LMFDB - Embedded newform 630.2.bv.c.577.3

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			577.3
Root			$-1.45333 + 1.51725i$ of defining polynomial
Character	$\chi$	$=$	630.577
Dual form			630.2.bv.c.523.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.264946 - 2.22032i) q^{5} +(0.698943 - 2.55176i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.264946 - 2.22032i) q^{5} +(0.698943 - 2.55176i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.21323 - 0.318742i) q^{10} +(0.371536 - 0.643519i) q^{11} +(-2.05532 - 2.05532i) q^{13} +(-2.28391 - 1.33557i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.69789 + 6.33660i) q^{17} +(-0.946027 - 1.63857i) q^{19} +(-0.880708 + 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(-5.11112 - 1.36952i) q^{23} +(-4.85961 + 1.17653i) q^{25} +(-2.51725 + 1.45333i) q^{26} +(-1.88118 + 1.86042i) q^{28} -9.69135i q^{29} +(2.96403 + 1.71129i) q^{31} +(0.965926 - 0.258819i) q^{32} +6.56014 q^{34} +(-5.85090 - 0.875795i) q^{35} +(-0.691342 + 2.58012i) q^{37} +(-1.82758 + 0.489700i) q^{38} +(1.75735 + 1.38266i) q^{40} -0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +(-0.643519 + 0.371536i) q^{44} +(-2.64571 + 4.58251i) q^{46} +(-4.54913 - 1.21894i) q^{47} +(-6.02296 - 3.56707i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(0.752300 + 2.80762i) q^{52} +(-1.29040 - 4.81583i) q^{53} +(-1.52725 - 0.654429i) q^{55} +(1.31014 + 2.29859i) q^{56} +(-9.36112 - 2.50831i) q^{58} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(2.42012 - 2.42012i) q^{62} -1.00000i q^{64} +(-4.01892 + 5.10802i) q^{65} +(13.2248 - 3.54358i) q^{67} +(1.69789 - 6.33660i) q^{68} +(-2.36028 + 5.42486i) q^{70} +16.0173 q^{71} +(-8.54906 + 2.29071i) q^{73} +(2.31328 + 1.33557i) q^{74} +1.89205i q^{76} +(-1.38242 - 1.39785i) q^{77} +(5.70091 - 3.29142i) q^{79} +(1.79038 - 1.33961i) q^{80} +(-0.789836 - 0.211636i) q^{82} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-1.12846 - 1.95456i) q^{86} +(0.192321 + 0.717752i) q^{88} +(3.01603 + 5.22392i) q^{89} +(-6.68124 + 3.80814i) q^{91} +(3.74160 + 3.74160i) q^{92} +(-2.35481 + 4.07864i) q^{94} +(-3.38749 + 2.53461i) q^{95} +(-3.16693 + 3.16693i) q^{97} +(-5.00438 + 4.89451i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.264946	−	2.22032i	−0.118487	−	0.992956i
$5$	−0.264946	−	2.22032i	−0.118487	−	0.992956i
$6$		0			0
$7$	0.698943	−	2.55176i	0.264175	−	0.964475i
$7$	0.698943	−	2.55176i	0.264175	−	0.964475i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−2.21323	−	0.318742i	−0.699886	−	0.100795i
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	−0.804563	−	0.593867i	$-0.797601\pi$
$11$	0.371536	−	0.643519i	0.112022	−	0.194028i	0.916586	+	0.399839i	$0.130934\pi$
$12$		0			0
$13$	−2.05532	−	2.05532i	−0.570044	−	0.570044i	0.362097	−	0.932141i	$-0.382061\pi$
$13$	−2.05532	−	2.05532i	−0.570044	−	0.570044i	−0.932141	+	0.362097i	$0.882061\pi$
$14$	−2.28391	−	1.33557i	−0.610401	−	0.356946i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.69789	+	6.33660i	0.411798	+	1.53685i	0.791163	+	0.611605i	$0.209476\pi$
$17$	1.69789	+	6.33660i	0.411798	+	1.53685i	−0.379365	+	0.925247i	$0.623857\pi$
$18$		0			0
$19$	−0.946027	−	1.63857i	−0.217033	−	0.375913i	0.736866	−	0.676039i	$-0.236305\pi$
$19$	−0.946027	−	1.63857i	−0.217033	−	0.375913i	−0.953900	+	0.300126i	$0.902971\pi$
$20$	−0.880708	+	2.05532i	−0.196932	+	0.459584i
$21$		0			0
$22$	−0.525431	−	0.525431i	−0.112022	−	0.112022i
$23$	−5.11112	−	1.36952i	−1.06574	−	0.285565i	−0.317000	−	0.948426i	$-0.602675\pi$
$23$	−5.11112	−	1.36952i	−1.06574	−	0.285565i	−0.748743	+	0.662861i	$0.769342\pi$
$24$		0			0
$25$	−4.85961	+	1.17653i	−0.971921	+	0.235306i
$26$	−2.51725	+	1.45333i	−0.493673	+	0.285022i
$27$		0			0
$28$	−1.88118	+	1.86042i	−0.355510	+	0.351586i
$29$		−	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	0.741975	−	0.670427i	$-0.233889\pi$
$31$	2.96403	+	1.71129i	0.532356	+	0.307356i	−0.209619	+	0.977783i	$0.567222\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$		0			0
$34$	6.56014			1.12505
$35$	−5.85090	−	0.875795i	−0.988982	−	0.148036i
$36$		0			0
$37$	−0.691342	+	2.58012i	−0.113656	+	0.424170i	−0.999183	−	0.0404183i	$-0.987131\pi$
$37$	−0.691342	+	2.58012i	−0.113656	+	0.424170i	0.885527	+	0.464588i	$0.153798\pi$
$38$	−1.82758	+	0.489700i	−0.296473	+	0.0794398i
$39$		0			0
$40$	1.75735	+	1.38266i	0.277861	+	0.218617i
$41$		−	0.817699i		−	0.127703i	−0.997959	−	0.0638515i	$-0.979662\pi$
$41$		−	0.817699i		−	0.127703i	0.997959	−	0.0638515i	$-0.0203384\pi$
$42$		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
$47$	−4.54913	−	1.21894i	−0.663560	−	0.177800i	−0.0887076	−	0.996058i	$-0.528274\pi$
$47$	−4.54913	−	1.21894i	−0.663560	−	0.177800i	−0.574852	+	0.818257i	$0.694940\pi$
$48$		0			0
$49$	−6.02296	−	3.56707i	−0.860423	−	0.509581i
$50$	−0.121320	+	4.99853i	−0.0171573	+	0.706899i
$51$		0			0
$52$	0.752300	+	2.80762i	0.104325	+	0.389347i
$53$	−1.29040	−	4.81583i	−0.177250	−	0.661505i	−0.996158	−	0.0875798i	$-0.972087\pi$
$53$	−1.29040	−	4.81583i	−0.177250	−	0.661505i	0.818908	−	0.573925i	$-0.194580\pi$
$54$		0			0
$55$	−1.52725	−	0.654429i	−0.205935	−	0.0882432i
$56$	1.31014	+	2.29859i	0.175075	+	0.307163i
$57$		0			0
$58$	−9.36112	−	2.50831i	−1.22918	−	0.329357i
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	−0.937001	−	0.349327i	$-0.886410\pi$
$59$	−1.27487	+	2.20815i	−0.165975	+	0.287476i	0.771026	+	0.636803i	$0.219744\pi$
$60$		0			0
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	−0.123927	−	0.992291i	$-0.539549\pi$
$61$	5.25989	−	3.03680i	0.673460	−	0.388822i	0.797386	+	0.603469i	$0.206215\pi$
$62$	2.42012	−	2.42012i	0.307356	−	0.307356i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.01892	+	5.10802i	−0.498485	+	0.633572i
$66$		0			0
$67$	13.2248	−	3.54358i	1.61567	−	0.432917i	0.665944	−	0.746002i	$-0.268029\pi$
$67$	13.2248	−	3.54358i	1.61567	−	0.432917i	0.949725	+	0.313084i	$0.101362\pi$
$68$	1.69789	−	6.33660i	0.205899	−	0.768426i
$69$		0			0
$70$	−2.36028	+	5.42486i	−0.282107	+	0.648395i
$71$	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
$73$	−8.54906	+	2.29071i	−1.00059	+	0.268108i	−0.721693	−	0.692213i	$-0.756636\pi$
$73$	−8.54906	+	2.29071i	−1.00059	+	0.268108i	−0.278898	+	0.960321i	$0.589969\pi$
$74$	2.31328	+	1.33557i	0.268913	+	0.155257i
$75$		0			0
$76$			1.89205i			0.217033i
$77$	−1.38242	−	1.39785i	−0.157542	−	0.159300i
$78$		0			0
