LMFDB - Embedded newform 875.2.bb.c.507.15

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 = [288,8] 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			507.15
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.c.768.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.49982 + 0.973996i) q^{2} +(-0.335932 - 0.128952i) q^{3} +(0.487325 + 1.09455i) q^{4} +(-0.378240 - 0.520602i) q^{6} +(-2.62695 + 0.314872i) q^{7} +(0.224327 - 1.41635i) q^{8} +(-2.13321 - 1.92075i) q^{9} +(-2.82518 - 3.13767i) q^{11} +(-0.0225635 - 0.430536i) q^{12} +(0.268631 - 0.527217i) q^{13} +(-4.24664 - 2.08638i) q^{14} +(3.31938 - 3.68655i) q^{16} +(0.675395 + 0.546924i) q^{17} +(-1.32863 - 4.95853i) q^{18} +(-5.83214 - 2.59663i) q^{19} +(0.923080 + 0.232975i) q^{21} +(-1.18118 - 7.45766i) q^{22} +(-0.882537 + 1.35899i) q^{23} +(-0.258000 + 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(0.959010 + 1.88216i) q^{27} +(-1.62482 - 2.72188i) q^{28} +(-0.996818 + 1.37200i) q^{29} +(8.94867 - 0.940543i) q^{31} +(5.79889 - 1.55381i) q^{32} +(0.544457 + 1.41836i) q^{33} +(0.480271 + 1.47812i) q^{34} +(1.06279 - 3.27094i) q^{36} +(-4.35142 + 0.228048i) q^{37} +(-6.21806 - 9.57497i) q^{38} +(-0.158228 + 0.142469i) q^{39} +(5.70437 - 1.85346i) q^{41} +(1.15754 + 1.24850i) q^{42} +(-3.73281 + 3.73281i) q^{43} +(2.05756 - 4.62136i) q^{44} +(-2.64730 + 1.17865i) q^{46} +(-6.06621 - 7.49114i) q^{47} +(-1.59048 + 0.810389i) q^{48} +(6.80171 - 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(0.707976 + 0.0371035i) q^{52} +(-3.03918 + 7.91735i) q^{53} +(-0.394875 + 3.75698i) q^{54} +(-0.143329 + 3.79131i) q^{56} +(1.62436 + 1.62436i) q^{57} +(-2.83137 + 1.08686i) q^{58} +(6.62786 + 1.40879i) q^{59} +(0.256792 + 1.20811i) q^{61} +(14.3375 + 7.30532i) q^{62} +(6.20863 + 4.37403i) q^{63} +(0.774814 + 0.251752i) q^{64} +(-0.564887 + 2.65758i) q^{66} +(7.21376 - 8.90825i) q^{67} +(-0.269499 + 1.00578i) q^{68} +(0.471717 - 0.342723i) q^{69} +(-11.3299 - 8.23164i) q^{71} +(-3.19899 + 2.59049i) q^{72} +(0.182500 - 3.48231i) q^{73} +(-6.74848 - 3.89623i) q^{74} -7.64897i q^{76} +(8.40955 + 7.35294i) q^{77} +(-0.376077 + 0.0595648i) q^{78} +(-14.0514 - 1.47686i) q^{79} +(0.820700 + 7.80844i) q^{81} +(10.3608 + 2.77617i) q^{82} +(3.01586 + 0.477665i) q^{83} +(0.194837 + 1.12389i) q^{84} +(-9.23428 + 1.96281i) q^{86} +(0.511786 - 0.332358i) q^{87} +(-5.07780 + 3.29756i) q^{88} +(16.6785 - 3.54513i) q^{89} +(-0.539673 + 1.46956i) q^{91} +(-1.91756 - 0.303712i) q^{92} +(-3.12743 - 0.837993i) q^{93} +(-1.80189 - 17.1438i) q^{94} +(-2.14840 - 0.225806i) q^{96} +(-11.5748 + 1.83327i) q^{97} +(11.8126 + 4.14368i) q^{98} +12.1198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.49982	+	0.973996i	1.06053	+	0.688719i	0.952225	−	0.305398i	$-0.0987895\pi$
$2$	1.49982	+	0.973996i	1.06053	+	0.688719i	0.108310	+	0.994117i	$0.465456\pi$
$3$	−0.335932	−	0.128952i	−0.193951	−	0.0744506i	0.259454	−	0.965755i	$-0.416457\pi$
$3$	−0.335932	−	0.128952i	−0.193951	−	0.0744506i	−0.453405	+	0.891305i	$0.649791\pi$
$4$	0.487325	+	1.09455i	0.243663	+	0.547275i
$5$		0			0
$5$		0			0
$6$	−0.378240	−	0.520602i	−0.154416	−	0.212535i
$7$	−2.62695	+	0.314872i	−0.992893	+	0.119010i
$7$	−2.62695	+	0.314872i	−0.992893	+	0.119010i
$8$	0.224327	−	1.41635i	0.0793117	−	0.500755i
$9$	−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	$0.986291\pi$
$12$	−0.0225635	−	0.430536i	−0.00651351	−	0.124285i
$13$	0.268631	−	0.527217i	0.0745047	−	0.146224i	−0.850749	−	0.525571i	$-0.823852\pi$
$13$	0.268631	−	0.527217i	0.0745047	−	0.146224i	0.925254	+	0.379348i	$0.123852\pi$
$14$	−4.24664	−	2.08638i	−1.13496	−	0.557610i
$15$		0			0
$16$	3.31938	−	3.68655i	0.829846	−	0.921638i
$17$	0.675395	+	0.546924i	0.163807	+	0.132649i	0.707719	−	0.706494i	$-0.249724\pi$
$17$	0.675395	+	0.546924i	0.163807	+	0.132649i	−0.543912	+	0.839142i	$0.683057\pi$
$18$	−1.32863	−	4.95853i	−0.313162	−	1.16874i
$19$	−5.83214	−	2.59663i	−1.33798	−	0.595709i	−0.392013	−	0.919960i	$-0.628221\pi$
$19$	−5.83214	−	2.59663i	−1.33798	−	0.595709i	−0.945971	+	0.324251i	$0.894888\pi$
$20$		0			0
$21$	0.923080	+	0.232975i	0.201433	+	0.0508394i
$22$	−1.18118	−	7.45766i	−0.251828	−	1.58998i
$23$	−0.882537	+	1.35899i	−0.184022	+	0.283369i	−0.918627	−	0.395126i	$-0.870701\pi$
$23$	−0.882537	+	1.35899i	−0.184022	+	0.283369i	0.734605	+	0.678495i	$0.237367\pi$
$24$	−0.258000	+	0.446869i	−0.0526640	+	0.0912168i
$25$		0			0
$26$	0.916406	−	0.529087i	0.179722	−	0.103762i
$27$	0.959010	+	1.88216i	0.184562	+	0.362223i
$28$	−1.62482	−	2.72188i	−0.307062	−	0.514387i
$29$	−0.996818	+	1.37200i	−0.185104	+	0.254774i	−0.891477	−	0.453066i	$-0.850330\pi$
$29$	−0.996818	+	1.37200i	−0.185104	+	0.254774i	0.706373	+	0.707840i	$0.250330\pi$
$30$		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	$0.167195\pi$
$32$	5.79889	−	1.55381i	1.02511	−	0.274677i
$33$	0.544457	+	1.41836i	0.0947778	+	0.246905i
$34$	0.480271	+	1.47812i	0.0823657	+	0.253496i
$35$		0			0
$36$	1.06279	−	3.27094i	0.177132	−	0.545157i
$37$	−4.35142	+	0.228048i	−0.715369	+	0.0374909i	−0.406548	−	0.913629i	$-0.633268\pi$
$37$	−4.35142	+	0.228048i	−0.715369	+	0.0374909i	−0.308821	+	0.951120i	$0.599934\pi$
$38$	−6.21806	−	9.57497i	−1.00870	−	1.55326i
$39$	−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	$0.244845\pi$
$42$	1.15754	+	1.24850i	0.178612	+	0.192647i
$43$	−3.73281	+	3.73281i	−0.569248	+	0.569248i	−0.931918	−	0.362670i	$-0.881865\pi$
$43$	−3.73281	+	3.73281i	−0.569248	+	0.569248i	0.362670	+	0.931918i	$0.381865\pi$
$44$	2.05756	−	4.62136i	0.310189	−	0.696697i
$45$		0			0
$46$	−2.64730	+	1.17865i	−0.390323	+	0.173783i
$47$	−6.06621	−	7.49114i	−0.884847	−	1.09270i	−0.995108	−	0.0987925i	$-0.968502\pi$
$47$	−6.06621	−	7.49114i	−0.884847	−	1.09270i	0.110261	−	0.993903i	$-0.464831\pi$
$48$	−1.59048	+	0.810389i	−0.229566	+	0.116970i
$49$	6.80171	−	1.65430i	0.971673	−	0.236329i
$50$		0			0
$51$	−0.156360	−	0.270823i	−0.0218948	−	0.0379228i
$52$	0.707976	+	0.0371035i	0.0981786	+	0.00514532i
$53$	−3.03918	+	7.91735i	−0.417464	+	1.08753i	0.550143	+	0.835070i	$0.314573\pi$
$53$	−3.03918	+	7.91735i	−0.417464	+	1.08753i	−0.967607	+	0.252461i	$0.918760\pi$
$54$	−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
$58$	−2.83137	+	1.08686i	−0.371778	+	0.142712i
$59$	6.62786	+	1.40879i	0.862874	+	0.183409i	0.618031	−	0.786153i	$-0.287930\pi$
$59$	6.62786	+	1.40879i	0.862874	+	0.183409i	0.244842	+	0.969563i	$0.421264\pi$
$60$		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	$0.908138\pi$
$62$	14.3375	+	7.30532i	1.82086	+	0.927777i
$63$	6.20863	+	4.37403i	0.782214	+	0.551076i
$64$	0.774814	+	0.251752i	0.0968517	+	0.0314690i
$65$		0			0
$66$	−0.564887	+	2.65758i	−0.0695328	+	0.327126i
$67$	7.21376	−	8.90825i	0.881301	−	1.08832i	−0.114189	−	0.993459i	$-0.536427\pi$
$67$	7.21376	−	8.90825i	0.881301	−	1.08832i	0.995491	−	0.0948576i	$-0.0302396\pi$
$68$	−0.269499	+	1.00578i	−0.0326815	+	0.121969i
$69$	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	$-0.612239\pi$
$72$	−3.19899	+	2.59049i	−0.377005	+	0.305293i
$73$	0.182500	−	3.48231i	0.0213601	−	0.407574i	−0.966935	−	0.255022i	$-0.917917\pi$
$73$	0.182500	−	3.48231i	0.0213601	−	0.407574i	0.988295	−	0.152552i	$-0.0487493\pi$
$74$	−6.74848	−	3.89623i	−0.784494	−	0.452928i
$75$		0			0
$76$		−	7.64897i		−	0.877397i
$77$	8.40955	+	7.35294i	0.958358	+	0.837945i
$78$	−0.376077	+	0.0595648i	−0.0425823	+	0.00674438i
$79$	−14.0514	−	1.47686i	−1.58090	−	0.166159i	−0.727016	−	0.686621i	$-0.759093\pi$
