LMFDB - Embedded newform 630.2.bw.a.103.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(103,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.18
Character	$\chi$	$=$	630.103
Dual form			630.2.bw.a.367.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.20754 + 1.24171i) q^{3} -1.00000i q^{4} +(2.21622 - 0.297244i) q^{5} +(-1.73188 - 0.0241584i) q^{6} +(-0.456895 + 2.60600i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0836789 + 2.99883i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.20754 + 1.24171i) q^{3} -1.00000i q^{4} +(2.21622 - 0.297244i) q^{5} +(-1.73188 - 0.0241584i) q^{6} +(-0.456895 + 2.60600i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0836789 + 2.99883i) q^{9} +(-1.35692 + 1.77729i) q^{10} +(0.952963 - 1.65058i) q^{11} +(1.24171 - 1.20754i) q^{12} +(-0.0332580 - 0.124120i) q^{13} +(-1.51965 - 2.16580i) q^{14} +(3.04528 + 2.39297i) q^{15} -1.00000 q^{16} +(-1.04234 + 3.89008i) q^{17} +(-2.06133 - 2.17966i) q^{18} +(1.12059 - 1.94092i) q^{19} +(-0.297244 - 2.21622i) q^{20} +(-3.78762 + 2.57953i) q^{21} +(0.493290 + 1.84098i) q^{22} +(-0.891242 + 3.32616i) q^{23} +(-0.0241584 + 1.73188i) q^{24} +(4.82329 - 1.31752i) q^{25} +(0.111283 + 0.0642495i) q^{26} +(-3.82472 + 3.51732i) q^{27} +(2.60600 + 0.456895i) q^{28} +(-0.734875 + 0.424280i) q^{29} +(-3.84542 + 0.461252i) q^{30} -5.46370i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.20028 - 0.809845i) q^{33} +(-2.01365 - 3.48775i) q^{34} +(-0.237963 + 5.91129i) q^{35} +(2.99883 + 0.0836789i) q^{36} +(-0.426494 - 1.59170i) q^{37} +(0.580061 + 2.16482i) q^{38} +(0.113961 - 0.191177i) q^{39} +(1.77729 + 1.35692i) q^{40} +(9.63896 + 5.56506i) q^{41} +(0.854246 - 4.50225i) q^{42} +(1.51359 - 5.64881i) q^{43} +(-1.65058 - 0.952963i) q^{44} +(0.705935 + 6.67096i) q^{45} +(-1.72175 - 2.98215i) q^{46} +(4.32073 + 4.32073i) q^{47} +(-1.20754 - 1.24171i) q^{48} +(-6.58249 - 2.38134i) q^{49} +(-2.47896 + 4.34221i) q^{50} +(-6.08901 + 3.40315i) q^{51} +(-0.124120 + 0.0332580i) q^{52} +(-0.0925928 + 0.345561i) q^{53} +(0.217369 - 5.19160i) q^{54} +(1.62135 - 3.94132i) q^{55} +(-2.16580 + 1.51965i) q^{56} +(3.76322 - 0.952299i) q^{57} +(0.219624 - 0.819646i) q^{58} -12.7246 q^{59} +(2.39297 - 3.04528i) q^{60} -5.80201i q^{61} +(3.86342 + 3.86342i) q^{62} +(-7.77673 - 1.58822i) q^{63} +1.00000i q^{64} +(-0.110601 - 0.265193i) q^{65} +(-1.69030 + 2.83559i) q^{66} +(-9.88643 + 9.88643i) q^{67} +(3.89008 + 1.04234i) q^{68} +(-5.20634 + 2.90982i) q^{69} +(-4.01165 - 4.34818i) q^{70} -6.15534 q^{71} +(-2.17966 + 2.06133i) q^{72} +(7.01525 + 1.87973i) q^{73} +(1.42708 + 0.823922i) q^{74} +(7.46031 + 4.39816i) q^{75} +(-1.94092 - 1.12059i) q^{76} +(3.86601 + 3.23757i) q^{77} +(0.0546003 + 0.215765i) q^{78} -10.0513i q^{79} +(-2.21622 + 0.297244i) q^{80} +(-8.98600 - 0.501878i) q^{81} +(-10.7509 + 2.88069i) q^{82} +(-4.80070 - 1.28634i) q^{83} +(2.57953 + 3.78762i) q^{84} +(-1.15376 + 8.93111i) q^{85} +(2.92404 + 5.06458i) q^{86} +(-1.41423 - 0.400164i) q^{87} +(1.84098 - 0.493290i) q^{88} +(0.774397 - 1.34130i) q^{89} +(-5.21625 - 4.21791i) q^{90} +(0.338653 - 0.0299603i) q^{91} +(3.32616 + 0.891242i) q^{92} +(6.78432 - 6.59765i) q^{93} -6.11044 q^{94} +(1.90655 - 4.63461i) q^{95} +(1.73188 + 0.0241584i) q^{96} +(3.66369 - 13.6731i) q^{97} +(6.33839 - 2.97066i) q^{98} +(4.87007 + 2.99590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.20754	+	1.24171i	0.697175	+	0.716901i
$3$	1.20754	+	1.24171i	0.697175	+	0.716901i
$4$		−	1.00000i		−	0.500000i
$5$	2.21622	−	0.297244i	0.991125	−	0.132932i
$5$	2.21622	−	0.297244i	0.991125	−	0.132932i
$6$	−1.73188	−	0.0241584i	−0.707038	−	0.00986261i
$7$	−0.456895	+	2.60600i	−0.172690	+	0.984976i
$7$	−0.456895	+	2.60600i	−0.172690	+	0.984976i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.0836789	+	2.99883i	−0.0278930	+	0.999611i
$10$	−1.35692	+	1.77729i	−0.429097	+	0.562028i
$11$	0.952963	−	1.65058i	0.287329	−	0.497669i	−0.685842	−	0.727750i	$-0.740566\pi$
$11$	0.952963	−	1.65058i	0.287329	−	0.497669i	0.973171	+	0.230081i	$0.0738993\pi$
$12$	1.24171	−	1.20754i	0.358450	−	0.348588i
$13$	−0.0332580	−	0.124120i	−0.00922410	−	0.0344248i	0.961160	−	0.275990i	$-0.0890058\pi$
$13$	−0.0332580	−	0.124120i	−0.00922410	−	0.0344248i	−0.970385	+	0.241566i	$0.922339\pi$
$14$	−1.51965	−	2.16580i	−0.406143	−	0.578833i
$15$	3.04528	+	2.39297i	0.786287	+	0.617862i
$16$	−1.00000			−0.250000
$17$	−1.04234	+	3.89008i	−0.252805	+	0.943482i	0.716493	+	0.697594i	$0.245746\pi$
$17$	−1.04234	+	3.89008i	−0.252805	+	0.943482i	−0.969298	+	0.245888i	$0.920921\pi$
$18$	−2.06133	−	2.17966i	−0.485859	−	0.513752i
$19$	1.12059	−	1.94092i	0.257081	−	0.445278i	−0.708377	−	0.705834i	$-0.750572\pi$
$19$	1.12059	−	1.94092i	0.257081	−	0.445278i	0.965459	+	0.260556i	$0.0839058\pi$
$20$	−0.297244	−	2.21622i	−0.0664658	−	0.495563i
$21$	−3.78762	+	2.57953i	−0.826525	+	0.562899i
$22$	0.493290	+	1.84098i	0.105170	+	0.392499i
$23$	−0.891242	+	3.32616i	−0.185837	+	0.693553i	0.808613	+	0.588341i	$0.200219\pi$
$23$	−0.891242	+	3.32616i	−0.185837	+	0.693553i	−0.994450	+	0.105212i	$0.966448\pi$
$24$	−0.0241584	+	1.73188i	−0.00493130	+	0.353519i
$25$	4.82329	−	1.31752i	0.964658	−	0.263504i
$26$	0.111283	+	0.0642495i	0.0218245	+	0.0126004i
$27$	−3.82472	+	3.51732i	−0.736068	+	0.676908i
$28$	2.60600	+	0.456895i	0.492488	+	0.0863451i
$29$	−0.734875	+	0.424280i	−0.136463	+	0.0787869i	−0.566677	−	0.823940i	$-0.691771\pi$
$29$	−0.734875	+	0.424280i	−0.136463	+	0.0787869i	0.430214	+	0.902727i	$0.358438\pi$
$30$	−3.84542	+	0.461252i	−0.702074	+	0.0842127i
$31$		−	5.46370i		−	0.981309i	−0.871354	−	0.490654i	$-0.836758\pi$
$31$		−	5.46370i		−	0.981309i	0.871354	−	0.490654i	$-0.163242\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	3.20028	−	0.809845i	0.557098	−	0.140976i
$34$	−2.01365	−	3.48775i	−0.345338	−	0.598144i
$35$	−0.237963	+	5.91129i	−0.0402230	+	0.999191i
$36$	2.99883	+	0.0836789i	0.499805	+	0.0139465i
$37$	−0.426494	−	1.59170i	−0.0701151	−	0.261673i	0.921966	−	0.387270i	$-0.126582\pi$
$37$	−0.426494	−	1.59170i	−0.0701151	−	0.261673i	−0.992081	+	0.125597i	$0.959915\pi$
$38$	0.580061	+	2.16482i	0.0940983	+	0.351180i
$39$	0.113961	−	0.191177i	0.0182484	−	0.0306129i
$40$	1.77729	+	1.35692i	0.281014	+	0.214548i
$41$	9.63896	+	5.56506i	1.50535	+	0.869116i	0.999981	+	0.00621495i	$0.00197829\pi$
$41$	9.63896	+	5.56506i	1.50535	+	0.869116i	0.505373	+	0.862901i	$0.331355\pi$
$42$	0.854246	−	4.50225i	0.131813	−	0.694712i
$43$	1.51359	−	5.64881i	0.230821	−	0.861435i	−0.749167	−	0.662381i	$-0.769546\pi$
$43$	1.51359	−	5.64881i	0.230821	−	0.861435i	0.979988	−	0.199055i	$-0.0637872\pi$
$44$	−1.65058	−	0.952963i	−0.248834	−	0.143665i
$45$	0.705935	+	6.67096i	0.105235	+	0.994447i
$46$	−1.72175	−	2.98215i	−0.253858	−	0.439695i
$47$	4.32073	+	4.32073i	0.630244	+	0.630244i	0.948129	−	0.317886i	$-0.102973\pi$
$47$	4.32073	+	4.32073i	0.630244	+	0.630244i	−0.317886	+	0.948129i	$0.602973\pi$
$48$	−1.20754	−	1.24171i	−0.174294	−	0.179225i
$49$	−6.58249	−	2.38134i	−0.940356	−	0.340191i
$50$	−2.47896	+	4.34221i	−0.350577	+	0.614081i
$51$	−6.08901	+	3.40315i	−0.852632	+	0.476536i
$52$	−0.124120	+	0.0332580i	−0.0172124	+	0.00461205i
$53$	−0.0925928	+	0.345561i	−0.0127186	+	0.0474665i	−0.971994	−	0.235008i	$-0.924488\pi$
$53$	−0.0925928	+	0.345561i	−0.0127186	+	0.0474665i	0.959275	+	0.282474i	$0.0911551\pi$
$54$	0.217369	−	5.19160i	0.0295802	−	0.706488i
$55$	1.62135	−	3.94132i	0.218623	−	0.531447i
$56$	−2.16580	+	1.51965i	−0.289417	+	0.203072i
$57$	3.76322	−	0.952299i	0.498451	−	0.126135i
$58$	0.219624	−	0.819646i	0.0288380	−	0.107625i
$59$	−12.7246			−1.65660			−0.828302	−	0.560281i	$-0.810693\pi$
$59$	−12.7246			−1.65660			−0.828302	+	0.560281i	$0.810693\pi$
$60$	2.39297	−	3.04528i	0.308931	−	0.393143i
$61$		−	5.80201i		−	0.742871i	−0.928459	−	0.371435i	$-0.878866\pi$
$61$		−	5.80201i		−	0.742871i	0.928459	−	0.371435i	$-0.121134\pi$
$62$	3.86342	+	3.86342i	0.490654	+	0.490654i
$63$	−7.77673	−	1.58822i	−0.979776	−	0.200097i
$64$			1.00000i			0.125000i
$65$	−0.110601	−	0.265193i	−0.0137184	−	0.0328931i
$66$	−1.69030	+	2.83559i	−0.208061	+	0.349037i
$67$	−9.88643	+	9.88643i	−1.20782	+	1.20782i	−0.236087	+	0.971732i	$0.575865\pi$
$67$	−9.88643	+	9.88643i	−1.20782	+	1.20782i	−0.971732	+	0.236087i	$0.924135\pi$
$68$	3.89008	+	1.04234i	0.471741	+	0.126403i
$69$	−5.20634	+	2.90982i	−0.626769	+	0.350301i
$70$	−4.01165	−	4.34818i	−0.479484	−	0.519707i
$71$	−6.15534			−0.730504			−0.365252	−	0.930909i	$-0.619017\pi$
$71$	−6.15534			−0.730504			−0.365252	+	0.930909i	$0.619017\pi$
$72$	−2.17966	+	2.06133i	−0.256876	+	0.242929i
$73$	7.01525	+	1.87973i	0.821073	+	0.220006i	0.644816	−	0.764338i	$-0.276934\pi$
$73$	7.01525	+	1.87973i	0.821073	+	0.220006i	0.176258	+	0.984344i	$0.443601\pi$
$74$	1.42708	+	0.823922i	0.165894	+	0.0957790i
$75$	7.46031	+	4.39816i	0.861442	+	0.507856i
$76$	−1.94092	−	1.12059i	−0.222639	−	0.128541i
$77$	3.86601	+	3.23757i	0.440573	+	0.368955i
$78$	0.0546003	+	0.215765i	0.00618227	+	0.0244306i
$79$		−	10.0513i		−	1.13085i	−0.824798	−	0.565427i	$-0.808711\pi$
$79$		−	10.0513i		−	1.13085i	0.824798	−	0.565427i	$-0.191289\pi$
$80$	−2.21622	+	0.297244i	−0.247781	+	0.0332329i
