LMFDB - Embedded newform 531.2.m.a.4.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(4,531)] 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("531.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(174)) chi = DirichletCharacter(H, H._module([58, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.m (of order $87$, degree $56$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$3248$
Relative dimension:	$58$ over $\Q(\zeta_{87})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{87}]$

Embedding invariants

Embedding label			4.15
Character	$\chi$	$=$	531.4
Dual form			531.2.m.a.133.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.700893 - 1.58966i) q^{2} +(-1.19780 + 1.25111i) q^{3} +(-0.686795 + 0.751772i) q^{4} +(-2.23191 + 0.936314i) q^{5} +(2.82836 + 1.02720i) q^{6} +(2.79042 - 0.405878i) q^{7} +(-1.61631 - 0.544599i) q^{8} +(-0.130538 - 2.99716i) q^{9} +(3.05275 + 2.89172i) q^{10} +(-2.16085 - 1.52275i) q^{11} +(-0.117904 - 1.75973i) q^{12} +(-1.65804 - 1.35759i) q^{13} +(-2.60099 - 4.15133i) q^{14} +(1.50196 - 3.91388i) q^{15} +(0.450735 + 4.97931i) q^{16} +(1.84760 + 4.63714i) q^{17} +(-4.67296 + 2.30820i) q^{18} +(3.38093 + 4.98651i) q^{19} +(0.828971 - 2.32095i) q^{20} +(-2.83457 + 3.97727i) q^{21} +(-0.906129 + 4.50229i) q^{22} +(2.39921 + 1.56423i) q^{23} +(2.61737 - 1.36986i) q^{24} +(0.601283 - 0.612239i) q^{25} +(-0.995990 + 3.58723i) q^{26} +(3.90613 + 3.42669i) q^{27} +(-1.61132 + 2.37651i) q^{28} +(5.72183 + 7.81592i) q^{29} +(-7.27444 + 0.355610i) q^{30} +(-1.95582 - 4.03465i) q^{31} +(4.61498 - 2.55450i) q^{32} +(4.49339 - 0.879494i) q^{33} +(6.07648 - 6.18719i) q^{34} +(-5.84795 + 3.51859i) q^{35} +(2.34283 + 1.96030i) q^{36} +(6.34219 - 2.13693i) q^{37} +(5.55715 - 8.86953i) q^{38} +(3.68449 - 0.448260i) q^{39} +(4.11738 - 0.297878i) q^{40} +(-0.491532 - 0.249331i) q^{41} +(8.30923 + 1.71835i) q^{42} +(0.725349 + 8.01299i) q^{43} +(2.62882 - 0.578647i) q^{44} +(3.09763 + 6.56718i) q^{45} +(0.804999 - 4.91028i) q^{46} +(-2.64269 - 1.10864i) q^{47} +(-6.76954 - 5.40031i) q^{48} +(0.911757 - 0.270970i) q^{49} +(-1.39468 - 0.526720i) q^{50} +(-8.01462 - 3.24282i) q^{51} +(2.15933 - 0.314083i) q^{52} +(-6.68363 + 6.33107i) q^{53} +(2.70948 - 8.61114i) q^{54} +(6.24860 + 1.37542i) q^{55} +(-4.73123 - 0.863634i) q^{56} +(-10.2883 - 1.74294i) q^{57} +(8.41423 - 14.5739i) q^{58} +(6.33585 - 4.34247i) q^{59} +(1.91081 + 3.81717i) q^{60} +(1.91197 + 4.33643i) q^{61} +(-5.04289 + 5.93695i) q^{62} +(-1.58074 - 8.31034i) q^{63} +(0.665020 + 0.505535i) q^{64} +(4.97173 + 1.47758i) q^{65} +(-4.54748 - 6.52652i) q^{66} +(-9.29504 + 8.18872i) q^{67} +(-4.75500 - 1.79578i) q^{68} +(-4.83080 + 1.12803i) q^{69} +(9.69214 + 6.83006i) q^{70} +(6.37233 - 4.84412i) q^{71} +(-1.42126 + 4.91543i) q^{72} +(0.147383 - 0.277994i) q^{73} +(-7.84219 - 8.58414i) q^{74} +(0.0457576 + 1.48561i) q^{75} +(-6.07073 - 0.883011i) q^{76} +(-6.64772 - 3.37208i) q^{77} +(-3.29501 - 5.54289i) q^{78} +(-0.0282886 + 0.0792022i) q^{79} +(-5.66820 - 10.6914i) q^{80} +(-8.96592 + 0.782486i) q^{81} +(-0.0518394 + 0.956122i) q^{82} +(9.49758 + 5.25712i) q^{83} +(-1.04323 - 4.86252i) q^{84} +(-8.46551 - 8.61975i) q^{85} +(12.2295 - 6.76930i) q^{86} +(-16.6322 - 2.20330i) q^{87} +(2.66331 + 3.63804i) q^{88} +(14.8383 - 1.61376i) q^{89} +(8.26844 - 9.52706i) q^{90} +(-5.17763 - 3.11528i) q^{91} +(-2.82371 + 0.729355i) q^{92} +(7.39048 + 2.38578i) q^{93} +(0.0898883 + 4.97800i) q^{94} +(-12.2149 - 7.96384i) q^{95} +(-2.33189 + 8.83362i) q^{96} +(2.16811 - 3.46043i) q^{97} +(-1.06979 - 1.25946i) q^{98} +(-4.28186 + 6.67518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) $ 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{29}\right)$

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 $

$2$	−0.700893	−	1.58966i	−0.495606	−	1.12406i	−0.969859	−	0.243668i	$-0.921649\pi$
$2$	−0.700893	−	1.58966i	−0.495606	−	1.12406i	0.474252	−	0.880389i	$-0.342718\pi$
$3$	−1.19780	+	1.25111i	−0.691552	+	0.722327i
$3$	−1.19780	+	1.25111i	−0.691552	+	0.722327i
$4$	−0.686795	+	0.751772i	−0.343397	+	0.375886i
$5$	−2.23191	+	0.936314i	−0.998142	+	0.418732i	−0.824369	−	0.566053i	$-0.808470\pi$
$5$	−2.23191	+	0.936314i	−0.998142	+	0.418732i	−0.173774	+	0.984786i	$0.555596\pi$
$6$	2.82836	+	1.02720i	1.15467	+	0.419353i
$7$	2.79042	−	0.405878i	1.05468	−	0.153407i	0.405540	−	0.914077i	$-0.367083\pi$
$7$	2.79042	−	0.405878i	1.05468	−	0.153407i	0.649139	+	0.760670i	$0.275129\pi$
$8$	−1.61631	−	0.544599i	−0.571452	−	0.192545i
$9$	−0.130538	−	2.99716i	−0.0435127	−	0.999053i
$10$	3.05275	+	2.89172i	0.965365	+	0.914442i
$11$	−2.16085	−	1.52275i	−0.651520	−	0.459127i	0.202559	−	0.979270i	$-0.435074\pi$
$11$	−2.16085	−	1.52275i	−0.651520	−	0.459127i	−0.854079	+	0.520143i	$0.825879\pi$
$12$	−0.117904	−	1.75973i	−0.0340358	−	0.507990i
$13$	−1.65804	−	1.35759i	−0.459857	−	0.376527i	0.374973	−	0.927036i	$-0.377652\pi$
$13$	−1.65804	−	1.35759i	−0.459857	−	0.376527i	−0.834829	+	0.550509i	$0.814434\pi$
$14$	−2.60099	−	4.15133i	−0.695144	−	1.10949i
$15$	1.50196	−	3.91388i	0.387805	−	1.01056i
$16$	0.450735	+	4.97931i	0.112684	+	1.24483i
$17$	1.84760	+	4.63714i	0.448110	+	1.12467i	0.963498	+	0.267714i	$0.0862683\pi$
$17$	1.84760	+	4.63714i	0.448110	+	1.12467i	−0.515389	+	0.856957i	$0.672352\pi$
$18$	−4.67296	+	2.30820i	−1.10143	+	0.544048i
$19$	3.38093	+	4.98651i	0.775640	+	1.14398i	0.986063	+	0.166372i	$0.0532054\pi$
$19$	3.38093	+	4.98651i	0.775640	+	1.14398i	−0.210423	+	0.977610i	$0.567484\pi$
$20$	0.828971	−	2.32095i	0.185364	−	0.518980i
$21$	−2.83457	+	3.97727i	−0.618555	+	0.867912i
$22$	−0.906129	+	4.50229i	−0.193187	+	0.959891i
$23$	2.39921	+	1.56423i	0.500270	+	0.326165i	0.771371	−	0.636386i	$-0.219572\pi$
$23$	2.39921	+	1.56423i	0.500270	+	0.326165i	−0.271101	+	0.962551i	$0.587388\pi$
$24$	2.61737	−	1.36986i	0.534269	−	0.279621i
$25$	0.601283	−	0.612239i	0.120257	−	0.122448i
$26$	−0.995990	+	3.58723i	−0.195330	+	0.703514i
$27$	3.90613	+	3.42669i	0.751734	+	0.659466i
$28$	−1.61132	+	2.37651i	−0.304510	+	0.449119i
$29$	5.72183	+	7.81592i	1.06252	+	1.45138i	0.884026	+	0.467438i	$0.154823\pi$
$29$	5.72183	+	7.81592i	1.06252	+	1.45138i	0.178491	+	0.983941i	$0.442878\pi$
$30$	−7.27444	+	0.355610i	−1.32813	+	0.0649251i
$31$	−1.95582	−	4.03465i	−0.351276	−	0.724645i	0.648040	−	0.761606i	$-0.275589\pi$
$31$	−1.95582	−	4.03465i	−0.351276	−	0.724645i	−0.999317	+	0.0369605i	$0.988232\pi$
$32$	4.61498	−	2.55450i	0.815821	−	0.451575i
$33$	4.49339	−	0.879494i	0.782200	−	0.153100i
$34$	6.07648	−	6.18719i	1.04211	−	1.06109i
$35$	−5.84795	+	3.51859i	−0.988483	+	0.594751i
$36$	2.34283	+	1.96030i	0.390472	+	0.326716i
$37$	6.34219	−	2.13693i	1.04265	−	0.351310i	0.254681	−	0.967025i	$-0.418029\pi$
$37$	6.34219	−	2.13693i	1.04265	−	0.351310i	0.787969	+	0.615715i	$0.211133\pi$
$38$	5.55715	−	8.86953i	0.901489	−	1.43883i
$39$	3.68449	−	0.448260i	0.589990	−	0.0717791i
$40$	4.11738	−	0.297878i	0.651016	−	0.0470986i
$41$	−0.491532	−	0.249331i	−0.0767644	−	0.0389390i	0.413580	−	0.910468i	$-0.364278\pi$
$41$	−0.491532	−	0.249331i	−0.0767644	−	0.0389390i	−0.490344	+	0.871529i	$0.663129\pi$
$42$	8.30923	+	1.71835i	1.28214	+	0.265148i
$43$	0.725349	+	8.01299i	0.110615	+	1.22197i	0.841800	+	0.539790i	$0.181496\pi$
$43$	0.725349	+	8.01299i	0.110615	+	1.22197i	−0.731185	+	0.682179i	$0.761032\pi$
$44$	2.62882	−	0.578647i	0.396310	−	0.0872344i
$45$	3.09763	+	6.56718i	0.461768	+	0.978977i
$46$	0.804999	−	4.91028i	0.118691	−	0.723981i
$47$	−2.64269	−	1.10864i	−0.385476	−	0.161712i	0.185568	−	0.982631i	$-0.440588\pi$
$47$	−2.64269	−	1.10864i	−0.385476	−	0.161712i	−0.571043	+	0.820920i	$0.693461\pi$
$48$	−6.76954	−	5.40031i	−0.977099	−	0.779467i
$49$	0.911757	−	0.270970i	0.130251	−	0.0387101i
$50$	−1.39468	−	0.526720i	−0.197238	−	0.0744894i
$51$	−8.01462	−	3.24282i	−1.12227	−	0.454086i
$52$	2.15933	−	0.314083i	0.299445	−	0.0435555i
$53$	−6.68363	+	6.33107i	−0.918068	+	0.869640i	−0.991821	−	0.127637i	$-0.959261\pi$
$53$	−6.68363	+	6.33107i	−0.918068	+	0.869640i	0.0737533	+	0.997277i	$0.476502\pi$
$54$	2.70948	−	8.61114i	0.368713	−	1.17183i
$55$	6.24860	+	1.37542i	0.842561	+	0.185462i
$56$	−4.73123	−	0.863634i	−0.632237	−	0.115408i
$57$	−10.2883	−	1.74294i	−1.36272	−	0.230858i
$58$	8.41423	−	14.5739i	1.10484	−	1.91364i
$59$	6.33585	−	4.34247i	0.824857	−	0.565341i
$59$	6.33585	−	4.34247i	0.824857	−	0.565341i
$60$	1.91081	+	3.81717i	0.246684	+	0.492794i
$61$	1.91197	+	4.33643i	0.244803	+	0.555223i	0.994280	−	0.106807i	$-0.0340628\pi$
$61$	1.91197	+	4.33643i	0.244803	+	0.555223i	−0.749477	+	0.662030i	$0.769695\pi$
$62$	−5.04289	+	5.93695i	−0.640448	+	0.753993i
$63$	−1.58074	−	8.31034i	−0.199154	−	1.04700i
$64$	0.665020	+	0.505535i	0.0831275	+	0.0631919i
$65$	4.97173	+	1.47758i	0.616667	+	0.183271i
$66$	−4.54748	−	6.52652i	−0.559757	−	0.803359i
$67$	−9.29504	+	8.18872i	−1.13557	+	1.00041i	−0.135616	+	0.990761i	$0.543301\pi$
$67$	−9.29504	+	8.18872i	−1.13557	+	1.00041i	−0.999953	+	0.00964952i	$0.996928\pi$
$68$	−4.75500	−	1.79578i	−0.576628	−	0.217771i
$69$	−4.83080	+	1.12803i	−0.581560	+	0.135799i
$70$	9.69214	+	6.83006i	1.15843	+	0.816349i
$71$	6.37233	−	4.84412i	0.756256	−	0.574891i	−0.154423	−	0.988005i	$-0.549352\pi$
$71$	6.37233	−	4.84412i	0.756256	−	0.574891i	0.910679	+	0.413114i	$0.135559\pi$
$72$	−1.42126	+	4.91543i	−0.167497	+	0.579289i
$73$	0.147383	−	0.277994i	0.0172499	−	0.0325367i	−0.874737	−	0.484597i	$-0.838966\pi$
$73$	0.147383	−	0.277994i	0.0172499	−	0.0325367i	0.891987	+	0.452061i	$0.149311\pi$
$74$	−7.84219	−	8.58414i	−0.911636	−	0.997886i
