LMFDB - Embedded newform 361.2.i.a.7.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(7,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(114)) chi = DirichletCharacter(H, H._module([50])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.i (of order $57$, degree $36$, 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$1080$
Relative dimension:	$30$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			7.8
Character	$\chi$	$=$	361.7
Dual form			361.2.i.a.258.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.301334 - 1.54266i) q^{2} +(-1.89976 + 0.210265i) q^{3} +(-0.436011 + 0.177092i) q^{4} +(-1.83532 + 1.78542i) q^{5} +(0.896828 + 2.86732i) q^{6} +(-0.330256 + 0.257049i) q^{7} +(-1.31482 - 2.01249i) q^{8} +(0.637470 - 0.142860i) q^{9} +(3.30734 + 2.29326i) q^{10} +(1.86914 - 2.03043i) q^{11} +(0.791078 - 0.428110i) q^{12} +(2.90641 + 3.95431i) q^{13} +(0.496056 + 0.432016i) q^{14} +(3.11124 - 3.77777i) q^{15} +(-3.38303 + 3.29106i) q^{16} +(6.70886 + 2.72490i) q^{17} +(-0.412476 - 0.940352i) q^{18} +(2.22135 + 3.75041i) q^{19} +(0.484033 - 1.10348i) q^{20} +(0.573358 - 0.557771i) q^{21} +(-3.69549 - 2.27161i) q^{22} +(4.00205 + 0.442946i) q^{23} +(2.92100 + 3.54678i) q^{24} +(0.0428780 - 1.55553i) q^{25} +(5.22436 - 5.67517i) q^{26} +(4.24238 - 1.45641i) q^{27} +(0.0984740 - 0.170562i) q^{28} +(-0.929559 - 6.70349i) q^{29} +(-6.76534 - 3.66122i) q^{30} +(-9.68378 + 3.32445i) q^{31} +(2.14541 + 1.48760i) q^{32} +(-3.12398 + 4.25033i) q^{33} +(2.18199 - 11.1706i) q^{34} +(0.147184 - 1.06141i) q^{35} +(-0.252645 + 0.175180i) q^{36} +(-1.45004 + 1.57516i) q^{37} +(5.11624 - 4.55692i) q^{38} +(-6.35292 - 6.90111i) q^{39} +(6.00626 + 1.34604i) q^{40} +(0.834318 + 2.22836i) q^{41} +(-1.03322 - 0.716421i) q^{42} +(1.54512 - 1.07136i) q^{43} +(-0.455392 + 1.21630i) q^{44} +(-0.914893 + 1.40035i) q^{45} +(-0.522635 - 6.30727i) q^{46} +(1.82260 + 5.82717i) q^{47} +(5.73493 - 6.96354i) q^{48} +(-1.67540 + 6.61602i) q^{49} +(-2.41258 + 0.402588i) q^{50} +(-13.3181 - 3.76601i) q^{51} +(-1.96750 - 1.20942i) q^{52} +(3.37567 + 10.7926i) q^{53} +(-3.52512 - 6.10569i) q^{54} +(0.194709 + 7.06368i) q^{55} +(0.951537 + 0.326663i) q^{56} +(-5.00861 - 6.65779i) q^{57} +(-10.0611 + 3.45398i) q^{58} +(-4.69699 - 12.5451i) q^{59} +(-0.687521 + 2.19813i) q^{60} +(3.48584 + 6.88820i) q^{61} +(8.04654 + 13.9370i) q^{62} +(-0.173806 + 0.211042i) q^{63} +(-2.14342 + 4.88651i) q^{64} +(-12.3943 - 2.06824i) q^{65} +(7.49817 + 3.53847i) q^{66} +(9.70593 - 0.535491i) q^{67} -3.40769 q^{68} -7.69604 q^{69} +(-1.68175 + 0.0927848i) q^{70} +(-3.75087 + 7.41193i) q^{71} +(-1.12567 - 1.09507i) q^{72} +(-0.116234 - 0.0472103i) q^{73} +(2.86689 + 1.76227i) q^{74} +(0.245616 + 2.96415i) q^{75} +(-1.63270 - 1.24184i) q^{76} +(-0.0953763 + 1.15102i) q^{77} +(-8.73172 + 11.8799i) q^{78} +(9.17460 - 6.36153i) q^{79} +(0.332990 - 12.0803i) q^{80} +(-9.52566 + 4.49527i) q^{81} +(3.18620 - 1.95855i) q^{82} +(2.23333 - 8.81923i) q^{83} +(-0.151213 + 0.344732i) q^{84} +(-17.1780 + 6.97709i) q^{85} +(-2.11835 - 2.06076i) q^{86} +(3.17544 + 12.5395i) q^{87} +(-6.54380 - 1.09197i) q^{88} +(-7.22359 + 2.93397i) q^{89} +(2.43595 + 0.989398i) q^{90} +(-1.97631 - 0.558847i) q^{91} +(-1.82338 + 0.515602i) q^{92} +(17.6978 - 8.35179i) q^{93} +(8.44014 - 4.56757i) q^{94} +(-10.7730 - 2.91714i) q^{95} +(-4.38855 - 2.37497i) q^{96} +(5.04975 + 0.278602i) q^{97} +(10.7111 + 0.590949i) q^{98} +(0.901453 - 1.56136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1080 q - 38 q^{2} - 19 q^{3} - 8 q^{4} - 37 q^{5} - 38 q^{6} - 40 q^{7} - 38 q^{8} + 49 q^{9} + 19 q^{10} - 40 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} - 8 q^{16} - 94 q^{17} - 38 q^{18} - 38 q^{19} - 46 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) $ 1080 * q - 38 * q^2 - 19 * q^3 - 8 * q^4 - 37 * q^5 - 38 * q^6 - 40 * q^7 - 38 * q^8 + 49 * q^9 + 19 * q^10 - 40 * q^11 - 38 * q^12 - 38 * q^13 - 38 * q^15 - 8 * q^16 - 94 * q^17 - 38 * q^18 - 38 * q^19 - 46 * q^20 - 38 * q^21 - 19 * q^22 - 34 * q^23 - 30 * q^24 - 7 * q^25 + 41 * q^26 - 76 * q^27 - 15 * q^28 + 60 * q^30 - 38 * q^31 - 38 * q^32 - 114 * q^33 - 38 * q^34 - 33 * q^35 - 38 * q^37 - 76 * q^38 + 26 * q^39 - 38 * q^40 - 38 * q^41 - 32 * q^42 + 43 * q^43 - 26 * q^44 + 47 * q^45 + 26 * q^47 - 456 * q^48 - 32 * q^49 + 38 * q^50 + 38 * q^51 - 38 * q^52 - 38 * q^53 - 214 * q^54 - 29 * q^55 + 304 * q^56 - 38 * q^57 - 46 * q^58 - 38 * q^59 - 33 * q^61 - 13 * q^62 + 68 * q^63 - 110 * q^64 + 38 * q^65 - 26 * q^66 - 38 * q^67 - 96 * q^68 - 228 * q^69 - 342 * q^70 - 38 * q^71 - 38 * q^72 - 29 * q^73 + 50 * q^74 + 190 * q^75 + 323 * q^76 - 60 * q^77 + 228 * q^78 - 38 * q^79 + 322 * q^80 + 129 * q^81 + 48 * q^82 - 35 * q^83 + 19 * q^84 - 23 * q^85 - 684 * q^86 + 37 * q^87 - 38 * q^88 + 76 * q^89 - 722 * q^90 - 114 * q^91 - 22 * q^92 - 30 * q^93 + 228 * q^94 - 152 * q^95 + 142 * q^96 + 19 * q^97 + 57 * q^98 + 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{57}\right)$

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 $

$2$	−0.301334	−	1.54266i	−0.213075	−	1.09083i	−0.922486	−	0.386031i	$-0.873846\pi$
$2$	−0.301334	−	1.54266i	−0.213075	−	1.09083i	0.709411	−	0.704795i	$-0.248961\pi$
$3$	−1.89976	+	0.210265i	−1.09682	+	0.121396i	−0.640159	−	0.768242i	$-0.721132\pi$
$3$	−1.89976	+	0.210265i	−1.09682	+	0.121396i	−0.456665	+	0.889639i	$0.650956\pi$
$4$	−0.436011	+	0.177092i	−0.218006	+	0.0885462i
$5$	−1.83532	+	1.78542i	−0.820778	+	0.798466i	−0.982085	−	0.188439i	$-0.939657\pi$
$5$	−1.83532	+	1.78542i	−0.820778	+	0.798466i	0.161306	+	0.986904i	$0.448429\pi$
$6$	0.896828	+	2.86732i	0.366128	+	1.17058i
$7$	−0.330256	+	0.257049i	−0.124825	+	0.0971553i	−0.674701	−	0.738091i	$-0.735728\pi$
$7$	−0.330256	+	0.257049i	−0.124825	+	0.0971553i	0.549876	+	0.835246i	$0.314675\pi$
$8$	−1.31482	−	2.01249i	−0.464861	−	0.711522i
$9$	0.637470	−	0.142860i	0.212490	−	0.0476201i
$10$	3.30734	+	2.29326i	1.04587	+	0.725193i
$11$	1.86914	−	2.03043i	0.563567	−	0.612196i	−0.387241	−	0.921979i	$-0.626572\pi$
$11$	1.86914	−	2.03043i	0.563567	−	0.612196i	0.950808	+	0.309782i	$0.100256\pi$
$12$	0.791078	−	0.428110i	0.228365	−	0.123585i
$13$	2.90641	+	3.95431i	0.806093	+	1.09673i	0.993431	+	0.114433i	$0.0365052\pi$
$13$	2.90641	+	3.95431i	0.806093	+	1.09673i	−0.187338	+	0.982295i	$0.559986\pi$
$14$	0.496056	+	0.432016i	0.132577	+	0.115461i
$15$	3.11124	−	3.77777i	0.803319	−	0.975416i
$16$	−3.38303	+	3.29106i	−0.845757	+	0.822765i
$17$	6.70886	+	2.72490i	1.62714	+	0.660886i	0.993613	−	0.112838i	$-0.0359942\pi$
$17$	6.70886	+	2.72490i	1.62714	+	0.660886i	0.633523	+	0.773724i	$0.281608\pi$
$18$	−0.412476	−	0.940352i	−0.0972216	−	0.221643i
$19$	2.22135	+	3.75041i	0.509613	+	0.860403i
$19$	2.22135	+	3.75041i	0.509613	+	0.860403i
$20$	0.484033	−	1.10348i	0.108233	−	0.246747i
$21$	0.573358	−	0.557771i	0.125117	−	0.121716i
$22$	−3.69549	−	2.27161i	−0.787882	−	0.484309i
$23$	4.00205	+	0.442946i	0.834484	+	0.0923607i	0.517088	−	0.855932i	$-0.327016\pi$
$23$	4.00205	+	0.442946i	0.834484	+	0.0923607i	0.317396	+	0.948293i	$0.397191\pi$
$24$	2.92100	+	3.54678i	0.596247	+	0.723983i
$25$	0.0428780	−	1.55553i	0.00857559	−	0.311107i
$26$	5.22436	−	5.67517i	1.02458	−	1.11299i
$27$	4.24238	−	1.45641i	0.816447	−	0.280287i
$28$	0.0984740	−	0.170562i	0.0186098	−	0.0322332i
$29$	−0.929559	−	6.70349i	−0.172615	−	1.24481i	−0.856858	−	0.515553i	$-0.827586\pi$
$29$	−0.929559	−	6.70349i	−0.172615	−	1.24481i	0.684243	−	0.729254i	$-0.260133\pi$
$30$	−6.76534	−	3.66122i	−1.23518	−	0.668444i
$31$	−9.68378	+	3.32445i	−1.73926	+	0.597088i	−0.997305	−	0.0733638i	$-0.976627\pi$
$31$	−9.68378	+	3.32445i	−1.73926	+	0.597088i	−0.741953	+	0.670452i	$0.766100\pi$
$32$	2.14541	+	1.48760i	0.379259	+	0.262973i
$33$	−3.12398	+	4.25033i	−0.543815	+	0.739887i
$34$	2.18199	−	11.1706i	0.374209	−	1.91574i
$35$	0.147184	−	1.06141i	0.0248786	−	0.179412i
$36$	−0.252645	+	0.175180i	−0.0421074	+	0.0291966i
$37$	−1.45004	+	1.57516i	−0.238385	+	0.258955i	−0.843434	−	0.537233i	$-0.819469\pi$
$37$	−1.45004	+	1.57516i	−0.238385	+	0.258955i	0.605049	+	0.796189i	$0.293154\pi$
$38$	5.11624	−	4.55692i	0.829964	−	0.739230i
$39$	−6.35292	−	6.90111i	−1.01728	−	1.10506i
$40$	6.00626	+	1.34604i	0.949674	+	0.212827i
$41$	0.834318	+	2.22836i	0.130299	+	0.348012i	0.985353	−	0.170526i	$-0.0545467\pi$
$41$	0.834318	+	2.22836i	0.130299	+	0.348012i	−0.855055	+	0.518538i	$0.826477\pi$
$42$	−1.03322	−	0.716421i	−0.159430	−	0.110546i
$43$	1.54512	−	1.07136i	0.235629	−	0.163382i	−0.446107	−	0.894979i	$-0.647190\pi$
$43$	1.54512	−	1.07136i	0.235629	−	0.163382i	0.681736	+	0.731598i	$0.261225\pi$
$44$	−0.455392	+	1.21630i	−0.0686529	+	0.183364i
$45$	−0.914893	+	1.40035i	−0.136384	+	0.208752i
$46$	−0.522635	−	6.30727i	−0.0770584	−	0.929956i
$47$	1.82260	+	5.82717i	0.265853	+	0.849981i	0.987486	+	0.157705i	$0.0504094\pi$
$47$	1.82260	+	5.82717i	0.265853	+	0.849981i	−0.721633	+	0.692276i	$0.756608\pi$
$48$	5.73493	−	6.96354i	0.827766	−	1.00510i
$49$	−1.67540	+	6.61602i	−0.239343	+	0.945145i
$50$	−2.41258	+	0.402588i	−0.341190	+	0.0569346i
$51$	−13.3181	−	3.76601i	−1.86491	−	0.527347i
$52$	−1.96750	−	1.20942i	−0.272844	−	0.167716i
$53$	3.37567	+	10.7926i	0.463684	+	1.48248i	0.833051	+	0.553196i	$0.186592\pi$
$53$	3.37567	+	10.7926i	0.463684	+	1.48248i	−0.369368	+	0.929283i	$0.620426\pi$
$54$	−3.52512	−	6.10569i	−0.479708	−	0.830879i
$55$	0.194709	+	7.06368i	0.0262545	+	0.952466i
$56$	0.951537	+	0.326663i	0.127154	+	0.0436522i
$57$	−5.00861	−	6.65779i	−0.663406	−	0.881846i
$58$	−10.0611	+	3.45398i	−1.32109	+	0.453530i
$59$	−4.69699	−	12.5451i	−0.611495	−	1.63323i	−0.764215	−	0.644962i	$-0.776873\pi$
$59$	−4.69699	−	12.5451i	−0.611495	−	1.63323i	0.152719	−	0.988270i	$-0.451197\pi$
