LMFDB - Embedded newform 490.2.g.c.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(97,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("490.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.3
Root			$-1.45333 - 1.51725i$ of defining polynomial
Character	$\chi$	$=$	490.97
Dual form			490.2.g.c.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.830578 + 0.830578i) q^{3} +1.00000i q^{4} +(2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 - 0.707107i) q^{8} -1.62028i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.830578 + 0.830578i) q^{3} +1.00000i q^{4} +(2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 - 0.707107i) q^{8} -1.62028i q^{9} +(-0.830578 - 2.07609i) q^{10} +0.743072 q^{11} +(-0.830578 + 0.830578i) q^{12} +(2.05532 + 2.05532i) q^{13} +(0.975610 + 2.43860i) q^{15} -1.00000 q^{16} +(4.63872 - 4.63872i) q^{17} +(-1.14571 + 1.14571i) q^{18} -1.89205 q^{19} +(-0.880708 + 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(-3.74160 + 3.74160i) q^{23} +1.17462 q^{24} +(3.44871 + 3.62028i) q^{25} -2.90667i q^{26} +(3.83750 - 3.83750i) q^{27} +9.69135i q^{29} +(1.03449 - 2.41421i) q^{30} +3.42257i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.617179 + 0.617179i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-1.88878 - 1.88878i) q^{37} +(1.33788 + 1.33788i) q^{38} +3.41421i q^{39} +(2.07609 - 0.830578i) q^{40} -0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +0.743072i q^{44} +(1.42699 - 3.33020i) q^{45} +5.29142 q^{46} +(3.33020 - 3.33020i) q^{47} +(-0.830578 - 0.830578i) q^{48} +(0.121320 - 4.99853i) q^{50} +7.70563 q^{51} +(-2.05532 + 2.05532i) q^{52} +(3.52543 - 3.52543i) q^{53} -5.42705 q^{54} +(1.52725 + 0.654429i) q^{55} +(-1.57150 - 1.57150i) q^{57} +(6.85282 - 6.85282i) q^{58} +2.54975 q^{59} +(-2.43860 + 0.975610i) q^{60} -6.07359i q^{61} +(2.42012 - 2.42012i) q^{62} -1.00000i q^{64} +(2.41421 + 6.03449i) q^{65} -0.872823i q^{66} +(-9.68124 - 9.68124i) q^{67} +(4.63872 + 4.63872i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-1.14571 - 1.14571i) q^{72} +(-6.25834 - 6.25834i) q^{73} +2.67114i q^{74} +(-0.142505 + 5.87135i) q^{75} -1.89205i q^{76} +(2.41421 - 2.41421i) q^{78} +6.58284i q^{79} +(-2.05532 - 0.880708i) q^{80} +1.51386 q^{81} +(-0.578200 + 0.578200i) q^{82} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} -2.25693 q^{86} +(-8.04942 + 8.04942i) q^{87} +(0.525431 - 0.525431i) q^{88} -6.03207 q^{89} +(-3.36384 + 1.34577i) q^{90} +(-3.74160 - 3.74160i) q^{92} +(-2.84271 + 2.84271i) q^{93} -4.70961 q^{94} +(-3.88878 - 1.66635i) q^{95} +1.17462i q^{96} +(3.16693 - 3.16693i) q^{97} -1.20398i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) $ 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.830578	+	0.830578i	0.479535	+	0.479535i	0.904983	−	0.425448i	$-0.139884\pi$
$3$	0.830578	+	0.830578i	0.479535	+	0.479535i	−0.425448	+	0.904983i	$0.639884\pi$
$4$			1.00000i			0.500000i
