LMFDB - Embedded newform 875.2.bb.c.768.15

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			768.15
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.c.507.15

$q$-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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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	0.108310	−	0.994117i	$-0.465456\pi$
$2$	1.49982	−	0.973996i	1.06053	−	0.688719i	0.952225	+	0.305398i	$0.0987895\pi$
$3$	−0.335932	+	0.128952i	−0.193951	+	0.0744506i	−0.453405	−	0.891305i	$-0.649791\pi$
$3$	−0.335932	+	0.128952i	−0.193951	+	0.0744506i	0.259454	+	0.965755i	$0.416457\pi$
$4$	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	−0.999073	−	0.0430546i	$-0.986291\pi$
$11$	−2.82518	+	3.13767i	−0.851822	+	0.946045i	0.147250	+	0.989099i	$0.452958\pi$
$12$	−0.0225635	+	0.430536i	−0.00651351	+	0.124285i
$13$	0.268631	+	0.527217i	0.0745047	+	0.146224i	0.925254	−	0.379348i	$-0.123852\pi$
$13$	0.268631	+	0.527217i	0.0745047	+	0.146224i	−0.850749	+	0.525571i	$0.823852\pi$
$14$	−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	−0.543912	−	0.839142i	$-0.683057\pi$
$17$	0.675395	−	0.546924i	0.163807	−	0.132649i	0.707719	+	0.706494i	$0.249724\pi$
$18$	−1.32863	+	4.95853i	−0.313162	+	1.16874i
$19$	−5.83214	+	2.59663i	−1.33798	+	0.595709i	−0.945971	−	0.324251i	$-0.894888\pi$
$19$	−5.83214	+	2.59663i	−1.33798	+	0.595709i	−0.392013	+	0.919960i	$0.628221\pi$
$20$		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	0.734605	−	0.678495i	$-0.237367\pi$
$23$	−0.882537	−	1.35899i	−0.184022	−	0.283369i	−0.918627	+	0.395126i	$0.870701\pi$
$24$	−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	0.706373	−	0.707840i	$-0.250330\pi$
$29$	−0.996818	−	1.37200i	−0.185104	−	0.254774i	−0.891477	+	0.453066i	$0.850330\pi$
$30$		0			0
$31$	8.94867	+	0.940543i	1.60723	+	0.168927i	0.865195	−	0.501436i	$-0.167195\pi$
$31$	8.94867	+	0.940543i	1.60723	+	0.168927i	0.742034	+	0.670362i	$0.233861\pi$
$32$	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	−0.308821	−	0.951120i	$-0.599934\pi$
$37$	−4.35142	−	0.228048i	−0.715369	−	0.0374909i	−0.406548	+	0.913629i	$0.633268\pi$
$38$	−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	0.718465	−	0.695563i	$-0.244845\pi$
$41$	5.70437	+	1.85346i	0.890873	+	0.289462i	0.172408	+	0.985026i	$0.444845\pi$
$42$	1.15754	−	1.24850i	0.178612	−	0.192647i
$43$	−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
$47$	−6.06621	+	7.49114i	−0.884847	+	1.09270i	0.110261	+	0.993903i	$0.464831\pi$
$47$	−6.06621	+	7.49114i	−0.884847	+	1.09270i	−0.995108	+	0.0987925i	$0.968502\pi$
$48$	−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	−0.967607	−	0.252461i	$-0.918760\pi$
$53$	−3.03918	−	7.91735i	−0.417464	−	1.08753i	0.550143	−	0.835070i	$-0.314573\pi$
$54$	−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	0.244842	−	0.969563i	$-0.421264\pi$
$59$	6.62786	−	1.40879i	0.862874	−	0.183409i	0.618031	+	0.786153i	$0.287930\pi$
$60$		0			0
$61$	0.256792	−	1.20811i	0.0328789	−	0.154683i	−0.958646	−	0.284602i	$-0.908138\pi$
$61$	0.256792	−	1.20811i	0.0328789	−	0.154683i	0.991525	+	0.129919i	$0.0414718\pi$
$62$	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	0.995491	+	0.0948576i	$0.0302396\pi$
$67$	7.21376	+	8.90825i	0.881301	+	1.08832i	−0.114189	+	0.993459i	$0.536427\pi$
$68$	−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	−0.345348	+	0.938475i	$0.612239\pi$
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.999261	+	0.0384406i	$0.987761\pi$
$72$	−3.19899	−	2.59049i	−0.377005	−	0.305293i
$73$	0.182500	+	3.48231i	0.0213601	+	0.407574i	0.988295	+	0.152552i	$0.0487493\pi$
$73$	0.182500	+	3.48231i	0.0213601	+	0.407574i	−0.966935	+	0.255022i	$0.917917\pi$
$74$	−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	−0.853885	−	0.520462i	$-0.825760\pi$
$79$	−14.0514	+	1.47686i	−1.58090	+	0.166159i	−0.727016	+	0.686621i	$0.759093\pi$
$80$		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	0.0112944	−	0.999936i	$-0.496405\pi$