$75$	0.0457576	+	1.48561i	0.00528363	+	0.171544i
$76$	−6.07073	−	0.883011i	−0.696360	−	0.101288i
$77$	−6.64772	−	3.37208i	−0.757578	−	0.384284i
$78$	−3.29501	−	5.54289i	−0.373087	−	0.627608i
$79$	−0.0282886	+	0.0792022i	−0.00318272	+	0.00891094i	−0.943315	−	0.331899i	$-0.892311\pi$
$79$	−0.0282886	+	0.0792022i	−0.00318272	+	0.00891094i	0.940132	+	0.340810i	$0.110701\pi$
$80$	−5.66820	−	10.6914i	−0.633724	−	1.19533i
$81$	−8.96592	+	0.782486i	−0.996213	+	0.0869429i
$82$	−0.0518394	+	0.956122i	−0.00572470	+	0.105586i
$83$	9.49758	+	5.25712i	1.04249	+	0.577044i	0.910201	−	0.414166i	$-0.135927\pi$
$83$	9.49758	+	5.25712i	1.04249	+	0.577044i	0.132293	+	0.991211i	$0.457766\pi$
$84$	−1.04323	−	4.86252i	−0.113826	−	0.530545i
$85$	−8.46551	−	8.61975i	−0.918213	−	0.934943i
$86$	12.2295	−	6.76930i	1.31874	−	0.729953i
$87$	−16.6322	−	2.20330i	−1.78316	−	0.236219i
$88$	2.66331	+	3.63804i	0.283910	+	0.387816i
$89$	14.8383	−	1.61376i	1.57286	−	0.171058i	0.720289	−	0.693675i	$-0.244009\pi$
$89$	14.8383	−	1.61376i	1.57286	−	0.171058i	0.852568	+	0.522616i	$0.175044\pi$
$90$	8.26844	−	9.52706i	0.871570	−	1.00424i
$91$	−5.17763	−	3.11528i	−0.542763	−	0.326570i
$92$	−2.82371	+	0.729355i	−0.294392	+	0.0760405i
$93$	7.39048	+	2.38578i	0.766357	+	0.247393i
$94$	0.0898883	+	4.97800i	0.00927127	+	0.513442i
$95$	−12.2149	−	7.96384i	−1.25322	−	0.817072i
$96$	−2.33189	+	8.83362i	−0.237997	+	0.901577i
$97$	2.16811	−	3.46043i	0.220139	−	0.351354i	−0.718931	−	0.695082i	$-0.755368\pi$
$97$	2.16811	−	3.46043i	0.220139	−	0.351354i	0.939069	+	0.343728i	$0.111690\pi$
$98$	−1.06979	−	1.25946i	−0.108066	−	0.127225i
$99$	−4.28186	+	6.67518i	−0.430343	+	0.670881i
$100$	0.0473061	+	0.872510i	0.00473061	+	0.0872510i
$101$	1.36704	−	1.73247i	0.136025	−	0.172387i	−0.712279	−	0.701897i	$-0.752337\pi$
$101$	1.36704	−	1.73247i	0.136025	−	0.172387i	0.848304	+	0.529510i	$0.177624\pi$
$102$	0.462419	+	15.0134i	0.0457863	+	1.48654i
$103$	0.783959	−	2.47342i	0.0772458	−	0.243713i	−0.906820	−	0.421518i	$-0.861497\pi$
$103$	0.783959	−	2.47342i	0.0772458	−	0.243713i	0.984066	+	0.177805i	$0.0568997\pi$
$104$	1.94056	+	3.09725i	0.190288	+	0.303710i
$105$	2.60255	−	11.5310i	0.253983	−	1.12531i
$106$	14.7487	+	6.18727i	1.43252	+	0.600961i
$107$	−14.8922	+	6.88988i	−1.43969	+	0.666070i	−0.975567	−	0.219702i	$-0.929492\pi$
$107$	−14.8922	+	6.88988i	−1.43969	+	0.666070i	−0.464120	+	0.885772i	$0.653629\pi$
$108$	−5.25879	+	0.583087i	−0.506028	+	0.0561076i
$109$	0.153116	+	0.933964i	0.0146658	+	0.0894575i	0.993145	−	0.116887i	$-0.0372915\pi$
$109$	0.153116	+	0.933964i	0.0146658	+	0.0894575i	−0.978479	+	0.206344i	$0.933843\pi$
$110$	−2.19316	−	10.8971i	−0.209109	−	1.03900i
$111$	−4.92316	+	10.4944i	−0.467286	+	0.996083i
$112$	3.27873	+	13.7114i	0.309811	+	1.29561i
$113$	−9.92880	+	4.16525i	−0.934023	+	0.391834i	−0.800582	−	0.599223i	$-0.795476\pi$
$113$	−9.92880	+	4.16525i	−0.934023	+	0.391834i	−0.133441	+	0.991057i	$0.542603\pi$
$114$	4.44036	+	17.5765i	0.415878	+	1.64619i
$115$	−6.81944	−	1.24482i	−0.635916	−	0.116080i
$116$	−9.80551	−	1.06641i	−0.910419	−	0.0990140i
$117$	−3.85247	+	5.14662i	−0.356161	+	0.475805i
$118$	−11.3438	−	7.02822i	−1.04428	−	0.647000i
$119$	7.03770	+	12.1896i	0.645145	+	1.11742i
$120$	−4.55914	+	5.50809i	−0.416190	+	0.502817i
$121$	−1.34946	−	3.77820i	−0.122678	−	0.343473i
$122$	5.55335	−	6.07875i	0.502776	−	0.550344i
$123$	0.900699	−	0.316310i	0.0812133	−	0.0285207i
$124$	4.37639	+	1.30064i	0.393012	+	0.116801i
$125$	3.71057	−	9.31282i	0.331883	−	0.832964i
$126$	−12.1027	+	8.33749i	−1.07819	+	0.742763i
$127$	2.60165	+	15.8694i	0.230859	+	1.40818i	0.806866	+	0.590734i	$0.201162\pi$
$127$	2.60165	+	15.8694i	0.230859	+	1.40818i	−0.576007	+	0.817444i	$0.695390\pi$
$128$	2.79101	−	11.6718i	0.246693	−	1.03165i
$129$	−10.8939	−	8.69049i	−0.959157	−	0.765155i
$130$	−1.13581	−	8.93896i	−0.0996173	−	0.783998i
$131$	−3.25247	−	2.66310i	−0.284170	−	0.232676i	0.480662	−	0.876906i	$-0.340396\pi$
$131$	−3.25247	−	2.66310i	−0.284170	−	0.232676i	−0.764832	+	0.644230i	$0.777178\pi$
$132$	−2.42486	+	3.98204i	−0.211057	+	0.346592i
$133$	11.4581	+	12.5422i	0.993546	+	1.08755i
$134$	19.5321	+	9.03650i	1.68731	+	0.780635i
$135$	−11.9266	−	3.99071i	−1.02648	−	0.343466i
$136$	−0.460925	−	8.50126i	−0.0395240	−	0.728977i
$137$	2.03624	−	4.20055i	0.173968	−	0.358878i	−0.794790	−	0.606884i	$-0.792419\pi$
$137$	2.03624	−	4.20055i	0.173968	−	0.358878i	0.968758	+	0.248007i	$0.0797755\pi$
$138$	5.17905	+	6.88869i	0.440870	+	0.586404i
$139$	−0.342344	−	0.0123675i	−0.0290372	−	0.00104900i	0.0215800	−	0.999767i	$-0.493130\pi$
$139$	−0.342344	−	0.0123675i	−0.0290372	−	0.00104900i	−0.0506172	+	0.998718i	$0.516119\pi$
$140$	1.37116	−	6.81287i	0.115884	−	0.575793i
$141$	4.55244	−	1.97836i	0.383385	−	0.166608i
$142$	−12.1668	−	6.73460i	−1.02102	−	0.565155i
$143$	1.51549	+	5.45832i	0.126732	+	0.456448i
$144$	14.8649	−	2.00091i	1.23874	−	0.166743i
$145$	−20.0888	−	12.0870i	−1.66828	−	1.00377i
$146$	−0.545214	−	0.0394442i	−0.0451222	−	0.00326443i
$147$	−0.753092	+	1.46528i	−0.0621140	+	0.120854i
$148$	−2.74930	+	6.23552i	−0.225991	+	0.512557i
$149$	−7.36182	−	15.1866i	−0.603104	−	1.24414i	−0.951747	−	0.306883i	$-0.900714\pi$
$149$	−7.36182	−	15.1866i	−0.603104	−	1.24414i	0.348644	−	0.937255i	$-0.386642\pi$
$150$	2.32954	−	1.11399i	0.190206	−	0.0909572i
$151$	−18.0596	+	4.66472i	−1.46967	+	0.379610i	−0.897678	−	0.440652i	$-0.854747\pi$
$151$	−18.0596	+	4.66472i	−1.46967	+	0.379610i	−0.571988	+	0.820262i	$0.693828\pi$
$152$	−2.74900	−	9.90100i	−0.222973	−	0.803077i
$153$	13.6570	−	6.14288i	1.10411	−	0.496623i
$154$	−0.701101	+	12.9311i	−0.0564963	+	1.04201i
$155$	8.14293	+	7.17374i	0.654056	+	0.576208i
$156$	−2.19350	+	3.07776i	−0.175620	+	0.246418i
$157$	16.3256	−	2.98006i	1.30292	−	0.237835i	0.516908	−	0.856041i	$-0.327083\pi$
$157$	16.3256	−	2.98006i	1.30292	−	0.237835i	0.786016	+	0.618206i	$0.212140\pi$
$158$	0.145731	−	0.0105431i	0.0115938	−	0.000838767i
$159$	0.0848217	−	15.9453i	0.00672680	−	1.26455i
$160$	−7.90843	+	10.0225i	−0.625216	+	0.792347i
$161$	7.32969	+	3.39107i	0.577660	+	0.267254i
$162$	7.52804	+	13.7043i	0.591458	+	1.07671i
$163$	−10.5788	+	19.9537i	−0.828596	+	1.56290i	−0.00206999	+	0.999998i	$0.500659\pi$
$163$	−10.5788	+	19.9537i	−0.828596	+	1.56290i	−0.826526	+	0.562899i	$0.809686\pi$
$164$	0.525022	−	0.198281i	0.0409973	−	0.0154831i
$165$	−9.20539	+	6.17018i	−0.716638	+	0.480348i
$166$	1.70023	−	18.7826i	0.131963	−	1.45781i
$167$	−4.73100	+	1.40603i	−0.366096	+	0.108802i	−0.462686	−	0.886522i	$-0.653114\pi$
$167$	−4.73100	+	1.40603i	−0.366096	+	0.108802i	0.0965903	+	0.995324i	$0.469206\pi$
$168$	6.74757	−	4.88481i	0.520587	−	0.376871i
$169$	−1.65890	−	8.24259i	−0.127608	−	0.634045i
$170$	−7.76902	+	19.4988i	−0.595857	+	1.49549i
$171$	14.5040	−	10.7841i	1.10915	−	0.824683i
$172$	−6.52211	−	4.95798i	−0.497306	−	0.378042i
$173$	1.65809	+	5.23134i	0.126063	+	0.397732i	0.995321	−	0.0966268i	$-0.0308053\pi$
$173$	1.65809	+	5.23134i	0.126063	+	0.397732i	−0.869258	+	0.494358i	$0.835403\pi$
$174$	8.15489	+	27.9837i	0.618220	+	2.12144i
$175$	1.42934	−	1.95245i	0.108048	−	0.147591i
$176$	6.60828	−	11.4459i	0.498118	−	0.862766i
$177$	−2.15621	+	13.1282i	−0.162070	+	0.986779i
$178$	−12.9654	−	22.4567i	−0.971797	−	1.68320i
$179$	−3.02946	−	0.329474i	−0.226433	−	0.0246261i	−0.00580082	−	0.999983i	$-0.501846\pi$
$179$	−3.02946	−	0.329474i	−0.226433	−	0.0246261i	−0.220632	+	0.975357i	$0.570812\pi$
$180$	−7.06446	−	2.18159i	−0.526554	−	0.162606i
$181$	−19.0666	−	4.19688i	−1.41721	−	0.311951i	−0.560673	−	0.828037i	$-0.689458\pi$
$181$	−19.0666	−	4.19688i	−1.41721	−	0.311951i	−0.856537	+	0.516086i	$0.827389\pi$
$182$	−1.32325	+	10.4141i	−0.0980860	+	0.771947i
$183$	−7.71550	−	2.80211i	−0.570346	−	0.207138i
$184$	−3.02599	−	3.83489i	−0.223079	−	0.282712i
$185$	−12.1544	+	10.7077i	−0.893608	+	0.787248i
$186$	−1.38737	−	13.4205i	−0.101727	−	0.984038i
$187$	3.06882	−	12.8336i	0.224414	−	0.938485i
$188$	2.64843	−	1.22529i	0.193156	−	0.0893637i
$189$	12.2905	+	7.97648i	0.894005	+	0.580204i
$190$	−4.09842	+	24.9993i	−0.297331	+	1.81364i
$191$	−10.0955	+	0.364709i	−0.730484	+	0.0263894i	−0.398847	−	0.917018i	$-0.630590\pi$
$191$	−10.0955	+	0.364709i	−0.730484	+	0.0263894i	−0.331637	+	0.943407i	$0.607601\pi$
$192$	−1.42904	+	0.226480i	−0.103132	+	0.0163448i
$193$	−16.3161	+	11.4980i	−1.17446	+	0.827644i	−0.987945	−	0.154808i	$-0.950524\pi$
$193$	−16.3161	+	11.4980i	−1.17446	+	0.827644i	−0.186516	+	0.982452i	$0.559720\pi$
$194$	−7.02051	−	1.02116i	−0.504043	−	0.0733151i
$195$	−7.80375	+	4.45032i	−0.558838	+	0.318694i
$196$	−0.422482	+	0.871535i	−0.0301773	+	0.0622525i
$197$	11.7030	+	13.7779i	0.833807	+	0.981633i	0.999990	−	0.00446143i	$-0.00142012\pi$
$197$	11.7030	+	13.7779i	0.833807	+	0.981633i	−0.166183	+	0.986095i	$0.553144\pi$
$198$	13.6124	+	2.12809i	0.967388	+	0.151237i
$199$	9.05246	−	3.05013i	0.641712	−	0.216218i	0.0204130	−	0.999792i	$-0.493502\pi$
$199$	9.05246	−	3.05013i	0.641712	−	0.216218i	0.621299	+	0.783574i	$0.286605\pi$
$200$	−1.30529	+	0.662110i	−0.0922976	+	0.0468183i
$201$	0.888661	−	21.4376i	0.0626813	−	1.51209i
$202$	−3.71218	−	0.958843i	−0.261188	−	0.0674639i
$203$	19.1386	+	19.4873i	1.34327	+	1.36774i
$204$	7.94226	−	3.79802i	0.556069	−	0.265914i
$205$	1.33051	+	0.0962575i	0.0929268	+	0.00672292i
$206$	−4.48135	+	0.487377i	−0.312231	+	0.0339571i
$207$	4.37506	−	7.39501i	0.304088	−	0.513989i
$208$	6.01251	−	8.86779i	0.416893	−	0.614871i
$209$	0.287530	−	15.9234i	0.0198889	−	1.10144i
$210$	−20.1544	+	3.94483i	−1.39079	+	0.272219i
$211$	4.28920	+	1.10789i	0.295281	+	0.0762700i	0.394804	−	0.918765i	$-0.370812\pi$