$81$	−8.98600	−	0.501878i	−0.998444	−	0.0557642i
$82$	−10.7509	+	2.88069i	−1.18723	+	0.318119i
$83$	−4.80070	−	1.28634i	−0.526945	−	0.141195i	−0.0144681	−	0.999895i	$-0.504605\pi$
$83$	−4.80070	−	1.28634i	−0.526945	−	0.141195i	−0.512477	+	0.858701i	$0.671272\pi$
$84$	2.57953	+	3.78762i	0.281450	+	0.413263i
$85$	−1.15376	+	8.93111i	−0.125143	+	0.968714i
$86$	2.92404	+	5.06458i	0.315307	+	0.546128i
$87$	−1.41423	−	0.400164i	−0.151621	−	0.0429020i
$88$	1.84098	−	0.493290i	0.196250	−	0.0525849i
$89$	0.774397	−	1.34130i	0.0820860	−	0.142177i	−0.822060	−	0.569401i	$-0.807175\pi$
$89$	0.774397	−	1.34130i	0.0820860	−	0.142177i	0.904146	+	0.427224i	$0.140508\pi$
$90$	−5.21625	−	4.21791i	−0.549841	−	0.444606i
$91$	0.338653	−	0.0299603i	0.0355005	−	0.00314069i
$92$	3.32616	+	0.891242i	0.346776	+	0.0929184i
$93$	6.78432	−	6.59765i	0.703501	−	0.684144i
$94$	−6.11044			−0.630244
$95$	1.90655	−	4.63461i	0.195608	−	0.475501i
$96$	1.73188	+	0.0241584i	0.176759	+	0.00246565i
$97$	3.66369	−	13.6731i	0.371992	−	1.38829i	−0.485699	−	0.874126i	$-0.661435\pi$
$97$	3.66369	−	13.6731i	0.371992	−	1.38829i	0.857691	−	0.514166i	$-0.171898\pi$
$98$	6.33839	−	2.97066i	0.640274	−	0.300082i
$99$	4.87007	+	2.99590i	0.489461	+	0.301099i
$100$	−1.31752	−	4.82329i	−0.131752	−	0.482329i
$101$	8.82250	+	5.09367i	0.877872	+	0.506839i	0.869956	−	0.493129i	$-0.164147\pi$
$101$	8.82250	+	5.09367i	0.877872	+	0.506839i	0.00791560	+	0.999969i	$0.497480\pi$
$102$	1.89919	−	6.71197i	0.188048	−	0.664584i
$103$	−2.44235	−	0.654425i	−0.240651	−	0.0644824i	0.136477	−	0.990643i	$-0.456422\pi$
$103$	−2.44235	−	0.654425i	−0.240651	−	0.0644824i	−0.377129	+	0.926161i	$0.623089\pi$
$104$	0.0642495	−	0.111283i	0.00630018	−	0.0109122i
$105$	−7.62745	+	6.84266i	−0.744363	+	0.667775i
$106$	−0.178876	−	0.309822i	−0.0173739	−	0.0300925i
$107$	−1.64660	−	6.14520i	−0.159183	−	0.594079i	−0.998711	−	0.0507622i	$-0.983835\pi$
$107$	−1.64660	−	6.14520i	−0.159183	−	0.594079i	0.839528	−	0.543317i	$-0.182832\pi$
$108$	3.51732	+	3.82472i	0.338454	+	0.368034i
$109$	−1.77647	+	1.02564i	−0.170154	+	0.0982387i	−0.582659	−	0.812717i	$-0.697988\pi$
$109$	−1.77647	+	1.02564i	−0.170154	+	0.0982387i	0.412504	+	0.910956i	$0.364654\pi$
$110$	1.64046	+	3.93340i	0.156412	+	0.375035i
$111$	1.46141	−	2.45162i	0.138711	−	0.232698i
$112$	0.456895	−	2.60600i	0.0431725	−	0.246244i
$113$	19.6336	−	5.26081i	1.84697	−	0.494895i	0.847612	−	0.530617i	$-0.178040\pi$
$113$	19.6336	−	5.26081i	1.84697	−	0.494895i	0.999362	+	0.0357214i	$0.0113729\pi$
$114$	−1.98762	+	3.33438i	−0.186158	+	0.312293i
$115$	−0.986509	+	7.63643i	−0.0919925	+	0.712101i
$116$	0.424280	+	0.734875i	0.0393934	+	0.0682314i
$117$	0.374999	−	0.0893488i	0.0346687	−	0.00826030i
$118$	8.99767	−	8.99767i	0.828302	−	0.828302i
$119$	−9.66130	−	4.49370i	−0.885650	−	0.411937i
$120$	0.461252	+	3.84542i	0.0421063	+	0.351037i
$121$	3.68372	+	6.38039i	0.334884	+	0.580036i
$122$	4.10264	+	4.10264i	0.371435	+	0.371435i
$123$	4.72929	+	18.6888i	0.426425	+	1.68512i
$124$	−5.46370			−0.490654
$125$	10.2979	−	4.35361i	0.921069	−	0.389399i
$126$	6.62202	−	4.37594i	0.589936	−	0.389840i
$127$	12.7660	−	12.7660i	1.13280	−	1.13280i	0.143088	−	0.989710i	$-0.454297\pi$
$127$	12.7660	−	12.7660i	1.13280	−	1.13280i	0.989710	−	0.143088i	$-0.0457032\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	8.84190	−	4.94174i	0.778486	−	0.435096i
$130$	0.265726	+	0.109313i	0.0233058	+	0.00958737i
$131$	11.8452	−	6.83882i	1.03492	−	0.597510i	0.116528	−	0.993187i	$-0.462823\pi$
$131$	11.8452	−	6.83882i	1.03492	−	0.597510i	0.918390	+	0.395677i	$0.129490\pi$
$132$	−0.809845	−	3.20028i	−0.0704880	−	0.278549i
$133$	4.54605	+	3.80706i	0.394193	+	0.330114i
$134$		−	13.9815i		−	1.20782i
$135$	−7.43093	+	8.93203i	−0.639553	+	0.768747i
$136$	−3.48775	+	2.01365i	−0.299072	+	0.172669i
$137$	−4.18988	−	15.6368i	−0.357966	−	1.33595i	−0.876711	−	0.481017i	$-0.840268\pi$
$137$	−4.18988	−	15.6368i	−0.357966	−	1.33595i	0.518746	−	0.854929i	$-0.326399\pi$
$138$	1.62388	−	5.73899i	0.138234	−	0.488535i
$139$	6.37489	−	11.0416i	0.540711	−	0.936539i	−0.458152	−	0.888874i	$-0.651489\pi$
$139$	6.37489	−	11.0416i	0.540711	−	0.936539i	0.998863	−	0.0476651i	$-0.0151780\pi$
$140$	5.91129	+	0.237963i	0.499595	+	0.0201115i
$141$	−0.147618	+	10.5826i	−0.0124317	+	0.891212i
$142$	4.35248	−	4.35248i	0.365252	−	0.365252i
$143$	−0.236564	−	0.0633873i	−0.0197825	−	0.00530071i
$144$	0.0836789	−	2.99883i	0.00697324	−	0.249903i
$145$	−1.50253	+	1.15874i	−0.124778	+	0.0962279i
$146$	−6.28970	+	3.63136i	−0.520540	+	0.300534i
$147$	−4.99172	−	11.0491i	−0.411710	−	0.911315i
$148$	−1.59170	+	0.426494i	−0.130837	+	0.0350576i
$149$	−13.6019	+	7.85304i	−1.11431	+	0.643346i	−0.939942	−	0.341335i	$-0.889121\pi$
$149$	−13.6019	+	7.85304i	−1.11431	+	0.643346i	−0.174366	+	0.984681i	$0.555788\pi$
$150$	−8.38520	+	2.16527i	−0.684649	+	0.176793i
$151$	−3.30729	+	5.72840i	−0.269144	+	0.466171i	−0.968641	−	0.248465i	$-0.920074\pi$
$151$	−3.30729	+	5.72840i	−0.269144	+	0.466171i	0.699497	+	0.714635i	$0.253407\pi$
$152$	2.16482	−	0.580061i	0.175590	−	0.0470492i
$153$	−11.5785	−	3.45133i	−0.936063	−	0.279023i
$154$	−5.02299	+	0.444378i	−0.404764	+	0.0358090i
$155$	−1.62405	−	12.1088i	−0.130447	−	0.972600i
$156$	−0.191177	−	0.113961i	−0.0153064	−	0.00912418i
$157$	−11.0742	−	11.0742i	−0.883817	−	0.883817i	0.110103	−	0.993920i	$-0.464882\pi$
$157$	−11.0742	−	11.0742i	−0.883817	−	0.883817i	−0.993920	+	0.110103i	$0.964882\pi$
$158$	7.10731	+	7.10731i	0.565427	+	0.565427i
$159$	−0.540896	+	0.302307i	−0.0428958	+	0.0239745i
$160$	1.35692	−	1.77729i	0.107274	−	0.140507i
$161$	−8.26078	−	3.84229i	−0.651041	−	0.302815i
$162$	6.70894	−	5.99918i	0.527104	−	0.471340i
$163$	5.09842	−	1.36612i	0.399339	−	0.107003i	−0.0535594	−	0.998565i	$-0.517057\pi$
$163$	5.09842	−	1.36612i	0.399339	−	0.107003i	0.452899	+	0.891562i	$0.350390\pi$
$164$	5.56506	−	9.63896i	0.434558	−	0.752677i
$165$	6.85182	−	2.74606i	0.533414	−	0.213781i
$166$	4.30419	−	2.48503i	0.334070	−	0.192875i
$167$	18.5917	−	4.98162i	1.43867	−	0.385489i	0.546600	−	0.837394i	$-0.315922\pi$
$167$	18.5917	−	4.98162i	1.43867	−	0.385489i	0.892066	+	0.451905i	$0.149255\pi$
$168$	−4.50225	−	0.854246i	−0.347356	−	0.0659065i
$169$	11.2440	−	6.49174i	0.864925	−	0.499365i
$170$	−5.49941	−	7.13108i	−0.421786	−	0.546929i
$171$	5.72673	+	3.52288i	0.437934	+	0.269402i
$172$	−5.64881	−	1.51359i	−0.430718	−	0.115410i
$173$	−11.7540	+	11.7540i	−0.893638	+	0.893638i	−0.994863	−	0.101226i	$-0.967724\pi$
$173$	−11.7540	+	11.7540i	−0.893638	+	0.893638i	0.101226	+	0.994863i	$0.467724\pi$
$174$	1.28297	−	0.717050i	0.0972615	−	0.0543594i
$175$	1.22972	+	13.1715i	0.0929581	+	0.995670i
$176$	−0.952963	+	1.65058i	−0.0718323	+	0.124417i
$177$	−15.3655	−	15.8003i	−1.15494	−	1.18762i
$178$	0.400858	+	1.49602i	0.0300455	+	0.112132i
$179$	−12.1906	+	7.03822i	−0.911165	+	0.526061i	−0.880806	−	0.473478i	$-0.842998\pi$
$179$	−12.1906	+	7.03822i	−0.911165	+	0.526061i	−0.0303590	+	0.999539i	$0.509665\pi$
$180$	6.67096	−	0.705935i	0.497224	−	0.0526173i
$181$		−	13.0807i		−	0.972280i	−0.873881	−	0.486140i	$-0.838404\pi$
$181$		−	13.0807i		−	0.972280i	0.873881	−	0.486140i	$-0.161596\pi$
$182$	−0.218279	+	0.260649i	−0.0161799	+	0.0193206i
$183$	7.20440	−	7.00617i	0.532564	−	0.517911i
$184$	−2.98215	+	1.72175i	−0.219847	+	0.126929i
$185$	−1.41833	−	3.40078i	−0.104278	−	0.250030i
$186$	−0.131994	+	9.46248i	−0.00967827	+	0.693823i
$187$	5.42757	+	5.42757i	0.396903	+	0.396903i
$188$	4.32073	−	4.32073i	0.315122	−	0.315122i
$189$	−7.41863	−	11.5743i	−0.539626	−	0.841905i
$190$	1.92902	+	4.62530i	0.139946	+	0.335554i
$191$	5.48323			0.396753			0.198376	−	0.980126i	$-0.436433\pi$
$191$	5.48323			0.396753			0.198376	+	0.980126i	$0.436433\pi$
$192$	−1.24171	+	1.20754i	−0.0896126	+	0.0871469i
$193$	10.5332	+	10.5332i	0.758196	+	0.758196i	0.975994	−	0.217798i	$-0.0698873\pi$
$193$	10.5332	+	10.5332i	0.758196	+	0.758196i	−0.217798	+	0.975994i	$0.569887\pi$
$194$	7.07771	+	12.2590i	0.508150	+	0.880142i
$195$	0.195736	−	0.457566i	0.0140170	−	0.0327670i
$196$	−2.38134	+	6.58249i	−0.170096	+	0.470178i
$197$	6.36311	−	6.36311i	0.453353	−	0.453353i	−0.443113	−	0.896466i	$-0.646126\pi$
$197$	6.36311	−	6.36311i	0.453353	−	0.453353i	0.896466	+	0.443113i	$0.146126\pi$
$198$	−5.56208	+	1.32524i	−0.395280	+	0.0941809i
$199$	−1.91970	−	3.32501i	−0.136084	−	0.235704i	0.789927	−	0.613201i	$-0.210118\pi$
$199$	−1.91970	−	3.32501i	−0.136084	−	0.235704i	−0.926011	+	0.377497i	$0.876785\pi$
$200$	4.34221	+	2.47896i	0.307041	+	0.175289i
$201$	−24.2143	−	0.337771i	−1.70795	−	0.0238245i
$202$	−9.84022	+	2.63668i	−0.692356	+	0.185516i
$203$	−0.769914	−	2.10894i	−0.0540374	−	0.148018i
$204$	3.40315	+	6.08901i	0.238268	+	0.426316i
$205$	23.0163	+	9.46829i	1.60753	+	0.661294i
$206$	2.18975	−	1.26425i	0.152567	−	0.0880846i
$207$	−9.90002	−	2.95102i	−0.688099	−	0.205110i
$208$	0.0332580	+	0.124120i	0.00230602	+	0.00860620i
$209$	−2.13577	−	3.69926i	−0.147734	−	0.255883i
$210$	0.554930	−	10.2319i	0.0382938	−	0.706069i
$211$	1.42343	−	2.46545i	0.0979928	−	0.169729i	−0.812861	−	0.582458i	$-0.802091\pi$
$211$	1.42343	−	2.46545i	0.0979928	−	0.169729i	0.910854	+	0.412729i	$0.135424\pi$