$79$	5.70091	−	3.29142i	0.641402	−	0.370314i	−0.143752	−	0.989614i	$-0.545917\pi$
$79$	5.70091	−	3.29142i	0.641402	−	0.370314i	0.785155	+	0.619300i	$0.212583\pi$
$80$	1.79038	−	1.33961i	0.200170	−	0.149773i
$81$		0			0
$82$	−0.789836	−	0.211636i	−0.0872228	−	0.0233713i
$83$	9.23519	+	9.23519i	1.01369	+	1.01369i	0.999905	+	0.0137887i	$0.00438921\pi$
$83$	9.23519	+	9.23519i	1.01369	+	1.01369i	0.0137887	+	0.999905i	$0.495611\pi$
$84$		0			0
$85$	13.6194	−	5.44871i	1.47723	−	0.590995i
$86$	−1.12846	−	1.95456i	−0.121685	−	0.210765i
$87$		0			0
$88$	0.192321	+	0.717752i	0.0205015	+	0.0765127i
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	0.980425	−	0.196892i	$-0.0630849\pi$
$89$	3.01603	+	5.22392i	0.319699	+	0.553735i	−0.660726	+	0.750627i	$0.729752\pi$
$90$		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
$95$	−3.38749	+	2.53461i	−0.347549	+	0.260046i
$96$		0			0
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	−0.849363	−	0.527810i	$-0.823013\pi$
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	0.527810	+	0.849363i	$0.323013\pi$
$98$	−5.00438	+	4.89451i	−0.505519	+	0.494420i
$99$		0			0
$100$	4.79681	+	1.41090i	0.479681	+	0.141090i
$101$	−9.68359	−	5.59083i	−0.963554	−	0.556308i	−0.0662887	−	0.997800i	$-0.521116\pi$
$101$	−9.68359	−	5.59083i	−0.963554	−	0.556308i	−0.897265	+	0.441493i	$0.854449\pi$
$102$		0			0
$103$	0.627940	−	2.34351i	0.0618728	−	0.230912i	−0.928064	−	0.372420i	$-0.878528\pi$
$103$	0.627940	−	2.34351i	0.0618728	−	0.230912i	0.989937	+	0.141507i	$0.0451949\pi$
$104$	2.90667			0.285022
$105$		0			0
$106$	−4.98571			−0.484255
$107$	1.71868	−	6.41422i	0.166151	−	0.620086i	−0.831739	−	0.555167i	$-0.812654\pi$
$107$	1.71868	−	6.41422i	0.166151	−	0.620086i	0.997891	−	0.0649189i	$-0.0206789\pi$
$108$		0			0
$109$	7.76000	+	4.48024i	0.743274	+	0.429129i	0.823258	−	0.567667i	$-0.192154\pi$
$109$	7.76000	+	4.48024i	0.743274	+	0.429129i	−0.0799848	+	0.996796i	$0.525487\pi$
$110$	−1.02741	+	1.30583i	−0.0979599	+	0.124506i
$111$		0			0
$112$	2.55936	−	0.670578i	0.241837	−	0.0633637i
$113$	−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
$115$	−1.68660	+	11.7112i	−0.157276	+	1.09207i
$116$	−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
$122$	−1.57196	−	5.86664i	−0.142319	−	0.531141i
$123$		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	$0.997548\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$		0			0
$130$	3.89379	+	5.20403i	0.341508	+	0.456423i
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	−0.0910579	−	0.995846i	$-0.529025\pi$
$131$	8.30763	−	4.79641i	0.725841	−	0.419064i	0.816899	+	0.576781i	$0.195692\pi$
$132$		0			0
$133$	−4.84245	+	1.26877i	−0.419893	+	0.110016i
$134$		−	13.6913i		−	1.18275i
$135$		0			0
$136$	−5.68124	−	3.28007i	−0.487163	−	0.281264i
$137$	8.99233	−	2.40949i	0.768267	−	0.205856i	0.146661	−	0.989187i	$-0.453147\pi$
$137$	8.99233	−	2.40949i	0.768267	−	0.205856i	0.621606	+	0.783330i	$0.286481\pi$
$138$		0			0
$139$	22.1714			1.88056			0.940278	−	0.340408i	$-0.110565\pi$
$139$	22.1714			1.88056			0.940278	+	0.340408i	$0.110565\pi$
$140$	4.62913	+	3.68391i	0.391233	+	0.311347i
$141$		0			0
$142$	4.14557	−	15.4715i	0.347889	−	1.29834i
$143$	−2.08627	+	0.559013i	−0.174462	+	0.0467470i
$144$		0			0
$145$	−21.5179	+	2.56768i	−1.78696	+	0.213235i
$146$			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	$-0.615038\pi$
$149$	3.41418	−	1.97118i	0.279701	−	0.161485i	0.633288	+	0.773916i	$0.281705\pi$
$150$		0			0
$151$	9.97267	−	17.2732i	0.811564	−	1.40567i	−0.100205	−	0.994967i	$-0.531950\pi$
$151$	9.97267	−	17.2732i	0.811564	−	1.40567i	0.911769	−	0.410703i	$-0.134717\pi$
$152$	1.82758	+	0.489700i	0.148237	+	0.0397199i
$153$		0			0
$154$	−1.70802	+	0.973528i	−0.137636	+	0.0784491i
$155$	3.01429	−	7.03449i	0.242113	−	0.565024i
$156$		0			0
$157$	−1.93165	−	7.20903i	−0.154163	−	0.575343i	−0.999176	−	0.0405972i	$-0.987074\pi$
$157$	−1.93165	−	7.20903i	−0.154163	−	0.575343i	0.845013	−	0.534746i	$-0.179593\pi$
$158$	−1.70376	−	6.35854i	−0.135544	−	0.505858i
$159$		0			0
$160$	−0.830578	−	2.07609i	−0.0656630	−	0.164129i
$161$	−7.06707	+	12.0851i	−0.556963	+	0.952442i
$162$		0			0
$163$	−11.7520	−	3.14893i	−0.920486	−	0.246644i	−0.232693	−	0.972550i	$-0.574754\pi$
$163$	−11.7520	−	3.14893i	−0.920486	−	0.246644i	−0.687793	+	0.725907i	$0.741420\pi$
$164$	−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	−0.648540	−	0.761181i	$-0.724620\pi$
$167$	1.45564	−	1.45564i	0.112641	−	0.112641i	0.761181	+	0.648540i	$0.224620\pi$
$168$		0			0
$169$		−	4.55129i		−	0.350099i
$170$	−1.73808	−	14.5656i	−0.133305	−	1.11713i
$171$		0			0
$172$	−2.18003	+	0.584136i	−0.166225	+	0.0445400i
$173$	−2.43499	+	9.08750i	−0.185129	+	0.690910i	0.809474	+	0.587155i	$0.199752\pi$
$173$	−2.43499	+	9.08750i	−0.185129	+	0.690910i	−0.994603	+	0.103754i	$0.966914\pi$
$174$		0			0
$175$	−0.394370	+	13.2229i	−0.0298116	+	0.999556i
$176$	0.743072			0.0560111
$177$		0			0
$178$	5.82653	−	1.56121i	0.436717	−	0.117018i
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	0.638447	−	0.769665i	$-0.279577\pi$
$179$	3.89494	+	2.24874i	0.291121	+	0.168079i	−0.347326	+	0.937744i	$0.612910\pi$
$180$		0			0
$181$			17.8850i			1.32938i	0.747118	+	0.664691i	$0.231437\pi$
$181$			17.8850i			1.32938i	−0.747118	+	0.664691i	$0.768563\pi$
$182$	1.94915	+	7.43921i	0.144480	+	0.551431i
$183$		0			0
$184$	4.58251	−	2.64571i	0.337827	−	0.195044i
$185$	5.91186	+	0.851405i	0.434649	+	0.0625965i
$186$		0			0
$187$	4.70855	+	1.26165i	0.344323	+	0.0922612i
$188$	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	0.811442	−	0.584433i	$-0.198683\pi$
$191$	−1.38774	−	2.40364i	−0.100413	−	0.173921i	−0.911855	+	0.410512i	$0.865350\pi$
$192$		0			0
$193$	−1.33034	−	4.96491i	−0.0957602	−	0.357382i	0.901373	−	0.433043i	$-0.142560\pi$
$193$	−1.33034	−	4.96491i	−0.0957602	−	0.357382i	−0.997134	+	0.0756607i	$0.975893\pi$
$194$	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	−0.485824	−	0.874057i	$-0.661480\pi$
$199$	7.25148	−	12.5599i	0.514043	−	0.890349i	0.999867	−	0.0162926i	$-0.00518634\pi$
$200$	2.60433	−	4.26819i	0.184154	−	0.301807i
$201$		0			0
$202$	−7.90662	+	7.90662i	−0.556308	+	0.556308i
$203$	−24.7300	−	6.77370i	−1.73571	−	0.475420i
$204$		0			0
$205$	−1.81555	+	0.216646i	−0.126803	+	0.0151312i
$206$	−2.10113	−	1.21309i	−0.146393	−	0.0845198i
$207$		0			0
$208$	0.752300	−	2.80762i	0.0521627	−	0.194674i
