LMFDB - Embedded newform 669.2.i.a.4.7

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)

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);

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")

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 = [648] 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:	$648$
Relative dimension:	$18$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	669.4
Dual form			669.2.i.a.502.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.871922 + 0.308070i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-0.890730 + 0.719214i) q^{4} +(1.42047 + 2.30699i) q^{5} +(0.0392473 - 0.923913i) q^{6} +(0.275779 - 2.15360i) q^{7} +(1.52478 - 2.47640i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-1.94925 - 1.57391i) q^{10} +(0.160487 - 3.77800i) q^{11} +(-0.335236 - 1.09466i) q^{12} +(-1.68380 - 4.19029i) q^{13} +(0.423001 + 1.96273i) q^{14} +(-2.67026 + 0.457862i) q^{15} +(-0.0841965 + 0.390673i) q^{16} +(0.121896 - 2.86952i) q^{17} +(0.842655 + 0.380904i) q^{18} +(-1.96150 + 0.510735i) q^{19} +(-2.92447 - 1.03328i) q^{20} +(1.89548 + 1.05888i) q^{21} +(1.02395 + 3.34356i) q^{22} +(-1.47571 - 2.39671i) q^{23} +(1.72930 + 2.33817i) q^{24} +(-1.05344 + 2.08937i) q^{25} +(2.75904 + 3.13488i) q^{26} +(0.911228 - 0.411901i) q^{27} +(1.30325 + 2.11662i) q^{28} +(1.23660 - 5.73786i) q^{29} +(2.18720 - 1.22185i) q^{30} +(0.507562 - 0.0431999i) q^{31} +(0.691840 + 5.40268i) q^{32} +(3.44573 + 1.55757i) q^{33} +(0.777728 + 2.53955i) q^{34} +(5.36006 - 2.42290i) q^{35} +(1.14072 + 0.0970896i) q^{36} +(0.218745 + 5.14942i) q^{37} +(1.55293 - 1.04960i) q^{38} +4.51594 q^{39} +7.87893 q^{40} +(-1.18930 + 0.803830i) q^{41} +(-1.97891 - 0.339319i) q^{42} +(-0.849049 - 1.68399i) q^{43} +(2.57424 + 3.48060i) q^{44} +(0.570778 - 2.64842i) q^{45} +(2.02506 + 1.63512i) q^{46} +(-11.3960 - 2.96728i) q^{47} +(-0.331108 - 0.223790i) q^{48} +(2.21220 + 0.576011i) q^{49} +(0.274845 - 2.14630i) q^{50} +(2.61714 + 1.18302i) q^{51} +(4.51352 + 2.52141i) q^{52} +(5.30521 - 6.02789i) q^{53} +(-0.667626 + 0.639868i) q^{54} +(8.94376 - 4.99628i) q^{55} +(-4.91268 - 3.96671i) q^{56} +(0.257453 - 2.01048i) q^{57} +(0.689439 + 5.38393i) q^{58} +(3.02663 - 9.88299i) q^{59} +(2.04918 - 2.32832i) q^{60} +(3.15698 + 7.85645i) q^{61} +(-0.429246 + 0.194032i) q^{62} +(-1.68926 + 1.36398i) q^{63} +(-2.62748 - 5.21129i) q^{64} +(7.27516 - 9.83667i) q^{65} +(-3.48424 - 0.296553i) q^{66} +(-9.95496 + 8.03807i) q^{67} +(1.95522 + 2.64363i) q^{68} +(2.77411 - 0.475670i) q^{69} +(-3.92713 + 3.76385i) q^{70} +(0.353503 - 1.15431i) q^{71} +(-2.81434 + 0.732798i) q^{72} +(-1.76969 - 0.988610i) q^{73} +(-1.77711 - 4.42250i) q^{74} +(-1.54592 - 1.75651i) q^{75} +(1.37984 - 1.86566i) q^{76} +(-8.09204 - 1.38752i) q^{77} +(-3.93755 + 1.39122i) q^{78} +(5.07801 - 3.43214i) q^{79} +(-1.02088 + 0.360698i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.789346 - 1.06727i) q^{82} +(1.92187 - 3.81180i) q^{83} +(-2.44991 + 0.420080i) q^{84} +(6.79309 - 3.79485i) q^{85} +(1.25909 + 1.20674i) q^{86} +(4.86302 + 3.28683i) q^{87} +(-9.11114 - 6.15806i) q^{88} +(-3.22284 + 5.23423i) q^{89} +(0.318224 + 2.48506i) q^{90} +(-9.48856 + 2.47063i) q^{91} +(3.03821 + 1.07347i) q^{92} +(-0.149163 + 0.487069i) q^{93} +(10.8505 - 0.923517i) q^{94} +(-3.96450 - 3.79967i) q^{95} +(-5.27105 - 1.37247i) q^{96} +(-3.94783 + 6.41168i) q^{97} +(-2.10631 + 0.179274i) q^{98} +(-2.73001 + 2.61650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * 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 $

$2$	−0.871922	+	0.308070i	−0.616542	+	0.217838i	−0.623102	−	0.782140i	$-0.714128\pi$
$2$	−0.871922	+	0.308070i	−0.616542	+	0.217838i	0.00656017	+	0.999978i	$0.497912\pi$
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$4$	−0.890730	+	0.719214i	−0.445365	+	0.359607i
$5$	1.42047	+	2.30699i	0.635253	+	1.03172i	0.995116	+	0.0987108i	$0.0314719\pi$
$5$	1.42047	+	2.30699i	0.635253	+	1.03172i	−0.359864	+	0.933005i	$0.617177\pi$
$6$	0.0392473	−	0.923913i	0.0160227	−	0.377186i
$7$	0.275779	−	2.15360i	0.104235	−	0.813984i	−0.852440	−	0.522825i	$-0.824878\pi$
$7$	0.275779	−	2.15360i	0.104235	−	0.813984i	0.956675	−	0.291159i	$-0.0940408\pi$
$8$	1.52478	−	2.47640i	0.539092	−	0.875541i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−1.94925	−	1.57391i	−0.616407	−	0.497714i
$11$	0.160487	−	3.77800i	0.0483888	−	1.13911i	−0.796662	−	0.604424i	$-0.793403\pi$
$11$	0.160487	−	3.77800i	0.0483888	−	1.13911i	0.845051	−	0.534685i	$-0.179570\pi$
$12$	−0.335236	−	1.09466i	−0.0967744	−	0.316002i
$13$	−1.68380	−	4.19029i	−0.467001	−	1.16218i	−0.956905	−	0.290401i	$-0.906211\pi$
$13$	−1.68380	−	4.19029i	−0.467001	−	1.16218i	0.489904	−	0.871776i	$-0.337032\pi$
$14$	0.423001	+	1.96273i	0.113052	+	0.524562i
$15$	−2.67026	+	0.457862i	−0.689458	+	0.118219i
$16$	−0.0841965	+	0.390673i	−0.0210491	+	0.0976683i
$17$	0.121896	−	2.86952i	0.0295640	−	0.695960i	−0.921759	−	0.387764i	$-0.873248\pi$
$17$	0.121896	−	2.86952i	0.0295640	−	0.695960i	0.951323	−	0.308196i	$-0.0997254\pi$
$18$	0.842655	+	0.380904i	0.198616	+	0.0897800i
$19$	−1.96150	+	0.510735i	−0.449999	+	0.117171i	−0.470072	−	0.882628i	$-0.655772\pi$
$19$	−1.96150	+	0.510735i	−0.449999	+	0.117171i	0.0200735	+	0.999799i	$0.493610\pi$
$20$	−2.92447	−	1.03328i	−0.653931	−	0.231049i
$21$	1.89548	+	1.05888i	0.413627	+	0.231066i
$22$	1.02395	+	3.34356i	0.218308	+	0.712850i
$23$	−1.47571	−	2.39671i	−0.307708	−	0.499749i	0.660188	−	0.751100i	$-0.270477\pi$
$23$	−1.47571	−	2.39671i	−0.307708	−	0.499749i	−0.967896	+	0.251351i	$0.919125\pi$
$24$	1.72930	+	2.33817i	0.352992	+	0.477277i
$25$	−1.05344	+	2.08937i	−0.210688	+	0.417874i
$26$	2.75904	+	3.13488i	0.541093	+	0.614801i
$27$	0.911228	−	0.411901i	0.175366	−	0.0792704i
$28$	1.30325	+	2.11662i	0.246292	+	0.400003i
$29$	1.23660	−	5.73786i	0.229631	−	1.06549i	−0.704815	−	0.709391i	$-0.748970\pi$
$29$	1.23660	−	5.73786i	0.229631	−	1.06549i	0.934447	−	0.356103i	$-0.115895\pi$
$30$	2.18720	−	1.22185i	0.399327	−	0.223077i
$31$	0.507562	−	0.0431999i	0.0911608	−	0.00775893i	−0.0391367	−	0.999234i	$-0.512461\pi$
$31$	0.507562	−	0.0431999i	0.0911608	−	0.00775893i	0.130298	+	0.991475i	$0.458407\pi$
$32$	0.691840	+	5.40268i	0.122301	+	0.955068i
$33$	3.44573	+	1.55757i	0.599824	+	0.271137i
$34$	0.777728	+	2.53955i	0.133379	+	0.435529i
$35$	5.36006	−	2.42290i	0.906015	−	0.409545i
$36$	1.14072	+	0.0970896i	0.190120	+	0.0161816i
$37$	0.218745	+	5.14942i	0.0359614	+	0.846559i	0.922985	+	0.384835i	$0.125742\pi$
$37$	0.218745	+	5.14942i	0.0359614	+	0.846559i	−0.887024	+	0.461724i	$0.847231\pi$
$38$	1.55293	−	1.04960i	0.251919	−	0.170268i
$39$	4.51594			0.723129
$40$	7.87893			1.24577
$41$	−1.18930	+	0.803830i	−0.185738	+	0.125537i	−0.649315	−	0.760520i	$-0.724944\pi$
$41$	−1.18930	+	0.803830i	−0.185738	+	0.125537i	0.463577	+	0.886057i	$0.346566\pi$
$42$	−1.97891	−	0.339319i	−0.305353	−	0.0523581i
$43$	−0.849049	−	1.68399i	−0.129479	−	0.256806i	0.818906	−	0.573928i	$-0.194581\pi$
$43$	−0.849049	−	1.68399i	−0.129479	−	0.256806i	−0.948385	+	0.317122i	$0.897284\pi$
$44$	2.57424	+	3.48060i	0.388081	+	0.524720i
$45$	0.570778	−	2.64842i	0.0850866	−	0.394803i
$46$	2.02506	+	1.63512i	0.298579	+	0.241086i
$47$	−11.3960	−	2.96728i	−1.66227	−	0.432823i	−0.702067	−	0.712111i	$-0.747739\pi$
$47$	−11.3960	−	2.96728i	−1.66227	−	0.432823i	−0.960207	+	0.279288i	$0.909901\pi$
$48$	−0.331108	−	0.223790i	−0.0477913	−	0.0323013i
$49$	2.21220	+	0.576011i	0.316028	+	0.0822873i
$50$	0.274845	−	2.14630i	0.0388689	−	0.303533i
$51$	2.61714	+	1.18302i	0.366474	+	0.165657i
$52$	4.51352	+	2.52141i	0.625913	+	0.349656i
$53$	5.30521	−	6.02789i	0.728727	−	0.827995i	−0.261827	−	0.965115i	$-0.584325\pi$
$53$	5.30521	−	6.02789i	0.728727	−	0.827995i	0.990554	+	0.137120i	$0.0437846\pi$
$54$	−0.667626	+	0.639868i	−0.0908524	+	0.0870750i
$55$	8.94376	−	4.99628i	1.20598	−	0.673699i
$56$	−4.91268	−	3.96671i	−0.656484	−	0.530074i
$57$	0.257453	−	2.01048i	0.0341004	−	0.266295i
$58$	0.689439	+	5.38393i	0.0905278	+	0.706944i
$59$	3.02663	−	9.88299i	0.394034	−	1.28666i	−0.510362	−	0.859960i	$-0.670488\pi$
$59$	3.02663	−	9.88299i	0.394034	−	1.28666i	0.904395	−	0.426695i	$-0.140322\pi$
$60$	2.04918	−	2.32832i	0.264548	−	0.300585i
$61$	3.15698	+	7.85645i	0.404210	+	1.00591i	0.981856	+	0.189628i	$0.0607281\pi$
$61$	3.15698	+	7.85645i	0.404210	+	1.00591i	−0.577646	+	0.816287i	$0.696029\pi$
$62$	−0.429246	+	0.194032i	−0.0545143	+	0.0246420i
$63$	−1.68926	+	1.36398i	−0.212827	+	0.171846i
$64$	−2.62748	−	5.21129i	−0.328434	−	0.651411i
$65$	7.27516	−	9.83667i	0.902373	−	1.22009i
$66$	−3.48424	−	0.296553i	−0.428881	−	0.0365031i
$67$	−9.95496	+	8.03807i	−1.21619	+	0.982007i	−0.216208	+	0.976347i	$0.569369\pi$
$67$	−9.95496	+	8.03807i	−1.21619	+	0.982007i	−0.999984	+	0.00565941i	$0.998199\pi$
$68$	1.95522	+	2.64363i	0.237105	+	0.320588i
$69$	2.77411	−	0.475670i	0.333964	−	0.0572639i
$70$	−3.92713	+	3.76385i	−0.469382	+	0.449866i
$71$	0.353503	−	1.15431i	0.0419531	−	0.136991i	−0.932734	−	0.360566i	$-0.882584\pi$
$71$	0.353503	−	1.15431i	0.0419531	−	0.136991i	0.974687	+	0.223575i	$0.0717727\pi$
$72$	−2.81434	+	0.732798i	−0.331674	+	0.0863611i
$73$	−1.76969	−	0.988610i	−0.207127	−	0.115708i	0.380688	−	0.924704i	$-0.375687\pi$
$73$	−1.76969	−	0.988610i	−0.207127	−	0.115708i	−0.587815	+	0.808996i	$0.700012\pi$