$79$	−14.0514	−	1.47686i	−1.58090	−	0.166159i	−0.853885	+	0.520462i	$0.825760\pi$
$80$		0			0
$81$	0.820700	+	7.80844i	0.0911889	+	0.867605i
$82$	10.3608	+	2.77617i	1.14416	+	0.306577i
$83$	3.01586	+	0.477665i	0.331033	+	0.0524305i	0.319739	−	0.947506i	$-0.396405\pi$
$83$	3.01586	+	0.477665i	0.331033	+	0.0524305i	0.0112944	+	0.999936i	$0.496405\pi$
$84$	0.194837	+	1.12389i	0.0212584	+	0.122627i
$85$		0			0
$86$	−9.23428	+	1.96281i	−0.995758	+	0.211655i
$87$	0.511786	−	0.332358i	0.0548692	−	0.0356325i
$88$	−5.07780	+	3.29756i	−0.541296	+	0.351522i
$89$	16.6785	−	3.54513i	1.76792	−	0.375783i	0.794944	−	0.606683i	$-0.207500\pi$
$89$	16.6785	−	3.54513i	1.76792	−	0.375783i	0.972977	+	0.230900i	$0.0741671\pi$
$90$		0			0
$91$	−0.539673	+	1.46956i	−0.0565731	+	0.154051i
$92$	−1.91756	−	0.303712i	−0.199920	−	0.0316642i
$93$	−3.12743	−	0.837993i	−0.324300	−	0.0868958i
$94$	−1.80189	−	17.1438i	−0.185851	−	1.76825i
$95$		0			0
$96$	−2.14840	−	0.225806i	−0.219270	−	0.0230462i
$97$	−11.5748	+	1.83327i	−1.17524	+	0.186140i	−0.713358	−	0.700800i	$-0.752826\pi$
$97$	−11.5748	+	1.83327i	−1.17524	+	0.186140i	−0.461884	+	0.886940i	$0.652826\pi$
$98$	11.8126	+	4.14368i	1.19326	+	0.418575i
$99$			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	$0.595700\pi$
$102$	0.0292687	−	0.558480i	0.00289803	−	0.0552978i
$103$	1.62888	−	1.31905i	0.160499	−	0.129969i	−0.545707	−	0.837976i	$-0.683739\pi$
$103$	1.62888	−	1.31905i	0.160499	−	0.129969i	0.706206	+	0.708007i	$0.250405\pi$
$104$	−0.686462	−	0.498744i	−0.0673131	−	0.0489058i
$105$		0			0
$106$	−12.2697	+	8.91446i	−1.19174	+	0.865849i
$107$	1.06590	−	3.97800i	0.103045	−	0.384568i	−0.895071	−	0.445923i	$-0.852876\pi$
$107$	1.06590	−	3.97800i	0.103045	−	0.384568i	0.998116	+	0.0613552i	$0.0195422\pi$
$108$	−1.59277	+	1.96691i	−0.153265	+	0.189266i
$109$	2.48271	−	11.6802i	0.237801	−	1.11876i	−0.683512	−	0.729940i	$-0.739548\pi$
$109$	2.48271	−	11.6802i	0.237801	−	1.11876i	0.921312	−	0.388824i	$-0.127119\pi$
$110$		0			0
$111$	1.49119	+	0.484517i	0.141537	+	0.0459883i
$112$	−7.55906	+	10.7296i	−0.714264	+	1.01385i
$113$	3.18186	+	1.62124i	0.299324	+	0.152513i	0.597202	−	0.802091i	$-0.296279\pi$
$113$	3.18186	+	1.62124i	0.299324	+	0.152513i	−0.297878	+	0.954604i	$0.596279\pi$
$114$	0.854131	+	4.01837i	0.0799967	+	0.376355i
$115$		0			0
$116$	−1.98750	−	0.422456i	−0.184535	−	0.0392241i
$117$	−1.58570	+	0.608693i	−0.146598	+	0.0562737i
$118$	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
$122$	−0.791555	+	2.06207i	−0.0716640	+	0.186691i
$123$	−2.15529	−	0.112954i	−0.194336	−	0.0101847i
$124$	5.39038	+	9.33642i	0.484071	+	0.838435i
$125$		0			0
$126$	5.05155	+	12.6074i	0.450028	+	1.12316i
$127$	2.93160	−	1.49373i	0.260138	−	0.132547i	−0.319058	−	0.947735i	$-0.603367\pi$
$127$	2.93160	−	1.49373i	0.260138	−	0.132547i	0.579196	+	0.815188i	$0.303367\pi$
$128$	−6.63931	−	8.19887i	−0.586838	−	0.724685i
$129$	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
$133$	16.1383	+	4.98485i	1.39937	+	0.432241i
$134$	19.4960	−	6.33462i	1.68419	−	0.547228i
$135$		0			0
$136$	0.926145	−	0.833904i	0.0794162	−	0.0715067i
$137$	−0.549457	−	0.846089i	−0.0469433	−	0.0722863i	0.814420	−	0.580276i	$-0.197055\pi$
$137$	−0.549457	−	0.846089i	−0.0469433	−	0.0722863i	−0.861363	+	0.507990i	$0.830389\pi$
$138$	1.04130	−	0.0545724i	0.0886416	−	0.00464551i
$139$	−3.10037	+	9.54195i	−0.262970	+	0.809337i	0.729185	+	0.684317i	$0.239900\pi$
$139$	−3.10037	+	9.54195i	−0.262970	+	0.809337i	−0.992154	+	0.125020i	$0.960100\pi$
$140$		0			0
$141$	1.07183	+	3.29877i	0.0902647	+	0.277806i
$142$	−8.97522	−	23.3812i	−0.753183	−	1.96211i
$143$	−2.41316	+	0.646606i	−0.201799	+	0.0540719i
$144$	−14.1619	+	1.48848i	−1.18016	+	0.124040i
$145$		0			0
$146$	3.66548	−	5.04510i	0.303357	−	0.417535i
$147$	−2.49824	−	0.321362i	−0.206051	−	0.0265055i
$148$	−2.37017	−	4.65171i	−0.194827	−	0.382369i
$149$	−6.19698	+	3.57783i	−0.507676	+	0.293107i	−0.731878	−	0.681436i	$-0.761356\pi$
$149$	−6.19698	+	3.57783i	−0.507676	+	0.293107i	0.224202	+	0.974543i	$0.428023\pi$
$150$		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	$-0.303553\pi$
$152$	−4.98605	+	7.67784i	−0.404422	+	0.622755i
$153$	−0.390255	−	2.46397i	−0.0315502	−	0.199200i
$154$	5.45110	+	19.2190i	0.439262	+	1.54871i
$155$		0			0
$156$	−0.233047	−	0.103759i	−0.0186587	−	0.00830740i
$157$	5.19791	+	19.3989i	0.414838	+	1.54820i	0.785159	+	0.619294i	$0.212581\pi$
$157$	5.19791	+	19.3989i	0.414838	+	1.54820i	−0.370321	+	0.928904i	$0.620752\pi$
$158$	−19.6361	−	15.9010i	−1.56216	−	1.26501i
$159$	2.04192	−	2.26778i	0.161935	−	0.179847i
$160$		0			0
$161$	1.89047	−	3.84788i	0.148990	−	0.303255i
$162$	−6.37449	+	12.5106i	−0.500827	+	0.982928i
$163$	0.844482	+	16.1137i	0.0661449	+	1.26212i	0.807039	+	0.590498i	$0.201069\pi$
$163$	0.844482	+	16.1137i	0.0661449	+	1.26212i	−0.740894	+	0.671622i	$0.765598\pi$
$164$	4.80859	+	5.34048i	0.375488	+	0.417021i
$165$		0			0
$166$	4.05801	+	3.65384i	0.314962	+	0.283593i
$167$	1.58959	−	10.0363i	0.123006	−	0.776630i	−0.846649	−	0.532152i	$-0.821383\pi$
$167$	1.58959	−	10.0363i	0.123006	−	0.776630i	0.969655	−	0.244478i	$-0.0786165\pi$
$168$	0.537046	−	1.25514i	0.0414340	−	0.0968361i
$169$	7.43541	+	10.2340i	0.571955	+	0.787228i
$170$		0			0
$171$	7.45369	+	16.7413i	0.569998	+	1.28024i
$172$	−5.90483	−	2.26665i	−0.450239	−	0.172831i
$173$	−2.81344	−	1.82707i	−0.213902	−	0.138909i	0.433241	−	0.901278i	$-0.357370\pi$
$173$	−2.81344	−	1.82707i	−0.213902	−	0.138909i	−0.647143	+	0.762368i	$0.724036\pi$
$174$	1.09130			0.0827315
$175$		0			0
$176$	−20.9450			−1.57879
$177$	−2.04484	−	1.32794i	−0.153700	−	0.0998138i
$178$	28.4678	+	10.9278i	2.13375	+	0.819070i
$179$	1.18133	+	2.65332i	0.0882971	+	0.198319i	0.952297	−	0.305174i	$-0.0987147\pi$
$179$	1.18133	+	2.65332i	0.0882971	+	0.198319i	−0.863999	+	0.503493i	$0.832048\pi$
$180$		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	$0.894974\pi$
$182$	−2.24076	+	1.67843i	−0.166096	+	0.124414i
$183$	0.0695242	−	0.438958i	0.00513937	−	0.0324487i
$184$	1.72682	+	1.55484i	0.127303	+	0.114624i
$185$		0			0
$186$	−3.87439	−	4.30295i	−0.284084	−	0.315507i
$187$	−0.192039	−	3.66433i	−0.0140433	−	0.267962i
$188$	5.24321	−	10.2904i	0.382401	−	0.750504i
$189$	−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	$0.409830\pi$
$192$	−0.227821	−	0.184486i	−0.0164416	−	0.0133141i
$193$	0.160877	+	0.600403i	0.0115802	+	0.0432179i	0.971474	−	0.237145i	$-0.0762117\pi$
$193$	0.160877	+	0.600403i	0.0115802	+	0.0432179i	−0.959894	+	0.280363i	$0.909545\pi$
$194$	−19.1457	−	8.52422i	−1.37458	−	0.612004i
$195$		0			0
$196$	5.12536	+	6.63863i	0.366097	+	0.474188i
$197$	−3.81776	−	24.1044i	−0.272004	−	1.71736i	−0.624052	−	0.781383i	$-0.714515\pi$
$197$	−3.81776	−	24.1044i	−0.272004	−	1.71736i	0.352048	−	0.935982i	$-0.385485\pi$
$198$	−11.8046	+	18.1775i	−0.838918	+	1.29182i
$199$	4.29215	−	7.43422i	0.304262	−	0.526998i	−0.672835	−	0.739793i	$-0.734923\pi$
$199$	4.29215	−	7.43422i	0.304262	−	0.526998i	0.977097	+	0.212795i	$0.0682568\pi$
$200$		0			0
$201$	−3.57207	+	2.06234i	−0.251955	+	0.145466i
$202$	3.60817	+	7.08143i	0.253870	+	0.498248i
$203$	2.18658	−	3.91805i	0.153468	−	0.274993i
$204$	0.220231	−	0.303123i	0.0154193	−	0.0212228i
$205$		0			0
$206$	3.72778	−	0.391806i	0.259727	−	0.0272984i
$207$	4.49292	−	1.20387i	0.312280	−	0.0836751i
$208$	−1.05192	−	2.74036i	−0.0729378	−	0.190010i
$209$	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	$0.0543046\pi$