$212$	0.345561	+	0.0925928i	0.0237332	+	0.00635930i
$213$	−7.43284	−	7.64313i	−0.509289	−	0.523699i
$214$	5.50964	+	3.18099i	0.376631	+	0.217448i
$215$	1.67539	−	12.9689i	0.114260	−	0.884474i
$216$	−5.19160	−	0.217369i	−0.353244	−	0.0147901i
$217$	14.2384	+	2.49634i	0.966566	+	0.169462i
$218$	0.530912	−	1.98139i	0.0359579	−	0.134197i
$219$	6.13714	+	10.9808i	0.414710	+	0.742011i
$220$	−3.94132	−	1.62135i	−0.265724	−	0.109312i
$221$	0.517504			0.0348111
$222$	0.700184	+	2.76693i	0.0469933	+	0.185704i
$223$	−23.2566	−	6.23160i	−1.55738	−	0.417299i	−0.625547	−	0.780186i	$-0.715124\pi$
$223$	−23.2566	−	6.23160i	−1.55738	−	0.417299i	−0.931833	+	0.362888i	$0.881791\pi$
$224$	1.51965	+	2.16580i	0.101536	+	0.144708i
$225$	3.54741	+	14.5745i	0.236494	+	0.971633i
$226$	−10.1631	+	17.6030i	−0.676039	+	1.17093i
$227$	−20.9398	+	5.61080i	−1.38982	+	0.372402i	−0.874679	−	0.484702i	$-0.838928\pi$
$227$	−20.9398	+	5.61080i	−1.38982	+	0.372402i	−0.515143	+	0.857104i	$0.672261\pi$
$228$	−0.952299	−	3.76322i	−0.0630675	−	0.249225i
$229$	−4.81983	−	8.34819i	−0.318503	−	0.551664i	0.661673	−	0.749793i	$-0.269847\pi$
$229$	−4.81983	−	8.34819i	−0.318503	−	0.551664i	−0.980176	+	0.198129i	$0.936514\pi$
$230$	−4.70221	−	6.09734i	−0.310054	−	0.402047i
$231$	0.648264	+	8.70996i	0.0426526	+	0.573074i
$232$	−0.819646	−	0.219624i	−0.0538124	−	0.0144190i
$233$	28.3917	−	7.60753i	1.86000	−	0.498386i	0.860072	−	0.510173i	$-0.170419\pi$
$233$	28.3917	−	7.60753i	1.86000	−	0.498386i	0.999931	+	0.0117869i	$0.00375196\pi$
$234$	−0.201985	+	0.328344i	−0.0132042	+	0.0214645i
$235$	10.8600	+	8.29139i	0.708430	+	0.540871i
$236$			12.7246i			0.828302i
$237$	12.4807	−	12.1373i	0.810710	−	0.788404i
$238$	10.0091	−	3.65404i	0.648794	−	0.236857i
$239$	7.33947	+	4.23744i	0.474751	+	0.274097i	0.718226	−	0.695810i	$-0.244954\pi$
$239$	7.33947	+	4.23744i	0.474751	+	0.274097i	−0.243476	+	0.969907i	$0.578288\pi$
$240$	−3.04528	−	2.39297i	−0.196572	−	0.154465i
$241$	−7.05696	−	4.07434i	−0.454579	−	0.262451i	0.255183	−	0.966893i	$-0.417864\pi$
$241$	−7.05696	−	4.07434i	−0.454579	−	0.262451i	−0.709762	+	0.704441i	$0.751198\pi$
$242$	−7.11640	−	1.90683i	−0.457460	−	0.122576i
$243$	−10.2278	−	11.7640i	−0.656113	−	0.754663i
$244$	−5.80201			−0.371435
$245$	−15.2961	−	3.32097i	−0.977233	−	0.212169i
$246$	−16.5591	−	9.87089i	−1.05577	−	0.629345i
$247$	−0.278177	−	0.0745372i	−0.0177000	−	0.00474269i
$248$	3.86342	−	3.86342i	0.245327	−	0.245327i
$249$	−4.19979	−	7.51439i	−0.266151	−	0.476205i
$250$	−4.20322	+	10.3602i	−0.265835	+	0.655234i
$251$			10.7148i			0.676315i	0.941090	+	0.338157i	$0.109804\pi$
$251$			10.7148i			0.676315i	−0.941090	+	0.338157i	$0.890196\pi$
$252$	−1.58822	+	7.77673i	−0.100048	+	0.489888i
$253$	4.64078	+	4.64078i	0.291763	+	0.291763i
$254$			18.0538i			1.13280i
$255$	−12.4830	+	9.35206i	−0.781719	+	0.585649i
$256$	1.00000			0.0625000
$257$	0.494721	−	1.84632i	0.0308599	−	0.115171i	−0.948778	−	0.315944i	$-0.897679\pi$
$257$	0.494721	−	1.84632i	0.0308599	−	0.115171i	0.979638	+	0.200773i	$0.0643455\pi$
$258$	−2.75783	+	9.74651i	−0.171695	+	0.606791i
$259$	4.34283	−	0.384205i	0.269850	−	0.0238733i
$260$	−0.265193	+	0.110601i	−0.0164466	+	0.00685919i
$261$	−1.21085	−	2.23927i	−0.0749499	−	0.138607i
$262$	−3.54003	+	13.2116i	−0.218704	+	0.816214i
$263$	−18.4095	+	4.93281i	−1.13518	+	0.304170i	−0.777011	−	0.629487i	$-0.783265\pi$
$263$	−18.4095	+	4.93281i	−1.13518	+	0.304170i	−0.358168	+	0.933657i	$0.616598\pi$
$264$	2.83559	+	1.69030i	0.174519	+	0.104031i
$265$	−0.102490	+	0.793363i	−0.00629593	+	0.0487359i
$266$	−5.90655	+	0.522546i	−0.362154	+	0.0320393i
$267$	2.60062	−	0.658097i	0.159155	−	0.0402749i
$268$	9.88643	+	9.88643i	0.603910	+	0.603910i
$269$	−11.4674	−	19.8622i	−0.699182	−	1.21102i	−0.968751	−	0.248037i	$-0.920215\pi$
$269$	−11.4674	−	19.8622i	−0.699182	−	1.21102i	0.269569	−	0.962981i	$-0.413119\pi$
$270$	−1.06144	−	11.5704i	−0.0645970	−	0.704150i
$271$	−17.0844	−	9.86371i	−1.03781	−	0.599178i	−0.118595	−	0.992943i	$-0.537839\pi$
$271$	−17.0844	−	9.86371i	−1.03781	−	0.599178i	−0.919211	+	0.393765i	$0.871172\pi$
$272$	1.04234	−	3.89008i	0.0632013	−	0.235870i
$273$	0.446141	+	0.384330i	0.0270017	+	0.0232607i
$274$	14.0196	+	8.09423i	0.846956	+	0.488990i
$275$	2.42175	−	9.21678i	0.146037	−	0.555793i
$276$	2.90982	+	5.20634i	0.175151	+	0.313385i
$277$	8.31828	+	31.0442i	0.499797	+	1.86527i	0.501308	+	0.865269i	$0.332852\pi$
$277$	8.31828	+	31.0442i	0.499797	+	1.86527i	−0.00151114	+	0.999999i	$0.500481\pi$
$278$	3.29988	+	12.3153i	0.197914	+	0.738625i
$279$	16.3847	+	0.457196i	0.980927	+	0.0273716i
$280$	−4.34818	+	4.01165i	−0.259853	+	0.239742i
$281$	6.88610	+	11.9271i	0.410790	+	0.711509i	0.994976	−	0.100110i	$-0.0319196\pi$
$281$	6.88610	+	11.9271i	0.410790	+	0.711509i	−0.584186	+	0.811620i	$0.698586\pi$
$282$	−7.37862	−	7.58738i	−0.439390	−	0.451822i
$283$	5.41131	−	5.41131i	0.321669	−	0.321669i	−0.527738	−	0.849407i	$-0.676960\pi$
$283$	5.41131	−	5.41131i	0.321669	−	0.321669i	0.849407	+	0.527738i	$0.176960\pi$
$284$			6.15534i			0.365252i
$285$	8.05708	−	3.22910i	0.477260	−	0.191276i
$286$	0.212098	−	0.122455i	0.0125416	−	0.00724090i
$287$	−18.9066	+	22.5765i	−1.11602	+	1.33265i
$288$	2.06133	+	2.17966i	0.121465	+	0.128438i
$289$	0.676223	+	0.390418i	0.0397778	+	0.0229657i
$290$	0.243100	−	1.88180i	0.0142753	−	0.110503i
$291$	21.4021	−	11.9616i	1.25461	−	0.701202i
$292$	1.87973	−	7.01525i	0.110003	−	0.410537i
$293$	−4.43606	−	16.5556i	−0.259158	−	0.967189i	−0.965730	−	0.259549i	$-0.916426\pi$
$293$	−4.43606	−	16.5556i	−0.259158	−	0.967189i	0.706572	−	0.707641i	$-0.250240\pi$
$294$	11.3426	+	4.28322i	0.661512	+	0.249803i
$295$	−28.2006	+	3.78232i	−1.64190	+	0.220215i
$296$	0.823922	−	1.42708i	0.0478895	−	0.0829471i
$297$	2.16079	+	9.66489i	0.125382	+	0.560814i
$298$	4.06503	−	15.1709i	0.235481	−	0.878827i
$299$	0.442485			0.0255896
$300$	4.39816	−	7.46031i	0.253928	−	0.430721i
$301$	14.0293	+	6.52534i	0.808633	+	0.376115i
$302$	−1.71198	−	6.38920i	−0.0985134	−	0.367657i
$303$	4.32869	+	17.1058i	0.248677	+	0.982703i
$304$	−1.12059	+	1.94092i	−0.0642704	+	0.111320i
$305$	−1.72461	−	12.8585i	−0.0987511	−	0.736278i
$306$	10.6277	−	5.74675i	0.607543	−	0.328520i
$307$	21.5298	+	21.5298i	1.22877	+	1.22877i	0.964428	+	0.264345i	$0.0851558\pi$
$307$	21.5298	+	21.5298i	1.22877	+	1.22877i	0.264345	+	0.964428i	$0.414844\pi$
$308$	3.23757	−	3.86601i	0.184478	−	0.220287i
$309$	−2.13663	−	3.82293i	−0.121549	−	0.217479i
$310$	9.71057	+	7.41382i	0.551523	+	0.421076i
$311$		−	2.06338i		−	0.117003i	−0.998287	−	0.0585017i	$-0.981368\pi$
$311$		−	2.06338i		−	0.117003i	0.998287	−	0.0585017i	$-0.0186323\pi$
$312$	0.215765	−	0.0546003i	0.0122153	−	0.00309114i
$313$	−6.64409	+	6.64409i	−0.375546	+	0.375546i	−0.869492	−	0.493946i	$-0.835554\pi$
$313$	−6.64409	+	6.64409i	−0.375546	+	0.375546i	0.493946	+	0.869492i	$0.335554\pi$
$314$	15.6613			0.883817
$315$	−17.7071	−	1.20826i	−0.997680	−	0.0680778i
$316$	−10.0513			−0.565427
$317$	−8.34375	+	8.34375i	−0.468631	+	0.468631i	−0.901471	−	0.432840i	$-0.857512\pi$
$317$	−8.34375	+	8.34375i	−0.468631	+	0.468631i	0.432840	+	0.901471i	$0.357512\pi$
$318$	0.168708	−	0.596234i	0.00946068	−	0.0334352i
$319$			1.61729i			0.0905511i
$320$	0.297244	+	2.21622i	0.0166165	+	0.123891i
$321$	5.64220	−	9.46519i	0.314917	−	0.528296i
$322$	8.55816	−	3.12435i	0.476928	−	0.174113i
$323$	6.38229	+	6.38229i	0.355120	+	0.355120i
$324$	−0.501878	+	8.98600i	−0.0278821	+	0.499222i
$325$	−0.323944	−	0.554851i	−0.0179692	−	0.0307776i
$326$	−2.63914	+	4.57112i	−0.146168	+	0.253171i
$327$	−3.41871	−	0.967344i	−0.189055	−	0.0534942i
$328$	2.88069	+	10.7509i	0.159059	+	0.593617i
$329$	−13.2340	+	9.28571i	−0.729612	+	0.511938i
$330$	−2.90321	+	6.78673i	−0.159816	+	0.373597i
$331$	−21.1731			−1.16378			−0.581890	−	0.813267i	$-0.697687\pi$
$331$	−21.1731			−1.16378			−0.581890	+	0.813267i	$0.697687\pi$
$332$	−1.28634	+	4.80070i	−0.0705973	+	0.263473i
$333$	4.80892	−	1.14579i	0.263527	−	0.0627890i
$334$	−9.62375	+	16.6688i	−0.526588	+	0.912077i
$335$	−18.9718	+	24.8492i	−1.03654	+	1.35766i
$336$	3.78762	−	2.57953i	0.206631	−	0.140725i
$337$	1.04798	+	3.91111i	0.0570870	+	0.213052i	0.988577	−	0.150715i	$-0.0481574\pi$
$337$	1.04798	+	3.91111i	0.0570870	+	0.213052i	−0.931490	+	0.363766i	$0.881491\pi$
$338$	−3.36037	+	12.5411i	−0.182780	+	0.682145i
$339$	30.2408	+	18.0266i	1.64246	+	0.979068i
$340$	8.93111	+	1.15376i	0.484357	+	0.0625715i
$341$	−9.01827	−	5.20670i	−0.488367	−	0.281959i
$342$	−6.54046	+	1.55836i	−0.353668	+	0.0842663i
$343$	9.21329	−	16.0660i	0.497471	−	0.867481i
$344$	5.06458	−	2.92404i	0.273064	−	0.157654i
$345$	−10.6735	+	7.99637i	−0.574641	+	0.430510i
$346$		−	16.6226i		−	0.893638i
$347$	−14.3097	+	14.3097i	−0.768183	+	0.768183i	−0.977787	−	0.209603i	$-0.932783\pi$
$347$	−14.3097	+	14.3097i	−0.768183	+	0.768183i	0.209603	+	0.977787i	$0.432783\pi$
$348$	−0.400164	+	1.41423i	−0.0214510	+	0.0758104i
$349$	−13.7657	−	23.8428i	−0.736860	−	1.27628i	−0.953903	−	0.300116i	$-0.902974\pi$
$349$	−13.7657	−	23.8428i	−0.736860	−	1.27628i	0.217043	−	0.976162i	$-0.430359\pi$
$350$	−10.1832	−	8.44410i	−0.544314	−	0.451356i