$74$	−1.77711	−	4.42250i	−0.206585	−	0.514106i
$75$	−1.54592	−	1.75651i	−0.178508	−	0.202824i
$76$	1.37984	−	1.86566i	0.158278	−	0.214006i
$77$	−8.09204	−	1.38752i	−0.922173	−	0.158122i
$78$	−3.93755	+	1.39122i	−0.445840	+	0.157525i
$79$	5.07801	−	3.43214i	0.571321	−	0.386146i	−0.239977	−	0.970779i	$-0.577140\pi$
$79$	5.07801	−	3.43214i	0.571321	−	0.386146i	0.811298	+	0.584633i	$0.198762\pi$
$80$	−1.02088	+	0.360698i	−0.114137	+	0.0403273i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	0.789346	−	1.06727i	0.0871687	−	0.117860i
$83$	1.92187	−	3.81180i	0.210953	−	0.418400i	−0.762597	−	0.646873i	$-0.776076\pi$
$83$	1.92187	−	3.81180i	0.210953	−	0.418400i	0.973550	+	0.228474i	$0.0733735\pi$
$84$	−2.44991	+	0.420080i	−0.267308	+	0.0458345i
$85$	6.79309	−	3.79485i	0.736814	−	0.411609i
$86$	1.25909	+	1.20674i	0.135771	+	0.130126i
$87$	4.86302	+	3.28683i	0.521370	+	0.352385i
$88$	−9.11114	−	6.15806i	−0.971251	−	0.656451i
$89$	−3.22284	+	5.23423i	−0.341621	+	0.554828i	−0.975884	−	0.218290i	$-0.929952\pi$
$89$	−3.22284	+	5.23423i	−0.341621	+	0.554828i	0.634263	+	0.773117i	$0.281304\pi$
$90$	0.318224	+	2.48506i	0.0335437	+	0.261948i
$91$	−9.48856	+	2.47063i	−0.994671	+	0.258992i
$92$	3.03821	+	1.07347i	0.316756	+	0.111917i
$93$	−0.149163	+	0.487069i	−0.0154675	+	0.0505067i
$94$	10.8505	−	0.923517i	1.11915	−	0.0952535i
$95$	−3.96450	−	3.79967i	−0.406750	−	0.389838i
$96$	−5.27105	−	1.37247i	−0.537974	−	0.140077i
$97$	−3.94783	+	6.41168i	−0.400841	+	0.651008i	−0.987281	−	0.158985i	$-0.949178\pi$
$97$	−3.94783	+	6.41168i	−0.400841	+	0.651008i	0.586440	+	0.809993i	$0.300529\pi$
$98$	−2.10631	+	0.179274i	−0.212770	+	0.0181094i
$99$	−2.73001	+	2.61650i	−0.274376	+	0.262968i
$100$	−0.564376	−	2.61871i	−0.0564376	−	0.261871i
$101$	0.163645	+	0.185936i	0.0162833	+	0.0185014i	0.758757	−	0.651374i	$-0.225807\pi$
$101$	0.163645	+	0.185936i	0.0162833	+	0.0185014i	−0.742474	+	0.669875i	$0.766348\pi$
$102$	−2.64640	−	0.225242i	−0.262033	−	0.0223023i
$103$	1.74454	−	4.34146i	0.171895	−	0.427777i	−0.816953	−	0.576704i	$-0.804339\pi$
$103$	1.74454	−	4.34146i	0.171895	−	0.427777i	0.988848	+	0.148927i	$0.0475819\pi$
$104$	−12.9443	−	2.21952i	−1.26929	−	0.217642i
$105$	0.249649	+	5.87693i	0.0243633	+	0.573530i
$106$	−2.76872	+	6.89023i	−0.268922	+	0.669238i
$107$	1.45606	+	2.88792i	0.140763	+	0.279186i	0.952328	−	0.305075i	$-0.0986817\pi$
$107$	1.45606	+	2.88792i	0.140763	+	0.279186i	−0.811566	+	0.584261i	$0.801384\pi$
$108$	−0.515413	+	1.02226i	−0.0495957	+	0.0983671i
$109$	2.38008	+	11.0436i	0.227971	+	1.05779i	0.936108	+	0.351713i	$0.114401\pi$
$109$	2.38008	+	11.0436i	0.227971	+	1.05779i	−0.708137	+	0.706075i	$0.750464\pi$
$110$	−6.25906	+	7.11167i	−0.596778	+	0.678072i
$111$	−4.85965	−	1.71702i	−0.461257	−	0.162973i
$112$	0.818134	+	0.289065i	0.0773064	+	0.0273141i
$113$	7.81847	−	8.88351i	0.735500	−	0.835690i	−0.255880	−	0.966709i	$-0.582365\pi$
$113$	7.81847	−	8.88351i	0.735500	−	0.835690i	0.991380	+	0.131018i	$0.0418246\pi$
$114$	0.394891	+	1.83230i	0.0369849	+	0.171611i
$115$	3.43298	−	6.80891i	0.320127	−	0.634934i
$116$	3.02527	+	6.00026i	0.280889	+	0.557110i
$117$	−1.68380	+	4.19029i	−0.155667	+	0.387392i
$118$	0.405663	+	9.54961i	0.0373443	+	0.879113i
$119$	−6.14618	−	1.05387i	−0.563419	−	0.0966079i
$120$	−2.93771	+	7.31077i	−0.268175	+	0.667379i
$121$	−3.28715	−	0.279778i	−0.298832	−	0.0254343i
$122$	−5.17298	−	5.87764i	−0.468339	−	0.532137i
$123$	−0.302425	−	1.40326i	−0.0272687	−	0.126527i
$124$	−0.421031	+	0.403525i	−0.0378097	+	0.0362376i
$125$	7.18081	−	0.611177i	0.642272	−	0.0546654i
$126$	1.05270	−	1.70970i	0.0937821	−	0.152312i
$127$	9.82190	+	2.55742i	0.871553	+	0.226935i	0.660761	−	0.750596i	$-0.270234\pi$
$127$	9.82190	+	2.55742i	0.871553	+	0.226935i	0.210792	+	0.977531i	$0.432396\pi$
$128$	−3.96830	−	3.80331i	−0.350752	−	0.336168i
$129$	1.87913	−	0.159937i	0.165448	−	0.0140817i
$130$	−3.31300	+	10.8181i	−0.290569	+	0.948807i
$131$	1.89211	+	0.668527i	0.165315	+	0.0584094i	0.414515	−	0.910043i	$-0.363951\pi$
$131$	1.89211	+	0.668527i	0.165315	+	0.0584094i	−0.249200	+	0.968452i	$0.580168\pi$
$132$	−4.18943	+	1.09084i	−0.364643	+	0.0949458i
$133$	0.558977	+	4.36513i	0.0484695	+	0.378505i
$134$	6.20367	−	10.0754i	0.535915	−	0.870382i
$135$	2.24462	+	1.51710i	0.193186	+	0.130571i
$136$	−6.92022	−	4.67725i	−0.593404	−	0.401071i
$137$	−8.50194	−	8.14845i	−0.726370	−	0.696169i	0.234826	−	0.972038i	$-0.424548\pi$
$137$	−8.50194	−	8.14845i	−0.726370	−	0.696169i	−0.961195	+	0.275868i	$0.911035\pi$
$138$	−2.27227	+	1.26937i	−0.193429	+	0.108056i
$139$	−12.0419	+	2.06479i	−1.02138	+	0.175133i	−0.655235	−	0.755425i	$-0.727431\pi$
$139$	−12.0419	+	2.06479i	−1.02138	+	0.175133i	−0.366145	+	0.930558i	$0.619322\pi$
$140$	−3.03178	+	6.01318i	−0.256232	+	0.508206i
$141$	7.00237	−	9.46783i	0.589706	−	0.797335i
$142$	0.0473804	+	1.11537i	0.00397607	+	0.0935998i
$143$	−16.1011	+	5.68889i	−1.34645	+	0.475729i
$144$	0.331108	−	0.223790i	0.0275923	−	0.0186492i
$145$	14.9937	−	5.29762i	1.24516	−	0.439943i
$146$	1.84760	+	0.316802i	0.152908	+	0.0262187i
$147$	−1.35931	+	1.83790i	−0.112114	+	0.151588i
$148$	−3.89838	−	4.42942i	−0.320445	−	0.364096i
$149$	6.38493	+	15.8895i	0.523074	+	1.30172i	0.922869	+	0.385115i	$0.125838\pi$
$149$	6.38493	+	15.8895i	0.523074	+	1.30172i	−0.399795	+	0.916605i	$0.630919\pi$
$150$	1.88905	+	1.05529i	0.154240	+	0.0861639i
$151$	−16.8671	+	4.39184i	−1.37262	+	0.357403i	−0.863959	−	0.503562i	$-0.832023\pi$
$151$	−16.8671	+	4.39184i	−1.37262	+	0.357403i	−0.508664	+	0.860965i	$0.669860\pi$
$152$	−1.72607	+	5.63622i	−0.140003	+	0.457158i
$153$	−2.07353	+	1.98732i	−0.167635	+	0.160665i
$154$	7.48308	−	1.28310i	0.603004	−	0.103395i
$155$	0.820637	+	1.10957i	0.0659152	+	0.0891232i
$156$	−4.02248	+	3.24793i	−0.322056	+	0.260042i
$157$	1.98385	+	0.168850i	0.158328	+	0.0134757i	0.163702	−	0.986510i	$-0.447656\pi$
$157$	1.98385	+	0.168850i	0.158328	+	0.0134757i	−0.00537374	+	0.999986i	$0.501711\pi$
$158$	−3.37029	+	4.55694i	−0.268126	+	0.362531i
$159$	3.61513	+	7.17019i	0.286699	+	0.568633i
$160$	−11.4812	+	9.27040i	−0.907667	+	0.732890i
$161$	−5.56853	+	2.51713i	−0.438862	+	0.198378i
$162$	−0.344798	−	0.858062i	−0.0270899	−	0.0674157i
$163$	14.3604	−	16.3165i	1.12479	−	1.27801i	0.168463	−	0.985708i	$-0.446120\pi$
$163$	14.3604	−	16.3165i	1.12479	−	1.27801i	0.956326	−	0.292301i	$-0.0944210\pi$
$164$	0.481223	−	1.57136i	0.0375772	−	0.122703i
$165$	1.30126	+	10.1617i	0.101303	+	0.791088i
$166$	−0.501421	+	3.91567i	−0.0389178	+	0.303915i
$167$	−2.35118	−	1.89844i	−0.181940	−	0.146906i	0.532941	−	0.846152i	$-0.321087\pi$
$167$	−2.35118	−	1.89844i	−0.181940	−	0.146906i	−0.714881	+	0.699246i	$0.753519\pi$
$168$	5.51239	−	3.07940i	0.425290	−	0.237581i
$169$	−5.33793	+	5.11599i	−0.410610	+	0.393538i
$170$	−4.75397	+	5.40156i	−0.364613	+	0.414281i
$171$	1.76951	+	0.988509i	0.135318	+	0.0755932i
$172$	1.96742	+	0.889331i	0.150015	+	0.0678108i
$173$	2.63812	−	20.6015i	0.200572	−	1.56630i	−0.508436	−	0.861100i	$-0.669776\pi$
$173$	2.63812	−	20.6015i	0.200572	−	1.56630i	0.709009	−	0.705200i	$-0.249143\pi$
$174$	−5.25275	−	1.36771i	−0.398210	−	0.103686i
$175$	4.20915	+	2.84489i	0.318182	+	0.215053i
$176$	1.46245	+	0.380793i	0.110236	+	0.0287033i
$177$	8.04182	+	6.49331i	0.604460	+	0.488067i
$178$	1.19756	−	5.55671i	0.0897610	−	0.416493i
$179$	11.7070	+	15.8289i	0.875023	+	1.18311i	0.982006	+	0.188848i	$0.0604754\pi$
$179$	11.7070	+	15.8289i	0.875023	+	1.18311i	−0.106983	+	0.994261i	$0.534119\pi$
$180$	1.39637	+	2.76954i	0.104079	+	0.206429i
$181$	−6.83964	−	1.17277i	−0.508386	−	0.0871716i	−0.0909094	−	0.995859i	$-0.528977\pi$
$181$	−6.83964	−	1.17277i	−0.508386	−	0.0871716i	−0.417477	+	0.908688i	$0.637085\pi$
$182$	7.51216	−	5.07734i	0.556839	−	0.376357i
$183$	−8.46701			−0.625899
$184$	−8.18537			−0.603433
$185$	−11.5689	+	7.81922i	−0.850564	+	0.574881i
$186$	−0.0199925	−	0.470639i	−0.00146592	−	0.0345089i
$187$	−10.8215	−	0.921043i	−0.791345	−	0.0673534i
$188$	12.2848	−	5.55310i	0.895965	−	0.405002i
$189$	−0.635772	−	2.07601i	−0.0462456	−	0.151008i
$190$	4.62730	+	2.09167i	0.335700	+	0.151746i
$191$	−0.668032	−	5.21676i	−0.0483371	−	0.377471i	−0.997947	−	0.0640383i	$-0.979602\pi$
$191$	−0.668032	−	5.21676i	−0.0483371	−	0.377471i	0.949610	−	0.313433i	$-0.101479\pi$
$192$	5.81517	−	0.494944i	0.419674	−	0.0357195i
$193$	−15.1793	+	8.47968i	−1.09263	+	0.610381i	−0.926717	−	0.375759i	$-0.877382\pi$
$193$	−15.1793	+	8.47968i	−1.09263	+	0.610381i	−0.165915	+	0.986140i	$0.553058\pi$
$194$	1.46696	−	6.80670i	0.105321	−	0.488692i
$195$	6.41475	+	10.4182i	0.459369	+	0.746063i
$196$	−2.38474	+	1.07797i	−0.170339	+	0.0769980i
$197$	−6.88135	−	7.81873i	−0.490276	−	0.557061i	0.451949	−	0.892044i	$-0.350729\pi$
$197$	−6.88135	−	7.81873i	−0.490276	−	0.557061i	−0.942224	+	0.334983i	$0.891270\pi$
$198$	1.57429	−	3.12242i	0.111880	−	0.221901i
$199$	−11.5864	−	15.6658i	−0.821338	−	1.11052i	−0.992130	−	0.125215i	$-0.960038\pi$
$199$	−11.5864	−	15.6658i	−0.821338	−	1.11052i	0.170792	−	0.985307i	$-0.445367\pi$
$200$	3.56786	+	5.79457i	0.252286	+	0.409738i
$201$	−3.74667	−	12.2341i	−0.264269	−	0.862930i
$202$	−0.199967	−	0.111708i	−0.0140696	−	0.00785976i
$203$	−12.0160	−	4.24553i	−0.843359	−	0.297978i
$204$	−3.18202	+	0.828533i	−0.222786	+	0.0580089i