$211$	4.28920	+	1.10789i	0.295281	+	0.0762700i	−0.0995237	+	0.995035i	$0.531732\pi$
$212$	−0.169244	−	9.37272i	−0.0116237	−	0.643721i
$213$	−1.57228	+	13.7748i	−0.107731	+	0.943831i
$214$	21.3904	+	18.8445i	1.46222	+	1.28818i
$215$	−9.12159	−	17.2051i	−0.622087	−	1.17338i
$216$	−4.44735	−	7.66587i	−0.302604	−	0.521596i
$217$	−7.09514	−	10.4645i	−0.481650	−	0.710380i
$218$	1.37736	−	0.898010i	0.0932868	−	0.0608209i
$219$	0.171264	+	0.517373i	0.0115730	+	0.0349608i
$220$	−5.32551	+	3.75289i	−0.359046	+	0.253020i
$221$	3.23192	−	10.1968i	0.217403	−	0.685913i
$222$	20.1331	+	0.470689i	1.35124	+	0.0315905i
$223$	13.9470	−	5.26724i	0.933957	−	0.352720i	0.160838	−	0.986981i	$-0.448580\pi$
$223$	13.9470	−	5.26724i	0.933957	−	0.352720i	0.773119	+	0.634261i	$0.218695\pi$
$224$	11.8409	−	9.00123i	0.791155	−	0.601420i
$225$	−1.91347	−	1.72222i	−0.127564	−	0.114815i
$226$	13.5803	+	12.8640i	0.903351	+	0.855700i
$227$	−18.5592	+	15.1962i	−1.23182	+	1.00860i	−0.232468	+	0.972604i	$0.574680\pi$
$227$	−18.5592	+	15.1962i	−1.23182	+	1.00860i	−0.999352	+	0.0360006i	$0.988538\pi$
$228$	8.37627	−	6.53745i	0.554732	−	0.432953i
$229$	5.95506	+	7.54695i	0.393522	+	0.498717i	0.941143	−	0.338010i	$-0.109754\pi$
$229$	5.95506	+	7.54695i	0.393522	+	0.498717i	−0.547621	+	0.836727i	$0.684466\pi$
$230$	2.80087	+	11.7131i	0.184684	+	0.772336i
$231$	12.1815	−	4.27793i	0.801483	−	0.281467i
$232$	−4.99172	−	15.7491i	−0.327723	−	1.03398i
$233$	12.8772	−	15.1602i	0.843612	−	0.993177i	−0.156373	−	0.987698i	$-0.549980\pi$
$233$	12.8772	−	15.1602i	0.843612	−	0.993177i	0.999985	−	0.00547904i	$-0.00174404\pi$
$234$	10.8815	+	2.51687i	0.711347	+	0.164533i
$235$	6.93629			0.452473
$236$	−1.08688	+	7.74550i	−0.0707499	+	0.504189i
$237$	−0.0652063	−	0.130261i	−0.00423560	−	0.00846134i
$238$	14.4447	−	19.7312i	0.936309	−	1.27898i
$239$	6.40224	+	17.9250i	0.414127	+	1.15947i	0.949203	+	0.314665i	$0.101892\pi$
$239$	6.40224	+	17.9250i	0.414127	+	1.15947i	−0.535076	+	0.844804i	$0.679717\pi$
$240$	20.1654	+	5.71461i	1.30167	+	0.368877i
$241$	2.14898	−	16.9127i	0.138428	−	1.08944i	−0.759876	−	0.650068i	$-0.774740\pi$
$241$	2.14898	−	16.9127i	0.138428	−	1.08944i	0.898304	−	0.439375i	$-0.144800\pi$
$242$	−5.06022	+	4.79329i	−0.325283	+	0.308125i
$243$	9.76043	−	12.1546i	0.626132	−	0.779717i
$244$	−4.57314	−	1.54087i	−0.292765	−	0.0986441i
$245$	−1.78125	+	1.45847i	−0.113800	+	0.0931785i
$246$	−1.13412	−	1.21010i	−0.0723087	−	0.0771533i
$247$	1.16390	−	12.8577i	0.0740574	−	0.818118i
$248$	0.963952	+	7.58640i	0.0612110	+	0.481737i
$249$	−17.9534	+	5.58549i	−1.13775	+	0.353966i
$250$	−17.4049	+	0.628768i	−1.10078	+	0.0397668i
$251$	17.9812	−	3.95797i	1.13497	−	0.249825i	0.392528	−	0.919740i	$-0.371600\pi$
$251$	17.9812	−	3.95797i	1.13497	−	0.249825i	0.742438	+	0.669915i	$0.233669\pi$
$252$	7.33313	+	4.51915i	0.461944	+	0.284679i
$253$	−2.80239	−	7.03347i	−0.176185	−	0.442190i
$254$	23.4034	−	15.2585i	1.46846	−	0.957401i
$255$	20.9242	−	0.266498i	1.31033	−	0.0166888i
$256$	−18.8668	+	3.44393i	−1.17918	+	0.215246i
$257$	24.9453	+	0.901171i	1.55604	+	0.0562135i	0.800679	−	0.599093i	$-0.204472\pi$
$257$	24.9453	+	0.901171i	1.55604	+	0.0562135i	0.755363	+	0.655307i	$0.227461\pi$
$258$	−6.17940	+	23.4087i	−0.384713	+	1.45736i
$259$	16.8300	−	8.53709i	1.04577	−	0.530469i
$260$	−4.52535	+	2.72282i	−0.280651	+	0.168862i
$261$	22.6786	−	18.1695i	1.40377	−	1.12466i
$262$	−1.95378	+	7.03686i	−0.120705	+	0.434739i
$263$	−0.108739	+	6.02195i	−0.00670512	+	0.371329i	0.979095	+	0.203405i	$0.0652007\pi$
$263$	−0.108739	+	6.02195i	−0.00670512	+	0.371329i	−0.985800	+	0.167924i	$0.946294\pi$
$264$	−7.74170	−	1.02556i	−0.476469	−	0.0631189i
$265$	8.98942	−	20.3884i	0.552216	−	1.25245i
$266$	11.9068	−	27.0052i	0.730055	−	1.65580i
$267$	−15.7544	+	20.4973i	−0.964151	+	1.25441i
$268$	0.227731	−	12.6117i	0.0139109	−	0.770383i
$269$	1.38531	−	4.98943i	0.0844638	−	0.304211i	−0.909237	−	0.416280i	$-0.863334\pi$
$269$	1.38531	−	4.98943i	0.0844638	−	0.304211i	0.993701	+	0.112068i	$0.0357476\pi$
$270$	2.01541	+	21.7562i	0.122654	+	1.32404i
$271$	16.6889	−	10.0414i	1.01378	−	0.609970i	0.0912206	−	0.995831i	$-0.470923\pi$
$271$	16.6889	−	10.0414i	1.01378	−	0.609970i	0.922557	+	0.385861i	$0.126096\pi$
$272$	−22.2569	+	11.2899i	−1.34953	+	0.684551i
$273$	10.0993	−	2.74628i	0.611239	−	0.166213i
$274$	−8.10462	−	0.292787i	−0.489618	−	0.0176879i
$275$	−2.23157	+	0.407349i	−0.134569	+	0.0245641i
$276$	2.46975	−	4.40639i	0.148661	−	0.265233i
$277$	11.3569	−	7.40447i	0.682373	−	0.444892i	−0.157613	−	0.987501i	$-0.550380\pi$
$277$	11.3569	−	7.40447i	0.682373	−	0.444892i	0.839985	+	0.542609i	$0.182564\pi$
$278$	0.220286	+	0.552877i	0.0132119	+	0.0331594i
$279$	−11.8372	+	6.38859i	−0.708674	+	0.382475i
$280$	11.3683	−	2.50236i	0.679387	−	0.149544i
$281$	3.56025	−	0.128617i	0.212386	−	0.00767267i	0.0702952	−	0.997526i	$-0.477606\pi$
$281$	3.56025	−	0.128617i	0.212386	−	0.00767267i	0.142091	+	0.989854i	$0.454617\pi$
$282$	−6.33568	−	5.85020i	−0.377284	−	0.348375i
$283$	0.00764838	+	0.0601935i	0.000454649	+	0.00357813i	0.992250	−	0.124260i	$-0.0396558\pi$
$283$	0.00764838	+	0.0601935i	0.000454649	+	0.00357813i	−0.991795	+	0.127839i	$0.959196\pi$
$284$	−0.734806	+	8.11745i	−0.0436027	+	0.481682i
$285$	24.5946	−	5.74304i	1.45686	−	0.340188i
$286$	7.61465	−	6.23481i	0.450264	−	0.368672i
$287$	−1.47278	−	0.496237i	−0.0869353	−	0.0292919i
$288$	−8.25866	−	13.4984i	−0.486646	−	0.795399i
$289$	−5.74746	+	5.44429i	−0.338086	+	0.320252i
$290$	−5.13411	+	40.4060i	−0.301485	+	2.37272i
$291$	1.73240	+	6.85746i	0.101555	+	0.401991i
$292$	0.107766	+	0.301723i	0.00630654	+	0.0176570i
$293$	9.56850	−	13.0704i	0.558998	−	0.763581i	−0.431350	−	0.902185i	$-0.641963\pi$
$293$	9.56850	−	13.0704i	0.558998	−	0.763581i	0.990348	+	0.138604i	$0.0442615\pi$
$294$	2.85712	+	0.170156i	0.166631	+	0.00992371i
$295$	−10.0752	+	15.6244i	−0.586599	+	0.909685i
$296$	−11.4147			−0.663468
$297$	−3.22254	−	13.3526i	−0.186991	−	0.774797i
$298$	−18.9817	+	22.3470i	−1.09958	+	1.29453i
$299$	−1.85440	−	5.85069i	−0.107243	−	0.338354i
$300$	−1.14827	−	0.985910i	−0.0662953	−	0.0569216i
$301$	5.27632	+	22.0652i	0.304122	+	1.27182i
$302$	20.0731	+	25.4390i	1.15508	+	1.46385i
$303$	0.530064	+	3.78547i	0.0304514	+	0.217469i
$304$	−23.3054	+	19.0823i	−1.33666	+	1.09445i
$305$	−8.32761	−	7.88833i	−0.476838	−	0.451685i
$306$	−19.3372	−	17.4045i	−1.10543	−	0.994949i
$307$	−4.91006	+	3.73253i	−0.280232	+	0.213027i	−0.735843	−	0.677152i	$-0.763214\pi$
$307$	−4.91006	+	3.73253i	−0.280232	+	0.213027i	0.455611	+	0.890179i	$0.349421\pi$
$308$	7.10065	−	2.68165i	0.404597	−	0.152801i
$309$	2.15548	+	3.94348i	0.122621	+	0.224337i
$310$	5.69645	−	17.9725i	0.323536	−	1.02077i
$311$	−23.9922	+	16.9073i	−1.36047	+	0.958726i	−0.360812	+	0.932639i	$0.617500\pi$
$311$	−23.9922	+	16.9073i	−1.36047	+	0.958726i	−0.999660	+	0.0260876i	$0.991695\pi$
$312$	−6.19940	−	1.28204i	−0.350972	−	0.0725812i
$313$	2.28937	−	1.49262i	0.129403	−	0.0843677i	−0.479819	−	0.877367i	$-0.659298\pi$
$313$	2.28937	−	1.49262i	0.129403	−	0.0843677i	0.609222	+	0.793000i	$0.291482\pi$
$314$	−16.1798	−	23.8634i	−0.913077	−	1.34669i
$315$	11.3092	+	17.0679i	0.637199	+	0.961668i
$316$	−0.0401136	−	0.0756622i	−0.00225656	−	0.00425633i
$317$	−11.5743	−	10.1967i	−0.650076	−	0.572702i	0.270763	−	0.962646i	$-0.412724\pi$
$317$	−11.5743	−	10.1967i	−0.650076	−	0.572702i	−0.920838	+	0.389944i	$0.872494\pi$
$318$	−25.4070	+	11.0411i	−1.42476	+	0.619156i
$319$	−0.462296	−	25.6019i	−0.0258836	−	1.43343i
$320$	−1.95761	−	0.505643i	−0.109434	−	0.0282663i
$321$	9.21798	−	26.8845i	0.514498	−	1.50055i
$322$	0.253313	−	14.0285i	0.0141166	−	0.781776i
$323$	−16.8765	+	24.8909i	−0.939032	+	1.38497i
$324$	5.56949	−	7.27774i	0.309416	−	0.404319i
$325$	−1.82812	+	0.198820i	−0.101406	+	0.0110285i
$326$	39.1342	+	2.83122i	2.16744	+	0.156807i
$327$	−1.35189	−	0.927140i	−0.0747597	−	0.0512710i
$328$	0.658684	+	0.670685i	0.0363697	+	0.0370324i
$329$	−7.82418	−	2.02096i	−0.431361	−	0.111419i
$330$	16.2605	+	10.3088i	0.895109	+	0.567478i
$331$	10.8211	−	5.48902i	0.594780	−	0.301704i	−0.129099	−	0.991632i	$-0.541208\pi$
$331$	10.8211	−	5.48902i	0.594780	−	0.301704i	0.723878	+	0.689928i	$0.242358\pi$
$332$	−10.4750	+	3.52945i	−0.574893	+	0.193704i
$333$	−7.23263	−	18.7296i	−0.396345	−	1.02638i
$334$	5.55104	+	6.53519i	0.303739	+	0.357590i
$335$	13.0785	−	26.9796i	0.714556	−	1.47405i
$336$	−21.0817	−	12.3215i	−1.15010	−	0.672194i
$337$	4.39299	+	0.638977i	0.239301	+	0.0348073i	0.262534	−	0.964923i	$-0.415442\pi$
$337$	4.39299	+	0.638977i	0.239301	+	0.0348073i	−0.0232327	+	0.999730i	$0.507396\pi$
$338$	−11.9402	+	8.41426i	−0.649460	+	0.457675i
$339$	6.68157	−	17.4111i	0.362893	−	0.945643i
$340$	12.2942	−	0.444138i	0.666744	−	0.0240868i
$341$	−1.91754	+	11.6965i	−0.103841	+	0.633401i
$342$	−27.3088	−	15.4979i	−1.47669	−	0.838028i
$343$	−15.4800	+	7.16179i	−0.835839	+	0.386700i
$344$	3.19147	−	13.3465i	0.172073	−	0.719595i
$345$	9.72575	−	7.04081i	0.523617	−	0.379065i
$346$	7.15389	−	6.30241i	0.384596	−	0.338820i
$347$	11.0682	+	14.0270i	0.594174	+	0.753007i	0.985948	−	0.167055i	$-0.0534256\pi$
$347$	11.0682	+	14.0270i	0.594174	+	0.753007i	−0.391773	+	0.920062i	$0.628138\pi$
$348$	13.0793	−	10.9904i	0.701122	−	0.589147i
$349$	−2.80791	+	22.0986i	−0.150304	+	1.18291i	0.721273	+	0.692651i	$0.243557\pi$
$349$	−2.80791	+	22.0986i	−0.150304	+	1.18291i	−0.871577	+	0.490258i	$0.836903\pi$
$350$	−4.10554	−	0.903697i	−0.219450	−	0.0483046i
$351$	−1.82447	−	10.9845i	−0.0973831	−	0.586308i