$209$	−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	$0.387767\pi$
$212$	−1.29040	+	4.81583i	−0.0886249	+	0.330752i
$213$		0			0
$214$	−5.75083	−	3.32024i	−0.393119	−	0.226967i
$215$	−3.96620	−	3.12055i	−0.270493	−	0.212820i
$216$		0			0
$217$	6.43848	−	6.36741i	0.437073	−	0.432248i
$218$	6.33602	−	6.33602i	0.429129	−	0.429129i
$219$		0			0
$220$	0.995425	+	1.33038i	0.0671115	+	0.0896941i
$221$	9.53406	−	16.5135i	0.641330	−	1.11082i
$222$		0			0
$223$	3.13756	+	3.13756i	0.210107	+	0.210107i	0.804313	−	0.594206i	$-0.202534\pi$
$223$	3.13756	+	3.13756i	0.210107	+	0.210107i	−0.594206	+	0.804313i	$0.702534\pi$
$224$	0.0146827	−	2.64571i	0.000981028	−	0.176774i
$225$		0			0
$226$	0.217641	+	0.376965i	0.0144772	+	0.0250753i
$227$	−0.173634	−	0.648012i	−0.0115245	−	0.0430101i	0.959924	−	0.280260i	$-0.0904207\pi$
$227$	−0.173634	−	0.648012i	−0.0115245	−	0.0430101i	−0.971449	+	0.237250i	$0.923754\pi$
$228$		0			0
$229$	6.60166	+	11.4344i	0.436250	+	0.755608i	0.997397	−	0.0721088i	$-0.0229729\pi$
$229$	6.60166	+	11.4344i	0.436250	+	0.755608i	−0.561146	+	0.827717i	$0.689640\pi$
$230$	10.8756	+	4.66020i	0.717115	+	0.307284i
$231$		0			0
$232$	6.85282	+	6.85282i	0.449910	+	0.449910i
$233$	−8.36389	−	2.24110i	−0.547937	−	0.146819i	−0.0257782	−	0.999668i	$-0.508206\pi$
$233$	−8.36389	−	2.24110i	−0.547937	−	0.146819i	−0.522158	+	0.852849i	$0.674873\pi$
$234$		0			0
$235$	−1.50115	+	10.4235i	−0.0979243	+	0.679952i
$236$	2.20815	−	1.27487i	0.143738	−	0.0829873i
$237$		0			0
$238$	4.58516	−	16.7399i	0.297212	−	1.08509i
$239$		−	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	−0.0683274	−	0.997663i	$-0.521766\pi$
$241$	−15.0040	−	8.66256i	−0.966493	−	0.558005i	−0.898165	+	0.439658i	$0.855100\pi$
$242$	10.0918	−	2.70410i	0.648728	−	0.173826i
$243$		0			0
$244$	−6.07359			−0.388822
$245$	−6.32426	+	14.3180i	−0.404042	+	0.914740i
$246$		0			0
$247$	−1.42339	+	5.31218i	−0.0905683	+	0.338006i
$248$	−3.30595	+	0.885827i	−0.209928	+	0.0562501i
$249$		0			0
$250$	11.1305	−	1.05497i	0.703952	−	0.0667222i
$251$			5.49938i			0.347118i	0.984824	+	0.173559i	$0.0555267\pi$
$251$			5.49938i			0.347118i	−0.984824	+	0.173559i	$0.944473\pi$
$252$		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
$257$	−15.9473	−	4.27307i	−0.994766	−	0.266547i	−0.275515	−	0.961297i	$-0.588848\pi$
$257$	−15.9473	−	4.27307i	−0.994766	−	0.266547i	−0.719251	+	0.694750i	$0.755515\pi$
$258$		0			0
$259$	6.10065	+	3.56750i	0.379076	+	0.221674i
$260$	6.03449	−	2.41421i	0.374243	−	0.149723i
$261$		0			0
$262$	−2.48280	−	9.26595i	−0.153388	−	0.572453i
$263$	2.55217	+	9.52484i	0.157374	+	0.587327i	0.998890	+	0.0470956i	$0.0149965\pi$
$263$	2.55217	+	9.52484i	0.157374	+	0.587327i	−0.841517	+	0.540231i	$0.818337\pi$
$264$		0			0
$265$	−10.3508	+	4.14102i	−0.635843	+	0.254381i
$266$	−0.0277804	+	5.00583i	−0.00170333	+	0.306927i
$267$		0			0
$268$	−13.2248	−	3.54358i	−0.807835	−	0.216459i
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	−0.969655	−	0.244478i	$-0.921383\pi$
$269$	−4.47922	+	7.75824i	−0.273103	+	0.473028i	0.696552	+	0.717506i	$0.254717\pi$
$270$		0			0
$271$	−19.7889	+	11.4251i	−1.20209	+	0.694027i	−0.961020	−	0.276480i	$-0.910832\pi$
$271$	−19.7889	+	11.4251i	−1.20209	+	0.694027i	−0.241071	+	0.970507i	$0.577499\pi$
$272$	−4.63872	+	4.63872i	−0.281264	+	0.281264i
$273$		0			0
$274$		−	9.30954i		−	0.562410i
$275$	−1.04840	+	3.56437i	−0.0632209	+	0.214940i
$276$		0			0
$277$	−20.7995	+	5.57320i	−1.24972	+	0.334861i	−0.822228	−	0.569158i	$-0.807269\pi$
$277$	−20.7995	+	5.57320i	−1.24972	+	0.334861i	−0.427491	+	0.904019i	$0.640603\pi$
$278$	5.73839	−	21.4160i	0.344166	−	1.28444i
$279$		0			0
$280$	4.75649	−	3.51793i	0.284255	−	0.210236i
$281$	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
$283$	−2.82870	+	0.757948i	−0.168149	+	0.0450553i	−0.341911	−	0.939732i	$-0.611074\pi$
$283$	−2.82870	+	0.757948i	−0.168149	+	0.0450553i	0.173762	+	0.984788i	$0.444408\pi$
$284$	−13.8714	−	8.00863i	−0.823113	−	0.475225i
$285$		0			0
$286$			2.15986i			0.127715i
$287$	−2.08657	−	0.571524i	−0.123166	−	0.0337360i
$288$		0			0
$289$	−22.5473	+	13.0177i	−1.32631	+	0.765747i
$290$	−3.08904	+	21.4492i	−0.181395	+	1.25954i
$291$		0			0
$292$	8.54906	+	2.29071i	0.500296	+	0.134054i
$293$	10.7875	+	10.7875i	0.630212	+	0.630212i	0.948121	−	0.317909i	$-0.102981\pi$
$293$	10.7875	+	10.7875i	0.630212	+	0.630212i	−0.317909	+	0.948121i	$0.602981\pi$
$294$		0			0
$295$	5.24056	+	2.24558i	0.305117	+	0.130743i
$296$	−1.33557	−	2.31328i	−0.0776285	−	0.134456i
$297$		0			0
$298$	−1.02036	−	3.80802i	−0.0591077	−	0.220593i
$299$	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
$305$	−8.13624	−	10.8740i	−0.465880	−	0.622645i
$306$		0			0
$307$	6.89201	−	6.89201i	0.393348	−	0.393348i	−0.482531	−	0.875879i	$-0.660282\pi$
$307$	6.89201	−	6.89201i	0.393348	−	0.393348i	0.875879	+	0.482531i	$0.160282\pi$
$308$	0.498288	+	1.90179i	0.0283926	+	0.108364i
$309$		0			0
$310$	−6.01464	−	4.73224i	−0.341609	−	0.268773i
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	0.503091	−	0.864233i	$-0.332196\pi$
$311$	0.109136	+	0.0630096i	0.00618852	+	0.00357294i	−0.496903	+	0.867806i	$0.665529\pi$
$312$		0			0
$313$	−3.02662	+	11.2955i	−0.171075	+	0.638459i	0.826112	+	0.563505i	$0.190548\pi$
$313$	−3.02662	+	11.2955i	−0.171075	+	0.638459i	−0.997187	+	0.0749536i	$0.976119\pi$
$314$	−7.46334			−0.421181
$315$		0			0
$316$	−6.58284			−0.370314
$317$	2.83308	−	10.5732i	0.159122	−	0.593851i	−0.839595	−	0.543212i	$-0.817208\pi$
$317$	2.83308	−	10.5732i	0.159122	−	0.593851i	0.998717	−	0.0506382i	$-0.0161255\pi$
$318$		0			0
$319$	−6.23657	−	3.60068i	−0.349181	−	0.201600i
$320$	−2.22032	+	0.264946i	−0.124119	+	0.0148109i
$321$		0			0
$322$	9.84425	+	9.95413i	0.548599	+	0.554722i
$323$	8.77670	−	8.77670i	0.488349	−	0.488349i
$324$		0			0
$325$	12.4062	+	7.56992i	0.688173	+	0.419904i
$326$	−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	0.931251	−	0.364378i	$-0.118718\pi$
$331$	2.73019	+	4.72883i	0.150065	+	0.259920i	−0.781186	+	0.624298i	$0.785385\pi$
$332$	−3.38031	−	12.6155i	−0.185519	−	0.692366i
$333$		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	$0.460625\pi$
$338$	−4.39621	−	1.17796i	−0.239122	−	0.0640727i
$339$		0			0
$340$	−14.5191	−	2.09099i	−0.787410	−	0.113400i
$341$	2.20249	−	1.27161i	0.119272	−	0.0688615i
$342$		0			0
$343$	−13.3120	+	12.8760i	−0.718781	+	0.695237i
$344$			2.25693i			0.121685i
$345$		0			0
$346$	8.14763	+	4.70404i	0.438019	+	0.252891i
