LMFDB - Embedded newform 875.2.bb.a.493.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			493.15
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.a.607.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.973996 - 1.49982i) q^{2} +(0.128952 - 0.335932i) q^{3} +(-0.487325 - 1.09455i) q^{4} +(-0.378240 - 0.520602i) q^{6} +(0.314872 + 2.62695i) q^{7} +(1.41635 + 0.224327i) q^{8} +(2.13321 + 1.92075i) q^{9} +(-2.82518 - 3.13767i) q^{11} +(-0.430536 + 0.0225635i) q^{12} +(0.527217 + 0.268631i) q^{13} +(4.24664 + 2.08638i) q^{14} +(3.31938 - 3.68655i) q^{16} +(0.546924 - 0.675395i) q^{17} +(4.95853 - 1.32863i) q^{18} +(5.83214 + 2.59663i) q^{19} +(0.923080 + 0.232975i) q^{21} +(-7.45766 + 1.18118i) q^{22} +(-1.35899 - 0.882537i) q^{23} +(0.258000 - 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(1.88216 - 0.959010i) q^{27} +(2.72188 - 1.62482i) q^{28} +(0.996818 - 1.37200i) q^{29} +(8.94867 - 0.940543i) q^{31} +(-1.55381 - 5.79889i) q^{32} +(-1.41836 + 0.544457i) q^{33} +(-0.480271 - 1.47812i) q^{34} +(1.06279 - 3.27094i) q^{36} +(0.228048 + 4.35142i) q^{37} +(9.57497 - 6.21806i) q^{38} +(0.158228 - 0.142469i) q^{39} +(5.70437 - 1.85346i) q^{41} +(1.24850 - 1.15754i) q^{42} +(-3.73281 - 3.73281i) q^{43} +(-2.05756 + 4.62136i) q^{44} +(-2.64730 + 1.17865i) q^{46} +(-7.49114 + 6.06621i) q^{47} +(-0.810389 - 1.59048i) q^{48} +(-6.80171 + 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(0.0371035 - 0.707976i) q^{52} +(-7.91735 - 3.03918i) q^{53} +(0.394875 - 3.75698i) q^{54} +(-0.143329 + 3.79131i) q^{56} +(1.62436 - 1.62436i) q^{57} +(-1.08686 - 2.83137i) q^{58} +(-6.62786 - 1.40879i) q^{59} +(0.256792 + 1.20811i) q^{61} +(7.30532 - 14.3375i) q^{62} +(-4.37403 + 6.20863i) q^{63} +(-0.774814 - 0.251752i) q^{64} +(-0.564887 + 2.65758i) q^{66} +(-8.90825 - 7.21376i) q^{67} +(-1.00578 - 0.269499i) q^{68} +(-0.471717 + 0.342723i) q^{69} +(-11.3299 - 8.23164i) q^{71} +(2.59049 + 3.19899i) q^{72} +(3.48231 + 0.182500i) q^{73} +(6.74848 + 3.89623i) q^{74} -7.64897i q^{76} +(7.35294 - 8.40955i) q^{77} +(-0.0595648 - 0.376077i) q^{78} +(14.0514 + 1.47686i) q^{79} +(0.820700 + 7.80844i) q^{81} +(2.77617 - 10.3608i) q^{82} +(-0.477665 + 3.01586i) q^{83} +(-0.194837 - 1.12389i) q^{84} +(-9.23428 + 1.96281i) q^{86} +(-0.332358 - 0.511786i) q^{87} +(-3.29756 - 5.07780i) q^{88} +(-16.6785 + 3.54513i) q^{89} +(-0.539673 + 1.46956i) q^{91} +(-0.303712 + 1.91756i) q^{92} +(0.837993 - 3.12743i) q^{93} +(1.80189 + 17.1438i) q^{94} +(-2.14840 - 0.225806i) q^{96} +(1.83327 + 11.5748i) q^{97} +(-4.14368 + 11.8126i) q^{98} -12.1198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.973996	−	1.49982i	0.688719	−	1.06053i	−0.305398	−	0.952225i	$-0.598790\pi$
$2$	0.973996	−	1.49982i	0.688719	−	1.06053i	0.994117	−	0.108310i	$-0.0345438\pi$
$3$	0.128952	−	0.335932i	0.0744506	−	0.193951i	−0.891305	−	0.453405i	$-0.850209\pi$
$3$	0.128952	−	0.335932i	0.0744506	−	0.193951i	0.965755	+	0.259454i	$0.0835426\pi$
$4$	−0.487325	−	1.09455i	−0.243663	−	0.547275i
$5$		0			0
$5$		0			0
$6$	−0.378240	−	0.520602i	−0.154416	−	0.212535i
$7$	0.314872	+	2.62695i	0.119010	+	0.992893i
$7$	0.314872	+	2.62695i	0.119010	+	0.992893i
$8$	1.41635	+	0.224327i	0.500755	+	0.0793117i
$9$	2.13321	+	1.92075i	0.711071	+	0.640251i
$10$		0			0
$11$	−2.82518	−	3.13767i	−0.851822	−	0.946045i	0.147250	−	0.989099i	$-0.452958\pi$
$11$	−2.82518	−	3.13767i	−0.851822	−	0.946045i	−0.999073	+	0.0430546i	$0.986291\pi$
$12$	−0.430536	+	0.0225635i	−0.124285	+	0.00651351i
$13$	0.527217	+	0.268631i	0.146224	+	0.0745047i	0.525571	−	0.850749i	$-0.323852\pi$
$13$	0.527217	+	0.268631i	0.146224	+	0.0745047i	−0.379348	+	0.925254i	$0.623852\pi$
$14$	4.24664	+	2.08638i	1.13496	+	0.557610i
$15$		0			0
$16$	3.31938	−	3.68655i	0.829846	−	0.921638i
$17$	0.546924	−	0.675395i	0.132649	−	0.163807i	−0.706494	−	0.707719i	$-0.749724\pi$
$17$	0.546924	−	0.675395i	0.132649	−	0.163807i	0.839142	+	0.543912i	$0.183057\pi$
$18$	4.95853	−	1.32863i	1.16874	−	0.313162i
$19$	5.83214	+	2.59663i	1.33798	+	0.595709i	0.945971	−	0.324251i	$-0.105112\pi$
$19$	5.83214	+	2.59663i	1.33798	+	0.595709i	0.392013	+	0.919960i	$0.371779\pi$
$20$		0			0
$21$	0.923080	+	0.232975i	0.201433	+	0.0508394i
$22$	−7.45766	+	1.18118i	−1.58998	+	0.251828i
$23$	−1.35899	−	0.882537i	−0.283369	−	0.184022i	0.395126	−	0.918627i	$-0.370701\pi$
$23$	−1.35899	−	0.882537i	−0.283369	−	0.184022i	−0.678495	+	0.734605i	$0.737367\pi$
$24$	0.258000	−	0.446869i	0.0526640	−	0.0912168i
$25$		0			0
$26$	0.916406	−	0.529087i	0.179722	−	0.103762i
$27$	1.88216	−	0.959010i	0.362223	−	0.184562i
$28$	2.72188	−	1.62482i	0.514387	−	0.307062i
$29$	0.996818	−	1.37200i	0.185104	−	0.254774i	−0.706373	−	0.707840i	$-0.749670\pi$
$29$	0.996818	−	1.37200i	0.185104	−	0.254774i	0.891477	+	0.453066i	$0.149670\pi$
$30$		0			0
$31$	8.94867	−	0.940543i	1.60723	−	0.168927i	0.742034	−	0.670362i	$-0.233861\pi$
$31$	8.94867	−	0.940543i	1.60723	−	0.168927i	0.865195	+	0.501436i	$0.167195\pi$
$32$	−1.55381	−	5.79889i	−0.274677	−	1.02511i
$33$	−1.41836	+	0.544457i	−0.246905	+	0.0947778i
$34$	−0.480271	−	1.47812i	−0.0823657	−	0.253496i
$35$		0			0
$36$	1.06279	−	3.27094i	0.177132	−	0.545157i
$37$	0.228048	+	4.35142i	0.0374909	+	0.715369i	0.951120	+	0.308821i	$0.0999344\pi$
$37$	0.228048	+	4.35142i	0.0374909	+	0.715369i	−0.913629	+	0.406548i	$0.866732\pi$
$38$	9.57497	−	6.21806i	1.55326	−	1.00870i
$39$	0.158228	−	0.142469i	0.0253367	−	0.0228133i
$40$		0			0
$41$	5.70437	−	1.85346i	0.890873	−	0.289462i	0.172408	−	0.985026i	$-0.444845\pi$
$41$	5.70437	−	1.85346i	0.890873	−	0.289462i	0.718465	+	0.695563i	$0.244845\pi$
$42$	1.24850	−	1.15754i	0.192647	−	0.178612i
$43$	−3.73281	−	3.73281i	−0.569248	−	0.569248i	0.362670	−	0.931918i	$-0.381865\pi$
$43$	−3.73281	−	3.73281i	−0.569248	−	0.569248i	−0.931918	+	0.362670i	$0.881865\pi$
$44$	−2.05756	+	4.62136i	−0.310189	+	0.696697i
$45$		0			0
$46$	−2.64730	+	1.17865i	−0.390323	+	0.173783i
$47$	−7.49114	+	6.06621i	−1.09270	+	0.884847i	−0.993903	−	0.110261i	$-0.964831\pi$
$47$	−7.49114	+	6.06621i	−1.09270	+	0.884847i	−0.0987925	+	0.995108i	$0.531498\pi$
$48$	−0.810389	−	1.59048i	−0.116970	−	0.229566i
$49$	−6.80171	+	1.65430i	−0.971673	+	0.236329i
$50$		0			0
$51$	−0.156360	−	0.270823i	−0.0218948	−	0.0379228i
$52$	0.0371035	−	0.707976i	0.00514532	−	0.0981786i
$53$	−7.91735	−	3.03918i	−1.08753	−	0.417464i	−0.252461	−	0.967607i	$-0.581240\pi$
$53$	−7.91735	−	3.03918i	−1.08753	−	0.417464i	−0.835070	+	0.550143i	$0.814573\pi$
$54$	0.394875	−	3.75698i	0.0537357	−	0.511261i
$55$		0			0
$56$	−0.143329	+	3.79131i	−0.0191531	+	0.506635i
$57$	1.62436	−	1.62436i	0.215152	−	0.215152i
$58$	−1.08686	−	2.83137i	−0.142712	−	0.371778i
$59$	−6.62786	−	1.40879i	−0.862874	−	0.183409i	−0.244842	−	0.969563i	$-0.578736\pi$
$59$	−6.62786	−	1.40879i	−0.862874	−	0.183409i	−0.618031	+	0.786153i	$0.712070\pi$
$60$		0			0
$61$	0.256792	+	1.20811i	0.0328789	+	0.154683i	0.991525	−	0.129919i	$-0.0414718\pi$
$61$	0.256792	+	1.20811i	0.0328789	+	0.154683i	−0.958646	+	0.284602i	$0.908138\pi$
$62$	7.30532	−	14.3375i	0.927777	−	1.82086i
$63$	−4.37403	+	6.20863i	−0.551076	+	0.782214i
$64$	−0.774814	−	0.251752i	−0.0968517	−	0.0314690i
$65$		0			0
$66$	−0.564887	+	2.65758i	−0.0695328	+	0.327126i
$67$	−8.90825	−	7.21376i	−1.08832	−	0.881301i	−0.0948576	−	0.995491i	$-0.530240\pi$
$67$	−8.90825	−	7.21376i	−1.08832	−	0.881301i	−0.993459	+	0.114189i	$0.963573\pi$
$68$	−1.00578	−	0.269499i	−0.121969	−	0.0326815i
$69$	−0.471717	+	0.342723i	−0.0567881	+	0.0412590i
$70$		0			0
$71$	−11.3299	−	8.23164i	−1.34461	−	0.976915i	−0.999261	−	0.0384406i	$-0.987761\pi$
$71$	−11.3299	−	8.23164i	−1.34461	−	0.976915i	−0.345348	−	0.938475i	$-0.612239\pi$
$72$	2.59049	+	3.19899i	0.305293	+	0.377005i
$73$	3.48231	+	0.182500i	0.407574	+	0.0213601i	0.255022	−	0.966935i	$-0.417917\pi$
$73$	3.48231	+	0.182500i	0.407574	+	0.0213601i	0.152552	+	0.988295i	$0.451251\pi$
$74$	6.74848	+	3.89623i	0.784494	+	0.452928i
$75$		0			0
$76$		−	7.64897i		−	0.877397i
$77$	7.35294	−	8.40955i	0.837945	−	0.958358i
$78$	−0.0595648	−	0.376077i	−0.00674438	−	0.0425823i
$79$	14.0514	+	1.47686i	1.58090	+	0.166159i	0.853885	−	0.520462i	$-0.174240\pi$
$79$	14.0514	+	1.47686i	1.58090	+	0.166159i	0.727016	+	0.686621i	$0.240907\pi$
$80$		0			0
$81$	0.820700	+	7.80844i	0.0911889	+	0.867605i
$82$	2.77617	−	10.3608i	0.306577	−	1.14416i
$83$	−0.477665	+	3.01586i	−0.0524305	+	0.331033i	0.947506	+	0.319739i	$0.103595\pi$