$212$	−10.1470	+	0.531782i	−0.696899	+	0.0365229i
$213$	2.74458	+	4.22628i	0.188056	+	0.289580i
$214$	5.47322	−	4.92811i	0.374141	−	0.336878i
$215$		0			0
$216$	2.88093	−	0.936071i	0.196023	−	0.0636916i
$217$	−23.2115	+	5.28844i	−1.57570	+	0.359003i
$218$	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
$222$	1.76460	+	2.17910i	0.118432	+	0.146252i
$223$	11.3328	−	5.77436i	0.758902	−	0.386680i	−0.0313132	−	0.999510i	$-0.509969\pi$
$223$	11.3328	−	5.77436i	0.758902	−	0.386680i	0.790215	+	0.612830i	$0.209969\pi$
$224$	−14.7441	+	5.90768i	−0.985134	+	0.394723i
$225$		0			0
$226$	3.19314	+	5.53069i	0.212405	+	0.367896i
$227$	−6.99268	−	0.366471i	−0.464120	−	0.0243235i	−0.181157	−	0.983454i	$-0.557984\pi$
$227$	−6.99268	−	0.366471i	−0.464120	−	0.0243235i	−0.282963	+	0.959131i	$0.591318\pi$
$228$	−0.986352	+	2.56954i	−0.0653228	+	0.170172i
$229$	−1.54623	+	14.7114i	−0.102178	+	0.972159i	0.816552	+	0.577272i	$0.195883\pi$
$229$	−1.54623	+	14.7114i	−0.102178	+	0.972159i	−0.918730	+	0.394887i	$0.870784\pi$
$230$		0			0
$231$	−1.87686	−	3.55452i	−0.123488	−	0.233870i
$232$	1.71962	+	1.71962i	0.112899	+	0.112899i
$233$	2.38168	−	0.914241i	0.156029	−	0.0598939i	−0.279100	−	0.960262i	$-0.590036\pi$
$233$	2.38168	−	0.914241i	0.156029	−	0.0598939i	0.435129	+	0.900368i	$0.356703\pi$
$234$	−2.97113	−	0.631534i	−0.194229	−	0.0412847i
$235$		0			0
$236$	1.68793	+	7.94106i	0.109875	+	0.516919i
$237$	4.52986	+	2.30808i	0.294246	+	0.149926i
$238$	−1.72706	−	3.73172i	−0.111949	−	0.241892i
$239$	−0.945911	−	0.307345i	−0.0611859	−	0.0198805i	0.278264	−	0.960505i	$-0.410241\pi$
$239$	−0.945911	−	0.307345i	−0.0611859	−	0.0198805i	−0.339450	+	0.940624i	$0.610241\pi$
$240$		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	$0.0114093\pi$
$242$	−7.68291	+	9.48761i	−0.493876	+	0.609886i
$243$	2.37141	−	8.85021i	0.152126	−	0.567741i
$244$	−1.19720	+	0.869816i	−0.0766428	+	0.0556843i
$245$		0			0
$246$	−3.12253	−	2.26865i	−0.199086	−	0.144644i
$247$	−2.93568	+	2.37727i	−0.186793	+	0.151262i
$248$	0.675296	−	12.8854i	0.0428814	−	0.818225i
$249$	−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	$-0.162784\pi$
$252$	−1.76197	+	8.92723i	−0.110994	+	0.562363i
$253$	6.75739	−	1.07026i	0.424833	−	0.0672870i
$254$	5.85177	+	0.615046i	0.367173	+	0.0385914i
$255$		0			0
$256$	−2.14244	−	20.3840i	−0.133903	−	1.27400i
$257$	−15.0766	−	4.03975i	−0.940449	−	0.251993i	−0.244145	−	0.969739i	$-0.578507\pi$
$257$	−15.0766	−	4.03975i	−0.940449	−	0.251993i	−0.696305	+	0.717746i	$0.745174\pi$
$258$	3.35520	+	0.531412i	0.208886	+	0.0330842i
$259$	11.3591	−	1.96921i	0.705823	−	0.122361i
$260$		0			0
$261$	4.76170	−	1.01213i	0.294742	−	0.0626494i
$262$	−5.53122	+	3.59202i	−0.341720	+	0.221916i
$263$	−3.44715	+	2.23861i	−0.212561	+	0.138038i	−0.646528	−	0.762890i	$-0.723780\pi$
$263$	−3.44715	+	2.23861i	−0.212561	+	0.138038i	0.433968	+	0.900928i	$0.357113\pi$
$264$	2.13103	−	0.452964i	0.131156	−	0.0278780i
$265$		0			0
$266$	19.3494	+	23.1951i	1.18639	+	1.42218i
$267$	−6.06001	−	0.959811i	−0.370866	−	0.0587395i
$268$	13.2660	+	3.55461i	0.810349	+	0.217132i
$269$	−1.23301	−	11.7313i	−0.0751780	−	0.715271i	−0.965582	−	0.260099i	$-0.916245\pi$
$269$	−1.23301	−	11.7313i	−0.0751780	−	0.715271i	0.890404	−	0.455171i	$-0.150422\pi$
$270$		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	$0.598912\pi$
$272$	4.25816	−	0.674426i	0.258189	−	0.0408931i
$273$	0.370796	−	0.424079i	0.0224416	−	0.0256664i
$274$		−	1.80415i		−	0.108993i
$275$		0			0
$276$	0.605007	+	0.349301i	0.0364171	+	0.0210254i
$277$	1.59392	−	30.4139i	0.0957696	−	1.82739i	−0.355130	−	0.934817i	$-0.615563\pi$
$277$	1.59392	−	30.4139i	0.0957696	−	1.82739i	0.450899	−	0.892575i	$-0.351103\pi$
$278$	−13.9438	+	11.2915i	−0.836294	+	0.677218i
$279$	−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	$0.255473\pi$
$282$	−1.60542	+	5.99152i	−0.0956016	+	0.356790i
$283$	−3.52471	+	4.35265i	−0.209522	+	0.258738i	−0.871064	−	0.491170i	$-0.836569\pi$
$283$	−3.52471	+	4.35265i	−0.209522	+	0.258738i	0.661541	+	0.749909i	$0.269903\pi$
$284$	3.48861	−	16.4126i	0.207011	−	0.973908i
$285$		0			0
$286$	−4.24911	−	1.38062i	−0.251255	−	0.0816377i
$287$	−14.4015	+	6.66509i	−0.850093	+	0.393428i
$288$	−15.3547	−	7.82364i	−0.904787	−	0.461012i
$289$	−3.37747	−	15.8897i	−0.198674	−	0.934690i
$290$		0			0
$291$	4.12475	+	0.876742i	0.241797	+	0.0513956i
$292$	3.90050	−	1.49726i	0.228260	−	0.0876207i
$293$	−7.38400	−	7.38400i	−0.431378	−	0.431378i	0.457719	−	0.889097i	$-0.348667\pi$
$293$	−7.38400	−	7.38400i	−0.431378	−	0.431378i	−0.889097	+	0.457719i	$0.848667\pi$
$294$	−3.43391	−	2.91526i	−0.200270	−	0.170022i
$295$		0			0
$296$	−0.653147	+	6.21428i	−0.0379634	+	0.361198i
$297$	3.19625	−	8.32650i	0.185465	−	0.483153i
$298$	−12.7792	−	0.669727i	−0.740277	−	0.0387962i
$299$	0.479406	+	0.830355i	0.0277247	+	0.0480207i
$300$		0			0
$301$	8.63053	−	10.9812i	0.497456	−	0.632948i
$302$	38.9892	−	19.8660i	2.24358	−	1.14316i
$303$	−1.00638	−	1.24278i	−0.0578152	−	0.0713959i
$304$	−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	0.115702	−	0.993284i	$-0.463088\pi$
$307$	19.4310	−	19.4310i	1.10899	−	1.10899i	0.993284	−	0.115702i	$-0.0369117\pi$
$308$	−3.94998	+	12.7880i	−0.225071	+	0.728661i
$309$	−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	$0.406520\pi$
$312$	0.166290	+	0.256065i	0.00941434	+	0.0144968i
$313$	30.4559	−	1.59613i	1.72147	−	0.0902185i	0.834199	−	0.551464i	$-0.185931\pi$
$313$	30.4559	−	1.59613i	1.72147	−	0.0902185i	0.887272	+	0.461246i	$0.152597\pi$
$314$	−11.0985	+	34.1576i	−0.626323	+	1.92762i
$315$		0			0
$316$	−5.23108	−	16.0996i	−0.294271	−	0.905674i
$317$	9.06260	+	23.6089i	0.509006	+	1.32601i	0.911769	+	0.410703i	$0.134717\pi$
$317$	9.06260	+	23.6089i	0.509006	+	1.32601i	−0.402763	+	0.915304i	$0.631950\pi$
$318$	5.27133	−	1.41245i	0.295601	−	0.0792061i
$319$	7.12108	−	0.748456i	0.398704	−	0.0419055i
$320$		0			0
$321$	−0.871043	+	1.19889i	−0.0486169	+	0.0669154i
$322$	6.58319	−	3.92982i	0.366867	−	0.219000i
$323$	−2.51883	−	4.94349i	−0.140152	−	0.275063i
$324$	−8.14678	+	4.70355i	−0.452599	+	0.261308i
$325$		0			0
$326$	−14.4281	+	24.9902i	−0.799097	+	1.38408i
$327$	−2.34022	+	3.60362i	−0.129414	+	0.199280i
$328$	−1.34550	−	8.49516i	−0.0742928	−	0.469066i
$329$	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	$0.691567\pi$
$332$	0.946875	+	3.53378i	0.0519665	+	0.193942i
$333$	9.72053	+	7.87153i	0.532682	+	0.431357i
$334$	12.1594	−	13.5044i	0.665332	−	0.738926i
$335$		0			0
$336$	3.92293	−	2.62965i	0.214014	−	0.143459i
$337$	−2.24236	+	4.40088i	−0.122149	+	0.239731i	−0.943982	−	0.329998i	$-0.892952\pi$
$337$	−2.24236	+	4.40088i	−0.122149	+	0.239731i	0.821833	+	0.569729i	$0.192952\pi$
$338$	1.18395	+	22.5912i	0.0643986	+	1.22880i
$339$	−0.859827	−	0.954934i	−0.0466994	−	0.0518649i
$340$		0			0
$341$	−28.2327	−	25.4208i	−1.52889	−	1.37661i
$342$	−5.12671	+	32.3688i	−0.277221	+	1.75030i
$343$	−17.3468	+	6.48744i	−0.936642	+	0.350289i
$344$	4.44958	+	6.12432i	0.239905	+	0.330201i
$345$		0			0
$346$	−2.44010	−	5.48056i	−0.131181	−	0.294637i
$347$	24.0377	+	9.22720i	1.29041	+	0.495342i	0.904216	−	0.427075i	$-0.140456\pi$
$347$	24.0377	+	9.22720i	1.29041	+	0.495342i	0.386194	+	0.922417i	$0.373789\pi$
$348$	0.613188	+	0.398209i	0.0328704	+	0.0213463i
$349$	23.8148			1.27478			0.637389	−	0.770543i	$-0.280015\pi$
$349$	23.8148			1.27478			0.637389	+	0.770543i	$0.280015\pi$
$350$		0			0
$351$	1.24993			0.0667163
$352$	−21.2582	−	13.8053i	−1.13307	−	0.735823i
