LMFDB - Embedded newform 875.2.bb.c.507.1

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			507.1
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.c.768.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.03786 - 1.32340i) q^{2} +(2.14641 + 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-3.28370 - 4.51962i) q^{6} +(-2.14884 - 1.54352i) q^{7} +(0.723845 - 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +(0.0112005 + 0.0124395i) q^{11} +(0.469788 + 8.96408i) q^{12} +(-1.39124 + 2.73047i) q^{13} +(2.33634 + 5.98928i) q^{14} +(-2.29834 + 2.55257i) q^{16} +(5.48928 + 4.44513i) q^{17} +(-1.43762 - 5.36527i) q^{18} +(2.90112 + 1.29166i) q^{19} +(-3.34055 - 5.08353i) q^{21} +(-0.00636273 - 0.0401727i) q^{22} +(-2.98285 + 4.59318i) q^{23} +(5.31918 - 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(-0.745322 - 1.46278i) q^{27} +(2.09295 - 10.1155i) q^{28} +(-0.0353871 + 0.0487062i) q^{29} +(8.96709 - 0.942479i) q^{31} +(-0.877177 + 0.235039i) q^{32} +(0.0137917 + 0.0359286i) q^{33} +(-5.30369 - 16.3231i) q^{34} +(-2.75796 + 8.48811i) q^{36} +(8.39052 - 0.439728i) q^{37} +(-4.20270 - 6.47159i) q^{38} +(-5.23590 + 4.71442i) q^{39} +(-5.83738 + 1.89668i) q^{41} +(0.0800095 + 14.7804i) q^{42} +(3.18681 - 3.18681i) q^{43} +(-0.0265816 + 0.0597034i) q^{44} +(12.1573 - 5.41276i) q^{46} +(2.89679 + 3.57724i) q^{47} +(-7.03633 + 3.58519i) q^{48} +(2.23507 + 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-11.9482 - 0.626178i) q^{52} +(-1.55951 + 4.06266i) q^{53} +(-0.416980 + 3.96730i) q^{54} +(-8.60961 + 8.70333i) q^{56} +(5.16276 + 5.16276i) q^{57} +(0.136572 - 0.0524250i) q^{58} +(2.45075 + 0.520924i) q^{59} +(2.77436 + 13.0523i) q^{61} +(-19.5210 - 9.94643i) q^{62} +(-1.28946 - 5.90896i) q^{63} +(8.63203 + 2.80472i) q^{64} +(0.0194425 - 0.0914696i) q^{66} +(-0.200158 + 0.247175i) q^{67} +(-7.13755 + 26.6377i) q^{68} +(-10.1869 + 7.40119i) q^{69} +(-6.35569 - 4.61768i) q^{71} +(8.22016 - 6.65655i) q^{72} +(-0.174974 + 3.33870i) q^{73} +(-17.6807 - 10.2079i) q^{74} +12.3987i q^{76} +(-0.00486761 - 0.0440188i) q^{77} +(16.9091 - 2.67814i) q^{78} +(-5.32825 - 0.560021i) q^{79} +(-1.11138 - 10.5741i) q^{81} +(14.4058 + 3.86003i) q^{82} +(8.63403 + 1.36750i) q^{83} +(12.8268 - 19.9876i) q^{84} +(-10.7117 + 2.27684i) q^{86} +(-0.116086 + 0.0753869i) q^{87} +(0.0649580 - 0.0421842i) q^{88} +(8.18738 - 1.74028i) q^{89} +(7.20412 - 3.71994i) q^{91} +(-21.1194 - 3.34499i) q^{92} +(20.0236 + 5.36531i) q^{93} +(-1.16913 - 11.1236i) q^{94} +(-2.07644 - 0.218242i) q^{96} +(6.79613 - 1.07640i) q^{97} +(4.22415 - 16.4762i) q^{98} +0.0382642i 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 $

$2$	−2.03786	−	1.32340i	−1.44099	−	0.935787i	−0.999253	−	0.0386405i	$-0.987697\pi$
$2$	−2.03786	−	1.32340i	−1.44099	−	0.935787i	−0.441733	−	0.897147i	$-0.645636\pi$
$3$	2.14641	+	0.823930i	1.23923	+	0.475696i	0.887675	−	0.460471i	$-0.152319\pi$
$3$	2.14641	+	0.823930i	1.23923	+	0.475696i	0.351556	+	0.936167i	$0.385653\pi$
$4$	1.58801	+	3.56673i	0.794006	+	1.78337i
$5$		0			0
$5$		0			0
$6$	−3.28370	−	4.51962i	−1.34056	−	1.84513i
$7$	−2.14884	−	1.54352i	−0.812187	−	0.583397i
$7$	−2.14884	−	1.54352i	−0.812187	−	0.583397i
$8$	0.723845	−	4.57018i	0.255918	−	1.61580i
$9$	1.69878	+	1.52959i	0.566261	+	0.509864i
$10$		0			0
$11$	0.0112005	+	0.0124395i	0.00337709	+	0.00375064i	0.744831	−	0.667253i	$-0.232530\pi$
$11$	0.0112005	+	0.0124395i	0.00337709	+	0.00375064i	−0.741454	+	0.671004i	$0.765863\pi$
$12$	0.469788	+	8.96408i	0.135616	+	2.58771i
$13$	−1.39124	+	2.73047i	−0.385862	+	0.757297i	−0.999478	−	0.0323079i	$-0.989714\pi$
$13$	−1.39124	+	2.73047i	−0.385862	+	0.757297i	0.613616	+	0.789605i	$0.289714\pi$
$14$	2.33634	+	5.98928i	0.624414	+	1.60070i
$15$		0			0
$16$	−2.29834	+	2.55257i	−0.574586	+	0.638142i
$17$	5.48928	+	4.44513i	1.33135	+	1.07810i	0.990431	+	0.138008i	$0.0440700\pi$
$17$	5.48928	+	4.44513i	1.33135	+	1.07810i	0.340914	+	0.940094i	$0.389263\pi$
$18$	−1.43762	−	5.36527i	−0.338850	−	1.26461i
$19$	2.90112	+	1.29166i	0.665563	+	0.296328i	0.711572	−	0.702613i	$-0.247984\pi$
$19$	2.90112	+	1.29166i	0.665563	+	0.296328i	−0.0460087	+	0.998941i	$0.514650\pi$
$20$		0			0
$21$	−3.34055	−	5.08353i	−0.728967	−	1.10932i
$22$	−0.00636273	−	0.0401727i	−0.00135654	−	0.00856485i
$23$	−2.98285	+	4.59318i	−0.621966	+	0.957744i	0.377530	+	0.925997i	$0.376774\pi$
$23$	−2.98285	+	4.59318i	−0.621966	+	0.957744i	−0.999496	+	0.0317465i	$0.989893\pi$
$24$	5.31918	−	9.21308i	1.08577	−	1.88061i
$25$		0			0
$26$	6.44868	−	3.72315i	1.26469	−	0.730169i
$27$	−0.745322	−	1.46278i	−0.143437	−	0.281512i
$28$	2.09295	−	10.1155i	0.395530	−	1.91165i
$29$	−0.0353871	+	0.0487062i	−0.00657122	+	0.00904451i	−0.812290	−	0.583254i	$-0.801779\pi$
$29$	−0.0353871	+	0.0487062i	−0.00657122	+	0.00904451i	0.805719	+	0.592298i	$0.201779\pi$
$30$		0			0
$31$	8.96709	−	0.942479i	1.61054	−	0.169274i	0.743927	−	0.668260i	$-0.232961\pi$
$31$	8.96709	−	0.942479i	1.61054	−	0.169274i	0.866610	+	0.498986i	$0.166294\pi$
$32$	−0.877177	+	0.235039i	−0.155065	+	0.0415494i
$33$	0.0137917	+	0.0359286i	0.00240083	+	0.00625437i
$34$	−5.30369	−	16.3231i	−0.909576	−	2.79939i
$35$		0			0
$36$	−2.75796	+	8.48811i	−0.459659	+	1.41469i
$37$	8.39052	−	0.439728i	1.37939	−	0.0722909i	0.651847	−	0.758350i	$-0.273994\pi$
$37$	8.39052	−	0.439728i	1.37939	−	0.0722909i	0.727546	+	0.686059i	$0.240661\pi$
$38$	−4.20270	−	6.47159i	−0.681768	−	1.04983i
$39$	−5.23590	+	4.71442i	−0.838415	+	0.754912i
$40$		0			0
$41$	−5.83738	+	1.89668i	−0.911646	+	0.296212i	−0.727035	−	0.686600i	$-0.759102\pi$
$41$	−5.83738	+	1.89668i	−0.911646	+	0.296212i	−0.184610	+	0.982812i	$0.559102\pi$
$42$	0.0800095	+	14.7804i	0.0123457	+	2.28067i
$43$	3.18681	−	3.18681i	0.485984	−	0.485984i	−0.421052	−	0.907036i	$-0.638339\pi$
$43$	3.18681	−	3.18681i	0.485984	−	0.485984i	0.907036	+	0.421052i	$0.138339\pi$
$44$	−0.0265816	+	0.0597034i	−0.00400733	+	0.00900062i
$45$		0			0
$46$	12.1573	−	5.41276i	1.79249	−	0.798068i
$47$	2.89679	+	3.57724i	0.422541	+	0.521794i	0.943314	−	0.331900i	$-0.107690\pi$
$47$	2.89679	+	3.57724i	0.422541	+	0.521794i	−0.520774	+	0.853695i	$0.674356\pi$
$48$	−7.03633	+	3.58519i	−1.01561	+	0.517477i
$49$	2.23507	+	6.63359i	0.319295	+	0.947655i
$50$		0			0
$51$	8.11977	+	14.0639i	1.13700	+	1.96933i
$52$	−11.9482	−	0.626178i	−1.65691	−	0.0868352i
$53$	−1.55951	+	4.06266i	−0.214215	+	0.558050i	−0.998016	−	0.0629629i	$-0.979945\pi$
$53$	−1.55951	+	4.06266i	−0.214215	+	0.558050i	0.783801	+	0.621012i	$0.213278\pi$
$54$	−0.416980	+	3.96730i	−0.0567438	+	0.539881i
$55$		0			0
$56$	−8.60961	+	8.70333i	−1.15051	+	1.16303i
$57$	5.16276	+	5.16276i	0.683825	+	0.683825i
$58$	0.136572	−	0.0524250i	0.0179328	−	0.00688374i
$59$	2.45075	+	0.520924i	0.319061	+	0.0678185i	0.364658	−	0.931141i	$-0.381186\pi$
$59$	2.45075	+	0.520924i	0.319061	+	0.0678185i	−0.0455974	+	0.998960i	$0.514519\pi$
$60$		0			0
$61$	2.77436	+	13.0523i	0.355221	+	1.67118i	0.686099	+	0.727509i	$0.259322\pi$
$61$	2.77436	+	13.0523i	0.355221	+	1.67118i	−0.330878	+	0.943674i	$0.607345\pi$
$62$	−19.5210	−	9.94643i	−2.47917	−	1.26320i
$63$	−1.28946	−	5.90896i	−0.162457	−	0.744460i
$64$	8.63203	+	2.80472i	1.07900	+	0.350590i
$65$		0			0
$66$	0.0194425	−	0.0914696i	0.00239320	−	0.0112591i
$67$	−0.200158	+	0.247175i	−0.0244532	+	0.0301972i	−0.789226	−	0.614103i	$-0.789518\pi$
$67$	−0.200158	+	0.247175i	−0.0244532	+	0.0301972i	0.764773	+	0.644300i	$0.222851\pi$
$68$	−7.13755	+	26.6377i	−0.865556	+	3.23030i
$69$	−10.1869	+	7.40119i	−1.22635	+	0.890999i
$70$		0			0
$71$	−6.35569	−	4.61768i	−0.754282	−	0.548018i	0.142869	−	0.989742i	$-0.454367\pi$
$71$	−6.35569	−	4.61768i	−0.754282	−	0.548018i	−0.897151	+	0.441724i	$0.854367\pi$
$72$	8.22016	−	6.65655i	0.968755	−	0.784482i
$73$	−0.174974	+	3.33870i	−0.0204791	+	0.390765i	0.969090	+	0.246707i	$0.0793485\pi$
$73$	−0.174974	+	3.33870i	−0.0204791	+	0.390765i	−0.989569	+	0.144058i	$0.953985\pi$
$74$	−17.6807	−	10.2079i	−2.05533	−	1.18665i
$75$		0			0
$76$			12.3987i			1.42223i
$77$	−0.00486761	−	0.0440188i	−0.000554716	−	0.00501640i
$78$	16.9091	−	2.67814i	1.91458	−	0.303240i
$79$	−5.32825	−	0.560021i	−0.599475	−	0.0630073i	−0.200069	−	0.979782i	$-0.564117\pi$
$79$	−5.32825	−	0.560021i	−0.599475	−	0.0630073i	−0.399405	+	0.916774i	$0.630783\pi$
$80$		0			0
$81$	−1.11138	−	10.5741i	−0.123486	−	1.17490i
$82$	14.4058	+	3.86003i	1.59086	+	0.426270i
