LMFDB - Embedded newform 630.2.bo.a.269.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(89,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("630.89");

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.bo (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 21 x^{14} - 54 x^{13} + 113 x^{12} - 168 x^{11} + 186 x^{10} - 84 x^{9} + \cdots + 390625 $ x^16 - 6x^15 + 21x^14 - 54x^13 + 113x^12 - 168x^11 + 186x^10 - 84x^9 - 6x^8 - 420x^7 + 4650x^6 - 21000x^5 + 70625x^4 - 168750x^3 + 328125x^2 - 468750*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.3
Root			$1.68760 + 1.46697i$ of defining polynomial
Character	$\chi$	$=$	630.269
Dual form			630.2.bo.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.68760 + 1.46697i) q^{5} +(-2.30608 - 1.29693i) q^{7} +1.00000 q^{8} +(2.11423 + 0.728019i) q^{10} +(1.11120 + 0.641550i) q^{11} +6.14864 q^{13} +(0.0298666 + 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.64871 - 3.26128i) q^{17} +(5.22868 - 3.01878i) q^{19} +(-0.426635 - 2.19499i) q^{20} -1.28310i q^{22} +(-1.43958 - 2.49343i) q^{23} +(0.695987 - 4.95132i) q^{25} +(-3.07432 - 5.32488i) q^{26} +(2.27621 - 1.34866i) q^{28} -1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(-0.500000 + 0.866025i) q^{32} +6.52257i q^{34} +(5.79429 - 1.19425i) q^{35} +(8.25652 - 4.76690i) q^{37} +(-5.22868 - 3.01878i) q^{38} +(-1.68760 + 1.46697i) q^{40} +8.71759 q^{41} -5.35859i q^{43} +(-1.11120 + 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(0.698165 - 0.403086i) q^{47} +(3.63597 + 5.98162i) q^{49} +(-4.63597 + 1.87292i) q^{50} +(-3.07432 + 5.32488i) q^{52} +(3.33413 - 5.77488i) q^{53} +(-2.81639 + 0.547415i) q^{55} +(-2.30608 - 1.29693i) q^{56} +(-1.16959 + 0.675260i) q^{58} +(-0.798110 + 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} +8.65515i q^{62} +1.00000 q^{64} +(-10.3764 + 9.01988i) q^{65} +(4.67188 + 2.69731i) q^{67} +(5.64871 - 3.26128i) q^{68} +(-3.93140 - 4.42087i) q^{70} -15.6787i q^{71} +(-6.20837 + 10.7532i) q^{73} +(-8.25652 - 4.76690i) q^{74} +6.03756i q^{76} +(-1.73046 - 2.92060i) q^{77} +(-5.59093 - 9.68377i) q^{79} +(2.11423 + 0.728019i) q^{80} +(-4.35880 - 7.54966i) q^{82} +3.74493i q^{83} +(14.3170 - 2.78275i) q^{85} +(-4.64067 + 2.67929i) q^{86} +(1.11120 + 0.641550i) q^{88} +(1.81971 + 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} +2.87917 q^{92} +(-0.698165 - 0.403086i) q^{94} +(-4.39545 + 12.7648i) q^{95} -8.76818 q^{97} +(3.36225 - 6.13965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50}+ \cdots + 20 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.68760	+	1.46697i	−0.754718	+	0.656050i
$5$	−1.68760	+	1.46697i	−0.754718	+	0.656050i
$6$		0			0
$7$	−2.30608	−	1.29693i	−0.871614	−	0.490192i
$7$	−2.30608	−	1.29693i	−0.871614	−	0.490192i
$8$	1.00000			0.353553
$9$		0			0
$10$	2.11423	+	0.728019i	0.668580	+	0.230220i
$11$	1.11120	+	0.641550i	0.335038	+	0.193435i	0.658076	−	0.752952i	$-0.271371\pi$
$11$	1.11120	+	0.641550i	0.335038	+	0.193435i	−0.323037	+	0.946386i	$0.604704\pi$
$12$		0			0
$13$	6.14864			1.70533			0.852663	−	0.522462i	$-0.174986\pi$
$13$	6.14864			1.70533			0.852663	+	0.522462i	$0.174986\pi$
$14$	0.0298666	+	2.64558i	0.00798219	+	0.707062i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.64871	−	3.26128i	−1.37001	−	0.790977i	−0.379084	−	0.925362i	$-0.623761\pi$
$17$	−5.64871	−	3.26128i	−1.37001	−	0.790977i	−0.990929	+	0.134385i	$0.957094\pi$
$18$		0			0
$19$	5.22868	−	3.01878i	1.19954	−	0.692555i	0.239088	−	0.970998i	$-0.423152\pi$
$19$	5.22868	−	3.01878i	1.19954	−	0.692555i	0.960453	+	0.278443i	$0.0898183\pi$
$20$	−0.426635	−	2.19499i	−0.0953985	−	0.490815i
$21$		0			0
$22$		−	1.28310i		−	0.273558i
$23$	−1.43958	−	2.49343i	−0.300174	−	0.519917i	0.676001	−	0.736901i	$-0.263711\pi$
$23$	−1.43958	−	2.49343i	−0.300174	−	0.519917i	−0.976175	+	0.216984i	$0.930378\pi$
$24$		0			0
$25$	0.695987	−	4.95132i	0.139197	−	0.990265i
$26$	−3.07432	−	5.32488i	−0.602923	−	1.04429i
$27$		0			0
$28$	2.27621	−	1.34866i	0.430163	−	0.254872i
$29$		−	1.35052i		−	0.250785i	−0.992107	−	0.125393i	$-0.959981\pi$
$29$		−	1.35052i		−	0.250785i	0.992107	−	0.125393i	$-0.0400191\pi$
$30$		0			0
$31$	−7.49558	−	4.32758i	−1.34625	−	0.777255i	−0.358530	−	0.933518i	$-0.616722\pi$
$31$	−7.49558	−	4.32758i	−1.34625	−	0.777255i	−0.987716	+	0.156263i	$0.950055\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$			6.52257i			1.11861i
$35$	5.79429	−	1.19425i	0.979413	−	0.201866i
$36$		0			0
$37$	8.25652	−	4.76690i	1.35736	−	0.783674i	0.368095	−	0.929788i	$-0.380010\pi$
$37$	8.25652	−	4.76690i	1.35736	−	0.783674i	0.989268	+	0.146114i	$0.0466766\pi$
$38$	−5.22868	−	3.01878i	−0.848203	−	0.489710i
$39$		0			0
$40$	−1.68760	+	1.46697i	−0.266833	+	0.231949i
$41$	8.71759			1.36146			0.680730	−	0.732535i	$-0.261663\pi$
$41$	8.71759			1.36146			0.680730	+	0.732535i	$0.261663\pi$
$42$		0			0
$43$		−	5.35859i		−	0.817177i	−0.912719	−	0.408588i	$-0.866021\pi$
$43$		−	5.35859i		−	0.817177i	0.912719	−	0.408588i	$-0.133979\pi$
$44$	−1.11120	+	0.641550i	−0.167519	+	0.0967173i
$45$		0			0
$46$	−1.43958	+	2.49343i	−0.212255	+	0.367637i
$47$	0.698165	−	0.403086i	0.101838	−	0.0587961i	−0.448216	−	0.893925i	$-0.647940\pi$
$47$	0.698165	−	0.403086i	0.101838	−	0.0587961i	0.550054	+	0.835129i	$0.314607\pi$
$48$		0			0
$49$	3.63597	+	5.98162i	0.519424	+	0.854517i
$50$	−4.63597	+	1.87292i	−0.655625	+	0.264871i
$51$		0			0
$52$	−3.07432	+	5.32488i	−0.426331	+	0.738427i
$53$	3.33413	−	5.77488i	0.457978	−	0.793241i	−0.540876	−	0.841102i	$-0.681907\pi$
$53$	3.33413	−	5.77488i	0.457978	−	0.793241i	0.998854	+	0.0478611i	$0.0152405\pi$
$54$		0			0
$55$	−2.81639	+	0.547415i	−0.379762	+	0.0738134i
$56$	−2.30608	−	1.29693i	−0.308162	−	0.173309i
$57$		0			0
$58$	−1.16959	+	0.675260i	−0.153574	+	0.0886660i
$59$	−0.798110	+	1.38237i	−0.103905	+	0.179969i	−0.913290	−	0.407309i	$-0.866467\pi$
$59$	−0.798110	+	1.38237i	−0.103905	+	0.179969i	0.809385	+	0.587278i	$0.199800\pi$
$60$		0			0
$61$	−5.50239	+	3.17681i	−0.704509	+	0.406748i	−0.809025	−	0.587775i	$-0.800004\pi$
$61$	−5.50239	+	3.17681i	−0.704509	+	0.406748i	0.104516	+	0.994523i	$0.466671\pi$
$62$			8.65515i			1.09921i
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.3764	+	9.01988i	−1.28704	+	1.11878i
$66$		0			0
$67$	4.67188	+	2.69731i	0.570761	+	0.329529i	0.757453	−	0.652889i	$-0.226443\pi$
$67$	4.67188	+	2.69731i	0.570761	+	0.329529i	−0.186692	+	0.982418i	$0.559777\pi$
$68$	5.64871	−	3.26128i	0.685006	−	0.395489i
$69$		0			0
$70$	−3.93140	−	4.42087i	−0.469892	−	0.528395i
$71$		−	15.6787i		−	1.86072i	−0.366650	−	0.930359i	$-0.619495\pi$
$71$		−	15.6787i		−	1.86072i	0.366650	−	0.930359i	$-0.380505\pi$
$72$		0			0
$73$	−6.20837	+	10.7532i	−0.726635	+	1.25857i	0.231663	+	0.972796i	$0.425583\pi$
$73$	−6.20837	+	10.7532i	−0.726635	+	1.25857i	−0.958298	+	0.285772i	$0.907750\pi$
$74$	−8.25652	−	4.76690i	−0.959801	−	0.554141i
$75$		0			0
$76$			6.03756i			0.692555i
$77$	−1.73046	−	2.92060i	−0.197204	−	0.332834i
$78$		0			0
$79$	−5.59093	−	9.68377i	−0.629028	−	1.08951i	−0.987747	−	0.156064i	$-0.950120\pi$
$79$	−5.59093	−	9.68377i	−0.629028	−	1.08951i	0.358719	−	0.933446i	$-0.383214\pi$
$80$	2.11423	+	0.728019i	0.236379	+	0.0813949i
$81$		0			0
$82$	−4.35880	−	7.54966i	−0.481349	−	0.833720i
$83$			3.74493i			0.411059i	0.978651	+	0.205530i	$0.0658917\pi$