$205$	−3.54379	−	1.60190i	−0.247509	−	0.111881i
$206$	−0.183633	+	4.32286i	−0.0127943	+	0.301188i
$207$	−0.592978	+	2.75143i	−0.0412148	+	0.191237i
$208$	1.77880	−	0.305007i	0.123338	−	0.0211484i
$209$	1.61476	+	7.49251i	0.111695	+	0.518268i
$210$	−2.02818	−	5.04732i	−0.139958	−	0.348298i
$211$	−4.59212	−	14.9948i	−0.316135	−	1.03229i	−0.962959	−	0.269649i	$-0.913092\pi$
$211$	−4.59212	−	14.9948i	−0.316135	−	1.03229i	0.646824	−	0.762639i	$-0.276097\pi$
$212$	−0.390166	+	9.18481i	−0.0267967	+	0.630815i
$213$	0.939264	+	0.758403i	0.0643573	+	0.0519649i
$214$	−2.15925	−	2.06948i	−0.147603	−	0.141466i
$215$	2.67889	−	4.35080i	0.182699	−	0.296722i
$216$	0.369391	−	2.88463i	0.0251339	−	0.196274i
$217$	0.0469398	−	1.10500i	0.00318648	−	0.0750122i
$218$	−5.47746	−	8.89596i	−0.370980	−	0.602510i
$219$	1.57716	−	1.27347i	0.106575	−	0.0860531i
$220$	−4.37308	+	10.8828i	−0.294833	+	0.733719i
$221$	−12.2294	+	4.32091i	−0.822636	+	0.290656i
$222$	4.76620			0.319886
$223$	−0.336681	−	14.9294i	−0.0225458	−	0.999746i
$223$	−0.336681	−	14.9294i	−0.0225458	−	0.999746i
$224$	11.8260			0.790158
$225$	2.20625	−	0.779519i	0.147084	−	0.0519679i
$226$	−4.08036	+	10.1544i	−0.271422	+	0.675459i
$227$	13.5083	−	10.9072i	0.896580	−	0.723938i	−0.0651676	−	0.997874i	$-0.520758\pi$
$227$	13.5083	−	10.9072i	0.896580	−	0.723938i	0.961748	+	0.273936i	$0.0883258\pi$
$228$	1.21665	+	1.97596i	0.0805745	+	0.130861i
$229$	−0.0865714	+	2.03796i	−0.00572080	+	0.134672i	0.993967	+	0.109681i	$0.0349828\pi$
$229$	−0.0865714	+	2.03796i	−0.00572080	+	0.134672i	−0.999688	+	0.0249913i	$0.992044\pi$
$230$	−0.895673	+	6.99444i	−0.0590589	+	0.461200i
$231$	4.30463	−	6.99117i	0.283224	−	0.459985i
$232$	−12.3237	−	11.8113i	−0.809090	−	0.775450i
$233$	14.7906	+	11.9426i	0.968964	+	0.782384i	0.976040	−	0.217591i	$-0.0698198\pi$
$233$	14.7906	+	11.9426i	0.968964	+	0.782384i	−0.00707567	+	0.999975i	$0.502252\pi$
$234$	0.177239	−	4.17233i	0.0115864	−	0.272754i
$235$	−9.34214	−	30.5053i	−0.609414	−	1.98995i
$236$	4.41207	+	10.9799i	0.287202	+	0.714728i
$237$	1.29127	+	5.99153i	0.0838772	+	0.389191i
$238$	5.68365	−	0.974560i	0.368417	−	0.0631714i
$239$	−2.48166	+	11.5149i	−0.160525	+	0.744839i	0.823573	+	0.567211i	$0.191977\pi$
$239$	−2.48166	+	11.5149i	−0.160525	+	0.744839i	−0.984098	+	0.177628i	$0.943158\pi$
$240$	0.0459521	−	1.08175i	0.00296620	−	0.0698266i
$241$	10.2446	+	4.63085i	0.659913	+	0.298299i	0.713906	−	0.700242i	$-0.246925\pi$
$241$	10.2446	+	4.63085i	0.659913	+	0.298299i	−0.0539929	+	0.998541i	$0.517195\pi$
$242$	2.95233	−	0.768727i	0.189783	−	0.0494157i
$243$	−0.942877	−	0.333140i	−0.0604856	−	0.0213709i
$244$	−8.46248	−	4.72743i	−0.541755	−	0.302642i
$245$	1.81350	+	5.92171i	0.115860	+	0.378324i
$246$	0.695992	+	1.13036i	0.0443748	+	0.0720693i
$247$	5.44289	+	7.35928i	0.346323	+	0.468259i
$248$	0.666941	−	1.32280i	0.0423508	−	0.0839978i
$249$	2.82035	+	3.20454i	0.178732	+	0.203079i
$250$	−6.07283	+	2.74509i	−0.384079	+	0.173615i
$251$	−13.6459	−	22.1624i	−0.861323	−	1.39888i	−0.916344	−	0.400392i	$-0.868874\pi$
$251$	−13.6459	−	22.1624i	−0.861323	−	1.39888i	0.0550212	−	0.998485i	$-0.482477\pi$
$252$	0.523679	−	2.42988i	0.0329887	−	0.153068i
$253$	−9.29162	+	5.19061i	−0.584159	+	0.326331i
$254$	−9.35180	+	0.795956i	−0.586784	+	0.0499427i
$255$	0.988350	+	7.71817i	0.0618929	+	0.483330i
$256$	15.2679	+	6.90155i	0.954247	+	0.431347i
$257$	3.05491	+	9.97534i	0.190560	+	0.622245i	0.999414	+	0.0342345i	$0.0108993\pi$
$257$	3.05491	+	9.97534i	0.190560	+	0.622245i	−0.808854	+	0.588010i	$0.799911\pi$
$258$	−1.58918	+	0.718356i	−0.0989382	+	0.0447229i
$259$	11.1501	+	0.949014i	0.692834	+	0.0589689i
$260$	0.594467	+	13.9942i	0.0368673	+	0.867884i
$261$	−4.86302	+	3.28683i	−0.301013	+	0.203450i
$262$	−1.85573			−0.114647
$263$	18.5961			1.14668			0.573341	−	0.819317i	$-0.305647\pi$
$263$	18.5961			1.14668			0.573341	+	0.819317i	$0.305647\pi$
$264$	9.11114	−	6.15806i	0.560752	−	0.379002i
$265$	21.4421	+	3.67663i	1.31718	+	0.225853i
$266$	−1.83215	−	3.63385i	−0.112336	−	0.222806i
$267$	−3.65513	−	4.94206i	−0.223690	−	0.302449i
$268$	3.08609	−	14.3195i	0.188513	−	0.874703i
$269$	−20.5007	−	16.5532i	−1.24995	−	1.00926i	−0.999150	−	0.0412262i	$-0.986874\pi$
$269$	−20.5007	−	16.5532i	−1.24995	−	1.00926i	−0.250801	−	0.968039i	$-0.580694\pi$
$270$	−2.42451	−	0.631293i	−0.147551	−	0.0384193i
$271$	15.3858	+	10.3990i	0.934623	+	0.631695i	0.929710	−	0.368293i	$-0.120058\pi$
$271$	15.3858	+	10.3990i	0.934623	+	0.631695i	0.00491358	+	0.999988i	$0.498436\pi$
$272$	1.11078	+	0.289225i	0.0673510	+	0.0175368i
$273$	1.24540	−	9.72552i	0.0753751	−	0.588615i
$274$	9.92332	+	4.48563i	0.599490	+	0.270987i
$275$	7.72458	+	4.31521i	0.465810	+	0.260217i
$276$	−2.12888	+	2.41887i	−0.128143	+	0.145599i
$277$	−8.08729	+	7.75104i	−0.485918	+	0.465715i	−0.894539	−	0.446989i	$-0.852496\pi$
$277$	−8.08729	+	7.75104i	−0.485918	+	0.465715i	0.408621	+	0.912704i	$0.366010\pi$
$278$	9.86350	−	5.51008i	0.591573	−	0.330473i
$279$	−0.396329	−	0.320013i	−0.0237276	−	0.0191587i
$280$	2.17284	−	16.9681i	0.129852	−	1.01404i
$281$	2.91378	+	22.7541i	0.173821	+	1.35740i	0.810261	+	0.586070i	$0.199325\pi$
$281$	2.91378	+	22.7541i	0.173821	+	1.35740i	−0.636439	+	0.771327i	$0.719593\pi$
$282$	−3.18877	+	10.4124i	−0.189889	+	0.620052i
$283$	−4.92412	+	5.59489i	−0.292709	+	0.332581i	−0.878376	−	0.477970i	$-0.841373\pi$
$283$	−4.92412	+	5.59489i	−0.292709	+	0.332581i	0.585668	+	0.810551i	$0.300832\pi$
$284$	0.515319	+	1.28242i	0.0305786	+	0.0760977i
$285$	5.00386	−	2.26189i	0.296403	−	0.133983i
$286$	12.2864	−	9.92055i	0.726508	−	0.586614i
$287$	1.40314	+	2.78296i	0.0828248	+	0.164273i
$288$	3.23885	−	4.37921i	0.190851	−	0.258047i
$289$	8.71948	+	0.742137i	0.512911	+	0.0436551i
$290$	−11.4413	+	9.23822i	−0.671858	+	0.542487i
$291$	−4.47736	−	6.05378i	−0.262467	−	0.354879i
$292$	2.28734	−	0.392204i	0.133857	−	0.0229520i
$293$	−4.89448	+	4.69098i	−0.285938	+	0.274050i	−0.821205	−	0.570633i	$-0.806698\pi$
$293$	−4.89448	+	4.69098i	−0.285938	+	0.274050i	0.535266	+	0.844683i	$0.320211\pi$
$294$	0.619007	−	2.02127i	0.0361012	−	0.117883i
$295$	27.0991	−	7.05607i	1.57777	−	0.410820i
$296$	13.0856	+	7.31004i	0.760583	+	0.424887i
$297$	−1.40992	−	3.50873i	−0.0818120	−	0.203597i
$298$	−10.4622	−	11.8874i	−0.606062	−	0.688620i
$299$	−7.55812	+	10.2193i	−0.437097	+	0.590995i
$300$	2.64031	+	0.452726i	0.152438	+	0.0261381i
$301$	−3.86079	+	1.36410i	−0.222532	+	0.0786256i
$302$	13.3538	−	9.02558i	0.768424	−	0.519364i
$303$	−0.233544	+	0.0825165i	−0.0134168	+	0.00474045i
$304$	−0.0343789	−	0.809307i	−0.00197177	−	0.0464169i
$305$	−13.6403	+	18.4429i	−0.781043	+	1.05604i
$306$	1.19573	−	2.37158i	0.0683552	−	0.135574i
$307$	22.0152	−	3.77489i	1.25648	−	0.215444i	0.498018	−	0.867167i	$-0.334061\pi$
$307$	22.0152	−	3.77489i	1.25648	−	0.215444i	0.758458	+	0.651722i	$0.225953\pi$
$308$	8.20574	−	4.58400i	0.467566	−	0.261198i
$309$	3.37793	+	3.23748i	0.192164	+	0.184174i
$310$	−1.05736	−	0.714650i	−0.0600539	−	0.0405894i
$311$	2.31709	+	1.56608i	0.131390	+	0.0888042i	0.623907	−	0.781499i	$-0.285545\pi$
$311$	2.31709	+	1.56608i	0.131390	+	0.0888042i	−0.492517	+	0.870303i	$0.663923\pi$
$312$	6.88582	−	11.1833i	0.389833	−	0.633129i
$313$	1.05199	+	8.21512i	0.0594619	+	0.464346i	0.994076	+	0.108684i	$0.0346636\pi$
$313$	1.05199	+	8.21512i	0.0594619	+	0.464346i	−0.934615	+	0.355662i	$0.884255\pi$
$314$	−1.78178	+	0.463939i	−0.100552	+	0.0261816i
$315$	−5.54623	−	1.95961i	−0.312494	−	0.110411i
$316$	−2.05469	+	6.70928i	−0.115586	+	0.377427i
$317$	25.0051	−	2.12825i	1.40443	−	0.119534i	0.642048	−	0.766664i	$-0.278085\pi$
$317$	25.0051	−	2.12825i	1.40443	−	0.119534i	0.762380	+	0.647130i	$0.224031\pi$
$318$	−5.36103	−	5.13813i	−0.300632	−	0.288132i
$319$	−21.4792	−	5.59274i	−1.20260	−	0.313133i
$320$	8.29012	−	13.4640i	0.463432	−	0.752661i
$321$	−3.22257	+	0.274281i	−0.179866	+	0.0153089i
$322$	4.07987	−	3.91024i	0.227362	−	0.217909i
$323$	1.22646	+	5.69081i	0.0682423	+	0.316645i
$324$	−0.756370	−	0.859403i	−0.0420205	−	0.0477446i
$325$	10.5288	+	0.896137i	0.584035	+	0.0497087i
$326$	−7.49448	+	18.6507i	−0.415081	+	1.03297i
$327$	−11.1347	−	1.90923i	−0.615750	−	0.105581i
$328$	0.177176	+	4.17086i	0.00978291	+	0.230297i
$329$	−9.53311	+	23.7241i	−0.525577	+	1.30795i
$330$	−4.26511	−	8.45935i	−0.234787	−	0.465672i
$331$	11.5390	−	22.8863i	0.634242	−	1.25794i	−0.316685	−	0.948531i	$-0.602570\pi$
$331$	11.5390	−	22.8863i	0.634242	−	1.25794i	0.950928	−	0.309414i	$-0.100133\pi$
$332$	1.02963	+	4.77752i	0.0565085	+	0.262201i
$333$	3.40516	−	3.86901i	0.186602	−	0.212021i
$334$	2.63490	+	0.930969i	0.144175	+	0.0509403i
$335$	−32.6844	−	11.5481i	−1.78574	−	0.630942i
$336$	−0.573267	+	0.651358i	−0.0312743	+	0.0355345i
$337$	−1.14244	−	5.30094i	−0.0622326	−	0.288760i	0.935718	−	0.352749i	$-0.114753\pi$
$337$	−1.14244	−	5.30094i	−0.0622326	−	0.288760i	−0.997951	+	0.0639885i	$0.979618\pi$
$338$	3.07818	−	6.10520i	0.167431	−	0.332079i
$339$	5.32774	+	10.5669i	0.289363	+	0.573918i
$340$	−3.32150	+	8.26587i	−0.180134	+	0.448280i
$341$	−0.0817519	−	1.92450i	−0.00442711	−	0.104218i
$342$	−1.84741	−	0.316770i	−0.0998964	−	0.0171290i
$343$	7.51736	−	18.7077i	0.405899	−	1.01012i
$344$	−5.46485	−	0.465127i	−0.294645	−	0.0250780i
$345$	5.03790	+	5.72417i	0.271232	+	0.308179i