$353$	−29.5626	−	11.3480i	−1.57346	−	0.603995i	−0.593792	−	0.804619i	$-0.702370\pi$
$353$	−29.5626	−	11.3480i	−1.57346	−	0.603995i	−0.979668	+	0.200624i	$0.935703\pi$
$354$	−1.77350	−	3.98334i	−0.0942603	−	0.211712i
$355$		0			0
$356$	12.0082	+	16.5279i	0.636433	+	0.875975i
$357$	0.496024	+	0.662205i	0.0262524	+	0.0350476i
$358$	−0.812532	+	5.13013i	−0.0429437	+	0.271136i
$359$	−9.42711	−	8.48821i	−0.497544	−	0.447990i	0.381753	−	0.924264i	$-0.375320\pi$
$359$	−9.42711	−	8.48821i	−0.497544	−	0.447990i	−0.879297	+	0.476274i	$0.841987\pi$
$360$		0			0
$361$	14.5578	+	16.1681i	0.766201	+	0.850953i
$362$	−0.740304	−	14.1258i	−0.0389095	−	0.742437i
$363$	1.11520	−	2.18870i	0.0585328	−	0.114877i
$364$	−1.87150	+	0.125453i	−0.0980932	+	0.00657552i
$365$		0			0
$366$	0.531817	−	0.590643i	0.0277985	−	0.0308734i
$367$	6.10039	+	4.94000i	0.318438	+	0.257866i	0.775190	−	0.631728i	$-0.217654\pi$
$367$	6.10039	+	4.94000i	0.318438	+	0.257866i	−0.456752	+	0.889594i	$0.650987\pi$
$368$	2.08050	+	7.76452i	0.108453	+	0.404754i
$369$	−15.7287	−	7.00286i	−0.818802	−	0.364554i
$370$		0			0
$371$	5.49083	−	21.7554i	0.285070	−	1.12948i
$372$	−0.606851	−	3.83151i	−0.0314638	−	0.198654i
$373$	1.98581	−	3.05789i	0.102822	−	0.158331i	−0.783515	−	0.621373i	$-0.786575\pi$
$373$	1.98581	−	3.05789i	0.102822	−	0.158331i	0.886337	+	0.463042i	$0.153242\pi$
$374$	3.28101	−	5.68288i	0.169657	−	0.293855i
$375$		0			0
$376$	−11.9709	+	6.91139i	−0.617351	+	0.356428i
$377$	0.455567	+	0.894102i	0.0234629	+	0.0460486i
$378$	−0.145652	−	9.99373i	−0.00749155	−	0.514022i
$379$	12.1944	−	16.7841i	0.626384	−	0.862143i	−0.371414	−	0.928467i	$-0.621127\pi$
$379$	12.1944	−	16.7841i	0.626384	−	0.862143i	0.997798	+	0.0663239i	$0.0211271\pi$
$380$		0			0
$381$	−1.17744	+	0.123754i	−0.0603221	+	0.00634010i
$382$	−25.1385	+	6.73584i	−1.28620	+	0.344636i
$383$	−6.96275	−	18.1386i	−0.355780	−	0.926838i	−0.988331	−	0.152320i	$-0.951326\pi$
$383$	−6.96275	−	18.1386i	−0.355780	−	0.926838i	0.632551	−	0.774518i	$-0.282008\pi$
$384$	1.17310	+	3.61042i	0.0598643	+	0.184243i
$385$		0			0
$386$	−0.343502	+	1.05719i	−0.0174838	+	0.0538096i
$387$	15.1327	−	0.793070i	0.769237	−	0.0403140i
$388$	−7.64729	−	11.7758i	−0.388232	−	0.597825i
$389$	11.3701	−	10.2377i	0.576487	−	0.519072i	−0.328503	−	0.944503i	$-0.606544\pi$
$389$	11.3701	−	10.2377i	0.576487	−	0.519072i	0.904991	+	0.425431i	$0.139878\pi$
$390$		0			0
$391$	−1.33933	+	0.435173i	−0.0677326	+	0.0220077i
$392$	−0.817259	−	10.0047i	−0.0412778	−	0.505313i
$393$	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
$397$	18.3983	+	22.7200i	0.923382	+	1.14028i	0.989796	+	0.142489i	$0.0455107\pi$
$397$	18.3983	+	22.7200i	0.923382	+	1.14028i	−0.0664145	+	0.997792i	$0.521156\pi$
$398$	13.6784	−	6.96947i	0.685634	−	0.349348i
$399$	−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	$0.649502\pi$
$402$	−7.36619	−	0.386045i	−0.367392	−	0.0192542i
$403$	1.90802	−	4.97055i	0.0950451	−	0.247601i
$404$	−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
$408$	−0.418656	+	0.160707i	−0.0207265	+	0.00795617i
$409$	30.0548	+	6.38835i	1.48611	+	0.315883i	0.878267	−	0.478170i	$-0.158700\pi$
$409$	30.0548	+	6.38835i	1.48611	+	0.315883i	0.607848	+	0.794054i	$0.292033\pi$
$410$		0			0
$411$	0.0754751	+	0.355082i	0.00372291	+	0.0175149i
$412$	2.23756	+	1.14009i	0.110237	+	0.0561683i
$413$	−17.8546	−	1.61390i	−0.878569	−	0.0794151i
$414$	7.91115	+	2.57049i	0.388812	+	0.126333i
$415$		0			0
$416$	0.738565	−	3.47468i	0.0362111	−	0.170360i
$417$	2.27197	−	2.80565i	0.111259	−	0.137393i
$418$	−12.4760	+	46.5612i	−0.610223	+	2.27738i
$419$	8.60424	−	6.25134i	0.420345	−	0.305398i	−0.357432	−	0.933939i	$-0.616348\pi$
$419$	8.60424	−	6.25134i	0.420345	−	0.305398i	0.777776	+	0.628541i	$0.216348\pi$
$420$		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	$0.525875\pi$
$422$	5.77633	−	4.67758i	0.281187	−	0.227701i
$423$	−1.44813	+	27.6319i	−0.0704103	+	1.34351i
$424$	10.5319	+	6.08062i	0.511476	+	0.295301i
$425$		0			0
$426$			9.01188i			0.436627i
$427$	−1.05498	−	3.09280i	−0.0510541	−	0.149671i
$428$	4.87356	−	0.771896i	0.235572	−	0.0373110i
$429$	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	$0.907570\pi$
$432$	10.1220	+	2.71219i	0.486996	+	0.130490i
$433$	20.2759	+	3.21139i	0.974399	+	0.154330i	0.623278	−	0.782000i	$-0.285801\pi$
$433$	20.2759	+	3.21139i	0.974399	+	0.154330i	0.351121	+	0.936330i	$0.385801\pi$
$434$	−39.9641	−	14.6762i	−1.91834	−	0.704481i
$435$		0			0
$436$	13.9945	−	2.97462i	0.670215	−	0.142458i
$437$	8.67588	−	5.63418i	0.415023	−	0.269519i
$438$	−1.88193	+	1.22214i	−0.0899220	+	0.0583961i
$439$	12.2397	−	2.60162i	0.584168	−	0.124169i	0.0936579	−	0.995604i	$-0.470144\pi$
$439$	12.2397	−	2.60162i	0.584168	−	0.124169i	0.490510	+	0.871436i	$0.336811\pi$
$440$		0			0
$441$	−17.6870	−	9.53543i	−0.842238	−	0.454068i
$442$	0.908306	+	0.143862i	0.0432037	+	0.00684280i
$443$	−33.8090	−	9.05910i	−1.60632	−	0.430411i	−0.659373	−	0.751816i	$-0.729178\pi$
$443$	−33.8090	−	9.05910i	−1.60632	−	0.430411i	−0.946942	+	0.321405i	$0.895845\pi$
$444$	0.196366	+	1.86830i	0.00931912	+	0.0886655i
$445$		0			0
$446$	22.6214	+	2.37761i	1.07115	+	0.112583i
$447$	2.54313	−	0.402793i	0.120286	−	0.0190514i
$448$	−2.11466	−	0.417373i	−0.0999085	−	0.0197190i
$449$		−	4.28525i		−	0.202233i	−0.994875	−	0.101117i	$-0.967758\pi$
$449$		−	4.28525i		−	0.202233i	0.994875	−	0.101117i	$-0.0322416\pi$
$450$		0			0
$451$	−21.9314	−	12.6621i	−1.03271	−	0.596235i
$452$	−0.223927	+	4.27278i	−0.0105326	+	0.200974i
$453$	−6.84254	+	5.54098i	−0.321491	+	0.260338i
$454$	−10.1308	−	7.36048i	−0.475464	−	0.345445i
$455$		0			0
$456$	2.66505	−	1.93627i	0.124802	−	0.0906742i
$457$	4.57736	−	17.0829i	0.214120	−	0.799107i	−0.772355	−	0.635192i	$-0.780921\pi$
$457$	4.57736	−	17.0829i	0.214120	−	0.799107i	0.986474	−	0.163915i	$-0.0524122\pi$
$458$	−16.6479	+	20.5585i	−0.777908	+	0.960636i
$459$	−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	$0.402006\pi$
$462$	0.647130	−	7.15920i	0.0301072	−	0.333076i
$463$	−24.3244	−	12.3939i	−1.13045	−	0.575994i	−0.214277	−	0.976773i	$-0.568740\pi$
$463$	−24.3244	−	12.3939i	−1.13045	−	0.575994i	−0.916175	+	0.400779i	$0.868740\pi$
$464$	1.74913	+	8.22902i	0.0812015	+	0.382023i
$465$		0			0
$466$	4.46256	+	0.948547i	0.206724	+	0.0439406i
$467$	6.60852	−	2.53677i	0.305806	−	0.117388i	−0.200626	−	0.979668i	$-0.564298\pi$
$467$	6.60852	−	2.53677i	0.305806	−	0.117388i	0.506432	+	0.862280i	$0.330964\pi$
$468$	−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
$472$	3.48215	−	9.07132i	0.160279	−	0.417541i
$473$	22.2582	+	1.16650i	1.02343	+	0.0536358i
$474$	4.54592	+	7.87377i	0.208801	+	0.361654i
$475$		0			0
$476$	0.391267	−	2.72700i	0.0179337	−	0.124992i
$477$	21.6905	−	11.0519i	0.993140	−	0.506030i
$478$	−1.11935	−	1.38228i	−0.0511977	−	0.0632239i
$479$	−34.5054	+	15.3628i	−1.57659	+	0.701943i	−0.993852	−	0.110717i	$-0.964685\pi$
$479$	−34.5054	+	15.3628i	−1.57659	+	0.701943i	−0.582738	+	0.812660i	$0.698019\pi$
$480$		0			0
$481$	−1.04869	+	2.35540i	−0.0478163	+	0.107397i
$482$	6.78154	−	6.78154i	0.308891	−	0.308891i
$483$	−1.13126	+	1.04885i	−0.0514743	+	0.0477241i
$484$	−7.77889	+	2.52751i	−0.353586	+	0.114887i
$485$		0			0
$486$	12.1768	−	10.9640i	0.552349	−	0.497337i
$487$	−7.15837	−	11.0229i	−0.324377	−	0.499496i	0.638433	−	0.769678i	$-0.279583\pi$
$487$	−7.15837	−	11.0229i	−0.324377	−	0.499496i	−0.962809	+	0.270181i	$0.912916\pi$
$488$	1.76871	−	0.0926944i	0.0800660	−	0.00419608i