$347$	−20.8040	+	5.57442i	−1.11682	+	0.299250i	−0.769595	−	0.638532i	$-0.779542\pi$
$347$	−20.8040	+	5.57442i	−1.11682	+	0.299250i	−0.347223	+	0.937783i	$0.612875\pi$
$348$		0			0
$349$	−12.5744			−0.673093			−0.336546	−	0.941667i	$-0.609259\pi$
$349$	−12.5744			−0.673093			−0.336546	+	0.941667i	$0.609259\pi$
$350$	12.6702	+	3.80326i	0.677253	+	0.203293i
$351$		0			0
$352$	0.192321	−	0.717752i	0.0102508	−	0.0382563i
$353$	−0.666012	+	0.178457i	−0.0354482	+	0.00949832i	−0.276500	−	0.961014i	$-0.589174\pi$
$353$	−0.666012	+	0.178457i	−0.0354482	+	0.00949832i	0.241051	+	0.970512i	$0.422508\pi$
$354$		0			0
$355$	−4.24371	−	35.5634i	−0.225233	−	1.88751i
$356$		−	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	$-0.864852\pi$
$359$	−19.1381	+	11.0494i	−1.01007	+	0.583165i	−0.0988582	+	0.995102i	$0.531519\pi$
$360$		0			0
$361$	7.71007	−	13.3542i	0.405793	−	0.702854i
$362$	17.2756	+	4.62898i	0.907985	+	0.243294i
$363$		0			0
$364$	7.69020	+	0.0426776i	0.403076	+	0.00223692i
$365$	7.35115	+	18.3747i	0.384777	+	0.961775i
$366$		0			0
$367$	3.47100	+	12.9539i	0.181185	+	0.676191i	0.995415	+	0.0956487i	$0.0304926\pi$
$367$	3.47100	+	12.9539i	0.181185	+	0.676191i	−0.814230	+	0.580542i	$0.802841\pi$
$368$	−1.36952	−	5.11112i	−0.0713912	−	0.266436i
$369$		0			0
$370$	2.35250	−	5.49006i	0.122300	−	0.285415i
$371$	−13.1908	−	0.0732036i	−0.684830	−	0.00380054i
$372$		0			0
$373$	14.4564	+	3.87359i	0.748526	+	0.200567i	0.612864	−	0.790188i	$-0.290017\pi$
$373$	14.4564	+	3.87359i	0.748526	+	0.200567i	0.135662	+	0.990755i	$0.456684\pi$
$374$	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	$0.985952\pi$
$380$	4.20096	−	0.501292i	0.215505	−	0.0257157i
$381$		0			0
$382$	−2.68091	+	0.718348i	−0.137167	+	0.0367539i
$383$	2.70676	−	10.1017i	0.138309	−	0.516175i	−0.861654	−	0.507497i	$-0.830571\pi$
$383$	2.70676	−	10.1017i	0.138309	−	0.516175i	0.999962	−	0.00867837i	$-0.00276245\pi$
$384$		0			0
$385$	−2.73741	+	3.43977i	−0.139511	+	0.175307i
$386$	−5.14005			−0.261622
$387$		0			0
$388$	4.32611	−	1.15918i	0.219625	−	0.0588483i
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.0610449	−	0.998135i	$-0.519443\pi$
$389$	−18.8548	−	10.8858i	−0.955978	−	0.551934i	−0.894933	+	0.446201i	$0.852777\pi$
$390$		0			0
$391$		−	34.7124i		−	1.75548i
$392$	6.78117	−	1.73658i	0.342501	−	0.0877104i
$393$		0			0
$394$	−1.64169	+	0.947829i	−0.0827071	+	0.0477510i
$395$	−8.81843	−	11.7858i	−0.443703	−	0.593006i
$396$		0			0
$397$	−30.6188	−	8.20427i	−1.53671	−	0.411761i	−0.611510	−	0.791237i	$-0.709438\pi$
$397$	−30.6188	−	8.20427i	−1.53671	−	0.411761i	−0.925202	+	0.379476i	$0.876104\pi$
$398$	−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	0.986042	−	0.166499i	$-0.0532463\pi$
$401$	6.98528	+	12.0989i	0.348828	+	0.604188i	−0.637213	+	0.770687i	$0.719913\pi$
$402$		0			0
$403$	−2.57480	−	9.60930i	−0.128260	−	0.478673i
$404$	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	$-0.986667\pi$
$409$	−9.36960	+	16.2286i	−0.463297	+	0.802454i	0.535826	+	0.844328i	$0.320000\pi$
$410$	−0.260635	+	1.80976i	−0.0128718	+	0.0893776i
$411$		0			0
$412$	−1.71557	+	1.71557i	−0.0845198	+	0.0845198i
$413$	4.74360	+	4.79654i	0.233417	+	0.236022i
$414$		0			0
$415$	18.0582	−	22.9519i	0.886443	−	1.12666i
$416$	−2.51725	−	1.45333i	−0.123418	−	0.0712555i
$417$		0			0
$418$	−0.363882	+	1.35803i	−0.0177981	+	0.0664232i
$419$	31.5744			1.54251			0.771255	−	0.636526i	$-0.219629\pi$
$419$	31.5744			1.54251			0.771255	+	0.636526i	$0.219629\pi$
$420$		0			0
$421$	−13.5569			−0.660722			−0.330361	−	0.943855i	$-0.607171\pi$
$421$	−13.5569			−0.660722			−0.330361	+	0.943855i	$0.607171\pi$
$422$	2.59658	−	9.69057i	0.126399	−	0.471729i
$423$		0			0
$424$	4.31775	+	2.49286i	0.209689	+	0.121064i
$425$	−15.7063	−	28.7958i	−0.761866	−	1.39680i
$426$		0			0
$427$	−4.07282	−	15.5445i	−0.197097	−	0.752252i
$428$	−4.69553	+	4.69553i	−0.226967	+	0.226967i
$429$		0			0
$430$	−4.04075	+	3.02340i	−0.194862	+	0.145801i
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	−0.660800	−	0.750562i	$-0.729783\pi$
$431$	6.63518	−	11.4925i	0.319605	−	0.553572i	0.980406	+	0.196989i	$0.0631164\pi$
$432$		0			0
$433$	12.0535	+	12.0535i	0.579252	+	0.579252i	0.934697	−	0.355445i	$-0.115671\pi$
$433$	12.0535	+	12.0535i	0.579252	+	0.579252i	−0.355445	+	0.934697i	$0.615671\pi$
$434$	−4.48405	−	7.86710i	−0.215241	−	0.377633i
$435$		0			0
$436$	−4.48024	−	7.76000i	−0.214565	−	0.371637i
$437$	2.59121	+	9.67052i	0.123954	+	0.462604i
$438$		0			0
$439$	17.5238	+	30.3521i	0.836366	+	1.44863i	0.892913	+	0.450228i	$0.148657\pi$
$439$	17.5238	+	30.3521i	0.836366	+	1.44863i	−0.0565475	+	0.998400i	$0.518009\pi$
$440$	1.54268	−	0.617179i	0.0735445	−	0.0294229i
$441$		0			0
$442$	−13.4832	−	13.4832i	−0.641330	−	0.641330i
$443$	−0.0609189	−	0.0163232i	−0.00289435	−	0.000775538i	0.257372	−	0.966313i	$-0.417144\pi$
$443$	−0.0609189	−	0.0163232i	−0.00289435	−	0.000775538i	−0.260266	+	0.965537i	$0.583810\pi$
$444$		0			0
$445$	10.7997	−	8.08060i	0.511954	−	0.383057i
$446$	3.84271	−	2.21859i	0.181958	−	0.105053i
$447$		0			0
$448$	−2.55176	−	0.698943i	−0.120559	−	0.0330219i
$449$			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
$452$	0.420450	−	0.112659i	0.0197763	−	0.00529904i
$453$		0			0
$454$	−0.670872			−0.0314856
$455$	10.2254	+	13.8255i	0.479376	+	0.648151i
$456$		0			0
$457$	5.19531	−	19.3892i	0.243027	−	0.906987i	−0.731339	−	0.682015i	$-0.761104\pi$
$457$	5.19531	−	19.3892i	0.243027	−	0.906987i	0.974365	−	0.224973i	$-0.0722293\pi$
$458$	12.7534	−	3.41727i	0.595929	−	0.159679i
$459$		0			0
$460$	7.31621	−	9.29886i	0.341120	−	0.433561i
$461$		−	11.6940i		−	0.544642i	−0.962207	−	0.272321i	$-0.912209\pi$
$461$		−	11.6940i		−	0.544642i	0.962207	−	0.272321i	$-0.0877912\pi$
$462$		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
$467$	20.2080	+	5.41472i	0.935116	+	0.250563i	0.694035	−	0.719942i	$-0.255831\pi$
$467$	20.2080	+	5.41472i	0.935116	+	0.250563i	0.241081	+	0.970505i	$0.422498\pi$
$468$		0			0
$469$	0.201026	−	36.2233i	0.00928250	−	1.67264i
$470$	9.67977	+	4.14779i	0.446495	+	0.191323i
$471$		0			0
$472$	−0.659924	−	2.46287i	−0.0303754	−	0.113363i
$473$	−0.434055	−	1.61992i	−0.0199579	−	0.0744838i
$474$		0			0
$475$	6.52514	+	6.84976i	0.299394	+	0.314289i
$476$	−14.9828	−	8.76153i	−0.686734	−	0.401584i
$477$		0			0
$478$	−3.86655	−	1.03604i	−0.176852	−	0.0473873i
