LMFDB - Embedded newform 630.2.bv.c.397.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(73,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("630.73");

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.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.2
Root			$1.45333 + 1.51725i$ of defining polynomial
Character	$\chi$	$=$	630.397
Dual form			630.2.bv.c.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.79038 - 1.33961i) q^{5} +(-2.55176 + 0.698943i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.79038 - 1.33961i) q^{5} +(-2.55176 + 0.698943i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.38266 + 1.75735i) q^{10} +(0.371536 + 0.643519i) q^{11} +(2.05532 + 2.05532i) q^{13} +(2.28391 - 1.33557i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.33660 + 1.69789i) q^{17} +(0.946027 - 1.63857i) q^{19} +(0.880708 - 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(1.36952 + 5.11112i) q^{23} +(1.41090 - 4.79681i) q^{25} +(-2.51725 - 1.45333i) q^{26} +(-1.86042 + 1.88118i) q^{28} -9.69135i q^{29} +(2.96403 - 1.71129i) q^{31} +(-0.258819 + 0.965926i) q^{32} -6.56014 q^{34} +(-3.63230 + 4.66973i) q^{35} +(2.58012 - 0.691342i) q^{37} +(-0.489700 + 1.82758i) q^{38} +(-0.318742 + 2.21323i) q^{40} +0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +(0.643519 + 0.371536i) q^{44} +(-2.64571 - 4.58251i) q^{46} +(-1.21894 - 4.54913i) q^{47} +(6.02296 - 3.56707i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(2.80762 + 0.752300i) q^{52} +(4.81583 + 1.29040i) q^{53} +(1.52725 + 0.654429i) q^{55} +(1.31014 - 2.29859i) q^{56} +(2.50831 + 9.36112i) q^{58} +(1.27487 + 2.20815i) q^{59} +(5.25989 + 3.03680i) q^{61} +(-2.42012 + 2.42012i) q^{62} -1.00000i q^{64} +(6.43313 + 0.926476i) q^{65} +(-3.54358 + 13.2248i) q^{67} +(6.33660 - 1.69789i) q^{68} +(2.29992 - 5.45072i) q^{70} +16.0173 q^{71} +(-2.29071 + 8.54906i) q^{73} +(-2.31328 + 1.33557i) q^{74} -1.89205i q^{76} +(-1.39785 - 1.38242i) q^{77} +(-5.70091 - 3.29142i) q^{79} +(-0.264946 - 2.22032i) q^{80} +(-0.211636 - 0.789836i) q^{82} +(-9.23519 - 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-1.12846 + 1.95456i) q^{86} +(-0.717752 - 0.192321i) q^{88} +(-3.01603 + 5.22392i) q^{89} +(-6.68124 - 3.80814i) q^{91} +(3.74160 + 3.74160i) q^{92} +(2.35481 + 4.07864i) q^{94} +(-0.501292 - 4.20096i) q^{95} +(3.16693 - 3.16693i) q^{97} +(-4.89451 + 5.00438i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 + 8 * q^7	$ 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.79038	−	1.33961i	0.800681	−	0.599091i
$5$	1.79038	−	1.33961i	0.800681	−	0.599091i
$6$		0			0
$7$	−2.55176	+	0.698943i	−0.964475	+	0.264175i
$7$	−2.55176	+	0.698943i	−0.964475	+	0.264175i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−1.38266	+	1.75735i	−0.437234	+	0.555722i
$11$	0.371536	+	0.643519i	0.112022	+	0.194028i	0.916586	−	0.399839i	$-0.130934\pi$
$11$	0.371536	+	0.643519i	0.112022	+	0.194028i	−0.804563	+	0.593867i	$0.797601\pi$
$12$		0			0
$13$	2.05532	+	2.05532i	0.570044	+	0.570044i	0.932141	−	0.362097i	$-0.117939\pi$
$13$	2.05532	+	2.05532i	0.570044	+	0.570044i	−0.362097	+	0.932141i	$0.617939\pi$
$14$	2.28391	−	1.33557i	0.610401	−	0.356946i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.33660	+	1.69789i	1.53685	+	0.411798i	0.925247	−	0.379365i	$-0.123857\pi$
$17$	6.33660	+	1.69789i	1.53685	+	0.411798i	0.611605	+	0.791163i	$0.290524\pi$
$18$		0			0
$19$	0.946027	−	1.63857i	0.217033	−	0.375913i	−0.736866	−	0.676039i	$-0.763695\pi$
$19$	0.946027	−	1.63857i	0.217033	−	0.375913i	0.953900	+	0.300126i	$0.0970286\pi$
$20$	0.880708	−	2.05532i	0.196932	−	0.459584i
$21$		0			0
$22$	−0.525431	−	0.525431i	−0.112022	−	0.112022i
$23$	1.36952	+	5.11112i	0.285565	+	1.06574i	0.948426	+	0.317000i	$0.102675\pi$
$23$	1.36952	+	5.11112i	0.285565	+	1.06574i	−0.662861	+	0.748743i	$0.730658\pi$
$24$		0			0
$25$	1.41090	−	4.79681i	0.282180	−	0.959361i
$26$	−2.51725	−	1.45333i	−0.493673	−	0.285022i
$27$		0			0
$28$	−1.86042	+	1.88118i	−0.351586	+	0.355510i
$29$		−	9.69135i		−	1.79964i	−0.436263	−	0.899819i	$-0.643698\pi$
$29$		−	9.69135i		−	1.79964i	0.436263	−	0.899819i	$-0.356302\pi$
$30$		0			0
$31$	2.96403	−	1.71129i	0.532356	−	0.307356i	−0.209619	−	0.977783i	$-0.567222\pi$
$31$	2.96403	−	1.71129i	0.532356	−	0.307356i	0.741975	+	0.670427i	$0.233889\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	−6.56014			−1.12505
$35$	−3.63230	+	4.66973i	−0.613971	+	0.789328i
$36$		0			0
$37$	2.58012	−	0.691342i	0.424170	−	0.113656i	−0.0404183	−	0.999183i	$-0.512869\pi$
$37$	2.58012	−	0.691342i	0.424170	−	0.113656i	0.464588	+	0.885527i	$0.346202\pi$
$38$	−0.489700	+	1.82758i	−0.0794398	+	0.296473i
$39$		0			0
$40$	−0.318742	+	2.21323i	−0.0503975	+	0.349943i
$41$			0.817699i			0.127703i	0.997959	+	0.0638515i	$0.0203384\pi$
$41$			0.817699i			0.127703i	−0.997959	+	0.0638515i	$0.979662\pi$
$42$		0			0
$43$	1.59589	−	1.59589i	0.243371	−	0.243371i	−0.574872	−	0.818243i	$-0.694948\pi$
$43$	1.59589	−	1.59589i	0.243371	−	0.243371i	0.818243	+	0.574872i	$0.194948\pi$
$44$	0.643519	+	0.371536i	0.0970142	+	0.0560111i
$45$		0			0
$46$	−2.64571	−	4.58251i	−0.390089	−	0.675654i
$47$	−1.21894	−	4.54913i	−0.177800	−	0.663560i	−0.996058	−	0.0887076i	$-0.971726\pi$
$47$	−1.21894	−	4.54913i	−0.177800	−	0.663560i	0.818257	−	0.574852i	$-0.194940\pi$
$48$		0			0
$49$	6.02296	−	3.56707i	0.860423	−	0.509581i
$50$	−0.121320	+	4.99853i	−0.0171573	+	0.706899i
$51$		0			0
$52$	2.80762	+	0.752300i	0.389347	+	0.104325i
$53$	4.81583	+	1.29040i	0.661505	+	0.177250i	0.573925	−	0.818908i	$-0.305420\pi$
$53$	4.81583	+	1.29040i	0.661505	+	0.177250i	0.0875798	+	0.996158i	$0.472087\pi$
$54$		0			0
$55$	1.52725	+	0.654429i	0.205935	+	0.0882432i
$56$	1.31014	−	2.29859i	0.175075	−	0.307163i
$57$		0			0
$58$	2.50831	+	9.36112i	0.329357	+	1.22918i
$59$	1.27487	+	2.20815i	0.165975	+	0.287476i	0.937001	−	0.349327i	$-0.113590\pi$
$59$	1.27487	+	2.20815i	0.165975	+	0.287476i	−0.771026	+	0.636803i	$0.780256\pi$
$60$		0			0
$61$	5.25989	+	3.03680i	0.673460	+	0.388822i	0.797386	−	0.603469i	$-0.206215\pi$
$61$	5.25989	+	3.03680i	0.673460	+	0.388822i	−0.123927	+	0.992291i	$0.539549\pi$
$62$	−2.42012	+	2.42012i	−0.307356	+	0.307356i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.43313	+	0.926476i	0.797932	+	0.114915i
$66$		0			0
$67$	−3.54358	+	13.2248i	−0.432917	+	1.61567i	0.313084	+	0.949725i	$0.398638\pi$
$67$	−3.54358	+	13.2248i	−0.432917	+	1.61567i	−0.746002	+	0.665944i	$0.768029\pi$
$68$	6.33660	−	1.69789i	0.768426	−	0.205899i
$69$		0			0
$70$	2.29992	−	5.45072i	0.274893	−	0.651486i
$71$	16.0173			1.90090			0.950450	−	0.310879i	$-0.100623\pi$
$71$	16.0173			1.90090			0.950450	+	0.310879i	$0.100623\pi$
$72$		0			0
$73$	−2.29071	+	8.54906i	−0.268108	+	1.00059i	0.692213	+	0.721693i	$0.256636\pi$
$73$	−2.29071	+	8.54906i	−0.268108	+	1.00059i	−0.960321	+	0.278898i	$0.910031\pi$
$74$	−2.31328	+	1.33557i	−0.268913	+	0.155257i
$75$		0			0
$76$		−	1.89205i		−	0.217033i
$77$	−1.39785	−	1.38242i	−0.159300	−	0.157542i
$78$		0			0
$79$	−5.70091	−	3.29142i	−0.641402	−	0.370314i	0.143752	−	0.989614i	$-0.454083\pi$
$79$	−5.70091	−	3.29142i	−0.641402	−	0.370314i	−0.785155	+	0.619300i	$0.787417\pi$
$80$	−0.264946	−	2.22032i	−0.0296219	−	0.248239i
$81$		0			0
$82$	−0.211636	−	0.789836i	−0.0233713	−	0.0872228i
$83$	−9.23519	−	9.23519i	−1.01369	−	1.01369i	−0.999905	−	0.0137887i	$-0.995611\pi$
$83$	−9.23519	−	9.23519i	−1.01369	−	1.01369i	−0.0137887	−	0.999905i	$-0.504389\pi$
$84$		0			0
$85$	13.6194	−	5.44871i	1.47723	−	0.590995i
$86$	−1.12846	+	1.95456i	−0.121685	+	0.210765i
$87$		0			0
$88$	−0.717752	−	0.192321i	−0.0765127	−	0.0205015i