$83$			3.74493i			0.411059i	−0.978651	+	0.205530i	$0.934108\pi$
$84$		0			0
$85$	14.3170	−	2.78275i	1.55289	−	0.301832i
$86$	−4.64067	+	2.67929i	−0.500417	+	0.288916i
$87$		0			0
$88$	1.11120	+	0.641550i	0.118454	+	0.0683894i
$89$	1.81971	+	3.15183i	0.192889	+	0.334093i	0.946206	−	0.323564i	$-0.104881\pi$
$89$	1.81971	+	3.15183i	0.192889	+	0.334093i	−0.753318	+	0.657657i	$0.771548\pi$
$90$		0			0
$91$	−14.1792	−	7.97433i	−1.48639	−	0.835937i
$92$	2.87917			0.300174
$93$		0			0
$94$	−0.698165	−	0.403086i	−0.0720102	−	0.0415751i
$95$	−4.39545	+	12.7648i	−0.450964	+	1.30964i
$96$		0			0
$97$	−8.76818			−0.890274			−0.445137	−	0.895463i	$-0.646845\pi$
$97$	−8.76818			−0.890274			−0.445137	+	0.895463i	$0.646845\pi$
$98$	3.36225	−	6.13965i	0.339639	−	0.620198i
$99$		0			0
$100$	3.93998	+	3.07840i	0.393998	+	0.307840i
$101$	0.853270	−	1.47791i	0.0849035	−	0.147057i	−0.820447	−	0.571723i	$-0.806275\pi$
$101$	0.853270	−	1.47791i	0.0849035	−	0.147057i	0.905350	+	0.424666i	$0.139608\pi$
$102$		0			0
$103$	5.18220	+	8.97583i	0.510617	+	0.884415i	0.999924	+	0.0123035i	$0.00391643\pi$
$103$	5.18220	+	8.97583i	0.510617	+	0.884415i	−0.489307	+	0.872112i	$0.662750\pi$
$104$	6.14864			0.602923
$105$		0			0
$106$	−6.66826			−0.647679
$107$	5.75680	+	9.97106i	0.556531	+	0.963939i	0.997783	+	0.0665560i	$0.0212011\pi$
$107$	5.75680	+	9.97106i	0.556531	+	0.963939i	−0.441252	+	0.897383i	$0.645466\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	1.88227	+	2.16536i	0.179468	+	0.206459i
$111$		0			0
$112$	0.0298666	+	2.64558i	0.00282213	+	0.249984i
$113$	13.3875			1.25939			0.629695	−	0.776843i	$-0.283180\pi$
$113$	13.3875			1.25939			0.629695	+	0.776843i	$0.283180\pi$
$114$		0			0
$115$	6.08724	+	2.09609i	0.567638	+	0.195461i
$116$	1.16959	+	0.675260i	0.108593	+	0.0626963i
$117$		0			0
$118$	1.59622			0.146944
$119$	8.79670	+	14.8467i	0.806392	+	1.36100i
$120$		0			0
$121$	−4.67683	−	8.10050i	−0.425166	−	0.736409i
$122$	5.50239	+	3.17681i	0.498163	+	0.287615i
$123$		0			0
$124$	7.49558	−	4.32758i	0.673123	−	0.388628i
$125$	6.08890	+	9.37685i	0.544608	+	0.838691i
$126$		0			0
$127$			5.65313i			0.501634i	0.968035	+	0.250817i	$0.0806992\pi$
$127$			5.65313i			0.501634i	−0.968035	+	0.250817i	$0.919301\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	12.9997	+	4.47632i	1.14015	+	0.392599i
$131$	−6.23366	−	10.7970i	−0.544638	−	0.943340i	−0.998630	−	0.0523344i	$-0.983334\pi$
$131$	−6.23366	−	10.7970i	−0.544638	−	0.943340i	0.453992	−	0.891006i	$-0.349999\pi$
$132$		0			0
$133$	−15.9729	+	0.180321i	−1.38502	+	0.0156358i
$134$		−	5.39463i		−	0.466025i
$135$		0			0
$136$	−5.64871	−	3.26128i	−0.484373	−	0.279653i
$137$	0.0254843	−	0.0441401i	0.00217727	−	0.00377114i	−0.864935	−	0.501884i	$-0.832640\pi$
$137$	0.0254843	−	0.0441401i	0.00217727	−	0.00377114i	0.867112	+	0.498113i	$0.165974\pi$
$138$		0			0
$139$			1.05069i			0.0891184i	0.999007	+	0.0445592i	$0.0141883\pi$
$139$			1.05069i			0.0891184i	−0.999007	+	0.0445592i	$0.985812\pi$
$140$	−1.86289	+	5.61513i	−0.157443	+	0.474565i
$141$		0			0
$142$	−13.5781	+	7.83934i	−1.13945	+	0.657863i
$143$	6.83235	+	3.94466i	0.571350	+	0.329869i
$144$		0			0
$145$	1.98118	+	2.27914i	0.164528	+	0.189272i
$146$	12.4167			1.02762
$147$		0			0
$148$			9.53381i			0.783674i
$149$	−7.12137	+	4.11153i	−0.583406	+	0.336829i	−0.762486	−	0.647005i	$-0.776021\pi$
$149$	−7.12137	+	4.11153i	−0.583406	+	0.336829i	0.179080	+	0.983835i	$0.442688\pi$
$150$		0			0
$151$	2.13357	−	3.69546i	0.173628	−	0.300732i	−0.766058	−	0.642772i	$-0.777784\pi$
$151$	2.13357	−	3.69546i	0.173628	−	0.300732i	0.939686	+	0.342040i	$0.111118\pi$
$152$	5.22868	−	3.01878i	0.424102	−	0.244855i
$153$		0			0
$154$	−1.66409	+	2.95892i	−0.134096	+	0.238437i
$155$	18.9980	−	3.69259i	1.52595	−	0.296596i
$156$		0			0
$157$	2.41601	−	4.18466i	0.192819	−	0.333972i	−0.753364	−	0.657603i	$-0.771570\pi$
$157$	2.41601	−	4.18466i	0.192819	−	0.333972i	0.946183	+	0.323631i	$0.104904\pi$
$158$	−5.59093	+	9.68377i	−0.444790	+	0.770399i
$159$		0			0
$160$	−0.426635	−	2.19499i	−0.0337285	−	0.173529i
$161$	0.0859910	+	7.61708i	0.00677704	+	0.600310i
$162$		0			0
$163$	9.31256	−	5.37661i	0.729416	−	0.421128i	−0.0887927	−	0.996050i	$-0.528301\pi$
$163$	9.31256	−	5.37661i	0.729416	−	0.421128i	0.818208	+	0.574922i	$0.194968\pi$
$164$	−4.35880	+	7.54966i	−0.340365	+	0.589529i
$165$		0			0
$166$	3.24320	−	1.87246i	0.251721	−	0.145331i
$167$		−	18.9267i		−	1.46459i	−0.680988	−	0.732295i	$-0.738449\pi$
$167$		−	18.9267i		−	1.46459i	0.680988	−	0.732295i	$-0.261551\pi$
$168$		0			0
$169$	24.8057			1.90813
$170$	−9.56842	−	11.0075i	−0.733864	−	0.844235i
$171$		0			0
$172$	4.64067	+	2.67929i	0.353848	+	0.204294i
$173$	−10.2568	+	5.92176i	−0.779810	+	0.450223i	−0.836363	−	0.548176i	$-0.815322\pi$
$173$	−10.2568	+	5.92176i	−0.779810	+	0.450223i	0.0565531	+	0.998400i	$0.481989\pi$
$174$		0			0
$175$	−8.02650	+	10.5155i	−0.606746	+	0.794896i
$176$		−	1.28310i		−	0.0967173i
$177$		0			0
$178$	1.81971	−	3.15183i	0.136393	−	0.236239i
$179$	−3.27843	−	1.89280i	−0.245041	−	0.141475i	0.372450	−	0.928052i	$-0.378518\pi$
$179$	−3.27843	−	1.89280i	−0.245041	−	0.141475i	−0.617492	+	0.786577i	$0.711851\pi$
$180$		0			0
$181$			19.0033i			1.41251i	0.707960	+	0.706253i	$0.249616\pi$
$181$			19.0033i			1.41251i	−0.707960	+	0.706253i	$0.750384\pi$
$182$	0.183639	+	16.2667i	0.0136122	+	1.20577i
$183$		0			0
$184$	−1.43958	−	2.49343i	−0.106128	−	0.183818i
$185$	−6.94079	+	20.1567i	−0.510297	+	1.48195i
$186$		0			0
$187$	−4.18455	−	7.24785i	−0.306005	−	0.530016i
$188$			0.806172i			0.0587961i
$189$		0			0
$190$	13.2524	−	2.57583i	0.961428	−	0.186871i
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	−0.585995	−	0.810315i	$-0.699296\pi$
$191$	−2.44949	+	1.41421i	−0.177239	+	0.102329i	0.408756	+	0.912644i	$0.365963\pi$
$192$		0			0
$193$	3.06479	+	1.76946i	0.220608	+	0.127368i	0.606232	−	0.795288i	$-0.292680\pi$
$193$	3.06479	+	1.76946i	0.220608	+	0.127368i	−0.385623	+	0.922656i	$0.626014\pi$
$194$	4.38409	+	7.59347i	0.314759	+	0.545179i
$195$		0			0
$196$	−6.99822	+	0.158029i	−0.499873	+	0.0112878i
$197$	−2.36728			−0.168662			−0.0843308	−	0.996438i	$-0.526875\pi$
$197$	−2.36728			−0.168662			−0.0843308	+	0.996438i	$0.526875\pi$
$198$		0			0
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	0.389885	−	0.920864i	$-0.372515\pi$
$199$	−3.00000	−	1.73205i	−0.212664	−	0.122782i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0.695987	−	4.95132i	0.0492137	−	0.350111i
$201$		0			0
$202$	−1.70654			−0.120072
$203$	−1.75153	+	3.11440i	−0.122933	+	0.218588i
$204$		0			0
$205$	−14.7118	+	12.7885i	−1.02752	+	0.893185i
$206$	5.18220	−	8.97583i	0.361061	−	0.625376i
$207$		0			0
$208$	−3.07432	−	5.32488i	−0.213166	−	0.369214i
$209$	7.74679			0.535856
$210$		0			0
$211$	−14.3620			−0.988721			−0.494361	−	0.869257i	$-0.664598\pi$
$211$	−14.3620			−0.988721			−0.494361	+	0.869257i	$0.664598\pi$
$212$	3.33413	+	5.77488i	0.228989	+	0.396621i
$213$		0			0
$214$	5.75680	−	9.97106i	0.393527	−	0.681608i
$215$	7.86090	+	9.04315i	0.536109	+	0.616738i
$216$		0			0
$217$	11.6728	+	19.7009i	0.792403	+	1.33739i
$218$	2.00000			0.135457
$219$		0			0
$220$	0.934120	−	2.71277i	0.0629784	−	0.182895i
$221$	−34.7319	−	20.0524i	−2.33632	−	1.34887i
$222$		0			0
$223$	−13.5975			−0.910557			−0.455279	−	0.890349i	$-0.650460\pi$
