LMFDB - Embedded newform 195.2.bf.a.62.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [195,2,Mod(17,195)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(195, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("195.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.bf (of order $12$, degree $4$, 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:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			62.14
Character	$\chi$	$=$	195.62
Dual form			195.2.bf.a.173.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0683265 - 0.254998i) q^{2} +(-0.131022 + 1.72709i) q^{3} +(1.67170 + 0.965154i) q^{4} +(0.374569 - 2.20447i) q^{5} +(0.431452 + 0.151416i) q^{6} +(0.894980 + 3.34011i) q^{7} +(0.733676 - 0.733676i) q^{8} +(-2.96567 - 0.452574i) q^{9} +(-0.536543 - 0.246138i) q^{10} +(-0.378689 - 0.655909i) q^{11} +(-1.88593 + 2.76071i) q^{12} +(-1.67516 - 3.19278i) q^{13} +0.912873 q^{14} +(3.75824 + 0.935748i) q^{15} +(1.79335 + 3.10618i) q^{16} +(1.89902 + 7.08724i) q^{17} +(-0.318039 + 0.725316i) q^{18} +(2.37830 - 4.11934i) q^{19} +(2.75382 - 3.32369i) q^{20} +(-5.88593 + 1.10808i) q^{21} +(-0.193130 + 0.0517490i) q^{22} +(-0.309199 + 1.15395i) q^{23} +(1.17100 + 1.36325i) q^{24} +(-4.71940 - 1.65145i) q^{25} +(-0.928610 + 0.209011i) q^{26} +(1.17020 - 5.06267i) q^{27} +(-1.72759 + 6.44744i) q^{28} +(-3.57287 - 6.18840i) q^{29} +(0.495401 - 0.894408i) q^{30} -3.75546i q^{31} +(2.91904 - 0.782155i) q^{32} +(1.18243 - 0.568091i) q^{33} +1.93698 q^{34} +(7.69841 - 0.721858i) q^{35} +(-4.52089 - 3.61889i) q^{36} +(-2.67900 - 0.717836i) q^{37} +(-0.887922 - 0.887922i) q^{38} +(5.73370 - 2.47482i) q^{39} +(-1.34256 - 1.89218i) q^{40} +(-2.69593 - 4.66949i) q^{41} +(-0.119607 + 1.57661i) q^{42} +(-1.48024 - 5.52432i) q^{43} -1.46197i q^{44} +(-2.10853 + 6.36821i) q^{45} +(0.273128 + 0.157690i) q^{46} +(2.28189 + 2.28189i) q^{47} +(-5.59961 + 2.69030i) q^{48} +(-4.29318 + 2.47867i) q^{49} +(-0.743577 + 1.09060i) q^{50} +(-12.4891 + 2.35119i) q^{51} +(0.281170 - 6.95414i) q^{52} +(-5.30126 - 5.30126i) q^{53} +(-1.21101 - 0.644314i) q^{54} +(-1.58778 + 0.589127i) q^{55} +(3.10719 + 1.79394i) q^{56} +(6.80285 + 4.64726i) q^{57} +(-1.82215 + 0.488244i) q^{58} +(4.58287 + 2.64592i) q^{59} +(5.37949 + 5.19157i) q^{60} +(-1.28268 + 2.22167i) q^{61} +(-0.957635 - 0.256597i) q^{62} +(-1.14256 - 10.3107i) q^{63} +6.37561i q^{64} +(-7.66586 + 2.49692i) q^{65} +(-0.0640708 - 0.340333i) q^{66} +(-5.60475 - 1.50179i) q^{67} +(-3.66569 + 13.6805i) q^{68} +(-1.95246 - 0.685208i) q^{69} +(0.341933 - 2.01240i) q^{70} +(0.328162 - 0.568393i) q^{71} +(-2.50788 + 1.84380i) q^{72} +(8.39721 + 8.39721i) q^{73} +(-0.366094 + 0.634093i) q^{74} +(3.47055 - 7.93444i) q^{75} +(7.95159 - 4.59085i) q^{76} +(1.85189 - 1.85189i) q^{77} +(-0.239311 - 1.63118i) q^{78} +6.35343i q^{79} +(7.51921 - 2.78992i) q^{80} +(8.59035 + 2.68437i) q^{81} +(-1.37491 + 0.368407i) q^{82} +(2.33630 - 2.33630i) q^{83} +(-10.9089 - 3.82845i) q^{84} +(16.3349 - 1.53168i) q^{85} -1.50983 q^{86} +(11.1560 - 5.35985i) q^{87} +(-0.759060 - 0.203390i) q^{88} +(9.05197 - 5.22616i) q^{89} +(1.47981 + 0.972789i) q^{90} +(9.16501 - 8.45269i) q^{91} +(-1.63062 + 1.63062i) q^{92} +(6.48601 + 0.492049i) q^{93} +(0.737790 - 0.425963i) q^{94} +(-8.19013 - 6.78588i) q^{95} +(0.968391 + 5.14392i) q^{96} +(2.29178 + 8.55305i) q^{97} +(0.338717 + 1.26411i) q^{98} +(0.826218 + 2.11659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) $ 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.0683265	−	0.254998i	0.0483141	−	0.180311i	−0.937552	−	0.347845i	$-0.886914\pi$
$2$	0.0683265	−	0.254998i	0.0483141	−	0.180311i	0.985866	+	0.167534i	$0.0535803\pi$
$3$	−0.131022	+	1.72709i	−0.0756458	+	0.997135i
$3$	−0.131022	+	1.72709i	−0.0756458	+	0.997135i
$4$	1.67170	+	0.965154i	0.835848	+	0.482577i
$5$	0.374569	−	2.20447i	0.167512	−	0.985870i
$5$	0.374569	−	2.20447i	0.167512	−	0.985870i
$6$	0.431452	+	0.151416i	0.176139	+	0.0618155i
$7$	0.894980	+	3.34011i	0.338271	+	1.26244i	0.900280	+	0.435312i	$0.143362\pi$
$7$	0.894980	+	3.34011i	0.338271	+	1.26244i	−0.562009	+	0.827131i	$0.689971\pi$
$8$	0.733676	−	0.733676i	0.259394	−	0.259394i
$9$	−2.96567	−	0.452574i	−0.988555	−	0.150858i
$10$	−0.536543	−	0.246138i	−0.169670	−	0.0778357i
$11$	−0.378689	−	0.655909i	−0.114179	−	0.197764i	0.803272	−	0.595612i	$-0.203090\pi$
$11$	−0.378689	−	0.655909i	−0.114179	−	0.197764i	−0.917451	+	0.397848i	$0.869757\pi$
$12$	−1.88593	+	2.76071i	−0.544423	+	0.796948i
$13$	−1.67516	−	3.19278i	−0.464605	−	0.885518i
$13$	−1.67516	−	3.19278i	−0.464605	−	0.885518i
$14$	0.912873			0.243975
$15$	3.75824	+	0.935748i	0.970374	+	0.241609i
$16$	1.79335	+	3.10618i	0.448338	+	0.776544i
$17$	1.89902	+	7.08724i	0.460580	+	1.71891i	0.671144	+	0.741327i	$0.265803\pi$
$17$	1.89902	+	7.08724i	0.460580	+	1.71891i	−0.210564	+	0.977580i	$0.567530\pi$
$18$	−0.318039	+	0.725316i	−0.0749625	+	0.170959i
$19$	2.37830	−	4.11934i	0.545620	−	0.945041i	−0.452948	−	0.891537i	$-0.649628\pi$
$19$	2.37830	−	4.11934i	0.545620	−	0.945041i	0.998568	−	0.0535042i	$-0.0170391\pi$
$20$	2.75382	−	3.32369i	0.615773	−	0.743200i
$21$	−5.88593	+	1.10808i	−1.28442	+	0.241803i
$22$	−0.193130	+	0.0517490i	−0.0411754	+	0.0110329i
$23$	−0.309199	+	1.15395i	−0.0644725	+	0.240615i	−0.990641	−	0.136496i	$-0.956416\pi$
$23$	−0.309199	+	1.15395i	−0.0644725	+	0.240615i	0.926168	+	0.377111i	$0.123082\pi$
$24$	1.17100	+	1.36325i	0.239029	+	0.278273i
$25$	−4.71940	−	1.65145i	−0.943879	−	0.330290i
$26$	−0.928610	+	0.209011i	−0.182115	+	0.0409903i
$27$	1.17020	−	5.06267i	0.225206	−	0.974311i
$28$	−1.72759	+	6.44744i	−0.326483	+	1.21845i
$29$	−3.57287	−	6.18840i	−0.663466	−	1.14916i	−0.979699	−	0.200475i	$-0.935751\pi$
$29$	−3.57287	−	6.18840i	−0.663466	−	1.14916i	0.316233	−	0.948682i	$-0.397582\pi$
$30$	0.495401	−	0.894408i	0.0904475	−	0.163296i
$31$		−	3.75546i		−	0.674500i	−0.941415	−	0.337250i	$-0.890503\pi$
$31$		−	3.75546i		−	0.674500i	0.941415	−	0.337250i	$-0.109497\pi$
$32$	2.91904	−	0.782155i	0.516019	−	0.138267i
$33$	1.18243	−	0.568091i	0.205834	−	0.0988919i
$34$	1.93698			0.332190
$35$	7.69841	−	0.721858i	1.30127	−	0.122016i
$36$	−4.52089	−	3.61889i	−0.753481	−	0.603148i
$37$	−2.67900	−	0.717836i	−0.440425	−	0.118012i	0.0317906	−	0.999495i	$-0.489879\pi$
$37$	−2.67900	−	0.717836i	−0.440425	−	0.118012i	−0.472216	+	0.881483i	$0.656546\pi$
$38$	−0.887922	−	0.887922i	−0.144040	−	0.144040i
$39$	5.73370	−	2.47482i	0.918126	−	0.396288i
$40$	−1.34256	−	1.89218i	−0.212277	−	0.299180i
$41$	−2.69593	−	4.66949i	−0.421033	−	0.729251i	0.575007	−	0.818148i	$-0.304999\pi$
$41$	−2.69593	−	4.66949i	−0.421033	−	0.729251i	−0.996041	+	0.0888969i	$0.971666\pi$
$42$	−0.119607	+	1.57661i	−0.0184557	+	0.243276i
$43$	−1.48024	−	5.52432i	−0.225734	−	0.842451i	−0.982109	−	0.188313i	$-0.939698\pi$
$43$	−1.48024	−	5.52432i	−0.225734	−	0.842451i	0.756375	−	0.654138i	$-0.226968\pi$
$44$		−	1.46197i		−	0.220401i
$45$	−2.10853	+	6.36821i	−0.314321	+	0.949317i
$46$	0.273128	+	0.157690i	0.0402705	+	0.0232502i
$47$	2.28189	+	2.28189i	0.332847	+	0.332847i	0.853667	−	0.520819i	$-0.174374\pi$
$47$	2.28189	+	2.28189i	0.332847	+	0.332847i	−0.520819	+	0.853667i	$0.674374\pi$
$48$	−5.59961	+	2.69030i	−0.808234	+	0.388311i
$49$	−4.29318	+	2.47867i	−0.613311	+	0.354095i
$50$	−0.743577	+	1.09060i	−0.105158	+	0.154234i
$51$	−12.4891	+	2.35119i	−1.74882	+	0.329232i
$52$	0.281170	−	6.95414i	0.0389912	−	0.964366i
$53$	−5.30126	−	5.30126i	−0.728185	−	0.728185i	0.242073	−	0.970258i	$-0.422173\pi$
$53$	−5.30126	−	5.30126i	−0.728185	−	0.728185i	−0.970258	+	0.242073i	$0.922173\pi$
$54$	−1.21101	−	0.644314i	−0.164798	−	0.0876801i
$55$	−1.58778	+	0.589127i	−0.214096	+	0.0794379i
$56$	3.10719	+	1.79394i	0.415215	+	0.239725i
$57$	6.80285	+	4.64726i	0.901060	+	0.615545i
$58$	−1.82215	+	0.488244i	−0.239260	+	0.0641096i
$59$	4.58287	+	2.64592i	0.596639	+	0.344470i	0.767718	−	0.640787i	$-0.221392\pi$
$59$	4.58287	+	2.64592i	0.596639	+	0.344470i	−0.171079	+	0.985257i	$0.554725\pi$
$60$	5.37949	+	5.19157i	0.694490	+	0.670228i
$61$	−1.28268	+	2.22167i	−0.164231	+	0.284456i	−0.936382	−	0.350983i	$-0.885847\pi$
$61$	−1.28268	+	2.22167i	−0.164231	+	0.284456i	0.772151	+	0.635439i	$0.219181\pi$
$62$	−0.957635	−	0.256597i	−0.121620	−	0.0325879i
$63$	−1.14256	−	10.3107i	−0.143950	−	1.29903i
$64$			6.37561i			0.796951i
$65$	−7.66586	+	2.49692i	−0.950833	+	0.309705i
$66$	−0.0640708	−	0.340333i	−0.00788657	−	0.0418921i
$67$	−5.60475	−	1.50179i	−0.684729	−	0.183473i	−0.100349	−	0.994952i	$-0.531996\pi$
$67$	−5.60475	−	1.50179i	−0.684729	−	0.183473i	−0.584381	+	0.811480i	$0.698662\pi$
$68$	−3.66569	+	13.6805i	−0.444530	+	1.65901i
$69$	−1.95246	−	0.685208i	−0.235048	−	0.0824893i
$70$	0.341933	−	2.01240i	0.0408689	−	0.240528i
$71$	0.328162	−	0.568393i	0.0389456	−	0.0674558i	−0.845896	−	0.533349i	$-0.820933\pi$
$71$	0.328162	−	0.568393i	0.0389456	−	0.0674558i	0.884841	+	0.465893i	$0.154267\pi$
$72$	−2.50788	+	1.84380i	−0.295557	+	0.217294i
$73$	8.39721	+	8.39721i	0.982819	+	0.982819i	0.999855	−	0.0170357i	$-0.00542289\pi$
$73$	8.39721	+	8.39721i	0.982819	+	0.982819i	−0.0170357	+	0.999855i	$0.505423\pi$
$74$	−0.366094	+	0.634093i	−0.0425575	+	0.0737118i
$75$	3.47055	−	7.93444i	0.400745	−	0.916190i
$76$	7.95159	−	4.59085i	0.912110	−	0.526607i
$77$	1.85189	−	1.85189i	0.211042	−	0.211042i