$352$	−13.8621	−	1.50760i	−0.738854	−	0.0803552i
$353$	13.1531	+	22.7818i	0.700067	+	1.21255i	0.968443	+	0.249237i	$0.0801797\pi$
$353$	13.1531	+	22.7818i	0.700067	+	1.21255i	−0.268376	+	0.963314i	$0.586487\pi$
$354$	22.3807	−	5.77387i	1.18952	−	0.306878i
$355$	−9.68687	+	16.7782i	−0.514126	+	0.890492i
$356$	−8.97768	+	12.2633i	−0.475816	+	0.649956i
$357$	−23.6803	−	5.79588i	−1.25330	−	0.306750i
$358$	1.59958	+	5.04673i	0.0845405	+	0.266728i
$359$	13.0950	+	9.95456i	0.691128	+	0.525382i	0.890751	−	0.454491i	$-0.150179\pi$
$359$	13.0950	+	9.95456i	0.691128	+	0.525382i	−0.199623	+	0.979873i	$0.563972\pi$
$360$	−1.43026	−	12.3016i	−0.0753814	−	0.648350i
$361$	−6.40189	+	16.0675i	−0.336942	+	0.845660i
$362$	6.69207	+	33.2509i	0.351727	+	1.74763i
$363$	6.34332	+	2.83723i	0.332938	+	0.148916i
$364$	5.89795	−	1.75285i	0.309137	−	0.0918741i
$365$	−0.0686566	+	0.758455i	−0.00359365	+	0.0396993i
$366$	0.953356	+	14.2290i	0.0498327	+	0.743760i
$367$	−32.3902	+	12.2325i	−1.69075	+	0.638533i	−0.996684	−	0.0813749i	$-0.974069\pi$
$367$	−32.3902	+	12.2325i	−1.69075	+	0.638533i	−0.694069	+	0.719908i	$0.744184\pi$
$368$	−6.70738	+	12.6515i	−0.349646	+	0.659503i
$369$	−0.683122	+	1.50575i	−0.0355619	+	0.0783861i
$370$	25.5405	+	11.8163i	1.32779	+	0.614301i
$371$	−16.0805	+	20.3791i	−0.834858	+	1.05803i
$372$	−6.86930	+	3.91742i	−0.356157	+	0.203109i
$373$	−15.9954	+	1.15721i	−0.828210	+	0.0599180i	−0.479750	−	0.877405i	$-0.659272\pi$
$373$	−15.9954	+	1.15721i	−0.828210	+	0.0599180i	−0.348461	+	0.937323i	$0.613295\pi$
$374$	−22.5519	+	4.11660i	−1.16613	+	0.212865i
$375$	7.20681	+	15.7972i	0.372158	+	0.815766i
$376$	3.66764	+	3.23111i	0.189144	+	0.166632i
$377$	1.12378	−	20.7270i	0.0578778	−	1.06749i
$378$	4.06551	−	25.1284i	0.209107	−	1.29247i
$379$	1.09502	+	3.94392i	0.0562475	+	0.202585i	0.986335	−	0.164753i	$-0.0526828\pi$
$379$	1.09502	+	3.94392i	0.0562475	+	0.202585i	−0.930087	+	0.367339i	$0.880269\pi$
$380$	14.3761	−	3.71330i	0.737479	−	0.190488i
$381$	−22.9705	−	15.7534i	−1.17682	−	0.807072i
$382$	7.65563	+	15.7927i	0.391696	+	0.808027i
$383$	−11.7852	+	26.7293i	−0.602194	+	1.36580i	0.307907	+	0.951416i	$0.400371\pi$
$383$	−11.7852	+	26.7293i	−0.602194	+	1.36580i	−0.910101	+	0.414386i	$0.863997\pi$
$384$	11.2596	+	17.4724i	0.574589	+	0.891634i
$385$	17.9945	+	1.30183i	0.917083	+	0.0663476i
$386$	29.7137	+	17.8782i	1.51239	+	0.909974i
$387$	23.9215	−	3.21999i	1.21600	−	0.163681i
$388$	1.11241	+	4.00653i	0.0564740	+	0.203401i
$389$	−9.16774	−	5.07455i	−0.464823	−	0.257290i	0.234472	−	0.972123i	$-0.424664\pi$
$389$	−9.16774	−	5.07455i	−0.464823	−	0.257290i	−0.699295	+	0.714833i	$0.746503\pi$
$390$	12.5441	+	9.28608i	0.635194	+	0.470219i
$391$	−2.82076	+	14.0155i	−0.142652	+	0.708797i
$392$	−1.62125	−	0.0585694i	−0.0818857	−	0.00295820i
$393$	7.22765	−	0.879326i	0.364587	−	0.0443561i
$394$	13.6995	−	28.2606i	0.690171	−	1.42375i
$395$	−0.0110204	−	0.203259i	−0.000554497	−	0.0102271i
$396$	−2.07746	−	7.80346i	−0.104396	−	0.392139i
$397$	20.7294	+	9.59043i	1.04038	+	0.481330i	0.864263	−	0.503040i	$-0.167785\pi$
$397$	20.7294	+	9.59043i	1.04038	+	0.481330i	0.176114	+	0.984370i	$0.443647\pi$
$398$	−11.1935	−	12.2525i	−0.561078	−	0.614161i
$399$	−29.4162	−	0.687718i	−1.47265	−	0.0344289i
$400$	3.31954	+	2.71802i	0.165977	+	0.135901i
$401$	0.903515	+	7.11076i	0.0451194	+	0.355094i	0.998566	+	0.0535326i	$0.0170481\pi$
$401$	0.903515	+	7.11076i	0.0451194	+	0.355094i	−0.953447	+	0.301562i	$0.902492\pi$
$402$	−34.7012	+	13.6128i	−1.73074	+	0.678943i
$403$	−2.23457	+	9.34481i	−0.111312	+	0.465498i
$404$	0.363549	+	2.21755i	0.0180872	+	0.110327i
$405$	19.2785	−	10.1414i	0.957957	−	0.503928i
$406$	17.5640	−	44.0823i	0.871687	−	2.18777i
$407$	−16.9585	−	5.04000i	−0.840603	−	0.249824i
$408$	11.1881	+	9.60616i	0.553893	+	0.475576i
$409$	9.38377	−	10.2716i	0.463997	−	0.507896i	−0.461245	−	0.887273i	$-0.652597\pi$
$409$	9.38377	−	10.2716i	0.463997	−	0.507896i	0.925242	+	0.379376i	$0.123861\pi$
$410$	−0.779529	−	2.18252i	−0.0384982	−	0.107787i
$411$	2.81632	+	7.57899i	0.138919	+	0.373844i
$412$	1.32103	+	2.28809i	0.0650824	+	0.112726i
$413$	15.9172	−	14.6889i	0.783232	−	0.722792i
$414$	−14.8220	−	1.77173i	−0.728460	−	0.0870759i
$415$	−26.1201	−	2.84073i	−1.28218	−	0.139446i
$416$	−11.1198	−	2.02979i	−0.545191	−	0.0995187i
$417$	0.425533	−	0.413495i	0.0208385	−	0.0202489i
$418$	−25.5143	+	10.7035i	−1.24794	+	0.523527i
$419$	7.65114	+	31.9965i	0.373783	+	1.56313i	0.765741	+	0.643149i	$0.222372\pi$
$419$	7.65114	+	31.9965i	0.373783	+	1.56313i	−0.391959	+	0.919983i	$0.628202\pi$
$420$	6.88126	+	9.87594i	0.335771	+	0.481897i
$421$	−5.43028	−	26.9815i	−0.264656	−	1.31500i	−0.859492	−	0.511149i	$-0.829220\pi$
$421$	−5.43028	−	26.9815i	−0.264656	−	1.31500i	0.594836	−	0.803847i	$-0.297217\pi$
$422$	−1.24511	−	7.59486i	−0.0606112	−	0.369712i
$423$	−2.97779	+	8.06528i	−0.144785	+	0.392147i
$424$	14.2507	−	6.59309i	0.692077	−	0.320189i
$425$	3.94997	+	1.65706i	0.191602	+	0.0803791i
$426$	22.9991	−	7.15525i	1.11431	−	0.346673i
$427$	7.09526	+	11.3244i	0.343364	+	0.548028i
$428$	5.04828	−	15.9275i	0.244018	−	0.769885i
$429$	−8.64421	−	4.64194i	−0.417346	−	0.224115i
$430$	−20.9570	+	26.5592i	−1.01064	+	1.28080i
$431$	−0.367640	−	6.78072i	−0.0177086	−	0.326616i	−0.993943	−	0.109898i	$-0.964948\pi$
$431$	−0.367640	−	6.78072i	−0.0177086	−	0.326616i	0.976234	−	0.216718i	$-0.0695352\pi$
$432$	−15.3019	+	20.9943i	−0.736213	+	1.01009i
$433$	−18.4168	−	21.6819i	−0.885055	−	1.04197i	−0.998825	−	0.0484603i	$-0.984569\pi$
$433$	−18.4168	−	21.6819i	−0.885055	−	1.04197i	0.113770	−	0.993507i	$-0.463707\pi$
$434$	−11.6621	+	18.6134i	−0.559799	+	0.893470i
$435$	39.1846	−	10.6554i	1.87876	−	0.510885i
$436$	−0.807287	−	0.526333i	−0.0386620	−	0.0252068i
$437$	0.311525	+	17.2522i	0.0149023	+	0.825287i
$438$	0.702408	−	0.634875i	0.0335623	−	0.0303355i
$439$	35.6130	−	9.19872i	1.69972	−	0.439031i	0.730037	−	0.683408i	$-0.239503\pi$
$439$	35.6130	−	9.19872i	1.69972	−	0.439031i	0.969680	+	0.244377i	$0.0785835\pi$
$440$	−9.35063	−	5.62609i	−0.445774	−	0.268213i
$441$	−0.931160	−	2.69731i	−0.0443410	−	0.128443i
$442$	−18.4747	+	2.00924i	−0.878751	+	0.0955699i
$443$	−14.9192	−	20.3793i	−0.708831	−	0.968250i	−0.999933	−	0.0115581i	$-0.996321\pi$
$443$	−14.9192	−	20.3793i	−0.708831	−	0.968250i	0.291102	−	0.956692i	$-0.405978\pi$
$444$	−4.50819	−	10.9086i	−0.213949	−	0.517699i
$445$	−31.6068	+	17.4951i	−1.49831	+	0.829347i
$446$	−18.1484	−	18.4791i	−0.859353	−	0.875010i
$447$	27.8181	+	8.98018i	1.31575	+	0.424748i
$448$	2.06087	+	1.14074i	0.0973669	+	0.0538948i
$449$	0.174394	−	3.21650i	0.00823015	−	0.151796i	−0.991530	−	0.129880i	$-0.958541\pi$
$449$	0.174394	−	3.21650i	0.00823015	−	0.151796i	0.999760	−	0.0219158i	$-0.00697658\pi$
$450$	−1.39660	+	4.24885i	−0.0658365	+	0.200293i
$451$	0.682456	+	1.28725i	0.0321356	+	0.0606142i
$452$	3.68773	−	10.3249i	0.173456	−	0.485641i
$453$	15.7957	−	28.1819i	0.742148	−	1.32410i
$454$	37.1647	+	18.8519i	1.74423	+	0.884765i
$455$	14.4729	+	2.10514i	0.678500	+	0.0986906i
$456$	15.6800	+	8.42015i	0.734282	+	0.394310i
$457$	22.5069	+	24.6363i	1.05283	+	1.15244i	0.987986	+	0.154543i	$0.0493906\pi$
$457$	22.5069	+	24.6363i	1.05283	+	1.15244i	0.0648441	+	0.997895i	$0.479345\pi$
$458$	7.82319	−	14.7561i	0.365554	−	0.689508i
$459$	−8.67304	+	24.4444i	−0.404823	+	1.14097i
$460$	5.61938	−	4.27174i	0.262005	−	0.199171i
$461$	−1.24903	−	0.880196i	−0.0581733	−	0.0409948i	0.546587	−	0.837402i	$-0.315927\pi$
$461$	−1.24903	−	0.880196i	−0.0581733	−	0.0409948i	−0.604761	+	0.796407i	$0.706731\pi$
$462$	−15.3383	−	16.3660i	−0.713605	−	0.761415i
$463$	−31.2323	−	11.7953i	−1.45149	−	0.548172i	−0.502804	−	0.864400i	$-0.667698\pi$
$463$	−31.2323	−	11.7953i	−1.45149	−	0.548172i	−0.948683	+	0.316228i	$0.897583\pi$
$464$	−36.3388	+	32.0137i	−1.68699	+	1.48620i
$465$	−18.7287	+	1.59496i	−0.868525	+	0.0739646i
$466$	−33.1250	−	9.84461i	−1.53449	−	0.456043i
$467$	−12.1085	−	9.20462i	−0.560313	−	0.425939i	0.286306	−	0.958138i	$-0.407573\pi$
$467$	−12.1085	−	9.20462i	−0.560313	−	0.425939i	−0.846619	+	0.532199i	$0.821366\pi$
$468$	−1.22323	−	6.43085i	−0.0565439	−	0.297266i
$469$	−22.6134	+	26.6226i	−1.04419	+	1.22932i
$470$	−4.86160	−	11.0263i	−0.224249	−	0.508606i
$471$	−15.8265	+	23.9946i	−0.729245	+	1.10561i
$472$	−12.6056	+	3.56828i	−0.580220	+	0.164243i
$473$	10.6344	−	18.4194i	0.488971	−	0.846923i
$474$	−0.161367	+	0.194954i	−0.00741183	+	0.00895455i
$475$	5.08583	+	0.928363i	0.233354	+	0.0425962i
$476$	−13.9973	−	3.08104i	−0.641565	−	0.141219i
$477$	19.8477	+	19.2055i	0.908764	+	0.879358i
$478$	24.0072	−	22.7408i	1.09806	−	1.04014i
$479$	−7.31635	+	1.06419i	−0.334292	+	0.0486242i	−0.309017	−	0.951056i	$-0.600000\pi$
$479$	−7.31635	+	1.06419i	−0.334292	+	0.0486242i	−0.0252750	+	0.999681i	$0.508046\pi$
$480$	−3.06647	−	21.8993i	−0.139964	−	0.999560i
$481$	−13.4167	−	5.06697i	−0.611747	−	0.231034i
$482$	−28.3916	+	8.43786i	−1.29320	+	0.384334i
$483$	−13.0221	+	5.10839i	−0.592527	+	0.232440i
$484$	3.76715	+	1.58036i	0.171234	+	0.0718347i
$485$	−1.59899	+	9.75342i	−0.0726065	+	0.442880i
$486$	−26.1626	−	6.99665i	−1.18676	−	0.317375i
$487$	21.3475	−	4.69895i	0.967349	−	0.212930i	0.296919	−	0.954903i	$-0.404041\pi$
$487$	21.3475	−	4.69895i	0.967349	−	0.212930i	0.670430	+	0.741973i	$0.266110\pi$
$488$	−0.728725	−	8.05028i	−0.0329878	−	0.364419i
$489$	−12.2929	−	37.1358i	−0.555906	−	1.67934i
$490$	3.56694	+	1.80934i	0.161138	+	0.0817377i
$491$	−14.2261	+	1.02921i	−0.642016	+	0.0464475i	−0.389326	−	0.921100i	$-0.627292\pi$
$491$	−14.2261	+	1.02921i	−0.642016	+	0.0464475i	−0.252689	+	0.967547i	$0.581315\pi$