$83$	−0.477665	+	3.01586i	−0.0524305	+	0.331033i	−0.999936	+	0.0112944i	$0.996405\pi$
$84$	−0.194837	−	1.12389i	−0.0212584	−	0.122627i
$85$		0			0
$86$	−9.23428	+	1.96281i	−0.995758	+	0.211655i
$87$	−0.332358	−	0.511786i	−0.0356325	−	0.0548692i
$88$	−3.29756	−	5.07780i	−0.351522	−	0.541296i
$89$	−16.6785	+	3.54513i	−1.76792	+	0.375783i	−0.972977	−	0.230900i	$-0.925833\pi$
$89$	−16.6785	+	3.54513i	−1.76792	+	0.375783i	−0.794944	+	0.606683i	$0.792500\pi$
$90$		0			0
$91$	−0.539673	+	1.46956i	−0.0565731	+	0.154051i
$92$	−0.303712	+	1.91756i	−0.0316642	+	0.199920i
$93$	0.837993	−	3.12743i	0.0868958	−	0.324300i
$94$	1.80189	+	17.1438i	0.185851	+	1.76825i
$95$		0			0
$96$	−2.14840	−	0.225806i	−0.219270	−	0.0230462i
$97$	1.83327	+	11.5748i	0.186140	+	1.17524i	0.886940	+	0.461884i	$0.152826\pi$
$97$	1.83327	+	11.5748i	0.186140	+	1.17524i	−0.700800	+	0.713358i	$0.747174\pi$
$98$	−4.14368	+	11.8126i	−0.418575	+	1.19326i
$99$		−	12.1198i		−	1.21809i
$100$		0			0
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	0.679109	−	0.734038i	$-0.262367\pi$
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	−0.296141	+	0.955144i	$0.595700\pi$
$102$	−0.558480	−	0.0292687i	−0.0552978	−	0.00289803i
$103$	1.31905	+	1.62888i	0.129969	+	0.160499i	0.837976	−	0.545707i	$-0.183739\pi$
$103$	1.31905	+	1.62888i	0.129969	+	0.160499i	−0.708007	+	0.706206i	$0.750405\pi$
$104$	0.686462	+	0.498744i	0.0673131	+	0.0489058i
$105$		0			0
$106$	−12.2697	+	8.91446i	−1.19174	+	0.865849i
$107$	−3.97800	−	1.06590i	−0.384568	−	0.103045i	0.0613552	−	0.998116i	$-0.480458\pi$
$107$	−3.97800	−	1.06590i	−0.384568	−	0.103045i	−0.445923	+	0.895071i	$0.647124\pi$
$108$	−1.96691	−	1.59277i	−0.189266	−	0.153265i
$109$	−2.48271	+	11.6802i	−0.237801	+	1.11876i	0.683512	+	0.729940i	$0.260452\pi$
$109$	−2.48271	+	11.6802i	−0.237801	+	1.11876i	−0.921312	+	0.388824i	$0.872881\pi$
$110$		0			0
$111$	1.49119	+	0.484517i	0.141537	+	0.0459883i
$112$	10.7296	+	7.55906i	1.01385	+	0.714264i
$113$	−1.62124	+	3.18186i	−0.152513	+	0.299324i	−0.954604	−	0.297878i	$-0.903721\pi$
$113$	−1.62124	+	3.18186i	−0.152513	+	0.299324i	0.802091	+	0.597202i	$0.203721\pi$
$114$	−0.854131	−	4.01837i	−0.0799967	−	0.376355i
$115$		0			0
$116$	−1.98750	−	0.422456i	−0.184535	−	0.0392241i
$117$	0.608693	+	1.58570i	0.0562737	+	0.146598i
$118$	−8.56845	+	8.56845i	−0.788789	+	0.788789i
$119$	1.94644	+	1.22408i	0.178430	+	0.112211i
$120$		0			0
$121$	−0.713576	+	6.78922i	−0.0648706	+	0.617202i
$122$	2.06207	+	0.791555i	0.186691	+	0.0716640i
$123$	0.112954	−	2.15529i	0.0101847	−	0.194336i
$124$	−5.39038	−	9.33642i	−0.484071	−	0.838435i
$125$		0			0
$126$	5.05155	+	12.6074i	0.450028	+	1.12316i
$127$	−1.49373	−	2.93160i	−0.132547	−	0.260138i	0.815188	−	0.579196i	$-0.196633\pi$
$127$	−1.49373	−	2.93160i	−0.132547	−	0.260138i	−0.947735	+	0.319058i	$0.896633\pi$
$128$	8.19887	−	6.63931i	0.724685	−	0.586838i
$129$	−1.73532	+	0.772616i	−0.152787	+	0.0680250i
$130$		0			0
$131$	−1.50001	+	3.36908i	−0.131057	+	0.294358i	−0.967140	−	0.254244i	$-0.918173\pi$
$131$	−1.50001	+	3.36908i	−0.131057	+	0.294358i	0.836083	+	0.548602i	$0.184840\pi$
$132$	1.28714	+	1.28714i	0.112031	+	0.112031i
$133$	−4.98485	+	16.1383i	−0.432241	+	1.39937i
$134$	−19.4960	+	6.33462i	−1.68419	+	0.547228i
$135$		0			0
$136$	0.926145	−	0.833904i	0.0794162	−	0.0715067i
$137$	−0.846089	+	0.549457i	−0.0722863	+	0.0469433i	−0.580276	−	0.814420i	$-0.697055\pi$
$137$	−0.846089	+	0.549457i	−0.0722863	+	0.0469433i	0.507990	+	0.861363i	$0.330389\pi$
$138$	0.0545724	+	1.04130i	0.00464551	+	0.0886416i
$139$	3.10037	−	9.54195i	0.262970	−	0.809337i	−0.729185	−	0.684317i	$-0.760100\pi$
$139$	3.10037	−	9.54195i	0.262970	−	0.809337i	0.992154	−	0.125020i	$-0.0398996\pi$
$140$		0			0
$141$	1.07183	+	3.29877i	0.0902647	+	0.277806i
$142$	−23.3812	+	8.97522i	−1.96211	+	0.753183i
$143$	−0.646606	−	2.41316i	−0.0540719	−	0.201799i
$144$	14.1619	−	1.48848i	1.18016	−	0.124040i
$145$		0			0
$146$	3.66548	−	5.04510i	0.303357	−	0.417535i
$147$	−0.321362	+	2.49824i	−0.0265055	+	0.206051i
$148$	4.65171	−	2.37017i	0.382369	−	0.194827i
$149$	6.19698	−	3.57783i	0.507676	−	0.293107i	−0.224202	−	0.974543i	$-0.571977\pi$
$149$	6.19698	−	3.57783i	0.507676	−	0.293107i	0.731878	+	0.681436i	$0.238644\pi$
$150$		0			0
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.416908	−	0.908949i	$-0.363114\pi$
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.578718	−	0.815527i	$-0.303553\pi$
$152$	7.67784	+	4.98605i	0.622755	+	0.404422i
$153$	2.46397	−	0.390255i	0.199200	−	0.0315502i
$154$	−5.45110	−	19.2190i	−0.439262	−	1.54871i
$155$		0			0
$156$	−0.233047	−	0.103759i	−0.0186587	−	0.00830740i
$157$	19.3989	−	5.19791i	1.54820	−	0.414838i	0.619294	−	0.785159i	$-0.287419\pi$
$157$	19.3989	−	5.19791i	1.54820	−	0.414838i	0.928904	+	0.370321i	$0.120752\pi$
$158$	15.9010	−	19.6361i	1.26501	−	1.56216i
$159$	−2.04192	+	2.26778i	−0.161935	+	0.179847i
$160$		0			0
$161$	1.89047	−	3.84788i	0.148990	−	0.303255i
$162$	12.5106	+	6.37449i	0.982928	+	0.500827i
$163$	−16.1137	+	0.844482i	−1.26212	+	0.0661449i	−0.671622	−	0.740894i	$-0.734402\pi$
$163$	−16.1137	+	0.844482i	−1.26212	+	0.0661449i	−0.590498	+	0.807039i	$0.701069\pi$
$164$	−4.80859	−	5.34048i	−0.375488	−	0.417021i
$165$		0			0
$166$	4.05801	+	3.65384i	0.314962	+	0.283593i
$167$	−10.0363	−	1.58959i	−0.776630	−	0.123006i	−0.244478	−	0.969655i	$-0.578617\pi$
$167$	−10.0363	−	1.58959i	−0.776630	−	0.123006i	−0.532152	+	0.846649i	$0.678617\pi$
$168$	1.25514	+	0.537046i	0.0968361	+	0.0414340i
$169$	−7.43541	−	10.2340i	−0.571955	−	0.787228i
$170$		0			0
$171$	7.45369	+	16.7413i	0.569998	+	1.28024i
$172$	−2.26665	+	5.90483i	−0.172831	+	0.450239i
$173$	1.82707	−	2.81344i	0.138909	−	0.213902i	−0.762368	−	0.647143i	$-0.775964\pi$
$173$	1.82707	−	2.81344i	0.138909	−	0.213902i	0.901278	+	0.433241i	$0.142630\pi$
$174$	−1.09130			−0.0827315
$175$		0			0
$176$	−20.9450			−1.57879
$177$	−1.32794	+	2.04484i	−0.0998138	+	0.153700i
$178$	−10.9278	+	28.4678i	−0.819070	+	2.13375i
$179$	−1.18133	−	2.65332i	−0.0882971	−	0.198319i	0.863999	−	0.503493i	$-0.167952\pi$
$179$	−1.18133	−	2.65332i	−0.0882971	−	0.198319i	−0.952297	+	0.305174i	$0.901285\pi$
$180$		0			0
$181$	−4.64922	−	6.39910i	−0.345574	−	0.475641i	0.600485	−	0.799636i	$-0.294974\pi$
$181$	−4.64922	−	6.39910i	−0.345574	−	0.475641i	−0.946059	+	0.323994i	$0.894974\pi$
$182$	1.67843	+	2.24076i	0.124414	+	0.166096i
$183$	0.438958	+	0.0695242i	0.0324487	+	0.00513937i
$184$	−1.72682	−	1.55484i	−0.127303	−	0.114624i
$185$		0			0
$186$	−3.87439	−	4.30295i	−0.284084	−	0.315507i
$187$	−3.66433	+	0.192039i	−0.267962	+	0.0140433i
$188$	10.2904	+	5.24321i	0.750504	+	0.382401i
$189$	3.11191	+	4.64238i	0.226358	+	0.337684i
$190$		0			0
$191$	−9.73774	+	10.8149i	−0.704598	+	0.782536i	−0.984101	−	0.177609i	$-0.943164\pi$
$191$	−9.73774	+	10.8149i	−0.704598	+	0.782536i	0.279503	+	0.960145i	$0.409830\pi$
$192$	−0.184486	+	0.227821i	−0.0133141	+	0.0164416i
$193$	−0.600403	+	0.160877i	−0.0432179	+	0.0115802i	−0.280363	−	0.959894i	$-0.590455\pi$
$193$	−0.600403	+	0.160877i	−0.0432179	+	0.0115802i	0.237145	+	0.971474i	$0.423788\pi$
$194$	19.1457	+	8.52422i	1.37458	+	0.612004i
$195$		0			0
$196$	5.12536	+	6.63863i	0.366097	+	0.474188i
$197$	−24.1044	+	3.81776i	−1.71736	+	0.272004i	−0.935982	−	0.352048i	$-0.885485\pi$
$197$	−24.1044	+	3.81776i	−1.71736	+	0.272004i	−0.781383	+	0.624052i	$0.785485\pi$
$198$	−18.1775	−	11.8046i	−1.29182	−	0.838918i
$199$	−4.29215	+	7.43422i	−0.304262	+	0.526998i	−0.977097	−	0.212795i	$-0.931743\pi$
$199$	−4.29215	+	7.43422i	−0.304262	+	0.526998i	0.672835	+	0.739793i	$0.265077\pi$
$200$		0			0
$201$	−3.57207	+	2.06234i	−0.251955	+	0.145466i
$202$	7.08143	−	3.60817i	0.498248	−	0.253870i
$203$	3.91805	+	2.18658i	0.274993	+	0.153468i
$204$	−0.220231	+	0.303123i	−0.0154193	+	0.0212228i
$205$		0			0
$206$	3.72778	−	0.391806i	0.259727	−	0.0272984i
$207$	−1.20387	−	4.49292i	−0.0836751	−	0.312280i
$208$	2.74036	−	1.05192i	0.190010	−	0.0729378i
$209$	−8.32941	−	25.6353i	−0.576158	−	1.77323i
$210$		0			0
$211$	1.28435	−	3.95282i	0.0884183	−	0.272123i	−0.897064	−	0.441900i	$-0.854305\pi$
$211$	1.28435	−	3.95282i	0.0884183	−	0.272123i	0.985483	+	0.169777i	$0.0543046\pi$
$212$	0.531782	+	10.1470i	0.0365229	+	0.696899i
$213$	−4.22628	+	2.74458i	−0.289580	+	0.188056i
$214$	−5.47322	+	4.92811i	−0.374141	+	0.336878i
$215$		0			0