$78$	−0.239311	−	1.63118i	−0.0270966	−	0.184694i
$79$			6.35343i			0.714816i	0.933948	+	0.357408i	$0.116340\pi$
$79$			6.35343i			0.714816i	−0.933948	+	0.357408i	$0.883660\pi$
$80$	7.51921	−	2.78992i	0.840673	−	0.311922i
$81$	8.59035	+	2.68437i	0.954484	+	0.298263i
$82$	−1.37491	+	0.368407i	−0.151834	+	0.0406837i
$83$	2.33630	−	2.33630i	0.256442	−	0.256442i	−0.567163	−	0.823605i	$-0.691959\pi$
$83$	2.33630	−	2.33630i	0.256442	−	0.256442i	0.823605	+	0.567163i	$0.191959\pi$
$84$	−10.9089	−	3.82845i	−1.19026	−	0.417719i
$85$	16.3349	−	1.53168i	1.77177	−	0.166134i
$86$	−1.50983			−0.162809
$87$	11.1560	−	5.35985i	1.19605	−	0.574636i
$88$	−0.759060	−	0.203390i	−0.0809161	−	0.0216814i
$89$	9.05197	−	5.22616i	0.959507	−	0.553971i	0.0634855	−	0.997983i	$-0.479778\pi$
$89$	9.05197	−	5.22616i	0.959507	−	0.553971i	0.896021	+	0.444011i	$0.146445\pi$
$90$	1.47981	+	0.972789i	0.155986	+	0.102541i
$91$	9.16501	−	8.45269i	0.960754	−	0.886083i
$92$	−1.63062	+	1.63062i	−0.170004	+	0.170004i
$93$	6.48601	+	0.492049i	0.672568	+	0.0510231i
$94$	0.737790	−	0.425963i	0.0760972	−	0.0439348i
$95$	−8.19013	−	6.78588i	−0.840290	−	0.696216i
$96$	0.968391	+	5.14392i	0.0988360	+	0.525000i
$97$	2.29178	+	8.55305i	0.232695	+	0.868430i	0.979174	+	0.203022i	$0.0650761\pi$
$97$	2.29178	+	8.55305i	0.232695	+	0.868430i	−0.746479	+	0.665409i	$0.768257\pi$
$98$	0.338717	+	1.26411i	0.0342156	+	0.127694i
$99$	0.826218	+	2.11659i	0.0830381	+	0.212725i
$100$	−6.29549	−	7.31567i	−0.629549	−	0.731567i
$101$	−10.7112	+	6.18411i	−1.06580	+	0.615342i	−0.927032	−	0.374983i	$-0.877649\pi$
$101$	−10.7112	+	6.18411i	−1.06580	+	0.615342i	−0.138772	+	0.990324i	$0.544315\pi$
$102$	−0.253788	+	3.34534i	−0.0251288	+	0.331238i
$103$	−11.9113	+	11.9113i	−1.17365	+	1.17365i	−0.192322	+	0.981332i	$0.561602\pi$
$103$	−11.9113	+	11.9113i	−1.17365	+	1.17365i	−0.981332	+	0.192322i	$0.938398\pi$
$104$	−3.57149	−	1.11344i	−0.350214	−	0.109182i
$105$	0.238049	+	13.3904i	0.0232312	+	1.30677i
$106$	−1.71403	+	0.989595i	−0.166481	+	0.0961180i
$107$	1.85116	+	0.496016i	0.178958	+	0.0479517i	0.347185	−	0.937797i	$-0.387138\pi$
$107$	1.85116	+	0.496016i	0.178958	+	0.0479517i	−0.168227	+	0.985748i	$0.553804\pi$
$108$	6.84248	−	7.33381i	0.658418	−	0.705697i
$109$	−7.27602			−0.696916			−0.348458	−	0.937324i	$-0.613295\pi$
$109$	−7.27602			−0.696916			−0.348458	+	0.937324i	$0.613295\pi$
$110$	0.0417389	+	0.445133i	0.00397964	+	0.0424418i
$111$	1.59078	−	4.53282i	0.150990	−	0.430236i
$112$	−8.76996	+	8.76996i	−0.828683	+	0.828683i
$113$	2.83327	−	0.759173i	0.266532	−	0.0714170i	−0.123078	−	0.992397i	$-0.539277\pi$
$113$	2.83327	−	0.759173i	0.266532	−	0.0714170i	0.389610	+	0.920980i	$0.372610\pi$
$114$	1.64986	−	1.41718i	0.154523	−	0.132731i
$115$	2.42803	+	1.11385i	0.226415	+	0.103867i
$116$		−	13.7935i		−	1.28069i
$117$	3.52299	+	10.2269i	0.325701	+	0.945473i
$118$	0.987837	−	0.987837i	0.0909378	−	0.0909378i
$119$	−21.9726	+	12.6859i	−2.01422	+	1.16291i
$120$	3.44387	−	2.07080i	0.314381	−	0.189037i
$121$	5.21319	−	9.02951i	0.473926	−	0.820864i
$122$	0.478880	+	0.478880i	0.0433558	+	0.0433558i
$123$	8.41784	−	4.04430i	0.759011	−	0.364662i
$124$	3.62460	−	6.27798i	0.325498	−	0.563780i
$125$	−5.40832	+	9.78520i	−0.483735	+	0.875215i
$126$	−2.70728	−	0.413143i	−0.241183	−	0.0368057i
$127$	3.31991	−	12.3901i	0.294594	−	1.09944i	−0.646945	−	0.762537i	$-0.723954\pi$
$127$	3.31991	−	12.3901i	0.294594	−	1.09944i	0.941539	−	0.336904i	$-0.109380\pi$
$128$	7.46386	+	1.99993i	0.659718	+	0.176771i
$129$	9.73493	−	1.83269i	0.857112	−	0.161359i
$130$	0.112930	+	2.12538i	0.00990458	+	0.186409i
$131$			17.7409i			1.55003i	0.631943	+	0.775015i	$0.282258\pi$
$131$			17.7409i			1.55003i	−0.631943	+	0.775015i	$0.717742\pi$
$132$	2.52496	+	0.191551i	0.219769	+	0.0166724i
$133$	15.8876	+	4.25707i	1.37763	+	0.369134i
$134$	−0.765906	+	1.32659i	−0.0661642	+	0.114600i
$135$	−10.7222	−	4.47600i	−0.922819	−	0.385233i
$136$	6.59301	+	3.80647i	0.565346	+	0.326402i
$137$	−20.7346	+	5.55583i	−1.77148	+	0.474666i	−0.988988	−	0.147996i	$-0.952718\pi$
$137$	−20.7346	+	5.55583i	−1.77148	+	0.474666i	−0.782490	+	0.622663i	$0.786051\pi$
$138$	−0.308131	+	0.451055i	−0.0262299	+	0.0383964i
$139$	8.79884	+	5.08001i	0.746308	+	0.430881i	0.824358	−	0.566068i	$-0.191536\pi$
$139$	8.79884	+	5.08001i	0.746308	+	0.430881i	−0.0780503	+	0.996949i	$0.524869\pi$
$140$	13.5661	+	6.22343i	1.14655	+	0.525976i
$141$	−4.24000	+	3.64204i	−0.357072	+	0.306715i
$142$	−0.122517	−	0.122517i	−0.0102814	−	0.0102814i
$143$	−1.45981	+	2.30782i	−0.122075	+	0.192990i
$144$	−3.91271	−	10.0235i	−0.326059	−	0.835292i
$145$	−14.9804	+	5.55832i	−1.24406	+	0.461593i
$146$	2.71502	−	1.56752i	0.224697	−	0.129729i
$147$	−3.71837	−	7.73946i	−0.306686	−	0.638340i
$148$	−3.78565	−	3.78565i	−0.311179	−	0.311179i
$149$	11.4427	+	6.60643i	0.937420	+	0.541220i	0.889151	−	0.457615i	$-0.151296\pi$
$149$	11.4427	+	6.60643i	0.937420	+	0.541220i	0.0482693	+	0.998834i	$0.484629\pi$
$150$	−1.78614	−	1.42712i	−0.145837	−	0.116524i
$151$			7.62730i			0.620701i	0.950622	+	0.310350i	$0.100446\pi$
$151$			7.62730i			0.620701i	−0.950622	+	0.310350i	$0.899554\pi$
$152$	−1.27736	−	4.76717i	−0.103607	−	0.386668i
$153$	−2.42436	−	21.8778i	−0.195998	−	1.76872i
$154$	−0.345695	−	0.598761i	−0.0278569	−	0.0482496i
$155$	−8.27881	−	1.40668i	−0.664970	−	0.112987i
$156$	11.9736	+	1.39675i	0.958653	+	0.111830i
$157$	−2.99534	−	2.99534i	−0.239054	−	0.239054i	0.577404	−	0.816458i	$-0.304066\pi$
$157$	−2.99534	−	2.99534i	−0.239054	−	0.239054i	−0.816458	+	0.577404i	$0.804066\pi$
$158$	1.62011	+	0.434108i	0.128889	+	0.0345357i
$159$	9.85033	−	8.46117i	0.781182	−	0.671014i
$160$	−0.630858	−	6.72792i	−0.0498737	−	0.531889i
$161$	−4.13104			−0.325572
$162$	1.27146	−	2.00711i	0.0998951	−	0.157693i
$163$	−15.8049	+	4.23491i	−1.23794	+	0.331704i	−0.817665	−	0.575695i	$-0.804732\pi$
$163$	−15.8049	+	4.23491i	−1.23794	+	0.331704i	−0.420271	+	0.907399i	$0.638065\pi$
$164$		−	10.4079i		−	0.812724i
$165$	−0.809440	−	2.81942i	−0.0630148	−	0.219492i
$166$	−0.436121	−	0.755383i	−0.0338495	−	0.0586291i
$167$	2.13487	−	7.96743i	0.165201	−	0.616538i	−0.832814	−	0.553553i	$-0.813271\pi$
$167$	2.13487	−	7.96743i	0.165201	−	0.616538i	0.998015	−	0.0629845i	$-0.0200619\pi$
$168$	−3.50539	+	5.13134i	−0.270447	+	0.395891i
$169$	−7.38769	+	10.6968i	−0.568284	+	0.822833i
$170$	0.725534	−	4.27003i	0.0556459	−	0.327496i
$171$	−8.91756	+	11.1402i	−0.681943	+	0.851915i
$172$	2.85731	−	10.6636i	0.217868	−	0.813094i
$173$	−11.7353	+	3.14446i	−0.892217	+	0.239069i	−0.675671	−	0.737204i	$-0.736146\pi$
$173$	−11.7353	+	3.14446i	−0.892217	+	0.239069i	−0.216546	+	0.976272i	$0.569479\pi$
$174$	−0.604498	−	3.21099i	−0.0458269	−	0.243424i
$175$	1.29227	−	17.2413i	0.0976863	−	1.30332i
$176$	1.35825	−	2.35255i	0.102382	−	0.177330i
$177$	−5.17020	+	7.56835i	−0.388616	+	0.568872i
$178$	−0.714170	−	2.66532i	−0.0535293	−	0.199774i
$179$	6.88190	+	11.9198i	0.514377	+	0.890927i	0.999861	+	0.0166817i	$0.00531018\pi$
$179$	6.88190	+	11.9198i	0.514377	+	0.890927i	−0.485484	+	0.874246i	$0.661356\pi$
$180$	−9.67113	+	8.61065i	−0.720843	+	0.641800i
$181$	−5.09406			−0.378639			−0.189319	−	0.981916i	$-0.560628\pi$
$181$	−5.09406			−0.378639			−0.189319	+	0.981916i	$0.560628\pi$
$182$	−1.52921	−	2.91460i	−0.113352	−	0.216045i
$183$	−3.66896	−	2.50639i	−0.271217	−	0.185278i
$184$	0.619772	+	1.07348i	0.0456902	+	0.0791378i
$185$	−2.58592	+	5.63691i	−0.190121	+	0.414434i
$186$	0.568638	−	1.62030i	0.0416946	−	0.118806i
$187$	3.92944	−	3.92944i	0.287349	−	0.287349i
$188$	1.61225	+	6.01699i	0.117585	+	0.438834i
$189$	17.9572	−	0.622378i	1.30619	−	0.0452713i
$190$	−2.28999	+	1.62481i	−0.166133	+	0.117876i
$191$	7.24923	+	4.18535i	0.524536	+	0.302841i	0.738789	−	0.673937i	$-0.235398\pi$
$191$	7.24923	+	4.18535i	0.524536	+	0.302841i	−0.214252	+	0.976778i	$0.568732\pi$
$192$	−11.0112	−	0.835347i	−0.794668	−	0.0602860i
$193$	−1.94577	+	7.26170i	−0.140059	+	0.522708i	0.859866	+	0.510519i	$0.170547\pi$
$193$	−1.94577	+	7.26170i	−0.140059	+	0.522708i	−0.999926	+	0.0121893i	$0.996120\pi$
$194$	2.33760			0.167830
$195$	−3.30801	−	13.5668i	−0.236892	−	0.971536i
$196$	−9.56918			−0.683513
$197$	4.83176	−	18.0324i	0.344249	−	1.28475i	−0.549238	−	0.835666i	$-0.685082\pi$
$197$	4.83176	−	18.0324i	0.344249	−	1.28475i	0.893487	−	0.449089i	$-0.148251\pi$
$198$	0.596179	−	0.0660647i	0.0423686	−	0.00469501i
$199$	0.308520	+	0.178124i	0.0218704	+	0.0126269i	0.510895	−	0.859643i	$-0.329314\pi$
$199$	0.308520	+	0.178124i	0.0218704	+	0.0126269i	−0.489025	+	0.872270i	$0.662647\pi$
$200$	−4.67414	+	2.25088i	−0.330512	+	0.159161i
$201$	3.32807	−	9.48313i	0.234744	−	0.668888i
$202$	0.845077	+	3.15387i	0.0594594	+	0.221906i
$203$	17.4723	−	17.4723i	1.22631	−	1.22631i
$204$	−23.1472	−	8.12343i	−1.62063	−	0.568754i
$205$	−11.3036	+	4.19406i	−0.789475	+	0.292926i
$206$	2.22350	+	3.85121i	0.154918	+	0.268327i
$207$	1.43923	−	3.28229i	0.100033	−	0.228135i
$208$	6.91319	−	10.9291i	0.479343	−	0.757797i
$209$	−3.60255			−0.249193
$210$	3.43080	+	0.854219i	0.236747	+	0.0589467i
$211$	4.03683	+	6.99199i	0.277907	+	0.481349i	0.970864	−	0.239630i	$-0.0770260\pi$
$211$	4.03683	+	6.99199i	0.277907	+	0.481349i	−0.692958	+	0.720978i	$0.743693\pi$
$212$	−3.74556	−	13.9786i	−0.257246	−	0.960056i
$213$	0.938668	+	0.641236i	0.0643165	+	0.0439368i