$223$	−13.5975			−0.910557			−0.455279	+	0.890349i	$0.650460\pi$
$224$	2.27621	−	1.34866i	0.152086	−	0.0901109i
$225$		0			0
$226$	−6.69375	−	11.5939i	−0.445261	−	0.771215i
$227$	−10.7006	−	6.17797i	−0.710221	−	0.410046i	0.100922	−	0.994894i	$-0.467821\pi$
$227$	−10.7006	−	6.17797i	−0.710221	−	0.410046i	−0.811143	+	0.584848i	$0.801154\pi$
$228$		0			0
$229$	−2.09008	+	1.20671i	−0.138116	+	0.0797414i	−0.567466	−	0.823397i	$-0.692076\pi$
$229$	−2.09008	+	1.20671i	−0.138116	+	0.0797414i	0.429350	+	0.903138i	$0.358743\pi$
$230$	−1.22835	−	6.31975i	−0.0809952	−	0.416712i
$231$		0			0
$232$		−	1.35052i		−	0.0886660i
$233$	6.43780	+	11.1506i	0.421754	+	0.730500i	0.996111	−	0.0881051i	$-0.0280811\pi$
$233$	6.43780	+	11.1506i	0.421754	+	0.730500i	−0.574357	+	0.818605i	$0.694748\pi$
$234$		0			0
$235$	−0.586908	+	1.70444i	−0.0382857	+	0.111185i
$236$	−0.798110	−	1.38237i	−0.0519525	−	0.0899844i
$237$		0			0
$238$	8.45929	−	15.0415i	0.548334	−	0.974997i
$239$		−	27.2546i		−	1.76296i	−0.472226	−	0.881478i	$-0.656549\pi$
$239$		−	27.2546i		−	1.76296i	0.472226	−	0.881478i	$-0.343451\pi$
$240$		0			0
$241$	2.26690	+	1.30880i	0.146024	+	0.0843070i	0.571232	−	0.820789i	$-0.306466\pi$
$241$	2.26690	+	1.30880i	0.146024	+	0.0843070i	−0.425208	+	0.905096i	$0.639799\pi$
$242$	−4.67683	+	8.10050i	−0.300638	+	0.520720i
$243$		0			0
$244$		−	6.35361i		−	0.406748i
$245$	−14.9109	−	4.76072i	−0.952624	−	0.304151i
$246$		0			0
$247$	32.1492	−	18.5614i	2.04561	−	1.18103i
$248$	−7.49558	−	4.32758i	−0.475970	−	0.274801i
$249$		0			0
$250$	5.07614	−	9.96157i	0.321043	−	0.630025i
$251$	26.7173			1.68638			0.843190	−	0.537615i	$-0.180675\pi$
$251$	26.7173			1.68638			0.843190	+	0.537615i	$0.180675\pi$
$252$		0			0
$253$		−	3.69426i		−	0.232256i
$254$	4.89575	−	2.82656i	0.307187	−	0.177354i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.14632	−	5.28063i	0.570532	−	0.329397i	−0.186830	−	0.982392i	$-0.559821\pi$
$257$	9.14632	−	5.28063i	0.570532	−	0.329397i	0.757362	+	0.652996i	$0.226488\pi$
$258$		0			0
$259$	−25.2225	+	0.284743i	−1.56725	+	0.0176930i
$260$	−2.62322	−	13.4962i	−0.162685	−	0.836999i
$261$		0			0
$262$	−6.23366	+	10.7970i	−0.385117	+	0.667042i
$263$	4.16587	−	7.21550i	0.256879	−	0.444927i	−0.708526	−	0.705685i	$-0.750639\pi$
$263$	4.16587	−	7.21550i	0.256879	−	0.444927i	0.965404	+	0.260759i	$0.0839726\pi$
$264$		0			0
$265$	2.84491	+	14.6368i	0.174762	+	0.899130i
$266$	8.14259	+	13.7427i	0.499254	+	0.842621i
$267$		0			0
$268$	−4.67188	+	2.69731i	−0.285381	+	0.164765i
$269$	−7.14171	+	12.3698i	−0.435438	+	0.754201i	−0.997331	−	0.0730091i	$-0.976740\pi$
$269$	−7.14171	+	12.3698i	−0.435438	+	0.754201i	0.561893	+	0.827210i	$0.310073\pi$
$270$		0			0
$271$	−6.58566	+	3.80223i	−0.400050	+	0.230969i	−0.686506	−	0.727125i	$-0.740856\pi$
$271$	−6.58566	+	3.80223i	−0.400050	+	0.230969i	0.286456	+	0.958094i	$0.407523\pi$
$272$			6.52257i			0.395489i
$273$		0			0
$274$	−0.0509686			−0.00307912
$275$	3.94990	−	5.05538i	0.238188	−	0.304851i
$276$		0			0
$277$	−10.4270	−	6.02002i	−0.626497	−	0.361708i	0.152897	−	0.988242i	$-0.451140\pi$
$277$	−10.4270	−	6.02002i	−0.626497	−	0.361708i	−0.779394	+	0.626534i	$0.784473\pi$
$278$	0.909924	−	0.525345i	0.0545736	−	0.0315081i
$279$		0			0
$280$	5.79429	−	1.19425i	0.346275	−	0.0713704i
$281$			12.7879i			0.762861i	0.924397	+	0.381431i	$0.124569\pi$
$281$			12.7879i			0.762861i	−0.924397	+	0.381431i	$0.875431\pi$
$282$		0			0
$283$	7.77607	−	13.4685i	0.462239	−	0.800622i	−0.536833	−	0.843689i	$-0.680379\pi$
$283$	7.77607	−	13.4685i	0.462239	−	0.800622i	0.999072	+	0.0430666i	$0.0137128\pi$
$284$	13.5781	+	7.83934i	0.805715	+	0.465180i
$285$		0			0
$286$		−	7.88931i		−	0.466505i
$287$	−20.1034	−	11.3061i	−1.18667	−	0.667376i
$288$		0			0
$289$	12.7719	+	22.1216i	0.751290	+	1.30127i
$290$	0.983204	−	2.85532i	0.0577357	−	0.167670i
$291$		0			0
$292$	−6.20837	−	10.7532i	−0.363317	−	0.629284i
$293$			11.5536i			0.674967i	0.941331	+	0.337483i	$0.109576\pi$
$293$			11.5536i			0.674967i	−0.941331	+	0.337483i	$0.890424\pi$
$294$		0			0
$295$	−0.681003	−	3.50369i	−0.0396495	−	0.203993i
$296$	8.25652	−	4.76690i	0.479900	−	0.277071i
$297$		0			0
$298$	7.12137	+	4.11153i	0.412530	+	0.238174i
$299$	−8.85148	−	15.3312i	−0.511894	−	0.886627i
$300$		0			0
$301$	−6.94969	+	12.3573i	−0.400573	+	0.712263i
$302$	−4.26715			−0.245547
$303$		0			0
$304$	−5.22868	−	3.01878i	−0.299885	−	0.173139i
$305$	4.62555	−	13.4330i	0.264858	−	0.769173i
$306$		0			0
$307$	−2.57617			−0.147030			−0.0735150	−	0.997294i	$-0.523422\pi$
$307$	−2.57617			−0.147030			−0.0735150	+	0.997294i	$0.523422\pi$
$308$	3.39455	−	0.0383219i	0.193422	−	0.00218359i
$309$		0			0
$310$	−12.6969	−	14.6064i	−0.721133	−	0.829590i
$311$	12.3570	−	21.4030i	0.700702	−	1.21365i	−0.267519	−	0.963553i	$-0.586204\pi$
$311$	12.3570	−	21.4030i	0.700702	−	1.21365i	0.968220	−	0.250098i	$-0.0804629\pi$
$312$		0			0
$313$	4.50087	+	7.79573i	0.254404	+	0.440641i	0.964733	−	0.263229i	$-0.0847874\pi$
$313$	4.50087	+	7.79573i	0.254404	+	0.440641i	−0.710329	+	0.703869i	$0.751454\pi$
$314$	−4.83203			−0.272687
$315$		0			0
$316$	11.1819			0.629028
$317$	−11.9529	−	20.7031i	−0.671344	−	1.16280i	−0.977523	−	0.210828i	$-0.932384\pi$
$317$	−11.9529	−	20.7031i	−0.671344	−	1.16280i	0.306180	−	0.951974i	$-0.400949\pi$
$318$		0			0
$319$	0.866426	−	1.50069i	0.0485106	−	0.0840227i
$320$	−1.68760	+	1.46697i	−0.0943397	+	0.0820062i
$321$		0			0
$322$	6.55359	−	3.88301i	0.365217	−	0.216392i
$323$	−39.3804			−2.19118
$324$		0			0
$325$	4.27937	−	30.4439i	0.237377	−	1.68872i
$326$	−9.31256	−	5.37661i	−0.515775	−	0.297783i
$327$		0			0
$328$	8.71759			0.481349
$329$	−2.13279	+	0.0240776i	−0.117585	+	0.00132744i
$330$		0			0
$331$	−2.18364	−	3.78217i	−0.120024	−	0.207887i	0.799753	−	0.600329i	$-0.204964\pi$
$331$	−2.18364	−	3.78217i	−0.120024	−	0.207887i	−0.919777	+	0.392442i	$0.871630\pi$
$332$	−3.24320	−	1.87246i	−0.177994	−	0.102765i
$333$		0			0
$334$	−16.3910	+	9.46334i	−0.896874	+	0.517811i
$335$	−11.8412	+	2.30154i	−0.646951	+	0.125746i
$336$		0			0
$337$		−	19.5159i		−	1.06310i	−0.847028	−	0.531549i	$-0.821610\pi$
$337$		−	19.5159i		−	1.06310i	0.847028	−	0.531549i	$-0.178390\pi$
$338$	−12.4029	−	21.4824i	−0.674627	−	1.16849i
$339$		0			0
$340$	−4.74855	+	13.7902i	−0.257526	+	0.747881i
$341$	−5.55271	−	9.61758i	−0.300696	−	0.520821i
$342$		0			0
$343$	−0.627092	−	18.5096i	−0.0338598	−	0.999427i
$344$		−	5.35859i		−	0.288916i
$345$		0			0
$346$	10.2568	+	5.92176i	0.551409	+	0.318356i
$347$	13.4574	−	23.3088i	0.722429	−	1.25128i	−0.237595	−	0.971364i	$-0.576359\pi$
$347$	13.4574	−	23.3088i	0.722429	−	1.25128i	0.960024	−	0.279919i	$-0.0903075\pi$
$348$		0			0
$349$			10.3821i			0.555741i	0.960619	+	0.277870i	$0.0896286\pi$
$349$			10.3821i			0.555741i	−0.960619	+	0.277870i	$0.910371\pi$
$350$	13.1199	+	1.69341i	0.701289	+	0.0905167i
$351$		0			0
$352$	−1.11120	+	0.641550i	−0.0592270	+	0.0341947i
$353$	−0.146316	−	0.0844756i	−0.00778761	−	0.00449618i	0.496101	−	0.868265i	$-0.334765\pi$
$353$	−0.146316	−	0.0844756i	−0.00778761	−	0.00449618i	−0.503889	+	0.863769i	$0.668098\pi$
$354$		0			0
$355$	23.0002	+	26.4594i	1.22072	+	1.40432i
$356$	−3.63941			−0.192889
$357$		0			0
$358$			3.78561i			0.200075i
$359$	−32.6198	+	18.8330i	−1.72161	+	0.993970i	−0.805975	+	0.591949i	$0.798359\pi$