$83$	3.01586	−	0.477665i	0.331033	−	0.0524305i	0.319739	+	0.947506i	$0.396405\pi$
$84$	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	0.972977	−	0.230900i	$-0.0741671\pi$
$89$	16.6785	+	3.54513i	1.76792	+	0.375783i	0.794944	+	0.606683i	$0.207500\pi$
$90$		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	−0.461884	−	0.886940i	$-0.652826\pi$
$97$	−11.5748	−	1.83327i	−1.17524	−	0.186140i	−0.713358	+	0.700800i	$0.752826\pi$
$98$	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	−0.296141	−	0.955144i	$-0.595700\pi$
$101$	3.84878	−	2.22209i	0.382967	−	0.221106i	0.679109	+	0.734038i	$0.262367\pi$
$102$	0.0292687	+	0.558480i	0.00289803	+	0.0552978i
$103$	1.62888	+	1.31905i	0.160499	+	0.129969i	0.706206	−	0.708007i	$-0.250405\pi$
$103$	1.62888	+	1.31905i	0.160499	+	0.129969i	−0.545707	+	0.837976i	$0.683739\pi$
$104$	−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	0.998116	−	0.0613552i	$-0.0195422\pi$
$107$	1.06590	+	3.97800i	0.103045	+	0.384568i	−0.895071	+	0.445923i	$0.852876\pi$
$108$	−1.59277	−	1.96691i	−0.153265	−	0.189266i
$109$	2.48271	+	11.6802i	0.237801	+	1.11876i	0.921312	+	0.388824i	$0.127119\pi$
$109$	2.48271	+	11.6802i	0.237801	+	1.11876i	−0.683512	+	0.729940i	$0.739548\pi$
$110$		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	−0.297878	−	0.954604i	$-0.596279\pi$
$113$	3.18186	−	1.62124i	0.299324	−	0.152513i	0.597202	+	0.802091i	$0.296279\pi$
$114$	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	0.579196	−	0.815188i	$-0.303367\pi$
$127$	2.93160	+	1.49373i	0.260138	+	0.132547i	−0.319058	+	0.947735i	$0.603367\pi$
$128$	−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	0.836083	−	0.548602i	$-0.184840\pi$
$131$	−1.50001	−	3.36908i	−0.131057	−	0.294358i	−0.967140	+	0.254244i	$0.918173\pi$
$132$	−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	−0.861363	−	0.507990i	$-0.830389\pi$
$137$	−0.549457	+	0.846089i	−0.0469433	+	0.0722863i	0.814420	+	0.580276i	$0.197055\pi$
$138$	1.04130	+	0.0545724i	0.0886416	+	0.00464551i
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	−0.992154	−	0.125020i	$-0.960100\pi$
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	0.729185	−	0.684317i	$-0.239900\pi$
$140$		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	0.224202	−	0.974543i	$-0.428023\pi$
$149$	−6.19698	−	3.57783i	−0.507676	−	0.293107i	−0.731878	+	0.681436i	$0.761356\pi$
$150$		0			0
$151$	12.2345	+	21.1907i	0.995627	+	1.72448i	0.578718	+	0.815527i	$0.303553\pi$
$151$	12.2345	+	21.1907i	0.995627	+	1.72448i	0.416908	+	0.908949i	$0.363114\pi$
$152$	−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	−0.370321	−	0.928904i	$-0.620752\pi$
$157$	5.19791	−	19.3989i	0.414838	−	1.54820i	0.785159	−	0.619294i	$-0.212581\pi$
$158$	−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	−0.740894	−	0.671622i	$-0.765598\pi$
$163$	0.844482	−	16.1137i	0.0661449	−	1.26212i	0.807039	−	0.590498i	$-0.201069\pi$
$164$	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	0.969655	+	0.244478i	$0.0786165\pi$
$167$	1.58959	+	10.0363i	0.123006	+	0.776630i	−0.846649	+	0.532152i	$0.821383\pi$
$168$	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	−0.647143	−	0.762368i	$-0.724036\pi$
$173$	−2.81344	+	1.82707i	−0.213902	+	0.138909i	0.433241	+	0.901278i	$0.357370\pi$
$174$	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	−0.863999	−	0.503493i	$-0.832048\pi$
$179$	1.18133	−	2.65332i	0.0882971	−	0.198319i	0.952297	+	0.305174i	$0.0987147\pi$
$180$		0			0
$181$	−4.64922	+	6.39910i	−0.345574	+	0.475641i	−0.946059	−	0.323994i	$-0.894974\pi$
$181$	−4.64922	+	6.39910i	−0.345574	+	0.475641i	0.600485	+	0.799636i	$0.294974\pi$
$182$	−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	0.279503	−	0.960145i	$-0.409830\pi$
$191$	−9.73774	−	10.8149i	−0.704598	−	0.782536i	−0.984101	+	0.177609i	$0.943164\pi$
$192$	−0.227821	+	0.184486i	−0.0164416	+	0.0133141i
$193$	0.160877	−	0.600403i	0.0115802	−	0.0432179i	−0.959894	−	0.280363i	$-0.909545\pi$
$193$	0.160877	−	0.600403i	0.0115802	−	0.0432179i	0.971474	+	0.237145i	$0.0762117\pi$
