LMFDB - Embedded newform 875.2.bb.a.493.1

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

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

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

Embedding invariants

Embedding label			493.1
Character	$\chi$	$=$	875.493
Dual form			875.2.bb.a.607.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.32340 + 2.03786i) q^{2} +(-0.823930 + 2.14641i) q^{3} +(-1.58801 - 3.56673i) q^{4} +(-3.28370 - 4.51962i) q^{6} +(-1.54352 + 2.14884i) q^{7} +(4.57018 + 0.723845i) q^{8} +(-1.69878 - 1.52959i) q^{9} +(0.0112005 + 0.0124395i) q^{11} +(8.96408 - 0.469788i) q^{12} +(-2.73047 - 1.39124i) q^{13} +(-2.33634 - 5.98928i) q^{14} +(-2.29834 + 2.55257i) q^{16} +(4.44513 - 5.48928i) q^{17} +(5.36527 - 1.43762i) q^{18} +(-2.90112 - 1.29166i) q^{19} +(-3.34055 - 5.08353i) q^{21} +(-0.0401727 + 0.00636273i) q^{22} +(-4.59318 - 2.98285i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(-1.46278 + 0.745322i) q^{27} +(10.1155 + 2.09295i) q^{28} +(0.0353871 - 0.0487062i) q^{29} +(8.96709 - 0.942479i) q^{31} +(0.235039 + 0.877177i) q^{32} +(-0.0359286 + 0.0137917i) q^{33} +(5.30369 + 16.3231i) q^{34} +(-2.75796 + 8.48811i) q^{36} +(-0.439728 - 8.39052i) q^{37} +(6.47159 - 4.20270i) q^{38} +(5.23590 - 4.71442i) q^{39} +(-5.83738 + 1.89668i) q^{41} +(14.7804 - 0.0800095i) q^{42} +(3.18681 + 3.18681i) q^{43} +(0.0265816 - 0.0597034i) q^{44} +(12.1573 - 5.41276i) q^{46} +(3.57724 - 2.89679i) q^{47} +(-3.58519 - 7.03633i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-0.626178 + 11.9482i) q^{52} +(-4.06266 - 1.55951i) q^{53} +(0.416980 - 3.96730i) q^{54} +(-8.60961 + 8.70333i) q^{56} +(5.16276 - 5.16276i) q^{57} +(0.0524250 + 0.136572i) q^{58} +(-2.45075 - 0.520924i) q^{59} +(2.77436 + 13.0523i) q^{61} +(-9.94643 + 19.5210i) q^{62} +(5.90896 - 1.28946i) q^{63} +(-8.63203 - 2.80472i) q^{64} +(0.0194425 - 0.0914696i) q^{66} +(0.247175 + 0.200158i) q^{67} +(-26.6377 - 7.13755i) q^{68} +(10.1869 - 7.40119i) q^{69} +(-6.35569 - 4.61768i) q^{71} +(-6.65655 - 8.22016i) q^{72} +(-3.33870 - 0.174974i) q^{73} +(17.6807 + 10.2079i) q^{74} +12.3987i q^{76} +(-0.0440188 + 0.00486761i) q^{77} +(2.67814 + 16.9091i) q^{78} +(5.32825 + 0.560021i) q^{79} +(-1.11138 - 10.5741i) q^{81} +(3.86003 - 14.4058i) q^{82} +(-1.36750 + 8.63403i) q^{83} +(-12.8268 + 19.9876i) q^{84} +(-10.7117 + 2.27684i) q^{86} +(0.0753869 + 0.116086i) q^{87} +(0.0421842 + 0.0649580i) q^{88} +(-8.18738 + 1.74028i) q^{89} +(7.20412 - 3.71994i) q^{91} +(-3.34499 + 21.1194i) q^{92} +(-5.36531 + 20.0236i) q^{93} +(1.16913 + 11.1236i) q^{94} +(-2.07644 - 0.218242i) q^{96} +(-1.07640 - 6.79613i) q^{97} +(16.4762 + 4.22415i) q^{98} -0.0382642i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32340	+	2.03786i	−0.935787	+	1.44099i	−0.0386405	+	0.999253i	$0.512303\pi$
$2$	−1.32340	+	2.03786i	−0.935787	+	1.44099i	−0.897147	+	0.441733i	$0.854364\pi$
$3$	−0.823930	+	2.14641i	−0.475696	+	1.23923i	0.460471	+	0.887675i	$0.347681\pi$
$3$	−0.823930	+	2.14641i	−0.475696	+	1.23923i	−0.936167	+	0.351556i	$0.885653\pi$
$4$	−1.58801	−	3.56673i	−0.794006	−	1.78337i
$5$		0			0
$5$		0			0
$6$	−3.28370	−	4.51962i	−1.34056	−	1.84513i
$7$	−1.54352	+	2.14884i	−0.583397	+	0.812187i
$7$	−1.54352	+	2.14884i	−0.583397	+	0.812187i
$8$	4.57018	+	0.723845i	1.61580	+	0.255918i
$9$	−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	$0.765863\pi$
$12$	8.96408	−	0.469788i	2.58771	−	0.135616i
$13$	−2.73047	−	1.39124i	−0.757297	−	0.385862i	0.0323079	−	0.999478i	$-0.489714\pi$
$13$	−2.73047	−	1.39124i	−0.757297	−	0.385862i	−0.789605	+	0.613616i	$0.789714\pi$
$14$	−2.33634	−	5.98928i	−0.624414	−	1.60070i
$15$		0			0
$16$	−2.29834	+	2.55257i	−0.574586	+	0.638142i
$17$	4.44513	−	5.48928i	1.07810	−	1.33135i	0.138008	−	0.990431i	$-0.455930\pi$
$17$	4.44513	−	5.48928i	1.07810	−	1.33135i	0.940094	−	0.340914i	$-0.110737\pi$
$18$	5.36527	−	1.43762i	1.26461	−	0.338850i
$19$	−2.90112	−	1.29166i	−0.665563	−	0.296328i	0.0460087	−	0.998941i	$-0.485350\pi$
$19$	−2.90112	−	1.29166i	−0.665563	−	0.296328i	−0.711572	+	0.702613i	$0.752016\pi$
$20$		0			0
$21$	−3.34055	−	5.08353i	−0.728967	−	1.10932i
$22$	−0.0401727	+	0.00636273i	−0.00856485	+	0.00135654i
$23$	−4.59318	−	2.98285i	−0.957744	−	0.621966i	−0.0317465	−	0.999496i	$-0.510107\pi$
$23$	−4.59318	−	2.98285i	−0.957744	−	0.621966i	−0.925997	+	0.377530i	$0.876774\pi$
$24$	−5.31918	+	9.21308i	−1.08577	+	1.88061i
$25$		0			0
$26$	6.44868	−	3.72315i	1.26469	−	0.730169i
$27$	−1.46278	+	0.745322i	−0.281512	+	0.143437i
$28$	10.1155	+	2.09295i	1.91165	+	0.395530i
$29$	0.0353871	−	0.0487062i	0.00657122	−	0.00904451i	−0.805719	−	0.592298i	$-0.798221\pi$
$29$	0.0353871	−	0.0487062i	0.00657122	−	0.00904451i	0.812290	+	0.583254i	$0.198221\pi$
$30$		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	$0.166294\pi$
$32$	0.235039	+	0.877177i	0.0415494	+	0.155065i
$33$	−0.0359286	+	0.0137917i	−0.00625437	+	0.00240083i
$34$	5.30369	+	16.3231i	0.909576	+	2.79939i
$35$		0			0
$36$	−2.75796	+	8.48811i	−0.459659	+	1.41469i
$37$	−0.439728	−	8.39052i	−0.0722909	−	1.37939i	−0.758350	−	0.651847i	$-0.773994\pi$
$37$	−0.439728	−	8.39052i	−0.0722909	−	1.37939i	0.686059	−	0.727546i	$-0.259339\pi$
$38$	6.47159	−	4.20270i	1.04983	−	0.681768i
$39$	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	$0.559102\pi$
$42$	14.7804	−	0.0800095i	2.28067	−	0.0123457i
$43$	3.18681	+	3.18681i	0.485984	+	0.485984i	0.907036	−	0.421052i	$-0.138339\pi$
$43$	3.18681	+	3.18681i	0.485984	+	0.485984i	−0.421052	+	0.907036i	$0.638339\pi$
$44$	0.0265816	−	0.0597034i	0.00400733	−	0.00900062i
$45$		0			0
$46$	12.1573	−	5.41276i	1.79249	−	0.798068i
$47$	3.57724	−	2.89679i	0.521794	−	0.422541i	−0.331900	−	0.943314i	$-0.607690\pi$
$47$	3.57724	−	2.89679i	0.521794	−	0.422541i	0.853695	+	0.520774i	$0.174356\pi$
$48$	−3.58519	−	7.03633i	−0.517477	−	1.01561i
$49$	−2.23507	−	6.63359i	−0.319295	−	0.947655i
$50$		0			0
$51$	8.11977	+	14.0639i	1.13700	+	1.96933i
$52$	−0.626178	+	11.9482i	−0.0868352	+	1.65691i
$53$	−4.06266	−	1.55951i	−0.558050	−	0.214215i	0.0629629	−	0.998016i	$-0.479945\pi$
$53$	−4.06266	−	1.55951i	−0.558050	−	0.214215i	−0.621012	+	0.783801i	$0.713278\pi$
$54$	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
$58$	0.0524250	+	0.136572i	0.00688374	+	0.0179328i
$59$	−2.45075	−	0.520924i	−0.319061	−	0.0678185i	0.0455974	−	0.998960i	$-0.485481\pi$
$59$	−2.45075	−	0.520924i	−0.319061	−	0.0678185i	−0.364658	+	0.931141i	$0.618814\pi$
$60$		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	$0.607345\pi$
$62$	−9.94643	+	19.5210i	−1.26320	+	2.47917i
$63$	5.90896	−	1.28946i	0.744460	−	0.162457i
$64$	−8.63203	−	2.80472i	−1.07900	−	0.350590i
$65$		0			0
$66$	0.0194425	−	0.0914696i	0.00239320	−	0.0112591i
$67$	0.247175	+	0.200158i	0.0301972	+	0.0244532i	0.644300	−	0.764773i	$-0.277149\pi$
$67$	0.247175	+	0.200158i	0.0301972	+	0.0244532i	−0.614103	+	0.789226i	$0.710482\pi$
$68$	−26.6377	−	7.13755i	−3.23030	−	0.865556i
$69$	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	$0.854367\pi$
$72$	−6.65655	−	8.22016i	−0.784482	−	0.968755i
$73$	−3.33870	−	0.174974i	−0.390765	−	0.0204791i	−0.144058	−	0.989569i	$-0.546015\pi$
$73$	−3.33870	−	0.174974i	−0.390765	−	0.0204791i	−0.246707	+	0.969090i	$0.579349\pi$
$74$	17.6807	+	10.2079i	2.05533	+	1.18665i
$75$		0			0
$76$			12.3987i			1.42223i
$77$	−0.0440188	+	0.00486761i	−0.00501640	+	0.000554716i
$78$	2.67814	+	16.9091i	0.303240	+	1.91458i