$216$	2.88093	−	0.936071i	0.196023	−	0.0636916i
$217$	5.28844	+	23.2115i	0.359003	+	1.57570i
$218$	15.1001	+	15.1001i	1.02271	+	1.02271i
$219$	0.510360	−	1.14629i	0.0344869	−	0.0774589i
$220$		0			0
$221$	0.469780	−	0.209159i	0.0316008	−	0.0140696i
$222$	2.17910	−	1.76460i	0.146252	−	0.118432i
$223$	5.77436	+	11.3328i	0.386680	+	0.758902i	0.999510	−	0.0313132i	$-0.00996893\pi$
$223$	5.77436	+	11.3328i	0.386680	+	0.758902i	−0.612830	+	0.790215i	$0.709969\pi$
$224$	14.7441	−	5.90768i	0.985134	−	0.394723i
$225$		0			0
$226$	3.19314	+	5.53069i	0.212405	+	0.367896i
$227$	−0.366471	+	6.99268i	−0.0243235	+	0.464120i	0.959131	+	0.282963i	$0.0913175\pi$
$227$	−0.366471	+	6.99268i	−0.0243235	+	0.464120i	−0.983454	+	0.181157i	$0.942016\pi$
$228$	−2.56954	−	0.986352i	−0.170172	−	0.0653228i
$229$	1.54623	−	14.7114i	0.102178	−	0.972159i	−0.816552	−	0.577272i	$-0.804117\pi$
$229$	1.54623	−	14.7114i	0.102178	−	0.972159i	0.918730	−	0.394887i	$-0.129216\pi$
$230$		0			0
$231$	−1.87686	−	3.55452i	−0.123488	−	0.233870i
$232$	1.71962	−	1.71962i	0.112899	−	0.112899i
$233$	0.914241	+	2.38168i	0.0598939	+	0.156029i	0.960262	−	0.279100i	$-0.0900361\pi$
$233$	0.914241	+	2.38168i	0.0598939	+	0.156029i	−0.900368	+	0.435129i	$0.856703\pi$
$234$	2.97113	+	0.631534i	0.194229	+	0.0412847i
$235$		0			0
$236$	1.68793	+	7.94106i	0.109875	+	0.516919i
$237$	2.30808	−	4.52986i	0.149926	−	0.294246i
$238$	3.73172	−	1.72706i	0.241892	−	0.111949i
$239$	0.945911	+	0.307345i	0.0611859	+	0.0198805i	0.339450	−	0.940624i	$-0.389759\pi$
$239$	0.945911	+	0.307345i	0.0611859	+	0.0198805i	−0.278264	+	0.960505i	$0.589759\pi$
$240$		0			0
$241$	1.11500	−	5.24565i	0.0718234	−	0.337902i	−0.927534	−	0.373738i	$-0.878076\pi$
$241$	1.11500	−	5.24565i	0.0718234	−	0.337902i	0.999358	+	0.0358356i	$0.0114093\pi$
$242$	9.48761	+	7.68291i	0.609886	+	0.493876i
$243$	8.85021	+	2.37141i	0.567741	+	0.152126i
$244$	1.19720	−	0.869816i	0.0766428	−	0.0556843i
$245$		0			0
$246$	−3.12253	−	2.26865i	−0.199086	−	0.144644i
$247$	2.37727	+	2.93568i	0.151262	+	0.186793i
$248$	12.8854	+	0.675296i	0.818225	+	0.0428814i
$249$	0.951527	+	0.549365i	0.0603006	+	0.0348146i
$250$		0			0
$251$		−	15.5071i		−	0.978800i	−0.872059	−	0.489400i	$-0.837216\pi$
$251$		−	15.5071i		−	0.978800i	0.872059	−	0.489400i	$-0.162784\pi$
$252$	8.92723	+	1.76197i	0.562363	+	0.110994i
$253$	1.07026	+	6.75739i	0.0672870	+	0.424833i
$254$	−5.85177	−	0.615046i	−0.367173	−	0.0385914i
$255$		0			0
$256$	−2.14244	−	20.3840i	−0.133903	−	1.27400i
$257$	−4.03975	+	15.0766i	−0.251993	+	0.940449i	0.717746	+	0.696305i	$0.245174\pi$
$257$	−4.03975	+	15.0766i	−0.251993	+	0.940449i	−0.969739	+	0.244145i	$0.921493\pi$
$258$	−0.531412	+	3.35520i	−0.0330842	+	0.208886i
$259$	−11.3591	+	1.96921i	−0.705823	+	0.122361i
$260$		0			0
$261$	4.76170	−	1.01213i	0.294742	−	0.0626494i
$262$	3.59202	+	5.53122i	0.221916	+	0.341720i
$263$	−2.23861	−	3.44715i	−0.138038	−	0.212561i	0.762890	−	0.646528i	$-0.223780\pi$
$263$	−2.23861	−	3.44715i	−0.138038	−	0.212561i	−0.900928	+	0.433968i	$0.857113\pi$
$264$	−2.13103	+	0.452964i	−0.131156	+	0.0278780i
$265$		0			0
$266$	19.3494	+	23.1951i	1.18639	+	1.42218i
$267$	−0.959811	+	6.06001i	−0.0587395	+	0.370866i
$268$	−3.55461	+	13.2660i	−0.217132	+	0.810349i
$269$	1.23301	+	11.7313i	0.0751780	+	0.715271i	0.965582	+	0.260099i	$0.0837554\pi$
$269$	1.23301	+	11.7313i	0.0751780	+	0.715271i	−0.890404	+	0.455171i	$0.849578\pi$
$270$		0			0
$271$	−6.69826	−	0.704015i	−0.406890	−	0.0427659i	−0.101127	−	0.994874i	$-0.532245\pi$
$271$	−6.69826	−	0.704015i	−0.406890	−	0.0427659i	−0.305763	+	0.952108i	$0.598912\pi$
$272$	−0.674426	−	4.25816i	−0.0408931	−	0.258189i
$273$	0.424079	+	0.370796i	0.0256664	+	0.0224416i
$274$			1.80415i			0.108993i
$275$		0			0
$276$	0.605007	+	0.349301i	0.0364171	+	0.0210254i
$277$	−30.4139	−	1.59392i	−1.82739	−	0.0957696i	−0.892575	−	0.450899i	$-0.851103\pi$
$277$	−30.4139	−	1.59392i	−1.82739	−	0.0957696i	−0.934817	+	0.355130i	$0.884437\pi$
$278$	−11.2915	−	13.9438i	−0.677218	−	0.836294i
$279$	20.8960	+	15.1818i	1.25101	+	0.908911i
$280$		0			0
$281$	3.78178	−	2.74762i	0.225602	−	0.163909i	−0.469243	−	0.883069i	$-0.655473\pi$
$281$	3.78178	−	2.74762i	0.225602	−	0.163909i	0.694845	+	0.719160i	$0.255473\pi$
$282$	5.99152	+	1.60542i	0.356790	+	0.0956016i
$283$	−4.35265	−	3.52471i	−0.258738	−	0.209522i	0.491170	−	0.871064i	$-0.336569\pi$
$283$	−4.35265	−	3.52471i	−0.258738	−	0.209522i	−0.749909	+	0.661541i	$0.769903\pi$
$284$	−3.48861	+	16.4126i	−0.207011	+	0.973908i
$285$		0			0
$286$	−4.24911	−	1.38062i	−0.251255	−	0.0816377i
$287$	6.66509	+	14.4015i	0.393428	+	0.850093i
$288$	7.82364	−	15.3547i	0.461012	−	0.904787i
$289$	3.37747	+	15.8897i	0.198674	+	0.934690i
$290$		0			0
$291$	4.12475	+	0.876742i	0.241797	+	0.0513956i
$292$	−1.49726	−	3.90050i	−0.0876207	−	0.228260i
$293$	7.38400	−	7.38400i	0.431378	−	0.431378i	−0.457719	−	0.889097i	$-0.651333\pi$
$293$	7.38400	−	7.38400i	0.431378	−	0.431378i	0.889097	+	0.457719i	$0.151333\pi$
$294$	3.43391	+	2.91526i	0.200270	+	0.170022i
$295$		0			0
$296$	−0.653147	+	6.21428i	−0.0379634	+	0.361198i
$297$	−8.32650	−	3.19625i	−0.483153	−	0.185465i
$298$	0.669727	−	12.7792i	0.0387962	−	0.740277i
$299$	−0.479406	−	0.830355i	−0.0277247	−	0.0480207i
$300$		0			0
$301$	8.63053	−	10.9812i	0.497456	−	0.632948i
$302$	−19.8660	−	38.9892i	−1.14316	−	2.24358i
$303$	1.24278	−	1.00638i	0.0713959	−	0.0578152i
$304$	28.9317	−	12.8812i	1.65935	−	0.738790i
$305$		0			0
$306$	1.81459	−	4.07563i	0.103733	−	0.232988i
$307$	−19.4310	−	19.4310i	−1.10899	−	1.10899i	−0.993284	−	0.115702i	$-0.963088\pi$
$307$	−19.4310	−	19.4310i	−1.10899	−	1.10899i	−0.115702	−	0.993284i	$-0.536912\pi$
$308$	−12.7880	−	3.94998i	−0.728661	−	0.225071i
$309$	0.717289	−	0.233061i	0.0408051	−	0.0132584i
$310$		0			0
$311$	−11.1492	+	10.0388i	−0.632212	+	0.569246i	−0.921685	−	0.387940i	$-0.873187\pi$
$311$	−11.1492	+	10.0388i	−0.632212	+	0.569246i	0.289473	+	0.957186i	$0.406520\pi$
$312$	0.256065	−	0.166290i	0.0144968	−	0.00941434i
$313$	1.59613	+	30.4559i	0.0902185	+	1.72147i	0.551464	+	0.834199i	$0.314069\pi$
$313$	1.59613	+	30.4559i	0.0902185	+	1.72147i	−0.461246	+	0.887272i	$0.652597\pi$
$314$	11.0985	−	34.1576i	0.626323	−	1.92762i
$315$		0			0
$316$	−5.23108	−	16.0996i	−0.294271	−	0.905674i
$317$	23.6089	−	9.06260i	1.32601	−	0.509006i	0.410703	−	0.911769i	$-0.365283\pi$
$317$	23.6089	−	9.06260i	1.32601	−	0.509006i	0.915304	+	0.402763i	$0.131950\pi$
$318$	1.41245	+	5.27133i	0.0792061	+	0.295601i
$319$	−7.12108	+	0.748456i	−0.398704	+	0.0419055i
$320$		0			0
$321$	−0.871043	+	1.19889i	−0.0486169	+	0.0669154i
$322$	−3.92982	−	6.58319i	−0.219000	−	0.366867i
$323$	4.94349	−	2.51883i	0.275063	−	0.140152i
$324$	8.14678	−	4.70355i	0.452599	−	0.261308i
$325$		0			0
$326$	−14.4281	+	24.9902i	−0.799097	+	1.38408i
$327$	3.60362	+	2.34022i	0.199280	+	0.129414i
$328$	8.49516	−	1.34550i	0.469066	−	0.0742928i
$329$	−18.2944	−	17.7688i	−1.00860	−	0.979623i
$330$		0			0
$331$	−6.04742	−	2.69249i	−0.332396	−	0.147992i	0.233751	−	0.972297i	$-0.424900\pi$
$331$	−6.04742	−	2.69249i	−0.332396	−	0.147992i	−0.566147	+	0.824304i	$0.691567\pi$
$332$	3.53378	−	0.946875i	0.193942	−	0.0519665i
$333$	−7.87153	+	9.72053i	−0.431357	+	0.532682i
$334$	−12.1594	+	13.5044i	−0.665332	+	0.738926i
$335$		0			0
$336$	3.92293	−	2.62965i	0.214014	−	0.143459i
$337$	4.40088	+	2.24236i	0.239731	+	0.122149i	0.569729	−	0.821833i	$-0.307048\pi$
$337$	4.40088	+	2.24236i	0.239731	+	0.122149i	−0.329998	+	0.943982i	$0.607048\pi$
$338$	−22.5912	+	1.18395i	−1.22880	+	0.0643986i
$339$	0.859827	+	0.954934i	0.0466994	+	0.0518649i
$340$		0			0
$341$	−28.2327	−	25.4208i	−1.52889	−	1.37661i
$342$	32.3688	+	5.12671i	1.75030	+	0.277221i
$343$	−6.48744	−	17.3468i	−0.350289	−	0.936642i
$344$	−4.44958	−	6.12432i	−0.239905	−	0.330201i
$345$		0			0
$346$	−2.44010	−	5.48056i	−0.131181	−	0.294637i
$347$	9.22720	−	24.0377i	0.495342	−	1.29041i	−0.427075	−	0.904216i	$-0.640456\pi$
$347$	9.22720	−	24.0377i	0.495342	−	1.29041i	0.922417	−	0.386194i	$-0.126211\pi$
$348$	−0.398209	+	0.613188i	−0.0213463	+	0.0328704i
$349$	−23.8148			−1.27478			−0.637389	−	0.770543i	$-0.719985\pi$
$349$	−23.8148			−1.27478			−0.637389	+	0.770543i	$0.719985\pi$
$350$		0			0
$351$	1.24993			0.0667163
$352$	−13.8053	+	21.2582i	−0.735823	+	1.13307i
$353$	11.3480	−	29.5626i	0.603995	−	1.57346i	−0.200624	−	0.979668i	$-0.564297\pi$