$351$	0.563773	+	0.357747i	0.0300920	+	0.0190951i
$352$	−0.493290	−	1.84098i	−0.0262925	−	0.0981248i
$353$	−2.38328	−	8.89451i	−0.126849	−	0.473407i	0.873050	−	0.487631i	$-0.162139\pi$
$353$	−2.38328	−	8.89451i	−0.126849	−	0.473407i	−0.999899	+	0.0142240i	$0.995472\pi$
$354$	22.0375	+	0.307406i	1.17128	+	0.0163384i
$355$	−13.6416	+	1.82964i	−0.724021	+	0.0971071i
$356$	−1.34130	−	0.774397i	−0.0710885	−	0.0410430i
$357$	−6.08657	−	17.4229i	−0.322136	−	0.922116i
$358$	3.64325	−	13.5968i	0.192552	−	0.718613i
$359$	10.0714	+	5.81471i	0.531547	+	0.306889i	0.741646	−	0.670791i	$-0.234045\pi$
$359$	10.0714	+	5.81471i	0.531547	+	0.306889i	−0.210099	+	0.977680i	$0.567379\pi$
$360$	−4.21791	+	5.21625i	−0.222303	+	0.274920i
$361$	6.98855	+	12.1045i	0.367818	+	0.637080i
$362$	9.24945	+	9.24945i	0.486140	+	0.486140i
$363$	−3.47433	+	12.2787i	−0.182355	+	0.644465i
$364$	−0.0299603	−	0.338653i	−0.00157035	−	0.0177503i
$365$	16.1061	+	2.08066i	0.843032	+	0.108907i
$366$	−0.140167	+	10.0484i	−0.00732664	+	0.525238i
$367$	−35.6524	+	9.55304i	−1.86104	+	0.498665i	−0.999952	−	0.00978777i	$-0.996884\pi$
$367$	−35.6524	+	9.55304i	−1.86104	+	0.498665i	−0.861090	+	0.508453i	$0.830218\pi$
$368$	0.891242	−	3.32616i	0.0464592	−	0.173388i
$369$	−17.4953	+	28.4400i	−0.910767	+	1.48053i
$370$	3.40762	+	1.40181i	0.177154	+	0.0728764i
$371$	−0.858228	−	0.399182i	−0.0445570	−	0.0207245i
$372$	−6.59765	−	6.78432i	−0.342072	−	0.351750i
$373$	−4.71509	+	17.5970i	−0.244138	+	0.911137i	0.729676	+	0.683793i	$0.239671\pi$
$373$	−4.71509	+	17.5970i	−0.244138	+	0.911137i	−0.973815	+	0.227344i	$0.926996\pi$
$374$	−7.67574			−0.396903
$375$	17.8410	+	7.52977i	0.921307	+	0.388836i
$376$			6.11044i			0.315122i
$377$	0.0771023	+	0.0771023i	0.00397097	+	0.00397097i
$378$	13.4300	+	2.93848i	0.690765	+	0.151139i
$379$			12.7439i			0.654612i	0.944918	+	0.327306i	$0.106141\pi$
$379$			12.7439i			0.654612i	−0.944918	+	0.327306i	$0.893859\pi$
$380$	−4.63461	−	1.90655i	−0.237750	−	0.0978041i
$381$	31.2671	+	0.436151i	1.60186	+	0.0223447i
$382$	−3.87723	+	3.87723i	−0.198376	+	0.198376i
$383$	−15.3140	−	4.10337i	−0.782509	−	0.209673i	−0.154618	−	0.987974i	$-0.549415\pi$
$383$	−15.3140	−	4.10337i	−0.782509	−	0.209673i	−0.627890	+	0.778302i	$0.716081\pi$
$384$	0.0241584	−	1.73188i	0.00123283	−	0.0883797i
$385$	9.53030	+	6.02602i	0.485709	+	0.307115i
$386$	−14.8962			−0.758196
$387$	16.8132	+	5.01170i	0.854662	+	0.254759i
$388$	−13.6731	−	3.66369i	−0.694146	−	0.185996i
$389$	9.48755	+	5.47764i	0.481038	+	0.277727i	0.720849	−	0.693092i	$-0.243752\pi$
$389$	9.48755	+	5.47764i	0.481038	+	0.277727i	−0.239811	+	0.970820i	$0.577085\pi$
$390$	0.185142	+	0.461955i	0.00937501	+	0.0233920i
$391$	−12.0100	−	6.93400i	−0.607374	−	0.350667i
$392$	−2.97066	−	6.33839i	−0.150041	−	0.320137i
$393$	22.7954	+	6.45009i	1.14987	+	0.325364i
$394$			8.99879i			0.453353i
$395$	−2.98768	−	22.2758i	−0.150326	−	1.12082i
$396$	2.99590	−	4.87007i	0.150549	−	0.244730i
$397$	6.92806	−	1.85637i	0.347710	−	0.0931685i	−0.0807374	−	0.996735i	$-0.525728\pi$
$397$	6.92806	−	1.85637i	0.347710	−	0.0931685i	0.428447	+	0.903567i	$0.359061\pi$
$398$	3.70857	+	0.993709i	0.185894	+	0.0498101i
$399$	0.762295	+	10.2421i	0.0381625	+	0.512745i
$400$	−4.82329	+	1.31752i	−0.241165	+	0.0658760i
$401$	1.20527	+	2.08759i	0.0601883	+	0.104249i	0.894549	−	0.446969i	$-0.147497\pi$
$401$	1.20527	+	2.08759i	0.0601883	+	0.104249i	−0.834361	+	0.551218i	$0.814163\pi$
$402$	17.3610	−	16.8833i	0.865886	−	0.842062i
$403$	−0.678156	+	0.181711i	−0.0337814	+	0.00905169i
$404$	5.09367	−	8.82250i	0.253420	−	0.438936i
$405$	−20.0642	+	1.55876i	−0.996996	+	0.0774555i
$406$	2.03566	+	0.946832i	0.101028	+	0.0469905i
$407$	−3.03366	−	0.812866i	−0.150373	−	0.0402923i
$408$	−6.71197	−	1.89919i	−0.332292	−	0.0940240i
$409$	3.87477			0.191595			0.0957975	−	0.995401i	$-0.469460\pi$
$409$	3.87477			0.191595			0.0957975	+	0.995401i	$0.469460\pi$
$410$	−22.9701	+	9.57988i	−1.13441	+	0.473116i
$411$	14.3569	−	24.0848i	0.708175	−	1.18801i
$412$	−0.654425	+	2.44235i	−0.0322412	+	0.120326i
$413$	5.81382	−	33.1604i	0.286079	−	1.63172i
$414$	9.08706	−	4.91369i	0.446604	−	0.241495i
$415$	−11.0218	−	1.42384i	−0.541038	−	0.0698938i
$416$	−0.111283	−	0.0642495i	−0.00545611	−	0.00315009i
$417$	21.4084	−	5.41749i	1.04838	−	0.265296i
$418$	4.12598	+	1.10555i	0.201808	+	0.0540744i
$419$	−19.8432	+	34.3694i	−0.969403	+	1.67905i	−0.272113	+	0.962265i	$0.587722\pi$
$419$	−19.8432	+	34.3694i	−0.969403	+	1.67905i	−0.697290	+	0.716789i	$0.745611\pi$
$420$	6.84266	+	7.62745i	0.333888	+	0.372181i
$421$	−15.5014	−	26.8491i	−0.755490	−	1.30855i	−0.945130	−	0.326694i	$-0.894065\pi$
$421$	−15.5014	−	26.8491i	−0.755490	−	1.30855i	0.189640	−	0.981854i	$-0.439268\pi$
$422$	0.736821	+	2.74985i	0.0358679	+	0.133861i
$423$	−13.3187	+	12.5956i	−0.647578	+	0.612419i
$424$	−0.309822	+	0.178876i	−0.0150463	+	0.00868697i
$425$	0.0977283	+	20.1363i	0.00474052	+	0.976753i
$426$	10.6603	+	0.148703i	0.516494	+	0.00720468i
$427$	15.1200	+	2.65091i	0.731710	+	0.128286i
$428$	−6.14520	+	1.64660i	−0.297039	+	0.0795915i
$429$	−0.206953	−	0.370287i	−0.00999180	−	0.0178776i
$430$	7.98574	+	10.3551i	0.385107	+	0.499367i
$431$	3.14435	+	5.44618i	0.151458	+	0.262333i	0.931764	−	0.363065i	$-0.118270\pi$
$431$	3.14435	+	5.44618i	0.151458	+	0.262333i	−0.780306	+	0.625398i	$0.784936\pi$
$432$	3.82472	−	3.51732i	0.184017	−	0.169227i
$433$	−29.0084	+	29.0084i	−1.39406	+	1.39406i	−0.578067	+	0.815989i	$0.696193\pi$
$433$	−29.0084	+	29.0084i	−1.39406	+	1.39406i	−0.815989	+	0.578067i	$0.803807\pi$
$434$	−11.8332	+	8.30290i	−0.568014	+	0.398552i
$435$	−3.25319	−	0.466481i	−0.155978	−	0.0223661i
$436$	1.02564	+	1.77647i	0.0491194	+	0.0850772i
$437$	5.45710	+	5.45710i	0.261049	+	0.261049i
$438$	−12.1042	−	3.42495i	−0.578360	−	0.163650i
$439$	10.5033			0.501293			0.250647	−	0.968079i	$-0.419357\pi$
$439$	10.5033			0.501293			0.250647	+	0.968079i	$0.419357\pi$
$440$	3.93340	−	1.64046i	0.187518	−	0.0782060i
$441$	7.69206	−	19.5405i	0.366288	−	0.930501i
$442$	−0.365931	+	0.365931i	−0.0174055	+	0.0174055i
$443$	−12.6724	−	12.6724i	−0.602085	−	0.602085i	0.338781	−	0.940865i	$-0.389986\pi$
$443$	−12.6724	−	12.6724i	−0.602085	−	0.602085i	−0.940865	+	0.338781i	$0.889986\pi$
$444$	−2.45162	−	1.46141i	−0.116349	−	0.0693556i
$445$	1.31755	−	3.20280i	0.0624576	−	0.151827i
$446$	20.8513	−	12.0385i	0.987339	−	0.570041i
$447$	−26.1760	−	7.40666i	−1.23808	−	0.350323i
$448$	−2.60600	−	0.456895i	−0.123122	−	0.0215863i
$449$		−	3.56418i		−	0.168204i	−0.996457	−	0.0841021i	$-0.973198\pi$
$449$		−	3.56418i		−	0.168204i	0.996457	−	0.0841021i	$-0.0268022\pi$
$450$	−12.8141	−	7.79732i	−0.604064	−	0.367569i
$451$	18.3712	−	10.6066i	0.865064	−	0.499445i
$452$	−5.26081	−	19.6336i	−0.247448	−	0.923487i
$453$	−11.1067	+	2.81060i	−0.521838	+	0.132053i
$454$	10.8392	−	18.7741i	0.508710	−	0.881112i
$455$	0.741626	−	0.167062i	0.0347680	−	0.00783197i
$456$	3.33438	+	1.98762i	0.156147	+	0.0930790i
$457$	−0.781369	+	0.781369i	−0.0365509	+	0.0365509i	−0.725146	−	0.688595i	$-0.758228\pi$
$457$	−0.781369	+	0.781369i	−0.0365509	+	0.0365509i	0.688595	+	0.725146i	$0.258228\pi$
$458$	9.31120	+	2.49493i	0.435084	+	0.116580i
$459$	−9.69595	−	18.5447i	−0.452568	−	0.865593i
$460$	7.63643	+	0.986509i	0.356051	+	0.0459962i
$461$	6.42804	−	3.71123i	0.299384	−	0.172849i	−0.342782	−	0.939415i	$-0.611369\pi$
$461$	6.42804	−	3.71123i	0.299384	−	0.172849i	0.642166	+	0.766566i	$0.278036\pi$
$462$	−6.61727	−	5.70048i	−0.307863	−	0.265210i
$463$	−23.8989	+	6.40368i	−1.11067	+	0.297604i	−0.767104	−	0.641522i	$-0.778303\pi$
$463$	−23.8989	+	6.40368i	−1.11067	+	0.297604i	−0.343571	+	0.939127i	$0.611636\pi$
$464$	0.734875	−	0.424280i	0.0341157	−	0.0196967i
$465$	13.0744	−	16.6385i	0.606313	−	0.771590i
$466$	−14.6966	+	25.4553i	−0.680808	+	1.17919i
$467$	19.0695	−	5.10964i	0.882429	−	0.236446i	0.210974	−	0.977492i	$-0.432336\pi$
$467$	19.0695	−	5.10964i	0.882429	−	0.236446i	0.671455	+	0.741045i	$0.265670\pi$
$468$	−0.0893488	−	0.374999i	−0.00413015	−	0.0173344i
$469$	−21.2470	−	30.2811i	−0.981095	−	1.39825i
$470$	−13.5421	+	1.81629i	−0.624650	+	0.0837793i
$471$	0.378351	−	27.1235i	0.0174335	−	1.24979i
$472$	−8.99767	−	8.99767i	−0.414151	−	0.414151i
$473$	−7.88142	−	7.88142i	−0.362388	−	0.362388i
$474$	−0.242822	+	17.4076i	−0.0111532	+	0.799557i
$475$	2.84774	−	10.8380i	0.130663	−	0.497283i
$476$	−4.49370	+	9.66130i	−0.205969	+	0.442825i
$477$	−1.02853	−	0.306587i	−0.0470932	−	0.0140376i
$478$	−8.18611	+	2.19346i	−0.374424	+	0.100327i
$479$	20.6912	−	35.8382i	0.945404	−	1.63749i	0.190464	−	0.981694i	$-0.439001\pi$
$479$	20.6912	−	35.8382i	0.945404	−	1.63749i	0.754940	−	0.655794i	$-0.227666\pi$
$480$	3.84542	−	0.461252i	0.175519	−	0.0210532i
$481$	−0.183378	+	0.105873i	−0.00836130	+	0.00482740i
$482$	7.87102	−	2.10903i	0.358515	−	0.0960638i
$483$	−5.20425	−	14.8972i	−0.236802	−	0.677846i
$484$	6.38039	−	3.68372i	0.290018	−	0.167442i
$485$	4.05531	−	31.3916i	0.184142	−	1.42542i
$486$	15.5506	+	1.08628i	0.705388	+	0.0492747i
$487$	14.9475	+	4.00517i	0.677336	+	0.181492i	0.581057	−	0.813863i	$-0.302639\pi$
$487$	14.9475	+	4.00517i	0.677336	+	0.181492i	0.0962791	+	0.995354i	$0.469306\pi$