$79$	5.32825	+	0.560021i	0.599475	+	0.0630073i	0.399405	−	0.916774i	$-0.369217\pi$
$79$	5.32825	+	0.560021i	0.599475	+	0.0630073i	0.200069	+	0.979782i	$0.435883\pi$
$80$		0			0
$81$	−1.11138	−	10.5741i	−0.123486	−	1.17490i
$82$	3.86003	−	14.4058i	0.426270	−	1.59086i
$83$	−1.36750	+	8.63403i	−0.150102	+	0.947708i	0.791546	+	0.611110i	$0.209277\pi$
$83$	−1.36750	+	8.63403i	−0.150102	+	0.947708i	−0.941648	+	0.336599i	$0.890723\pi$
$84$	−12.8268	+	19.9876i	−1.39952	+	2.18082i
$85$		0			0
$86$	−10.7117	+	2.27684i	−1.15507	+	0.245518i
$87$	0.0753869	+	0.116086i	0.00808233	+	0.0124457i
$88$	0.0421842	+	0.0649580i	0.00449685	+	0.00692455i
$89$	−8.18738	+	1.74028i	−0.867861	+	0.184470i	−0.620264	−	0.784394i	$-0.712974\pi$
$89$	−8.18738	+	1.74028i	−0.867861	+	0.184470i	−0.247597	+	0.968863i	$0.579641\pi$
$90$		0			0
$91$	7.20412	−	3.71994i	0.755197	−	0.389956i
$92$	−3.34499	+	21.1194i	−0.348739	+	2.20185i
$93$	−5.36531	+	20.0236i	−0.556356	+	2.07635i
$94$	1.16913	+	11.1236i	0.120587	+	1.14731i
$95$		0			0
$96$	−2.07644	−	0.218242i	−0.211926	−	0.0222743i
$97$	−1.07640	−	6.79613i	−0.109292	−	0.690043i	−0.980113	−	0.198442i	$-0.936412\pi$
$97$	−1.07640	−	6.79613i	−0.109292	−	0.690043i	0.870821	−	0.491601i	$-0.163588\pi$
$98$	16.4762	+	4.22415i	1.66435	+	0.426704i
$99$		−	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	$0.843561\pi$
$102$	−39.4059	−	2.06518i	−3.90177	−	0.204483i
$103$	−0.137698	−	0.170043i	−0.0135678	−	0.0167548i	0.770317	−	0.637661i	$-0.220098\pi$
$103$	−0.137698	−	0.170043i	−0.0135678	−	0.0167548i	−0.783885	+	0.620906i	$0.786765\pi$
$104$	−11.4717	−	8.33468i	−1.12489	−	0.817282i
$105$		0			0
$106$	8.55461	−	6.21528i	0.830897	−	0.603682i
$107$	−4.72847	−	1.26699i	−0.457119	−	0.122485i	0.0229097	−	0.999738i	$-0.492707\pi$
$107$	−4.72847	−	1.26699i	−0.457119	−	0.122485i	−0.480028	+	0.877253i	$0.659374\pi$
$108$	4.98127	+	4.03376i	0.479323	+	0.388148i
$109$	1.60438	−	7.54803i	0.153672	−	0.722970i	−0.832065	−	0.554678i	$-0.812842\pi$
$109$	1.60438	−	7.54803i	0.153672	−	0.722970i	0.985737	−	0.168292i	$-0.0538252\pi$
$110$		0			0
$111$	18.3718	+	5.96936i	1.74377	+	0.566587i
$112$	−1.93753	−	8.87874i	−0.183079	−	0.838962i
$113$	−1.81771	+	3.56746i	−0.170996	+	0.335599i	−0.960561	−	0.278068i	$-0.910306\pi$
$113$	−1.81771	+	3.56746i	−0.170996	+	0.335599i	0.789565	+	0.613666i	$0.210306\pi$
$114$	3.68858	+	17.3534i	0.345467	+	1.62530i
$115$		0			0
$116$	−0.229917	−	0.0488704i	−0.0213473	−	0.00453750i
$117$	2.51044	+	6.53993i	0.232091	+	0.604616i
$118$	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
$122$	−30.2705	−	11.6198i	−2.74056	−	1.05200i
$123$	0.738538	−	14.0921i	0.0665917	−	1.27065i
$124$	−17.6014	−	30.4866i	−1.58065	−	2.73777i
$125$		0			0
$126$	−5.19220	+	13.7481i	−0.462558	+	1.22478i
$127$	3.30790	+	6.49211i	0.293528	+	0.576082i	0.989928	−	0.141572i	$-0.0452158\pi$
$127$	3.30790	+	6.49211i	0.293528	+	0.576082i	−0.696399	+	0.717654i	$0.745216\pi$
$128$	15.7278	−	12.7361i	1.39015	−	1.12572i
$129$	−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
$133$	7.25354	−	4.24035i	0.628962	−	0.367685i
$134$	−0.735006	+	0.238818i	−0.0634949	+	0.0206307i
$135$		0			0
$136$	24.2884	−	21.8694i	2.08272	−	1.87529i
$137$	2.76276	−	1.79416i	0.236039	−	0.153285i	−0.421200	−	0.906968i	$-0.638391\pi$
$137$	2.76276	−	1.79416i	0.236039	−	0.153285i	0.657239	+	0.753682i	$0.271724\pi$
$138$	1.60128	+	30.5542i	0.136310	+	2.60094i
$139$	−1.40509	+	4.32443i	−0.119179	+	0.366794i	−0.992796	−	0.119820i	$-0.961768\pi$
$139$	−1.40509	+	4.32443i	−0.119179	+	0.366794i	0.873617	+	0.486614i	$0.161768\pi$
$140$		0			0
$141$	3.27031	+	10.0650i	0.275410	+	0.847625i
$142$	17.8213	−	6.84097i	1.49553	−	0.574082i
$143$	−0.0132764	−	0.0495483i	−0.00111023	−	0.00414344i
$144$	7.80877	−	0.820735i	0.650731	−	0.0683946i
$145$		0			0
$146$	4.77502	−	6.57225i	0.395183	−	0.543923i
$147$	16.0799	+	0.668241i	1.32625	+	0.0551156i
$148$	−29.2285	+	14.8926i	−2.40256	+	1.22417i
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.311491	−	0.950249i	$-0.399172\pi$
$149$	15.7486	−	9.09246i	1.29018	−	0.744884i	0.978685	+	0.205366i	$0.0658384\pi$
$150$		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	$-0.112590\pi$
$152$	−12.3237	−	8.00310i	−0.999583	−	0.649137i
$153$	−15.9477	+	2.52586i	−1.28929	+	0.204204i
$154$	0.0483350	−	0.0961460i	0.00389495	−	0.00774766i
$155$		0			0
$156$	−25.1298	−	11.1885i	−2.01199	−	0.895796i
$157$	15.7038	−	4.20781i	1.25330	−	0.335820i	0.429688	−	0.902978i	$-0.358624\pi$
$157$	15.7038	−	4.20781i	1.25330	−	0.335820i	0.823609	+	0.567158i	$0.191957\pi$
$158$	−8.19266	+	10.1171i	−0.651773	+	0.804873i
$159$	6.69470	−	7.43521i	0.530924	−	0.589651i
$160$		0			0
$161$	13.4994	−	5.26593i	1.06390	−	0.415014i
$162$	23.0193	+	11.7289i	1.80856	+	0.921510i
$163$	9.35413	−	0.490229i	0.732672	−	0.0383977i	0.317649	−	0.948208i	$-0.397107\pi$
$163$	9.35413	−	0.490229i	0.732672	−	0.0383977i	0.415023	+	0.909811i	$0.363773\pi$
$164$	16.0348	+	17.8084i	1.25211	+	1.39060i
$165$		0			0
$166$	−15.7852	−	14.2131i	−1.22517	−	1.10315i
$167$	−7.46435	−	1.18224i	−0.577608	−	0.0914842i	−0.139207	−	0.990263i	$-0.544455\pi$
$167$	−7.46435	−	1.18224i	−0.577608	−	0.0914842i	−0.438402	+	0.898779i	$0.644455\pi$
$168$	−11.5872	−	25.6507i	−0.893972	−	1.97899i
$169$	−2.12129	−	2.91971i	−0.163177	−	0.224593i
$170$		0			0
$171$	2.95266	+	6.63179i	0.225796	+	0.507145i
$172$	6.30581	−	16.4272i	0.480813	−	1.25256i
$173$	12.7463	−	19.6275i	0.969080	−	1.49225i	0.101572	−	0.994828i	$-0.467613\pi$
$173$	12.7463	−	19.6275i	0.969080	−	1.49225i	0.867508	−	0.497423i	$-0.165720\pi$
$174$	−0.336334			−0.0254974
$175$		0			0
$176$	−0.0574953			−0.00433387
$177$	3.13737	−	4.83112i	0.235819	−	0.363129i
$178$	7.28875	−	18.9878i	0.546315	−	1.42320i
$179$	−5.54190	−	12.4473i	−0.414221	−	0.930356i	−0.993351	−	0.115121i	$-0.963274\pi$
$179$	−5.54190	−	12.4473i	−0.414221	−	0.930356i	0.579130	−	0.815235i	$-0.303392\pi$
$180$		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	$0.868559\pi$
$182$	−1.95323	+	19.6040i	−0.144783	+	1.45314i
$183$	−30.3016	−	4.79930i	−2.23996	−	0.354774i
$184$	−18.8325	−	16.9569i	−1.38835	−	1.25008i
$185$		0			0
$186$	−33.7049	−	37.4330i	−2.47136	−	2.74472i
$187$	0.118072	−	0.00618787i	0.00863424	−	0.000452502i
$188$	−16.0128	−	8.15893i	−1.16785	−	0.595051i
$189$	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	$0.413442\pi$
$192$	13.1323	−	16.2170i	0.947740	−	1.17036i
$193$	16.0726	−	4.30663i	1.15693	−	0.309998i	0.371191	−	0.928557i	$-0.378950\pi$
$193$	16.0726	−	4.30663i	1.15693	−	0.309998i	0.785739	+	0.618558i	$0.212283\pi$
$194$	15.2741	+	6.80046i	1.09662	+	0.488245i
$195$		0			0
$196$	−20.1109	+	18.5061i	−1.43649	+	1.32186i
$197$	−15.3662	+	2.43376i	−1.09479	+	0.173398i	−0.677608	−	0.735423i	$-0.736983\pi$
$197$	−15.3662	+	2.43376i	−1.09479	+	0.173398i	−0.417185	+	0.908821i	$0.636983\pi$
$198$	0.0779771	+	0.0506389i	0.00554159	+	0.00359875i
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	−0.828842	−	0.559482i	$-0.811000\pi$
$199$	0.988951	−	1.71291i	0.0701049	−	0.121425i	0.898947	+	0.438057i	$0.144333\pi$
$200$		0			0
$201$	−0.633276	+	0.365622i	−0.0446678	+	0.0257890i
$202$	22.9578	−	11.6976i	1.61531	−	0.823039i
$203$	0.0500411	+	0.151221i	0.00351220	+	0.0106136i
$204$	37.2677	−	51.2946i	2.60926	−	3.59134i
$205$		0			0
$206$	0.528754	−	0.0555743i	0.0368401	−	0.00387205i
$207$	3.24028	+	12.0929i	0.225215	+	0.840514i
$208$	9.82681	−	3.77216i	0.681367	−	0.261552i
$209$	−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	$-0.00187554\pi$