$5$	2.05532	+	0.880708i	0.919168	+	0.393865i
$5$	2.05532	+	0.880708i	0.919168	+	0.393865i
$6$		−	1.17462i		−	0.479535i
$7$		0			0
$7$		0			0
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.62028i		−	0.540093i
$10$	−0.830578	−	2.07609i	−0.262652	−	0.656517i
$11$	0.743072			0.224045			0.112022	−	0.993706i	$-0.464267\pi$
$11$	0.743072			0.224045			0.112022	+	0.993706i	$0.464267\pi$
$12$	−0.830578	+	0.830578i	−0.239767	+	0.239767i
$13$	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	$0.617939\pi$
$14$		0			0
$15$	0.975610	+	2.43860i	0.251901	+	0.629645i
$16$	−1.00000			−0.250000
$17$	4.63872	−	4.63872i	1.12505	−	1.12505i	0.134084	−	0.990970i	$-0.457191\pi$
$17$	4.63872	−	4.63872i	1.12505	−	1.12505i	0.990970	−	0.134084i	$-0.0428092\pi$
$18$	−1.14571	+	1.14571i	−0.270047	+	0.270047i
$19$	−1.89205			−0.434067			−0.217033	−	0.976164i	$-0.569638\pi$
$19$	−1.89205			−0.434067			−0.217033	+	0.976164i	$0.569638\pi$
$20$	−0.880708	+	2.05532i	−0.196932	+	0.459584i
$21$		0			0
$22$	−0.525431	−	0.525431i	−0.112022	−	0.112022i
$23$	−3.74160	+	3.74160i	−0.780177	+	0.780177i	−0.979861	−	0.199683i	$-0.936009\pi$
$23$	−3.74160	+	3.74160i	−0.780177	+	0.780177i	0.199683	+	0.979861i	$0.436009\pi$
$24$	1.17462			0.239767
$25$	3.44871	+	3.62028i	0.689741	+	0.724056i
$26$		−	2.90667i		−	0.570044i
$27$	3.83750	−	3.83750i	0.738528	−	0.738528i
$28$		0			0
$29$			9.69135i			1.79964i	0.436263	+	0.899819i	$0.356302\pi$
$29$			9.69135i			1.79964i	−0.436263	+	0.899819i	$0.643698\pi$
$30$	1.03449	−	2.41421i	0.188872	−	0.440773i
$31$			3.42257i			0.614712i	0.951595	+	0.307356i	$0.0994443\pi$
$31$			3.42257i			0.614712i	−0.951595	+	0.307356i	$0.900556\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.617179	+	0.617179i	0.107437	+	0.107437i
$34$	−6.56014			−1.12505
$35$		0			0
$36$	1.62028			0.270047
$37$	−1.88878	−	1.88878i	−0.310514	−	0.310514i	0.534595	−	0.845109i	$-0.320464\pi$
$37$	−1.88878	−	1.88878i	−0.310514	−	0.310514i	−0.845109	+	0.534595i	$0.820464\pi$
$38$	1.33788	+	1.33788i	0.217033	+	0.217033i
$39$			3.41421i			0.546712i
$40$	2.07609	−	0.830578i	0.328258	−	0.131326i
$41$		−	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	$0.194948\pi$
$44$			0.743072i			0.112022i
$45$	1.42699	−	3.33020i	0.212724	−	0.496437i
$46$	5.29142			0.780177
$47$	3.33020	−	3.33020i	0.485759	−	0.485759i	−0.421206	−	0.906965i	$-0.638393\pi$
$47$	3.33020	−	3.33020i	0.485759	−	0.485759i	0.906965	+	0.421206i	$0.138393\pi$
$48$	−0.830578	−	0.830578i	−0.119884	−	0.119884i
$49$		0			0
$50$	0.121320	−	4.99853i	0.0171573	−	0.706899i
$51$	7.70563			1.07900
$52$	−2.05532	+	2.05532i	−0.285022	+	0.285022i
$53$	3.52543	−	3.52543i	0.484255	−	0.484255i	−0.422232	−	0.906488i	$-0.638753\pi$
$53$	3.52543	−	3.52543i	0.484255	−	0.484255i	0.906488	+	0.422232i	$0.138753\pi$
$54$	−5.42705			−0.738528
$55$	1.52725	+	0.654429i	0.205935	+	0.0882432i
$56$		0			0
$57$	−1.57150	−	1.57150i	−0.208150	−	0.208150i