$89$	−3.01603	+	5.22392i	−0.319699	+	0.553735i	−0.980425	−	0.196892i	$-0.936915\pi$
$89$	−3.01603	+	5.22392i	−0.319699	+	0.553735i	0.660726	+	0.750627i	$0.270248\pi$
$90$		0			0
$91$	−6.68124	−	3.80814i	−0.700385	−	0.399201i
$92$	3.74160	+	3.74160i	0.390089	+	0.390089i
$93$		0			0
$94$	2.35481	+	4.07864i	0.242880	+	0.420680i
$95$	−0.501292	−	4.20096i	−0.0514315	−	0.431009i
$96$		0			0
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	−0.527810	−	0.849363i	$-0.676987\pi$
$97$	3.16693	−	3.16693i	0.321553	−	0.321553i	0.849363	+	0.527810i	$0.176987\pi$
$98$	−4.89451	+	5.00438i	−0.494420	+	0.505519i
$99$		0			0
$100$	−1.17653	−	4.85961i	−0.117653	−	0.485961i
$101$	−9.68359	+	5.59083i	−0.963554	+	0.556308i	−0.897265	−	0.441493i	$-0.854449\pi$
$101$	−9.68359	+	5.59083i	−0.963554	+	0.556308i	−0.0662887	+	0.997800i	$0.521116\pi$
$102$		0			0
$103$	2.34351	−	0.627940i	0.230912	−	0.0618728i	−0.141507	−	0.989937i	$-0.545195\pi$
$103$	2.34351	−	0.627940i	0.230912	−	0.0618728i	0.372420	+	0.928064i	$0.378528\pi$
$104$	−2.90667			−0.285022
$105$		0			0
$106$	−4.98571			−0.484255
$107$	−6.41422	+	1.71868i	−0.620086	+	0.166151i	−0.555167	−	0.831739i	$-0.687346\pi$
$107$	−6.41422	+	1.71868i	−0.620086	+	0.166151i	−0.0649189	+	0.997891i	$0.520679\pi$
$108$		0			0
$109$	−7.76000	+	4.48024i	−0.743274	+	0.429129i	−0.823258	−	0.567667i	$-0.807846\pi$
$109$	−7.76000	+	4.48024i	−0.743274	+	0.429129i	0.0799848	+	0.996796i	$0.474513\pi$
$110$	−1.64459	−	0.236848i	−0.156806	−	0.0225826i
$111$		0			0
$112$	−0.670578	+	2.55936i	−0.0633637	+	0.241837i
$113$	−0.307790	+	0.307790i	−0.0289545	+	0.0289545i	−0.721436	−	0.692481i	$-0.756518\pi$
$113$	−0.307790	+	0.307790i	−0.0289545	+	0.0289545i	0.692481	+	0.721436i	$0.256518\pi$
$114$		0			0
$115$	9.29886	+	7.31621i	0.867123	+	0.682240i
$116$	−4.84567	−	8.39295i	−0.449910	−	0.779266i
$117$		0			0
$118$	−1.80295	−	1.80295i	−0.165975	−	0.165975i
$119$	−17.3562	+	0.0963204i	−1.59104	+	0.00882967i
$120$		0			0
$121$	5.22392	−	9.04810i	0.474902	−	0.822554i
$122$	−5.86664	−	1.57196i	−0.531141	−	0.142319i
$123$		0			0
$124$	1.71129	−	2.96403i	0.153678	−	0.266178i
$125$	−3.89980	−	10.4781i	−0.348808	−	0.937194i
$126$		0			0
$127$	−11.1823	−	11.1823i	−0.992267	−	0.992267i	0.00770296	−	0.999970i	$-0.497548\pi$
$127$	−11.1823	−	11.1823i	−0.992267	−	0.992267i	−0.999970	+	0.00770296i	$0.997548\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	−6.45372	+	0.770110i	−0.566028	+	0.0675431i
$131$	8.30763	+	4.79641i	0.725841	+	0.419064i	0.816899	−	0.576781i	$-0.195692\pi$
$131$	8.30763	+	4.79641i	0.725841	+	0.419064i	−0.0910579	+	0.995846i	$0.529025\pi$
$132$		0			0
$133$	−1.26877	+	4.84245i	−0.110016	+	0.419893i
$134$		−	13.6913i		−	1.18275i
$135$		0			0
$136$	−5.68124	+	3.28007i	−0.487163	+	0.281264i
$137$	−2.40949	+	8.99233i	−0.205856	+	0.768267i	0.783330	+	0.621606i	$0.213519\pi$
$137$	−2.40949	+	8.99233i	−0.205856	+	0.768267i	−0.989187	+	0.146661i	$0.953147\pi$
$138$		0			0
$139$	−22.1714			−1.88056			−0.940278	−	0.340408i	$-0.889435\pi$
$139$	−22.1714			−1.88056			−0.940278	+	0.340408i	$0.889435\pi$
$140$	−0.810803	+	5.86026i	−0.0685253	+	0.495282i
$141$		0			0
$142$	−15.4715	+	4.14557i	−1.29834	+	0.347889i
$143$	−0.559013	+	2.08627i	−0.0467470	+	0.174462i
$144$		0			0
$145$	−12.9826	−	17.3512i	−1.07815	−	1.44094i
$146$		−	8.85064i		−	0.732484i
$147$		0			0
$148$	1.88878	−	1.88878i	0.155257	−	0.155257i
$149$	−3.41418	−	1.97118i	−0.279701	−	0.161485i	0.353587	−	0.935402i	$-0.384962\pi$
$149$	−3.41418	−	1.97118i	−0.279701	−	0.161485i	−0.633288	+	0.773916i	$0.718295\pi$
$150$		0			0
$151$	9.97267	+	17.2732i	0.811564	+	1.40567i	0.911769	+	0.410703i	$0.134717\pi$
$151$	9.97267	+	17.2732i	0.811564	+	1.40567i	−0.100205	+	0.994967i	$0.531950\pi$
$152$	0.489700	+	1.82758i	0.0397199	+	0.148237i
$153$		0			0
$154$	1.70802	+	0.973528i	0.137636	+	0.0784491i
$155$	3.01429	−	7.03449i	0.242113	−	0.565024i
$156$		0			0
$157$	−7.20903	−	1.93165i	−0.575343	−	0.154163i	−0.0405972	−	0.999176i	$-0.512926\pi$
$157$	−7.20903	−	1.93165i	−0.575343	−	0.154163i	−0.534746	+	0.845013i	$0.679593\pi$
$158$	6.35854	+	1.70376i	0.505858	+	0.135544i
$159$		0			0
$160$	0.830578	+	2.07609i	0.0656630	+	0.164129i
$161$	−7.06707	−	12.0851i	−0.556963	−	0.952442i
$162$		0			0
$163$	3.14893	+	11.7520i	0.246644	+	0.920486i	0.972550	+	0.232693i	$0.0747537\pi$
$163$	3.14893	+	11.7520i	0.246644	+	0.920486i	−0.725907	+	0.687793i	$0.758580\pi$
$164$	0.408849	+	0.708148i	0.0319258	+	0.0552970i
$165$		0			0
$166$	11.3107	+	6.53026i	0.877884	+	0.506847i
$167$	−1.45564	+	1.45564i	−0.112641	+	0.112641i	−0.761181	−	0.648540i	$-0.775380\pi$
$167$	−1.45564	+	1.45564i	−0.112641	+	0.112641i	0.648540	+	0.761181i	$0.275380\pi$
$168$		0			0
$169$		−	4.55129i		−	0.350099i
$170$	−11.7451	+	8.78801i	−0.900809	+	0.674010i
$171$		0			0
$172$	0.584136	−	2.18003i	0.0445400	−	0.166225i
$173$	−9.08750	+	2.43499i	−0.690910	+	0.185129i	−0.587155	−	0.809474i	$-0.699752\pi$
$173$	−9.08750	+	2.43499i	−0.690910	+	0.185129i	−0.103754	+	0.994603i	$0.533086\pi$
$174$		0			0
$175$	−0.247587	+	13.2264i	−0.0187158	+	0.999825i
$176$	0.743072			0.0560111
$177$		0			0
$178$	1.56121	−	5.82653i	0.117018	−	0.436717i
$179$	−3.89494	+	2.24874i	−0.291121	+	0.168079i	−0.638447	−	0.769665i	$-0.720423\pi$
$179$	−3.89494	+	2.24874i	−0.291121	+	0.168079i	0.347326	+	0.937744i	$0.387090\pi$
$180$		0			0
$181$		−	17.8850i		−	1.32938i	−0.747118	−	0.664691i	$-0.768563\pi$
$181$		−	17.8850i		−	1.32938i	0.747118	−	0.664691i	$-0.231437\pi$
$182$	7.43921	+	1.94915i	0.551431	+	0.144480i
$183$		0			0
$184$	−4.58251	−	2.64571i	−0.337827	−	0.195044i
$185$	3.69327	−	4.69412i	0.271535	−	0.345119i
$186$		0			0
$187$	1.26165	+	4.70855i	0.0922612	+	0.344323i
$188$	−3.33020	−	3.33020i	−0.242880	−	0.242880i
$189$		0			0
$190$	1.57150	+	3.92807i	0.114009	+	0.284972i
$191$	−1.38774	+	2.40364i	−0.100413	+	0.173921i	−0.911855	−	0.410512i	$-0.865350\pi$
$191$	−1.38774	+	2.40364i	−0.100413	+	0.173921i	0.811442	+	0.584433i	$0.198683\pi$
$192$		0			0
$193$	4.96491	+	1.33034i	0.357382	+	0.0957602i	0.433043	−	0.901373i	$-0.357440\pi$
$193$	4.96491	+	1.33034i	0.357382	+	0.0957602i	−0.0756607	+	0.997134i	$0.524107\pi$
$194$	−2.23936	+	3.87868i	−0.160776	+	0.278473i
$195$		0			0
$196$	3.43250	−	6.10065i	0.245179	−	0.435761i
$197$	−1.34043	−	1.34043i	−0.0955019	−	0.0955019i	0.657742	−	0.753244i	$-0.271512\pi$
$197$	−1.34043	−	1.34043i	−0.0955019	−	0.0955019i	−0.753244	+	0.657742i	$0.771512\pi$
$198$		0			0
$199$	−7.25148	−	12.5599i	−0.514043	−	0.890349i	−0.999867	−	0.0162926i	$-0.994814\pi$
$199$	−7.25148	−	12.5599i	−0.514043	−	0.890349i	0.485824	−	0.874057i	$-0.338520\pi$
$200$	2.39420	+	4.38951i	0.169295	+	0.310385i
$201$		0			0
$202$	7.90662	−	7.90662i	0.556308	−	0.556308i
$203$	6.77370	+	24.7300i	0.475420	+	1.73571i
$204$		0			0
$205$	1.09540	+	1.46399i	0.0765057	+	0.102249i
$206$	−2.10113	+	1.21309i	−0.146393	+	0.0845198i
$207$		0			0
$208$	2.80762	−	0.752300i	0.194674	−	0.0521627i
$209$	1.40593			0.0972504
$210$		0			0
$211$	10.0324			0.690660			0.345330	−	0.938481i	$-0.387767\pi$
$211$	10.0324			0.690660			0.345330	+	0.938481i	$0.387767\pi$
$212$	4.81583	−	1.29040i	0.330752	−	0.0886249i
$213$		0			0
$214$	5.75083	−	3.32024i	0.393119	−	0.226967i
$215$	0.719378	−	4.99511i	0.0490611	−	0.340664i
$216$		0			0
$217$	−6.36741	+	6.43848i	−0.432248	+	0.437073i
$218$	6.33602	−	6.33602i	0.429129	−	0.429129i
$219$		0			0
$220$	1.64985	−	0.196874i	0.111233	−	0.0132732i
$221$	9.53406	+	16.5135i	0.641330	+	1.11082i
$222$		0			0
$223$	−3.13756	−	3.13756i	−0.210107	−	0.210107i	0.594206	−	0.804313i	$-0.297466\pi$
$223$	−3.13756	−	3.13756i	−0.210107	−	0.210107i	−0.804313	+	0.594206i	$0.797466\pi$