$346$	4.04645	+	18.7756i	0.217538	+	1.00938i
$347$	15.3013	−	14.6651i	0.821415	−	0.787263i	−0.158356	−	0.987382i	$-0.550619\pi$
$347$	15.3013	−	14.6651i	0.821415	−	0.787263i	0.979772	+	0.200119i	$0.0641330\pi$
$348$	−6.69557	+	0.569877i	−0.358920	+	0.0305486i
$349$	8.64230	−	14.0360i	0.462612	−	0.751329i	−0.532879	−	0.846192i	$-0.678890\pi$
$349$	8.64230	−	14.0360i	0.462612	−	0.751329i	0.995490	+	0.0948627i	$0.0302412\pi$
$350$	−4.54648	−	1.18381i	−0.243019	−	0.0632773i
$351$	−3.26031	−	3.12475i	−0.174022	−	0.166787i
$352$	20.5224	−	1.74671i	1.09385	−	0.0931000i
$353$	8.55573	−	27.9374i	0.455376	−	1.48696i	−0.373556	−	0.927608i	$-0.621862\pi$
$353$	8.55573	−	27.9374i	0.455376	−	1.48696i	0.828932	−	0.559350i	$-0.188949\pi$
$354$	−9.01223	−	3.18422i	−0.478995	−	0.169240i
$355$	3.16511	−	0.824131i	0.167987	−	0.0437403i
$356$	−0.893850	−	6.98020i	−0.0473739	−	0.369950i
$357$	3.26951	−	5.31003i	0.173041	−	0.281036i
$358$	−15.0840	−	10.1950i	−0.797215	−	0.538823i
$359$	2.70357	+	1.82729i	0.142689	+	0.0964408i	0.629239	−	0.777212i	$-0.283367\pi$
$359$	2.70357	+	1.82729i	0.142689	+	0.0964408i	−0.486550	+	0.873653i	$0.661745\pi$
$360$	−5.68824	−	5.45174i	−0.299797	−	0.287332i
$361$	−13.0006	+	7.26259i	−0.684244	+	0.382242i
$362$	6.32493	−	1.08452i	0.332431	−	0.0570010i
$363$	1.48524	−	2.94579i	0.0779548	−	0.154614i
$364$	6.67483	−	9.02497i	0.349856	−	0.473037i
$365$	−0.233083	−	5.48695i	−0.0122001	−	0.287200i
$366$	7.38258	−	2.60843i	0.385893	−	0.136345i
$367$	5.27444	−	3.56490i	0.275324	−	0.186086i	−0.414529	−	0.910036i	$-0.636054\pi$
$367$	5.27444	−	3.56490i	0.275324	−	0.186086i	0.689853	+	0.723950i	$0.257675\pi$
$368$	1.06058	−	0.374727i	0.0552866	−	0.0195340i
$369$	1.41483	+	0.242596i	0.0736529	+	0.0126291i
$370$	7.67833	−	10.3818i	0.399178	−	0.539724i
$371$	−11.5186	−	13.0877i	−0.598016	−	0.679478i
$372$	−0.217443	−	0.541127i	−0.0112739	−	0.0280561i
$373$	−10.7649	−	6.01365i	−0.557387	−	0.311375i	0.183483	−	0.983023i	$-0.441263\pi$
$373$	−10.7649	−	6.01365i	−0.557387	−	0.311375i	−0.740871	+	0.671648i	$0.765587\pi$
$374$	9.71923	−	2.53069i	0.502570	−	0.130859i
$375$	−2.11031	+	6.89088i	−0.108976	+	0.355844i
$376$	−24.7246	+	23.6966i	−1.27507	+	1.22206i
$377$	−26.1255	+	4.47966i	−1.34553	+	0.230714i
$378$	1.19390	+	1.61426i	0.0614077	+	0.0830287i
$379$	18.8149	−	15.1920i	0.966459	−	0.780361i	−0.00913171	−	0.999958i	$-0.502907\pi$
$379$	18.8149	−	15.1920i	0.966459	−	0.780361i	0.975591	+	0.219597i	$0.0704743\pi$
$380$	6.26408	+	0.533152i	0.321340	+	0.0273501i
$381$	−6.03517	+	8.16008i	−0.309191	+	0.418054i
$382$	2.18960	+	4.34281i	0.112030	+	0.222197i
$383$	7.76157	−	6.26703i	0.396598	−	0.320230i	−0.409174	−	0.912456i	$-0.634183\pi$
$383$	7.76157	−	6.26703i	0.396598	−	0.320230i	0.805772	+	0.592226i	$0.201751\pi$
$384$	5.00866	−	2.26406i	0.255597	−	0.115537i
$385$	−8.29349	−	20.6391i	−0.422675	−	1.05187i
$386$	10.6229	−	12.0699i	0.540689	−	0.614343i
$387$	−0.552241	+	1.80326i	−0.0280720	+	0.0916647i
$388$	−1.09492	−	8.55041i	−0.0555863	−	0.434081i
$389$	−1.27356	+	9.94544i	−0.0645722	+	0.504254i	0.927036	+	0.374973i	$0.122348\pi$
$389$	−1.27356	+	9.94544i	−0.0645722	+	0.504254i	−0.991608	+	0.129281i	$0.958733\pi$
$390$	−8.80270	−	7.10768i	−0.445742	−	0.359911i
$391$	−7.05730	+	3.94244i	−0.356903	+	0.199378i
$392$	4.79955	−	4.60000i	0.242414	−	0.232335i
$393$	−1.32581	+	1.50641i	−0.0668780	+	0.0759882i
$394$	8.40872	+	4.69739i	0.423625	+	0.236651i
$395$	15.1310	+	6.83966i	0.761325	+	0.344141i
$396$	0.549876	−	4.29406i	0.0276323	−	0.215785i
$397$	32.7488	+	8.52713i	1.64362	+	0.427964i	0.954867	−	0.297035i	$-0.0959979\pi$
$397$	32.7488	+	8.52713i	1.64362	+	0.427964i	0.688749	+	0.725000i	$0.258160\pi$
$398$	14.9286	+	10.0900i	0.748304	+	0.505765i
$399$	−4.25878	−	1.10890i	−0.213206	−	0.0555144i
$400$	−0.727565	−	0.587468i	−0.0363783	−	0.0293734i
$401$	−7.10170	+	32.9520i	−0.354642	+	1.64555i	0.350561	+	0.936540i	$0.385991\pi$
$401$	−7.10170	+	32.9520i	−0.354642	+	1.64555i	−0.705203	+	0.709005i	$0.749144\pi$
$402$	7.03577	+	9.51299i	0.350912	+	0.474465i
$403$	−1.03565	−	2.05409i	−0.0515895	−	0.102322i
$404$	−0.279491	−	0.0479236i	−0.0139052	−	0.00238429i
$405$	−2.24462	+	1.51710i	−0.111536	+	0.0753853i
$406$	11.7850			0.584877
$407$	19.4896			0.966064
$408$	6.92022	−	4.67725i	0.342602	−	0.231558i
$409$	−0.407519	−	9.59331i	−0.0201505	−	0.474359i	−0.980614	−	0.195951i	$-0.937220\pi$
$409$	−0.407519	−	9.59331i	−0.0201505	−	0.474359i	0.960463	−	0.278407i	$-0.0898065\pi$
$410$	3.58341	+	0.304993i	0.176972	+	0.0150625i
$411$	10.7309	−	4.85066i	0.529314	−	0.239265i
$412$	1.56852	+	5.12177i	0.0772756	+	0.252331i
$413$	−20.4493	−	9.24367i	−1.00624	−	0.454851i
$414$	−0.330601	−	2.58171i	−0.0162481	−	0.126884i
$415$	11.5237	−	0.980814i	0.565678	−	0.0481463i
$416$	21.4739	−	11.9960i	1.05284	−	0.588154i
$417$	2.57400	−	11.9434i	0.126049	−	0.584871i
$418$	−3.71616	−	6.03543i	−0.181763	−	0.295202i
$419$	−19.5870	+	8.85390i	−0.956890	+	0.432541i	−0.829001	−	0.559247i	$-0.811090\pi$
$419$	−19.5870	+	8.85390i	−0.956890	+	0.432541i	−0.127889	+	0.991789i	$0.540820\pi$
$420$	−4.44914	−	5.05521i	−0.217096	−	0.246669i
$421$	−13.3995	+	26.5764i	−0.653054	+	1.29526i	0.288205	+	0.957569i	$0.406942\pi$
$421$	−13.3995	+	26.5764i	−0.653054	+	1.29526i	−0.941259	+	0.337686i	$0.890356\pi$
$422$	8.62343	+	11.6597i	0.419782	+	0.567583i
$423$	6.17422	+	10.0276i	0.300201	+	0.487557i
$424$	−6.83820	−	22.3291i	−0.332092	−	1.08440i
$425$	5.86708	+	3.27755i	0.284595	+	0.158984i
$426$	−1.05261	−	0.371910i	−0.0509989	−	0.0180191i
$427$	17.7903	−	4.63222i	0.860931	−	0.224169i
$428$	−3.37399	−	1.52514i	−0.163088	−	0.0737204i
$429$	0.724751	−	17.0612i	0.0349913	−	0.823723i
$430$	−0.995437	+	4.61884i	−0.0480042	+	0.222740i
$431$	30.5337	−	5.23553i	1.47076	−	0.252187i	0.622854	−	0.782338i	$-0.285973\pi$
$431$	30.5337	−	5.23553i	1.47076	−	0.252187i	0.847903	+	0.530151i	$0.177865\pi$
$432$	0.0841965	+	0.390673i	0.00405091	+	0.0187963i
$433$	−11.6011	−	28.8704i	−0.557512	−	1.38742i	−0.894989	−	0.446088i	$-0.852817\pi$
$433$	−11.6011	−	28.8704i	−0.557512	−	1.38742i	0.337478	−	0.941334i	$-0.390426\pi$
$434$	0.299489	+	0.977934i	0.0143759	+	0.0469423i
$435$	−0.674904	+	15.8878i	−0.0323591	+	0.761760i
$436$	−10.0627	−	8.12510i	−0.481918	−	0.389122i
$437$	4.11870	+	3.94745i	0.197024	+	0.188832i
$438$	−0.982846	+	1.59624i	−0.0469622	+	0.0762714i
$439$	−3.20119	+	24.9985i	−0.152784	+	1.19312i	0.716063	+	0.698036i	$0.245942\pi$
$439$	−3.20119	+	24.9985i	−0.152784	+	1.19312i	−0.868847	+	0.495080i	$0.835139\pi$
$440$	1.26447	−	29.7666i	0.0602812	−	1.41907i
$441$	−1.19854	−	1.94656i	−0.0570735	−	0.0926933i
$442$	9.33191	−	7.53499i	0.443874	−	0.358403i
$443$	5.52891	−	13.7592i	0.262686	−	0.653720i	−0.737070	−	0.675817i	$-0.763791\pi$
$443$	5.52891	−	13.7592i	0.262686	−	0.653720i	0.999756	+	0.0220970i	$0.00703425\pi$
$444$	5.56354	−	1.96572i	0.264034	−	0.0932891i
$445$	−16.6532			−0.789440
$446$	4.89285	+	12.9135i	0.231683	+	0.611474i
$447$	−17.1244			−0.809955
$448$	−11.9476	+	4.22137i	−0.564472	+	0.199441i
$449$	−1.09429	+	2.72324i	−0.0516427	+	0.128518i	−0.951483	−	0.307702i	$-0.900440\pi$
$449$	−1.09429	+	2.72324i	−0.0516427	+	0.128518i	0.899840	+	0.436220i	$0.143683\pi$
$450$	−1.68354	+	1.35936i	−0.0793626	+	0.0640808i
$451$	2.84600	+	4.62220i	0.134013	+	0.217651i
$452$	−0.575001	+	13.5360i	−0.0270458	+	0.636678i
$453$	2.21385	−	17.2883i	0.104016	−	0.812275i
$454$	−8.41804	+	13.6718i	−0.395078	+	0.641648i
$455$	−19.1779	−	18.3805i	−0.899074	−	0.861693i
$456$	−4.58621	−	3.70311i	−0.214769	−	0.173414i
$457$	−1.54047	+	36.2639i	−0.0720601	+	1.69635i	0.491982	+	0.870605i	$0.336273\pi$
$457$	−1.54047	+	36.2639i	−0.0720601	+	1.69635i	−0.564042	+	0.825746i	$0.690754\pi$
$458$	−0.552350	−	1.80361i	−0.0258096	−	0.0842772i
$459$	−1.07088	−	2.66500i	−0.0499846	−	0.124391i
$460$	1.83921	+	8.53394i	0.0857534	+	0.397897i
$461$	5.19912	−	0.891479i	0.242147	−	0.0415203i	−0.0466473	−	0.998911i	$-0.514854\pi$
$461$	5.19912	−	0.891479i	0.242147	−	0.0415203i	0.288794	+	0.957391i	$0.406746\pi$
$462$	−1.59954	+	7.42188i	−0.0744172	+	0.345297i
$463$	−1.73600	+	40.8668i	−0.0806787	+	1.89924i	0.270177	+	0.962811i	$0.412918\pi$
$463$	−1.73600	+	40.8668i	−0.0806787	+	1.89924i	−0.350855	+	0.936430i	$0.614109\pi$
$464$	2.13751	+	0.966215i	0.0992314	+	0.0448554i
$465$	−1.33554	+	0.347748i	−0.0619343	+	0.0161264i
$466$	−16.5754	−	5.85646i	−0.767841	−	0.271295i
$467$	−32.4335	−	18.1185i	−1.50084	−	0.838422i	−0.501207	−	0.865328i	$-0.667110\pi$
$467$	−32.4335	−	18.1185i	−1.50084	−	0.838422i	−0.999638	+	0.0269056i	$0.991435\pi$
$468$	−1.51391	−	4.94343i	−0.0699804	−	0.228510i
$469$	14.5654	+	23.6557i	0.672568	+	1.09232i
$470$	17.5434	+	23.7202i	0.809216	+	1.09413i
$471$	−0.896364	+	1.77783i	−0.0413023	+	0.0819182i
$472$	−19.8593	−	22.5646i	−0.914099	−	1.03862i
$473$	−6.49837	+	2.93745i	−0.298795	+	0.135064i
$474$	−2.97170	−	4.82634i	−0.136495	−	0.221681i
$475$	0.999205	−	4.63633i	0.0458467	−	0.212729i
$476$	6.23254	−	3.48170i	0.285668	−	0.159584i
$477$	−8.00106	+	0.680991i	−0.366344	+	0.0311804i
$478$	−1.38359	−	10.8046i	−0.0632839	−	0.494193i
$479$	15.1062	+	6.82843i	0.690220	+	0.311999i	0.726327	−	0.687349i	$-0.241226\pi$
$479$	15.1062	+	6.82843i	0.690220	+	0.311999i	−0.0361075	+	0.999348i	$0.511496\pi$
$480$	−4.32107	−	14.1098i	−0.197229	−	0.644021i
