LMFDB - Embedded newform 630.2.ce.b.53.4

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			53.4
Root			$0.0537601 + 1.73122i$ of defining polynomial
Character	$\chi$	$=$	630.53
Dual form			630.2.ce.b.107.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.99004 - 1.01969i) q^{5} +(1.79000 + 1.94831i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.469882 - 2.18614i) q^{10} +(2.64338 + 1.52616i) q^{11} +(1.00000 + 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.16954 - 1.11722i) q^{17} +(-5.47036 + 3.15831i) q^{19} +(-2.23326 - 0.111944i) q^{20} +(2.15831 - 2.15831i) q^{22} +(-1.62602 - 0.435690i) q^{23} +(2.92048 - 4.05842i) q^{25} +(1.22474 - 0.707107i) q^{26} +(-0.576028 - 2.58228i) q^{28} +5.88074 q^{29} +(1.50000 - 2.59808i) q^{31} +(0.965926 - 0.258819i) q^{32} -4.31662i q^{34} +(5.54882 + 2.05197i) q^{35} +(-6.83013 - 1.83013i) q^{37} +(1.63486 + 6.10139i) q^{38} +(-0.686141 + 2.12819i) q^{40} -2.82843i q^{41} +(-7.63325 - 7.63325i) q^{43} +(-1.52616 - 2.64338i) q^{44} +(-0.841688 + 1.45785i) q^{46} +(-0.0819485 + 0.305836i) q^{47} +(-0.591820 + 6.97494i) q^{49} +(-3.16426 - 3.87137i) q^{50} +(-0.366025 - 1.36603i) q^{52} +(0.422716 + 1.57760i) q^{53} +(6.81662 + 0.341688i) q^{55} +(-2.64338 - 0.111944i) q^{56} +(1.52205 - 5.68036i) q^{58} +(5.99269 - 10.3796i) q^{59} +(-3.15831 - 5.47036i) q^{61} +(-2.12132 - 2.12132i) q^{62} -1.00000i q^{64} +(3.00972 + 0.970349i) q^{65} +(3.89204 + 14.5253i) q^{67} +(-4.16954 - 1.11722i) q^{68} +(3.41819 - 4.82866i) q^{70} -1.86199i q^{71} +(3.66556 - 0.982183i) q^{73} +(-3.53553 + 6.12372i) q^{74} +6.31662 q^{76} +(1.75822 + 7.88194i) q^{77} +(-3.14649 + 1.81662i) q^{79} +(1.87809 + 1.21358i) q^{80} +(-2.73205 - 0.732051i) q^{82} +(-8.67372 + 8.67372i) q^{83} +(7.15831 - 6.47494i) q^{85} +(-9.34878 + 5.39752i) q^{86} +(-2.94831 + 0.789997i) q^{88} +(-6.32852 - 10.9613i) q^{89} +(-0.158312 + 3.73831i) q^{91} +(1.19033 + 1.19033i) q^{92} +(0.274205 + 0.158312i) q^{94} +(-7.66572 + 11.8632i) q^{95} +(-5.84169 + 5.84169i) q^{97} +(6.58410 + 2.37690i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.99004	−	1.01969i	0.889971	−	0.456017i
$5$	1.99004	−	1.01969i	0.889971	−	0.456017i
$6$		0			0
$7$	1.79000	+	1.94831i	0.676555	+	0.736392i
$7$	1.79000	+	1.94831i	0.676555	+	0.736392i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.469882	−	2.18614i	−0.148590	−	0.691318i
$11$	2.64338	+	1.52616i	0.797010	+	0.460154i	0.842424	−	0.538814i	$-0.181128\pi$
$11$	2.64338	+	1.52616i	0.797010	+	0.460154i	−0.0454148	+	0.998968i	$0.514461\pi$
$12$		0			0
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	0.832050	−	0.554700i	$-0.187167\pi$
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.34521	−	1.22474i	0.626783	−	0.327327i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.16954	−	1.11722i	1.01126	−	0.270967i	0.285105	−	0.958496i	$-0.407971\pi$
$17$	4.16954	−	1.11722i	1.01126	−	0.270967i	0.726157	+	0.687529i	$0.241305\pi$
$18$		0			0
$19$	−5.47036	+	3.15831i	−1.25499	+	0.724567i	−0.972095	−	0.234586i	$-0.924627\pi$
$19$	−5.47036	+	3.15831i	−1.25499	+	0.724567i	−0.282891	+	0.959152i	$0.591293\pi$
$20$	−2.23326	−	0.111944i	−0.499373	−	0.0250314i
$21$		0			0
$22$	2.15831	−	2.15831i	0.460154	−	0.460154i
$23$	−1.62602	−	0.435690i	−0.339048	−	0.0908476i	0.0852780	−	0.996357i	$-0.472822\pi$
$23$	−1.62602	−	0.435690i	−0.339048	−	0.0908476i	−0.424326	+	0.905510i	$0.639489\pi$
$24$		0			0
$25$	2.92048	−	4.05842i	0.584096	−	0.811684i
$26$	1.22474	−	0.707107i	0.240192	−	0.138675i
$27$		0			0
$28$	−0.576028	−	2.58228i	−0.108859	−	0.488006i
$29$	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	$0.0798387\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$		−	4.31662i		−	0.740295i
$35$	5.54882	+	2.05197i	0.937922	+	0.346846i
$36$		0			0
$37$	−6.83013	−	1.83013i	−1.12287	−	0.300871i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	−6.83013	−	1.83013i	−1.12287	−	0.300871i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	1.63486	+	6.10139i	0.265210	+	0.989776i
$39$		0			0
$40$	−0.686141	+	2.12819i	−0.108488	+	0.336497i
$41$		−	2.82843i		−	0.441726i	−0.975305	−	0.220863i	$-0.929113\pi$
$41$		−	2.82843i		−	0.441726i	0.975305	−	0.220863i	$-0.0708874\pi$
$42$		0			0
$43$	−7.63325	−	7.63325i	−1.16406	−	1.16406i	−0.983578	−	0.180481i	$-0.942234\pi$
$43$	−7.63325	−	7.63325i	−1.16406	−	1.16406i	−0.180481	−	0.983578i	$-0.557766\pi$
$44$	−1.52616	−	2.64338i	−0.230077	−	0.398505i
$45$		0			0
$46$	−0.841688	+	1.45785i	−0.124100	+	0.214948i
$47$	−0.0819485	+	0.305836i	−0.0119534	+	0.0446108i	−0.971645	−	0.236445i	$-0.924018\pi$
$47$	−0.0819485	+	0.305836i	−0.0119534	+	0.0446108i	0.959692	+	0.281055i	$0.0906845\pi$
$48$		0			0
$49$	−0.591820	+	6.97494i	−0.0845458	+	0.996420i
$50$	−3.16426	−	3.87137i	−0.447494	−	0.547494i
$51$		0			0
$52$	−0.366025	−	1.36603i	−0.0507586	−	0.189434i
$53$	0.422716	+	1.57760i	0.0580645	+	0.216700i	0.988862	−	0.148836i	$-0.0475526\pi$
$53$	0.422716	+	1.57760i	0.0580645	+	0.216700i	−0.930797	+	0.365535i	$0.880886\pi$
$54$		0			0
$55$	6.81662	+	0.341688i	0.919153	+	0.0460731i
$56$	−2.64338	−	0.111944i	−0.353237	−	0.0149591i
$57$		0			0
$58$	1.52205	−	5.68036i	0.199855	−	0.745868i
$59$	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
$65$	3.00972	+	0.970349i	0.373310	+	0.120357i
$66$		0			0
$67$	3.89204	+	14.5253i	0.475488	+	1.77455i	0.619528	+	0.784975i	$0.287324\pi$
$67$	3.89204	+	14.5253i	0.475488	+	1.77455i	−0.144040	+	0.989572i	$0.546009\pi$
$68$	−4.16954	−	1.11722i	−0.505631	−	0.135483i
$69$		0			0
$70$	3.41819	−	4.82866i	0.408552	−	0.577135i
$71$		−	1.86199i		−	0.220977i	−0.993877	−	0.110489i	$-0.964758\pi$
$71$		−	1.86199i		−	0.220977i	0.993877	−	0.110489i	$-0.0352416\pi$
$72$		0			0
$73$	3.66556	−	0.982183i	0.429021	−	0.114956i	−0.0378455	−	0.999284i	$-0.512049\pi$
$73$	3.66556	−	0.982183i	0.429021	−	0.114956i	0.466867	+	0.884328i	$0.345383\pi$
$74$	−3.53553	+	6.12372i	−0.410997	+	0.711868i
$75$		0			0
$76$	6.31662			0.724567
$77$	1.75822	+	7.88194i	0.200368	+	0.898231i
$78$		0			0
$79$	−3.14649	+	1.81662i	−0.354007	+	0.204386i	−0.666449	−	0.745551i	$-0.732187\pi$