$224$	−0.0146827	−	2.64571i	−0.000981028	−	0.176774i
$225$		0			0
$226$	0.217641	−	0.376965i	0.0144772	−	0.0250753i
$227$	−0.648012	−	0.173634i	−0.0430101	−	0.0115245i	0.237250	−	0.971449i	$-0.423754\pi$
$227$	−0.648012	−	0.173634i	−0.0430101	−	0.0115245i	−0.280260	+	0.959924i	$0.590421\pi$
$228$		0			0
$229$	−6.60166	+	11.4344i	−0.436250	+	0.755608i	−0.997397	−	0.0721088i	$-0.977027\pi$
$229$	−6.60166	+	11.4344i	−0.436250	+	0.755608i	0.561146	+	0.827717i	$0.310360\pi$
$230$	−10.8756	−	4.66020i	−0.717115	−	0.307284i
$231$		0			0
$232$	6.85282	+	6.85282i	0.449910	+	0.449910i
$233$	2.24110	+	8.36389i	0.146819	+	0.547937i	0.999668	+	0.0257782i	$0.00820637\pi$
$233$	2.24110	+	8.36389i	0.146819	+	0.547937i	−0.852849	+	0.522158i	$0.825127\pi$
$234$		0			0
$235$	−8.27641	−	6.51177i	−0.539894	−	0.424781i
$236$	2.20815	+	1.27487i	0.143738	+	0.0829873i
$237$		0			0
$238$	16.7399	−	4.58516i	1.08509	−	0.297212i
$239$		−	4.00294i		−	0.258929i	−0.991584	−	0.129464i	$-0.958674\pi$
$239$		−	4.00294i		−	0.258929i	0.991584	−	0.129464i	$-0.0413258\pi$
$240$		0			0
$241$	−15.0040	+	8.66256i	−0.966493	+	0.558005i	−0.898165	−	0.439658i	$-0.855100\pi$
$241$	−15.0040	+	8.66256i	−0.966493	+	0.558005i	−0.0683274	+	0.997663i	$0.521766\pi$
$242$	−2.70410	+	10.0918i	−0.173826	+	0.648728i
$243$		0			0
$244$	6.07359			0.388822
$245$	6.00489	−	14.4548i	0.383639	−	0.923483i
$246$		0			0
$247$	5.31218	−	1.42339i	0.338006	−	0.0905683i
$248$	−0.885827	+	3.30595i	−0.0562501	+	0.209928i
$249$		0			0
$250$	6.47886	+	9.11177i	0.409759	+	0.576279i
$251$		−	5.49938i		−	0.347118i	−0.984824	−	0.173559i	$-0.944473\pi$
$251$		−	5.49938i		−	0.347118i	0.984824	−	0.173559i	$-0.0555267\pi$
$252$		0			0
$253$	−2.78028	+	2.78028i	−0.174795	+	0.174795i
$254$	13.6954	+	7.90707i	0.859329	+	0.496134i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.27307	−	15.9473i	−0.266547	−	0.994766i	−0.961297	−	0.275515i	$-0.911152\pi$
$257$	−4.27307	−	15.9473i	−0.266547	−	0.994766i	0.694750	−	0.719251i	$-0.255515\pi$
$258$		0			0
$259$	−6.10065	+	3.56750i	−0.379076	+	0.221674i
$260$	6.03449	−	2.41421i	0.374243	−	0.149723i
$261$		0			0
$262$	−9.26595	−	2.48280i	−0.572453	−	0.153388i
$263$	−9.52484	−	2.55217i	−0.587327	−	0.157374i	−0.0470956	−	0.998890i	$-0.514997\pi$
$263$	−9.52484	−	2.55217i	−0.587327	−	0.157374i	−0.540231	+	0.841517i	$0.681663\pi$
$264$		0			0
$265$	10.3508	−	4.14102i	0.635843	−	0.254381i
$266$	−0.0277804	−	5.00583i	−0.00170333	−	0.306927i
$267$		0			0
$268$	3.54358	+	13.2248i	0.216459	+	0.807835i
$269$	4.47922	+	7.75824i	0.273103	+	0.473028i	0.969655	−	0.244478i	$-0.0786167\pi$
$269$	4.47922	+	7.75824i	0.273103	+	0.473028i	−0.696552	+	0.717506i	$0.745283\pi$
$270$		0			0
$271$	−19.7889	−	11.4251i	−1.20209	−	0.694027i	−0.241071	−	0.970507i	$-0.577499\pi$
$271$	−19.7889	−	11.4251i	−1.20209	−	0.694027i	−0.961020	+	0.276480i	$0.910832\pi$
$272$	4.63872	−	4.63872i	0.281264	−	0.281264i
$273$		0			0
$274$		−	9.30954i		−	0.562410i
$275$	3.61104	−	0.874245i	0.217754	−	0.0527189i
$276$		0			0
$277$	5.57320	−	20.7995i	0.334861	−	1.24972i	−0.569158	−	0.822228i	$-0.692731\pi$
$277$	5.57320	−	20.7995i	0.334861	−	1.24972i	0.904019	−	0.427491i	$-0.140603\pi$
$278$	21.4160	−	5.73839i	1.28444	−	0.344166i
$279$		0			0
$280$	−0.733571	−	5.87042i	−0.0438392	−	0.350825i
$281$	5.64885			0.336982			0.168491	−	0.985703i	$-0.446111\pi$
$281$	5.64885			0.336982			0.168491	+	0.985703i	$0.446111\pi$
$282$		0			0
$283$	−0.757948	+	2.82870i	−0.0450553	+	0.168149i	−0.984788	−	0.173762i	$-0.944408\pi$
$283$	−0.757948	+	2.82870i	−0.0450553	+	0.168149i	0.939732	+	0.341911i	$0.111074\pi$
$284$	13.8714	−	8.00863i	0.823113	−	0.475225i
$285$		0			0
$286$		−	2.15986i		−	0.127715i
$287$	−0.571524	−	2.08657i	−0.0337360	−	0.123166i
$288$		0			0
$289$	22.5473	+	13.0177i	1.32631	+	0.765747i
$290$	17.0310	+	13.3998i	1.00010	+	0.786863i
$291$		0			0
$292$	2.29071	+	8.54906i	0.134054	+	0.500296i
$293$	−10.7875	−	10.7875i	−0.630212	−	0.630212i	0.317909	−	0.948121i	$-0.397019\pi$
$293$	−10.7875	−	10.7875i	−0.630212	−	0.630212i	−0.948121	+	0.317909i	$0.897019\pi$
$294$		0			0
$295$	5.24056	+	2.24558i	0.305117	+	0.130743i
$296$	−1.33557	+	2.31328i	−0.0776285	+	0.134456i
$297$		0			0
$298$	3.80802	+	1.02036i	0.220593	+	0.0591077i
$299$	−7.69020	+	13.3198i	−0.444736	+	0.770305i
$300$		0			0
$301$	−2.95689	+	5.18776i	−0.170432	+	0.299018i
$302$	−14.1035	−	14.1035i	−0.811564	−	0.811564i
$303$		0			0
$304$	−0.946027	−	1.63857i	−0.0542584	−	0.0939783i
$305$	13.4853	−	1.60917i	0.772166	−	0.0921411i
$306$		0			0
$307$	−6.89201	+	6.89201i	−0.393348	+	0.393348i	−0.875879	−	0.482531i	$-0.839718\pi$
$307$	−6.89201	+	6.89201i	−0.393348	+	0.393348i	0.482531	+	0.875879i	$0.339718\pi$
$308$	−1.90179	−	0.498288i	−0.108364	−	0.0283926i
$309$		0			0
$310$	−1.09092	+	7.57495i	−0.0619599	+	0.430228i
$311$	0.109136	−	0.0630096i	0.00618852	−	0.00357294i	−0.496903	−	0.867806i	$-0.665529\pi$
$311$	0.109136	−	0.0630096i	0.00618852	−	0.00357294i	0.503091	+	0.864233i	$0.332196\pi$
$312$		0			0
$313$	−11.2955	+	3.02662i	−0.638459	+	0.171075i	−0.563505	−	0.826112i	$-0.690548\pi$
$313$	−11.2955	+	3.02662i	−0.638459	+	0.171075i	−0.0749536	+	0.997187i	$0.523881\pi$
$314$	7.46334			0.421181
$315$		0			0
$316$	−6.58284			−0.370314
$317$	−10.5732	+	2.83308i	−0.593851	+	0.159122i	−0.543212	−	0.839595i	$-0.682792\pi$
$317$	−10.5732	+	2.83308i	−0.593851	+	0.159122i	−0.0506382	+	0.998717i	$0.516126\pi$
$318$		0			0
$319$	6.23657	−	3.60068i	0.349181	−	0.201600i
$320$	−1.33961	−	1.79038i	−0.0748864	−	0.100085i
$321$		0			0
$322$	9.95413	+	9.84425i	0.554722	+	0.548599i
$323$	8.77670	−	8.77670i	0.488349	−	0.488349i
$324$		0			0
$325$	12.7588	−	6.95913i	0.707733	−	0.386023i
$326$	−6.08327	−	10.5365i	−0.336921	−	0.583565i
$327$		0			0
$328$	−0.578200	−	0.578200i	−0.0319258	−	0.0319258i
$329$	6.29002	+	10.7563i	0.346780	+	0.593016i
$330$		0			0
$331$	2.73019	−	4.72883i	0.150065	−	0.259920i	−0.781186	−	0.624298i	$-0.785385\pi$
$331$	2.73019	−	4.72883i	0.150065	−	0.259920i	0.931251	+	0.364378i	$0.118718\pi$
$332$	−12.6155	−	3.38031i	−0.692366	−	0.185519i
$333$		0			0
$334$	1.02929	−	1.78279i	0.0563205	−	0.0975500i
$335$	11.3717	+	28.4244i	0.621304	+	1.55299i
$336$		0			0
$337$	20.4823	+	20.4823i	1.11574	+	1.11574i	0.992359	+	0.123385i	$0.0393751\pi$
$337$	20.4823	+	20.4823i	1.11574	+	1.11574i	0.123385	+	0.992359i	$0.460625\pi$
$338$	1.17796	+	4.39621i	0.0640727	+	0.239122i
$339$		0			0
$340$	9.07041	−	11.5284i	0.491912	−	0.625217i
$341$	2.20249	+	1.27161i	0.119272	+	0.0688615i
$342$		0			0
$343$	−12.8760	+	13.3120i	−0.695237	+	0.718781i
$344$			2.25693i			0.121685i
$345$		0			0
$346$	8.14763	−	4.70404i	0.438019	−	0.252891i
$347$	5.57442	−	20.8040i	0.299250	−	1.11682i	−0.638532	−	0.769595i	$-0.720458\pi$
$347$	5.57442	−	20.8040i	0.299250	−	1.11682i	0.937783	−	0.347223i	$-0.112875\pi$
$348$		0			0
$349$	12.5744			0.673093			0.336546	−	0.941667i	$-0.390741\pi$
$349$	12.5744			0.673093			0.336546	+	0.941667i	$0.390741\pi$
$350$	−3.18410	−	12.8398i	−0.170198	−	0.686318i
$351$		0			0
$352$	−0.717752	+	0.192321i	−0.0382563	+	0.0102508i
$353$	−0.178457	+	0.666012i	−0.00949832	+	0.0354482i	−0.970512	−	0.241051i	$-0.922508\pi$
$353$	−0.178457	+	0.666012i	−0.00949832	+	0.0354482i	0.961014	+	0.276500i	$0.0891744\pi$
$354$		0			0
$355$	28.6769	−	21.4569i	1.52201	−	1.13881i
$356$			6.03207i			0.319699i
$357$		0			0
$358$	3.18020	−	3.18020i	0.168079	−	0.168079i
$359$	19.1381	+	11.0494i	1.01007	+	0.583165i	0.911212	−	0.411937i	$-0.135148\pi$
$359$	19.1381	+	11.0494i	1.01007	+	0.583165i	0.0988582	+	0.995102i	$0.468481\pi$
$360$		0			0
$361$	7.71007	+	13.3542i	0.405793	+	0.702854i
$362$	4.62898	+	17.2756i	0.243294	+	0.907985i