$489$	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	$-0.276743\pi$
$492$	−0.926693	−	2.41412i	−0.0417785	−	0.108837i
$493$	−1.42363	+	0.381460i	−0.0641170	+	0.0171801i
$494$	−6.71845	+	0.706137i	−0.302277	+	0.0317706i
$495$		0			0
$496$	26.2367	−	36.1118i	1.17806	−	1.62147i
$497$	32.3549	+	18.0566i	1.45132	+	0.809950i
$498$	−0.892043	−	1.75073i	−0.0399734	−	0.0784522i
$499$	7.78986	−	4.49748i	0.348722	−	0.201335i	−0.315400	−	0.948959i	$-0.602139\pi$
$499$	7.78986	−	4.49748i	0.348722	−	0.201335i	0.664122	+	0.747624i	$0.268805\pi$
$500$		0			0
$501$	−1.82819	+	3.16652i	−0.0816777	+	0.141470i
$502$	15.1039	−	23.2579i	0.674119	−	1.03805i
$503$	5.63363	+	35.5693i	0.251191	+	1.58596i	0.714419	+	0.699718i	$0.246691\pi$
$503$	5.63363	+	35.5693i	0.251191	+	1.58596i	−0.463228	+	0.886239i	$0.653309\pi$
$504$	7.58792	−	7.81236i	0.337993	−	0.347990i
$505$		0			0
$506$	11.1773	+	4.97646i	0.496892	+	0.221231i
$507$	−1.17810	−	4.39673i	−0.0523213	−	0.195266i
$508$	3.06360	+	2.48086i	0.135925	+	0.110070i
$509$	−6.14407	+	6.82368i	−0.272331	+	0.302454i	−0.863761	−	0.503902i	$-0.831897\pi$
$509$	−6.14407	+	6.82368i	−0.272331	+	0.302454i	0.591429	+	0.806357i	$0.298564\pi$
$510$		0			0
$511$	0.617064	+	9.20532i	0.0272973	+	0.407220i
$512$	7.06144	−	13.8588i	0.312074	−	0.612480i
$513$	−0.705788	−	13.4672i	−0.0311613	−	0.594593i
$514$	−18.6774	−	20.7434i	−0.823827	−	0.914952i
$515$		0			0
$516$	1.69133	+	1.52288i	0.0744568	+	0.0670412i
$517$	−6.36667	+	40.1976i	−0.280006	+	1.76789i
$518$	18.9547	+	8.11030i	0.832822	+	0.356346i
$519$	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	$0.952808\pi$
$522$	8.12752	+	3.11986i	0.355732	+	0.136553i
$523$	−17.1195	−	11.1175i	−0.748582	−	0.486135i	0.113100	−	0.993584i	$-0.463922\pi$
$523$	−17.1195	−	11.1175i	−0.748582	−	0.486135i	−0.861682	+	0.507449i	$0.830589\pi$
$524$	−4.41862			−0.193028
$525$		0			0
$526$	−7.35051			−0.320498
$527$	6.55830	+	4.25901i	0.285684	+	0.185525i
$528$	7.03611	+	2.70091i	0.306208	+	0.117542i
$529$	8.28697	+	18.6128i	0.360303	+	0.809253i
$530$		0			0
$531$	−11.4327	−	15.7357i	−0.496136	−	0.682873i
$532$	2.40845	+	20.0934i	0.104419	+	0.871162i
$533$	0.555191	−	3.50534i	0.0240480	−	0.151833i
$534$	−8.15408	−	7.34197i	−0.352862	−	0.317718i
$535$		0			0
$536$	−10.9989	−	12.2156i	−0.475082	−	0.527632i
$537$	−0.0546965	−	1.04367i	−0.00236033	−	0.0450378i
$538$	9.57695	−	18.7958i	0.412892	−	0.810346i
$539$	−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	$0.357165\pi$
$542$	−9.36049	−	7.57997i	−0.402067	−	0.325588i
$543$	0.736644	+	2.74919i	0.0316124	+	0.117979i
$544$	4.76636	+	2.12212i	0.204356	+	0.0909851i
$545$		0			0
$546$	0.969180	−	0.274890i	0.0414771	−	0.0117642i
$547$	−0.468776	−	2.95974i	−0.0200434	−	0.126549i	0.975638	−	0.219388i	$-0.0704060\pi$
$547$	−0.468776	−	2.95974i	−0.0200434	−	0.126549i	−0.995681	+	0.0928385i	$0.970406\pi$
$548$	0.658323	−	1.01373i	0.0281222	−	0.0433043i
$549$	1.77270	−	3.07040i	0.0756568	−	0.131041i
$550$		0			0
$551$	9.37617	−	5.41333i	0.399438	−	0.230616i
$552$	−0.379595	−	0.744998i	−0.0161567	−	0.0317092i
$553$	37.3772	−	0.544749i	1.58944	−	0.0231651i
$554$	32.0136	−	44.0629i	1.36013	−	1.87205i
$555$		0			0
$556$	−11.9550	+	1.25652i	−0.507006	+	0.0532885i
$557$	−30.2559	+	8.10705i	−1.28198	+	0.343507i	−0.834610	−	0.550841i	$-0.814307\pi$
$557$	−30.2559	+	8.10705i	−1.28198	+	0.343507i	−0.447373	+	0.894347i	$0.647641\pi$
$558$	−16.5532	−	43.1226i	−0.700754	−	1.82553i
$559$	0.965254	+	2.97075i	0.0408259	+	0.125649i
$560$		0			0
$561$	−0.408011	+	1.25573i	−0.0172262	+	0.0530169i
$562$	8.34817	−	0.437509i	0.352146	−	0.0184552i
$563$	10.1341	+	15.6052i	0.427103	+	0.657680i	0.985064	−	0.172186i	$-0.0550831\pi$
$563$	10.1341	+	15.6052i	0.427103	+	0.657680i	−0.557962	+	0.829867i	$0.688416\pi$
$564$	−3.08833	+	2.78075i	−0.130042	+	0.117091i
$565$		0			0
$566$	−9.52590	+	3.09515i	−0.400404	+	0.130099i
$567$	−4.61460	−	20.2540i	−0.193795	−	0.850586i
$568$	−14.2005	+	14.2005i	−0.595838	+	0.595838i
$569$	0.637171	−	1.43111i	0.0267116	−	0.0599952i	−0.899697	−	0.436515i	$-0.856213\pi$
$569$	0.637171	−	1.43111i	0.0267116	−	0.0599952i	0.926409	+	0.376520i	$0.122879\pi$
$570$		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	$0.455904\pi$
$572$	−1.88374	−	2.32622i	−0.0787630	−	0.0972643i
$573$	4.66582	−	2.37736i	0.194918	−	0.0993154i
$574$	−28.0914	−	4.03053i	−1.17251	−	0.168231i
$575$		0			0
$576$	−1.16929	−	2.02527i	−0.0487204	−	0.0843861i
$577$	−9.27556	−	0.486112i	−0.386147	−	0.0202371i	−0.141725	−	0.989906i	$-0.545265\pi$
$577$	−9.27556	−	0.486112i	−0.386147	−	0.0202371i	−0.244422	+	0.969669i	$0.578598\pi$
$578$	10.4109	−	27.1214i	0.433038	−	1.12810i
$579$	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
$583$	33.4283	−	12.8319i	1.38446	−	0.531444i
$584$	−4.89123	−	1.03966i	−0.202400	−	0.0430216i
$585$		0			0
$586$	−3.88270	−	18.2667i	−0.160393	−	0.754589i
$587$	11.8830	+	6.05467i	0.490462	+	0.249903i	0.681688	−	0.731643i	$-0.261246\pi$
$587$	11.8830	+	6.05467i	0.490462	+	0.249903i	−0.191226	+	0.981546i	$0.561246\pi$
$588$	−0.865708	−	2.89106i	−0.0357012	−	0.119225i
$589$	−54.6321	−	17.7511i	−2.25108	−	0.731419i
$590$		0			0
$591$	−1.82581	+	8.58974i	−0.0751036	+	0.353335i
$592$	−13.6033	+	16.7987i	−0.559093	+	0.690423i
$593$	9.45404	−	35.2829i	0.388231	−	1.44890i	−0.444780	−	0.895640i	$-0.646718\pi$
$593$	9.45404	−	35.2829i	0.388231	−	1.44890i	0.833011	−	0.553257i	$-0.186615\pi$
$594$	12.9038	−	9.37515i	0.529449	−	0.384667i
$595$		0			0
$596$	−6.93605	−	5.03934i	−0.284112	−	0.206419i
$597$	−2.40053	+	1.94391i	−0.0982471	+	0.0795589i
$598$	−0.0897391	+	1.71232i	−0.00366970	+	0.0700221i
$599$	−0.214739	−	0.123980i	−0.00877399	−	0.00506567i	0.495607	−	0.868547i	$-0.334946\pi$
$599$	−0.214739	−	0.123980i	−0.00877399	−	0.00506567i	−0.504381	+	0.863481i	$0.668279\pi$
$600$		0			0
$601$			19.3484i			0.789237i	0.918845	+	0.394618i	$0.129123\pi$
$601$			19.3484i			0.789237i	−0.918845	+	0.394618i	$0.870877\pi$
$602$	23.6400	−	8.06381i	0.963492	−	0.328656i
$603$	−32.4991	+	5.14734i	−1.32346	+	0.209616i
$604$	29.1565	+	3.06447i	1.18636	+	0.124691i
$605$		0			0
$606$	−0.298934	−	2.84416i	−0.0121433	−	0.115536i
$607$	−34.8976	−	9.35079i	−1.41645	−	0.379537i	−0.532227	−	0.846601i	$-0.678645\pi$
$607$	−34.8976	−	9.35079i	−1.41645	−	0.379537i	−0.884223	+	0.467065i	$0.845312\pi$
$608$	−37.8546	−	5.99558i	−1.53521	−	0.243153i
$609$	−1.23979	+	1.03423i	−0.0502386	+	0.0419093i
$610$		0			0
$611$	−5.57903	+	1.18586i	−0.225703	+	0.0479747i
$612$	2.50676	−	1.62791i	0.101330	−	0.0658043i
$613$	13.0930	−	8.50267i	0.528820	−	0.343420i	−0.252453	−	0.967609i	$-0.581237\pi$
$613$	13.0930	−	8.50267i	0.528820	−	0.343420i	0.781273	+	0.624189i	$0.214571\pi$
$614$	48.0688	−	10.2173i	1.93990	−	0.412338i
$615$		0			0
$616$	12.3008	−	10.2614i	0.495614	−	0.413443i
$617$	−27.4606	−	4.34934i	−1.10552	−	0.175098i	−0.423120	−	0.906074i	$-0.639065\pi$
$617$	−27.4606	−	4.34934i	−1.10552	−	0.175098i	−0.682403	+	0.730976i	$0.739065\pi$
$618$	−1.30281	−	0.349086i	−0.0524065	−	0.0140423i
$619$	3.75824	+	35.7573i	0.151056	+	1.43721i	0.763048	+	0.646342i	$0.223702\pi$
$619$	3.75824	+	35.7573i	0.151056	+	1.43721i	−0.611992	+	0.790864i	$0.709631\pi$
$620$		0			0
$621$	−3.40420	−	0.357796i	−0.136606	−	0.0143579i
$622$	−26.4995	+	4.19711i	−1.06253	+	0.168289i
$623$	−42.6974	+	14.5645i	−1.71063	+	0.583513i
$624$			1.05622i			0.0422827i
$625$		0			0
$626$	47.2331	+	27.2700i	1.88781	+	1.08993i
$627$	0.507612	−	9.68582i	0.0202721	−	0.386814i
