) q^{25} +(2.16562 + 2.46062i) q^{26} +(-0.911228 + 0.411901i) q^{27} +(0.109338 + 0.177575i) q^{28} +(0.811534 - 3.76553i) q^{29} +(4.74331 - 2.64977i) q^{30} +(8.90974 - 0.758330i) q^{31} +(0.367093 + 2.86668i) q^{32} +(4.59557 + 2.07733i) q^{33} +(-1.93277 - 6.31114i) q^{34} +(-1.24201 + 0.561424i) q^{35} +(-0.521426 - 0.0443799i) q^{36} +(-0.214565 - 5.05103i) q^{37} +(2.54640 - 1.72107i) q^{38} +2.06352 q^{39} -8.02323 q^{40} +(-0.973745 + 0.658137i) q^{41} +(0.623902 + 0.106979i) q^{42} +(-3.55532 - 7.05156i) q^{43} +(1.56936 + 2.12191i) q^{44} +(0.720604 - 3.34362i) q^{45} +(-10.6328 - 8.58535i) q^{46} +(2.36046 + 0.614617i) q^{47} +(3.95428 + 2.67263i) q^{48} +(6.62046 + 1.72383i) q^{49} +(-1.35164 + 10.5552i) q^{50} +(-3.78631 - 1.71152i) q^{51} +(0.942735 + 0.526643i) q^{52} +(1.70710 - 1.93965i) q^{53} +(-1.14682 + 1.09914i) q^{54} +(-15.0594 + 8.41271i) q^{55} +(-0.727273 - 0.587232i) q^{56} +(0.245759 - 1.91916i) q^{57} +(-0.777204 - 6.06930i) q^{58} +(-1.00383 + 3.27783i) q^{59} +(1.18256 - 1.34365i) q^{60} +(2.81183 + 6.99752i) q^{61} +(12.9433 - 5.85074i) q^{62} +(0.310044 - 0.250343i) q^{63} +(-2.23060 - 4.42413i) q^{64} +(-4.19694 + 5.67463i) q^{65} +(7.98235 + 0.679398i) q^{66} +(5.75150 - 4.64401i) q^{67} +(-1.29300 - 1.74825i) q^{68} +(-8.47947 + 1.45395i) q^{69} +(-1.56313 + 1.49814i) q^{70} +(0.00464403 - 0.0151643i) q^{71} +(2.27002 - 0.591068i) q^{72} +(-4.71715 - 2.63516i) q^{73} +(-2.99432 - 7.45165i) q^{74} +(4.42588 + 5.02878i) q^{75} +(0.602079 - 0.814064i) q^{76} +(-1.98081 - 0.339645i) q^{77} +(3.09064 - 1.09199i) q^{78} +(12.3062 - 8.31751i) q^{79} +(-15.3922 + 5.43841i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(-1.11015 + 1.50102i) q^{82} +(0.146775 - 0.291110i) q^{83} +(0.205537 - 0.0352429i) q^{84} +(12.4075 - 6.93126i) q^{85} +(-9.05662 - 8.68007i) q^{86} +(-3.19141 - 2.15702i) q^{87} +(-9.80132 - 6.62453i) q^{88} +(-1.39719 + 2.26918i) q^{89} +(-0.690121 - 5.38925i) q^{90} +(-0.795769 + 0.207202i) q^{91} +(-4.24499 - 1.49985i) q^{92} +(2.61841 - 8.55000i) q^{93} +(3.86065 - 0.328589i) q^{94} +(4.77782 + 4.57917i) q^{95} +(2.79683 + 0.728239i) q^{96} +(-6.00702 + 9.75602i) q^{97} +(10.8281 - 0.921603i) q^{98} +(3.64102 - 3.48964i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - q^{2} - 20 q^{3} - 23 q^{4} - 4 q^{5} - q^{6} - 12 q^{7} - 9 q^{8} - 20 q^{9} - 16 q^{10} - 14 q^{11} - 23 q^{12} - 14 q^{13} - 28 q^{14} - 4 q^{15} - 37 q^{16} - 20 q^{17} - q^{18} + 42 q^{19}+ \cdots - 14 q^{99}+O(q^{100}) \) 720 * q - q^2 - 20 * q^3 - 23 * q^4 - 4 * q^5 - q^6 - 12 * q^7 - 9 * q^8 - 20 * q^9 - 16 * q^10 - 14 * q^11 - 23 * q^12 - 14 * q^13 - 28 * q^14 - 4 * q^15 - 37 * q^16 - 20 * q^17 - q^18 + 42 * q^19 - 34 * q^20 - 12 * q^21 - 32 * q^22 - 18 * q^23 - 9 * q^24 - 48 * q^25 - 48 * q^26 - 20 * q^27 - 80 * q^28 + 7 * q^29 - 16 * q^30 - 40 * q^31 - 59 * q^32 - 14 * q^33 + 22 * q^34 - 32 * q^35 - 23 * q^36 - 44 * q^37 - 36 * q^38 + 60 * q^39 + 124 * q^40 + 176 * q^41 + 46 * q^42 - 42 * q^43 + 76 * q^44 - 4 * q^45 - 88 * q^46 - 26 * q^47 - 37 * q^48 - 94 * q^49 - 87 * q^50 + 54 * q^51 + 206 * q^52 - 54 * q^53 - q^54 - 74 * q^55 - 107 * q^56 - 32 * q^57 + 13 * q^58 - 50 * q^59 - 34 * q^60 - 86 * q^61 - 83 * q^62 - 12 * q^63 + 99 * q^64 + 52 * q^65 + 42 * q^66 - 68 * q^67 + 63 * q^68 - 18 * q^69 - 62 * q^70 - 68 * q^71 - 9 * q^72 - 58 * q^73 - 82 * q^74 - 48 * q^75 - 145 * q^76 + 40 * q^77 + 26 * q^78 - 90 * q^79 + 325 * q^80 - 20 * q^81 + 62 * q^82 + 58 * q^83 - 80 * q^84 - 14 * q^85 - 153 * q^86 - 30 * q^87 - 152 * q^88 - 110 * q^89 - 16 * q^90 - 114 * q^91 - 110 * q^92 - 40 * q^93 + 102 * q^94 - 118 * q^95 - 59 * q^96 - 110 * q^97 - 154 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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