$58$	6.85282	−	6.85282i	0.899819	−	0.899819i
$59$	2.54975			0.331949			0.165975	−	0.986130i	$-0.446923\pi$
$59$	2.54975			0.331949			0.165975	+	0.986130i	$0.446923\pi$
$60$	−2.43860	+	0.975610i	−0.314822	+	0.125951i
$61$		−	6.07359i		−	0.777644i	−0.921313	−	0.388822i	$-0.872882\pi$
$61$		−	6.07359i		−	0.777644i	0.921313	−	0.388822i	$-0.127118\pi$
$62$	2.42012	−	2.42012i	0.307356	−	0.307356i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	2.41421	+	6.03449i	0.299446	+	0.748487i
$66$		−	0.872823i		−	0.107437i
$67$	−9.68124	−	9.68124i	−1.18275	−	1.18275i	−0.979028	−	0.203724i	$-0.934696\pi$
$67$	−9.68124	−	9.68124i	−1.18275	−	1.18275i	−0.203724	−	0.979028i	$-0.565304\pi$
$68$	4.63872	+	4.63872i	0.562527	+	0.562527i
$69$	−6.21538			−0.748244
$70$		0			0
$71$	−16.0173			−1.90090			−0.950450	−	0.310879i	$-0.899377\pi$
$71$	−16.0173			−1.90090			−0.950450	+	0.310879i	$0.899377\pi$
$72$	−1.14571	−	1.14571i	−0.135023	−	0.135023i
$73$	−6.25834	−	6.25834i	−0.732484	−	0.732484i	0.238627	−	0.971111i	$-0.423303\pi$
$73$	−6.25834	−	6.25834i	−0.732484	−	0.732484i	−0.971111	+	0.238627i	$0.923303\pi$
$74$			2.67114i			0.310514i
$75$	−0.142505	+	5.87135i	−0.0164550	+	0.677965i
$76$		−	1.89205i		−	0.217033i
$77$		0			0
$78$	2.41421	−	2.41421i	0.273356	−	0.273356i
$79$			6.58284i			0.740628i	0.928907	+	0.370314i	$0.120750\pi$
$79$			6.58284i			0.740628i	−0.928907	+	0.370314i	$0.879250\pi$
$80$	−2.05532	−	0.880708i	−0.229792	−	0.0984662i
$81$	1.51386			0.168206
$82$	−0.578200	+	0.578200i	−0.0638515	+	0.0638515i
$83$	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
$86$	−2.25693			−0.243371
$87$	−8.04942	+	8.04942i	−0.862989	+	0.862989i
$88$	0.525431	−	0.525431i	0.0560111	−	0.0560111i
$89$	−6.03207			−0.639398			−0.319699	−	0.947519i	$-0.603582\pi$
$89$	−6.03207			−0.639398			−0.319699	+	0.947519i	$0.603582\pi$
$90$	−3.36384	+	1.34577i	−0.354580	+	0.141856i
$91$		0			0
$92$	−3.74160	−	3.74160i	−0.390089	−	0.390089i
$93$	−2.84271	+	2.84271i	−0.294776	+	0.294776i
$94$	−4.70961			−0.485759
$95$	−3.88878	−	1.66635i	−0.398981	−	0.170964i
$96$			1.17462i			0.119884i
$97$	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	$0.176987\pi$
$98$		0			0
$99$		−	1.20398i		−	0.121005i
$100$	−3.62028	+	3.44871i	−0.362028	+	0.344871i
$101$			11.1817i			1.11262i	0.830976	+	0.556308i	$0.187782\pi$
$101$			11.1817i			1.11262i	−0.830976	+	0.556308i	$0.812218\pi$
$102$	−5.44871	−	5.44871i	−0.539502	−	0.539502i
$103$	−1.71557	−	1.71557i	−0.169040	−	0.169040i	0.617517	−	0.786557i	$-0.288138\pi$
$103$	−1.71557	−	1.71557i	−0.169040	−	0.169040i	−0.786557	+	0.617517i	$0.788138\pi$
$104$	2.90667			0.285022
$105$		0			0
$106$	−4.98571			−0.484255
$107$	−4.69553	−	4.69553i	−0.453934	−	0.453934i	0.442724	−	0.896658i	$-0.354012\pi$
$107$	−4.69553	−	4.69553i	−0.453934	−	0.453934i	−0.896658	+	0.442724i	$0.854012\pi$
$108$	3.83750	+	3.83750i	0.369264	+	0.369264i