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	−0.443145	−	0.896450i	$-0.646137\pi$
$479$	12.1419	−	21.0303i	0.554775	−	0.960899i	0.997921	−	0.0644496i	$-0.0205292\pi$
$480$		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
$485$	7.87065	+	6.19252i	0.357388	+	0.281188i
$486$		0			0
$487$	−2.46890	+	0.661539i	−0.111876	+	0.0299772i	−0.314323	−	0.949316i	$-0.601777\pi$
$487$	−2.46890	+	0.661539i	−0.111876	+	0.0299772i	0.202446	+	0.979293i	$0.435111\pi$
$488$	−1.57196	+	5.86664i	−0.0711594	+	0.265570i
$489$		0			0
$490$	12.1932	+	9.81452i	0.550834	+	0.443375i
$491$	−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
$493$	61.4102	−	16.4548i	2.76578	−	0.741088i
$494$	4.76277	+	2.74978i	0.214287	+	0.123719i
$495$		0			0
$496$			3.42257i			0.153678i
$497$	11.1951	−	40.8722i	0.502171	−	1.83337i
$498$		0			0
$499$	−26.0565	+	15.0437i	−1.16645	+	0.673450i	−0.952841	−	0.303469i	$-0.901855\pi$
$499$	−26.0565	+	15.0437i	−1.16645	+	0.673450i	−0.213608	+	0.976919i	$0.568522\pi$
$500$	1.86175	−	11.0242i	0.0832600	−	0.493019i
$501$		0			0
$502$	5.31199	+	1.42334i	0.237086	+	0.0635269i
$503$	24.6819	+	24.6819i	1.10051	+	1.10051i	0.994349	+	0.106161i	$0.0338558\pi$
$503$	24.6819	+	24.6819i	1.10051	+	1.10051i	0.106161	+	0.994349i	$0.466144\pi$
$504$		0			0
$505$	−9.84777	+	22.9819i	−0.438220	+	1.02268i
$506$	1.96595	+	3.40513i	0.0873973	+	0.151377i
$507$		0			0
$508$	4.09300	+	15.2753i	0.181598	+	0.677731i
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	0.694441	−	0.719549i	$-0.255652\pi$
$509$	−6.22521	−	10.7824i	−0.275927	−	0.477920i	−0.970369	+	0.241629i	$0.922318\pi$
$510$		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
$515$	−5.36969	−	0.773324i	−0.236617	−	0.0340767i
$516$		0			0
$517$	−2.47458	+	2.47458i	−0.108832	+	0.108832i
$518$	5.02490	−	4.96944i	0.220782	−	0.218345i
$519$		0			0
$520$	−0.770110	−	6.45372i	−0.0337715	−	0.283014i
$521$	−30.6011	−	17.6676i	−1.34066	−	0.774030i	−0.353756	−	0.935338i	$-0.615096\pi$
$521$	−30.6011	−	17.6676i	−1.34066	−	0.774030i	−0.986904	+	0.161308i	$0.948429\pi$
$522$		0			0
$523$	−4.25513	+	15.8804i	−0.186064	+	0.694400i	0.808336	+	0.588721i	$0.200368\pi$
$523$	−4.25513	+	15.8804i	−0.186064	+	0.694400i	−0.994400	+	0.105679i	$0.966298\pi$
$524$	−9.59282			−0.419064
$525$		0			0
$526$	9.86084			0.429953
$527$	−5.81115	+	21.6875i	−0.253137	+	0.944722i
$528$		0			0
$529$	4.32938	+	2.49957i	0.188234	+	0.108677i
$530$	1.32094	+	11.0699i	0.0573782	+	0.480844i
$531$		0			0
$532$	4.82807	+	1.32244i	0.209323	+	0.0573349i
$533$	−1.68063	+	1.68063i	−0.0727964	+	0.0727964i
$534$		0			0
$535$	−14.6969	−	2.11660i	−0.635404	−	0.0915086i
$536$	−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	0.996568	+	0.0827763i	$0.0263787\pi$
$541$	13.2572	+	22.9621i	0.569970	+	0.987218i	−0.426598	+	0.904441i	$0.640288\pi$
$542$	5.91408	+	22.0717i	0.254032	+	0.948059i
$543$		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	$0.760338\pi$
$548$	−8.99233	−	2.40949i	−0.384133	−	0.102928i
$549$		0			0
$550$	3.17157	+	1.93520i	0.135236	+	0.0825174i
$551$	−15.8799	+	9.16828i	−0.676507	+	0.390582i
$552$		0			0
$553$	−4.41431	−	16.8479i	−0.187715	−	0.716444i
$554$			21.5332i			0.914858i
$555$		0			0
$556$	−19.2010	−	11.0857i	−0.814305	−	0.470139i
$557$	15.0145	−	4.02313i	0.636186	−	0.170466i	0.0737108	−	0.997280i	$-0.476516\pi$
$557$	15.0145	−	4.02313i	0.636186	−	0.170466i	0.562475	+	0.826814i	$0.309849\pi$
$558$		0			0
$559$	−6.56014			−0.277464
$560$	−2.16699	−	5.50492i	−0.0915719	−	0.232625i
$561$		0			0
$562$	1.46203	−	5.45637i	0.0616721	−	0.230163i
$563$	26.5108	−	7.10355i	1.11730	−	0.299379i	0.347508	−	0.937677i	$-0.387028\pi$
$563$	26.5108	−	7.10355i	1.11730	−	0.299379i	0.769789	+	0.638298i	$0.220361\pi$
$564$		0			0
$565$	0.764940	+	0.601844i	0.0321813	+	0.0253198i
$566$			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	$-0.711905\pi$
$569$	−5.85207	+	3.37869i	−0.245332	+	0.141642i	0.372293	+	0.928115i	$0.378572\pi$
$570$		0			0
$571$	−5.87721	+	10.1796i	−0.245953	+	0.426004i	−0.962399	−	0.271639i	$-0.912434\pi$
$571$	−5.87721	+	10.1796i	−0.245953	+	0.426004i	0.716446	+	0.697643i	$0.245768\pi$
$572$	2.08627	+	0.559013i	0.0872312	+	0.0233735i
$573$		0			0
$574$	−1.09209	+	1.86755i	−0.0455831	+	0.0779501i
$575$	26.4493	+	0.641957i	1.10301	+	0.0267715i
$576$		0			0
$577$	0.583767	+	2.17865i	0.0243025	+	0.0906983i	0.977012	−	0.213184i	$-0.0683835\pi$
$577$	0.583767	+	2.17865i	0.0243025	+	0.0906983i	−0.952709	+	0.303883i	$0.901717\pi$
$578$	6.73845	+	25.1483i	0.280283	+	1.04603i
$579$		0			0
$580$	19.9189	+	8.53525i	0.827085	+	0.354407i
$581$	30.0209	−	17.1111i	1.24547	−	0.709889i
$582$		0			0
$583$	−3.57851	−	0.958858i	−0.148207	−	0.0397118i
$584$	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	−0.390680	−	0.920527i	$-0.627760\pi$
$587$	12.8372	−	12.8372i	0.529847	−	0.529847i	0.920527	+	0.390680i	$0.127760\pi$
$588$		0			0
$589$		−	6.47569i		−	0.266826i
$590$	3.52542	−	4.48079i	0.145139	−	0.184471i
$591$		0			0
$592$	−2.58012	+	0.691342i	−0.106042	+	0.0284140i
$593$	−9.40957	+	35.1170i	−0.386405	+	1.44208i	0.449535	+	0.893262i	$0.351590\pi$
$593$	−9.40957	+	35.1170i	−0.386405	+	1.44208i	−0.835940	+	0.548820i	$0.815077\pi$
$594$		0			0
$595$	−4.38460	−	38.5618i	−0.179751	−	1.58088i
$596$	−3.94236			−0.161485
$597$		0			0
$598$	14.8563	−	3.98074i	0.607520	−	0.162785i
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.974186	−	0.225748i	$-0.0724826\pi$
$599$	30.9792	+	17.8858i	1.26578	+	0.730796i	0.291589	+	0.956544i	$0.405816\pi$
$600$		0			0
$601$		−	45.6631i		−	1.86264i	−0.364204	−	0.931319i	$-0.618659\pi$
$601$		−	45.6631i		−	1.86264i	0.364204	−	0.931319i	$-0.381341\pi$
$602$	−5.77629	+	1.51345i	−0.235424	+	0.0616835i
$603$		0			0
$604$	−17.2732	+	9.97267i	−0.702835	+	0.405782i
$605$	18.7056	−	13.9960i	0.760490	−	0.569019i
$606$		0			0
$607$	−1.13151	−	0.303188i	−0.0459267	−	0.0123060i	0.235783	−	0.971806i	$-0.424235\pi$
$607$	−1.13151	−	0.303188i	−0.0459267	−	0.0123060i	−0.281709	+	0.959500i	$0.590901\pi$
$608$	−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
$613$	−3.60737	−	13.4629i	−0.145700	−	0.543760i	−0.999723	−	0.0235253i	$-0.992511\pi$
$613$	−3.60737	−	13.4629i	−0.145700	−	0.543760i	0.854023	−	0.520235i	$-0.174156\pi$
$614$	−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	$-0.682709\pi$
$619$	11.3386	−	19.6391i	0.455738	−	0.789361i	0.998730	+	0.0503763i	$0.0160421\pi$
$620$	−6.12770	+	4.58491i	−0.246094	+	0.184134i