$83$	8.63403	+	1.36750i	0.947708	+	0.150102i	0.611110	−	0.791546i	$-0.290723\pi$
$83$	8.63403	+	1.36750i	0.947708	+	0.150102i	0.336599	+	0.941648i	$0.390723\pi$
$84$	12.8268	−	19.9876i	1.39952	−	2.18082i
$85$		0			0
$86$	−10.7117	+	2.27684i	−1.15507	+	0.245518i
$87$	−0.116086	+	0.0753869i	−0.0124457	+	0.00808233i
$88$	0.0649580	−	0.0421842i	0.00692455	−	0.00449685i
$89$	8.18738	−	1.74028i	0.867861	−	0.184470i	0.247597	−	0.968863i	$-0.420359\pi$
$89$	8.18738	−	1.74028i	0.867861	−	0.184470i	0.620264	+	0.784394i	$0.287026\pi$
$90$		0			0
$91$	7.20412	−	3.71994i	0.755197	−	0.389956i
$92$	−21.1194	−	3.34499i	−2.20185	−	0.348739i
$93$	20.0236	+	5.36531i	2.07635	+	0.556356i
$94$	−1.16913	−	11.1236i	−0.120587	−	1.14731i
$95$		0			0
$96$	−2.07644	−	0.218242i	−0.211926	−	0.0222743i
$97$	6.79613	−	1.07640i	0.690043	−	0.109292i	0.198442	−	0.980113i	$-0.436412\pi$
$97$	6.79613	−	1.07640i	0.690043	−	0.109292i	0.491601	+	0.870821i	$0.336412\pi$
$98$	4.22415	−	16.4762i	0.426704	−	1.66435i
$99$			0.0382642i			0.00384569i
$100$		0			0
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.0321267	−	0.999484i	$-0.510228\pi$
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.881642	+	0.471919i	$0.843561\pi$
$102$	2.06518	−	39.4059i	0.204483	−	3.90177i
$103$	−0.170043	+	0.137698i	−0.0167548	+	0.0135678i	−0.637661	−	0.770317i	$-0.720098\pi$
$103$	−0.170043	+	0.137698i	−0.0167548	+	0.0135678i	0.620906	+	0.783885i	$0.286765\pi$
$104$	11.4717	+	8.33468i	1.12489	+	0.817282i
$105$		0			0
$106$	8.55461	−	6.21528i	0.830897	−	0.603682i
$107$	1.26699	−	4.72847i	0.122485	−	0.457119i	−0.877253	−	0.480028i	$-0.840626\pi$
$107$	1.26699	−	4.72847i	0.122485	−	0.457119i	0.999738	+	0.0229097i	$0.00729301\pi$
$108$	4.03376	−	4.98127i	0.388148	−	0.479323i
$109$	−1.60438	+	7.54803i	−0.153672	+	0.722970i	0.832065	+	0.554678i	$0.187158\pi$
$109$	−1.60438	+	7.54803i	−0.153672	+	0.722970i	−0.985737	+	0.168292i	$0.946175\pi$
$110$		0			0
$111$	18.3718	+	5.96936i	1.74377	+	0.566587i
$112$	8.87874	−	1.93753i	0.838962	−	0.183079i
$113$	3.56746	+	1.81771i	0.335599	+	0.170996i	0.613666	−	0.789565i	$-0.289694\pi$
$113$	3.56746	+	1.81771i	0.335599	+	0.170996i	−0.278068	+	0.960561i	$0.589694\pi$
$114$	−3.68858	−	17.3534i	−0.345467	−	1.62530i
$115$		0			0
$116$	−0.229917	−	0.0488704i	−0.0213473	−	0.00453750i
$117$	−6.53993	+	2.51044i	−0.604616	+	0.232091i
$118$	−4.30491	−	4.30491i	−0.396299	−	0.396299i
$119$	−4.93444	−	18.0247i	−0.452339	−	1.65232i
$120$		0			0
$121$	1.14978	−	10.9395i	0.104526	−	0.994497i
$122$	11.6198	−	30.2705i	1.05200	−	2.74056i
$123$	−14.0921	−	0.738538i	−1.27065	−	0.0665917i
$124$	17.6014	+	30.4866i	1.58065	+	2.73777i
$125$		0			0
$126$	−5.19220	+	13.7481i	−0.462558	+	1.22478i
$127$	−6.49211	+	3.30790i	−0.576082	+	0.293528i	−0.717654	−	0.696399i	$-0.754784\pi$
$127$	−6.49211	+	3.30790i	−0.576082	+	0.293528i	0.141572	+	0.989928i	$0.454784\pi$
$128$	−12.7361	−	15.7278i	−1.12572	−	1.39015i
$129$	9.46591	−	4.21449i	0.833427	−	0.371065i
$130$		0			0
$131$	−4.81183	+	10.8075i	−0.420412	+	0.944260i	0.571880	+	0.820337i	$0.306214\pi$
$131$	−4.81183	+	10.8075i	−0.420412	+	0.944260i	−0.992292	+	0.123923i	$0.960452\pi$
$132$	−0.106246	+	0.106246i	−0.00924757	+	0.00924757i
$133$	−4.24035	−	7.25354i	−0.367685	−	0.628962i
$134$	0.735006	−	0.238818i	0.0634949	−	0.0206307i
$135$		0			0
$136$	24.2884	−	21.8694i	2.08272	−	1.87529i
$137$	1.79416	+	2.76276i	0.153285	+	0.236039i	0.906968	−	0.421200i	$-0.138391\pi$
$137$	1.79416	+	2.76276i	0.153285	+	0.236039i	−0.753682	+	0.657239i	$0.771724\pi$
$138$	30.5542	−	1.60128i	2.60094	−	0.136310i
$139$	1.40509	−	4.32443i	0.119179	−	0.366794i	−0.873617	−	0.486614i	$-0.838232\pi$
$139$	1.40509	−	4.32443i	0.119179	−	0.366794i	0.992796	+	0.119820i	$0.0382318\pi$
$140$		0			0
$141$	3.27031	+	10.0650i	0.275410	+	0.847625i
$142$	6.84097	+	17.8213i	0.574082	+	1.49553i
$143$	−0.0495483	+	0.0132764i	−0.00414344	+	0.00111023i
$144$	−7.80877	+	0.820735i	−0.650731	+	0.0683946i
$145$		0			0
$146$	4.77502	−	6.57225i	0.395183	−	0.543923i
$147$	−0.668241	+	16.0799i	−0.0551156	+	1.32625i
$148$	14.8926	+	29.2285i	1.22417	+	2.40256i
$149$	−15.7486	+	9.09246i	−1.29018	+	0.744884i	−0.978685	−	0.205366i	$-0.934162\pi$
$149$	−15.7486	+	9.09246i	−1.29018	+	0.744884i	−0.311491	+	0.950249i	$0.600828\pi$
$150$		0			0
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	−0.169072	−	0.985604i	$-0.554077\pi$
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	0.938094	−	0.346381i	$-0.112590\pi$
$152$	8.00310	−	12.3237i	0.649137	−	0.999583i
$153$	2.52586	+	15.9477i	0.204204	+	1.28929i
$154$	−0.0483350	+	0.0961460i	−0.00389495	+	0.00774766i
$155$		0			0
$156$	−25.1298	−	11.1885i	−2.01199	−	0.895796i
$157$	4.20781	+	15.7038i	0.335820	+	1.25330i	0.902978	+	0.429688i	$0.141376\pi$
$157$	4.20781	+	15.7038i	0.335820	+	1.25330i	−0.567158	+	0.823609i	$0.691957\pi$
$158$	10.1171	+	8.19266i	0.804873	+	0.651773i
$159$	−6.69470	+	7.43521i	−0.530924	+	0.589651i
$160$		0			0
$161$	13.4994	−	5.26593i	1.06390	−	0.415014i
$162$	−11.7289	+	23.0193i	−0.921510	+	1.80856i
$163$	−0.490229	−	9.35413i	−0.0383977	−	0.732672i	−0.948208	−	0.317649i	$-0.897107\pi$
$163$	−0.490229	−	9.35413i	−0.0383977	−	0.732672i	0.909811	−	0.415023i	$-0.136227\pi$
$164$	−16.0348	−	17.8084i	−1.25211	−	1.39060i
$165$		0			0
$166$	−15.7852	−	14.2131i	−1.22517	−	1.10315i
$167$	1.18224	−	7.46435i	0.0914842	−	0.577608i	−0.898779	−	0.438402i	$-0.855545\pi$
$167$	1.18224	−	7.46435i	0.0914842	−	0.577608i	0.990263	−	0.139207i	$-0.0444553\pi$
$168$	−25.6507	+	11.5872i	−1.97899	+	0.893972i
$169$	2.12129	+	2.91971i	0.163177	+	0.224593i
$170$		0			0
$171$	2.95266	+	6.63179i	0.225796	+	0.507145i
$172$	16.4272	+	6.30581i	1.25256	+	0.480813i
$173$	−19.6275	−	12.7463i	−1.49225	−	0.969080i	−0.994828	−	0.101572i	$-0.967613\pi$
$173$	−19.6275	−	12.7463i	−1.49225	−	0.969080i	−0.497423	−	0.867508i	$-0.665720\pi$
$174$	0.336334			0.0254974
$175$		0			0
$176$	−0.0574953			−0.00433387
$177$	4.83112	+	3.13737i	0.363129	+	0.235819i
$178$	−18.9878	−	7.28875i	−1.42320	−	0.546315i
$179$	5.54190	+	12.4473i	0.414221	+	0.930356i	0.993351	+	0.115121i	$0.0367256\pi$
$179$	5.54190	+	12.4473i	0.414221	+	0.930356i	−0.579130	+	0.815235i	$0.696608\pi$
$180$		0			0
$181$	−3.38018	−	4.65241i	−0.251247	−	0.345811i	0.664701	−	0.747110i	$-0.268559\pi$
$181$	−3.38018	−	4.65241i	−0.251247	−	0.345811i	−0.915947	+	0.401298i	$0.868559\pi$
$182$	−19.6040	−	1.95323i	−1.45314	−	0.144783i
$183$	−4.79930	+	30.3016i	−0.354774	+	2.23996i
$184$	18.8325	+	16.9569i	1.38835	+	1.25008i
$185$		0			0
$186$	−33.7049	−	37.4330i	−2.47136	−	2.74472i
$187$	0.00618787	+	0.118072i	0.000452502	+	0.00863424i
$188$	−8.15893	+	16.0128i	−0.595051	+	1.16785i
$189$	−0.656250	+	4.29370i	−0.0477352	+	0.312321i
$190$		0			0
$191$	−9.91552	+	11.0123i	−0.717462	+	0.796822i	−0.986053	−	0.166432i	$-0.946775\pi$
$191$	−9.91552	+	11.0123i	−0.717462	+	0.796822i	0.268591	+	0.963254i	$0.413442\pi$
$192$	16.2170	+	13.1323i	1.17036	+	0.947740i
$193$	−4.30663	−	16.0726i	−0.309998	−	1.15693i	−0.928557	−	0.371191i	$-0.878950\pi$
$193$	−4.30663	−	16.0726i	−0.309998	−	1.15693i	0.618558	−	0.785739i	$-0.287717\pi$
$194$	−15.2741	−	6.80046i	−1.09662	−	0.488245i
$195$		0			0
$196$	−20.1109	+	18.5061i	−1.43649	+	1.32186i
$197$	−2.43376	−	15.3662i	−0.173398	−	1.09479i	−0.908821	−	0.417185i	$-0.863017\pi$
$197$	−2.43376	−	15.3662i	−0.173398	−	1.09479i	0.735423	−	0.677608i	$-0.236983\pi$
$198$	0.0506389	−	0.0779771i	0.00359875	−	0.00554159i
$199$	−0.988951	+	1.71291i	−0.0701049	+	0.121425i	−0.898947	−	0.438057i	$-0.855667\pi$
$199$	−0.988951	+	1.71291i	−0.0701049	+	0.121425i	0.828842	+	0.559482i	$0.189000\pi$
$200$		0			0
$201$	−0.633276	+	0.365622i	−0.0446678	+	0.0257890i
$202$	11.6976	+	22.9578i	0.823039	+	1.61531i
$203$	0.151221	−	0.0500411i	0.0106136	−	0.00351220i
$204$	−37.2677	+	51.2946i	−2.60926	+	3.59134i
$205$		0			0
$206$	0.528754	−	0.0555743i	0.0368401	−	0.00387205i
$207$	−12.0929	+	3.24028i	−0.840514	+	0.225215i
$208$	−3.77216	−	9.82681i	−0.261552	−	0.681367i
$209$	0.0164266	+	0.0505557i	0.00113625	+	0.00349701i
$210$		0			0
$211$	2.82445	−	8.69276i	0.194443	−	0.598434i	−0.805540	−	0.592542i	$-0.798124\pi$
$211$	2.82445	−	8.69276i	0.194443	−	0.598434i	0.999983	−	0.00589215i	$-0.00187554\pi$
$212$	−16.9670	+	0.889200i	−1.16530	+	0.0610705i
$213$	−9.83728	−	15.1481i	−0.674040	−	1.03793i
$214$	−8.83963	+	7.95924i	−0.604264	+	0.544082i