$359$	−32.6198	+	18.8330i	−1.72161	+	0.993970i	−0.915631	+	0.402021i	$0.868308\pi$
$360$		0			0
$361$	8.72604	−	15.1139i	0.459265	−	0.795471i
$362$	16.4574	−	9.50166i	0.864979	−	0.499396i
$363$		0			0
$364$	13.9956	−	8.29240i	0.733568	−	0.434640i
$365$	−5.29741	−	27.2546i	−0.277279	−	1.42657i
$366$		0			0
$367$	−7.57787	+	13.1253i	−0.395562	+	0.685133i	−0.993173	−	0.116653i	$-0.962783\pi$
$367$	−7.57787	+	13.1253i	−0.395562	+	0.685133i	0.597611	+	0.801786i	$0.296117\pi$
$368$	−1.43958	+	2.49343i	−0.0750435	+	0.129979i
$369$		0			0
$370$	20.9266	−	4.06745i	1.08792	−	0.211457i
$371$	−15.1784	+	8.99319i	−0.788021	+	0.466903i
$372$		0			0
$373$	−10.4270	+	6.02002i	−0.539889	+	0.311705i	−0.745034	−	0.667027i	$-0.767567\pi$
$373$	−10.4270	+	6.02002i	−0.539889	+	0.311705i	0.205145	+	0.978732i	$0.434233\pi$
$374$	−4.18455	+	7.24785i	−0.216378	+	0.374778i
$375$		0			0
$376$	0.698165	−	0.403086i	0.0360051	−	0.0207876i
$377$		−	8.30386i		−	0.427671i
$378$		0			0
$379$	18.0918			0.929312			0.464656	−	0.885491i	$-0.346178\pi$
$379$	18.0918			0.929312			0.464656	+	0.885491i	$0.346178\pi$
$380$	−8.85692	−	10.1890i	−0.454351	−	0.522684i
$381$		0			0
$382$	2.44949	+	1.41421i	0.125327	+	0.0723575i
$383$	−25.2480	+	14.5769i	−1.29011	+	0.744846i	−0.978674	−	0.205421i	$-0.934144\pi$
$383$	−25.2480	+	14.5769i	−1.29011	+	0.744846i	−0.311437	+	0.950267i	$0.600810\pi$
$384$		0			0
$385$	7.20477	+	2.39027i	0.367189	+	0.121819i
$386$		−	3.53892i		−	0.180126i
$387$		0			0
$388$	4.38409	−	7.59347i	0.222568	−	0.385500i
$389$	17.0297	+	9.83207i	0.863438	+	0.498506i	0.865162	−	0.501493i	$-0.167216\pi$
$389$	17.0297	+	9.83207i	0.863438	+	0.498506i	−0.00172432	+	0.999999i	$0.500549\pi$
$390$		0			0
$391$			18.7796i			0.949723i
$392$	3.63597	+	5.98162i	0.183644	+	0.302117i
$393$		0			0
$394$	1.18364	+	2.05012i	0.0596309	+	0.103284i
$395$	23.6411	+	8.14060i	1.18951	+	0.409598i
$396$		0			0
$397$	2.84227	+	4.92295i	0.142649	+	0.247076i	0.928493	−	0.371349i	$-0.121105\pi$
$397$	2.84227	+	4.92295i	0.142649	+	0.247076i	−0.785844	+	0.618425i	$0.787771\pi$
$398$			3.46410i			0.173640i
$399$		0			0
$400$	−4.63597	+	1.87292i	−0.231798	+	0.0936460i
$401$	−8.84787	+	5.10832i	−0.441842	+	0.255097i	−0.704378	−	0.709825i	$-0.748774\pi$
$401$	−8.84787	+	5.10832i	−0.441842	+	0.255097i	0.262537	+	0.964922i	$0.415441\pi$
$402$		0			0
$403$	−46.0876	−	26.6087i	−2.29579	−	1.32547i
$404$	0.853270	+	1.47791i	0.0424518	+	0.0735286i
$405$		0			0
$406$	3.57291	−	0.0403355i	0.177321	−	0.00200182i
$407$	12.2328			0.606359
$408$		0			0
$409$	12.0969	+	6.98414i	0.598153	+	0.345344i	0.768314	−	0.640073i	$-0.221096\pi$
$409$	12.0969	+	6.98414i	0.598153	+	0.345344i	−0.170162	+	0.985416i	$0.554429\pi$
$410$	18.4310	+	6.34657i	0.910244	+	0.313435i
$411$		0			0
$412$	−10.3644			−0.510617
$413$	3.63333	−	2.15275i	0.178784	−	0.105930i
$414$		0			0
$415$	−5.49370	−	6.31994i	−0.269675	−	0.310234i
$416$	−3.07432	+	5.32488i	−0.150731	+	0.261074i
$417$		0			0
$418$	−3.87339	−	6.70891i	−0.189454	−	0.328144i
$419$	11.3181			0.552924			0.276462	−	0.961025i	$-0.410838\pi$
$419$	11.3181			0.552924			0.276462	+	0.961025i	$0.410838\pi$
$420$		0			0
$421$	−13.9099			−0.677928			−0.338964	−	0.940799i	$-0.610077\pi$
$421$	−13.9099			−0.677928			−0.338964	+	0.940799i	$0.610077\pi$
$422$	7.18100	+	12.4379i	0.349566	+	0.605466i
$423$		0			0
$424$	3.33413	−	5.77488i	0.161920	−	0.280453i
$425$	−20.0791	+	25.6988i	−0.973979	+	1.24657i
$426$		0			0
$427$	16.8090	−	0.189761i	0.813445	−	0.00918318i
$428$	−11.5136			−0.556531
$429$		0			0
$430$	3.90115	−	11.3293i	0.188130	−	0.546348i
$431$	22.5947	+	13.0451i	1.08835	+	0.628359i	0.933137	−	0.359522i	$-0.117060\pi$
$431$	22.5947	+	13.0451i	1.08835	+	0.628359i	0.155213	+	0.987881i	$0.450394\pi$
$432$		0			0
$433$	8.42614			0.404935			0.202467	−	0.979289i	$-0.435104\pi$
$433$	8.42614			0.404935			0.202467	+	0.979289i	$0.435104\pi$
$434$	11.2251	−	19.9594i	0.538822	−	0.958083i
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−15.0542	−	8.69157i	−0.720142	−	0.415774i
$438$		0			0
$439$	−23.9529	+	13.8292i	−1.14321	+	0.660033i	−0.947224	−	0.320573i	$-0.896125\pi$
$439$	−23.9529	+	13.8292i	−1.14321	+	0.660033i	−0.195987	+	0.980606i	$0.562791\pi$
$440$	−2.81639	+	0.547415i	−0.134266	+	0.0260970i
$441$		0			0
$442$			40.1049i			1.90759i
$443$	−1.17861	−	2.04142i	−0.0559975	−	0.0969906i	0.836668	−	0.547711i	$-0.184501\pi$
$443$	−1.17861	−	2.04142i	−0.0559975	−	0.0969906i	−0.892665	+	0.450720i	$0.851167\pi$
$444$		0			0
$445$	−7.69458	−	2.64956i	−0.364758	−	0.125601i
$446$	6.79876	+	11.7758i	0.321931	+	0.557600i
$447$		0			0
$448$	−2.30608	−	1.29693i	−0.108952	−	0.0612740i
$449$			12.8021i			0.604169i	0.953281	+	0.302084i	$0.0976824\pi$
$449$			12.8021i			0.604169i	−0.953281	+	0.302084i	$0.902318\pi$
$450$		0			0
$451$	9.68696	+	5.59277i	0.456141	+	0.263353i
$452$	−6.69375	+	11.5939i	−0.314847	+	0.545332i
$453$		0			0
$454$			12.3559i			0.579893i
$455$	35.6270	−	7.34304i	1.67022	−	0.344247i
$456$		0			0
$457$	29.8989	−	17.2621i	1.39861	−	0.807488i	0.404363	−	0.914599i	$-0.367493\pi$
$457$	29.8989	−	17.2621i	1.39861	−	0.807488i	0.994247	+	0.107111i	$0.0341601\pi$
$458$	2.09008	+	1.20671i	0.0976628	+	0.0563857i
$459$		0			0
$460$	−4.85888	+	4.22366i	−0.226547	+	0.196929i
$461$	20.2692			0.944032			0.472016	−	0.881590i	$-0.343526\pi$
$461$	20.2692			0.944032			0.472016	+	0.881590i	$0.343526\pi$
$462$		0			0
$463$			13.1246i			0.609952i	0.952360	+	0.304976i	$0.0986485\pi$
$463$			13.1246i			0.609952i	−0.952360	+	0.304976i	$0.901352\pi$
$464$	−1.16959	+	0.675260i	−0.0542966	+	0.0313482i
$465$		0			0
$466$	6.43780	−	11.1506i	0.298225	−	0.516541i
$467$	1.32647	−	0.765836i	0.0613816	−	0.0354387i	−0.468995	−	0.883201i	$-0.655384\pi$
$467$	1.32647	−	0.765836i	0.0613816	−	0.0354387i	0.530377	+	0.847762i	$0.322050\pi$
$468$		0			0
$469$	−7.27550	−	12.2793i	−0.335951	−	0.567005i
$470$	1.76954	−	0.343941i	0.0816228	−	0.0158648i
$471$		0			0
$472$	−0.798110	+	1.38237i	−0.0367360	+	0.0636286i
$473$	3.43780	−	5.95444i	0.158070	−	0.273786i
$474$		0			0
$475$	−11.3079	−	27.9899i	−0.518840	−	1.28426i
$476$	−17.2560	+	0.194807i	−0.790927	+	0.00892896i
$477$		0			0
$478$	−23.6032	+	13.6273i	−1.07959	+	0.623299i
$479$	14.6585	−	25.3893i	0.669764	−	1.16007i	−0.308205	−	0.951320i	$-0.599728\pi$
$479$	14.6585	−	25.3893i	0.669764	−	1.16007i	0.977970	−	0.208746i	$-0.0669382\pi$
$480$		0			0
$481$	50.7663	−	29.3100i	2.31475	−	1.33642i
$482$		−	2.61759i		−	0.119228i
$483$		0			0
$484$	9.35366			0.425166
$485$	14.7972	−	12.8627i	0.671905	−	0.584064i
$486$		0			0
$487$	−7.09743	−	4.09770i	−0.321615	−	0.185685i	0.330497	−	0.943807i	$-0.392784\pi$
$487$	−7.09743	−	4.09770i	−0.321615	−	0.185685i	−0.652112	+	0.758122i	$0.726117\pi$
$488$	−5.50239	+	3.17681i	−0.249082	+	0.143807i
$489$		0			0
$490$	3.33256	+	15.2936i	0.150550	+	0.690894i
$491$			40.4383i			1.82495i	0.409129	+	0.912477i	$0.365833\pi$
$491$			40.4383i			1.82495i	−0.409129	+	0.912477i	$0.634167\pi$
$492$		0			0
$493$	−4.40443	+	7.62869i	−0.198366	+	0.343579i
$494$	−32.1492	−	18.5614i	−1.44646	−	0.835116i
$495$		0			0
$496$			8.65515i			0.388628i
$497$	−20.3341	+	36.1562i	−0.912109	+	1.62183i
$498$		0			0
$499$	−8.72450	−	15.1113i	−0.390562	−	0.676474i	0.601961	−	0.798525i	$-0.294386\pi$
$499$	−8.72450	−	15.1113i	−0.390562	−	0.676474i	−0.992524	+	0.122051i	$0.961053\pi$