$481$	21.2092	−	9.58718i	0.967058	−	0.437138i
$482$	−10.3591	−	0.881691i	−0.471845	−	0.0401599i
$483$	−0.259359	−	6.10551i	−0.0118012	−	0.277810i
$484$	3.12918	−	2.11496i	0.142236	−	0.0961345i
$485$	−20.3994			−0.926290
$486$	0.924746			0.0419473
$487$	−26.3203	+	17.7894i	−1.19268	+	0.806114i	−0.985080	−	0.172099i	$-0.944945\pi$
$487$	−26.3203	+	17.7894i	−1.19268	+	0.806114i	−0.207605	+	0.978213i	$0.566567\pi$
$488$	24.2694	+	4.16141i	1.09863	+	0.188378i
$489$	9.78558	+	19.4085i	0.442519	+	0.877684i
$490$	−3.40553	−	4.60459i	−0.153846	−	0.208014i
$491$	−1.96539	+	9.11944i	−0.0886968	+	0.411554i	−1.00000		0.000181459i	$-0.999942\pi$
$491$	−1.96539	+	9.11944i	−0.0886968	+	0.411554i	0.911303	+	0.411736i	$0.135077\pi$
$492$	1.27862	+	1.03241i	0.0576446	+	0.0465448i
$493$	−16.3142	−	4.24787i	−0.734752	−	0.191315i
$494$	−7.01295	−	4.73993i	−0.315528	−	0.213259i
$495$	−9.91413	−	2.58144i	−0.445607	−	0.116027i
$496$	−0.0258579	+	0.201928i	−0.00116105	+	0.00906684i
$497$	−2.38843	−	1.07964i	−0.107136	−	0.0484284i
$498$	−3.44634	−	1.92524i	−0.154434	−	0.0862722i
$499$	−22.1802	+	25.2016i	−0.992921	+	1.12818i	−0.00117020	+	0.999999i	$0.500372\pi$
$499$	−22.1802	+	25.2016i	−0.992921	+	1.12818i	−0.991751	+	0.128178i	$0.959087\pi$
$500$	−5.95660	+	5.70894i	−0.266387	+	0.255311i
$501$	2.63820	−	1.47379i	0.117866	−	0.0658439i
$502$	18.7257	+	15.1200i	0.835771	+	0.674838i
$503$	−4.37177	+	34.1398i	−0.194927	+	1.52222i	0.538603	+	0.842560i	$0.318952\pi$
$503$	−4.37177	+	34.1398i	−0.194927	+	1.52222i	−0.733530	+	0.679657i	$0.762129\pi$
$504$	0.802016	+	6.26306i	0.0357246	+	0.278979i
$505$	−0.196501	+	0.641643i	−0.00874417	+	0.0285527i
$506$	6.50250	−	7.38827i	0.289071	−	0.328449i
$507$	−2.75679	−	6.86053i	−0.122433	−	0.304687i
$508$	−10.5880	+	4.78608i	−0.469766	+	0.212348i
$509$	7.06690	−	5.70613i	0.313235	−	0.252920i	−0.458743	−	0.888569i	$-0.651700\pi$
$509$	7.06690	−	5.70613i	0.313235	−	0.252920i	0.771978	+	0.635649i	$0.219268\pi$
$510$	−3.23950	−	6.42516i	−0.143447	−	0.284511i
$511$	−2.61712	+	3.53857i	−0.115774	+	0.156537i
$512$	−4.48503	−	0.381732i	−0.198212	−	0.0168703i
$513$	−1.57700	+	1.27334i	−0.0696263	+	0.0562193i
$514$	−5.73675	−	7.75660i	−0.253037	−	0.342129i
$515$	12.4938	−	2.14227i	0.550541	−	0.0943997i
$516$	−1.55877	+	1.49396i	−0.0686209	+	0.0657678i
$517$	−13.0393	+	42.5778i	−0.573468	+	1.87257i
$518$	−10.0144	+	2.60754i	−0.440007	+	0.114569i
$519$	18.1322	+	10.1293i	0.795916	+	0.444625i
$520$	−13.2665	−	33.0150i	−0.581775	−	1.44780i
$521$	17.2425	+	19.5913i	0.755408	+	0.858310i	0.993606	−	0.112907i	$-0.0360161\pi$
$521$	17.2425	+	19.5913i	0.755408	+	0.858310i	−0.238198	+	0.971217i	$0.576557\pi$
$522$	3.22760	−	4.36401i	0.141268	−	0.191007i
$523$	−10.3239	−	1.77021i	−0.451431	−	0.0774057i	−0.0612062	−	0.998125i	$-0.519495\pi$
$523$	−10.3239	−	1.77021i	−0.451431	−	0.0774057i	−0.390225	+	0.920719i	$0.627603\pi$
$524$	−2.16618	+	0.765359i	−0.0946299	+	0.0334349i
$525$	−4.20915	+	2.84489i	−0.183702	+	0.124161i
$526$	−16.2143	+	5.72889i	−0.706978	+	0.249791i
$527$	−0.0620933	−	1.46172i	−0.00270483	−	0.0636737i
$528$	−0.898617	+	1.21501i	−0.0391073	+	0.0528766i
$529$	6.78819	−	13.4636i	0.295139	−	0.585372i
$530$	−19.8285	+	3.39995i	−0.861297	+	0.147684i
$531$	−9.02352	+	5.04084i	−0.391587	+	0.218754i
$532$	−3.63736	−	3.48613i	−0.157700	−	0.151143i
$533$	5.37083	+	3.63004i	0.232636	+	0.157235i
$534$	4.70949	+	3.18306i	0.203799	+	0.137744i
$535$	−4.59411	+	7.46131i	−0.198621	+	0.322580i
$536$	4.72636	+	36.9088i	0.204148	+	1.59422i
$537$	−19.0525	+	4.96089i	−0.822177	+	0.214078i
$538$	22.9746	+	8.11743i	0.990504	+	0.349967i
$539$	2.53120	−	8.26523i	0.109026	−	0.356009i
$540$	−3.09047	+	0.263038i	−0.132993	+	0.0113193i
$541$	18.8900	+	18.1046i	0.812144	+	0.778377i	0.978184	−	0.207742i	$-0.0666116\pi$
$541$	18.8900	+	18.1046i	0.812144	+	0.778377i	−0.166040	+	0.986119i	$0.553098\pi$
$542$	−16.6189	−	4.32722i	−0.713842	−	0.185870i
$543$	3.63841	−	5.90915i	0.156139	−	0.253586i
$544$	15.5874	−	1.32669i	0.668305	−	0.0568812i
$545$	−22.0967	+	21.1779i	−0.946517	+	0.907163i
$546$	1.91025	+	8.86357i	0.0817510	+	0.379326i
$547$	15.5269	+	17.6420i	0.663882	+	0.754317i	0.980987	−	0.194074i	$-0.0621701\pi$
$547$	15.5269	+	17.6420i	0.663882	+	0.754317i	−0.317105	+	0.948391i	$0.602711\pi$
$548$	13.4334	+	1.14335i	0.573847	+	0.0488416i
$549$	3.15698	−	7.85645i	0.134737	−	0.335305i
$550$	−8.06462	−	1.38282i	−0.343876	−	0.0589635i
$551$	0.504927	+	11.8864i	0.0215106	+	0.506377i
$552$	3.05197	−	7.59512i	0.129900	−	0.323270i
$553$	−5.99104	−	11.8825i	−0.254765	−	0.505296i
$554$	4.66363	−	9.24976i	0.198139	−	0.392984i
$555$	−2.94183	−	13.6501i	−0.124874	−	0.579415i
$556$	9.24105	−	10.4999i	0.391908	−	0.445294i
$557$	−40.3287	−	14.2490i	−1.70878	−	0.603751i	−0.713488	−	0.700667i	$-0.752886\pi$
$557$	−40.3287	−	14.2490i	−1.70878	−	0.603751i	−0.995293	+	0.0969166i	$0.969102\pi$
$558$	0.444155	+	0.156930i	0.0188026	+	0.00664337i
$559$	−5.62677	+	6.39326i	−0.237987	+	0.270406i
$560$	0.495264	+	2.29803i	0.0209287	+	0.0971095i
$561$	4.88948	−	9.69771i	0.206434	−	0.409438i
$562$	−9.55044	−	18.9422i	−0.402861	−	0.799027i
$563$	5.42860	−	13.5096i	0.228788	−	0.569361i	−0.768745	−	0.639555i	$-0.779119\pi$
$563$	5.42860	−	13.5096i	0.228788	−	0.569361i	0.997533	+	0.0701941i	$0.0223619\pi$
$564$	0.572177	+	13.4695i	0.0240930	+	0.567168i
$565$	31.6000	+	5.41837i	1.32942	+	0.227952i
$566$	2.56983	−	6.39528i	0.108018	−	0.268814i
$567$	2.16336	+	0.184129i	0.0908527	+	0.00773271i
$568$	−2.31952	−	2.63548i	−0.0973248	−	0.110582i
$569$	5.89622	+	27.3586i	0.247182	+	1.14693i	0.915268	+	0.402846i	$0.131979\pi$
$569$	5.89622	+	27.3586i	0.247182	+	1.14693i	−0.668085	+	0.744085i	$0.732886\pi$
$570$	−3.66616	+	3.51373i	−0.153559	+	0.147174i
$571$	−28.6640	+	2.43967i	−1.19955	+	0.102097i	−0.667496	−	0.744613i	$-0.732634\pi$
$571$	−28.6640	+	2.43967i	−1.19955	+	0.102097i	−0.532055	+	0.846710i	$0.678580\pi$
$572$	10.2502	−	16.6474i	0.428584	−	0.696064i
$573$	5.08965	+	1.32524i	0.212623	+	0.0553628i
$574$	−2.08078	−	1.99426i	−0.0868500	−	0.0832390i
$575$	6.56220	−	0.558525i	0.273663	−	0.0232921i
$576$	−1.70897	+	5.58037i	−0.0712071	+	0.232516i
$577$	−30.2094	−	10.6737i	−1.25764	−	0.444351i	−0.380583	−	0.924747i	$-0.624277\pi$
$577$	−30.2094	−	10.6737i	−1.25764	−	0.444351i	−0.877052	+	0.480396i	$0.840493\pi$
$578$	−7.83134	+	2.03912i	−0.325741	+	0.0848163i
$579$	−2.20849	−	17.2464i	−0.0917818	−	0.716737i
$580$	−9.54523	+	15.5024i	−0.396344	+	0.643704i
$581$	−7.67908	−	5.19015i	−0.318582	−	0.215324i
$582$	5.76889	+	3.89909i	0.239128	+	0.161623i
$583$	−21.9220	−	21.0105i	−0.907915	−	0.870166i
$584$	−5.14659	+	2.87506i	−0.212968	+	0.118971i
$585$	−12.0587	+	2.06768i	−0.498567	+	0.0854879i
$586$	2.82246	−	5.59801i	0.116595	−	0.231252i
$587$	6.30183	−	8.52064i	0.260104	−	0.351684i	−0.654480	−	0.756079i	$-0.727112\pi$
$587$	6.30183	−	8.52064i	0.260104	−	0.351684i	0.914584	+	0.404395i	$0.132518\pi$
$588$	−0.111071	−	2.61471i	−0.00458050	−	0.107829i
$589$	−0.973519	+	0.343966i	−0.0401131	+	0.0141729i
$590$	−21.4546	+	14.5008i	−0.883272	+	0.596987i
$591$	9.82067	−	3.46986i	0.403968	−	0.142731i
$592$	−2.03016	−	0.348105i	−0.0834389	−	0.0143070i
$593$	−3.21741	+	4.35022i	−0.132123	+	0.178642i	−0.865082	−	0.501631i	$-0.832733\pi$
$593$	−3.21741	+	4.35022i	−0.132123	+	0.178642i	0.732959	+	0.680273i	$0.238139\pi$
$594$	2.31027	+	2.62498i	0.0947917	+	0.107704i
$595$	−6.29919	−	15.6761i	−0.258241	−	0.642659i
$596$	−17.1152	−	9.56113i	−0.701066	−	0.391639i
$597$	18.8562	−	4.90978i	0.771734	−	0.200944i
$598$	3.44185	−	11.2388i	0.140748	−	0.459590i
$599$	−18.4751	+	17.7069i	−0.754871	+	0.723485i	−0.967284	−	0.253695i	$-0.918354\pi$
$599$	−18.4751	+	17.7069i	−0.754871	+	0.723485i	0.212413	+	0.977180i	$0.431868\pi$
$600$	−6.70702	+	1.15003i	−0.273813	+	0.0469499i
$601$	10.7755	+	14.5694i	0.439540	+	0.594298i	0.966840	−	0.255381i	$-0.0822010\pi$
$601$	10.7755	+	14.5694i	0.439540	+	0.594298i	−0.527300	+	0.849679i	$0.676796\pi$
$602$	2.94607	−	2.37878i	0.120073	−	0.0969520i
$603$	12.7489	+	1.08509i	0.519175	+	0.0441883i
$604$	11.8653	−	16.0430i	0.482793	−	0.652780i
$605$	−4.02385	−	7.98083i	−0.163593	−	0.324467i
$606$	0.178212	−	0.143896i	0.00723936	−	0.00584537i
$607$	9.51830	−	4.30254i	0.386336	−	0.174635i	−0.209372	−	0.977836i	$-0.567142\pi$
$607$	9.51830	−	4.30254i	0.386336	−	0.174635i	0.595708	+	0.803201i	$0.296872\pi$
$608$	−4.11638	−	10.2440i	−0.166941	−	0.415449i
$609$	8.41963	−	9.56656i	0.341181	−	0.387656i
$610$	6.21159	−	20.2830i	0.251500	−	0.821234i
$611$	6.75474	+	52.7488i	0.273268	+	2.13399i
$612$	0.417649	−	3.26148i	0.0168825	−	0.131838i
$613$	12.9473	+	10.4542i	0.522938	+	0.422243i	0.853151	−	0.521663i	$-0.174688\pi$
$613$	12.9473	+	10.4542i	0.522938	+	0.422243i	−0.330213	+	0.943906i	$0.607121\pi$
$614$	−18.0326	+	10.0736i	−0.727738	+	0.406539i
$615$	2.80771	−	2.69097i	0.113218	−	0.108510i
$616$	−15.7746	+	17.9235i	−0.635579	+	0.722158i
$617$	7.70071	+	4.30187i	0.310019	+	0.173187i	0.634955	−	0.772549i	$-0.281019\pi$
$617$	7.70071	+	4.30187i	0.310019	+	0.173187i	−0.324936	+	0.945736i	$0.605343\pi$
$618$	−3.94266	−	1.78220i	−0.158597	−	0.0716904i
$619$	−5.93044	+	46.3117i	−0.238365	+	1.86142i	0.223807	+	0.974633i	$0.428151\pi$
$619$	−5.93044	+	46.3117i	−0.238365	+	1.86142i	−0.462172	+	0.886790i	$0.652930\pi$