$214$	0.252966	−	0.438150i	0.0172924	−	0.0299513i
$215$	−12.7327	+	1.19390i	−0.868360	+	0.0814236i
$216$	−2.85581	−	4.57291i	−0.194313	−	0.311147i
$217$	12.5437	−	3.36106i	0.851519	−	0.228164i
$218$	−0.497145	+	1.85537i	−0.0336709	+	0.125662i
$219$	−15.6029	+	13.4025i	−1.05435	+	0.905657i
$220$	−3.22288	−	0.547609i	−0.217286	−	0.0369198i
$221$	19.4468	−	17.9354i	1.30814	−	1.20647i
$222$	−1.04717	−	0.715356i	−0.0702813	−	0.0480116i
$223$	1.50273	−	5.60827i	0.100630	−	0.375557i	−0.897183	−	0.441660i	$-0.854390\pi$
$223$	1.50273	−	5.60827i	0.100630	−	0.375557i	0.997813	+	0.0661025i	$0.0210564\pi$
$224$	5.22497	+	9.04992i	0.349108	+	0.604673i
$225$	13.2488	+	7.03353i	0.883250	+	0.468902i
$226$		−	0.774351i		−	0.0515091i
$227$	−5.01188	+	1.34293i	−0.332650	+	0.0891333i	−0.421278	−	0.906931i	$-0.638418\pi$
$227$	−5.01188	+	1.34293i	−0.332650	+	0.0891333i	0.0886282	+	0.996065i	$0.471752\pi$
$228$	6.88697	+	14.3346i	0.456101	+	0.949332i
$229$	16.0682			1.06182			0.530908	−	0.847429i	$-0.321851\pi$
$229$	16.0682			1.06182			0.530908	+	0.847429i	$0.321851\pi$
$230$	0.449929	−	0.543037i	0.0296675	−	0.0358068i
$231$	2.95574	+	3.44101i	0.194473	+	0.226402i
$232$	−7.16161	−	1.91895i	−0.470183	−	0.125985i
$233$	−5.72175	−	5.72175i	−0.374844	−	0.374844i	0.494394	−	0.869238i	$-0.335390\pi$
$233$	−5.72175	−	5.72175i	−0.374844	−	0.374844i	−0.869238	+	0.494394i	$0.835390\pi$
$234$	2.84854	−	0.199590i	0.186215	−	0.0130476i
$235$	5.88508	−	4.17563i	0.383900	−	0.272388i
$236$	5.10745	+	8.84636i	0.332466	+	0.575849i
$237$	−10.9729	−	0.832441i	−0.712768	−	0.0540728i
$238$	1.73356	+	6.46975i	0.112370	+	0.419371i
$239$		−	14.1799i		−	0.917222i	−0.888637	−	0.458611i	$-0.848347\pi$
$239$		−	14.1799i		−	0.917222i	0.888637	−	0.458611i	$-0.151653\pi$
$240$	3.83325	+	13.3519i	0.247435	+	0.861860i
$241$	−1.38091	−	0.797270i	−0.0889523	−	0.0513567i	0.454864	−	0.890561i	$-0.349688\pi$
$241$	−1.38091	−	0.797270i	−0.0889523	−	0.0513567i	−0.543816	+	0.839204i	$0.683021\pi$
$242$	−1.94631	−	1.94631i	−0.125113	−	0.125113i
$243$	−5.76167	+	14.4846i	−0.369611	+	0.929187i
$244$	−4.28851	+	2.47597i	−0.274543	+	0.158508i
$245$	3.85606	+	10.3926i	0.246355	+	0.663960i
$246$	−0.456127	−	2.42287i	−0.0290816	−	0.154476i
$247$	−17.1362	−	0.692849i	−1.09035	−	0.0440849i
$248$	−2.75529	−	2.75529i	−0.174961	−	0.174961i
$249$	3.72889	+	4.34110i	0.236309	+	0.275106i
$250$	2.12567	+	2.04770i	0.134439	+	0.129508i
$251$	10.7131	+	6.18523i	0.676207	+	0.390408i	0.798424	−	0.602095i	$-0.205667\pi$
$251$	10.7131	+	6.18523i	0.676207	+	0.390408i	−0.122217	+	0.992503i	$0.539000\pi$
$252$	8.04139	−	18.3391i	0.506560	−	1.15525i
$253$	0.873975	−	0.234181i	0.0549463	−	0.0147228i
$254$	−2.93260	−	1.69314i	−0.184008	−	0.106237i
$255$	0.505105	+	28.4125i	0.0316309	+	1.77926i
$256$	−5.35565	+	9.27626i	−0.334728	+	0.579766i
$257$	16.7703	+	4.49358i	1.04610	+	0.280302i	0.740639	−	0.671903i	$-0.234523\pi$
$257$	16.7703	+	4.49358i	1.04610	+	0.280302i	0.305461	+	0.952205i	$0.401190\pi$
$258$	0.197821	−	2.60761i	0.0123158	−	0.162343i
$259$		−	9.59061i		−	0.595932i
$260$	−15.2249	−	3.22463i	−0.944208	−	0.199983i
$261$	7.79524	+	19.9697i	0.482513	+	1.23609i
$262$	4.52390	+	1.21217i	0.279487	+	0.0748884i
$263$	4.53603	−	16.9287i	0.279704	−	1.04387i	−0.672920	−	0.739716i	$-0.734960\pi$
$263$	4.53603	−	16.9287i	0.279704	−	1.04387i	0.952623	−	0.304153i	$-0.0983733\pi$
$264$	0.450725	−	1.28432i	0.0277402	−	0.0790441i
$265$	−13.6722	+	9.70080i	−0.839875	+	0.595916i
$266$	2.17109	−	3.76043i	0.133118	−	0.230567i
$267$	7.84002	+	16.3183i	0.479802	+	0.998663i
$268$	−7.91998	−	7.91998i	−0.483790	−	0.483790i
$269$	−2.88285	+	4.99325i	−0.175771	+	0.304444i	−0.940428	−	0.339994i	$-0.889575\pi$
$269$	−2.88285	+	4.99325i	−0.175771	+	0.304444i	0.764657	+	0.644437i	$0.222908\pi$
$270$	−1.87398	+	2.42831i	−0.114047	+	0.147782i
$271$	18.2632	−	10.5443i	1.10941	−	0.640518i	0.170733	−	0.985317i	$-0.445386\pi$
$271$	18.2632	−	10.5443i	1.10941	−	0.640518i	0.938676	+	0.344800i	$0.112053\pi$
$272$	−18.6086	+	18.6086i	−1.12831	+	1.12831i
$273$	13.3977	+	16.9363i	0.810867	+	1.02503i
$274$			5.66690i			0.342350i
$275$	0.703982	+	3.72088i	0.0424517	+	0.224378i
$276$	−2.60258	−	3.02988i	−0.156657	−	0.182377i
$277$	5.36578	−	1.43776i	0.322399	−	0.0863865i	−0.0939901	−	0.995573i	$-0.529962\pi$
$277$	5.36578	−	1.43776i	0.322399	−	0.0863865i	0.416389	+	0.909187i	$0.363296\pi$
$278$	1.89659	−	1.89659i	0.113750	−	0.113750i
$279$	−1.69962	+	11.1374i	−0.101754	+	0.666781i
$280$	5.11854	−	6.17776i	0.305891	−	0.369192i
$281$	−13.3268			−0.795013			−0.397506	−	0.917599i	$-0.630124\pi$
$281$	−13.3268			−0.795013			−0.397506	+	0.917599i	$0.630124\pi$
$282$	0.639009	+	1.33004i	0.0380524	+	0.0792027i
$283$	13.4493	+	3.60372i	0.799475	+	0.214219i	0.635354	−	0.772221i	$-0.280854\pi$
$283$	13.4493	+	3.60372i	0.799475	+	0.214219i	0.164122	+	0.986440i	$0.447521\pi$
$284$	1.09717	−	0.633453i	0.0651052	−	0.0375885i
$285$	12.7929	−	13.2560i	0.757786	−	0.785216i
$286$	0.488746	+	0.529934i	0.0289002	+	0.0313356i
$287$	13.1838	−	13.1838i	0.778215	−	0.778215i
$288$	−9.01089	+	0.998528i	−0.530972	+	0.0588388i
$289$	−31.9002	+	18.4176i	−1.87648	+	1.08339i
$290$	0.393800	+	4.19976i	0.0231247	+	0.246619i
$291$	−15.0721	+	2.83747i	−0.883545	+	0.166335i
$292$	5.93298	+	22.1422i	0.347201	+	1.29577i
$293$	−3.86933	−	14.4405i	−0.226049	−	0.843626i	−0.981982	−	0.188976i	$-0.939483\pi$
$293$	−3.86933	−	14.4405i	−0.226049	−	0.843626i	0.755933	−	0.654649i	$-0.227184\pi$
$294$	−2.22761	+	0.419368i	−0.129917	+	0.0244580i
$295$	7.54947	−	9.11174i	0.439547	−	0.530506i
$296$	−2.49218	+	1.43886i	−0.144855	+	0.0836321i
$297$	−3.76379	+	1.14963i	−0.218397	+	0.0667084i
$298$	2.46646	−	2.46646i	0.142878	−	0.142878i
$299$	4.20226	−	0.945840i	0.243023	−	0.0546993i
$300$	13.4597	−	9.91435i	0.777093	−	0.572405i
$301$	17.1271	−	9.88831i	0.987187	−	0.569953i
$302$	1.94495	+	0.521147i	0.111919	+	0.0299886i
$303$	−9.27710	−	19.3094i	−0.532955	−	1.10930i
$304$	17.0605			0.978488
$305$	4.41716	+	3.65980i	0.252926	+	0.209560i
$306$	−5.74445	−	0.876629i	−0.328388	−	0.0501136i
$307$	7.71849	−	7.71849i	0.440517	−	0.440517i	−0.451668	−	0.892186i	$-0.649171\pi$
$307$	7.71849	−	7.71849i	0.440517	−	0.440517i	0.892186	+	0.451668i	$0.149171\pi$
$308$	4.88315	−	1.30844i	0.278243	−	0.0745551i
$309$	−19.0112	−	22.1325i	−1.08151	−	1.25907i
$310$	−0.924362	+	2.01497i	−0.0525002	+	0.114442i
$311$			4.84533i			0.274753i	0.990519	+	0.137377i	$0.0438671\pi$
$311$			4.84533i			0.274753i	−0.990519	+	0.137377i	$0.956133\pi$
$312$	2.39096	−	6.02239i	0.135361	−	0.340951i
$313$	−1.11868	+	1.11868i	−0.0632313	+	0.0632313i	−0.738015	−	0.674784i	$-0.764237\pi$
$313$	−1.11868	+	1.11868i	−0.0632313	+	0.0632313i	0.674784	+	0.738015i	$0.264237\pi$
$314$	−0.968466	+	0.559144i	−0.0546537	+	0.0315543i
$315$	−23.1576	−	1.34331i	−1.30478	−	0.0756871i
$316$	−6.13203	+	10.6210i	−0.344954	+	0.597478i
$317$	3.06846	+	3.06846i	0.172342	+	0.172342i	0.788007	−	0.615666i	$-0.211113\pi$
$317$	3.06846	+	3.06846i	0.172342	+	0.172342i	−0.615666	+	0.788007i	$0.711113\pi$
$318$	−1.48454	−	3.08994i	−0.0832490	−	0.173275i
$319$	−2.70602	+	4.68696i	−0.151508	+	0.262419i
$320$	14.0549	+	2.38810i	0.785691	+	0.133499i
$321$	−1.09921	+	3.13212i	−0.0613517	+	0.174818i
$322$	−0.282260	+	1.05341i	−0.0157297	+	0.0587041i
$323$	33.7112	+	9.03288i	1.87574	+	0.502603i
$324$	11.7696	+	12.7785i	0.653868	+	0.709914i
$325$	2.63301	+	17.8344i	0.146053	+	0.989277i
$326$			4.31958i			0.239239i
$327$	0.953321	−	12.5663i	0.0527188	−	0.694920i
$328$	−5.40383	−	1.44795i	−0.298377	−	0.0799498i
$329$	−5.57951	+	9.66400i	−0.307608	+	0.532794i
$330$	−0.774253	+	0.0137643i	−0.0426212	+	0.000757701i
$331$	−13.7926	−	7.96315i	−0.758109	−	0.437694i	0.0705077	−	0.997511i	$-0.477538\pi$
$331$	−13.7926	−	7.96315i	−0.758109	−	0.437694i	−0.828616	+	0.559817i	$0.810871\pi$
$332$	6.16047	−	1.65069i	0.338100	−	0.0905936i
$333$	7.62015	+	3.34131i	0.417582	+	0.183103i
$334$	−1.88581	−	1.08877i	−0.103187	−	0.0595750i
$335$	−5.41001	+	11.7930i	−0.295581	+	0.644320i
$336$	−13.9974	−	16.2955i	−0.763622	−	0.888995i
$337$	5.75666	+	5.75666i	0.313585	+	0.313585i	0.846297	−	0.532712i	$-0.178827\pi$
$337$	5.75666	+	5.75666i	0.313585	+	0.313585i	−0.532712	+	0.846297i	$0.678827\pi$
$338$	2.22289	+	2.61472i	0.120909	+	0.142222i
$339$	0.939937	+	4.99278i	0.0510504	+	0.271171i
$340$	28.7853	+	13.2052i	1.56110	+	0.716154i
$341$	−2.46324	+	1.42215i	−0.133392	+	0.0770138i
$342$	2.23143	+	3.03513i	0.120662	+	0.164121i
$343$	4.99459	+	4.99459i	0.269682	+	0.269682i
$344$	−5.13908	−	2.96705i	−0.277080	−	0.159972i
$345$	−2.24185	+	4.04748i	−0.120697	+	0.217909i
$346$			3.20732i			0.172427i
$347$	−0.703627	−	2.62597i	−0.0377727	−	0.140970i	0.944464	−	0.328614i	$-0.106581\pi$
$347$	−0.703627	−	2.62597i	−0.0377727	−	0.140970i	−0.982237	+	0.187644i	$0.939915\pi$
$348$	23.8226	+	1.80725i	1.27702	+	0.0968790i
$349$	−10.1053	−	17.5028i	−0.540922	−	0.936905i	−0.998851	−	0.0479160i	$-0.984742\pi$
$349$	−10.1053	−	17.5028i	−0.540922	−	0.936905i	0.457929	−	0.888989i	$-0.348591\pi$
$350$	−4.30821	−	1.50757i	−0.230283	−	0.0805828i
$351$	−18.1243	+	4.74457i	−0.967402	+	0.253246i
$352$	−1.61843	−	1.61843i	−0.0862627	−	0.0862627i
$353$	−28.2021	−	7.55673i	−1.50105	−	0.402204i	−0.587596	−	0.809155i	$-0.699925\pi$
$353$	−28.2021	−	7.55673i	−1.50105	−	0.402204i	−0.913450	+	0.406951i	$0.866592\pi$