$488$	4.10264	−	4.10264i	0.185718	−	0.185718i
$489$	7.85288	+	4.68110i	0.355120	+	0.211687i
$490$	13.1643	−	8.46770i	0.594701	−	0.382532i
$491$	−2.15176	+	3.72696i	−0.0971077	+	0.168195i	−0.910486	−	0.413539i	$-0.864292\pi$
$491$	−2.15176	+	3.72696i	−0.0971077	+	0.168195i	0.813379	+	0.581735i	$0.197626\pi$
$492$	18.6888	−	4.72929i	0.842558	−	0.213213i
$493$	−0.884491	−	3.30096i	−0.0398355	−	0.148668i
$494$	0.249406	−	0.143995i	0.0112213	−	0.00647863i
$495$	11.6837	+	5.19197i	0.525143	+	0.233362i
$496$			5.46370i			0.245327i
$497$	2.81234	−	16.0408i	0.126151	−	0.719529i
$498$	8.28317	+	2.34377i	0.371178	+	0.105027i
$499$	27.9994	−	16.1655i	1.25343	−	0.723666i	0.281638	−	0.959521i	$-0.409122\pi$
$499$	27.9994	−	16.1655i	1.25343	−	0.723666i	0.971788	+	0.235855i	$0.0757889\pi$
$500$	−4.35361	−	10.2979i	−0.194700	−	0.460535i
$501$	28.6359	+	17.0699i	1.27936	+	0.762627i
$502$	−7.57654	−	7.57654i	−0.338157	−	0.338157i
$503$	−7.60770	+	7.60770i	−0.339210	+	0.339210i	−0.856070	−	0.516860i	$-0.827101\pi$
$503$	−7.60770	+	7.60770i	−0.339210	+	0.339210i	0.516860	+	0.856070i	$0.327101\pi$
$504$	−4.37594	−	6.62202i	−0.194920	−	0.294968i
$505$	21.0667	+	8.66628i	0.937456	+	0.385644i
$506$	−6.56305			−0.291763
$507$	21.6385	+	6.12274i	0.961000	+	0.271921i
$508$	−12.7660	−	12.7660i	−0.566399	−	0.566399i
$509$	−11.1692	−	19.3457i	−0.495068	−	0.857483i	0.504916	−	0.863169i	$-0.331524\pi$
$509$	−11.1692	−	19.3457i	−0.495068	−	0.857483i	−0.999984	+	0.00568564i	$0.998190\pi$
$510$	2.21394	−	15.4398i	0.0980349	−	0.683684i
$511$	−8.10382	+	17.4229i	−0.358492	+	0.770745i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.54088	+	11.3650i	0.112183	+	0.501775i
$514$	0.955728	+	1.65537i	0.0421553	+	0.0730152i
$515$	−5.60731	−	0.724378i	−0.247087	−	0.0319199i
$516$	−4.94174	−	8.84190i	−0.217548	−	0.389243i
$517$	11.2492	−	3.01422i	0.494740	−	0.132565i
$518$	−2.79917	+	3.34252i	−0.122988	+	0.146862i
$519$	−28.7884	−	0.401575i	−1.26367	−	0.0176272i
$520$	0.109313	−	0.265726i	0.00479368	−	0.0116529i
$521$	23.5834	−	13.6159i	1.03321	−	0.596523i	0.115306	−	0.993330i	$-0.463215\pi$
$521$	23.5834	−	13.6159i	1.03321	−	0.596523i	0.917902	+	0.396807i	$0.129882\pi$
$522$	2.43960	+	0.727202i	0.106779	+	0.0318287i
$523$	0.248721	+	0.928240i	0.0108758	+	0.0405891i	0.971151	−	0.238467i	$-0.0766450\pi$
$523$	0.248721	+	0.928240i	0.0108758	+	0.0405891i	−0.960275	+	0.279056i	$0.909978\pi$
$524$	−6.83882	−	11.8452i	−0.298755	−	0.517459i
$525$	−14.8702	+	17.4321i	−0.648988	+	0.760798i
$526$	9.52946	−	16.5055i	0.415504	−	0.719674i
$527$	21.2542	+	5.69504i	0.925847	+	0.248080i
$528$	−3.20028	+	0.809845i	−0.139275	+	0.0352440i
$529$	9.64955	+	5.57117i	0.419546	+	0.242225i
$530$	−0.488521	−	0.633464i	−0.0212200	−	0.0275159i
$531$	1.06478	−	38.1590i	0.0462076	−	1.65596i
$532$	3.80706	−	4.54605i	0.165057	−	0.197096i
$533$	0.370165	−	1.38147i	0.0160336	−	0.0598383i
$534$	−1.37357	+	2.30426i	−0.0594401	+	0.0997150i
$535$	−5.47586	−	13.1297i	−0.236742	−	0.567646i
$536$	−13.9815			−0.603910
$537$	−23.4600	−	6.63816i	−1.01238	−	0.286458i
$538$	22.1534	+	5.93598i	0.955100	+	0.255918i
$539$	−10.2035	+	8.59561i	−0.439495	+	0.370239i
$540$	8.93203	+	7.43093i	0.384373	+	0.319777i
$541$	−10.8824	+	18.8488i	−0.467869	+	0.810373i	−0.999326	−	0.0367122i	$-0.988312\pi$
$541$	−10.8824	+	18.8488i	−0.467869	+	0.810373i	0.531457	+	0.847086i	$0.321645\pi$
$542$	19.0552	−	5.10583i	0.818492	−	0.219314i
$543$	16.2424	−	15.7955i	0.697028	−	0.677850i
$544$	2.01365	+	3.48775i	0.0863346	+	0.149536i
$545$	−3.63218	+	2.80110i	−0.155585	+	0.119986i
$546$	−0.587232	+	0.0437064i	−0.0251312	+	0.00187046i
$547$	−16.0667	−	4.30506i	−0.686963	−	0.184071i	−0.101579	−	0.994827i	$-0.532390\pi$
$547$	−16.0667	−	4.30506i	−0.686963	−	0.184071i	−0.585384	+	0.810756i	$0.699056\pi$
$548$	−15.6368	+	4.18988i	−0.667973	+	0.178983i
$549$	17.3992	+	0.485505i	0.742582	+	0.0207209i
$550$	4.80482	+	8.22968i	0.204878	+	0.350915i
$551$			1.90178i			0.0810186i
$552$	−5.73899	−	1.62388i	−0.244268	−	0.0691170i
$553$	26.1936	+	4.59237i	1.11386	+	0.195287i
$554$	−27.8335	−	16.0697i	−1.18253	−	0.682735i
$555$	2.51009	−	5.86774i	0.106547	−	0.249072i
$556$	−11.0416	−	6.37489i	−0.468269	−	0.270355i
$557$	−26.8483	−	7.19398i	−1.13760	−	0.304819i	−0.359614	−	0.933101i	$-0.617092\pi$
$557$	−26.8483	−	7.19398i	−1.13760	−	0.304819i	−0.777985	+	0.628282i	$0.783758\pi$
$558$	−11.9090	+	11.2625i	−0.504149	+	0.476778i
$559$	−0.751472			−0.0317839
$560$	0.237963	−	5.91129i	0.0100558	−	0.249798i
$561$	−0.185433	+	13.2935i	−0.00782900	+	0.561251i
$562$	−13.3029	−	3.56451i	−0.561150	−	0.150360i
$563$	−19.4908	+	19.4908i	−0.821439	+	0.821439i	−0.986314	−	0.164875i	$-0.947278\pi$
$563$	−19.4908	+	19.4908i	−0.821439	+	0.821439i	0.164875	+	0.986314i	$0.447278\pi$
$564$	10.5826	+	0.147618i	0.445606	+	0.00621585i
$565$	41.9487	−	17.4951i	1.76479	−	0.736024i
$566$			7.65275i			0.321669i
$567$	5.41355	−	23.1882i	0.227348	−	0.973814i
$568$	−4.35248	−	4.35248i	−0.182626	−	0.182626i
$569$			29.4265i			1.23362i	0.787112	+	0.616811i	$0.211576\pi$
$569$			29.4265i			1.23362i	−0.787112	+	0.616811i	$0.788424\pi$
$570$	−3.41389	+	7.98053i	−0.142992	+	0.334268i
$571$	−19.4442			−0.813715			−0.406858	−	0.913492i	$-0.633375\pi$
$571$	−19.4442			−0.813715			−0.406858	+	0.913492i	$0.633375\pi$
$572$	−0.0633873	+	0.236564i	−0.00265035	+	0.00989126i
$573$	6.62124	+	6.80857i	0.276606	+	0.284432i
$574$	−2.59505	−	29.3330i	−0.108315	−	1.22433i
$575$	0.0835614	+	17.2173i	0.00348475	+	0.718010i
$576$	−2.99883	−	0.0836789i	−0.124951	−	0.00348662i
$577$	−7.69885	+	28.7325i	−0.320507	+	1.19615i	0.598245	+	0.801314i	$0.295865\pi$
$577$	−7.69885	+	28.7325i	−0.320507	+	1.19615i	−0.918752	+	0.394836i	$0.870802\pi$
$578$	−0.754229	+	0.202095i	−0.0313718	+	0.00840604i
$579$	−0.359868	+	25.7985i	−0.0149556	+	1.07215i
$580$	1.15874	+	1.50253i	0.0481139	+	0.0623892i
$581$	5.54563	−	11.9229i	0.230072	−	0.494646i
$582$	−6.67540	+	23.5917i	−0.276704	+	0.977906i
$583$	0.482139	+	0.482139i	0.0199682	+	0.0199682i
$584$	3.63136	+	6.28970i	0.150267	+	0.260270i
$585$	0.804524	−	0.309483i	0.0332630	−	0.0127956i
$586$	14.8434	+	8.56982i	0.613174	+	0.354016i
$587$	−6.42058	+	23.9619i	−0.265006	+	0.989015i	0.697241	+	0.716837i	$0.254411\pi$
$587$	−6.42058	+	23.9619i	−0.265006	+	0.989015i	−0.962247	+	0.272178i	$0.912256\pi$
$588$	−11.0491	+	4.99172i	−0.455658	+	0.205855i
$589$	−10.6046	−	6.12257i	−0.436955	−	0.252276i
$590$	17.2663	−	22.6153i	0.710844	−	0.931059i
$591$	15.5848	+	0.217396i	0.641075	+	0.00894248i
$592$	0.426494	+	1.59170i	0.0175288	+	0.0654183i
$593$	−9.92623	−	37.0452i	−0.407621	−	1.52126i	−0.799169	−	0.601106i	$-0.794727\pi$
$593$	−9.92623	−	37.0452i	−0.407621	−	1.52126i	0.391548	−	0.920158i	$-0.371940\pi$
$594$	−8.36202	−	5.30619i	−0.343098	−	0.217716i
$595$	−22.7473	−	7.08728i	−0.932550	−	0.290550i
$596$	7.85304	+	13.6019i	0.321673	+	0.557154i
$597$	1.81058	−	6.39880i	0.0741021	−	0.261886i
$598$	−0.312884	+	0.312884i	−0.0127948	+	0.0127948i
$599$			25.2785i			1.03285i	0.856332	+	0.516427i	$0.172738\pi$
$599$			25.2785i			1.03285i	−0.856332	+	0.516427i	$0.827262\pi$
$600$	2.16527	+	8.38520i	0.0883966	+	0.342324i
$601$	8.00455	−	4.62143i	0.326512	−	0.188512i	−0.327779	−	0.944754i	$-0.606300\pi$
$601$	8.00455	−	4.62143i	0.326512	−	0.188512i	0.654292	+	0.756242i	$0.272967\pi$
$602$	−14.5343	+	5.30607i	−0.592374	+	0.216259i
$603$	−28.8205	−	30.4750i	−1.17366	−	1.24104i
$604$	5.72840	+	3.30729i	0.233085	+	0.134572i
$605$	10.0605	+	13.0454i	0.409017	+	0.530371i
$606$	−15.1565	−	9.03478i	−0.615690	−	0.367013i
$607$	−5.94403	+	22.1834i	−0.241261	+	0.900398i	0.733965	+	0.679187i	$0.237667\pi$
$607$	−5.94403	+	22.1834i	−0.241261	+	0.900398i	−0.975226	+	0.221211i	$0.928999\pi$
$608$	−0.580061	−	2.16482i	−0.0235246	−	0.0877949i
$609$	1.68898	−	3.50264i	0.0684409	−	0.141934i
$610$	10.3118	+	7.87288i	0.417514	+	0.318763i
$611$	0.392592	−	0.679990i	0.0158826	−	0.0275094i
$612$	−3.45133	+	11.5785i	−0.139512	+	0.468032i
$613$	−3.09511	+	11.5511i	−0.125010	+	0.466544i	−0.999840	−	0.0178860i	$-0.994306\pi$
$613$	−3.09511	+	11.5511i	−0.125010	+	0.466544i	0.874830	+	0.484430i	$0.160973\pi$
$614$	−30.4478			−1.22877
$615$	16.0363	+	40.0129i	0.646646	+	1.61347i
$616$	0.444378	+	5.02299i	0.0179045	+	0.202382i
$617$	11.3792	+	42.4679i	0.458111	+	1.70969i	0.678778	+	0.734344i	$0.262510\pi$
$617$	11.3792	+	42.4679i	0.458111	+	1.70969i	−0.220667	+	0.975349i	$0.570823\pi$
$618$	4.21405	+	1.19239i	0.169514	+	0.0479649i
$619$	2.51539	−	4.35678i	0.101102	−	0.175114i	−0.811037	−	0.584995i	$-0.801096\pi$
$619$	2.51539	−	4.35678i	0.101102	−	0.175114i	0.912139	+	0.409881i	$0.134430\pi$
$620$	−12.1088	+	1.62405i	−0.486300	+	0.0652235i
$621$	−8.29041	−	15.8564i	−0.332683	−	0.636296i
$622$	1.45903	+	1.45903i	0.0585017	+	0.0585017i
$623$	3.14160	+	2.63091i	0.125866	+	0.105405i
$624$	−0.113961	+	0.191177i	−0.00456209	+	0.00765322i
$625$	21.5283	−	12.7096i	0.861131	−	0.508382i
$626$		−	9.39616i		−	0.375546i
$627$	2.01437	−	7.11901i	0.0804460	−	0.284306i
$628$	−11.0742	+	11.0742i	−0.441909	+	0.441909i
$629$	6.63637			0.264609
$630$	13.3752	−	11.6664i	0.532879	−	0.464801i