$621$		0			0
$622$	0.0891090	−	0.0891090i	0.00357294	−	0.00357294i
$623$	15.4382	−	4.04497i	0.618520	−	0.162058i
$624$		0			0
$625$	22.2316	−	11.4349i	0.889263	−	0.457397i
$626$	10.1273	+	5.84698i	0.404767	+	0.233692i
$627$		0			0
$628$	−1.93165	+	7.20903i	−0.0770814	+	0.287672i
$629$	−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	$0.276720\pi$
$632$	−1.70376	+	6.35854i	−0.0677721	+	0.252929i
$633$		0			0
$634$	−9.47968	−	5.47310i	−0.376486	−	0.217364i
$635$	−21.8655	+	27.7909i	−0.867706	+	1.10285i
$636$		0			0
$637$	5.04765	+	19.7106i	0.199995	+	0.780963i
$638$	−5.09214	+	5.09214i	−0.201600	+	0.201600i
$639$		0			0
$640$	−0.318742	+	2.21323i	−0.0125994	+	0.0874857i
$641$	−0.428070	+	0.741439i	−0.0169077	+	0.0292851i	−0.874355	−	0.485286i	$-0.838715\pi$
$641$	−0.428070	+	0.741439i	−0.0169077	+	0.0292851i	0.857448	+	0.514571i	$0.172049\pi$
$642$		0			0
$643$	16.4254	+	16.4254i	0.647754	+	0.647754i	0.952450	−	0.304696i	$-0.0985548\pi$
$643$	16.4254	+	16.4254i	0.647754	+	0.647754i	−0.304696	+	0.952450i	$0.598555\pi$
$644$	12.1628	−	6.93250i	0.479283	−	0.273179i
$645$		0			0
$646$	−6.20607	−	10.7492i	−0.244174	−	0.422922i
$647$	12.2805	+	45.8316i	0.482798	+	1.80183i	0.589779	+	0.807564i	$0.299215\pi$
$647$	12.2805	+	45.8316i	0.482798	+	1.80183i	−0.106982	+	0.994261i	$0.534119\pi$
$648$		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
$653$	25.3781	+	6.80004i	0.993121	+	0.266106i	0.718561	−	0.695464i	$-0.244801\pi$
$653$	25.3781	+	6.80004i	0.993121	+	0.266106i	0.274560	+	0.961570i	$0.411468\pi$
$654$		0			0
$655$	−12.8506	−	17.1748i	−0.502115	−	0.671074i
$656$	0.708148	−	0.408849i	0.0276485	−	0.0159629i
$657$		0			0
$658$	8.76184	+	8.85964i	0.341572	+	0.345385i
$659$		−	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	0.234078	−	0.972218i	$-0.424793\pi$
$661$	−12.6197	−	7.28597i	−0.490848	−	0.283391i	−0.724926	+	0.688827i	$0.758126\pi$
$662$	5.27432	−	1.41325i	0.204992	−	0.0549275i
$663$		0			0
$664$	−13.0605			−0.506847
$665$	4.10006	+	10.4156i	0.158993	+	0.403900i
$666$		0			0
$667$	−13.2725	+	49.5336i	−0.513913	+	1.91795i
$668$	−1.98844	+	0.532802i	−0.0769352	+	0.0206147i
$669$		0			0
$670$	−30.3991	+	3.62747i	−1.17442	+	0.140141i
$671$		−	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
$677$	21.9882	+	5.89172i	0.845075	+	0.226437i	0.655280	−	0.755386i	$-0.272551\pi$
$677$	21.9882	+	5.89172i	0.845075	+	0.226437i	0.189796	+	0.981824i	$0.439217\pi$
$678$		0			0
$679$	5.86774	+	10.2947i	0.225183	+	0.395076i
$680$	−5.77756	+	13.4832i	−0.221559	+	0.517057i
$681$		0			0
$682$	−0.658233	−	2.45656i	−0.0252050	−	0.0940665i
$683$	−7.93034	−	29.5964i	−0.303446	−	1.13248i	−0.934275	−	0.356554i	$-0.883952\pi$
$683$	−7.93034	−	29.5964i	−0.303446	−	1.13248i	0.630829	−	0.775922i	$-0.282715\pi$
$684$		0			0
$685$	−7.73231	−	19.3274i	−0.295436	−	0.738463i
$686$	8.99183	+	16.1910i	0.343310	+	0.618173i
$687$		0			0
$688$	2.18003	+	0.584136i	0.0831127	+	0.0222700i
$689$	−7.24590	+	12.5503i	−0.276047	+	0.478127i
$690$		0			0
$691$	27.7284	−	16.0090i	1.05484	−	0.609012i	0.130839	−	0.991404i	$-0.458233\pi$
$691$	27.7284	−	16.0090i	1.05484	−	0.609012i	0.924000	+	0.382392i	$0.124900\pi$
$692$	6.65251	−	6.65251i	0.252891	−	0.252891i
$693$		0			0
$694$			21.5379i			0.817567i
$695$	−5.87423	−	49.2276i	−0.222822	−	1.86731i
$696$		0			0
$697$	5.18143	−	1.38836i	0.196261	−	0.0525879i
$698$	−3.25450	+	12.1459i	−0.123184	+	0.459731i
$699$		0			0
$700$	6.95297	−	11.2542i	0.262798	−	0.425367i
$701$	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
$703$	4.88174	−	1.30806i	0.184118	−	0.0493343i
$704$	−0.643519	−	0.371536i	−0.0242535	−	0.0140028i
$705$		0			0
$706$			0.689506i			0.0259499i
$707$	−21.0347	+	20.8025i	−0.791092	+	0.782360i
$708$		0			0
$709$	23.1074	−	13.3411i	0.867818	−	0.501035i	0.00119522	−	0.999999i	$-0.499620\pi$
$709$	23.1074	−	13.3411i	0.867818	−	0.501035i	0.866622	+	0.498965i	$0.166286\pi$
$710$	−35.4499	−	5.10537i	−1.33041	−	0.191601i
$711$		0			0
$712$	−5.82653	−	1.56121i	−0.218358	−	0.0585089i
$713$	−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
$718$	5.71959	+	21.3458i	0.213453	+	0.796618i
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	−0.993364	−	0.115015i	$-0.963308\pi$
$719$	−15.9890	−	27.6937i	−0.596288	−	1.03280i	0.397076	−	0.917786i	$-0.370025\pi$
$720$		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
$725$	11.4021	+	47.0961i	0.423465	+	1.74911i
$726$		0			0
$727$	−21.4539	+	21.4539i	−0.795683	+	0.795683i	−0.982412	−	0.186729i	$-0.940211\pi$
$727$	−21.4539	+	21.4539i	−0.795683	+	0.795683i	0.186729	+	0.982412i	$0.440211\pi$
$728$	2.03159	−	7.41711i	0.0752958	−	0.274897i
$729$		0			0
$730$	19.6512	−	2.34494i	0.727324	−	0.0867901i
$731$	12.8222	+	7.40288i	0.474245	+	0.273805i
$732$		0			0
$733$	−3.36789	+	12.5691i	−0.124396	+	0.464252i	−0.999817	−	0.0191085i	$-0.993917\pi$
$733$	−3.36789	+	12.5691i	−0.124396	+	0.464252i	0.875422	+	0.483360i	$0.160584\pi$
$734$	13.4109			0.495006
$735$		0			0
$736$	−5.29142			−0.195044
$737$	2.63314	−	9.82700i	0.0969928	−	0.361982i
$738$		0			0
$739$	3.12136	+	1.80212i	0.114821	+	0.0662920i	0.556311	−	0.830974i	$-0.312216\pi$
$739$	3.12136	+	1.80212i	0.114821	+	0.0662920i	−0.441490	+	0.897266i	$0.645550\pi$
$740$	−4.69412	−	3.69327i	−0.172559	−	0.135767i
$741$		0			0
$742$	−3.48473	+	12.7223i	−0.127928	+	0.467052i
$743$	−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
$745$	−5.28121	−	7.05831i	−0.193489	−	0.258596i
$746$	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	0.781576	+	0.623810i	$0.214416\pi$
$751$	25.5141	+	44.1917i	0.931023	+	1.61258i	0.149447	+	0.988770i	$0.452251\pi$
$752$	−1.21894	−	4.54913i	−0.0444501	−	0.165890i
$753$		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	$0.507993\pi$
$758$	1.65931	+	0.444610i	0.0602687	+	0.0161490i
$759$		0			0
$760$	0.603077	−	4.18756i	0.0218759	−	0.151899i
$761$	25.8753	−	14.9391i	0.937980	−	0.541543i	0.0486532	−	0.998816i	$-0.484507\pi$
$761$	25.8753	−	14.9391i	0.937980	−	0.541543i	0.889326	+	0.457273i	$0.151174\pi$
$762$		0			0
$763$	16.8563	−	16.6702i	0.610239	−	0.603503i
$764$			2.77548i			0.100413i
$765$		0			0
$766$	−9.05698	−	5.22905i	−0.327242	−	0.188933i
$767$	7.15874	−	1.91818i	0.258487	−	0.0692614i
$768$		0			0
$769$	−44.7341			−1.61315			−0.806576	−	0.591130i	$-0.798682\pi$
$769$	−44.7341			−1.61315			−0.806576	+	0.591130i	$0.798682\pi$
$770$	2.61407	+	3.53441i	0.0942047	+	0.127371i
$771$		0			0