$79$	−3.14649	+	1.81662i	−0.354007	+	0.204386i	0.312441	+	0.949937i	$0.398853\pi$
$80$	1.87809	+	1.21358i	0.209977	+	0.135682i
$81$		0			0
$82$	−2.73205	−	0.732051i	−0.301705	−	0.0808415i
$83$	−8.67372	+	8.67372i	−0.952065	+	0.952065i	−0.998903	−	0.0468375i	$-0.985086\pi$
$83$	−8.67372	+	8.67372i	−0.952065	+	0.952065i	0.0468375	+	0.998903i	$0.485086\pi$
$84$		0			0
$85$	7.15831	−	6.47494i	0.776428	−	0.702306i
$86$	−9.34878	+	5.39752i	−1.00811	+	0.582030i
$87$		0			0
$88$	−2.94831	+	0.789997i	−0.314291	+	0.0842140i
$89$	−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
$95$	−7.66572	+	11.8632i	−0.786486	+	1.21714i
$96$		0			0
$97$	−5.84169	+	5.84169i	−0.593134	+	0.593134i	−0.938477	−	0.345343i	$-0.887763\pi$
$97$	−5.84169	+	5.84169i	−0.593134	+	0.593134i	0.345343	+	0.938477i	$0.387763\pi$
$98$	6.58410	+	2.37690i	0.665094	+	0.240103i
$99$		0			0
$100$	−4.55842	+	2.05446i	−0.455842	+	0.205446i
$101$	−14.6355	−	8.44984i	−1.45629	−	0.840790i	−0.457465	−	0.889228i	$-0.651243\pi$
$101$	−14.6355	−	8.44984i	−1.45629	−	0.840790i	−0.998826	+	0.0484373i	$0.984576\pi$
$102$		0			0
$103$	−1.32986	+	4.96311i	−0.131035	+	0.489030i	−0.999983	−	0.00587425i	$-0.998130\pi$
$103$	−1.32986	+	4.96311i	−0.131035	+	0.489030i	0.868948	+	0.494904i	$0.164797\pi$
$104$	−1.41421			−0.138675
$105$		0			0
$106$	1.63325			0.158635
$107$	−3.52854	+	13.1687i	−0.341117	+	1.27307i	0.555966	+	0.831205i	$0.312349\pi$
$107$	−3.52854	+	13.1687i	−0.341117	+	1.27307i	−0.897083	+	0.441862i	$0.854318\pi$
$108$		0			0
$109$	14.9532	+	8.63325i	1.43226	+	0.826915i	0.997293	−	0.0735313i	$-0.0234269\pi$
$109$	14.9532	+	8.63325i	1.43226	+	0.826915i	0.434966	+	0.900447i	$0.356760\pi$
$110$	2.09432	−	6.49592i	0.199685	−	0.619362i
$111$		0			0
$112$	−0.792287	+	2.52434i	−0.0748641	+	0.238528i
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	−0.770490	−	0.637452i	$-0.779988\pi$
$113$	−1.41421	+	1.41421i	−0.133038	+	0.133038i	0.637452	+	0.770490i	$0.279988\pi$
$114$		0			0
$115$	−3.68009	+	0.790988i	−0.343171	+	0.0737600i
$116$	−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
$122$	−6.10139	+	1.63486i	−0.552394	+	0.148014i
$123$		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	−0.886983	−	0.461801i	$-0.847203\pi$
$127$	−4.79156	+	4.79156i	−0.425182	+	0.425182i	0.461801	+	0.886983i	$0.347203\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	1.71626	−	2.65602i	0.150526	−	0.232949i
$131$	10.8288	−	6.25202i	0.946118	−	0.546241i	0.0542449	−	0.998528i	$-0.482725\pi$
$131$	10.8288	−	6.25202i	0.946118	−	0.546241i	0.891873	+	0.452286i	$0.149392\pi$
$132$		0			0
$133$	−15.9453	−	5.00458i	−1.38263	−	0.433952i
$134$	15.0377			1.29906
$135$		0			0
$136$	−2.15831	+	3.73831i	−0.185074	+	0.320557i
$137$	−17.3867	+	4.65874i	−1.48544	+	0.398023i	−0.908196	−	0.418546i	$-0.862540\pi$
$137$	−17.3867	+	4.65874i	−1.48544	+	0.398023i	−0.577247	+	0.816569i	$0.695873\pi$
$138$		0			0
$139$			13.2665i			1.12525i	0.826712	+	0.562625i	$0.190208\pi$
$139$			13.2665i			1.12525i	−0.826712	+	0.562625i	$0.809792\pi$
$140$	−3.77944	−	4.55147i	−0.319421	−	0.384669i
$141$		0			0
$142$	−1.79854	−	0.481918i	−0.150930	−	0.0404417i
$143$	1.11722	+	4.16954i	0.0934270	+	0.348674i
$144$		0			0
$145$	11.7029	−	5.99651i	0.971872	−	0.497983i
$146$		−	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	$0.929151\pi$
$152$	1.63486	−	6.10139i	0.132605	−	0.494888i
$153$		0			0
$154$	8.06843	+	0.341688i	0.650173	+	0.0275340i
$155$	0.335831	−	6.69979i	0.0269746	−	0.538140i
$156$		0			0
$157$	−1.34821	−	5.03158i	−0.107599	−	0.401564i	0.891028	−	0.453948i	$-0.149985\pi$
$157$	−1.34821	−	5.03158i	−0.107599	−	0.401564i	−0.998627	+	0.0523837i	$0.983318\pi$
$158$	0.940354	+	3.50945i	0.0748106	+	0.279197i
$159$		0			0
$160$	1.65831	−	1.50000i	0.131101	−	0.118585i
$161$	−2.06171	−	3.94786i	−0.162485	−	0.311135i
$162$		0			0
$163$	−2.90986	+	10.8597i	−0.227918	+	0.850600i	0.753297	+	0.657680i	$0.228462\pi$
$163$	−2.90986	+	10.8597i	−0.227918	+	0.850600i	−0.981215	+	0.192919i	$0.938204\pi$
$164$	−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	0.453510	−	0.891251i	$-0.350171\pi$
$167$	−5.65685	−	5.65685i	−0.437741	−	0.437741i	−0.891251	+	0.453510i	$0.850171\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$	−4.40160	−	8.59024i	−0.337587	−	0.658841i
$171$		0			0
$172$	2.79396	+	10.4272i	0.213038	+	0.795068i
$173$	−19.2217	−	5.15043i	−1.46140	−	0.391580i	−0.561425	−	0.827528i	$-0.689747\pi$
$173$	−19.2217	−	5.15043i	−1.46140	−	0.391580i	−0.899972	+	0.435947i	$0.856413\pi$
$174$		0			0
$175$	13.1347	−	1.57456i	0.992891	−	0.119026i
$176$			3.05231i			0.230077i
$177$		0			0
$178$	−12.2258	+	3.27588i	−0.916359	+	0.245538i
$179$	−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	$0.131805\pi$
$182$	3.56995	+	1.12046i	0.264623	+	0.0830542i
$183$		0			0
$184$	1.45785	−	0.841688i	0.107474	−	0.0620500i
$185$	−15.4583	+	3.32257i	−1.13652	+	0.244280i
$186$		0			0
$187$	12.7267	+	3.41012i	0.930672	+	0.249373i
$188$	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	0.316942	−	0.948445i	$-0.397344\pi$
$191$	17.9220	−	10.3473i	1.29679	−	0.748702i	0.979848	+	0.199743i	$0.0640107\pi$
$192$		0			0
$193$	10.2110	−	2.73602i	0.735001	−	0.196943i	0.128146	−	0.991755i	$-0.459098\pi$
$193$	10.2110	−	2.73602i	0.735001	−	0.196943i	0.606855	+	0.794813i	$0.292431\pi$
$194$	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	0.925109	+	0.379701i	$0.123973\pi$
$197$	18.3139	+	18.3139i	1.30481	+	1.30481i	0.379701	+	0.925109i	$0.376027\pi$
$198$		0			0
$199$	−4.01251	−	2.31662i	−0.284439	−	0.164221i	0.350992	−	0.936378i	$-0.385844\pi$
$199$	−4.01251	−	2.31662i	−0.284439	−	0.164221i	−0.635431	+	0.772157i	$0.719178\pi$
$200$	0.804646	+	4.93483i	0.0568970	+	0.348945i
$201$		0			0
$202$	−11.9499	+	11.9499i	−0.840790	+	0.840790i
$203$	10.5265	+	11.4575i	0.738816	+	0.804159i
$204$		0			0
$205$	−2.88411	−	5.62867i	−0.201435	−	0.393123i
$206$	4.44980	+	2.56910i	0.310033	+	0.178997i
$207$		0			0
$208$	−0.366025	+	1.36603i	−0.0253793	+	0.0947168i
$209$	−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	$0.554500\pi$
$212$	0.422716	−	1.57760i	0.0290323	−	0.108350i