$194$	−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	0.352048	+	0.935982i	$0.385485\pi$
$197$	−3.81776	+	24.1044i	−0.272004	+	1.71736i	−0.624052	+	0.781383i	$0.714515\pi$
$198$	−11.8046	−	18.1775i	−0.838918	−	1.29182i
$199$	4.29215	+	7.43422i	0.304262	+	0.526998i	0.977097	−	0.212795i	$-0.0682568\pi$
$199$	4.29215	+	7.43422i	0.304262	+	0.526998i	−0.672835	+	0.739793i	$0.734923\pi$
$200$		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	0.985483	−	0.169777i	$-0.0543046\pi$
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	−0.897064	+	0.441900i	$0.854305\pi$
$212$	−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	0.790215	−	0.612830i	$-0.209969\pi$
$223$	11.3328	+	5.77436i	0.758902	+	0.386680i	−0.0313132	+	0.999510i	$0.509969\pi$
$224$	−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	−0.282963	−	0.959131i	$-0.591318\pi$
$227$	−6.99268	+	0.366471i	−0.464120	+	0.0243235i	−0.181157	+	0.983454i	$0.557984\pi$
$228$	−0.986352	−	2.56954i	−0.0653228	−	0.170172i
$229$	−1.54623	−	14.7114i	−0.102178	−	0.972159i	−0.918730	−	0.394887i	$-0.870784\pi$
$229$	−1.54623	−	14.7114i	−0.102178	−	0.972159i	0.816552	−	0.577272i	$-0.195883\pi$
$230$		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	0.435129	−	0.900368i	$-0.356703\pi$
$233$	2.38168	+	0.914241i	0.156029	+	0.0598939i	−0.279100	+	0.960262i	$0.590036\pi$
$234$	−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	−0.339450	−	0.940624i	$-0.610241\pi$
$239$	−0.945911	+	0.307345i	−0.0611859	+	0.0198805i	0.278264	+	0.960505i	$0.410241\pi$
$240$		0			0
$241$	1.11500	+	5.24565i	0.0718234	+	0.337902i	0.999358	−	0.0358356i	$-0.0114093\pi$
$241$	1.11500	+	5.24565i	0.0718234	+	0.337902i	−0.927534	+	0.373738i	$0.878076\pi$
$242$	−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	$0.162784\pi$
$251$			15.5071i			0.978800i	−0.872059	+	0.489400i	$0.837216\pi$
$252$	−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	−0.696305	−	0.717746i	$-0.745174\pi$
$257$	−15.0766	+	4.03975i	−0.940449	+	0.251993i	−0.244145	+	0.969739i	$0.578507\pi$
$258$	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	0.433968	−	0.900928i	$-0.357113\pi$
$263$	−3.44715	−	2.23861i	−0.212561	−	0.138038i	−0.646528	+	0.762890i	$0.723780\pi$
$264$	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	0.890404	+	0.455171i	$0.150422\pi$
$269$	−1.23301	+	11.7313i	−0.0751780	+	0.715271i	−0.965582	+	0.260099i	$0.916245\pi$
$270$		0			0
$271$	−6.69826	+	0.704015i	−0.406890	+	0.0427659i	−0.305763	−	0.952108i	$-0.598912\pi$
$271$	−6.69826	+	0.704015i	−0.406890	+	0.0427659i	−0.101127	+	0.994874i	$0.532245\pi$
$272$	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	0.450899	+	0.892575i	$0.351103\pi$
$277$	1.59392	+	30.4139i	0.0957696	+	1.82739i	−0.355130	+	0.934817i	$0.615563\pi$
$278$	−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	0.694845	−	0.719160i	$-0.255473\pi$
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	−0.469243	+	0.883069i	$0.655473\pi$
$282$	−1.60542	−	5.99152i	−0.0956016	−	0.356790i
$283$	−3.52471	−	4.35265i	−0.209522	−	0.258738i	0.661541	−	0.749909i	$-0.269903\pi$
$283$	−3.52471	−	4.35265i	−0.209522	−	0.258738i	−0.871064	+	0.491170i	$0.836569\pi$
$284$	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	−0.889097	−	0.457719i	$-0.848667\pi$
$293$	−7.38400	+	7.38400i	−0.431378	+	0.431378i	0.457719	+	0.889097i	$0.348667\pi$
$294$	−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	0.993284	+	0.115702i	$0.0369117\pi$
$307$	19.4310	+	19.4310i	1.10899	+	1.10899i	0.115702	+	0.993284i	$0.463088\pi$
$308$	−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	0.289473	−	0.957186i	$-0.406520\pi$
$311$	−11.1492	−	10.0388i	−0.632212	−	0.569246i	−0.921685	+	0.387940i	$0.873187\pi$
$312$	0.166290	−	0.256065i	0.00941434	−	0.0144968i
$313$	30.4559	+	1.59613i	1.72147	+	0.0902185i	0.887272	−	0.461246i	$-0.152597\pi$
$313$	30.4559	+	1.59613i	1.72147	+	0.0902185i	0.834199	+	0.551464i	$0.185931\pi$
