LMFDB - Embedded newform 630.2.ce.b.557.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(53,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.53"); 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.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.6040479020157644046336.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$1.47240 + 0.912166i$ of defining polynomial
Character	$\chi$	$=$	630.557
Dual form			630.2.ce.b.233.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-1.87809 + 1.21358i) q^{5} +(-1.94831 + 1.79000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.12819 - 0.686141i) q^{10} +(-2.64338 - 1.52616i) q^{11} +(1.00000 - 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.11722 - 4.16954i) q^{17} +(5.47036 - 3.15831i) q^{19} +(-2.23326 + 0.111944i) q^{20} +(2.15831 + 2.15831i) q^{22} +(0.435690 - 1.62602i) q^{23} +(2.05446 - 4.55842i) q^{25} +(-1.22474 + 0.707107i) q^{26} +(-2.58228 + 0.576028i) q^{28} +5.88074 q^{29} +(1.50000 - 2.59808i) q^{31} +(-0.258819 - 0.965926i) q^{32} +4.31662i q^{34} +(1.48680 - 5.72620i) q^{35} +(1.83013 - 6.83013i) q^{37} +(-6.10139 + 1.63486i) q^{38} +(2.18614 + 0.469882i) q^{40} +2.82843i q^{41} +(-7.63325 + 7.63325i) q^{43} +(-1.52616 - 2.64338i) q^{44} +(-0.841688 + 1.45785i) q^{46} +(0.305836 + 0.0819485i) q^{47} +(0.591820 - 6.97494i) q^{49} +(-3.16426 + 3.87137i) q^{50} +(1.36603 - 0.366025i) q^{52} +(-1.57760 + 0.422716i) q^{53} +(6.81662 - 0.341688i) q^{55} +(2.64338 + 0.111944i) q^{56} +(-5.68036 - 1.52205i) q^{58} +(5.99269 - 10.3796i) q^{59} +(-3.15831 - 5.47036i) q^{61} +(-2.12132 + 2.12132i) q^{62} +1.00000i q^{64} +(-0.664513 + 3.09167i) q^{65} +(-14.5253 + 3.89204i) q^{67} +(1.11722 - 4.16954i) q^{68} +(-2.91819 + 5.14628i) q^{70} +1.86199i q^{71} +(-0.982183 - 3.66556i) q^{73} +(-3.53553 + 6.12372i) q^{74} +6.31662 q^{76} +(7.88194 - 1.75822i) q^{77} +(3.14649 - 1.81662i) q^{79} +(-1.99004 - 1.01969i) q^{80} +(0.732051 - 2.73205i) q^{82} +(-8.67372 - 8.67372i) q^{83} +(7.15831 + 6.47494i) q^{85} +(9.34878 - 5.39752i) q^{86} +(0.789997 + 2.94831i) q^{88} +(-6.32852 - 10.9613i) q^{89} +(-0.158312 + 3.73831i) q^{91} +(1.19033 - 1.19033i) q^{92} +(-0.274205 - 0.158312i) q^{94} +(-6.44097 + 12.5703i) q^{95} +(-5.84169 - 5.84169i) q^{97} +(-2.37690 + 6.58410i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{7} + 16 q^{13} + 8 q^{16} + 8 q^{22} - 12 q^{28} + 24 q^{31} - 40 q^{37} + 12 q^{40} - 16 q^{43} - 40 q^{46} + 8 q^{52} + 56 q^{55} - 20 q^{58} - 24 q^{61} - 32 q^{67} + 4 q^{70} + 48 q^{73}+ \cdots - 120 q^{97}+O(q^{100}) $ 16 * q + 12 * q^7 + 16 * q^13 + 8 * q^16 + 8 * q^22 - 12 * q^28 + 24 * q^31 - 40 * q^37 + 12 * q^40 - 16 * q^43 - 40 * q^46 + 8 * q^52 + 56 * q^55 - 20 * q^58 - 24 * q^61 - 32 * q^67 + 4 * q^70 + 48 * q^73 + 48 * q^76 - 16 * q^82 + 88 * q^85 - 4 * q^88 + 24 * q^91 - 120 * q^97

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.87809	+	1.21358i	−0.839908	+	0.542729i
$5$	−1.87809	+	1.21358i	−0.839908	+	0.542729i
$6$		0			0
$7$	−1.94831	+	1.79000i	−0.736392	+	0.676555i
$7$	−1.94831	+	1.79000i	−0.736392	+	0.676555i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.12819	−	0.686141i	0.672994	−	0.216977i
$11$	−2.64338	−	1.52616i	−0.797010	−	0.460154i	0.0454148	−	0.998968i	$-0.485539\pi$
$11$	−2.64338	−	1.52616i	−0.797010	−	0.460154i	−0.842424	+	0.538814i	$0.818872\pi$
$12$		0			0
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	1.00000	−	1.00000i	0.277350	−	0.277350i	0.832050	+	0.554700i	$0.187167\pi$
$14$	2.34521	−	1.22474i	0.626783	−	0.327327i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.11722	−	4.16954i	−0.270967	−	1.01126i	−0.958496	−	0.285105i	$-0.907971\pi$
$17$	−1.11722	−	4.16954i	−0.270967	−	1.01126i	0.687529	−	0.726157i	$-0.258695\pi$
$18$		0			0
$19$	5.47036	−	3.15831i	1.25499	−	0.724567i	0.282891	−	0.959152i	$-0.408707\pi$
$19$	5.47036	−	3.15831i	1.25499	−	0.724567i	0.972095	+	0.234586i	$0.0753733\pi$
$20$	−2.23326	+	0.111944i	−0.499373	+	0.0250314i
$21$		0			0
$22$	2.15831	+	2.15831i	0.460154	+	0.460154i
$23$	0.435690	−	1.62602i	0.0908476	−	0.339048i	−0.905510	−	0.424326i	$-0.860511\pi$
$23$	0.435690	−	1.62602i	0.0908476	−	0.339048i	0.996357	+	0.0852780i	$0.0271778\pi$
$24$		0			0
$25$	2.05446	−	4.55842i	0.410891	−	0.911684i
$26$	−1.22474	+	0.707107i	−0.240192	+	0.138675i
$27$		0			0
$28$	−2.58228	+	0.576028i	−0.488006	+	0.108859i
$29$	5.88074			1.09203			0.546013	−	0.837777i	$-0.316145\pi$
$29$	5.88074			1.09203			0.546013	+	0.837777i	$0.316145\pi$
$30$		0			0
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	−0.699301	−	0.714827i	$-0.746505\pi$
$31$	1.50000	−	2.59808i	0.269408	−	0.466628i	0.968709	+	0.248199i	$0.0798387\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$			4.31662i			0.740295i
$35$	1.48680	−	5.72620i	0.251315	−	0.967905i
$36$		0			0
$37$	1.83013	−	6.83013i	0.300871	−	1.12287i	−0.635571	−	0.772043i	$-0.719235\pi$
$37$	1.83013	−	6.83013i	0.300871	−	1.12287i	0.936442	−	0.350823i	$-0.114098\pi$
$38$	−6.10139	+	1.63486i	−0.989776	+	0.265210i
$39$		0			0
$40$	2.18614	+	0.469882i	0.345659	+	0.0742949i
$41$			2.82843i			0.441726i	0.975305	+	0.220863i	$0.0708874\pi$
$41$			2.82843i			0.441726i	−0.975305	+	0.220863i	$0.929113\pi$
$42$		0			0
$43$	−7.63325	+	7.63325i	−1.16406	+	1.16406i	−0.180481	+	0.983578i	$0.557766\pi$
$43$	−7.63325	+	7.63325i	−1.16406	+	1.16406i	−0.983578	+	0.180481i	$0.942234\pi$
$44$	−1.52616	−	2.64338i	−0.230077	−	0.398505i
$45$		0			0
$46$	−0.841688	+	1.45785i	−0.124100	+	0.214948i
$47$	0.305836	+	0.0819485i	0.0446108	+	0.0119534i	0.281055	−	0.959692i	$-0.409316\pi$
$47$	0.305836	+	0.0819485i	0.0446108	+	0.0119534i	−0.236445	+	0.971645i	$0.575982\pi$
$48$		0			0
$49$	0.591820	−	6.97494i	0.0845458	−	0.996420i
$50$	−3.16426	+	3.87137i	−0.447494	+	0.547494i
$51$		0			0
$52$	1.36603	−	0.366025i	0.189434	−	0.0507586i
$53$	−1.57760	+	0.422716i	−0.216700	+	0.0580645i	−0.365535	−	0.930797i	$-0.619114\pi$
$53$	−1.57760	+	0.422716i	−0.216700	+	0.0580645i	0.148836	+	0.988862i	$0.452447\pi$
$54$		0			0
$55$	6.81662	−	0.341688i	0.919153	−	0.0460731i
$56$	2.64338	+	0.111944i	0.353237	+	0.0149591i
$57$		0			0
$58$	−5.68036	−	1.52205i	−0.745868	−	0.199855i
$59$	5.99269	−	10.3796i	0.780181	−	1.35131i	−0.151655	−	0.988434i	$-0.548460\pi$
$59$	5.99269	−	10.3796i	0.780181	−	1.35131i	0.931836	−	0.362880i	$-0.118206\pi$
$60$		0			0
$61$	−3.15831	−	5.47036i	−0.404380	−	0.700408i	0.589869	−	0.807499i	$-0.299179\pi$
$61$	−3.15831	−	5.47036i	−0.404380	−	0.700408i	−0.994249	+	0.107092i	$0.965846\pi$
$62$	−2.12132	+	2.12132i	−0.269408	+	0.269408i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−0.664513	+	3.09167i	−0.0824227	+	0.383474i
$66$		0			0
$67$	−14.5253	+	3.89204i	−1.77455	+	0.475488i	−0.989572	−	0.144040i	$-0.953991\pi$
$67$	−14.5253	+	3.89204i	−1.77455	+	0.475488i	−0.784975	+	0.619528i	$0.787324\pi$
$68$	1.11722	−	4.16954i	0.135483	−	0.505631i
$69$		0			0
$70$	−2.91819	+	5.14628i	−0.348791	+	0.615098i
$71$			1.86199i			0.220977i	0.993877	+	0.110489i	$0.0352416\pi$
$71$			1.86199i			0.220977i	−0.993877	+	0.110489i	$0.964758\pi$
$72$		0			0
$73$	−0.982183	−	3.66556i	−0.114956	−	0.429021i	0.884328	−	0.466867i	$-0.154617\pi$
$73$	−0.982183	−	3.66556i	−0.114956	−	0.429021i	−0.999284	+	0.0378455i	$0.987951\pi$
$74$	−3.53553	+	6.12372i	−0.410997	+	0.711868i
$75$		0			0
$76$	6.31662			0.724567
$77$	7.88194	−	1.75822i	0.898231	−	0.200368i
$78$		0			0
$79$	3.14649	−	1.81662i	0.354007	−	0.204386i	−0.312441	−	0.949937i	$-0.601147\pi$