$492$	−0.380802	+	0.894360i	−0.0171679	+	0.0403209i
$493$	−25.6718	+	40.9736i	−1.15620	+	1.84536i
$494$	−21.2551	+	7.16169i	−0.956314	+	0.322220i
$495$	3.30667	−	18.9076i	0.148624	−	0.849833i
$496$	19.2082	−	11.5572i	0.862475	−	0.518934i
$497$	15.8153	−	16.1035i	0.709415	−	0.722341i
$498$	21.4625	+	24.6250i	0.961756	+	1.10347i
$499$	2.11933	−	1.17310i	0.0948741	−	0.0525150i	−0.436134	−	0.899882i	$-0.643653\pi$
$499$	2.11933	−	1.17310i	0.0948741	−	0.0525150i	0.531008	+	0.847367i	$0.321813\pi$
$500$	4.45272	+	9.18549i	0.199132	+	0.410788i
$501$	3.90771	−	7.60315i	0.174584	−	0.339683i
$502$	−18.8947	−	25.8099i	−0.843314	−	1.15195i
$503$	21.9679	−	32.4003i	0.979501	−	1.44466i	0.0856323	−	0.996327i	$-0.472709\pi$
$503$	21.9679	−	32.4003i	0.979501	−	1.44466i	0.893869	−	0.448329i	$-0.147981\pi$
$504$	−1.97084	+	14.2930i	−0.0877883	+	0.636660i
$505$	−1.42897	+	5.14670i	−0.0635885	+	0.229025i
$506$	−9.21662	+	9.38455i	−0.409729	+	0.417194i
$507$	12.2994	+	7.79753i	0.546235	+	0.346301i
$508$	−13.7169	−	8.94314i	−0.608591	−	0.396788i
$509$	−1.59476	+	7.92392i	−0.0706867	+	0.351221i	−0.999829	−	0.0185013i	$-0.994111\pi$
$509$	−1.59476	+	7.92392i	−0.0706867	+	0.351221i	0.929142	+	0.369723i	$0.120547\pi$
$510$	−15.0893	−	33.0756i	−0.668165	−	1.46461i
$511$	0.298429	−	0.835538i	0.0132017	−	0.0369620i
$512$	5.22882	+	7.71194i	0.231084	+	0.340823i
$513$	−3.88084	+	31.0633i	−0.171343	+	1.37148i
$514$	−16.0514	−	40.2860i	−0.707997	−	1.77694i
$515$	0.566167	+	6.25449i	0.0249483	+	0.275606i
$516$	14.0152	−	2.22118i	0.616983	−	0.0977819i
$517$	4.02226	+	6.41976i	0.176899	+	0.282341i
$518$	−25.3671	−	20.7704i	−1.11457	−	0.912598i
$519$	−8.53104	−	4.19166i	−0.374471	−	0.183994i
$520$	−7.23117	−	5.09582i	−0.317108	−	0.223466i
$521$	27.8125	+	26.3454i	1.21849	+	1.15421i	0.983247	+	0.182278i	$0.0583469\pi$
$521$	27.8125	+	26.3454i	1.21849	+	1.15421i	0.235242	+	0.971937i	$0.424412\pi$
$522$	−44.7786	−	23.3163i	−1.95990	−	1.02053i
$523$	−13.6958	−	4.61466i	−0.598876	−	0.201785i	0.00350444	−	0.999994i	$-0.498885\pi$
$523$	−13.6958	−	4.61466i	−0.598876	−	0.201785i	−0.602381	+	0.798209i	$0.705781\pi$
$524$	4.23583	−	0.616118i	0.185043	−	0.0269152i
$525$	0.730659	+	4.12690i	0.0318886	+	0.180113i
$526$	9.64904	−	4.04788i	0.420718	−	0.176496i
$527$	15.0957	−	16.5239i	0.657577	−	0.719791i
$528$	6.40460	+	21.9776i	0.278725	+	0.956451i
$529$	−5.96962	−	13.5393i	−0.259549	−	0.588667i
$530$	−38.7112			−1.68151
$531$	−13.8421	−	18.4227i	−0.600697	−	0.799477i
$532$	−17.2983			−0.749975
$533$	0.476489	+	1.08070i	0.0206390	+	0.0468102i
$534$	43.6257	+	10.6776i	1.88787	+	0.462066i
$535$	26.7871	−	29.3214i	1.15811	−	1.26768i
$536$	19.4832	−	8.17345i	0.841548	−	0.353039i
$537$	4.04091	−	3.39554i	0.174378	−	0.146528i
$538$	−8.90244	+	1.29490i	−0.383811	+	0.0558269i
$539$	−2.38279	−	0.802855i	−0.102634	−	0.0345814i
$540$	11.1912	−	6.22528i	0.481594	−	0.267894i
$541$	−5.48091	−	5.19179i	−0.235643	−	0.223213i	0.560761	−	0.827977i	$-0.310508\pi$
$541$	−5.48091	−	5.19179i	−0.235643	−	0.223213i	−0.796404	+	0.604765i	$0.793267\pi$
$542$	−27.6594	−	19.4917i	−1.18808	−	0.837238i
$543$	28.0888	−	18.8273i	1.20540	−	0.807958i
$544$	20.3722	+	16.6806i	0.873451	+	0.715175i
$545$	−1.21622	−	1.94116i	−0.0520973	−	0.0831502i
$546$	−11.4442	−	14.1296i	−0.489766	−	0.604691i
$547$	−1.45152	−	16.0351i	−0.0620626	−	0.685611i	−0.966102	−	0.258161i	$-0.916883\pi$
$547$	−1.45152	−	16.0351i	−0.0620626	−	0.685611i	0.904039	−	0.427450i	$-0.140588\pi$
$548$	1.75938	+	4.41571i	0.0751570	+	0.188630i
$549$	12.7474	−	6.29655i	0.544045	−	0.268730i
$550$	2.21164	+	3.26192i	0.0943045	+	0.139089i
$551$	−19.6290	+	54.9570i	−0.836222	+	2.34125i
$552$	8.42241	+	0.807603i	0.358481	+	0.0343738i
$553$	−0.0467906	+	0.232489i	−0.00198974	+	0.00988643i
$554$	−19.7306	−	12.8639i	−0.838272	−	0.546534i
$555$	1.16203	−	28.0322i	0.0493255	−	1.18990i
$556$	0.244417	−	0.248871i	0.0103656	−	0.0105545i
$557$	−1.76802	+	6.36783i	−0.0749133	+	0.269813i	−0.991516	−	0.129986i	$-0.958507\pi$
$557$	−1.76802	+	6.36783i	−0.0749133	+	0.269813i	0.916602	+	0.399800i	$0.130920\pi$
$558$	18.4523	+	14.3393i	0.781147	+	0.607033i
$559$	9.67568	−	14.2706i	0.409237	−	0.603580i
$560$	−20.1560	−	27.5328i	−0.851748	−	1.16347i
$561$	12.3803	+	19.2115i	0.522699	+	0.811111i
$562$	−2.69981	−	5.56942i	−0.113885	−	0.234932i
$563$	−16.0567	+	8.88775i	−0.676710	+	0.374574i	−0.784957	−	0.619550i	$-0.787315\pi$
$563$	−16.0567	+	8.88775i	−0.676710	+	0.374574i	0.108247	+	0.994124i	$0.465476\pi$
$564$	−1.63932	+	4.78113i	−0.0690278	+	0.201322i
$565$	18.2603	−	18.5930i	0.768215	−	0.782211i
$566$	0.0903263	−	0.0543475i	0.00379670	−	0.00228440i
$567$	−24.7011	+	5.82253i	−1.03735	+	0.244523i
$568$	−12.9378	+	4.35924i	−0.542857	+	0.182910i
$569$	13.4156	−	21.4120i	0.562410	−	0.897639i	−0.437588	−	0.899175i	$-0.644167\pi$
$569$	13.4156	−	21.4120i	0.562410	−	0.897639i	0.999999	+	0.00153670i	$0.000489145\pi$
$570$	−26.3677	−	35.0718i	−1.10442	−	1.46899i
$571$	−6.89722	+	0.498989i	−0.288640	+	0.0208820i	−0.215718	−	0.976456i	$-0.569209\pi$
$571$	−6.89722	+	0.498989i	−0.288640	+	0.0208820i	−0.0729215	+	0.997338i	$0.523232\pi$
$572$	−5.14425	−	2.60944i	−0.215092	−	0.109106i
$573$	11.6361	−	13.0674i	0.486106	−	0.545898i
$574$	0.243415	+	2.68902i	0.0101599	+	0.112238i
$575$	2.40029	−	0.528343i	0.100099	−	0.0220334i
$576$	1.42836	−	2.05916i	0.0595149	−	0.0857984i
$577$	−5.78226	+	35.2702i	−0.240719	+	1.46832i	0.539062	+	0.842266i	$0.318779\pi$
$577$	−5.78226	+	35.2702i	−0.240719	+	1.46832i	−0.779780	+	0.626053i	$0.784669\pi$
$578$	12.6829	+	5.32063i	0.527539	+	0.221309i
$579$	5.15827	−	34.1856i	0.214370	−	1.42070i
$580$	22.8836	−	6.80090i	0.950188	−	0.282392i
$581$	28.6360	+	10.8147i	1.18802	+	0.448670i
$582$	9.68677	−	7.56026i	0.401530	−	0.313383i
$583$	24.0830	−	3.50296i	0.997415	−	0.145078i
$584$	−0.389612	+	0.369060i	−0.0161222	+	0.0152718i
$585$	3.77953	−	15.0939i	0.156264	−	0.624057i
$586$	−27.4839	−	6.04967i	−1.13535	−	0.249910i
$587$	−24.7292	−	4.51405i	−1.02068	−	0.186315i	−0.356824	−	0.934172i	$-0.616140\pi$
$587$	−24.7292	−	4.51405i	−1.02068	−	0.186315i	−0.663860	+	0.747857i	$0.731083\pi$
$588$	−0.584334	−	1.57250i	−0.0240975	−	0.0648487i
$589$	13.5063	−	23.3936i	0.556518	−	0.963918i
$590$	31.8990	+	5.06503i	1.31326	+	0.208524i
$591$	−31.2555	−	1.86143i	−1.28568	−	0.0765689i
$592$	13.4991	+	30.6165i	0.554810	+	1.25833i
$593$	6.72285	−	7.91476i	0.276075	−	0.325020i	−0.606598	−	0.795009i	$-0.707466\pi$
$593$	6.72285	−	7.91476i	0.276075	−	0.325020i	0.882672	+	0.469989i	$0.155742\pi$
$594$	−18.9674	+	14.4815i	−0.778242	+	0.594183i
$595$	−27.1209	−	20.6168i	−1.11185	−	0.845204i
$596$	16.4730	+	4.89569i	0.674759	+	0.200535i
$597$	−7.02702	+	14.9790i	−0.287597	+	0.613052i
$598$	−8.00085	+	7.04857i	−0.327179	+	0.288237i
$599$	26.2118	+	9.89922i	1.07099	+	0.404471i	0.825193	−	0.564851i	$-0.191066\pi$
$599$	26.2118	+	9.89922i	1.07099	+	0.404471i	0.245794	+	0.969322i	$0.420951\pi$
$600$	0.735103	−	2.42613i	0.0300105	−	0.0990463i
$601$	6.87904	+	4.84767i	0.280602	+	0.197741i	0.707791	−	0.706421i	$-0.249692\pi$
$601$	6.87904	+	4.84767i	0.280602	+	0.197741i	−0.427189	+	0.904162i	$0.640496\pi$
$602$	31.3779	−	23.8529i	1.27887	−	0.972170i
$603$	25.7562	+	26.7898i	1.04888	+	1.09096i
$604$	8.89640	−	16.7804i	0.361989	−	0.682784i
$605$	6.54946	+	7.16911i	0.266274	+	0.291466i
$606$	5.64607	−	3.49583i	0.229356	−	0.142008i
$607$	23.4747	+	3.41448i	0.952807	+	0.138590i	0.602565	−	0.798070i	$-0.294145\pi$
$607$	23.4747	+	3.41448i	0.952807	+	0.138590i	0.350242	+	0.936659i	$0.386099\pi$
$608$	28.3410	+	14.3760i	1.14938	+	0.583026i
$609$	−47.3050	+	0.602492i	−1.91689	+	0.0244142i
$610$	−6.70297	+	18.7669i	−0.271395	+	0.759850i
$611$	2.87660	+	5.42585i	0.116375	+	0.219506i
$612$	−4.76154	+	14.4859i	−0.192474	+	0.585557i
$613$	0.304432	−	5.61492i	0.0122959	−	0.226785i	−0.985926	−	0.167181i	$-0.946534\pi$
$613$	0.304432	−	5.61492i	0.0122959	−	0.226785i	0.998222	−	0.0596036i	$-0.0189837\pi$
$614$	9.37488	+	5.18921i	0.378339	+	0.209419i
$615$	−1.71412	+	1.54931i	−0.0691199	+	0.0624743i
$616$	8.90836	+	9.07067i	0.358928	+	0.365468i
$617$	−6.60146	+	3.65405i	−0.265765	+	0.147107i	−0.611547	−	0.791208i	$-0.709453\pi$
$617$	−6.60146	+	3.65405i	−0.265765	+	0.147107i	0.345783	+	0.938315i	$0.387613\pi$
$618$	4.75802	−	6.19044i	0.191396	−	0.249016i
$619$	−19.6405	−	26.8285i	−0.789416	−	1.07833i	−0.995018	−	0.0996927i	$-0.968214\pi$
$619$	−19.6405	−	26.8285i	−0.789416	−	1.07833i	0.205602	−	0.978636i	$-0.434085\pi$
$620$	−10.9855	+	1.19475i	−0.441190	+	0.0479823i
$621$	4.01149	+	14.3314i	0.160975	+	0.575100i
$622$	43.6928	+	26.2891i	1.75192	+	1.05410i
$623$	40.7501	−	10.5256i	1.63262	−	0.421699i
$624$	3.89275	+	18.1442i	0.155835	+	0.726348i
$625$	0.515523	+	28.5496i	0.0206209	+	1.14198i
$626$	−3.97735	−	2.59314i	−0.158967	−	0.103643i
$627$	19.5775	+	19.4328i	0.781849	+	0.776072i
$628$	−8.97200	+	14.3198i	−0.358022	+	0.571423i
$629$	21.6271	+	25.4614i	0.862329	+	1.01521i
$630$	19.2056	−	29.9405i	0.765169	−	1.19286i
$631$	1.66012	+	30.6191i	0.0660884	+	1.21893i	0.824007	+	0.566580i	$0.191734\pi$
$631$	1.66012	+	30.6191i	0.0660884	+	1.21893i	−0.757919	+	0.652349i	$0.773784\pi$
$632$	0.0888566	−	0.112609i	0.00353453	−	0.00447936i
$633$	−6.52370	+	4.03922i	−0.259294	+	0.160545i
$634$	−8.09686	+	25.5459i	−0.321567	+	1.01456i
$635$	−20.6654	−	32.9831i	−0.820080	−	1.30889i
$636$	11.9290	+	11.0149i	0.473015	+	0.436770i
$637$	−1.87959	−	0.788512i	−0.0744722	−	0.0312420i
$638$	−40.3742	+	18.6791i	−1.59843	+	0.739513i
$639$	−15.3504	−	18.4665i	−0.607253	−	0.730525i