$212$	0.889200	+	16.9670i	0.0610705	+	1.16530i
$213$	15.1481	−	9.83728i	1.03793	−	0.674040i
$214$	8.83963	−	7.95924i	0.604264	−	0.544082i
$215$		0			0
$216$	−7.22465	+	2.34743i	−0.491575	+	0.159722i
$217$	−11.8157	+	20.7236i	−0.802101	+	1.40681i
$218$	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
$222$	−36.4780	+	29.5393i	−2.44824	+	1.98255i
$223$	3.37676	+	6.62726i	0.226124	+	0.443794i	0.975996	−	0.217789i	$-0.0698846\pi$
$223$	3.37676	+	6.62726i	0.226124	+	0.443794i	−0.749871	+	0.661584i	$0.769885\pi$
$224$	−2.24771	−	0.848882i	−0.150181	−	0.0567183i
$225$		0			0
$226$	−4.86443	−	8.42544i	−0.323577	−	0.560452i
$227$	0.613246	−	11.7014i	0.0407026	−	0.776651i	−0.899684	−	0.436543i	$-0.856203\pi$
$227$	0.613246	−	11.7014i	0.0407026	−	0.776651i	0.940386	−	0.340109i	$-0.110464\pi$
$228$	−26.6127	−	10.2157i	−1.76247	−	0.676549i
$229$	−2.81607	+	26.7931i	−0.186091	+	1.77054i	0.360134	+	0.932901i	$0.382731\pi$
$229$	−2.81607	+	26.7931i	−0.186091	+	1.77054i	−0.546225	+	0.837638i	$0.683936\pi$
$230$		0			0
$231$	0.0258205	−	0.0984929i	0.00169886	−	0.00648036i
$232$	0.196981	−	0.196981i	0.0129324	−	0.0129324i
$233$	−7.82907	−	20.3954i	−0.512900	−	1.33615i	−0.908561	−	0.417753i	$-0.862818\pi$
$233$	−7.82907	−	20.3954i	−0.512900	−	1.33615i	0.395661	−	0.918397i	$-0.370515\pi$
$234$	−16.6498	−	3.53902i	−1.08843	−	0.231353i
$235$		0			0
$236$	2.03383	+	9.56842i	0.132391	+	0.622851i
$237$	−5.59214	+	10.9752i	−0.363248	+	0.712915i
$238$	−43.2622	−	13.7983i	−2.80427	−	0.894409i
$239$	4.05851	+	1.31869i	0.262523	+	0.0852989i	0.437321	−	0.899305i	$-0.355927\pi$
$239$	4.05851	+	1.31869i	0.262523	+	0.0852989i	−0.174798	+	0.984604i	$0.555927\pi$
$240$		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	$0.0649831\pi$
$242$	20.7715	+	16.8204i	1.33524	+	1.08126i
$243$	18.8546	+	5.05209i	1.20953	+	0.324092i
$244$	42.1485	−	30.6227i	2.69828	−	1.96042i
$245$		0			0
$246$	27.7405	+	20.1546i	1.76867	+	1.28501i
$247$	6.12442	+	7.56302i	0.389687	+	0.481224i
$248$	41.6634	+	2.18349i	2.64563	+	0.138652i
$249$	−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	$-0.00132910\pi$
$252$	−13.9827	−	19.0280i	−0.880825	−	1.19865i
$253$	−0.0143411	−	0.0905461i	−0.000901617	−	0.00569259i
$254$	−17.6077	−	1.85065i	−1.10481	−	0.116120i
$255$		0			0
$256$	3.24278	+	30.8530i	0.202674	+	1.92831i
$257$	2.37849	−	8.87663i	0.148366	−	0.553709i	−0.851217	−	0.524815i	$-0.824135\pi$
$257$	2.37849	−	8.87663i	0.148366	−	0.553709i	0.999582	−	0.0288944i	$-0.00919866\pi$
$258$	3.93865	−	24.8677i	0.245210	−	1.54819i
$259$	18.7087	+	12.0061i	1.16250	+	0.746020i
$260$		0			0
$261$	−0.134615	+	0.0286134i	−0.00833249	+	0.00177113i
$262$	−15.6563	−	24.1086i	−0.967249	−	1.48943i
$263$	−11.3926	−	17.5431i	−0.702499	−	1.08175i	−0.992202	−	0.124637i	$-0.960223\pi$
$263$	−11.3926	−	17.5431i	−0.702499	−	1.08175i	0.289703	−	0.957117i	$-0.406443\pi$
$264$	−0.174183	+	0.0370238i	−0.0107202	+	0.00227866i
$265$		0			0
$266$	−0.958107	+	20.3934i	−0.0587453	+	1.25040i
$267$	3.01047	−	19.0074i	0.184238	−	1.16323i
$268$	0.321394	−	1.19946i	0.0196323	−	0.0732687i
$269$	−0.158106	−	1.50428i	−0.00963991	−	0.0917176i	0.988644	−	0.150276i	$-0.0480163\pi$
$269$	−0.158106	−	1.50428i	−0.00963991	−	0.0917176i	−0.998284	+	0.0585585i	$0.981350\pi$
$270$		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	$0.444328\pi$
$272$	3.79533	+	23.9627i	0.230125	+	1.45295i
$273$	2.04883	+	18.5280i	0.124001	+	1.12136i
$274$			8.00453i			0.483571i
$275$		0			0
$276$	−42.5749	−	24.5807i	−2.56271	−	1.47958i
$277$	−13.6454	−	0.715125i	−0.819872	−	0.0429677i	−0.362213	−	0.932095i	$-0.617979\pi$
$277$	−13.6454	−	0.715125i	−0.819872	−	0.0429677i	−0.457659	+	0.889128i	$0.651312\pi$
$278$	−6.95309	−	8.58636i	−0.417019	−	0.514975i
$279$	−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	$0.337933\pi$
$282$	−24.8390	−	6.65559i	−1.47914	−	0.396334i
$283$	−14.6857	−	11.8922i	−0.872974	−	0.706920i	0.0841955	−	0.996449i	$-0.473168\pi$
$283$	−14.6857	−	11.8922i	−0.872974	−	0.706920i	−0.957169	+	0.289529i	$0.906501\pi$
$284$	−6.37712	+	30.0020i	−0.378413	+	1.78029i
$285$		0			0
$286$	0.118543	+	0.0385168i	0.00700957	+	0.00227755i
$287$	4.93447	−	15.4712i	0.291272	−	0.913236i
$288$	0.942442	−	1.84965i	0.0555339	−	0.108991i
$289$	−6.83850	−	32.1726i	−0.402265	−	1.89251i
$290$		0			0
$291$	15.4742	+	3.28914i	0.907112	+	0.192813i
$292$	4.67781	+	12.1861i	0.273748	+	0.713138i
$293$	−4.94524	+	4.94524i	−0.288904	+	0.288904i	−0.836647	−	0.547743i	$-0.815487\pi$
$293$	−4.94524	+	4.94524i	−0.288904	+	0.288904i	0.547743	+	0.836647i	$0.315487\pi$
$294$	−22.6420	+	31.8843i	−1.32051	+	1.85953i
$295$		0			0
$296$	4.06380	−	38.6645i	0.236204	−	2.24733i
$297$	−0.0256553	−	0.00984815i	−0.00148867	−	0.000571447i
$298$	−2.31257	+	44.1265i	−0.133964	+	2.55618i
$299$	8.39168	+	14.5348i	0.485303	+	0.840570i
$300$		0			0
$301$	−11.7669	+	1.92904i	−0.678231	+	0.111188i
$302$	20.8491	+	40.9187i	1.19973	+	2.35460i
$303$	18.9465	−	15.3426i	1.08845	−	0.881409i
$304$	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	$-0.311591\pi$
$307$	−4.76473	−	4.76473i	−0.271938	−	0.271938i	−0.829880	+	0.557942i	$0.811591\pi$
$308$	0.0872638	+	0.149273i	0.00497232	+	0.00850564i
$309$	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	$0.242919\pi$
$312$	27.3415	−	17.7558i	1.54791	−	1.00522i
$313$	0.227616	+	4.34316i	0.0128656	+	0.245490i	0.997490	+	0.0708059i	$0.0225571\pi$
$313$	0.227616	+	4.34316i	0.0128656	+	0.245490i	−0.984625	+	0.174684i	$0.944110\pi$
$314$	−12.2075	+	37.5707i	−0.688908	+	2.12024i
$315$		0			0
$316$	−6.46387	−	19.8938i	−0.363621	−	1.11911i
$317$	−19.3720	+	7.43621i	−1.08804	+	0.417659i	−0.835254	−	0.549864i	$-0.814680\pi$
$317$	−19.3720	+	7.43621i	−1.08804	+	0.417659i	−0.252784	+	0.967523i	$0.581346\pi$
$318$	6.29216	+	23.4827i	0.352847	+	1.31684i
$319$	0.00100223		0.000105339i	5.61143e−5		5.89785e-6i
$320$		0			0
$321$	6.61541	−	9.10533i	0.369236	−	0.508210i
$322$	−7.13384	+	34.4788i	−0.397553	+	1.92143i
$323$	−19.9862	+	10.1835i	−1.11206	+	0.566623i
$324$	−35.9500	+	20.7557i	−1.99722	+	1.15310i
$325$		0			0
$326$	−11.3803	+	19.7112i	−0.630295	+	1.09170i
$327$	14.8793	+	9.66271i	0.822825	+	0.534349i
$328$	−28.0508	+	4.44281i	−1.54884	+	0.245313i
$329$	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	$0.489465\pi$
$332$	32.9669	−	8.83346i	1.80929	−	0.484799i
$333$	−12.0871	+	14.9263i	−0.662367	+	0.817955i
$334$	12.2876	−	13.6467i	0.672346	−	0.746716i
$335$		0			0
$336$	20.6538	+	3.15673i	1.12676	+	0.172214i
$337$	−22.7884	−	11.6113i	−1.24137	−	0.632508i	−0.294967	−	0.955507i	$-0.595309\pi$
$337$	−22.7884	−	11.6113i	−1.24137	−	0.632508i	−0.946399	+	0.323000i	$0.895309\pi$
$338$	8.75730	−	0.458951i	0.476334	−	0.0249636i
$339$	−6.15957	−	6.84090i	−0.334542	−	0.371547i
$340$		0			0
$341$	0.112160	+	0.100989i	0.00607382	+	0.00546889i
$342$	−17.4222	−	2.75941i	−0.942086	−	0.149212i
$343$	17.7044	+	5.43629i	0.955949	+	0.293532i
$344$	12.2575	+	16.8710i	0.660882	+	0.909626i
$345$		0			0
$346$	23.1297	+	51.9502i	1.24346	+	2.79286i
$347$	5.43034	−	14.1465i	0.291516	−	0.759425i	−0.707114	−	0.707099i	$-0.750003\pi$
$347$	5.43034	−	14.1465i	0.291516	−	0.759425i	0.998630	−	0.0523255i	$-0.0166633\pi$
$348$	0.294331	−	0.453231i	0.0157778	−	0.0242957i
$349$	1.48928			0.0797192			0.0398596	−	0.999205i	$-0.487309\pi$
$349$	1.48928			0.0797192			0.0398596	+	0.999205i	$0.487309\pi$
$350$		0			0
$351$	5.03100			0.268535
$352$	−0.00827905	+	0.0127486i	−0.000441275	+	0.000679504i