$314$	−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	−0.402763	−	0.915304i	$-0.631950\pi$
$317$	9.06260	−	23.6089i	0.509006	−	1.32601i	0.911769	−	0.410703i	$-0.134717\pi$
$318$	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	−0.566147	−	0.824304i	$-0.691567\pi$
$331$	−6.04742	+	2.69249i	−0.332396	+	0.147992i	0.233751	+	0.972297i	$0.424900\pi$
$332$	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	0.821833	−	0.569729i	$-0.192952\pi$
$337$	−2.24236	−	4.40088i	−0.122149	−	0.239731i	−0.943982	+	0.329998i	$0.892952\pi$
$338$	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	0.386194	−	0.922417i	$-0.373789\pi$
$347$	24.0377	−	9.22720i	1.29041	−	0.495342i	0.904216	+	0.427075i	$0.140456\pi$
$348$	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	−0.979668	−	0.200624i	$-0.935703\pi$
$353$	−29.5626	+	11.3480i	−1.57346	+	0.603995i	−0.593792	+	0.804619i	$0.702370\pi$
$354$	−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	−0.879297	−	0.476274i	$-0.841987\pi$
$359$	−9.42711	+	8.48821i	−0.497544	+	0.447990i	0.381753	+	0.924264i	$0.375320\pi$
$360$		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	−0.456752	−	0.889594i	$-0.650987\pi$
$367$	6.10039	−	4.94000i	0.318438	−	0.257866i	0.775190	+	0.631728i	$0.217654\pi$
$368$	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	0.886337	−	0.463042i	$-0.153242\pi$
$373$	1.98581	+	3.05789i	0.102822	+	0.158331i	−0.783515	+	0.621373i	$0.786575\pi$
$374$	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	0.997798	−	0.0663239i	$-0.0211271\pi$
$379$	12.1944	+	16.7841i	0.626384	+	0.862143i	−0.371414	+	0.928467i	$0.621127\pi$
$380$		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	0.632551	+	0.774518i	$0.282008\pi$
$383$	−6.96275	+	18.1386i	−0.355780	+	0.926838i	−0.988331	+	0.152320i	$0.951326\pi$
$384$	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	0.904991	−	0.425431i	$-0.139878\pi$
$389$	11.3701	+	10.2377i	0.576487	+	0.519072i	−0.328503	+	0.944503i	$0.606544\pi$
$390$		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	−0.0664145	−	0.997792i	$-0.521156\pi$
$397$	18.3983	−	22.7200i	0.923382	−	1.14028i	0.989796	−	0.142489i	$-0.0455107\pi$
$398$	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	−0.452595	−	0.891716i	$-0.649502\pi$
$401$	10.9327	−	18.9359i	0.545952	−	0.945616i	0.998546	−	0.0538996i	$-0.0171651\pi$
$402$	−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	0.607848	−	0.794054i	$-0.292033\pi$
$409$	30.0548	−	6.38835i	1.48611	−	0.315883i	0.878267	+	0.478170i	$0.158700\pi$
$410$		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	0.777776	−	0.628541i	$-0.216348\pi$
$419$	8.60424	+	6.25134i	0.420345	+	0.305398i	−0.357432	+	0.933939i	$0.616348\pi$
$420$		0			0
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	−0.0812007	−	0.996698i	$-0.525875\pi$
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	0.922824	+	0.385223i	$0.125875\pi$
$422$	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	−0.958136	−	0.286314i	$-0.907570\pi$
$431$	0.801158	−	7.62251i	0.0385904	−	0.367164i	0.996726	−	0.0808496i	$-0.0257634\pi$
$432$	10.1220	−	2.71219i	0.486996	−	0.130490i
$433$	20.2759	−	3.21139i	0.974399	−	0.154330i	0.351121	−	0.936330i	$-0.385801\pi$
$433$	20.2759	−	3.21139i	0.974399	−	0.154330i	0.623278	+	0.782000i	$0.285801\pi$
$434$	−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	0.490510	−	0.871436i	$-0.336811\pi$
$439$	12.2397	+	2.60162i	0.584168	+	0.124169i	0.0936579	+	0.995604i	$0.470144\pi$
$440$		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	−0.946942	−	0.321405i	$-0.895845\pi$
$443$	−33.8090	+	9.05910i	−1.60632	+	0.430411i	−0.659373	+	0.751816i	$0.729178\pi$
$444$	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	$0.0322416\pi$
$449$			4.28525i			0.202233i	−0.994875	+	0.101117i	$0.967758\pi$
$450$		0			0
$451$	−21.9314	+	12.6621i	−1.03271	+	0.596235i
$452$	−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	0.986474	+	0.163915i	$0.0524122\pi$
$457$	4.57736	+	17.0829i	0.214120	+	0.799107i	−0.772355	+	0.635192i	$0.780921\pi$