$363$		0			0
$364$	−7.69020	+	0.0426776i	−0.403076	+	0.00223692i
$365$	7.35115	+	18.3747i	0.384777	+	0.961775i
$366$		0			0
$367$	12.9539	+	3.47100i	0.676191	+	0.181185i	0.580542	−	0.814230i	$-0.302841\pi$
$367$	12.9539	+	3.47100i	0.676191	+	0.181185i	0.0956487	+	0.995415i	$0.469507\pi$
$368$	5.11112	+	1.36952i	0.266436	+	0.0713912i
$369$		0			0
$370$	−2.35250	+	5.49006i	−0.122300	+	0.285415i
$371$	−13.1908	+	0.0732036i	−0.684830	+	0.00380054i
$372$		0			0
$373$	−3.87359	−	14.4564i	−0.200567	−	0.748526i	−0.990755	−	0.135662i	$-0.956684\pi$
$373$	−3.87359	−	14.4564i	−0.200567	−	0.748526i	0.790188	−	0.612864i	$-0.209983\pi$
$374$	−2.43733	−	4.22157i	−0.126031	−	0.218292i
$375$		0			0
$376$	4.07864	+	2.35481i	0.210340	+	0.121440i
$377$	19.9189	−	19.9189i	1.02587	−	1.02587i
$378$		0			0
$379$			1.71784i			0.0882395i	0.999026	+	0.0441198i	$0.0140483\pi$
$379$			1.71784i			0.0882395i	−0.999026	+	0.0441198i	$0.985952\pi$
$380$	−2.53461	−	3.38749i	−0.130023	−	0.173775i
$381$		0			0
$382$	0.718348	−	2.68091i	0.0367539	−	0.137167i
$383$	10.1017	−	2.70676i	0.516175	−	0.138309i	0.00867837	−	0.999962i	$-0.497238\pi$
$383$	10.1017	−	2.70676i	0.516175	−	0.138309i	0.507497	+	0.861654i	$0.330571\pi$
$384$		0			0
$385$	−4.35459	−	0.602485i	−0.221931	−	0.0307055i
$386$	−5.14005			−0.261622
$387$		0			0
$388$	1.15918	−	4.32611i	0.0588483	−	0.219625i
$389$	18.8548	−	10.8858i	0.955978	−	0.551934i	0.0610449	−	0.998135i	$-0.480557\pi$
$389$	18.8548	−	10.8858i	0.955978	−	0.551934i	0.894933	+	0.446201i	$0.147223\pi$
$390$		0			0
$391$			34.7124i			1.75548i
$392$	−1.73658	+	6.78117i	−0.0877104	+	0.342501i
$393$		0			0
$394$	1.64169	+	0.947829i	0.0827071	+	0.0477510i
$395$	−14.6160	+	1.74410i	−0.735410	+	0.0877551i
$396$		0			0
$397$	−8.20427	−	30.6188i	−0.411761	−	1.53671i	−0.791237	−	0.611510i	$-0.790562\pi$
$397$	−8.20427	−	30.6188i	−0.411761	−	1.53671i	0.379476	−	0.925202i	$-0.376104\pi$
$398$	10.2551	+	10.2551i	0.514043	+	0.514043i
$399$		0			0
$400$	−3.44871	−	3.62028i	−0.172435	−	0.181014i
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	−0.637213	−	0.770687i	$-0.719913\pi$
$401$	6.98528	−	12.0989i	0.348828	−	0.604188i	0.986042	+	0.166499i	$0.0532463\pi$
$402$		0			0
$403$	9.60930	+	2.57480i	0.478673	+	0.128260i
$404$	−5.59083	+	9.68359i	−0.278154	+	0.481777i
$405$		0			0
$406$	−12.9435	−	22.1342i	−0.642374	−	1.09850i
$407$	1.40350	+	1.40350i	0.0695690	+	0.0695690i
$408$		0			0
$409$	9.36960	+	16.2286i	0.463297	+	0.802454i	0.999123	−	0.0418748i	$-0.0133330\pi$
$409$	9.36960	+	16.2286i	0.463297	+	0.802454i	−0.535826	+	0.844328i	$0.680000\pi$
$410$	−1.43698	−	1.13060i	−0.0709673	−	0.0558361i
$411$		0			0
$412$	1.71557	−	1.71557i	0.0845198	−	0.0845198i
$413$	−4.79654	−	4.74360i	−0.236022	−	0.233417i
$414$		0			0
$415$	−28.9060	−	4.16294i	−1.41894	−	0.204351i
$416$	−2.51725	+	1.45333i	−0.123418	+	0.0712555i
$417$		0			0
$418$	−1.35803	+	0.363882i	−0.0664232	+	0.0177981i
$419$	−31.5744			−1.54251			−0.771255	−	0.636526i	$-0.780371\pi$
$419$	−31.5744			−1.54251			−0.771255	+	0.636526i	$0.780371\pi$
$420$		0			0
$421$	−13.5569			−0.660722			−0.330361	−	0.943855i	$-0.607171\pi$
$421$	−13.5569			−0.660722			−0.330361	+	0.943855i	$0.607171\pi$
$422$	−9.69057	+	2.59658i	−0.471729	+	0.126399i
$423$		0			0
$424$	−4.31775	+	2.49286i	−0.209689	+	0.121064i
$425$	17.0848	−	27.9999i	0.828733	−	1.35820i
$426$		0			0
$427$	−15.5445	−	4.07282i	−0.752252	−	0.197097i
$428$	−4.69553	+	4.69553i	−0.226967	+	0.226967i
$429$		0			0
$430$	0.597964	+	5.01109i	0.0288364	+	0.241656i
$431$	6.63518	+	11.4925i	0.319605	+	0.553572i	0.980406	−	0.196989i	$-0.0631164\pi$
$431$	6.63518	+	11.4925i	0.319605	+	0.553572i	−0.660800	+	0.750562i	$0.729783\pi$
$432$		0			0
$433$	−12.0535	−	12.0535i	−0.579252	−	0.579252i	0.355445	−	0.934697i	$-0.384329\pi$
$433$	−12.0535	−	12.0535i	−0.579252	−	0.579252i	−0.934697	+	0.355445i	$0.884329\pi$
$434$	4.48405	−	7.86710i	0.215241	−	0.377633i
$435$		0			0
$436$	−4.48024	+	7.76000i	−0.214565	+	0.371637i
$437$	9.67052	+	2.59121i	0.462604	+	0.123954i
$438$		0			0
$439$	−17.5238	+	30.3521i	−0.836366	+	1.44863i	0.0565475	+	0.998400i	$0.481991\pi$
$439$	−17.5238	+	30.3521i	−0.836366	+	1.44863i	−0.892913	+	0.450228i	$0.851343\pi$
$440$	−1.54268	+	0.617179i	−0.0735445	+	0.0294229i
$441$		0			0
$442$	−13.4832	−	13.4832i	−0.641330	−	0.641330i
$443$	0.0163232	+	0.0609189i	0.000775538	+	0.00289435i	0.966313	−	0.257372i	$-0.0828564\pi$
$443$	0.0163232	+	0.0609189i	0.000775538	+	0.00289435i	−0.965537	+	0.260266i	$0.916190\pi$
$444$		0			0
$445$	1.59817	+	13.3931i	0.0757606	+	0.634893i
$446$	3.84271	+	2.21859i	0.181958	+	0.105053i
$447$		0			0
$448$	0.698943	+	2.55176i	0.0330219	+	0.120559i
$449$			24.5207i			1.15720i	0.815611	+	0.578601i	$0.196401\pi$
$449$			24.5207i			1.15720i	−0.815611	+	0.578601i	$0.803599\pi$
$450$		0			0
$451$	−0.526205	+	0.303804i	−0.0247780	+	0.0143056i
$452$	−0.112659	+	0.420450i	−0.00529904	+	0.0197763i
$453$		0			0
$454$	0.670872			0.0314856
$455$	−17.0634	+	2.13224i	−0.799943	+	0.0999612i
$456$		0			0
$457$	−19.3892	+	5.19531i	−0.906987	+	0.243027i	−0.682015	−	0.731339i	$-0.738896\pi$
$457$	−19.3892	+	5.19531i	−0.906987	+	0.243027i	−0.224973	+	0.974365i	$0.572229\pi$
$458$	3.41727	−	12.7534i	0.159679	−	0.595929i
$459$		0			0
$460$	11.7112	+	1.68660i	0.546035	+	0.0786380i
$461$			11.6940i			0.544642i	0.962207	+	0.272321i	$0.0877912\pi$
$461$			11.6940i			0.544642i	−0.962207	+	0.272321i	$0.912209\pi$
$462$		0			0
$463$	2.77226	−	2.77226i	0.128838	−	0.128838i	−0.639747	−	0.768585i	$-0.720961\pi$
$463$	2.77226	−	2.77226i	0.128838	−	0.128838i	0.768585	+	0.639747i	$0.220961\pi$
$464$	−8.39295	−	4.84567i	−0.389633	−	0.224955i
$465$		0			0
$466$	−4.32947	−	7.49886i	−0.200559	−	0.347378i
$467$	5.41472	+	20.2080i	0.250563	+	0.935116i	0.970505	+	0.241081i	$0.0775019\pi$
$467$	5.41472	+	20.2080i	0.250563	+	0.935116i	−0.719942	+	0.694035i	$0.755831\pi$
$468$		0			0
$469$	−0.201026	−	36.2233i	−0.00928250	−	1.67264i
$470$	9.67977	+	4.14779i	0.446495	+	0.191323i
$471$		0			0
$472$	−2.46287	−	0.659924i	−0.113363	−	0.0303754i
$473$	1.61992	+	0.434055i	0.0744838	+	0.0199579i
$474$		0			0
$475$	−6.52514	−	6.84976i	−0.299394	−	0.314289i
$476$	−14.9828	+	8.76153i	−0.686734	+	0.401584i
$477$		0			0
$478$	1.03604	+	3.86655i	0.0473873	+	0.176852i
$479$	−12.1419	−	21.0303i	−0.554775	−	0.960899i	−0.997921	−	0.0644496i	$-0.979471\pi$
$479$	−12.1419	−	21.0303i	−0.554775	−	0.960899i	0.443145	−	0.896450i	$-0.353863\pi$
$480$		0			0
$481$	6.72392	+	3.88206i	0.306584	+	0.177007i
$482$	12.2507	−	12.2507i	0.558005	−	0.558005i
$483$		0			0
$484$		−	10.4478i		−	0.474902i
$485$	1.42755	−	9.91244i	0.0648219	−	0.450101i
$486$		0			0
$487$	0.661539	−	2.46890i	0.0299772	−	0.111876i	−0.949316	−	0.314323i	$-0.898223\pi$
$487$	0.661539	−	2.46890i	0.0299772	−	0.111876i	0.979293	+	0.202446i	$0.0648892\pi$
$488$	−5.86664	+	1.57196i	−0.265570	+	0.0711594i
$489$		0			0
$490$	−2.05910	+	15.5164i	−0.0930209	+	0.700962i
$491$	−14.5668			−0.657391			−0.328695	−	0.944436i	$-0.606609\pi$
$491$	−14.5668			−0.657391			−0.328695	+	0.944436i	$0.606609\pi$
$492$		0			0
$493$	16.4548	−	61.4102i	0.741088	−	2.76578i
$494$	−4.76277	+	2.74978i	−0.214287	+	0.123719i
$495$		0			0
$496$		−	3.42257i		−	0.153678i
$497$	−40.8722	+	11.1951i	−1.83337	+	0.502171i
$498$		0			0
$499$	26.0565	+	15.0437i	1.16645	+	0.673450i	0.952841	−	0.303469i	$-0.0981450\pi$
$499$	26.0565	+	15.0437i	1.16645	+	0.673450i	0.213608	+	0.976919i	$0.431478\pi$
$500$	−8.61640	−	7.12444i	−0.385337	−	0.318615i
$501$		0			0
$502$	1.42334	+	5.31199i	0.0635269	+	0.237086i
$503$	−24.6819	−	24.6819i	−1.10051	−	1.10051i	−0.994349	−	0.106161i	$-0.966144\pi$