$631$	33.7283			1.34270			0.671351	−	0.741140i	$-0.265714\pi$
$631$	33.7283			1.34270			0.671351	+	0.741140i	$0.265714\pi$
$632$	7.10731	−	7.10731i	0.282714	−	0.282714i
$633$	4.78022	−	1.20965i	0.189997	−	0.0480795i
$634$		−	11.7998i		−	0.468631i
$635$	24.4977	−	32.0869i	0.972160	−	1.27333i
$636$	0.302307	+	0.540896i	0.0119872	+	0.0214479i
$637$	−0.0766526	+	0.896220i	−0.00303708	+	0.0355095i
$638$	−1.14360	−	1.14360i	−0.0452755	−	0.0452755i
$639$	0.515072	−	18.4588i	0.0203759	−	0.730220i
$640$	−1.77729	−	1.35692i	−0.0702536	−	0.0536371i
$641$	19.8478	−	34.3774i	0.783942	−	1.35783i	−0.145688	−	0.989331i	$-0.546539\pi$
$641$	19.8478	−	34.3774i	0.783942	−	1.35783i	0.929629	−	0.368496i	$-0.120127\pi$
$642$	2.70326	+	10.6825i	0.106689	+	0.421606i
$643$	9.16800	+	34.2155i	0.361551	+	1.34933i	0.872037	+	0.489440i	$0.162799\pi$
$643$	9.16800	+	34.2155i	0.361551	+	1.34933i	−0.510486	+	0.859886i	$0.670535\pi$
$644$	−3.84229	+	8.26078i	−0.151407	+	0.325520i
$645$	18.1267	−	13.5802i	0.713739	−	0.534720i
$646$	−9.02593			−0.355120
$647$	2.85785	−	10.6656i	0.112354	−	0.419310i	−0.886722	−	0.462304i	$-0.847023\pi$
$647$	2.85785	−	10.6656i	0.112354	−	0.419310i	0.999075	+	0.0429940i	$0.0136896\pi$
$648$	−5.99918	−	6.70894i	−0.235670	−	0.263552i
$649$	−12.1261	+	21.0030i	−0.475991	+	0.824441i
$650$	0.621402	+	0.163276i	0.0243734	+	0.00640421i
$651$	14.0938	+	20.6944i	0.552378	+	0.811077i
$652$	−1.36612	−	5.09842i	−0.0535013	−	0.199670i
$653$	−1.00417	+	3.74760i	−0.0392961	+	0.146655i	−0.982787	−	0.184745i	$-0.940854\pi$
$653$	−1.00417	+	3.74760i	−0.0392961	+	0.146655i	0.943490	+	0.331400i	$0.107521\pi$
$654$	3.10141	−	1.73338i	0.121275	−	0.0677804i
$655$	24.2188	−	18.6773i	0.946305	−	0.729781i
$656$	−9.63896	−	5.56506i	−0.376338	−	0.217279i
$657$	−6.22403	+	20.8803i	−0.242822	+	0.814617i
$658$	2.79183	−	15.9238i	0.108837	−	0.620775i
$659$	−9.35772	+	5.40268i	−0.364525	+	0.210459i	−0.671064	−	0.741399i	$-0.734162\pi$
$659$	−9.35772	+	5.40268i	−0.364525	+	0.210459i	0.306539	+	0.951858i	$0.400829\pi$
$660$	−2.74606	−	6.85182i	−0.106890	−	0.266707i
$661$			32.1003i			1.24856i	0.781203	+	0.624278i	$0.214607\pi$
$661$			32.1003i			1.24856i	−0.781203	+	0.624278i	$0.785393\pi$
$662$	14.9717	−	14.9717i	0.581890	−	0.581890i
$663$	0.624908	+	0.642589i	0.0242694	+	0.0249561i
$664$	−2.48503	−	4.30419i	−0.0964377	−	0.167035i
$665$	11.2067	+	7.08601i	0.434577	+	0.274784i
$666$	−2.59022	+	4.21062i	−0.100369	+	0.163158i
$667$	−0.756273	−	2.82245i	−0.0292830	−	0.109286i
$668$	−4.98162	−	18.5917i	−0.192745	−	0.719333i
$669$	−20.3456	−	36.4029i	−0.786605	−	1.40742i
$670$	−4.15593	−	30.9862i	−0.160557	−	1.19710i
$671$	−9.57668	−	5.52910i	−0.369704	−	0.213449i
$672$	−0.854246	+	4.50225i	−0.0329532	+	0.173678i
$673$	−4.75708	+	17.7537i	−0.183372	+	0.684354i	0.811601	+	0.584212i	$0.198596\pi$
$673$	−4.75708	+	17.7537i	−0.183372	+	0.684354i	−0.994973	+	0.100142i	$0.968070\pi$
$674$	−3.50660	−	2.02454i	−0.135069	−	0.0779823i
$675$	−13.8136	+	22.0042i	−0.531686	+	0.846941i
$676$	−6.49174	−	11.2440i	−0.249682	−	0.432463i
$677$	26.2021	+	26.2021i	1.00703	+	1.00703i	0.999975	+	0.00705196i	$0.00224473\pi$
$677$	26.2021	+	26.2021i	1.00703	+	1.00703i	0.00705196	+	0.999975i	$0.497755\pi$
$678$	−34.1302	+	8.63678i	−1.31076	+	0.331694i
$679$	33.9582	+	15.7948i	1.30319	+	0.606147i
$680$	−7.13108	+	5.49941i	−0.273464	+	0.210893i
$681$	−32.2527	−	19.2258i	−1.23593	−	0.736735i
$682$	10.0586	−	2.69519i	0.385163	−	0.103204i
$683$	−8.12146	+	30.3097i	−0.310759	+	1.15977i	0.617115	+	0.786873i	$0.288301\pi$
$683$	−8.12146	+	30.3097i	−0.310759	+	1.15977i	−0.927874	+	0.372895i	$0.878365\pi$
$684$	3.52288	−	5.72673i	0.134701	−	0.218967i
$685$	−13.9337	−	33.4093i	−0.532378	−	1.27650i
$686$	4.84558	+	17.8751i	0.185005	+	0.682476i
$687$	4.54587	−	16.0656i	0.173436	−	0.612942i
$688$	−1.51359	+	5.64881i	−0.0577052	+	0.215359i
$689$	0.0459706			0.00175134
$690$	1.89300	−	13.2016i	0.0720653	−	0.502575i
$691$		−	27.5897i		−	1.04956i	−0.851237	−	0.524781i	$-0.824147\pi$
$691$		−	27.5897i		−	1.04956i	0.851237	−	0.524781i	$-0.175853\pi$
$692$	11.7540	+	11.7540i	0.446819	+	0.446819i
$693$	−10.0324	+	11.3226i	−0.381100	+	0.430110i
$694$		−	20.2369i		−	0.768183i
$695$	10.8461	−	26.3656i	0.411417	−	1.00010i
$696$	−0.717050	−	1.28297i	−0.0271797	−	0.0486307i
$697$	−31.6956	+	31.6956i	−1.20056	+	1.20056i
$698$	26.5932	+	7.12564i	1.00657	+	0.269709i
$699$	43.7305	+	26.0678i	1.65404	+	0.985974i
$700$	13.1715	−	1.22972i	0.497835	−	0.0464790i
$701$	−11.7518			−0.443858			−0.221929	−	0.975063i	$-0.571235\pi$
$701$	−11.7518			−0.443858			−0.221929	+	0.975063i	$0.571235\pi$
$702$	−0.651613	+	0.145682i	−0.0245936	+	0.00549842i
$703$	−3.56728	−	0.955851i	−0.134543	−	0.0360506i
$704$	1.65058	+	0.952963i	0.0622086	+	0.0359162i
$705$	2.81845	+	23.4972i	0.106149	+	0.884956i
$706$	7.97460	+	4.60414i	0.300128	+	0.173279i
$707$	−17.3051	+	20.6642i	−0.650825	+	0.777157i
$708$	−15.8003	+	15.3655i	−0.593810	+	0.577472i
$709$			19.7415i			0.741407i	0.928751	+	0.370704i	$0.120883\pi$
$709$			19.7415i			0.741407i	−0.928751	+	0.370704i	$0.879117\pi$
$710$	8.35232	−	10.9398i	0.313457	−	0.410564i
$711$	30.1420	+	0.841078i	1.13041	+	0.0315429i
$712$	1.49602	−	0.400858i	0.0560658	−	0.0150228i
$713$	18.1731	+	4.86948i	0.680589	+	0.182363i
$714$	16.6237	+	8.01597i	0.622126	+	0.299990i
$715$	−0.543121	−	0.0701629i	−0.0203116	−	0.00262394i
$716$	7.03822	+	12.1906i	0.263031	+	0.455582i
$717$	3.60106	+	14.2304i	0.134484	+	0.531443i
$718$	−11.2332	+	3.00991i	−0.419218	+	0.112329i
$719$	−15.4175	+	26.7039i	−0.574977	+	0.995889i	0.421067	+	0.907029i	$0.361656\pi$
$719$	−15.4175	+	26.7039i	−0.574977	+	0.995889i	−0.996044	+	0.0888596i	$0.971678\pi$
$720$	−0.705935	−	6.67096i	−0.0263086	−	0.248612i
$721$	2.82133	−	6.06575i	0.105072	−	0.225900i
$722$	−13.5008	−	3.61754i	−0.502449	−	0.134631i
$723$	−3.46245	−	13.6826i	−0.128770	−	0.508862i
$724$	−13.0807			−0.486140
$725$	−2.98552	+	3.01464i	−0.110879	+	0.111961i
$726$	−6.22563	−	11.1391i	−0.231055	−	0.413410i
$727$	9.09686	−	33.9500i	0.337384	−	1.25913i	−0.563877	−	0.825859i	$-0.690691\pi$
$727$	9.09686	−	33.9500i	0.337384	−	1.25913i	0.901261	−	0.433276i	$-0.142642\pi$
$728$	0.260649	+	0.218279i	0.00966031	+	0.00808996i
$729$	2.25699	−	26.9055i	0.0835921	−	0.996500i
$730$	−12.8600	+	9.91749i	−0.475969	+	0.367063i
$731$	20.3966	+	11.7760i	0.754396	+	0.435551i
$732$	−7.00617	−	7.20440i	−0.258956	−	0.266282i
$733$	−8.25158	−	2.21100i	−0.304779	−	0.0816653i	0.103188	−	0.994662i	$-0.467096\pi$
$733$	−8.25158	−	2.21100i	−0.304779	−	0.0816653i	−0.407967	+	0.912997i	$0.633762\pi$
$734$	18.4551	−	31.9651i	0.681189	−	1.17985i
$735$	−14.3470	−	23.0035i	−0.529199	−	0.848498i
$736$	1.72175	+	2.98215i	0.0634645	+	0.109924i
$737$	6.89695	+	25.7398i	0.254052	+	0.948136i
$738$	−7.73908	−	32.4811i	−0.284879	−	1.19565i
$739$	11.2226	−	6.47938i	0.412831	−	0.238348i	−0.279174	−	0.960240i	$-0.590061\pi$
$739$	11.2226	−	6.47938i	0.412831	−	0.238348i	0.692005	+	0.721892i	$0.256727\pi$
$740$	−3.40078	+	1.41833i	−0.125015	+	0.0521388i
$741$	−0.243357	−	0.435421i	−0.00893994	−	0.0159956i
$742$	0.889123	−	0.324594i	0.0326407	−	0.0119162i
$743$	−4.58590	+	1.22879i	−0.168241	+	0.0450799i	−0.341956	−	0.939716i	$-0.611089\pi$
$743$	−4.58590	+	1.22879i	−0.168241	+	0.0450799i	0.173715	+	0.984796i	$0.444423\pi$
$744$	9.46248	+	0.131994i	0.346911	+	0.00483913i
$745$	−27.8105	+	21.4472i	−1.01890	+	0.785763i
$746$	−9.10886	−	15.7770i	−0.333499	−	0.577637i
$747$	4.25925	−	14.2889i	0.155838	−	0.522802i
$748$	5.42757	−	5.42757i	0.198452	−	0.198452i
$749$	16.7667	−	1.48333i	0.612643	−	0.0541998i
$750$	−17.9399	+	7.29117i	−0.655071	+	0.266236i
$751$	−15.6200	−	27.0547i	−0.569982	−	0.987238i	−0.996567	−	0.0827907i	$-0.973617\pi$
$751$	−15.6200	−	27.0547i	−0.569982	−	0.987238i	0.426585	−	0.904448i	$-0.359717\pi$
$752$	−4.32073	−	4.32073i	−0.157561	−	0.157561i
$753$	−13.3047	+	12.9386i	−0.484850	+	0.471510i
$754$	−0.109039			−0.00397097
$755$	−5.62697	+	13.6785i	−0.204786	+	0.497811i
$756$	−11.5743	+	7.41863i	−0.420952	+	0.269813i
$757$	−23.4870	+	23.4870i	−0.853651	+	0.853651i	−0.990581	−	0.136929i	$-0.956277\pi$
$757$	−23.4870	+	23.4870i	−0.853651	+	0.853651i	0.136929	+	0.990581i	$0.456277\pi$
$758$	−9.01132	−	9.01132i	−0.327306	−	0.327306i
$759$	−0.158553	+	11.3664i	−0.00575509	+	0.412575i
$760$	4.62530	−	1.92902i	0.167777	−	0.0699731i
$761$	−1.18659	+	0.685080i	−0.0430139	+	0.0248341i	−0.521353	−	0.853341i	$-0.674572\pi$
$761$	−1.18659	+	0.685080i	−0.0430139	+	0.0248341i	0.478339	+	0.878175i	$0.341239\pi$
$762$	−22.4176	+	21.8008i	−0.812103	+	0.789759i
$763$	−1.86117	−	5.09808i	−0.0673788	−	0.184563i
$764$		−	5.48323i		−	0.198376i
$765$	−26.6863	−	4.20728i	−0.964847	−	0.152115i
$766$	13.7302	−	7.92711i	0.496091	−	0.286418i
$767$	0.423195	+	1.57939i	0.0152807	+	0.0570283i
$768$	1.20754	+	1.24171i	0.0435735	+	0.0448063i
$769$	17.7995	−	30.8297i	0.641868	−	1.11175i	−0.343147	−	0.939282i	$-0.611493\pi$
$769$	17.7995	−	30.8297i	0.641868	−	1.11175i	0.985015	−	0.172467i	$-0.0551737\pi$
$770$	−11.0000	+	2.47790i	−0.396412	+	0.0892972i
$771$	2.88999	−	1.61522i	0.104081	−	0.0581706i
$772$	10.5332	−	10.5332i	0.379098	−	0.379098i