$353$	11.3480	−	29.5626i	0.603995	−	1.57346i	0.804619	−	0.593792i	$-0.202370\pi$
$354$	1.77350	+	3.98334i	0.0942603	+	0.211712i
$355$		0			0
$356$	12.0082	+	16.5279i	0.636433	+	0.875975i
$357$	0.662205	−	0.496024i	0.0350476	−	0.0262524i
$358$	−5.13013	−	0.812532i	−0.271136	−	0.0429437i
$359$	9.42711	+	8.48821i	0.497544	+	0.447990i	0.879297	−	0.476274i	$-0.158013\pi$
$359$	9.42711	+	8.48821i	0.497544	+	0.447990i	−0.381753	+	0.924264i	$0.624680\pi$
$360$		0			0
$361$	14.5578	+	16.1681i	0.766201	+	0.850953i
$362$	−14.1258	+	0.740304i	−0.742437	+	0.0389095i
$363$	2.18870	+	1.11520i	0.114877	+	0.0585328i
$364$	1.87150	−	0.125453i	0.0980932	−	0.00657552i
$365$		0			0
$366$	0.531817	−	0.590643i	0.0277985	−	0.0308734i
$367$	4.94000	−	6.10039i	0.257866	−	0.318438i	−0.631728	−	0.775190i	$-0.717654\pi$
$367$	4.94000	−	6.10039i	0.257866	−	0.318438i	0.889594	+	0.456752i	$0.150987\pi$
$368$	−7.76452	+	2.08050i	−0.404754	+	0.108453i
$369$	15.7287	+	7.00286i	0.818802	+	0.364554i
$370$		0			0
$371$	5.49083	−	21.7554i	0.285070	−	1.12948i
$372$	−3.83151	+	0.606851i	−0.198654	+	0.0314638i
$373$	3.05789	+	1.98581i	0.158331	+	0.102822i	0.621373	−	0.783515i	$-0.286575\pi$
$373$	3.05789	+	1.98581i	0.158331	+	0.102822i	−0.463042	+	0.886337i	$0.653242\pi$
$374$	−3.28101	+	5.68288i	−0.169657	+	0.293855i
$375$		0			0
$376$	−11.9709	+	6.91139i	−0.617351	+	0.356428i
$377$	0.894102	−	0.455567i	0.0460486	−	0.0234629i
$378$	9.99373	−	0.145652i	0.514022	−	0.00749155i
$379$	−12.1944	+	16.7841i	−0.626384	+	0.862143i	−0.997798	−	0.0663239i	$-0.978873\pi$
$379$	−12.1944	+	16.7841i	−0.626384	+	0.862143i	0.371414	+	0.928467i	$0.378873\pi$
$380$		0			0
$381$	−1.17744	+	0.123754i	−0.0603221	+	0.00634010i
$382$	6.73584	+	25.1385i	0.344636	+	1.28620i
$383$	18.1386	−	6.96275i	0.926838	−	0.355780i	0.152320	−	0.988331i	$-0.451326\pi$
$383$	18.1386	−	6.96275i	0.926838	−	0.355780i	0.774518	+	0.632551i	$0.217992\pi$
$384$	−1.17310	−	3.61042i	−0.0598643	−	0.184243i
$385$		0			0
$386$	−0.343502	+	1.05719i	−0.0174838	+	0.0538096i
$387$	−0.793070	−	15.1327i	−0.0403140	−	0.769237i
$388$	11.7758	−	7.64729i	0.597825	−	0.388232i
$389$	−11.3701	+	10.2377i	−0.576487	+	0.519072i	−0.904991	−	0.425431i	$-0.860122\pi$
$389$	−11.3701	+	10.2377i	−0.576487	+	0.519072i	0.328503	+	0.944503i	$0.393456\pi$
$390$		0			0
$391$	−1.33933	+	0.435173i	−0.0677326	+	0.0220077i
$392$	−10.0047	+	0.817259i	−0.505313	+	0.0412778i
$393$	0.938353	+	0.938353i	0.0473337	+	0.0473337i
$394$	−17.7516	+	39.8707i	−0.894312	+	2.00866i
$395$		0			0
$396$	−13.2657	+	5.90628i	−0.666628	+	0.296802i
$397$	22.7200	−	18.3983i	1.14028	−	0.923382i	0.142489	−	0.989796i	$-0.454489\pi$
$397$	22.7200	−	18.3983i	1.14028	−	0.923382i	0.997792	+	0.0664145i	$0.0211560\pi$
$398$	6.96947	+	13.6784i	0.349348	+	0.685634i
$399$	4.77858	+	3.75565i	0.239228	+	0.188017i
$400$		0			0
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	0.998546	+	0.0538996i	$0.0171651\pi$
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	−0.452595	+	0.891716i	$0.649502\pi$
$402$	−0.386045	+	7.36619i	−0.0192542	+	0.367392i
$403$	4.97055	+	1.90802i	0.247601	+	0.0950451i
$404$	0.556586	−	5.29556i	0.0276912	−	0.263464i
$405$		0			0
$406$	7.09565	−	3.74665i	0.352151	−	0.185943i
$407$	13.0091	−	13.0091i	0.644836	−	0.644836i
$408$	−0.160707	−	0.418656i	−0.00795617	−	0.0207265i
$409$	−30.0548	−	6.38835i	−1.48611	−	0.315883i	−0.607848	−	0.794054i	$-0.707967\pi$
$409$	−30.0548	−	6.38835i	−1.48611	−	0.315883i	−0.878267	+	0.478170i	$0.841300\pi$
$410$		0			0
$411$	0.0754751	+	0.355082i	0.00372291	+	0.0175149i
$412$	1.14009	−	2.23756i	0.0561683	−	0.110237i
$413$	1.61390	−	17.8546i	0.0794151	−	0.878569i
$414$	−7.91115	−	2.57049i	−0.388812	−	0.126333i
$415$		0			0
$416$	0.738565	−	3.47468i	0.0362111	−	0.170360i
$417$	−2.80565	−	2.27197i	−0.137393	−	0.111259i
$418$	−46.5612	−	12.4760i	−2.27738	−	0.610223i
$419$	−8.60424	+	6.25134i	−0.420345	+	0.305398i	−0.777776	−	0.628541i	$-0.783652\pi$
$419$	−8.60424	+	6.25134i	−0.420345	+	0.305398i	0.357432	+	0.933939i	$0.383652\pi$
$420$		0			0
$421$	17.2687	+	12.5464i	0.841623	+	0.611475i	0.922824	−	0.385223i	$-0.125875\pi$
$421$	17.2687	+	12.5464i	0.841623	+	0.611475i	−0.0812007	+	0.996698i	$0.525875\pi$
$422$	−4.67758	−	5.77633i	−0.227701	−	0.281187i
$423$	−27.6319	−	1.44813i	−1.34351	−	0.0704103i
$424$	−10.5319	−	6.08062i	−0.511476	−	0.295301i
$425$		0			0
$426$			9.01188i			0.436627i
$427$	−3.09280	+	1.05498i	−0.149671	+	0.0510541i
$428$	0.771896	+	4.87356i	0.0373110	+	0.235572i
$429$	−0.894041	−	0.0939675i	−0.0431647	−	0.00453679i
$430$		0			0
$431$	0.801158	+	7.62251i	0.0385904	+	0.367164i	0.996726	+	0.0808496i	$0.0257634\pi$
$431$	0.801158	+	7.62251i	0.0385904	+	0.367164i	−0.958136	+	0.286314i	$0.907570\pi$
$432$	2.71219	−	10.1220i	0.130490	−	0.486996i
$433$	−3.21139	+	20.2759i	−0.154330	+	0.974399i	0.782000	+	0.623278i	$0.214199\pi$
$433$	−3.21139	+	20.2759i	−0.154330	+	0.974399i	−0.936330	+	0.351121i	$0.885801\pi$
$434$	39.9641	+	14.6762i	1.91834	+	0.704481i
$435$		0			0
$436$	13.9945	−	2.97462i	0.670215	−	0.142458i
$437$	−5.63418	−	8.67588i	−0.269519	−	0.415023i
$438$	−1.22214	−	1.88193i	−0.0583961	−	0.0899220i
$439$	−12.2397	+	2.60162i	−0.584168	+	0.124169i	−0.490510	−	0.871436i	$-0.663189\pi$
$439$	−12.2397	+	2.60162i	−0.584168	+	0.124169i	−0.0936579	+	0.995604i	$0.529856\pi$
$440$		0			0
$441$	−17.6870	−	9.53543i	−0.842238	−	0.454068i
$442$	0.143862	−	0.908306i	0.00684280	−	0.0432037i
$443$	9.05910	−	33.8090i	0.430411	−	1.60632i	−0.321405	−	0.946942i	$-0.604155\pi$
$443$	9.05910	−	33.8090i	0.430411	−	1.60632i	0.751816	−	0.659373i	$-0.229178\pi$
$444$	−0.196366	−	1.86830i	−0.00931912	−	0.0886655i
$445$		0			0
$446$	22.6214	+	2.37761i	1.07115	+	0.112583i
$447$	−0.402793	−	2.54313i	−0.0190514	−	0.120286i
$448$	0.417373	−	2.11466i	0.0197190	−	0.0999085i
$449$			4.28525i			0.202233i	0.994875	+	0.101117i	$0.0322416\pi$
$449$			4.28525i			0.202233i	−0.994875	+	0.101117i	$0.967758\pi$
$450$		0			0
$451$	−21.9314	−	12.6621i	−1.03271	−	0.596235i
$452$	4.27278	+	0.223927i	0.200974	+	0.0105326i
$453$	−5.54098	−	6.84254i	−0.260338	−	0.321491i
$454$	10.1308	+	7.36048i	0.475464	+	0.345445i
$455$		0			0
$456$	2.66505	−	1.93627i	0.124802	−	0.0906742i
$457$	−17.0829	−	4.57736i	−0.799107	−	0.214120i	−0.163915	−	0.986474i	$-0.552412\pi$
$457$	−17.0829	−	4.57736i	−0.799107	−	0.214120i	−0.635192	+	0.772355i	$0.719079\pi$
$458$	−20.5585	−	16.6479i	−0.960636	−	0.777908i
$459$	0.381690	−	1.79571i	0.0178158	−	0.0838166i
$460$		0			0
$461$	23.7965	+	7.73195i	1.10831	+	0.360113i	0.805297	−	0.592872i	$-0.202006\pi$
$461$	23.7965	+	7.73195i	1.10831	+	0.360113i	0.303017	+	0.952985i	$0.402006\pi$
$462$	−7.15920	−	0.647130i	−0.333076	−	0.0301072i
$463$	12.3939	−	24.3244i	0.575994	−	1.13045i	−0.400779	−	0.916175i	$-0.631260\pi$
$463$	12.3939	−	24.3244i	0.575994	−	1.13045i	0.976773	−	0.214277i	$-0.0687396\pi$
$464$	−1.74913	−	8.22902i	−0.0812015	−	0.382023i
$465$		0			0
$466$	4.46256	+	0.948547i	0.206724	+	0.0439406i
$467$	−2.53677	−	6.60852i	−0.117388	−	0.305806i	0.862280	−	0.506432i	$-0.169036\pi$
$467$	−2.53677	−	6.60852i	−0.117388	−	0.305806i	−0.979668	+	0.200626i	$0.935702\pi$
$468$	1.43900	−	1.43900i	0.0665177	−	0.0665177i
$469$	16.1452	−	25.6729i	0.745517	−	1.18547i
$470$		0			0
$471$	0.755382	−	7.18698i	0.0348062	−	0.331159i
$472$	−9.07132	−	3.48215i	−0.417541	−	0.160279i
$473$	−1.16650	+	22.2582i	−0.0536358	+	1.02343i
$474$	−4.54592	−	7.87377i	−0.208801	−	0.361654i
$475$		0			0
$476$	0.391267	−	2.72700i	0.0179337	−	0.124992i
$477$	−11.0519	−	21.6905i	−0.506030	−	0.993140i
$478$	1.38228	−	1.11935i	0.0632239	−	0.0511977i
$479$	34.5054	−	15.3628i	1.57659	−	0.701943i	0.582738	−	0.812660i	$-0.301981\pi$
$479$	34.5054	−	15.3628i	1.57659	−	0.701943i	0.993852	+	0.110717i	$0.0353146\pi$
$480$		0			0
$481$	−1.04869	+	2.35540i	−0.0478163	+	0.107397i
$482$	−6.78154	−	6.78154i	−0.308891	−	0.308891i
$483$	−1.04885	−	1.13126i	−0.0477241	−	0.0514743i
$484$	7.77889	−	2.52751i	0.353586	−	0.114887i
$485$		0			0
$486$	12.1768	−	10.9640i	0.552349	−	0.497337i
$487$	−11.0229	+	7.15837i	−0.499496	+	0.324377i	−0.769678	−	0.638433i	$-0.779583\pi$
$487$	−11.0229	+	7.15837i	−0.499496	+	0.324377i	0.270181	+	0.962809i	$0.412916\pi$
$488$	0.0926944	+	1.76871i	0.00419608	+	0.0800660i
$489$	−1.79421	+	5.52200i	−0.0811368	+	0.249713i
$490$		0			0
$491$	−7.21929	−	22.2187i	−0.325802	−	1.00272i	−0.971077	−	0.238765i	$-0.923257\pi$