$628$	−18.7000	+	15.1429i	−0.746209	+	0.604268i
$629$	−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	$0.106520\pi$
$632$	−5.24385	+	19.5703i	−0.208589	+	0.778465i
$633$	−0.941179	+	1.16226i	−0.0374085	+	0.0461957i
$634$	−9.40266	+	44.2361i	−0.373427	+	1.75684i
$635$		0			0
$636$	3.47728	+	1.12984i	0.137883	+	0.0448009i
$637$	0.954970	−	4.03038i	0.0378373	−	0.159689i
$638$	11.4094	+	5.81335i	0.451701	+	0.230153i
$639$	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	$0.682303\pi$
$642$	−2.47412	+	0.949726i	−0.0976457	+	0.0374827i
$643$	−9.47610	−	9.47610i	−0.373701	−	0.373701i	0.495122	−	0.868823i	$-0.335123\pi$
$643$	−9.47610	−	9.47610i	−0.373701	−	0.373701i	−0.868823	+	0.495122i	$0.835123\pi$
$644$	5.13297	+	0.194050i	0.202267	+	0.00764662i
$645$		0			0
$646$	1.03714	−	9.86769i	0.0408056	−	0.388239i
$647$	−4.96466	+	12.9334i	−0.195181	+	0.508464i	−0.995888	−	0.0905921i	$-0.971124\pi$
$647$	−4.96466	+	12.9334i	−0.195181	+	0.508464i	0.800707	+	0.599056i	$0.204457\pi$
$648$	11.2436	+	0.589251i	0.441689	+	0.0231480i
$649$	−14.3045	−	24.7762i	−0.561502	−	0.972549i
$650$		0			0
$651$	8.47946	+	1.21662i	0.332336	+	0.0476832i
$652$	−17.2257	+	8.77692i	−0.674610	+	0.343731i
$653$	−23.0993	−	28.5253i	−0.903947	−	1.11628i	−0.992746	−	0.120231i	$-0.961636\pi$
$653$	−23.0993	−	28.5253i	−0.903947	−	1.11628i	0.0887994	−	0.996050i	$-0.471697\pi$
$654$	−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
$658$	10.1316	+	44.4686i	0.394970	+	1.73357i
$659$	−17.1826	+	5.58297i	−0.669340	+	0.217482i	−0.623922	−	0.781486i	$-0.714462\pi$
$659$	−17.1826	+	5.58297i	−0.669340	+	0.217482i	−0.0454175	+	0.998968i	$0.514462\pi$
$660$		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	$0.437830\pi$
$662$	−6.44759	−	9.92841i	−0.250593	−	0.385879i
$663$	−0.184786	+	0.00968421i	−0.00717648	+	0.000376103i
$664$	1.35308	−	4.16435i	0.0525097	−	0.161608i
$665$		0			0
$666$	6.91223	+	21.2737i	0.267843	+	0.824337i
$667$	−0.984806	−	2.56551i	−0.0381318	−	0.0993369i
$668$	11.7598	−	3.15104i	0.455002	−	0.121917i
$669$	−4.55167	+	0.478400i	−0.175978	+	0.0184960i
$670$		0			0
$671$	3.06518	−	4.21886i	0.118330	−	0.162867i
$672$	5.71484	−	0.0832901i	0.220455	−	0.00321299i
$673$	−23.2205	−	45.5727i	−0.895083	−	1.75670i	−0.597187	−	0.802102i	$-0.703715\pi$
$673$	−23.2205	−	45.5727i	−0.895083	−	1.75670i	−0.297896	−	0.954598i	$-0.596285\pi$
$674$	−7.64957	+	4.41648i	−0.294651	+	0.170117i
$675$		0			0
$676$	−7.57813	+	13.1257i	−0.291466	+	0.504835i
$677$	−21.5376	+	33.1651i	−0.827759	+	1.27464i	0.131275	+	0.991346i	$0.458093\pi$
$677$	−21.5376	+	33.1651i	−0.827759	+	1.27464i	−0.959034	+	0.283291i	$0.908574\pi$
$678$	−0.359485	−	2.26970i	−0.0138059	−	0.0871673i
$679$	29.8291	−	8.46047i	1.14474	−	0.324683i
$680$		0			0
$681$	2.30181	+	1.02483i	0.0882055	+	0.0392716i
$682$	−17.5842	−	65.6252i	−0.673335	−	2.51292i
$683$	8.47008	+	6.85894i	0.324099	+	0.262450i	0.777536	−	0.628838i	$-0.216469\pi$
$683$	8.47008	+	6.85894i	0.324099	+	0.262450i	−0.453438	+	0.891288i	$0.649802\pi$
$684$	−14.6918	+	16.3169i	−0.561755	+	0.623892i
$685$		0			0
$686$	−32.3359	−	7.16576i	−1.23459	−	0.273590i
$687$	2.41650	−	4.74265i	0.0921953	−	0.180943i
$688$	1.37056	+	26.1518i	0.0522520	+	0.997028i
$689$	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	$0.505202\pi$
$692$	0.628759	−	3.96983i	0.0239018	−	0.150910i
$693$	−3.81618	−	31.8381i	−0.144965	−	1.20943i
$694$	27.0650	+	37.2518i	1.02737	+	1.41406i
$695$		0			0
$696$	−0.355927	−	0.799424i	−0.0134914	−	0.0303021i
$697$	4.86641	+	1.86804i	0.184328	+	0.0707570i
$698$	35.7180	+	23.1955i	1.35195	+	0.877963i
$699$	−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	$0.398211\pi$
$702$	1.87467	+	1.21743i	0.0707549	+	0.0459488i
$703$	25.9702	+	9.96904i	0.979486	+	0.375989i
$704$	−1.39907	−	3.14236i	−0.0527293	−	0.118432i
$705$		0			0
$706$	−33.2858	−	45.8139i	−1.25273	−	1.72423i
$707$	−10.8102	−	4.62545i	−0.406560	−	0.173958i
$708$	0.456990	−	2.88532i	0.0171747	−	0.108437i
$709$	−13.9859	−	12.5930i	−0.525253	−	0.472940i	0.363327	−	0.931662i	$-0.381641\pi$
$709$	−13.9859	−	12.5930i	−0.525253	−	0.472940i	−0.888580	+	0.458722i	$0.848308\pi$
$710$		0			0
$711$	27.1378	+	30.1396i	1.01775	+	1.13032i
$712$	−1.27969	−	24.4179i	−0.0479583	−	0.915099i
$713$	−6.61935	+	12.9912i	−0.247897	+	0.486525i
$714$	0.0989623	+	1.47631i	0.00370357	+	0.0552497i
$715$		0			0
$716$	−2.32850	+	2.58606i	−0.0870201	+	0.0966456i
$717$	0.278129	+	0.225225i	0.0103869	+	0.00841116i
$718$	−5.87151	−	21.9128i	−0.219123	−	0.817777i
$719$	−37.9155	−	16.8811i	−1.41401	−	0.629558i	−0.449423	−	0.893319i	$-0.648370\pi$
$719$	−37.9155	−	16.8811i	−1.41401	−	0.629558i	−0.964588	+	0.263761i	$0.915037\pi$
$720$		0			0
$721$	−3.86367	+	3.97795i	−0.143890	+	0.148147i
$722$	6.08648	+	38.4285i	0.226515	+	1.43016i
$723$	−1.05100	+	1.61840i	−0.0390872	+	0.0601890i
$724$	4.73846	−	8.20725i	0.176103	−	0.305020i
$725$		0			0
$726$	3.80439	−	2.19646i	0.141194	−	0.0815184i
$727$	−9.01500	−	17.6929i	−0.334348	−	0.656195i	0.661225	−	0.750188i	$-0.270037\pi$
$727$	−9.01500	−	17.6929i	−0.334348	−	0.656195i	−0.995573	+	0.0939929i	$0.970037\pi$
$728$	1.96034	+	1.09403i	0.0726550	+	0.0405473i
$729$	11.9070	−	16.3886i	0.441001	−	0.606985i
$730$		0			0
$731$	−4.56268	+	0.479557i	−0.168757	+	0.0177371i
$732$	0.514343	−	0.137818i	0.0190107	−	0.00509389i
$733$	−3.55260	−	9.25483i	−0.131218	−	0.341835i	0.852192	−	0.523228i	$-0.175273\pi$
$733$	−3.55260	−	9.25483i	−0.131218	−	0.341835i	−0.983411	+	0.181394i	$0.941939\pi$
$734$	4.33796	+	13.3509i	0.160117	+	0.492790i
$735$		0			0
$736$	−3.00613	+	9.25192i	−0.110807	+	0.341030i
$737$	−48.3314	+	2.53294i	−1.78031	+	0.0933020i
$738$	−16.7695	−	25.8227i	−0.617293	−	0.950547i
$739$	6.85463	−	6.17193i	0.252152	−	0.227038i	−0.533355	−	0.845891i	$-0.679069\pi$
$739$	6.85463	−	6.17193i	0.252152	−	0.227038i	0.785507	+	0.618853i	$0.212402\pi$
$740$		0			0
$741$	1.29274	−	0.420038i	0.0474901	−	0.0154305i
$742$	29.4250	−	27.2812i	1.08022	−	1.00152i
$743$	31.8855	−	31.8855i	1.16976	−	1.16976i	0.187500	−	0.982265i	$-0.439962\pi$
$743$	31.8855	−	31.8855i	1.16976	−	1.16976i	0.982265	−	0.187500i	$-0.0600383\pi$
$744$	−1.88846	+	4.24155i	−0.0692342	+	0.155503i
$745$		0			0
$746$	5.95674	−	2.65211i	0.218092	−	0.0971006i
$747$	−5.51599	−	6.81168i	−0.201819	−	0.249226i
$748$	3.91720	−	1.99592i	0.143227	−	0.0729779i
$749$	−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	$0.889779\pi$
$752$	−47.7525	−	2.50260i	−1.74136	−	0.0912606i
$753$	−1.99968	+	5.20934i	−0.0728723	+	0.189839i
$754$	−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	0.998082	+	0.0619022i	$0.0197167\pi$
$757$	29.1640	+	29.1640i	1.05998	+	1.05998i	0.0619022	+	0.998082i	$0.480283\pi$
$758$	34.6371	−	13.2959i	1.25808	−	0.482930i
$759$	−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	$0.911725\pi$
$762$	−1.88649	−	0.961213i	−0.0683402	−	0.0348211i
$763$	−2.84418	+	31.4651i	−0.102966	+	1.13911i
$764$	−16.5829	−	5.38810i	−0.599947	−	0.194934i
$765$		0			0
$766$	7.22402	−	33.9863i	0.261014	−	1.22798i
$767$	2.52319	−	3.11588i	0.0911070	−	0.112508i
$768$	−1.90884	+	7.12390i	−0.0688795	+	0.257062i
$769$	16.8695	−	12.2564i	0.608330	−	0.441977i	−0.240496	−	0.970650i	$-0.577310\pi$
$769$	16.8695	−	12.2564i	0.608330	−	0.441977i	0.848826	+	0.528673i	$0.177310\pi$
$770$		0			0
$771$	4.54376	+	3.30124i	0.163640	+	0.118891i
$772$	−0.578771	+	0.468680i	−0.0208304	+	0.0168682i
$773$	−0.993051	+	18.9485i	−0.0357176	+	0.681532i	0.920832	+	0.389961i	$0.127511\pi$