$60$	−0.687521	+	2.19813i	−0.0887586	+	0.283777i
$61$	3.48584	+	6.88820i	0.446316	+	0.881944i	0.998826	+	0.0484377i	$0.0154242\pi$
$61$	3.48584	+	6.88820i	0.446316	+	0.881944i	−0.552511	+	0.833506i	$0.686330\pi$
$62$	8.04654	+	13.9370i	1.02191	+	1.77000i
$63$	−0.173806	+	0.211042i	−0.0218976	+	0.0265887i
$64$	−2.14342	+	4.88651i	−0.267928	+	0.610814i
$65$	−12.3943	−	2.06824i	−1.53732	−	0.256534i
$66$	7.49817	+	3.53847i	0.922961	+	0.435556i
$67$	9.70593	−	0.535491i	1.18577	−	0.0654206i	0.548559	−	0.836112i	$-0.315177\pi$
$67$	9.70593	−	0.535491i	1.18577	−	0.0654206i	0.637209	+	0.770691i	$0.280089\pi$
$68$	−3.40769			−0.413244
$69$	−7.69604			−0.926495
$70$	−1.68175	+	0.0927848i	−0.201008	+	0.0110899i
$71$	−3.75087	+	7.41193i	−0.445147	+	0.879634i	0.553751	+	0.832683i	$0.313196\pi$
$71$	−3.75087	+	7.41193i	−0.445147	+	0.879634i	−0.998897	+	0.0469511i	$0.985049\pi$
$72$	−1.12567	−	1.09507i	−0.132661	−	0.129055i
$73$	−0.116234	−	0.0472103i	−0.0136042	−	0.00552555i	0.369497	−	0.929232i	$-0.379530\pi$
$73$	−0.116234	−	0.0472103i	−0.0136042	−	0.00552555i	−0.383101	+	0.923706i	$0.625144\pi$
$74$	2.86689	+	1.76227i	0.333269	+	0.204860i
$75$	0.245616	+	2.96415i	0.0283613	+	0.342270i
$76$	−1.63270	−	1.24184i	−0.187284	−	0.142448i
$77$	−0.0953763	+	1.15102i	−0.0108691	+	0.131171i
$78$	−8.73172	+	11.8799i	−0.988673	+	1.34514i
$79$	9.17460	−	6.36153i	1.03222	−	0.715728i	0.0726994	−	0.997354i	$-0.476839\pi$
$79$	9.17460	−	6.36153i	1.03222	−	0.715728i	0.959524	+	0.281626i	$0.0908737\pi$
$80$	0.332990	−	12.0803i	0.0372294	−	1.35062i
$81$	−9.52566	+	4.49527i	−1.05841	+	0.499474i
$82$	3.18620	−	1.95855i	0.351857	−	0.216286i
$83$	2.23333	−	8.81923i	0.245140	−	0.968036i	−0.717349	−	0.696714i	$-0.754644\pi$
$83$	2.23333	−	8.81923i	0.245140	−	0.968036i	0.962489	−	0.271322i	$-0.0874608\pi$
$84$	−0.151213	+	0.344732i	−0.0164987	+	0.0376133i
$85$	−17.1780	+	6.97709i	−1.86321	+	0.756772i
$86$	−2.11835	−	2.06076i	−0.228427	−	0.222218i
$87$	3.17544	+	12.5395i	0.340443	+	1.34438i
$88$	−6.54380	−	1.09197i	−0.697571	−	0.116404i
$89$	−7.22359	+	2.93397i	−0.765699	+	0.311000i	−0.725528	−	0.688193i	$-0.758404\pi$
$89$	−7.22359	+	2.93397i	−0.765699	+	0.311000i	−0.0401709	+	0.999193i	$0.512790\pi$
$90$	2.43595	+	0.989398i	0.256772	+	0.104292i
$91$	−1.97631	−	0.558847i	−0.207174	−	0.0585831i
$92$	−1.82338	+	0.515602i	−0.190100	+	0.0537553i
$93$	17.6978	−	8.35179i	1.83518	−	0.866041i
$94$	8.44014	−	4.56757i	0.870534	−	0.471109i
$95$	−10.7730	−	2.91714i	−1.10528	−	0.299292i
$96$	−4.38855	−	2.37497i	−0.447905	−	0.242394i
$97$	5.04975	+	0.278602i	0.512724	+	0.0282878i	0.309603	−	0.950866i	$-0.399804\pi$
$97$	5.04975	+	0.278602i	0.512724	+	0.0282878i	0.203121	+	0.979154i	$0.434892\pi$
$98$	10.7111	+	0.590949i	1.08199	+	0.0596949i
$99$	0.901453	−	1.56136i	0.0905994	−	0.156923i
$100$	0.256778	+	0.685823i	0.0256778	+	0.0685823i
$101$	−4.20818	+	0.943076i	−0.418730	+	0.0938395i	−0.422953	−	0.906152i	$-0.639007\pi$
$101$	−4.20818	+	0.943076i	−0.418730	+	0.0938395i	0.00422339	+	0.999991i	$0.498656\pi$
$102$	−1.79647	+	21.6802i	−0.177877	+	2.14666i
$103$	−2.90531	−	2.26129i	−0.286268	−	0.222811i	0.460891	−	0.887457i	$-0.347530\pi$
$103$	−2.90531	−	2.26129i	−0.286268	−	0.222811i	−0.747159	+	0.664645i	$0.768583\pi$
$104$	4.13659	−	11.0483i	0.405626	−	1.08338i
$105$	−0.0564354	+	2.04737i	−0.00550754	+	0.199803i
$106$	15.6321	−	8.45969i	1.51833	−	0.821677i
$107$	14.7625	+	5.06797i	1.42714	+	0.489939i	0.926691	−	0.375825i	$-0.122641\pi$
$107$	14.7625	+	5.06797i	1.42714	+	0.489939i	0.500453	+	0.865764i	$0.333167\pi$
$108$	−1.59181	+	1.38630i	−0.153172	+	0.133397i
$109$	2.05535	−	6.57131i	0.196866	−	0.629417i	−0.802593	−	0.596528i	$-0.796547\pi$
$109$	2.05535	−	6.57131i	0.196866	−	0.629417i	0.999459	−	0.0328894i	$-0.0104709\pi$
$110$	10.8382	−	2.42889i	1.03338	−	0.231586i
$111$	2.42352	−	3.29732i	0.230030	−	0.312968i
$112$	0.271303	−	1.95650i	0.0256357	−	0.184871i
$113$	−12.9784	−	10.1015i	−1.22091	−	0.950269i	−0.221216	−	0.975225i	$-0.571003\pi$
$113$	−12.9784	−	10.1015i	−1.22091	−	0.950269i	−0.999689	+	0.0249562i	$0.992055\pi$
$114$	−8.76145	+	9.73280i	−0.820585	+	0.911560i
$115$	−8.13587	+	6.33240i	−0.758673	+	0.590499i
$116$	1.59244	+	2.75818i	0.147854	+	0.256090i
$117$	2.41766	+	2.10555i	0.223513	+	0.194658i
$118$	−17.9375	+	11.0261i	−1.65128	+	1.01504i
$119$	−2.91607	+	0.824587i	−0.267316	+	0.0755898i
$120$	−11.6935	−	1.29423i	−1.06746	−	0.118147i
$121$	0.279423	+	3.37213i	0.0254021	+	0.306558i
$122$	9.57575	−	7.45311i	0.866948	−	0.674773i
$123$	−2.05355	−	4.05792i	−0.185162	−	0.365890i
$124$	3.63350	−	3.16442i	0.326298	−	0.284173i
$125$	−5.97228	−	6.48763i	−0.534177	−	0.580271i
$126$	0.377939	+	0.204530i	0.0336695	+	0.0182210i
$127$	−2.88556	+	4.99794i	−0.256052	+	0.443496i	−0.965181	−	0.261584i	$-0.915755\pi$
$127$	−2.88556	+	4.99794i	−0.256052	+	0.443496i	0.709129	+	0.705079i	$0.249089\pi$
$128$	13.2791	+	2.97592i	1.17372	+	0.263037i
$129$	−2.71009	+	2.36022i	−0.238610	+	0.207805i
$130$	0.544224	+	19.7434i	0.0477316	+	1.73161i
$131$	16.0212	+	13.9528i	1.39977	+	1.21906i	0.944414	+	0.328757i	$0.106630\pi$
$131$	16.0212	+	13.9528i	1.39977	+	1.21906i	0.455360	+	0.890307i	$0.349511\pi$
$132$	0.609389	−	2.40642i	0.0530405	−	0.209452i
$133$	−1.69765	−	0.667601i	−0.147205	−	0.0578883i
$134$	−3.75080	−	14.8116i	−0.324020	−	1.27953i
$135$	−5.18580	+	10.2474i	−0.446323	+	0.881958i
$136$	−3.33713	−	17.0843i	−0.286157	−	1.46496i
$137$	−17.0498	+	0.940662i	−1.45666	+	0.0803662i	−0.766013	−	0.642825i	$-0.777762\pi$
$137$	−17.0498	+	0.940662i	−1.45666	+	0.0803662i	−0.690648	+	0.723191i	$0.742674\pi$
$138$	2.31908	+	11.8724i	0.197413	+	1.01064i
$139$	7.82909	+	3.69463i	0.664054	+	0.313375i	0.729000	−	0.684514i	$-0.239986\pi$
$139$	7.82909	+	3.69463i	0.664054	+	0.313375i	−0.0649454	+	0.997889i	$0.520687\pi$
$140$	0.123794	+	0.488853i	0.0104625	+	0.0413156i
$141$	−4.68774	−	10.6870i	−0.394779	−	0.900006i
$142$	12.5643	+	3.55286i	1.05438	+	0.298149i
$143$	13.4614	+	1.48991i	1.12570	+	0.124592i
$144$	−1.68642	+	2.58125i	−0.140535	+	0.215104i
$145$	13.6746	+	10.6434i	1.13561	+	0.883884i
$146$	−0.0378042	+	0.193536i	−0.00312869	+	0.0160172i
$147$	1.79174	−	12.9211i	0.147780	−	1.06571i
$148$	0.353284	−	0.943580i	0.0290398	−	0.0775618i
$149$	3.59270	+	4.36238i	0.294326	+	0.357380i	0.898112	−	0.439766i	$-0.144939\pi$
$149$	3.59270	+	4.36238i	0.294326	+	0.357380i	−0.603787	+	0.797146i	$0.706342\pi$
$150$	4.49866	−	1.27210i	0.367314	−	0.103867i
$151$	−0.0856046	+	0.0142849i	−0.00696640	+	0.00116249i	−0.168077	−	0.985774i	$-0.553756\pi$
$151$	−0.0856046	+	0.0142849i	−0.00696640	+	0.00116249i	0.161110	+	0.986936i	$0.448492\pi$
$152$	4.62697	−	9.40158i	0.375297	−	0.762569i
$153$	4.66598	+	0.778614i	0.377222	+	0.0629472i
$154$	1.80437	−	0.199708i	0.145401	−	0.0160929i
$155$	11.8373	−	23.3911i	0.950791	−	1.87882i
$156$	3.99208	+	1.88391i	0.319622	+	0.150833i
$157$	−10.4453	+	1.15609i	−0.833627	+	0.0922658i	−0.516681	−	0.856178i	$-0.672833\pi$
$157$	−10.4453	+	1.15609i	−0.833627	+	0.0922658i	−0.316946	+	0.948444i	$0.602657\pi$
$158$	−12.5783	−	12.2364i	−1.00068	−	0.973472i
$159$	−8.68225	−	19.7935i	−0.688547	−	1.56973i
$160$	−6.59351	+	1.10026i	−0.521262	+	0.0869833i
$161$	−1.43556	+	0.882435i	−0.113138	+	0.0695456i
$162$	9.80507	+	13.3403i	0.770359	+	1.04811i
$163$	−1.17690	−	0.404030i	−0.0921818	−	0.0316460i	0.278223	−	0.960517i	$-0.410255\pi$
$163$	−1.17690	−	0.404030i	−0.0921818	−	0.0316460i	−0.370405	+	0.928871i	$0.620781\pi$
$164$	−0.758398	−	0.823840i	−0.0592209	−	0.0643311i
$165$	−1.85514	−	13.3783i	−0.144423	−	1.04150i
$166$	−14.2781	−	0.787742i	−1.10819	−	0.0611407i
$167$	−2.55306	−	18.4113i	−0.197562	−	1.42471i	−0.787028	−	0.616918i	$-0.788381\pi$
$167$	−2.55306	−	18.4113i	−0.197562	−	1.42471i	0.589466	−	0.807793i	$-0.299338\pi$
$168$	−1.87637	−	0.420505i	−0.144765	−	0.0324427i
$169$	−3.30868	+	10.5784i	−0.254514	+	0.813726i
$170$	15.9396	+	24.3973i	1.22251	+	1.87119i
$171$	1.95183	+	2.07343i	0.149260	+	0.158559i
$172$	−0.483960	+	0.740756i	−0.0369016	+	0.0564821i
$173$	1.75523	+	2.13126i	0.133448	+	0.162036i	0.834377	−	0.551194i	$-0.185828\pi$
$173$	1.75523	+	2.13126i	0.133448	+	0.162036i	−0.700929	+	0.713231i	$0.747231\pi$
$174$	18.3874	−	8.67722i	1.39394	−	0.657818i
$175$	0.385687	+	0.524746i	0.0291552	+	0.0396671i
$176$	0.358906	+	13.0204i	0.0270535	+	0.981452i
$177$	11.5609	+	22.8450i	0.868972	+	1.71713i
$178$	6.70283	+	10.2594i	0.502398	+	0.768977i
$179$	1.83953	−	22.1999i	0.137493	−	1.65930i	−0.483399	−	0.875400i	$-0.660598\pi$
$179$	1.83953	−	22.1999i	0.137493	−	1.65930i	0.620893	−	0.783896i	$-0.286770\pi$
$180$	0.150913	−	0.772588i	0.0112484	−	0.0575853i
$181$	2.64631	−	13.5476i	0.196699	−	1.00699i	−0.744112	−	0.668055i	$-0.767127\pi$
$181$	2.64631	−	13.5476i	0.196699	−	1.00699i	0.940811	−	0.338932i	$-0.110066\pi$
$182$	−0.266583	+	3.21718i	−0.0197604	+	0.238473i
$183$	−8.07058	−	12.3529i	−0.596595	−	0.913156i
$184$	−4.37056	−	8.63647i	−0.322202	−	0.636689i
$185$	−0.151051	−	5.47986i	−0.0111055	−	0.402887i
$186$	−18.2169	−	24.7850i	−1.33573	−	1.81733i
$187$	18.0725	−	8.52861i	1.32159	−	0.623674i
$188$	−1.82662	−	2.21794i	−0.133220	−	0.161760i
$189$	−1.02670	+	1.57149i	−0.0746818	+	0.114309i
$190$	−1.25389	+	17.4981i	−0.0909671	+	1.26944i
$191$	−6.42727	−	9.83766i	−0.465061	−	0.711828i	0.525212	−	0.850972i	$-0.323986\pi$
$191$	−6.42727	−	9.83766i	−0.465061	−	0.711828i	−0.990272	+	0.139143i	$0.955565\pi$
$192$	3.04452	−	9.73387i	0.219719	−	0.702481i
$193$	17.7833	+	3.98532i	1.28007	+	0.286870i	0.805103	−	0.593135i	$-0.202110\pi$
$193$	17.7833	+	3.98532i	1.28007	+	0.286870i	0.474964	+	0.880005i	$0.342461\pi$
$194$	−1.09187	−	7.87399i	−0.0783917	−	0.565320i