$491$	−7.21929	−	22.2187i	−0.325802	−	1.00272i	0.645275	−	0.763950i	$-0.276743\pi$
$492$	−2.41412	+	0.926693i	−0.108837	+	0.0417785i
$493$	−0.381460	−	1.42363i	−0.0171801	−	0.0641170i
$494$	6.71845	−	0.706137i	0.302277	−	0.0317706i
$495$		0			0
$496$	26.2367	−	36.1118i	1.17806	−	1.62147i
$497$	18.0566	−	32.3549i	0.809950	−	1.45132i
$498$	1.75073	−	0.892043i	0.0784522	−	0.0399734i
$499$	−7.78986	+	4.49748i	−0.348722	+	0.201335i	−0.664122	−	0.747624i	$-0.731195\pi$
$499$	−7.78986	+	4.49748i	−0.348722	+	0.201335i	0.315400	+	0.948959i	$0.397861\pi$
$500$		0			0
$501$	−1.82819	+	3.16652i	−0.0816777	+	0.141470i
$502$	−23.2579	−	15.1039i	−1.03805	−	0.674119i
$503$	−35.5693	+	5.63363i	−1.58596	+	0.251191i	−0.886239	−	0.463228i	$-0.846691\pi$
$503$	−35.5693	+	5.63363i	−1.58596	+	0.251191i	−0.699718	+	0.714419i	$0.746691\pi$
$504$	−7.58792	+	7.81236i	−0.337993	+	0.347990i
$505$		0			0
$506$	11.1773	+	4.97646i	0.496892	+	0.221231i
$507$	−4.39673	+	1.17810i	−0.195266	+	0.0523213i
$508$	−2.48086	+	3.06360i	−0.110070	+	0.135925i
$509$	6.14407	−	6.82368i	0.272331	−	0.302454i	−0.591429	−	0.806357i	$-0.701436\pi$
$509$	6.14407	−	6.82368i	0.272331	−	0.302454i	0.863761	+	0.503902i	$0.168103\pi$
$510$		0			0
$511$	0.617064	+	9.20532i	0.0272973	+	0.407220i
$512$	−13.8588	−	7.06144i	−0.612480	−	0.312074i
$513$	13.4672	−	0.705788i	0.594593	−	0.0311613i
$514$	18.6774	+	20.7434i	0.823827	+	0.914952i
$515$		0			0
$516$	1.69133	+	1.52288i	0.0744568	+	0.0670412i
$517$	40.1976	+	6.36667i	1.76789	+	0.280006i
$518$	−8.11030	+	18.9547i	−0.356346	+	0.832822i
$519$	−0.709520	−	0.976571i	−0.0311445	−	0.0428667i
$520$		0			0
$521$	−4.96375	−	11.1488i	−0.217466	−	0.488437i	0.771564	−	0.636152i	$-0.219475\pi$
$521$	−4.96375	−	11.1488i	−0.217466	−	0.488437i	−0.989030	+	0.147715i	$0.952808\pi$
$522$	3.11986	−	8.12752i	0.136553	−	0.355732i
$523$	11.1175	−	17.1195i	0.486135	−	0.748582i	−0.507449	−	0.861682i	$-0.669411\pi$
$523$	11.1175	−	17.1195i	0.486135	−	0.748582i	0.993584	+	0.113100i	$0.0360779\pi$
$524$	4.41862			0.193028
$525$		0			0
$526$	−7.35051			−0.320498
$527$	4.25901	−	6.55830i	0.185525	−	0.285684i
$528$	−2.70091	+	7.03611i	−0.117542	+	0.306208i
$529$	−8.28697	−	18.6128i	−0.360303	−	0.809253i
$530$		0			0
$531$	−11.4327	−	15.7357i	−0.496136	−	0.682873i
$532$	20.0934	−	2.40845i	0.871162	−	0.104419i
$533$	3.50534	+	0.555191i	0.151833	+	0.0240480i
$534$	8.15408	+	7.34197i	0.352862	+	0.317718i
$535$		0			0
$536$	−10.9989	−	12.2156i	−0.475082	−	0.527632i
$537$	−1.04367	+	0.0546965i	−0.0450378	+	0.00236033i
$538$	18.7958	+	9.57695i	0.810346	+	0.412892i
$539$	24.4067	+	16.6679i	1.05127	+	0.717936i
$540$		0			0
$541$	−11.8063	+	13.1122i	−0.507591	+	0.563737i	−0.941410	−	0.337263i	$-0.890499\pi$
$541$	−11.8063	+	13.1122i	−0.507591	+	0.563737i	0.433820	+	0.901000i	$0.357165\pi$
$542$	−7.57997	+	9.36049i	−0.325588	+	0.402067i
$543$	−2.74919	+	0.736644i	−0.117979	+	0.0316124i
$544$	−4.76636	−	2.12212i	−0.204356	−	0.0909851i
$545$		0			0
$546$	0.969180	−	0.274890i	0.0414771	−	0.0117642i
$547$	−2.95974	+	0.468776i	−0.126549	+	0.0200434i	−0.219388	−	0.975638i	$-0.570406\pi$
$547$	−2.95974	+	0.468776i	−0.126549	+	0.0200434i	0.0928385	+	0.995681i	$0.470406\pi$
$548$	1.01373	+	0.658323i	0.0433043	+	0.0281222i
$549$	−1.77270	+	3.07040i	−0.0756568	+	0.131041i
$550$		0			0
$551$	9.37617	−	5.41333i	0.399438	−	0.230616i
$552$	−0.744998	+	0.379595i	−0.0317092	+	0.0161567i
$553$	0.544749	+	37.3772i	0.0231651	+	1.58944i
$554$	−32.0136	+	44.0629i	−1.36013	+	1.87205i
$555$		0			0
$556$	−11.9550	+	1.25652i	−0.507006	+	0.0532885i
$557$	8.10705	+	30.2559i	0.343507	+	1.28198i	0.894347	+	0.447373i	$0.147641\pi$
$557$	8.10705	+	30.2559i	0.343507	+	1.28198i	−0.550841	+	0.834610i	$0.685693\pi$
$558$	43.1226	−	16.5532i	1.82553	−	0.700754i
$559$	−0.965254	−	2.97075i	−0.0408259	−	0.125649i
$560$		0			0
$561$	−0.408011	+	1.25573i	−0.0172262	+	0.0530169i
$562$	−0.437509	−	8.34817i	−0.0184552	−	0.352146i
$563$	−15.6052	+	10.1341i	−0.657680	+	0.427103i	−0.829867	−	0.557962i	$-0.811584\pi$
$563$	−15.6052	+	10.1341i	−0.657680	+	0.427103i	0.172186	+	0.985064i	$0.444917\pi$
$564$	3.08833	−	2.78075i	0.130042	−	0.117091i
$565$		0			0
$566$	−9.52590	+	3.09515i	−0.400404	+	0.130099i
$567$	−20.2540	+	4.61460i	−0.850586	+	0.193795i
$568$	−14.2005	−	14.2005i	−0.595838	−	0.595838i
$569$	−0.637171	+	1.43111i	−0.0267116	+	0.0599952i	−0.926409	−	0.376520i	$-0.877121\pi$
$569$	−0.637171	+	1.43111i	−0.0267116	+	0.0599952i	0.899697	+	0.436515i	$0.143787\pi$
$570$		0			0
$571$	−12.0801	+	5.37840i	−0.505536	+	0.225079i	−0.643625	−	0.765341i	$-0.722570\pi$
$571$	−12.0801	+	5.37840i	−0.505536	+	0.225079i	0.138090	+	0.990420i	$0.455904\pi$
$572$	−2.32622	+	1.88374i	−0.0972643	+	0.0787630i
$573$	2.37736	+	4.66582i	0.0993154	+	0.194918i
$574$	28.0914	+	4.03053i	1.17251	+	0.168231i
$575$		0			0
$576$	−1.16929	−	2.02527i	−0.0487204	−	0.0843861i
$577$	−0.486112	+	9.27556i	−0.0202371	+	0.386147i	0.969669	+	0.244422i	$0.0785982\pi$
$577$	−0.486112	+	9.27556i	−0.0202371	+	0.386147i	−0.989906	+	0.141725i	$0.954735\pi$
$578$	27.1214	+	10.4109i	1.12810	+	0.433038i
$579$	−0.0233794	+	0.222440i	−0.000971615	+	0.00924430i
$580$		0			0
$581$	−8.07290	−	0.305192i	−0.334920	−	0.0126615i
$582$	5.33245	−	5.33245i	0.221037	−	0.221037i
$583$	12.8319	+	33.4283i	0.531444	+	1.38446i
$584$	4.89123	+	1.03966i	0.202400	+	0.0430216i
$585$		0			0
$586$	−3.88270	−	18.2667i	−0.160393	−	0.754589i
$587$	6.05467	−	11.8830i	0.249903	−	0.490462i	−0.731643	−	0.681688i	$-0.761246\pi$
$587$	6.05467	−	11.8830i	0.249903	−	0.490462i	0.981546	+	0.191226i	$0.0612462\pi$
$588$	2.89106	−	0.865708i	0.119225	−	0.0357012i
$589$	54.6321	+	17.7511i	2.25108	+	0.731419i
$590$		0			0
$591$	−1.82581	+	8.58974i	−0.0751036	+	0.353335i
$592$	16.7987	+	13.6033i	0.690423	+	0.559093i
$593$	35.2829	+	9.45404i	1.44890	+	0.388231i	0.895640	−	0.444780i	$-0.146718\pi$
$593$	35.2829	+	9.45404i	1.44890	+	0.388231i	0.553257	+	0.833011i	$0.313385\pi$
$594$	−12.9038	+	9.37515i	−0.529449	+	0.384667i
$595$		0			0
$596$	−6.93605	−	5.03934i	−0.284112	−	0.206419i
$597$	1.94391	+	2.40053i	0.0795589	+	0.0982471i
$598$	−1.71232	−	0.0897391i	−0.0700221	−	0.00366970i
$599$	0.214739	+	0.123980i	0.00877399	+	0.00506567i	0.504381	−	0.863481i	$-0.331721\pi$
$599$	0.214739	+	0.123980i	0.00877399	+	0.00506567i	−0.495607	+	0.868547i	$0.665054\pi$
$600$		0			0
$601$			19.3484i			0.789237i	0.918845	+	0.394618i	$0.129123\pi$
$601$			19.3484i			0.789237i	−0.918845	+	0.394618i	$0.870877\pi$
$602$	−8.06381	−	23.6400i	−0.328656	−	0.963492i
$603$	−5.14734	−	32.4991i	−0.209616	−	1.32346i
$604$	−29.1565	−	3.06447i	−1.18636	−	0.124691i
$605$		0			0
$606$	−0.298934	−	2.84416i	−0.0121433	−	0.115536i
$607$	−9.35079	+	34.8976i	−0.379537	+	1.41645i	0.467065	+	0.884223i	$0.345312\pi$
$607$	−9.35079	+	34.8976i	−0.379537	+	1.41645i	−0.846601	+	0.532227i	$0.821355\pi$
$608$	5.99558	−	37.8546i	0.243153	−	1.53521i
$609$	1.23979	−	1.03423i	0.0502386	−	0.0419093i
$610$		0			0
$611$	−5.57903	+	1.18586i	−0.225703	+	0.0479747i
$612$	−1.62791	−	2.50676i	−0.0658043	−	0.101330i
$613$	8.50267	+	13.0930i	0.343420	+	0.528820i	0.967609	−	0.252453i	$-0.0812373\pi$
$613$	8.50267	+	13.0930i	0.343420	+	0.528820i	−0.624189	+	0.781273i	$0.714571\pi$
$614$	−48.0688	+	10.2173i	−1.93990	+	0.412338i
$615$		0			0
$616$	12.3008	−	10.2614i	0.495614	−	0.413443i
$617$	−4.34934	+	27.4606i	−0.175098	+	1.10552i	0.730976	+	0.682403i	$0.239065\pi$
$617$	−4.34934	+	27.4606i	−0.175098	+	1.10552i	−0.906074	+	0.423120i	$0.860935\pi$
$618$	0.349086	−	1.30281i	0.0140423	−	0.0524065i
$619$	−3.75824	−	35.7573i	−0.151056	−	1.43721i	−0.763048	−	0.646342i	$-0.776298\pi$
$619$	−3.75824	−	35.7573i	−0.151056	−	1.43721i	0.611992	−	0.790864i	$-0.290369\pi$
$620$		0			0
$621$	−3.40420	−	0.357796i	−0.136606	−	0.0143579i
$622$	4.19711	+	26.4995i	0.168289	+	1.06253i
$623$	−14.5645	−	42.6974i	−0.583513	−	1.71063i
$624$		−	1.05622i		−	0.0422827i
$625$		0			0
$626$	47.2331	+	27.2700i	1.88781	+	1.08993i
$627$	−9.68582	−	0.507612i	−0.386814	−	0.0202721i
$628$	−15.1429	−	18.7000i	−0.604268	−	0.746209i
$629$	3.06365	+	2.22587i	0.122156	+	0.0887514i
$630$		0			0
$631$	23.2118	−	16.8644i	0.924048	−	0.671360i	−0.0204802	−	0.999790i	$-0.506520\pi$
$631$	23.2118	−	16.8644i	0.924048	−	0.671360i	0.944528	+	0.328430i	$0.106520\pi$
$632$	19.5703	+	5.24385i	0.778465	+	0.208589i