$213$		0			0
$214$	11.8067	+	6.81662i	0.807092	+	0.465975i
$215$	−22.9740	−	7.40692i	−1.56681	−	0.505148i
$216$		0			0
$217$	7.74685	−	1.72808i	0.525891	−	0.117310i
$218$	12.2093	−	12.2093i	0.826915	−	0.826915i
$219$		0			0
$220$	−5.73253	−	3.70422i	−0.386487	−	0.249739i
$221$	5.28676	+	3.05231i	0.355626	+	0.205321i
$222$		0			0
$223$	−16.1583	−	16.1583i	−1.08204	−	1.08204i	−0.996319	−	0.0857215i	$-0.972680\pi$
$223$	−16.1583	−	16.1583i	−1.08204	−	1.08204i	−0.0857215	−	0.996319i	$-0.527320\pi$
$224$	2.23326	+	1.41864i	0.149216	+	0.0947867i
$225$		0			0
$226$	1.00000	+	1.73205i	0.0665190	+	0.115214i
$227$	16.1149	−	4.31798i	1.06958	−	0.286594i	0.319262	−	0.947667i	$-0.396565\pi$
$227$	16.1149	−	4.31798i	1.06958	−	0.286594i	0.750322	+	0.661073i	$0.229898\pi$
$228$		0			0
$229$	−22.5167	+	13.0000i	−1.48794	+	0.859064i	−0.999905	−	0.0137585i	$-0.995620\pi$
$229$	−22.5167	+	13.0000i	−1.48794	+	0.859064i	−0.488037	+	0.872823i	$0.662287\pi$
$230$	−0.188443	+	3.75942i	−0.0124256	+	0.247889i
$231$		0			0
$232$	−4.15831	+	4.15831i	−0.273007	+	0.273007i
$233$	−20.2360	−	5.42223i	−1.32571	−	0.355222i	−0.474593	−	0.880205i	$-0.657405\pi$
$233$	−20.2360	−	5.42223i	−1.32571	−	0.355222i	−0.851113	+	0.524983i	$0.824072\pi$
$234$		0			0
$235$	0.148776	+	0.692186i	0.00970509	+	0.0451533i
$236$	−10.3796	+	5.99269i	−0.675657	+	0.390091i
$237$		0			0
$238$	8.41012	−	7.72675i	0.545147	−	0.500851i
$239$	−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	$0.0986598\pi$
$242$	−1.62602	+	0.435690i	−0.104524	+	0.0280072i
$243$		0			0
$244$			6.31662i			0.404380i
$245$	5.93450	+	14.4838i	0.379141	+	0.925339i
$246$		0			0
$247$	−8.62867	−	2.31205i	−0.549029	−	0.147112i
$248$	0.776457	+	2.89778i	0.0493051	+	0.184009i
$249$		0			0
$250$	−10.2446	−	4.47760i	−0.647923	−	0.283189i
$251$		−	17.1236i		−	1.08083i	−0.841399	−	0.540415i	$-0.818267\pi$
$251$		−	17.1236i		−	1.08083i	0.841399	−	0.540415i	$-0.181733\pi$
$252$		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
$257$	5.50418	−	20.5419i	0.343341	−	1.28137i	−0.551197	−	0.834375i	$-0.685829\pi$
$257$	5.50418	−	20.5419i	0.343341	−	1.28137i	0.894538	−	0.446991i	$-0.147504\pi$
$258$		0			0
$259$	−8.66025	−	16.5831i	−0.538122	−	1.03043i
$260$	−2.12132	−	2.34521i	−0.131559	−	0.145444i
$261$		0			0
$262$	−3.23628	−	12.0780i	−0.199938	−	0.746179i
$263$	1.44502	+	5.39288i	0.0891037	+	0.332539i	0.996060	−	0.0886860i	$-0.0282668\pi$
$263$	1.44502	+	5.39288i	0.0891037	+	0.332539i	−0.906956	+	0.421225i	$0.861600\pi$
$264$		0			0
$265$	2.44987	+	2.70844i	0.150495	+	0.166378i
$266$	−8.96100	+	14.1067i	−0.549434	+	0.864937i
$267$		0			0
$268$	3.89204	−	14.5253i	0.237744	−	0.887273i
$269$	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
$275$	13.9137	−	6.27085i	0.839030	−	0.378146i
$276$		0			0
$277$	−4.85588	−	18.1224i	−0.291761	−	1.08887i	−0.943756	−	0.330644i	$-0.892734\pi$
$277$	−4.85588	−	18.1224i	−0.291761	−	1.08887i	0.651994	−	0.758224i	$-0.273933\pi$
$278$	12.8145	+	3.43362i	0.768560	+	0.205935i
$279$		0			0
$280$	−5.37457	+	2.47265i	−0.321192	+	0.147769i
$281$			19.7990i			1.18111i	0.806998	+	0.590554i	$0.201091\pi$
$281$			19.7990i			1.18111i	−0.806998	+	0.590554i	$0.798909\pi$
$282$		0			0
$283$	1.79854	−	0.481918i	0.106912	−	0.0286471i	−0.204966	−	0.978769i	$-0.565708\pi$
$283$	1.79854	−	0.481918i	0.106912	−	0.0286471i	0.311879	+	0.950122i	$0.399042\pi$
$284$	−0.930994	+	1.61253i	−0.0552443	+	0.0956860i
$285$		0			0
$286$	4.31662			0.255247
$287$	5.51065	−	5.06288i	0.325283	−	0.298852i
$288$		0			0
$289$	1.41444	−	0.816625i	0.0832021	−	0.0480368i
$290$	−2.76325	−	12.8561i	−0.162264	−	0.754938i
$291$		0			0
$292$	−3.66556	−	0.982183i	−0.214511	−	0.0574779i
$293$	0.707107	−	0.707107i	0.0413096	−	0.0413096i	−0.686150	−	0.727460i	$-0.740701\pi$
$293$	0.707107	−	0.707107i	0.0413096	−	0.0413096i	0.727460	+	0.686150i	$0.240701\pi$
$294$		0			0
$295$	1.34169	−	26.7665i	0.0781161	−	1.55841i
$296$	6.12372	−	3.53553i	0.355934	−	0.205499i
$297$		0			0
$298$	6.83013	−	1.83013i	0.395659	−	0.106016i
$299$	−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
$305$	−11.8632	−	7.66572i	−0.679285	−	0.438938i
$306$		0			0
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	−0.915645	−	0.401988i	$-0.868319\pi$
$307$	−9.00000	+	9.00000i	−0.513657	+	0.513657i	0.401988	+	0.915645i	$0.368319\pi$
$308$	2.41831	−	7.70507i	0.137796	−	0.439037i
$309$		0			0
$310$	−6.38458	−	2.05842i	−0.362620	−	0.116911i
$311$	12.6352	+	7.29496i	0.716478	+	0.413659i	0.813455	−	0.581628i	$-0.197584\pi$
$311$	12.6352	+	7.29496i	0.716478	+	0.413659i	−0.0969768	+	0.995287i	$0.530917\pi$
$312$		0			0
$313$	1.63794	−	6.11288i	0.0925819	−	0.345520i	−0.904060	−	0.427406i	$-0.859428\pi$
$313$	1.63794	−	6.11288i	0.0925819	−	0.345520i	0.996642	+	0.0818856i	$0.0260942\pi$
$314$	−5.20908			−0.293965
$315$		0			0
$316$	3.63325			0.204386
$317$	1.02230	−	3.81529i	0.0574182	−	0.214288i	−0.931256	−	0.364366i	$-0.881286\pi$
$317$	1.02230	−	3.81529i	0.0574182	−	0.214288i	0.988674	+	0.150078i	$0.0479525\pi$
$318$		0			0
$319$	15.5450	+	8.97494i	0.870356	+	0.502500i
$320$	−1.01969	−	1.99004i	−0.0570022	−	0.111246i
$321$		0			0
$322$	−4.34695	+	0.969672i	−0.242246	+	0.0540377i
$323$	−19.2803	+	19.2803i	−1.07279	+	1.07279i
$324$		0			0
$325$	6.97890	−	1.13794i	0.387120	−	0.0631216i
$326$	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	$0.803839\pi$
$332$	11.8485	−	3.17480i	0.650272	−	0.174240i
$333$		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	−0.0658849	−	0.997827i	$-0.520987\pi$
$337$	17.1082	−	17.1082i	0.931942	−	0.931942i	0.997827	+	0.0658849i	$0.0209870\pi$
$338$	−10.6252	−	2.84701i	−0.577934	−	0.154857i
$339$		0			0
$340$	−9.43675	+	2.02830i	−0.511780	+	0.110000i
$341$	7.93015	−	4.57847i	0.429441	−	0.247938i
$342$		0			0
$343$	−14.6487	+	11.3321i	−0.790955	+	0.611874i
$344$	10.7950			0.582030
$345$		0			0
$346$	−9.94987	+	17.2337i	−0.534909	+	0.926489i
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$		−	4.00000i		−	0.214115i	−0.994253	−	0.107058i	$-0.965857\pi$
$349$		−	4.00000i		−	0.214115i	0.994253	−	0.107058i	$-0.0341429\pi$