$353$	−3.36856	+	8.77541i	−0.179291	+	0.467068i	−0.993545	−	0.113441i	$-0.963813\pi$
$353$	−3.36856	+	8.77541i	−0.179291	+	0.467068i	0.814254	+	0.580509i	$0.197146\pi$
$354$	5.69315	+	12.7870i	0.302588	+	0.679623i
$355$		0			0
$356$	19.2088	+	26.4386i	1.01806	+	1.40124i
$357$	−42.7541	−	4.25978i	−2.26279	−	0.225451i
$358$	32.7001	+	5.17918i	1.72825	+	0.273728i
$359$	4.56543	+	4.11073i	0.240954	+	0.216956i	0.780756	−	0.624836i	$-0.214834\pi$
$359$	4.56543	+	4.11073i	0.240954	+	0.216956i	−0.539802	+	0.841792i	$0.681501\pi$
$360$		0			0
$361$	−5.96536	−	6.62520i	−0.313966	−	0.348695i
$362$	13.9543	−	0.731315i	0.733422	−	0.0384370i
$363$	22.5332	+	11.4813i	1.18269	+	0.602610i
$364$	−24.7083	−	19.7879i	−1.29506	−	1.03717i
$365$		0			0
$366$	49.8815	−	55.3990i	2.60735	−	2.89575i
$367$	−22.7079	+	28.0420i	−1.18534	+	1.46378i	−0.331341	+	0.943511i	$0.607501\pi$
$367$	−22.7079	+	28.0420i	−1.18534	+	1.46378i	−0.854003	+	0.520267i	$0.825832\pi$
$368$	18.1706	−	4.86880i	0.947209	−	0.253804i
$369$	12.8176	+	5.70676i	0.667257	+	0.297082i
$370$		0			0
$371$	9.62196	−	6.32289i	0.499547	−	0.328268i
$372$	79.9390	−	12.6611i	4.14464	−	0.656447i
$373$	−15.5909	−	10.1248i	−0.807264	−	0.524244i	0.0737815	−	0.997274i	$-0.476493\pi$
$373$	−15.5909	−	10.1248i	−0.807264	−	0.524244i	−0.881046	+	0.473031i	$0.843160\pi$
$374$	−0.143646	+	0.248802i	−0.00742777	+	0.0128653i
$375$		0			0
$376$	18.4455	−	10.6495i	0.951252	−	0.549206i
$377$	−0.164386	+	0.0837587i	−0.00846629	+	0.00431379i
$378$	7.88149	+	7.01965i	0.405380	+	0.361052i
$379$	13.0838	−	18.0083i	0.672068	−	0.925022i	−0.327737	−	0.944769i	$-0.606286\pi$
$379$	13.0838	−	18.0083i	0.672068	−	0.925022i	0.999805	+	0.0197466i	$0.00628593\pi$
$380$		0			0
$381$	−16.6602	+	1.75106i	−0.853529	+	0.0897095i
$382$	−9.31932	−	34.7802i	−0.476818	−	1.77951i
$383$	14.3726	−	5.51711i	0.734403	−	0.281911i	0.0377184	−	0.999288i	$-0.487991\pi$
$383$	14.3726	−	5.51711i	0.734403	−	0.281911i	0.696685	+	0.717377i	$0.254658\pi$
$384$	14.3783	+	44.2520i	0.733742	+	2.25822i
$385$		0			0
$386$	−12.4942	+	38.4531i	−0.635937	+	1.95721i
$387$	−0.539182	−	10.2882i	−0.0274082	−	0.522979i
$388$	−22.5307	+	14.6316i	−1.14382	+	0.742806i
$389$	−8.85903	+	7.97670i	−0.449171	+	0.404435i	−0.862428	−	0.506179i	$-0.831057\pi$
$389$	−8.85903	+	7.97670i	−0.449171	+	0.404435i	0.413258	+	0.910614i	$0.364391\pi$
$390$		0			0
$391$	−36.7909	+	11.9541i	−1.86060	+	0.604545i
$392$	−5.41296	−	31.9345i	−0.273396	−	1.61294i
$393$	−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
$397$	−5.26807	+	4.26600i	−0.264397	+	0.214105i	−0.752347	−	0.658767i	$-0.771078\pi$
$397$	−5.26807	+	4.26600i	−0.264397	+	0.214105i	0.487950	+	0.872872i	$0.337745\pi$
$398$	2.18190	+	4.28222i	0.109369	+	0.214648i
$399$	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	$0.984251\pi$
$402$	0.0929920	−	1.77439i	0.00463802	−	0.0884987i
$403$	−25.7956	−	9.90201i	−1.28497	−	0.493254i
$404$	−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
$408$	26.9287	+	70.1518i	1.33317	+	3.47303i
$409$	15.5613	+	3.30765i	0.769456	+	0.163553i	0.575882	−	0.817533i	$-0.304659\pi$
$409$	15.5613	+	3.30765i	0.769456	+	0.163553i	0.193574	+	0.981086i	$0.437992\pi$
$410$		0			0
$411$	1.57468	+	7.40829i	0.0776732	+	0.365424i
$412$	−0.387832	+	0.761163i	−0.0191071	+	0.0374998i
$413$	4.90218	−	4.46223i	0.241221	−	0.219572i
$414$	−28.9318	−	9.40052i	−1.42192	−	0.462010i
$415$		0			0
$416$	0.578601	−	2.72210i	0.0283683	−	0.133462i
$417$	−8.12431	−	6.57894i	−0.397849	−	0.322172i
$418$	0.124765	+	0.0334306i	0.00610243	+	0.00163514i
$419$	−28.7560	+	20.8925i	−1.40482	+	1.02066i	−0.410773	+	0.911738i	$0.634741\pi$
$419$	−28.7560	+	20.8925i	−1.40482	+	1.02066i	−0.994050	+	0.108926i	$0.965259\pi$
$420$		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	$0.811244\pi$
$422$	13.9768	+	17.2599i	0.680378	+	0.840197i
$423$	−10.5079	−	0.550694i	−0.510910	−	0.0267757i
$424$	−17.4383	−	10.0680i	−0.846876	−	0.488944i
$425$		0			0
$426$			43.8884i			2.12640i
$427$	−32.3298	−	14.1849i	−1.56455	−	0.686458i
$428$	2.98985	+	18.8772i	0.144520	+	0.912464i
$429$	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	$0.995883\pi$
$432$	1.45948	−	5.44685i	0.0702192	−	0.262061i
$433$	0.194066	−	1.22529i	0.00932624	−	0.0588836i	−0.982586	−	0.185807i	$-0.940510\pi$
$433$	0.194066	−	1.22529i	0.00932624	−	0.0588836i	0.991913	+	0.126923i	$0.0405102\pi$
$434$	−26.5950	−	51.5044i	−1.27660	−	2.47229i
$435$		0			0
$436$	−29.4696	+	6.26395i	−1.41134	+	0.299989i
$437$	9.47255	+	14.5864i	0.453133	+	0.697764i
$438$	10.1725	+	15.6642i	0.486059	+	0.748465i
$439$	5.32727	−	1.13235i	0.254257	−	0.0540439i	−0.0790199	−	0.996873i	$-0.525179\pi$
$439$	5.32727	−	1.13235i	0.254257	−	0.0540439i	0.333277	+	0.942829i	$0.391846\pi$
$440$		0			0
$441$	−6.34978	+	14.6878i	−0.302371	+	0.699417i
$442$	8.22783	−	51.9485i	0.391358	−	2.47094i
$443$	4.73507	−	17.6715i	0.224970	−	0.839599i	−0.757447	−	0.652897i	$-0.773553\pi$
$443$	4.73507	−	17.6715i	0.224970	−	0.839599i	0.982417	−	0.186702i	$-0.0597799\pi$
$444$	−7.88353	−	75.0067i	−0.374136	−	3.55966i
$445$		0			0
$446$	−17.9743	−	1.88917i	−0.851106	−	0.0894548i
$447$	6.54041	+	41.2945i	0.309351	+	1.95316i
$448$	19.3507	−	14.2197i	0.914233	−	0.671820i
$449$		−	7.28927i		−	0.344002i	−0.985097	−	0.172001i	$-0.944977\pi$
$449$		−	7.28927i		−	0.344002i	0.985097	−	0.172001i	$-0.0550232\pi$
$450$		0			0
$451$	−0.0889755	−	0.0513700i	−0.00418969	−	0.00241892i
$452$	15.6107	+	0.818124i	0.734267	+	0.0384813i
$453$	27.3458	+	33.7692i	1.28482	+	1.58662i
$454$	23.0343	+	16.7354i	1.08105	+	0.785432i
$455$		0			0
$456$	27.3318	−	19.8577i	1.27993	−	0.929922i
$457$	11.4145	+	3.05849i	0.533946	+	0.143070i	0.515710	−	0.856763i	$-0.327528\pi$
$457$	11.4145	+	3.05849i	0.533946	+	0.143070i	0.0182361	+	0.999834i	$0.494195\pi$
$458$	−50.8739	−	41.1969i	−2.37718	−	1.92500i
$459$	−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	$0.606310\pi$
$462$	0.166544	+	0.182964i	0.00774833	+	0.00851227i
$463$	17.5466	−	34.4372i	0.815460	−	1.60043i	0.0158788	−	0.999874i	$-0.494945\pi$
$463$	17.5466	−	34.4372i	0.815460	−	1.60043i	0.799582	−	0.600557i	$-0.205055\pi$
$464$	0.0429941	+	0.202271i	0.00199595	+	0.00939022i
$465$		0			0
$466$	51.9241	+	11.0368i	2.40534	+	0.511270i
$467$	−3.20499	−	8.34928i	−0.148309	−	0.386358i	0.839221	−	0.543791i	$-0.183012\pi$
$467$	−3.20499	−	8.34928i	−0.148309	−	0.386358i	−0.987530	+	0.157433i	$0.949678\pi$
$468$	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
$472$	−10.8233	−	4.15468i	−0.498183	−	0.191235i
$473$	−0.00394820	+	0.0753362i	−0.000181538	+	0.00346396i
$474$	−14.9653	−	25.9206i	−0.687377	−	1.19057i
$475$		0			0
$476$	56.4535	−	46.2233i	2.58754	−	2.11864i
$477$	4.51617	+	8.86348i	0.206781	+	0.405831i
$478$	−8.05835	+	6.52552i	−0.368580	+	0.298470i
$479$	−0.885419	+	0.394214i	−0.0404558	+	0.0180121i	−0.426865	−	0.904315i	$-0.640382\pi$
$479$	−0.885419	+	0.394214i	−0.0404558	+	0.0180121i	0.386409	+	0.922328i	$0.373715\pi$
$480$		0			0
$481$	−10.4726	+	23.5218i	−0.477509	+	1.07250i
$482$	0.282157	+	0.282157i	0.0128519	+	0.0128519i
$483$	0.180335	+	33.3139i	0.00820553	+	1.51584i
$484$	−40.8440	+	13.2710i	−1.85655	+	0.603228i
$485$		0			0
$486$	−35.2477	+	31.7372i	−1.59887	+	1.43963i
$487$	29.0780	−	18.8835i	1.31765	−	0.855691i	0.321808	−	0.946805i	$-0.395709\pi$
$487$	29.0780	−	18.8835i	1.31765	−	0.855691i	0.995840	+	0.0911139i	$0.0290427\pi$
$488$	3.23145	+	61.6598i	0.146281	+	2.79121i
$489$	−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	$0.863152\pi$