$195$	23.9810	+	1.32307i	1.71732	+	0.0947470i
$196$	−0.441152	−	3.18136i	−0.0315109	−	0.227240i
$197$	4.87648	+	5.29727i	0.347435	+	0.377415i	0.884829	−	0.465917i	$-0.154275\pi$
$197$	4.87648	+	5.29727i	0.347435	+	0.377415i	−0.537394	+	0.843331i	$0.680591\pi$
$198$	−2.68029	−	0.920145i	−0.190480	−	0.0653918i
$199$	−1.70845	−	2.32443i	−0.121109	−	0.164775i	0.740988	−	0.671519i	$-0.234358\pi$
$199$	−1.70845	−	2.32443i	−0.121109	−	0.164775i	−0.862097	+	0.506744i	$0.830849\pi$
$200$	−3.18687	+	1.95896i	−0.225346	+	0.138519i
$201$	−18.3263	+	3.05812i	−1.29264	+	0.215703i
$202$	2.72291	+	6.20762i	0.191583	+	0.436766i
$203$	2.03012	+	1.97493i	0.142486	+	0.138613i
$204$	6.47378	−	0.716518i	0.453256	−	0.0501663i
$205$	−5.50981	−	2.60014i	−0.384822	−	0.181602i
$206$	−2.61294	+	5.16330i	−0.182052	+	0.359744i
$207$	2.61446	−	0.289369i	0.181718	−	0.0201125i
$208$	−22.8463	−	3.81238i	−1.58411	−	0.264341i
$209$	11.7670	+	2.49975i	0.813937	+	0.172911i
$210$	3.17541	−	0.529882i	0.219124	−	0.0365653i
$211$	−9.33333	+	2.63921i	−0.642533	+	0.181691i	−0.577757	−	0.816209i	$-0.696072\pi$
$211$	−9.33333	+	2.63921i	−0.642533	+	0.181691i	−0.0647759	+	0.997900i	$0.520633\pi$
$212$	−3.38312	−	4.10789i	−0.232353	−	0.282131i
$213$	5.56727	−	14.8695i	0.381463	−	1.01884i
$214$	3.36972	−	24.3006i	0.230349	−	1.66116i
$215$	−0.922950	+	4.72499i	−0.0629447	+	0.322242i
$216$	−8.50900	−	6.62282i	−0.578964	−	0.450626i
$217$	2.34358	−	3.58712i	0.159093	−	0.243510i
$218$	−10.7566	−	1.19054i	−0.728532	−	0.0806339i
$219$	0.230744	+	0.0652481i	0.0155922	+	0.00440905i
$220$	−1.33582	−	3.04536i	−0.0900609	−	0.205318i
$221$	8.72357	+	34.4486i	0.586811	+	2.31726i
$222$	−5.81693	−	2.74508i	−0.390407	−	0.184237i
$223$	2.51890	+	12.8953i	0.168678	+	0.863536i	0.965715	+	0.259606i	$0.0835926\pi$
$223$	2.51890	+	12.8953i	0.168678	+	0.863536i	−0.797037	+	0.603931i	$0.793600\pi$
$224$	−1.09092	+	0.0601878i	−0.0728903	+	0.00402147i
$225$	−0.194891	−	0.997731i	−0.0129927	−	0.0665154i
$226$	−11.6723	+	23.0652i	−0.776433	+	1.53427i
$227$	2.03293	+	8.02787i	0.134931	+	0.532829i	0.999538	+	0.0303814i	$0.00967219\pi$
$227$	2.03293	+	8.02787i	0.134931	+	0.532829i	−0.864608	+	0.502447i	$0.832433\pi$
$228$	3.36285	+	2.01588i	0.222710	+	0.133505i
$229$	1.69778	−	6.70437i	0.112192	−	0.443037i	−0.887655	−	0.460509i	$-0.847667\pi$
$229$	1.69778	−	6.70437i	0.112192	−	0.443037i	0.999847	+	0.0174717i	$0.00556169\pi$
$230$	12.2204	+	10.6427i	0.805786	+	0.701760i
$231$	−0.0608276	−	2.20671i	−0.00400216	−	0.145191i
$232$	−12.2685	+	10.6846i	−0.805466	+	0.701481i
$233$	21.4942	+	4.81697i	1.40813	+	0.315570i	0.855478	−	0.517839i	$-0.173264\pi$
$233$	21.4942	+	4.81697i	1.40813	+	0.315570i	0.552656	+	0.833410i	$0.313614\pi$
$234$	2.51962	−	4.36411i	0.164713	−	0.285291i
$235$	−13.7490	−	7.44060i	−0.896887	−	0.485371i
$236$	4.26958	+	4.63800i	0.277926	+	0.301908i
$237$	−16.0919	+	14.0144i	−1.04528	+	0.910336i
$238$	2.15077	+	4.25004i	0.139414	+	0.275489i
$239$	4.67199	−	3.63636i	0.302206	−	0.235216i	−0.451745	−	0.892147i	$-0.649198\pi$
$239$	4.67199	−	3.63636i	0.302206	−	0.235216i	0.753951	+	0.656931i	$0.228146\pi$
$240$	1.90746	+	23.0196i	0.123126	+	1.48591i
$241$	7.50113	+	0.830225i	0.483190	+	0.0534795i	0.348304	−	0.937382i	$-0.386758\pi$
$241$	7.50113	+	0.830225i	0.483190	+	0.0534795i	0.134886	+	0.990861i	$0.456933\pi$
$242$	5.11786	−	1.44719i	0.328988	−	0.0930290i
$243$	5.68759	−	3.49615i	0.364859	−	0.224278i
$244$	−2.73971	−	2.38602i	−0.175392	−	0.152749i
$245$	−8.73750	−	15.1338i	−0.558218	−	0.966862i
$246$	−5.64119	+	4.39071i	−0.359669	+	0.279942i
$247$	−8.37414	+	19.6842i	−0.532834	+	1.25247i
$248$	19.4229	+	15.1174i	1.23335	+	0.959958i
$249$	−2.38841	+	17.2240i	−0.151359	+	1.09152i
$250$	−8.20856	+	11.1681i	−0.519155	+	0.706336i
$251$	−1.70547	+	0.382205i	−0.107648	+	0.0241246i	−0.272172	−	0.962249i	$-0.587742\pi$
$251$	−1.70547	+	0.382205i	−0.107648	+	0.0241246i	0.164524	+	0.986373i	$0.447391\pi$
$252$	0.0384077	−	0.122796i	0.00241946	−	0.00773543i
$253$	8.37975	−	7.29793i	0.526830	−	0.458817i
$254$	8.57964	+	2.94540i	0.538335	+	0.184811i
$255$	31.1669	−	16.8667i	1.95175	−	1.05623i
$256$	0.295332	−	10.7141i	0.0184583	−	0.669632i
$257$	−7.44454	+	19.8835i	−0.464377	+	1.24030i	0.469573	+	0.882894i	$0.344408\pi$
$257$	−7.44454	+	19.8835i	−0.464377	+	1.24030i	−0.933950	+	0.357403i	$0.883662\pi$
$258$	4.45765	+	3.46953i	0.277521	+	0.216003i
$259$	0.0739910	−	0.892939i	0.00459758	−	0.0554845i
$260$	5.77032	−	1.29316i	0.357860	−	0.0801983i
$261$	−1.55023	−	4.14048i	−0.0959568	−	0.256289i
$262$	16.6968	−	28.9197i	1.03153	−	1.78666i
$263$	−19.2332	−	1.06112i	−1.18597	−	0.0654316i	−0.548663	−	0.836044i	$-0.684863\pi$
$263$	−19.2332	−	1.06112i	−1.18597	−	0.0654316i	−0.637304	+	0.770612i	$0.719951\pi$
$264$	12.6612	+	0.698539i	0.779244	+	0.0429921i
$265$	−25.4648	−	13.7809i	−1.56429	−	0.846551i
$266$	−0.518321	+	2.82008i	−0.0317803	+	0.172910i
$267$	13.1061	−	7.09269i	0.802083	−	0.434065i
$268$	−4.13706	+	1.95233i	−0.252711	+	0.119257i
$269$	−5.77590	+	1.63327i	−0.352163	+	0.0995822i	−0.443591	−	0.896229i	$-0.646296\pi$
$269$	−5.77590	+	1.63327i	−0.352163	+	0.0995822i	0.0914276	+	0.995812i	$0.470857\pi$
$270$	17.3710	+	4.91204i	1.05716	+	0.298937i
$271$	−5.26773	−	2.13957i	−0.319992	−	0.129969i	0.210660	−	0.977559i	$-0.432439\pi$
$271$	−5.26773	−	2.13957i	−0.319992	−	0.129969i	−0.530652	+	0.847590i	$0.678053\pi$
$272$	−31.6640	+	12.8608i	−1.91991	+	0.779802i
$273$	3.87201	+	0.646125i	0.234345	+	0.0391053i
$274$	6.58879	+	26.0186i	0.398044	+	1.57184i
$275$	−3.07825	−	2.99457i	−0.185625	−	0.180579i
$276$	3.35556	−	1.36291i	0.201981	−	0.0820376i
$277$	5.30461	−	12.0933i	0.318723	−	0.726615i	−0.681262	−	0.732039i	$-0.738569\pi$
$277$	5.30461	−	12.0933i	0.318723	−	0.726615i	0.999985	+	0.00542438i	$0.00172664\pi$
$278$	3.34040	−	13.1909i	0.200344	−	0.791140i
$279$	−5.69819	+	3.50266i	−0.341142	+	0.209699i
$280$	−2.32960	+	1.09937i	−0.139220	+	0.0656997i
$281$	−0.287701	+	10.4373i	−0.0171628	+	0.622635i	0.941325	+	0.337502i	$0.109582\pi$
$281$	−0.287701	+	10.4373i	−0.0171628	+	0.622635i	−0.958488	+	0.285134i	$0.907962\pi$
$282$	−15.0738	+	10.4519i	−0.897632	+	0.622404i
$283$	15.8145	−	21.5164i	0.940072	−	1.27901i	−0.0201557	−	0.999797i	$-0.506416\pi$
$283$	15.8145	−	21.5164i	0.940072	−	1.27901i	0.960228	−	0.279217i	$-0.0900750\pi$
$284$	0.322826	−	3.89593i	0.0191562	−	0.231181i
$285$	21.0794	+	3.27667i	1.24863	+	0.194093i
$286$	−1.75795	−	21.2154i	−0.103950	−	1.25449i
$287$	−0.848337	−	0.521471i	−0.0500757	−	0.0307814i
$288$	1.58016	+	0.641804i	0.0931116	+	0.0378187i
$289$	25.3983	+	24.7079i	1.49402	+	1.45341i
$290$	12.2985	−	24.3025i	0.722192	−	1.42709i
$291$	−9.65186	+	0.532508i	−0.565802	+	0.0312162i
$292$	0.0590400			0.00345506
$293$	−26.8246			−1.56711			−0.783556	−	0.621321i	$-0.786596\pi$
$293$	−26.8246			−1.56711			−0.783556	+	0.621321i	$0.786596\pi$
$294$	−20.4728	+	1.12951i	−1.19400	+	0.0658746i
$295$	31.0188	+	14.6381i	1.80598	+	0.852263i
$296$	5.07655	+	0.847126i	0.295068	+	0.0492382i
$297$	4.97246	−	11.3361i	0.288532	−	0.657786i
$298$	5.64707	−	6.85686i	0.327126	−	0.397207i
$299$	9.88003	+	17.1127i	0.571377	+	0.989654i
$300$	−0.632019	−	1.24890i	−0.0364896	−	0.0721055i
$301$	−0.234894	+	0.750997i	−0.0135390	+	0.0432867i
$302$	0.0478322	+	0.127754i	0.00275244	+	0.00735143i
$303$	7.79622	−	2.67645i	0.447881	−	0.153758i
$304$	−19.8577	−	5.37714i	−1.13892	−	0.308400i
$305$	−18.6960	−	6.41833i	−1.07053	−	0.367513i
$306$	−0.204879	−	7.43264i	−0.0117122	−	0.424896i
$307$	−3.51955	−	6.09604i	−0.200871	−	0.347919i	0.747938	−	0.663768i	$-0.231044\pi$
$307$	−3.51955	−	6.09604i	−0.200871	−	0.347919i	−0.948809	+	0.315849i	$0.897711\pi$
$308$	−0.162252	−	0.518748i	−0.00924516	−	0.0295584i
$309$	5.99484	+	3.68501i	0.341034	+	0.209633i
$310$	−39.6514	−	11.2124i	−2.25205	−	0.636819i
$311$	4.67661	−	0.780388i	0.265186	−	0.0442517i	−0.0305076	−	0.999535i	$-0.509712\pi$
$311$	4.67661	−	0.780388i	0.265186	−	0.0442517i	0.295694	+	0.955283i	$0.404449\pi$
$312$	−5.53543	+	21.8589i	−0.313382	+	1.23752i
$313$	7.19751	−	8.73945i	0.406827	−	0.493983i	−0.527921	−	0.849293i	$-0.677028\pi$
$313$	7.19751	−	8.73945i	0.406827	−	0.493983i	0.934748	+	0.355310i	$0.115625\pi$
$314$	4.93097	+	15.7652i	0.278271	+	0.889682i
$315$	−0.0578086	−	0.697646i	−0.00325715	−	0.0393079i
$316$	−2.87365	+	4.39845i	−0.161655	+	0.247432i
$317$	−2.11381	+	5.64573i	−0.118723	+	0.317096i	−0.982355	−	0.187028i	$-0.940114\pi$
$317$	−2.11381	+	5.64573i	−0.118723	+	0.317096i	0.863631	+	0.504124i	$0.168185\pi$
$318$	−27.9184	+	19.3582i	−1.56559	+	1.08556i
$319$	−15.3484	−	10.6424i	−0.859347	−	0.595858i
$320$	−4.79063	−	12.7952i	−0.267805	−	0.715274i
$321$	−29.1107	−	6.52387i	−1.62480	−	0.364127i
$322$	1.79388	+	1.94867i	0.0999690	+	0.108595i
$323$	4.68324	+	31.2139i	0.260582	+	1.73679i
$324$	3.35721	−	3.64691i	0.186512	−	0.202606i
$325$	6.27568	−	4.35146i	0.348112	−	0.241376i
$326$	−0.268641	+	1.93730i	−0.0148787	+	0.107297i
$327$	−2.52294	+	12.9160i	−0.139519	+	0.714259i
$328$	3.38758	−	4.60896i	0.187048	−	0.254487i
$329$	−2.09979	−	1.45596i	−0.115765	−	0.0802699i
$330$	−20.0792	+	6.89319i	−1.10532	+	0.379458i
$331$	−20.6248	−	11.1616i	−1.13364	−	0.613497i	−0.202911	−	0.979197i	$-0.565040\pi$
$331$	−20.6248	−	11.1616i	−1.13364	−	0.613497i	−0.930733	+	0.365700i	$0.880830\pi$
$332$	0.588061	+	4.24079i	0.0322740	+	0.232743i
$333$	−0.699329	+	1.21127i	−0.0383230	+	0.0663774i
$334$	−27.6331	+	9.48645i	−1.51202	+	0.519076i
$335$	−16.8574	+	18.3120i	−0.921016	+	1.00049i
$336$	−0.104027	+	3.77391i	−0.00567514	+	0.205884i
$337$	−10.3947	−	12.6215i	−0.566233	−	0.687538i	0.408026	−	0.912970i	$-0.366217\pi$
$337$	−10.3947	−	12.6215i	−0.566233	−	0.687538i	−0.974259	+	0.225432i	$0.927621\pi$