$500$	−11.1650	+	0.584722i	−0.499316	+	0.0261496i
$501$		0			0
$502$	−13.3586	−	23.1379i	−0.596226	−	1.03269i
$503$			1.91949i			0.0855860i	0.999084	+	0.0427930i	$0.0136256\pi$
$503$			1.91949i			0.0855860i	−0.999084	+	0.0427930i	$0.986374\pi$
$504$		0			0
$505$	0.728069	+	3.74584i	0.0323987	+	0.166688i
$506$	−3.19932	+	1.84713i	−0.142227	+	0.0821149i
$507$		0			0
$508$	−4.89575	−	2.82656i	−0.217214	−	0.125408i
$509$	−5.54549	−	9.60508i	−0.245800	−	0.425737i	0.716556	−	0.697529i	$-0.245717\pi$
$509$	−5.54549	−	9.60508i	−0.245800	−	0.425737i	−0.962356	+	0.271792i	$0.912384\pi$
$510$		0			0
$511$	28.2631	−	16.7459i	1.25029	−	0.740796i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−9.14632	−	5.28063i	−0.403427	−	0.232919i
$515$	−21.9128	−	7.54547i	−0.965592	−	0.332493i
$516$		0			0
$517$	1.03440			0.0454928
$518$	12.8578	+	21.7009i	0.564941	+	0.953484i
$519$		0			0
$520$	−10.3764	+	9.01988i	−0.455037	+	0.395548i
$521$	−19.8706	+	34.4168i	−0.870546	+	1.50783i	−0.00911254	+	0.999958i	$0.502901\pi$
$521$	−19.8706	+	34.4168i	−0.870546	+	1.50783i	−0.861433	+	0.507871i	$0.830433\pi$
$522$		0			0
$523$	15.6404	+	27.0900i	0.683907	+	1.18456i	0.973779	+	0.227496i	$0.0730538\pi$
$523$	15.6404	+	27.0900i	0.683907	+	1.18456i	−0.289872	+	0.957065i	$0.593613\pi$
$524$	12.4673			0.544638
$525$		0			0
$526$	−8.33174			−0.363281
$527$	28.2269	+	48.8904i	1.22958	+	2.12970i
$528$		0			0
$529$	7.35519	−	12.7396i	0.319791	−	0.553894i
$530$	11.2534	−	9.78215i	0.488815	−	0.424909i
$531$		0			0
$532$	7.83026	−	13.9231i	0.339485	−	0.603641i
$533$	53.6013			2.32173
$534$		0			0
$535$	−24.3424	−	8.38211i	−1.05242	−	0.362390i
$536$	4.67188	+	2.69731i	0.201795	+	0.116506i
$537$		0			0
$538$	14.2834			0.615802
$539$	0.202767	+	8.97941i	0.00873380	+	0.386771i
$540$		0			0
$541$	12.3987	+	21.4752i	0.533061	+	0.923290i	0.999254	+	0.0386065i	$0.0122919\pi$
$541$	12.3987	+	21.4752i	0.533061	+	0.923290i	−0.466193	+	0.884683i	$0.654375\pi$
$542$	6.58566	+	3.80223i	0.282878	+	0.163320i
$543$		0			0
$544$	5.64871	−	3.26128i	0.242186	−	0.139826i
$545$	−0.853270	−	4.38998i	−0.0365501	−	0.188046i
$546$		0			0
$547$			40.5380i			1.73328i	0.498934	+	0.866640i	$0.333725\pi$
$547$			40.5380i			1.73328i	−0.498934	+	0.866640i	$0.666275\pi$
$548$	0.0254843	+	0.0441401i	0.00108863	+	0.00188557i
$549$		0			0
$550$	−6.35304	−	0.893021i	−0.270895	−	0.0380785i
$551$	−4.07692	−	7.06144i	−0.173683	−	0.300827i
$552$		0			0
$553$	0.333964	+	29.5825i	0.0142016	+	1.25798i
$554$			12.0400i			0.511532i
$555$		0			0
$556$	−0.909924	−	0.525345i	−0.0385894	−	0.0222796i
$557$	11.8732	−	20.5650i	0.503084	−	0.871367i	−0.496910	−	0.867802i	$-0.665532\pi$
$557$	11.8732	−	20.5650i	0.503084	−	0.871367i	0.999994	−	0.00356477i	$-0.00113470\pi$
$558$		0			0
$559$		−	32.9480i		−	1.39355i
$560$	−3.93140	−	4.42087i	−0.166132	−	0.186816i
$561$		0			0
$562$	11.0746	−	6.39394i	0.467155	−	0.269712i
$563$	7.29944	+	4.21434i	0.307635	+	0.177613i	0.645868	−	0.763449i	$-0.276496\pi$
$563$	7.29944	+	4.21434i	0.307635	+	0.177613i	−0.338233	+	0.941062i	$0.609829\pi$
$564$		0			0
$565$	−22.5927	+	19.6391i	−0.950483	+	0.826222i
$566$	−15.5521			−0.653705
$567$		0			0
$568$		−	15.6787i		−	0.657863i
$569$	20.3139	−	11.7283i	0.851605	−	0.491674i	−0.00958727	−	0.999954i	$-0.503052\pi$
$569$	20.3139	−	11.7283i	0.851605	−	0.491674i	0.861192	+	0.508280i	$0.169718\pi$
$570$		0			0
$571$	−7.67946	+	13.3012i	−0.321376	+	0.556639i	−0.980772	−	0.195157i	$-0.937479\pi$
$571$	−7.67946	+	13.3012i	−0.321376	+	0.556639i	0.659397	+	0.751795i	$0.270812\pi$
$572$	−6.83235	+	3.94466i	−0.285675	+	0.164934i
$573$		0			0
$574$	0.260365	+	23.0631i	0.0108674	+	0.962636i
$575$	−13.3477	+	5.39245i	−0.556639	+	0.224881i
$576$		0			0
$577$	−7.12041	+	12.3329i	−0.296426	+	0.513426i	−0.975316	−	0.220815i	$-0.929128\pi$
$577$	−7.12041	+	12.3329i	−0.296426	+	0.513426i	0.678889	+	0.734241i	$0.262462\pi$
$578$	12.7719	−	22.1216i	0.531242	−	0.920139i
$579$		0			0
$580$	−2.96438	+	0.576179i	−0.123089	+	0.0239245i
$581$	4.85690	−	8.63609i	0.201498	−	0.358285i
$582$		0			0
$583$	7.40975	−	4.27802i	0.306881	−	0.177178i
$584$	−6.20837	+	10.7532i	−0.256904	+	0.444971i
$585$		0			0
$586$	10.0057	−	5.77679i	0.413331	−	0.238637i
$587$		−	12.5249i		−	0.516958i	−0.966017	−	0.258479i	$-0.916779\pi$
$587$		−	12.5249i		−	0.516958i	0.966017	−	0.258479i	$-0.0832212\pi$
$588$		0			0
$589$	−52.2560			−2.15317
$590$	−2.69378	+	2.34161i	−0.110901	+	0.0964025i
$591$		0			0
$592$	−8.25652	−	4.76690i	−0.339341	−	0.195919i
$593$	12.7436	−	7.35750i	0.523316	−	0.302136i	−0.214975	−	0.976620i	$-0.568967\pi$
$593$	12.7436	−	7.35750i	0.523316	−	0.302136i	0.738290	+	0.674483i	$0.235634\pi$
$594$		0			0
$595$	−36.6250	−	12.1508i	−1.50148	−	0.498135i
$596$		−	8.22305i		−	0.336829i
$597$		0			0
$598$	−8.85148	+	15.3312i	−0.361964	+	0.626940i
$599$	23.9304	+	13.8162i	0.977769	+	0.564515i	0.901596	−	0.432579i	$-0.142396\pi$
$599$	23.9304	+	13.8162i	0.977769	+	0.564515i	0.0761732	+	0.997095i	$0.475730\pi$
$600$		0			0
$601$			8.82137i			0.359831i	0.983682	+	0.179916i	$0.0575825\pi$
$601$			8.82137i			0.359831i	−0.983682	+	0.179916i	$0.942418\pi$
$602$	14.1766	−	0.160043i	0.577794	−	0.00652286i
$603$		0			0
$604$	2.13357	+	3.69546i	0.0868139	+	0.150366i
$605$	19.7758	+	6.80963i	0.804002	+	0.276851i
$606$		0			0
$607$	−13.2677	−	22.9803i	−0.538519	−	0.932743i	−0.998984	−	0.0450649i	$-0.985651\pi$
$607$	−13.2677	−	22.9803i	−0.538519	−	0.932743i	0.460465	−	0.887678i	$-0.347683\pi$
$608$			6.03756i			0.244855i
$609$		0			0
$610$	−13.9461	+	2.71067i	−0.564662	+	0.109752i
$611$	4.29276	−	2.47843i	0.173667	−	0.100266i
$612$		0			0
$613$	0.791273	+	0.456842i	0.0319592	+	0.0184517i	0.515894	−	0.856652i	$-0.327460\pi$
$613$	0.791273	+	0.456842i	0.0319592	+	0.0184517i	−0.483935	+	0.875104i	$0.660793\pi$
$614$	1.28809	+	2.23103i	0.0519830	+	0.0900371i
$615$		0			0
$616$	−1.73046	−	2.92060i	−0.0697223	−	0.117674i
$617$	−35.0558			−1.41129			−0.705646	−	0.708565i	$-0.749343\pi$
$617$	−35.0558			−1.41129			−0.705646	+	0.708565i	$0.749343\pi$
$618$		0			0
$619$	16.5382	+	9.54835i	0.664727	+	0.383781i	0.794076	−	0.607819i	$-0.207955\pi$
$619$	16.5382	+	9.54835i	0.664727	+	0.383781i	−0.129348	+	0.991599i	$0.541289\pi$
$620$	−6.30111	+	18.2990i	−0.253059	+	0.734906i
$621$		0			0
$622$	−24.7140			−0.990942
$623$	−0.108697	−	9.62837i	−0.00435485	−	0.385753i
$624$		0			0
$625$	−24.0312	−	6.89212i	−0.961248	−	0.275685i
$626$	4.50087	−	7.79573i	0.179891	−	0.311580i
$627$		0			0
$628$	2.41601	+	4.18466i	0.0964095	+	0.166986i
$629$	−62.1849			−2.47947
$630$		0			0
$631$	21.5350			0.857296			0.428648	−	0.903472i	$-0.358990\pi$
$631$	21.5350			0.857296			0.428648	+	0.903472i	$0.358990\pi$
$632$	−5.59093	−	9.68377i	−0.222395	−	0.385200i
$633$		0			0
$634$	−11.9529	+	20.7031i	−0.474712	+	0.822225i
$635$	−8.29298	−	9.54022i	−0.329097	−	0.378592i
$636$		0			0
$637$	22.3562	+	36.7788i	0.885786	+	1.45723i
$638$	−1.73285			−0.0686043
$639$		0			0
$640$	2.11423	+	0.728019i	0.0835725	+	0.0287775i
$641$	28.6767	+	16.5565i	1.13266	+	0.653943i	0.944603	−	0.328214i	$-0.106447\pi$
$641$	28.6767	+	16.5565i	1.13266	+	0.653943i	0.188060	+	0.982158i	$0.439780\pi$
$642$		0			0
$643$	−3.31191			−0.130609			−0.0653044	−	0.997865i	$-0.520802\pi$
$643$	−3.31191			−0.130609			−0.0653044	+	0.997865i	$0.520802\pi$
$644$	−6.63958	−	3.73407i	−0.261636	−	0.147143i