$350$	1.87860	−	13.0947i	0.100416	−	0.699940i
$351$		0			0
$352$	2.94831	+	0.789997i	0.157145	+	0.0421070i
$353$	−4.11516	−	15.3580i	−0.219028	−	0.817423i	−0.984710	−	0.174203i	$-0.944265\pi$
$353$	−4.11516	−	15.3580i	−0.219028	−	0.817423i	0.765682	−	0.643219i	$-0.222402\pi$
$354$		0			0
$355$	−1.89864	−	3.70542i	−0.100770	−	0.196663i
$356$			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
$362$	6.37555	−	23.7939i	0.335092	−	1.25058i
$363$		0			0
$364$	2.00626	−	3.15831i	0.105156	−	0.165541i
$365$	6.29307	−	5.69230i	0.329394	−	0.297949i
$366$		0			0
$367$	−2.36999	−	8.84493i	−0.123713	−	0.461702i	0.876078	−	0.482169i	$-0.160151\pi$
$367$	−2.36999	−	8.84493i	−0.123713	−	0.461702i	−0.999791	+	0.0204680i	$0.993484\pi$
$368$	−0.435690	−	1.62602i	−0.0227119	−	0.0847619i
$369$		0			0
$370$	−0.791562	+	15.7916i	−0.0411513	+	0.820964i
$371$	−2.31699	+	3.64748i	−0.120292	+	0.189368i
$372$		0			0
$373$	−5.97230	+	22.2889i	−0.309234	+	1.15408i	0.620005	+	0.784598i	$0.287130\pi$
$373$	−5.97230	+	22.2889i	−0.309234	+	1.15408i	−0.929239	+	0.369479i	$0.879536\pi$
$374$	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	$-0.711756\pi$
$379$		−	30.6332i		−	1.57352i	0.617256	−	0.786762i	$-0.288244\pi$
$380$	12.5703	−	6.44097i	0.644843	−	0.330415i
$381$		0			0
$382$	−5.35614	−	19.9894i	−0.274044	−	1.02275i
$383$	1.93185	+	0.517638i	0.0987130	+	0.0264501i	0.307837	−	0.951439i	$-0.400395\pi$
$383$	1.93185	+	0.517638i	0.0987130	+	0.0264501i	−0.209124	+	0.977889i	$0.567061\pi$
$384$		0			0
$385$	11.5360	+	13.8925i	0.587930	+	0.708028i
$386$		−	10.5712i		−	0.538058i
$387$		0			0
$388$	7.97989	−	2.13821i	0.405118	−	0.108551i
$389$	−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
$392$	−4.51355	−	5.35051i	−0.227968	−	0.270241i
$393$		0			0
$394$	22.4298	−	12.9499i	1.13000	−	0.652405i
$395$	−4.40923	+	6.82358i	−0.221853	+	0.343331i
$396$		0			0
$397$	−7.19417	−	1.92767i	−0.361065	−	0.0967471i	0.0737258	−	0.997279i	$-0.476511\pi$
$397$	−7.19417	−	1.92767i	−0.361065	−	0.0967471i	−0.434791	+	0.900531i	$0.643178\pi$
$398$	−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	0.0325197	−	0.999471i	$-0.489647\pi$
$401$	18.3098	−	10.5712i	0.914347	−	0.527898i	0.881827	+	0.471573i	$0.156314\pi$
$402$		0			0
$403$	4.09808	−	1.09808i	0.204140	−	0.0546991i
$404$	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	0.998452	−	0.0556140i	$-0.0177116\pi$
$409$	29.3146	+	16.9248i	1.44952	+	0.836878i	0.451063	+	0.892492i	$0.351045\pi$
$410$	−6.18334	+	1.32903i	−0.305373	+	0.0656360i
$411$		0			0
$412$	3.63325	−	3.63325i	0.178997	−	0.178997i
$413$	30.9496	−	6.90391i	1.52293	−	0.339719i
$414$		0			0
$415$	−8.41654	+	26.1055i	−0.413152	+	1.28147i
$416$	1.22474	+	0.707107i	0.0600481	+	0.0346688i
$417$		0			0
$418$	−4.99012	+	18.6234i	−0.244075	+	0.910899i
$419$	−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	$0.779561\pi$
$422$	−1.28112	+	4.78121i	−0.0623640	+	0.232746i
$423$		0			0
$424$	−1.41444	−	0.816625i	−0.0686911	−	0.0396588i
$425$	7.64289	−	20.1846i	0.370735	−	0.979096i
$426$		0			0
$427$	5.00458	−	15.9453i	0.242189	−	0.771647i
$428$	9.64016	−	9.64016i	0.465975	−	0.465975i
$429$		0			0
$430$	−13.1006	+	20.2741i	−0.631769	+	0.977703i
$431$	11.0841	+	6.39941i	0.533902	+	0.308249i	0.742604	−	0.669731i	$-0.233591\pi$
$431$	11.0841	+	6.39941i	0.533902	+	0.308249i	−0.208702	+	0.977979i	$0.566924\pi$
$432$		0			0
$433$	−6.05013	−	6.05013i	−0.290750	−	0.290750i	0.546626	−	0.837377i	$-0.315912\pi$
$433$	−6.05013	−	6.05013i	−0.290750	−	0.290750i	−0.837377	+	0.546626i	$0.815912\pi$
$434$	0.335831	−	7.93015i	0.0161204	−	0.380659i
$435$		0			0
$436$	−8.63325	−	14.9532i	−0.413458	−	0.716130i
$437$	10.2709	−	2.75209i	0.491325	−	0.131650i
$438$		0			0
$439$	−3.96910	+	2.29156i	−0.189435	+	0.109370i	−0.591718	−	0.806145i	$-0.701550\pi$
$439$	−3.96910	+	2.29156i	−0.189435	+	0.109370i	0.402283	+	0.915515i	$0.368217\pi$
$440$	−5.06169	+	4.57847i	−0.241307	+	0.218270i
$441$		0			0
$442$	4.31662	−	4.31662i	0.205321	−	0.205321i
$443$	−21.2020	−	5.68105i	−1.00734	−	0.269915i	−0.282820	−	0.959173i	$-0.591270\pi$
$443$	−21.2020	−	5.68105i	−1.00734	−	0.269915i	−0.724515	+	0.689259i	$0.757936\pi$
$444$		0			0
$445$	−23.7711	−	15.3603i	−1.12686	−	0.728148i
$446$	−19.7898	+	11.4257i	−0.937075	+	0.541020i
$447$		0			0
$448$	1.94831	−	1.79000i	0.0920490	−	0.0845694i
$449$	−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
$452$	1.93185	−	0.517638i	0.0908667	−	0.0243476i
$453$		0			0
$454$		−	16.6834i		−	0.782990i
$455$	3.49685	+	7.60079i	0.163935	+	0.356331i
$456$		0			0
$457$	32.4314	+	8.68997i	1.51708	+	0.406500i	0.918778	−	0.394774i	$-0.129177\pi$
$457$	32.4314	+	8.68997i	1.51708	+	0.406500i	0.598299	+	0.801273i	$0.295844\pi$
$458$	6.72930	+	25.1141i	0.314439	+	1.17350i
$459$		0			0
$460$	3.58255	+	1.15503i	0.167037	+	0.0538537i
$461$		−	0.0708883i		−	0.00330160i	−0.999999	−	0.00165080i	$-0.999475\pi$
$461$		−	0.0708883i		−	0.00330160i	0.999999	−	0.00165080i	$-0.000525466\pi$
$462$		0			0
$463$	27.6332	+	27.6332i	1.28423	+	1.28423i	0.938239	+	0.345987i	$0.112456\pi$
$463$	27.6332	+	27.6332i	1.28423	+	1.28423i	0.345987	+	0.938239i	$0.387544\pi$
$464$	2.94037	+	5.09287i	0.136503	+	0.236431i
$465$		0			0
$466$	−10.4749	+	18.1431i	−0.485242	+	0.840464i
$467$	−9.97307	+	37.2200i	−0.461499	+	1.72234i	0.206745	+	0.978395i	$0.433713\pi$
$467$	−9.97307	+	37.2200i	−0.461499	+	1.72234i	−0.668244	+	0.743942i	$0.732954\pi$
$468$		0			0
$469$	−21.3330	+	33.5831i	−0.985067	+	1.55072i
$470$	0.707107	+	0.0354442i	0.0326164	+	0.00163492i
$471$		0			0
$472$	3.10204	+	11.5770i	0.142783	+	0.532874i
$473$	−8.52806	−	31.8271i	−0.392120	−	1.46341i
$474$		0			0
$475$	−3.15831	+	31.4248i	−0.144913	+	1.44187i
$476$	−5.28676	−	10.1234i	−0.242318	−	0.464004i
$477$		0			0
$478$	−0.250133	+	0.933508i	−0.0114408	+	0.0426977i
$479$	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
$485$	−5.66848	+	17.5819i	−0.257392	+	0.798351i
$486$		0			0
$487$	4.20012	+	15.6751i	0.190326	+	0.710305i	0.993428	+	0.114463i	$0.0365147\pi$
$487$	4.20012	+	15.6751i	0.190326	+	0.710305i	−0.803102	+	0.595842i	$0.796819\pi$
$488$	6.10139	+	1.63486i	0.276197	+	0.0740068i