$354$	1.57665	+	1.83551i	0.0837982	+	0.0975563i
$355$	−1.13009	−	0.936326i	−0.0599788	−	0.0496950i
$356$	20.1762			1.06934
$357$	−19.0307	−	39.6107i	−1.00721	−	2.09642i
$358$	3.50974	−	0.940432i	0.185496	−	0.0497034i
$359$		−	29.4575i		−	1.55471i	−0.629063	−	0.777355i	$-0.716561\pi$
$359$		−	29.4575i		−	1.55471i	0.629063	−	0.777355i	$-0.283439\pi$
$360$	3.12522	+	6.21919i	0.164714	+	0.327780i
$361$	−1.81264	−	3.13958i	−0.0954020	−	0.165241i
$362$	−0.348060	+	1.29898i	−0.0182936	+	0.0682727i
$363$	14.9117	+	10.1867i	0.782662	+	0.534663i
$364$	23.4792	−	5.28468i	1.23065	−	0.276993i
$365$	21.6568	−	15.3661i	1.13357	−	0.804298i
$366$	−0.889812	+	0.764324i	−0.0465112	+	0.0399519i
$367$	−1.66608	+	6.21790i	−0.0869688	+	0.324572i	−0.995680	−	0.0928540i	$-0.970401\pi$
$367$	−1.66608	+	6.21790i	−0.0869688	+	0.324572i	0.908711	+	0.417426i	$0.137068\pi$
$368$	−4.13887	+	1.10901i	−0.215753	+	0.0578109i
$369$	5.88194	+	15.0682i	0.306201	+	0.784422i
$370$	1.26071	+	1.04455i	0.0655413	+	0.0543038i
$371$	12.9623	−	22.4513i	0.672968	−	1.16562i
$372$	10.3677	+	7.08255i	0.537542	+	0.367213i
$373$	−2.50087	−	9.33338i	−0.129490	−	0.483264i	0.870470	−	0.492222i	$-0.163815\pi$
$373$	−2.50087	−	9.33338i	−0.129490	−	0.483264i	−0.999960	+	0.00895787i	$0.997149\pi$
$374$	−0.733515	−	1.27049i	−0.0379292	−	0.0656952i
$375$	−16.1913	−	10.6227i	−0.836115	−	0.548555i
$376$	3.34833			0.172677
$377$	−13.7731	+	21.7739i	−0.709349	+	1.12142i
$378$	1.06825	−	4.62157i	0.0549447	−	0.237708i
$379$	−7.67284	−	13.2897i	−0.394127	−	0.682649i	0.598862	−	0.800852i	$-0.295620\pi$
$379$	−7.67284	−	13.2897i	−0.394127	−	0.682649i	−0.992989	+	0.118204i	$0.962286\pi$
$380$	−7.14199	−	19.2487i	−0.366377	−	0.987435i
$381$	20.9638	+	7.35715i	1.07401	+	0.376918i
$382$	1.56257	−	1.56257i	0.0799481	−	0.0799481i
$383$	5.85583	+	21.8543i	0.299219	+	1.11670i	0.937808	+	0.347153i	$0.112852\pi$
$383$	5.85583	+	21.8543i	0.299219	+	1.11670i	−0.638589	+	0.769548i	$0.720482\pi$
$384$	−4.43199	+	12.6287i	−0.226169	+	0.644456i
$385$	−3.38878	−	4.77610i	−0.172708	−	0.243413i
$386$	1.71877	+	0.992333i	0.0874832	+	0.0505084i
$387$	1.88972	+	17.0532i	0.0960601	+	0.866863i
$388$	−4.42384	+	16.5100i	−0.224587	+	0.838169i
$389$	−11.0104			−0.558251			−0.279126	−	0.960255i	$-0.590045\pi$
$389$	−11.0104			−0.558251			−0.279126	+	0.960255i	$0.590045\pi$
$390$	−3.68552	−	0.0834334i	−0.186624	−	0.00422481i
$391$	−8.76548			−0.443289
$392$	−1.33126	+	4.96834i	−0.0672390	+	0.250939i
$393$	−30.6401	−	2.32445i	−1.54559	−	0.117253i
$394$	−4.26809	−	2.46418i	−0.215023	−	0.124144i
$395$	14.0060	+	2.37979i	0.704716	+	0.119740i
$396$	−0.661651	+	4.33572i	−0.0332492	+	0.217878i
$397$	−2.08456	−	7.77969i	−0.104621	−	0.390451i	0.893681	−	0.448703i	$-0.148114\pi$
$397$	−2.08456	−	7.77969i	−0.104621	−	0.390451i	−0.998302	+	0.0582519i	$0.981447\pi$
$398$	0.0665015	−	0.0665015i	0.00333342	−	0.00333342i
$399$	−9.43396	+	26.8815i	−0.472288	+	1.34576i
$400$	−3.33384	−	17.6209i	−0.166692	−	0.881045i
$401$	−18.6776	−	32.3506i	−0.932716	−	1.61551i	−0.778656	−	0.627451i	$-0.784098\pi$
$401$	−18.6776	−	32.3506i	−0.932716	−	1.61551i	−0.154060	−	0.988061i	$-0.549235\pi$
$402$	−2.19078	−	1.49660i	−0.109266	−	0.0746436i
$403$	−11.9904	+	6.29099i	−0.597282	+	0.313376i
$404$	−23.8745			−1.18780
$405$	9.13529	−	17.9317i	0.453936	−	0.891034i
$406$	−3.26158	−	5.64922i	−0.161869	−	0.280366i
$407$	0.543674	+	2.02902i	0.0269489	+	0.100575i
$408$	−7.43795	+	10.8880i	−0.368233	+	0.539035i
$409$	6.94769	−	12.0338i	0.343541	−	0.595031i	−0.641546	−	0.767084i	$-0.721707\pi$
$409$	6.94769	−	12.0338i	0.343541	−	0.595031i	0.985088	+	0.172053i	$0.0550401\pi$
$410$	0.297144	+	3.16895i	0.0146749	+	0.156503i
$411$	−6.87870	−	36.5385i	−0.339301	−	1.80231i
$412$	−31.4083	+	8.41582i	−1.54737	+	0.414618i
$413$	−4.73610	+	17.6754i	−0.233048	+	0.869748i
$414$	−0.738640	−	0.591268i	−0.0363022	−	0.0290592i
$415$	−4.27521	−	6.02541i	−0.209862	−	0.295776i
$416$	−7.38711	−	8.00963i	−0.362183	−	0.392704i
$417$	−9.92648	+	14.5308i	−0.486102	+	0.711575i
$418$	−0.246150	+	0.918643i	−0.0120396	+	0.0449323i
$419$	16.7332	+	28.9828i	0.817472	+	1.41590i	0.907539	+	0.419967i	$0.137958\pi$
$419$	16.7332	+	28.9828i	0.817472	+	1.41590i	−0.0900677	+	0.995936i	$0.528708\pi$
$420$	−12.5259	+	22.6145i	−0.611200	+	1.10347i
$421$			16.6235i			0.810182i	0.914276	+	0.405091i	$0.132760\pi$
$421$			16.6235i			0.810182i	−0.914276	+	0.405091i	$0.867240\pi$
$422$	2.05877	−	0.551645i	0.100219	−	0.0268537i
$423$	−5.73459	−	7.80004i	−0.278825	−	0.379251i
$424$	−7.77882			−0.377773
$425$	2.74201	−	36.5836i	0.133007	−	1.77457i
$426$	0.227650	−	0.195545i	0.0110297	−	0.00947419i
$427$	−8.56860	−	2.29595i	−0.414664	−	0.111109i
$428$	2.61584	+	2.61584i	0.126441	+	0.126441i
$429$	−3.79454	−	2.82359i	−0.183202	−	0.136324i
$430$	−0.565535	+	3.32838i	−0.0272725	+	0.160509i
$431$	17.3517	+	30.0540i	0.835801	+	1.44765i	0.893377	+	0.449309i	$0.148330\pi$
$431$	17.3517	+	30.0540i	0.835801	+	1.44765i	−0.0575757	+	0.998341i	$0.518337\pi$
$432$	17.8241	−	5.44429i	0.857564	−	0.261938i
$433$	5.49011	+	20.4894i	0.263838	+	0.984656i	0.962958	+	0.269652i	$0.0869087\pi$
$433$	5.49011	+	20.4894i	0.263838	+	0.984656i	−0.699120	+	0.715004i	$0.746425\pi$
$434$		−	3.42826i		−	0.164562i
$435$	−7.63694	−	26.6008i	−0.366163	−	1.27541i
$436$	−12.1633	−	7.02248i	−0.582516	−	0.336316i
$437$	4.01813	+	4.01813i	0.192213	+	0.192213i
$438$	2.35152	+	4.89447i	0.112360	+	0.233867i
$439$	15.3686	−	8.87309i	0.733505	−	0.423489i	−0.0861981	−	0.996278i	$-0.527472\pi$
$439$	15.3686	−	8.87309i	0.733505	−	0.423489i	0.819703	+	0.572789i	$0.194138\pi$
$440$	−0.732687	+	1.59714i	−0.0349295	+	0.0761408i
$441$	13.8539	−	5.40792i	0.659710	−	0.257520i
$442$	−3.24476	−	6.18437i	−0.154337	−	0.294160i
$443$	−12.3374	−	12.3374i	−0.586169	−	0.586169i	0.350422	−	0.936592i	$-0.386038\pi$
$443$	−12.3374	−	12.3374i	−0.586169	−	0.586169i	−0.936592	+	0.350422i	$0.886038\pi$
$444$	7.03416	−	6.04215i	0.333826	−	0.286748i
$445$	−8.13033	−	21.9124i	−0.385415	−	1.03875i
$446$	−1.32742	−	0.766387i	−0.0628552	−	0.0362895i
$447$	−12.9091	+	18.8969i	−0.610581	+	0.893793i
$448$	−21.2953	+	5.70605i	−1.00611	+	0.269585i
$449$	11.9704	+	6.91114i	0.564920	+	0.326157i	0.755118	−	0.655589i	$-0.227580\pi$
$449$	11.9704	+	6.91114i	0.564920	+	0.326157i	−0.190198	+	0.981746i	$0.560913\pi$
$450$	2.69878	−	2.89783i	0.127222	−	0.136605i
$451$	−2.04184	+	3.53657i	−0.0961464	+	0.166530i
$452$	5.46909	+	1.46544i	0.257244	+	0.0689284i
$453$	−13.1730	−	0.999347i	−0.618923	−	0.0469534i
$454$			1.36978i			0.0642868i
$455$	−15.2008	−	23.3701i	−0.712624	−	1.09561i
$456$	8.40068	−	1.58151i	0.393398	−	0.0740608i
$457$	1.27310	+	0.341127i	0.0595532	+	0.0159572i	0.288473	−	0.957488i	$-0.406853\pi$
$457$	1.27310	+	0.341127i	0.0595532	+	0.0159572i	−0.228919	+	0.973445i	$0.573519\pi$
$458$	1.09788	−	4.09736i	0.0513008	−	0.191457i
$459$	38.1026	−	1.32060i	1.77848	−	0.0616402i
$460$	2.98389	+	4.20545i	0.139124	+	0.196080i
$461$	−5.56011	+	9.63039i	−0.258960	+	0.448532i	−0.965964	−	0.258678i	$-0.916713\pi$
$461$	−5.56011	+	9.63039i	−0.258960	+	0.448532i	0.707003	+	0.707210i	$0.250046\pi$
$462$	1.07941	−	0.518595i	0.0502186	−	0.0241272i
$463$	−20.2693	−	20.2693i	−0.941994	−	0.941994i	0.0564134	−	0.998407i	$-0.482034\pi$
$463$	−20.2693	−	20.2693i	−0.941994	−	0.941994i	−0.998407	+	0.0564134i	$0.982034\pi$
$464$	12.8148	−	22.1959i	0.594914	−	1.03042i
$465$	3.51416	−	14.1139i	0.162965	−	0.654517i
$466$	−1.84998	+	1.06809i	−0.0856987	+	0.0494782i
$467$	6.97119	−	6.97119i	0.322588	−	0.322588i	−0.527171	−	0.849759i	$-0.676747\pi$
$467$	6.97119	−	6.97119i	0.322588	−	0.322588i	0.849759	+	0.527171i	$0.176747\pi$
$468$	−3.98112	+	20.4964i	−0.184027	+	0.947447i
$469$		−	20.0646i		−	0.926495i
$470$	−0.662671	−	1.78599i	−0.0305667	−	0.0823816i
$471$	5.56567	−	4.78076i	0.256453	−	0.220286i
$472$	5.30360	−	1.42110i	0.244118	−	0.0654112i
$473$	−3.06290	+	3.06290i	−0.140832	+	0.140832i
$474$	−0.962013	+	2.74120i	−0.0441867	+	0.125907i
$475$	−18.0270	+	15.5131i	−0.827137	+	0.711792i
$476$	−48.9753			−2.24478
$477$	13.3226	+	18.1210i	0.609998	+	0.829703i
$478$	−3.61585	−	0.968864i	−0.165385	−	0.0443148i
$479$	29.8923	−	17.2583i	1.36582	−	0.788554i	0.375425	−	0.926853i	$-0.377497\pi$
$479$	29.8923	−	17.2583i	1.36582	−	0.788554i	0.990391	+	0.138299i	$0.0441635\pi$
$480$	11.7024	−	0.208039i	0.534138	−	0.00949566i
$481$	2.19586	+	9.75595i	0.100123	+	0.444833i
$482$	−0.297655	+	0.297655i	−0.0135578	+	0.0135578i
$483$	0.541259	−	7.13467i	0.0246281	−	0.324639i
$484$	17.4297	−	10.0631i	0.792260	−	0.457412i
$485$	19.7134	−	1.84847i	0.895139	−	0.0839346i
$486$	3.29987	+	2.45889i	0.149685	+	0.111538i
$487$	1.59523	+	5.95347i	0.0722867	+	0.269778i	0.992604	−	0.121394i	$-0.0387365\pi$
$487$	1.59523	+	5.95347i	0.0722867	+	0.269778i	−0.920318	+	0.391172i	$0.872070\pi$
$488$	0.688913	+	2.57106i	0.0311856	+	0.116386i
$489$	−5.24327	−	27.8513i	−0.237109	−	1.25948i
$490$	2.91357	−	0.273197i	0.131622	−	0.0123418i
$491$	−33.2103	+	19.1739i	−1.49876	+	0.865308i	−0.999999	−	0.00143268i	$-0.999544\pi$
$491$	−33.2103	+	19.1739i	−1.49876	+	0.865308i	−0.498759	+	0.866741i	$0.666211\pi$
$492$	17.9754	+	1.36367i	0.810395	+	0.0614791i
$493$	37.0737	−	37.0737i	1.66971	−	1.66971i
$494$	−1.34753	+	4.32235i	−0.0606283	+	0.194472i
$495$	4.97544	−	1.02857i	0.223630	−	0.0462306i