$633$	−1.16226	−	0.941179i	−0.0461957	−	0.0374085i
$634$	9.40266	−	44.2361i	0.373427	−	1.75684i
$635$		0			0
$636$	3.47728	+	1.12984i	0.137883	+	0.0448009i
$637$	−4.03038	−	0.954970i	−0.159689	−	0.0378373i
$638$	−5.81335	+	11.4094i	−0.230153	+	0.451701i
$639$	−8.35809	−	39.3217i	−0.330641	−	1.55554i
$640$		0			0
$641$	−17.6000	−	3.74101i	−0.695160	−	0.147761i	−0.153238	−	0.988189i	$-0.548970\pi$
$641$	−17.6000	−	3.74101i	−0.695160	−	0.147761i	−0.541922	+	0.840429i	$0.682303\pi$
$642$	0.949726	+	2.47412i	0.0374827	+	0.0976457i
$643$	9.47610	−	9.47610i	0.373701	−	0.373701i	−0.495122	−	0.868823i	$-0.664877\pi$
$643$	9.47610	−	9.47610i	0.373701	−	0.373701i	0.868823	+	0.495122i	$0.164877\pi$
$644$	−5.13297	−	0.194050i	−0.202267	−	0.00764662i
$645$		0			0
$646$	1.03714	−	9.86769i	0.0408056	−	0.388239i
$647$	12.9334	+	4.96466i	0.508464	+	0.195181i	0.599056	−	0.800707i	$-0.295543\pi$
$647$	12.9334	+	4.96466i	0.508464	+	0.195181i	−0.0905921	+	0.995888i	$0.528876\pi$
$648$	−0.589251	+	11.2436i	−0.0231480	+	0.441689i
$649$	14.3045	+	24.7762i	0.561502	+	0.972549i
$650$		0			0
$651$	8.47946	+	1.21662i	0.332336	+	0.0476832i
$652$	8.77692	+	17.2257i	0.343731	+	0.674610i
$653$	28.5253	−	23.0993i	1.11628	−	0.903947i	0.120231	−	0.992746i	$-0.461636\pi$
$653$	28.5253	−	23.0993i	1.11628	−	0.903947i	0.996050	+	0.0887994i	$0.0283030\pi$
$654$	7.01981	−	3.12542i	0.274496	−	0.122214i
$655$		0			0
$656$	12.1021	−	27.1818i	0.472508	−	1.06127i
$657$	7.07798	+	7.07798i	0.276138	+	0.276138i
$658$	−44.4686	+	10.1316i	−1.73357	+	0.394970i
$659$	17.1826	−	5.58297i	0.669340	−	0.217482i	0.0454175	−	0.998968i	$-0.485538\pi$
$659$	17.1826	−	5.58297i	0.669340	−	0.217482i	0.623922	+	0.781486i	$0.285538\pi$
$660$		0			0
$661$	−19.5718	+	17.6225i	−0.761253	+	0.685435i	−0.955327	−	0.295552i	$-0.904497\pi$
$661$	−19.5718	+	17.6225i	−0.761253	+	0.685435i	0.194074	+	0.980987i	$0.437830\pi$
$662$	−9.92841	+	6.44759i	−0.385879	+	0.250593i
$663$	−0.00968421	−	0.184786i	−0.000376103	−	0.00717648i
$664$	−1.35308	+	4.16435i	−0.0525097	+	0.161608i
$665$		0			0
$666$	6.91223	+	21.2737i	0.267843	+	0.824337i
$667$	−2.56551	+	0.984806i	−0.0993369	+	0.0381318i
$668$	3.15104	+	11.7598i	0.121917	+	0.455002i
$669$	4.55167	−	0.478400i	0.175978	−	0.0184960i
$670$		0			0
$671$	3.06518	−	4.21886i	0.118330	−	0.162867i
$672$	−0.0832901	−	5.71484i	−0.00321299	−	0.220455i
$673$	45.5727	−	23.2205i	1.75670	−	0.895083i	0.802102	−	0.597187i	$-0.203715\pi$
$673$	45.5727	−	23.2205i	1.75670	−	0.895083i	0.954598	−	0.297896i	$-0.0962850\pi$
$674$	7.64957	−	4.41648i	0.294651	−	0.170117i
$675$		0			0
$676$	−7.57813	+	13.1257i	−0.291466	+	0.504835i
$677$	33.1651	+	21.5376i	1.27464	+	0.827759i	0.991346	−	0.131275i	$-0.0419072\pi$
$677$	33.1651	+	21.5376i	1.27464	+	0.827759i	0.283291	+	0.959034i	$0.408574\pi$
$678$	2.26970	−	0.359485i	0.0871673	−	0.0138059i
$679$	−29.8291	+	8.46047i	−1.14474	+	0.324683i
$680$		0			0
$681$	2.30181	+	1.02483i	0.0882055	+	0.0392716i
$682$	−65.6252	+	17.5842i	−2.51292	+	0.673335i
$683$	−6.85894	+	8.47008i	−0.262450	+	0.324099i	−0.891288	−	0.453438i	$-0.850198\pi$
$683$	−6.85894	+	8.47008i	−0.262450	+	0.324099i	0.628838	+	0.777536i	$0.283531\pi$
$684$	14.6918	−	16.3169i	0.561755	−	0.623892i
$685$		0			0
$686$	−32.3359	−	7.16576i	−1.23459	−	0.273590i
$687$	−4.74265	−	2.41650i	−0.180943	−	0.0921953i
$688$	−26.1518	+	1.37056i	−0.997028	+	0.0522520i
$689$	−3.35774	−	3.72915i	−0.127920	−	0.142069i
$690$		0			0
$691$	25.6649	+	23.1088i	0.976340	+	0.879101i	0.992681	−	0.120766i	$-0.0385350\pi$
$691$	25.6649	+	23.1088i	0.976340	+	0.879101i	−0.0163408	+	0.999866i	$0.505202\pi$
$692$	−3.96983	−	0.628759i	−0.150910	−	0.0239018i
$693$	31.8381	−	3.81618i	1.20943	−	0.144965i
$694$	−27.0650	−	37.2518i	−1.02737	−	1.41406i
$695$		0			0
$696$	−0.355927	−	0.799424i	−0.0134914	−	0.0303021i
$697$	1.86804	−	4.86641i	0.0707570	−	0.184328i
$698$	−23.1955	+	35.7180i	−0.877963	+	1.35195i
$699$	0.917976			0.0347211
$700$		0			0
$701$	16.6461			0.628716			0.314358	−	0.949305i	$-0.398211\pi$
$701$	16.6461			0.628716			0.314358	+	0.949305i	$0.398211\pi$
$702$	1.21743	−	1.87467i	0.0459488	−	0.0707549i
$703$	−9.96904	+	25.9702i	−0.375989	+	0.979486i
$704$	1.39907	+	3.14236i	0.0527293	+	0.118432i
$705$		0			0
$706$	−33.2858	−	45.8139i	−1.25273	−	1.72423i
$707$	−4.62545	+	10.8102i	−0.173958	+	0.406560i
$708$	2.88532	+	0.456990i	0.108437	+	0.0171747i
$709$	13.9859	+	12.5930i	0.525253	+	0.472940i	0.888580	−	0.458722i	$-0.151692\pi$
$709$	13.9859	+	12.5930i	0.525253	+	0.472940i	−0.363327	+	0.931662i	$0.618359\pi$
$710$		0			0
$711$	27.1378	+	30.1396i	1.01775	+	1.13032i
$712$	−24.4179	+	1.27969i	−0.915099	+	0.0479583i
$713$	−12.9912	−	6.61935i	−0.486525	−	0.247897i
$714$	−0.0989623	−	1.47631i	−0.00370357	−	0.0552497i
$715$		0			0
$716$	−2.32850	+	2.58606i	−0.0870201	+	0.0966456i
$717$	0.225225	−	0.278129i	0.00841116	−	0.0103869i
$718$	21.9128	−	5.87151i	0.817777	−	0.219123i
$719$	37.9155	+	16.8811i	1.41401	+	0.629558i	0.964588	−	0.263761i	$-0.0849630\pi$
$719$	37.9155	+	16.8811i	1.41401	+	0.629558i	0.449423	+	0.893319i	$0.351630\pi$
$720$		0			0
$721$	−3.86367	+	3.97795i	−0.143890	+	0.148147i
$722$	38.4285	−	6.08648i	1.43016	−	0.226515i
$723$	−1.61840	−	1.05100i	−0.0601890	−	0.0390872i
$724$	−4.73846	+	8.20725i	−0.176103	+	0.305020i
$725$		0			0
$726$	3.80439	−	2.19646i	0.141194	−	0.0815184i
$727$	−17.6929	+	9.01500i	−0.656195	+	0.334348i	−0.750188	−	0.661225i	$-0.770037\pi$
$727$	−17.6929	+	9.01500i	−0.656195	+	0.334348i	0.0939929	+	0.995573i	$0.470037\pi$
$728$	−1.09403	+	1.96034i	−0.0405473	+	0.0726550i
$729$	−11.9070	+	16.3886i	−0.441001	+	0.606985i
$730$		0			0
$731$	−4.56268	+	0.479557i	−0.168757	+	0.0177371i
$732$	−0.137818	−	0.514343i	−0.00509389	−	0.0190107i
$733$	9.25483	−	3.55260i	0.341835	−	0.131218i	−0.181394	−	0.983411i	$-0.558061\pi$
$733$	9.25483	−	3.55260i	0.341835	−	0.131218i	0.523228	+	0.852192i	$0.324727\pi$
$734$	−4.33796	−	13.3509i	−0.160117	−	0.492790i
$735$		0			0
$736$	−3.00613	+	9.25192i	−0.110807	+	0.341030i
$737$	2.53294	+	48.3314i	0.0933020	+	1.78031i
$738$	25.8227	−	16.7695i	0.950547	−	0.617293i
$739$	−6.85463	+	6.17193i	−0.252152	+	0.227038i	−0.785507	−	0.618853i	$-0.787598\pi$
$739$	−6.85463	+	6.17193i	−0.252152	+	0.227038i	0.533355	+	0.845891i	$0.320931\pi$
$740$		0			0
$741$	1.29274	−	0.420038i	0.0474901	−	0.0154305i
$742$	−27.2812	−	29.4250i	−1.00152	−	1.08022i
$743$	31.8855	+	31.8855i	1.16976	+	1.16976i	0.982265	+	0.187500i	$0.0600383\pi$
$743$	31.8855	+	31.8855i	1.16976	+	1.16976i	0.187500	+	0.982265i	$0.439962\pi$
$744$	1.88846	−	4.24155i	0.0692342	−	0.155503i
$745$		0			0
$746$	5.95674	−	2.65211i	0.218092	−	0.0971006i
$747$	−6.81168	+	5.51599i	−0.249226	+	0.201819i
$748$	1.99592	+	3.91720i	0.0729779	+	0.143227i
$749$	1.54751	−	10.7856i	0.0565447	−	0.394098i
$750$		0			0
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	0.764243	−	0.644928i	$-0.223113\pi$
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	−0.940646	+	0.339390i	$0.889779\pi$
$752$	−2.50260	+	47.7525i	−0.0912606	+	1.74136i
$753$	−5.20934	−	1.99968i	−0.189839	−	0.0728723i
$754$	0.187581	−	1.78471i	0.00683130	−	0.0649955i
$755$		0			0
$756$	3.56481	−	5.66849i	0.129651	−	0.206161i
$757$	29.1640	−	29.1640i	1.05998	−	1.05998i	0.0619022	−	0.998082i	$-0.480283\pi$
$757$	29.1640	−	29.1640i	1.05998	−	1.05998i	0.998082	−	0.0619022i	$-0.0197167\pi$
$758$	13.2959	+	34.6371i	0.482930	+	1.25808i
$759$	2.40804	+	0.511844i	0.0874062	+	0.0185788i
$760$		0			0
$761$	0.778111	+	3.66072i	0.0282065	+	0.132701i	0.989998	−	0.141082i	$-0.0450582\pi$
$761$	0.778111	+	3.66072i	0.0282065	+	0.132701i	−0.961791	+	0.273783i	$0.911725\pi$
$762$	−0.961213	+	1.88649i	−0.0348211	+	0.0683402i
$763$	−31.4651	−	2.84418i	−1.13911	−	0.102966i
$764$	16.5829	+	5.38810i	0.599947	+	0.194934i
$765$		0			0
$766$	7.22402	−	33.9863i	0.261014	−	1.22798i
$767$	−3.11588	−	2.52319i	−0.112508	−	0.0911070i
$768$	−7.12390	−	1.90884i	−0.257062	−	0.0688795i
$769$	−16.8695	+	12.2564i	−0.608330	+	0.441977i	−0.848826	−	0.528673i	$-0.822690\pi$
$769$	−16.8695	+	12.2564i	−0.608330	+	0.441977i	0.240496	+	0.970650i	$0.422690\pi$
$770$		0			0
$771$	4.54376	+	3.30124i	0.163640	+	0.118891i
$772$	0.468680	+	0.578771i	0.0168682	+	0.0208304i
$773$	−18.9485	−	0.993051i	−0.681532	−	0.0357176i	−0.291571	−	0.956549i	$-0.594178\pi$
$773$	−18.9485	−	0.993051i	−0.681532	−	0.0357176i	−0.389961	+	0.920832i	$0.627511\pi$