$338$	17.3159	+	1.91653i	0.941863	+	0.104245i
$339$	26.7798	+	16.4615i	1.45448	+	0.894064i
$340$	6.25420	−	6.08418i	0.339181	−	0.329961i
$341$	−11.3503	+	25.8760i	−0.614653	+	1.40127i
$342$	2.61045	−	3.63581i	0.141157	−	0.196602i
$343$	−2.32410	−	5.29841i	−0.125489	−	0.286087i
$344$	−4.18767	−	1.70089i	−0.225784	−	0.0917057i
$345$	14.1247	−	13.7407i	0.760447	−	0.739774i
$346$	2.75890	−	3.34994i	0.148319	−	0.180094i
$347$	−11.8552	−	10.3247i	−0.636418	−	0.554257i	0.277209	−	0.960810i	$-0.410590\pi$
$347$	−11.8552	−	10.3247i	−0.636418	−	0.554257i	−0.913627	+	0.406553i	$0.866731\pi$
$348$	−3.60519	−	4.90503i	−0.193258	−	0.262937i
$349$	−7.09945	+	3.84203i	−0.380025	+	0.205659i	−0.654719	−	0.755872i	$-0.727213\pi$
$349$	−7.09945	+	3.84203i	−0.380025	+	0.205659i	0.274694	+	0.961532i	$0.411424\pi$
$350$	0.693285	−	0.753108i	0.0370576	−	0.0402553i
$351$	18.0892	+	12.5428i	0.965530	+	0.669484i
$352$	7.03053	−	1.57558i	0.374729	−	0.0839787i
$353$	−6.46457	−	9.89476i	−0.344074	−	0.526645i	0.622638	−	0.782510i	$-0.286061\pi$
$353$	−6.46457	−	9.89476i	−0.344074	−	0.526645i	−0.966713	+	0.255865i	$0.917640\pi$
$354$	31.7584	−	24.7185i	1.68794	−	1.31378i
$355$	−6.34939	−	20.3001i	−0.336991	−	1.07742i
$356$	2.62998	−	2.55848i	0.139389	−	0.135599i
$357$	5.36645	−	2.17966i	0.284022	−	0.115360i
$358$	−34.8012	+	3.85179i	−1.83930	+	0.203574i
$359$	0.158214	+	0.809965i	0.00835019	+	0.0427483i	0.985394	−	0.170291i	$-0.0544708\pi$
$359$	0.158214	+	0.809965i	0.00835019	+	0.0427483i	−0.977044	+	0.213039i	$0.931664\pi$
$360$	4.02111			0.211931
$361$	−9.13118	+	16.6620i	−0.480588	+	0.876946i
$362$	−21.6968			−1.14036
$363$	−1.23988	−	6.34748i	−0.0650766	−	0.333156i
$364$	0.960661	−	0.106326i	0.0503523	−	0.00557299i
$365$	0.297617	−	0.120882i	0.0155780	−	0.00632724i
$366$	−16.6245	+	16.1725i	−0.868974	+	0.845351i
$367$	4.04157	+	12.9216i	0.210968	+	0.674503i	0.998317	+	0.0579951i	$0.0184708\pi$
$367$	4.04157	+	12.9216i	0.210968	+	0.674503i	−0.787349	+	0.616508i	$0.788547\pi$
$368$	−14.9968	+	11.6725i	−0.781762	+	0.608469i
$369$	0.850198	+	1.30132i	0.0442595	+	0.0677442i
$370$	−8.40805	+	1.88429i	−0.437113	+	0.0979594i
$371$	−3.88906	−	2.69662i	−0.201910	−	0.140001i
$372$	−6.23740	+	6.77562i	−0.323394	+	0.351299i
$373$	2.74921	−	1.48780i	0.142349	−	0.0770352i	−0.403212	−	0.915107i	$-0.632106\pi$
$373$	2.74921	−	1.48780i	0.142349	−	0.0770352i	0.545561	+	0.838071i	$0.316317\pi$
$374$	−18.6026	−	25.3098i	−0.961918	−	1.30874i
$375$	12.7100	+	11.0691i	0.656341	+	0.571608i
$376$	9.33072	−	11.3297i	0.481195	−	0.584283i
$377$	23.8060	−	23.1589i	1.22607	−	1.19274i
$378$	2.73365	+	1.11031i	0.140604	+	0.0571084i
$379$	−7.62345	−	17.3797i	−0.391590	−	0.892736i	−0.995418	−	0.0956210i	$-0.969516\pi$
$379$	−7.62345	−	17.3797i	−0.391590	−	0.892736i	0.603828	−	0.797115i	$-0.293642\pi$
$380$	5.21373	−	0.635906i	0.267459	−	0.0326213i
$381$	4.43097	−	10.1016i	0.227006	−	0.517521i
$382$	−13.2394	+	12.8795i	−0.677388	+	0.658973i
$383$	−17.6711	−	10.8624i	−0.902950	−	0.555041i	−0.00738536	−	0.999973i	$-0.502351\pi$
$383$	−17.6711	−	10.8624i	−0.902950	−	0.555041i	−0.895565	+	0.444931i	$0.853228\pi$
$384$	−25.8528	−	2.86139i	−1.31930	−	0.146020i
$385$	−1.88001	−	2.28277i	−0.0958144	−	0.116341i
$386$	0.789303	−	28.6344i	0.0401745	−	1.45745i
$387$	0.831914	−	0.903700i	0.0422886	−	0.0459376i
$388$	−2.25108	+	0.772798i	−0.114281	+	0.0392329i
$389$	10.2766	−	17.7996i	0.521045	−	0.902476i	−0.478656	−	0.878003i	$-0.658876\pi$
$389$	10.2766	−	17.7996i	0.521045	−	0.902476i	0.999700	−	0.0244732i	$-0.00779083\pi$
$390$	−5.18524	−	37.3933i	−0.262565	−	1.89348i
$391$	25.6422	+	13.8768i	1.29678	+	0.701782i
$392$	15.5175	−	5.32717i	0.783753	−	0.269063i
$393$	−33.3701	−	23.1383i	−1.68330	−	1.16717i
$394$	6.70244	−	9.11900i	0.337664	−	0.459408i
$395$	−5.48028	+	28.0560i	−0.275743	+	1.41165i
$396$	−0.116538	+	0.840412i	−0.00585626	+	0.0422323i
$397$	1.64007	−	1.13720i	0.0823126	−	0.0570743i	−0.527937	−	0.849284i	$-0.677034\pi$
$397$	1.64007	−	1.13720i	0.0823126	−	0.0570743i	0.610249	+	0.792209i	$0.291069\pi$
$398$	−3.07100	+	3.33599i	−0.153935	+	0.167218i
$399$	3.36550	+	0.911321i	0.168486	+	0.0456231i
$400$	4.97429	+	5.40352i	0.248715	+	0.270176i
$401$	3.79587	+	0.850675i	0.189557	+	0.0424807i	0.312426	−	0.949942i	$-0.398859\pi$
$401$	3.79587	+	0.850675i	0.189557	+	0.0424807i	−0.122869	+	0.992423i	$0.539209\pi$
$402$	10.2400	+	27.3497i	0.510723	+	1.36408i
$403$	−41.2909	−	28.6305i	−2.05685	−	1.42619i
$404$	1.66780	−	1.15643i	0.0829763	−	0.0575345i
$405$	9.45664	−	25.2576i	0.469904	−	1.25506i
$406$	2.43490	−	3.72689i	0.120842	−	0.184963i
$407$	0.487927	+	5.88840i	0.0241856	+	0.291877i
$408$	9.93196	+	31.7542i	0.491705	+	1.57207i
$409$	13.7408	−	16.6846i	0.679441	−	0.825000i	−0.312736	−	0.949840i	$-0.601245\pi$
$409$	13.7408	−	16.6846i	0.679441	−	0.825000i	0.992177	+	0.124841i	$0.0398419\pi$
$410$	−2.35084	+	9.28327i	−0.116100	+	0.458468i
$411$	32.1926	−	5.37200i	1.58794	−	0.264981i
$412$	1.66720	+	0.471440i	0.0821372	+	0.0232262i
$413$	4.77591	+	2.93574i	0.235007	+	0.144458i
$414$	−1.23422	−	3.94603i	−0.0606588	−	0.193937i
$415$	11.6472	+	20.1735i	0.571738	+	0.990279i
$416$	0.353028	+	12.8072i	0.0173086	+	0.627925i
$417$	−15.6502	−	5.37272i	−0.766394	−	0.263103i
$418$	0.310481	−	18.9057i	0.0151861	−	0.924706i
$419$	−4.74411	+	1.62866i	−0.231765	+	0.0795650i	−0.438136	−	0.898909i	$-0.644361\pi$
$419$	−4.74411	+	1.62866i	−0.231765	+	0.0795650i	0.206371	+	0.978474i	$0.433835\pi$
$420$	−0.337968	−	0.902671i	−0.0164911	−	0.0440459i
$421$	−7.93708	+	25.3762i	−0.386829	+	1.23676i	0.533561	+	0.845762i	$0.320854\pi$
$421$	−7.93708	+	25.3762i	−0.386829	+	1.23676i	−0.920390	+	0.391001i	$0.872129\pi$
$422$	6.88386	+	13.6029i	0.335101	+	0.662178i
$423$	1.99433	+	3.45427i	0.0969674	+	0.167952i
$424$	17.2816	−	20.9839i	0.839269	−	1.01907i
$425$	4.52634	−	10.3190i	0.219560	−	0.500545i
$426$	−24.6162	−	4.10772i	−1.19266	−	0.199020i
$427$	−2.92182	−	1.37884i	−0.141397	−	0.0667268i
$428$	−7.33410	+	0.404634i	−0.354507	+	0.0195587i
$429$	−25.8867			−1.24982
$430$	7.56717			0.364922
$431$	24.7677	−	1.36647i	1.19302	−	0.0658207i	0.552333	−	0.833623i	$-0.313738\pi$
$431$	24.7677	−	1.36647i	1.19302	−	0.0658207i	0.640686	+	0.767803i	$0.278650\pi$
$432$	−9.55895	+	18.8890i	−0.459905	+	0.908798i
$433$	26.7347	+	26.0080i	1.28479	+	1.24986i	0.951722	+	0.306960i	$0.0993118\pi$
$433$	26.7347	+	26.0080i	1.28479	+	1.24986i	0.333067	+	0.942903i	$0.391916\pi$
$434$	−6.23991	−	2.53443i	−0.299525	−	0.121657i
$435$	−28.2163	−	17.3445i	−1.35287	−	0.831606i
$436$	0.267575	+	3.22915i	0.0128145	+	0.154648i
$437$	7.22873	+	15.9933i	0.345797	+	0.765061i
$438$	0.0311248	−	0.375620i	0.00148720	−	0.0179478i
$439$	−12.0106	+	16.3411i	−0.573237	+	0.779917i	−0.991735	−	0.128301i	$-0.959048\pi$
$439$	−12.0106	+	16.3411i	−0.573237	+	0.779917i	0.418498	+	0.908218i	$0.362557\pi$
$440$	13.9596	−	9.67935i	0.665496	−	0.461445i
$441$	−0.122853	+	4.45686i	−0.00585012	+	0.212232i
$442$	50.5138	−	23.8380i	2.40269	−	1.13386i
$443$	5.18178	−	3.18523i	0.246194	−	0.151335i	−0.395081	−	0.918646i	$-0.629283\pi$
$443$	5.18178	−	3.18523i	0.246194	−	0.151335i	0.641274	+	0.767312i	$0.278406\pi$
$444$	−0.472752	+	1.86685i	−0.0224358	+	0.0885970i
$445$	8.01919	−	18.2819i	0.380146	−	0.866646i
$446$	19.1341	−	7.77160i	0.906026	−	0.367996i
$447$	−7.74252	−	7.53204i	−0.366208	−	0.356253i
$448$	−0.548193	−	2.16477i	−0.0258997	−	0.102276i
$449$	4.31317	+	0.719741i	0.203551	+	0.0339667i	0.265492	−	0.964113i	$-0.414466\pi$
$449$	4.31317	+	0.719741i	0.203551	+	0.0339667i	−0.0619405	+	0.998080i	$0.519729\pi$
$450$	−1.48043	+	0.601300i	−0.0697883	+	0.0283456i
$451$	6.08398	+	2.47110i	0.286484	+	0.116360i
$452$	7.44762	+	2.10599i	0.350307	+	0.0990573i
$453$	0.159624	−	0.0451374i	0.00749979	−	0.00212074i
$454$	11.7717	−	5.55520i	0.552473	−	0.260718i
$455$	4.62494	−	2.50289i	0.216820	−	0.117337i
$456$	−6.81329	+	18.8336i	−0.319062	+	0.881964i
$457$	14.8694	+	8.04690i	0.695560	+	0.376418i	0.784934	−	0.619580i	$-0.212697\pi$
$457$	14.8694	+	8.04690i	0.695560	+	0.376418i	−0.0893736	+	0.995998i	$0.528487\pi$
$458$	−10.8542	−	0.598841i	−0.507182	−	0.0279820i
$459$	32.4301	+	1.78922i	1.51371	+	0.0835136i
$460$	2.42591	−	4.20180i	0.113109	−	0.195910i
$461$	−3.21349	−	8.58284i	−0.149667	−	0.399743i	0.840101	−	0.542430i	$-0.182496\pi$
$461$	−3.21349	−	8.58284i	−0.149667	−	0.399743i	−0.989768	+	0.142688i	$0.954426\pi$
$462$	−3.38588	+	0.758793i	−0.157525	+	0.0353022i
$463$	−1.49152	+	18.0000i	−0.0693169	+	0.836531i	0.869905	+	0.493220i	$0.164180\pi$
$463$	−1.49152	+	18.0000i	−0.0693169	+	0.836531i	−0.939222	+	0.343311i	$0.888451\pi$
$464$	25.2063	+	19.6189i	1.17017	+	0.910783i
$465$	−17.5696	+	46.9263i	−0.814770	+	2.17615i
$466$	0.954013	−	34.6098i	0.0441938	−	1.60327i
$467$	−19.4562	+	10.5292i	−0.900325	+	0.487231i	−0.859036	−	0.511916i	$-0.828936\pi$
$467$	−19.4562	+	10.5292i	−0.900325	+	0.487231i	−0.0412891	+	0.999147i	$0.513146\pi$
$468$	−1.42700	−	0.489891i	−0.0659633	−	0.0226452i
$469$	−3.06780	+	2.67175i	−0.141658	+	0.123370i
$470$	−7.33527	+	23.4522i	−0.338351	+	1.08177i
$471$	19.6005	−	4.39256i	0.903141	−	0.202399i
$472$	−19.0711	+	25.9472i	−0.877821	+	1.19432i
$473$	0.712723	−	5.13979i	0.0327710	−	0.236328i
$474$	26.4686	+	20.6013i	1.21574	+	0.946249i
$475$	5.92914	−	3.29458i	0.272047	−	0.151166i
$476$	1.12541	−	0.875944i	0.0515832	−	0.0401488i
$477$	3.69372	+	6.39772i	0.169124	+	0.292931i
$478$	−7.01749	−	6.11154i	−0.320973	−	0.279535i
$479$	0.782703	−	0.481126i	0.0357626	−	0.0219832i	−0.505676	−	0.862723i	$-0.668757\pi$
$479$	0.782703	−	0.481126i	0.0357626	−	0.0219832i	0.541439	+	0.840740i	$0.317880\pi$
$480$	12.2947	−	3.47661i	0.561174	−	0.158685i
$481$	−10.4431	−	1.15584i	−0.476164	−	0.0527019i