$492$	−51.4357	+	19.7443i	−2.31890	+	0.890143i
$493$	−0.110061	−	0.410755i	−0.00495692	−	0.0184995i
$494$	−23.5175	+	2.47179i	−1.05810	+	0.111211i
$495$		0			0
$496$	−18.2037	+	25.0553i	−0.817371	+	1.12501i
$497$	19.7329	−	6.52990i	0.885139	−	0.292906i
$498$	43.5130	−	22.1710i	1.94986	−	0.993506i
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.995612	−	0.0935745i	$-0.970171\pi$
$499$	−31.5502	+	18.2155i	−1.41238	+	0.815438i	−0.416768	+	0.909013i	$0.636837\pi$
$500$		0			0
$501$	8.68766	−	15.0475i	0.388136	−	0.672271i
$502$	0.269618	+	0.175092i	0.0120336	+	0.00781474i
$503$	1.32059	−	0.209162i	0.0588824	−	0.00932605i	−0.126924	−	0.991912i	$-0.540510\pi$
$503$	1.32059	−	0.209162i	0.0588824	−	0.00932605i	0.185806	+	0.982586i	$0.440510\pi$
$504$	27.9384	−	1.61588i	1.24448	−	0.0719772i
$505$		0			0
$506$	0.203500	+	0.0906038i	0.00904666	+	0.00402783i
$507$	8.01470	−	2.14753i	0.355945	−	0.0953752i
$508$	17.9027	−	22.1079i	0.794302	−	0.980882i
$509$	12.8202	−	14.2382i	0.568244	−	0.631098i	−0.388703	−	0.921363i	$-0.627077\pi$
$509$	12.8202	−	14.2382i	0.568244	−	0.631098i	0.956946	+	0.290265i	$0.0937434\pi$
$510$		0			0
$511$	5.52935	−	6.90427i	0.244604	−	0.305427i
$512$	−31.1015	−	15.8470i	−1.37451	−	0.700346i
$513$	5.20640	−	0.272856i	0.229868	−	0.0120469i
$514$	14.9417	+	16.5944i	0.659048	+	0.731947i
$515$		0			0
$516$	30.0640	+	27.0697i	1.32349	+	1.19168i
$517$	0.0761016	+	0.0120533i	0.00334694	+	0.000530104i
$518$	−49.2258	+	22.2368i	−2.16286	+	0.977028i
$519$	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	$0.762953\pi$
$522$	0.119840	−	0.312195i	0.00524527	−	0.0136644i
$523$	−18.9558	+	29.1893i	−0.828877	+	1.27636i	0.129707	+	0.991552i	$0.458596\pi$
$523$	−18.9558	+	29.1893i	−0.828877	+	1.27636i	−0.958585	+	0.284807i	$0.908070\pi$
$524$	46.1889			2.01777
$525$		0			0
$526$	50.8274			2.21618
$527$	34.6864	−	53.4123i	1.51096	−	2.32668i
$528$	0.0473721	−	0.123408i	0.00206160	−	0.00537066i
$529$	2.84498	+	6.38993i	0.123695	+	0.277823i
$530$		0			0
$531$	3.36650	+	4.63359i	0.146094	+	0.201081i
$532$	−26.6429	−	19.1377i	−1.15512	−	0.829725i
$533$	18.5775	+	2.94239i	0.804683	+	0.127449i
$534$	34.7503	+	31.2893i	1.50379	+	1.35402i
$535$		0			0
$536$	0.984749	+	1.09367i	0.0425347	+	0.0472395i
$537$	31.2832	−	1.63948i	1.34997	−	0.0707489i
$538$	3.27475	+	1.66857i	0.141185	+	0.0719372i
$539$	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	$0.354711\pi$
$542$	−13.8951	+	17.1590i	−0.596846	+	0.737043i
$543$	12.7710	−	3.42198i	0.548057	−	0.146851i
$544$	5.85985	+	2.60897i	0.251239	+	0.111859i
$545$		0			0
$546$	−40.4689	−	20.3447i	−1.73191	−	0.870674i
$547$	−9.77211	+	1.54775i	−0.417825	+	0.0661770i	−0.361808	−	0.932253i	$-0.617840\pi$
$547$	−9.77211	+	1.54775i	−0.417825	+	0.0661770i	−0.0560177	+	0.998430i	$0.517840\pi$
$548$	−10.7866	−	7.00490i	−0.460781	−	0.299234i
$549$	15.2517	−	26.4167i	0.650927	−	1.12744i
$550$		0			0
$551$	−0.165574	+	0.0955944i	−0.00705370	+	0.00407246i
$552$	51.9131	−	26.4511i	2.20957	−	1.12583i
$553$	−9.42768	+	10.5852i	−0.400906	+	0.450127i
$554$	19.5157	−	26.8610i	0.829142	−	1.14122i
$555$		0			0
$556$	17.6554	−	1.85566i	0.748756	−	0.0786975i
$557$	4.19928	+	15.6719i	0.177929	+	0.664041i	0.996034	+	0.0889717i	$0.0283581\pi$
$557$	4.19928	+	15.6719i	0.177929	+	0.664041i	−0.818105	+	0.575069i	$0.804975\pi$
$558$	46.7559	−	17.9479i	1.97934	−	0.759796i
$559$	−4.26786	−	13.1351i	−0.180511	−	0.555557i
$560$		0			0
$561$	−0.0840009	+	0.258528i	−0.00354652	+	0.0109151i
$562$	−0.506879	−	9.67182i	−0.0213814	−	0.407981i
$563$	26.0064	−	16.8888i	1.09604	−	0.711776i	0.135739	−	0.990745i	$-0.456659\pi$
$563$	26.0064	−	16.8888i	1.09604	−	0.711776i	0.960300	+	0.278969i	$0.0899926\pi$
$564$	30.7058	−	27.6476i	1.29295	−	1.16418i
$565$		0			0
$566$	43.6698	−	14.1892i	1.83558	−	0.596416i
$567$	24.4374	+	13.9331i	1.02628	+	0.585137i
$568$	−25.7042	−	25.7042i	−1.07852	−	1.07852i
$569$	−5.42165	+	12.1772i	−0.227287	+	0.510496i	−0.990806	−	0.135290i	$-0.956803\pi$
$569$	−5.42165	+	12.1772i	−0.227287	+	0.510496i	0.763519	+	0.645786i	$0.223470\pi$
$570$		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	$0.310772\pi$
$572$	−0.155642	+	0.126037i	−0.00650774	+	0.00526986i
$573$	−15.4672	−	30.3562i	−0.646153	−	1.26815i
$574$	24.9979	+	30.5304i	1.04339	+	1.27431i
$575$		0			0
$576$	10.3739	+	17.9681i	0.432245	+	0.748670i
$577$	−1.81100	+	34.5559i	−0.0753928	+	1.43858i	0.655039	+	0.755595i	$0.272652\pi$
$577$	−1.81100	+	34.5559i	−0.0753928	+	1.43858i	−0.730432	+	0.682986i	$0.760681\pi$
$578$	74.6134	+	28.6414i	3.10351	+	1.19133i
$579$	−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
$583$	−0.0261045	−	0.0680047i	−0.00108114	−	0.00281647i
$584$	−15.1318	−	3.21636i	−0.626158	−	0.133094i
$585$		0			0
$586$	−3.53317	−	16.6222i	−0.145954	−	0.686659i
$587$	−9.11097	+	17.8813i	−0.376050	+	0.738039i	−0.999023	−	0.0442042i	$-0.985925\pi$
$587$	−9.11097	+	17.8813i	−0.376050	+	0.738039i	0.622973	+	0.782244i	$0.285925\pi$
$588$	−23.1517	−	58.4140i	−0.954760	−	2.40895i
$589$	−27.2320	−	8.84822i	−1.12208	−	0.364584i
$590$		0			0
$591$	7.43679	−	34.9873i	0.305908	−	1.43919i
$592$	22.4280	+	18.1619i	0.921786	+	0.746448i
$593$	−17.9557	−	4.81121i	−0.737352	−	0.197573i	−0.129451	−	0.991586i	$-0.541322\pi$
$593$	−17.9557	−	4.81121i	−0.737352	−	0.197573i	−0.607901	+	0.794013i	$0.707988\pi$
$594$	0.0540215	−	0.0392489i	0.00221653	−	0.00161040i
$595$		0			0
$596$	−57.4394	−	41.7321i	−2.35281	−	1.70942i
$597$	2.86179	+	3.53401i	0.117125	+	0.144638i
$598$	−40.7255	−	2.13433i	−1.66539	−	0.0872794i
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.279241	−	0.960221i	$-0.590083\pi$
$599$	−30.6038	−	17.6691i	−1.25044	−	0.721941i	−0.971196	+	0.238280i	$0.923416\pi$
$600$		0			0
$601$		−	0.819532i		−	0.0334294i	−0.999860	−	0.0167147i	$-0.994679\pi$
$601$		−	0.819532i		−	0.0334294i	0.999860	−	0.0167147i	$-0.00532070\pi$
$602$	11.6412	−	26.5322i	0.474460	−	1.08137i
$603$	−0.113736	−	0.718101i	−0.00463169	−	0.0292433i
$604$	−73.3858	−	7.71316i	−2.98603	−	0.313844i
$605$		0			0
$606$	6.19220	+	58.9149i	0.251541	+	2.39325i
$607$	−3.58282	+	13.3713i	−0.145422	+	0.542724i	0.854314	+	0.519757i	$0.173978\pi$
$607$	−3.58282	+	13.3713i	−0.145422	+	0.542724i	−0.999736	+	0.0229662i	$0.992689\pi$
$608$	0.451141	−	2.84839i	0.0182962	−	0.115518i
$609$	−0.365812	−	0.0171863i	−0.0148234	−	0.000696423i
$610$		0			0
$611$	−13.7977	+	2.93279i	−0.558196	+	0.118648i
$612$	34.3341	+	52.8700i	1.38788	+	2.13714i
$613$	20.8766	+	32.1471i	0.843197	+	1.29841i	0.952542	+	0.304406i	$0.0984580\pi$
$613$	20.8766	+	32.1471i	0.843197	+	1.29841i	−0.109345	+	0.994004i	$0.534875\pi$
$614$	16.0155	−	3.40421i	0.646334	−	0.137383i
$615$		0			0
$616$	−0.204697	−	0.00961692i	−0.00824748	−	0.000387477i
$617$	2.62812	−	16.5933i	0.105804	−	0.668022i	−0.876595	−	0.481229i	$-0.840191\pi$
$617$	2.62812	−	16.5933i	0.105804	−	0.668022i	0.982399	−	0.186793i	$-0.0598094\pi$
$618$	−0.316371	+	1.18071i	−0.0127263	+	0.0474952i
$619$	0.649827	+	6.18269i	0.0261187	+	0.248503i	0.999789	+	0.0205421i	$0.00653923\pi$
$619$	0.649827	+	6.18269i	0.0261187	+	0.248503i	−0.973670	+	0.227961i	$0.926794\pi$
$620$		0			0
$621$	8.94198	+	0.939840i	0.358829	+	0.0377145i
$622$	0.999300	+	6.30933i	0.0400683	+	0.252981i
$623$	8.89783	−	20.2796i	0.356484	−	0.812484i
$624$			24.2004i			0.968790i
$625$		0			0
$626$	−9.15199	−	5.28391i	−0.365787	−	0.211187i
$627$	0.122048	+	0.00639625i	0.00487411	+	0.000255442i