$215$		0			0
$216$	−7.22465	+	2.34743i	−0.491575	+	0.159722i
$217$	−20.7236	−	11.8157i	−1.40681	−	0.802101i
$218$	13.2586	−	13.2586i	0.897985	−	0.897985i
$219$	−3.12642	+	7.02205i	−0.211264	+	0.474506i
$220$		0			0
$221$	−19.7742	+	8.80405i	−1.33016	+	0.592225i
$222$	−29.5393	−	36.4780i	−1.98255	−	2.44824i
$223$	6.62726	−	3.37676i	0.443794	−	0.226124i	−0.217789	−	0.975996i	$-0.569885\pi$
$223$	6.62726	−	3.37676i	0.443794	−	0.226124i	0.661584	+	0.749871i	$0.269885\pi$
$224$	2.24771	+	0.848882i	0.150181	+	0.0567183i
$225$		0			0
$226$	−4.86443	−	8.42544i	−0.323577	−	0.560452i
$227$	11.7014	+	0.613246i	0.776651	+	0.0407026i	0.436543	−	0.899684i	$-0.356203\pi$
$227$	11.7014	+	0.613246i	0.776651	+	0.0407026i	0.340109	+	0.940386i	$0.389536\pi$
$228$	−10.2157	+	26.6127i	−0.676549	+	1.76247i
$229$	2.81607	−	26.7931i	0.186091	−	1.77054i	−0.360134	−	0.932901i	$-0.617269\pi$
$229$	2.81607	−	26.7931i	0.186091	−	1.77054i	0.546225	−	0.837638i	$-0.316064\pi$
$230$		0			0
$231$	0.0258205	−	0.0984929i	0.00169886	−	0.00648036i
$232$	0.196981	+	0.196981i	0.0129324	+	0.0129324i
$233$	−20.3954	+	7.82907i	−1.33615	+	0.512900i	−0.918397	−	0.395661i	$-0.870515\pi$
$233$	−20.3954	+	7.82907i	−1.33615	+	0.512900i	−0.417753	+	0.908561i	$0.637182\pi$
$234$	16.6498	+	3.53902i	1.08843	+	0.231353i
$235$		0			0
$236$	2.03383	+	9.56842i	0.132391	+	0.622851i
$237$	−10.9752	−	5.59214i	−0.712915	−	0.363248i
$238$	−13.7983	+	43.2622i	−0.894409	+	2.80427i
$239$	−4.05851	−	1.31869i	−0.262523	−	0.0852989i	0.174798	−	0.984604i	$-0.444073\pi$
$239$	−4.05851	−	1.31869i	−0.262523	−	0.0852989i	−0.437321	+	0.899305i	$0.644073\pi$
$240$		0			0
$241$	0.0341430	−	0.160630i	0.00219934	−	0.0103471i	−0.977034	−	0.213082i	$-0.931650\pi$
$241$	0.0341430	−	0.160630i	0.00219934	−	0.0103471i	0.979234	+	0.202735i	$0.0649831\pi$
$242$	−16.8204	+	20.7715i	−1.08126	+	1.33524i
$243$	5.05209	−	18.8546i	0.324092	−	1.20953i
$244$	−42.1485	+	30.6227i	−2.69828	+	1.96042i
$245$		0			0
$246$	27.7405	+	20.1546i	1.76867	+	1.28501i
$247$	−7.56302	+	6.12442i	−0.481224	+	0.389687i
$248$	2.18349	−	41.6634i	0.138652	−	2.64563i
$249$	17.4055	+	10.0490i	1.10303	+	0.636832i
$250$		0			0
$251$		−	0.132304i		−	0.00835098i	−0.999991	−	0.00417549i	$-0.998671\pi$
$251$		−	0.132304i		−	0.00835098i	0.999991	−	0.00417549i	$-0.00132910\pi$
$252$	19.0280	−	13.9827i	1.19865	−	0.880825i
$253$	−0.0905461	+	0.0143411i	−0.00569259	+	0.000901617i
$254$	17.6077	+	1.85065i	1.10481	+	0.116120i
$255$		0			0
$256$	3.24278	+	30.8530i	0.202674	+	1.92831i
$257$	8.87663	+	2.37849i	0.553709	+	0.148366i	0.524815	−	0.851217i	$-0.324135\pi$
$257$	8.87663	+	2.37849i	0.553709	+	0.148366i	0.0288944	+	0.999582i	$0.490801\pi$
$258$	−24.8677	−	3.93865i	−1.54819	−	0.245210i
$259$	−18.7087	−	12.0061i	−1.16250	−	0.746020i
$260$		0			0
$261$	−0.134615	+	0.0286134i	−0.00833249	+	0.00177113i
$262$	24.1086	−	15.6563i	1.48943	−	0.967249i
$263$	−17.5431	+	11.3926i	−1.08175	+	0.702499i	−0.957117	−	0.289703i	$-0.906443\pi$
$263$	−17.5431	+	11.3926i	−1.08175	+	0.702499i	−0.124637	+	0.992202i	$0.539777\pi$
$264$	0.174183	−	0.0370238i	0.0107202	−	0.00227866i
$265$		0			0
$266$	−0.958107	+	20.3934i	−0.0587453	+	1.25040i
$267$	19.0074	+	3.01047i	1.16323	+	0.184238i
$268$	−1.19946	−	0.321394i	−0.0732687	−	0.0196323i
$269$	0.158106	+	1.50428i	0.00963991	+	0.0917176i	0.998284	−	0.0585585i	$-0.0186504\pi$
$269$	0.158106	+	1.50428i	0.00963991	+	0.0917176i	−0.988644	+	0.150276i	$0.951984\pi$
$270$		0			0
$271$	9.03693	+	0.949820i	0.548955	+	0.0576974i	0.374946	−	0.927047i	$-0.377661\pi$
$271$	9.03693	+	0.949820i	0.548955	+	0.0576974i	0.174009	+	0.984744i	$0.444328\pi$
$272$	−23.9627	+	3.79533i	−1.45295	+	0.230125i
$273$	18.5280	−	2.04883i	1.12136	−	0.124001i
$274$		−	8.00453i		−	0.483571i
$275$		0			0
$276$	−42.5749	−	24.5807i	−2.56271	−	1.47958i
$277$	0.715125	−	13.6454i	0.0429677	−	0.819872i	−0.889128	−	0.457659i	$-0.848688\pi$
$277$	0.715125	−	13.6454i	0.0429677	−	0.819872i	0.932095	−	0.362213i	$-0.117979\pi$
$278$	−8.58636	+	6.95309i	−0.514975	+	0.417019i
$279$	16.6747	+	12.1149i	0.998291	+	0.725301i
$280$		0			0
$281$	−3.22462	+	2.34282i	−0.192365	+	0.139761i	−0.679799	−	0.733399i	$-0.737933\pi$
$281$	−3.22462	+	2.34282i	−0.192365	+	0.139761i	0.487434	+	0.873160i	$0.337933\pi$
$282$	6.65559	−	24.8390i	0.396334	−	1.47914i
$283$	−11.8922	+	14.6857i	−0.706920	+	0.872974i	−0.996449	−	0.0841955i	$-0.973168\pi$
$283$	−11.8922	+	14.6857i	−0.706920	+	0.872974i	0.289529	+	0.957169i	$0.406501\pi$
$284$	6.37712	−	30.0020i	0.378413	−	1.78029i
$285$		0			0
$286$	0.118543	+	0.0385168i	0.00700957	+	0.00227755i
$287$	15.4712	+	4.93447i	0.913236	+	0.291272i
$288$	−1.84965	−	0.942442i	−0.108991	−	0.0555339i
$289$	6.83850	+	32.1726i	0.402265	+	1.89251i
$290$		0			0
$291$	15.4742	+	3.28914i	0.907112	+	0.192813i
$292$	−12.1861	+	4.67781i	−0.713138	+	0.273748i
$293$	4.94524	+	4.94524i	0.288904	+	0.288904i	0.836647	−	0.547743i	$-0.184513\pi$
$293$	4.94524	+	4.94524i	0.288904	+	0.288904i	−0.547743	+	0.836647i	$0.684513\pi$
$294$	22.6420	−	31.8843i	1.32051	−	1.85953i
$295$		0			0
$296$	4.06380	−	38.6645i	0.236204	−	2.24733i
$297$	0.00984815	−	0.0256553i	0.000571447	−	0.00148867i
$298$	44.1265	+	2.31257i	2.55618	+	0.133964i
$299$	−8.39168	−	14.5348i	−0.485303	−	0.840570i
$300$		0			0
$301$	−11.7669	+	1.92904i	−0.678231	+	0.111188i
$302$	−40.9187	+	20.8491i	−2.35460	+	1.19973i
$303$	−15.3426	−	18.9465i	−0.881409	−	1.08845i
$304$	−9.96484	+	4.43663i	−0.571523	+	0.254458i
$305$		0			0
$306$	15.9578	−	35.8419i	0.912248	−	2.04894i
$307$	4.76473	−	4.76473i	0.271938	−	0.271938i	−0.557942	−	0.829880i	$-0.688409\pi$
$307$	4.76473	−	4.76473i	0.271938	−	0.271938i	0.829880	+	0.557942i	$0.188409\pi$
$308$	0.149273	−	0.0872638i	0.00850564	−	0.00497232i
$309$	−0.478436	+	0.155453i	−0.0272173	+	0.00884342i
$310$		0			0
$311$	1.95368	−	1.75910i	0.110783	−	0.0997496i	−0.611878	−	0.790952i	$-0.709586\pi$
$311$	1.95368	−	1.75910i	0.110783	−	0.0997496i	0.722661	+	0.691203i	$0.242919\pi$
$312$	17.7558	+	27.3415i	1.00522	+	1.54791i
$313$	4.34316	−	0.227616i	0.245490	−	0.0128656i	0.0708059	−	0.997490i	$-0.477443\pi$
$313$	4.34316	−	0.227616i	0.245490	−	0.0128656i	0.174684	+	0.984625i	$0.444110\pi$
$314$	12.2075	−	37.5707i	0.688908	−	2.12024i
$315$		0			0
$316$	−6.46387	−	19.8938i	−0.363621	−	1.11911i
$317$	−7.43621	−	19.3720i	−0.417659	−	1.08804i	−0.967523	−	0.252784i	$-0.918654\pi$
$317$	−7.43621	−	19.3720i	−0.417659	−	1.08804i	0.549864	−	0.835254i	$-0.314680\pi$
$318$	23.4827	−	6.29216i	1.31684	−	0.352847i
$319$	−0.00100223		0.000105339i	−5.61143e−5		5.89785e-6i
$320$		0			0
$321$	6.61541	−	9.10533i	0.369236	−	0.508210i
$322$	−34.4788	−	7.13384i	−1.92143	−	0.397553i
$323$	10.1835	+	19.9862i	0.566623	+	1.11206i
$324$	35.9500	−	20.7557i	1.99722	−	1.15310i
$325$		0			0
$326$	−11.3803	+	19.7112i	−0.630295	+	1.09170i
$327$	−9.66271	+	14.8793i	−0.534349	+	0.822825i
$328$	4.44281	+	28.0508i	0.245313	+	1.54884i
$329$	−0.703199	−	12.1582i	−0.0387686	−	0.670304i
$330$		0			0
$331$	14.5178	+	6.46376i	0.797972	+	0.355280i	0.764881	−	0.644172i	$-0.222798\pi$
$331$	14.5178	+	6.46376i	0.797972	+	0.355280i	0.0330919	+	0.999452i	$0.489465\pi$
$332$	8.83346	+	32.9669i	0.484799	+	1.80929i
$333$	14.9263	+	12.0871i	0.817955	+	0.662367i
$334$	−12.2876	+	13.6467i	−0.672346	+	0.746716i
$335$		0			0
$336$	20.6538	+	3.15673i	1.12676	+	0.172214i
$337$	11.6113	−	22.7884i	0.632508	−	1.24137i	−0.323000	−	0.946399i	$-0.604691\pi$
$337$	11.6113	−	22.7884i	0.632508	−	1.24137i	0.955507	−	0.294967i	$-0.0953086\pi$
$338$	−0.458951	−	8.75730i	−0.0249636	−	0.476334i
$339$	6.15957	+	6.84090i	0.334542	+	0.371547i
$340$		0			0
$341$	0.112160	+	0.100989i	0.00607382	+	0.00546889i
$342$	2.75941	−	17.4222i	0.149212	−	0.942086i
$343$	5.43629	−	17.7044i	0.293532	−	0.955949i
$344$	−12.2575	−	16.8710i	−0.660882	−	0.909626i
$345$		0			0
$346$	23.1297	+	51.9502i	1.24346	+	2.79286i
$347$	14.1465	+	5.43034i	0.759425	+	0.291516i	0.707099	−	0.707114i	$-0.250003\pi$
$347$	14.1465	+	5.43034i	0.759425	+	0.291516i	0.0523255	+	0.998630i	$0.483337\pi$
$348$	−0.453231	−	0.294331i	−0.0242957	−	0.0157778i
$349$	−1.48928			−0.0797192			−0.0398596	−	0.999205i	$-0.512691\pi$
$349$	−1.48928			−0.0797192			−0.0398596	+	0.999205i	$0.512691\pi$
$350$		0			0
$351$	5.03100			0.268535
$352$	−0.0127486	−	0.00827905i	−0.000679504	−	0.000441275i
$353$	8.77541	+	3.36856i	0.467068	+	0.179291i	0.580509	−	0.814254i	$-0.302854\pi$