$79$	3.14649	−	1.81662i	0.354007	−	0.204386i	0.666449	+	0.745551i	$0.267813\pi$
$80$	−1.99004	−	1.01969i	−0.222493	−	0.114004i
$81$		0			0
$82$	0.732051	−	2.73205i	0.0808415	−	0.301705i
$83$	−8.67372	−	8.67372i	−0.952065	−	0.952065i	0.0468375	−	0.998903i	$-0.485086\pi$
$83$	−8.67372	−	8.67372i	−0.952065	−	0.952065i	−0.998903	+	0.0468375i	$0.985086\pi$
$84$		0			0
$85$	7.15831	+	6.47494i	0.776428	+	0.702306i
$86$	9.34878	−	5.39752i	1.00811	−	0.582030i
$87$		0			0
$88$	0.789997	+	2.94831i	0.0842140	+	0.314291i
$89$	−6.32852	−	10.9613i	−0.670821	−	1.16190i	−0.977672	−	0.210139i	$-0.932608\pi$
$89$	−6.32852	−	10.9613i	−0.670821	−	1.16190i	0.306850	−	0.951758i	$-0.400725\pi$
$90$		0			0
$91$	−0.158312	+	3.73831i	−0.0165956	+	0.391881i
$92$	1.19033	−	1.19033i	0.124100	−	0.124100i
$93$		0			0
$94$	−0.274205	−	0.158312i	−0.0282821	−	0.0163287i
$95$	−6.44097	+	12.5703i	−0.660830	+	1.28969i
$96$		0			0
$97$	−5.84169	−	5.84169i	−0.593134	−	0.593134i	0.345343	−	0.938477i	$-0.387763\pi$
$97$	−5.84169	−	5.84169i	−0.593134	−	0.593134i	−0.938477	+	0.345343i	$0.887763\pi$
$98$	−2.37690	+	6.58410i	−0.240103	+	0.665094i
$99$		0			0
$100$	4.05842	−	2.92048i	0.405842	−	0.292048i
$101$	14.6355	+	8.44984i	1.45629	+	0.840790i	0.998826	−	0.0484373i	$-0.0154241\pi$
$101$	14.6355	+	8.44984i	1.45629	+	0.840790i	0.457465	+	0.889228i	$0.348757\pi$
$102$		0			0
$103$	4.96311	+	1.32986i	0.489030	+	0.131035i	0.494904	−	0.868948i	$-0.335203\pi$
$103$	4.96311	+	1.32986i	0.489030	+	0.131035i	−0.00587425	+	0.999983i	$0.501870\pi$
$104$	−1.41421			−0.138675
$105$		0			0
$106$	1.63325			0.158635
$107$	13.1687	+	3.52854i	1.27307	+	0.341117i	0.831205	−	0.555966i	$-0.187651\pi$
$107$	13.1687	+	3.52854i	1.27307	+	0.341117i	0.441862	+	0.897083i	$0.354318\pi$
$108$		0			0
$109$	−14.9532	−	8.63325i	−1.43226	−	0.826915i	−0.434966	−	0.900447i	$-0.643240\pi$
$109$	−14.9532	−	8.63325i	−1.43226	−	0.826915i	−0.997293	+	0.0735313i	$0.976573\pi$
$110$	−6.67279	−	1.43423i	−0.636225	−	0.136748i
$111$		0			0
$112$	−2.52434	−	0.792287i	−0.238528	−	0.0748641i
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	0.637452	−	0.770490i	$-0.279988\pi$
$113$	−1.41421	−	1.41421i	−0.133038	−	0.133038i	−0.770490	+	0.637452i	$0.779988\pi$
$114$		0			0
$115$	1.15503	+	3.58255i	0.107707	+	0.334074i
$116$	5.09287	+	2.94037i	0.472861	+	0.273007i
$117$		0			0
$118$	−8.47494	+	8.47494i	−0.780181	+	0.780181i
$119$	9.64016	+	6.12372i	0.883712	+	0.561361i
$120$		0			0
$121$	−0.841688	−	1.45785i	−0.0765171	−	0.132531i
$122$	1.63486	+	6.10139i	0.148014	+	0.552394i
$123$		0			0
$124$	2.59808	−	1.50000i	0.233314	−	0.134704i
$125$	1.67355	+	11.0544i	0.149686	+	0.988734i
$126$		0			0
$127$	−4.79156	−	4.79156i	−0.425182	−	0.425182i	0.461801	−	0.886983i	$-0.347203\pi$
$127$	−4.79156	−	4.79156i	−0.425182	−	0.425182i	−0.886983	+	0.461801i	$0.847203\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$	1.44205	−	2.81433i	0.126476	−	0.246834i
$131$	−10.8288	+	6.25202i	−0.946118	+	0.546241i	−0.891873	−	0.452286i	$-0.850608\pi$
$131$	−10.8288	+	6.25202i	−0.946118	+	0.546241i	−0.0542449	+	0.998528i	$0.517275\pi$
$132$		0			0
$133$	−5.00458	+	15.9453i	−0.433952	+	1.38263i
$134$	15.0377			1.29906
$135$		0			0
$136$	−2.15831	+	3.73831i	−0.185074	+	0.320557i
$137$	4.65874	+	17.3867i	0.398023	+	1.48544i	0.816569	+	0.577247i	$0.195873\pi$
$137$	4.65874	+	17.3867i	0.398023	+	1.48544i	−0.418546	+	0.908196i	$0.637460\pi$
$138$		0			0
$139$		−	13.2665i		−	1.12525i	−0.826712	−	0.562625i	$-0.809792\pi$
$139$		−	13.2665i		−	1.12525i	0.826712	−	0.562625i	$-0.190208\pi$
$140$	4.15071	−	4.21564i	0.350799	−	0.356286i
$141$		0			0
$142$	0.481918	−	1.79854i	0.0404417	−	0.150930i
$143$	−4.16954	+	1.11722i	−0.348674	+	0.0934270i
$144$		0			0
$145$	−11.0446	+	7.13674i	−0.917202	+	0.592674i
$146$			3.79487i			0.314065i
$147$		0			0
$148$	5.00000	−	5.00000i	0.410997	−	0.410997i
$149$	3.53553	+	6.12372i	0.289642	+	0.501675i	0.973724	−	0.227730i	$-0.0731303\pi$
$149$	3.53553	+	6.12372i	0.289642	+	0.501675i	−0.684082	+	0.729405i	$0.739797\pi$
$150$		0			0
$151$	−8.34169	+	14.4482i	−0.678837	+	1.17578i	0.296495	+	0.955035i	$0.404182\pi$
$151$	−8.34169	+	14.4482i	−0.678837	+	1.17578i	−0.975331	+	0.220745i	$0.929151\pi$
$152$	−6.10139	−	1.63486i	−0.494888	−	0.132605i
$153$		0			0
$154$	−8.06843	−	0.341688i	−0.650173	−	0.0275340i
$155$	0.335831	+	6.69979i	0.0269746	+	0.538140i
$156$		0			0
$157$	5.03158	−	1.34821i	0.401564	−	0.107599i	−0.0523837	−	0.998627i	$-0.516682\pi$
$157$	5.03158	−	1.34821i	0.401564	−	0.107599i	0.453948	+	0.891028i	$0.350015\pi$
$158$	−3.50945	+	0.940354i	−0.279197	+	0.0748106i
$159$		0			0
$160$	1.65831	+	1.50000i	0.131101	+	0.118585i
$161$	2.06171	+	3.94786i	0.162485	+	0.311135i
$162$		0			0
$163$	10.8597	+	2.90986i	0.850600	+	0.227918i	0.657680	−	0.753297i	$-0.271538\pi$
$163$	10.8597	+	2.90986i	0.850600	+	0.227918i	0.192919	+	0.981215i	$0.438204\pi$
$164$	−1.41421	+	2.44949i	−0.110432	+	0.191273i
$165$		0			0
$166$	6.13325	+	10.6231i	0.476032	+	0.824512i
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	−0.891251	−	0.453510i	$-0.850171\pi$
$167$	−5.65685	+	5.65685i	−0.437741	+	0.437741i	0.453510	+	0.891251i	$0.350171\pi$
$168$		0			0
$169$			11.0000i			0.846154i
$170$	−5.23856	−	8.10702i	−0.401779	−	0.621780i
$171$		0			0
$172$	−10.4272	+	2.79396i	−0.795068	+	0.213038i
$173$	5.15043	−	19.2217i	0.391580	−	1.46140i	−0.435947	−	0.899972i	$-0.643587\pi$
$173$	5.15043	−	19.2217i	0.391580	−	1.46140i	0.827528	−	0.561425i	$-0.189747\pi$
$174$		0			0
$175$	4.15685	+	12.5587i	0.314228	+	0.949348i
$176$		−	3.05231i		−	0.230077i
$177$		0			0
$178$	3.27588	+	12.2258i	0.245538	+	0.916359i
$179$	−0.707107	+	1.22474i	−0.0528516	+	0.0915417i	−0.891241	−	0.453530i	$-0.850164\pi$
$179$	−0.707107	+	1.22474i	−0.0528516	+	0.0915417i	0.838389	+	0.545072i	$0.183498\pi$
$180$		0			0
$181$	24.6332			1.83098			0.915488	−	0.402346i	$-0.131805\pi$
$181$	24.6332			1.83098			0.915488	+	0.402346i	$0.131805\pi$
$182$	1.12046	−	3.56995i	0.0830542	−	0.264623i
$183$		0			0
$184$	−1.45785	+	0.841688i	−0.107474	+	0.0620500i
$185$	4.85175	+	15.0486i	0.356708	+	1.10640i
$186$		0			0
$187$	−3.41012	+	12.7267i	−0.249373	+	0.930672i
$188$	0.223888	+	0.223888i	0.0163287	+	0.0163287i
$189$		0			0
$190$	9.47494	−	10.4749i	0.687384	−	0.759932i
$191$	−17.9220	+	10.3473i	−1.29679	+	0.748702i	−0.979848	−	0.199743i	$-0.935989\pi$
$191$	−17.9220	+	10.3473i	−1.29679	+	0.748702i	−0.316942	+	0.948445i	$0.602656\pi$
$192$		0			0
$193$	−2.73602	−	10.2110i	−0.196943	−	0.735001i	−0.991755	−	0.128146i	$-0.959098\pi$
$193$	−2.73602	−	10.2110i	−0.196943	−	0.735001i	0.794813	−	0.606855i	$-0.207569\pi$
$194$	4.13070	+	7.15458i	0.296567	+	0.513669i
$195$		0			0
$196$	4.00000	−	5.74456i	0.285714	−	0.410326i
$197$	18.3139	−	18.3139i	1.30481	−	1.30481i	0.379701	−	0.925109i	$-0.376027\pi$
$197$	18.3139	−	18.3139i	1.30481	−	1.30481i	0.925109	−	0.379701i	$-0.123973\pi$
$198$		0			0
$199$	4.01251	+	2.31662i	0.284439	+	0.164221i	0.635431	−	0.772157i	$-0.280822\pi$
$199$	4.01251	+	2.31662i	0.284439	+	0.164221i	−0.350992	+	0.936378i	$0.614156\pi$
$200$	−4.67601	+	1.77057i	−0.330644	+	0.125198i
$201$		0			0
$202$	−11.9499	−	11.9499i	−0.840790	−	0.840790i
$203$	−11.4575	+	10.5265i	−0.804159	+	0.738816i
$204$		0			0
$205$	−3.43252	−	5.31205i	−0.239737	−	0.371009i
$206$	−4.44980	−	2.56910i	−0.310033	−	0.178997i
$207$		0			0
$208$	1.36603	+	0.366025i	0.0947168	+	0.0253793i
$209$	−19.2803			−1.33365
$210$		0			0