$458$	−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	0.303017	−	0.952985i	$-0.402006\pi$
$461$	23.7965	−	7.73195i	1.10831	−	0.360113i	0.805297	+	0.592872i	$0.202006\pi$
$462$	0.647130	+	7.15920i	0.0301072	+	0.333076i
$463$	−24.3244	+	12.3939i	−1.13045	+	0.575994i	−0.916175	−	0.400779i	$-0.868740\pi$
$463$	−24.3244	+	12.3939i	−1.13045	+	0.575994i	−0.214277	+	0.976773i	$0.568740\pi$
$464$	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	0.506432	−	0.862280i	$-0.330964\pi$
$467$	6.60852	+	2.53677i	0.305806	+	0.117388i	−0.200626	+	0.979668i	$0.564298\pi$
$468$	−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	−0.582738	−	0.812660i	$-0.698019\pi$
$479$	−34.5054	−	15.3628i	−1.57659	−	0.701943i	−0.993852	+	0.110717i	$0.964685\pi$
$480$		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	−0.962809	−	0.270181i	$-0.912916\pi$
$487$	−7.15837	+	11.0229i	−0.324377	+	0.499496i	0.638433	+	0.769678i	$0.279583\pi$
$488$	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	0.645275	+	0.763950i	$0.276743\pi$
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	−0.971077	+	0.238765i	$0.923257\pi$
$492$	−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	0.664122	−	0.747624i	$-0.268805\pi$
$499$	7.78986	+	4.49748i	0.348722	+	0.201335i	−0.315400	+	0.948959i	$0.602139\pi$
$500$		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	−0.463228	−	0.886239i	$-0.653309\pi$
$503$	5.63363	−	35.5693i	0.251191	−	1.58596i	0.714419	−	0.699718i	$-0.246691\pi$
$504$	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	0.591429	−	0.806357i	$-0.298564\pi$
$509$	−6.14407	−	6.82368i	−0.272331	−	0.302454i	−0.863761	+	0.503902i	$0.831897\pi$
$510$		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	−0.989030	−	0.147715i	$-0.952808\pi$
$521$	−4.96375	+	11.1488i	−0.217466	+	0.488437i	0.771564	+	0.636152i	$0.219475\pi$
$522$	8.12752	−	3.11986i	0.355732	−	0.136553i
$523$	−17.1195	+	11.1175i	−0.748582	+	0.486135i	−0.861682	−	0.507449i	$-0.830589\pi$
$523$	−17.1195	+	11.1175i	−0.748582	+	0.486135i	0.113100	+	0.993584i	$0.463922\pi$
$524$	−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	0.433820	−	0.901000i	$-0.357165\pi$
$541$	−11.8063	−	13.1122i	−0.507591	−	0.563737i	−0.941410	+	0.337263i	$0.890499\pi$
$542$	−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	−0.995681	−	0.0928385i	$-0.970406\pi$
$547$	−0.468776	+	2.95974i	−0.0200434	+	0.126549i	0.975638	+	0.219388i	$0.0704060\pi$
$548$	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	−0.447373	−	0.894347i	$-0.647641\pi$
$557$	−30.2559	−	8.10705i	−1.28198	−	0.343507i	−0.834610	+	0.550841i	$0.814307\pi$
$558$	−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	−0.557962	−	0.829867i	$-0.688416\pi$
$563$	10.1341	−	15.6052i	0.427103	−	0.657680i	0.985064	+	0.172186i	$0.0550831\pi$
$564$	−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	0.926409	−	0.376520i	$-0.122879\pi$
$569$	0.637171	+	1.43111i	0.0267116	+	0.0599952i	−0.899697	+	0.436515i	$0.856213\pi$
$570$		0			0
$571$	−12.0801	−	5.37840i	−0.505536	−	0.225079i	0.138090	−	0.990420i	$-0.455904\pi$
$571$	−12.0801	−	5.37840i	−0.505536	−	0.225079i	−0.643625	+	0.765341i	$0.722570\pi$
$572$	−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	−0.244422	−	0.969669i	$-0.578598\pi$
$577$	−9.27556	+	0.486112i	−0.386147	+	0.0202371i	−0.141725	+	0.989906i	$0.545265\pi$
$578$	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	−0.191226	−	0.981546i	$-0.561246\pi$
$587$	11.8830	−	6.05467i	0.490462	−	0.249903i	0.681688	+	0.731643i	$0.261246\pi$
$588$	−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	0.833011	+	0.553257i	$0.186615\pi$
$593$	9.45404	+	35.2829i	0.388231	+	1.44890i	−0.444780	+	0.895640i	$0.646718\pi$
$594$	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	−0.504381	−	0.863481i	$-0.668279\pi$
$599$	−0.214739	+	0.123980i	−0.00877399	+	0.00506567i	0.495607	+	0.868547i	$0.334946\pi$
$600$		0			0
$601$		−	19.3484i		−	0.789237i	−0.918845	−	0.394618i	$-0.870877\pi$