$628$	−39.9459	−	49.3291i	−1.59402	−	1.96845i
$629$	−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	$0.434022\pi$
$632$	23.9457	+	6.41622i	0.952508	+	0.255224i
$633$	16.3311	+	13.2246i	0.649102	+	0.525632i
$634$	10.4830	−	49.3185i	0.416332	−	1.95869i
$635$		0			0
$636$	−37.1507	−	12.0710i	−1.47312	−	0.478646i
$637$	−3.12616	+	21.2223i	−0.123863	+	0.840860i
$638$	−0.00111169	+	0.00218182i	−4.40123e−5	+	8.63790e-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	$0.625465\pi$
$642$	9.80055	+	25.5313i	0.386797	+	1.00764i
$643$	−10.6811	+	10.6811i	−0.421223	+	0.421223i	−0.885625	−	0.464402i	$-0.846269\pi$
$643$	−10.6811	+	10.6811i	−0.421223	+	0.421223i	0.464402	+	0.885625i	$0.346269\pi$
$644$	−40.2193	−	39.7862i	−1.58486	−	1.56780i
$645$		0			0
$646$	5.69727	−	54.2059i	0.224156	−	2.13270i
$647$	−14.1458	−	5.43005i	−0.556127	−	0.213477i	0.0640393	−	0.997947i	$-0.479602\pi$
$647$	−14.1458	−	5.43005i	−0.556127	−	0.213477i	−0.620167	+	0.784470i	$0.712935\pi$
$648$	2.57478	−	49.1298i	0.101147	−	1.93000i
$649$	−0.0209698	−	0.0363207i	−0.000823135	−	0.00142571i
$650$		0			0
$651$	−34.7461	−	42.4361i	−1.36181	−	1.66320i
$652$	−16.6030	−	32.5852i	−0.650223	−	1.27614i
$653$	−28.0257	+	22.6948i	−1.09673	+	0.888116i	−0.994299	−	0.106624i	$-0.965996\pi$
$653$	−28.0257	+	22.6948i	−1.09673	+	0.888116i	−0.102432	+	0.994740i	$0.532663\pi$
$654$	−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
$658$	−25.7074	−	14.6572i	−1.00218	−	0.571397i
$659$	−30.6779	+	9.96786i	−1.19504	+	0.388293i	−0.837935	−	0.545771i	$-0.816237\pi$
$659$	−30.6779	+	9.96786i	−1.19504	+	0.388293i	−0.357107	+	0.934063i	$0.616237\pi$
$660$		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	$0.381953\pi$
$662$	−32.3852	+	21.0312i	−1.25869	+	0.817400i
$663$	−2.60454	−	49.6975i	−0.101152	−	1.93009i
$664$	−12.4994	+	38.4692i	−0.485071	+	1.49290i
$665$		0			0
$666$	−14.4216	−	44.3852i	−0.558827	−	1.71989i
$667$	−0.307822	+	0.118162i	−0.0119189	+	0.00457525i
$668$	7.63675	+	28.5007i	0.295475	+	1.10273i
$669$	−17.0070	+	1.78751i	−0.657530	+	0.0691092i
$670$		0			0
$671$	−0.131290	+	0.180705i	−0.00506839	+	0.00697604i
$672$	3.67400	−	4.12508i	0.141728	−	0.159128i
$673$	−17.1076	+	8.71675i	−0.659449	+	0.336006i	−0.751485	−	0.659750i	$-0.770662\pi$
$673$	−17.1076	+	8.71675i	−0.659449	+	0.336006i	0.0920367	+	0.995756i	$0.470662\pi$
$674$	53.8205	−	31.0733i	2.07309	−	1.19690i
$675$		0			0
$676$	−7.04519	+	12.2026i	−0.270969	+	0.469332i
$677$	29.7649	+	19.3296i	1.14396	+	0.742895i	0.970299	−	0.241911i	$-0.0777741\pi$
$677$	29.7649	+	19.3296i	1.14396	+	0.742895i	0.173660	+	0.984806i	$0.444441\pi$
$678$	22.0924	−	3.49909i	0.848453	−	0.134382i
$679$	16.2653	+	8.17698i	0.624204	+	0.313804i
$680$		0			0
$681$	24.6108	+	10.9574i	0.943088	+	0.419890i
$682$	−0.354236	+	0.0949172i	−0.0135644	+	0.00363457i
$683$	−6.00704	+	7.41808i	−0.229853	+	0.283845i	−0.879004	−	0.476815i	$-0.841791\pi$
$683$	−6.00704	+	7.41808i	−0.229853	+	0.283845i	0.649151	+	0.760660i	$0.275124\pi$
$684$	18.9650	−	21.0627i	0.725143	−	0.805353i
$685$		0			0
$686$	−34.5085	+	28.8848i	−1.31754	+	1.10283i
$687$	−55.1888	−	28.1201i	−2.10558	−	1.07285i
$688$	−15.4589	+	0.810168i	−0.589366	+	0.0308874i
$689$	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	$-0.674748\pi$
$692$	−90.2473	−	14.2938i	−3.43069	−	0.543367i
$693$	0.0822238	+	0.0590617i	0.00312342	+	0.00224357i
$694$	21.6421	+	29.7878i	0.821524	+	1.13073i
$695$		0			0
$696$	0.260504	+	0.585101i	0.00987437	+	0.0221782i
$697$	−15.5365	+	40.4740i	−0.588487	+	1.53306i
$698$	−1.97091	+	3.03494i	−0.0746002	+	0.114874i
$699$	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	$0.215381\pi$
$702$	−6.65804	+	10.2525i	−0.251291	+	0.386955i
$703$	−9.56202	+	24.9099i	−0.360638	+	0.939495i
$704$	−0.0617943	−	0.138792i	−0.00232896	−	0.00523093i
$705$		0			0
$706$	−13.4251	−	18.4781i	−0.505261	−	0.695431i
$707$	25.5677	−	11.5497i	0.961571	−	0.434371i
$708$	−22.2135	−	3.51827i	−0.834834	−	0.132225i
$709$	−1.43178	−	1.28918i	−0.0537715	−	0.0484161i	0.641807	−	0.766866i	$-0.278185\pi$
$709$	−1.43178	−	1.28918i	−0.0537715	−	0.0484161i	−0.695578	+	0.718450i	$0.744852\pi$
$710$		0			0
$711$	−8.19493	−	9.10139i	−0.307334	−	0.341329i
$712$	−38.6775	+	2.02700i	−1.44950	+	0.0759651i
$713$	−43.9987	−	22.4185i	−1.64777	−	0.839578i
$714$	65.2617	−	81.4895i	2.44236	−	3.04967i
$715$		0			0
$716$	−35.5957	+	39.5330i	−1.33027	+	1.47742i
$717$	−6.17437	+	7.62472i	−0.230586	+	0.284750i
$718$	−14.4190	+	3.86356i	−0.538112	+	0.144187i
$719$	−44.2991	−	19.7232i	−1.65208	−	0.735552i	−0.652327	−	0.757938i	$-0.726207\pi$
$719$	−44.2991	−	19.7232i	−1.65208	−	0.735552i	−0.999749	+	0.0223865i	$0.992874\pi$
$720$		0			0
$721$	0.577936	−	0.0334263i	0.0215235	−	0.00124486i
$722$	21.3958	−	3.38876i	0.796270	−	0.126117i
$723$	0.316647	+	0.205633i	0.0117762	+	0.00764756i
$724$	−11.2262	+	19.4443i	−0.417217	+	0.722641i
$725$		0			0
$726$	−53.2178	+	30.7253i	−1.97510	+	1.14032i
$727$	6.51342	−	3.31875i	0.241569	−	0.123086i	−0.329015	−	0.944325i	$-0.606717\pi$
$727$	6.51342	−	3.31875i	0.241569	−	0.123086i	0.570584	+	0.821239i	$0.306717\pi$
$728$	35.6168	−	11.7861i	1.32005	−	0.436823i
$729$	−7.63022	+	10.5021i	−0.282601	+	0.388967i
$730$		0			0
$731$	31.6591	−	3.32750i	1.17095	−	0.123072i
$732$	31.0015	+	115.699i	1.14585	+	4.27636i
$733$	9.62129	−	3.69327i	0.355371	−	0.136414i	−0.174132	−	0.984722i	$-0.555712\pi$
$733$	9.62129	−	3.69327i	0.355371	−	0.136414i	0.529503	+	0.848308i	$0.322379\pi$
$734$	−27.0939	−	83.3864i	−1.00005	−	3.07785i
$735$		0			0
$736$	1.53691	−	4.73012i	0.0566512	−	0.174354i
$737$	0.000278631		0.00531660i	1.02635e−5		0.000195839i
$738$	−28.5924	+	18.5681i	−1.05250	+	0.683502i
$739$	−16.3525	+	14.7239i	−0.601537	+	0.541626i	−0.912648	−	0.408747i	$-0.865966\pi$
$739$	−16.3525	+	14.7239i	−0.601537	+	0.541626i	0.311111	+	0.950374i	$0.399299\pi$
$740$		0			0
$741$	−21.2794	+	6.91411i	−0.781720	+	0.253996i
$742$	0.151440	+	27.9760i	0.00555953	+	1.02703i
$743$	32.3075	+	32.3075i	1.18525	+	1.18525i	0.978366	+	0.206883i	$0.0663319\pi$
$743$	32.3075	+	32.3075i	1.18525	+	1.18525i	0.206883	+	0.978366i	$0.433668\pi$
$744$	−39.0144	+	87.6278i	−1.43034	+	3.21259i
$745$		0			0
$746$	41.2660	−	18.3728i	1.51086	−	0.672676i
$747$	15.5296	−	12.5756i	0.568199	−	0.460119i
$748$	−0.209569	−	0.411303i	−0.00766262	−	0.0150387i
$749$	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	$0.965300\pi$
$752$	−0.827466	+	15.7890i	−0.0301746	+	0.575765i
$753$	0.283980	+	0.109010i	0.0103488	+	0.00397253i
$754$	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	−0.748792	−	0.662805i	$-0.769366\pi$
$757$	−2.36580	+	2.36580i	−0.0859865	+	0.0859865i	0.662805	+	0.748792i	$0.269366\pi$
$758$	19.3833	+	50.4951i	0.704032	+	1.83406i
$759$	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	$-0.303999\pi$
$762$	18.4798	−	36.2686i	0.669451	−	1.31387i
$763$	13.7431	+	15.0981i	0.497535	+	0.546589i
$764$	55.0239	+	17.8784i	1.99070	+	0.646816i
$765$		0			0
$766$	−7.77758	+	36.5906i	−0.281015	+	1.32207i
$767$	5.96698	+	4.83197i	0.215455	+	0.174472i
$768$	−68.8951	−	18.4604i	−2.48604	−	0.666132i
$769$	31.5396	−	22.9148i	1.13735	−	0.826330i	0.150599	−	0.988595i	$-0.451880\pi$
$769$	31.5396	−	22.9148i	1.13735	−	0.826330i	0.986747	+	0.162264i	$0.0518798\pi$
$770$		0			0
$771$	17.0932	+	12.4189i	0.615596	+	0.447257i
$772$	−40.8841	−	50.4876i	−1.47145	−	1.81709i
$773$	23.2158	+	1.21669i	0.835014	+	0.0437612i	0.465049	−	0.885285i	$-0.346037\pi$