$211$	−4.94987			−0.340763			−0.170382	−	0.985378i	$-0.554500\pi$
$211$	−4.94987			−0.340763			−0.170382	+	0.985378i	$0.554500\pi$
$212$	−1.57760	−	0.422716i	−0.108350	−	0.0290323i
$213$		0			0
$214$	−11.8067	−	6.81662i	−0.807092	−	0.465975i
$215$	5.07240	−	23.5995i	0.345935	−	1.60947i
$216$		0			0
$217$	1.72808	+	7.74685i	0.117310	+	0.525891i
$218$	12.2093	+	12.2093i	0.826915	+	0.826915i
$219$		0			0
$220$	6.07421	+	3.11240i	0.409523	+	0.209838i
$221$	−5.28676	−	3.05231i	−0.355626	−	0.205321i
$222$		0			0
$223$	−16.1583	+	16.1583i	−1.08204	+	1.08204i	−0.0857215	+	0.996319i	$0.527320\pi$
$223$	−16.1583	+	16.1583i	−1.08204	+	1.08204i	−0.996319	+	0.0857215i	$0.972680\pi$
$224$	2.23326	+	1.41864i	0.149216	+	0.0947867i
$225$		0			0
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$	−4.31798	−	16.1149i	−0.286594	−	1.06958i	−0.947667	−	0.319262i	$-0.896565\pi$
$227$	−4.31798	−	16.1149i	−0.286594	−	1.06958i	0.661073	−	0.750322i	$-0.270102\pi$
$228$		0			0
$229$	22.5167	−	13.0000i	1.48794	−	0.859064i	0.488037	−	0.872823i	$-0.337713\pi$
$229$	22.5167	−	13.0000i	1.48794	−	0.859064i	0.999905	+	0.0137585i	$0.00437961\pi$
$230$	−0.188443	−	3.75942i	−0.0124256	−	0.247889i
$231$		0			0
$232$	−4.15831	−	4.15831i	−0.273007	−	0.273007i
$233$	5.42223	−	20.2360i	0.355222	−	1.32571i	−0.524983	−	0.851113i	$-0.675928\pi$
$233$	5.42223	−	20.2360i	0.355222	−	1.32571i	0.880205	−	0.474593i	$-0.157405\pi$
$234$		0			0
$235$	−0.673839	+	0.217249i	−0.0439564	+	0.0141718i
$236$	10.3796	−	5.99269i	0.675657	−	0.390091i
$237$		0			0
$238$	−7.72675	−	8.41012i	−0.500851	−	0.545147i
$239$	−0.966438			−0.0625137			−0.0312569	−	0.999511i	$-0.509951\pi$
$239$	−0.966438			−0.0625137			−0.0312569	+	0.999511i	$0.509951\pi$
$240$		0			0
$241$	3.29156	−	5.70115i	0.212028	−	0.367244i	−0.740321	−	0.672254i	$-0.765326\pi$
$241$	3.29156	−	5.70115i	0.212028	−	0.367244i	0.952349	+	0.305010i	$0.0986598\pi$
$242$	0.435690	+	1.62602i	0.0280072	+	0.104524i
$243$		0			0
$244$		−	6.31662i		−	0.404380i
$245$	7.35314	+	13.8178i	0.469775	+	0.882786i
$246$		0			0
$247$	2.31205	−	8.62867i	0.147112	−	0.549029i
$248$	−2.89778	+	0.776457i	−0.184009	+	0.0493051i
$249$		0			0
$250$	1.24456	−	11.1109i	0.0787131	−	0.702712i
$251$			17.1236i			1.08083i	0.841399	+	0.540415i	$0.181733\pi$
$251$			17.1236i			1.08083i	−0.841399	+	0.540415i	$0.818267\pi$
$252$		0			0
$253$	−3.63325	+	3.63325i	−0.228420	+	0.228420i
$254$	3.38815	+	5.86844i	0.212591	+	0.368219i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−20.5419	−	5.50418i	−1.28137	−	0.343341i	−0.446991	−	0.894538i	$-0.647504\pi$
$257$	−20.5419	−	5.50418i	−1.28137	−	0.343341i	−0.834375	+	0.551197i	$0.814171\pi$
$258$		0			0
$259$	8.66025	+	16.5831i	0.538122	+	1.03043i
$260$	−2.12132	+	2.34521i	−0.131559	+	0.145444i
$261$		0			0
$262$	12.0780	−	3.23628i	0.746179	−	0.199938i
$263$	−5.39288	+	1.44502i	−0.332539	+	0.0891037i	−0.421225	−	0.906956i	$-0.638400\pi$
$263$	−5.39288	+	1.44502i	−0.332539	+	0.0891037i	0.0886860	+	0.996060i	$0.471733\pi$
$264$		0			0
$265$	2.44987	−	2.70844i	0.150495	−	0.166378i
$266$	8.96100	−	14.1067i	0.549434	−	0.864937i
$267$		0			0
$268$	−14.5253	−	3.89204i	−0.887273	−	0.237744i
$269$	6.73524	−	11.6658i	0.410655	−	0.711275i	−0.584307	−	0.811533i	$-0.698634\pi$
$269$	6.73524	−	11.6658i	0.410655	−	0.711275i	0.994961	+	0.100258i	$0.0319669\pi$
$270$		0			0
$271$	−8.65831	−	14.9966i	−0.525955	−	0.910981i	−0.999543	−	0.0302342i	$-0.990375\pi$
$271$	−8.65831	−	14.9966i	−0.525955	−	0.910981i	0.473588	−	0.880747i	$-0.342959\pi$
$272$	3.05231	−	3.05231i	0.185074	−	0.185074i
$273$		0			0
$274$		−	18.0000i		−	1.08742i
$275$	−12.3876	+	8.91423i	−0.746999	+	0.537548i
$276$		0			0
$277$	18.1224	−	4.85588i	1.08887	−	0.291761i	0.330644	−	0.943756i	$-0.392734\pi$
$277$	18.1224	−	4.85588i	1.08887	−	0.291761i	0.758224	+	0.651994i	$0.226067\pi$
$278$	−3.43362	+	12.8145i	−0.205935	+	0.768560i
$279$		0			0
$280$	−5.10037	+	2.99771i	−0.304805	+	0.179147i
$281$		−	19.7990i		−	1.18111i	−0.806998	−	0.590554i	$-0.798909\pi$
$281$		−	19.7990i		−	1.18111i	0.806998	−	0.590554i	$-0.201091\pi$
$282$		0			0
$283$	−0.481918	−	1.79854i	−0.0286471	−	0.106912i	0.950122	−	0.311879i	$-0.100958\pi$
$283$	−0.481918	−	1.79854i	−0.0286471	−	0.106912i	−0.978769	+	0.204966i	$0.934292\pi$
$284$	−0.930994	+	1.61253i	−0.0552443	+	0.0956860i
$285$		0			0
$286$	4.31662			0.255247
$287$	−5.06288	−	5.51065i	−0.298852	−	0.325283i
$288$		0			0
$289$	−1.41444	+	0.816625i	−0.0832021	+	0.0480368i
$290$	12.5154	−	4.03502i	0.734927	−	0.236944i
$291$		0			0
$292$	0.982183	−	3.66556i	0.0574779	−	0.214511i
$293$	0.707107	+	0.707107i	0.0413096	+	0.0413096i	0.727460	−	0.686150i	$-0.240701\pi$
$293$	0.707107	+	0.707107i	0.0413096	+	0.0413096i	−0.686150	+	0.727460i	$0.740701\pi$
$294$		0			0
$295$	1.34169	+	26.7665i	0.0781161	+	1.55841i
$296$	−6.12372	+	3.53553i	−0.355934	+	0.205499i
$297$		0			0
$298$	−1.83013	−	6.83013i	−0.106016	−	0.395659i
$299$	−1.19033	−	2.06171i	−0.0688383	−	0.119231i
$300$		0			0
$301$	1.20844	−	28.5354i	0.0696532	−	1.64475i
$302$	11.7969	−	11.7969i	0.678837	−	0.678837i
$303$		0			0
$304$	5.47036	+	3.15831i	0.313747	+	0.181142i
$305$	12.5703	+	6.44097i	0.719774	+	0.368809i
$306$		0			0
$307$	−9.00000	−	9.00000i	−0.513657	−	0.513657i	0.401988	−	0.915645i	$-0.368319\pi$
$307$	−9.00000	−	9.00000i	−0.513657	−	0.513657i	−0.915645	+	0.401988i	$0.868319\pi$
$308$	7.70507	+	2.41831i	0.439037	+	0.137796i
$309$		0			0
$310$	1.40965	−	6.55842i	0.0800625	−	0.372493i
$311$	−12.6352	−	7.29496i	−0.716478	−	0.413659i	0.0969768	−	0.995287i	$-0.469083\pi$
$311$	−12.6352	−	7.29496i	−0.716478	−	0.413659i	−0.813455	+	0.581628i	$0.802416\pi$
$312$		0			0
$313$	−6.11288	−	1.63794i	−0.345520	−	0.0925819i	0.0818856	−	0.996642i	$-0.473906\pi$
$313$	−6.11288	−	1.63794i	−0.345520	−	0.0925819i	−0.427406	+	0.904060i	$0.640572\pi$
$314$	−5.20908			−0.293965
$315$		0			0
$316$	3.63325			0.204386
$317$	−3.81529	−	1.02230i	−0.214288	−	0.0574182i	0.150078	−	0.988674i	$-0.452048\pi$
$317$	−3.81529	−	1.02230i	−0.214288	−	0.0574182i	−0.364366	+	0.931256i	$0.618714\pi$
$318$		0			0
$319$	−15.5450	−	8.97494i	−0.870356	−	0.502500i
$320$	−1.21358	−	1.87809i	−0.0678411	−	0.104989i
$321$		0			0
$322$	−0.969672	−	4.34695i	−0.0540377	−	0.242246i
$323$	−19.2803	−	19.2803i	−1.07279	−	1.07279i
$324$		0			0
$325$	−2.50397	−	6.61288i	−0.138895	−	0.366816i
$326$	−9.73657	−	5.62141i	−0.539259	−	0.311341i
$327$		0			0
$328$	2.00000	−	2.00000i	0.110432	−	0.110432i
$329$	−0.742551	+	0.387785i	−0.0409382	+	0.0213793i
$330$		0			0
$331$	1.68338	+	2.91569i	0.0925267	+	0.160261i	0.908574	−	0.417725i	$-0.137172\pi$
$331$	1.68338	+	2.91569i	0.0925267	+	0.160261i	−0.816047	+	0.577986i	$0.803839\pi$
$332$	−3.17480	−	11.8485i	−0.174240	−	0.650272i
$333$		0			0
$334$	6.92820	−	4.00000i	0.379094	−	0.218870i
$335$	22.5565	−	24.9372i	1.23239	−	1.36246i
$336$		0			0
$337$	17.1082	+	17.1082i	0.931942	+	0.931942i	0.997827	−	0.0658849i	$-0.0209870\pi$
$337$	17.1082	+	17.1082i	0.931942	+	0.931942i	−0.0658849	+	0.997827i	$0.520987\pi$
$338$	2.84701	−	10.6252i	0.154857	−	0.577934i
$339$		0			0
$340$	2.96181	+	9.18662i	0.160627	+	0.498214i
$341$	−7.93015	+	4.57847i	−0.429441	+	0.247938i
$342$		0			0
$343$	11.3321	+	14.6487i	0.611874	+	0.790955i
$344$	10.7950			0.582030
$345$		0			0
$346$	−9.94987	+	17.2337i	−0.534909	+	0.926489i
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$			4.00000i			0.214115i	0.994253	+	0.107058i	$0.0341429\pi$