$620$	−1.52899	−	0.398117i	−0.0614056	−	0.0159888i
$621$	−2.33192	−	1.57610i	−0.0935768	−	0.0632469i
$622$	−2.50278	−	0.651674i	−0.100353	−	0.0261298i
$623$	10.3836	+	8.38421i	0.416012	+	0.335906i
$624$	−0.380226	+	1.76426i	−0.0152212	+	0.0706268i
$625$	18.5670	+	25.1043i	0.742682	+	1.00417i
$626$	−3.44808	−	6.83886i	−0.137813	−	0.273336i
$627$	−7.55429	−	1.29531i	−0.301689	−	0.0517298i
$628$	−1.88851	+	1.27641i	−0.0753598	+	0.0509343i
$629$	14.8030			0.590235
$630$	5.43957			0.216718
$631$	−14.6204	+	9.88164i	−0.582027	+	0.393382i	−0.815308	−	0.579028i	$-0.803432\pi$
$631$	−14.6204	+	9.88164i	−0.582027	+	0.393382i	0.233281	+	0.972409i	$0.425054\pi$
$632$	−0.756494	−	17.8085i	−0.0300917	−	0.708382i
$633$	15.6258	+	1.32995i	0.621068	+	0.0528607i
$634$	−21.1469	+	9.55899i	−0.839850	+	0.379636i
$635$	8.05175	+	26.2917i	0.319524	+	1.04336i
$636$	−8.37701	−	3.78665i	−0.332170	−	0.150150i
$637$	−1.31124	−	10.2396i	−0.0519530	−	0.405709i
$638$	20.4511	−	1.74065i	0.809668	−	0.0689129i
$639$	−1.05392	+	0.588757i	−0.0416926	+	0.0232909i
$640$	3.13734	−	14.5573i	0.124014	−	0.575428i
$641$	−9.03571	−	14.6749i	−0.356889	−	0.579624i	0.622249	−	0.782819i	$-0.286219\pi$
$641$	−9.03571	−	14.6749i	−0.356889	−	0.579624i	−0.979138	+	0.203195i	$0.934868\pi$
$642$	2.72533	−	1.23193i	0.107560	−	0.0486204i
$643$	−29.3904	−	33.3940i	−1.15904	−	1.31693i	−0.939984	−	0.341218i	$-0.889160\pi$
$643$	−29.3904	−	33.3940i	−1.15904	−	1.31693i	−0.219060	−	0.975711i	$-0.570299\pi$
$644$	3.14970	−	6.24705i	0.124115	−	0.246168i
$645$	3.03821	+	4.10794i	0.119630	+	0.161750i
$646$	−2.82255	−	4.58411i	−0.111052	−	0.180359i
$647$	−12.4347	−	40.6035i	−0.488858	−	1.59629i	−0.770946	−	0.636901i	$-0.780216\pi$
$647$	−12.4347	−	40.6035i	−0.488858	−	1.59629i	0.282088	−	0.959389i	$-0.408973\pi$
$648$	2.53888	+	1.41831i	0.0997368	+	0.0557163i
$649$	−36.8522	−	13.0207i	−1.44657	−	0.511107i
$650$	−9.45641	+	2.46226i	−0.370911	+	0.0965777i
$651$	1.00781	+	0.455561i	0.0394994	+	0.0178548i
$652$	−1.05612	+	24.8618i	−0.0413607	+	0.973663i
$653$	7.15897	−	33.2177i	0.280152	−	1.29991i	−0.590110	−	0.807323i	$-0.700916\pi$
$653$	7.15897	−	33.2177i	0.280152	−	1.29991i	0.870263	−	0.492588i	$-0.163949\pi$
$654$	10.2968	−	1.76556i	0.402635	−	0.0690388i
$655$	1.14541	+	5.31470i	0.0447547	+	0.207663i
$656$	−0.213899	−	0.532309i	−0.00835137	−	0.0207832i
$657$	0.593583	+	1.93825i	0.0231579	+	0.0756185i
$658$	1.00347	−	23.6224i	0.0391192	−	0.920897i
$659$	28.9538	+	23.3785i	1.12788	+	0.910698i	0.996741	−	0.0806659i	$-0.0257047\pi$
$659$	28.9538	+	23.3785i	1.12788	+	0.910698i	0.131137	+	0.991364i	$0.458137\pi$
$660$	−8.46752	−	8.11546i	−0.329598	−	0.315894i
$661$	14.6554	−	23.8019i	0.570030	−	0.925788i	−0.429709	−	0.902967i	$-0.641384\pi$
$661$	14.6554	−	23.8019i	0.570030	−	0.925788i	0.999740	−	0.0228209i	$-0.00726476\pi$
$662$	−3.01056	+	23.5099i	−0.117009	+	0.913738i
$663$	0.550473	−	12.9586i	0.0213786	−	0.503269i
$664$	−6.50912	−	10.5715i	−0.252603	−	0.410253i
$665$	−9.27629	+	7.49008i	−0.359719	+	0.290453i
$666$	−1.77711	+	4.42250i	−0.0688616	+	0.171369i
$667$	−15.5769	+	5.50366i	−0.603139	+	0.213103i
$668$	3.45965			0.133858
$669$	13.9783	+	5.25412i	0.540434	+	0.203136i
$670$	32.0559			1.23843
$671$	30.1883	−	10.6662i	1.16541	−	0.411764i
$672$	−4.40940	+	10.9732i	−0.170096	+	0.423301i
$673$	12.8338	−	10.3626i	0.494707	−	0.399448i	−0.348273	−	0.937393i	$-0.613232\pi$
$673$	12.8338	−	10.3626i	0.494707	−	0.399448i	0.842980	+	0.537945i	$0.180799\pi$
$674$	2.62918	+	4.27006i	0.101272	+	0.164476i
$675$	−0.0993088	+	2.33781i	−0.00382240	+	0.0899822i
$676$	1.07516	−	8.39607i	0.0413523	−	0.322926i
$677$	3.28399	−	5.33354i	0.126214	−	0.204985i	−0.782232	−	0.622988i	$-0.785919\pi$
$677$	3.28399	−	5.33354i	0.126214	−	0.204985i	0.908446	+	0.418003i	$0.137270\pi$
$678$	−7.90074	−	7.57224i	−0.303426	−	0.290810i
$679$	12.7195	+	10.2703i	0.488128	+	0.394136i
$680$	0.960407	−	22.6087i	0.0368299	−	0.867005i
$681$	5.08402	+	16.6011i	0.194820	+	0.636154i
$682$	0.664162	+	1.65283i	0.0254321	+	0.0632902i
$683$	−2.59354	−	12.0341i	−0.0992391	−	0.460471i	−0.999675	−	0.0254829i	$-0.991888\pi$
$683$	−2.59354	−	12.0341i	−0.0992391	−	0.460471i	0.900436	−	0.434988i	$-0.143247\pi$
$684$	−2.28711	+	0.392164i	−0.0874498	+	0.0149948i
$685$	6.72163	−	31.1885i	0.256820	−	1.19165i
$686$	−0.791286	+	18.6275i	−0.0302115	+	0.711201i
$687$	−1.85872	−	0.840194i	−0.0709146	−	0.0320554i
$688$	0.729376	−	0.189915i	0.0278072	−	0.00724043i
$689$	−34.1915	−	12.0806i	−1.30259	−	0.460235i
$690$	−6.15610	−	3.43901i	−0.234359	−	0.130921i
$691$	0.394411	+	1.28789i	0.0150041	+	0.0489935i	0.963355	−	0.268230i	$-0.0864387\pi$
$691$	0.394411	+	1.28789i	0.0150041	+	0.0489935i	−0.948351	+	0.317223i	$0.897249\pi$
$692$	12.4670	+	20.2477i	0.473924	+	0.769702i
$693$	4.88202	+	6.60092i	0.185453	+	0.250748i
$694$	−8.82365	+	17.5007i	−0.334941	+	0.664316i
$695$	−21.8686	−	24.8475i	−0.829522	−	0.942520i
$696$	15.5546	−	7.03110i	0.589594	−	0.266513i
$697$	2.16163	+	3.51071i	0.0818777	+	0.132978i
$698$	−3.21135	+	14.9007i	−0.121551	+	0.564000i
$699$	−16.5962	+	9.27117i	−0.627724	+	0.350668i
$700$	−5.79530	+	0.493253i	−0.219042	+	0.0186432i
$701$	−2.11693	−	16.5314i	−0.0799555	−	0.624384i	−0.981467	−	0.191629i	$-0.938623\pi$
$701$	−2.11693	−	16.5314i	−0.0799555	−	0.624384i	0.901512	−	0.432754i	$-0.142458\pi$
$702$	3.80538	+	1.72014i	0.143625	+	0.0649225i
$703$	−3.05905	−	9.98886i	−0.115374	−	0.376737i
$704$	−20.1099	+	9.09026i	−0.757921	+	0.342602i
$705$	31.7888	+	2.70563i	1.19724	+	0.101900i
$706$	1.14673	+	26.9950i	0.0431579	+	1.01597i
$707$	0.445562	−	0.301148i	0.0167571	−	0.0113258i
$708$	−11.8332			−0.444718
$709$	8.56963			0.321839			0.160920	−	0.986968i	$-0.448554\pi$
$709$	8.56963			0.321839			0.160920	+	0.986968i	$0.448554\pi$
$710$	−2.50584	+	1.69365i	−0.0940426	+	0.0635617i
$711$	−6.04093	−	1.03582i	−0.226553	−	0.0388463i
$712$	8.04793	+	15.9621i	0.301609	+	0.598206i
$713$	−0.852555	−	1.15273i	−0.0319284	−	0.0431701i
$714$	−1.21490	+	5.63717i	−0.0454666	+	0.210966i
$715$	−35.9954	−	29.0642i	−1.34615	−	1.08694i
$716$	−21.8122	−	5.67945i	−0.815159	−	0.212251i
$717$	−9.75927	−	6.59612i	−0.364467	−	0.246336i
$718$	−2.92023	−	0.760370i	−0.108982	−	0.0283768i
$719$	4.92136	−	38.4316i	0.183536	−	1.43326i	−0.594024	−	0.804448i	$-0.702461\pi$
$719$	4.92136	−	38.4316i	0.183536	−	1.43326i	0.777559	−	0.628810i	$-0.216458\pi$
$720$	0.986609	+	0.445975i	0.0367687	+	0.0166205i
$721$	−8.86866	−	4.95433i	−0.330286	−	0.184509i
$722$	9.09816	−	10.3375i	0.338599	−	0.384723i
$723$	−8.11668	+	7.77921i	−0.301863	+	0.289312i
$724$	6.93574	−	3.87454i	0.257765	−	0.143996i
$725$	10.6858	+	8.62820i	0.396862	+	0.320443i
$726$	−0.387502	+	3.02606i	−0.0143816	+	0.112308i
$727$	5.48181	+	42.8083i	0.203309	+	1.58767i	0.696375	+	0.717678i	$0.254795\pi$
$727$	5.48181	+	42.8083i	0.203309	+	1.58767i	−0.493065	+	0.869992i	$0.664124\pi$
$728$	−8.34971	+	27.2647i	−0.309461	+	1.01050i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	1.89359	+	4.71239i	0.0700850	+	0.174413i
$731$	−4.93573	+	2.23109i	−0.182555	+	0.0825199i
$732$	7.54182	−	6.08959i	0.278754	−	0.225078i
$733$	4.87498	+	9.66895i	0.180062	+	0.357131i	0.964920	−	0.262544i	$-0.0845616\pi$
$733$	4.87498	+	9.66895i	0.180062	+	0.357131i	−0.784858	+	0.619675i	$0.787264\pi$
$734$	−3.50066	+	4.73321i	−0.129212	+	0.174706i
$735$	−6.17086	−	0.525218i	−0.227616	−	0.0193730i
$736$	11.9277	−	9.63096i	0.439662	−	0.355002i
$737$	28.7702	+	38.8999i	1.05976	+	1.43289i
$738$	−1.30836	+	0.224340i	−0.0481612	+	0.00825807i
$739$	−14.1250	+	13.5377i	−0.519596	+	0.497992i	−0.905383	−	0.424596i	$-0.860416\pi$
$739$	−14.1250	+	13.5377i	−0.519596	+	0.497992i	0.385788	+	0.922588i	$0.373930\pi$
$740$	4.68108	−	15.2853i	0.172080	−	0.561900i
$741$	−8.85801	+	2.30645i	−0.325407	+	0.0847294i
$742$	14.0752	+	7.86290i	0.516718	+	0.288656i
$743$	5.34813	+	13.3093i	0.196204	+	0.488272i	0.993298	−	0.115583i	$-0.0368738\pi$
$743$	5.34813	+	13.3093i	0.196204	+	0.488272i	−0.797094	+	0.603855i	$0.793631\pi$
$744$	0.978737	+	1.11206i	0.0358822	+	0.0407701i
$745$	−27.5873	+	37.3005i	−1.01072	+	1.36658i
$746$	11.2388	+	1.92709i	0.411482	+	0.0705557i
$747$	−4.02504	+	1.42214i	−0.147268	+	0.0520333i
$748$	10.3014	−	6.96256i	0.376658	−	0.254576i
$749$	6.62098	−	2.33934i	0.241925	−	0.0854776i
$750$	−0.282847	−	6.65843i	−0.0103281	−	0.243132i
$751$	15.3618	−	20.7705i	0.560560	−	0.757927i	−0.428803	−	0.903398i	$-0.641064\pi$
$751$	15.3618	−	20.7705i	0.560560	−	0.757927i	0.989362	+	0.145471i	$0.0464698\pi$
$752$	2.11874	−	4.20227i	0.0772625	−	0.153241i
$753$	25.6522	−	4.39851i	0.934818	−	0.160291i
$754$	21.3993	−	11.9544i	0.779318	−	0.435353i
$755$	−34.0911	−	32.6736i	−1.24070	−	1.18912i
$756$	2.05940	+	1.39191i	0.0748997	+	0.0506233i
$757$	5.67395	+	3.83492i	0.206223	+	0.139383i	0.658733	−	0.752377i	$-0.271093\pi$
$757$	5.67395	+	3.83492i	0.206223	+	0.139383i	−0.452510	+	0.891760i	$0.649471\pi$
$758$	−11.7250	+	19.0426i	−0.425870	+	0.691657i
$759$	−1.35187	−	10.5569i	−0.0490697	−	0.383193i
$760$	−15.4545	+	4.02404i	−0.560594	+	0.145967i
$761$	19.6620	+	6.94702i	0.712746	+	0.251829i	0.664801	−	0.747021i	$-0.268516\pi$
$761$	19.6620	+	6.94702i	0.712746	+	0.251829i	0.0479454	+	0.998850i	$0.484733\pi$
$762$	2.74832	−	8.97421i	0.0995612	−	0.325101i