$489$		0			0
$490$	15.5263	−	1.98359i	0.701406	−	0.0896097i
$491$		−	13.8474i		−	0.624923i	−0.949930	−	0.312461i	$-0.898847\pi$
$491$		−	13.8474i		−	0.624923i	0.949930	−	0.312461i	$-0.101153\pi$
$492$		0			0
$493$	24.5200	−	6.57011i	1.10432	−	0.295903i
$494$	−4.46653	+	7.73625i	−0.200959	+	0.348071i
$495$		0			0
$496$	3.00000			0.134704
$497$	3.62773	−	3.33295i	0.162726	−	0.149503i
$498$		0			0
$499$	19.0526	−	11.0000i	0.852910	−	0.492428i	−0.00872186	−	0.999962i	$-0.502776\pi$
$499$	19.0526	−	11.0000i	0.852910	−	0.492428i	0.861632	+	0.507534i	$0.169443\pi$
$500$	−6.97652	+	8.73660i	−0.312000	+	0.390713i
$501$		0			0
$502$	−16.5401	−	4.43190i	−0.738220	−	0.197806i
$503$	12.4331	−	12.4331i	0.554367	−	0.554367i	−0.373331	−	0.927698i	$-0.621785\pi$
$503$	12.4331	−	12.4331i	0.554367	−	0.554367i	0.927698	+	0.373331i	$0.121785\pi$
$504$		0			0
$505$	−37.7414	−	1.89181i	−1.67947	−	0.0841846i
$506$	−4.44980	+	2.56910i	−0.197818	+	0.114210i
$507$		0			0
$508$	6.54540	−	1.75383i	0.290405	−	0.0778138i
$509$	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
$515$	2.41434	+	11.2328i	0.106389	+	0.494977i
$516$		0			0
$517$	−0.683375	+	0.683375i	−0.0300548	+	0.0300548i
$518$	−18.2595	+	4.07313i	−0.802277	+	0.178963i
$519$		0			0
$520$	−2.81433	+	1.44205i	−0.123417	+	0.0632382i
$521$	14.6355	+	8.44984i	0.641195	+	0.370194i	0.785075	−	0.619401i	$-0.212625\pi$
$521$	14.6355	+	8.44984i	0.641195	+	0.370194i	−0.143880	+	0.989595i	$0.545958\pi$
$522$		0			0
$523$	−4.14217	+	15.4588i	−0.181125	+	0.675966i	0.814302	+	0.580441i	$0.197120\pi$
$523$	−4.14217	+	15.4588i	−0.181125	+	0.675966i	−0.995427	+	0.0955252i	$0.969547\pi$
$524$	−12.5040			−0.546241
$525$		0			0
$526$	5.58312			0.243436
$527$	3.35167	−	12.5086i	0.146001	−	0.544884i
$528$		0			0
$529$	−17.4645	−	10.0831i	−0.759325	−	0.438397i
$530$	3.25022	−	1.66540i	0.141181	−	0.0723404i
$531$		0			0
$532$	11.3067	+	12.3067i	0.490209	+	0.533565i
$533$	2.82843	−	2.82843i	0.122513	−	0.122513i
$534$		0			0
$535$	6.40602	+	29.8042i	0.276956	+	1.28855i
$536$	−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	$0.613946\pi$
$542$	−16.7266	+	4.48187i	−0.718468	+	0.192513i
$543$		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	−0.774447	−	0.632639i	$-0.781972\pi$
$547$	−3.31662	+	3.31662i	−0.141809	+	0.141809i	0.632639	+	0.774447i	$0.281972\pi$
$548$	17.3867	+	4.65874i	0.742722	+	0.199012i
$549$		0			0
$550$	−2.45603	−	15.0627i	−0.104726	−	0.642274i
$551$	−32.1698	+	18.5732i	−1.37048	+	0.791246i
$552$		0			0
$553$	−9.17155	−	2.87858i	−0.390014	−	0.122410i
$554$	−18.7617			−0.797107
$555$		0			0
$556$	6.63325	−	11.4891i	0.281312	−	0.487247i
$557$	−35.0307	+	9.38646i	−1.48430	+	0.397717i	−0.907808	−	0.419386i	$-0.862246\pi$
$557$	−35.0307	+	9.38646i	−1.48430	+	0.397717i	−0.576492	+	0.817103i	$0.695579\pi$
$558$		0			0
$559$		−	15.2665i		−	0.645704i
$560$	0.997353	+	5.83141i	0.0421458	+	0.246422i
$561$		0			0
$562$	19.1244	+	5.12436i	0.806712	+	0.216158i
$563$	−1.53994	−	5.74714i	−0.0649008	−	0.242213i	0.925853	−	0.377883i	$-0.123348\pi$
$563$	−1.53994	−	5.74714i	−0.0649008	−	0.242213i	−0.990754	+	0.135670i	$0.956681\pi$
$564$		0			0
$565$	−1.37228	+	4.25639i	−0.0577323	+	0.179068i
$566$		−	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	$0.840376\pi$
$572$	1.11722	−	4.16954i	0.0467135	−	0.174337i
$573$		0			0
$574$	−3.46410	−	6.63325i	−0.144589	−	0.276866i
$575$	−6.51696	+	5.32663i	−0.271776	+	0.222136i
$576$		0			0
$577$	0.558212	+	2.08327i	0.0232387	+	0.0867279i	0.976571	−	0.215194i	$-0.0690384\pi$
$577$	0.558212	+	2.08327i	0.0232387	+	0.0867279i	−0.953333	+	0.301922i	$0.902372\pi$
$578$	−0.422716	−	1.57760i	−0.0175827	−	0.0656194i
$579$		0			0
$580$	−13.1332	−	0.658312i	−0.545329	−	0.0273349i
$581$	−32.4250	−	1.37316i	−1.34522	−	0.0569682i
$582$		0			0
$583$	−1.29026	+	4.81533i	−0.0534372	+	0.199430i
$584$	−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	0.682871	−	0.730539i	$-0.260731\pi$
$587$	−1.15488	−	1.15488i	−0.0476671	−	0.0476671i	−0.730539	+	0.682871i	$0.760731\pi$
$588$		0			0
$589$			18.9499i			0.780816i
$590$	−25.5072	−	8.22365i	−1.05011	−	0.338562i
$591$		0			0
$592$	−1.83013	−	6.83013i	−0.0752178	−	0.280716i
$593$	27.3518	+	7.32888i	1.12320	+	0.300961i	0.772179	−	0.635406i	$-0.219167\pi$
$593$	27.3518	+	7.32888i	1.12320	+	0.300961i	0.351024	+	0.936367i	$0.385834\pi$
$594$		0			0
$595$	25.4285	+	2.35649i	1.04247	+	0.0966066i
$596$		−	7.07107i		−	0.289642i
$597$		0			0
$598$	−2.29953	+	0.616158i	−0.0940349	+	0.0251966i
$599$	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	$0.377781\pi$
$602$	−27.2503	−	8.55277i	−1.11064	−	0.348585i
$603$		0			0
$604$	14.4482	−	8.34169i	0.587890	−	0.339418i
$605$	−3.16153	−	2.04291i	−0.128535	−	0.0830560i
$606$		0			0
$607$	14.8100	+	3.96833i	0.601120	+	0.161070i	0.546530	−	0.837439i	$-0.315948\pi$
$607$	14.8100	+	3.96833i	0.601120	+	0.161070i	0.0545897	+	0.998509i	$0.482615\pi$
$608$	−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
$613$	22.3574	−	5.99065i	0.903007	−	0.241960i	0.222700	−	0.974887i	$-0.428513\pi$
$613$	22.3574	−	5.99065i	0.903007	−	0.241960i	0.680307	+	0.732927i	$0.261846\pi$
$614$	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	0.459662	−	0.888094i	$-0.347971\pi$
$617$	−10.6420	−	10.6420i	−0.428433	−	0.428433i	−0.888094	+	0.459662i	$0.847971\pi$
$618$		0			0
$619$	−4.83513	−	2.79156i	−0.194340	−	0.112202i	0.399673	−	0.916658i	$-0.369124\pi$
$619$	−4.83513	−	2.79156i	−0.194340	−	0.112202i	−0.594013	+	0.804456i	$0.702457\pi$
$620$	−3.64073	+	5.63427i	−0.146215	+	0.226278i
$621$		0			0
$622$	10.3166	−	10.3166i	0.413659	−	0.413659i
$623$	10.0280	−	31.9506i	0.401763	−	1.28007i
$624$		0			0
$625$	−7.94158	−	23.7051i	−0.317663	−	0.948204i
$626$	−5.48066	−	3.16426i	−0.219051	−	0.126469i
$627$		0			0
$628$	−1.34821	+	5.03158i	−0.0537994	+	0.200782i
$629$	−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	$0.715985\pi$
$632$	0.940354	−	3.50945i	0.0374053	−	0.139598i
$633$		0			0
$634$	−3.42069	−	1.97494i	−0.135853	−	0.0784348i
$635$	−4.64949	+	14.4213i	−0.184509	+	0.572290i
$636$		0			0
$637$	−7.56676	+	6.38312i	−0.299806	+	0.252908i