$772$	−1.33034	+	4.96491i	−0.0478801	+	0.178691i
$773$	23.3328	−	6.25202i	0.839224	−	0.224869i	0.186490	−	0.982457i	$-0.440289\pi$
$773$	23.3328	−	6.25202i	0.839224	−	0.224869i	0.652734	+	0.757587i	$0.273622\pi$
$774$		0			0
$775$	−16.4174	−	4.82891i	−0.589731	−	0.173460i
$776$		−	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
$782$	−33.5296	−	8.98424i	−1.19902	−	0.321276i
$783$		0			0
$784$	0.0776922	−	6.99957i	0.00277472	−	0.249985i
$785$	−15.4945	+	6.19889i	−0.553024	+	0.221248i
$786$		0			0
$787$	3.28689	+	12.2669i	0.117165	+	0.437266i	0.999440	−	0.0334688i	$-0.0106554\pi$
$787$	3.28689	+	12.2669i	0.117165	+	0.437266i	−0.882275	+	0.470735i	$0.843989\pi$
$788$	0.490633	+	1.83107i	0.0174781	+	0.0652290i
$789$		0			0
$790$	−13.6666	+	5.46757i	−0.486234	+	0.194527i
$791$	0.570279	+	1.00054i	0.0202768	+	0.0355749i
$792$		0			0
$793$	−17.0524	−	4.56917i	−0.605547	−	0.162256i
$794$	−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	−0.848193	−	0.529687i	$-0.822310\pi$
$797$	−8.99183	+	8.99183i	−0.318507	+	0.318507i	0.529687	+	0.848193i	$0.322310\pi$
$798$		0			0
$799$		−	30.8957i		−	1.09301i
$800$	−4.38951	+	2.39420i	−0.155193	+	0.0846477i
$801$		0			0
$802$	13.4945	−	3.61585i	0.476508	−	0.127680i
$803$	−1.70216	+	6.35256i	−0.0600681	+	0.224177i
$804$		0			0
$805$	28.7052	+	12.4892i	1.01173	+	0.440187i
$806$	−9.94828			−0.350413
$807$		0			0
$808$	10.8006	−	2.89402i	0.379965	−	0.101811i
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	0.855902	−	0.517139i	$-0.173003\pi$
$809$	23.7782	+	13.7284i	0.835997	+	0.482663i	−0.0199044	+	0.999802i	$0.506336\pi$
$810$		0			0
$811$		−	12.7335i		−	0.447132i	−0.974689	−	0.223566i	$-0.928230\pi$
$811$		−	12.7335i		−	0.447132i	0.974689	−	0.223566i	$-0.0717699\pi$
$812$	18.0300	+	18.2312i	0.632727	+	0.639789i
$813$		0			0
$814$	1.71893	−	0.992425i	0.0602485	−	0.0347845i
$815$	−3.87799	+	26.9274i	−0.135840	+	0.943226i
$816$		0			0
$817$	−4.12473	−	1.10522i	−0.144306	−	0.0386666i
$818$	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	0.999410	+	0.0343601i	$0.0109393\pi$
$821$	15.1707	+	26.2764i	0.529461	+	0.917054i	−0.469948	+	0.882694i	$0.655727\pi$
$822$		0			0
$823$	2.63314	+	9.82702i	0.0917856	+	0.342549i	0.996513	−	0.0834435i	$-0.0265918\pi$
$823$	2.63314	+	9.82702i	0.0917856	+	0.342549i	−0.904727	+	0.425992i	$0.859925\pi$
$824$	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	$-0.868500\pi$
$829$	−3.17447	+	5.49835i	−0.110254	+	0.190966i	0.805619	+	0.592435i	$0.201833\pi$
$830$	−17.4960	−	23.3833i	−0.607295	−	0.811645i
$831$		0			0
$832$	−2.05532	+	2.05532i	−0.0712555	+	0.0712555i
$833$	12.3768	−	44.2216i	0.428830	−	1.53219i
$834$		0			0
$835$	−3.61765	−	2.84632i	−0.125194	−	0.0985009i
$836$	1.21757	+	0.702966i	0.0421106	+	0.0243126i
$837$		0			0
$838$	8.17206	−	30.4985i	0.282299	−	1.05355i
$839$	−39.7411			−1.37202			−0.686008	−	0.727594i	$-0.740638\pi$
$839$	−39.7411			−1.37202			−0.686008	+	0.727594i	$0.740638\pi$
$840$		0			0
$841$	−64.9222			−2.23870
$842$	−3.50878	+	13.0949i	−0.120921	+	0.451282i
$843$		0			0
$844$	−8.68832	−	5.01621i	−0.299064	−	0.172665i
$845$	−10.1053	+	1.20585i	−0.347633	+	0.0414824i
$846$		0			0
$847$	26.7398	−	7.00609i	0.918790	−	0.240732i
$848$	3.52543	−	3.52543i	0.121064	−	0.121064i
$849$		0			0
$850$	−31.8797	+	7.71818i	−1.09346	+	0.264731i
$851$	7.06707	−	12.2405i	0.242256	−	0.419600i
$852$		0			0
$853$	17.1451	+	17.1451i	0.587036	+	0.587036i	0.936828	−	0.349791i	$-0.113748\pi$
$853$	17.1451	+	17.1451i	0.587036	+	0.587036i	−0.349791	+	0.936828i	$0.613748\pi$
$854$	−16.0690	−	0.0891766i	−0.549869	−	0.00305156i
$855$		0			0
$856$	3.32024	+	5.75083i	0.113484	+	0.196559i
$857$	−4.35890	−	16.2677i	−0.148897	−	0.555692i	−0.999551	−	0.0299658i	$-0.990460\pi$
$857$	−4.35890	−	16.2677i	−0.148897	−	0.555692i	0.850654	−	0.525727i	$-0.176206\pi$
$858$		0			0
$859$	−15.4345	−	26.7333i	−0.526619	−	0.912130i	−0.999519	−	0.0310142i	$-0.990126\pi$
$859$	−15.4345	−	26.7333i	−0.526619	−	0.912130i	0.472900	−	0.881116i	$-0.343207\pi$
$860$	1.87456	+	4.68558i	0.0639218	+	0.159777i
$861$		0			0
$862$	−9.38356	−	9.38356i	−0.319605	−	0.319605i
$863$	−1.24908	−	0.334691i	−0.0425193	−	0.0113930i	0.237497	−	0.971388i	$-0.423673\pi$
$863$	−1.24908	−	0.334691i	−0.0425193	−	0.0113930i	−0.280016	+	0.959995i	$0.590340\pi$
$864$		0			0
$865$	20.8223	+	2.99875i	0.707978	+	0.101960i
$866$	14.7624	−	8.52308i	0.501647	−	0.289626i
$867$		0			0
$868$	−8.75960	+	2.29510i	−0.297320	+	0.0779008i
$869$		−	4.89152i		−	0.165934i
$870$		0			0
$871$	−34.4645	−	19.8981i	−1.16778	−	0.674221i
$872$	−8.65516	+	2.31914i	−0.293101	+	0.0785361i
$873$		0			0
$874$	10.0117			0.338649
$875$	29.4635	−	2.62772i	0.996047	−	0.0888332i
$876$		0			0
$877$	2.51177	−	9.37406i	0.0848165	−	0.316540i	−0.910463	−	0.413591i	$-0.864274\pi$
$877$	2.51177	−	9.37406i	0.0848165	−	0.316540i	0.995279	+	0.0970513i	$0.0309411\pi$
$878$	33.8534	−	9.07099i	1.14250	−	0.306131i
$879$		0			0
$880$	−0.196874	−	1.64985i	−0.00663662	−	0.0556166i
$881$		−	18.3500i		−	0.618227i	−0.951025	−	0.309113i	$-0.899968\pi$
$881$		−	18.3500i		−	0.618227i	0.951025	−	0.309113i	$-0.100032\pi$
$882$		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
$887$	−37.5247	−	10.0547i	−1.25996	−	0.337604i	−0.433781	−	0.901018i	$-0.642821\pi$
$887$	−37.5247	−	10.0547i	−1.25996	−	0.337604i	−0.826175	+	0.563414i	$0.809488\pi$
$888$		0			0
$889$	−36.3503	+	20.7187i	−1.21915	+	0.694884i
$890$	−5.01010	−	12.5231i	−0.167939	−	0.419775i
$891$		0			0
$892$	−1.14843	−	4.28599i	−0.0384522	−	0.143506i
$893$	2.30629	+	8.60721i	0.0771772	+	0.288029i
$894$		0			0
$895$	3.96097	−	9.24379i	0.132401	−	0.308986i
$896$	−1.33557	+	2.28391i	−0.0446183	+	0.0763001i
$897$		0			0
$898$	23.6851	+	6.34642i	0.790384	+	0.211783i
$899$	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
$905$	39.7104	−	4.73856i	1.32002	−	0.157515i
$906$		0			0
$907$	−33.5044	+	8.97748i	−1.11250	+	0.298092i	−0.767843	−	0.640638i	$-0.778670\pi$
$907$	−33.5044	+	8.97748i	−1.11250	+	0.298092i	−0.344653	+	0.938730i	$0.612003\pi$
$908$	−0.173634	+	0.648012i	−0.00576226	+	0.0215050i
$909$		0			0
$910$	16.0010	−	6.29871i	0.530427	−	0.208800i
$911$	−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
$913$	9.37422	−	2.51182i	0.310242	−	0.0831290i
$914$	−17.3839	−	10.0366i	−0.575007	−	0.331980i
$915$		0			0
$916$		−	13.2033i		−	0.436250i
$917$	−6.43273	−	24.5515i	−0.212428	−	0.810761i
$918$		0			0