$353$	8.77541	+	3.36856i	0.467068	+	0.179291i	−0.113441	+	0.993545i	$0.536187\pi$
$354$	−5.69315	−	12.7870i	−0.302588	−	0.679623i
$355$		0			0
$356$	19.2088	+	26.4386i	1.01806	+	1.40124i
$357$	4.25978	−	42.7541i	0.225451	−	2.26279i
$358$	5.17918	−	32.7001i	0.273728	−	1.72825i
$359$	−4.56543	−	4.11073i	−0.240954	−	0.216956i	0.539802	−	0.841792i	$-0.318499\pi$
$359$	−4.56543	−	4.11073i	−0.240954	−	0.216956i	−0.780756	+	0.624836i	$0.785166\pi$
$360$		0			0
$361$	−5.96536	−	6.62520i	−0.313966	−	0.348695i
$362$	0.731315	+	13.9543i	0.0384370	+	0.733422i
$363$	11.4813	−	22.5332i	0.602610	−	1.18269i
$364$	24.7083	+	19.7879i	1.29506	+	1.03717i
$365$		0			0
$366$	49.8815	−	55.3990i	2.60735	−	2.89575i
$367$	−28.0420	−	22.7079i	−1.46378	−	1.18534i	−0.943511	−	0.331341i	$-0.892499\pi$
$367$	−28.0420	−	22.7079i	−1.46378	−	1.18534i	−0.520267	−	0.854003i	$-0.674168\pi$
$368$	−4.86880	−	18.1706i	−0.253804	−	0.947209i
$369$	−12.8176	−	5.70676i	−0.667257	−	0.297082i
$370$		0			0
$371$	9.62196	−	6.32289i	0.499547	−	0.328268i
$372$	12.6611	+	79.9390i	0.656447	+	4.14464i
$373$	−10.1248	+	15.5909i	−0.524244	+	0.807264i	−0.997274	−	0.0737815i	$-0.976493\pi$
$373$	−10.1248	+	15.5909i	−0.524244	+	0.807264i	0.473031	+	0.881046i	$0.343160\pi$
$374$	0.143646	−	0.248802i	0.00742777	−	0.0128653i
$375$		0			0
$376$	18.4455	−	10.6495i	0.951252	−	0.549206i
$377$	−0.0837587	−	0.164386i	−0.00431379	−	0.00846629i
$378$	7.01965	−	7.88149i	0.361052	−	0.405380i
$379$	−13.0838	+	18.0083i	−0.672068	+	0.925022i	−0.999805	−	0.0197466i	$-0.993714\pi$
$379$	−13.0838	+	18.0083i	−0.672068	+	0.925022i	0.327737	+	0.944769i	$0.393714\pi$
$380$		0			0
$381$	−16.6602	+	1.75106i	−0.853529	+	0.0897095i
$382$	34.7802	−	9.31932i	1.77951	−	0.476818i
$383$	−5.51711	−	14.3726i	−0.281911	−	0.734403i	−0.999288	−	0.0377184i	$-0.987991\pi$
$383$	−5.51711	−	14.3726i	−0.281911	−	0.734403i	0.717377	−	0.696685i	$-0.245342\pi$
$384$	−14.3783	−	44.2520i	−0.733742	−	2.25822i
$385$		0			0
$386$	−12.4942	+	38.4531i	−0.635937	+	1.95721i
$387$	10.2882	−	0.539182i	0.522979	−	0.0274082i
$388$	14.6316	+	22.5307i	0.742806	+	1.14382i
$389$	8.85903	−	7.97670i	0.449171	−	0.404435i	−0.413258	−	0.910614i	$-0.635609\pi$
$389$	8.85903	−	7.97670i	0.449171	−	0.404435i	0.862428	+	0.506179i	$0.168943\pi$
$390$		0			0
$391$	−36.7909	+	11.9541i	−1.86060	+	0.604545i
$392$	31.9345	−	5.41296i	1.61294	−	0.273396i
$393$	−19.2328	+	19.2328i	−0.970168	+	0.970168i
$394$	−15.3760	+	34.5350i	−0.774629	+	1.73985i
$395$		0			0
$396$	−0.136478	+	0.0607640i	−0.00685828	+	0.00305350i
$397$	−4.26600	−	5.26807i	−0.214105	−	0.264397i	0.658767	−	0.752347i	$-0.271078\pi$
$397$	−4.26600	−	5.26807i	−0.214105	−	0.264397i	−0.872872	+	0.487950i	$0.837745\pi$
$398$	4.28222	−	2.18190i	0.214648	−	0.109369i
$399$	−3.12512	−	19.0628i	−0.156452	−	0.954335i
$400$		0			0
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	0.542220	−	0.840237i	$-0.317584\pi$
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	−0.998776	+	0.0494575i	$0.984251\pi$
$402$	1.77439	+	0.0929920i	0.0884987	+	0.00463802i
$403$	−9.90201	+	25.7956i	−0.493254	+	1.28497i
$404$	4.32754	−	41.1738i	0.215303	−	2.04847i
$405$		0			0
$406$	−0.374391	−	0.0981488i	−0.0185807	−	0.00487104i
$407$	0.0994483	+	0.0994483i	0.00492947	+	0.00492947i
$408$	70.1518	−	26.9287i	3.47303	−	1.33317i
$409$	−15.5613	−	3.30765i	−0.769456	−	0.163553i	−0.193574	−	0.981086i	$-0.562008\pi$
$409$	−15.5613	−	3.30765i	−0.769456	−	0.163553i	−0.575882	+	0.817533i	$0.695341\pi$
$410$		0			0
$411$	1.57468	+	7.40829i	0.0776732	+	0.365424i
$412$	−0.761163	−	0.387832i	−0.0374998	−	0.0191071i
$413$	−4.46223	−	4.90218i	−0.219572	−	0.241221i
$414$	28.9318	+	9.40052i	1.42192	+	0.462010i
$415$		0			0
$416$	0.578601	−	2.72210i	0.0283683	−	0.133462i
$417$	6.57894	−	8.12431i	0.322172	−	0.397849i
$418$	0.0334306	−	0.124765i	0.00163514	−	0.00610243i
$419$	28.7560	−	20.8925i	1.40482	−	1.02066i	0.410773	−	0.911738i	$-0.365259\pi$
$419$	28.7560	−	20.8925i	1.40482	−	1.02066i	0.994050	−	0.108926i	$-0.0347411\pi$
$420$		0			0
$421$	−11.3679	−	8.25925i	−0.554037	−	0.402531i	0.275235	−	0.961377i	$-0.411244\pi$
$421$	−11.3679	−	8.25925i	−0.554037	−	0.402531i	−0.829272	+	0.558846i	$0.811244\pi$
$422$	−17.2599	+	13.9768i	−0.840197	+	0.680378i
$423$	−0.550694	+	10.5079i	−0.0267757	+	0.510910i
$424$	17.4383	+	10.0680i	0.846876	+	0.488944i
$425$		0			0
$426$			43.8884i			2.12640i
$427$	14.1849	−	32.3298i	0.686458	−	1.56455i
$428$	18.8772	−	2.98985i	0.912464	−	0.144520i
$429$	−0.117290	−	0.0123277i	−0.00566280	−	0.000595185i
$430$		0			0
$431$	−0.397806	−	3.78487i	−0.0191616	−	0.182311i	0.980755	−	0.195244i	$-0.0625498\pi$
$431$	−0.397806	−	3.78487i	−0.0191616	−	0.182311i	−0.999916	+	0.0129330i	$0.995883\pi$
$432$	5.44685	+	1.45948i	0.262061	+	0.0702192i
$433$	−1.22529	−	0.194066i	−0.0588836	−	0.00932624i	0.126923	−	0.991913i	$-0.459490\pi$
$433$	−1.22529	−	0.194066i	−0.0588836	−	0.00932624i	−0.185807	+	0.982586i	$0.559490\pi$
$434$	26.5950	+	51.5044i	1.27660	+	2.47229i
$435$		0			0
$436$	−29.4696	+	6.26395i	−1.41134	+	0.299989i
$437$	−14.5864	+	9.47255i	−0.697764	+	0.453133i
$438$	15.6642	−	10.1725i	0.748465	−	0.486059i
$439$	−5.32727	+	1.13235i	−0.254257	+	0.0540439i	−0.333277	−	0.942829i	$-0.608154\pi$
$439$	−5.32727	+	1.13235i	−0.254257	+	0.0540439i	0.0790199	+	0.996873i	$0.474821\pi$
$440$		0			0
$441$	−6.34978	+	14.6878i	−0.302371	+	0.699417i
$442$	51.9485	+	8.22783i	2.47094	+	0.391358i
$443$	−17.6715	−	4.73507i	−0.839599	−	0.224970i	−0.186702	−	0.982417i	$-0.559780\pi$
$443$	−17.6715	−	4.73507i	−0.839599	−	0.224970i	−0.652897	+	0.757447i	$0.726447\pi$
$444$	7.88353	+	75.0067i	0.374136	+	3.55966i
$445$		0			0
$446$	−17.9743	−	1.88917i	−0.851106	−	0.0894548i
$447$	−41.2945	+	6.54041i	−1.95316	+	0.309351i
$448$	−14.2197	−	19.3507i	−0.671820	−	0.914233i
$449$			7.28927i			0.344002i	0.985097	+	0.172001i	$0.0550232\pi$
$449$			7.28927i			0.344002i	−0.985097	+	0.172001i	$0.944977\pi$
$450$		0			0
$451$	−0.0889755	−	0.0513700i	−0.00418969	−	0.00241892i
$452$	−0.818124	+	15.6107i	−0.0384813	+	0.734267i
$453$	33.7692	−	27.3458i	1.58662	−	1.28482i
$454$	−23.0343	−	16.7354i	−1.08105	−	0.785432i
$455$		0			0
$456$	27.3318	−	19.8577i	1.27993	−	0.929922i
$457$	−3.05849	+	11.4145i	−0.143070	+	0.533946i	0.856763	+	0.515710i	$0.172472\pi$
$457$	−3.05849	+	11.4145i	−0.143070	+	0.533946i	−0.999834	+	0.0182361i	$0.994195\pi$
$458$	−41.1969	+	50.8739i	−1.92500	+	2.37718i
$459$	2.41095	−	11.3426i	0.112534	−	0.529429i
$460$		0			0
$461$	−0.809532	−	0.263033i	−0.0377037	−	0.0122507i	0.290104	−	0.956995i	$-0.406310\pi$
$461$	−0.809532	−	0.263033i	−0.0377037	−	0.0122507i	−0.327808	+	0.944744i	$0.606310\pi$
$462$	−0.182964	+	0.166544i	−0.00851227	+	0.00774833i
$463$	−34.4372	−	17.5466i	−1.60043	−	0.815460i	−0.999874	−	0.0158788i	$-0.994945\pi$
$463$	−34.4372	−	17.5466i	−1.60043	−	0.815460i	−0.600557	−	0.799582i	$-0.705055\pi$
$464$	−0.0429941	−	0.202271i	−0.00199595	−	0.00939022i
$465$		0			0
$466$	51.9241	+	11.0368i	2.40534	+	0.511270i
$467$	8.34928	−	3.20499i	0.386358	−	0.148309i	−0.157433	−	0.987530i	$-0.550322\pi$
$467$	8.34928	−	3.20499i	0.386358	−	0.148309i	0.543791	+	0.839221i	$0.316988\pi$
$468$	−19.3396	−	19.3396i	−0.893972	−	0.893972i
$469$	0.811629	−	0.222191i	0.0374775	−	0.0102598i
$470$		0			0
$471$	−3.90711	+	37.1737i	−0.180030	+	1.71287i
$472$	4.15468	−	10.8233i	0.191235	−	0.498183i
$473$	0.0753362	+	0.00394820i	0.00346396	+	0.000181538i
$474$	14.9653	+	25.9206i	0.687377	+	1.19057i
$475$		0			0
$476$	56.4535	−	46.2233i	2.58754	−	2.11864i
$477$	−8.86348	+	4.51617i	−0.405831	+	0.206781i
$478$	6.52552	+	8.05835i	0.298470	+	0.368580i
$479$	0.885419	−	0.394214i	0.0404558	−	0.0180121i	−0.386409	−	0.922328i	$-0.626285\pi$
$479$	0.885419	−	0.394214i	0.0404558	−	0.0180121i	0.426865	+	0.904315i	$0.359618\pi$
$480$		0			0
$481$	−10.4726	+	23.5218i	−0.477509	+	1.07250i
$482$	−0.282157	+	0.282157i	−0.0128519	+	0.0128519i
$483$	33.3139	−	0.180335i	1.51584	−	0.00820553i
$484$	40.8440	−	13.2710i	1.85655	−	0.603228i
$485$		0			0
$486$	−35.2477	+	31.7372i	−1.59887	+	1.43963i
$487$	18.8835	+	29.0780i	0.855691	+	1.31765i	0.946805	+	0.321808i	$0.104291\pi$
$487$	18.8835	+	29.0780i	0.855691	+	1.31765i	−0.0911139	+	0.995840i	$0.529043\pi$
$488$	61.6598	−	3.23145i	2.79121	−	0.146281i
$489$	6.65491	−	20.4817i	0.300946	−	0.926215i
$490$		0			0