$763$	24.4399	−	2.08014i	0.884785	−	0.0753063i
$764$	4.34700	+	4.16626i	0.157269	+	0.150730i
$765$	−7.53011	−	1.96069i	−0.272252	−	0.0708889i
$766$	−4.83680	+	7.85547i	−0.174761	+	0.283830i
$767$	−46.5088	+	3.95848i	−1.67934	+	0.142933i
$768$	−12.0966	+	11.5937i	−0.436499	+	0.418351i
$769$	2.96276	+	13.7473i	0.106840	+	0.495739i	0.999028	+	0.0440751i	$0.0140341\pi$
$769$	2.96276	+	13.7473i	0.106840	+	0.495739i	−0.892188	+	0.451663i	$0.850831\pi$
$770$	13.5896	+	15.4408i	0.489734	+	0.556446i
$771$	−10.3951	−	0.884750i	−0.374369	−	0.0318635i
$772$	7.42197	−	18.4703i	0.267123	−	0.664760i
$773$	−2.22694	−	0.381847i	−0.0800975	−	0.0137341i	0.128813	−	0.991669i	$-0.458883\pi$
$773$	−2.22694	−	0.381847i	−0.0800975	−	0.0137341i	−0.208910	+	0.977935i	$0.566992\pi$
$774$	−0.0740174	−	1.74243i	−0.00266050	−	0.0626303i
$775$	−0.444425	+	1.10599i	−0.0159642	+	0.0397285i
$776$	9.85833	+	19.5528i	0.353893	+	0.701906i
$777$	−5.03797	+	9.99222i	−0.180736	+	0.358469i
$778$	−1.95344	−	9.06400i	−0.0700343	−	0.324960i
$779$	1.92228	−	2.18413i	0.0688727	−	0.0782546i
$780$	−13.2067	−	4.66623i	−0.472877	−	0.167078i
$781$	−4.30424	−	1.52079i	−0.154018	−	0.0544180i
$782$	4.93887	−	5.61164i	0.176614	−	0.200672i
$783$	−1.23660	−	5.73786i	−0.0441926	−	0.205054i
$784$	−0.411291	+	0.815747i	−0.0146890	+	0.0291338i
$785$	2.42846	+	4.81655i	0.0866753	+	0.171910i
$786$	0.691921	−	1.72191i	0.0246800	−	0.0614185i
$787$	−0.515241	−	12.1292i	−0.0183663	−	0.432358i	−0.984614	−	0.174743i	$-0.944090\pi$
$787$	−0.515241	−	12.1292i	−0.0183663	−	0.432358i	0.966248	−	0.257615i	$-0.0829365\pi$
$788$	11.7528	+	2.01521i	0.418675	+	0.0717890i
$789$	−6.93366	+	17.2551i	−0.246845	+	0.614297i
$790$	−15.3002	−	1.30224i	−0.544356	−	0.0463316i
$791$	−16.9754	−	19.2877i	−0.603574	−	0.685793i
$792$	2.31684	+	10.7502i	0.0823255	+	0.381992i
$793$	27.6051	−	26.4573i	0.980285	−	0.939527i
$794$	−31.1814	+	2.65393i	−1.10659	+	0.0941843i
$795$	−11.4063	+	18.5251i	−0.404541	+	0.657017i
$796$	21.5874	+	5.62093i	0.765147	+	0.199229i
$797$	−2.91433	−	2.79316i	−0.103231	−	0.0989388i	0.638553	−	0.769578i	$-0.279533\pi$
$797$	−2.91433	−	2.79316i	−0.103231	−	0.0989388i	−0.741784	+	0.670639i	$0.766020\pi$
$798$	4.05494	−	0.345126i	0.143543	−	0.0122173i
$799$	−9.90379	+	32.3393i	−0.350371	+	1.14408i
$800$	−12.0170	−	4.24588i	−0.424866	−	0.150115i
$801$	5.94852	−	1.54887i	0.210181	−	0.0547268i
$802$	−3.95939	−	30.9194i	−0.139811	−	1.09180i
$803$	−4.01898	+	6.52724i	−0.141827	+	0.230341i
$804$	12.1362	+	8.20266i	0.428012	+	0.289286i
$805$	−13.7169	−	9.27102i	−0.483458	−	0.326760i
$806$	1.53581	+	1.47196i	0.0540967	+	0.0518474i
$807$	23.0033	−	12.8504i	0.809756	−	0.452357i
$808$	0.709976	−	0.121738i	0.0249769	−	0.00428271i
$809$	8.21916	−	16.3017i	0.288970	−	0.573138i	−0.701207	−	0.712958i	$-0.747355\pi$
$809$	8.21916	−	16.3017i	0.288970	−	0.573138i	0.990177	+	0.139820i	$0.0446523\pi$
$810$	1.48976	−	2.01429i	0.0523449	−	0.0707750i
$811$	−1.26958	−	29.8868i	−0.0445809	−	1.04947i	−0.872498	−	0.488618i	$-0.837501\pi$
$811$	−1.26958	−	29.8868i	−0.0445809	−	1.04947i	0.827917	−	0.560851i	$-0.189526\pi$
$812$	13.7565	−	4.86047i	0.482757	−	0.170569i
$813$	−15.3858	+	10.3990i	−0.539605	+	0.364709i
$814$	−16.9934	+	6.00416i	−0.595619	+	0.210446i
$815$	58.0404	+	9.95203i	2.03307	+	0.348604i
$816$	−0.682530	+	0.922842i	−0.0238933	+	0.0323059i
$817$	2.52548	+	2.86950i	0.0883554	+	0.100391i
$818$	3.31074	+	8.23908i	0.115757	+	0.288073i
$819$	8.55985	+	4.78182i	0.299105	+	0.167090i
$820$	4.30867	−	1.12189i	0.150465	−	0.0391781i
$821$	−1.79345	+	5.85621i	−0.0625917	+	0.204383i	−0.981986	−	0.188954i	$-0.939490\pi$
$821$	−1.79345	+	5.85621i	−0.0625917	+	0.204383i	0.919394	+	0.393337i	$0.128680\pi$
$822$	−7.86214	+	7.53525i	−0.274224	+	0.262822i
$823$	−15.5008	+	2.65787i	−0.540322	+	0.0926476i	−0.432689	−	0.901543i	$-0.642435\pi$
$823$	−15.5008	+	2.65787i	−0.540322	+	0.0926476i	−0.107633	+	0.994191i	$0.534327\pi$
$824$	−8.09116	−	10.9400i	−0.281869	−	0.381112i
$825$	−6.88419	+	5.55860i	−0.239677	+	0.193526i
$826$	20.6779	+	1.75995i	0.719477	+	0.0612365i
$827$	8.01808	−	10.8412i	0.278816	−	0.376984i	−0.642181	−	0.766553i	$-0.721970\pi$
$827$	8.01808	−	10.8412i	0.278816	−	0.376984i	0.920997	+	0.389568i	$0.127376\pi$
$828$	−1.45068	−	2.87726i	−0.0504147	−	0.0999915i
$829$	−8.76710	+	7.07894i	−0.304494	+	0.245862i	−0.768322	−	0.640064i	$-0.778908\pi$
$829$	−8.76710	+	7.07894i	−0.304494	+	0.245862i	0.463828	+	0.885925i	$0.346476\pi$
$830$	−9.74564	+	4.40531i	−0.338276	+	0.152910i
$831$	−4.17671	−	10.3941i	−0.144888	−	0.360569i
$832$	−17.4127	+	19.7846i	−0.603676	+	0.685909i
$833$	1.92253	−	6.27772i	0.0666117	−	0.217510i
$834$	1.43507	+	11.2067i	0.0496925	+	0.388056i
$835$	1.03991	−	8.12081i	0.0359876	−	0.281032i
$836$	−6.82703	−	5.51244i	−0.236118	−	0.190652i
$837$	0.444711	−	0.248430i	0.0153715	−	0.00858701i
$838$	14.3508	−	13.7541i	0.495739	−	0.475127i
$839$	−11.7171	+	13.3132i	−0.404519	+	0.459622i	−0.916889	−	0.399142i	$-0.869308\pi$
$839$	−11.7171	+	13.3132i	−0.404519	+	0.459622i	0.512370	+	0.858765i	$0.328767\pi$
$840$	14.9343	+	8.34281i	0.515283	+	0.287854i
$841$	−4.96820	−	2.24577i	−0.171317	−	0.0774403i
$842$	3.49597	−	27.3006i	0.120479	−	0.940840i
$843$	−22.1997	−	5.78035i	−0.764599	−	0.199086i
$844$	14.8748	+	10.0536i	0.512013	+	0.346061i
$845$	−19.3849	−	5.04743i	−0.666860	−	0.173637i
$846$	−8.47263	−	6.84117i	−0.291295	−	0.235204i
$847$	−1.50906	+	7.00205i	−0.0518518	+	0.240593i
$848$	1.90826	+	2.58013i	0.0655298	+	0.0886021i
$849$	−3.35544	−	6.65513i	−0.115159	−	0.228403i
$850$	−6.12535	−	1.05030i	−0.210098	−	0.0360249i
$851$	12.0189	−	8.12334i	0.412002	−	0.278465i
$852$	−1.38208			−0.0473494
$853$	32.9325			1.12759			0.563793	−	0.825916i	$-0.309341\pi$
$853$	32.9325			1.12759			0.563793	+	0.825916i	$0.309341\pi$
$854$	−14.0847	+	9.51958i	−0.481968	+	0.325753i
$855$	0.233059	+	5.48639i	0.00797045	+	0.187631i
$856$	9.37183	+	0.797660i	0.320322	+	0.0272635i
$857$	38.4943	−	17.4005i	1.31494	−	0.594390i	0.372272	−	0.928124i	$-0.378579\pi$
$857$	38.4943	−	17.4005i	1.31494	−	0.594390i	0.942667	+	0.333733i	$0.108309\pi$
$858$	4.62412	+	15.0993i	0.157865	+	0.515483i
$859$	−19.2195	−	8.68774i	−0.655759	−	0.296422i	0.0564329	−	0.998406i	$-0.482027\pi$
$859$	−19.2195	−	8.68774i	−0.655759	−	0.296422i	−0.712192	+	0.701984i	$0.752298\pi$
$860$	0.742986	+	5.80208i	0.0253356	+	0.197849i
$861$	−3.10545	+	0.264313i	−0.105834	+	0.00900776i
$862$	−25.0101	+	13.9715i	−0.851848	+	0.475871i
$863$	3.38417	−	15.7026i	0.115198	−	0.534522i	−0.882712	−	0.469914i	$-0.844285\pi$
$863$	3.38417	−	15.7026i	0.115198	−	0.534522i	0.997911	−	0.0646085i	$-0.0205799\pi$
$864$	2.85580	+	4.63811i	0.0971561	+	0.157792i
$865$	51.2746	−	23.1776i	1.74339	−	0.788062i
$866$	19.0093	+	21.5988i	0.645963	+	0.733956i
$867$	−3.93974	+	7.81400i	−0.133800	+	0.265377i
$868$	0.752920	+	1.01802i	0.0255558	+	0.0345537i
$869$	−12.1517	−	19.7355i	−0.412217	−	0.669482i
$870$	−4.30607	−	14.0608i	−0.145990	−	0.476706i
$871$	50.4440	+	28.1797i	1.70923	+	0.954833i
$872$	30.9776	+	10.9451i	1.04903	+	0.370647i
$873$	7.28665	−	1.89730i	0.246616	−	0.0642138i
$874$	−4.80728	−	2.17303i	−0.162609	−	0.0735037i
$875$	0.664088	−	15.6331i	0.0224503	−	0.528497i
$876$	−0.488928	+	2.26863i	−0.0165194	+	0.0766501i
$877$	55.3924	−	9.49798i	1.87047	−	0.320724i	0.881892	−	0.471451i	$-0.156270\pi$
$877$	55.3924	−	9.49798i	1.87047	−	0.320724i	0.988575	+	0.150727i	$0.0481615\pi$
$878$	−4.91011	−	22.7830i	−0.165708	−	0.768889i
$879$	−2.52777	−	6.29059i	−0.0852595	−	0.212176i
$880$	1.19888	+	3.91476i	0.0404143	+	0.131966i
$881$	−1.73172	+	40.7660i	−0.0583431	+	1.37344i	0.696509	+	0.717548i	$0.254736\pi$
$881$	−1.73172	+	40.7660i	−0.0583431	+	1.37344i	−0.754852	+	0.655895i	$0.772291\pi$
$882$	1.64471	+	1.32801i	0.0553804	+	0.0447165i
$883$	17.6942	+	16.9586i	0.595459	+	0.570701i	0.928090	−	0.372356i	$-0.121450\pi$
$883$	17.6942	+	16.9586i	0.595459	+	0.570701i	−0.332631	+	0.943057i	$0.607936\pi$
$884$	7.78540	−	12.6443i	0.261851	−	0.425273i
$885$	−3.55684	+	27.7759i	−0.119562	+	0.933677i
$886$	−0.581980	+	13.7003i	−0.0195520	+	0.460269i
$887$	12.3196	+	20.0083i	0.413651	+	0.671812i	0.989302	−	0.145884i	$-0.0466026\pi$
$887$	12.3196	+	20.0083i	0.413651	+	0.671812i	−0.575651	+	0.817696i	$0.695251\pi$
$888$	−11.6619	+	9.41636i	−0.391349	+	0.315992i
$889$	8.21634	−	20.4472i	0.275567	−	0.685776i
$890$	14.5203	−	5.13036i	0.486723	−	0.171970i
$891$	3.78141			0.126682
$892$	11.0373	+	13.0559i	0.369557	+	0.437144i
$893$	23.8687			0.798735
$894$	14.9311	−	5.27550i	0.499371	−	0.176439i
$895$	−19.8877	+	49.4924i	−0.664772	+	1.65435i
$896$	−9.28518	+	7.49726i	−0.310196	+	0.250466i
$897$	−6.66424	−	10.8234i	−0.222512	−	0.361383i
$898$	0.115186	−	2.71157i	0.00384382	−	0.0904864i
$899$	0.379778	−	2.96574i	0.0126663	−	0.0989130i
$900$	−1.40453	+	2.28111i	−0.0468178	+	0.0760370i
$901$	−16.6505	−	15.9582i	−0.554707	−	0.531644i
$902$	−3.90545	−	3.15343i	−0.130037	−	0.104998i
$903$	0.173783	−	4.09100i	0.00578315	−	0.136140i
$904$	−10.0777	−	32.9071i	−0.335179	−	1.09447i
$905$	−7.00991	−	17.4448i	−0.233017	−	0.579886i
$906$	3.39569	+	15.7561i	0.112814	+	0.523461i
$907$	24.4545	−	4.19314i	0.811997	−	0.139231i	0.252002	−	0.967727i	$-0.418911\pi$
$907$	24.4545	−	4.19314i	0.811997	−	0.139231i	0.559995	+	0.828496i	$0.310803\pi$