$601$		−	19.3484i		−	0.789237i	0.918845	−	0.394618i	$-0.129123\pi$
$602$	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	−0.884223	−	0.467065i	$-0.845312\pi$
$607$	−34.8976	+	9.35079i	−1.41645	+	0.379537i	−0.532227	+	0.846601i	$0.678645\pi$
$608$	−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	0.781273	−	0.624189i	$-0.214571\pi$
$613$	13.0930	+	8.50267i	0.528820	+	0.343420i	−0.252453	+	0.967609i	$0.581237\pi$
$614$	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	−0.682403	−	0.730976i	$-0.739065\pi$
$617$	−27.4606	+	4.34934i	−1.10552	+	0.175098i	−0.423120	+	0.906074i	$0.639065\pi$
$618$	−1.30281	+	0.349086i	−0.0524065	+	0.0140423i
$619$	3.75824	−	35.7573i	0.151056	−	1.43721i	−0.611992	−	0.790864i	$-0.709631\pi$
$619$	3.75824	−	35.7573i	0.151056	−	1.43721i	0.763048	−	0.646342i	$-0.223702\pi$
$620$		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	0.944528	−	0.328430i	$-0.106520\pi$
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	−0.0204802	+	0.999790i	$0.506520\pi$
$632$	−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	−0.541922	−	0.840429i	$-0.682303\pi$
$641$	−17.6000	+	3.74101i	−0.695160	+	0.147761i	−0.153238	+	0.988189i	$0.548970\pi$
$642$	−2.47412	−	0.949726i	−0.0976457	−	0.0374827i
$643$	−9.47610	+	9.47610i	−0.373701	+	0.373701i	−0.868823	−	0.495122i	$-0.835123\pi$
$643$	−9.47610	+	9.47610i	−0.373701	+	0.373701i	0.495122	+	0.868823i	$0.335123\pi$
$644$	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	0.800707	−	0.599056i	$-0.204457\pi$
$647$	−4.96466	−	12.9334i	−0.195181	−	0.508464i	−0.995888	+	0.0905921i	$0.971124\pi$
$648$	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	0.0887994	+	0.996050i	$0.471697\pi$
$653$	−23.0993	+	28.5253i	−0.903947	+	1.11628i	−0.992746	+	0.120231i	$0.961636\pi$
$654$	−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	−0.0454175	−	0.998968i	$-0.514462\pi$
$659$	−17.1826	−	5.58297i	−0.669340	−	0.217482i	−0.623922	+	0.781486i	$0.714462\pi$
$660$		0			0
$661$	−19.5718	−	17.6225i	−0.761253	−	0.685435i	0.194074	−	0.980987i	$-0.437830\pi$
$661$	−19.5718	−	17.6225i	−0.761253	−	0.685435i	−0.955327	+	0.295552i	$0.904497\pi$
$662$	−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	−0.297896	+	0.954598i	$0.596285\pi$
$673$	−23.2205	+	45.5727i	−0.895083	+	1.75670i	−0.597187	+	0.802102i	$0.703715\pi$
$674$	−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	−0.959034	−	0.283291i	$-0.908574\pi$
$677$	−21.5376	−	33.1651i	−0.827759	−	1.27464i	0.131275	−	0.991346i	$-0.458093\pi$
$678$	−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	−0.453438	−	0.891288i	$-0.649802\pi$
$683$	8.47008	−	6.85894i	0.324099	−	0.262450i	0.777536	+	0.628838i	$0.216469\pi$
$684$	−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	−0.0163408	−	0.999866i	$-0.505202\pi$
$691$	25.6649	−	23.1088i	0.976340	−	0.879101i	0.992681	+	0.120766i	$0.0385350\pi$
$692$	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	−0.888580	−	0.458722i	$-0.848308\pi$
$709$	−13.9859	+	12.5930i	−0.525253	+	0.472940i	0.363327	+	0.931662i	$0.381641\pi$
$710$		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	−0.964588	−	0.263761i	$-0.915037\pi$
$719$	−37.9155	+	16.8811i	−1.41401	+	0.629558i	−0.449423	+	0.893319i	$0.648370\pi$
$720$		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	−0.995573	−	0.0939929i	$-0.970037\pi$
$727$	−9.01500	+	17.6929i	−0.334348	+	0.656195i	0.661225	+	0.750188i	$0.270037\pi$
$728$	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	−0.983411	−	0.181394i	$-0.941939\pi$
$733$	−3.55260	+	9.25483i	−0.131218	+	0.341835i	0.852192	+	0.523228i	$0.175273\pi$
$734$	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	0.785507	−	0.618853i	$-0.212402\pi$
$739$	6.85463	+	6.17193i	0.252152	+	0.227038i	−0.533355	+	0.845891i	$0.679069\pi$
$740$		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	0.982265	+	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
$747$	−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	−0.940646	−	0.339390i	$-0.889779\pi$