$773$	23.2158	+	1.21669i	0.835014	+	0.0437612i	0.369964	+	0.929046i	$0.379370\pi$
$774$	21.6795	+	12.5167i	0.779254	+	0.449902i
$775$		0			0
$776$		−	31.8387i		−	1.14294i
$777$	−41.1845	+	30.2643i	−1.47749	+	1.08573i
$778$	−4.53136	−	28.6099i	−0.162457	−	1.02571i
$779$	19.3848	+	2.03743i	0.694534	+	0.0729984i
$780$		0			0
$781$	−0.0137457	−	0.130782i	−0.000491861	−	0.00467975i
$782$	24.3284	−	90.7949i	0.869983	−	3.24682i
$783$	−0.0154617	+	0.0976210i	−0.000552554	+	0.00348869i
$784$	22.0696	+	9.54110i	0.788201	+	0.340754i
$785$		0			0
$786$	64.6466	−	13.7411i	2.30587	−	0.490127i
$787$	−8.99124	−	13.8453i	−0.320503	−	0.493531i	0.641294	−	0.767295i	$-0.278398\pi$
$787$	−8.99124	−	13.8453i	−0.320503	−	0.493531i	−0.961797	+	0.273764i	$0.911731\pi$
$788$	33.0822	+	50.9422i	1.17851	+	1.81474i
$789$	47.0414	−	9.99896i	1.67472	−	0.355972i
$790$		0			0
$791$	−4.86024	−	9.41245i	−0.172810	−	0.334668i
$792$	0.0276973	−	0.174874i	0.000984182	−	0.00621388i
$793$	10.5837	−	39.4989i	0.375838	−	1.40265i
$794$	−1.72174	−	16.3812i	−0.0611022	−	0.581349i
$795$		0			0
$796$	−7.67997	−	0.807198i	−0.272209	−	0.0286104i
$797$	−6.82142	−	43.0687i	−0.241627	−	1.52557i	−0.748257	−	0.663409i	$-0.769109\pi$
$797$	−6.82142	−	43.0687i	−0.241627	−	1.52557i	0.506630	−	0.862164i	$-0.330891\pi$
$798$	−42.9832	−	18.8592i	−1.52159	−	0.667609i
$799$		−	32.5131i		−	1.15023i
$800$		0			0
$801$	16.5705	+	9.56698i	0.585490	+	0.338033i
$802$	44.3695	+	2.32531i	1.56674	+	0.0821095i
$803$	−0.0352186	−	0.0434914i	−0.00124284	−	0.00153478i
$804$	2.30973	+	1.67811i	0.0814578	+	0.0591825i
$805$		0			0
$806$	54.3169	−	39.4635i	1.91323	−	1.39004i
$807$	3.35907	+	0.900061i	0.118245	+	0.0316836i
$808$	−38.1313	−	30.8782i	−1.34146	−	1.08629i
$809$	−3.06134	+	14.4025i	−0.107631	+	0.506364i	0.890997	+	0.454008i	$0.150006\pi$
$809$	−3.06134	+	14.4025i	−0.107631	+	0.506364i	−0.998628	+	0.0523559i	$0.983327\pi$
$810$		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	$0.449782\pi$
$812$	0.459897	−	0.418623i	0.0161392	−	0.0146908i
$813$	−9.48450	+	18.6144i	−0.332636	+	0.652835i
$814$	0.0710517	+	0.334272i	0.00249036	+	0.0117162i
$815$		0			0
$816$	−54.5610	−	11.5973i	−1.91002	−	0.405986i
$817$	−5.12904	−	13.3616i	−0.179442	−	0.467464i
$818$	−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	$0.706690\pi$
$822$	−17.1810	−	6.59517i	−0.599256	−	0.230033i
$823$	−2.77167	+	52.8866i	−0.0966142	+	1.84351i	0.335918	+	0.941891i	$0.390953\pi$
$823$	−2.77167	+	52.8866i	−0.0966142	+	1.84351i	−0.432533	+	0.901618i	$0.642380\pi$
$824$	−0.506220	−	0.876799i	−0.0176350	−	0.0305447i
$825$		0			0
$826$	2.60585	+	15.8953i	0.0906690	+	0.553068i
$827$	2.43786	+	4.78458i	0.0847728	+	0.166376i	0.929501	−	0.368819i	$-0.120238\pi$
$827$	2.43786	+	4.78458i	0.0847728	+	0.166376i	−0.844728	+	0.535196i	$0.820238\pi$
$828$	37.9865	−	30.7609i	1.32012	−	1.06901i
$829$	32.0214	−	14.2568i	1.11215	−	0.495161i	0.233369	−	0.972388i	$-0.425025\pi$
$829$	32.0214	−	14.2568i	1.11215	−	0.495161i	0.878780	+	0.477228i	$0.158358\pi$
$830$		0			0
$831$	12.7778	−	28.6994i	0.443257	−	0.995571i
$832$	19.6675	+	19.6675i	0.681847	+	0.681847i
$833$	−46.3488	−	17.2183i	−1.60589	−	0.596577i
$834$	24.1587	−	7.84964i	0.836548	−	0.271811i
$835$		0			0
$836$	−0.154233	+	0.138872i	−0.00533427	+	0.00480300i
$837$	−12.4144	+	8.06201i	−0.429105	+	0.278664i
$838$	−4.52017	−	86.2499i	−0.156147	−	2.97945i
$839$	4.17081	−	12.8364i	0.143992	−	0.443163i	−0.852888	−	0.522095i	$-0.825151\pi$
$839$	4.17081	−	12.8364i	0.143992	−	0.443163i	0.996880	+	0.0789314i	$0.0251508\pi$
$840$		0			0
$841$	8.96037	+	27.5772i	0.308978	+	0.950938i
$842$	31.8755	−	12.2359i	1.09850	−	0.421675i
$843$	−2.37180	−	8.85167i	−0.0816891	−	0.304868i
$844$	−35.4900	+	3.73015i	−1.22162	+	0.128397i
$845$		0			0
$846$	15.0284	−	20.6848i	0.516686	−	0.711158i
$847$	21.7325	+	19.3560i	0.746737	+	0.665081i
$848$	13.3182	−	6.78594i	0.457347	−	0.233030i
$849$	37.6256	−	21.7232i	1.29131	−	0.745537i
$850$		0			0
$851$	−23.0079	+	39.8508i	−0.788699	+	1.36607i
$852$	−59.1423	−	38.4075i	−2.02618	−	1.31582i
$853$	33.7053	−	5.33840i	1.15405	−	0.182783i	0.450063	−	0.892997i	$-0.351402\pi$
$853$	33.7053	−	5.33840i	1.15405	−	0.182783i	0.703986	+	0.710214i	$0.251402\pi$
$854$	71.6923	−	47.1112i	2.45326	−	1.61211i
$855$		0			0
$856$	−20.6929	−	9.21306i	−0.707268	−	0.314896i
$857$	−6.63141	+	1.77688i	−0.226525	+	0.0606971i	−0.370296	−	0.928914i	$-0.620744\pi$
$857$	−6.63141	+	1.77688i	−0.226525	+	0.0606971i	0.143771	+	0.989611i	$0.454077\pi$
$858$	−0.180344	+	0.222706i	−0.00615683	+	0.00760305i
$859$	−29.6526	+	32.9326i	−1.01174	+	1.12365i	−0.0194321	+	0.999811i	$0.506186\pi$
$859$	−29.6526	+	32.9326i	−1.01174	+	1.12365i	−0.992303	+	0.123834i	$0.960481\pi$
$860$		0			0
$861$	29.1419	+	23.3386i	0.993152	+	0.795376i
$862$	8.23950	+	4.19824i	0.280639	+	0.142993i
$863$	2.01642	−	0.105676i	0.0686398	−	0.00359726i	−0.0179852	−	0.999838i	$-0.505725\pi$
$863$	2.01642	−	0.105676i	0.0686398	−	0.00359726i	0.0866249	+	0.996241i	$0.472392\pi$
$864$	−0.997589	−	1.10794i	−0.0339387	−	0.0376927i
$865$		0			0
$866$	2.24014	+	2.01703i	0.0761230	+	0.0685415i
$867$	74.6900	+	11.8297i	2.53661	+	0.401759i
$868$	92.6791	+	9.23402i	3.14573	+	0.313423i
$869$	0.0527129	+	0.0725531i	0.00178816	+	0.00246119i
$870$		0			0
$871$	−0.396434	−	0.890406i	−0.0134327	−	0.0301703i
$872$	12.7959	−	33.3345i	0.433324	−	1.12885i
$873$	−8.56673	+	13.1916i	−0.289940	+	0.446468i
$874$	−42.2612			−1.42950
$875$		0			0
$876$	−30.0106			−1.01396
$877$	25.5614	−	39.3610i	0.863146	−	1.32913i	−0.0800162	−	0.996794i	$-0.525497\pi$
$877$	25.5614	−	39.3610i	0.863146	−	1.32913i	0.943162	−	0.332334i	$-0.107836\pi$
$878$	−4.74256	+	12.3548i	−0.160054	+	0.416954i
$879$	−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	$0.921469\pi$
$882$	−21.5283	−	32.3778i	−0.724896	−	1.09022i
$883$	−15.6869	−	2.48456i	−0.527906	−	0.0836122i	−0.113208	−	0.993571i	$-0.536113\pi$
$883$	−15.6869	−	2.48456i	−0.527906	−	0.0836122i	−0.414698	+	0.909959i	$0.636113\pi$
$884$	62.8034	+	56.5485i	2.11231	+	1.90193i
$885$		0			0
$886$	29.7457	+	33.0360i	0.999327	+	1.10986i
$887$	−17.5270	+	0.918554i	−0.588501	+	0.0308420i	−0.344263	−	0.938873i	$-0.611871\pi$
$887$	−17.5270	+	0.918554i	−0.588501	+	0.0308420i	−0.244238	+	0.969715i	$0.578538\pi$
$888$	79.6415	+	40.5794i	2.67259	+	1.36175i
$889$	−19.0564	−	2.91258i	−0.639130	−	0.0976848i
$890$		0			0
$891$	0.119088	−	0.132260i	0.00398958	−	0.00443088i
$892$	18.2753	−	22.5682i	0.611904	−	0.755638i
$893$	−14.1197	+	3.78336i	−0.472498	+	0.126605i
$894$	−92.8081	−	41.3208i	−3.10397	−	1.38198i
$895$		0			0
$896$	3.09170	+	53.4551i	0.103287	+	1.78581i
$897$	−38.1118	+	6.03632i	−1.27252	+	0.201547i
$898$	14.8545	+	9.64664i	0.495702	+	0.321912i
$899$	0.271415	−	0.470104i	0.00905219	−	0.0156789i
$900$		0			0
$901$	−26.6196	+	15.3689i	−0.886829	+	0.512011i
$902$	0.222435	−	0.113336i	0.00740629	−	0.00377369i
$903$	5.55457	−	26.8459i	0.184844	−	0.893377i
$904$	−10.8896	+	14.9882i	−0.362182	+	0.498500i
$905$		0			0
$906$	−105.006	+	11.0366i	−3.48860	+	0.366667i
$907$	−7.69450	−	28.7163i	−0.255492	−	0.953508i	−0.967816	−	0.251658i	$-0.919024\pi$
$907$	−7.69450	−	28.7163i	−0.255492	−	0.953508i	0.712325	−	0.701850i	$-0.247642\pi$
$908$	−42.7097	+	16.3947i	−1.41737	+	0.544078i
$909$	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	$-0.126847\pi$
$912$	1.31251	+	25.0441i	0.0434614	+	0.829293i
$913$	−0.122719	+	0.0796949i	−0.00406142	+	0.00263752i
$914$	−21.3387	+	19.2135i	−0.705822	+	0.635525i
$915$		0			0