$496$	11.6651	−	6.73486i	0.523779	−	0.302404i
$497$	2.19219	+	0.587397i	0.0983333	+	0.0263483i
$498$	1.36176	−	0.654247i	0.0610217	−	0.0293175i
$499$	−15.3354			−0.686509			−0.343254	−	0.939242i	$-0.611529\pi$
$499$	−15.3354			−0.686509			−0.343254	+	0.939242i	$0.611529\pi$
$500$	−18.4853	+	11.1380i	−0.826687	+	0.498107i
$501$	13.4807	+	4.73101i	0.602275	+	0.211366i
$502$	2.30921	−	2.30921i	0.103065	−	0.103065i
$503$	−14.0783	+	3.77227i	−0.627721	+	0.168197i	−0.558635	−	0.829413i	$-0.688675\pi$
$503$	−14.0783	+	3.77227i	−0.627721	+	0.168197i	−0.0690858	+	0.997611i	$0.522008\pi$
$504$	−8.40299	−	6.72645i	−0.374299	−	0.299620i
$505$	9.62062	+	25.9289i	0.428112	+	1.15382i
$506$		−	0.238863i		−	0.0106187i
$507$	−17.5064	−	14.1607i	−0.777487	−	0.628899i
$508$	17.5082	−	17.5082i	0.776800	−	0.776800i
$509$	14.2026	−	8.19989i	0.629520	−	0.363454i	−0.151046	−	0.988527i	$-0.548264\pi$
$509$	14.2026	−	8.19989i	0.629520	−	0.363454i	0.780566	+	0.625073i	$0.214931\pi$
$510$	7.27966	+	1.81253i	0.322349	+	0.0802602i
$511$	−20.5323	+	35.5630i	−0.908295	+	1.57321i
$512$	12.9273	+	12.9273i	0.571313	+	0.571313i
$513$	−18.0718	−	16.8610i	−0.797888	−	0.744432i
$514$	2.29171	−	3.96935i	0.101083	−	0.175081i
$515$	21.7965	+	30.7197i	0.960469	+	1.35367i
$516$	18.0427	+	6.33200i	0.794284	+	0.278751i
$517$	0.632584	−	2.36084i	0.0278210	−	0.103829i
$518$	−2.44559	−	0.655293i	−0.107453	−	0.0287919i
$519$	−3.89317	−	20.6799i	−0.170891	−	0.907745i
$520$	−3.79232	+	7.45619i	−0.166304	+	0.326976i
$521$		−	1.84827i		−	0.0809740i	−0.999180	−	0.0404870i	$-0.987109\pi$
$521$		−	1.84827i		−	0.0809740i	0.999180	−	0.0404870i	$-0.0128909\pi$
$522$	5.62486	−	0.623310i	0.246193	−	0.0272815i
$523$	22.5196	+	6.03412i	0.984715	+	0.263854i	0.715029	−	0.699095i	$-0.246413\pi$
$523$	22.5196	+	6.03412i	0.984715	+	0.263854i	0.269686	+	0.962948i	$0.413080\pi$
$524$	−17.1227	+	29.6574i	−0.748009	+	1.29559i
$525$	29.6080	+	4.49086i	1.29220	+	0.195997i
$526$	−4.00685	−	2.31336i	−0.174707	−	0.100867i
$527$	26.6158	−	7.13169i	1.15940	−	0.310661i
$528$	3.88510	+	2.65405i	0.169077	+	0.115502i
$529$	18.6826	+	10.7864i	0.812287	+	0.468974i
$530$	1.53951	+	4.14920i	0.0668722	+	0.180230i
$531$	−12.3938	−	9.92102i	−0.537845	−	0.430535i
$532$	22.4505	+	22.4505i	0.973352	+	0.973352i
$533$	−10.3925	+	16.4296i	−0.450151	+	0.711647i
$534$	4.69681	−	0.884218i	0.203251	−	0.0382639i
$535$	1.78684	−	3.89503i	0.0772518	−	0.168397i
$536$	−5.21390	+	3.01025i	−0.225206	+	0.130023i
$537$	−21.4882	+	10.3239i	−0.927285	+	0.445508i
$538$	1.07629	+	1.07629i	0.0464023	+	0.0464023i
$539$	3.25156	+	1.87729i	0.140055	+	0.0808605i
$540$	−13.6042	−	17.8311i	−0.585432	−	0.767327i
$541$		−	30.2686i		−	1.30135i	−0.759357	−	0.650674i	$-0.774487\pi$
$541$		−	30.2686i		−	1.30135i	0.759357	−	0.650674i	$-0.225513\pi$
$542$	−1.44090	−	5.37753i	−0.0618921	−	0.230985i
$543$	0.667436	−	8.79790i	0.0286424	−	0.377554i
$544$	11.0866	+	19.2026i	0.475336	+	0.823306i
$545$	−2.72537	+	16.0398i	−0.116742	+	0.687069i
$546$	5.23413	−	2.25920i	0.224000	−	0.0966847i
$547$	22.9924	+	22.9924i	0.983084	+	0.983084i	0.999859	−	0.0167753i	$-0.00533998\pi$
$547$	22.9924	+	22.9924i	0.983084	+	0.983084i	−0.0167753	+	0.999859i	$0.505340\pi$
$548$	−40.0242	−	10.7245i	−1.70975	−	0.458126i
$549$	4.80948	−	6.00822i	0.205263	−	0.256425i
$550$	0.996918	+	0.0747207i	0.0425087	+	0.00318610i
$551$	−33.9895			−1.44800
$552$	−1.93519	+	0.929752i	−0.0823673	+	0.0395729i
$553$	−21.2212	+	5.68619i	−0.902415	+	0.241801i
$554$		−	1.46650i		−	0.0623057i
$555$	−9.39662	−	5.20467i	−0.398864	−	0.220926i
$556$	9.80599	+	16.9845i	0.415867	+	0.720302i
$557$	−7.31770	+	27.3100i	−0.310061	+	1.15716i	0.618440	+	0.785832i	$0.287765\pi$
$557$	−7.31770	+	27.3100i	−0.310061	+	1.15716i	−0.928501	+	0.371331i	$0.878902\pi$
$558$	2.72390	+	1.19438i	0.115312	+	0.0505623i
$559$	−15.1583	+	13.9802i	−0.641128	+	0.591298i
$560$	16.0482	+	22.6181i	0.678159	+	0.955788i
$561$	6.27165	+	7.30134i	0.264789	+	0.308263i
$562$	−0.910577	+	3.39832i	−0.0384104	+	0.143349i
$563$	−26.1208	+	6.99906i	−1.10086	+	0.294975i	−0.763116	−	0.646262i	$-0.776331\pi$
$563$	−26.1208	+	6.99906i	−1.10086	+	0.294975i	−0.337747	+	0.941237i	$0.609665\pi$
$564$	−10.6031	+	1.99613i	−0.446472	+	0.0840524i
$565$	−0.612321	−	6.53024i	−0.0257606	−	0.274729i
$566$	1.83788	−	3.18330i	0.0772519	−	0.133804i
$567$	−1.27789	+	31.0952i	−0.0536664	+	1.30588i
$568$	−0.176252	−	0.657781i	−0.00739537	−	0.0275999i
$569$	−4.95492	−	8.58218i	−0.207721	−	0.359784i	0.743275	−	0.668986i	$-0.233271\pi$
$569$	−4.95492	−	8.58218i	−0.207721	−	0.359784i	−0.950996	+	0.309202i	$0.899938\pi$
$570$	−2.50615	−	4.16790i	−0.104971	−	0.174574i
$571$	23.1555			0.969026			0.484513	−	0.874784i	$-0.338997\pi$
$571$	23.1555			0.969026			0.484513	+	0.874784i	$0.338997\pi$
$572$	−4.66776	+	2.44904i	−0.195169	+	0.102399i
$573$	−8.17828	+	11.9717i	−0.341652	+	0.500125i
$574$	−2.46104	−	4.26265i	−0.102722	−	0.177919i
$575$	3.36492	−	4.93531i	0.140327	−	0.205817i
$576$	2.88544	−	18.9079i	0.120227	−	0.787831i
$577$	−7.88984	+	7.88984i	−0.328458	+	0.328458i	−0.852000	−	0.523542i	$-0.824610\pi$
$577$	−7.88984	+	7.88984i	−0.328458	+	0.328458i	0.523542	+	0.852000i	$0.324610\pi$
$578$	2.51682	+	9.39291i	0.104686	+	0.390693i
$579$	−12.2867	−	4.31195i	−0.510616	−	0.179199i
$580$	−30.4074	−	5.16661i	−1.26260	−	0.214532i
$581$	9.89445	+	5.71256i	0.410491	+	0.236997i
$582$	−0.306278	+	4.03724i	−0.0126956	+	0.167349i
$583$	−1.46961	+	5.48468i	−0.0608652	+	0.227152i
$584$	12.3217			0.509874
$585$	23.8644	−	3.93568i	0.986672	−	0.162720i
$586$	−3.94669			−0.163036
$587$	−4.63260	+	17.2891i	−0.191208	+	0.713597i	0.802008	+	0.597313i	$0.203765\pi$
$587$	−4.63260	+	17.2891i	−0.191208	+	0.713597i	−0.993216	+	0.116284i	$0.962902\pi$
$588$	1.25378	−	16.5268i	0.0517048	−	0.681554i
$589$	−15.4700	−	8.93162i	−0.637431	−	0.368021i
$590$	−1.80765	−	2.54767i	−0.0744197	−	0.104886i
$591$	30.5105	+	10.7075i	1.25503	+	0.440449i
$592$	−2.57466	−	9.60878i	−0.105818	−	0.394918i
$593$	18.2825	−	18.2825i	0.750773	−	0.750773i	−0.223851	−	0.974623i	$-0.571863\pi$
$593$	18.2825	−	18.2825i	0.750773	−	0.750773i	0.974623	+	0.223851i	$0.0718628\pi$
$594$	0.0359868	+	1.03831i	0.00147656	+	0.0426024i
$595$	19.7354	+	53.1897i	0.809073	+	2.18056i
$596$	12.7524	+	22.0879i	0.522360	+	0.904754i
$597$	−0.348060	+	0.509504i	−0.0142451	+	0.0208526i
$598$	0.0459385	−	1.13619i	0.00187857	−	0.0464624i
$599$	−28.6851			−1.17204			−0.586021	−	0.810296i	$-0.699306\pi$
$599$	−28.6851			−1.17204			−0.586021	+	0.810296i	$0.699306\pi$
$600$	−3.27505	−	8.36757i	−0.133703	−	0.341605i
$601$	−22.4909	−	38.9554i	−0.917423	−	1.58902i	−0.803315	−	0.595554i	$-0.796933\pi$
$601$	−22.4909	−	38.9554i	−0.917423	−	1.58902i	−0.114107	−	0.993468i	$-0.536401\pi$
$602$	−1.35127	−	5.04300i	−0.0550735	−	0.205537i
$603$	15.9422	+	6.99037i	0.649215	+	0.284670i
$604$	−7.36152	+	12.7505i	−0.299536	+	0.518811i
$605$	−17.9526	−	14.8745i	−0.729877	−	0.604734i
$606$	−5.55774	+	1.04630i	−0.225768	+	0.0425028i
$607$	22.9328	−	6.14482i	0.930813	−	0.249411i	0.238612	−	0.971115i	$-0.423308\pi$
$607$	22.9328	−	6.14482i	0.930813	−	0.249411i	0.692201	+	0.721704i	$0.256641\pi$
$608$	3.72040	−	13.8847i	0.150882	−	0.563100i
$609$	27.8869	+	32.4654i	1.13004	+	1.31557i
$610$	1.23505	−	0.876305i	0.0500058	−	0.0354805i
$611$	3.46304	−	11.1081i	0.140100	−	0.449385i
$612$	17.0627	−	38.9129i	0.689718	−	1.57296i
$613$	9.31036	−	34.7467i	0.376042	−	1.40341i	−0.475775	−	0.879567i	$-0.657832\pi$
$613$	9.31036	−	34.7467i	0.376042	−	1.40341i	0.851817	−	0.523840i	$-0.175501\pi$
$614$	−1.44082	−	2.49558i	−0.0581468	−	0.100713i
$615$	−5.76249	−	20.0718i	−0.232366	−	0.809372i
$616$		−	2.71738i		−	0.109486i
$617$	−17.2574	+	4.62410i	−0.694756	+	0.186159i	−0.588881	−	0.808220i	$-0.700431\pi$
$617$	−17.2574	+	4.62410i	−0.694756	+	0.186159i	−0.105876	+	0.994379i	$0.533765\pi$
$618$	−6.94271	+	3.33558i	−0.279277	+	0.134177i
$619$	2.34719			0.0943415			0.0471707	−	0.998887i	$-0.484980\pi$
$619$	2.34719			0.0943415			0.0471707	+	0.998887i	$0.484980\pi$
$620$	−12.4820	−	10.3419i	−0.501288	−	0.415339i
$621$	5.48023	+	2.91573i	0.219914	+	0.117004i
$622$	1.23555	+	0.331065i	0.0495410	+	0.0132745i
$623$	25.5573	+	25.5573i	1.02393	+	1.02393i
$624$	17.9698	+	13.3716i	0.719366	+	0.535294i
$625$	19.5454	+	15.5877i	0.781816	+	0.623509i
$626$	0.208825	+	0.361695i	0.00834632	+	0.0144563i
$627$	0.472014	−	6.22192i	0.0188504	−	0.248479i
$628$	−2.11633	−	7.89826i	−0.0844508	−	0.315175i
$629$		−	20.3499i		−	0.811404i
$630$	−1.92482	+	5.81336i	−0.0766867	+	0.231610i
$631$	11.6065	+	6.70099i	0.462046	+	0.266762i	0.712904	−	0.701262i	$-0.247379\pi$
$631$	11.6065	+	6.70099i	0.462046	+	0.266762i	−0.250858	+	0.968024i	$0.580713\pi$
$632$	4.66136	+	4.66136i	0.185419	+	0.185419i
$633$	−12.6047	+	6.05585i	−0.500992	+	0.240699i
$634$	0.992107	−	0.572793i	0.0394016	−	0.0227485i
$635$	−26.0700	−	11.9596i	−1.03456	−	0.474601i
$636$	24.6331	−	4.63740i	0.976765	−	0.183885i
$637$	15.1056	+	9.55501i	0.598505	+	0.378583i
$638$	1.01027	+	1.01027i	0.0399971	+	0.0399971i
$639$	−1.23046	+	1.53715i	−0.0486762	+	0.0608086i
$640$	7.20452	−	15.7047i	0.284784	−	0.620785i
$641$	−7.29316	−	4.21071i	−0.288062	−	0.166313i	0.349005	−	0.937121i	$-0.386520\pi$
$641$	−7.29316	−	4.21071i	−0.288062	−	0.166313i	−0.637068	+	0.770808i	$0.719853\pi$