$482$	−0.979589	−	11.8219i	−0.0446190	−	0.538472i
$483$	2.54167	−	1.97826i	0.115650	−	0.0900139i
$484$	−0.719011	−	1.42080i	−0.0326823	−	0.0645820i
$485$	−9.76530	+	8.50461i	−0.443420	+	0.386174i
$486$	−7.10723	−	7.72051i	−0.322391	−	0.350209i
$487$	−18.8384	−	10.1949i	−0.853652	−	0.461973i	−0.0106875	−	0.999943i	$-0.503402\pi$
$487$	−18.8384	−	10.1949i	−0.853652	−	0.461973i	−0.842964	+	0.537970i	$0.819191\pi$
$488$	9.27916	−	16.0720i	0.420048	−	0.727544i
$489$	2.32077	+	0.520097i	0.104949	+	0.0235196i
$490$	−20.7134	+	18.0393i	−0.935736	+	0.814933i
$491$	−0.644165	−	23.3691i	−0.0290707	−	1.05463i	−0.863758	−	0.503908i	$-0.831895\pi$
$491$	−0.644165	−	23.3691i	−0.0290707	−	1.05463i	0.834687	−	0.550725i	$-0.185649\pi$
$492$	1.61399	+	1.40563i	0.0727645	+	0.0633707i
$493$	12.0301	−	47.5057i	0.541808	−	2.13955i
$494$	32.8894	+	6.98695i	1.47976	+	0.314358i
$495$	1.13324	+	4.47507i	0.0509354	+	0.201139i
$496$	21.8195	−	43.1166i	0.979726	−	1.93599i
$497$	−0.666477	−	3.41199i	−0.0298956	−	0.153049i
$498$	27.2905	−	1.50566i	1.22291	−	0.0674701i
$499$	0.494684	+	2.53251i	0.0221451	+	0.113371i	0.990886	−	0.134705i	$-0.0430088\pi$
$499$	0.494684	+	2.53251i	0.0221451	+	0.113371i	−0.968741	+	0.248076i	$0.920202\pi$
$500$	3.75289	+	1.77103i	0.167834	+	0.0792030i
$501$	8.72144	+	34.4402i	0.389645	+	1.53867i
$502$	1.10353	+	2.51579i	0.0492529	+	0.112285i
$503$	13.8246	+	3.90922i	0.616407	+	0.174303i	0.565973	−	0.824424i	$-0.308501\pi$
$503$	13.8246	+	3.90922i	0.616407	+	0.174303i	0.0504344	+	0.998727i	$0.483939\pi$
$504$	0.653244	+	0.0723010i	0.0290978	+	0.00322054i
$505$	6.03956	−	9.24423i	0.268757	−	0.411363i
$506$	−13.7833	−	10.7280i	−0.612744	−	0.476917i
$507$	4.06141	−	20.7921i	0.180373	−	0.923411i
$508$	0.373040	−	2.69017i	0.0165510	−	0.119357i
$509$	−0.679422	+	1.81466i	−0.0301149	+	0.0804332i	−0.950705	−	0.310097i	$-0.899638\pi$
$509$	−0.679422	+	1.81466i	−0.0301149	+	0.0804332i	0.920590	+	0.390531i	$0.127708\pi$
$510$	−35.4112	−	42.9975i	−1.56804	−	1.90396i
$511$	0.0505225	−	0.0142864i	0.00223498	−	0.000631993i
$512$	10.2286	−	1.70685i	0.452044	−	0.0754328i
$513$	14.8860	+	12.6755i	0.657232	+	0.559636i
$514$	32.9167	+	5.49283i	1.45190	+	0.242278i
$515$	9.36951	−	1.03702i	0.412870	−	0.0456965i
$516$	0.763651	−	1.50902i	0.0336179	−	0.0664307i
$517$	15.2383	+	7.19114i	0.670181	+	0.316266i
$518$	−1.39980	+	0.154930i	−0.0615036	+	0.00680721i
$519$	−3.78263	−	3.67980i	−0.166039	−	0.161525i
$520$	12.1340	+	27.6628i	0.532112	+	1.21309i
$521$	16.1525	−	2.69538i	0.707656	−	0.118087i	0.200188	−	0.979758i	$-0.435845\pi$
$521$	16.1525	−	2.69538i	0.707656	−	0.118087i	0.507468	+	0.861671i	$0.330582\pi$
$522$	−5.92022	+	3.63914i	−0.259121	+	0.159281i
$523$	−5.40658	−	7.35592i	−0.236413	−	0.321652i	0.671345	−	0.741145i	$-0.265717\pi$
$523$	−5.40658	−	7.35592i	−0.236413	−	0.321652i	−0.907759	+	0.419493i	$0.862208\pi$
$524$	−9.45634	−	3.24636i	−0.413102	−	0.141818i
$525$	−0.843047	−	0.915793i	−0.0367936	−	0.0399685i
$526$	4.15865	+	29.9900i	0.181326	+	1.30763i
$527$	−74.0259	−	4.08412i	−3.22462	−	0.177907i
$528$	−3.41957	−	24.6602i	−0.148818	−	1.07320i
$529$	−6.62315	−	1.48428i	−0.287963	−	0.0645340i
$530$	−13.5858	+	43.4362i	−0.590129	+	1.88675i
$531$	−4.78639	−	7.32611i	−0.207711	−	0.317926i
$532$	0.858423	−	0.00956037i	0.0372174	−	0.000414495i
$533$	−6.38678	+	9.77569i	−0.276642	+	0.423432i
$534$	−14.8909	−	18.0811i	−0.644394	−	0.782444i
$535$	−36.1423	+	17.0560i	−1.56257	+	0.737394i
$536$	−13.8393	−	18.8290i	−0.597765	−	0.813289i
$537$	1.17319	+	42.5611i	0.0506268	+	1.83665i
$538$	4.26006	+	8.41810i	0.183664	+	0.362930i
$539$	10.3018	+	15.7680i	0.443729	+	0.679177i
$540$	0.446326	−	5.38636i	0.0192068	−	0.231792i
$541$	2.37302	−	12.1485i	0.102024	−	0.522306i	−0.895057	−	0.445952i	$-0.852865\pi$
$541$	2.37302	−	12.1485i	0.102024	−	0.522306i	0.997081	−	0.0763539i	$-0.0243279\pi$
$542$	−1.71328	+	8.77104i	−0.0735917	+	0.376749i
$543$	−2.17875	+	26.2936i	−0.0934991	+	1.12837i
$544$	10.3397	+	15.8261i	0.443312	+	0.678539i
$545$	7.96035	+	15.7301i	0.340984	+	0.673803i
$546$	−0.170017	−	6.16790i	−0.00727606	−	0.263962i
$547$	24.5743	+	33.4346i	1.05072	+	1.42956i	0.897313	+	0.441396i	$0.145516\pi$
$547$	24.5743	+	33.4346i	1.05072	+	1.42956i	0.153409	+	0.988163i	$0.450975\pi$
$548$	7.26730	−	3.42952i	0.310444	−	0.146502i
$549$	3.20617	+	3.89303i	0.136836	+	0.166151i
$550$	−3.69202	+	5.65106i	−0.157428	+	0.240962i
$551$	23.0760	−	18.3771i	0.983070	−	0.782889i
$552$	10.1189	+	15.4882i	0.430691	+	0.659222i
$553$	−1.39475	+	4.45926i	−0.0593107	+	0.189627i
$554$	−20.2543	−	4.53909i	−0.860522	−	0.192848i
$555$	1.43918	+	10.3786i	0.0610899	+	0.440548i
$556$	−4.06786	−	0.224430i	−0.172516	−	0.00951795i
$557$	1.31361	+	9.47308i	0.0556595	+	0.401387i	0.997807	+	0.0661889i	$0.0210840\pi$
$557$	1.31361	+	9.47308i	0.0556595	+	0.401387i	−0.942148	+	0.335198i	$0.891197\pi$
$558$	7.12048	+	7.73490i	0.301434	+	0.327445i
$559$	8.72727	+	2.99608i	0.369124	+	0.126720i
$560$	2.99525	+	4.07518i	0.126572	+	0.172208i
$561$	−32.5400	+	20.0023i	−1.37384	+	0.844497i
$562$	16.1879	−	2.70127i	0.682843	−	0.113946i
$563$	12.8097	+	29.2031i	0.539864	+	1.23077i	0.948124	+	0.317900i	$0.102978\pi$
$563$	12.8097	+	29.2031i	0.539864	+	1.23077i	−0.408260	+	0.912866i	$0.633864\pi$
$564$	3.93649	+	3.82948i	0.165756	+	0.161250i
$565$	41.8549	−	4.63250i	1.76085	−	0.194891i
$566$	−37.9579	−	17.9127i	−1.59549	−	0.752929i
$567$	1.99041	−	3.93315i	0.0835892	−	0.165177i
$568$	19.8482	−	2.19679i	0.832810	−	0.0921754i
$569$	−32.1309	−	5.36170i	−1.34700	−	0.224774i	−0.553246	−	0.833018i	$-0.686611\pi$
$569$	−32.1309	−	5.36170i	−1.34700	−	0.224774i	−0.793750	+	0.608244i	$0.791874\pi$
$570$	−1.29713	−	33.5057i	−0.0543309	−	1.40340i
$571$	−8.70996	+	1.45344i	−0.364500	+	0.0608244i	−0.344011	−	0.938966i	$-0.611786\pi$
$571$	−8.70996	+	1.45344i	−0.364500	+	0.0608244i	−0.0204897	+	0.999790i	$0.506523\pi$
$572$	−6.13318	+	1.73430i	−0.256441	+	0.0725146i
$573$	14.2787	+	17.3377i	0.596503	+	0.724294i
$574$	−0.548820	+	1.46583i	−0.0229073	+	0.0611826i
$575$	0.860617	−	6.20632i	0.0358902	−	0.258821i
$576$	−0.668279	+	3.42122i	−0.0278450	+	0.142551i
$577$	22.7582	+	17.7134i	0.947435	+	0.737418i	0.964951	−	0.262428i	$-0.0845234\pi$
$577$	22.7582	+	17.7134i	0.947435	+	0.737418i	−0.0175166	+	0.999847i	$0.505576\pi$
$578$	30.4625	−	46.6263i	1.26707	−	1.93940i
$579$	−34.6218	−	3.83194i	−1.43883	−	0.159250i
$580$	−7.84714	−	2.21896i	−0.325835	−	0.0921373i
$581$	1.52940	+	3.48668i	0.0634502	+	0.144652i
$582$	3.72991	+	14.7291i	0.154610	+	0.610540i
$583$	28.2232	+	13.3188i	1.16888	+	0.551610i
$584$	0.0578176	+	0.295994i	0.00239251	+	0.0122483i
$585$	−8.19647	+	0.452212i	−0.338882	+	0.0186967i
$586$	8.08316	+	41.3813i	0.333912	+	1.70945i
$587$	14.9589	−	29.5596i	0.617420	−	1.22005i	−0.342431	−	0.939543i	$-0.611250\pi$
$587$	14.9589	−	29.5596i	0.617420	−	1.22005i	0.959851	−	0.280511i	$-0.0905041\pi$
$588$	1.50701	+	5.95104i	0.0621480	+	0.245417i
$589$	−33.9791	−	28.9334i	−1.40009	−	1.19218i
$590$	13.2346	−	52.2624i	0.544861	−	2.15161i
$591$	−10.3779	−	9.03816i	−0.426892	−	0.371780i
$592$	−0.278432	−	10.1010i	−0.0114435	−	0.415148i
$593$	−22.0542	+	19.2070i	−0.905658	+	0.788738i	−0.977992	−	0.208642i	$-0.933096\pi$
$593$	−22.0542	+	19.2070i	−0.905658	+	0.788738i	0.0723341	+	0.997380i	$0.476955\pi$
$594$	−18.9861	−	4.25488i	−0.779009	−	0.174580i
$595$	3.87968	−	6.71981i	0.159051	−	0.275485i
$596$	−2.33900	−	1.26581i	−0.0958093	−	0.0518494i
$597$	3.73439	+	4.05663i	0.152838	+	0.166027i
$598$	23.4219	−	20.3982i	0.957794	−	0.834143i
$599$	−8.37190	−	16.5433i	−0.342067	−	0.675942i	0.654735	−	0.755859i	$-0.272780\pi$
$599$	−8.37190	−	16.5433i	−0.342067	−	0.675942i	−0.996802	+	0.0799165i	$0.974535\pi$
$600$	5.64237	−	4.39163i	0.230349	−	0.179288i
$601$	−3.15337	−	38.0555i	−0.128629	−	1.55232i	−0.689422	−	0.724360i	$-0.742136\pi$
$601$	−3.15337	−	38.0555i	−0.128629	−	1.55232i	0.560794	−	0.827956i	$-0.310496\pi$
$602$	1.22931	+	0.136060i	0.0501031	+	0.00554541i
$603$	6.11074	−	1.72795i	0.248849	−	0.0703677i
$604$	0.0347948	−	0.0213883i	0.00141578	−	0.000870277i
$605$	−6.53352	−	5.69004i	−0.265625	−	0.231333i
$606$	−6.47811	−	11.2204i	−0.263155	−	0.455798i
$607$	−19.2087	+	14.9508i	−0.779659	+	0.606833i	−0.923867	−	0.382715i	$-0.874989\pi$
$607$	−19.2087	+	14.9508i	−0.779659	+	0.606833i	0.144208	+	0.989547i	$0.453937\pi$
$608$	−0.813379	+	11.3507i	−0.0329869	+	0.460330i
$609$	−4.27198	−	3.32502i	−0.173110	−	0.134737i
$610$	−4.26758	+	30.7756i	−0.172789	+	1.24607i
$611$	−17.7452	+	24.1433i	−0.717896	+	0.976732i
$612$	−2.17230	+	0.486825i	−0.0878102	+	0.0196787i
$613$	12.5740	−	40.2012i	0.507858	−	1.62371i	−0.247846	−	0.968799i	$-0.579723\pi$
$613$	12.5740	−	40.2012i	0.507858	−	1.62371i	0.755704	−	0.654913i	$-0.227295\pi$
$614$	−8.34356	+	7.26641i	−0.336719	+	0.293248i
$615$	11.0140	+	3.78111i	0.444128	+	0.152469i
$616$	2.44182	−	1.32145i	0.0983837	−	0.0532426i
$617$	0.139523	−	5.06162i	0.00561697	−	0.203773i	−0.991606	−	0.129297i	$-0.958728\pi$
$617$	0.139523	−	5.06162i	0.00561697	−	0.203773i	0.997223	−	0.0744758i	$-0.0237283\pi$
$618$	3.87828	−	10.3584i	0.156007	−	0.416677i
$619$	−0.0316648	−	0.0246457i	−0.00127272	−	0.000990595i	0.613576	−	0.789636i	$-0.289730\pi$
$619$	−0.0316648	−	0.0246457i	−0.00127272	−	0.000990595i	−0.614849	+	0.788645i	$0.710783\pi$
$620$	−1.01880	+	12.2950i	−0.0409159	+	0.493781i
$621$	17.6233	−	3.94948i	0.707199	−	0.158487i
$622$	−2.61309	−	6.97926i	−0.104775	−	0.279843i
$623$	1.63146	−	2.82578i	0.0653631	−	0.113212i
$624$	44.2041	+	2.43881i	1.76958	+	0.0976304i
$625$	30.3130	+	1.67241i	1.21252	+	0.0668966i
$626$	−15.6509	−	8.46982i	−0.625534	−	0.338522i
$627$	−22.8799	−	2.27473i	−0.913737	−	0.0908440i