$773$	−29.1413	−	7.80839i	−1.04814	−	0.280848i	−0.306657	−	0.951820i	$-0.599211\pi$
$773$	−29.1413	−	7.80839i	−1.04814	−	0.280848i	−0.741483	+	0.670972i	$0.765877\pi$
$774$	−15.4325	+	8.34491i	−0.554711	+	0.299951i
$775$	−7.19853	−	26.3530i	−0.258579	−	0.946628i
$776$	12.2590	−	7.07771i	0.440071	−	0.254075i
$777$	5.72122	+	4.92858i	0.205248	+	0.176812i
$778$	−10.5820	+	2.83543i	−0.379383	+	0.101655i
$779$	21.6027	−	12.4723i	0.773997	−	0.446867i
$780$	−0.457566	−	0.195736i	−0.0163835	−	0.00700849i
$781$	−5.86581	+	10.1599i	−0.209895	+	0.363549i
$782$	13.3955	−	3.58930i	0.479021	−	0.128353i
$783$	1.31836	−	4.20754i	0.0471145	−	0.150365i
$784$	6.58249	+	2.38134i	0.235089	+	0.0850479i
$785$	−27.8346	−	21.2512i	−0.993461	−	0.758486i
$786$	−20.6797	+	11.5579i	−0.737619	+	0.412255i
$787$	7.17749	+	7.17749i	0.255850	+	0.255850i	0.823364	−	0.567514i	$-0.192095\pi$
$787$	7.17749	+	7.17749i	0.255850	+	0.255850i	−0.567514	+	0.823364i	$0.692095\pi$
$788$	−6.36311	−	6.36311i	−0.226676	−	0.226676i
$789$	−28.3554	−	16.9027i	−1.00948	−	0.601750i
$790$	17.8640	+	13.6388i	0.635572	+	0.485246i
$791$	4.73918	+	53.5688i	0.168506	+	1.90469i
$792$	1.32524	+	5.56208i	0.0470905	+	0.197640i
$793$	−0.720147	+	0.192963i	−0.0255732	+	0.00685231i
$794$	−3.58623	+	6.21153i	−0.127271	+	0.220439i
$795$	−1.10889	+	0.830757i	−0.0393282	+	0.0294639i
$796$	−3.32501	+	1.91970i	−0.117852	+	0.0680419i
$797$	0.0307123	−	0.00822932i	0.00108788	−	0.000291498i	−0.258275	−	0.966071i	$-0.583154\pi$
$797$	0.0307123	−	0.00822932i	0.00108788	−	0.000291498i	0.259363	+	0.965780i	$0.416487\pi$
$798$	−7.78126	−	6.70321i	−0.275454	−	0.237291i
$799$	−21.3117	+	12.3043i	−0.753952	+	0.435295i
$800$	2.47896	−	4.34221i	0.0876443	−	0.153520i
$801$	3.95752	+	2.43453i	0.139832	+	0.0860198i
$802$	−2.32840	−	0.623893i	−0.0822187	−	0.0220304i
$803$	9.78793	−	9.78793i	0.345409	−	0.345409i
$804$	−0.337771	+	24.2143i	−0.0119122	+	0.853974i
$805$	−19.4498	−	6.05990i	−0.685516	−	0.213583i
$806$	0.351040	−	0.608018i	0.0123648	−	0.0214165i
$807$	10.8156	−	38.2236i	0.380727	−	1.34554i
$808$	2.63668	+	9.84022i	0.0927581	+	0.346178i
$809$	−20.3222	+	11.7330i	−0.714491	+	0.412512i	−0.812722	−	0.582652i	$-0.802015\pi$
$809$	−20.3222	+	11.7330i	−0.714491	+	0.412512i	0.0982306	+	0.995164i	$0.468682\pi$
$810$	13.0853	−	15.2897i	0.459770	−	0.537226i
$811$		−	47.9808i		−	1.68483i	−0.538827	−	0.842416i	$-0.681132\pi$
$811$		−	47.9808i		−	1.68483i	0.538827	−	0.842416i	$-0.318868\pi$
$812$	−2.10894	+	0.769914i	−0.0740092	+	0.0270187i
$813$	−8.38236	−	33.1248i	−0.293982	−	1.16174i
$814$	2.71990	−	1.57034i	0.0953325	−	0.0550402i
$815$	10.8932	−	4.54310i	0.381571	−	0.159138i
$816$	6.08901	−	3.40315i	0.213158	−	0.119134i
$817$	−9.26778	−	9.26778i	−0.324239	−	0.324239i
$818$	−2.73987	+	2.73987i	−0.0957975	+	0.0957975i
$819$	0.0615078	+	1.01807i	0.00214926	+	0.0355743i
$820$	9.46829	−	23.0163i	0.330647	−	0.803763i
$821$	−52.9361			−1.84748			−0.923742	−	0.383016i	$-0.874886\pi$
$821$	−52.9361			−1.84748			−0.923742	+	0.383016i	$0.874886\pi$
$822$	6.87862	+	27.1824i	0.239919	+	0.948095i
$823$	5.54836	+	5.54836i	0.193404	+	0.193404i	0.797165	−	0.603761i	$-0.206332\pi$
$823$	5.54836	+	5.54836i	0.193404	+	0.193404i	−0.603761	+	0.797165i	$0.706332\pi$
$824$	−1.26425	−	2.18975i	−0.0440423	−	0.0762835i
$825$	14.3689	−	8.12256i	0.500262	−	0.282791i
$826$	19.3369	+	27.5589i	0.672818	+	0.958898i
$827$	38.3952	−	38.3952i	1.33513	−	1.33513i	0.434421	−	0.900710i	$-0.356953\pi$
$827$	38.3952	−	38.3952i	1.33513	−	1.33513i	0.900710	−	0.434421i	$-0.143047\pi$
$828$	−2.95102	+	9.90002i	−0.102555	+	0.344050i
$829$	−19.6761	−	34.0801i	−0.683380	−	1.18365i	−0.973943	−	0.226794i	$-0.927176\pi$
$829$	−19.6761	−	34.0801i	−0.683380	−	1.18365i	0.290562	−	0.956856i	$-0.406158\pi$
$830$	8.80039	−	6.78677i	0.305466	−	0.235572i
$831$	−28.5032	+	47.8161i	−0.988765	+	1.65872i
$832$	0.124120	−	0.0332580i	0.00430310	−	0.00115301i
$833$	16.1248	−	23.1242i	0.558691	−	0.801207i
$834$	−11.3073	+	18.9688i	−0.391540	+	0.656836i
$835$	39.7225	−	16.5666i	1.37465	−	0.573312i
$836$	−3.69926	+	2.13577i	−0.127941	+	0.0738670i
$837$	19.2175	+	20.8971i	0.664255	+	0.722310i
$838$	−10.2716	−	38.3341i	−0.354826	−	1.32423i
$839$	14.2996	+	24.7676i	0.493676	+	0.855072i	0.999973	−	0.00728714i	$-0.00231959\pi$
$839$	14.2996	+	24.7676i	0.493676	+	0.855072i	−0.506298	+	0.862359i	$0.668986\pi$
$840$	−10.2319	−	0.554930i	−0.353035	−	0.0191469i
$841$	−14.1400	+	24.4912i	−0.487585	+	0.844522i
$842$	29.9463	+	8.02410i	1.03202	+	0.276529i
$843$	−6.49468	+	22.9530i	−0.223689	+	0.790542i
$844$	−2.46545	−	1.42343i	−0.0848643	−	0.0489964i
$845$	22.9896	−	17.7294i	0.790868	−	0.609909i
$846$	0.511315	−	18.3242i	0.0175794	−	0.629998i
$847$	−18.3104	+	6.68461i	−0.629152	+	0.229686i
$848$	0.0925928	−	0.345561i	0.00317965	−	0.0118666i
$849$	13.2537	+	0.184878i	0.454864	+	0.00634499i
$850$	−14.3076	−	14.1694i	−0.490747	−	0.486006i
$851$	5.67435			0.194514
$852$	−7.64313	+	7.43284i	−0.261849	+	0.254645i
$853$	3.27982	+	0.878825i	0.112299	+	0.0300904i	0.314531	−	0.949247i	$-0.398153\pi$
$853$	3.27982	+	0.878825i	0.112299	+	0.0300904i	−0.202232	+	0.979338i	$0.564819\pi$
$854$	−12.5660	+	8.81701i	−0.429998	+	0.301712i
$855$	13.7389	+	6.10525i	0.469859	+	0.208795i
$856$	3.18099	−	5.50964i	0.108724	−	0.188315i
$857$	−2.29807	+	0.615766i	−0.0785006	+	0.0210342i	−0.297856	−	0.954611i	$-0.596271\pi$
$857$	−2.29807	+	0.615766i	−0.0785006	+	0.0210342i	0.219355	+	0.975645i	$0.429605\pi$
$858$	0.408170	+	0.115494i	0.0139347	+	0.00394291i
$859$	5.83506	+	10.1066i	0.199090	+	0.344833i	0.948234	−	0.317574i	$-0.102868\pi$
$859$	5.83506	+	10.1066i	0.199090	+	0.344833i	−0.749144	+	0.662407i	$0.769535\pi$
$860$	−12.9689	−	1.67539i	−0.442237	−	0.0571302i
$861$	−50.8639	+	3.78569i	−1.73344	+	0.129016i
$862$	−6.07442	−	1.62764i	−0.206896	−	0.0554375i
$863$	4.86937	−	1.30474i	0.165755	−	0.0444140i	−0.174987	−	0.984571i	$-0.555988\pi$
$863$	4.86937	−	1.30474i	0.165755	−	0.0444140i	0.340742	+	0.940157i	$0.389322\pi$
$864$	−0.217369	+	5.19160i	−0.00739504	+	0.176622i
$865$	−22.5556	+	29.5432i	−0.766914	+	1.00450i
$866$		−	41.0241i		−	1.39406i
$867$	0.331784	+	1.31112i	0.0112680	+	0.0445279i
$868$	2.49634	−	14.2384i	0.0847312	−	0.483283i
$869$	−16.5904	−	9.57848i	−0.562791	−	0.324928i
$870$	2.63020	−	1.97050i	0.0891722	−	0.0668061i
$871$	1.55591	+	0.898305i	0.0527200	+	0.0304379i
$872$	−1.98139	−	0.530912i	−0.0670983	−	0.0179789i
$873$	40.6967	+	12.1309i	1.37738	+	0.410570i
$874$	−7.71751			−0.261049
$875$	6.64048	+	28.8254i	0.224489	+	0.974477i
$876$	10.9808	−	6.13714i	0.371005	−	0.207355i
$877$	−34.0157	−	9.11447i	−1.14863	−	0.307774i	−0.366213	−	0.930531i	$-0.619346\pi$
$877$	−34.0157	−	9.11447i	−1.14863	−	0.307774i	−0.782415	+	0.622757i	$0.786012\pi$
$878$	−7.42692	+	7.42692i	−0.250647	+	0.250647i
$879$	15.2005	−	25.4999i	0.512700	−	0.860091i
$880$	−1.62135	+	3.94132i	−0.0546558	+	0.132862i
$881$			46.9281i			1.58105i	0.612430	+	0.790524i	$0.290192\pi$
$881$			46.9281i			1.58105i	−0.612430	+	0.790524i	$0.709808\pi$
$882$	8.37814	+	19.2563i	0.282107	+	0.648395i
$883$	1.20209	+	1.20209i	0.0404535	+	0.0404535i	0.727044	−	0.686591i	$-0.240894\pi$
$883$	1.20209	+	1.20209i	0.0404535	+	0.0404535i	−0.686591	+	0.727044i	$0.740894\pi$
$884$		−	0.517504i		−	0.0174055i
$885$	−38.7500	−	30.4496i	−1.30257	−	1.02355i
$886$	17.9215			0.602085
$887$	2.61798	−	9.77042i	0.0879031	−	0.328059i	−0.907945	−	0.419089i	$-0.862349\pi$
$887$	2.61798	−	9.77042i	0.0879031	−	0.328059i	0.995848	+	0.0910306i	$0.0290161\pi$
$888$	2.76693	−	0.700184i	0.0928522	−	0.0234966i
$889$	27.4355	+	39.1009i	0.920156	+	1.31140i
$890$	1.33307	+	3.19636i	0.0446847	+	0.107142i
$891$	−9.39172	+	14.3538i	−0.314634	+	0.480872i
$892$	−6.23160	+	23.2566i	−0.208649	+	0.778690i
$893$	13.2280	−	3.54443i	0.442658	−	0.118610i
$894$	23.7465	−	13.2719i	0.794203	−	0.443880i
$895$	−24.9249	+	19.2218i	−0.833148	+	0.642515i
$896$	2.16580	−	1.51965i	0.0723541	−	0.0507679i
$897$	0.534320	+	0.549438i	0.0178404	+	0.0183452i
$898$	2.52026	+	2.52026i	0.0841021	+	0.0841021i
$899$	2.31814	+	4.01513i	0.0773142	+	0.133912i
$900$	14.5745	−	3.54741i	0.485816	−	0.118247i
$901$	−1.24775	−	0.720386i	−0.0415684	−	0.0239995i
$902$	−5.49038	+	20.4904i	−0.182810	+	0.682255i
$903$	8.83836	+	25.2999i	0.294122	+	0.841927i
$904$	17.6030	+	10.1631i	0.585467	+	0.338020i
$905$	−3.88816	−	28.9897i	−0.129247	−	0.963651i
$906$	5.86623	−	9.84102i	0.194892	−	0.326946i
$907$	−3.91922	−	14.6267i	−0.130136	−	0.485672i	0.869835	−	0.493343i	$-0.164225\pi$
$907$	−3.91922	−	14.6267i	−0.130136	−	0.485672i	−0.999971	+	0.00767029i	$0.997558\pi$
$908$	5.61080	+	20.9398i	0.186201	+	0.694911i
$909$	−16.0133	+	26.0310i	−0.531129	+	0.863393i
$910$	−0.406279	+	0.642539i	−0.0134680	+	0.0213000i
$911$	7.49062	+	12.9741i	0.248175	+	0.429852i	0.963020	−	0.269432i	$-0.0868358\pi$
$911$	7.49062	+	12.9741i	0.248175	+	0.429852i	−0.714844	+	0.699284i	$0.753502\pi$
$912$	−3.76322	+	0.952299i	−0.124613	+	0.0315338i
$913$	−6.69811	+	6.69811i	−0.221675	+	0.221675i
$914$		−	1.10502i		−	0.0365509i
$915$	13.8840	−	17.6687i	0.458991	−	0.584109i
$916$	−8.34819	+	4.81983i	−0.275832	+	0.159252i
$917$	12.4100	+	33.9932i	0.409813	+	1.12255i