$642$	0.723580	+	0.494303i	0.0285574	+	0.0195086i
$643$	27.1243	−	7.26793i	1.06968	−	0.286619i	0.319316	−	0.947648i	$-0.396547\pi$
$643$	27.1243	−	7.26793i	1.06968	−	0.286619i	0.750360	+	0.661029i	$0.229880\pi$
$644$	−6.90584	−	3.98709i	−0.272128	−	0.157113i
$645$	−0.393717	−	22.1468i	−0.0155026	−	0.872031i
$646$	4.60673	−	7.97910i	0.181250	−	0.313933i
$647$	12.8340	+	3.43885i	0.504555	+	0.135195i	0.502113	−	0.864802i	$-0.332556\pi$
$647$	12.8340	+	3.43885i	0.504555	+	0.135195i	0.00244197	+	0.999997i	$0.499223\pi$
$648$	8.27200	−	4.33308i	0.324955	−	0.170220i
$649$		−	4.00793i		−	0.157325i
$650$	4.72765	+	0.547152i	0.185434	+	0.0214611i
$651$	4.16135	+	22.1044i	0.163096	+	0.866338i
$652$	−30.5083	−	8.17468i	−1.19480	−	0.320145i
$653$	−10.1122	+	37.7391i	−0.395719	+	1.47685i	0.424832	+	0.905272i	$0.360333\pi$
$653$	−10.1122	+	37.7391i	−0.395719	+	1.47685i	−0.820551	+	0.571573i	$0.806333\pi$
$654$	−3.13925	−	1.10171i	−0.122754	−	0.0430802i
$655$	39.1093	+	6.64519i	1.52813	+	0.259649i
$656$	9.66949	−	16.7481i	0.377530	−	0.653902i
$657$	−21.1030	−	28.7037i	−0.823305	−	1.11984i
$658$	2.08307	+	2.08307i	0.0812066	+	0.0812066i
$659$	0.692965	−	1.20025i	0.0269941	−	0.0467551i	−0.852213	−	0.523195i	$-0.824740\pi$
$659$	0.692965	−	1.20025i	0.0269941	−	0.0467551i	0.879207	+	0.476440i	$0.158073\pi$
$660$	1.36804	−	5.49445i	0.0532508	−	0.213871i
$661$	−36.2520	+	20.9301i	−1.41004	+	0.814087i	−0.995392	−	0.0958938i	$-0.969429\pi$
$661$	−36.2520	+	20.9301i	−1.41004	+	0.814087i	−0.414649	+	0.909981i	$0.636096\pi$
$662$	−2.97299	+	2.97299i	−0.115548	+	0.115548i
$663$	28.4280	+	35.9363i	1.10405	+	1.39565i
$664$		−	3.42818i		−	0.133039i
$665$	15.3356	−	33.4292i	0.594688	−	1.29633i
$666$	1.37269	−	1.71482i	0.0531905	−	0.0664481i
$667$	8.24582	−	2.20946i	0.319279	−	0.0855507i
$668$	11.2586	−	11.2586i	0.435610	−	0.435610i
$669$	9.48908	+	3.33016i	0.366869	+	0.128751i
$670$	2.63754	+	2.18532i	0.101897	+	0.0844262i
$671$	1.94295			0.0750068
$672$	−16.3146	+	7.83825i	−0.629349	+	0.302367i
$673$	−21.7288	−	5.82222i	−0.837585	−	0.224430i	−0.185565	−	0.982632i	$-0.559412\pi$
$673$	−21.7288	−	5.82222i	−0.837585	−	0.224430i	−0.652020	+	0.758202i	$0.726078\pi$
$674$	1.86127	−	1.07460i	0.0716934	−	0.0413922i
$675$	−13.8834	+	21.9602i	−0.534373	+	0.845249i
$676$	−22.6740	+	10.7516i	−0.872079	+	0.413522i
$677$	9.66307	−	9.66307i	0.371382	−	0.371382i	−0.496599	−	0.867980i	$-0.665418\pi$
$677$	9.66307	−	9.66307i	0.371382	−	0.371382i	0.867980	+	0.496599i	$0.165418\pi$
$678$	1.33737	+	0.101457i	0.0513615	+	0.00389644i
$679$	−26.5170	+	15.3096i	−1.01763	+	0.587529i
$680$	10.8608	−	13.1083i	0.416493	−	0.502681i
$681$	−1.66269	−	8.83191i	−0.0637143	−	0.338439i
$682$	0.194341	+	0.725292i	0.00744171	+	0.0277729i
$683$	10.5914	+	39.5275i	0.405267	+	1.51248i	0.803562	+	0.595221i	$0.202935\pi$
$683$	10.5914	+	39.5275i	0.405267	+	1.51248i	−0.398295	+	0.917257i	$0.630398\pi$
$684$	−25.6595	+	10.0163i	−0.981114	+	0.382981i
$685$	4.48113	+	47.7899i	0.171215	+	1.82596i
$686$	1.61487	−	0.932347i	0.0616561	−	0.0355972i
$687$	−2.10529	+	27.7512i	−0.0803219	+	1.05877i
$688$	14.5049	−	14.5049i	0.552995	−	0.552995i
$689$	−8.04531	+	25.8062i	−0.306502	+	0.983139i
$690$	0.878922	+	0.848218i	0.0334600	+	0.0322911i
$691$	−35.2096	+	20.3283i	−1.33944	+	0.773323i	−0.986724	−	0.162409i	$-0.948074\pi$
$691$	−35.2096	+	20.3283i	−1.33944	+	0.773323i	−0.352712	+	0.935732i	$0.614740\pi$
$692$	−22.6527	−	6.06977i	−0.861127	−	0.230738i
$693$	−6.33020	+	4.65397i	−0.240465	+	0.176790i
$694$	−0.717694			−0.0272433
$695$	14.4945	−	17.4940i	0.549809	−	0.663585i
$696$	4.25252	−	12.1173i	0.161192	−	0.459306i
$697$	27.9741	−	27.9741i	1.05960	−	1.05960i
$698$	−5.15364	+	1.38091i	−0.195068	+	0.0522684i
$699$	10.6316	−	9.13228i	0.402125	−	0.345415i
$700$	18.8008	−	27.5750i	0.710604	−	1.04224i
$701$		−	49.6743i		−	1.87617i	−0.346401	−	0.938086i	$-0.612596\pi$
$701$		−	49.6743i		−	1.87617i	0.346401	−	0.938086i	$-0.387404\pi$
$702$	−0.0285122	+	4.94583i	−0.00107612	+	0.186668i
$703$	−9.32848	+	9.32848i	−0.351830	+	0.351830i
$704$	4.18182	−	2.41437i	0.157608	−	0.0909952i
$705$	6.44061	+	10.7112i	0.242567	+	0.403405i
$706$	−3.85390	+	6.67515i	−0.145044	+	0.251223i
$707$	−30.2419	−	30.2419i	−1.13736	−	1.13736i
$708$	−15.9476	+	7.66194i	−0.599349	+	0.287953i
$709$	−0.0385950	+	0.0668486i	−0.00144947	+	0.00251055i	−0.866749	−	0.498744i	$-0.833795\pi$
$709$	−0.0385950	+	0.0668486i	−0.00144947	+	0.00251055i	0.865300	+	0.501255i	$0.167128\pi$
$710$	−0.315976	+	0.224194i	−0.0118584	+	0.00841386i
$711$	2.87540	−	18.8421i	0.107836	−	0.706636i
$712$	2.80691	−	10.4755i	0.105193	−	0.392587i
$713$	4.33360	+	1.16119i	0.162295	+	0.0434868i
$714$	−11.4010	+	2.14634i	−0.426670	+	0.0803246i
$715$	4.54073	+	4.08254i	0.169814	+	0.152679i
$716$			26.5684i			0.992906i
$717$	24.4900	+	1.85788i	0.914594	+	0.0693840i
$718$	−7.51161	−	2.01273i	−0.280331	−	0.0751144i
$719$	1.97524	−	3.42122i	0.0736641	−	0.127590i	−0.826840	−	0.562437i	$-0.809864\pi$
$719$	1.97524	−	3.42122i	0.0736641	−	0.127590i	0.900505	+	0.434847i	$0.143197\pi$
$720$	−23.5621	+	4.87096i	−0.878108	+	0.181530i
$721$	−50.4454	−	29.1247i	−1.87868	−	1.08466i
$722$	−0.924438	+	0.247702i	−0.0344040	+	0.00921853i
$723$	1.55789	−	2.28050i	0.0579384	−	0.0848126i
$724$	−8.51572	−	4.91655i	−0.316484	−	0.182722i
$725$	6.64196	+	35.1059i	0.246676	+	1.30380i
$726$	3.61645	−	3.10644i	0.134219	−	0.115291i
$727$	−26.2031	−	26.2031i	−0.971818	−	0.971818i	0.0277959	−	0.999614i	$-0.491151\pi$
$727$	−26.2031	−	26.2031i	−0.971818	−	0.971818i	−0.999614	+	0.0277959i	$0.991151\pi$
$728$	0.522611	−	12.9257i	0.0193693	−	0.479058i
$729$	−24.2612	−	11.8487i	−0.898565	−	0.438841i
$730$	−2.43859	−	6.57234i	−0.0902563	−	0.243253i
$731$	36.3412	−	20.9816i	1.34413	−	0.776032i
$732$	−3.71433	−	7.73103i	−0.137286	−	0.285747i
$733$	−4.40376	−	4.40376i	−0.162656	−	0.162656i	0.621086	−	0.783742i	$-0.286692\pi$
$733$	−4.40376	−	4.40376i	−0.162656	−	0.162656i	−0.783742	+	0.621086i	$0.786692\pi$
$734$	1.47172	+	0.849695i	0.0543220	+	0.0313628i
$735$	−18.4542	+	5.29810i	−0.680694	+	0.195423i
$736$			3.61027i			0.133076i
$737$	1.13742	+	4.24492i	0.0418975	+	0.156364i
$738$	4.24427	−	0.470322i	0.156234	−	0.0173128i
$739$	−19.3253	−	33.4724i	−0.710892	−	1.23130i	−0.964523	−	0.264000i	$-0.914958\pi$
$739$	−19.3253	−	33.4724i	−0.710892	−	1.23130i	0.253630	−	0.967301i	$-0.418375\pi$
$740$	−9.76335	+	6.92738i	−0.358908	+	0.254655i
$741$	3.44183	−	29.5049i	0.126439	−	1.08389i
$742$	−4.83938	−	4.83938i	−0.177659	−	0.177659i
$743$	40.6962	+	10.9045i	1.49300	+	0.400048i	0.910749	−	0.412961i	$-0.135506\pi$
$743$	40.6962	+	10.9045i	1.49300	+	0.400048i	0.582251	+	0.813009i	$0.302172\pi$
$744$	5.11964	−	4.39763i	0.187695	−	0.161225i
$745$	18.8498	−	22.7505i	0.690601	−	0.833513i
$746$	−2.55087			−0.0933940
$747$	−7.98604	+	5.87134i	−0.292194	+	0.214821i
$748$	10.3613	−	2.77632i	0.378848	−	0.101512i
$749$			6.62700i			0.242145i
$750$	−3.81507	+	3.40293i	−0.139307	+	0.124258i
$751$	8.97373	+	15.5430i	0.327456	+	0.567170i	0.982006	−	0.188848i	$-0.0604754\pi$
$751$	8.97373	+	15.5430i	0.327456	+	0.567170i	−0.654550	+	0.756018i	$0.727142\pi$
$752$	−2.99572	+	11.1802i	−0.109243	+	0.407699i
$753$	−12.0861	+	17.6921i	−0.440442	+	0.644737i
$754$	4.61125	+	4.99984i	0.167932	+	0.182084i
$755$	16.8142	+	2.85695i	0.611930	+	0.103975i
$756$	30.6196	+	16.2910i	1.11363	+	0.592499i
$757$	−1.65482	+	6.17589i	−0.0601456	+	0.224466i	−0.989456	−	0.144833i	$-0.953736\pi$
$757$	−1.65482	+	6.17589i	−0.0601456	+	0.224466i	0.929311	+	0.369299i	$0.120402\pi$
$758$	−3.91312	+	1.04852i	−0.142131	+	0.0380838i
$759$	0.289941	+	1.54011i	0.0105242	+	0.0559026i
$760$	−10.9875	+	1.03027i	−0.398560	+	0.0373718i
$761$	−1.79494	+	3.10892i	−0.0650664	+	0.112698i	−0.896723	−	0.442591i	$-0.854059\pi$
$761$	−1.79494	+	3.10892i	−0.0650664	+	0.112698i	0.831657	+	0.555290i	$0.187393\pi$
$762$	3.30844	−	4.84303i	0.119852	−	0.175444i
$763$	−6.51189	−	24.3027i	−0.235746	−	0.879818i
$764$	8.07901	+	13.9933i	0.292288	+	0.506258i
$765$	−49.1372	−	2.85032i	−1.77656	−	0.103053i
$766$	5.97290			0.215810
$767$	0.770813	−	19.0645i	0.0278324	−	0.688377i
$768$	−15.3192	−	10.4651i	−0.552785	−	0.377626i
$769$	3.66193	+	6.34265i	0.132053	+	0.228722i	0.924468	−	0.381260i	$-0.124510\pi$
$769$	3.66193	+	6.34265i	0.132053	+	0.228722i	−0.792415	+	0.609982i	$0.791177\pi$
$770$	−1.44944	+	0.537798i	−0.0522342	+	0.0193809i
$771$	−9.95808	+	28.3750i	−0.358631	+	1.02190i
$772$	−10.2614	+	10.2614i	−0.369315	+	0.369315i
$773$	−8.46631	−	31.5967i	−0.304512	−	1.13645i	−0.933364	−	0.358930i	$-0.883142\pi$
$773$	−8.46631	−	31.5967i	−0.304512	−	1.13645i	0.628852	−	0.777525i	$-0.283525\pi$
$774$	4.47765	+	0.683310i	0.160946	+	0.0245611i
$775$	−6.20196	+	17.7235i	−0.222781	+	0.636647i
$776$	7.95660	+	4.59374i	0.285625	+	0.164906i
$777$	16.5638	+	1.25658i	0.594224	+	0.0450797i
$778$	−0.752305	+	2.80764i	−0.0269714	+	0.100659i
$779$	−25.6469			−0.918897
$780$	7.56403	−	25.8722i	0.270836	−	0.926375i
$781$	−0.497085			−0.0177871
$782$	−0.598915	+	2.23518i	−0.0214171	+	0.0799299i
$783$	−35.5108	+	10.8466i	−1.26905	+	0.387625i
$784$	−15.3983	−	8.89024i	−0.549941	−	0.317509i
$785$	−7.72510	+	5.48118i	−0.275721	+	0.195632i
$786$	−2.68626	+	7.65435i	−0.0958158	+	0.273021i
$787$	−6.60933	−	24.6663i	−0.235597	−	0.879260i	−0.977879	−	0.209172i	$-0.932923\pi$