$491$	1.58176	+	4.86817i	0.0713840	+	0.219697i	0.980383	−	0.197100i	$-0.0631524\pi$
$491$	1.58176	+	4.86817i	0.0713840	+	0.219697i	−0.908999	+	0.416798i	$0.863152\pi$
$492$	−19.7443	−	51.4357i	−0.890143	−	2.31890i
$493$	−0.410755	+	0.110061i	−0.0184995	+	0.00495692i
$494$	23.5175	−	2.47179i	1.05810	−	0.111211i
$495$		0			0
$496$	−18.2037	+	25.0553i	−0.817371	+	1.12501i
$497$	6.52990	+	19.7329i	0.292906	+	0.885139i
$498$	−22.1710	−	43.5130i	−0.993506	−	1.94986i
$499$	31.5502	−	18.2155i	1.41238	−	0.815438i	0.416768	−	0.909013i	$-0.363163\pi$
$499$	31.5502	−	18.2155i	1.41238	−	0.815438i	0.995612	+	0.0935745i	$0.0298293\pi$
$500$		0			0
$501$	8.68766	−	15.0475i	0.388136	−	0.672271i
$502$	−0.175092	+	0.269618i	−0.00781474	+	0.0120336i
$503$	−0.209162	−	1.32059i	−0.00932605	−	0.0588824i	0.982586	−	0.185806i	$-0.0594896\pi$
$503$	−0.209162	−	1.32059i	−0.00932605	−	0.0588824i	−0.991912	+	0.126924i	$0.959490\pi$
$504$	−27.9384	+	1.61588i	−1.24448	+	0.0719772i
$505$		0			0
$506$	0.203500	+	0.0906038i	0.00904666	+	0.00402783i
$507$	2.14753	+	8.01470i	0.0953752	+	0.355945i
$508$	−22.1079	−	17.9027i	−0.980882	−	0.794302i
$509$	−12.8202	+	14.2382i	−0.568244	+	0.631098i	−0.956946	−	0.290265i	$-0.906257\pi$
$509$	−12.8202	+	14.2382i	−0.568244	+	0.631098i	0.388703	+	0.921363i	$0.372923\pi$
$510$		0			0
$511$	5.52935	−	6.90427i	0.244604	−	0.305427i
$512$	15.8470	−	31.1015i	0.700346	−	1.37451i
$513$	−0.272856	−	5.20640i	−0.0120469	−	0.229868i
$514$	−14.9417	−	16.5944i	−0.659048	−	0.731947i
$515$		0			0
$516$	30.0640	+	27.0697i	1.32349	+	1.19168i
$517$	−0.0120533	+	0.0761016i	−0.000530104	+	0.00334694i
$518$	22.2368	+	49.2258i	0.977028	+	2.16286i
$519$	−31.6267	−	43.5304i	−1.38826	−	1.91077i
$520$		0			0
$521$	5.94344	+	13.3492i	0.260387	+	0.584838i	0.995674	−	0.0929175i	$-0.0296193\pi$
$521$	5.94344	+	13.3492i	0.260387	+	0.584838i	−0.735287	+	0.677756i	$0.762953\pi$
$522$	0.312195	+	0.119840i	0.0136644	+	0.00524527i
$523$	29.1893	+	18.9558i	1.27636	+	0.828877i	0.991552	−	0.129707i	$-0.0414038\pi$
$523$	29.1893	+	18.9558i	1.27636	+	0.828877i	0.284807	+	0.958585i	$0.408070\pi$
$524$	−46.1889			−2.01777
$525$		0			0
$526$	50.8274			2.21618
$527$	53.4123	+	34.6864i	2.32668	+	1.51096i
$528$	−0.123408	−	0.0473721i	−0.00537066	−	0.00206160i
$529$	−2.84498	−	6.38993i	−0.123695	−	0.277823i
$530$		0			0
$531$	3.36650	+	4.63359i	0.146094	+	0.201081i
$532$	19.1377	−	26.6429i	0.829725	−	1.15512i
$533$	2.94239	−	18.5775i	0.127449	−	0.804683i
$534$	−34.7503	−	31.2893i	−1.50379	−	1.35402i
$535$		0			0
$536$	0.984749	+	1.09367i	0.0425347	+	0.0472395i
$537$	1.63948	+	31.2832i	0.0707489	+	1.34997i
$538$	1.66857	−	3.27475i	0.0719372	−	0.141185i
$539$	−0.0574843	+	0.102103i	−0.00247602	+	0.00439788i
$540$		0			0
$541$	−11.5839	+	12.8652i	−0.498029	+	0.553117i	−0.938782	−	0.344511i	$-0.888045\pi$
$541$	−11.5839	+	12.8652i	−0.498029	+	0.553117i	0.440753	+	0.897628i	$0.354711\pi$
$542$	−17.1590	−	13.8951i	−0.737043	−	0.596846i
$543$	−3.42198	−	12.7710i	−0.146851	−	0.548057i
$544$	−5.85985	−	2.60897i	−0.251239	−	0.111859i
$545$		0			0
$546$	−40.4689	−	20.3447i	−1.73191	−	0.870674i
$547$	−1.54775	−	9.77211i	−0.0661770	−	0.417825i	−0.998430	−	0.0560177i	$-0.982160\pi$
$547$	−1.54775	−	9.77211i	−0.0661770	−	0.417825i	0.932253	−	0.361808i	$-0.117840\pi$
$548$	−7.00490	+	10.7866i	−0.299234	+	0.460781i
$549$	−15.2517	+	26.4167i	−0.650927	+	1.12744i
$550$		0			0
$551$	−0.165574	+	0.0955944i	−0.00705370	+	0.00407246i
$552$	26.4511	+	51.9131i	1.12583	+	2.20957i
$553$	10.5852	+	9.42768i	0.450127	+	0.400906i
$554$	−19.5157	+	26.8610i	−0.829142	+	1.14122i
$555$		0			0
$556$	17.6554	−	1.85566i	0.748756	−	0.0786975i
$557$	−15.6719	+	4.19928i	−0.664041	+	0.177929i	−0.575069	−	0.818105i	$-0.695025\pi$
$557$	−15.6719	+	4.19928i	−0.664041	+	0.177929i	−0.0889717	+	0.996034i	$0.528358\pi$
$558$	−17.9479	−	46.7559i	−0.759796	−	1.97934i
$559$	4.26786	+	13.1351i	0.180511	+	0.555557i
$560$		0			0
$561$	−0.0840009	+	0.258528i	−0.00354652	+	0.0109151i
$562$	9.67182	−	0.506879i	0.407981	−	0.0213814i
$563$	−16.8888	−	26.0064i	−0.711776	−	1.09604i	−0.990745	−	0.135739i	$-0.956659\pi$
$563$	−16.8888	−	26.0064i	−0.711776	−	1.09604i	0.278969	−	0.960300i	$-0.410007\pi$
$564$	−30.7058	+	27.6476i	−1.29295	+	1.16418i
$565$		0			0
$566$	43.6698	−	14.1892i	1.83558	−	0.596416i
$567$	−13.9331	+	24.4374i	−0.585137	+	1.02628i
$568$	−25.7042	+	25.7042i	−1.07852	+	1.07852i
$569$	5.42165	−	12.1772i	0.227287	−	0.510496i	−0.763519	−	0.645786i	$-0.776530\pi$
$569$	5.42165	−	12.1772i	0.227287	−	0.510496i	0.990806	+	0.135290i	$0.0431966\pi$
$570$		0			0
$571$	7.62713	−	3.39582i	0.319185	−	0.142110i	−0.240889	−	0.970553i	$-0.577439\pi$
$571$	7.62713	−	3.39582i	0.319185	−	0.142110i	0.560075	+	0.828442i	$0.310772\pi$
$572$	−0.126037	−	0.155642i	−0.00526986	−	0.00650774i
$573$	−30.3562	+	15.4672i	−1.26815	+	0.646153i
$574$	−24.9979	−	30.5304i	−1.04339	−	1.27431i
$575$		0			0
$576$	10.3739	+	17.9681i	0.432245	+	0.748670i
$577$	−34.5559	−	1.81100i	−1.43858	−	0.0753928i	−0.682986	−	0.730432i	$-0.739319\pi$
$577$	−34.5559	−	1.81100i	−1.43858	−	0.0753928i	−0.755595	+	0.655039i	$0.772652\pi$
$578$	28.6414	−	74.6134i	1.19133	−	3.10351i
$579$	3.99887	−	38.0467i	0.166187	−	1.58117i
$580$		0			0
$581$	−16.4424	−	16.2654i	−0.682147	−	0.674802i
$582$	−27.1814	−	27.1814i	−1.12670	−	1.12670i
$583$	−0.0680047	+	0.0261045i	−0.00281647	+	0.00108114i
$584$	15.1318	+	3.21636i	0.626158	+	0.133094i
$585$		0			0
$586$	−3.53317	−	16.6222i	−0.145954	−	0.686659i
$587$	−17.8813	−	9.11097i	−0.738039	−	0.376050i	0.0442042	−	0.999023i	$-0.485925\pi$
$587$	−17.8813	−	9.11097i	−0.738039	−	0.376050i	−0.782244	+	0.622973i	$0.785925\pi$
$588$	−58.4140	+	23.1517i	−2.40895	+	0.954760i
$589$	27.2320	+	8.84822i	1.12208	+	0.364584i
$590$		0			0
$591$	7.43679	−	34.9873i	0.305908	−	1.43919i
$592$	−18.1619	+	22.4280i	−0.746448	+	0.921786i
$593$	−4.81121	+	17.9557i	−0.197573	+	0.737352i	0.794013	+	0.607901i	$0.207988\pi$
$593$	−4.81121	+	17.9557i	−0.197573	+	0.737352i	−0.991586	+	0.129451i	$0.958678\pi$
$594$	−0.0540215	+	0.0392489i	−0.00221653	+	0.00161040i
$595$		0			0
$596$	−57.4394	−	41.7321i	−2.35281	−	1.70942i
$597$	−3.53401	+	2.86179i	−0.144638	+	0.117125i
$598$	−2.13433	+	40.7255i	−0.0872794	+	1.66539i
$599$	30.6038	+	17.6691i	1.25044	+	0.721941i	0.971196	−	0.238280i	$-0.0765837\pi$
$599$	30.6038	+	17.6691i	1.25044	+	0.721941i	0.279241	+	0.960221i	$0.409917\pi$
$600$		0			0
$601$		−	0.819532i		−	0.0334294i	−0.999860	−	0.0167147i	$-0.994679\pi$
$601$		−	0.819532i		−	0.0334294i	0.999860	−	0.0167147i	$-0.00532070\pi$
$602$	26.5322	+	11.6412i	1.08137	+	0.474460i
$603$	−0.718101	+	0.113736i	−0.0292433	+	0.00463169i
$604$	73.3858	+	7.71316i	2.98603	+	0.313844i
$605$		0			0
$606$	6.19220	+	58.9149i	0.251541	+	2.39325i
$607$	−13.3713	−	3.58282i	−0.542724	−	0.145422i	−0.0229662	−	0.999736i	$-0.507311\pi$
$607$	−13.3713	−	3.58282i	−0.542724	−	0.145422i	−0.519757	+	0.854314i	$0.673978\pi$
$608$	−2.84839	−	0.451141i	−0.115518	−	0.0182962i
$609$	0.365812	+	0.0171863i	0.0148234	+	0.000696423i
$610$		0			0
$611$	−13.7977	+	2.93279i	−0.558196	+	0.118648i
$612$	−52.8700	+	34.3341i	−2.13714	+	1.38788i
$613$	32.1471	−	20.8766i	1.29841	−	0.843197i	0.304406	−	0.952542i	$-0.401542\pi$
$613$	32.1471	−	20.8766i	1.29841	−	0.843197i	0.994004	+	0.109345i	$0.0348753\pi$
$614$	−16.0155	+	3.40421i	−0.646334	+	0.137383i
$615$		0			0
$616$	−0.204697	−	0.00961692i	−0.00824748	−	0.000387477i
$617$	16.5933	+	2.62812i	0.668022	+	0.105804i	0.481229	−	0.876595i	$-0.340191\pi$
$617$	16.5933	+	2.62812i	0.668022	+	0.105804i	0.186793	+	0.982399i	$0.440191\pi$
$618$	1.18071	+	0.316371i	0.0474952	+	0.0127263i
$619$	−0.649827	−	6.18269i	−0.0261187	−	0.248503i	−0.999789	−	0.0205421i	$-0.993461\pi$
$619$	−0.649827	−	6.18269i	−0.0261187	−	0.248503i	0.973670	−	0.227961i	$-0.0732059\pi$
$620$		0			0
$621$	8.94198	+	0.939840i	0.358829	+	0.0377145i
$622$	−6.30933	+	0.999300i	−0.252981	+	0.0400683i
$623$	−20.2796	−	8.89783i	−0.812484	−	0.356484i
$624$		−	24.2004i		−	0.968790i
$625$		0			0
$626$	−9.15199	−	5.28391i	−0.365787	−	0.211187i
$627$	−0.00639625	+	0.122048i	−0.000255442	+	0.00487411i
$628$	−49.3291	+	39.9459i	−1.96845	+	1.59402i
$629$	48.0125	+	34.8832i	1.91439	+	1.39088i
$630$		0			0
$631$	−16.6120	+	12.0693i	−0.661312	+	0.480471i	−0.867106	−	0.498124i	$-0.834022\pi$
$631$	−16.6120	+	12.0693i	−0.661312	+	0.480471i	0.205794	+	0.978595i	$0.434022\pi$