$919$	−15.4242	+	8.90515i	−0.508797	+	0.293754i	−0.732339	−	0.680940i	$-0.761571\pi$
$919$	−15.4242	+	8.90515i	−0.508797	+	0.293754i	0.223542	+	0.974694i	$0.428238\pi$
$920$	−7.08843	−	9.47364i	−0.233699	−	0.312337i
$921$		0			0
$922$	−11.2955	−	3.02662i	−0.371997	−	0.0996763i
$923$	−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
$928$	−2.50831	−	9.36112i	−0.0823392	−	0.307294i
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	0.999416	+	0.0341607i	$0.0108758\pi$
$929$	16.1326	+	27.9424i	0.529292	+	0.916761i	−0.470124	+	0.882600i	$0.655791\pi$
$930$		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
$935$	1.55376	−	10.7887i	0.0508133	−	0.352830i
$936$		0			0
$937$	28.9650	−	28.9650i	0.946244	−	0.946244i	−0.0523829	−	0.998627i	$-0.516682\pi$
$937$	28.9650	−	28.9650i	0.946244	−	0.946244i	0.998627	+	0.0523829i	$0.0166816\pi$
$938$	−34.9370	−	9.56947i	−1.14073	−	0.312454i
$939$		0			0
$940$	6.51177	−	8.27641i	0.212390	−	0.269947i
$941$	−30.8629	−	17.8187i	−1.00610	−	0.580874i	−0.0960550	−	0.995376i	$-0.530622\pi$
$941$	−30.8629	−	17.8187i	−1.00610	−	0.580874i	−0.910048	+	0.414502i	$0.863956\pi$
$942$		0			0
$943$	−1.11985	+	4.17936i	−0.0364675	+	0.136099i
$944$	−2.54975			−0.0829873
$945$		0			0
$946$	−1.67706			−0.0545259
$947$	−3.61149	+	13.4783i	−0.117358	+	0.437985i	−0.999452	−	0.0330871i	$-0.989466\pi$
$947$	−3.61149	+	13.4783i	−0.117358	+	0.437985i	0.882095	+	0.471072i	$0.156133\pi$
$948$		0			0
$949$	22.2792	+	12.8629i	0.723214	+	0.417548i
$950$	8.30519	−	4.52995i	0.269456	−	0.146971i
$951$		0			0
$952$	−12.3408	+	12.2046i	−0.399968	+	0.395553i
$953$	−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
$955$	−4.96916	+	3.71806i	−0.160798	+	0.120314i
$956$	−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
$962$	−2.00950	−	7.49956i	−0.0647889	−	0.241796i
$963$		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	$-0.532149\pi$
$968$	−10.0918	−	2.70410i	−0.324364	−	0.0869131i
$969$		0			0
$970$	8.01859	−	5.99972i	0.257461	−	0.192639i
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	−0.563966	−	0.825798i	$-0.690725\pi$
$971$	−4.07547	+	2.35297i	−0.130788	+	0.0755105i	0.433179	+	0.901308i	$0.357392\pi$
$972$		0			0
$973$	15.4966	−	56.5762i	0.496797	−	1.81375i
$974$			2.55599i			0.0818993i
$975$		0			0
$976$	5.25989	+	3.03680i	0.168365	+	0.0972055i
$977$	−26.5853	+	7.12351i	−0.850540	+	0.227901i	−0.657654	−	0.753320i	$-0.728451\pi$
$977$	−26.5853	+	7.12351i	−0.850540	+	0.227901i	−0.192885	+	0.981221i	$0.561785\pi$
$978$		0			0
$979$	4.48226			0.143254
$980$	12.6359	−	9.23758i	0.403640	−	0.295084i
$981$		0			0
$982$	−3.77017	+	14.0704i	−0.120311	+	0.449006i
$983$	−43.3874	+	11.6256i	−1.38384	+	0.370799i	−0.872515	−	0.488587i	$-0.837513\pi$
$983$	−43.3874	+	11.6256i	−1.38384	+	0.370799i	−0.511327	+	0.859386i	$0.670846\pi$
$984$		0			0
$985$	−2.62104	+	3.33133i	−0.0835134	+	0.106145i
$986$		−	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	−0.812858	−	0.582462i	$-0.802090\pi$
$991$	3.08498	−	5.34334i	0.0979975	−	0.169737i	0.910856	+	0.412725i	$0.135423\pi$
$992$	3.30595	+	0.885827i	0.104964	+	0.0281250i
$993$		0			0
$994$	−36.5820	−	21.3922i	−1.16031	−	0.678519i
$995$	−29.8083	−	12.7729i	−0.944985	−	0.404927i
$996$		0			0
$997$	4.87184	+	18.1820i	0.154293	+	0.575829i	0.999165	+	0.0408602i	$0.0130098\pi$
$997$	4.87184	+	18.1820i	0.154293	+	0.575829i	−0.844872	+	0.534968i	$0.820324\pi$
$998$	7.78721	+	29.0623i	0.246500	+	0.919950i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.4	✓	16	15.8	even	4
70.2.k.a.17.2	yes	16	3.2	odd	2
70.2.k.a.33.2	yes	16	105.68	odd	12
70.2.k.a.47.4	yes	16	21.5	even	6
350.2.o.c.143.1		16	15.2	even	4
350.2.o.c.157.3		16	15.14	odd	2
350.2.o.c.243.3		16	105.47	odd	12
350.2.o.c.257.1		16	105.89	even	6
490.2.g.c.97.2		16	21.11	odd	6
490.2.g.c.97.3		16	21.17	even	6
490.2.g.c.293.2		16	105.38	odd	12
490.2.g.c.293.3		16	105.53	even	12
490.2.l.c.117.3		16	21.2	odd	6
490.2.l.c.227.1		16	21.20	even	2
490.2.l.c.313.1		16	105.23	even	12
490.2.l.c.423.3		16	105.83	odd	4
560.2.ci.c.17.2		16	12.11	even	2
560.2.ci.c.33.2		16	420.383	even	12
560.2.ci.c.257.2		16	84.47	odd	6
560.2.ci.c.353.2		16	60.23	odd	4
630.2.bv.c.73.2		16	5.3	odd	4	inner
630.2.bv.c.397.2		16	7.5	odd	6	inner
630.2.bv.c.523.3		16	35.33	even	12	inner
630.2.bv.c.577.3		16	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.264946 - 2.22032i) q^{5} +(0.698943 - 2.55176i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.264946 - 2.22032i) q^{5} +(0.698943 - 2.55176i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.21323 - 0.318742i) q^{10} +(0.371536 - 0.643519i) q^{11} +(-2.05532 - 2.05532i) q^{13} +(-2.28391 - 1.33557i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.69789 + 6.33660i) q^{17} +(-0.946027 - 1.63857i) q^{19} +(-0.880708 + 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(-5.11112 - 1.36952i) q^{23} +(-4.85961 + 1.17653i) q^{25} +(-2.51725 + 1.45333i) q^{26} +(-1.88118 + 1.86042i) q^{28} -9.69135i q^{29} +(2.96403 + 1.71129i) q^{31} +(0.965926 - 0.258819i) q^{32} +6.56014 q^{34} +(-5.85090 - 0.875795i) q^{35} +(-0.691342 + 2.58012i) q^{37} +(-1.82758 + 0.489700i) q^{38} +(1.75735 + 1.38266i) q^{40} -0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +(-0.643519 + 0.371536i) q^{44} +(-2.64571 + 4.58251i) q^{46} +(-4.54913 - 1.21894i) q^{47} +(-6.02296 - 3.56707i) q^{49} +(-0.121320 + 4.99853i) q^{50} +(0.752300 + 2.80762i) q^{52} +(-1.29040 - 4.81583i) q^{53} +(-1.52725 - 0.654429i) q^{55} +(1.31014 + 2.29859i) q^{56} +(-9.36112 - 2.50831i) q^{58} +(-1.27487 + 2.20815i) q^{59} +(5.25989 - 3.03680i) q^{61} +(2.42012 - 2.42012i) q^{62} -1.00000i q^{64} +(-4.01892 + 5.10802i) q^{65} +(13.2248 - 3.54358i) q^{67} +(1.69789 - 6.33660i) q^{68} +(-2.36028 + 5.42486i) q^{70} +16.0173 q^{71} +(-8.54906 + 2.29071i) q^{73} +(2.31328 + 1.33557i) q^{74} +1.89205i q^{76} +(-1.38242 - 1.39785i) q^{77} +(5.70091 - 3.29142i) q^{79} +(1.79038 - 1.33961i) q^{80} +(-0.789836 - 0.211636i) q^{82} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} +(-1.12846 - 1.95456i) q^{86} +(0.192321 + 0.717752i) q^{88} +(3.01603 + 5.22392i) q^{89} +(-6.68124 + 3.80814i) q^{91} +(3.74160 + 3.74160i) q^{92} +(-2.35481 + 4.07864i) q^{94} +(-3.38749 + 2.53461i) q^{95} +(-3.16693 + 3.16693i) q^{97} +(-5.00438 + 4.89451i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} + 8 q^{7}+O(q^{10}) \) 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