$503$	−24.6819	−	24.6819i	−1.10051	−	1.10051i	−0.106161	−	0.994349i	$-0.533856\pi$
$504$		0			0
$505$	−9.84777	+	22.9819i	−0.438220	+	1.02268i
$506$	1.96595	−	3.40513i	0.0873973	−	0.151377i
$507$		0			0
$508$	−15.2753	−	4.09300i	−0.677731	−	0.181598i
$509$	6.22521	−	10.7824i	0.275927	−	0.477920i	−0.694441	−	0.719549i	$-0.744348\pi$
$509$	6.22521	−	10.7824i	0.275927	−	0.477920i	0.970369	+	0.241629i	$0.0776817\pi$
$510$		0			0
$511$	−0.129951	−	23.4162i	−0.00574869	−	1.03587i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	8.25494	+	14.2980i	0.364110	+	0.630656i
$515$	3.35456	−	4.26363i	0.147820	−	0.187878i
$516$		0			0
$517$	2.47458	−	2.47458i	0.108832	−	0.108832i
$518$	4.96944	−	5.02490i	0.218345	−	0.220782i
$519$		0			0
$520$	−5.20403	+	3.89379i	−0.228212	+	0.170754i
$521$	−30.6011	+	17.6676i	−1.34066	+	0.774030i	−0.986904	−	0.161308i	$-0.948429\pi$
$521$	−30.6011	+	17.6676i	−1.34066	+	0.774030i	−0.353756	+	0.935338i	$0.615096\pi$
$522$		0			0
$523$	−15.8804	+	4.25513i	−0.694400	+	0.186064i	−0.588721	−	0.808336i	$-0.700368\pi$
$523$	−15.8804	+	4.25513i	−0.694400	+	0.186064i	−0.105679	+	0.994400i	$0.533702\pi$
$524$	9.59282			0.419064
$525$		0			0
$526$	9.86084			0.429953
$527$	21.6875	−	5.81115i	0.944722	−	0.253137i
$528$		0			0
$529$	−4.32938	+	2.49957i	−0.188234	+	0.108677i
$530$	−8.92631	+	6.67890i	−0.387734	+	0.290113i
$531$		0			0
$532$	1.32244	+	4.82807i	0.0573349	+	0.209323i
$533$	−1.68063	+	1.68063i	−0.0727964	+	0.0727964i
$534$		0			0
$535$	−9.18150	+	11.6696i	−0.396951	+	0.504522i
$536$	−6.84567	−	11.8571i	−0.295688	−	0.512147i
$537$		0			0
$538$	−6.33457	−	6.33457i	−0.273103	−	0.273103i
$539$	4.53322	+	2.55059i	0.195260	+	0.109862i
$540$		0			0
$541$	13.2572	−	22.9621i	0.569970	−	0.987218i	−0.426598	−	0.904441i	$-0.640288\pi$
$541$	13.2572	−	22.9621i	0.569970	−	0.987218i	0.996568	−	0.0827763i	$-0.0263787\pi$
$542$	22.0717	+	5.91408i	0.948059	+	0.254032i
$543$		0			0
$544$	−3.28007	+	5.68124i	−0.140632	+	0.243581i
$545$	−7.89157	+	18.4167i	−0.338038	+	0.788884i
$546$		0			0
$547$	−1.07403	−	1.07403i	−0.0459223	−	0.0459223i	0.683773	−	0.729695i	$-0.260338\pi$
$547$	−1.07403	−	1.07403i	−0.0459223	−	0.0459223i	−0.729695	+	0.683773i	$0.760338\pi$
$548$	2.40949	+	8.99233i	0.102928	+	0.384133i
$549$		0			0
$550$	−3.26172	+	1.77906i	−0.139080	+	0.0758594i
$551$	−15.8799	−	9.16828i	−0.676507	−	0.390582i
$552$		0			0
$553$	16.8479	+	4.41431i	0.716444	+	0.187715i
$554$			21.5332i			0.914858i
$555$		0			0
$556$	−19.2010	+	11.0857i	−0.814305	+	0.470139i
$557$	−4.02313	+	15.0145i	−0.170466	+	0.636186i	0.826814	+	0.562475i	$0.190151\pi$
$557$	−4.02313	+	15.0145i	−0.170466	+	0.636186i	−0.997280	+	0.0737108i	$0.976516\pi$
$558$		0			0
$559$	6.56014			0.277464
$560$	2.22795	+	5.48053i	0.0941482	+	0.231595i
$561$		0			0
$562$	−5.45637	+	1.46203i	−0.230163	+	0.0616721i
$563$	7.10355	−	26.5108i	0.299379	−	1.11730i	−0.638298	−	0.769789i	$-0.720361\pi$
$563$	7.10355	−	26.5108i	0.299379	−	1.11730i	0.937677	−	0.347508i	$-0.112972\pi$
$564$		0			0
$565$	−0.138742	+	0.963380i	−0.00583694	+	0.0405297i
$566$		−	2.92849i		−	0.123093i
$567$		0			0
$568$	−11.3259	+	11.3259i	−0.475225	+	0.475225i
$569$	5.85207	+	3.37869i	0.245332	+	0.141642i	0.617625	−	0.786473i	$-0.288095\pi$
$569$	5.85207	+	3.37869i	0.245332	+	0.141642i	−0.372293	+	0.928115i	$0.621428\pi$
$570$		0			0
$571$	−5.87721	−	10.1796i	−0.245953	−	0.426004i	0.716446	−	0.697643i	$-0.245768\pi$
$571$	−5.87721	−	10.1796i	−0.245953	−	0.426004i	−0.962399	+	0.271639i	$0.912434\pi$
$572$	0.559013	+	2.08627i	0.0233735	+	0.0872312i
$573$		0			0
$574$	1.09209	+	1.86755i	0.0455831	+	0.0779501i
$575$	26.4493	+	0.641957i	1.10301	+	0.0267715i
$576$		0			0
$577$	2.17865	+	0.583767i	0.0906983	+	0.0243025i	0.303883	−	0.952709i	$-0.401717\pi$
$577$	2.17865	+	0.583767i	0.0906983	+	0.0243025i	−0.213184	+	0.977012i	$0.568384\pi$
$578$	−25.1483	−	6.73845i	−1.04603	−	0.280283i
$579$		0			0
$580$	−19.9189	−	8.53525i	−0.827085	−	0.354407i
$581$	30.0209	+	17.1111i	1.24547	+	0.709889i
$582$		0			0
$583$	0.958858	+	3.57851i	0.0397118	+	0.148207i
$584$	−4.42532	−	7.66488i	−0.183121	−	0.317175i
$585$		0			0
$586$	13.2119	+	7.62790i	0.545779	+	0.315106i
$587$	−12.8372	+	12.8372i	−0.529847	+	0.529847i	−0.920527	−	0.390680i	$-0.872240\pi$
$587$	−12.8372	+	12.8372i	−0.529847	+	0.529847i	0.390680	+	0.920527i	$0.372240\pi$
$588$		0			0
$589$		−	6.47569i		−	0.266826i
$590$	−5.64319	−	0.812712i	−0.232327	−	0.0334588i
$591$		0			0
$592$	0.691342	−	2.58012i	0.0284140	−	0.106042i
$593$	−35.1170	+	9.40957i	−1.44208	+	0.386405i	−0.893262	−	0.449535i	$-0.851590\pi$
$593$	−35.1170	+	9.40957i	−1.44208	+	0.386405i	−0.548820	+	0.835940i	$0.684923\pi$
$594$		0			0
$595$	−30.9452	+	23.4230i	−1.26863	+	0.960249i
$596$	−3.94236			−0.161485
$597$		0			0
$598$	3.98074	−	14.8563i	0.162785	−	0.607520i
$599$	−30.9792	+	17.8858i	−1.26578	+	0.730796i	−0.974186	−	0.225748i	$-0.927517\pi$
$599$	−30.9792	+	17.8858i	−1.26578	+	0.730796i	−0.291589	+	0.956544i	$0.594184\pi$
$600$		0			0
$601$			45.6631i			1.86264i	0.364204	+	0.931319i	$0.381341\pi$
$601$			45.6631i			1.86264i	−0.364204	+	0.931319i	$0.618659\pi$
$602$	1.51345	−	5.77629i	0.0616835	−	0.235424i
$603$		0			0
$604$	17.2732	+	9.97267i	0.702835	+	0.405782i
$605$	−2.76811	−	23.1975i	−0.112540	−	0.943113i
$606$		0			0
$607$	−0.303188	−	1.13151i	−0.0123060	−	0.0459267i	0.959500	−	0.281709i	$-0.0909014\pi$
$607$	−0.303188	−	1.13151i	−0.0123060	−	0.0459267i	−0.971806	+	0.235783i	$0.924235\pi$
$608$	1.33788	+	1.33788i	0.0542584	+	0.0542584i
$609$		0			0
$610$	−12.6093	+	5.04460i	−0.510536	+	0.204250i
$611$	6.84463	−	11.8553i	0.276904	−	0.479612i
$612$		0			0
$613$	13.4629	+	3.60737i	0.543760	+	0.145700i	0.520235	−	0.854023i	$-0.325844\pi$
$613$	13.4629	+	3.60737i	0.543760	+	0.145700i	0.0235253	+	0.999723i	$0.492511\pi$
$614$	4.87339	−	8.44095i	0.196674	−	0.340649i
$615$		0			0
$616$	1.96595	−	0.0109103i	0.0792105	−	0.000439588i
$617$	−22.7725	−	22.7725i	−0.916788	−	0.916788i	0.0800065	−	0.996794i	$-0.474506\pi$
$617$	−22.7725	−	22.7725i	−0.916788	−	0.916788i	−0.996794	+	0.0800065i	$0.974506\pi$
$618$		0			0
$619$	−11.3386	−	19.6391i	−0.455738	−	0.789361i	0.542992	−	0.839738i	$-0.317291\pi$
$619$	−11.3386	−	19.6391i	−0.455738	−	0.789361i	−0.998730	+	0.0503763i	$0.983958\pi$
$620$	−0.906797	−	7.59919i	−0.0364178	−	0.305191i
$621$		0			0
$622$	−0.0891090	+	0.0891090i	−0.00357294	+	0.00357294i
$623$	4.04497	−	15.4382i	0.162058	−	0.618520i
$624$		0			0
$625$	−21.0187	−	13.5356i	−0.840749	−	0.541425i
$626$	10.1273	−	5.84698i	0.404767	−	0.233692i
$627$		0			0
$628$	−7.20903	+	1.93165i	−0.287672	+	0.0770814i
$629$	17.5231			0.698690
$630$		0			0
$631$	32.4210			1.29066			0.645330	−	0.763904i	$-0.276720\pi$
$631$	32.4210			1.29066			0.645330	+	0.763904i	$0.276720\pi$
$632$	6.35854	−	1.70376i	0.252929	−	0.0677721i
$633$		0			0
$634$	9.47968	−	5.47310i	0.376486	−	0.217364i
$635$	−35.0004	−	5.04063i	−1.38895	−	0.200031i
$636$		0			0
$637$	19.7106	+	5.04765i	0.780963	+	0.199995i
$638$	−5.09214	+	5.09214i	−0.201600	+	0.201600i
$639$		0			0
$640$	1.75735	+	1.38266i	0.0694652	+	0.0546543i
$641$	−0.428070	−	0.741439i	−0.0169077	−	0.0292851i	0.857448	−	0.514571i	$-0.172049\pi$
$641$	−0.428070	−	0.741439i	−0.0169077	−	0.0292851i	−0.874355	+	0.485286i	$0.838715\pi$
$642$		0			0
$643$	−16.4254	−	16.4254i	−0.647754	−	0.647754i	0.304696	−	0.952450i	$-0.401445\pi$
$643$	−16.4254	−	16.4254i	−0.647754	−	0.647754i	−0.952450	+	0.304696i	$0.901445\pi$
$644$	−12.1628	−	6.93250i	−0.479283	−	0.273179i
$645$		0			0
$646$	−6.20607	+	10.7492i	−0.244174	+	0.422922i
$647$	45.8316	+	12.2805i	1.80183	+	0.482798i	0.994261	−	0.106982i	$-0.0341186\pi$