$751$	−4.83420	+	8.37308i	−0.176403	+	0.305538i	0.764243	+	0.644928i	$0.223113\pi$
$752$	−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	0.0619022	−	0.998082i	$-0.480283\pi$
$757$	29.1640	−	29.1640i	1.05998	−	1.05998i	0.998082	−	0.0619022i	$-0.0197167\pi$
$758$	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	−0.961791	−	0.273783i	$-0.911725\pi$
$761$	0.778111	−	3.66072i	0.0282065	−	0.132701i	0.989998	+	0.141082i	$0.0450582\pi$
$762$	−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	0.848826	−	0.528673i	$-0.177310\pi$
$769$	16.8695	+	12.2564i	0.608330	+	0.441977i	−0.240496	+	0.970650i	$0.577310\pi$
$770$		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	−0.956549	−	0.291571i	$-0.905822\pi$
$773$	−0.993051	−	18.9485i	−0.0357176	−	0.681532i	0.920832	−	0.389961i	$-0.127511\pi$
$774$	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	0.777865	−	0.628431i	$-0.216303\pi$
$787$	14.5921	+	9.47620i	0.520151	+	0.337790i	−0.257714	+	0.966221i	$0.582969\pi$
$788$	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	0.132854	−	0.991136i	$-0.457586\pi$
$797$	−1.32890	−	0.210477i	−0.0470720	−	0.00745547i	−0.179926	+	0.983680i	$0.557586\pi$
$798$	−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	−0.998914	−	0.0465911i	$-0.985164\pi$
$809$	−2.99535	−	14.0920i	−0.105311	−	0.495449i	0.893603	−	0.448858i	$-0.148169\pi$
$810$		0			0
$811$	−6.31358	+	2.05141i	−0.221700	+	0.0720346i	−0.417761	−	0.908557i	$-0.637185\pi$
$811$	−6.31358	+	2.05141i	−0.221700	+	0.0720346i	0.196061	+	0.980592i	$0.437185\pi$
$812$	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	−0.969333	−	0.245752i	$-0.920965\pi$
$821$	−2.07096	−	19.7039i	−0.0722771	−	0.687670i	0.897056	−	0.441918i	$-0.145702\pi$
$822$	−0.232650	−	0.606073i	−0.00811458	−	0.0211392i
$823$	−23.0145	+	1.20614i	−0.802235	+	0.0420434i	−0.449046	−	0.893509i	$-0.648236\pi$
$823$	−23.0145	+	1.20614i	−0.802235	+	0.0420434i	−0.353189	+	0.935552i	$0.614903\pi$
$824$	−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	−0.301698	−	0.953403i	$-0.597554\pi$
$827$	−35.9571	−	18.3211i	−1.25035	−	0.637086i	−0.948653	+	0.316317i	$0.897554\pi$
$828$	3.50721	−	4.33105i	0.121884	−	0.150514i
$829$	11.3227	+	5.04117i	0.393252	+	0.175087i	0.593830	−	0.804591i	$-0.297615\pi$
$829$	11.3227	+	5.04117i	0.393252	+	0.175087i	−0.200578	+	0.979678i	$0.564282\pi$
$830$		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	−0.982781	−	0.184772i	$-0.940845\pi$
$839$	−8.58250	−	26.4142i	−0.296301	−	0.911920i	0.686481	−	0.727148i	$-0.259155\pi$
$840$		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	−0.796928	−	0.604074i	$-0.793543\pi$
$853$	4.31272	−	27.2295i	0.147665	−	0.932319i	0.944593	−	0.328245i	$-0.106457\pi$
$854$	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	−0.989877	−	0.141929i	$-0.954669\pi$
$857$	−1.80489	+	6.73593i	−0.0616538	+	0.230095i	0.928223	+	0.372024i	$0.121336\pi$
$858$	1.24938	−	1.01173i	0.0426531	−	0.0345398i
$859$	5.29128	+	5.87656i	0.180536	+	0.200506i	0.826620	−	0.562761i	$-0.190261\pi$
$859$	5.29128	+	5.87656i	0.180536	+	0.200506i	−0.646083	+	0.763267i	$0.723594\pi$
$860$		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	−0.952597	−	0.304235i	$-0.901599\pi$
$863$	0.780920	−	14.9008i	0.0265828	−	0.507230i	0.979180	−	0.202995i	$-0.0650675\pi$
$864$	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	−0.0664179	−	0.997792i	$-0.521157\pi$
$877$	24.2272	−	15.7334i	0.818096	−	0.531278i	0.884514	+	0.466514i	$0.154490\pi$
$878$	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	−0.0737612	−	0.997276i	$-0.523500\pi$
$881$	26.6392	−	36.6657i	0.897498	−	1.23530i	0.971259	−	0.238024i	$-0.0764997\pi$
$882$	−17.2399	+	31.5285i	−0.580497	+	1.06162i
$883$	0.361222	+	2.28067i	0.0121561	+	0.0767506i	0.993021	−	0.117941i	$-0.0376294\pi$
$883$	0.361222	+	2.28067i	0.0121561	+	0.0767506i	−0.980865	+	0.194692i	$0.937629\pi$
$884$	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	−0.733354	−	0.679847i	$-0.762046\pi$