$638$	12.6925	−	12.6925i	0.502500	−	0.502500i
$639$		0			0
$640$	−2.18614	+	0.469882i	−0.0864148	+	0.0185737i
$641$	26.8830	+	15.5209i	1.06181	+	0.613039i	0.925934	−	0.377686i	$-0.123280\pi$
$641$	26.8830	+	15.5209i	1.06181	+	0.613039i	0.135881	+	0.990725i	$0.456614\pi$
$642$		0			0
$643$	7.89975	+	7.89975i	0.311536	+	0.311536i	0.845504	−	0.533969i	$-0.179300\pi$
$643$	7.89975	+	7.89975i	0.311536	+	0.311536i	−0.533969	+	0.845504i	$0.679300\pi$
$644$	−0.188443	+	4.44980i	−0.00742571	+	0.175347i
$645$		0			0
$646$	13.6332	+	23.6135i	0.536393	+	0.929060i
$647$	−31.1186	+	8.33821i	−1.22340	+	0.327809i	−0.812006	−	0.583649i	$-0.801624\pi$
$647$	−31.1186	+	8.33821i	−1.22340	+	0.327809i	−0.411393	+	0.911458i	$0.634958\pi$
$648$		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
$653$	21.8136	+	5.84494i	0.853633	+	0.228730i	0.658997	−	0.752145i	$-0.270981\pi$
$653$	21.8136	+	5.84494i	0.853633	+	0.228730i	0.194636	+	0.980876i	$0.437648\pi$
$654$		0			0
$655$	15.1746	−	23.4837i	0.592922	−	0.917585i
$656$	2.44949	−	1.41421i	0.0956365	−	0.0552158i
$657$		0			0
$658$	0.182385	+	0.817615i	0.00711010	+	0.0318740i
$659$	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	$0.779618\pi$
$662$	3.25203	−	0.871379i	0.126394	−	0.0338671i
$663$		0			0
$664$		−	12.2665i		−	0.476032i
$665$	−36.8348	+	6.29990i	−1.42839	+	0.244300i
$666$		0			0
$667$	−9.56218	−	2.56218i	−0.370249	−	0.0992079i
$668$	2.07055	+	7.72741i	0.0801121	+	0.298982i
$669$		0			0
$670$	29.9255	−	15.3337i	1.15612	−	0.592393i
$671$		−	19.2803i		−	0.744309i
$672$		0			0
$673$	10.7414	+	10.7414i	0.414052	+	0.414052i	0.883147	−	0.469096i	$-0.155420\pi$
$673$	10.7414	+	10.7414i	0.414052	+	0.414052i	−0.469096	+	0.883147i	$0.655420\pi$
$674$	−12.0973	−	20.9532i	−0.465971	−	0.807086i
$675$		0			0
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	−1.72978	+	6.45564i	−0.0664810	+	0.248111i	−0.991167	−	0.132620i	$-0.957661\pi$
$677$	−1.72978	+	6.45564i	−0.0664810	+	0.248111i	0.924686	+	0.380731i	$0.124328\pi$
$678$		0			0
$679$	−21.8380	−	0.924812i	−0.838066	−	0.0354910i
$680$	−0.483219	+	9.64016i	−0.0185306	+	0.369683i
$681$		0			0
$682$	−2.36999	−	8.84493i	−0.0907517	−	0.338690i
$683$	−8.48913	−	31.6819i	−0.324828	−	1.21227i	−0.914485	−	0.404620i	$-0.867404\pi$
$683$	−8.48913	−	31.6819i	−0.324828	−	1.21227i	0.589657	−	0.807654i	$-0.299263\pi$
$684$		0			0
$685$	−29.8496	+	27.0000i	−1.14050	+	1.03162i
$686$	7.15458	+	17.0825i	0.273163	+	0.652213i
$687$		0			0
$688$	2.79396	−	10.4272i	0.106519	−	0.397534i
$689$	−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
$695$	13.5277	+	26.4008i	0.513133	+	1.00144i
$696$		0			0
$697$	−3.15999	−	11.7932i	−0.119693	−	0.446701i
$698$	−3.86370	−	1.03528i	−0.146243	−	0.0391858i
$699$		0			0
$700$	−12.1623	−	5.20375i	−0.459691	−	0.196683i
$701$			29.3328i			1.10789i	0.832555	+	0.553943i	$0.186877\pi$
$701$			29.3328i			1.10789i	−0.832555	+	0.553943i	$0.813123\pi$
$702$		0			0
$703$	43.1433	−	11.5602i	1.62718	−	0.436002i
$704$	1.52616	−	2.64338i	0.0575192	−	0.0996262i
$705$		0			0
$706$	−15.8997			−0.598395
$707$	−9.73469	−	43.6398i	−0.366111	−	1.64124i
$708$		0			0
$709$	−13.2212	+	7.63325i	−0.496532	+	0.286673i	−0.727280	−	0.686341i	$-0.759216\pi$
$709$	−13.2212	+	7.63325i	−0.496532	+	0.286673i	0.230748	+	0.973013i	$0.425883\pi$
$710$	−4.07057	+	0.874915i	−0.152766	+	0.0328350i
$711$		0			0
$712$	12.2258	+	3.27588i	0.458180	+	0.122769i
$713$	−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
$718$	−6.32914	+	1.69589i	−0.236201	+	0.0632899i
$719$	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
$725$	17.1746	−	23.8665i	0.637848	−	0.886381i
$726$		0			0
$727$	−31.1082	+	31.1082i	−1.15374	+	1.15374i	−0.167942	+	0.985797i	$0.553712\pi$
$727$	−31.1082	+	31.1082i	−1.15374	+	1.15374i	−0.985797	+	0.167942i	$0.946288\pi$
$728$	−2.53144	−	2.75533i	−0.0938213	−	0.102119i
$729$		0			0
$730$	−3.86957	−	7.55192i	−0.143219	−	0.279509i
$731$	−40.3552	−	23.2991i	−1.49259	−	0.861748i
$732$		0			0
$733$	−2.09861	+	7.83211i	−0.0775138	+	0.289286i	−0.993792	−	0.111258i	$-0.964512\pi$
$733$	−2.09861	+	7.83211i	−0.0775138	+	0.289286i	0.916278	+	0.400544i	$0.131179\pi$
$734$	−9.15694			−0.337989
$735$		0			0
$736$	−1.68338			−0.0620500
$737$	−11.8797	+	44.3358i	−0.437595	+	1.63313i
$738$		0			0
$739$	−12.0375	−	6.94987i	−0.442808	−	0.255655i	0.261980	−	0.965073i	$-0.415625\pi$
$739$	−12.0375	−	6.94987i	−0.442808	−	0.255655i	−0.704788	+	0.709418i	$0.748958\pi$
$740$	15.0486	+	4.85175i	0.553198	+	0.178354i
$741$		0			0
$742$	2.92351	+	3.18208i	0.107326	+	0.116818i
$743$	−21.1423	+	21.1423i	−0.775636	+	0.775636i	−0.979086	−	0.203449i	$-0.934785\pi$
$743$	−21.1423	+	21.1423i	−0.775636	+	0.775636i	0.203449	+	0.979086i	$0.434785\pi$
$744$		0			0
$745$	13.2801	+	8.58129i	0.486546	+	0.314394i
$746$	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	$0.839141\pi$
$752$	−0.305836	+	0.0819485i	−0.0111527	+	0.00298836i
$753$		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	−0.893967	−	0.448133i	$-0.852089\pi$
$757$	−12.2665	+	12.2665i	−0.445833	+	0.445833i	0.448133	+	0.893967i	$0.352089\pi$
$758$	−29.5894	−	7.92847i	−1.07474	−	0.287975i
$759$		0			0
$760$	−2.96807	−	13.8090i	−0.107663	−	0.500906i
$761$	−2.12310	+	1.22577i	−0.0769622	+	0.0444341i	−0.537987	−	0.842953i	$-0.680815\pi$
$761$	−2.12310	+	1.22577i	−0.0769622	+	0.0444341i	0.461025	+	0.887387i	$0.347482\pi$
$762$		0			0
$763$	9.94599	+	44.5870i	0.360069	+	1.61416i
$764$	−20.6945			−0.748702
$765$		0			0
$766$	1.00000	−	1.73205i	0.0361315	−	0.0625815i
$767$	16.3723	−	4.38695i	0.591170	−	0.158404i
$768$		0			0
$769$		−	35.6332i		−	1.28497i	−0.766299	−	0.642484i	$-0.777904\pi$
$769$		−	35.6332i		−	1.28497i	0.766299	−	0.642484i	$-0.222096\pi$
$770$	16.4049	−	7.54730i	0.591191	−	0.271986i
$771$		0			0
$772$	−10.2110	−	2.73602i	−0.367500	−	0.0984714i
$773$	6.53945	+	24.4056i	0.235208	+	0.877807i	0.978055	+	0.208346i	$0.0668081\pi$
$773$	6.53945	+	24.4056i	0.235208	+	0.877807i	−0.742847	+	0.669461i	$0.766525\pi$
$774$		0			0
$775$	−6.16337	−	13.6753i	−0.221395	−	0.491230i
$776$		−	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