$349$			4.00000i			0.214115i	−0.994253	+	0.107058i	$0.965857\pi$
$350$	−0.764778	−	13.2066i	−0.0408791	−	0.705924i
$351$		0			0
$352$	−0.789997	+	2.94831i	−0.0421070	+	0.157145i
$353$	15.3580	−	4.11516i	0.817423	−	0.219028i	0.174203	−	0.984710i	$-0.444265\pi$
$353$	15.3580	−	4.11516i	0.817423	−	0.219028i	0.643219	+	0.765682i	$0.277598\pi$
$354$		0			0
$355$	−2.25967	−	3.49699i	−0.119931	−	0.185601i
$356$		−	12.6570i		−	0.670821i
$357$		0			0
$358$	1.00000	−	1.00000i	0.0528516	−	0.0528516i
$359$	−3.27620	−	5.67455i	−0.172911	−	0.299491i	0.766525	−	0.642214i	$-0.221984\pi$
$359$	−3.27620	−	5.67455i	−0.172911	−	0.299491i	−0.939436	+	0.342723i	$0.888651\pi$
$360$		0			0
$361$	10.4499	−	18.0997i	0.549993	−	0.952616i
$362$	−23.7939	−	6.37555i	−1.25058	−	0.335092i
$363$		0			0
$364$	−2.00626	+	3.15831i	−0.105156	+	0.165541i
$365$	6.29307	+	5.69230i	0.329394	+	0.297949i
$366$		0			0
$367$	8.84493	−	2.36999i	0.461702	−	0.123713i	−0.0204680	−	0.999791i	$-0.506516\pi$
$367$	8.84493	−	2.36999i	0.461702	−	0.123713i	0.482169	+	0.876078i	$0.339849\pi$
$368$	1.62602	−	0.435690i	0.0847619	−	0.0227119i
$369$		0			0
$370$	−0.791562	−	15.7916i	−0.0411513	−	0.820964i
$371$	2.31699	−	3.64748i	0.120292	−	0.189368i
$372$		0			0
$373$	22.2889	+	5.97230i	1.15408	+	0.309234i	0.784598	−	0.620005i	$-0.212870\pi$
$373$	22.2889	+	5.97230i	1.15408	+	0.309234i	0.369479	+	0.929239i	$0.379536\pi$
$374$	6.58785	−	11.4105i	0.340650	−	0.590022i
$375$		0			0
$376$	−0.158312	−	0.274205i	−0.00816434	−	0.0141410i
$377$	5.88074	−	5.88074i	0.302874	−	0.302874i
$378$		0			0
$379$			30.6332i			1.57352i	0.617256	+	0.786762i	$0.288244\pi$
$379$			30.6332i			1.57352i	−0.617256	+	0.786762i	$0.711756\pi$
$380$	−11.8632	+	7.66572i	−0.608569	+	0.393243i
$381$		0			0
$382$	19.9894	−	5.35614i	1.02275	−	0.274044i
$383$	−0.517638	+	1.93185i	−0.0264501	+	0.0987130i	−0.977889	−	0.209124i	$-0.932939\pi$
$383$	−0.517638	+	1.93185i	−0.0264501	+	0.0987130i	0.951439	+	0.307837i	$0.0996053\pi$
$384$		0			0
$385$	−12.6693	+	12.8675i	−0.645686	+	0.655786i
$386$			10.5712i			0.538058i
$387$		0			0
$388$	−2.13821	−	7.97989i	−0.108551	−	0.405118i
$389$	−13.1403	+	22.7596i	−0.666237	+	1.15396i	0.312711	+	0.949848i	$0.398763\pi$
$389$	−13.1403	+	22.7596i	−0.666237	+	1.15396i	−0.978948	+	0.204108i	$0.934570\pi$
$390$		0			0
$391$	−7.26650			−0.367483
$392$	−5.35051	+	4.51355i	−0.270241	+	0.227968i
$393$		0			0
$394$	−22.4298	+	12.9499i	−1.13000	+	0.652405i
$395$	−3.70477	+	7.23030i	−0.186407	+	0.363796i
$396$		0			0
$397$	1.92767	−	7.19417i	0.0967471	−	0.361065i	−0.900531	−	0.434791i	$-0.856822\pi$
$397$	1.92767	−	7.19417i	0.0967471	−	0.361065i	0.997279	+	0.0737258i	$0.0234890\pi$
$398$	−3.27620	−	3.27620i	−0.164221	−	0.164221i
$399$		0			0
$400$	4.97494	−	0.500000i	0.248747	−	0.0250000i
$401$	−18.3098	+	10.5712i	−0.914347	+	0.527898i	−0.881827	−	0.471573i	$-0.843686\pi$
$401$	−18.3098	+	10.5712i	−0.914347	+	0.527898i	−0.0325197	+	0.999471i	$0.510353\pi$
$402$		0			0
$403$	−1.09808	−	4.09808i	−0.0546991	−	0.204140i
$404$	8.44984	+	14.6355i	0.420395	+	0.728146i
$405$		0			0
$406$	13.7916	−	7.20241i	0.684464	−	0.357450i
$407$	−15.2616	+	15.2616i	−0.756488	+	0.756488i
$408$		0			0
$409$	−29.3146	−	16.9248i	−1.44952	−	0.836878i	−0.451063	−	0.892492i	$-0.648955\pi$
$409$	−29.3146	−	16.9248i	−1.44952	−	0.836878i	−0.998452	+	0.0556140i	$0.982288\pi$
$410$	1.94070	+	6.01944i	0.0958443	+	0.297279i
$411$		0			0
$412$	3.63325	+	3.63325i	0.178997	+	0.178997i
$413$	6.90391	+	30.9496i	0.339719	+	1.52293i
$414$		0			0
$415$	26.8163	+	5.76381i	1.31636	+	0.282934i
$416$	−1.22474	−	0.707107i	−0.0600481	−	0.0346688i
$417$		0			0
$418$	18.6234	+	4.99012i	0.910899	+	0.244075i
$419$	−6.17552			−0.301694			−0.150847	−	0.988557i	$-0.548200\pi$
$419$	−6.17552			−0.301694			−0.150847	+	0.988557i	$0.548200\pi$
$420$		0			0
$421$	−31.5831			−1.53927			−0.769634	−	0.638486i	$-0.779561\pi$
$421$	−31.5831			−1.53927			−0.769634	+	0.638486i	$0.779561\pi$
$422$	4.78121	+	1.28112i	0.232746	+	0.0623640i
$423$		0			0
$424$	1.41444	+	0.816625i	0.0686911	+	0.0396588i
$425$	−21.3018	−	3.47335i	−1.03329	−	0.168482i
$426$		0			0
$427$	15.9453	+	5.00458i	0.771647	+	0.242189i
$428$	9.64016	+	9.64016i	0.465975	+	0.465975i
$429$		0			0
$430$	−11.0076	+	21.4825i	−0.530831	+	1.03598i
$431$	−11.0841	−	6.39941i	−0.533902	−	0.308249i	0.208702	−	0.977979i	$-0.433076\pi$
$431$	−11.0841	−	6.39941i	−0.533902	−	0.308249i	−0.742604	+	0.669731i	$0.766409\pi$
$432$		0			0
$433$	−6.05013	+	6.05013i	−0.290750	+	0.290750i	−0.837377	−	0.546626i	$-0.815912\pi$
$433$	−6.05013	+	6.05013i	−0.290750	+	0.290750i	0.546626	+	0.837377i	$0.315912\pi$
$434$	0.335831	−	7.93015i	0.0161204	−	0.380659i
$435$		0			0
$436$	−8.63325	−	14.9532i	−0.413458	−	0.716130i
$437$	−2.75209	−	10.2709i	−0.131650	−	0.491325i
$438$		0			0
$439$	3.96910	−	2.29156i	0.189435	−	0.109370i	−0.402283	−	0.915515i	$-0.631783\pi$
$439$	3.96910	−	2.29156i	0.189435	−	0.109370i	0.591718	+	0.806145i	$0.298450\pi$
$440$	−5.06169	−	4.57847i	−0.241307	−	0.218270i
$441$		0			0
$442$	4.31662	+	4.31662i	0.205321	+	0.205321i
$443$	5.68105	−	21.2020i	0.269915	−	1.00734i	−0.689259	−	0.724515i	$-0.742064\pi$
$443$	5.68105	−	21.2020i	0.269915	−	1.00734i	0.959173	−	0.282820i	$-0.0912698\pi$
$444$		0			0
$445$	25.1879	+	12.9062i	1.19402	+	0.611813i
$446$	19.7898	−	11.4257i	0.937075	−	0.541020i
$447$		0			0
$448$	−1.79000	−	1.94831i	−0.0845694	−	0.0920490i
$449$	−23.4521			−1.10677			−0.553386	−	0.832925i	$-0.686665\pi$
$449$	−23.4521			−1.10677			−0.553386	+	0.832925i	$0.686665\pi$
$450$		0			0
$451$	4.31662	−	7.47661i	0.203262	−	0.352060i
$452$	−0.517638	−	1.93185i	−0.0243476	−	0.0908667i
$453$		0			0
$454$			16.6834i			0.782990i
$455$	−4.23940	−	7.21301i	−0.198746	−	0.338151i
$456$		0			0
$457$	−8.68997	+	32.4314i	−0.406500	+	1.51708i	0.394774	+	0.918778i	$0.370823\pi$
$457$	−8.68997	+	32.4314i	−0.406500	+	1.51708i	−0.801273	+	0.598299i	$0.795844\pi$
$458$	−25.1141	+	6.72930i	−1.17350	+	0.314439i
$459$		0			0
$460$	−0.790988	+	3.68009i	−0.0368800	+	0.171585i
$461$			0.0708883i			0.00330160i	0.999999	+	0.00165080i	$0.000525466\pi$
$461$			0.0708883i			0.00330160i	−0.999999	+	0.00165080i	$0.999475\pi$
$462$		0			0
$463$	27.6332	−	27.6332i	1.28423	−	1.28423i	0.345987	−	0.938239i	$-0.387544\pi$
$463$	27.6332	−	27.6332i	1.28423	−	1.28423i	0.938239	−	0.345987i	$-0.112456\pi$
$464$	2.94037	+	5.09287i	0.136503	+	0.236431i
$465$		0			0
$466$	−10.4749	+	18.1431i	−0.485242	+	0.840464i
$467$	37.2200	+	9.97307i	1.72234	+	0.461499i	0.978395	−	0.206745i	$-0.0662871\pi$
$467$	37.2200	+	9.97307i	1.72234	+	0.461499i	0.743942	+	0.668244i	$0.232954\pi$
$468$		0			0
$469$	21.3330	−	33.5831i	0.985067	−	1.55072i
$470$	0.707107	−	0.0354442i	0.0326164	−	0.00163492i
$471$		0			0
$472$	−11.5770	+	3.10204i	−0.532874	+	0.142783i
$473$	31.8271	−	8.52806i	1.46341	−	0.392120i
$474$		0			0
$475$	−3.15831	−	31.4248i	−0.144913	−	1.44187i
$476$	5.28676	+	10.1234i	0.242318	+	0.464004i
$477$		0			0
$478$	0.933508	+	0.250133i	0.0426977	+	0.0114408i
$479$	5.17364	−	8.96100i	0.236389	−	0.409438i	−0.723286	−	0.690548i	$-0.757369\pi$
$479$	5.17364	−	8.96100i	0.236389	−	0.409438i	0.959676	+	0.281110i	$0.0907026\pi$
$480$		0			0
$481$	−5.00000	−	8.66025i	−0.227980	−	0.394874i
$482$	−4.65497	+	4.65497i	−0.212028	+	0.212028i
$483$		0			0
$484$		−	1.68338i		−	0.0765171i
$485$	18.0606	+	3.88188i	0.820088	+	0.176267i
$486$		0			0
$487$	−15.6751	+	4.20012i	−0.710305	+	0.190326i	−0.595842	−	0.803102i	$-0.703181\pi$