$773$	−0.993051	+	18.9485i	−0.0357176	+	0.681532i	−0.956549	+	0.291571i	$0.905822\pi$
$774$	23.4688	+	13.5497i	0.843567	+	0.487034i
$775$		0			0
$776$			16.8052i			0.603271i
$777$	−4.06984	−	0.803267i	−0.146005	−	0.0288170i
$778$	27.0246	−	4.28028i	0.968879	−	0.153455i
$779$	−38.0814	−	4.00252i	−1.36441	−	0.143405i
$780$		0			0
$781$	6.18068	+	58.8053i	0.221162	+	2.10422i
$782$	−2.43261	−	0.651815i	−0.0869898	−	0.0233089i
$783$	−3.53829	−	0.560410i	−0.126448	−	0.0200274i
$784$	16.4788	−	30.5661i	0.588529	−	1.09165i
$785$		0			0
$786$	2.32132	−	0.493411i	0.0827986	−	0.0175994i
$787$	14.5921	−	9.47620i	0.520151	−	0.337790i	−0.257714	−	0.966221i	$-0.582969\pi$
$787$	14.5921	−	9.47620i	0.520151	−	0.337790i	0.777865	+	0.628431i	$0.216303\pi$
$788$	24.5229	−	15.9254i	0.873594	−	0.567318i
$789$	1.44668	−	0.307502i	0.0515033	−	0.0109474i
$790$		0			0
$791$	−8.86906	−	3.25703i	−0.315348	−	0.115807i
$792$	17.1658	+	2.71880i	0.609962	+	0.0966084i
$793$	0.705921	+	0.189151i	0.0250680	+	0.00671694i
$794$	5.46497	+	51.9957i	0.193944	+	1.84526i
$795$		0			0
$796$	10.2288	+	1.07509i	0.362550	+	0.0381055i
$797$	−1.32890	+	0.210477i	−0.0470720	+	0.00745547i	−0.179926	−	0.983680i	$-0.557586\pi$
$797$	−1.32890	+	0.210477i	−0.0470720	+	0.00745547i	0.132854	+	0.991136i	$0.457586\pi$
$798$	−3.50903	−	10.2871i	−0.124218	−	0.364160i
$799$		−	8.37724i		−	0.296365i
$800$		0			0
$801$	−42.3882	−	24.4728i	−1.49771	−	0.864705i
$802$	−2.04647	+	39.0489i	−0.0722633	+	1.37887i
$803$	−11.4420	+	9.26552i	−0.403778	+	0.326973i
$804$	−3.99809	−	2.90479i	−0.141002	−	0.102444i
$805$		0			0
$806$	7.70298	−	5.59655i	0.271326	−	0.197130i
$807$	−1.09857	+	4.09993i	−0.0386716	+	0.144324i
$808$	4.01064	−	4.95273i	0.141094	−	0.174236i
$809$	−2.99535	+	14.0920i	−0.105311	+	0.495449i	0.893603	+	0.448858i	$0.148169\pi$
$809$	−2.99535	+	14.0920i	−0.105311	+	0.495449i	−0.998914	+	0.0465911i	$0.985164\pi$
$810$		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	$0.637185\pi$
$812$	5.35408	+	0.483963i	0.187891	+	0.0169838i
$813$	2.15938	+	1.10026i	0.0757326	+	0.0385877i
$814$	6.84051	+	32.1821i	0.239760	+	1.12798i
$815$		0			0
$816$	−1.51742	−	0.322538i	−0.0531204	−	0.0112911i
$817$	31.4630	−	12.0775i	1.10075	−	0.422538i
$818$	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	$0.920965\pi$
$822$	−0.232650	+	0.606073i	−0.00811458	+	0.0211392i
$823$	−23.0145	−	1.20614i	−0.802235	−	0.0420434i	−0.353189	−	0.935552i	$-0.614903\pi$
$823$	−23.0145	−	1.20614i	−0.802235	−	0.0420434i	−0.449046	+	0.893509i	$0.648236\pi$
$824$	−1.50282	−	2.60297i	−0.0523533	−	0.0906786i
$825$		0			0
$826$	−25.2068	−	19.8109i	−0.877058	−	0.689309i
$827$	−35.9571	+	18.3211i	−1.25035	+	0.637086i	−0.948653	−	0.316317i	$-0.897554\pi$
$827$	−35.9571	+	18.3211i	−1.25035	+	0.637086i	−0.301698	+	0.953403i	$0.597554\pi$
$828$	3.50721	+	4.33105i	0.121884	+	0.150514i
$829$	11.3227	−	5.04117i	0.393252	−	0.175087i	−0.200578	−	0.979678i	$-0.564282\pi$
$829$	11.3227	−	5.04117i	0.393252	−	0.175087i	0.593830	+	0.804591i	$0.297615\pi$
$830$		0			0
$831$	−4.45739	+	10.0115i	−0.154625	+	0.347294i
$832$	0.340867	−	0.340867i	0.0118174	−	0.0118174i
$833$	5.49862	+	2.60271i	0.190516	+	0.0901786i
$834$	6.14024	−	1.99508i	0.212619	−	0.0690841i
$835$		0			0
$836$	−24.0000	+	21.6097i	−0.830057	+	0.747387i
$837$	10.3521	+	15.9409i	0.357822	+	0.550997i
$838$	18.9936	−	0.995413i	0.656123	−	0.0343860i
$839$	−8.58250	+	26.4142i	−0.296301	+	0.911920i	0.686481	+	0.727148i	$0.259155\pi$
$839$	−8.58250	+	26.4142i	−0.296301	+	0.911920i	−0.982781	+	0.184772i	$0.940845\pi$
$840$		0			0
$841$	8.07275	+	24.8454i	0.278371	+	0.856737i
$842$	13.6798	+	35.6370i	0.471436	+	1.22813i
$843$	−1.62473	+	0.435346i	−0.0559588	+	0.0149941i
$844$	4.95246	−	0.520524i	0.170471	−	0.0179172i
$845$		0			0
$846$	−29.0853	+	40.0324i	−0.999972	+	1.37634i
$847$	−0.263207	−	18.0596i	−0.00904392	−	0.620536i
$848$	19.0995	+	37.4848i	0.655879	+	1.28723i
$849$	1.74535	−	1.00768i	0.0599002	−	0.0345834i
$850$		0			0
$851$	3.53038	−	6.11479i	0.121020	−	0.209612i
$852$	−3.28838	+	5.06366i	−0.112658	+	0.173478i
$853$	4.31272	+	27.2295i	0.147665	+	0.932319i	0.944593	+	0.328245i	$0.106457\pi$
$853$	4.31272	+	27.2295i	0.147665	+	0.932319i	−0.796928	+	0.604074i	$0.793543\pi$
$854$	1.43009	−	5.66619i	0.0489365	−	0.193893i
$855$		0			0
$856$	−5.39512	−	2.40206i	−0.184401	−	0.0821008i
$857$	−1.80489	−	6.73593i	−0.0616538	−	0.230095i	0.928223	−	0.372024i	$-0.121336\pi$
$857$	−1.80489	−	6.73593i	−0.0616538	−	0.230095i	−0.989877	+	0.141929i	$0.954669\pi$
$858$	1.24938	+	1.01173i	0.0426531	+	0.0345398i
$859$	5.29128	−	5.87656i	0.180536	−	0.200506i	−0.646083	−	0.763267i	$-0.723594\pi$
$859$	5.29128	−	5.87656i	0.180536	−	0.200506i	0.826620	+	0.562761i	$0.190261\pi$
$860$		0			0
$861$	5.69740	−	0.381916i	0.194167	−	0.0130157i
$862$	−6.22270	+	12.2127i	−0.211946	+	0.415968i
$863$	0.780920	+	14.9008i	0.0265828	+	0.507230i	0.979180	+	0.202995i	$0.0650675\pi$
$863$	0.780920	+	14.9008i	0.0265828	+	0.507230i	−0.952597	+	0.304235i	$0.901599\pi$
$864$	8.48572	+	9.42434i	0.288690	+	0.320623i
$865$		0			0
$866$	27.2824	+	24.5652i	0.927094	+	0.834759i
$867$	−0.914417	+	5.77340i	−0.0310552	+	0.196075i
$868$	−17.1000	−	22.8290i	−0.580413	−	0.774867i
$869$	35.0636	+	48.2610i	1.18945	+	1.63714i
$870$		0			0
$871$	−2.75875	−	6.19625i	−0.0934766	−	0.209952i
$872$	−15.9863	−	6.13658i	−0.541366	−	0.207811i
$873$	28.2127	+	18.3216i	0.954857	+	0.620091i
$874$	18.4999			0.625770
$875$		0			0
$876$	−1.50338			−0.0507945
$877$	24.2272	+	15.7334i	0.818096	+	0.531278i	0.884514	−	0.466514i	$-0.154490\pi$
$877$	24.2272	+	15.7334i	0.818096	+	0.531278i	−0.0664179	+	0.997792i	$0.521157\pi$
$878$	20.8913	+	8.01942i	0.705047	+	0.270642i
$879$	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	$0.523500\pi$
$882$	−17.2399	−	31.5285i	−0.580497	−	1.06162i
$883$	0.361222	−	2.28067i	0.0121561	−	0.0767506i	−0.980865	−	0.194692i	$-0.937629\pi$
$883$	0.361222	−	2.28067i	0.0121561	−	0.0767506i	0.993021	+	0.117941i	$0.0376294\pi$
$884$	0.457871	+	0.412269i	0.0153999	+	0.0138661i
$885$		0			0
$886$	−41.8840	−	46.5169i	−1.40712	−	1.56277i
$887$	1.99680	+	38.1012i	0.0670460	+	1.27931i	0.800400	+	0.599466i	$0.204621\pi$
$887$	1.99680	+	38.1012i	0.0670460	+	1.27931i	−0.733354	+	0.679847i	$0.762046\pi$
$888$	1.02076	−	2.00335i	0.0342544	−	0.0672281i
$889$	−7.23084	+	4.84702i	−0.242515	+	0.162564i
$890$		0			0
$891$	22.1817	−	24.6353i	0.743116	−	0.825314i
$892$	11.8431	+	9.59035i	0.396536	+	0.321109i
$893$	15.9272	+	59.4411i	0.532983	+	1.98912i
$894$	4.20657	+	1.87288i	0.140689	+	0.0626386i
$895$		0			0
$896$	20.0227	+	19.4475i	0.668912	+	0.649694i
$897$	−0.0539716	−	0.340763i	−0.00180206	−	0.0113778i
$898$	4.17382	−	6.42711i	0.139282	−	0.214476i
$899$	−7.62977	+	13.2152i	−0.254467	+	0.440750i
$900$		0			0
$901$	−6.38284	+	3.68513i	−0.212643	+	0.122770i
$902$	−20.5604	−	40.3520i	−0.684586	−	1.34357i
$903$	−4.31533	+	2.57603i	−0.143605	+	0.0857248i
$904$	3.01002	−	4.14293i	0.100112	−	0.137792i
$905$		0			0
$906$	−15.6595	+	1.64588i	−0.520252	+	0.0546806i
$907$	33.3004	−	8.92281i	1.10572	−	0.296277i	0.340629	−	0.940198i	$-0.389360\pi$
$907$	33.3004	−	8.92281i	1.10572	−	0.296277i	0.765092	+	0.643921i	$0.222693\pi$
$908$	−3.00659	−	7.83243i	−0.0997771	−	0.259928i
$909$	−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	$0.0123984\pi$
$912$	11.3802	−	0.596409i	0.376835	−	0.0197491i
$913$	−7.02157	−	10.8123i	−0.232380	−	0.357834i
$914$	23.5039	−	21.1630i	0.777441	−	0.700011i
$915$		0			0