$782$	−1.88071	+	7.01890i	−0.0672540	+	0.250995i
$783$		0			0
$784$	−6.33638	+	2.97494i	−0.226299	+	0.106248i
$785$	−7.81362	−	8.63828i	−0.278880	−	0.308313i
$786$		0			0
$787$	−8.03421	−	29.9841i	−0.286389	−	1.06882i	−0.947819	−	0.318810i	$-0.896717\pi$
$787$	−8.03421	−	29.9841i	−0.286389	−	1.06882i	0.661430	−	0.750007i	$-0.269950\pi$
$788$	−6.70335	−	25.0172i	−0.238797	−	0.891202i
$789$		0			0
$790$	5.44987	+	6.02506i	0.193898	+	0.214362i
$791$	−5.28676	−	0.223888i	−0.187976	−	0.00796052i
$792$		0			0
$793$	2.31205	−	8.62867i	0.0821031	−	0.306413i
$794$	−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	0.999453	−	0.0330615i	$-0.0105257\pi$
$797$	27.2824	+	27.2824i	0.966392	+	0.966392i	−0.0330615	+	0.999453i	$0.510526\pi$
$798$		0			0
$799$			1.36675i			0.0483522i
$800$	1.77057	−	4.67601i	0.0625992	−	0.165322i
$801$		0			0
$802$	−5.47203	−	20.4219i	−0.193224	−	0.721123i
$803$	11.1884	+	2.99793i	0.394831	+	0.105795i
$804$		0			0
$805$	−8.12845	−	5.75410i	−0.286490	−	0.202805i
$806$		−	4.24264i		−	0.149441i
$807$		0			0
$808$	16.3238	−	4.37396i	0.574270	−	0.153875i
$809$	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	$0.160131\pi$
$812$	−3.38747	−	15.1857i	−0.118877	−	0.532915i
$813$		0			0
$814$	−18.6915	+	10.7916i	−0.655138	+	0.378244i
$815$	5.28280	+	24.5784i	0.185048	+	0.860943i
$816$		0			0
$817$	65.8648	+	17.6484i	2.30432	+	0.617440i
$818$	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	−0.537800	−	0.843072i	$-0.680745\pi$
$821$	−2.19421	+	1.26683i	−0.0765783	+	0.0442125i	0.461222	+	0.887285i	$0.347411\pi$
$822$		0			0
$823$	28.5496	−	7.64984i	0.995176	−	0.266657i	0.275753	−	0.961229i	$-0.411073\pi$
$823$	28.5496	−	7.64984i	0.995176	−	0.266657i	0.719423	+	0.694572i	$0.244406\pi$
$824$	−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	0.0327270	−	0.999464i	$-0.489581\pi$
$827$	−27.8011	−	27.8011i	−0.966737	−	0.966737i	−0.999464	+	0.0327270i	$0.989581\pi$
$828$		0			0
$829$	−14.5922	−	8.42481i	−0.506808	−	0.292606i	0.224713	−	0.974425i	$-0.427856\pi$
$829$	−14.5922	−	8.42481i	−0.506808	−	0.292606i	−0.731521	+	0.681819i	$0.761189\pi$
$830$	23.0376	+	14.8864i	0.799647	+	0.516713i
$831$		0			0
$832$	1.00000	−	1.00000i	0.0346688	−	0.0346688i
$833$	5.32495	+	29.7435i	0.184499	+	1.03055i
$834$		0			0
$835$	−17.0256	−	5.48913i	−0.589194	−	0.189959i
$836$	16.6973	+	9.64016i	0.577487	+	0.333412i
$837$		0			0
$838$	−1.59834	+	5.96509i	−0.0552138	+	0.206061i
$839$	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
$842$	−8.17431	+	30.5070i	−0.281705	+	1.05134i
$843$		0			0
$844$	4.28672	+	2.47494i	0.147555	+	0.0851909i
$845$	−11.2165	−	21.8904i	−0.385861	−	0.753052i
$846$		0			0
$847$	1.33372	−	4.24941i	0.0458270	−	0.146011i
$848$	−1.15488	+	1.15488i	−0.0396588	+	0.0396588i
$849$		0			0
$850$	−17.5187	−	12.6066i	−0.600886	−	0.432404i
$851$	10.3085	+	5.95163i	0.353372	+	0.204019i
$852$		0			0
$853$	15.6834	+	15.6834i	0.536989	+	0.536989i	0.922643	−	0.385655i	$-0.126024\pi$
$853$	15.6834	+	15.6834i	0.536989	+	0.536989i	−0.385655	+	0.922643i	$0.626024\pi$
$854$	−14.1067	−	8.96100i	−0.482721	−	0.306639i
$855$		0			0
$856$	−6.81662	−	11.8067i	−0.232987	−	0.403546i
$857$	42.1949	−	11.3061i	1.44135	−	0.386209i	0.548344	−	0.836253i	$-0.315258\pi$
$857$	42.1949	−	11.3061i	1.44135	−	0.386209i	0.893006	+	0.450044i	$0.148592\pi$
$858$		0			0
$859$	11.1281	−	6.42481i	0.379686	−	0.219212i	−0.297996	−	0.954567i	$-0.596318\pi$
$859$	11.1281	−	6.42481i	0.379686	−	0.219212i	0.677682	+	0.735355i	$0.262985\pi$
$860$	16.1926	+	17.9016i	0.552162	+	0.610438i
$861$		0			0
$862$	9.05013	−	9.05013i	0.308249	−	0.308249i
$863$	24.9204	+	6.67740i	0.848300	+	0.227301i	0.656681	−	0.754168i	$-0.271960\pi$
$863$	24.9204	+	6.67740i	0.848300	+	0.227301i	0.191619	+	0.981469i	$0.438626\pi$
$864$		0			0
$865$	−43.5036	+	9.35053i	−1.47917	+	0.317928i
$866$	−7.40986	+	4.27808i	−0.251797	+	0.145375i
$867$		0			0
$868$	−7.57301	−	2.37686i	−0.257045	−	0.0806759i
$869$	−11.0898			−0.376196
$870$		0			0
$871$	−10.6332	+	18.4173i	−0.360294	+	0.624047i
$872$	−16.6782	+	4.46890i	−0.564794	+	0.151336i
$873$		0			0
$874$		−	10.6332i		−	0.359675i
$875$	24.5330	−	16.5267i	0.829366	−	0.558705i
$876$		0			0
$877$	−16.2554	−	4.35561i	−0.548904	−	0.147079i	−0.0263005	−	0.999654i	$-0.508373\pi$
$877$	−16.2554	−	4.35561i	−0.548904	−	0.147079i	−0.522604	+	0.852576i	$0.675039\pi$
$878$	1.18620	+	4.42696i	0.0400323	+	0.149403i
$879$		0			0
$880$	3.11240	+	6.07421i	0.104919	+	0.204762i
$881$		−	20.6945i		−	0.697217i	−0.937268	−	0.348608i	$-0.886654\pi$
$881$		−	20.6945i		−	0.697217i	0.937268	−	0.348608i	$-0.113346\pi$
$882$		0			0
$883$	3.68338	+	3.68338i	0.123955	+	0.123955i	0.766363	−	0.642408i	$-0.222064\pi$
$883$	3.68338	+	3.68338i	0.123955	+	0.123955i	−0.642408	+	0.766363i	$0.722064\pi$
$884$	−3.05231	−	5.28676i	−0.102660	−	0.177813i
$885$		0			0
$886$	−10.9749	+	19.0091i	−0.368710	+	0.638625i
$887$	0.245846	−	0.917508i	0.00825469	−	0.0308069i	−0.961676	−	0.274190i	$-0.911590\pi$
$887$	0.245846	−	0.917508i	0.00825469	−	0.0308069i	0.969930	+	0.243383i	$0.0782571\pi$
$888$		0			0
$889$	−17.9123	−	0.758564i	−0.600760	−	0.0254414i
$890$	−20.9893	+	18.9856i	−0.703563	+	0.636397i
$891$		0			0
$892$	5.91435	+	22.0727i	0.198027	+	0.739047i
$893$	−0.517638	−	1.93185i	−0.0173221	−	0.0646470i
$894$		0			0
$895$	−0.158312	+	3.15831i	−0.00529180	+	0.105571i
$896$	−1.22474	−	2.34521i	−0.0409159	−	0.0783479i
$897$		0			0
$898$	−6.06984	+	22.6530i	−0.202553	+	0.755939i
$899$	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
$905$	49.0210	−	25.1182i	1.62951	−	0.834956i
$906$		0			0
$907$	−5.02681	−	18.7603i	−0.166912	−	0.622926i	−0.997789	−	0.0664684i	$-0.978827\pi$
$907$	−5.02681	−	18.7603i	−0.166912	−	0.622926i	0.830876	−	0.556458i	$-0.187840\pi$
$908$	−16.1149	−	4.31798i	−0.534792	−	0.143297i
$909$		0			0
$910$	8.24685	−	1.41047i	0.273380	−	0.0467566i
$911$			6.48152i			0.214742i	0.994219	+	0.107371i	$0.0342433\pi$
$911$			6.48152i			0.214742i	−0.994219	+	0.107371i	$0.965757\pi$
$912$		0			0
$913$	−36.1654	+	9.69050i	−1.19690	+	0.320709i
$914$	16.7877	−	29.0772i	0.555289	−	0.961788i