$774$	−23.4688	−	13.5497i	−0.843567	−	0.487034i
$775$		0			0
$776$			16.8052i			0.603271i
$777$	−0.803267	+	4.06984i	−0.0288170	+	0.146005i
$778$	4.28028	+	27.0246i	0.153455	+	0.968879i
$779$	38.0814	+	4.00252i	1.36441	+	0.143405i
$780$		0			0
$781$	6.18068	+	58.8053i	0.221162	+	2.10422i
$782$	−0.651815	+	2.43261i	−0.0233089	+	0.0869898i
$783$	0.560410	−	3.53829i	0.0200274	−	0.126448i
$784$	−16.4788	+	30.5661i	−0.588529	+	1.09165i
$785$		0			0
$786$	2.32132	−	0.493411i	0.0827986	−	0.0175994i
$787$	−9.47620	−	14.5921i	−0.337790	−	0.520151i	0.628431	−	0.777865i	$-0.283697\pi$
$787$	−9.47620	−	14.5921i	−0.337790	−	0.520151i	−0.966221	+	0.257714i	$0.917031\pi$
$788$	15.9254	+	24.5229i	0.567318	+	0.873594i
$789$	−1.44668	+	0.307502i	−0.0515033	+	0.0109474i
$790$		0			0
$791$	−8.86906	−	3.25703i	−0.315348	−	0.115807i
$792$	2.71880	−	17.1658i	0.0966084	−	0.609962i
$793$	−0.189151	+	0.705921i	−0.00671694	+	0.0250680i
$794$	−5.46497	−	51.9957i	−0.193944	−	1.84526i
$795$		0			0
$796$	10.2288	+	1.07509i	0.362550	+	0.0381055i
$797$	0.210477	+	1.32890i	0.00745547	+	0.0470720i	0.991136	−	0.132854i	$-0.0424142\pi$
$797$	0.210477	+	1.32890i	0.00745547	+	0.0470720i	−0.983680	+	0.179926i	$0.942414\pi$
$798$	10.2871	−	3.50903i	0.364160	−	0.124218i
$799$			8.37724i			0.296365i
$800$		0			0
$801$	−42.3882	−	24.4728i	−1.49771	−	0.864705i
$802$	39.0489	+	2.04647i	1.37887	+	0.0722633i
$803$	−9.26552	−	11.4420i	−0.326973	−	0.403778i
$804$	3.99809	+	2.90479i	0.141002	+	0.102444i
$805$		0			0
$806$	7.70298	−	5.59655i	0.271326	−	0.197130i
$807$	4.09993	+	1.09857i	0.144324	+	0.0386716i
$808$	4.95273	+	4.01064i	0.174236	+	0.141094i
$809$	2.99535	−	14.0920i	0.105311	−	0.495449i	−0.893603	−	0.448858i	$-0.851831\pi$
$809$	2.99535	−	14.0920i	0.105311	−	0.495449i	0.998914	−	0.0465911i	$-0.0148358\pi$
$810$		0			0
$811$	−6.31358	−	2.05141i	−0.221700	−	0.0720346i	0.196061	−	0.980592i	$-0.437185\pi$
$811$	−6.31358	−	2.05141i	−0.221700	−	0.0720346i	−0.417761	+	0.908557i	$0.637185\pi$
$812$	0.483963	−	5.35408i	0.0169838	−	0.187891i
$813$	−1.10026	+	2.15938i	−0.0385877	+	0.0757326i
$814$	−6.84051	−	32.1821i	−0.239760	−	1.12798i
$815$		0			0
$816$	−1.51742	−	0.322538i	−0.0531204	−	0.0112911i
$817$	−12.0775	−	31.4630i	−0.422538	−	1.10075i
$818$	−38.8546	+	38.8546i	−1.35852	+	1.35852i
$819$	−3.97389	+	2.09830i	−0.138859	+	0.0733205i
$820$		0			0
$821$	−2.07096	+	19.7039i	−0.0722771	+	0.687670i	0.897056	+	0.441918i	$0.145702\pi$
$821$	−2.07096	+	19.7039i	−0.0722771	+	0.687670i	−0.969333	+	0.245752i	$0.920965\pi$
$822$	0.606073	+	0.232650i	0.0211392	+	0.00811458i
$823$	1.20614	−	23.0145i	0.0420434	−	0.802235i	−0.893509	−	0.449046i	$-0.851764\pi$
$823$	1.20614	−	23.0145i	0.0420434	−	0.802235i	0.935552	−	0.353189i	$-0.114903\pi$
$824$	1.50282	+	2.60297i	0.0523533	+	0.0906786i
$825$		0			0
$826$	−25.2068	−	19.8109i	−0.877058	−	0.689309i
$827$	18.3211	+	35.9571i	0.637086	+	1.25035i	0.953403	+	0.301698i	$0.0975536\pi$
$827$	18.3211	+	35.9571i	0.637086	+	1.25035i	−0.316317	+	0.948653i	$0.602446\pi$
$828$	−4.33105	+	3.50721i	−0.150514	+	0.121884i
$829$	−11.3227	+	5.04117i	−0.393252	+	0.175087i	−0.593830	−	0.804591i	$-0.702385\pi$
$829$	−11.3227	+	5.04117i	−0.393252	+	0.175087i	0.200578	+	0.979678i	$0.435718\pi$
$830$		0			0
$831$	−4.45739	+	10.0115i	−0.154625	+	0.347294i
$832$	−0.340867	−	0.340867i	−0.0118174	−	0.0118174i
$833$	−2.60271	+	5.49862i	−0.0901786	+	0.190516i
$834$	−6.14024	+	1.99508i	−0.212619	+	0.0690841i
$835$		0			0
$836$	−24.0000	+	21.6097i	−0.830057	+	0.747387i
$837$	15.9409	−	10.3521i	0.550997	−	0.357822i
$838$	0.995413	+	18.9936i	0.0343860	+	0.656123i
$839$	8.58250	−	26.4142i	0.296301	−	0.911920i	−0.686481	−	0.727148i	$-0.740845\pi$
$839$	8.58250	−	26.4142i	0.296301	−	0.911920i	0.982781	−	0.184772i	$-0.0591547\pi$
$840$		0			0
$841$	8.07275	+	24.8454i	0.278371	+	0.856737i
$842$	35.6370	−	13.6798i	1.22813	−	0.471436i
$843$	−0.435346	−	1.62473i	−0.0149941	−	0.0559588i
$844$	−4.95246	+	0.520524i	−0.170471	+	0.0179172i
$845$		0			0
$846$	−29.0853	+	40.0324i	−0.999972	+	1.37634i
$847$	−18.0596	+	0.263207i	−0.620536	+	0.00904392i
$848$	−37.4848	+	19.0995i	−1.28723	+	0.655879i
$849$	−1.74535	+	1.00768i	−0.0599002	+	0.0345834i
$850$		0			0
$851$	3.53038	−	6.11479i	0.121020	−	0.209612i
$852$	5.06366	+	3.28838i	0.173478	+	0.112658i
$853$	−27.2295	+	4.31272i	−0.932319	+	0.147665i	−0.604074	−	0.796928i	$-0.706457\pi$
$853$	−27.2295	+	4.31272i	−0.932319	+	0.147665i	−0.328245	+	0.944593i	$0.606457\pi$
$854$	−1.43009	+	5.66619i	−0.0489365	+	0.193893i
$855$		0			0
$856$	−5.39512	−	2.40206i	−0.184401	−	0.0821008i
$857$	−6.73593	+	1.80489i	−0.230095	+	0.0616538i	−0.372024	−	0.928223i	$-0.621336\pi$
$857$	−6.73593	+	1.80489i	−0.230095	+	0.0616538i	0.141929	+	0.989877i	$0.454669\pi$
$858$	−1.01173	+	1.24938i	−0.0345398	+	0.0426531i
$859$	−5.29128	+	5.87656i	−0.180536	+	0.200506i	−0.826620	−	0.562761i	$-0.809739\pi$
$859$	−5.29128	+	5.87656i	−0.180536	+	0.200506i	0.646083	+	0.763267i	$0.276406\pi$
$860$		0			0
$861$	5.69740	−	0.381916i	0.194167	−	0.0130157i
$862$	12.2127	+	6.22270i	0.415968	+	0.211946i
$863$	−14.9008	+	0.780920i	−0.507230	+	0.0265828i	−0.304235	−	0.952597i	$-0.598401\pi$
$863$	−14.9008	+	0.780920i	−0.507230	+	0.0265828i	−0.202995	+	0.979180i	$0.565068\pi$
$864$	−8.48572	−	9.42434i	−0.288690	−	0.320623i
$865$		0			0
$866$	27.2824	+	24.5652i	0.927094	+	0.834759i
$867$	5.77340	+	0.914417i	0.196075	+	0.0310552i
$868$	22.8290	−	17.1000i	0.774867	−	0.580413i
$869$	−35.0636	−	48.2610i	−1.18945	−	1.63714i
$870$		0			0
$871$	−2.75875	−	6.19625i	−0.0934766	−	0.209952i
$872$	−6.13658	+	15.9863i	−0.207811	+	0.541366i
$873$	−18.3216	+	28.2127i	−0.620091	+	0.954857i
$874$	−18.4999			−0.625770
$875$		0			0
$876$	−1.50338			−0.0507945
$877$	15.7334	−	24.2272i	0.531278	−	0.818096i	−0.466514	−	0.884514i	$-0.654490\pi$
$877$	15.7334	−	24.2272i	0.531278	−	0.818096i	0.997792	+	0.0664179i	$0.0211570\pi$
$878$	−8.01942	+	20.8913i	−0.270642	+	0.705047i
$879$	−1.52834	−	3.43271i	−0.0515496	−	0.115782i
$880$		0			0
$881$	26.6392	+	36.6657i	0.897498	+	1.23530i	0.971259	+	0.238024i	$0.0764997\pi$
$881$	26.6392	+	36.6657i	0.897498	+	1.23530i	−0.0737612	+	0.997276i	$0.523500\pi$
$882$	−31.5285	+	17.2399i	−1.06162	+	0.580497i
$883$	2.28067	+	0.361222i	0.0767506	+	0.0121561i	0.194692	−	0.980865i	$-0.437629\pi$
$883$	2.28067	+	0.361222i	0.0767506	+	0.0121561i	−0.117941	+	0.993021i	$0.537629\pi$
$884$	−0.457871	−	0.412269i	−0.0153999	−	0.0138661i
$885$		0			0
$886$	−41.8840	−	46.5169i	−1.40712	−	1.56277i
$887$	38.1012	−	1.99680i	1.27931	−	0.0670460i	0.599466	−	0.800400i	$-0.295379\pi$
$887$	38.1012	−	1.99680i	1.27931	−	0.0670460i	0.679847	+	0.733354i	$0.262046\pi$
$888$	2.00335	+	1.02076i	0.0672281	+	0.0342544i
$889$	7.23084	−	4.84702i	0.242515	−	0.162564i
$890$		0			0
$891$	22.1817	−	24.6353i	0.743116	−	0.825314i
$892$	9.59035	−	11.8431i	0.321109	−	0.396536i
$893$	−59.4411	+	15.9272i	−1.98912	+	0.532983i
$894$	−4.20657	−	1.87288i	−0.140689	−	0.0626386i
$895$		0			0
$896$	20.0227	+	19.4475i	0.668912	+	0.649694i
$897$	−0.340763	+	0.0539716i	−0.0113778	+	0.00180206i
$898$	6.42711	+	4.17382i	0.214476	+	0.139282i
$899$	7.62977	−	13.2152i	0.254467	−	0.440750i
$900$		0			0
$901$	−6.38284	+	3.68513i	−0.212643	+	0.122770i
$902$	−40.3520	+	20.5604i	−1.34357	+	0.684586i
$903$	−2.57603	−	4.31533i	−0.0857248	−	0.143605i
$904$	−3.01002	+	4.14293i	−0.100112	+	0.137792i
$905$		0			0
$906$	−15.6595	+	1.64588i	−0.520252	+	0.0546806i
$907$	−8.92281	−	33.3004i	−0.296277	−	1.10572i	−0.940198	−	0.340629i	$-0.889360\pi$
$907$	−8.92281	−	33.3004i	−0.296277	−	1.10572i	0.643921	−	0.765092i	$-0.277307\pi$
$908$	7.83243	−	3.00659i	0.259928	−	0.0997771i
$909$	3.94217	+	12.1327i	0.130753	+	0.402418i
$910$		0			0
$911$	5.06918	−	15.6013i	0.167949	−	0.516895i	−0.831292	−	0.555836i	$-0.812398\pi$
$911$	5.06918	−	15.6013i	0.167949	−	0.516895i	0.999242	+	0.0389409i	$0.0123984\pi$
$912$	−0.596409	−	11.3802i	−0.0197491	−	0.376835i
$913$	10.8123	−	7.02157i	0.357834	−	0.232380i
$914$	−23.5039	+	21.1630i	−0.777441	+	0.700011i
$915$		0			0
$916$	−16.8559	+	5.47682i	−0.556935	+	0.180959i
$917$	−9.32272	−	2.87963i	−0.307863	−	0.0950936i
$918$	−2.32148	−	2.32148i	−0.0766203	−	0.0766203i
$919$	−0.325410	+	0.730883i	−0.0107343	+	0.0241096i	−0.918833	−	0.394646i	$-0.870867\pi$
$919$	−0.325410	+	0.730883i	−0.0107343	+	0.0241096i	0.908099	+	0.418756i	$0.137534\pi$
$920$		0			0