$628$	4.34954	−	2.35385i	0.173565	−	0.0939289i
$629$	−14.0203	+	6.61633i	−0.559025	+	0.263810i
$630$	−1.05881	+	0.299403i	−0.0421841	+	0.0119285i
$631$	16.6352	+	4.70398i	0.662236	+	0.187263i	0.586605	−	0.809873i	$-0.300464\pi$
$631$	16.6352	+	4.70398i	0.662236	+	0.187263i	0.0756315	+	0.997136i	$0.475903\pi$
$632$	−24.8655	−	10.0995i	−0.989097	−	0.401736i
$633$	17.1761	−	6.97633i	0.682689	−	0.277284i
$634$	9.34640	+	1.55964i	0.371193	+	0.0619412i
$635$	−3.62752	−	14.3248i	−0.143954	−	0.568461i
$636$	7.29084	+	7.09264i	0.289101	+	0.281241i
$637$	−31.0312	+	12.6038i	−1.22950	+	0.499380i
$638$	−11.7925	+	26.8843i	−0.466871	+	1.06436i
$639$	−1.33220	+	5.26073i	−0.0527010	+	0.208111i
$640$	−29.6847	+	18.2471i	−1.17339	+	0.721281i
$641$	10.5128	−	4.96111i	0.415230	−	0.195952i	−0.207763	−	0.978179i	$-0.566618\pi$
$641$	10.5128	−	4.96111i	0.415230	−	0.195952i	0.622993	+	0.782227i	$0.285916\pi$
$642$	−1.29207	+	46.8738i	−0.0509939	+	1.84996i
$643$	−3.26474	+	2.26372i	−0.128749	+	0.0892723i	−0.632431	−	0.774616i	$-0.717943\pi$
$643$	−3.26474	+	2.26372i	−0.128749	+	0.0892723i	0.503683	+	0.863889i	$0.331978\pi$
$644$	0.469647	−	0.638978i	0.0185067	−	0.0251793i
$645$	0.759880	−	9.17039i	0.0299203	−	0.361084i
$646$	46.7413	−	16.6305i	1.83901	−	0.654316i
$647$	0.729508	+	8.80386i	0.0286799	+	0.346115i	0.995784	+	0.0917329i	$0.0292406\pi$
$647$	0.729508	+	8.80386i	0.0286799	+	0.346115i	−0.967104	+	0.254382i	$0.918128\pi$
$648$	21.5712	+	13.2598i	0.847398	+	0.520894i
$649$	−34.2512	−	13.9116i	−1.34448	−	0.546079i
$650$	−8.60390	−	8.37001i	−0.337473	−	0.328299i
$651$	−3.69799	+	7.30743i	−0.144936	+	0.286401i
$652$	0.584691	−	0.0322583i	0.0228983	−	0.00126333i
$653$	15.6973			0.614283			0.307141	−	0.951664i	$-0.400628\pi$
$653$	15.6973			0.614283			0.307141	+	0.951664i	$0.400628\pi$
$654$	20.6853			0.808860
$655$	−54.3156	+	2.99667i	−2.12229	+	0.117090i
$656$	−10.1562	−	4.79282i	−0.396533	−	0.187128i
$657$	−0.0808404	−	0.0134899i	−0.00315389	−	0.000526290i
$658$	−1.61332	+	3.67800i	−0.0628937	+	0.143383i
$659$	14.7036	−	17.8536i	0.572771	−	0.695477i	−0.402769	−	0.915302i	$-0.631952\pi$
$659$	14.7036	−	17.8536i	0.572771	−	0.695477i	0.975539	+	0.219825i	$0.0705485\pi$
$660$	3.17806	+	5.50456i	0.123706	+	0.214265i
$661$	5.35826	+	10.5882i	0.208412	+	0.411834i	0.972374	−	0.233427i	$-0.0749941\pi$
$661$	5.35826	+	10.5882i	0.208412	+	0.411834i	−0.763962	+	0.645261i	$0.776749\pi$
$662$	−11.0036	+	35.1805i	−0.427667	+	1.36733i
$663$	−23.8160	−	63.6096i	−0.924936	−	2.47039i
$664$	−20.6850	+	7.10119i	−0.802735	+	0.275579i
$665$	4.30768	−	1.80577i	0.167045	−	0.0700249i
$666$	2.07931	+	0.713830i	0.0805718	+	0.0276603i
$667$	−0.750850	−	27.2394i	−0.0290730	−	1.05471i
$668$	4.37367	+	7.57541i	0.169222	+	0.293101i
$669$	−7.49673	−	23.9684i	−0.289840	−	0.926671i
$670$	33.3289	+	20.4872i	1.28761	+	0.791489i
$671$	20.5015	+	5.79727i	0.791451	+	0.223801i
$672$	2.05983	−	0.343725i	0.0794596	−	0.0132595i
$673$	4.78599	−	18.8995i	0.184486	−	0.728520i	−0.806117	−	0.591756i	$-0.798435\pi$
$673$	4.78599	−	18.8995i	0.184486	−	0.728520i	0.990604	−	0.136764i	$-0.0436704\pi$
$674$	−16.3385	+	19.8387i	−0.629334	+	0.764158i
$675$	−2.08359	−	6.66161i	−0.0801974	−	0.256406i
$676$	−0.430740	−	5.19825i	−0.0165669	−	0.199933i
$677$	24.5240	−	37.5367i	0.942532	−	1.44265i	0.0463709	−	0.998924i	$-0.485234\pi$
$677$	24.5240	−	37.5367i	0.942532	−	1.44265i	0.896161	−	0.443729i	$-0.146345\pi$
$678$	17.3248	−	46.2725i	0.665355	−	1.77708i
$679$	−1.73932	+	1.20602i	−0.0667491	+	0.0462828i
$680$	36.6273	+	25.3968i	1.40459	+	0.973924i
$681$	−5.55006	−	14.8235i	−0.212679	−	0.568039i
$682$	43.3382	+	9.71231i	1.65950	+	0.371904i
$683$	−31.7667	−	34.5078i	−1.21552	−	1.32040i	−0.932448	−	0.361304i	$-0.882332\pi$
$683$	−31.7667	−	34.5078i	−1.21552	−	1.32040i	−0.283069	−	0.959099i	$-0.591353\pi$
$684$	−1.21821	−	0.558385i	−0.0465794	−	0.0213504i
$685$	29.6122	−	32.1675i	1.13143	−	1.22906i
$686$	−7.47331	+	5.18188i	−0.285332	+	0.197845i
$687$	−1.81567	+	13.0936i	−0.0692720	+	0.499554i
$688$	−1.70127	+	8.70954i	−0.0648602	+	0.332048i
$689$	−32.8663	+	44.7162i	−1.25211	+	1.70355i
$690$	−25.4535	−	17.6490i	−0.968997	−	0.671888i
$691$	27.8162	−	9.54931i	1.05818	−	0.363273i	0.259946	−	0.965623i	$-0.416295\pi$
$691$	27.8162	−	9.54931i	1.05818	−	0.363273i	0.798232	+	0.602350i	$0.205769\pi$
$692$	−1.14273	−	0.618414i	−0.0434400	−	0.0235086i
$693$	0.103636	+	0.747367i	0.00393680	+	0.0283901i
$694$	−12.3551	+	21.3996i	−0.468993	+	0.812319i
$695$	−20.9653	+	7.19741i	−0.795261	+	0.273013i
$696$	21.0605	−	22.8778i	0.798298	−	0.867183i
$697$	−0.474754	+	17.2232i	−0.0179826	+	0.652375i
$698$	8.06626	+	9.79431i	0.305312	+	0.370720i
$699$	−41.8466	−	4.63158i	−1.58278	−	0.175183i
$700$	−0.261092	−	0.160493i	−0.00986836	−	0.00606606i
$701$	27.8884	−	27.1303i	1.05333	−	1.02470i	0.0536732	−	0.998559i	$-0.482907\pi$
$701$	27.8884	−	27.1303i	1.05333	−	1.02470i	0.999658	−	0.0261382i	$-0.00832101\pi$
$702$	13.8984	−	31.6851i	0.524560	−	1.19588i
$703$	−9.12856	−	1.93925i	−0.344290	−	0.0731403i
$704$	5.91535	+	13.4856i	0.222943	+	0.508259i
$705$	27.6843	+	11.2444i	1.04265	+	0.423488i
$706$	−13.3163	+	12.9543i	−0.501164	+	0.487540i
$707$	1.14736	−	1.39316i	0.0431510	−	0.0523954i
$708$	−9.08636	−	7.91332i	−0.341486	−	0.297401i
$709$	2.52849	+	3.44014i	0.0949594	+	0.129197i	0.850651	−	0.525730i	$-0.176208\pi$
$709$	2.52849	+	3.44014i	0.0949594	+	0.129197i	−0.755692	+	0.654927i	$0.772699\pi$
$710$	−29.4029	+	15.9121i	−1.10347	+	0.597169i
$711$	4.93973	−	5.36597i	0.185254	−	0.201240i
$712$	15.4023	+	10.6797i	0.577227	+	0.400240i
$713$	−40.2275	+	9.01519i	−1.50653	+	0.337621i
$714$	−4.97957	−	7.62180i	−0.186356	−	0.285239i
$715$	−27.3661	+	21.2999i	−1.02343	+	0.796570i
$716$	3.12937	+	10.0052i	0.116950	+	0.373910i
$717$	−8.11104	+	7.89054i	−0.302912	+	0.294678i
$718$	1.20183	−	0.488140i	0.0448518	−	0.0182172i
$719$	−32.1302	+	3.55617i	−1.19825	+	0.132623i	−0.686903	−	0.726749i	$-0.741030\pi$
$719$	−32.1302	+	3.55617i	−1.19825	+	0.132623i	−0.511351	+	0.859372i	$0.670855\pi$
$720$	−1.51352	−	7.74838i	−0.0564056	−	0.288765i
$721$	1.54076			0.0573808
$722$	28.4553	+	9.06549i	1.05900	+	0.337383i
$723$	−14.4249			−0.536467
$724$	1.24536	+	6.37555i	0.0462835	+	0.236946i
$725$	−10.4674	+	1.15853i	−0.388748	+	0.0430266i
$726$	−9.41838	+	3.82542i	−0.349549	+	0.141975i
$727$	−2.32332	+	2.26016i	−0.0861671	+	0.0838246i	−0.739120	−	0.673574i	$-0.764758\pi$
$727$	−2.32332	+	2.26016i	−0.0861671	+	0.0838246i	0.652953	+	0.757399i	$0.273530\pi$
$728$	1.47383	+	4.71209i	0.0546237	+	0.174642i
$729$	14.8663	−	11.5709i	0.550604	−	0.428552i
$730$	−0.276161	−	0.422697i	−0.0102212	−	0.0156447i
$731$	13.2854	−	2.97732i	0.491377	−	0.110120i
$732$	5.70647	+	3.95678i	0.210917	+	0.146247i
$733$	22.1498	−	24.0611i	0.818122	−	0.888718i	−0.177313	−	0.984154i	$-0.556741\pi$
$733$	22.1498	−	24.0611i	0.818122	−	0.888718i	0.995436	+	0.0954366i	$0.0304247\pi$
$734$	18.7158	−	10.1285i	0.690813	−	0.373849i
$735$	19.7812	+	26.9133i	0.729641	+	0.992713i
$736$	7.92712	+	6.90374i	0.292198	+	0.254475i
$737$	17.0544	−	20.7081i	0.628209	−	0.762792i
$738$	1.75131	−	1.70370i	0.0644666	−	0.0627140i
$739$	−26.0375	−	10.5755i	−0.957804	−	0.389027i	−0.156763	−	0.987636i	$-0.550106\pi$
$739$	−26.0375	−	10.5755i	−0.957804	−	0.389027i	−0.801041	+	0.598610i	$0.795720\pi$
$740$	1.03630	+	2.36253i	0.0380952	+	0.0868483i
$741$	11.7699	−	39.1559i	0.432379	−	1.43843i
$742$	−2.98806	+	6.81208i	−0.109695	+	0.250079i
$743$	−35.4599	+	34.4959i	−1.30090	+	1.26553i	−0.357480	+	0.933921i	$0.616364\pi$
$743$	−35.4599	+	34.4959i	−1.30090	+	1.26553i	−0.943416	+	0.331610i	$0.892408\pi$
$744$	−40.0774	−	24.6355i	−1.46931	−	0.903181i
$745$	−14.3824	−	1.59185i	−0.526932	−	0.0583208i
$746$	−3.12359	−	3.79277i	−0.114363	−	0.138863i
$747$	0.163764	−	5.94105i	0.00599181	−	0.217372i
$748$	−6.36945	+	6.91907i	−0.232890	+	0.252986i
$749$	−6.17812	+	2.12095i	−0.225744	+	0.0774978i
$750$	13.2460	−	22.9427i	0.483675	−	0.837750i
$751$	−0.0139999	−	0.100960i	−0.000510864	−	0.00368408i	0.990265	−	0.139195i	$-0.0444516\pi$
$751$	−0.0139999	−	0.100960i	−0.000510864	−	0.00368408i	−0.990776	+	0.135511i	$0.956732\pi$
$752$	−25.3435	−	13.7152i	−0.924181	−	0.500142i
$753$	3.15961	−	1.08470i	0.115143	−	0.0395285i
$754$	−42.8998	−	29.7461i	−1.56232	−	1.08329i
$755$	0.131607	−	0.179058i	0.00478967	−	0.00651657i
$756$	0.169356	−	0.867008i	0.00615941	−	0.0315328i
$757$	1.14213	−	8.23643i	0.0415113	−	0.299358i	−0.958392	−	0.285455i	$-0.907855\pi$
$757$	1.14213	−	8.23643i	0.0415113	−	0.299358i	0.999903	−	0.0139027i	$-0.00442552\pi$
$758$	−24.5138	+	16.9975i	−0.890381	+	0.617377i
$759$	−14.3850	+	15.6262i	−0.522141	+	0.567197i
$760$	8.29385	+	25.5160i	0.300850	+	0.925562i
$761$	18.0928	+	19.6540i	0.655863	+	0.712457i	0.971664	−	0.236368i	$-0.0759572\pi$
$761$	18.0928	+	19.6540i	0.655863	+	0.712457i	−0.315800	+	0.948826i	$0.602273\pi$
$762$	−16.9185	−	3.79153i	−0.612894	−	0.137353i
$763$	1.01036	+	2.69854i	0.0365773	+	0.0976937i
$764$	4.54453	+	3.15111i	0.164415	+	0.114003i
$765$	−9.95370	+	6.90174i	−0.359877	+	0.249533i
$766$	−11.4321	+	30.5337i	−0.413057	+	1.10323i
$767$	35.9558	−	55.0345i	1.29829	−	1.98718i
$768$	1.69174	+	20.4163i	0.0610455	+	0.736710i
$769$	−9.40969	−	30.0845i	−0.339322	−	1.08487i	−0.954933	−	0.296823i	$-0.904073\pi$
$769$	−9.40969	−	30.0845i	−0.339322	−	1.08487i	0.615610	−	0.788051i	$-0.288910\pi$
$770$	−2.95503	+	3.58810i	−0.106492	+	0.129306i
$771$	9.96200	−	39.3391i	0.358773	−	1.41676i
$772$	−8.45947	+	1.41164i	−0.304463	+	0.0508059i
$773$	−13.5441	−	3.82989i	−0.487146	−	0.137752i	0.0196693	−	0.999807i	$-0.493739\pi$
$773$	−13.5441	−	3.82989i	−0.487146	−	0.137752i	−0.506815	+	0.862055i	$0.669177\pi$