$109$		−	8.96048i		−	0.858258i	−0.903243	−	0.429129i	$-0.858820\pi$
$109$		−	8.96048i		−	0.858258i	0.903243	−	0.429129i	$-0.141180\pi$
$110$	−0.617179	−	1.54268i	−0.0588457	−	0.147089i
$111$		−	3.13756i		−	0.297804i
$112$		0			0
$113$	0.307790	−	0.307790i	0.0289545	−	0.0289545i	−0.692481	−	0.721436i	$-0.743482\pi$
$113$	0.307790	−	0.307790i	0.0289545	−	0.0289545i	0.721436	+	0.692481i	$0.243482\pi$
$114$			2.22244i			0.208150i
$115$	−10.9855	+	4.39494i	−1.02440	+	0.409830i
$116$	−9.69135			−0.899819
$117$	3.33020	−	3.33020i	0.307877	−	0.307877i
$118$	−1.80295	−	1.80295i	−0.165975	−	0.165975i
$119$		0			0
$120$	2.41421	+	1.03449i	0.220387	+	0.0944359i
$121$	−10.4478			−0.949804
$122$	−4.29468	+	4.29468i	−0.388822	+	0.388822i
$123$	0.679163	−	0.679163i	0.0612380	−	0.0612380i
$124$	−3.42257			−0.307356
$125$	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	$0.997548\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	2.65102			0.233409
$130$	2.55992	−	5.97414i	0.224520	−	0.523967i
$131$			9.59282i			0.838129i	0.907957	+	0.419064i	$0.137642\pi$
$131$			9.59282i			0.838129i	−0.907957	+	0.419064i	$0.862358\pi$
$132$	−0.617179	+	0.617179i	−0.0537186	+	0.0537186i
$133$		0			0
$134$			13.6913i			1.18275i
$135$	11.2670	−	4.50759i	0.969712	−	0.387952i
$136$		−	6.56014i		−	0.562527i
$137$	6.58284	+	6.58284i	0.562410	+	0.562410i	0.929991	−	0.367581i	$-0.119814\pi$
$137$	6.58284	+	6.58284i	0.562410	+	0.562410i	−0.367581	+	0.929991i	$0.619814\pi$
$138$	4.39494	+	4.39494i	0.374122	+	0.374122i
$139$	−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			0
$141$	5.53198			0.465877
$142$	11.3259	+	11.3259i	0.950450	+	0.950450i
$143$	1.52725	+	1.52725i	0.127715	+	0.127715i
$144$			1.62028i			0.135023i
$145$	−8.53525	+	19.9189i	−0.708814	+	1.65417i
$146$			8.85064i			0.732484i
$147$		0			0
$148$	1.88878	−	1.88878i	0.155257	−	0.155257i
$149$		−	3.94236i		−	0.322970i	−0.986875	−	0.161485i	$-0.948372\pi$
$149$		−	3.94236i		−	0.322970i	0.986875	−	0.161485i	$-0.0516284\pi$
$150$	4.25243	−	4.05090i	0.347210	−	0.330755i
$151$	−19.9453			−1.62313			−0.811564	−	0.584264i	$-0.801383\pi$
$151$	−19.9453			−1.62313			−0.811564	+	0.584264i	$0.801383\pi$
$152$	−1.33788	+	1.33788i	−0.108517	+	0.108517i
$153$	−7.51602	−	7.51602i	−0.607634	−	0.607634i
$154$		0			0
$155$	−3.01429	+	7.03449i	−0.242113	+	0.565024i
$156$	−3.41421			−0.273356
$157$	5.27738	−	5.27738i	0.421181	−	0.421181i	−0.464430	−	0.885610i	$-0.653741\pi$
$157$	5.27738	−	5.27738i	0.421181	−	0.421181i	0.885610	+	0.464430i	$0.153741\pi$
$158$	4.65477	−	4.65477i	0.370314	−	0.370314i
$159$	5.85629			0.464434
$160$	0.830578	+	2.07609i	0.0656630	+	0.164129i
$161$		0			0
$162$	−1.07046	−	1.07046i	−0.0841031	−	0.0841031i
$163$	8.60305	−	8.60305i	0.673843	−	0.673843i	−0.284757	−	0.958600i	$-0.591913\pi$
$163$	8.60305	−	8.60305i	0.673843	−	0.673843i	0.958600	+	0.284757i	$0.0919129\pi$
$164$	0.817699			0.0638515
$165$	0.724948	+	1.81206i	0.0564371	+	0.141069i