$487$	−15.6751	+	4.20012i	−0.710305	+	0.190326i	−0.114463	+	0.993428i	$0.536515\pi$
$488$	−1.63486	+	6.10139i	−0.0740068	+	0.276197i
$489$		0			0
$490$	−3.52628	−	15.2501i	−0.159301	−	0.688929i
$491$			13.8474i			0.624923i	0.949930	+	0.312461i	$0.101153\pi$
$491$			13.8474i			0.624923i	−0.949930	+	0.312461i	$0.898847\pi$
$492$		0			0
$493$	−6.57011	−	24.5200i	−0.295903	−	1.10432i
$494$	−4.46653	+	7.73625i	−0.200959	+	0.348071i
$495$		0			0
$496$	3.00000			0.134704
$497$	−3.33295	−	3.62773i	−0.149503	−	0.162726i
$498$		0			0
$499$	−19.0526	+	11.0000i	−0.852910	+	0.492428i	−0.861632	−	0.507534i	$-0.830557\pi$
$499$	−19.0526	+	11.0000i	−0.852910	+	0.492428i	0.00872186	+	0.999962i	$0.497224\pi$
$500$	−4.07786	+	10.4101i	−0.182367	+	0.465556i
$501$		0			0
$502$	4.43190	−	16.5401i	0.197806	−	0.738220i
$503$	12.4331	+	12.4331i	0.554367	+	0.554367i	0.927698	−	0.373331i	$-0.121785\pi$
$503$	12.4331	+	12.4331i	0.554367	+	0.554367i	−0.373331	+	0.927698i	$0.621785\pi$
$504$		0			0
$505$	−37.7414	+	1.89181i	−1.67947	+	0.0841846i
$506$	4.44980	−	2.56910i	0.197818	−	0.114210i
$507$		0			0
$508$	−1.75383	−	6.54540i	−0.0778138	−	0.290405i
$509$	7.40690	+	12.8291i	0.328305	+	0.568641i	0.982176	−	0.187965i	$-0.0601893\pi$
$509$	7.40690	+	12.8291i	0.328305	+	0.568641i	−0.653871	+	0.756606i	$0.726856\pi$
$510$		0			0
$511$	8.47494	+	5.38354i	0.374909	+	0.238154i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	18.4173	+	10.6332i	0.812354	+	0.469013i
$515$	−10.9351	+	3.52552i	−0.481857	+	0.155353i
$516$		0			0
$517$	−0.683375	−	0.683375i	−0.0300548	−	0.0300548i
$518$	−4.07313	−	18.2595i	−0.178963	−	0.802277i
$519$		0			0
$520$	2.65602	−	1.71626i	0.116474	−	0.0752629i
$521$	−14.6355	−	8.44984i	−0.641195	−	0.370194i	0.143880	−	0.989595i	$-0.454042\pi$
$521$	−14.6355	−	8.44984i	−0.641195	−	0.370194i	−0.785075	+	0.619401i	$0.787375\pi$
$522$		0			0
$523$	15.4588	+	4.14217i	0.675966	+	0.181125i	0.580441	−	0.814302i	$-0.302880\pi$
$523$	15.4588	+	4.14217i	0.675966	+	0.181125i	0.0955252	+	0.995427i	$0.469547\pi$
$524$	−12.5040			−0.546241
$525$		0			0
$526$	5.58312			0.243436
$527$	−12.5086	−	3.35167i	−0.544884	−	0.146001i
$528$		0			0
$529$	17.4645	+	10.0831i	0.759325	+	0.438397i
$530$	−3.06739	+	1.98208i	−0.133239	+	0.0860959i
$531$		0			0
$532$	−12.3067	+	11.3067i	−0.533565	+	0.490209i
$533$	2.82843	+	2.82843i	0.122513	+	0.122513i
$534$		0			0
$535$	−29.0142	+	9.35433i	−1.25439	+	0.404423i
$536$	13.0230	+	7.51884i	0.562509	+	0.324765i
$537$		0			0
$538$	−9.52506	+	9.52506i	−0.410655	+	0.410655i
$539$	−12.2093	+	17.5342i	−0.525890	+	0.755252i
$540$		0			0
$541$	14.7916	+	25.6197i	0.635939	+	1.10148i	0.986315	+	0.164870i	$0.0527203\pi$
$541$	14.7916	+	25.6197i	0.635939	+	1.10148i	−0.350376	+	0.936609i	$0.613946\pi$
$542$	4.48187	+	16.7266i	0.192513	+	0.718468i
$543$		0			0
$544$	−3.73831	+	2.15831i	−0.160279	+	0.0925369i
$545$	38.5607	−	1.93288i	1.65176	−	0.0827954i
$546$		0			0
$547$	−3.31662	−	3.31662i	−0.141809	−	0.141809i	0.632639	−	0.774447i	$-0.281972\pi$
$547$	−3.31662	−	3.31662i	−0.141809	−	0.141809i	−0.774447	+	0.632639i	$0.781972\pi$
$548$	−4.65874	+	17.3867i	−0.199012	+	0.742722i
$549$		0			0
$550$	14.2727	−	5.40434i	0.608588	−	0.230442i
$551$	32.1698	−	18.5732i	1.37048	−	0.791246i
$552$		0			0
$553$	−2.87858	+	9.17155i	−0.122410	+	0.390014i
$554$	−18.7617			−0.797107
$555$		0			0
$556$	6.63325	−	11.4891i	0.281312	−	0.487247i
$557$	9.38646	+	35.0307i	0.397717	+	1.48430i	0.817103	+	0.576492i	$0.195579\pi$
$557$	9.38646	+	35.0307i	0.397717	+	1.48430i	−0.419386	+	0.907808i	$0.637754\pi$
$558$		0			0
$559$			15.2665i			0.645704i
$560$	5.70244	−	1.57549i	0.240972	−	0.0665768i
$561$		0			0
$562$	−5.12436	+	19.1244i	−0.216158	+	0.806712i
$563$	5.74714	−	1.53994i	0.242213	−	0.0649008i	−0.135670	−	0.990754i	$-0.543319\pi$
$563$	5.74714	−	1.53994i	0.242213	−	0.0649008i	0.377883	+	0.925853i	$0.376652\pi$
$564$		0			0
$565$	4.37228	+	0.939764i	0.183943	+	0.0395362i
$566$			1.86199i			0.0782652i
$567$		0			0
$568$	1.31662	−	1.31662i	0.0552443	−	0.0552443i
$569$	−8.44984	−	14.6355i	−0.354236	−	0.613554i	0.632751	−	0.774355i	$-0.281926\pi$
$569$	−8.44984	−	14.6355i	−0.354236	−	0.613554i	−0.986987	+	0.160801i	$0.948592\pi$
$570$		0			0
$571$	−20.4248	+	35.3768i	−0.854752	+	1.48047i	0.0221234	+	0.999755i	$0.492957\pi$
$571$	−20.4248	+	35.3768i	−0.854752	+	1.48047i	−0.876875	+	0.480718i	$0.840376\pi$
$572$	−4.16954	−	1.11722i	−0.174337	−	0.0467135i
$573$		0			0
$574$	3.46410	+	6.63325i	0.144589	+	0.276866i
$575$	−6.51696	−	5.32663i	−0.271776	−	0.222136i
$576$		0			0
$577$	−2.08327	+	0.558212i	−0.0867279	+	0.0232387i	−0.301922	−	0.953333i	$-0.597628\pi$
$577$	−2.08327	+	0.558212i	−0.0867279	+	0.0232387i	0.215194	+	0.976571i	$0.430962\pi$
$578$	1.57760	−	0.422716i	0.0656194	−	0.0175827i
$579$		0			0
$580$	−13.1332	+	0.658312i	−0.545329	+	0.0273349i
$581$	32.4250	+	1.37316i	1.34522	+	0.0569682i
$582$		0			0
$583$	4.81533	+	1.29026i	0.199430	+	0.0534372i
$584$	−1.89743	+	3.28645i	−0.0785163	+	0.135994i
$585$		0			0
$586$	−0.500000	−	0.866025i	−0.0206548	−	0.0357752i
$587$	−1.15488	+	1.15488i	−0.0476671	+	0.0476671i	−0.730539	−	0.682871i	$-0.760731\pi$
$587$	−1.15488	+	1.15488i	−0.0476671	+	0.0476671i	0.682871	+	0.730539i	$0.260731\pi$
$588$		0			0
$589$		−	18.9499i		−	0.780816i
$590$	5.63171	−	26.2017i	0.231854	−	1.07871i
$591$		0			0
$592$	6.83013	−	1.83013i	0.280716	−	0.0752178i
$593$	−7.32888	+	27.3518i	−0.300961	+	1.12320i	0.635406	+	0.772179i	$0.280833\pi$
$593$	−7.32888	+	27.3518i	−0.300961	+	1.12320i	−0.936367	+	0.351024i	$0.885834\pi$
$594$		0			0
$595$	−25.5367	+	0.198177i	−1.04690	+	0.00812446i
$596$			7.07107i			0.289642i
$597$		0			0
$598$	0.616158	+	2.29953i	0.0251966	+	0.0940349i
$599$	11.7615	−	20.3715i	0.480561	−	0.832356i	−0.519190	−	0.854659i	$-0.673766\pi$
$599$	11.7615	−	20.3715i	0.480561	−	0.832356i	0.999751	+	0.0223024i	$0.00709966\pi$
$600$		0			0
$601$	18.3668			0.749195			0.374598	−	0.927187i	$-0.377781\pi$
$601$	18.3668			0.749195			0.374598	+	0.927187i	$0.377781\pi$
$602$	−8.55277	+	27.2503i	−0.348585	+	1.11064i
$603$		0			0
$604$	−14.4482	+	8.34169i	−0.587890	+	0.339418i
$605$	3.34998	+	1.71651i	0.136196	+	0.0697862i
$606$		0			0
$607$	−3.96833	+	14.8100i	−0.161070	+	0.601120i	0.837439	+	0.546530i	$0.184052\pi$
$607$	−3.96833	+	14.8100i	−0.161070	+	0.601120i	−0.998509	+	0.0545897i	$0.982615\pi$
$608$	−4.46653	−	4.46653i	−0.181142	−	0.181142i
$609$		0			0
$610$	−10.4749	−	9.47494i	−0.424118	−	0.383629i
$611$	0.387785	−	0.223888i	0.0156881	−	0.00905752i
$612$		0			0
$613$	−5.99065	−	22.3574i	−0.241960	−	0.903007i	−0.974887	−	0.222700i	$-0.928513\pi$
$613$	−5.99065	−	22.3574i	−0.241960	−	0.903007i	0.732927	−	0.680307i	$-0.238154\pi$
$614$	6.36396	+	11.0227i	0.256829	+	0.444840i
$615$		0			0
$616$	−6.81662	−	4.33013i	−0.274650	−	0.174466i
$617$	−10.6420	+	10.6420i	−0.428433	+	0.428433i	−0.888094	−	0.459662i	$-0.847971\pi$
$617$	−10.6420	+	10.6420i	−0.428433	+	0.428433i	0.459662	+	0.888094i	$0.347971\pi$
$618$		0			0
$619$	4.83513	+	2.79156i	0.194340	+	0.112202i	0.594013	−	0.804456i	$-0.297543\pi$
$619$	4.83513	+	2.79156i	0.194340	+	0.112202i	−0.399673	+	0.916658i	$0.630876\pi$
$620$	−3.05906	+	5.97011i	−0.122855	+	0.239765i
$621$		0			0
$622$	10.3166	+	10.3166i	0.413659	+	0.413659i
$623$	31.9506	+	10.0280i	1.28007	+	0.401763i
$624$		0			0
$625$	−16.5584	−	18.7302i	−0.662337	−	0.749206i
$626$	5.48066	+	3.16426i	0.219051	+	0.126469i
$627$		0			0
$628$	5.03158	+	1.34821i	0.200782	+	0.0537994i