$774$	−1.64479	−	1.01105i	−0.0591206	−	0.0363413i
$775$	4.75606	+	15.2060i	0.170843	+	0.546215i
$776$	−6.07885	−	10.5289i	−0.218218	−	0.377964i
$777$	0.0471888	+	1.71192i	0.00169289	+	0.0614149i
$778$	−30.5554	−	10.4897i	−1.09547	−	0.376074i
$779$	−6.50397	+	8.07902i	−0.233029	+	0.289461i
$780$	−10.6903	+	3.66998i	−0.382774	+	0.131406i
$781$	8.03847	+	21.4698i	0.287639	+	0.768249i
$782$	13.6804	−	43.7387i	0.489210	−	1.56409i
$783$	−13.7066	−	27.0850i	−0.489833	−	0.967937i
$784$	−16.1058	−	27.8960i	−0.575206	−	0.996286i
$785$	17.1063	−	20.7711i	0.610552	−	0.741352i
$786$	−25.6390	+	58.4510i	−0.914513	+	2.08488i
$787$	25.1109	+	4.19028i	0.895109	+	0.149367i	0.594230	−	0.804295i	$-0.297457\pi$
$787$	25.1109	+	4.19028i	0.895109	+	0.149367i	0.300879	+	0.953662i	$0.402720\pi$
$788$	−3.06430	−	1.44608i	−0.109161	−	0.0515145i
$789$	36.7614	−	2.02818i	1.30874	−	0.0722052i
$790$	44.9322			1.59862
$791$	6.88277			0.244723
$792$	−4.32748	+	0.238754i	−0.153770	+	0.00848374i
$793$	−17.1068	+	33.8040i	−0.607481	+	1.20042i
$794$	−2.24852	−	2.18739i	−0.0797968	−	0.0776275i
$795$	51.2745	+	20.8259i	1.81852	+	0.738619i
$796$	1.15654	+	0.710925i	0.0409926	+	0.0251981i
$797$	2.27144	+	27.4123i	0.0804587	+	0.970992i	0.910559	+	0.413378i	$0.135651\pi$
$797$	2.27144	+	27.4123i	0.0804587	+	0.970992i	−0.830101	+	0.557613i	$0.811717\pi$
$798$	0.391720	−	5.46644i	0.0138667	−	0.193510i
$799$	−3.65092	+	44.0601i	−0.129160	+	1.55873i
$800$	2.40600	−	3.27348i	0.0850648	−	0.115735i
$801$	−4.18567	+	2.90228i	−0.147894	+	0.102547i
$802$	0.168478	−	6.11208i	0.00594918	−	0.215825i
$803$	−0.313115	+	0.147763i	−0.0110496	+	0.00521443i
$804$	7.44890	−	4.57882i	0.262702	−	0.161482i
$805$	1.05919	−	4.18263i	0.0373314	−	0.147418i
$806$	−31.7248	+	72.3252i	−1.11746	+	2.54755i
$807$	10.6294	−	4.31728i	0.374172	−	0.151976i
$808$	7.43095	+	7.22894i	0.261420	+	0.254313i
$809$	0.719731	+	2.84215i	0.0253044	+	0.0999248i	0.980764	−	0.195197i	$-0.0625346\pi$
$809$	0.719731	+	2.84215i	0.0253044	+	0.0999248i	−0.955460	+	0.295122i	$0.904640\pi$
$810$	−41.8134	−	6.97743i	−1.46917	−	0.245162i
$811$	9.30172	−	3.77803i	0.326628	−	0.132665i	−0.207103	−	0.978319i	$-0.566404\pi$
$811$	9.30172	−	3.77803i	0.326628	−	0.132665i	0.533731	+	0.845654i	$0.320790\pi$
$812$	−1.23490	−	0.501572i	−0.0433364	−	0.0176017i
$813$	10.4573	+	2.95704i	0.366753	+	0.103708i
$814$	8.93677	−	2.52708i	0.313234	−	0.0885740i
$815$	2.88134	−	1.35974i	0.100929	−	0.0476296i
$816$	57.4498	−	31.0903i	2.01114	−	1.08838i
$817$	7.45032	+	3.41497i	0.260654	+	0.119475i
$818$	−29.8792	−	16.1698i	−1.04470	−	0.565365i
$819$	−1.33968	−	0.0739120i	−0.0468121	−	0.00258270i
$820$	2.86280	+	0.157945i	0.0999734	+	0.00551569i
$821$	−7.37117	+	12.7672i	−0.257256	+	0.445580i	−0.965506	−	0.260382i	$-0.916152\pi$
$821$	−7.37117	+	12.7672i	−0.257256	+	0.445580i	0.708250	+	0.705962i	$0.249485\pi$
$822$	−17.9879	−	48.0435i	−0.627400	−	1.67571i
$823$	−1.86604	+	0.418190i	−0.0650461	+	0.0145772i	−0.251083	−	0.967966i	$-0.580787\pi$
$823$	−1.86604	+	0.418190i	−0.0650461	+	0.0145772i	0.186037	+	0.982543i	$0.440436\pi$
$824$	−0.730854	+	8.82009i	−0.0254605	+	0.307263i
$825$	6.47757	+	5.04170i	0.225520	+	0.175529i
$826$	3.08971	−	8.25224i	0.107505	−	0.287132i
$827$	1.18242	−	42.8958i	0.0411166	−	1.49163i	−0.645022	−	0.764164i	$-0.723152\pi$
$827$	1.18242	−	42.8958i	0.0411166	−	1.49163i	0.686139	−	0.727471i	$-0.259304\pi$
$828$	−1.08869	+	0.589170i	−0.0378346	+	0.0204751i
$829$	−10.9121	−	3.74614i	−0.378994	−	0.130109i	0.128619	−	0.991694i	$-0.458946\pi$
$829$	−10.9121	−	3.74614i	−0.378994	−	0.130109i	−0.507613	+	0.861585i	$0.669472\pi$
$830$	27.6112	−	24.0466i	0.958399	−	0.834670i
$831$	−7.53466	+	24.0896i	−0.261374	+	0.835661i
$832$	−25.5525	+	5.72644i	−0.885872	+	0.198529i
$833$	−29.2680	+	39.8206i	−1.01408	+	1.37970i
$834$	−3.57235	+	25.7619i	−0.123700	+	0.892062i
$835$	37.5577	+	29.2323i	1.29974	+	1.01163i
$836$	−5.57321	+	0.993920i	−0.192753	+	0.0343755i
$837$	−36.2405	+	28.2071i	−1.25266	+	0.974981i
$838$	3.94202	+	6.82778i	0.136175	+	0.235862i
$839$	3.72099	+	3.24062i	0.128463	+	0.111878i	0.718597	−	0.695427i	$-0.244785\pi$
$839$	3.72099	+	3.24062i	0.128463	+	0.111878i	−0.590134	+	0.807305i	$0.700925\pi$
$840$	4.19452	−	2.57836i	0.144725	−	0.0889619i
$841$	−16.1670	+	4.57158i	−0.557482	+	0.157641i
$842$	41.5386	+	4.59750i	1.43152	+	0.158440i
$843$	−1.64803	−	19.8887i	−0.0567611	−	0.685005i
$844$	3.60205	−	2.80359i	0.123988	−	0.0965035i
$845$	−12.8145	−	25.3222i	−0.440833	−	0.871109i
$846$	4.72781	−	4.11745i	0.162546	−	0.141561i
$847$	−0.959084	−	1.04184i	−0.0329545	−	0.0357981i
$848$	−46.9391	−	25.4022i	−1.61189	−	0.872314i
$849$	−25.5195	+	44.2010i	−0.875826	+	1.51698i
$850$	−17.2827	−	3.87313i	−0.592790	−	0.132847i
$851$	−6.50084	+	5.66159i	−0.222846	+	0.194077i
$852$	0.205887	+	7.46920i	0.00705357	+	0.255890i
$853$	34.4947	+	30.0415i	1.18108	+	1.02860i	0.998972	+	0.0453223i	$0.0144315\pi$
$853$	34.4947	+	30.0415i	1.18108	+	1.02860i	0.182105	+	0.983279i	$0.441709\pi$
$854$	−1.24664	+	4.92287i	−0.0426591	+	0.168457i
$855$	−7.28419	−	0.320558i	−0.249114	−	0.0109628i
$856$	−9.21085	−	36.3728i	−0.314820	−	1.24320i
$857$	4.46150	−	8.81616i	0.152402	−	0.301154i	−0.803256	−	0.595634i	$-0.796901\pi$
$857$	4.46150	−	8.81616i	0.152402	−	0.301154i	0.955658	+	0.294480i	$0.0951464\pi$
$858$	7.80053	+	39.9344i	0.266306	+	1.36334i
$859$	−12.6371	+	0.697208i	−0.431172	+	0.0237884i	−0.269374	−	0.963036i	$-0.586817\pi$
$859$	−12.6371	+	0.697208i	−0.431172	+	0.0237884i	−0.161798	+	0.986824i	$0.551729\pi$
$860$	−0.434343	−	2.22360i	−0.0148110	−	0.0758240i
$861$	1.72128	+	0.812291i	0.0586610	+	0.0276828i
$862$	−9.57136	−	37.7964i	−0.326002	−	1.28735i
$863$	0.126375	+	0.288105i	0.00430184	+	0.00980721i	0.917911	−	0.396786i	$-0.129875\pi$
$863$	0.126375	+	0.288105i	0.00430184	+	0.00980721i	−0.913609	+	0.406593i	$0.866717\pi$
$864$	11.2682	+	3.18635i	0.383353	+	0.108402i
$865$	−7.02660	−	0.777704i	−0.238911	−	0.0264427i
$866$	32.0654	−	49.0797i	1.08963	−	1.66780i
$867$	−53.4458	−	41.5986i	−1.81512	−	1.41276i
$868$	−0.386576	+	1.97906i	−0.0131213	+	0.0671735i
$869$	4.23199	−	30.5189i	0.143561	−	1.03528i
$870$	−18.2542	+	48.7547i	−0.618874	+	1.65294i
$871$	30.3269	+	36.8239i	1.02759	+	1.24773i
$872$	−15.9271	+	4.50376i	−0.539360	+	0.152516i
$873$	3.25886	−	0.543808i	0.110296	−	0.0184051i
$874$	22.4939	−	15.9708i	0.760868	−	0.540220i
$875$	3.64002	+	0.607412i	0.123055	+	0.0205343i
$876$	−0.112162	+	0.0124140i	−0.00378959	+	0.000419432i
$877$	−20.5772	+	40.6616i	−0.694841	+	1.37304i	0.222496	+	0.974934i	$0.428580\pi$
$877$	−20.5772	+	40.6616i	−0.694841	+	1.37304i	−0.917337	+	0.398111i	$0.869666\pi$
$878$	28.8279	+	13.6042i	0.972896	+	0.459121i
$879$	50.9602	−	5.64028i	1.71885	−	0.190242i
$880$	−23.9057	−	23.2558i	−0.805861	−	0.783953i
$881$	−18.7774	−	42.8083i	−0.632628	−	1.44225i	−0.880780	−	0.473526i	$-0.842981\pi$
$881$	−18.7774	−	42.8083i	−0.632628	−	1.44225i	0.248152	−	0.968721i	$-0.420177\pi$
$882$	6.91245	−	1.15348i	0.232754	−	0.0388398i
$883$	−39.3635	+	24.1967i	−1.32469	+	0.814282i	−0.991691	−	0.128646i	$-0.958937\pi$
$883$	−39.3635	+	24.1967i	−1.32469	+	0.814282i	−0.332997	+	0.942928i	$0.608060\pi$
$884$	−9.90415	−	13.4751i	−0.333113	−	0.453216i
$885$	−62.0059	−	21.2867i	−2.08431	−	0.715543i
$886$	−6.47517	−	7.03391i	−0.217537	−	0.236309i
$887$	2.26343	+	16.3227i	0.0759986	+	0.548063i	0.989861	+	0.142039i	$0.0453657\pi$
$887$	2.26343	+	16.3227i	0.0759986	+	0.548063i	−0.913862	+	0.406024i	$0.866915\pi$
$888$	−9.82232	−	0.541913i	−0.329615	−	0.0181854i
$889$	−0.331739	−	2.39233i	−0.0111262	−	0.0802362i
$890$	−30.6192	−	6.86193i	−1.02636	−	0.230013i
$891$	−8.67747	+	27.7434i	−0.290706	+	0.929439i
$892$	−3.38193	−	5.17644i	−0.113236	−	0.173320i
$893$	−17.8057	+	19.7797i	−0.595844	+	0.661903i
$894$	−9.28629	+	14.2137i	−0.310580	+	0.475378i
$895$	36.2600	+	44.0281i	1.21204	+	1.47170i
$896$	−5.15048	+	2.43057i	−0.172065	+	0.0811996i
$897$	−22.3679	−	30.4326i	−0.746841	−	1.01611i
$898$	−0.189388	−	6.87064i	−0.00631996	−	0.229276i
$899$	31.2870	+	61.8249i	1.04348	+	2.06198i
$900$	0.261665	+	0.400508i	0.00872217	+	0.0133503i
$901$	−6.76193	+	81.6044i	−0.225273	+	2.71864i
$902$	1.97876	−	10.1301i	0.0658855	−	0.337297i
$903$	0.288332	−	1.47610i	0.00959510	−	0.0491215i
$904$	−3.26482	+	39.4006i	−0.108586	+	1.31044i
$905$	19.3314	+	29.5890i	0.642598	+	0.983570i
$906$	−0.117732	−	0.232644i	−0.00391138	−	0.00772909i
$907$	−0.00712217	−	0.258379i	−0.000236488	−	0.00857934i	0.999493	−	0.0318438i	$-0.0101379\pi$
$907$	−0.00712217	−	0.258379i	−0.000236488	−	0.00857934i	−0.999729	+	0.0232644i	$0.992594\pi$
$908$	−2.30806	−	3.14022i	−0.0765956	−	0.104212i
$909$	−2.54786	+	1.20237i	−0.0845073	+	0.0398799i
$910$	−5.25476	−	6.38050i	−0.174194	−	0.211512i
$911$	4.86446	−	7.44560i	0.161167	−	0.246684i	−0.747447	−	0.664321i	$-0.768721\pi$
$911$	4.86446	−	7.44560i	0.161167	−	0.246684i	0.908614	+	0.417637i	$0.137142\pi$
$912$	38.8554	+	6.03986i	1.28663	+	0.200000i
$913$	−13.7324	−	21.0190i	−0.454476	−	0.695627i
$914$	7.93299	−	25.3632i	0.262400	−	0.838940i
$915$	36.8673	+	8.26216i	1.21880	+	0.273138i
$916$	0.447043	+	3.22384i	0.0147707	+	0.106519i
$917$	−8.87764	−	0.489793i	−0.293166	−	0.0161744i
$918$	−7.01213	−	50.5678i	−0.231435	−	1.66899i
$919$	−14.7501	−	16.0228i	−0.486560	−	0.528545i	0.443342	−	0.896352i	$-0.353793\pi$
$919$	−14.7501	−	16.0228i	−0.486560	−	0.528545i	−0.929902	+	0.367808i	$0.880108\pi$
$920$	23.4411	+	8.04735i	0.772831	+	0.265313i
$921$	7.96806	+	10.8409i	0.262557	+	0.357221i
$922$	−12.2721	+	7.54361i	−0.404159	+	0.248436i
$923$	−40.2106	+	6.70997i	−1.32355	+	0.220861i
$924$	0.417313	+	0.951379i	0.0137286	+	0.0312981i
$925$	2.38804	+	2.32312i	0.0785184	+	0.0763839i