$640$	4.69918	+	28.6637i	0.185751	+	1.13303i
$641$	−7.11048	−	35.3299i	−0.280847	−	1.39545i	−0.829084	−	0.559124i	$-0.811137\pi$
$641$	−7.11048	−	35.3299i	−0.280847	−	1.39545i	0.548237	−	0.836323i	$-0.315299\pi$
$642$	−49.1979	+	4.18975i	−1.94169	+	0.165356i
$643$	−3.17378	−	13.2725i	−0.125162	−	0.523417i	−0.999288	−	0.0377193i	$-0.987991\pi$
$643$	−3.17378	−	13.2725i	−0.125162	−	0.523417i	0.874127	−	0.485698i	$-0.161435\pi$
$644$	−7.58331	+	3.18129i	−0.298824	+	0.125360i
$645$	32.4513	+	9.19628i	1.27777	+	0.362103i
$646$	51.3966	+	9.38190i	2.02217	+	0.369126i
$647$	18.6192	+	2.02496i	0.731997	+	0.0796095i	0.466524	−	0.884509i	$-0.345506\pi$
$647$	18.6192	+	2.02496i	0.731997	+	0.0796095i	0.265473	+	0.964118i	$0.414472\pi$
$648$	14.9179	+	3.61809i	0.586029	+	0.142132i
$649$	−20.3033	−	0.264526i	−0.796974	−	0.0103836i
$650$	1.59737	+	2.76673i	0.0626540	+	0.108520i
$651$	21.5909	+	3.65768i	0.846212	+	0.143356i
$652$	−7.73521	−	21.6570i	−0.302934	−	0.848152i
$653$	16.2132	−	17.7471i	0.634470	−	0.694497i	−0.334298	−	0.942467i	$-0.608499\pi$
$653$	16.2132	−	17.7471i	0.634470	−	0.694497i	0.968768	+	0.247970i	$0.0797635\pi$
$654$	−0.526303	+	2.79887i	−0.0205801	+	0.109444i
$655$	9.75274	+	2.89847i	0.381071	+	0.113253i
$656$	1.01995	−	2.55987i	0.0398222	−	0.0999462i
$657$	−0.852430	−	0.405441i	−0.0332565	−	0.0158178i
$658$	2.27129	+	13.8542i	0.0885439	+	0.540094i
$659$	−0.115763	+	0.484111i	−0.00450948	+	0.0188583i	−0.974789	−	0.223127i	$-0.928373\pi$
$659$	−0.115763	+	0.484111i	−0.00450948	+	0.0188583i	0.970280	+	0.241986i	$0.0777987\pi$
$660$	1.68363	−	11.1580i	0.0655354	−	0.434325i
$661$	−5.98258	−	47.0835i	−0.232696	−	1.83134i	−0.498005	−	0.867174i	$-0.665934\pi$
$661$	−5.98258	−	47.0835i	−0.232696	−	1.83134i	0.265309	−	0.964163i	$-0.414526\pi$
$662$	−16.3101	−	13.3546i	−0.633909	−	0.519039i
$663$	8.88612	+	16.2573i	0.345108	+	0.631380i
$664$	−12.4880	−	13.6695i	−0.484629	−	0.530480i
$665$	−37.3170	−	17.2647i	−1.44709	−	0.669496i
$666$	−24.7043	+	24.6248i	−0.957273	+	0.954193i
$667$	1.50198	+	27.7023i	0.0581567	+	1.07264i
$668$	2.19221	−	4.52230i	0.0848192	−	0.174973i
$669$	−10.1158	+	23.7582i	−0.391100	+	0.918547i
$670$	−52.0549	−	1.88053i	−2.01106	−	0.0726514i
$671$	2.47183	−	12.2818i	0.0954241	−	0.474134i
$672$	−2.92158	+	25.5960i	−0.112702	+	0.987385i
$673$	−40.4045	−	22.3648i	−1.55748	−	0.862101i	−0.999479	−	0.0322608i	$-0.989729\pi$
$673$	−40.4045	−	22.3648i	−1.55748	−	0.862101i	−0.558001	−	0.829840i	$-0.688432\pi$
$674$	−2.06326	−	7.43119i	−0.0794738	−	0.286239i
$675$	4.44664	−	0.331071i	0.171151	−	0.0127429i
$676$	7.33588	+	4.41385i	0.282149	+	0.169763i
$677$	19.2260	+	1.39093i	0.738916	+	0.0534579i	0.436483	−	0.899713i	$-0.356224\pi$
$677$	19.2260	+	1.39093i	0.738916	+	0.0534579i	0.302433	+	0.953171i	$0.402201\pi$
$678$	−32.3608	+	1.58195i	−1.24281	+	0.0607544i
$679$	4.64543	−	10.5360i	0.178275	−	0.404336i
$680$	8.98859	+	18.5425i	0.344697	+	0.711073i
$681$	3.21828	−	41.4216i	0.123325	−	1.58728i
$682$	19.9374	−	5.14977i	0.763443	−	0.197195i
$683$	−10.7907	−	38.8646i	−0.412895	−	1.48711i	−0.819270	−	0.573408i	$-0.805621\pi$
$683$	−10.7907	−	38.8646i	−0.412895	−	1.48711i	0.406375	−	0.913706i	$-0.366793\pi$
$684$	−1.85406	+	18.3102i	−0.0708919	+	0.700108i
$685$	−0.611684	+	11.2818i	−0.0233712	+	0.431057i
$686$	22.2346	+	19.5881i	0.848920	+	0.747879i
$687$	−16.5750	−	1.58934i	−0.632377	−	0.0606370i
$688$	−39.5722	+	7.22347i	−1.50868	+	0.275392i
$689$	19.6767	−	1.42354i	0.749623	−	0.0542325i
$690$	−18.0092	−	10.5257i	−0.685598	−	0.400708i
$691$	−7.20811	+	9.13496i	−0.274209	+	0.347510i	−0.902672	−	0.430330i	$-0.858397\pi$
$691$	−7.20811	+	9.13496i	−0.274209	+	0.347510i	0.628462	+	0.777840i	$0.283685\pi$
$692$	−5.07155	−	2.34635i	−0.192791	−	0.0891948i
$693$	−9.23887	+	20.3644i	−0.350956	+	0.773581i
$694$	14.5404	−	27.4261i	0.551946	−	1.04108i
$695$	0.775662	−	0.292938i	0.0294225	−	0.0111118i
$696$	25.6829	+	12.6191i	0.973506	+	0.478325i
$697$	0.248026	−	2.73997i	0.00939467	−	0.103784i
$698$	37.0972	−	11.0251i	1.40415	−	0.417307i
$699$	3.54270	+	34.2697i	0.133997	+	1.29620i
$700$	0.486136	+	2.41547i	0.0183742	+	0.0912961i
$701$	−3.17034	+	7.95694i	−0.119742	+	0.300530i	−0.976614	−	0.214999i	$-0.931025\pi$
$701$	−3.17034	+	7.95694i	−0.119742	+	0.300530i	0.856872	+	0.515529i	$0.172404\pi$
$702$	−16.1828	+	10.5992i	−0.610780	+	0.400042i
$703$	32.0984	+	24.4005i	1.21061	+	0.920284i
$704$	−0.667201	−	2.10504i	−0.0251461	−	0.0793368i
$705$	−8.30830	+	8.67804i	−0.312909	+	0.326834i
$706$	26.9963	−	36.8764i	1.01602	−	1.38786i
$707$	3.11143	−	5.38916i	0.117018	−	0.202680i
$708$	−8.38858	−	10.6374i	−0.315262	−	0.399777i
$709$	14.1855	+	24.5701i	0.532749	+	0.922749i	0.999269	+	0.0382378i	$0.0121744\pi$
$709$	14.1855	+	24.5701i	0.532749	+	0.922749i	−0.466519	+	0.884511i	$0.654492\pi$
$710$	33.4610	+	3.63910i	1.25577	+	0.136573i
$711$	0.241074	+	0.0744465i	0.00904099	+	0.00279196i
$712$	−24.8622	−	5.47258i	−0.931749	−	0.205094i
$713$	1.61870	−	12.7393i	0.0606209	−	0.477092i
$714$	7.38393	+	41.7059i	0.276337	+	1.56080i
$715$	−8.49316	−	10.7635i	−0.317626	−	0.402533i
$716$	2.32831	−	2.05119i	0.0870130	−	0.0766565i
$717$	−30.0947	−	13.4607i	−1.12391	−	0.502698i
$718$	6.64613	−	27.7936i	0.248031	−	1.03725i
$719$	−2.22343	+	1.02867i	−0.0829199	+	0.0383628i	−0.460911	−	0.887447i	$-0.652477\pi$
$719$	−2.22343	+	1.02867i	−0.0829199	+	0.0383628i	0.377991	+	0.925809i	$0.376615\pi$
$720$	−31.3038	+	18.3841i	−1.16662	+	0.685136i
$721$	1.18367	−	7.22006i	0.0440821	−	0.268889i
$722$	30.0289	−	1.08482i	1.11756	−	0.0403729i
$723$	18.5856	+	22.9467i	0.691204	+	0.853397i
$724$	16.2499	−	11.4514i	0.603924	−	0.425586i
$725$	8.22565	+	1.19645i	0.305493	+	0.0444352i
$726$	0.0642190	−	12.0723i	0.00238339	−	0.448045i
$727$	4.93010	−	10.1703i	0.182847	−	0.377194i	−0.788437	−	0.615115i	$-0.789110\pi$
$727$	4.93010	−	10.1703i	0.182847	−	0.377194i	0.971285	+	0.237921i	$0.0764658\pi$
$728$	6.67209	+	7.85499i	0.247284	+	0.291125i
$729$	3.51563	+	26.7701i	0.130208	+	0.991487i
$730$	1.25380	−	0.422455i	0.0464053	−	0.0156358i
$731$	−35.8171	+	18.1684i	−1.32475	+	0.671981i
$732$	7.40551	−	3.87583i	0.273716	−	0.143255i
$733$	−23.8654	−	6.16434i	−0.881487	−	0.227685i	−0.218069	−	0.975933i	$-0.569976\pi$
$733$	−23.8654	−	6.16434i	−0.881487	−	0.227685i	−0.663419	+	0.748248i	$0.730895\pi$
$734$	42.1476	+	42.9155i	1.55570	+	1.58404i
$735$	0.308880	−	3.97550i	0.0113932	−	0.146639i
$736$	15.0681	+	1.09012i	0.555419	+	0.0401825i
$737$	32.5545	−	3.54052i	1.19916	−	0.130417i
$738$	2.87242	+	0.0305607i	0.105735	+	0.00112495i
$739$	7.79115	−	11.4911i	0.286602	−	0.422707i	−0.656948	−	0.753936i	$-0.728153\pi$
$739$	7.79115	−	11.4911i	0.286602	−	0.422707i	0.943550	+	0.331229i	$0.107463\pi$
$740$	0.297786	−	16.4913i	0.0109468	−	0.606234i
$741$	14.6923	+	16.8572i	0.539734	+	0.619264i
$742$	43.6664	+	11.2789i	1.60305	+	0.414061i
$743$	−0.825143	−	45.6963i	−0.0302716	−	1.67644i	−0.560172	−	0.828376i	$-0.689265\pi$
$743$	−0.825143	−	45.6963i	−0.0302716	−	1.67644i	0.529900	−	0.848060i	$-0.322229\pi$
$744$	−10.6460	−	7.88100i	−0.390302	−	0.288932i
$745$	30.6504	+	27.0023i	1.12294	+	0.989288i
$746$	13.0506	+	24.6161i	0.477817	+	0.901259i
$747$	14.5166	−	29.1520i	0.531136	−	1.06662i
$748$	7.54029	+	11.1211i	0.275700	+	0.406627i
$749$	−38.7591	+	25.2701i	−1.41623	+	0.923349i
$750$	20.0610	−	22.5285i	0.732523	−	0.822625i
$751$	16.5700	−	11.6769i	0.604646	−	0.426095i	−0.232870	−	0.972508i	$-0.574812\pi$
$751$	16.5700	−	11.6769i	0.604646	−	0.426095i	0.837516	+	0.546413i	$0.184007\pi$
$752$	4.32910	−	13.6585i	0.157866	−	0.498073i
$753$	−16.5861	+	27.2373i	−0.604432	+	0.992584i
$754$	−33.7364	+	12.7410i	−1.22861	+	0.463999i
$755$	35.9397	−	27.3207i	1.30798	−	0.994301i
$756$	−14.4376	+	3.76148i	−0.525090	+	0.136804i
$757$	−5.71229	−	5.41097i	−0.207617	−	0.196665i	0.576825	−	0.816868i	$-0.304292\pi$
$757$	−5.71229	−	5.41097i	−0.207617	−	0.196665i	−0.784441	+	0.620203i	$0.787050\pi$
$758$	5.50197	−	4.50497i	0.199841	−	0.163628i
$759$	12.1563	+	4.91862i	0.441247	+	0.178534i
$760$	15.4060	+	19.5243i	0.558834	+	0.708219i
$761$	0.990804	+	4.14347i	0.0359166	+	0.150201i	0.987635	−	0.156773i	$-0.0501090\pi$
$761$	0.990804	+	4.14347i	0.0359166	+	0.150201i	−0.951718	+	0.306973i	$0.900684\pi$
$762$	−8.94263	+	47.5567i	−0.323957	+	1.72280i
$763$	0.806331	+	2.54400i	0.0291912	+	0.0920991i
$764$	6.65935	−	7.83999i	0.240927	−	0.283641i
$765$	−24.7297	+	26.4977i	−0.894104	+	0.958026i
$766$	50.7505			1.83369
$767$	−16.4004	−	1.40150i	−0.592182	−	0.0506053i
$768$	18.2900	−	27.7296i	0.659983	−	1.00060i
$769$	2.03270	−	2.77663i	0.0733010	−	0.100128i	−0.768684	−	0.639629i	$-0.779088\pi$
$769$	2.03270	−	2.77663i	0.0733010	−	0.100128i	0.841985	+	0.539501i	$0.181387\pi$
$770$	−10.5427	−	29.5174i	−0.379934	−	1.06373i
$771$	−31.0070	+	30.1298i	−1.11669	+	1.08510i
$772$	2.56195	−	20.1628i	0.0922065	−	0.725674i
$773$	−16.3945	+	15.5297i	−0.589668	+	0.558563i	−0.923270	−	0.384151i	$-0.874494\pi$
$773$	−16.3945	+	15.5297i	−0.589668	+	0.558563i	0.333602	+	0.942714i	$0.391736\pi$
$774$	−21.8851	−	35.7701i	−0.786643	−	1.28573i
$775$	−3.64618	−	1.22854i	−0.130975	−	0.0441304i
$776$	−5.38889	+	4.41238i	−0.193450	+	0.158395i
$777$	−9.47825	+	31.2819i	−0.340030	+	1.12223i
$778$	−1.64118	+	18.1303i	−0.0588393	+	0.650002i
$779$	−0.418546	−	3.29400i	−0.0149960	−	0.118020i
$780$	2.01395	−	8.92310i	0.0721109	−	0.319498i
$781$	−21.1460	+	0.763920i	−0.756664	+	0.0273352i
$782$	24.2570	−	5.33936i	0.867427	−	0.190935i
$783$	−4.43251	+	50.1369i	−0.158405	+	1.79175i
$784$	1.76021	+	4.41778i	0.0628645	+	0.157778i