$629$	−30.5231			−1.21704
$630$		0			0
$631$	−31.5330			−1.25531			−0.627654	−	0.778492i	$-0.715985\pi$
$631$	−31.5330			−1.25531			−0.627654	+	0.778492i	$0.715985\pi$
$632$	−3.50945	−	0.940354i	−0.139598	−	0.0374053i
$633$		0			0
$634$	3.42069	+	1.97494i	0.135853	+	0.0784348i
$635$	14.8139	+	3.18406i	0.587873	+	0.126355i
$636$		0			0
$637$	−6.38312	−	7.56676i	−0.252908	−	0.299806i
$638$	12.6925	+	12.6925i	0.502500	+	0.502500i
$639$		0			0
$640$	0.686141	+	2.12819i	0.0271221	+	0.0841243i
$641$	−26.8830	−	15.5209i	−1.06181	−	0.613039i	−0.135881	−	0.990725i	$-0.543386\pi$
$641$	−26.8830	−	15.5209i	−1.06181	−	0.613039i	−0.925934	+	0.377686i	$0.876720\pi$
$642$		0			0
$643$	7.89975	−	7.89975i	0.311536	−	0.311536i	−0.533969	−	0.845504i	$-0.679300\pi$
$643$	7.89975	−	7.89975i	0.311536	−	0.311536i	0.845504	+	0.533969i	$0.179300\pi$
$644$	−0.188443	+	4.44980i	−0.00742571	+	0.175347i
$645$		0			0
$646$	13.6332	+	23.6135i	0.536393	+	0.929060i
$647$	8.33821	+	31.1186i	0.327809	+	1.22340i	0.911458	+	0.411393i	$0.134958\pi$
$647$	8.33821	+	31.1186i	0.327809	+	1.22340i	−0.583649	+	0.812006i	$0.698376\pi$
$648$		0			0
$649$	−31.6819	+	18.2916i	−1.24362	+	0.718007i
$650$	0.707107	+	7.03562i	0.0277350	+	0.275960i
$651$		0			0
$652$	7.94987	+	7.94987i	0.311341	+	0.311341i
$653$	−5.84494	+	21.8136i	−0.228730	+	0.853633i	0.752145	+	0.658997i	$0.229019\pi$
$653$	−5.84494	+	21.8136i	−0.228730	+	0.853633i	−0.980876	+	0.194636i	$0.937648\pi$
$654$		0			0
$655$	12.7502	−	24.8835i	0.498191	−	0.972278i
$656$	−2.44949	+	1.41421i	−0.0956365	+	0.0552158i
$657$		0			0
$658$	0.817615	−	0.182385i	0.0318740	−	0.00711010i
$659$	47.5646			1.85285			0.926427	−	0.376475i	$-0.122864\pi$
$659$	47.5646			1.85285			0.926427	+	0.376475i	$0.122864\pi$
$660$		0			0
$661$	−24.1082	+	41.7566i	−0.937700	+	1.62414i	−0.167952	+	0.985795i	$0.553715\pi$
$661$	−24.1082	+	41.7566i	−0.937700	+	1.62414i	−0.769747	+	0.638349i	$0.779618\pi$
$662$	−0.871379	−	3.25203i	−0.0338671	−	0.126394i
$663$		0			0
$664$			12.2665i			0.476032i
$665$	−9.95180	−	36.0202i	−0.385914	−	1.39680i
$666$		0			0
$667$	2.56218	−	9.56218i	0.0992079	−	0.370249i
$668$	−7.72741	+	2.07055i	−0.298982	+	0.0801121i
$669$		0			0
$670$	−28.2422	+	18.2494i	−1.09109	+	0.705036i
$671$			19.2803i			0.744309i
$672$		0			0
$673$	10.7414	−	10.7414i	0.414052	−	0.414052i	−0.469096	−	0.883147i	$-0.655420\pi$
$673$	10.7414	−	10.7414i	0.414052	−	0.414052i	0.883147	+	0.469096i	$0.155420\pi$
$674$	−12.0973	−	20.9532i	−0.465971	−	0.807086i
$675$		0			0
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	6.45564	+	1.72978i	0.248111	+	0.0664810i	0.380731	−	0.924686i	$-0.375672\pi$
$677$	6.45564	+	1.72978i	0.248111	+	0.0664810i	−0.132620	+	0.991167i	$0.542339\pi$
$678$		0			0
$679$	21.8380	+	0.924812i	0.838066	+	0.0354910i
$680$	−0.483219	−	9.64016i	−0.0185306	−	0.369683i
$681$		0			0
$682$	8.84493	−	2.36999i	0.338690	−	0.0907517i
$683$	31.6819	−	8.48913i	1.21227	−	0.324828i	0.404620	−	0.914485i	$-0.367404\pi$
$683$	31.6819	−	8.48913i	1.21227	−	0.324828i	0.807654	+	0.589657i	$0.200737\pi$
$684$		0			0
$685$	−29.8496	−	27.0000i	−1.14050	−	1.03162i
$686$	−7.15458	−	17.0825i	−0.273163	−	0.652213i
$687$		0			0
$688$	−10.4272	−	2.79396i	−0.397534	−	0.106519i
$689$	−1.15488	+	2.00031i	−0.0439975	+	0.0762059i
$690$		0			0
$691$	−24.0000	−	41.5692i	−0.913003	−	1.58137i	−0.809799	−	0.586707i	$-0.800424\pi$
$691$	−24.0000	−	41.5692i	−0.913003	−	1.58137i	−0.103204	−	0.994660i	$-0.532909\pi$
$692$	14.0712	−	14.0712i	0.534909	−	0.534909i
$693$		0			0
$694$		0			0
$695$	16.0999	+	24.9157i	0.610705	+	0.945106i
$696$		0			0
$697$	11.7932	−	3.15999i	0.446701	−	0.119693i
$698$	1.03528	−	3.86370i	0.0391858	−	0.146243i
$699$		0			0
$700$	−2.67941	+	12.9546i	−0.101272	+	0.489637i
$701$		−	29.3328i		−	1.10789i	−0.832555	−	0.553943i	$-0.813123\pi$
$701$		−	29.3328i		−	1.10789i	0.832555	−	0.553943i	$-0.186877\pi$
$702$		0			0
$703$	−11.5602	−	43.1433i	−0.436002	−	1.62718i
$704$	1.52616	−	2.64338i	0.0575192	−	0.0996262i
$705$		0			0
$706$	−15.8997			−0.598395
$707$	−43.6398	+	9.73469i	−1.64124	+	0.366111i
$708$		0			0
$709$	13.2212	−	7.63325i	0.496532	−	0.286673i	−0.230748	−	0.973013i	$-0.574117\pi$
$709$	13.2212	−	7.63325i	0.496532	−	0.286673i	0.727280	+	0.686341i	$0.240784\pi$
$710$	1.27759	+	3.96267i	0.0479470	+	0.148716i
$711$		0			0
$712$	−3.27588	+	12.2258i	−0.122769	+	0.458180i
$713$	−3.57098	−	3.57098i	−0.133734	−	0.133734i
$714$		0			0
$715$	6.47494	−	7.15831i	0.242149	−	0.267706i
$716$	−1.22474	+	0.707107i	−0.0457709	+	0.0264258i
$717$		0			0
$718$	1.69589	+	6.32914i	0.0632899	+	0.236201i
$719$	6.62329	+	11.4719i	0.247007	+	0.427829i	0.962694	−	0.270592i	$-0.0872196\pi$
$719$	6.62329	+	11.4719i	0.247007	+	0.427829i	−0.715687	+	0.698421i	$0.753886\pi$
$720$		0			0
$721$	−12.0501	+	6.29297i	−0.448770	+	0.234363i
$722$	−14.7784	+	14.7784i	−0.549993	+	0.549993i
$723$		0			0
$724$	21.3330	+	12.3166i	0.792835	+	0.457744i
$725$	12.0817	−	26.8069i	0.448704	−	0.995583i
$726$		0			0
$727$	−31.1082	−	31.1082i	−1.15374	−	1.15374i	−0.985797	−	0.167942i	$-0.946288\pi$
$727$	−31.1082	−	31.1082i	−1.15374	−	1.15374i	−0.167942	−	0.985797i	$-0.553712\pi$
$728$	2.75533	−	2.53144i	0.102119	−	0.0938213i
$729$		0			0
$730$	−4.60537	−	7.12711i	−0.170452	−	0.263786i
$731$	40.3552	+	23.2991i	1.49259	+	0.861748i
$732$		0			0
$733$	7.83211	+	2.09861i	0.289286	+	0.0775138i	0.400544	−	0.916278i	$-0.368821\pi$
$733$	7.83211	+	2.09861i	0.289286	+	0.0775138i	−0.111258	+	0.993792i	$0.535488\pi$
$734$	−9.15694			−0.337989
$735$		0			0
$736$	−1.68338			−0.0620500
$737$	44.3358	+	11.8797i	1.63313	+	0.437595i
$738$		0			0
$739$	12.0375	+	6.94987i	0.442808	+	0.255655i	0.704788	−	0.709418i	$-0.251042\pi$
$739$	12.0375	+	6.94987i	0.442808	+	0.255655i	−0.261980	+	0.965073i	$0.584375\pi$
$740$	−3.32257	+	15.4583i	−0.122140	+	0.568260i
$741$		0			0
$742$	−3.18208	+	2.92351i	−0.116818	+	0.107326i
$743$	−21.1423	−	21.1423i	−0.775636	−	0.775636i	0.203449	−	0.979086i	$-0.434785\pi$
$743$	−21.1423	−	21.1423i	−0.775636	−	0.775636i	−0.979086	+	0.203449i	$0.934785\pi$
$744$		0			0
$745$	−14.0717	−	7.21027i	−0.515546	−	0.264164i
$746$	−19.9837	−	11.5376i	−0.731655	−	0.422421i
$747$		0			0
$748$	−9.31662	+	9.31662i	−0.340650	+	0.340650i
$749$	−31.9728	+	16.6973i	−1.16826	+	0.610104i
$750$		0			0
$751$	−0.500000	−	0.866025i	−0.0182453	−	0.0316017i	0.856759	−	0.515718i	$-0.172475\pi$
$751$	−0.500000	−	0.866025i	−0.0182453	−	0.0316017i	−0.875004	+	0.484116i	$0.839141\pi$
$752$	0.0819485	+	0.305836i	0.00298836	+	0.0111527i
$753$		0			0
$754$	−7.20241	+	4.15831i	−0.262296	+	0.151437i
$755$	−1.86760	−	37.2584i	−0.0679689	−	1.35597i
$756$		0			0
$757$	−12.2665	−	12.2665i	−0.445833	−	0.445833i	0.448133	−	0.893967i	$-0.352089\pi$
$757$	−12.2665	−	12.2665i	−0.445833	−	0.445833i	−0.893967	+	0.448133i	$0.852089\pi$
$758$	7.92847	−	29.5894i	0.287975	−	1.07474i
$759$		0			0
$760$	13.4430	−	4.33409i	0.487629	−	0.157214i
$761$	2.12310	−	1.22577i	0.0769622	−	0.0444341i	−0.461025	−	0.887387i	$-0.652518\pi$
$761$	2.12310	−	1.22577i	0.0769622	−	0.0444341i	0.537987	+	0.842953i	$0.319185\pi$
$762$		0			0
$763$	44.5870	−	9.94599i	1.61416	−	0.360069i
$764$	−20.6945			−0.748702
$765$		0			0
$766$	1.00000	−	1.73205i	0.0361315	−	0.0625815i
$767$	−4.38695	−	16.3723i	−0.158404	−	0.591170i
$768$		0			0
$769$			35.6332i			1.28497i	0.766299	+	0.642484i	$0.222096\pi$
$769$			35.6332i			1.28497i	−0.766299	+	0.642484i	$0.777904\pi$
$770$	15.5679	−	9.14995i	0.561029	−	0.329741i