$166$		−	13.0605i		−	1.01369i
$167$	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
$170$	−13.4832	−	5.77756i	−1.03411	−	0.443119i
$171$			3.06566i			0.234437i
$172$	1.59589	+	1.59589i	0.121685	+	0.121685i
$173$	−6.65251	−	6.65251i	−0.505781	−	0.505781i	0.407448	−	0.913229i	$-0.366419\pi$
$173$	−6.65251	−	6.65251i	−0.505781	−	0.505781i	−0.913229	+	0.407448i	$0.866419\pi$
$174$	11.3836			0.862989
$175$		0			0
$176$	−0.743072			−0.0560111
$177$	2.11777	+	2.11777i	0.159181	+	0.159181i
$178$	4.26531	+	4.26531i	0.319699	+	0.319699i
$179$			4.49749i			0.336158i	0.985774	+	0.168079i	$0.0537564\pi$
$179$			4.49749i			0.336158i	−0.985774	+	0.168079i	$0.946244\pi$
$180$	3.33020	+	1.42699i	0.248218	+	0.106362i
$181$		−	17.8850i		−	1.32938i	−0.747118	−	0.664691i	$-0.768563\pi$
$181$		−	17.8850i		−	1.32938i	0.747118	−	0.664691i	$-0.231437\pi$
$182$		0			0
$183$	5.04460	−	5.04460i	0.372907	−	0.372907i
$184$			5.29142i			0.390089i
$185$	−2.21859	−	5.54552i	−0.163114	−	0.407715i
$186$	4.02021			0.294776
$187$	3.44690	−	3.44690i	0.252062	−	0.252062i
$188$	3.33020	+	3.33020i	0.242880	+	0.242880i
$189$		0			0
$190$	1.57150	+	3.92807i	0.114009	+	0.284972i
$191$	−2.77548			−0.200827			−0.100413	−	0.994946i	$-0.532017\pi$
$191$	−2.77548			−0.200827			−0.100413	+	0.994946i	$0.532017\pi$
$192$	0.830578	−	0.830578i	0.0599418	−	0.0599418i
$193$	−3.63457	+	3.63457i	−0.261622	+	0.261622i	−0.825713	−	0.564091i	$-0.809227\pi$
$193$	−3.63457	+	3.63457i	−0.261622	+	0.261622i	0.564091	+	0.825713i	$0.309227\pi$
$194$	−4.47871			−0.321553
$195$	−3.00693	+	7.01731i	−0.215330	+	0.502520i
$196$		0			0
$197$	1.34043	+	1.34043i	0.0955019	+	0.0955019i	0.753244	−	0.657742i	$-0.228488\pi$
$197$	1.34043	+	1.34043i	0.0955019	+	0.0955019i	−0.657742	+	0.753244i	$0.728488\pi$
$198$	−0.851345	+	0.851345i	−0.0605025	+	0.0605025i
$199$	14.5030			1.02809			0.514043	−	0.857764i	$-0.328147\pi$
$199$	14.5030			1.02809			0.514043	+	0.857764i	$0.328147\pi$
$200$	4.99853	+	0.121320i	0.353449	+	0.00857864i
$201$		−	16.0821i		−	1.13434i
$202$	7.90662	−	7.90662i	0.556308	−	0.556308i
$203$		0			0
$204$			7.70563i			0.539502i
$205$	0.720154	−	1.68063i	0.0502977	−	0.117381i
$206$			2.42618i			0.169040i
$207$	6.06244	+	6.06244i	0.421369	+	0.421369i
$208$	−2.05532	−	2.05532i	−0.142511	−	0.142511i
$209$	−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	$0.387767\pi$
$212$	3.52543	+	3.52543i	0.242128	+	0.242128i
$213$	−13.3036	−	13.3036i	−0.911547	−	0.911547i
$214$			6.64048i			0.453934i
$215$	4.68558	−	1.87456i	0.319554	−	0.127844i
$216$		−	5.42705i		−	0.369264i
$217$		0			0
$218$	−6.33602	+	6.33602i	−0.429129	+	0.429129i
$219$		−	10.3961i		−	0.702503i
$220$	−0.654429	+	1.52725i	−0.0441216	+	0.102967i
$221$	19.0681			1.28266
$222$	−2.21859	+	2.21859i	−0.148902	+	0.148902i
$223$	−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			0
$225$	5.86586	−	5.58787i	0.391058	−	0.372525i