$647$	45.8316	+	12.2805i	1.80183	+	0.482798i	0.807564	+	0.589779i	$0.200785\pi$
$648$		0			0
$649$	−0.947323	+	1.64081i	−0.0371857	+	0.0644075i
$650$	−10.5229	+	10.0242i	−0.412744	+	0.393183i
$651$		0			0
$652$	8.60305	+	8.60305i	0.336921	+	0.336921i
$653$	−6.80004	−	25.3781i	−0.266106	−	0.993121i	−0.961570	−	0.274560i	$-0.911468\pi$
$653$	−6.80004	−	25.3781i	−0.266106	−	0.993121i	0.695464	−	0.718561i	$-0.255199\pi$
$654$		0			0
$655$	21.2991	−	2.54158i	0.832225	−	0.0993077i
$656$	0.708148	+	0.408849i	0.0276485	+	0.0159629i
$657$		0			0
$658$	−8.85964	−	8.76184i	−0.345385	−	0.341572i
$659$		−	26.2355i		−	1.02199i	−0.859583	−	0.510996i	$-0.829277\pi$
$659$		−	26.2355i		−	1.02199i	0.859583	−	0.510996i	$-0.170723\pi$
$660$		0			0
$661$	−12.6197	+	7.28597i	−0.490848	+	0.283391i	−0.724926	−	0.688827i	$-0.758126\pi$
$661$	−12.6197	+	7.28597i	−0.490848	+	0.283391i	0.234078	+	0.972218i	$0.424793\pi$
$662$	−1.41325	+	5.27432i	−0.0549275	+	0.204992i
$663$		0			0
$664$	13.0605			0.506847
$665$	4.21541	+	10.3695i	0.163466	+	0.402110i
$666$		0			0
$667$	49.5336	−	13.2725i	1.91795	−	0.513913i
$668$	−0.532802	+	1.98844i	−0.0206147	+	0.0769352i
$669$		0			0
$670$	−18.3410	−	24.5127i	−0.708576	−	0.947007i
$671$			4.51312i			0.174227i
$672$		0			0
$673$	−16.4201	+	16.4201i	−0.632950	+	0.632950i	−0.948807	−	0.315857i	$-0.897708\pi$
$673$	−16.4201	+	16.4201i	−0.632950	+	0.632950i	0.315857	+	0.948807i	$0.397708\pi$
$674$	−25.0856	−	14.4832i	−0.966263	−	0.557872i
$675$		0			0
$676$	−2.27565	−	3.94154i	−0.0875249	−	0.151598i
$677$	5.89172	+	21.9882i	0.226437	+	0.845075i	0.981824	+	0.189796i	$0.0607825\pi$
$677$	5.89172	+	21.9882i	0.226437	+	0.845075i	−0.755386	+	0.655280i	$0.772551\pi$
$678$		0			0
$679$	−5.86774	+	10.2947i	−0.225183	+	0.395076i
$680$	−5.77756	+	13.4832i	−0.221559	+	0.517057i
$681$		0			0
$682$	−2.45656	−	0.658233i	−0.0940665	−	0.0252050i
$683$	29.5964	+	7.93034i	1.13248	+	0.303446i	0.775922	−	0.630829i	$-0.217285\pi$
$683$	29.5964	+	7.93034i	1.13248	+	0.303446i	0.356554	+	0.934275i	$0.383952\pi$
$684$		0			0
$685$	7.73231	+	19.3274i	0.295436	+	0.738463i
$686$	8.99183	−	16.1910i	0.343310	−	0.618173i
$687$		0			0
$688$	−0.584136	−	2.18003i	−0.0222700	−	0.0831127i
$689$	7.24590	+	12.5503i	0.276047	+	0.478127i
$690$		0			0
$691$	27.7284	+	16.0090i	1.05484	+	0.609012i	0.924000	−	0.382392i	$-0.124900\pi$
$691$	27.7284	+	16.0090i	1.05484	+	0.609012i	0.130839	+	0.991404i	$0.458233\pi$
$692$	−6.65251	+	6.65251i	−0.252891	+	0.252891i
$693$		0			0
$694$			21.5379i			0.817567i
$695$	−39.6952	+	29.7010i	−1.50573	+	1.12662i
$696$		0			0
$697$	−1.38836	+	5.18143i	−0.0525879	+	0.196261i
$698$	−12.1459	+	3.25450i	−0.459731	+	0.123184i
$699$		0			0
$700$	6.39880	+	11.5782i	0.241852	+	0.437616i
$701$	18.5294			0.699844			0.349922	−	0.936779i	$-0.386208\pi$
$701$	18.5294			0.699844			0.349922	+	0.936779i	$0.386208\pi$
$702$		0			0
$703$	1.30806	−	4.88174i	0.0493343	−	0.184118i
$704$	0.643519	−	0.371536i	0.0242535	−	0.0140028i
$705$		0			0
$706$		−	0.689506i		−	0.0259499i
$707$	20.8025	−	21.0347i	0.782360	−	0.791092i
$708$		0			0
$709$	−23.1074	−	13.3411i	−0.867818	−	0.501035i	−0.00119522	−	0.999999i	$-0.500380\pi$
$709$	−23.1074	−	13.3411i	−0.867818	−	0.501035i	−0.866622	+	0.498965i	$0.833714\pi$
$710$	−22.1464	+	28.1479i	−0.831138	+	1.05637i
$711$		0			0
$712$	−1.56121	−	5.82653i	−0.0585089	−	0.218358i
$713$	12.8059	+	12.8059i	0.479585	+	0.479585i
$714$		0			0
$715$	1.79393	+	4.48406i	0.0670893	+	0.167694i
$716$	−2.24874	+	3.89494i	−0.0840395	+	0.145561i
$717$		0			0
$718$	−21.3458	−	5.71959i	−0.796618	−	0.213453i
$719$	15.9890	−	27.6937i	0.596288	−	1.03280i	−0.397076	−	0.917786i	$-0.629975\pi$
$719$	15.9890	−	27.6937i	0.596288	−	1.03280i	0.993364	−	0.115015i	$-0.0366917\pi$
$720$		0			0
$721$	−5.54117	+	3.24033i	−0.206364	+	0.120676i
$722$	−10.9037	−	10.9037i	−0.405793	−	0.405793i
$723$		0			0
$724$	−8.94250	−	15.4889i	−0.332346	−	0.575639i
$725$	−46.4875	−	13.6735i	−1.72650	−	0.507822i
$726$		0			0
$727$	21.4539	−	21.4539i	0.795683	−	0.795683i	−0.186729	−	0.982412i	$-0.559789\pi$
$727$	21.4539	−	21.4539i	0.795683	−	0.795683i	0.982412	+	0.186729i	$0.0597885\pi$
$728$	7.41711	−	2.03159i	0.274897	−	0.0752958i
$729$		0			0
$730$	−11.8564	−	15.8460i	−0.438824	−	0.586486i
$731$	12.8222	−	7.40288i	0.474245	−	0.273805i
$732$		0			0
$733$	−12.5691	+	3.36789i	−0.464252	+	0.124396i	−0.483360	−	0.875422i	$-0.660584\pi$
$733$	−12.5691	+	3.36789i	−0.464252	+	0.124396i	0.0191085	+	0.999817i	$0.493917\pi$
$734$	−13.4109			−0.495006
$735$		0			0
$736$	−5.29142			−0.195044
$737$	−9.82700	+	2.63314i	−0.361982	+	0.0969928i
$738$		0			0
$739$	−3.12136	+	1.80212i	−0.114821	+	0.0662920i	−0.556311	−	0.830974i	$-0.687784\pi$
$739$	−3.12136	+	1.80212i	−0.114821	+	0.0662920i	0.441490	+	0.897266i	$0.354450\pi$
$740$	0.851405	−	5.91186i	0.0312983	−	0.217324i
$741$		0			0
$742$	12.7223	−	3.48473i	0.467052	−	0.127928i
$743$	−31.1070	+	31.1070i	−1.14121	+	1.14121i	−0.152977	+	0.988230i	$0.548886\pi$
$743$	−31.1070	+	31.1070i	−1.14121	+	1.14121i	−0.988230	+	0.152977i	$0.951114\pi$
$744$		0			0
$745$	−8.75328	+	1.04451i	−0.320695	+	0.0382680i
$746$	7.48320	+	12.9613i	0.273979	+	0.474546i
$747$		0			0
$748$	3.44690	+	3.44690i	0.126031	+	0.126031i
$749$	15.1663	−	8.86884i	0.554164	−	0.324060i
$750$		0			0
$751$	25.5141	−	44.1917i	0.931023	−	1.61258i	0.149447	−	0.988770i	$-0.452251\pi$
$751$	25.5141	−	44.1917i	0.931023	−	1.61258i	0.781576	−	0.623810i	$-0.214416\pi$
$752$	−4.54913	−	1.21894i	−0.165890	−	0.0444501i
$753$		0			0
$754$	−14.0848	+	24.3955i	−0.512936	+	0.888432i
$755$	40.9941	+	17.5660i	1.49193	+	0.639293i
$756$		0			0
$757$	26.8141	+	26.8141i	0.974576	+	0.974576i	0.999685	−	0.0251083i	$-0.00799305\pi$
$757$	26.8141	+	26.8141i	0.974576	+	0.974576i	−0.0251083	+	0.999685i	$0.507993\pi$
$758$	−0.444610	−	1.65931i	−0.0161490	−	0.0602687i
$759$		0			0
$760$	3.32499	+	2.61606i	0.120610	+	0.0948944i
$761$	25.8753	+	14.9391i	0.937980	+	0.541543i	0.889326	−	0.457273i	$-0.151174\pi$
$761$	25.8753	+	14.9391i	0.937980	+	0.541543i	0.0486532	+	0.998816i	$0.484507\pi$
$762$		0			0
$763$	16.6702	−	16.8563i	0.603503	−	0.610239i
$764$			2.77548i			0.100413i
$765$		0			0
$766$	−9.05698	+	5.22905i	−0.327242	+	0.188933i
$767$	−1.91818	+	7.15874i	−0.0692614	+	0.258487i
$768$		0			0
$769$	44.7341			1.61315			0.806576	−	0.591130i	$-0.201318\pi$
$769$	44.7341			1.61315			0.806576	+	0.591130i	$0.201318\pi$
$770$	4.36215	−	0.545096i	0.157201	−	0.0196439i
$771$		0			0
$772$	4.96491	−	1.33034i	0.178691	−	0.0478801i
$773$	6.25202	−	23.3328i	0.224869	−	0.839224i	−0.757587	−	0.652734i	$-0.773622\pi$
$773$	6.25202	−	23.3328i	0.224869	−	0.839224i	0.982457	−	0.186490i	$-0.0597113\pi$
$774$		0			0
$775$	−4.02675	−	16.6324i	−0.144645	−	0.597452i
$776$			4.47871i			0.160776i
$777$		0			0
$778$	−15.3949	+	15.3949i	−0.551934	+	0.551934i
$779$	1.33985	+	0.773565i	0.0480052	+	0.0277158i
$780$		0			0
$781$	5.95099	+	10.3074i	0.212943	+	0.368828i
$782$	−8.98424	−	33.5296i	−0.321276	−	1.19902i
$783$		0			0
$784$	−0.0776922	−	6.99957i	−0.00277472	−	0.249985i
$785$	−15.4945	+	6.19889i	−0.553024	+	0.221248i
$786$		0			0
$787$	12.2669	+	3.28689i	0.437266	+	0.117165i	0.470735	−	0.882275i	$-0.343989\pi$
$787$	12.2669	+	3.28689i	0.437266	+	0.117165i	−0.0334688	+	0.999440i	$0.510655\pi$
$788$	−1.83107	−	0.490633i	−0.0652290	−	0.0174781i
$789$		0			0
$790$	13.6666	−	5.46757i	0.486234	−	0.194527i
$791$	0.570279	−	1.00054i	0.0202768	−	0.0355749i
$792$		0			0
$793$	4.56917	+	17.0524i	0.162256	+	0.605547i
$794$	15.8494	+	27.4520i	0.562475	+	0.974236i
$795$		0			0
$796$	−12.5599	−	7.25148i	−0.445175	−	0.257022i
$797$	8.99183	−	8.99183i	0.318507	−	0.318507i	−0.529687	−	0.848193i	$-0.677690\pi$