$785$	−33.6471	+	21.9371i	−1.20091	+	0.782969i
$786$	−6.46363	−	10.8732i	−0.230550	−	0.387833i
$787$	−15.8629	+	2.89560i	−0.565452	+	0.103217i	−0.454722	−	0.890633i	$-0.650261\pi$
$787$	−15.8629	+	2.89560i	−0.565452	+	0.103217i	−0.110730	+	0.993851i	$0.535319\pi$
$788$	−18.3954	−	0.664552i	−0.655310	−	0.0236737i
$789$	−7.40385	−	7.34915i	−0.263584	−	0.261637i
$790$	−0.315388	+	0.159982i	−0.0112210	+	0.00569190i
$791$	−26.0149	+	15.6527i	−0.924984	+	0.556545i
$792$	10.5561	−	8.45727i	0.375095	−	0.300516i
$793$	2.71697	−	9.78563i	0.0964823	−	0.347498i
$794$	0.716405	−	39.6744i	0.0254243	−	1.40799i
$795$	14.7405	+	35.6680i	0.522792	+	1.26501i
$796$	−3.92418	+	8.90020i	−0.139089	+	0.315459i
$797$	−0.0660154	+	0.149726i	−0.00233839	+	0.00530356i	−0.916174	−	0.400782i	$-0.868739\pi$
$797$	−0.0660154	+	0.149726i	−0.00233839	+	0.00530356i	0.913835	+	0.406085i	$0.133106\pi$
$798$	19.5244	+	47.2437i	0.691156	+	1.67241i
$799$	0.258267	−	14.3028i	0.00913685	−	0.505998i
$800$	1.21095	−	4.36145i	0.0428135	−	0.154200i
$801$	−6.77366	−	44.2621i	−0.239336	−	1.56392i
$802$	10.6704	−	6.42016i	0.376784	−	0.226704i
$803$	−0.741787	+	0.376274i	−0.0261771	+	0.0132784i
$804$	15.5058	+	15.3913i	0.546849	+	0.542808i
$805$	−19.5343	−	0.705697i	−0.688495	−	0.0248726i
$806$	16.4212	−	2.99752i	0.578413	−	0.105583i
$807$	4.58299	+	7.70953i	0.161329	+	0.271388i
$808$	−3.15306	+	2.05572i	−0.110924	+	0.0723201i
$809$	−14.6646	−	36.8053i	−0.515580	−	1.29401i	−0.924411	−	0.381397i	$-0.875443\pi$
$809$	−14.6646	−	36.8053i	−0.515580	−	1.29401i	0.408832	−	0.912610i	$-0.365936\pi$
$810$	−29.6335	−	23.5382i	−1.04121	−	0.827048i
$811$	−14.8648	+	3.27200i	−0.521975	+	0.114895i	−0.468140	−	0.883655i	$-0.655076\pi$
$811$	−14.8648	+	3.27200i	−0.521975	+	0.114895i	−0.0538350	+	0.998550i	$0.517145\pi$
$812$	−27.7943	+	1.00410i	−0.975389	+	0.0352369i
$813$	−7.42716	+	32.9072i	−0.260482	+	1.15410i
$814$	3.87425	+	30.4907i	0.135792	+	1.06870i
$815$	4.92801	−	54.4401i	0.172621	−	1.90695i
$816$	12.5345	−	41.3689i	0.438797	−	1.44820i
$817$	−37.5044	+	30.7083i	−1.31211	+	1.07435i
$818$	−22.9053	−	7.71769i	−0.800865	−	0.269843i
$819$	−8.66110	+	15.9248i	−0.302643	+	0.556459i
$820$	−0.986151	+	0.934132i	−0.0344379	+	0.0326213i
$821$	−1.79164	+	14.1004i	−0.0625288	+	0.492108i	0.929761	+	0.368165i	$0.120014\pi$
$821$	−1.79164	+	14.1004i	−0.0625288	+	0.492108i	−0.992289	+	0.123943i	$0.960446\pi$
$822$	10.0740	−	9.78905i	0.351373	−	0.341432i
$823$	12.7780	+	35.7757i	0.445412	+	1.24706i	0.928449	+	0.371461i	$0.121143\pi$
$823$	12.7780	+	35.7757i	0.445412	+	1.24706i	−0.483037	+	0.875600i	$0.660466\pi$
$824$	−2.61414	+	3.57087i	−0.0910680	+	0.124397i
$825$	2.16334	−	3.27986i	0.0753179	−	0.114190i
$826$	−34.5065	−	15.0075i	−1.20063	−	0.522177i
$827$	26.9823			0.938265			0.469133	−	0.883128i	$-0.344567\pi$
$827$	26.9823			0.938265			0.469133	+	0.883128i	$0.344567\pi$
$828$	2.55459	+	8.36790i	0.0887783	+	0.290805i
$829$	0.0857939	−	0.101004i	0.00297975	−	0.00350803i	−0.760670	−	0.649139i	$-0.775130\pi$
$829$	0.0857939	−	0.101004i	0.00297975	−	0.00350803i	0.763650	+	0.645631i	$0.223405\pi$
$830$	13.7916	+	43.5130i	0.478714	+	1.51036i
$831$	−4.33959	+	23.0778i	−0.150539	+	0.800562i
$832$	−0.416320	−	1.74102i	−0.0144333	−	0.0603589i
$833$	2.94109	+	3.72730i	0.101903	+	0.129143i
$834$	−0.955568	−	0.386636i	−0.0330886	−	0.0133881i
$835$	9.24271	−	7.56785i	0.319857	−	0.261896i
$836$	11.7733	+	11.1523i	0.407188	+	0.385709i
$837$	6.18581	−	22.4619i	0.213813	−	0.776396i
$838$	45.5008	−	34.5888i	1.57180	−	1.19485i
$839$	−5.25593	+	1.98497i	−0.181455	+	0.0685286i	−0.442368	−	0.896834i	$-0.645861\pi$
$839$	−5.25593	+	1.98497i	−0.181455	+	0.0685286i	0.260913	+	0.965362i	$0.415976\pi$
$840$	−10.4863	+	17.2203i	−0.361811	+	0.594157i
$841$	−19.5871	+	61.7981i	−0.675418	+	2.13097i
$842$	−39.0852	+	27.5434i	−1.34696	+	0.949208i
$843$	−4.10356	+	4.60831i	−0.141334	+	0.158719i
$844$	−3.77868	+	2.46361i	−0.130067	+	0.0848011i
$845$	11.4202	+	16.8435i	0.392866	+	0.579434i
$846$	14.9081	−	0.919228i	0.512552	−	0.0316037i
$847$	−5.29904	−	9.99506i	−0.182077	−	0.343434i
$848$	−34.5369	−	30.4262i	−1.18600	−	1.04484i
$849$	−0.0844698	−	0.0625310i	−0.00289900	−	0.00214606i
$850$	−0.134354	−	7.44051i	−0.00460830	−	0.255207i
$851$	18.5589	+	4.79370i	0.636191	+	0.164326i
$852$	−9.27565	−	10.6424i	−0.317779	−	0.364604i
$853$	−0.361359	+	20.0120i	−0.0123727	+	0.685199i	0.933122	+	0.359561i	$0.117073\pi$
$853$	−0.361359	+	20.0120i	−0.0123727	+	0.685199i	−0.945494	+	0.325638i	$0.894421\pi$
$854$	13.0289	−	19.2162i	0.445841	−	0.657566i
$855$	−22.2744	+	37.6496i	−0.761767	+	1.28759i
$856$	27.8227	−	3.02590i	0.950961	−	0.103423i
$857$	−23.9882	−	1.73546i	−0.819421	−	0.0592821i	−0.343922	−	0.938998i	$-0.611756\pi$
$857$	−23.9882	−	1.73546i	−0.819421	−	0.0592821i	−0.475499	+	0.879716i	$0.657733\pi$
$858$	−1.32043	+	16.9948i	−0.0450786	+	0.580194i
$859$	35.0242	+	35.6624i	1.19501	+	1.21678i	0.970180	+	0.242387i	$0.0779305\pi$
$859$	35.0242	+	35.6624i	1.19501	+	1.21678i	0.224832	+	0.974398i	$0.427817\pi$
$860$	19.1990	+	4.95904i	0.654681	+	0.169102i
$861$	2.38494	−	1.24821i	0.0812786	−	0.0425389i
$862$	−10.5213	+	5.33699i	−0.358358	+	0.181778i
$863$	33.0221	−	11.1264i	1.12409	−	0.378748i	0.304961	−	0.952365i	$-0.401356\pi$
$863$	33.0221	−	11.1264i	1.12409	−	0.378748i	0.819124	+	0.573616i	$0.194460\pi$
$864$	26.7802	+	5.83592i	0.911079	+	0.198542i
$865$	−8.59890	−	10.1234i	−0.292372	−	0.344206i
$866$	−21.5586	+	44.4731i	−0.732591	+	1.51126i
$867$	0.0729408	−	13.7119i	0.00247720	−	0.465680i
$868$	12.7399	+	1.85306i	0.432419	+	0.0628971i
$869$	0.181733	−	0.128067i	0.00616486	−	0.00434438i
$870$	−44.4026	−	54.8217i	−1.50539	−	1.85863i
$871$	26.5284	−	0.958365i	0.898881	−	0.0324730i
$872$	0.261153	−	1.59296i	0.00884376	−	0.0539445i
$873$	−10.6545	−	6.04646i	−0.360600	−	0.204642i
$874$	27.2068	−	12.5872i	0.920283	−	0.425768i
$875$	6.57417	−	27.4927i	0.222247	−	0.929423i
$876$	−0.506570	−	0.226577i	−0.0171154	−	0.00765534i
$877$	29.9170	−	26.3562i	1.01022	−	0.889985i	0.0162800	−	0.999867i	$-0.494818\pi$
$877$	29.9170	−	26.3562i	1.01022	−	0.889985i	0.993945	+	0.109883i	$0.0350476\pi$
$878$	−39.5837	−	50.1651i	−1.33589	−	1.69299i
$879$	4.89129	+	27.6270i	0.164979	+	0.931835i
$880$	−4.03218	+	31.7336i	−0.135925	+	1.06974i
$881$	−4.95373	−	1.09040i	−0.166895	−	0.0367365i	0.130737	−	0.991417i	$-0.458266\pi$
$881$	−4.95373	−	1.09040i	−0.166895	−	0.0367365i	−0.297632	+	0.954681i	$0.596197\pi$
$882$	−3.63515	+	3.37075i	−0.122402	+	0.113499i
$883$	−26.8722	−	2.92253i	−0.904323	−	0.0983510i	−0.355873	−	0.934534i	$-0.615816\pi$
$883$	−26.8722	−	2.92253i	−0.904323	−	0.0983510i	−0.548450	+	0.836183i	$0.684782\pi$
$884$	5.44603	+	9.43280i	0.183170	+	0.317259i
$885$	−7.47969	−	31.3200i	−0.251427	−	1.05281i
$886$	−21.9393	+	38.0001i	−0.737067	+	1.27664i
$887$	−21.8533	+	29.8512i	−0.733763	+	1.00231i	0.265507	+	0.964109i	$0.414461\pi$
$887$	−21.8533	+	29.8512i	−0.733763	+	1.00231i	−0.999270	+	0.0381978i	$0.987838\pi$
$888$	13.6726	−	14.2811i	0.458822	−	0.479241i
$889$	13.7007	+	43.2262i	0.459507	+	1.44976i
$890$	49.9642	+	37.9818i	1.67480	+	1.27315i
$891$	20.5655	+	11.9620i	0.688971	+	0.400743i
$892$	−5.61893	+	14.1024i	−0.188136	+	0.472185i
$893$	−3.40652	−	16.9260i	−0.113995	−	0.566407i
$894$	−5.22214	−	50.5154i	−0.174655	−	1.68949i
$895$	7.07000	−	2.10117i	0.236324	−	0.0702345i
$896$	3.05077	−	33.7020i	0.101919	−	1.12591i
$897$	9.54105	+	4.68792i	0.318566	+	0.156525i
$898$	−5.23537	+	1.97720i	−0.174706	+	0.0659800i
$899$	20.3436	−	38.3722i	0.678498	−	1.27978i
$900$	2.60888	−	0.255680i	0.0869626	−	0.00852266i
$901$	−41.7068	−	19.2956i	−1.38945	−	0.642830i
$902$	1.56795	−	1.98709i	0.0522071	−	0.0661630i
$903$	−33.9259	−	19.8285i	−1.12898	−	0.659851i
$904$	18.3164	−	1.32513i	0.609195	−	0.0440731i
$905$	46.4846	−	8.48526i	1.54520	−	0.282060i
$906$	−55.8706	−	5.35728i	−1.85618	−	0.177984i
$907$	−28.0164	−	24.6818i	−0.930271	−	0.819547i	0.0535751	−	0.998564i	$-0.482938\pi$
$907$	−28.0164	−	24.6818i	−0.930271	−	0.819547i	−0.983846	+	0.179016i	$0.942708\pi$
$908$	1.32233	−	24.3890i	0.0438831	−	0.809376i
$909$	−5.37094	−	3.87107i	−0.178143	−	0.128395i
$910$	−6.79751	−	24.4824i	−0.225335	−	0.811584i
$911$	18.3900	−	4.75009i	0.609289	−	0.157377i	0.0672581	−	0.997736i	$-0.478575\pi$
$911$	18.3900	−	4.75009i	0.609289	−	0.157377i	0.542031	+	0.840358i	$0.317655\pi$
$912$	4.04130	−	52.0144i	0.133821	−	1.72237i
$913$	−12.5175	−	25.8223i	−0.414269	−	0.854593i
$914$	23.3883	−	53.0457i	0.773617	−	1.75460i
$915$	19.8440	−	0.970069i	0.656022	−	0.0320695i
$916$	−9.76350	−	0.706353i	−0.322595	−	0.0233386i
$917$	−10.1567	−	6.11106i	−0.335402	−	0.201805i
$918$	44.9371	−	3.34576i	1.48314	−	0.110426i
$919$	−12.7409	−	45.8887i	−0.420285	−	1.51373i	−0.806451	−	0.591301i	$-0.798615\pi$
$919$	−12.7409	−	45.8887i	−0.420285	−	1.51373i	0.386166	−	0.922429i	$-0.373799\pi$
$920$	10.3444	+	5.72587i	0.341046	+	0.188776i
$921$	1.21149	−	10.6139i	0.0399199	−	0.349738i
$922$	−0.523770	+	2.60246i	−0.0172494	+	0.0857074i
$923$	−17.1419	−	0.619267i	−0.564231	−	0.0203834i
$924$	−5.15015	+	12.0958i	−0.169427	+	0.397921i
$925$	2.50514	−	5.16784i	0.0823685	−	0.169917i
$926$	3.14010	+	57.9158i	0.103190	+	1.90323i
$927$	−7.51556	−	2.02677i	−0.246843	−	0.0665680i
$928$	46.3719	+	21.4539i	1.52223	+	0.704259i
$929$	−16.5326	−	18.0968i	−0.542417	−	0.593736i	0.404769	−	0.914419i	$-0.367352\pi$
$929$	−16.5326	−	18.0968i	−0.542417	−	0.593736i	−0.947186	+	0.320683i	$0.896087\pi$
$930$	15.6623	+	28.6544i	0.513587	+	0.939613i
$931$	4.43379	+	3.63035i	0.145312	+	0.118980i