$887$	1.99680	−	38.1012i	0.0670460	−	1.27931i	0.800400	−	0.599466i	$-0.204621\pi$
$888$	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	0.765092	−	0.643921i	$-0.222693\pi$
$907$	33.3004	+	8.92281i	1.10572	+	0.296277i	0.340629	+	0.940198i	$0.389360\pi$
$908$	−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	0.999242	−	0.0389409i	$-0.0123984\pi$
$911$	5.06918	+	15.6013i	0.167949	+	0.516895i	−0.831292	+	0.555836i	$0.812398\pi$
$912$	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	0.918833	−	0.394646i	$-0.129133\pi$
$919$	0.325410	+	0.730883i	0.0107343	+	0.0241096i	−0.908099	+	0.418756i	$0.862466\pi$
$920$		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	0.904036	+	0.427455i	$0.140590\pi$
$929$	3.31094	+	31.5015i	0.108628	+	1.03353i	−0.795408	+	0.606074i	$0.792743\pi$
$930$		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	−0.711457	−	0.702730i	$-0.751964\pi$
$937$	−17.1761	+	8.75168i	−0.561120	+	0.285905i	0.150337	+	0.988635i	$0.451964\pi$
$938$	−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	−0.703030	−	0.711160i	$-0.748170\pi$
$941$	−10.7376	−	50.5163i	−0.350035	−	1.64679i	0.352995	−	0.935625i	$-0.385163\pi$
$942$	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	−0.205268	−	0.978706i	$-0.565807\pi$
$947$	−37.0901	−	30.0349i	−1.20526	−	0.976004i	−0.999996	+	0.00270147i	$0.999140\pi$
$948$	−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	0.133418	−	0.991060i	$-0.457405\pi$
$953$	−1.41848	−	0.224666i	−0.0459492	−	0.00727764i	−0.179367	+	0.983782i	$0.557405\pi$
$954$	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	−0.272619	−	0.962122i	$-0.587890\pi$
$967$	−7.29472	+	1.15537i	−0.234582	+	0.0371542i	0.0380364	+	0.999276i	$0.487890\pi$
$968$	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	−0.579166	−	0.815209i	$-0.696622\pi$
$971$	−30.4188	+	3.19714i	−0.976185	+	0.102601i	−0.397019	+	0.917811i	$0.629955\pi$
$972$	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	−0.816410	−	0.577473i	$-0.804039\pi$
$977$	−2.02654	−	38.6687i	−0.0648347	−	1.23712i	0.751575	−	0.659647i	$-0.229294\pi$
$978$	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	−0.943582	−	0.331138i	$-0.892568\pi$
$983$	−33.5884	−	41.4782i	−1.07130	−	1.32295i	−0.127720	−	0.991810i	$-0.540766\pi$
$984$	−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	−0.483280	−	0.875466i	$-0.660555\pi$
$991$	−17.9026	+	3.80531i	−0.568694	+	0.120880i	−0.0854140	+	0.996346i	$0.527221\pi$
$992$	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	−0.924490	−	0.381207i	$-0.875509\pi$
$997$	−15.5520	−	40.5144i	−0.492537	−	1.28310i	0.431953	−	0.901896i	$-0.357825\pi$
$998$	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.768.15		288
5.2	odd	4		875.2.bb.a.607.15		288
5.3	odd	4		875.2.bb.b.607.4		288
5.4	even	2		175.2.x.a.33.4	✓	288
7.3	odd	6	inner	875.2.bb.c.143.15		288
25.3	odd	20		175.2.x.a.47.4	yes	288
25.4	even	10		875.2.bb.b.243.15		288
25.21	even	5		875.2.bb.a.243.4		288
25.22	odd	20	inner	875.2.bb.c.257.15		288
35.3	even	12		875.2.bb.b.857.15		288
35.17	even	12		875.2.bb.a.857.4		288
35.24	odd	6		175.2.x.a.108.4	yes	288
175.3	even	60		175.2.x.a.122.4	yes	288
175.122	even	60	inner	875.2.bb.c.507.15		288
175.129	odd	30		875.2.bb.b.493.4		288
175.171	odd	30		875.2.bb.a.493.15		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.4	✓	288	5.4	even	2
175.2.x.a.47.4	yes	288	25.3	odd	20
175.2.x.a.108.4	yes	288	35.24	odd	6
175.2.x.a.122.4	yes	288	175.3	even	60
875.2.bb.a.243.4		288	25.21	even	5
875.2.bb.a.493.15		288	175.171	odd	30
875.2.bb.a.607.15		288	5.2	odd	4
875.2.bb.a.857.4		288	35.17	even	12
875.2.bb.b.243.15		288	25.4	even	10
875.2.bb.b.493.4		288	175.129	odd	30
875.2.bb.b.607.4		288	5.3	odd	4
875.2.bb.b.857.15		288	35.3	even	12
875.2.bb.c.143.15		288	7.3	odd	6	inner
875.2.bb.c.257.15		288	25.22	odd	20	inner
875.2.bb.c.507.15		288	175.122	even	60	inner
875.2.bb.c.768.15		288	1.1	even	1	trivial

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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