$797$	8.99183	−	8.99183i	0.318507	−	0.318507i	0.848193	+	0.529687i	$0.177690\pi$
$798$		0			0
$799$		−	30.8957i		−	1.09301i
$800$	4.26819	+	2.60433i	0.150903	+	0.0920770i
$801$		0			0
$802$	−3.61585	+	13.4945i	−0.127680	+	0.476508i
$803$	−6.35256	+	1.70216i	−0.224177	+	0.0600681i
$804$		0			0
$805$	−28.8421	−	12.1699i	−1.01655	−	0.428931i
$806$	−9.94828			−0.350413
$807$		0			0
$808$	2.89402	−	10.8006i	0.101811	−	0.379965i
$809$	−23.7782	+	13.7284i	−0.835997	+	0.482663i	−0.855902	−	0.517139i	$-0.826997\pi$
$809$	−23.7782	+	13.7284i	−0.835997	+	0.482663i	0.0199044	+	0.999802i	$0.493664\pi$
$810$		0			0
$811$			12.7335i			0.447132i	0.974689	+	0.223566i	$0.0717699\pi$
$811$			12.7335i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$812$	18.2312	+	18.0300i	0.639789	+	0.632727i
$813$		0			0
$814$	−1.71893	−	0.992425i	−0.0602485	−	0.0347845i
$815$	21.3808	+	16.8221i	0.748938	+	0.589254i
$816$		0			0
$817$	−1.10522	−	4.12473i	−0.0386666	−	0.144306i
$818$	−13.2506	−	13.2506i	−0.463297	−	0.463297i
$819$		0			0
$820$	1.68063	+	0.720154i	0.0586903	+	0.0251489i
$821$	15.1707	−	26.2764i	0.529461	−	0.917054i	−0.469948	−	0.882694i	$-0.655727\pi$
$821$	15.1707	−	26.2764i	0.529461	−	0.917054i	0.999410	−	0.0343601i	$-0.0109393\pi$
$822$		0			0
$823$	−9.82702	−	2.63314i	−0.342549	−	0.0917856i	0.0834435	−	0.996513i	$-0.473408\pi$
$823$	−9.82702	−	2.63314i	−0.342549	−	0.0917856i	−0.425992	+	0.904727i	$0.640075\pi$
$824$	−1.21309	+	2.10113i	−0.0422599	+	0.0731963i
$825$		0			0
$826$	5.86084	+	3.34053i	0.203925	+	0.116232i
$827$	15.9794	+	15.9794i	0.555660	+	0.555660i	0.928069	−	0.372409i	$-0.121468\pi$
$827$	15.9794	+	15.9794i	0.555660	+	0.555660i	−0.372409	+	0.928069i	$0.621468\pi$
$828$		0			0
$829$	3.17447	+	5.49835i	0.110254	+	0.190966i	0.915873	−	0.401469i	$-0.131500\pi$
$829$	3.17447	+	5.49835i	0.110254	+	0.190966i	−0.805619	+	0.592435i	$0.798167\pi$
$830$	28.9985	−	3.46033i	1.00655	−	0.120110i
$831$		0			0
$832$	2.05532	−	2.05532i	0.0712555	−	0.0712555i
$833$	44.2216	−	12.3768i	1.53219	−	0.428830i
$834$		0			0
$835$	−0.656159	+	4.55614i	−0.0227073	+	0.157672i
$836$	1.21757	−	0.702966i	0.0421106	−	0.0243126i
$837$		0			0
$838$	30.4985	−	8.17206i	1.05355	−	0.282299i
$839$	39.7411			1.37202			0.686008	−	0.727594i	$-0.259362\pi$
$839$	39.7411			1.37202			0.686008	+	0.727594i	$0.259362\pi$
$840$		0			0
$841$	−64.9222			−2.23870
$842$	13.0949	−	3.50878i	0.451282	−	0.120921i
$843$		0			0
$844$	8.68832	−	5.01621i	0.299064	−	0.172665i
$845$	−6.09695	−	8.14853i	−0.209741	−	0.280318i
$846$		0			0
$847$	−7.00609	+	26.7398i	−0.240732	+	0.918790i
$848$	3.52543	−	3.52543i	0.121064	−	0.121064i
$849$		0			0
$850$	−9.25570	+	31.4677i	−0.317468	+	1.07933i
$851$	7.06707	+	12.2405i	0.242256	+	0.419600i
$852$		0			0
$853$	−17.1451	−	17.1451i	−0.587036	−	0.587036i	0.349791	−	0.936828i	$-0.386252\pi$
$853$	−17.1451	−	17.1451i	−0.587036	−	0.587036i	−0.936828	+	0.349791i	$0.886252\pi$
$854$	16.0690	−	0.0891766i	0.549869	−	0.00305156i
$855$		0			0
$856$	3.32024	−	5.75083i	0.113484	−	0.196559i
$857$	−16.2677	−	4.35890i	−0.555692	−	0.148897i	−0.0299658	−	0.999551i	$-0.509540\pi$
$857$	−16.2677	−	4.35890i	−0.555692	−	0.148897i	−0.525727	+	0.850654i	$0.676206\pi$
$858$		0			0
$859$	15.4345	−	26.7333i	0.526619	−	0.912130i	−0.472900	−	0.881116i	$-0.656793\pi$
$859$	15.4345	−	26.7333i	0.526619	−	0.912130i	0.999519	−	0.0310142i	$-0.00987370\pi$
$860$	−1.87456	−	4.68558i	−0.0639218	−	0.159777i
$861$		0			0
$862$	−9.38356	−	9.38356i	−0.319605	−	0.319605i
$863$	0.334691	+	1.24908i	0.0113930	+	0.0425193i	0.971388	−	0.237497i	$-0.0763269\pi$
$863$	0.334691	+	1.24908i	0.0113930	+	0.0425193i	−0.959995	+	0.280016i	$0.909660\pi$
$864$		0			0
$865$	−13.0081	+	16.5332i	−0.442289	+	0.562147i
$866$	14.7624	+	8.52308i	0.501647	+	0.289626i
$867$		0			0
$868$	−2.29510	+	8.75960i	−0.0779008	+	0.297320i
$869$		−	4.89152i		−	0.165934i
$870$		0			0
$871$	−34.4645	+	19.8981i	−1.16778	+	0.674221i
$872$	2.31914	−	8.65516i	0.0785361	−	0.293101i
$873$		0			0
$874$	−10.0117			−0.338649
$875$	17.2750	+	24.0120i	0.584001	+	0.811753i
$876$		0			0
$877$	−9.37406	+	2.51177i	−0.316540	+	0.0848165i	−0.413591	−	0.910463i	$-0.635726\pi$
$877$	−9.37406	+	2.51177i	−0.316540	+	0.0848165i	0.0970513	+	0.995279i	$0.469059\pi$
$878$	9.07099	−	33.8534i	0.306131	−	1.14250i
$879$		0			0
$880$	1.33038	−	0.995425i	0.0448471	−	0.0335558i
$881$			18.3500i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$881$			18.3500i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$882$		0			0
$883$	23.7527	−	23.7527i	0.799342	−	0.799342i	−0.183650	−	0.982992i	$-0.558791\pi$
$883$	23.7527	−	23.7527i	0.799342	−	0.799342i	0.982992	+	0.183650i	$0.0587913\pi$
$884$	16.5135	+	9.53406i	0.555408	+	0.320665i
$885$		0			0
$886$	−0.0315340	−	0.0546184i	−0.00105940	−	0.00183494i
$887$	−10.0547	−	37.5247i	−0.337604	−	1.25996i	−0.901018	−	0.433781i	$-0.857179\pi$
$887$	−10.0547	−	37.5247i	−0.337604	−	1.25996i	0.563414	−	0.826175i	$-0.309488\pi$
$888$		0			0
$889$	36.3503	+	20.7187i	1.21915	+	0.694884i
$890$	−5.01010	−	12.5231i	−0.167939	−	0.419775i
$891$		0			0
$892$	−4.28599	−	1.14843i	−0.143506	−	0.0384522i
$893$	−8.60721	−	2.30629i	−0.288029	−	0.0771772i
$894$		0			0
$895$	−3.96097	+	9.24379i	−0.132401	+	0.308986i
$896$	−1.33557	−	2.28391i	−0.0446183	−	0.0763001i
$897$		0			0
$898$	−6.34642	−	23.6851i	−0.211783	−	0.790384i
$899$	−16.5847	−	28.7255i	−0.553130	−	0.958049i
$900$		0			0
$901$	28.3251	+	16.3535i	0.943644	+	0.544813i
$902$	0.429644	−	0.429644i	0.0143056	−	0.0143056i
$903$		0			0
$904$		−	0.435281i		−	0.0144772i
$905$	−23.9589	−	32.0209i	−0.796421	−	1.06441i
$906$		0			0
$907$	8.97748	−	33.5044i	0.298092	−	1.11250i	−0.640638	−	0.767843i	$-0.721330\pi$
$907$	8.97748	−	33.5044i	0.298092	−	1.11250i	0.938730	−	0.344653i	$-0.112003\pi$
$908$	−0.648012	+	0.173634i	−0.0215050	+	0.00576226i
$909$		0			0
$910$	15.9301	−	6.47591i	0.528077	−	0.214674i
$911$	−48.1523			−1.59536			−0.797678	−	0.603083i	$-0.793939\pi$
$911$	−48.1523			−1.59536			−0.797678	+	0.603083i	$0.793939\pi$
$912$		0			0
$913$	2.51182	−	9.37422i	0.0831290	−	0.310242i
$914$	17.3839	−	10.0366i	0.575007	−	0.331980i
$915$		0			0
$916$			13.2033i			0.436250i
$917$	−24.5515	−	6.43273i	−0.810761	−	0.212428i
$918$		0			0
$919$	15.4242	+	8.90515i	0.508797	+	0.293754i	0.732339	−	0.680940i	$-0.238429\pi$
$919$	15.4242	+	8.90515i	0.508797	+	0.293754i	−0.223542	+	0.974694i	$0.571762\pi$
$920$	−11.7486	+	1.40194i	−0.387341	+	0.0462206i
$921$		0			0
$922$	−3.02662	−	11.2955i	−0.0996763	−	0.371997i
$923$	32.9206	+	32.9206i	1.08360	+	1.08360i
$924$		0			0
$925$	0.324064	−	13.3518i	0.0106552	−	0.439004i
$926$	−1.96028	+	3.39531i	−0.0644188	+	0.111577i
$927$		0			0
$928$	9.36112	+	2.50831i	0.307294	+	0.0823392i
$929$	−16.1326	+	27.9424i	−0.529292	+	0.916761i	0.470124	+	0.882600i	$0.344209\pi$
$929$	−16.1326	+	27.9424i	−0.529292	+	0.916761i	−0.999416	+	0.0341607i	$0.989124\pi$
$930$		0			0
$931$	−0.146998	−	13.2436i	−0.00481766	−	0.434040i
$932$	6.12279	+	6.12279i	0.200559	+	0.200559i
$933$		0			0
$934$	−10.4604	−	18.1180i	−0.342276	−	0.592839i
$935$	8.56645	+	6.73996i	0.280153	+	0.220420i
$936$		0			0
$937$	−28.9650	+	28.9650i	−0.946244	+	0.946244i	−0.998627	−	0.0523829i	$-0.983318\pi$
$937$	−28.9650	+	28.9650i	−0.946244	+	0.946244i	0.0523829	+	0.998627i	$0.483318\pi$
$938$	9.56947	+	34.9370i	0.312454	+	1.14073i
$939$		0			0
$940$	−10.4235	−	1.50115i	−0.339976	−	0.0489621i
$941$	−30.8629	+	17.8187i	−1.00610	+	0.580874i	−0.910048	−	0.414502i	$-0.863956\pi$
$941$	−30.8629	+	17.8187i	−1.00610	+	0.580874i	−0.0960550	+	0.995376i	$0.530622\pi$
$942$		0			0