$921$	−9.03317	+	4.02183i	−0.297653	+	0.132524i
$922$	34.7743	−	28.1596i	1.14523	−	0.927388i
$923$	−3.76204	−	7.38341i	−0.123829	−	0.243028i
$924$	−2.97596	+	3.78653i	−0.0979019	+	0.124568i
$925$		0			0
$926$	−24.4107	−	42.2806i	−0.802185	−	1.38943i
$927$	−0.314883	+	6.00832i	−0.0103421	+	0.197339i
$928$	−9.50496	−	3.64861i	−0.312015	−	0.119772i
$929$	−3.31094	+	31.5015i	−0.108628	+	1.03353i	0.795408	+	0.606074i	$0.207257\pi$
$929$	−3.31094	+	31.5015i	−0.108628	+	1.03353i	−0.904036	+	0.427455i	$0.859410\pi$
$930$		0			0
$931$	−43.9641	−	8.01343i	−1.44087	−	0.262630i
$932$	2.16134	−	2.16134i	0.0707969	−	0.0707969i
$933$	1.93463	+	5.03989i	0.0633370	+	0.164999i
$934$	−12.3824	−	2.63196i	−0.405165	−	0.0861204i
$935$		0			0
$936$	0.506405	+	2.38245i	0.0165524	+	0.0778728i
$937$	−8.75168	+	17.1761i	−0.285905	+	0.561120i	−0.988635	−	0.150337i	$-0.951964\pi$
$937$	−8.75168	+	17.1761i	−0.285905	+	0.561120i	0.702730	+	0.711457i	$0.251964\pi$
$938$	−22.7795	−	49.2203i	−0.743776	−	1.60710i
$939$	10.4370	+	3.39117i	0.340597	+	0.110667i
$940$		0			0
$941$	−10.7376	+	50.5163i	−0.350035	+	1.64679i	0.352995	+	0.935625i	$0.385163\pi$
$941$	−10.7376	+	50.5163i	−0.350035	+	1.64679i	−0.703030	+	0.711160i	$0.748170\pi$
$942$	−10.0435	−	8.13303i	−0.327233	−	0.264988i
$943$	−9.38792	−	2.51549i	−0.305713	−	0.0819155i
$944$	−27.1940	+	19.7576i	−0.885089	+	0.643055i
$945$		0			0
$946$	32.2471	+	23.4289i	1.04844	+	0.761739i
$947$	30.0349	+	37.0901i	0.976004	+	1.20526i	0.978706	+	0.205268i	$0.0658068\pi$
$947$	30.0349	+	37.0901i	0.976004	+	1.20526i	−0.00270147	+	0.999996i	$0.500860\pi$
$948$	−6.08294	−	0.318793i	−0.197565	−	0.0103539i
$949$	1.78691	+	1.03167i	0.0580056	+	0.0334895i
$950$		0			0
$951$		−	9.09962i		−	0.295076i
$952$	2.48224	+	2.17036i	0.0804499	+	0.0703418i
$953$	−0.224666	−	1.41848i	−0.00727764	−	0.0459492i	0.983782	−	0.179367i	$-0.0574049\pi$
$953$	−0.224666	−	1.41848i	−0.00727764	−	0.0459492i	−0.991060	+	0.133418i	$0.957405\pi$
$954$	−43.2964	−	4.55063i	−1.40177	−	0.147332i
$955$		0			0
$956$	−0.124562	−	1.18512i	−0.00402861	−	0.0383297i
$957$	−0.666849	+	2.48872i	−0.0215562	+	0.0804488i
$958$	10.5666	−	66.7152i	0.341393	−	2.15547i
$959$	−1.70980	−	2.04962i	−0.0552125	−	0.0661858i
$960$		0			0
$961$	48.8715	−	10.3880i	1.57650	−	0.335096i
$962$	2.51126	+	3.86701i	0.0809664	+	0.124677i
$963$	−6.43858	−	9.91455i	−0.207480	−	0.319492i
$964$	−6.28500	+	1.33592i	−0.202426	+	0.0430270i
$965$		0			0
$966$	−2.71826	+	0.471236i	−0.0874587	+	0.0151618i
$967$	−1.15537	+	7.29472i	−0.0371542	+	0.234582i	−0.999276	−	0.0380364i	$-0.987890\pi$
$967$	−1.15537	+	7.29472i	−0.0371542	+	0.234582i	0.962122	+	0.272619i	$0.0878897\pi$
$968$	−2.53368	+	9.45583i	−0.0814356	+	0.303922i
$969$	−0.208683	−	1.98549i	−0.00670387	−	0.0637830i
$970$		0			0
$971$	−30.4188	−	3.19714i	−0.976185	−	0.102601i	−0.397019	−	0.917811i	$-0.629955\pi$
$971$	−30.4188	−	3.19714i	−0.976185	−	0.102601i	−0.579166	+	0.815209i	$0.696622\pi$
$972$	−1.71731	−	10.8426i	−0.0550826	−	0.347778i
$973$	26.0424	+	5.14001i	0.834881	+	0.164781i
$974$			23.5047i			0.753138i
$975$		0			0
$976$	5.30617	+	3.06352i	0.169846	+	0.0980608i
$977$	38.6687	+	2.02654i	1.23712	+	0.0648347i	0.659647	−	0.751575i	$-0.270706\pi$
$977$	38.6687	+	2.02654i	1.23712	+	0.0648347i	0.577473	+	0.816410i	$0.304039\pi$
$978$	6.53447	+	8.06939i	0.208949	+	0.258031i
$979$	58.2432	+	42.3162i	1.86146	+	1.35243i
$980$		0			0
$981$	−27.7310	+	20.1478i	−0.885383	+	0.643268i
$982$	−40.3556	−	10.8133i	−1.28780	−	0.345065i
$983$	−41.4782	−	33.5884i	−1.32295	−	1.07130i	−0.991810	−	0.127720i	$-0.959234\pi$
$983$	−41.4782	−	33.5884i	−1.32295	−	1.07130i	−0.331138	−	0.943582i	$-0.607432\pi$
$984$	0.643473	−	3.02730i	0.0205132	−	0.0965068i
$985$		0			0
$986$	−2.50673	−	0.814485i	−0.0798305	−	0.0259385i
$987$	−8.32820	+	3.85434i	−0.265089	+	0.122685i
$988$	2.05475	−	4.03267i	0.0653702	−	0.128296i
$989$	1.77850	+	8.36718i	0.0565530	+	0.266061i
$990$		0			0
$991$	−17.9026	−	3.80531i	−0.568694	−	0.120880i	−0.0854140	−	0.996346i	$-0.527221\pi$
$991$	−17.9026	−	3.80531i	−0.568694	−	0.120880i	−0.483280	+	0.875466i	$0.660555\pi$
$992$	−19.3586	−	50.4310i	−0.614637	−	1.60118i
$993$	−1.68432	+	1.68432i	−0.0534503	+	0.0534503i
$994$	−30.9395	−	58.5953i	−0.981342	−	1.85853i
$995$		0			0
$996$	0.137604	−	1.30921i	0.00436015	−	0.0414840i
$997$	40.5144	+	15.5520i	1.28310	+	0.492537i	0.901896	−	0.431953i	$-0.142175\pi$
$997$	40.5144	+	15.5520i	1.28310	+	0.492537i	0.381207	+	0.924490i	$0.375509\pi$
$998$	−0.841875	+	16.0639i	−0.0266491	+	0.508495i
$999$	4.60228	+	7.97139i	0.145610	+	0.252203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.493.15		288
5.2	odd	4		875.2.bb.c.507.15		288
5.3	odd	4		175.2.x.a.122.4	yes	288
5.4	even	2		875.2.bb.b.493.4		288
7.5	odd	6	inner	875.2.bb.a.243.4		288
25.6	even	5		875.2.bb.c.143.15		288
25.8	odd	20		875.2.bb.b.857.15		288
25.17	odd	20	inner	875.2.bb.a.857.4		288
25.19	even	10		175.2.x.a.108.4	yes	288
35.12	even	12		875.2.bb.c.257.15		288
35.19	odd	6		875.2.bb.b.243.15		288
35.33	even	12		175.2.x.a.47.4	yes	288
175.19	odd	30		175.2.x.a.33.4	✓	288
175.33	even	60		875.2.bb.b.607.4		288
175.117	even	60	inner	875.2.bb.a.607.15		288
175.131	odd	30		875.2.bb.c.768.15		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.4	✓	288	175.19	odd	30
175.2.x.a.47.4	yes	288	35.33	even	12
175.2.x.a.108.4	yes	288	25.19	even	10
175.2.x.a.122.4	yes	288	5.3	odd	4
875.2.bb.a.243.4		288	7.5	odd	6	inner
875.2.bb.a.493.15		288	1.1	even	1	trivial
875.2.bb.a.607.15		288	175.117	even	60	inner
875.2.bb.a.857.4		288	25.17	odd	20	inner
875.2.bb.b.243.15		288	35.19	odd	6
875.2.bb.b.493.4		288	5.4	even	2
875.2.bb.b.607.4		288	175.33	even	60
875.2.bb.b.857.15		288	25.8	odd	20
875.2.bb.c.143.15		288	25.6	even	5
875.2.bb.c.257.15		288	35.12	even	12
875.2.bb.c.507.15		288	5.2	odd	4
875.2.bb.c.768.15		288	175.131	odd	30

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.973996 - 1.49982i) q^{2} +(0.128952 - 0.335932i) q^{3} +(-0.487325 - 1.09455i) q^{4} +(-0.378240 - 0.520602i) q^{6} +(0.314872 + 2.62695i) q^{7} +(1.41635 + 0.224327i) q^{8} +(2.13321 + 1.92075i) q^{9} +(-2.82518 - 3.13767i) q^{11} +(-0.430536 + 0.0225635i) q^{12} +(0.527217 + 0.268631i) q^{13} +(4.24664 + 2.08638i) q^{14} +(3.31938 - 3.68655i) q^{16} +(0.546924 - 0.675395i) q^{17} +(4.95853 - 1.32863i) q^{18} +(5.83214 + 2.59663i) q^{19} +(0.923080 + 0.232975i) q^{21} +(-7.45766 + 1.18118i) q^{22} +(-1.35899 - 0.882537i) q^{23} +(0.258000 - 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(1.88216 - 0.959010i) q^{27} +(2.72188 - 1.62482i) q^{28} +(0.996818 - 1.37200i) q^{29} +(8.94867 - 0.940543i) q^{31} +(-1.55381 - 5.79889i) q^{32} +(-1.41836 + 0.544457i) q^{33} +(-0.480271 - 1.47812i) q^{34} +(1.06279 - 3.27094i) q^{36} +(0.228048 + 4.35142i) q^{37} +(9.57497 - 6.21806i) q^{38} +(0.158228 - 0.142469i) q^{39} +(5.70437 - 1.85346i) q^{41} +(1.24850 - 1.15754i) q^{42} +(-3.73281 - 3.73281i) q^{43} +(-2.05756 + 4.62136i) q^{44} +(-2.64730 + 1.17865i) q^{46} +(-7.49114 + 6.06621i) q^{47} +(-0.810389 - 1.59048i) q^{48} +(-6.80171 + 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(0.0371035 - 0.707976i) q^{52} +(-7.91735 - 3.03918i) q^{53} +(0.394875 - 3.75698i) q^{54} +(-0.143329 + 3.79131i) q^{56} +(1.62436 - 1.62436i) q^{57} +(-1.08686 - 2.83137i) q^{58} +(-6.62786 - 1.40879i) q^{59} +(0.256792 + 1.20811i) q^{61} +(7.30532 - 14.3375i) q^{62} +(-4.37403 + 6.20863i) q^{63} +(-0.774814 - 0.251752i) q^{64} +(-0.564887 + 2.65758i) q^{66} +(-8.90825 - 7.21376i) q^{67} +(-1.00578 - 0.269499i) q^{68} +(-0.471717 + 0.342723i) q^{69} +(-11.3299 - 8.23164i) q^{71} +(2.59049 + 3.19899i) q^{72} +(3.48231 + 0.182500i) q^{73} +(6.74848 + 3.89623i) q^{74} -7.64897i q^{76} +(7.35294 - 8.40955i) q^{77} +(-0.0595648 - 0.376077i) q^{78} +(14.0514 + 1.47686i) q^{79} +(0.820700 + 7.80844i) q^{81} +(2.77617 - 10.3608i) q^{82} +(-0.477665 + 3.01586i) q^{83} +(-0.194837 - 1.12389i) q^{84} +(-9.23428 + 1.96281i) q^{86} +(-0.332358 - 0.511786i) q^{87} +(-3.29756 - 5.07780i) q^{88} +(-16.6785 + 3.54513i) q^{89} +(-0.539673 + 1.46956i) q^{91} +(-0.303712 + 1.91756i) q^{92} +(0.837993 - 3.12743i) q^{93} +(1.80189 + 17.1438i) q^{94} +(-2.14840 - 0.225806i) q^{96} +(1.83327 + 11.5748i) q^{97} +(-4.14368 + 11.8126i) q^{98} -12.1198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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