$918$	19.9692	+	6.25701i	0.659080	+	0.206512i
$919$	8.10093	+	4.67707i	0.267225	+	0.154282i	0.627626	−	0.778515i	$-0.284027\pi$
$919$	8.10093	+	4.67707i	0.267225	+	0.154282i	−0.360401	+	0.932798i	$0.617360\pi$
$920$	−6.09734	+	4.70221i	−0.201023	+	0.155027i
$921$	−0.735569	+	52.7320i	−0.0242378	+	1.73758i
$922$	−1.92107	+	7.16955i	−0.0632672	+	0.236116i
$923$	0.204714	+	0.764003i	0.00673824	+	0.0251475i
$924$	8.70996	−	0.648264i	0.286537	−	0.0213263i
$925$	−4.15419	−	7.11530i	−0.136589	−	0.233950i
$926$	12.3710	−	21.4271i	0.406535	−	0.704140i
$927$	2.16688	−	7.26942i	0.0711698	−	0.238759i
$928$	−0.219624	+	0.819646i	−0.00720950	+	0.0269062i
$929$	32.7951			1.07597			0.537987	−	0.842953i	$-0.319185\pi$
$929$	32.7951			1.07597			0.537987	+	0.842953i	$0.319185\pi$
$930$	2.52014	+	21.0102i	0.0826386	+	0.688952i
$931$	−11.9983	+	10.1076i	−0.393228	+	0.331263i
$932$	−7.60753	−	28.3917i	−0.249193	−	0.930001i
$933$	2.56211	−	2.49162i	0.0838798	−	0.0815719i
$934$	−9.87107	+	17.0972i	−0.322991	+	0.559438i
$935$	13.6420	+	10.4154i	0.446142	+	0.340620i
$936$	0.328344	+	0.201985i	0.0107323	+	0.00660210i
$937$	4.64907	+	4.64907i	0.151879	+	0.151879i	0.778957	−	0.627078i	$-0.215749\pi$
$937$	4.64907	+	4.64907i	0.151879	+	0.151879i	−0.627078	+	0.778957i	$0.715749\pi$
$938$	36.4359	+	6.38809i	1.18967	+	0.208578i
$939$	−16.2730	−	0.226996i	−0.531051	−	0.00740773i
$940$	8.29139	−	10.8600i	0.270435	−	0.354215i
$941$			3.96146i			0.129140i	0.997913	+	0.0645700i	$0.0205676\pi$
$941$			3.96146i			0.129140i	−0.997913	+	0.0645700i	$0.979432\pi$
$942$	18.9117	+	19.4467i	0.616176	+	0.633609i
$943$	−27.1009	+	27.1009i	−0.882528	+	0.882528i
$944$	12.7246			0.414151
$945$	−19.8817	−	23.4460i	−0.646753	−	0.762700i
$946$	11.1460			0.362388
$947$	10.8303	−	10.8303i	0.351938	−	0.351938i	−0.508892	−	0.860830i	$-0.669945\pi$
$947$	10.8303	−	10.8303i	0.351938	−	0.351938i	0.860830	+	0.508892i	$0.169945\pi$
$948$	−12.1373	−	12.4807i	−0.394202	−	0.405355i
$949$		−	0.933252i		−	0.0302946i
$950$	5.64999	+	9.67730i	0.183310	+	0.313973i
$951$	−20.4359	−	0.285065i	−0.662680	−	0.00924386i
$952$	−3.65404	−	10.0091i	−0.118428	−	0.324397i
$953$	28.0246	+	28.0246i	0.907805	+	0.907805i	0.996095	−	0.0882895i	$-0.0281401\pi$
$953$	28.0246	+	28.0246i	0.907805	+	0.907805i	−0.0882895	+	0.996095i	$0.528140\pi$
$954$	0.944071	−	0.510492i	0.0305654	−	0.0165278i
$955$	12.1521	−	1.62986i	0.393231	−	0.0527410i
$956$	4.23744	−	7.33947i	0.137049	−	0.237375i
$957$	−2.00821	+	1.95295i	−0.0649161	+	0.0631300i
$958$	10.7105	+	39.9723i	0.346042	+	1.29145i
$959$	42.6640	−	3.77444i	1.37769	−	0.121883i
$960$	−2.39297	+	3.04528i	−0.0772327	+	0.0982859i
$961$	1.14802			0.0370330
$962$	0.0548040	−	0.204531i	0.00176695	−	0.00659435i
$963$	18.5662	−	4.42366i	0.598288	−	0.142550i
$964$	−4.07434	+	7.05696i	−0.131226	+	0.227289i
$965$	26.4749	+	20.2130i	0.852256	+	0.650679i
$966$	14.2139	+	6.85395i	0.457324	+	0.220522i
$967$	−12.4863	−	46.5997i	−0.401534	−	1.49855i	−0.810360	−	0.585933i	$-0.800728\pi$
$967$	−12.4863	−	46.5997i	−0.401534	−	1.49855i	0.408826	−	0.912612i	$-0.365938\pi$
$968$	−1.90683	+	7.11640i	−0.0612880	+	0.228730i
$969$	−0.218052	+	15.6318i	−0.00700483	+	0.502167i
$970$	19.3297	+	25.0648i	0.620639	+	0.804781i
$971$	−19.7579	−	11.4072i	−0.634060	−	0.366075i	0.148263	−	0.988948i	$-0.452632\pi$
$971$	−19.7579	−	11.4072i	−0.634060	−	0.366075i	−0.782323	+	0.622873i	$0.785965\pi$
$972$	−11.7640	+	10.2278i	−0.377331	+	0.328057i
$973$	25.8619	+	21.6578i	0.829093	+	0.694318i
$974$	−13.4016	+	7.73740i	−0.429414	+	0.247922i
$975$	0.297787	−	1.07225i	0.00953681	−	0.0343395i
$976$			5.80201i			0.185718i
$977$	9.45293	−	9.45293i	0.302426	−	0.302426i	−0.539536	−	0.841962i	$-0.681400\pi$
$977$	9.45293	−	9.45293i	0.302426	−	0.302426i	0.841962	+	0.539536i	$0.181400\pi$
$978$	−8.86287	+	2.24279i	−0.283403	+	0.0717164i
$979$	−1.47594	−	2.55641i	−0.0471714	−	0.0817033i
$980$	−3.32097	+	15.2961i	−0.106085	+	0.488616i
$981$	−2.92708	−	5.41315i	−0.0934544	−	0.172828i
$982$	−1.11383	−	4.15689i	−0.0355439	−	0.132652i
$983$	−4.42342	−	16.5084i	−0.141085	−	0.526537i	−0.999898	−	0.0142485i	$-0.995464\pi$
$983$	−4.42342	−	16.5084i	−0.141085	−	0.526537i	0.858813	−	0.512289i	$-0.171202\pi$
$984$	−9.87089	+	16.5591i	−0.314672	+	0.527885i
$985$	12.2107	−	15.9935i	0.389064	−	0.509594i
$986$	2.95956	+	1.70870i	0.0942517	+	0.0544162i
$987$	−27.5107	−	5.21981i	−0.875676	−	0.166149i
$988$	−0.0745372	+	0.278177i	−0.00237134	+	0.00884998i
$989$	17.4399	+	10.0689i	0.554556	+	0.320173i
$990$	−11.9329	+	4.59033i	−0.379252	+	0.145890i
$991$	−21.9476	−	38.0143i	−0.697188	−	1.20756i	−0.969438	−	0.245338i	$-0.921101\pi$
$991$	−21.9476	−	38.0143i	−0.697188	−	1.20756i	0.272250	−	0.962227i	$-0.412232\pi$
$992$	−3.86342	−	3.86342i	−0.122664	−	0.122664i
$993$	−25.5675	−	26.2908i	−0.811359	−	0.834315i
$994$	9.35395	+	13.3312i	0.296689	+	0.422840i
$995$	−5.24282	−	6.79836i	−0.166209	−	0.215522i
$996$	−7.51439	+	4.19979i	−0.238102	+	0.133075i
$997$	−27.4984	+	7.36817i	−0.870883	+	0.233352i	−0.666470	−	0.745532i	$-0.732195\pi$
$997$	−27.4984	+	7.36817i	−0.870883	+	0.233352i	−0.204413	+	0.978885i	$0.565529\pi$
$998$	−8.36787	+	31.2293i	−0.264880	+	0.988546i
$999$	7.22972	+	4.58768i	0.228738	+	0.145148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.103.18	✓	192
5.2	odd	4	inner	630.2.bw.a.607.20	yes	192
7.3	odd	6		630.2.cg.a.283.9	yes	192
9.7	even	3		630.2.cg.a.313.46	yes	192
35.17	even	12		630.2.cg.a.157.46	yes	192
45.7	odd	12		630.2.cg.a.187.9	yes	192
63.52	odd	6	inner	630.2.bw.a.493.20	yes	192
315.52	even	12	inner	630.2.bw.a.367.18	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.18	✓	192	1.1	even	1	trivial
630.2.bw.a.367.18	yes	192	315.52	even	12	inner
630.2.bw.a.493.20	yes	192	63.52	odd	6	inner
630.2.bw.a.607.20	yes	192	5.2	odd	4	inner
630.2.cg.a.157.46	yes	192	35.17	even	12
630.2.cg.a.187.9	yes	192	45.7	odd	12
630.2.cg.a.283.9	yes	192	7.3	odd	6
630.2.cg.a.313.46	yes	192	9.7	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.20754 + 1.24171i) q^{3} -1.00000i q^{4} +(2.21622 - 0.297244i) q^{5} +(-1.73188 - 0.0241584i) q^{6} +(-0.456895 + 2.60600i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0836789 + 2.99883i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.20754 + 1.24171i) q^{3} -1.00000i q^{4} +(2.21622 - 0.297244i) q^{5} +(-1.73188 - 0.0241584i) q^{6} +(-0.456895 + 2.60600i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.0836789 + 2.99883i) q^{9} +(-1.35692 + 1.77729i) q^{10} +(0.952963 - 1.65058i) q^{11} +(1.24171 - 1.20754i) q^{12} +(-0.0332580 - 0.124120i) q^{13} +(-1.51965 - 2.16580i) q^{14} +(3.04528 + 2.39297i) q^{15} -1.00000 q^{16} +(-1.04234 + 3.89008i) q^{17} +(-2.06133 - 2.17966i) q^{18} +(1.12059 - 1.94092i) q^{19} +(-0.297244 - 2.21622i) q^{20} +(-3.78762 + 2.57953i) q^{21} +(0.493290 + 1.84098i) q^{22} +(-0.891242 + 3.32616i) q^{23} +(-0.0241584 + 1.73188i) q^{24} +(4.82329 - 1.31752i) q^{25} +(0.111283 + 0.0642495i) q^{26} +(-3.82472 + 3.51732i) q^{27} +(2.60600 + 0.456895i) q^{28} +(-0.734875 + 0.424280i) q^{29} +(-3.84542 + 0.461252i) q^{30} -5.46370i q^{31} +(0.707107 - 0.707107i) q^{32} +(3.20028 - 0.809845i) q^{33} +(-2.01365 - 3.48775i) q^{34} +(-0.237963 + 5.91129i) q^{35} +(2.99883 + 0.0836789i) q^{36} +(-0.426494 - 1.59170i) q^{37} +(0.580061 + 2.16482i) q^{38} +(0.113961 - 0.191177i) q^{39} +(1.77729 + 1.35692i) q^{40} +(9.63896 + 5.56506i) q^{41} +(0.854246 - 4.50225i) q^{42} +(1.51359 - 5.64881i) q^{43} +(-1.65058 - 0.952963i) q^{44} +(0.705935 + 6.67096i) q^{45} +(-1.72175 - 2.98215i) q^{46} +(4.32073 + 4.32073i) q^{47} +(-1.20754 - 1.24171i) q^{48} +(-6.58249 - 2.38134i) q^{49} +(-2.47896 + 4.34221i) q^{50} +(-6.08901 + 3.40315i) q^{51} +(-0.124120 + 0.0332580i) q^{52} +(-0.0925928 + 0.345561i) q^{53} +(0.217369 - 5.19160i) q^{54} +(1.62135 - 3.94132i) q^{55} +(-2.16580 + 1.51965i) q^{56} +(3.76322 - 0.952299i) q^{57} +(0.219624 - 0.819646i) q^{58} -12.7246 q^{59} +(2.39297 - 3.04528i) q^{60} -5.80201i q^{61} +(3.86342 + 3.86342i) q^{62} +(-7.77673 - 1.58822i) q^{63} +1.00000i q^{64} +(-0.110601 - 0.265193i) q^{65} +(-1.69030 + 2.83559i) q^{66} +(-9.88643 + 9.88643i) q^{67} +(3.89008 + 1.04234i) q^{68} +(-5.20634 + 2.90982i) q^{69} +(-4.01165 - 4.34818i) q^{70} -6.15534 q^{71} +(-2.17966 + 2.06133i) q^{72} +(7.01525 + 1.87973i) q^{73} +(1.42708 + 0.823922i) q^{74} +(7.46031 + 4.39816i) q^{75} +(-1.94092 - 1.12059i) q^{76} +(3.86601 + 3.23757i) q^{77} +(0.0546003 + 0.215765i) q^{78} -10.0513i q^{79} +(-2.21622 + 0.297244i) q^{80} +(-8.98600 - 0.501878i) q^{81} +(-10.7509 + 2.88069i) q^{82} +(-4.80070 - 1.28634i) q^{83} +(2.57953 + 3.78762i) q^{84} +(-1.15376 + 8.93111i) q^{85} +(2.92404 + 5.06458i) q^{86} +(-1.41423 - 0.400164i) q^{87} +(1.84098 - 0.493290i) q^{88} +(0.774397 - 1.34130i) q^{89} +(-5.21625 - 4.21791i) q^{90} +(0.338653 - 0.0299603i) q^{91} +(3.32616 + 0.891242i) q^{92} +(6.78432 - 6.59765i) q^{93} -6.11044 q^{94} +(1.90655 - 4.63461i) q^{95} +(1.73188 + 0.0241584i) q^{96} +(3.66369 - 13.6731i) q^{97} +(6.33839 - 2.97066i) q^{98} +(4.87007 + 2.99590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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