$908$	−4.18765	+	19.4308i	−0.138972	+	0.644833i
$909$	0.0105124	−	0.247470i	0.000348674	−	0.00820806i
$910$	22.3841	+	10.1183i	0.742027	+	0.335417i
$911$	−35.4328	+	9.22599i	−1.17394	+	0.305671i	−0.787307	−	0.616562i	$-0.788525\pi$
$911$	−35.4328	+	9.22599i	−1.17394	+	0.305671i	−0.386636	+	0.922233i	$0.626363\pi$
$912$	0.763766	+	0.269856i	0.0252908	+	0.00893581i
$913$	−14.0925	−	7.87257i	−0.466395	−	0.260544i
$914$	−9.82863	−	32.0938i	−0.325102	−	1.06157i
$915$	−12.0271	−	19.5333i	−0.397604	−	0.645750i
$916$	−1.38862	−	1.87753i	−0.0458812	−	0.0620354i
$917$	1.96154	−	3.89049i	0.0647759	−	0.128475i
$918$	1.75473	+	1.99376i	0.0579148	+	0.0658040i
$919$	9.32753	−	4.21631i	0.307687	−	0.139083i	−0.252145	−	0.967689i	$-0.581136\pi$
$919$	9.32753	−	4.21631i	0.307687	−	0.139083i	0.559832	+	0.828606i	$0.310866\pi$
$920$	−11.6271	−	18.8835i	−0.383333	−	0.622572i
$921$	−4.70584	+	21.8352i	−0.155063	+	0.719494i
$922$	−4.25859	+	2.37899i	−0.140249	+	0.0783479i
$923$	−5.43211	+	0.462341i	−0.178800	+	0.0152181i
$924$	1.19388	+	9.32319i	0.0392758	+	0.306711i
$925$	−10.9895	−	4.96756i	−0.361332	−	0.163332i
$926$	−11.0762	−	36.1675i	−0.363985	−	1.18854i
$927$	−4.26351	+	1.92723i	−0.140032	+	0.0632984i
$928$	31.8553	+	2.71129i	1.04570	+	0.0890024i
$929$	0.227436	+	5.35402i	0.00746193	+	0.175660i	0.998962	+	0.0455530i	$0.0145050\pi$
$929$	0.227436	+	5.35402i	0.00746193	+	0.175660i	−0.991500	+	0.130107i	$0.958468\pi$
$930$	1.05736	−	0.714650i	0.0346721	−	0.0234343i
$931$	−4.63341			−0.151854
$932$	−21.7637			−0.712894
$933$	−2.31709	+	1.56608i	−0.0758581	+	0.0512711i
$934$	33.8613	+	5.80610i	1.10797	+	0.189981i
$935$	−13.2467	−	26.2733i	−0.433214	−	0.859229i
$936$	7.80942	+	10.5590i	0.255259	+	0.345133i
$937$	−5.39046	+	25.0118i	−0.176099	+	0.817101i	0.800039	+	0.599948i	$0.204812\pi$
$937$	−5.39046	+	25.0118i	−0.176099	+	0.817101i	−0.976138	+	0.217153i	$0.930323\pi$
$938$	−19.9875	−	16.1388i	−0.652616	−	0.526951i
$939$	−8.01496	−	2.08693i	−0.261558	−	0.0681045i
$940$	30.2612	+	20.4530i	0.987010	+	0.667102i
$941$	22.7925	+	5.93472i	0.743016	+	0.193466i	0.604179	−	0.796849i	$-0.293501\pi$
$941$	22.7925	+	5.93472i	0.743016	+	0.193466i	0.138837	+	0.990315i	$0.455664\pi$
$942$	0.233864	−	1.82627i	0.00761969	−	0.0595033i
$943$	3.68162	+	1.66420i	0.119890	+	0.0541938i
$944$	3.60619	+	2.01454i	0.117371	+	0.0655676i
$945$	3.88624	−	4.41563i	0.126420	−	0.143640i
$946$	4.76114	−	4.56318i	0.154798	−	0.148362i
$947$	−30.8662	+	17.2429i	−1.00302	+	0.560319i	−0.900704	−	0.434434i	$-0.856949\pi$
$947$	−30.8662	+	17.2429i	−1.00302	+	0.560319i	−0.102313	+	0.994752i	$0.532624\pi$
$948$	−5.45936	−	4.40813i	−0.177312	−	0.143169i
$949$	−1.16276	+	9.08015i	−0.0377447	+	0.294754i
$950$	0.557083	+	4.35034i	0.0180742	+	0.141144i
$951$	−7.34854	+	23.9955i	−0.238293	+	0.778108i
$952$	−11.9814	+	13.6135i	−0.388319	+	0.441216i
$953$	−13.9827	−	34.7972i	−0.452943	−	1.12719i	−0.963586	−	0.267400i	$-0.913836\pi$
$953$	−13.9827	−	34.7972i	−0.452943	−	1.12719i	0.510642	−	0.859793i	$-0.329408\pi$
$954$	6.76651	−	3.05866i	0.219074	−	0.0990277i
$955$	11.0861	−	8.95137i	0.358737	−	0.289660i
$956$	−6.07121	−	12.0415i	−0.196357	−	0.389451i
$957$	13.1981	−	17.8450i	0.426634	−	0.576847i
$958$	−15.2751	−	1.30010i	−0.493515	−	0.0420043i
$959$	−19.8932	+	16.0626i	−0.642383	+	0.518688i
$960$	9.40209	+	12.7125i	0.303451	+	0.410293i
$961$	−30.2983	+	5.19517i	−0.977366	+	0.167586i
$962$	−15.5393	+	14.8932i	−0.501007	+	0.480176i
$963$	0.947054	−	3.09246i	0.0305184	−	0.0996530i
$964$	−12.4557	+	3.24322i	−0.401172	+	0.104457i
$965$	−41.1243	−	22.9734i	−1.32384	−	0.739539i
$966$	2.10706	+	5.24363i	0.0677937	+	0.168711i
$967$	−4.73952	−	5.38514i	−0.152413	−	0.173174i	0.669456	−	0.742852i	$-0.266527\pi$
$967$	−4.73952	−	5.38514i	−0.152413	−	0.173174i	−0.821868	+	0.569678i	$0.807068\pi$
$968$	−5.70503	+	7.71371i	−0.183367	+	0.247928i
$969$	−5.73774	−	0.983834i	−0.184323	−	0.0316053i
$970$	17.7867	−	6.28445i	0.571097	−	0.201781i
$971$	−3.55908	+	2.40552i	−0.114216	+	0.0771967i	−0.615751	−	0.787941i	$-0.711147\pi$
$971$	−3.55908	+	2.40552i	−0.114216	+	0.0771967i	0.501535	+	0.865137i	$0.332769\pi$
$972$	1.07945	−	0.381393i	0.0346233	−	0.0122332i
$973$	1.12583	+	26.5028i	0.0360923	+	0.849642i
$974$	17.4688	−	23.6194i	0.559738	−	0.756816i
$975$	−4.75726	+	9.43547i	−0.152354	+	0.302177i
$976$	−3.33511	+	0.571862i	−0.106754	+	0.0183049i
$977$	17.7859	−	9.93580i	0.569021	−	0.317874i	−0.176559	−	0.984290i	$-0.556497\pi$
$977$	17.7859	−	9.93580i	0.569021	−	0.317874i	0.745580	+	0.666416i	$0.232172\pi$
$978$	−14.5114	−	13.9081i	−0.464025	−	0.444732i
$979$	19.2577	+	13.0159i	0.615479	+	0.415991i
$980$	−5.87432	−	3.97035i	−0.187648	−	0.126828i
$981$	5.92320	−	9.61989i	0.189113	−	0.307139i
$982$	−1.09576	−	8.55692i	−0.0349670	−	0.273062i
$983$	23.7890	−	6.19418i	0.758752	−	0.197564i	0.147568	−	0.989052i	$-0.452856\pi$
$983$	23.7890	−	6.19418i	0.758752	−	0.197564i	0.611184	+	0.791488i	$0.290693\pi$
$984$	−3.93616	−	1.39073i	−0.125480	−	0.0443350i
$985$	8.26297	−	26.9814i	0.263280	−	0.859700i
$986$	15.5333	−	1.32208i	0.494682	−	0.0421036i
$987$	−18.4588	−	17.6913i	−0.587550	−	0.563121i
$988$	−10.1410	−	2.64052i	−0.322629	−	0.0840062i
$989$	−2.78308	+	4.52001i	−0.0884969	+	0.143728i
$990$	9.43961	−	0.803429i	0.300011	−	0.0255347i
$991$	26.7876	−	25.6739i	0.850937	−	0.815557i	−0.133545	−	0.991043i	$-0.542636\pi$
$991$	26.7876	−	25.6739i	0.850937	−	0.815557i	0.984482	+	0.175485i	$0.0561495\pi$
$992$	0.584547	+	2.71231i	0.0185594	+	0.0861159i
$993$	16.9335	+	19.2402i	0.537370	+	0.610570i
$994$	2.41513	+	0.205558i	0.0766032	+	0.00651989i
$995$	19.6828	−	48.9825i	0.623986	−	1.55285i
$996$	−4.81691	−	0.825943i	−0.152630	−	0.0261710i
$997$	−0.183816	−	4.32718i	−0.00582152	−	0.137043i	−0.999657	−	0.0261803i	$-0.991666\pi$
$997$	−0.183816	−	4.32718i	−0.00582152	−	0.137043i	0.993836	−	0.110863i	$-0.0353614\pi$
$998$	11.5756	−	28.8069i	0.366418	−	0.911866i
$999$	2.32038	+	4.60220i	0.0734135	+	0.145607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.a.4.7	✓	648
223.56	even	37	inner	669.2.i.a.502.7	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.a.4.7	✓	648	1.1	even	1	trivial
669.2.i.a.502.7	yes	648	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+(-0.871922 + 0.308070i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-0.890730 + 0.719214i) q^{4} +(1.42047 + 2.30699i) q^{5} +(0.0392473 - 0.923913i) q^{6} +(0.275779 - 2.15360i) q^{7} +(1.52478 - 2.47640i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-1.94925 - 1.57391i) q^{10} +(0.160487 - 3.77800i) q^{11} +(-0.335236 - 1.09466i) q^{12} +(-1.68380 - 4.19029i) q^{13} +(0.423001 + 1.96273i) q^{14} +(-2.67026 + 0.457862i) q^{15} +(-0.0841965 + 0.390673i) q^{16} +(0.121896 - 2.86952i) q^{17} +(0.842655 + 0.380904i) q^{18} +(-1.96150 + 0.510735i) q^{19} +(-2.92447 - 1.03328i) q^{20} +(1.89548 + 1.05888i) q^{21} +(1.02395 + 3.34356i) q^{22} +(-1.47571 - 2.39671i) q^{23} +(1.72930 + 2.33817i) q^{24} +(-1.05344 + 2.08937i) q^{25} +(2.75904 + 3.13488i) q^{26} +(0.911228 - 0.411901i) q^{27} +(1.30325 + 2.11662i) q^{28} +(1.23660 - 5.73786i) q^{29} +(2.18720 - 1.22185i) q^{30} +(0.507562 - 0.0431999i) q^{31} +(0.691840 + 5.40268i) q^{32} +(3.44573 + 1.55757i) q^{33} +(0.777728 + 2.53955i) q^{34} +(5.36006 - 2.42290i) q^{35} +(1.14072 + 0.0970896i) q^{36} +(0.218745 + 5.14942i) q^{37} +(1.55293 - 1.04960i) q^{38} +4.51594 q^{39} +7.87893 q^{40} +(-1.18930 + 0.803830i) q^{41} +(-1.97891 - 0.339319i) q^{42} +(-0.849049 - 1.68399i) q^{43} +(2.57424 + 3.48060i) q^{44} +(0.570778 - 2.64842i) q^{45} +(2.02506 + 1.63512i) q^{46} +(-11.3960 - 2.96728i) q^{47} +(-0.331108 - 0.223790i) q^{48} +(2.21220 + 0.576011i) q^{49} +(0.274845 - 2.14630i) q^{50} +(2.61714 + 1.18302i) q^{51} +(4.51352 + 2.52141i) q^{52} +(5.30521 - 6.02789i) q^{53} +(-0.667626 + 0.639868i) q^{54} +(8.94376 - 4.99628i) q^{55} +(-4.91268 - 3.96671i) q^{56} +(0.257453 - 2.01048i) q^{57} +(0.689439 + 5.38393i) q^{58} +(3.02663 - 9.88299i) q^{59} +(2.04918 - 2.32832i) q^{60} +(3.15698 + 7.85645i) q^{61} +(-0.429246 + 0.194032i) q^{62} +(-1.68926 + 1.36398i) q^{63} +(-2.62748 - 5.21129i) q^{64} +(7.27516 - 9.83667i) q^{65} +(-3.48424 - 0.296553i) q^{66} +(-9.95496 + 8.03807i) q^{67} +(1.95522 + 2.64363i) q^{68} +(2.77411 - 0.475670i) q^{69} +(-3.92713 + 3.76385i) q^{70} +(0.353503 - 1.15431i) q^{71} +(-2.81434 + 0.732798i) q^{72} +(-1.76969 - 0.988610i) q^{73} +(-1.77711 - 4.42250i) q^{74} +(-1.54592 - 1.75651i) q^{75} +(1.37984 - 1.86566i) q^{76} +(-8.09204 - 1.38752i) q^{77} +(-3.93755 + 1.39122i) q^{78} +(5.07801 - 3.43214i) q^{79} +(-1.02088 + 0.360698i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.789346 - 1.06727i) q^{82} +(1.92187 - 3.81180i) q^{83} +(-2.44991 + 0.420080i) q^{84} +(6.79309 - 3.79485i) q^{85} +(1.25909 + 1.20674i) q^{86} +(4.86302 + 3.28683i) q^{87} +(-9.11114 - 6.15806i) q^{88} +(-3.22284 + 5.23423i) q^{89} +(0.318224 + 2.48506i) q^{90} +(-9.48856 + 2.47063i) q^{91} +(3.03821 + 1.07347i) q^{92} +(-0.149163 + 0.487069i) q^{93} +(10.8505 - 0.923517i) q^{94} +(-3.96450 - 3.79967i) q^{95} +(-5.27105 - 1.37247i) q^{96} +(-3.94783 + 6.41168i) q^{97} +(-2.10631 + 0.179274i) q^{98} +(-2.73001 + 2.61650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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