$787$	−6.60933	−	24.6663i	−0.235597	−	0.879260i	0.742282	−	0.670088i	$-0.233744\pi$
$788$	25.4813	−	25.4813i	0.907732	−	0.907732i
$789$	28.6430	+	10.0522i	1.01972	+	0.357866i
$790$	1.56382	−	3.40889i	0.0556383	−	0.121283i
$791$	5.07145	+	8.78400i	0.180320	+	0.312323i
$792$	2.15907	+	0.946716i	0.0767192	+	0.0336401i
$793$	9.24200	+	0.373672i	0.328193	+	0.0132695i
$794$	−2.12624			−0.0754573
$795$	−14.9628	−	24.8841i	−0.530675	−	0.882547i
$796$	0.343835	+	0.595539i	0.0121869	+	0.0211083i
$797$	−0.338010	−	1.26147i	−0.0119729	−	0.0446836i	0.959681	−	0.281092i	$-0.0906965\pi$
$797$	−0.338010	−	1.26147i	−0.0119729	−	0.0446836i	−0.971654	+	0.236408i	$0.924030\pi$
$798$	6.21014	+	4.24236i	0.219836	+	0.150178i
$799$	−11.8389	+	20.5056i	−0.418831	+	0.725437i
$800$	−15.0678	−	1.12936i	−0.532728	−	0.0399289i
$801$	−29.2103	+	11.4023i	−1.03210	+	0.402882i
$802$	−9.52552	+	2.55235i	−0.336358	+	0.0901268i
$803$	2.32787	−	8.68774i	0.0821488	−	0.306584i
$804$	14.7162	−	12.6408i	0.519000	−	0.445807i
$805$	−1.54736	+	9.10677i	−0.0545372	+	0.320971i
$806$	0.784930	+	3.48736i	0.0276480	+	0.122837i
$807$	−8.24606	−	5.63317i	−0.290275	−	0.198297i
$808$	−3.32141	+	12.3957i	−0.116847	+	0.436079i
$809$	−14.5548	−	25.2097i	−0.511720	−	0.886326i	−0.999908	−	0.0135868i	$-0.995675\pi$
$809$	−14.5548	−	25.2097i	−0.511720	−	0.886326i	0.488187	−	0.872739i	$-0.337658\pi$
$810$	−3.94837	−	3.55469i	−0.138732	−	0.124899i
$811$		−	40.2274i		−	1.41257i	−0.707926	−	0.706287i	$-0.750369\pi$
$811$		−	40.2274i		−	1.41257i	0.707926	−	0.706287i	$-0.249631\pi$
$812$	46.0718	−	12.3449i	1.61680	−	0.433221i
$813$	15.8180	+	32.9237i	0.554760	+	1.15468i
$814$	0.554543			0.0194367
$815$	3.41572	+	36.4277i	0.119648	+	1.27601i
$816$	−29.7005	−	34.5768i	−1.03973	−	1.21043i
$817$	−26.2770	−	7.04090i	−0.919315	−	0.246330i
$818$	−2.59387	−	2.59387i	−0.0906927	−	0.0906927i
$819$	−31.0058	+	20.9200i	−1.08343	+	0.731004i
$820$	−22.9440	−	3.89849i	−0.801240	−	0.136141i
$821$	10.4818	+	18.1550i	0.365818	+	0.633615i	0.988907	−	0.148536i	$-0.0474561\pi$
$821$	10.4818	+	18.1550i	0.365818	+	0.633615i	−0.623089	+	0.782151i	$0.714123\pi$
$822$	−9.78723	−	0.742490i	−0.341369	−	0.0258973i
$823$	10.3440	+	38.6043i	0.360569	+	1.34566i	0.873329	+	0.487130i	$0.161956\pi$
$823$	10.3440	+	38.6043i	0.360569	+	1.34566i	−0.512760	+	0.858532i	$0.671377\pi$
$824$			17.4781i			0.608877i
$825$	−6.51853	+	0.728321i	−0.226946	+	0.0253569i
$826$	4.18358	+	2.41539i	0.145565	+	0.0840422i
$827$	−0.968029	−	0.968029i	−0.0336617	−	0.0336617i	0.690076	−	0.723737i	$-0.257577\pi$
$827$	−0.968029	−	0.968029i	−0.0336617	−	0.0336617i	−0.723737	+	0.690076i	$0.757577\pi$
$828$	5.57387	−	4.09791i	0.193705	−	0.142412i
$829$	23.0443	−	13.3046i	0.800362	−	0.462089i	−0.0432359	−	0.999065i	$-0.513767\pi$
$829$	23.0443	−	13.3046i	0.800362	−	0.462089i	0.843598	+	0.536976i	$0.180433\pi$
$830$	−1.82858	+	0.678473i	−0.0634709	+	0.0235502i
$831$	1.78010	+	9.45556i	0.0617509	+	0.328010i
$832$	20.3559	−	10.6802i	0.705715	−	0.370268i
$833$	−25.7197	−	25.7197i	−0.891136	−	0.891136i
$834$	3.02708	+	3.52407i	0.104819	+	0.122029i
$835$	−16.7643	−	7.69060i	−0.580153	−	0.266144i
$836$	−6.02236	−	3.47701i	−0.208288	−	0.120255i
$837$	−19.0127	−	4.39465i	−0.657173	−	0.151901i
$838$	8.53388	−	2.28665i	0.294798	−	0.0789909i
$839$	−10.1710	−	5.87220i	−0.351140	−	0.202731i	0.314047	−	0.949407i	$-0.398315\pi$
$839$	−10.1710	−	5.87220i	−0.351140	−	0.202731i	−0.665187	+	0.746676i	$0.731648\pi$
$840$	9.99889	+	9.64959i	0.344994	+	0.332942i
$841$	−11.0308	+	19.1060i	−0.380374	+	0.658827i
$842$	4.23897	+	1.13583i	0.146085	+	0.0391432i
$843$	1.74611	−	23.0166i	0.0601394	−	0.792735i
$844$			15.5846i			0.536446i
$845$	20.8137	+	20.2927i	0.716012	+	0.698088i
$846$	−2.38082	+	0.929360i	−0.0818542	+	0.0319521i
$847$	34.8253	+	9.33140i	1.19661	+	0.320631i
$848$	6.95963	−	25.9737i	0.238995	−	0.891940i
$849$	−7.98609	+	22.7559i	−0.274082	+	0.780980i
$850$	−9.14140	−	3.19884i	−0.313547	−	0.109719i
$851$	1.65669	−	2.86947i	0.0567907	−	0.0983643i
$852$	0.950275	+	1.97791i	0.0325559	+	0.0677621i
$853$	12.6463	+	12.6463i	0.433001	+	0.433001i	0.889648	−	0.456647i	$-0.150950\pi$
$853$	12.6463	+	12.6463i	0.433001	+	0.433001i	−0.456647	+	0.889648i	$0.650950\pi$
$854$	−1.17092	+	2.02810i	−0.0400682	+	0.0694002i
$855$	21.2181	+	23.8313i	0.725643	+	0.815013i
$856$	1.72207	−	0.994235i	0.0588590	−	0.0339823i
$857$	17.5943	−	17.5943i	0.601008	−	0.601008i	−0.339572	−	0.940580i	$-0.610282\pi$
$857$	17.5943	−	17.5943i	0.601008	−	0.601008i	0.940580	+	0.339572i	$0.110282\pi$
$858$	−0.979279	+	0.774675i	−0.0334320	+	0.0264470i
$859$		−	0.150593i		−	0.00513817i	−0.999997	−	0.00256909i	$-0.999182\pi$
$859$		−	0.150593i		−	0.00513817i	0.999997	−	0.00256909i	$-0.000817767\pi$
$860$	−22.4374	−	10.2931i	−0.765110	−	0.350993i
$861$	21.0422	+	24.4970i	0.717117	+	0.834854i
$862$	8.84929	−	2.37116i	0.301408	−	0.0807620i
$863$	21.1115	−	21.1115i	0.718643	−	0.718643i	−0.249685	−	0.968327i	$-0.580327\pi$
$863$	21.1115	−	21.1115i	0.718643	−	0.718643i	0.968327	+	0.249685i	$0.0803269\pi$
$864$	−0.543918	−	15.6934i	−0.0185045	−	0.533901i
$865$	2.53621	+	27.0479i	0.0862336	+	0.919657i
$866$	5.59987			0.190291
$867$	−27.6292	−	57.5076i	−0.938336	−	1.95306i
$868$	24.2131	+	6.48788i	0.821846	+	0.220213i
$869$	4.16727	−	2.40597i	0.141365	−	0.0816171i
$870$	−7.30496	+	0.129864i	−0.247661	+	0.00440281i
$871$	4.59396	+	20.4105i	0.155661	+	0.691582i
$872$	−5.33824	+	5.33824i	−0.180776	+	0.180776i
$873$	−2.92577	−	26.4027i	−0.0990224	−	0.893596i
$874$	1.29916	−	0.750071i	0.0439448	−	0.0253715i
$875$	−37.5240	−	9.30683i	−1.26854	−	0.314628i
$876$	−39.0188	+	7.34566i	−1.31832	+	0.248187i
$877$	2.56493	+	9.57243i	0.0866114	+	0.323238i	0.995614	−	0.0935514i	$-0.0298219\pi$
$877$	2.56493	+	9.57243i	0.0866114	+	0.323238i	−0.909003	+	0.416789i	$0.863155\pi$
$878$	−1.21253	−	4.52524i	−0.0409210	−	0.152719i
$879$	25.4471	−	4.79064i	0.858308	−	0.161584i
$880$	−4.67737	−	3.87540i	−0.157674	−	0.130640i
$881$	41.0035	−	23.6734i	1.38144	−	0.797576i	0.389112	−	0.921190i	$-0.372782\pi$
$881$	41.0035	−	23.6734i	1.38144	−	0.797576i	0.992330	+	0.123614i	$0.0394485\pi$
$882$	−0.432419	−	3.90222i	−0.0145603	−	0.131395i
$883$	−8.67634	+	8.67634i	−0.291982	+	0.291982i	−0.837863	−	0.545881i	$-0.816195\pi$
$883$	−8.67634	+	8.67634i	−0.291982	+	0.291982i	0.545881	+	0.837863i	$0.316195\pi$
$884$	49.8196	−	11.2133i	1.67561	−	0.377145i
$885$	14.7476	+	14.2324i	0.495736	+	0.478418i
$886$	−3.98900	+	2.30305i	−0.134013	+	0.0773724i
$887$	−16.6020	−	4.44848i	−0.557439	−	0.149365i	−0.0309097	−	0.999522i	$-0.509840\pi$
$887$	−16.6020	−	4.44848i	−0.557439	−	0.149365i	−0.526530	+	0.850157i	$0.676507\pi$
$888$	−2.15851	−	4.49274i	−0.0724348	−	0.150766i
$889$	44.3554			1.48763
$890$	−6.14313	+	0.576023i	−0.205918	+	0.0193084i
$891$	−1.49237	−	6.65103i	−0.0499964	−	0.222818i
$892$	7.92495	−	7.92495i	0.265347	−	0.265347i
$893$	14.8269	−	3.97285i	0.496163	−	0.132946i
$894$	3.93664	+	4.58296i	0.131661	+	0.153277i
$895$	28.8546	−	10.7062i	0.964503	−	0.357868i
$896$			26.7200i			0.892653i
$897$	1.08296	+	7.38160i	0.0361589	+	0.246464i
$898$	2.58022	−	2.58022i	0.0861032	−	0.0861032i
$899$	−23.2403	+	13.4178i	−0.775107	+	0.447508i
$900$	15.3594	+	24.5450i	0.511981	+	0.818167i
$901$	27.5041	−	47.6385i	0.916295	−	1.58707i
$902$	0.762306	+	0.762306i	0.0253820	+	0.0253820i
$903$	14.8340	+	30.8755i	0.493643	+	1.02747i
$904$	1.52172	−	2.63569i	0.0506116	−	0.0876619i
$905$	−1.90808	+	11.2297i	−0.0634266	+	0.373289i
$906$	−1.15490	+	3.29081i	−0.0383689	+	0.109330i
$907$	−11.2857	+	42.1187i	−0.374735	+	1.39853i	0.478997	+	0.877817i	$0.341001\pi$
$907$	−11.2857	+	42.1187i	−0.374735	+	1.39853i	−0.853732	+	0.520713i	$0.825666\pi$
$908$	−9.67446	−	2.59226i	−0.321058	−	0.0860273i
$909$	34.5646	−	13.4924i	1.14644	−	0.447515i
$910$	−6.99795	+	2.27937i	−0.231980	+	0.0755605i
$911$			17.9743i			0.595516i	0.954641	+	0.297758i	$0.0962388\pi$
$911$			17.9743i			0.595516i	−0.954641	+	0.297758i	$0.903761\pi$
$912$	−2.23531	+	29.4650i	−0.0740185	+	0.975684i
$913$	−2.41713	−	0.647668i	−0.0799954	−	0.0214347i
$914$	0.173973	−	0.301331i	0.00575452	−	0.00996713i
$915$	−6.89955	+	7.14930i	−0.228092	+	0.236349i
$916$	26.8611	+	15.5083i	0.887517	+	0.512408i
$917$	−59.2566	+	15.8778i	−1.95683	+	0.524330i
$918$	2.26667	−	9.80631i	0.0748112	−	0.323657i
$919$	−26.6383	−	15.3796i	−0.878716	−	0.507327i	−0.00848144	−	0.999964i	$-0.502700\pi$
$919$	−26.6383	−	15.3796i	−0.878716	−	0.507327i	−0.870235	+	0.492637i	$0.836033\pi$
$920$	2.59860	−	0.964180i	0.0856732	−	0.0317881i
$921$	12.3192	+	14.3418i	0.405932	+	0.472579i
$922$	2.07583	+	2.07583i	0.0683638	+	0.0683638i
$923$	−2.36448	−	0.0956004i	−0.0778277	−	0.00314673i
$924$	1.61998	+	8.60507i	0.0532935	+	0.283086i
$925$	11.4578	+	7.81200i	0.376730	+	0.256857i
$926$	−6.55356	+	3.78370i	−0.215363	+	0.124340i
$927$	40.7156	−	29.9342i	1.33728	−	0.983167i
$928$	−15.2697	−	15.2697i	−0.501251	−	0.501251i
$929$	35.1545	+	20.2965i	1.15338	+	0.665906i	0.949709	−	0.313133i	$-0.101379\pi$
$929$	35.1545	+	20.2965i	1.15338	+	0.665906i	0.203673	+	0.979039i	$0.434712\pi$
$930$	−3.35891	−	1.86046i	−0.110143	−	0.0610069i
$931$			23.5801i			0.772806i
$932$	−4.04265	−	15.0874i	−0.132421	−	0.494204i
$933$	−8.36831	−	0.634846i	−0.273966	−	0.0207839i
$934$	−1.30132	−	2.25396i	−0.0425806	−	0.0737517i
$935$	−7.19050	−	10.1342i	−0.235155	−	0.331424i