$916$	100.036	−	32.5036i	3.30528	−	1.07395i
$917$	−15.7966	−	27.0216i	−0.521648	−	0.892331i
$918$	−19.9241	−	19.9241i	−0.657593	−	0.657593i
$919$	−6.01760	+	13.5158i	−0.198502	+	0.445844i	−0.985181	−	0.171519i	$-0.945132\pi$
$919$	−6.01760	+	13.5158i	−0.198502	+	0.445844i	0.786678	+	0.617363i	$0.211799\pi$
$920$		0			0
$921$	14.1529	−	6.30127i	0.466353	−	0.207634i
$922$	1.60736	−	1.30162i	0.0529356	−	0.0428664i
$923$	10.9297	+	21.4508i	0.359756	+	0.706061i
$924$	−0.392301	+	0.0643132i	−0.0129058	+	0.00211575i
$925$		0			0
$926$	46.9570	+	81.3318i	1.54310	+	2.67273i
$927$	−0.0261771	+	0.499488i	−0.000859767	+	0.0164053i
$928$	0.0510413	+	0.0195929i	0.00167551	+	0.000643169i
$929$	−1.81026	+	17.2234i	−0.0593925	+	0.565082i	0.923847	+	0.382763i	$0.125027\pi$
$929$	−1.81026	+	17.2234i	−0.0593925	+	0.565082i	−0.983239	+	0.182320i	$0.941639\pi$
$930$		0			0
$931$	−2.08416	+	22.1318i	−0.0683056	+	0.725341i
$932$	−60.3124	+	60.3124i	−1.97560	+	1.97560i
$933$	2.16606	+	5.64278i	0.0709136	+	0.184736i
$934$	21.2562	+	4.51814i	0.695523	+	0.147838i
$935$		0			0
$936$	6.73928	+	31.7058i	0.220280	+	1.03634i
$937$	−15.2256	+	29.8820i	−0.497400	+	0.976202i	0.496719	+	0.867911i	$0.334538\pi$
$937$	−15.2256	+	29.8820i	−0.497400	+	0.976202i	−0.994119	+	0.108291i	$0.965462\pi$
$938$	0.621317	−	1.94804i	0.0202867	−	0.0636056i
$939$	−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	$-0.184814\pi$
$942$	−70.5841	−	57.1579i	−2.29975	−	1.86230i
$943$	32.4696	+	8.70021i	1.05736	+	0.283318i
$944$	6.96237	−	5.05846i	0.226606	−	0.164639i
$945$		0			0
$946$	−0.148300	−	0.107746i	−0.00482164	−	0.00350312i
$947$	−3.46839	−	4.28310i	−0.112707	−	0.139182i	0.717670	−	0.696383i	$-0.245209\pi$
$947$	−3.46839	−	4.28310i	−0.112707	−	0.139182i	−0.830378	+	0.557201i	$0.811875\pi$
$948$	48.0259	+	2.51693i	1.55981	+	0.0817462i
$949$	8.87279	+	5.12271i	0.288023	+	0.166290i
$950$		0			0
$951$		−	47.7071i		−	1.54701i
$952$	9.50416	+	85.9480i	0.308032	+	2.78559i
$953$	1.05931	+	6.68823i	0.0343145	+	0.216653i	0.998887	−	0.0471642i	$-0.0150184\pi$
$953$	1.05931	+	6.68823i	0.0343145	+	0.216653i	−0.964573	+	0.263817i	$0.915018\pi$
$954$	−24.0393	−	2.52663i	−0.778300	−	0.0818026i
$955$		0			0
$956$	−1.74155	−	16.5697i	−0.0563257	−	0.535903i
$957$	−0.000599669		0.00223799i	−1.93845e−5		7.23441e-5i
$958$	0.368413	−	2.32607i	0.0119029	−	0.0751518i
$959$	−0.409023	+	8.70608i	−0.0132080	+	0.281134i
$960$		0			0
$961$	49.1979	−	10.4573i	1.58703	−	0.337333i
$962$	−34.0748	−	52.4706i	−1.09862	−	1.69172i
$963$	6.09467	+	9.38497i	0.196398	+	0.302426i
$964$	−0.627144	+	0.133304i	−0.0201989	+	0.00429342i
$965$		0			0
$966$	−68.1278	−	43.7202i	−2.19198	−	1.40668i
$967$	9.03458	−	57.0421i	0.290533	−	1.83435i	−0.221228	−	0.975222i	$-0.571006\pi$
$967$	9.03458	−	57.0421i	0.290533	−	1.83435i	0.511760	−	0.859128i	$-0.328994\pi$
$968$	13.1732	−	49.1630i	0.423403	−	1.58016i
$969$	−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	$0.635335\pi$
$972$	−11.9220	−	75.2723i	−0.382397	−	2.41436i
$973$	−7.12374	−	9.69420i	−0.228377	−	0.310782i
$974$			84.2473i			2.69946i
$975$		0			0
$976$	−39.6935	−	22.9170i	−1.27056	−	0.733556i
$977$	−24.5758	−	1.28796i	−0.786249	−	0.0412056i	−0.345014	−	0.938597i	$-0.612126\pi$
$977$	−24.5758	−	1.28796i	−0.786249	−	0.0412056i	−0.441235	+	0.897392i	$0.645459\pi$
$978$	−32.9318	−	40.6674i	−1.05304	−	1.30040i
$979$	−0.113351	−	0.0823545i	−0.00362272	−	0.00263206i
$980$		0			0
$981$	−14.2709	+	10.3684i	−0.455634	+	0.331038i
$982$	−12.0140	−	3.21913i	−0.383381	−	0.102727i
$983$	34.9053	+	28.2657i	1.11331	+	0.901537i	0.995802	−	0.0915351i	$-0.0291774\pi$
$983$	34.9053	+	28.2657i	1.11331	+	0.901537i	0.117504	+	0.993072i	$0.462511\pi$
$984$	13.5758	−	63.8690i	0.432780	−	2.03607i
$985$		0			0
$986$	0.982717	+	0.319304i	0.0312961	+	0.0101687i
$987$	−26.6759	−	8.50816i	−0.849103	−	0.270818i
$988$	17.2496	−	33.8543i	0.548784	−	1.07705i
$989$	−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	$0.303454\pi$
$992$	2.93434	+	7.64421i	0.0931653	+	0.242704i
$993$	−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
$997$	23.1061	+	8.86960i	0.731778	+	0.280903i	0.695587	−	0.718442i	$-0.255144\pi$
$997$	23.1061	+	8.86960i	0.731778	+	0.280903i	0.0361906	+	0.999345i	$0.488478\pi$
$998$	4.63292	−	88.4014i	0.146653	−	2.79830i
$999$	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.a.493.1		288
5.2	odd	4		875.2.bb.c.507.1		288
5.3	odd	4		175.2.x.a.122.18	yes	288
5.4	even	2		875.2.bb.b.493.18		288
7.5	odd	6	inner	875.2.bb.a.243.18		288
25.6	even	5		875.2.bb.c.143.1		288
25.8	odd	20		875.2.bb.b.857.1		288
25.17	odd	20	inner	875.2.bb.a.857.18		288
25.19	even	10		175.2.x.a.108.18	yes	288
35.12	even	12		875.2.bb.c.257.1		288
35.19	odd	6		875.2.bb.b.243.1		288
35.33	even	12		175.2.x.a.47.18	yes	288
175.19	odd	30		175.2.x.a.33.18	✓	288
175.33	even	60		875.2.bb.b.607.18		288
175.117	even	60	inner	875.2.bb.a.607.1		288
175.131	odd	30		875.2.bb.c.768.1		288

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.32340 + 2.03786i) q^{2} +(-0.823930 + 2.14641i) q^{3} +(-1.58801 - 3.56673i) q^{4} +(-3.28370 - 4.51962i) q^{6} +(-1.54352 + 2.14884i) q^{7} +(4.57018 + 0.723845i) q^{8} +(-1.69878 - 1.52959i) q^{9} +(0.0112005 + 0.0124395i) q^{11} +(8.96408 - 0.469788i) q^{12} +(-2.73047 - 1.39124i) q^{13} +(-2.33634 - 5.98928i) q^{14} +(-2.29834 + 2.55257i) q^{16} +(4.44513 - 5.48928i) q^{17} +(5.36527 - 1.43762i) q^{18} +(-2.90112 - 1.29166i) q^{19} +(-3.34055 - 5.08353i) q^{21} +(-0.0401727 + 0.00636273i) q^{22} +(-4.59318 - 2.98285i) q^{23} +(-5.31918 + 9.21308i) q^{24} +(6.44868 - 3.72315i) q^{26} +(-1.46278 + 0.745322i) q^{27} +(10.1155 + 2.09295i) q^{28} +(0.0353871 - 0.0487062i) q^{29} +(8.96709 - 0.942479i) q^{31} +(0.235039 + 0.877177i) q^{32} +(-0.0359286 + 0.0137917i) q^{33} +(5.30369 + 16.3231i) q^{34} +(-2.75796 + 8.48811i) q^{36} +(-0.439728 - 8.39052i) q^{37} +(6.47159 - 4.20270i) q^{38} +(5.23590 - 4.71442i) q^{39} +(-5.83738 + 1.89668i) q^{41} +(14.7804 - 0.0800095i) q^{42} +(3.18681 + 3.18681i) q^{43} +(0.0265816 - 0.0597034i) q^{44} +(12.1573 - 5.41276i) q^{46} +(3.57724 - 2.89679i) q^{47} +(-3.58519 - 7.03633i) q^{48} +(-2.23507 - 6.63359i) q^{49} +(8.11977 + 14.0639i) q^{51} +(-0.626178 + 11.9482i) q^{52} +(-4.06266 - 1.55951i) q^{53} +(0.416980 - 3.96730i) q^{54} +(-8.60961 + 8.70333i) q^{56} +(5.16276 - 5.16276i) q^{57} +(0.0524250 + 0.136572i) q^{58} +(-2.45075 - 0.520924i) q^{59} +(2.77436 + 13.0523i) q^{61} +(-9.94643 + 19.5210i) q^{62} +(5.90896 - 1.28946i) q^{63} +(-8.63203 - 2.80472i) q^{64} +(0.0194425 - 0.0914696i) q^{66} +(0.247175 + 0.200158i) q^{67} +(-26.6377 - 7.13755i) q^{68} +(10.1869 - 7.40119i) q^{69} +(-6.35569 - 4.61768i) q^{71} +(-6.65655 - 8.22016i) q^{72} +(-3.33870 - 0.174974i) q^{73} +(17.6807 + 10.2079i) q^{74} +12.3987i q^{76} +(-0.0440188 + 0.00486761i) q^{77} +(2.67814 + 16.9091i) q^{78} +(5.32825 + 0.560021i) q^{79} +(-1.11138 - 10.5741i) q^{81} +(3.86003 - 14.4058i) q^{82} +(-1.36750 + 8.63403i) q^{83} +(-12.8268 + 19.9876i) q^{84} +(-10.7117 + 2.27684i) q^{86} +(0.0753869 + 0.116086i) q^{87} +(0.0421842 + 0.0649580i) q^{88} +(-8.18738 + 1.74028i) q^{89} +(7.20412 - 3.71994i) q^{91} +(-3.34499 + 21.1194i) q^{92} +(-5.36531 + 20.0236i) q^{93} +(1.16913 + 11.1236i) q^{94} +(-2.07644 - 0.218242i) q^{96} +(-1.07640 - 6.79613i) q^{97} +(16.4762 + 4.22415i) q^{98} -0.0382642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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