$645$		0			0
$646$	19.6902	+	34.1044i	0.774700	+	1.34182i
$647$	20.2077	+	11.6669i	0.794447	+	0.458674i	0.841526	−	0.540217i	$-0.181658\pi$
$647$	20.2077	+	11.6669i	0.794447	+	0.458674i	−0.0470789	+	0.998891i	$0.514991\pi$
$648$		0			0
$649$	−1.77371	+	1.02405i	−0.0696244	+	0.0401977i
$650$	−28.5049	+	11.5159i	−1.11805	+	0.451691i
$651$		0			0
$652$			10.7532i			0.421128i
$653$	8.73019	+	15.1211i	0.341639	+	0.591735i	0.984737	−	0.174048i	$-0.0556848\pi$
$653$	8.73019	+	15.1211i	0.341639	+	0.591735i	−0.643099	+	0.765783i	$0.722351\pi$
$654$		0			0
$655$	26.3589	+	9.07644i	1.02993	+	0.354646i
$656$	−4.35880	−	7.54966i	−0.170182	−	0.294765i
$657$		0			0
$658$	1.08725	+	1.83501i	0.0423854	+	0.0715363i
$659$		−	1.29864i		−	0.0505877i	−0.999680	−	0.0252939i	$-0.991948\pi$
$659$		−	1.29864i		−	0.0505877i	0.999680	−	0.0252939i	$-0.00805215\pi$
$660$		0			0
$661$	4.39869	+	2.53959i	0.171089	+	0.0987785i	0.583099	−	0.812401i	$-0.301840\pi$
$661$	4.39869	+	2.53959i	0.171089	+	0.0987785i	−0.412010	+	0.911179i	$0.635173\pi$
$662$	−2.18364	+	3.78217i	−0.0848695	+	0.146998i
$663$		0			0
$664$			3.74493i			0.145331i
$665$	26.6913	−	23.7360i	1.03504	−	0.920444i
$666$		0			0
$667$	−3.36743	+	1.94419i	−0.130387	+	0.0752793i
$668$	16.3910	+	9.46334i	0.634186	+	0.366147i
$669$		0			0
$670$	7.91377	+	9.10397i	0.305735	+	0.351717i
$671$	−8.15232			−0.314717
$672$		0			0
$673$		−	18.4124i		−	0.709747i	−0.934914	−	0.354873i	$-0.884524\pi$
$673$		−	18.4124i		−	0.709747i	0.934914	−	0.354873i	$-0.115476\pi$
$674$	−16.9012	+	9.75794i	−0.651012	+	0.375862i
$675$		0			0
$676$	−12.4029	+	21.4824i	−0.477033	+	0.826246i
$677$	35.7491	−	20.6397i	1.37395	−	0.793250i	0.382526	−	0.923945i	$-0.375054\pi$
$677$	35.7491	−	20.6397i	1.37395	−	0.793250i	0.991423	+	0.130695i	$0.0417208\pi$
$678$		0			0
$679$	20.2201	+	11.3717i	0.775976	+	0.436405i
$680$	14.3170	−	2.78275i	0.549031	−	0.106714i
$681$		0			0
$682$	−5.55271	+	9.61758i	−0.212624	+	0.368276i
$683$	−11.4896	+	19.9007i	−0.439639	+	0.761477i	−0.997662	−	0.0683485i	$-0.978227\pi$
$683$	−11.4896	+	19.9007i	−0.439639	+	0.761477i	0.558022	+	0.829826i	$0.311560\pi$
$684$		0			0
$685$	0.0217450	+	0.111876i	0.000830833	+	0.00427454i
$686$	−15.7163	+	9.79790i	−0.600050	+	0.374085i
$687$		0			0
$688$	−4.64067	+	2.67929i	−0.176924	+	0.102147i
$689$	20.5004	−	35.5077i	0.781001	−	1.35273i
$690$		0			0
$691$	11.0048	−	6.35361i	0.418642	−	0.241703i	−0.275854	−	0.961199i	$-0.588961\pi$
$691$	11.0048	−	6.35361i	0.418642	−	0.241703i	0.694496	+	0.719497i	$0.255627\pi$
$692$		−	11.8435i		−	0.450223i
$693$		0			0
$694$	−26.9147			−1.02167
$695$	−1.54133	−	1.77314i	−0.0584661	−	0.0672592i
$696$		0			0
$697$	−49.2431	−	28.4305i	−1.86522	−	1.07688i
$698$	8.99116	−	5.19105i	0.340320	−	0.196484i
$699$		0			0
$700$	−5.09342	−	12.2089i	−0.192513	−	0.461453i
$701$			26.5441i			1.00256i	0.865286	+	0.501279i	$0.167137\pi$
$701$			26.5441i			1.00256i	−0.865286	+	0.501279i	$0.832863\pi$
$702$		0			0
$703$	28.7804	−	49.8492i	1.08548	−	1.88010i
$704$	1.11120	+	0.641550i	0.0418798	+	0.0241793i
$705$		0			0
$706$			0.168951i			0.00635856i
$707$	−3.88444	+	2.30154i	−0.146089	+	0.0865582i
$708$		0			0
$709$	−21.1766	−	36.6789i	−0.795303	−	1.37751i	−0.922646	−	0.385647i	$-0.873978\pi$
$709$	−21.1766	−	36.6789i	−0.795303	−	1.37751i	0.127343	−	0.991859i	$-0.459355\pi$
$710$	11.4144	−	33.1484i	0.428374	−	1.24404i
$711$		0			0
$712$	1.81971	+	3.15183i	0.0681964	+	0.118120i
$713$			24.9196i			0.933248i
$714$		0			0
$715$	−17.3170	+	3.36586i	−0.647618	+	0.125876i
$716$	3.27843	−	1.89280i	0.122521	−	0.0707374i
$717$		0			0
$718$	32.6198	+	18.8330i	1.21736	+	0.702843i
$719$	11.9507	+	20.6992i	0.445686	+	0.771951i	0.998100	−	0.0616189i	$-0.0196263\pi$
$719$	11.9507	+	20.6992i	0.445686	+	0.771951i	−0.552413	+	0.833570i	$0.686293\pi$
$720$		0			0
$721$	−0.309550	−	27.4199i	−0.0115282	−	1.02117i
$722$	−17.4521			−0.649499
$723$		0			0
$724$	−16.4574	−	9.50166i	−0.611633	−	0.353126i
$725$	−6.68686	−	0.939945i	−0.248344	−	0.0349087i
$726$		0			0
$727$	−22.4529			−0.832731			−0.416365	−	0.909197i	$-0.636696\pi$
$727$	−22.4529			−0.832731			−0.416365	+	0.909197i	$0.636696\pi$
$728$	−14.1792	−	7.97433i	−0.525517	−	0.295548i
$729$		0			0
$730$	−20.9545	+	18.2150i	−0.775560	+	0.674168i
$731$	−17.4759	+	30.2691i	−0.646368	+	1.11954i
$732$		0			0
$733$	13.7725	+	23.8547i	0.508700	+	0.881094i	0.999949	+	0.0100750i	$0.00320702\pi$
$733$	13.7725	+	23.8547i	0.508700	+	0.881094i	−0.491249	+	0.871019i	$0.663460\pi$
$734$	15.1557			0.559409
$735$		0			0
$736$	2.87917			0.106128
$737$	3.46092	+	5.99449i	0.127485	+	0.220810i
$738$		0			0
$739$	−15.5456	+	26.9258i	−0.571856	+	0.990483i	0.424520	+	0.905419i	$0.360443\pi$
$739$	−15.5456	+	26.9258i	−0.571856	+	0.990483i	−0.996375	+	0.0850646i	$0.972890\pi$
$740$	−13.9858	−	16.0893i	−0.514129	−	0.591453i
$741$		0			0
$742$	15.3775	+	8.64824i	0.564526	+	0.317487i
$743$	1.12610			0.0413127			0.0206564	−	0.999787i	$-0.493424\pi$
$743$	1.12610			0.0413127			0.0206564	+	0.999787i	$0.493424\pi$
$744$		0			0
$745$	5.98654	−	17.3855i	0.219330	−	0.636954i
$746$	10.4270	+	6.02002i	0.381759	+	0.220409i
$747$		0			0
$748$	8.36910			0.306005
$749$	−0.343872	−	30.4602i	−0.0125648	−	1.11299i
$750$		0			0
$751$	4.77108	+	8.26375i	0.174099	+	0.301549i	0.939849	−	0.341590i	$-0.110965\pi$
$751$	4.77108	+	8.26375i	0.174099	+	0.301549i	−0.765750	+	0.643138i	$0.777632\pi$
$752$	−0.698165	−	0.403086i	−0.0254595	−	0.0146990i
$753$		0			0
$754$	−7.19135	+	4.15193i	−0.261894	+	0.151204i
$755$	1.82051	+	9.36635i	0.0662553	+	0.340876i
$756$		0			0
$757$		−	33.1687i		−	1.20554i	−0.797917	−	0.602768i	$-0.794065\pi$
$757$		−	33.1687i		−	1.20554i	0.797917	−	0.602768i	$-0.205935\pi$
$758$	−9.04589	−	15.6679i	−0.328562	−	0.569085i
$759$		0			0
$760$	−4.39545	+	12.7648i	−0.159440	+	0.463028i
$761$	−2.17122	−	3.76067i	−0.0787068	−	0.136324i	0.823985	−	0.566611i	$-0.191746\pi$
$761$	−2.17122	−	3.76067i	−0.0787068	−	0.136324i	−0.902692	+	0.430287i	$0.858412\pi$
$762$		0			0
$763$	4.55242	−	2.69731i	0.164809	−	0.0976493i
$764$		−	2.82843i		−	0.102329i
$765$		0			0
$766$	25.2480	+	14.5769i	0.912246	+	0.526685i
$767$	−4.90729	+	8.49967i	−0.177192	+	0.306905i
$768$		0			0
$769$		−	46.1795i		−	1.66528i	−0.553818	−	0.832638i	$-0.686830\pi$
$769$		−	46.1795i		−	1.66528i	0.553818	−	0.832638i	$-0.313170\pi$
$770$	−1.53235	−	7.43465i	−0.0552220	−	0.267926i
$771$		0			0
$772$	−3.06479	+	1.76946i	−0.110304	+	0.0636842i
$773$	15.5663	+	8.98723i	0.559883	+	0.323248i	0.753098	−	0.657908i	$-0.228558\pi$
$773$	15.5663	+	8.98723i	0.559883	+	0.323248i	−0.193216	+	0.981156i	$0.561892\pi$
$774$		0			0
$775$	−26.6441	+	34.1011i	−0.957083	+	1.22495i
$776$	−8.76818			−0.314759
$777$		0			0
$778$		−	19.6641i		−	0.704994i
$779$	45.5815	−	26.3165i	1.63313	−	0.942886i
$780$		0			0
$781$	10.0587	−	17.4221i	0.359927	−	0.623412i
$782$	16.2636	−	9.38978i	0.581584	−	0.335778i
$783$		0			0
$784$	3.36225	−	6.13965i	0.120080	−	0.219273i
$785$	2.06151	+	10.6063i	0.0735785	+	0.378554i
$786$		0			0
$787$	−6.92087	+	11.9873i	−0.246702	+	0.427301i	−0.962609	−	0.270895i	$-0.912680\pi$
$787$	−6.92087	+	11.9873i	−0.246702	+	0.427301i	0.715907	+	0.698196i	$0.246014\pi$
$788$	1.18364	−	2.05012i	0.0421654	−	0.0730326i
$789$		0			0
$790$	−4.77057	−	24.5441i	−0.169729	−	0.873239i
$791$	−30.8726	−	17.3626i	−1.09770	−	0.617342i