$771$		0			0
$772$	2.73602	−	10.2110i	0.0984714	−	0.367500i
$773$	−24.4056	+	6.53945i	−0.877807	+	0.235208i	−0.669461	−	0.742847i	$-0.733475\pi$
$773$	−24.4056	+	6.53945i	−0.877807	+	0.235208i	−0.208346	+	0.978055i	$0.566808\pi$
$774$		0			0
$775$	−8.76144	−	12.1753i	−0.314720	−	0.437348i
$776$			8.26139i			0.296567i
$777$		0			0
$778$	18.5831	−	18.5831i	0.666237	−	0.666237i
$779$	8.93306	+	15.4725i	0.320060	+	0.554360i
$780$		0			0
$781$	2.84169	−	4.92195i	0.101684	−	0.176121i
$782$	7.01890	+	1.88071i	0.250995	+	0.0672540i
$783$		0			0
$784$	6.33638	−	2.97494i	0.226299	−	0.106248i
$785$	−7.81362	+	8.63828i	−0.278880	+	0.308313i
$786$		0			0
$787$	29.9841	−	8.03421i	1.06882	−	0.286389i	0.318810	−	0.947819i	$-0.396717\pi$
$787$	29.9841	−	8.03421i	1.06882	−	0.286389i	0.750007	+	0.661430i	$0.230050\pi$
$788$	25.0172	−	6.70335i	0.891202	−	0.238797i
$789$		0			0
$790$	5.44987	−	6.02506i	0.193898	−	0.214362i
$791$	5.28676	+	0.223888i	0.187976	+	0.00796052i
$792$		0			0
$793$	−8.62867	−	2.31205i	−0.306413	−	0.0821031i
$794$	−3.72398	+	6.45012i	−0.132159	+	0.228906i
$795$		0			0
$796$	2.31662	+	4.01251i	0.0821106	+	0.142220i
$797$	27.2824	−	27.2824i	0.966392	−	0.966392i	−0.0330615	−	0.999453i	$-0.510526\pi$
$797$	27.2824	−	27.2824i	0.966392	−	0.966392i	0.999453	+	0.0330615i	$0.0105257\pi$
$798$		0			0
$799$		−	1.36675i		−	0.0483522i
$800$	−4.93483	−	0.804646i	−0.174473	−	0.0284485i
$801$		0			0
$802$	20.4219	−	5.47203i	0.721123	−	0.193224i
$803$	−2.99793	+	11.1884i	−0.105795	+	0.394831i
$804$		0			0
$805$	−8.66311	−	4.91241i	−0.305335	−	0.173140i
$806$			4.24264i			0.149441i
$807$		0			0
$808$	−4.37396	−	16.3238i	−0.153875	−	0.574270i
$809$	27.3178	−	47.3159i	0.960444	−	1.66354i	0.239057	−	0.971006i	$-0.423162\pi$
$809$	27.3178	−	47.3159i	0.960444	−	1.66354i	0.721387	−	0.692532i	$-0.243505\pi$
$810$		0			0
$811$	49.8997			1.75222			0.876109	−	0.482114i	$-0.160131\pi$
$811$	49.8997			1.75222			0.876109	+	0.482114i	$0.160131\pi$
$812$	−15.1857	+	3.38747i	−0.532915	+	0.118877i
$813$		0			0
$814$	18.6915	−	10.7916i	0.655138	−	0.378244i
$815$	−23.9269	+	7.71416i	−0.838123	+	0.270215i
$816$		0			0
$817$	−17.6484	+	65.8648i	−0.617440	+	2.30432i
$818$	23.9353	+	23.9353i	0.836878	+	0.836878i
$819$		0			0
$820$	−0.316625	−	6.31662i	−0.0110570	−	0.220586i
$821$	2.19421	−	1.26683i	0.0765783	−	0.0442125i	−0.461222	−	0.887285i	$-0.652589\pi$
$821$	2.19421	−	1.26683i	0.0765783	−	0.0442125i	0.537800	+	0.843072i	$0.319255\pi$
$822$		0			0
$823$	−7.64984	−	28.5496i	−0.266657	−	0.995176i	−0.961229	−	0.275753i	$-0.911073\pi$
$823$	−7.64984	−	28.5496i	−0.266657	−	0.995176i	0.694572	−	0.719423i	$-0.255594\pi$
$824$	−2.56910	−	4.44980i	−0.0894987	−	0.155016i
$825$		0			0
$826$	1.34169	−	31.6819i	0.0466833	−	1.10235i
$827$	−27.8011	+	27.8011i	−0.966737	+	0.966737i	−0.999464	−	0.0327270i	$-0.989581\pi$
$827$	−27.8011	+	27.8011i	−0.966737	+	0.966737i	0.0327270	+	0.999464i	$0.489581\pi$
$828$		0			0
$829$	14.5922	+	8.42481i	0.506808	+	0.292606i	0.731521	−	0.681819i	$-0.238811\pi$
$829$	14.5922	+	8.42481i	0.506808	+	0.292606i	−0.224713	+	0.974425i	$0.572144\pi$
$830$	−24.4108	−	12.5080i	−0.847310	−	0.434158i
$831$		0			0
$832$	1.00000	+	1.00000i	0.0346688	+	0.0346688i
$833$	−29.7435	+	5.32495i	−1.03055	+	0.184499i
$834$		0			0
$835$	3.75906	−	17.4891i	0.130087	−	0.605236i
$836$	−16.6973	−	9.64016i	−0.577487	−	0.333412i
$837$		0			0
$838$	5.96509	+	1.59834i	0.206061	+	0.0552138i
$839$	24.3476			0.840573			0.420287	−	0.907391i	$-0.361929\pi$
$839$	24.3476			0.840573			0.420287	+	0.907391i	$0.361929\pi$
$840$		0			0
$841$	5.58312			0.192522
$842$	30.5070	+	8.17431i	1.05134	+	0.281705i
$843$		0			0
$844$	−4.28672	−	2.47494i	−0.147555	−	0.0851909i
$845$	−13.3494	−	20.6590i	−0.459232	−	0.710691i
$846$		0			0
$847$	4.24941	+	1.33372i	0.146011	+	0.0458270i
$848$	−1.15488	−	1.15488i	−0.0396588	−	0.0396588i
$849$		0			0
$850$	19.6770	+	8.86832i	0.674915	+	0.304181i
$851$	−10.3085	−	5.95163i	−0.353372	−	0.204019i
$852$		0			0
$853$	15.6834	−	15.6834i	0.536989	−	0.536989i	−0.385655	−	0.922643i	$-0.626024\pi$
$853$	15.6834	−	15.6834i	0.536989	−	0.536989i	0.922643	+	0.385655i	$0.126024\pi$
$854$	−14.1067	−	8.96100i	−0.482721	−	0.306639i
$855$		0			0
$856$	−6.81662	−	11.8067i	−0.232987	−	0.403546i
$857$	−11.3061	−	42.1949i	−0.386209	−	1.44135i	−0.836253	−	0.548344i	$-0.815258\pi$
$857$	−11.3061	−	42.1949i	−0.386209	−	1.44135i	0.450044	−	0.893006i	$-0.351408\pi$
$858$		0			0
$859$	−11.1281	+	6.42481i	−0.379686	+	0.219212i	−0.677682	−	0.735355i	$-0.737015\pi$
$859$	−11.1281	+	6.42481i	−0.379686	+	0.219212i	0.297996	+	0.954567i	$0.403682\pi$
$860$	16.1926	−	17.9016i	0.552162	−	0.610438i
$861$		0			0
$862$	9.05013	+	9.05013i	0.308249	+	0.308249i
$863$	−6.67740	+	24.9204i	−0.227301	+	0.848300i	0.754168	+	0.656681i	$0.228040\pi$
$863$	−6.67740	+	24.9204i	−0.227301	+	0.848300i	−0.981469	+	0.191619i	$0.938626\pi$
$864$		0			0
$865$	13.6540	+	42.3505i	0.464251	+	1.43996i
$866$	7.40986	−	4.27808i	0.251797	−	0.145375i
$867$		0			0
$868$	−2.37686	+	7.57301i	−0.0806759	+	0.257045i
$869$	−11.0898			−0.376196
$870$		0			0
$871$	−10.6332	+	18.4173i	−0.360294	+	0.624047i
$872$	4.46890	+	16.6782i	0.151336	+	0.564794i
$873$		0			0
$874$			10.6332i			0.359675i
$875$	−23.0479	−	18.5417i	−0.779161	−	0.626824i
$876$		0			0
$877$	4.35561	−	16.2554i	0.147079	−	0.548904i	−0.852576	−	0.522604i	$-0.824961\pi$
$877$	4.35561	−	16.2554i	0.147079	−	0.548904i	0.999654	−	0.0263005i	$-0.00837268\pi$
$878$	−4.42696	+	1.18620i	−0.149403	+	0.0400323i
$879$		0			0
$880$	3.70422	+	5.73253i	0.124869	+	0.193243i
$881$			20.6945i			0.697217i	0.937268	+	0.348608i	$0.113346\pi$
$881$			20.6945i			0.697217i	−0.937268	+	0.348608i	$0.886654\pi$
$882$		0			0
$883$	3.68338	−	3.68338i	0.123955	−	0.123955i	−0.642408	−	0.766363i	$-0.722064\pi$
$883$	3.68338	−	3.68338i	0.123955	−	0.123955i	0.766363	+	0.642408i	$0.222064\pi$
$884$	−3.05231	−	5.28676i	−0.102660	−	0.177813i
$885$		0			0
$886$	−10.9749	+	19.0091i	−0.368710	+	0.638625i
$887$	−0.917508	−	0.245846i	−0.0308069	−	0.00825469i	0.243383	−	0.969930i	$-0.421743\pi$
$887$	−0.917508	−	0.245846i	−0.0308069	−	0.00825469i	−0.274190	+	0.961676i	$0.588410\pi$
$888$		0			0
$889$	17.9123	+	0.758564i	0.600760	+	0.0254414i
$890$	−20.9893	−	18.9856i	−0.703563	−	0.636397i
$891$		0			0
$892$	−22.0727	+	5.91435i	−0.739047	+	0.198027i
$893$	1.93185	−	0.517638i	0.0646470	−	0.0173221i
$894$		0			0
$895$	−0.158312	−	3.15831i	−0.00529180	−	0.105571i
$896$	1.22474	+	2.34521i	0.0409159	+	0.0783479i
$897$		0			0
$898$	22.6530	+	6.06984i	0.755939	+	0.202553i
$899$	8.82111	−	15.2786i	0.294201	−	0.509570i
$900$		0			0
$901$	3.52506	+	6.10559i	0.117437	+	0.203407i
$902$	−6.10463	+	6.10463i	−0.203262	+	0.203262i
$903$		0			0
$904$			2.00000i			0.0665190i
$905$	−46.2635	+	29.8944i	−1.53785	+	0.993723i
$906$		0			0
$907$	18.7603	−	5.02681i	0.622926	−	0.166912i	0.0664684	−	0.997789i	$-0.478827\pi$
$907$	18.7603	−	5.02681i	0.622926	−	0.166912i	0.556458	+	0.830876i	$0.312160\pi$
$908$	4.31798	−	16.1149i	0.143297	−	0.534792i
$909$		0			0
$910$	2.22808	+	8.06447i	0.0738603	+	0.267334i
$911$		−	6.48152i		−	0.214742i	−0.994219	−	0.107371i	$-0.965757\pi$
$911$		−	6.48152i		−	0.214742i	0.994219	−	0.107371i	$-0.0342433\pi$
$912$		0			0
$913$	9.69050	+	36.1654i	0.320709	+	1.19690i
$914$	16.7877	−	29.0772i	0.555289	−	0.961788i
$915$		0			0
$916$	26.0000			0.859064
$917$	9.90678	−	31.5644i	0.327151	−	1.04235i
$918$		0			0