$632$	−6.41622	+	23.9457i	−0.255224	+	0.952508i
$633$	13.2246	−	16.3311i	0.525632	−	0.649102i
$634$	−10.4830	+	49.3185i	−0.416332	+	1.95869i
$635$		0			0
$636$	−37.1507	−	12.0710i	−1.47312	−	0.478646i
$637$	−21.2223	−	3.12616i	−0.840860	−	0.123863i
$638$	0.00218182	+	0.00111169i	8.63790e−5	+	4.40123e-5i
$639$	−3.73378	−	17.5661i	−0.147706	−	0.694902i
$640$		0			0
$641$	−9.09717	−	1.93366i	−0.359317	−	0.0763751i	0.0247163	−	0.999695i	$-0.492132\pi$
$641$	−9.09717	−	1.93366i	−0.359317	−	0.0763751i	−0.384033	+	0.923319i	$0.625465\pi$
$642$	−25.5313	+	9.80055i	−1.00764	+	0.386797i
$643$	10.6811	+	10.6811i	0.421223	+	0.421223i	0.885625	−	0.464402i	$-0.153731\pi$
$643$	10.6811	+	10.6811i	0.421223	+	0.421223i	−0.464402	+	0.885625i	$0.653731\pi$
$644$	40.2193	+	39.7862i	1.58486	+	1.56780i
$645$		0			0
$646$	5.69727	−	54.2059i	0.224156	−	2.13270i
$647$	5.43005	−	14.1458i	0.213477	−	0.556127i	−0.784470	−	0.620167i	$-0.787065\pi$
$647$	5.43005	−	14.1458i	0.213477	−	0.556127i	0.997947	+	0.0640393i	$0.0203983\pi$
$648$	−49.1298	−	2.57478i	−1.93000	−	0.101147i
$649$	0.0209698	+	0.0363207i	0.000823135	+	0.00142571i
$650$		0			0
$651$	−34.7461	−	42.4361i	−1.36181	−	1.66320i
$652$	32.5852	−	16.6030i	1.27614	−	0.650223i
$653$	22.6948	+	28.0257i	0.888116	+	1.09673i	0.994740	+	0.102432i	$0.0326626\pi$
$653$	22.6948	+	28.0257i	0.888116	+	1.09673i	−0.106624	+	0.994299i	$0.534004\pi$
$654$	39.3825	−	17.5342i	1.53998	−	0.685643i
$655$		0			0
$656$	8.57490	−	19.2595i	0.334794	−	0.751959i
$657$	−5.40409	+	5.40409i	−0.210833	+	0.210833i
$658$	−14.6572	+	25.7074i	−0.571397	+	1.00218i
$659$	30.6779	−	9.96786i	1.19504	−	0.388293i	0.357107	−	0.934063i	$-0.383763\pi$
$659$	30.6779	−	9.96786i	1.19504	−	0.388293i	0.837935	+	0.545771i	$0.183763\pi$
$660$		0			0
$661$	−13.5393	+	12.1908i	−0.526618	+	0.474169i	−0.889030	−	0.457849i	$-0.848620\pi$
$661$	−13.5393	+	12.1908i	−0.526618	+	0.474169i	0.362412	+	0.932018i	$0.381953\pi$
$662$	−21.0312	−	32.3852i	−0.817400	−	1.25869i
$663$	−49.6975	+	2.60454i	−1.93009	+	0.101152i
$664$	12.4994	−	38.4692i	0.485071	−	1.49290i
$665$		0			0
$666$	−14.4216	−	44.3852i	−0.558827	−	1.71989i
$667$	−0.118162	−	0.307822i	−0.00457525	−	0.0119189i
$668$	28.5007	−	7.63675i	1.10273	−	0.295475i
$669$	17.0070	−	1.78751i	0.657530	−	0.0691092i
$670$		0			0
$671$	−0.131290	+	0.180705i	−0.00506839	+	0.00697604i
$672$	4.12508	+	3.67400i	0.159128	+	0.141728i
$673$	8.71675	+	17.1076i	0.336006	+	0.659449i	0.995756	−	0.0920367i	$-0.0293377\pi$
$673$	8.71675	+	17.1076i	0.336006	+	0.659449i	−0.659750	+	0.751485i	$0.729338\pi$
$674$	−53.8205	+	31.0733i	−2.07309	+	1.19690i
$675$		0			0
$676$	−7.04519	+	12.2026i	−0.270969	+	0.469332i
$677$	−19.3296	+	29.7649i	−0.742895	+	1.14396i	0.241911	+	0.970299i	$0.422226\pi$
$677$	−19.3296	+	29.7649i	−0.742895	+	1.14396i	−0.984806	+	0.173660i	$0.944441\pi$
$678$	−3.49909	−	22.0924i	−0.134382	−	0.848453i
$679$	−16.2653	−	8.17698i	−0.624204	−	0.313804i
$680$		0			0
$681$	24.6108	+	10.9574i	0.943088	+	0.419890i
$682$	−0.0949172	−	0.354236i	−0.00363457	−	0.0135644i
$683$	7.41808	+	6.00704i	0.283845	+	0.229853i	0.760660	−	0.649151i	$-0.224876\pi$
$683$	7.41808	+	6.00704i	0.283845	+	0.229853i	−0.476815	+	0.879004i	$0.658209\pi$
$684$	−18.9650	+	21.0627i	−0.725143	+	0.805353i
$685$		0			0
$686$	−34.5085	+	28.8848i	−1.31754	+	1.10283i
$687$	28.1201	−	55.1888i	1.07285	−	2.10558i
$688$	0.810168	+	15.4589i	0.0308874	+	0.589366i
$689$	−8.92332	−	9.91036i	−0.339952	−	0.377554i
$690$		0			0
$691$	−37.4522	−	33.7221i	−1.42475	−	1.28285i	−0.902926	−	0.429796i	$-0.858585\pi$
$691$	−37.4522	−	33.7221i	−1.42475	−	1.28285i	−0.521823	−	0.853054i	$-0.674748\pi$
$692$	14.2938	−	90.2473i	0.543367	−	3.43069i
$693$	0.0590617	−	0.0822238i	0.00224357	−	0.00312342i
$694$	−21.6421	−	29.7878i	−0.821524	−	1.13073i
$695$		0			0
$696$	0.260504	+	0.585101i	0.00987437	+	0.0221782i
$697$	−40.4740	−	15.5365i	−1.53306	−	0.588487i
$698$	3.03494	+	1.97091i	0.114874	+	0.0746002i
$699$	−50.2276			−1.89978
$700$		0			0
$701$	41.2864			1.55936			0.779682	−	0.626176i	$-0.215381\pi$
$701$	41.2864			1.55936			0.779682	+	0.626176i	$0.215381\pi$
$702$	−10.2525	−	6.65804i	−0.386955	−	0.251291i
$703$	24.9099	+	9.56202i	0.939495	+	0.360638i
$704$	0.0617943	+	0.138792i	0.00232896	+	0.00523093i
$705$		0			0
$706$	−13.4251	−	18.4781i	−0.505261	−	0.695431i
$707$	11.5497	+	25.5677i	0.434371	+	0.961571i
$708$	−3.51827	+	22.2135i	−0.132225	+	0.834834i
$709$	1.43178	+	1.28918i	0.0537715	+	0.0484161i	0.695578	−	0.718450i	$-0.255148\pi$
$709$	1.43178	+	1.28918i	0.0537715	+	0.0484161i	−0.641807	+	0.766866i	$0.721815\pi$
$710$		0			0
$711$	−8.19493	−	9.10139i	−0.307334	−	0.341329i
$712$	−2.02700	−	38.6775i	−0.0759651	−	1.44950i
$713$	−22.4185	+	43.9987i	−0.839578	+	1.64777i
$714$	−65.2617	+	81.4895i	−2.44236	+	3.04967i
$715$		0			0
$716$	−35.5957	+	39.5330i	−1.33027	+	1.47742i
$717$	−7.62472	−	6.17437i	−0.284750	−	0.230586i
$718$	3.86356	+	14.4190i	0.144187	+	0.538112i
$719$	44.2991	+	19.7232i	1.65208	+	0.735552i	0.999749	−	0.0223865i	$-0.00712643\pi$
$719$	44.2991	+	19.7232i	1.65208	+	0.735552i	0.652327	+	0.757938i	$0.273793\pi$
$720$		0			0
$721$	0.577936	−	0.0334263i	0.0215235	−	0.00124486i
$722$	3.38876	+	21.3958i	0.126117	+	0.796270i
$723$	0.205633	−	0.316647i	0.00764756	−	0.0117762i
$724$	11.2262	−	19.4443i	0.417217	−	0.722641i
$725$		0			0
$726$	−53.2178	+	30.7253i	−1.97510	+	1.14032i
$727$	3.31875	+	6.51342i	0.123086	+	0.241569i	0.944325	−	0.329015i	$-0.106717\pi$
$727$	3.31875	+	6.51342i	0.123086	+	0.241569i	−0.821239	+	0.570584i	$0.806717\pi$
$728$	−11.7861	−	35.6168i	−0.436823	−	1.32005i
$729$	7.63022	−	10.5021i	0.282601	−	0.388967i
$730$		0			0
$731$	31.6591	−	3.32750i	1.17095	−	0.123072i
$732$	−115.699	+	31.0015i	−4.27636	+	1.14585i
$733$	−3.69327	−	9.62129i	−0.136414	−	0.355371i	0.848308	−	0.529503i	$-0.177621\pi$
$733$	−3.69327	−	9.62129i	−0.136414	−	0.355371i	−0.984722	+	0.174132i	$0.944288\pi$
$734$	27.0939	+	83.3864i	1.00005	+	3.07785i
$735$		0			0
$736$	1.53691	−	4.73012i	0.0566512	−	0.174354i
$737$	−0.00531660		0.000278631i	−0.000195839		1.02635e-5i
$738$	18.5681	+	28.5924i	0.683502	+	1.05250i
$739$	16.3525	−	14.7239i	0.601537	−	0.541626i	−0.311111	−	0.950374i	$-0.600701\pi$
$739$	16.3525	−	14.7239i	0.601537	−	0.541626i	0.912648	+	0.408747i	$0.134034\pi$
$740$		0			0
$741$	−21.2794	+	6.91411i	−0.781720	+	0.253996i
$742$	−27.9760	+	0.151440i	−1.02703	+	0.00555953i
$743$	32.3075	−	32.3075i	1.18525	−	1.18525i	0.206883	−	0.978366i	$-0.433668\pi$
$743$	32.3075	−	32.3075i	1.18525	−	1.18525i	0.978366	−	0.206883i	$-0.0663319\pi$
$744$	39.0144	−	87.6278i	1.43034	−	3.21259i
$745$		0			0
$746$	41.2660	−	18.3728i	1.51086	−	0.672676i
$747$	12.5756	+	15.5296i	0.460119	+	0.568199i
$748$	−0.411303	+	0.209569i	−0.0150387	+	0.00766262i
$749$	−10.0211	+	8.20512i	−0.366162	+	0.299809i
$750$		0			0
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	0.591254	−	0.806485i	$-0.298633\pi$
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	−0.994064	+	0.108798i	$0.965300\pi$
$752$	−15.7890	−	0.827466i	−0.575765	−	0.0301746i
$753$	0.109010	−	0.283980i	0.00397253	−	0.0103488i
$754$	−0.0468599	+	0.445842i	−0.00170654	+	0.0162366i
$755$		0			0
$756$	−16.3566	+	4.47778i	−0.594885	+	0.162855i
$757$	−2.36580	−	2.36580i	−0.0859865	−	0.0859865i	0.662805	−	0.748792i	$-0.269366\pi$
$757$	−2.36580	−	2.36580i	−0.0859865	−	0.0859865i	−0.748792	+	0.662805i	$0.769366\pi$
$758$	50.4951	−	19.3833i	1.83406	−	0.704032i
$759$	−0.206165	−	0.0438218i	−0.00748332	−	0.00159063i
$760$		0			0
$761$	−7.78209	−	36.6118i	−0.282101	−	1.32718i	−0.859675	−	0.510841i	$-0.829334\pi$
$761$	−7.78209	−	36.6118i	−0.282101	−	1.32718i	0.577575	−	0.816338i	$-0.303999\pi$
$762$	36.2686	+	18.4798i	1.31387	+	0.669451i
$763$	15.0981	−	13.7431i	0.546589	−	0.497535i
$764$	−55.0239	−	17.8784i	−1.99070	−	0.646816i
$765$		0			0
$766$	−7.77758	+	36.5906i	−0.281015	+	1.32207i
$767$	−4.83197	+	5.96698i	−0.174472	+	0.215455i
$768$	−18.4604	+	68.8951i	−0.666132	+	2.48604i
$769$	−31.5396	+	22.9148i	−1.13735	+	0.826330i	−0.986747	−	0.162264i	$-0.948120\pi$
$769$	−31.5396	+	22.9148i	−1.13735	+	0.826330i	−0.150599	+	0.988595i	$0.548120\pi$
$770$		0			0
$771$	17.0932	+	12.4189i	0.615596	+	0.447257i
$772$	50.4876	−	40.8841i	1.81709	−	1.47145i
$773$	1.21669	−	23.2158i	0.0437612	−	0.835014i	−0.885285	−	0.465049i	$-0.846037\pi$