$943$	−4.17936	+	1.11985i	−0.136099	+	0.0364675i
$944$	2.54975			0.0829873
$945$		0			0
$946$	−1.67706			−0.0545259
$947$	13.4783	−	3.61149i	0.437985	−	0.117358i	−0.0330871	−	0.999452i	$-0.510534\pi$
$947$	13.4783	−	3.61149i	0.437985	−	0.117358i	0.471072	+	0.882095i	$0.343867\pi$
$948$		0			0
$949$	−22.2792	+	12.8629i	−0.723214	+	0.417548i
$950$	8.07565	+	4.92753i	0.262009	+	0.159870i
$951$		0			0
$952$	12.2046	−	12.3408i	0.395553	−	0.399968i
$953$	−25.4475	+	25.4475i	−0.824326	+	0.824326i	−0.986725	−	0.162399i	$-0.948077\pi$
$953$	−25.4475	+	25.4475i	−0.824326	+	0.824326i	0.162399	+	0.986725i	$0.448077\pi$
$954$		0			0
$955$	0.735353	+	6.16245i	0.0237955	+	0.199412i
$956$	−2.00147	−	3.46665i	−0.0647322	−	0.112120i
$957$		0			0
$958$	17.1712	+	17.1712i	0.554775	+	0.554775i
$959$	−0.136689	−	24.6304i	−0.00441392	−	0.795356i
$960$		0			0
$961$	−9.64300	+	16.7022i	−0.311064	+	0.538779i
$962$	−7.49956	−	2.00950i	−0.241796	−	0.0647889i
$963$		0			0
$964$	−8.66256	+	15.0040i	−0.279002	+	0.483246i
$965$	10.6712	−	4.26922i	0.343518	−	0.137431i
$966$		0			0
$967$	−34.0735	−	34.0735i	−1.09573	−	1.09573i	−0.994904	−	0.100827i	$-0.967851\pi$
$967$	−34.0735	−	34.0735i	−1.09573	−	1.09573i	−0.100827	−	0.994904i	$-0.532149\pi$
$968$	2.70410	+	10.0918i	0.0869131	+	0.324364i
$969$		0			0
$970$	1.18662	+	9.94416i	0.0381000	+	0.319288i
$971$	−4.07547	−	2.35297i	−0.130788	−	0.0755105i	0.433179	−	0.901308i	$-0.357392\pi$
$971$	−4.07547	−	2.35297i	−0.130788	−	0.0755105i	−0.563966	+	0.825798i	$0.690725\pi$
$972$		0			0
$973$	56.5762	−	15.4966i	1.81375	−	0.496797i
$974$			2.55599i			0.0818993i
$975$		0			0
$976$	5.25989	−	3.03680i	0.168365	−	0.0972055i
$977$	7.12351	−	26.5853i	0.227901	−	0.850540i	−0.753320	−	0.657654i	$-0.771549\pi$
$977$	7.12351	−	26.5853i	0.227901	−	0.850540i	0.981221	−	0.192885i	$-0.0617846\pi$
$978$		0			0
$979$	−4.48226			−0.143254
$980$	−2.02701	−	15.5207i	−0.0647504	−	0.495790i
$981$		0			0
$982$	14.0704	−	3.77017i	0.449006	−	0.120311i
$983$	−11.6256	+	43.3874i	−0.370799	+	1.38384i	0.488587	+	0.872515i	$0.337513\pi$
$983$	−11.6256	+	43.3874i	−0.370799	+	1.38384i	−0.859386	+	0.511327i	$0.829154\pi$
$984$		0			0
$985$	−4.19554	−	0.604226i	−0.133681	−	0.0192522i
$986$			63.5766i			2.02469i
$987$		0			0
$988$	3.88878	−	3.88878i	0.123719	−	0.123719i
$989$	10.3424	+	5.97118i	0.328869	+	0.189872i
$990$		0			0
$991$	3.08498	+	5.34334i	0.0979975	+	0.169737i	0.910856	−	0.412725i	$-0.135423\pi$
$991$	3.08498	+	5.34334i	0.0979975	+	0.169737i	−0.812858	+	0.582462i	$0.802090\pi$
$992$	0.885827	+	3.30595i	0.0281250	+	0.104964i
$993$		0			0
$994$	36.5820	−	21.3922i	1.16031	−	0.678519i
$995$	−29.8083	−	12.7729i	−0.944985	−	0.404927i
$996$		0			0
$997$	18.1820	+	4.87184i	0.575829	+	0.154293i	0.534968	−	0.844872i	$-0.320324\pi$
$997$	18.1820	+	4.87184i	0.575829	+	0.154293i	0.0408602	+	0.999165i	$0.486990\pi$
$998$	−29.0623	−	7.78721i	−0.919950	−	0.246500i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.c.397.2		16
3.2	odd	2		70.2.k.a.47.4	yes	16
5.3	odd	4	inner	630.2.bv.c.523.3		16
7.3	odd	6	inner	630.2.bv.c.577.3		16
12.11	even	2		560.2.ci.c.257.2		16
15.2	even	4		350.2.o.c.243.3		16
15.8	even	4		70.2.k.a.33.2	yes	16
15.14	odd	2		350.2.o.c.257.1		16
21.2	odd	6		490.2.g.c.97.3		16
21.5	even	6		490.2.g.c.97.2		16
21.11	odd	6		490.2.l.c.227.1		16
21.17	even	6		70.2.k.a.17.2	yes	16
21.20	even	2		490.2.l.c.117.3		16
35.3	even	12	inner	630.2.bv.c.73.2		16
60.23	odd	4		560.2.ci.c.33.2		16
84.59	odd	6		560.2.ci.c.17.2		16
105.17	odd	12		350.2.o.c.143.1		16
105.23	even	12		490.2.g.c.293.2		16
105.38	odd	12		70.2.k.a.3.4	✓	16
105.53	even	12		490.2.l.c.423.3		16
105.59	even	6		350.2.o.c.157.3		16
105.68	odd	12		490.2.g.c.293.3		16
105.83	odd	4		490.2.l.c.313.1		16
420.143	even	12		560.2.ci.c.353.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	105.38	odd	12
70.2.k.a.17.2	yes	16	21.17	even	6
70.2.k.a.33.2	yes	16	15.8	even	4
70.2.k.a.47.4	yes	16	3.2	odd	2
350.2.o.c.143.1		16	105.17	odd	12
350.2.o.c.157.3		16	105.59	even	6
350.2.o.c.243.3		16	15.2	even	4
350.2.o.c.257.1		16	15.14	odd	2
490.2.g.c.97.2		16	21.5	even	6
490.2.g.c.97.3		16	21.2	odd	6
490.2.g.c.293.2		16	105.23	even	12
490.2.g.c.293.3		16	105.68	odd	12
490.2.l.c.117.3		16	21.20	even	2
490.2.l.c.227.1		16	21.11	odd	6
490.2.l.c.313.1		16	105.83	odd	4
490.2.l.c.423.3		16	105.53	even	12
560.2.ci.c.17.2		16	84.59	odd	6
560.2.ci.c.33.2		16	60.23	odd	4
560.2.ci.c.257.2		16	12.11	even	2
560.2.ci.c.353.2		16	420.143	even	12
630.2.bv.c.73.2		16	35.3	even	12	inner
630.2.bv.c.397.2		16	1.1	even	1	trivial
630.2.bv.c.523.3		16	5.3	odd	4	inner
630.2.bv.c.577.3		16	7.3	odd	6	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.79038 - 1.33961i) q^{5} +(-2.55176 + 0.698943i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(1.79038 - 1.33961i) q^{5} +(-2.55176 + 0.698943i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-1.38266 + 1.75735i) q^{10} +(0.371536 + 0.643519i) q^{11} +(2.05532 + 2.05532i) q^{13} +(2.28391 - 1.33557i) q^{14} +(0.500000 - 0.866025i) q^{16} +(6.33660 + 1.69789i) q^{17} +(0.946027 - 1.63857i) q^{19} +(0.880708 - 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(1.36952 + 5.11112i) q^{23} +(1.41090 - 4.79681i) q^{25} +(-2.51725 - 1.45333i) q^{26} +(-1.86042 + 1.88118i) q^{28} -9.69135i q^{29} +(2.96403 - 1.71129i) q^{31} +(-0.258819 + 0.965926i) q^{32} -6.56014 q^{34} +(-3.63230 + 4.66973i) q^{35} +(2.58012 - 0.691342i) q^{37} +(-0.489700 + 1.82758i) q^{38} +(-0.318742 + 2.21323i) q^{40} +0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +(0.643519 + 0.371536i) q^{44} +(-2.64571 - 4.58251i) q^{46} +(-1.21894 - 4.54913i) q^{47} +(6.02296 - 3.56707i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(2.80762 + 0.752300i) q^{52} +(4.81583 + 1.29040i) q^{53} +(1.52725 + 0.654429i) q^{55} +(1.31014 - 2.29859i) q^{56} +(2.50831 + 9.36112i) q^{58} +(1.27487 + 2.20815i) q^{59} +(5.25989 + 3.03680i) q^{61} +(-2.42012 + 2.42012i) q^{62} -1.00000i q^{64} +(6.43313 + 0.926476i) q^{65} +(-3.54358 + 13.2248i) q^{67} +(6.33660 - 1.69789i) q^{68} +(2.29992 - 5.45072i) q^{70} +16.0173 q^{71} +(-2.29071 + 8.54906i) q^{73} +(-2.31328 + 1.33557i) q^{74} -1.89205i q^{76} +(-1.39785 - 1.38242i) q^{77} +(-5.70091 - 3.29142i) q^{79} +(-0.264946 - 2.22032i) q^{80} +(-0.211636 - 0.789836i) q^{82} +(-9.23519 - 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-1.12846 + 1.95456i) q^{86} +(-0.717752 - 0.192321i) q^{88} +(-3.01603 + 5.22392i) q^{89} +(-6.68124 - 3.80814i) q^{91} +(3.74160 + 3.74160i) q^{92} +(2.35481 + 4.07864i) q^{94} +(-0.501292 - 4.20096i) q^{95} +(3.16693 - 3.16693i) q^{97} +(-4.89451 + 5.00438i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 + 8 * q^7	\( 16 q + 12 q^{5} + 8 q^{7} - 12 q^{10} + 12 q^{11} + 8 q^{16} + 36 q^{17} - 8 q^{22} + 4 q^{23} + 12 q^{25} - 12 q^{26} + 4 q^{28} + 24 q^{31} - 8 q^{35} + 4 q^{37} - 24 q^{38} - 8 q^{43} - 8 q^{46} - 12 q^{47} + 32 q^{50} + 28 q^{53} + 4 q^{56} - 32 q^{58} - 12 q^{61} + 8 q^{65} + 32 q^{67} + 36 q^{68} - 12 q^{70} - 16 q^{71} - 12 q^{73} - 16 q^{77} + 12 q^{80} - 48 q^{82} + 24 q^{85} - 12 q^{86} - 4 q^{88} - 16 q^{91} - 8 q^{92} - 20 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 + 8 * q^7 - 12 * q^10 + 12 * q^11 + 8 * q^16 + 36 * q^17 - 8 * q^22 + 4 * q^23 + 12 * q^25 - 12 * q^26 + 4 * q^28 + 24 * q^31 - 8 * q^35 + 4 * q^37 - 24 * q^38 - 8 * q^43 - 8 * q^46 - 12 * q^47 + 32 * q^50 + 28 * q^53 + 4 * q^56 - 32 * q^58 - 12 * q^61 + 8 * q^65 + 32 * q^67 + 36 * q^68 - 12 * q^70 - 16 * q^71 - 12 * q^73 - 16 * q^77 + 12 * q^80 - 48 * q^82 + 24 * q^85 - 12 * q^86 - 4 * q^88 - 16 * q^91 - 8 * q^92 - 20 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more