$792$		0			0
$793$	−33.8322	+	19.5330i	−1.20142	+	0.693638i
$794$	2.84227	−	4.92295i	0.100868	−	0.174709i
$795$		0			0
$796$	3.00000	−	1.73205i	0.106332	−	0.0613909i
$797$			7.46138i			0.264296i	0.991230	+	0.132148i	$0.0421874\pi$
$797$			7.46138i			0.264296i	−0.991230	+	0.132148i	$0.957813\pi$
$798$		0			0
$799$	−5.25831			−0.186026
$800$	3.93998	+	3.07840i	0.139299	+	0.108838i
$801$		0			0
$802$	8.84787	+	5.10832i	0.312429	+	0.180381i
$803$	−13.7974	+	7.96596i	−0.486901	+	0.281113i
$804$		0			0
$805$	−11.3192	−	12.7284i	−0.398948	−	0.448618i
$806$			53.2174i			1.87450i
$807$		0			0
$808$	0.853270	−	1.47791i	0.0300179	−	0.0519926i
$809$	1.28750	+	0.743340i	0.0452662	+	0.0261344i	0.522462	−	0.852662i	$-0.325014\pi$
$809$	1.28750	+	0.743340i	0.0452662	+	0.0261344i	−0.477196	+	0.878797i	$0.658347\pi$
$810$		0			0
$811$		−	31.5494i		−	1.10785i	−0.832567	−	0.553925i	$-0.813129\pi$
$811$		−	31.5494i		−	1.10785i	0.832567	−	0.553925i	$-0.186871\pi$
$812$	−1.82139	−	3.07407i	−0.0639182	−	0.107879i
$813$		0			0
$814$	−6.11641	−	10.5939i	−0.214380	−	0.371317i
$815$	−7.82854	+	22.7348i	−0.274222	+	0.796366i
$816$		0			0
$817$	−16.1764	−	28.0183i	−0.565940	−	0.980237i
$818$		−	13.9683i		−	0.488390i
$819$		0			0
$820$	−3.71923	−	19.1350i	−0.129881	−	0.668224i
$821$	27.5430	−	15.9020i	0.961257	−	0.554982i	0.0646976	−	0.997905i	$-0.479392\pi$
$821$	27.5430	−	15.9020i	0.961257	−	0.554982i	0.896560	+	0.442923i	$0.146058\pi$
$822$		0			0
$823$	31.7287	+	18.3186i	1.10599	+	0.638545i	0.937788	−	0.347207i	$-0.112870\pi$
$823$	31.7287	+	18.3186i	1.10599	+	0.638545i	0.168204	+	0.985752i	$0.446203\pi$
$824$	5.18220	+	8.97583i	0.180530	+	0.312688i
$825$		0			0
$826$	−3.68100	−	2.07018i	−0.128078	−	0.0720308i
$827$	−21.9864			−0.764541			−0.382271	−	0.924050i	$-0.624858\pi$
$827$	−21.9864			−0.764541			−0.382271	+	0.924050i	$0.624858\pi$
$828$		0			0
$829$	−21.0498	−	12.1531i	−0.731090	−	0.422095i	0.0877305	−	0.996144i	$-0.472039\pi$
$829$	−21.0498	−	12.1531i	−0.731090	−	0.422095i	−0.818821	+	0.574049i	$0.805372\pi$
$830$	−2.72638	+	7.91766i	−0.0946339	+	0.274826i
$831$		0			0
$832$	6.14864			0.213166
$833$	−1.03076	−	45.6463i	−0.0357136	−	1.58155i
$834$		0			0
$835$	27.7649	+	31.9406i	0.960844	+	1.10535i
$836$	−3.87339	+	6.70891i	−0.133964	+	0.232033i
$837$		0			0
$838$	−5.65904	−	9.80175i	−0.195488	−	0.338596i
$839$	−27.3914			−0.945655			−0.472827	−	0.881155i	$-0.656767\pi$
$839$	−27.3914			−0.945655			−0.472827	+	0.881155i	$0.656767\pi$
$840$		0			0
$841$	27.1761			0.937107
$842$	6.95496	+	12.0463i	0.239684	+	0.415145i
$843$		0			0
$844$	7.18100	−	12.4379i	0.247180	−	0.428129i
$845$	−41.8622	+	36.3893i	−1.44010	+	1.25183i
$846$		0			0
$847$	0.279362	+	24.7459i	0.00959899	+	0.850278i
$848$	−6.66826			−0.228989
$849$		0			0
$850$	32.2953	+	4.53962i	1.10772	+	0.155708i
$851$	−23.7719	−	13.7247i	−0.814890	−	0.470477i
$852$		0			0
$853$	22.6073			0.774060			0.387030	−	0.922067i	$-0.373501\pi$
$853$	22.6073			0.774060			0.387030	+	0.922067i	$0.373501\pi$
$854$	−8.56884	−	14.4622i	−0.293220	−	0.494885i
$855$		0			0
$856$	5.75680	+	9.97106i	0.196763	+	0.340804i
$857$	−41.4461	−	23.9289i	−1.41577	−	0.817396i	−0.419848	−	0.907595i	$-0.637917\pi$
$857$	−41.4461	−	23.9289i	−1.41577	−	0.817396i	−0.995924	+	0.0901984i	$0.971250\pi$
$858$		0			0
$859$	41.5770	−	24.0045i	1.41859	−	0.819022i	0.422413	−	0.906403i	$-0.361183\pi$
$859$	41.5770	−	24.0045i	1.41859	−	0.819022i	0.996175	+	0.0873810i	$0.0278498\pi$
$860$	−11.7620	+	2.28616i	−0.401082	+	0.0779574i
$861$		0			0
$862$		−	26.0901i		−	0.888634i
$863$	−23.7785	−	41.1855i	−0.809428	−	1.40197i	−0.913260	−	0.407376i	$-0.866444\pi$
$863$	−23.7785	−	41.1855i	−0.809428	−	1.40197i	0.103832	−	0.994595i	$-0.466890\pi$
$864$		0			0
$865$	8.62231	−	25.0400i	0.293167	−	0.851386i
$866$	−4.21307	−	7.29726i	−0.143166	−	0.247971i
$867$		0			0
$868$	−22.8979	+	0.258500i	−0.777206	+	0.00877406i
$869$		−	14.3474i		−	0.486703i
$870$		0			0
$871$	28.7257	+	16.5848i	0.973334	+	0.561955i
$872$	−1.00000	+	1.73205i	−0.0338643	+	0.0586546i
$873$		0			0
$874$			17.3831i			0.587993i
$875$	−1.88039	−	29.5206i	−0.0635689	−	0.997977i
$876$		0			0
$877$	32.0433	−	18.5002i	1.08202	−	0.624707i	0.150583	−	0.988597i	$-0.451885\pi$
$877$	32.0433	−	18.5002i	1.08202	−	0.624707i	0.931442	+	0.363890i	$0.118552\pi$
$878$	23.9529	+	13.8292i	0.808372	+	0.466714i
$879$		0			0
$880$	1.88227	+	2.16536i	0.0634513	+	0.0729942i
$881$	5.97213			0.201206			0.100603	−	0.994927i	$-0.467923\pi$
$881$	5.97213			0.201206			0.100603	+	0.994927i	$0.467923\pi$
$882$		0			0
$883$			11.0589i			0.372163i	0.982534	+	0.186081i	$0.0595788\pi$
$883$			11.0589i			0.372163i	−0.982534	+	0.186081i	$0.940421\pi$
$884$	34.7319	−	20.0524i	1.16816	−	0.674437i
$885$		0			0
$886$	−1.17861	+	2.04142i	−0.0395962	+	0.0685827i
$887$	−5.15346	+	2.97535i	−0.173036	+	0.0999026i	−0.584017	−	0.811742i	$-0.698520\pi$
$887$	−5.15346	+	2.97535i	−0.173036	+	0.0999026i	0.410980	+	0.911644i	$0.365186\pi$
$888$		0			0
$889$	7.33169	−	13.0365i	0.245897	−	0.437231i
$890$	1.55270	+	7.98848i	0.0520467	+	0.267774i
$891$		0			0
$892$	6.79876	−	11.7758i	0.227639	−	0.394283i
$893$	2.43365	−	4.21521i	0.0814391	−	0.141057i
$894$		0			0
$895$	8.30937	−	1.61507i	0.277752	−	0.0539859i
$896$	0.0298666	+	2.64558i	0.000997774	+	0.0883827i
$897$		0			0
$898$	11.0869	−	6.40105i	0.369976	−	0.213606i
$899$	−5.84448	+	10.1229i	−0.194924	+	0.337619i
$900$		0			0
$901$	−37.6671	+	21.7471i	−1.25487	+	0.724500i
$902$		−	11.1855i		−	0.372438i
$903$		0			0
$904$	13.3875			0.445261
$905$	−27.8773	−	32.0700i	−0.926674	−	1.06604i
$906$		0			0
$907$	47.9037	+	27.6572i	1.59062	+	0.918343i	0.993201	+	0.116411i	$0.0371388\pi$
$907$	47.9037	+	27.6572i	1.59062	+	0.918343i	0.597415	+	0.801932i	$0.296195\pi$
$908$	10.7006	−	6.17797i	0.355110	−	0.205023i
$909$		0			0
$910$	−24.1727	−	27.1823i	−0.801319	−	0.901086i
$911$			35.2080i			1.16649i	0.812295	+	0.583246i	$0.198218\pi$
$911$			35.2080i			1.16649i	−0.812295	+	0.583246i	$0.801782\pi$
$912$		0			0
$913$	−2.40256	+	4.16135i	−0.0795131	+	0.137721i
$914$	−29.8989	−	17.2621i	−0.988966	−	0.570980i
$915$		0			0
$916$		−	2.41341i		−	0.0797414i
$917$	0.372357	+	32.9833i	0.0122963	+	1.08921i
$918$		0			0
$919$	25.4437	+	44.0698i	0.839311	+	1.45373i	0.890471	+	0.455039i	$0.150375\pi$
$919$	25.4437	+	44.0698i	0.839311	+	1.45373i	−0.0511601	+	0.998690i	$0.516292\pi$
$920$	6.08724	+	2.09609i	0.200690	+	0.0691060i
$921$		0			0
$922$	−10.1346	−	17.5537i	−0.333766	−	0.578099i
$923$		−	96.4026i		−	3.17313i
$924$		0			0
$925$	−17.8560	−	44.1984i	−0.587103	−	1.45323i
$926$	11.3662	−	6.56230i	0.373518	−	0.215651i
$927$		0			0
$928$	1.16959	+	0.675260i	0.0383935	+	0.0221665i
$929$	29.8405	+	51.6853i	0.979036	+	1.69574i	0.665918	+	0.746025i	$0.268040\pi$
$929$	29.8405	+	51.6853i	0.979036	+	1.69574i	0.313118	+	0.949714i	$0.398627\pi$
$930$		0			0
$931$	37.0685	+	20.2998i	1.21487	+	0.665298i
$932$	−12.8756			−0.421754
$933$		0			0
$934$	−1.32647	−	0.765836i	−0.0434033	−	0.0250589i
$935$	17.6942	+	6.09286i	0.578664	+	0.199258i
$936$		0			0
$937$	24.2579			0.792471			0.396235	−	0.918149i	$-0.370316\pi$
$937$	24.2579			0.792471			0.396235	+	0.918149i	$0.370316\pi$
$938$	−6.99643	+	12.4404i	−0.228442	+	0.406194i
$939$		0			0
$940$	−1.18263	−	1.36050i	−0.0385732	−	0.0443745i