$919$	−16.6853	+	9.63325i	−0.550397	+	0.317772i	−0.749282	−	0.662251i	$-0.769601\pi$
$919$	−16.6853	+	9.63325i	−0.550397	+	0.317772i	0.198885	+	0.980023i	$0.436268\pi$
$920$	1.71651	−	3.34998i	0.0565918	−	0.110445i
$921$		0			0
$922$	0.0183473	−	0.0684729i	0.000604235	−	0.00225503i
$923$	1.86199	+	1.86199i	0.0612881	+	0.0612881i
$924$		0			0
$925$	−27.3747	−	22.3747i	−0.900074	−	0.735675i
$926$	−33.8437	+	19.5397i	−1.11217	+	0.642113i
$927$		0			0
$928$	−1.52205	−	5.68036i	−0.0499637	−	0.186467i
$929$	−14.1776	−	24.5563i	−0.465151	−	0.805666i	0.534057	−	0.845448i	$-0.320667\pi$
$929$	−14.1776	−	24.5563i	−0.465151	−	0.805666i	−0.999208	+	0.0397827i	$0.987333\pi$
$930$		0			0
$931$	−18.7916	−	40.0246i	−0.615869	−	1.31175i
$932$	14.8138	−	14.8138i	0.485242	−	0.485242i
$933$		0			0
$934$	−33.3706	−	19.2665i	−1.09192	−	0.630419i
$935$	−9.04038	−	28.0404i	−0.295652	−	0.917021i
$936$		0			0
$937$	33.3747	+	33.3747i	1.09030	+	1.09030i	0.995496	+	0.0948079i	$0.0302237\pi$
$937$	33.3747	+	33.3747i	1.09030	+	1.09030i	0.0948079	+	0.995496i	$0.469776\pi$
$938$	−29.2981	+	26.9174i	−0.956616	+	0.878885i
$939$		0			0
$940$	−0.692186	−	0.148776i	−0.0225766	−	0.00485255i
$941$	−4.19452	−	2.42171i	−0.136737	−	0.0789454i	0.430071	−	0.902795i	$-0.358489\pi$
$941$	−4.19452	−	2.42171i	−0.136737	−	0.0789454i	−0.566808	+	0.823850i	$0.691822\pi$
$942$		0			0
$943$	4.59907	+	1.23232i	0.149766	+	0.0401297i
$944$	11.9854			0.390091
$945$		0			0
$946$	−32.9499			−1.07129
$947$	−23.7939	−	6.37555i	−0.773198	−	0.207178i	−0.149414	−	0.988775i	$-0.547739\pi$
$947$	−23.7939	−	6.37555i	−0.773198	−	0.207178i	−0.623784	+	0.781597i	$0.714405\pi$
$948$		0			0
$949$	−4.64774	−	2.68338i	−0.150872	−	0.0871060i
$950$	−5.08264	+	31.1715i	−0.164903	+	1.01134i
$951$		0			0
$952$	−2.48650	−	11.1468i	−0.0805879	−	0.361268i
$953$	24.1237	+	24.1237i	0.781445	+	0.781445i	0.980075	−	0.198630i	$-0.0636492\pi$
$953$	24.1237	+	24.1237i	0.781445	+	0.781445i	−0.198630	+	0.980075i	$0.563649\pi$
$954$		0			0
$955$	21.1019	−	41.1829i	0.682842	−	1.33265i
$956$	−0.836960	−	0.483219i	−0.0270692	−	0.0156284i
$957$		0			0
$958$	−7.31662	+	7.31662i	−0.236389	+	0.236389i
$959$	−40.1988	−	25.5355i	−1.29809	−	0.824583i
$960$		0			0
$961$	11.0000	+	19.0526i	0.354839	+	0.614599i
$962$	2.58819	+	9.65926i	0.0834466	+	0.311427i
$963$		0			0
$964$	5.70115	−	3.29156i	0.183622	−	0.106014i
$965$	17.5303	+	15.8567i	0.564320	+	0.510446i
$966$		0			0
$967$	27.6913	+	27.6913i	0.890493	+	0.890493i	0.994569	−	0.104077i	$-0.0331888\pi$
$967$	27.6913	+	27.6913i	0.890493	+	0.890493i	−0.104077	+	0.994569i	$0.533189\pi$
$968$	−0.435690	+	1.62602i	−0.0140036	+	0.0522621i
$969$		0			0
$970$	−16.4405	−	8.42403i	−0.527872	−	0.270479i
$971$	−24.9538	+	14.4071i	−0.800805	+	0.462345i	−0.843753	−	0.536732i	$-0.819659\pi$
$971$	−24.9538	+	14.4071i	−0.800805	+	0.462345i	0.0429474	+	0.999077i	$0.486325\pi$
$972$		0			0
$973$	23.7470	+	25.8472i	0.761294	+	0.828625i
$974$	16.2280			0.519979
$975$		0			0
$976$	3.15831	−	5.47036i	0.101095	−	0.175102i
$977$	−3.02388	−	11.2853i	−0.0967425	−	0.361048i	0.900535	−	0.434783i	$-0.143175\pi$
$977$	−3.02388	−	11.2853i	−0.0967425	−	0.361048i	−0.997278	+	0.0737348i	$0.976508\pi$
$978$		0			0
$979$			38.6332i			1.23472i
$980$	−0.540890	+	15.6431i	−0.0172781	+	0.499701i
$981$		0			0
$982$	3.58396	−	13.3755i	0.114369	−	0.426830i
$983$	8.43591	−	2.26040i	0.269064	−	0.0720954i	−0.121764	−	0.992559i	$-0.538855\pi$
$983$	8.43591	−	2.26040i	0.269064	−	0.0720954i	0.390828	+	0.920464i	$0.372189\pi$
$984$		0			0
$985$	−12.1698	+	56.6205i	−0.387763	+	1.80408i
$986$			25.3850i			0.808422i
$987$		0			0
$988$	6.31662	−	6.31662i	0.200959	−	0.200959i
$989$	9.08606	+	15.7375i	0.288920	+	0.500424i
$990$		0			0
$991$	−8.65831	+	14.9966i	−0.275040	+	0.476384i	−0.970145	−	0.242524i	$-0.922025\pi$
$991$	−8.65831	+	14.9966i	−0.275040	+	0.476384i	0.695105	+	0.718908i	$0.255358\pi$
$992$	−2.89778	−	0.776457i	−0.0920045	−	0.0246525i
$993$		0			0
$994$	2.28046	+	4.36675i	0.0723318	+	0.138505i
$995$	−10.3473	+	0.518663i	−0.328031	+	0.0164427i
$996$		0			0
$997$	11.3607	−	3.04410i	0.359798	−	0.0964075i	−0.0743918	−	0.997229i	$-0.523702\pi$
$997$	11.3607	−	3.04410i	0.359798	−	0.0964075i	0.434189	+	0.900822i	$0.357035\pi$
$998$	21.2504	−	5.69402i	0.672669	−	0.180241i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.b.557.1	yes	16
3.2	odd	2	inner	630.2.ce.b.557.4	yes	16
5.3	odd	4	inner	630.2.ce.b.53.1	✓	16
7.2	even	3	inner	630.2.ce.b.107.4	yes	16
15.8	even	4	inner	630.2.ce.b.53.4	yes	16
21.2	odd	6	inner	630.2.ce.b.107.1	yes	16
35.23	odd	12	inner	630.2.ce.b.233.4	yes	16
105.23	even	12	inner	630.2.ce.b.233.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.b.53.1	✓	16	5.3	odd	4	inner
630.2.ce.b.53.4	yes	16	15.8	even	4	inner
630.2.ce.b.107.1	yes	16	21.2	odd	6	inner
630.2.ce.b.107.4	yes	16	7.2	even	3	inner
630.2.ce.b.233.1	yes	16	105.23	even	12	inner
630.2.ce.b.233.4	yes	16	35.23	odd	12	inner
630.2.ce.b.557.1	yes	16	1.1	even	1	trivial
630.2.ce.b.557.4	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-1.87809 + 1.21358i) q^{5} +(-1.94831 + 1.79000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.12819 - 0.686141i) q^{10} +(-2.64338 - 1.52616i) q^{11} +(1.00000 - 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.11722 - 4.16954i) q^{17} +(5.47036 - 3.15831i) q^{19} +(-2.23326 + 0.111944i) q^{20} +(2.15831 + 2.15831i) q^{22} +(0.435690 - 1.62602i) q^{23} +(2.05446 - 4.55842i) q^{25} +(-1.22474 + 0.707107i) q^{26} +(-2.58228 + 0.576028i) q^{28} +5.88074 q^{29} +(1.50000 - 2.59808i) q^{31} +(-0.258819 - 0.965926i) q^{32} +4.31662i q^{34} +(1.48680 - 5.72620i) q^{35} +(1.83013 - 6.83013i) q^{37} +(-6.10139 + 1.63486i) q^{38} +(2.18614 + 0.469882i) q^{40} +2.82843i q^{41} +(-7.63325 + 7.63325i) q^{43} +(-1.52616 - 2.64338i) q^{44} +(-0.841688 + 1.45785i) q^{46} +(0.305836 + 0.0819485i) q^{47} +(0.591820 - 6.97494i) q^{49} +(-3.16426 + 3.87137i) q^{50} +(1.36603 - 0.366025i) q^{52} +(-1.57760 + 0.422716i) q^{53} +(6.81662 - 0.341688i) q^{55} +(2.64338 + 0.111944i) q^{56} +(-5.68036 - 1.52205i) q^{58} +(5.99269 - 10.3796i) q^{59} +(-3.15831 - 5.47036i) q^{61} +(-2.12132 + 2.12132i) q^{62} +1.00000i q^{64} +(-0.664513 + 3.09167i) q^{65} +(-14.5253 + 3.89204i) q^{67} +(1.11722 - 4.16954i) q^{68} +(-2.91819 + 5.14628i) q^{70} +1.86199i q^{71} +(-0.982183 - 3.66556i) q^{73} +(-3.53553 + 6.12372i) q^{74} +6.31662 q^{76} +(7.88194 - 1.75822i) q^{77} +(3.14649 - 1.81662i) q^{79} +(-1.99004 - 1.01969i) q^{80} +(0.732051 - 2.73205i) q^{82} +(-8.67372 - 8.67372i) q^{83} +(7.15831 + 6.47494i) q^{85} +(9.34878 - 5.39752i) q^{86} +(0.789997 + 2.94831i) q^{88} +(-6.32852 - 10.9613i) q^{89} +(-0.158312 + 3.73831i) q^{91} +(1.19033 - 1.19033i) q^{92} +(-0.274205 - 0.158312i) q^{94} +(-6.44097 + 12.5703i) q^{95} +(-5.84169 - 5.84169i) q^{97} +(-2.37690 + 6.58410i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7} + 16 q^{13} + 8 q^{16} + 8 q^{22} - 12 q^{28} + 24 q^{31} - 40 q^{37} + 12 q^{40} - 16 q^{43} - 40 q^{46} + 8 q^{52} + 56 q^{55} - 20 q^{58} - 24 q^{61} - 32 q^{67} + 4 q^{70} + 48 q^{73}+ \cdots - 120 q^{97}+O(q^{100}) \) 16 * q + 12 * q^7 + 16 * q^13 + 8 * q^16 + 8 * q^22 - 12 * q^28 + 24 * q^31 - 40 * q^37 + 12 * q^40 - 16 * q^43 - 40 * q^46 + 8 * q^52 + 56 * q^55 - 20 * q^58 - 24 * q^61 - 32 * q^67 + 4 * q^70 + 48 * q^73 + 48 * q^76 - 16 * q^82 + 88 * q^85 - 4 * q^88 + 24 * q^91 - 120 * q^97

Introduction

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