$915$		0			0
$916$	26.0000			0.859064
$917$	31.5644	+	9.90678i	1.04235	+	0.327151i
$918$		0			0
$919$	16.6853	−	9.63325i	0.550397	−	0.317772i	−0.198885	−	0.980023i	$-0.563732\pi$
$919$	16.6853	−	9.63325i	0.550397	−	0.317772i	0.749282	+	0.662251i	$0.230399\pi$
$920$	2.04291	−	3.16153i	0.0673527	−	0.104233i
$921$		0			0
$922$	−0.0684729	−	0.0183473i	−0.00225503	−	0.000604235i
$923$	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
$928$	5.68036	−	1.52205i	0.186467	−	0.0499637i
$929$	−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
$935$	28.8039	−	6.19102i	0.941989	−	0.202468i
$936$		0			0
$937$	33.3747	−	33.3747i	1.09030	−	1.09030i	0.0948079	−	0.995496i	$-0.469776\pi$
$937$	33.3747	−	33.3747i	1.09030	−	1.09030i	0.995496	−	0.0948079i	$-0.0302237\pi$
$938$	26.9174	+	29.2981i	0.878885	+	0.956616i
$939$		0			0
$940$	0.217249	−	0.673839i	0.00708589	−	0.0219782i
$941$	4.19452	+	2.42171i	0.136737	+	0.0789454i	0.566808	−	0.823850i	$-0.308178\pi$
$941$	4.19452	+	2.42171i	0.136737	+	0.0789454i	−0.430071	+	0.902795i	$0.641511\pi$
$942$		0			0
$943$	−1.23232	+	4.59907i	−0.0401297	+	0.149766i
$944$	11.9854			0.390091
$945$		0			0
$946$	−32.9499			−1.07129
$947$	6.37555	−	23.7939i	0.207178	−	0.773198i	−0.781597	−	0.623784i	$-0.785595\pi$
$947$	6.37555	−	23.7939i	0.207178	−	0.773198i	0.988775	−	0.149414i	$-0.0477387\pi$
$948$		0			0
$949$	4.64774	+	2.68338i	0.150872	+	0.0871060i
$950$	29.5366	+	11.1840i	0.958294	+	0.362858i
$951$		0			0
$952$	−11.1468	+	2.48650i	−0.361268	+	0.0805879i
$953$	24.1237	−	24.1237i	0.781445	−	0.781445i	−0.198630	−	0.980075i	$-0.563649\pi$
$953$	24.1237	−	24.1237i	0.781445	−	0.781445i	0.980075	+	0.198630i	$0.0636492\pi$
$954$		0			0
$955$	25.1144	−	38.8662i	0.812684	−	1.25768i
$956$	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
$962$	−9.65926	+	2.58819i	−0.311427	+	0.0834466i
$963$		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	−0.104077	−	0.994569i	$-0.533189\pi$
$967$	27.6913	−	27.6913i	0.890493	−	0.890493i	0.994569	+	0.104077i	$0.0331888\pi$
$968$	1.62602	+	0.435690i	0.0522621	+	0.0140036i
$969$		0			0
$970$	15.5157	+	10.0258i	0.498178	+	0.321911i
$971$	24.9538	−	14.4071i	0.800805	−	0.462345i	−0.0429474	−	0.999077i	$-0.513675\pi$
$971$	24.9538	−	14.4071i	0.800805	−	0.462345i	0.843753	+	0.536732i	$0.180341\pi$
$972$		0			0
$973$	−25.8472	+	23.7470i	−0.828625	+	0.761294i
$974$	16.2280			0.519979
$975$		0			0
$976$	3.15831	−	5.47036i	0.101095	−	0.175102i
$977$	11.2853	−	3.02388i	0.361048	−	0.0967425i	−0.0737348	−	0.997278i	$-0.523492\pi$
$977$	11.2853	−	3.02388i	0.361048	−	0.0967425i	0.434783	+	0.900535i	$0.356825\pi$
$978$		0			0
$979$		−	38.6332i		−	1.23472i
$980$	2.10249	−	15.5106i	0.0671616	−	0.495469i
$981$		0			0
$982$	−13.3755	−	3.58396i	−0.426830	−	0.114369i
$983$	−2.26040	−	8.43591i	−0.0720954	−	0.269064i	0.920464	−	0.390828i	$-0.127811\pi$
$983$	−2.26040	−	8.43591i	−0.0720954	−	0.269064i	−0.992559	+	0.121764i	$0.961145\pi$
$984$		0			0
$985$	55.1197	+	17.7709i	1.75626	+	0.566227i
$986$		−	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	$0.255358\pi$
$992$	0.776457	−	2.89778i	0.0246525	−	0.0920045i
$993$		0			0
$994$	−2.28046	−	4.36675i	−0.0723318	−	0.138505i
$995$	−10.3473	−	0.518663i	−0.328031	−	0.0164427i
$996$		0			0
$997$	−3.04410	−	11.3607i	−0.0964075	−	0.359798i	0.900822	−	0.434189i	$-0.142965\pi$
$997$	−3.04410	−	11.3607i	−0.0964075	−	0.359798i	−0.997229	+	0.0743918i	$0.976298\pi$
$998$	−5.69402	−	21.2504i	−0.180241	−	0.672669i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.b.53.1	✓	16	3.2	odd	2	inner
630.2.ce.b.53.4	yes	16	1.1	even	1	trivial
630.2.ce.b.107.1	yes	16	35.2	odd	12	inner
630.2.ce.b.107.4	yes	16	105.2	even	12	inner
630.2.ce.b.233.1	yes	16	7.2	even	3	inner
630.2.ce.b.233.4	yes	16	21.2	odd	6	inner
630.2.ce.b.557.1	yes	16	15.2	even	4	inner
630.2.ce.b.557.4	yes	16	5.2	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(1.99004 - 1.01969i) q^{5} +(1.79000 + 1.94831i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.469882 - 2.18614i) q^{10} +(2.64338 + 1.52616i) q^{11} +(1.00000 + 1.00000i) q^{13} +(2.34521 - 1.22474i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.16954 - 1.11722i) q^{17} +(-5.47036 + 3.15831i) q^{19} +(-2.23326 - 0.111944i) q^{20} +(2.15831 - 2.15831i) q^{22} +(-1.62602 - 0.435690i) q^{23} +(2.92048 - 4.05842i) q^{25} +(1.22474 - 0.707107i) q^{26} +(-0.576028 - 2.58228i) q^{28} +5.88074 q^{29} +(1.50000 - 2.59808i) q^{31} +(0.965926 - 0.258819i) q^{32} -4.31662i q^{34} +(5.54882 + 2.05197i) q^{35} +(-6.83013 - 1.83013i) q^{37} +(1.63486 + 6.10139i) q^{38} +(-0.686141 + 2.12819i) q^{40} -2.82843i q^{41} +(-7.63325 - 7.63325i) q^{43} +(-1.52616 - 2.64338i) q^{44} +(-0.841688 + 1.45785i) q^{46} +(-0.0819485 + 0.305836i) q^{47} +(-0.591820 + 6.97494i) q^{49} +(-3.16426 - 3.87137i) q^{50} +(-0.366025 - 1.36603i) q^{52} +(0.422716 + 1.57760i) q^{53} +(6.81662 + 0.341688i) q^{55} +(-2.64338 - 0.111944i) q^{56} +(1.52205 - 5.68036i) q^{58} +(5.99269 - 10.3796i) q^{59} +(-3.15831 - 5.47036i) q^{61} +(-2.12132 - 2.12132i) q^{62} -1.00000i q^{64} +(3.00972 + 0.970349i) q^{65} +(3.89204 + 14.5253i) q^{67} +(-4.16954 - 1.11722i) q^{68} +(3.41819 - 4.82866i) q^{70} -1.86199i q^{71} +(3.66556 - 0.982183i) q^{73} +(-3.53553 + 6.12372i) q^{74} +6.31662 q^{76} +(1.75822 + 7.88194i) q^{77} +(-3.14649 + 1.81662i) q^{79} +(1.87809 + 1.21358i) q^{80} +(-2.73205 - 0.732051i) q^{82} +(-8.67372 + 8.67372i) q^{83} +(7.15831 - 6.47494i) q^{85} +(-9.34878 + 5.39752i) q^{86} +(-2.94831 + 0.789997i) q^{88} +(-6.32852 - 10.9613i) q^{89} +(-0.158312 + 3.73831i) q^{91} +(1.19033 + 1.19033i) q^{92} +(0.274205 + 0.158312i) q^{94} +(-7.66572 + 11.8632i) q^{95} +(-5.84169 + 5.84169i) q^{97} +(6.58410 + 2.37690i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{7} + 16 q^{13} + 8 q^{16} + 8 q^{22} - 12 q^{28} + 24 q^{31} - 40 q^{37} + 12 q^{40} - 16 q^{43} - 40 q^{46} + 8 q^{52} + 56 q^{55} - 20 q^{58} - 24 q^{61} - 32 q^{67} + 4 q^{70} + 48 q^{73}+ \cdots - 120 q^{97}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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