$941$	15.0539	−	26.0742i	0.490744	−	0.849994i	−0.509199	−	0.860649i	$-0.670058\pi$
$941$	15.0539	−	26.0742i	0.490744	−	0.849994i	0.999943	+	0.0106549i	$0.00339164\pi$
$942$		0			0
$943$	−12.5497	−	21.7367i	−0.408675	−	0.707845i
$944$	1.59622			0.0519525
$945$		0			0
$946$	−6.87560			−0.223545
$947$	23.0812	+	39.9779i	0.750039	+	1.29911i	0.947803	+	0.318857i	$0.103299\pi$
$947$	23.0812	+	39.9779i	0.750039	+	1.29911i	−0.197764	+	0.980250i	$0.563368\pi$
$948$		0			0
$949$	−38.1730	+	66.1176i	−1.23915	+	2.14627i
$950$	−18.5860	+	23.7878i	−0.603011	+	0.771779i
$951$		0			0
$952$	8.79670	+	14.8467i	0.285103	+	0.481185i
$953$	23.7121			0.768110			0.384055	−	0.923310i	$-0.374527\pi$
$953$	23.7121			0.768110			0.384055	+	0.923310i	$0.374527\pi$
$954$		0			0
$955$	2.05915	−	5.97996i	0.0666324	−	0.193507i
$956$	23.6032	+	13.6273i	0.763382	+	0.440739i
$957$		0			0
$958$	−29.3170			−0.947190
$959$	−0.116015	+	0.0687391i	−0.00374632	+	0.00221970i
$960$		0			0
$961$	21.9558	+	38.0286i	0.708252	+	1.22673i
$962$	−50.7663	−	29.3100i	−1.63677	−	0.944991i
$963$		0			0
$964$	−2.26690	+	1.30880i	−0.0730120	+	0.0421535i
$965$	−7.76789	+	1.50983i	−0.250057	+	0.0486030i
$966$		0			0
$967$		−	0.0922780i		−	0.00296746i	−0.999999	−	0.00148373i	$-0.999528\pi$
$967$		−	0.0922780i		−	0.00296746i	0.999999	−	0.00148373i	$-0.000472286\pi$
$968$	−4.67683	−	8.10050i	−0.150319	−	0.260360i
$969$		0			0
$970$	−18.5380	−	6.38340i	−0.595219	−	0.204959i
$971$	19.8502	+	34.3816i	0.637024	+	1.10336i	0.986082	+	0.166257i	$0.0531683\pi$
$971$	19.8502	+	34.3816i	0.637024	+	1.10336i	−0.349058	+	0.937101i	$0.613498\pi$
$972$		0			0
$973$	1.36267	−	2.42297i	0.0436851	−	0.0776769i
$974$			8.19540i			0.262598i
$975$		0			0
$976$	5.50239	+	3.17681i	0.176127	+	0.101687i
$977$	−18.4035	+	31.8758i	−0.588779	+	1.01980i	0.405613	+	0.914045i	$0.367058\pi$
$977$	−18.4035	+	31.8758i	−0.588779	+	1.01980i	−0.994393	+	0.105751i	$0.966275\pi$
$978$		0			0
$979$			4.66973i			0.149245i
$980$	11.5784	−	10.5329i	0.369857	−	0.336460i
$981$		0			0
$982$	35.0206	−	20.2191i	1.11755	−	0.645218i
$983$	−54.1899	−	31.2865i	−1.72839	−	0.997885i	−0.896694	−	0.442650i	$-0.854038\pi$
$983$	−54.1899	−	31.2865i	−1.72839	−	0.997885i	−0.831693	−	0.555235i	$-0.812628\pi$
$984$		0			0
$985$	3.99502	−	3.47273i	0.127292	−	0.110650i
$986$	8.80886			0.280531
$987$		0			0
$988$			37.1227i			1.18103i
$989$	−13.3613	+	7.71414i	−0.424864	+	0.245295i
$990$		0			0
$991$	17.4019	−	30.1410i	0.552791	−	0.957462i	−0.445281	−	0.895391i	$-0.646896\pi$
$991$	17.4019	−	30.1410i	0.552791	−	0.957462i	0.998072	−	0.0620708i	$-0.0197704\pi$
$992$	7.49558	−	4.32758i	0.237985	−	0.137401i
$993$		0			0
$994$	41.4793	−	0.468269i	1.31564	−	0.0148526i
$995$	7.60367	−	1.47791i	0.241053	−	0.0468528i
$996$		0			0
$997$	−24.4316	+	42.3167i	−0.773755	+	1.34018i	0.161736	+	0.986834i	$0.448291\pi$
$997$	−24.4316	+	42.3167i	−0.773755	+	1.34018i	−0.935492	+	0.353349i	$0.885043\pi$
$998$	−8.72450	+	15.1113i	−0.276169	+	0.478339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bo.a.269.3	yes	16
3.2	odd	2		630.2.bo.b.269.6	yes	16
5.2	odd	4		3150.2.bf.f.1151.10		32
5.3	odd	4		3150.2.bf.f.1151.7		32
5.4	even	2		630.2.bo.b.269.8	yes	16
7.3	odd	6		4410.2.d.b.4409.10		16
7.4	even	3		4410.2.d.b.4409.7		16
7.5	odd	6	inner	630.2.bo.a.89.1	✓	16
15.2	even	4		3150.2.bf.f.1151.8		32
15.8	even	4		3150.2.bf.f.1151.9		32
15.14	odd	2	inner	630.2.bo.a.269.1	yes	16
21.5	even	6		630.2.bo.b.89.8	yes	16
21.11	odd	6		4410.2.d.a.4409.10		16
21.17	even	6		4410.2.d.a.4409.7		16
35.4	even	6		4410.2.d.a.4409.8		16
35.12	even	12		3150.2.bf.f.1601.8		32
35.19	odd	6		630.2.bo.b.89.6	yes	16
35.24	odd	6		4410.2.d.a.4409.9		16
35.33	even	12		3150.2.bf.f.1601.9		32
105.47	odd	12		3150.2.bf.f.1601.10		32
105.59	even	6		4410.2.d.b.4409.8		16
105.68	odd	12		3150.2.bf.f.1601.7		32
105.74	odd	6		4410.2.d.b.4409.9		16
105.89	even	6	inner	630.2.bo.a.89.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bo.a.89.1	✓	16	7.5	odd	6	inner
630.2.bo.a.89.3	yes	16	105.89	even	6	inner
630.2.bo.a.269.1	yes	16	15.14	odd	2	inner
630.2.bo.a.269.3	yes	16	1.1	even	1	trivial
630.2.bo.b.89.6	yes	16	35.19	odd	6
630.2.bo.b.89.8	yes	16	21.5	even	6
630.2.bo.b.269.6	yes	16	3.2	odd	2
630.2.bo.b.269.8	yes	16	5.4	even	2
3150.2.bf.f.1151.7		32	5.3	odd	4
3150.2.bf.f.1151.8		32	15.2	even	4
3150.2.bf.f.1151.9		32	15.8	even	4
3150.2.bf.f.1151.10		32	5.2	odd	4
3150.2.bf.f.1601.7		32	105.68	odd	12
3150.2.bf.f.1601.8		32	35.12	even	12
3150.2.bf.f.1601.9		32	35.33	even	12
3150.2.bf.f.1601.10		32	105.47	odd	12
4410.2.d.a.4409.7		16	21.17	even	6
4410.2.d.a.4409.8		16	35.4	even	6
4410.2.d.a.4409.9		16	35.24	odd	6
4410.2.d.a.4409.10		16	21.11	odd	6
4410.2.d.b.4409.7		16	7.4	even	3
4410.2.d.b.4409.8		16	105.59	even	6
4410.2.d.b.4409.9		16	105.74	odd	6
4410.2.d.b.4409.10		16	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bo (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.68760 + 1.46697i) q^{5} +(-2.30608 - 1.29693i) q^{7} +1.00000 q^{8} +(2.11423 + 0.728019i) q^{10} +(1.11120 + 0.641550i) q^{11} +6.14864 q^{13} +(0.0298666 + 2.64558i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-5.64871 - 3.26128i) q^{17} +(5.22868 - 3.01878i) q^{19} +(-0.426635 - 2.19499i) q^{20} -1.28310i q^{22} +(-1.43958 - 2.49343i) q^{23} +(0.695987 - 4.95132i) q^{25} +(-3.07432 - 5.32488i) q^{26} +(2.27621 - 1.34866i) q^{28} -1.35052i q^{29} +(-7.49558 - 4.32758i) q^{31} +(-0.500000 + 0.866025i) q^{32} +6.52257i q^{34} +(5.79429 - 1.19425i) q^{35} +(8.25652 - 4.76690i) q^{37} +(-5.22868 - 3.01878i) q^{38} +(-1.68760 + 1.46697i) q^{40} +8.71759 q^{41} -5.35859i q^{43} +(-1.11120 + 0.641550i) q^{44} +(-1.43958 + 2.49343i) q^{46} +(0.698165 - 0.403086i) q^{47} +(3.63597 + 5.98162i) q^{49} +(-4.63597 + 1.87292i) q^{50} +(-3.07432 + 5.32488i) q^{52} +(3.33413 - 5.77488i) q^{53} +(-2.81639 + 0.547415i) q^{55} +(-2.30608 - 1.29693i) q^{56} +(-1.16959 + 0.675260i) q^{58} +(-0.798110 + 1.38237i) q^{59} +(-5.50239 + 3.17681i) q^{61} +8.65515i q^{62} +1.00000 q^{64} +(-10.3764 + 9.01988i) q^{65} +(4.67188 + 2.69731i) q^{67} +(5.64871 - 3.26128i) q^{68} +(-3.93140 - 4.42087i) q^{70} -15.6787i q^{71} +(-6.20837 + 10.7532i) q^{73} +(-8.25652 - 4.76690i) q^{74} +6.03756i q^{76} +(-1.73046 - 2.92060i) q^{77} +(-5.59093 - 9.68377i) q^{79} +(2.11423 + 0.728019i) q^{80} +(-4.35880 - 7.54966i) q^{82} +3.74493i q^{83} +(14.3170 - 2.78275i) q^{85} +(-4.64067 + 2.67929i) q^{86} +(1.11120 + 0.641550i) q^{88} +(1.81971 + 3.15183i) q^{89} +(-14.1792 - 7.97433i) q^{91} +2.87917 q^{92} +(-0.698165 - 0.403086i) q^{94} +(-4.39545 + 12.7648i) q^{95} -8.76818 q^{97} +(3.36225 - 6.13965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} - 6 q^{5} + 16 q^{8} + 6 q^{10} - 8 q^{16} + 24 q^{19} - 8 q^{23} - 6 q^{25} + 12 q^{31} - 8 q^{32} + 4 q^{35} - 24 q^{38} - 6 q^{40} - 8 q^{46} + 60 q^{47} - 28 q^{49} + 12 q^{50}+ \cdots + 20 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 - 6 * q^5 + 16 * q^8 + 6 * q^10 - 8 * q^16 + 24 * q^19 - 8 * q^23 - 6 * q^25 + 12 * q^31 - 8 * q^32 + 4 * q^35 - 24 * q^38 - 6 * q^40 - 8 * q^46 + 60 * q^47 - 28 * q^49 + 12 * q^50 + 16 * q^53 + 24 * q^61 + 16 * q^64 - 20 * q^65 - 14 * q^70 - 88 * q^77 + 4 * q^79 + 6 * q^80 + 64 * q^85 - 28 * q^91 + 16 * q^92 - 60 * q^94 - 12 * q^95 + 20 * q^98

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