$773$	1.21669	−	23.2158i	0.0437612	−	0.835014i	0.929046	−	0.369964i	$-0.120630\pi$
$774$	−21.6795	−	12.5167i	−0.779254	−	0.449902i
$775$		0			0
$776$		−	31.8387i		−	1.14294i
$777$	−30.2643	−	41.1845i	−1.08573	−	1.47749i
$778$	−28.6099	+	4.53136i	−1.02571	+	0.162457i
$779$	−19.3848	−	2.03743i	−0.694534	−	0.0729984i
$780$		0			0
$781$	−0.0137457	−	0.130782i	−0.000491861	−	0.00467975i
$782$	90.7949	+	24.3284i	3.24682	+	0.869983i
$783$	0.0976210	+	0.0154617i	0.00348869	+	0.000552554i
$784$	−22.0696	−	9.54110i	−0.788201	−	0.340754i
$785$		0			0
$786$	64.6466	−	13.7411i	2.30587	−	0.490127i
$787$	13.8453	−	8.99124i	0.493531	−	0.320503i	−0.273764	−	0.961797i	$-0.588269\pi$
$787$	13.8453	−	8.99124i	0.493531	−	0.320503i	0.767295	+	0.641294i	$0.221602\pi$
$788$	50.9422	−	33.0822i	1.81474	−	1.17851i
$789$	−47.0414	+	9.99896i	−1.67472	+	0.355972i
$790$		0			0
$791$	−4.86024	−	9.41245i	−0.172810	−	0.334668i
$792$	0.174874	+	0.0276973i	0.00621388	+	0.000984182i
$793$	−39.4989	−	10.5837i	−1.40265	−	0.375838i
$794$	1.72174	+	16.3812i	0.0611022	+	0.581349i
$795$		0			0
$796$	−7.67997	−	0.807198i	−0.272209	−	0.0286104i
$797$	43.0687	−	6.82142i	1.52557	−	0.241627i	0.663409	−	0.748257i	$-0.269109\pi$
$797$	43.0687	−	6.82142i	1.52557	−	0.241627i	0.862164	+	0.506630i	$0.169109\pi$
$798$	−18.8592	+	42.9832i	−0.667609	+	1.52159i
$799$			32.5131i			1.15023i
$800$		0			0
$801$	16.5705	+	9.56698i	0.585490	+	0.338033i
$802$	−2.32531	+	44.3695i	−0.0821095	+	1.56674i
$803$	−0.0434914	+	0.0352186i	−0.00153478	+	0.00124284i
$804$	−2.30973	−	1.67811i	−0.0814578	−	0.0591825i
$805$		0			0
$806$	54.3169	−	39.4635i	1.91323	−	1.39004i
$807$	−0.900061	+	3.35907i	−0.0316836	+	0.118245i
$808$	−30.8782	+	38.1313i	−1.08629	+	1.34146i
$809$	3.06134	−	14.4025i	0.107631	−	0.506364i	−0.890997	−	0.454008i	$-0.849994\pi$
$809$	3.06134	−	14.4025i	0.107631	−	0.506364i	0.998628	−	0.0523559i	$-0.0166730\pi$
$810$		0			0
$811$	24.6251	+	8.00118i	0.864704	+	0.280959i	0.707592	−	0.706621i	$-0.249782\pi$
$811$	24.6251	+	8.00118i	0.864704	+	0.280959i	0.157112	+	0.987581i	$0.449782\pi$
$812$	0.418623	+	0.459897i	0.0146908	+	0.0161392i
$813$	18.6144	+	9.48450i	0.652835	+	0.332636i
$814$	−0.0710517	−	0.334272i	−0.00249036	−	0.0117162i
$815$		0			0
$816$	−54.5610	−	11.5973i	−1.91002	−	0.405986i
$817$	13.3616	−	5.12904i	0.467464	−	0.179442i
$818$	27.3344	+	27.3344i	0.955725	+	0.955725i
$819$	17.9282	+	4.69998i	0.626463	+	0.164231i
$820$		0			0
$821$	−5.12351	+	48.7470i	−0.178812	+	1.70128i	0.425846	+	0.904796i	$0.359977\pi$
$821$	−5.12351	+	48.7470i	−0.178812	+	1.70128i	−0.604657	+	0.796486i	$0.706690\pi$
$822$	6.59517	−	17.1810i	0.230033	−	0.599256i
$823$	52.8866	+	2.77167i	1.84351	+	0.0966142i	0.941891	−	0.335918i	$-0.109047\pi$
$823$	52.8866	+	2.77167i	1.84351	+	0.0966142i	0.901618	+	0.432533i	$0.142380\pi$
$824$	0.506220	+	0.876799i	0.0176350	+	0.0305447i
$825$		0			0
$826$	2.60585	+	15.8953i	0.0906690	+	0.553068i
$827$	−4.78458	+	2.43786i	−0.166376	+	0.0847728i	−0.535196	−	0.844728i	$-0.679762\pi$
$827$	−4.78458	+	2.43786i	−0.166376	+	0.0847728i	0.368819	+	0.929501i	$0.379762\pi$
$828$	−30.7609	−	37.9865i	−1.06901	−	1.32012i
$829$	−32.0214	+	14.2568i	−1.11215	+	0.495161i	−0.878780	−	0.477228i	$-0.841642\pi$
$829$	−32.0214	+	14.2568i	−1.11215	+	0.495161i	−0.233369	+	0.972388i	$0.574975\pi$
$830$		0			0
$831$	12.7778	−	28.6994i	0.443257	−	0.995571i
$832$	−19.6675	+	19.6675i	−0.681847	+	0.681847i
$833$	−17.2183	+	46.3488i	−0.596577	+	1.60589i
$834$	−24.1587	+	7.84964i	−0.836548	+	0.271811i
$835$		0			0
$836$	−0.154233	+	0.138872i	−0.00533427	+	0.00480300i
$837$	−8.06201	−	12.4144i	−0.278664	−	0.429105i
$838$	−86.2499	+	4.52017i	−2.97945	+	0.156147i
$839$	−4.17081	+	12.8364i	−0.143992	+	0.443163i	−0.996880	−	0.0789314i	$-0.974849\pi$
$839$	−4.17081	+	12.8364i	−0.143992	+	0.443163i	0.852888	+	0.522095i	$0.174849\pi$
$840$		0			0
$841$	8.96037	+	27.5772i	0.308978	+	0.950938i
$842$	12.2359	+	31.8755i	0.421675	+	1.09850i
$843$	−8.85167	+	2.37180i	−0.304868	+	0.0816891i
$844$	35.4900	−	3.73015i	1.22162	−	0.128397i
$845$		0			0
$846$	15.0284	−	20.6848i	0.516686	−	0.711158i
$847$	−19.3560	+	21.7325i	−0.665081	+	0.746737i
$848$	−6.78594	−	13.3182i	−0.233030	−	0.457347i
$849$	−37.6256	+	21.7232i	−1.29131	+	0.745537i
$850$		0			0
$851$	−23.0079	+	39.8508i	−0.788699	+	1.36607i
$852$	38.4075	−	59.1423i	1.31582	−	2.02618i
$853$	−5.33840	−	33.7053i	−0.182783	−	1.15405i	−0.892997	−	0.450063i	$-0.851402\pi$
$853$	−5.33840	−	33.7053i	−0.182783	−	1.15405i	0.710214	−	0.703986i	$-0.248598\pi$
$854$	−71.6923	+	47.1112i	−2.45326	+	1.61211i
$855$		0			0
$856$	−20.6929	−	9.21306i	−0.707268	−	0.314896i
$857$	−1.77688	−	6.63141i	−0.0606971	−	0.226525i	0.928914	−	0.370296i	$-0.120744\pi$
$857$	−1.77688	−	6.63141i	−0.0606971	−	0.226525i	−0.989611	+	0.143771i	$0.954077\pi$
$858$	0.222706	+	0.180344i	0.00760305	+	0.00615683i
$859$	29.6526	−	32.9326i	1.01174	−	1.12365i	0.0194321	−	0.999811i	$-0.493814\pi$
$859$	29.6526	−	32.9326i	1.01174	−	1.12365i	0.992303	−	0.123834i	$-0.0395192\pi$
$860$		0			0
$861$	29.1419	+	23.3386i	0.993152	+	0.795376i
$862$	−4.19824	+	8.23950i	−0.142993	+	0.280639i
$863$	−0.105676	−	2.01642i	−0.00359726	−	0.0686398i	0.996241	−	0.0866249i	$-0.0276082\pi$
$863$	−0.105676	−	2.01642i	−0.00359726	−	0.0686398i	−0.999838	+	0.0179852i	$0.994275\pi$
$864$	0.997589	+	1.10794i	0.0339387	+	0.0376927i
$865$		0			0
$866$	2.24014	+	2.01703i	0.0761230	+	0.0685415i
$867$	−11.8297	+	74.6900i	−0.401759	+	2.53661i
$868$	9.23402	−	92.6791i	0.313423	−	3.14573i
$869$	−0.0527129	−	0.0725531i	−0.00178816	−	0.00246119i
$870$		0			0
$871$	−0.396434	−	0.890406i	−0.0134327	−	0.0301703i
$872$	33.3345	+	12.7959i	1.12885	+	0.433324i
$873$	13.1916	+	8.56673i	0.446468	+	0.289940i
$874$	42.2612			1.42950
$875$		0			0
$876$	−30.0106			−1.01396
$877$	39.3610	+	25.5614i	1.32913	+	0.863146i	0.996794	−	0.0800162i	$-0.0254972\pi$
$877$	39.3610	+	25.5614i	1.32913	+	0.863146i	0.332334	+	0.943162i	$0.392164\pi$
$878$	12.3548	+	4.74256i	0.416954	+	0.160054i
$879$	6.53998	+	14.6890i	0.220588	+	0.495449i
$880$		0			0
$881$	−12.9945	−	17.8855i	−0.437797	−	0.602576i	0.531924	−	0.846792i	$-0.321469\pi$
$881$	−12.9945	−	17.8855i	−0.437797	−	0.602576i	−0.969721	+	0.244216i	$0.921469\pi$
$882$	32.3778	−	21.5283i	1.09022	−	0.724896i
$883$	−2.48456	+	15.6869i	−0.0836122	+	0.527906i	0.909959	+	0.414698i	$0.136113\pi$
$883$	−2.48456	+	15.6869i	−0.0836122	+	0.527906i	−0.993571	+	0.113208i	$0.963887\pi$
$884$	−62.8034	−	56.5485i	−2.11231	−	1.90193i
$885$		0			0
$886$	29.7457	+	33.0360i	0.999327	+	1.10986i
$887$	−0.918554	−	17.5270i	−0.0308420	−	0.588501i	−0.969715	−	0.244238i	$-0.921462\pi$
$887$	−0.918554	−	17.5270i	−0.0308420	−	0.588501i	0.938873	−	0.344263i	$-0.111871\pi$
$888$	40.5794	−	79.6415i	1.36175	−	2.67259i
$889$	19.0564	+	2.91258i	0.639130	+	0.0976848i
$890$		0			0
$891$	0.119088	−	0.132260i	0.00398958	−	0.00443088i
$892$	22.5682	+	18.2753i	0.755638	+	0.611904i
$893$	3.78336	+	14.1197i	0.126605	+	0.472498i
$894$	92.8081	+	41.3208i	3.10397	+	1.38198i
$895$		0			0
$896$	3.09170	+	53.4551i	0.103287	+	1.78581i
$897$	−6.03632	−	38.1118i	−0.201547	−	1.27252i
$898$	9.64664	−	14.8545i	0.321912	−	0.495702i
$899$	−0.271415	+	0.470104i	−0.00905219	+	0.0156789i
$900$		0			0
$901$	−26.6196	+	15.3689i	−0.886829	+	0.512011i
$902$	0.113336	+	0.222435i	0.00377369	+	0.00740629i
$903$	−26.8459	−	5.55457i	−0.893377	−	0.184844i
$904$	10.8896	−	14.9882i	0.362182	−	0.498500i
$905$		0			0
$906$	−105.006	+	11.0366i	−3.48860	+	0.366667i
$907$	28.7163	−	7.69450i	0.953508	−	0.255492i	0.251658	−	0.967816i	$-0.419024\pi$
$907$	28.7163	−	7.69450i	0.953508	−	0.255492i	0.701850	+	0.712325i	$0.252358\pi$
$908$	16.3947	+	42.7097i	0.544078	+	1.41737i
$909$	−7.49054	−	23.0535i	−0.248445	−	0.764636i
$910$		0			0
$911$	12.1969	−	37.5382i	0.404101	−	1.24370i	−0.517542	−	0.855658i	$-0.673153\pi$
$911$	12.1969	−	37.5382i	0.404101	−	1.24370i	0.921643	−	0.388038i	$-0.126847\pi$
$912$	−25.0441	+	1.31251i	−0.829293	+	0.0434614i
$913$	0.0796949	+	0.122719i	0.00263752	+	0.00406142i
$914$	21.3387	−	19.2135i	0.705822	−	0.635525i
$915$		0			0
$916$	100.036	−	32.5036i	3.30528	−	1.07395i
$917$	27.0216	−	15.7966i	0.892331	−	0.521648i
$918$	−19.9241	+	19.9241i	−0.657593	+	0.657593i
$919$	6.01760	−	13.5158i	0.198502	−	0.445844i	−0.786678	−	0.617363i	$-0.788201\pi$
$919$	6.01760	−	13.5158i	0.198502	−	0.445844i	0.985181	+	0.171519i	$0.0548676\pi$