$932$	2.55304	+	20.0926i	0.0836275	+	0.658157i
$933$	7.58502	−	50.2684i	0.248322	−	1.64571i
$934$	−6.14543	+	25.6998i	−0.201085	+	0.840922i
$935$	5.16692	+	31.5168i	0.168976	+	1.03071i
$936$	9.02963	−	6.22049i	0.295143	−	0.203323i
$937$	5.38792	−	13.5227i	0.176016	−	0.441766i	−0.814327	−	0.580406i	$-0.802894\pi$
$937$	5.38792	−	13.5227i	0.176016	−	0.441766i	0.990343	+	0.138640i	$0.0442731\pi$
$938$	58.1704	+	17.2880i	1.89933	+	0.564473i
$939$	−0.874788	+	4.65211i	−0.0285476	+	0.151816i
$940$	−4.76380	+	5.21451i	−0.155378	+	0.170079i
$941$	7.74730	+	21.6908i	0.252555	+	0.707101i	0.999126	+	0.0417955i	$0.0133078\pi$
$941$	7.74730	+	21.6908i	0.252555	+	0.707101i	−0.746571	+	0.665305i	$0.768301\pi$
$942$	49.2358	+	8.34099i	1.60419	+	0.271764i
$943$	−0.789277	−	1.36707i	−0.0257024	−	0.0445179i
$944$	24.4783	+	29.5908i	0.796700	+	0.963100i
$945$	−34.8999	−	6.29502i	−1.13529	−	0.204777i
$946$	−36.7340	−	3.99507i	−1.19433	−	0.129891i
$947$	−5.89408	−	1.07590i	−0.191532	−	0.0349621i	0.0829531	−	0.996553i	$-0.473565\pi$
$947$	−5.89408	−	1.07590i	−0.191532	−	0.0349621i	−0.274485	+	0.961591i	$0.588507\pi$
$948$	0.142710	+	0.0404420i	0.00463499	+	0.00131350i
$949$	−0.621767	+	0.260839i	−0.0201834	+	0.00846718i
$950$	−2.08885	−	8.73541i	−0.0677711	−	0.283414i
$951$	26.6208	−	2.26706i	0.863239	−	0.0735144i
$952$	−4.73664	−	23.5350i	−0.153515	−	0.762773i
$953$	−4.22329	−	25.7610i	−0.136806	−	0.834479i	−0.962684	−	0.270630i	$-0.912768\pi$
$953$	−4.22329	−	25.7610i	−0.136806	−	0.834479i	0.825878	−	0.563849i	$-0.190680\pi$
$954$	16.6190	−	45.0120i	0.538059	−	1.45732i
$955$	22.1908	−	10.2666i	0.718077	−	0.332218i
$956$	−17.8725	−	7.49773i	−0.578038	−	0.242494i
$957$	32.5845	+	30.0877i	1.05331	+	0.972596i
$958$	6.81968	+	10.8846i	0.220334	+	0.351665i
$959$	3.97706	−	12.5478i	0.128426	−	0.405189i
$960$	2.97744	−	1.84351i	0.0960964	−	0.0594992i
$961$	6.74971	−	8.55402i	0.217732	−	0.275936i
$962$	1.34892	+	24.8793i	0.0434908	+	0.802140i
$963$	22.5941	+	43.7350i	0.728084	+	1.40934i
$964$	11.2386	+	13.2311i	0.361971	+	0.426145i
$965$	25.6505	−	40.9396i	0.825717	−	1.31789i
$966$	17.2477	+	17.1203i	0.554935	+	0.550835i
$967$	7.46629	+	4.86786i	0.240100	+	0.156540i	0.660565	−	0.750769i	$-0.270317\pi$
$967$	7.46629	+	4.86786i	0.240100	+	0.156540i	−0.420465	+	0.907309i	$0.638133\pi$
$968$	0.123541	+	6.84167i	0.00397075	+	0.219900i
$969$	−10.9265	−	50.9287i	−0.351011	−	1.63607i
$970$	16.6253	−	4.29426i	0.533806	−	0.137880i
$971$	−18.7269	−	11.2676i	−0.600974	−	0.361594i	0.182326	−	0.983238i	$-0.441637\pi$
$971$	−18.7269	−	11.2676i	−0.600974	−	0.361594i	−0.783300	+	0.621644i	$0.786465\pi$
$972$	2.43408	+	15.6853i	0.0780731	+	0.503107i
$973$	−0.960302	+	0.104439i	−0.0307859	+	0.00334816i
$974$	−22.4320	−	30.6418i	−0.718769	−	0.981825i
$975$	1.94098	−	2.52532i	0.0621611	−	0.0808749i
$976$	−20.7306	+	11.4749i	−0.663571	+	0.367302i
$977$	−37.6644	−	38.3507i	−1.20499	−	1.22695i	−0.966745	−	0.255743i	$-0.917680\pi$
$977$	−37.6644	−	38.3507i	−1.20499	−	1.22695i	−0.238247	−	0.971205i	$-0.576573\pi$
$978$	−50.4172	+	45.5698i	−1.61216	+	1.45716i
$979$	−34.5207	−	19.1080i	−1.10328	−	0.610693i
$980$	0.126913	−	2.34077i	0.00405408	−	0.0747731i
$981$	2.77925	−	0.580829i	0.0887346	−	0.0185445i
$982$	11.6071	+	21.8933i	0.370397	+	0.698642i
$983$	12.1663	−	34.0631i	0.388044	−	1.08644i	−0.575246	−	0.817981i	$-0.695094\pi$
$983$	12.1663	−	34.0631i	0.388044	−	1.08644i	0.963290	−	0.268463i	$-0.0865156\pi$
$984$	−1.62807	+	0.0207357i	−0.0519010	+	0.000661029i
$985$	−39.0206	−	19.7933i	−1.24330	−	0.630668i
$986$	83.1272	+	12.0912i	2.64731	+	0.385062i
$987$	11.9003	−	7.36817i	0.378789	−	0.234532i
$988$	8.86672	+	9.70561i	0.282088	+	0.308776i
$989$	−10.7939	+	20.3595i	−0.343226	+	0.647393i
$990$	−32.3742	+	7.99573i	−1.02892	+	0.254121i
$991$	1.03436	−	0.786301i	0.0328576	−	0.0249777i	−0.588617	−	0.808412i	$-0.700327\pi$
$991$	1.03436	−	0.786301i	0.0328576	−	0.0249777i	0.621474	+	0.783435i	$0.286534\pi$
$992$	−19.3326	−	13.6237i	−0.613811	−	0.432553i
$993$	−6.09415	+	20.1131i	−0.193392	+	0.638269i
$994$	−36.6839	−	13.8541i	−1.16354	−	0.439426i
$995$	−17.3484	+	15.2836i	−0.549982	+	0.484522i
$996$	8.13131	−	17.3330i	0.257650	−	0.549217i
$997$	26.3221	+	7.82283i	0.833630	+	0.247751i	0.673354	−	0.739321i	$-0.264853\pi$
$997$	26.3221	+	7.82283i	0.833630	+	0.247751i	0.160277	+	0.987072i	$0.448761\pi$
$998$	−3.35024	−	2.54679i	−0.106050	−	0.0806171i
$999$	32.0960	+	13.3856i	1.01547	+	0.423501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.m.a.4.15	✓	3248
9.7	even	3	inner	531.2.m.a.358.15	yes	3248
59.15	even	29	inner	531.2.m.a.310.15	yes	3248
531.133	even	87	inner	531.2.m.a.133.15	yes	3248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
531.2.m.a.4.15	✓	3248	1.1	even	1	trivial
531.2.m.a.133.15	yes	3248	531.133	even	87	inner
531.2.m.a.310.15	yes	3248	59.15	even	29	inner
531.2.m.a.358.15	yes	3248	9.7	even	3	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.m (of order \(87\), degree \(56\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.700893 - 1.58966i) q^{2} +(-1.19780 + 1.25111i) q^{3} +(-0.686795 + 0.751772i) q^{4} +(-2.23191 + 0.936314i) q^{5} +(2.82836 + 1.02720i) q^{6} +(2.79042 - 0.405878i) q^{7} +(-1.61631 - 0.544599i) q^{8} +(-0.130538 - 2.99716i) q^{9} +(3.05275 + 2.89172i) q^{10} +(-2.16085 - 1.52275i) q^{11} +(-0.117904 - 1.75973i) q^{12} +(-1.65804 - 1.35759i) q^{13} +(-2.60099 - 4.15133i) q^{14} +(1.50196 - 3.91388i) q^{15} +(0.450735 + 4.97931i) q^{16} +(1.84760 + 4.63714i) q^{17} +(-4.67296 + 2.30820i) q^{18} +(3.38093 + 4.98651i) q^{19} +(0.828971 - 2.32095i) q^{20} +(-2.83457 + 3.97727i) q^{21} +(-0.906129 + 4.50229i) q^{22} +(2.39921 + 1.56423i) q^{23} +(2.61737 - 1.36986i) q^{24} +(0.601283 - 0.612239i) q^{25} +(-0.995990 + 3.58723i) q^{26} +(3.90613 + 3.42669i) q^{27} +(-1.61132 + 2.37651i) q^{28} +(5.72183 + 7.81592i) q^{29} +(-7.27444 + 0.355610i) q^{30} +(-1.95582 - 4.03465i) q^{31} +(4.61498 - 2.55450i) q^{32} +(4.49339 - 0.879494i) q^{33} +(6.07648 - 6.18719i) q^{34} +(-5.84795 + 3.51859i) q^{35} +(2.34283 + 1.96030i) q^{36} +(6.34219 - 2.13693i) q^{37} +(5.55715 - 8.86953i) q^{38} +(3.68449 - 0.448260i) q^{39} +(4.11738 - 0.297878i) q^{40} +(-0.491532 - 0.249331i) q^{41} +(8.30923 + 1.71835i) q^{42} +(0.725349 + 8.01299i) q^{43} +(2.62882 - 0.578647i) q^{44} +(3.09763 + 6.56718i) q^{45} +(0.804999 - 4.91028i) q^{46} +(-2.64269 - 1.10864i) q^{47} +(-6.76954 - 5.40031i) q^{48} +(0.911757 - 0.270970i) q^{49} +(-1.39468 - 0.526720i) q^{50} +(-8.01462 - 3.24282i) q^{51} +(2.15933 - 0.314083i) q^{52} +(-6.68363 + 6.33107i) q^{53} +(2.70948 - 8.61114i) q^{54} +(6.24860 + 1.37542i) q^{55} +(-4.73123 - 0.863634i) q^{56} +(-10.2883 - 1.74294i) q^{57} +(8.41423 - 14.5739i) q^{58} +(6.33585 - 4.34247i) q^{59} +(1.91081 + 3.81717i) q^{60} +(1.91197 + 4.33643i) q^{61} +(-5.04289 + 5.93695i) q^{62} +(-1.58074 - 8.31034i) q^{63} +(0.665020 + 0.505535i) q^{64} +(4.97173 + 1.47758i) q^{65} +(-4.54748 - 6.52652i) q^{66} +(-9.29504 + 8.18872i) q^{67} +(-4.75500 - 1.79578i) q^{68} +(-4.83080 + 1.12803i) q^{69} +(9.69214 + 6.83006i) q^{70} +(6.37233 - 4.84412i) q^{71} +(-1.42126 + 4.91543i) q^{72} +(0.147383 - 0.277994i) q^{73} +(-7.84219 - 8.58414i) q^{74} +(0.0457576 + 1.48561i) q^{75} +(-6.07073 - 0.883011i) q^{76} +(-6.64772 - 3.37208i) q^{77} +(-3.29501 - 5.54289i) q^{78} +(-0.0282886 + 0.0792022i) q^{79} +(-5.66820 - 10.6914i) q^{80} +(-8.96592 + 0.782486i) q^{81} +(-0.0518394 + 0.956122i) q^{82} +(9.49758 + 5.25712i) q^{83} +(-1.04323 - 4.86252i) q^{84} +(-8.46551 - 8.61975i) q^{85} +(12.2295 - 6.76930i) q^{86} +(-16.6322 - 2.20330i) q^{87} +(2.66331 + 3.63804i) q^{88} +(14.8383 - 1.61376i) q^{89} +(8.26844 - 9.52706i) q^{90} +(-5.17763 - 3.11528i) q^{91} +(-2.82371 + 0.729355i) q^{92} +(7.39048 + 2.38578i) q^{93} +(0.0898883 + 4.97800i) q^{94} +(-12.2149 - 7.96384i) q^{95} +(-2.33189 + 8.83362i) q^{96} +(2.16811 - 3.46043i) q^{97} +(-1.06979 - 1.25946i) q^{98} +(-4.28186 + 6.67518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3248 q - 29 q^{2} - 58 q^{3} + 29 q^{4} - 25 q^{5} - 66 q^{6} - 27 q^{7} - 116 q^{8} - 62 q^{9} - 116 q^{10} - 33 q^{11} - 58 q^{12} - 27 q^{13} - 33 q^{14} - 51 q^{15} + 29 q^{16} - 126 q^{17} - 78 q^{18}+ \cdots - 86 q^{99}+O(q^{100}) \) 3248 * q - 29 * q^2 - 58 * q^3 + 29 * q^4 - 25 * q^5 - 66 * q^6 - 27 * q^7 - 116 * q^8 - 62 * q^9 - 116 * q^10 - 33 * q^11 - 58 * q^12 - 27 * q^13 - 33 * q^14 - 51 * q^15 + 29 * q^16 - 126 * q^17 - 78 * q^18 - 120 * q^19 - 31 * q^20 - 60 * q^21 - 29 * q^22 - 29 * q^23 - 16 * q^24 + 29 * q^25 - 92 * q^26 - 55 * q^27 - 132 * q^28 - 27 * q^29 - 64 * q^30 - 21 * q^31 - 49 * q^32 - 32 * q^33 - 17 * q^34 - 136 * q^35 - 70 * q^36 - 120 * q^37 - 33 * q^38 - 80 * q^39 - 17 * q^40 - 17 * q^41 - 68 * q^42 - 21 * q^43 - 104 * q^44 - 58 * q^45 - 116 * q^46 - 17 * q^47 + 106 * q^48 + 19 * q^49 - 5 * q^50 - 250 * q^51 - 21 * q^52 - 108 * q^53 + 175 * q^54 - 116 * q^55 - q^56 + 63 * q^57 - 58 * q^58 - 17 * q^59 - 816 * q^60 - 27 * q^61 - 128 * q^62 + 95 * q^63 - 256 * q^64 - 59 * q^65 + 67 * q^66 - 15 * q^67 - 43 * q^68 - 302 * q^69 - 41 * q^70 - 134 * q^71 + 210 * q^72 - 144 * q^73 - 51 * q^74 - 47 * q^75 - 9 * q^76 - 85 * q^77 + 36 * q^78 - 39 * q^79 - 128 * q^80 - 22 * q^81 - 164 * q^82 - 35 * q^83 - 190 * q^84 - 17 * q^85 + 31 * q^86 - 75 * q^87 - 29 * q^88 - 36 * q^89 - 86 * q^90 - 136 * q^91 - 31 * q^92 - 41 * q^94 - 13 * q^95 - 30 * q^96 - 3 * q^97 - 156 * q^98 - 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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