$936$	10.0879	+	4.91847i	0.329735	+	0.160765i
$937$	25.1017	+	25.1017i	0.820037	+	0.820037i	0.986113	−	0.166076i	$-0.0531098\pi$
$937$	25.1017	+	25.1017i	0.820037	+	0.820037i	−0.166076	+	0.986113i	$0.553110\pi$
$938$	−5.11642	−	1.37094i	−0.167057	−	0.0447628i
$939$	−1.78548	−	2.07862i	−0.0582669	−	0.0678333i
$940$	13.8682	−	1.30038i	0.452330	−	0.0424137i
$941$	8.19014			0.266991			0.133495	−	0.991049i	$-0.457380\pi$
$941$	8.19014			0.266991			0.133495	+	0.991049i	$0.457380\pi$
$942$	−0.838801	−	1.74589i	−0.0273296	−	0.0568841i
$943$	6.22192	−	1.66716i	0.202614	−	0.0542902i
$944$			18.9803i			0.617756i
$945$	5.35418	−	39.8193i	0.174172	−	1.29532i
$946$	0.571756	+	0.990310i	0.0185894	+	0.0321978i
$947$	10.0422	−	37.4781i	0.326328	−	1.21787i	−0.586642	−	0.809847i	$-0.699550\pi$
$947$	10.0422	−	37.4781i	0.326328	−	1.21787i	0.912970	−	0.408027i	$-0.133783\pi$
$948$	−17.5400	−	11.9822i	−0.569671	−	0.389162i
$949$	12.7438	−	40.8771i	0.413681	−	1.32693i
$950$	2.72410	+	5.65682i	0.0883814	+	0.183531i
$951$	−5.70153	+	4.89746i	−0.184885	+	0.158811i
$952$	−6.81344	+	25.4281i	−0.220825	+	0.824129i
$953$	31.2837	−	8.38243i	1.01338	−	0.271534i	0.286338	−	0.958129i	$-0.407562\pi$
$953$	31.2837	−	8.38243i	1.01338	−	0.271534i	0.727040	+	0.686595i	$0.240895\pi$
$954$	5.53110	−	2.15908i	0.179076	−	0.0699029i
$955$	11.9418	−	14.4130i	0.386428	−	0.466395i
$956$	13.6858	−	23.7045i	0.442630	−	0.766658i
$957$	−7.74024	−	5.28762i	−0.250206	−	0.170925i
$958$	−2.35841	−	8.80169i	−0.0761966	−	0.284370i
$959$	−37.1142	−	64.2836i	−1.19848	−	2.07583i
$960$	−5.96597	+	23.9611i	−0.192551	+	0.773341i
$961$	16.8965			0.545049
$962$	2.63778	+	0.106651i	0.0850456	+	0.00343856i
$963$	−5.26543	−	2.30880i	−0.169676	−	0.0744002i
$964$	−1.53898	−	2.66558i	−0.0495671	−	0.0858527i
$965$	15.2794	+	7.00939i	0.491861	+	0.225640i
$966$	−1.78235	−	0.625507i	−0.0573460	−	0.0201254i
$967$	−0.363600	+	0.363600i	−0.0116926	+	0.0116926i	−0.712929	−	0.701236i	$-0.752632\pi$
$967$	−0.363600	+	0.363600i	−0.0116926	+	0.0116926i	0.701236	+	0.712929i	$0.252632\pi$
$968$	−2.79994	−	10.4495i	−0.0899936	−	0.335861i
$969$	−20.0175	+	57.0387i	−0.643055	+	1.83235i
$970$	0.875591	−	5.15317i	0.0281135	−	0.165458i
$971$	51.2520	+	29.5904i	1.64476	+	0.949600i	0.979110	+	0.203332i	$0.0651770\pi$
$971$	51.2520	+	29.5904i	1.64476	+	0.949600i	0.665645	+	0.746268i	$0.268156\pi$
$972$	−23.6116	+	18.6529i	−0.757343	+	0.598293i
$973$	−9.09302	+	33.9356i	−0.291509	+	1.08793i
$974$	1.62712			0.0521363
$975$	−31.1466	+	2.21074i	−0.997491	+	0.0708002i
$976$	−9.20119			−0.294523
$977$	−1.99334	+	7.43926i	−0.0637727	+	0.238003i	−0.990454	−	0.137846i	$-0.955982\pi$
$977$	−1.99334	+	7.43926i	−0.0637727	+	0.238003i	0.926681	+	0.375849i	$0.122649\pi$
$978$	−7.46029	−	0.565961i	−0.238554	−	0.0180974i
$979$	−6.85576	−	3.95818i	−0.219111	−	0.126504i
$980$	−3.58431	+	21.0950i	−0.114497	+	0.673855i
$981$	21.5782	+	3.29294i	0.688940	+	0.105135i
$982$	2.62018	+	9.77864i	0.0836132	+	0.312049i
$983$	−0.396618	+	0.396618i	−0.0126502	+	0.0126502i	−0.713404	−	0.700753i	$-0.752847\pi$
$983$	−0.396618	+	0.396618i	−0.0126502	+	0.0126502i	0.700753	+	0.713404i	$0.252847\pi$
$984$	3.20876	−	9.14318i	0.102292	−	0.291474i
$985$	−37.9421	−	17.4059i	−1.20894	−	0.554597i
$986$	−6.92060	−	11.9868i	−0.220397	−	0.381739i
$987$	−15.9595	−	10.9025i	−0.507998	−	0.347031i
$988$	−27.9778	−	17.6973i	−0.890091	−	0.563025i
$989$	6.83246			0.217260
$990$	0.0776722	−	1.33901i	0.00246859	−	0.0425564i
$991$	17.3190	+	29.9974i	0.550157	+	0.952900i	0.998263	+	0.0589191i	$0.0187654\pi$
$991$	17.3190	+	29.9974i	0.550157	+	0.952900i	−0.448106	+	0.893980i	$0.647901\pi$
$992$	−2.93735	−	10.9623i	−0.0932610	−	0.348055i
$993$	15.5602	−	22.7776i	0.493788	−	0.722827i
$994$	0.299570	−	0.518870i	0.00950178	−	0.0164576i
$995$	0.508232	−	0.613405i	0.0161120	−	0.0194462i
$996$	2.04373	+	10.8560i	0.0647582	+	0.343984i
$997$	−18.2994	+	4.90330i	−0.579546	+	0.155289i	−0.536671	−	0.843791i	$-0.680318\pi$
$997$	−18.2994	+	4.90330i	−0.579546	+	0.155289i	−0.0428751	+	0.999080i	$0.513652\pi$
$998$	−1.04782	+	3.91051i	−0.0331681	+	0.123785i
$999$	−6.76915	+	12.7229i	−0.214166	+	0.402534i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.bf.a.62.14	yes	96
3.2	odd	2	inner	195.2.bf.a.62.11	yes	96
5.2	odd	4		975.2.bn.d.218.14		96
5.3	odd	4	inner	195.2.bf.a.23.11	yes	96
5.4	even	2		975.2.bn.d.257.11		96
13.4	even	6	inner	195.2.bf.a.17.14	yes	96
15.2	even	4		975.2.bn.d.218.11		96
15.8	even	4	inner	195.2.bf.a.23.14	yes	96
15.14	odd	2		975.2.bn.d.257.14		96
39.17	odd	6	inner	195.2.bf.a.17.11	✓	96
65.4	even	6		975.2.bn.d.407.11		96
65.17	odd	12		975.2.bn.d.368.14		96
65.43	odd	12	inner	195.2.bf.a.173.11	yes	96
195.17	even	12		975.2.bn.d.368.11		96
195.134	odd	6		975.2.bn.d.407.14		96
195.173	even	12	inner	195.2.bf.a.173.14	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.11	✓	96	39.17	odd	6	inner
195.2.bf.a.17.14	yes	96	13.4	even	6	inner
195.2.bf.a.23.11	yes	96	5.3	odd	4	inner
195.2.bf.a.23.14	yes	96	15.8	even	4	inner
195.2.bf.a.62.11	yes	96	3.2	odd	2	inner
195.2.bf.a.62.14	yes	96	1.1	even	1	trivial
195.2.bf.a.173.11	yes	96	65.43	odd	12	inner
195.2.bf.a.173.14	yes	96	195.173	even	12	inner
975.2.bn.d.218.11		96	15.2	even	4
975.2.bn.d.218.14		96	5.2	odd	4
975.2.bn.d.257.11		96	5.4	even	2
975.2.bn.d.257.14		96	15.14	odd	2
975.2.bn.d.368.11		96	195.17	even	12
975.2.bn.d.368.14		96	65.17	odd	12
975.2.bn.d.407.11		96	65.4	even	6
975.2.bn.d.407.14		96	195.134	odd	6

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:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0683265 - 0.254998i) q^{2} +(-0.131022 + 1.72709i) q^{3} +(1.67170 + 0.965154i) q^{4} +(0.374569 - 2.20447i) q^{5} +(0.431452 + 0.151416i) q^{6} +(0.894980 + 3.34011i) q^{7} +(0.733676 - 0.733676i) q^{8} +(-2.96567 - 0.452574i) q^{9} +(-0.536543 - 0.246138i) q^{10} +(-0.378689 - 0.655909i) q^{11} +(-1.88593 + 2.76071i) q^{12} +(-1.67516 - 3.19278i) q^{13} +0.912873 q^{14} +(3.75824 + 0.935748i) q^{15} +(1.79335 + 3.10618i) q^{16} +(1.89902 + 7.08724i) q^{17} +(-0.318039 + 0.725316i) q^{18} +(2.37830 - 4.11934i) q^{19} +(2.75382 - 3.32369i) q^{20} +(-5.88593 + 1.10808i) q^{21} +(-0.193130 + 0.0517490i) q^{22} +(-0.309199 + 1.15395i) q^{23} +(1.17100 + 1.36325i) q^{24} +(-4.71940 - 1.65145i) q^{25} +(-0.928610 + 0.209011i) q^{26} +(1.17020 - 5.06267i) q^{27} +(-1.72759 + 6.44744i) q^{28} +(-3.57287 - 6.18840i) q^{29} +(0.495401 - 0.894408i) q^{30} -3.75546i q^{31} +(2.91904 - 0.782155i) q^{32} +(1.18243 - 0.568091i) q^{33} +1.93698 q^{34} +(7.69841 - 0.721858i) q^{35} +(-4.52089 - 3.61889i) q^{36} +(-2.67900 - 0.717836i) q^{37} +(-0.887922 - 0.887922i) q^{38} +(5.73370 - 2.47482i) q^{39} +(-1.34256 - 1.89218i) q^{40} +(-2.69593 - 4.66949i) q^{41} +(-0.119607 + 1.57661i) q^{42} +(-1.48024 - 5.52432i) q^{43} -1.46197i q^{44} +(-2.10853 + 6.36821i) q^{45} +(0.273128 + 0.157690i) q^{46} +(2.28189 + 2.28189i) q^{47} +(-5.59961 + 2.69030i) q^{48} +(-4.29318 + 2.47867i) q^{49} +(-0.743577 + 1.09060i) q^{50} +(-12.4891 + 2.35119i) q^{51} +(0.281170 - 6.95414i) q^{52} +(-5.30126 - 5.30126i) q^{53} +(-1.21101 - 0.644314i) q^{54} +(-1.58778 + 0.589127i) q^{55} +(3.10719 + 1.79394i) q^{56} +(6.80285 + 4.64726i) q^{57} +(-1.82215 + 0.488244i) q^{58} +(4.58287 + 2.64592i) q^{59} +(5.37949 + 5.19157i) q^{60} +(-1.28268 + 2.22167i) q^{61} +(-0.957635 - 0.256597i) q^{62} +(-1.14256 - 10.3107i) q^{63} +6.37561i q^{64} +(-7.66586 + 2.49692i) q^{65} +(-0.0640708 - 0.340333i) q^{66} +(-5.60475 - 1.50179i) q^{67} +(-3.66569 + 13.6805i) q^{68} +(-1.95246 - 0.685208i) q^{69} +(0.341933 - 2.01240i) q^{70} +(0.328162 - 0.568393i) q^{71} +(-2.50788 + 1.84380i) q^{72} +(8.39721 + 8.39721i) q^{73} +(-0.366094 + 0.634093i) q^{74} +(3.47055 - 7.93444i) q^{75} +(7.95159 - 4.59085i) q^{76} +(1.85189 - 1.85189i) q^{77} +(-0.239311 - 1.63118i) q^{78} +6.35343i q^{79} +(7.51921 - 2.78992i) q^{80} +(8.59035 + 2.68437i) q^{81} +(-1.37491 + 0.368407i) q^{82} +(2.33630 - 2.33630i) q^{83} +(-10.9089 - 3.82845i) q^{84} +(16.3349 - 1.53168i) q^{85} -1.50983 q^{86} +(11.1560 - 5.35985i) q^{87} +(-0.759060 - 0.203390i) q^{88} +(9.05197 - 5.22616i) q^{89} +(1.47981 + 0.972789i) q^{90} +(9.16501 - 8.45269i) q^{91} +(-1.63062 + 1.63062i) q^{92} +(6.48601 + 0.492049i) q^{93} +(0.737790 - 0.425963i) q^{94} +(-8.19013 - 6.78588i) q^{95} +(0.968391 + 5.14392i) q^{96} +(2.29178 + 8.55305i) q^{97} +(0.338717 + 1.26411i) q^{98} +(0.826218 + 2.11659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{3} - 12 q^{6} - 12 q^{7} + 4 q^{10} - 12 q^{12} - 24 q^{13} - 6 q^{15} + 16 q^{16} + 20 q^{22} - 16 q^{25} - 32 q^{27} - 36 q^{28} + 30 q^{33} - 4 q^{36} - 84 q^{37} - 152 q^{40} - 48 q^{42}+ \cdots - 48 q^{97}+O(q^{100}) \) 96 * q - 2 * q^3 - 12 * q^6 - 12 * q^7 + 4 * q^10 - 12 * q^12 - 24 * q^13 - 6 * q^15 + 16 * q^16 + 20 * q^22 - 16 * q^25 - 32 * q^27 - 36 * q^28 + 30 * q^33 - 4 * q^36 - 84 * q^37 - 152 * q^40 - 48 * q^42 + 8 * q^43 + 54 * q^45 - 28 * q^48 - 16 * q^51 + 28 * q^52 - 40 * q^55 + 84 * q^58 - 32 * q^61 + 90 * q^63 + 36 * q^67 + 90 * q^72 - 20 * q^75 + 72 * q^76 + 60 * q^78 + 32 * q^81 - 68 * q^82 + 84 * q^85 - 26 * q^87 - 108 * q^88 - 20 * q^90 - 80 * q^91 + 48 * q^93 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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