$920$		0			0
$921$	14.1529	−	6.30127i	0.466353	−	0.207634i
$922$	1.30162	+	1.60736i	0.0428664	+	0.0529356i
$923$	21.4508	−	10.9297i	0.706061	−	0.359756i
$924$	0.392301	−	0.0643132i	0.0129058	−	0.00211575i
$925$		0			0
$926$	46.9570	+	81.3318i	1.54310	+	2.67273i
$927$	−0.499488	−	0.0261771i	−0.0164053	−	0.000859767i
$928$	0.0195929	−	0.0510413i	0.000643169	−	0.00167551i
$929$	1.81026	−	17.2234i	0.0593925	−	0.565082i	−0.923847	−	0.382763i	$-0.874973\pi$
$929$	1.81026	−	17.2234i	0.0593925	−	0.565082i	0.983239	−	0.182320i	$-0.0583606\pi$
$930$		0			0
$931$	−2.08416	+	22.1318i	−0.0683056	+	0.725341i
$932$	−60.3124	−	60.3124i	−1.97560	−	1.97560i
$933$	5.64278	−	2.16606i	0.184736	−	0.0709136i
$934$	−21.2562	−	4.51814i	−0.695523	−	0.147838i
$935$		0			0
$936$	6.73928	+	31.7058i	0.220280	+	1.03634i
$937$	−29.8820	−	15.2256i	−0.976202	−	0.497400i	−0.108291	−	0.994119i	$-0.534538\pi$
$937$	−29.8820	−	15.2256i	−0.976202	−	0.497400i	−0.867911	+	0.496719i	$0.834538\pi$
$938$	−1.94804	−	0.621317i	−0.0636056	−	0.0202867i
$939$	9.50975	+	3.08990i	0.310339	+	0.100835i
$940$		0			0
$941$	9.06149	−	42.6310i	0.295396	−	1.38973i	−0.540732	−	0.841195i	$-0.681853\pi$
$941$	9.06149	−	42.6310i	0.295396	−	1.38973i	0.836128	−	0.548534i	$-0.184814\pi$
$942$	57.1579	−	70.5841i	1.86230	−	2.29975i
$943$	8.70021	−	32.4696i	0.283318	−	1.05736i
$944$	−6.96237	+	5.05846i	−0.226606	+	0.164639i
$945$		0			0
$946$	−0.148300	−	0.107746i	−0.00482164	−	0.00350312i
$947$	4.28310	−	3.46839i	0.139182	−	0.112707i	−0.557201	−	0.830378i	$-0.688125\pi$
$947$	4.28310	−	3.46839i	0.139182	−	0.112707i	0.696383	+	0.717670i	$0.254791\pi$
$948$	2.51693	−	48.0259i	0.0817462	−	1.55981i
$949$	−8.87279	−	5.12271i	−0.288023	−	0.166290i
$950$		0			0
$951$		−	47.7071i		−	1.54701i
$952$	−85.9480	+	9.50416i	−2.78559	+	0.308032i
$953$	6.68823	−	1.05931i	0.216653	−	0.0343145i	−0.0471642	−	0.998887i	$-0.515018\pi$
$953$	6.68823	−	1.05931i	0.216653	−	0.0343145i	0.263817	+	0.964573i	$0.415018\pi$
$954$	24.0393	+	2.52663i	0.778300	+	0.0818026i
$955$		0			0
$956$	−1.74155	−	16.5697i	−0.0563257	−	0.535903i
$957$	−0.00223799		0.000599669i	−7.23441e−5		1.93845e-5i
$958$	−2.32607	−	0.368413i	−0.0751518	−	0.0119029i
$959$	0.409023	−	8.70608i	0.0132080	−	0.281134i
$960$		0			0
$961$	49.1979	−	10.4573i	1.58703	−	0.337333i
$962$	52.4706	−	34.0748i	1.69172	−	1.09862i
$963$	9.38497	−	6.09467i	0.302426	−	0.196398i
$964$	0.627144	−	0.133304i	0.0201989	−	0.00429342i
$965$		0			0
$966$	−68.1278	−	43.7202i	−2.19198	−	1.40668i
$967$	57.0421	+	9.03458i	1.83435	+	0.290533i	0.975222	−	0.221228i	$-0.0710065\pi$
$967$	57.0421	+	9.03458i	1.83435	+	0.290533i	0.859128	+	0.511760i	$0.171006\pi$
$968$	−49.1630	−	13.1732i	−1.58016	−	0.423403i
$969$	5.39069	+	51.2890i	0.173174	+	1.64764i
$970$		0			0
$971$	−19.5233	−	2.05199i	−0.626534	−	0.0658514i	−0.214060	−	0.976821i	$-0.568669\pi$
$971$	−19.5233	−	2.05199i	−0.626534	−	0.0658514i	−0.412474	+	0.910969i	$0.635335\pi$
$972$	75.2723	−	11.9220i	2.41436	−	0.382397i
$973$	−9.69420	+	7.12374i	−0.310782	+	0.228377i
$974$		−	84.2473i		−	2.69946i
$975$		0			0
$976$	−39.6935	−	22.9170i	−1.27056	−	0.733556i
$977$	1.28796	−	24.5758i	0.0412056	−	0.786249i	−0.897392	−	0.441235i	$-0.854541\pi$
$977$	1.28796	−	24.5758i	0.0412056	−	0.786249i	0.938597	−	0.345014i	$-0.112126\pi$
$978$	−40.6674	+	32.9318i	−1.30040	+	1.05304i
$979$	0.113351	+	0.0823545i	0.00362272	+	0.00263206i
$980$		0			0
$981$	−14.2709	+	10.3684i	−0.455634	+	0.331038i
$982$	3.21913	−	12.0140i	0.102727	−	0.383381i
$983$	28.2657	−	34.9053i	0.901537	−	1.11331i	−0.0915351	−	0.995802i	$-0.529177\pi$
$983$	28.2657	−	34.9053i	0.901537	−	1.11331i	0.993072	−	0.117504i	$-0.0374893\pi$
$984$	−13.5758	+	63.8690i	−0.432780	+	2.03607i
$985$		0			0
$986$	0.982717	+	0.319304i	0.0312961	+	0.0101687i
$987$	8.50816	−	26.6759i	0.270818	−	0.849103i
$988$	−33.8543	−	17.2496i	−1.07705	−	0.548784i
$989$	5.13183	+	24.1433i	0.163183	+	0.767714i
$990$		0			0
$991$	45.3163	+	9.63229i	1.43952	+	0.305980i	0.860549	−	0.509368i	$-0.170121\pi$
$991$	45.3163	+	9.63229i	1.43952	+	0.305980i	0.578972	+	0.815347i	$0.303454\pi$
$992$	−7.64421	+	2.93434i	−0.242704	+	0.0931653i
$993$	25.8356	+	25.8356i	0.819867	+	0.819867i
$994$	12.8075	−	48.8545i	0.406229	−	1.54957i
$995$		0			0
$996$	−8.20219	+	78.0386i	−0.259896	+	2.47275i
$997$	−8.86960	+	23.1061i	−0.280903	+	0.731778i	0.718442	+	0.695587i	$0.244856\pi$
$997$	−8.86960	+	23.1061i	−0.280903	+	0.731778i	−0.999345	+	0.0361906i	$0.988478\pi$
$998$	−88.4014	−	4.63292i	−2.79830	−	0.146653i
$999$	−6.89686	−	11.9457i	−0.218207	−	0.377946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.507.1		288
5.2	odd	4		875.2.bb.b.493.18		288
5.3	odd	4		875.2.bb.a.493.1		288
5.4	even	2		175.2.x.a.122.18	yes	288
7.5	odd	6	inner	875.2.bb.c.257.1		288
25.6	even	5		875.2.bb.a.857.18		288
25.8	odd	20	inner	875.2.bb.c.143.1		288
25.17	odd	20		175.2.x.a.108.18	yes	288
25.19	even	10		875.2.bb.b.857.1		288
35.12	even	12		875.2.bb.b.243.1		288
35.19	odd	6		175.2.x.a.47.18	yes	288
35.33	even	12		875.2.bb.a.243.18		288
175.19	odd	30		875.2.bb.b.607.18		288
175.33	even	60	inner	875.2.bb.c.768.1		288
175.117	even	60		175.2.x.a.33.18	✓	288
175.131	odd	30		875.2.bb.a.607.1		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.18	✓	288	175.117	even	60
175.2.x.a.47.18	yes	288	35.19	odd	6
175.2.x.a.108.18	yes	288	25.17	odd	20
175.2.x.a.122.18	yes	288	5.4	even	2
875.2.bb.a.243.18		288	35.33	even	12
875.2.bb.a.493.1		288	5.3	odd	4
875.2.bb.a.607.1		288	175.131	odd	30
875.2.bb.a.857.18		288	25.6	even	5
875.2.bb.b.243.1		288	35.12	even	12
875.2.bb.b.493.18		288	5.2	odd	4
875.2.bb.b.607.18		288	175.19	odd	30
875.2.bb.b.857.1		288	25.19	even	10
875.2.bb.c.143.1		288	25.8	odd	20	inner
875.2.bb.c.257.1		288	7.5	odd	6	inner
875.2.bb.c.507.1		288	1.1	even	1	trivial
875.2.bb.c.768.1		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+(-2.03786 - 1.32340i) q^{2} +(2.14641 + 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-3.28370 - 4.51962i) q^{6} +(-2.14884 - 1.54352i) q^{7} +(0.723845 - 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +(0.0112005 + 0.0124395i) q^{11} +(0.469788 + 8.96408i) q^{12} +(-1.39124 + 2.73047i) q^{13} +(2.33634 + 5.98928i) q^{14} +(-2.29834 + 2.55257i) q^{16} +(5.48928 + 4.44513i) q^{17} +(-1.43762 - 5.36527i) q^{18} +(2.90112 + 1.29166i) q^{19} +(-3.34055 - 5.08353i) q^{21} +(-0.00636273 - 0.0401727i) q^{22} +(-2.98285 + 4.59318i) q^{23} +(5.31918 - 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(-0.745322 - 1.46278i) q^{27} +(2.09295 - 10.1155i) q^{28} +(-0.0353871 + 0.0487062i) q^{29} +(8.96709 - 0.942479i) q^{31} +(-0.877177 + 0.235039i) q^{32} +(0.0137917 + 0.0359286i) q^{33} +(-5.30369 - 16.3231i) q^{34} +(-2.75796 + 8.48811i) q^{36} +(8.39052 - 0.439728i) q^{37} +(-4.20270 - 6.47159i) q^{38} +(-5.23590 + 4.71442i) q^{39} +(-5.83738 + 1.89668i) q^{41} +(0.0800095 + 14.7804i) q^{42} +(3.18681 - 3.18681i) q^{43} +(-0.0265816 + 0.0597034i) q^{44} +(12.1573 - 5.41276i) q^{46} +(2.89679 + 3.57724i) q^{47} +(-7.03633 + 3.58519i) q^{48} +(2.23507 + 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-11.9482 - 0.626178i) q^{52} +(-1.55951 + 4.06266i) q^{53} +(-0.416980 + 3.96730i) q^{54} +(-8.60961 + 8.70333i) q^{56} +(5.16276 + 5.16276i) q^{57} +(0.136572 - 0.0524250i) q^{58} +(2.45075 + 0.520924i) q^{59} +(2.77436 + 13.0523i) q^{61} +(-19.5210 - 9.94643i) q^{62} +(-1.28946 - 5.90896i) q^{63} +(8.63203 + 2.80472i) q^{64} +(0.0194425 - 0.0914696i) q^{66} +(-0.200158 + 0.247175i) q^{67} +(-7.13755 + 26.6377i) q^{68} +(-10.1869 + 7.40119i) q^{69} +(-6.35569 - 4.61768i) q^{71} +(8.22016 - 6.65655i) q^{72} +(-0.174974 + 3.33870i) q^{73} +(-17.6807 - 10.2079i) q^{74} +12.3987i q^{76} +(-0.00486761 - 0.0440188i) q^{77} +(16.9091 - 2.67814i) q^{78} +(-5.32825 - 0.560021i) q^{79} +(-1.11138 - 10.5741i) q^{81} +(14.4058 + 3.86003i) q^{82} +(8.63403 + 1.36750i) q^{83} +(12.8268 - 19.9876i) q^{84} +(-10.7117 + 2.27684i) q^{86} +(-0.116086 + 0.0753869i) q^{87} +(0.0649580 - 0.0421842i) q^{88} +(8.18738 - 1.74028i) q^{89} +(7.20412 - 3.71994i) q^{91} +(-21.1194 - 3.34499i) q^{92} +(20.0236 + 5.36531i) q^{93} +(-1.16913 - 11.1236i) q^{94} +(-2.07644 - 0.218242i) q^{96} +(6.79613 - 1.07640i) q^{97} +(4.22415 - 16.4762i) q^{98} +0.0382642i 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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