$916$	−16.8559	+	5.47682i	−0.556935	+	0.180959i
$917$	2.87963	−	9.32272i	0.0950936	−	0.307863i
$918$	−2.32148	+	2.32148i	−0.0766203	+	0.0766203i
$919$	0.325410	−	0.730883i	0.0107343	−	0.0241096i	−0.908099	−	0.418756i	$-0.862466\pi$
$919$	0.325410	−	0.730883i	0.0107343	−	0.0241096i	0.918833	+	0.394646i	$0.129133\pi$
$920$		0			0
$921$	−9.03317	+	4.02183i	−0.297653	+	0.132524i
$922$	28.1596	+	34.7743i	0.927388	+	1.14523i
$923$	−7.38341	+	3.76204i	−0.243028	+	0.123829i
$924$	2.97596	−	3.78653i	0.0979019	−	0.124568i
$925$		0			0
$926$	−24.4107	−	42.2806i	−0.802185	−	1.38943i
$927$	−6.00832	−	0.314883i	−0.197339	−	0.0103421i
$928$	−3.64861	+	9.50496i	−0.119772	+	0.312015i
$929$	3.31094	−	31.5015i	0.108628	−	1.03353i	−0.795408	−	0.606074i	$-0.792743\pi$
$929$	3.31094	−	31.5015i	0.108628	−	1.03353i	0.904036	−	0.427455i	$-0.140590\pi$
$930$		0			0
$931$	−43.9641	−	8.01343i	−1.44087	−	0.262630i
$932$	2.16134	+	2.16134i	0.0707969	+	0.0707969i
$933$	5.03989	−	1.93463i	0.164999	−	0.0633370i
$934$	12.3824	+	2.63196i	0.405165	+	0.0861204i
$935$		0			0
$936$	0.506405	+	2.38245i	0.0165524	+	0.0778728i
$937$	−17.1761	−	8.75168i	−0.561120	−	0.285905i	0.150337	−	0.988635i	$-0.451964\pi$
$937$	−17.1761	−	8.75168i	−0.561120	−	0.285905i	−0.711457	+	0.702730i	$0.751964\pi$
$938$	−49.2203	+	22.7795i	−1.60710	+	0.743776i
$939$	−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	$0.748170\pi$
$942$	8.13303	−	10.0435i	0.264988	−	0.327233i
$943$	−2.51549	+	9.38792i	−0.0819155	+	0.305713i
$944$	27.1940	−	19.7576i	0.885089	−	0.643055i
$945$		0			0
$946$	32.2471	+	23.4289i	1.04844	+	0.761739i
$947$	−37.0901	+	30.0349i	−1.20526	+	0.976004i	−0.999996	−	0.00270147i	$-0.999140\pi$
$947$	−37.0901	+	30.0349i	−1.20526	+	0.976004i	−0.205268	+	0.978706i	$0.565807\pi$
$948$	−0.318793	+	6.08294i	−0.0103539	+	0.197565i
$949$	−1.78691	−	1.03167i	−0.0580056	−	0.0334895i
$950$		0			0
$951$		−	9.09962i		−	0.295076i
$952$	−2.17036	+	2.48224i	−0.0703418	+	0.0804499i
$953$	−1.41848	+	0.224666i	−0.0459492	+	0.00727764i	−0.179367	−	0.983782i	$-0.557405\pi$
$953$	−1.41848	+	0.224666i	−0.0459492	+	0.00727764i	0.133418	+	0.991060i	$0.457405\pi$
$954$	43.2964	+	4.55063i	1.40177	+	0.147332i
$955$		0			0
$956$	−0.124562	−	1.18512i	−0.00402861	−	0.0383297i
$957$	−2.48872	−	0.666849i	−0.0804488	−	0.0215562i
$958$	−66.7152	−	10.5666i	−2.15547	−	0.341393i
$959$	1.70980	+	2.04962i	0.0552125	+	0.0661858i
$960$		0			0
$961$	48.8715	−	10.3880i	1.57650	−	0.335096i
$962$	−3.86701	+	2.51126i	−0.124677	+	0.0809664i
$963$	−9.91455	+	6.43858i	−0.319492	+	0.207480i
$964$	6.28500	−	1.33592i	0.202426	−	0.0430270i
$965$		0			0
$966$	−2.71826	+	0.471236i	−0.0874587	+	0.0151618i
$967$	−7.29472	−	1.15537i	−0.234582	−	0.0371542i	0.0380364	−	0.999276i	$-0.487890\pi$
$967$	−7.29472	−	1.15537i	−0.234582	−	0.0371542i	−0.272619	+	0.962122i	$0.587890\pi$
$968$	9.45583	+	2.53368i	0.303922	+	0.0814356i
$969$	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	$0.696622\pi$
$972$	10.8426	−	1.71731i	0.347778	−	0.0550826i
$973$	5.14001	−	26.0424i	0.164781	−	0.834881i
$974$		−	23.5047i		−	0.753138i
$975$		0			0
$976$	5.30617	+	3.06352i	0.169846	+	0.0980608i
$977$	−2.02654	+	38.6687i	−0.0648347	+	1.23712i	0.751575	+	0.659647i	$0.229294\pi$
$977$	−2.02654	+	38.6687i	−0.0648347	+	1.23712i	−0.816410	+	0.577473i	$0.804039\pi$
$978$	8.06939	−	6.53447i	0.258031	−	0.208949i
$979$	−58.2432	−	42.3162i	−1.86146	−	1.35243i
$980$		0			0
$981$	−27.7310	+	20.1478i	−0.885383	+	0.643268i
$982$	10.8133	−	40.3556i	0.345065	−	1.28780i
$983$	−33.5884	+	41.4782i	−1.07130	+	1.32295i	−0.127720	+	0.991810i	$0.540766\pi$
$983$	−33.5884	+	41.4782i	−1.07130	+	1.32295i	−0.943582	+	0.331138i	$0.892568\pi$
$984$	−0.643473	+	3.02730i	−0.0205132	+	0.0965068i
$985$		0			0
$986$	−2.50673	−	0.814485i	−0.0798305	−	0.0259385i
$987$	−3.85434	−	8.32820i	−0.122685	−	0.265089i
$988$	−4.03267	−	2.05475i	−0.128296	−	0.0653702i
$989$	−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	$0.660555\pi$
$992$	50.4310	−	19.3586i	1.60118	−	0.614637i
$993$	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
$997$	−15.5520	+	40.5144i	−0.492537	+	1.28310i	0.431953	+	0.901896i	$0.357825\pi$
$997$	−15.5520	+	40.5144i	−0.492537	+	1.28310i	−0.924490	+	0.381207i	$0.875509\pi$
$998$	16.0639	+	0.841875i	0.508495	+	0.0266491i
$999$	−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.c.507.15		288
5.2	odd	4		875.2.bb.b.493.4		288
5.3	odd	4		875.2.bb.a.493.15		288
5.4	even	2		175.2.x.a.122.4	yes	288
7.5	odd	6	inner	875.2.bb.c.257.15		288
25.6	even	5		875.2.bb.a.857.4		288
25.8	odd	20	inner	875.2.bb.c.143.15		288
25.17	odd	20		175.2.x.a.108.4	yes	288
25.19	even	10		875.2.bb.b.857.15		288
35.12	even	12		875.2.bb.b.243.15		288
35.19	odd	6		175.2.x.a.47.4	yes	288
35.33	even	12		875.2.bb.a.243.4		288
175.19	odd	30		875.2.bb.b.607.4		288
175.33	even	60	inner	875.2.bb.c.768.15		288
175.117	even	60		175.2.x.a.33.4	✓	288
175.131	odd	30		875.2.bb.a.607.15		288

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(1.49982 + 0.973996i) q^{2} +(-0.335932 - 0.128952i) q^{3} +(0.487325 + 1.09455i) q^{4} +(-0.378240 - 0.520602i) q^{6} +(-2.62695 + 0.314872i) q^{7} +(0.224327 - 1.41635i) q^{8} +(-2.13321 - 1.92075i) q^{9} +(-2.82518 - 3.13767i) q^{11} +(-0.0225635 - 0.430536i) q^{12} +(0.268631 - 0.527217i) q^{13} +(-4.24664 - 2.08638i) q^{14} +(3.31938 - 3.68655i) q^{16} +(0.675395 + 0.546924i) q^{17} +(-1.32863 - 4.95853i) q^{18} +(-5.83214 - 2.59663i) q^{19} +(0.923080 + 0.232975i) q^{21} +(-1.18118 - 7.45766i) q^{22} +(-0.882537 + 1.35899i) q^{23} +(-0.258000 + 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(0.959010 + 1.88216i) q^{27} +(-1.62482 - 2.72188i) q^{28} +(-0.996818 + 1.37200i) q^{29} +(8.94867 - 0.940543i) q^{31} +(5.79889 - 1.55381i) q^{32} +(0.544457 + 1.41836i) q^{33} +(0.480271 + 1.47812i) q^{34} +(1.06279 - 3.27094i) q^{36} +(-4.35142 + 0.228048i) q^{37} +(-6.21806 - 9.57497i) q^{38} +(-0.158228 + 0.142469i) q^{39} +(5.70437 - 1.85346i) q^{41} +(1.15754 + 1.24850i) q^{42} +(-3.73281 + 3.73281i) q^{43} +(2.05756 - 4.62136i) q^{44} +(-2.64730 + 1.17865i) q^{46} +(-6.06621 - 7.49114i) q^{47} +(-1.59048 + 0.810389i) q^{48} +(6.80171 - 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(0.707976 + 0.0371035i) q^{52} +(-3.03918 + 7.91735i) q^{53} +(-0.394875 + 3.75698i) q^{54} +(-0.143329 + 3.79131i) q^{56} +(1.62436 + 1.62436i) q^{57} +(-2.83137 + 1.08686i) q^{58} +(6.62786 + 1.40879i) q^{59} +(0.256792 + 1.20811i) q^{61} +(14.3375 + 7.30532i) q^{62} +(6.20863 + 4.37403i) q^{63} +(0.774814 + 0.251752i) q^{64} +(-0.564887 + 2.65758i) q^{66} +(7.21376 - 8.90825i) q^{67} +(-0.269499 + 1.00578i) q^{68} +(0.471717 - 0.342723i) q^{69} +(-11.3299 - 8.23164i) q^{71} +(-3.19899 + 2.59049i) q^{72} +(0.182500 - 3.48231i) q^{73} +(-6.74848 - 3.89623i) q^{74} -7.64897i q^{76} +(8.40955 + 7.35294i) q^{77} +(-0.376077 + 0.0595648i) q^{78} +(-14.0514 - 1.47686i) q^{79} +(0.820700 + 7.80844i) q^{81} +(10.3608 + 2.77617i) q^{82} +(3.01586 + 0.477665i) q^{83} +(0.194837 + 1.12389i) q^{84} +(-9.23428 + 1.96281i) q^{86} +(0.511786 - 0.332358i) q^{87} +(-5.07780 + 3.29756i) q^{88} +(16.6785 - 3.54513i) q^{89} +(-0.539673 + 1.46956i) q^{91} +(-1.91756 - 0.303712i) q^{92} +(-3.12743 - 0.837993i) q^{93} +(-1.80189 - 17.1438i) q^{94} +(-2.14840 - 0.225806i) q^{96} +(-11.5748 + 1.83327i) q^{97} +(11.8126 + 4.14368i) q^{98} +12.1198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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