$926$	28.2173	−	3.12309i	0.927279	−	0.102631i
$927$	−2.17509	−	1.02645i	−0.0714395	−	0.0337131i
$928$	7.97781	−	15.7646i	0.261884	−	0.517498i
$929$	−54.0924	+	5.98695i	−1.77471	+	0.196425i	−0.936916	−	0.349554i	$-0.886333\pi$
$929$	−54.0924	+	5.98695i	−1.77471	+	0.196425i	−0.837798	+	0.545980i	$0.816158\pi$
$930$	77.6856	+	12.9634i	2.54741	+	0.425088i
$931$	−28.5345	+	8.41306i	−0.935179	+	0.275727i
$932$	−10.2248	+	1.70621i	−0.334923	+	0.0558888i
$933$	−8.72032	+	2.46587i	−0.285491	+	0.0807290i
$934$	22.1057	+	26.8415i	0.723321	+	0.878280i
$935$	−17.9416	+	47.9198i	−0.586752	+	1.56714i
$936$	1.05858	−	7.63395i	0.0346009	−	0.249523i
$937$	8.97050	−	45.9239i	0.293053	−	1.50027i	−0.486359	−	0.873759i	$-0.661675\pi$
$937$	8.97050	−	45.9239i	0.293053	−	1.50027i	0.779413	−	0.626511i	$-0.215518\pi$
$938$	5.04603	+	3.92748i	0.164759	+	0.128237i
$939$	−11.8359	+	18.1162i	−0.386250	+	0.591200i
$940$	7.31240	+	0.809336i	0.238504	+	0.0263976i
$941$	43.1655	+	12.2060i	1.40715	+	0.397905i	0.889206	−	0.457507i	$-0.151258\pi$
$941$	43.1655	+	12.2060i	1.40715	+	0.397905i	0.517948	+	0.855412i	$0.326696\pi$
$942$	−12.6825	−	28.9132i	−0.413219	−	0.942043i
$943$	2.35193	+	9.28757i	0.0765894	+	0.302445i
$944$	57.1767	+	26.9823i	1.86094	+	0.878200i
$945$	−0.921444	−	4.71728i	−0.0299746	−	0.153453i
$946$	−8.14371	+	0.449301i	−0.264775	+	0.0146080i
$947$	−1.90981	−	9.77717i	−0.0620605	−	0.317715i	0.937480	−	0.348040i	$-0.113153\pi$
$947$	−1.90981	−	9.77717i	−0.0620605	−	0.317715i	−0.999540	+	0.0303250i	$0.990346\pi$
$948$	4.53439	−	8.96021i	0.147270	−	0.291014i
$949$	−0.151140	−	0.596839i	−0.00490622	−	0.0193742i
$950$	−6.86906	−	8.15387i	−0.222862	−	0.264547i
$951$	2.82862	−	11.1700i	0.0917242	−	0.362211i
$952$	5.49360	+	4.78438i	0.178049	+	0.155063i
$953$	−0.742966	−	26.9534i	−0.0240670	−	0.873107i	−0.911290	−	0.411766i	$-0.864912\pi$
$953$	−0.742966	−	26.9534i	−0.0240670	−	0.873107i	0.887223	−	0.461341i	$-0.152632\pi$
$954$	8.75646	−	7.62601i	0.283501	−	0.246901i
$955$	29.3605	+	6.57983i	0.950082	+	0.212918i
$956$	−1.39307	+	2.41287i	−0.0450551	+	0.0780377i
$957$	31.3960	+	16.9906i	1.01489	+	0.549230i
$958$	−0.978068	−	1.06247i	−0.0315999	−	0.0343267i
$959$	5.38900	−	4.69328i	0.174020	−	0.151554i
$960$	11.7914	+	23.3005i	0.380566	+	0.752020i
$961$	58.2603	−	45.3458i	1.87936	−	1.46277i
$962$	1.36379	+	16.4584i	0.0439702	+	0.530642i
$963$	10.1347	+	1.12170i	0.326585	+	0.0361464i
$964$	−3.41760	+	0.966406i	−0.110074	+	0.0311258i
$965$	−39.7534	+	24.4363i	−1.27971	+	0.786633i
$966$	−3.81767	−	3.32481i	−0.122832	−	0.106974i
$967$	−5.24052	−	9.07684i	−0.168524	−	0.291892i	0.769377	−	0.638795i	$-0.220567\pi$
$967$	−5.24052	−	9.07684i	−0.168524	−	0.291892i	−0.937901	+	0.346903i	$0.887233\pi$
$968$	6.41899	−	4.99610i	0.206314	−	0.160581i
$969$	−15.4602	−	58.3141i	−0.496653	−	1.87332i
$970$	16.0623	+	12.5018i	0.515731	+	0.401409i
$971$	−0.781740	+	5.63750i	−0.0250872	+	0.180916i	−0.998927	−	0.0463216i	$-0.985250\pi$
$971$	−0.781740	+	5.63750i	−0.0250872	+	0.180916i	0.973839	+	0.227238i	$0.0729694\pi$
$972$	−1.86071	+	2.53159i	−0.0596823	+	0.0812007i
$973$	−3.53531	+	0.792281i	−0.113337	+	0.0253993i
$974$	−10.0505	+	32.1334i	−0.322040	+	1.02962i
$975$	−11.0073	+	9.58627i	−0.352516	+	0.307006i
$976$	−34.4621	−	11.8309i	−1.10311	−	0.378697i
$977$	−34.4370	+	18.6363i	−1.10174	+	0.596230i	−0.921885	−	0.387464i	$-0.873351\pi$
$977$	−34.4370	+	18.6363i	−1.10174	+	0.596230i	−0.179851	+	0.983694i	$0.557562\pi$
$978$	0.103007	−	3.73689i	0.00329379	−	0.119492i
$979$	−7.54468	+	20.1510i	−0.241129	+	0.644027i
$980$	6.48972	+	5.05116i	0.207307	+	0.161353i
$981$	0.371442	−	4.48264i	0.0118592	−	0.143120i
$982$	−35.8565	+	8.03562i	−1.14423	+	0.256427i
$983$	10.8096	+	28.8712i	0.344773	+	0.920848i	0.987901	+	0.155089i	$0.0495664\pi$
$983$	10.8096	+	28.8712i	0.344773	+	0.920848i	−0.643127	+	0.765759i	$0.722363\pi$
$984$	−5.46646	+	9.46819i	−0.174264	+	0.301835i
$985$	−18.4077	−	1.01558i	−0.586520	−	0.0323592i
$986$	−76.9103	−	4.24326i	−2.44932	−	0.135133i
$987$	4.29523	+	2.32446i	0.136719	+	0.0739884i
$988$	0.165302	−	10.0655i	0.00525896	−	0.320226i
$989$	6.65821	−	3.60324i	0.211719	−	0.114576i
$990$	6.56203	−	3.09670i	0.208555	−	0.0984194i
$991$	7.49581	−	2.11961i	0.238112	−	0.0673317i	−0.150957	−	0.988540i	$-0.548235\pi$
$991$	7.49581	−	2.11961i	0.238112	−	0.0673317i	0.389069	+	0.921209i	$0.372797\pi$
$992$	−25.7212	−	7.27325i	−0.816648	−	0.230926i
$993$	41.5290	+	16.8676i	1.31788	+	0.535278i
$994$	−5.06271	+	2.05630i	−0.160580	+	0.0652218i
$995$	7.28565	+	1.21576i	0.230971	+	0.0385422i
$996$	−2.00886	−	7.93281i	−0.0636532	−	0.251361i
$997$	−25.0908	−	24.4087i	−0.794635	−	0.773033i	0.183052	−	0.983103i	$-0.441402\pi$
$997$	−25.0908	−	24.4087i	−0.794635	−	0.773033i	−0.977686	+	0.210071i	$0.932631\pi$
$998$	3.75773	−	1.52626i	0.118949	−	0.0483129i
$999$	−3.85754	+	8.79430i	−0.122047	+	0.278239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.i.a.7.8	✓	1080
361.258	even	57	inner	361.2.i.a.258.8	yes	1080

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.i.a.7.8	✓	1080	1.1	even	1	trivial
361.2.i.a.258.8	yes	1080	361.258	even	57	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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.301334 - 1.54266i) q^{2} +(-1.89976 + 0.210265i) q^{3} +(-0.436011 + 0.177092i) q^{4} +(-1.83532 + 1.78542i) q^{5} +(0.896828 + 2.86732i) q^{6} +(-0.330256 + 0.257049i) q^{7} +(-1.31482 - 2.01249i) q^{8} +(0.637470 - 0.142860i) q^{9} +(3.30734 + 2.29326i) q^{10} +(1.86914 - 2.03043i) q^{11} +(0.791078 - 0.428110i) q^{12} +(2.90641 + 3.95431i) q^{13} +(0.496056 + 0.432016i) q^{14} +(3.11124 - 3.77777i) q^{15} +(-3.38303 + 3.29106i) q^{16} +(6.70886 + 2.72490i) q^{17} +(-0.412476 - 0.940352i) q^{18} +(2.22135 + 3.75041i) q^{19} +(0.484033 - 1.10348i) q^{20} +(0.573358 - 0.557771i) q^{21} +(-3.69549 - 2.27161i) q^{22} +(4.00205 + 0.442946i) q^{23} +(2.92100 + 3.54678i) q^{24} +(0.0428780 - 1.55553i) q^{25} +(5.22436 - 5.67517i) q^{26} +(4.24238 - 1.45641i) q^{27} +(0.0984740 - 0.170562i) q^{28} +(-0.929559 - 6.70349i) q^{29} +(-6.76534 - 3.66122i) q^{30} +(-9.68378 + 3.32445i) q^{31} +(2.14541 + 1.48760i) q^{32} +(-3.12398 + 4.25033i) q^{33} +(2.18199 - 11.1706i) q^{34} +(0.147184 - 1.06141i) q^{35} +(-0.252645 + 0.175180i) q^{36} +(-1.45004 + 1.57516i) q^{37} +(5.11624 - 4.55692i) q^{38} +(-6.35292 - 6.90111i) q^{39} +(6.00626 + 1.34604i) q^{40} +(0.834318 + 2.22836i) q^{41} +(-1.03322 - 0.716421i) q^{42} +(1.54512 - 1.07136i) q^{43} +(-0.455392 + 1.21630i) q^{44} +(-0.914893 + 1.40035i) q^{45} +(-0.522635 - 6.30727i) q^{46} +(1.82260 + 5.82717i) q^{47} +(5.73493 - 6.96354i) q^{48} +(-1.67540 + 6.61602i) q^{49} +(-2.41258 + 0.402588i) q^{50} +(-13.3181 - 3.76601i) q^{51} +(-1.96750 - 1.20942i) q^{52} +(3.37567 + 10.7926i) q^{53} +(-3.52512 - 6.10569i) q^{54} +(0.194709 + 7.06368i) q^{55} +(0.951537 + 0.326663i) q^{56} +(-5.00861 - 6.65779i) q^{57} +(-10.0611 + 3.45398i) q^{58} +(-4.69699 - 12.5451i) q^{59} +(-0.687521 + 2.19813i) q^{60} +(3.48584 + 6.88820i) q^{61} +(8.04654 + 13.9370i) q^{62} +(-0.173806 + 0.211042i) q^{63} +(-2.14342 + 4.88651i) q^{64} +(-12.3943 - 2.06824i) q^{65} +(7.49817 + 3.53847i) q^{66} +(9.70593 - 0.535491i) q^{67} -3.40769 q^{68} -7.69604 q^{69} +(-1.68175 + 0.0927848i) q^{70} +(-3.75087 + 7.41193i) q^{71} +(-1.12567 - 1.09507i) q^{72} +(-0.116234 - 0.0472103i) q^{73} +(2.86689 + 1.76227i) q^{74} +(0.245616 + 2.96415i) q^{75} +(-1.63270 - 1.24184i) q^{76} +(-0.0953763 + 1.15102i) q^{77} +(-8.73172 + 11.8799i) q^{78} +(9.17460 - 6.36153i) q^{79} +(0.332990 - 12.0803i) q^{80} +(-9.52566 + 4.49527i) q^{81} +(3.18620 - 1.95855i) q^{82} +(2.23333 - 8.81923i) q^{83} +(-0.151213 + 0.344732i) q^{84} +(-17.1780 + 6.97709i) q^{85} +(-2.11835 - 2.06076i) q^{86} +(3.17544 + 12.5395i) q^{87} +(-6.54380 - 1.09197i) q^{88} +(-7.22359 + 2.93397i) q^{89} +(2.43595 + 0.989398i) q^{90} +(-1.97631 - 0.558847i) q^{91} +(-1.82338 + 0.515602i) q^{92} +(17.6978 - 8.35179i) q^{93} +(8.44014 - 4.56757i) q^{94} +(-10.7730 - 2.91714i) q^{95} +(-4.38855 - 2.37497i) q^{96} +(5.04975 + 0.278602i) q^{97} +(10.7111 + 0.590949i) q^{98} +(0.901453 - 1.56136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1080 q - 38 q^{2} - 19 q^{3} - 8 q^{4} - 37 q^{5} - 38 q^{6} - 40 q^{7} - 38 q^{8} + 49 q^{9} + 19 q^{10} - 40 q^{11} - 38 q^{12} - 38 q^{13} - 38 q^{15} - 8 q^{16} - 94 q^{17} - 38 q^{18} - 38 q^{19} - 46 q^{20}+ \cdots + 2 q^{99}+O(q^{100}) \) 1080 * q - 38 * q^2 - 19 * q^3 - 8 * q^4 - 37 * q^5 - 38 * q^6 - 40 * q^7 - 38 * q^8 + 49 * q^9 + 19 * q^10 - 40 * q^11 - 38 * q^12 - 38 * q^13 - 38 * q^15 - 8 * q^16 - 94 * q^17 - 38 * q^18 - 38 * q^19 - 46 * q^20 - 38 * q^21 - 19 * q^22 - 34 * q^23 - 30 * q^24 - 7 * q^25 + 41 * q^26 - 76 * q^27 - 15 * q^28 + 60 * q^30 - 38 * q^31 - 38 * q^32 - 114 * q^33 - 38 * q^34 - 33 * q^35 - 38 * q^37 - 76 * q^38 + 26 * q^39 - 38 * q^40 - 38 * q^41 - 32 * q^42 + 43 * q^43 - 26 * q^44 + 47 * q^45 + 26 * q^47 - 456 * q^48 - 32 * q^49 + 38 * q^50 + 38 * q^51 - 38 * q^52 - 38 * q^53 - 214 * q^54 - 29 * q^55 + 304 * q^56 - 38 * q^57 - 46 * q^58 - 38 * q^59 - 33 * q^61 - 13 * q^62 + 68 * q^63 - 110 * q^64 + 38 * q^65 - 26 * q^66 - 38 * q^67 - 96 * q^68 - 228 * q^69 - 342 * q^70 - 38 * q^71 - 38 * q^72 - 29 * q^73 + 50 * q^74 + 190 * q^75 + 323 * q^76 - 60 * q^77 + 228 * q^78 - 38 * q^79 + 322 * q^80 + 129 * q^81 + 48 * q^82 - 35 * q^83 + 19 * q^84 - 23 * q^85 - 684 * q^86 + 37 * q^87 - 38 * q^88 + 76 * q^89 - 722 * q^90 - 114 * q^91 - 22 * q^92 - 30 * q^93 + 228 * q^94 - 152 * q^95 + 142 * q^96 + 19 * q^97 + 57 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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