$226$	−0.435281			−0.0289545
$227$	−0.474378	+	0.474378i	−0.0314856	+	0.0314856i	−0.722674	−	0.691189i	$-0.757087\pi$
$227$	−0.474378	+	0.474378i	−0.0314856	+	0.0314856i	0.691189	+	0.722674i	$0.257087\pi$
$228$	1.57150	−	1.57150i	0.104075	−	0.104075i
$229$	13.2033			0.872501			0.436250	−	0.899825i	$-0.356306\pi$
$229$	13.2033			0.872501			0.436250	+	0.899825i	$0.356306\pi$
$230$	10.8756	+	4.66020i	0.717115	+	0.307284i
$231$		0			0
$232$	6.85282	+	6.85282i	0.449910	+	0.449910i
$233$	−6.12279	+	6.12279i	−0.401117	+	0.401117i	−0.878627	−	0.477509i	$-0.841540\pi$
$233$	−6.12279	+	6.12279i	−0.401117	+	0.401117i	0.477509	+	0.878627i	$0.341540\pi$
$234$	−4.70961			−0.307877
$235$	9.77756	−	3.91170i	0.637818	−	0.255171i
$236$			2.54975i			0.165975i
$237$	−5.46757	+	5.46757i	−0.355157	+	0.355157i
$238$		0			0
$239$			4.00294i			0.258929i	0.991584	+	0.129464i	$0.0413258\pi$
$239$			4.00294i			0.258929i	−0.991584	+	0.129464i	$0.958674\pi$
$240$	−0.975610	−	2.43860i	−0.0629753	−	0.157411i
$241$		−	17.3251i		−	1.11601i	−0.829838	−	0.558005i	$-0.811567\pi$
$241$		−	17.3251i		−	1.11601i	0.829838	−	0.558005i	$-0.188433\pi$
$242$	7.38774	+	7.38774i	0.474902	+	0.474902i
$243$	−10.2551	−	10.2551i	−0.657867	−	0.657867i
$244$	6.07359			0.388822
$245$		0			0
$246$	−0.960481			−0.0612380
$247$	−3.88878	−	3.88878i	−0.247437	−	0.247437i
$248$	2.42012	+	2.42012i	0.153678	+	0.153678i
$249$			15.3411i			0.972202i
$250$	4.65160	−	10.1667i	0.294193	−	0.643001i
$251$			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
$254$			15.8141i			0.992267i
$255$	15.8376	+	6.78641i	0.991787	+	0.424982i
$256$	1.00000			0.0625000
$257$	11.6742	−	11.6742i	0.728219	−	0.728219i	−0.242046	−	0.970265i	$-0.577818\pi$
$257$	11.6742	−	11.6742i	0.728219	−	0.728219i	0.970265	+	0.242046i	$0.0778184\pi$
$258$	−1.87456	−	1.87456i	−0.116705	−	0.116705i
$259$		0			0
$260$	−6.03449	+	2.41421i	−0.374243	+	0.149723i
$261$	15.7027			0.971972
$262$	6.78315	−	6.78315i	0.419064	−	0.419064i
$263$	−6.97267	+	6.97267i	−0.429953	+	0.429953i	−0.888612	−	0.458659i	$-0.848330\pi$
$263$	−6.97267	+	6.97267i	−0.429953	+	0.429953i	0.458659	+	0.888612i	$0.348330\pi$
$264$	0.872823			0.0537186
$265$	10.3508	−	4.14102i	0.635843	−	0.254381i
$266$		0			0
$267$	−5.01010	−	5.01010i	−0.306613	−	0.306613i
$268$	9.68124	−	9.68124i	0.591376	−	0.591376i
$269$	8.95844			0.546206			0.273103	−	0.961985i	$-0.411950\pi$
$269$	8.95844			0.546206			0.273103	+	0.961985i	$0.411950\pi$
$270$	−11.1543	−	4.77965i	−0.678832	−	0.290880i
$271$			22.8503i			1.38805i	0.719949	+	0.694027i	$0.244165\pi$
$271$			22.8503i			1.38805i	−0.719949	+	0.694027i	$0.755835\pi$
$272$	−4.63872	+	4.63872i	−0.281264	+	0.281264i
$273$		0			0
$274$		−	9.30954i		−	0.562410i
$275$	2.56264	+	2.69013i	0.154533	+	0.162221i
$276$		−	6.21538i		−	0.374122i
$277$	15.2263	+	15.2263i	0.914858	+	0.914858i	0.996649	−	0.0817915i	$-0.0260642\pi$
$277$	15.2263	+	15.2263i	0.914858	+	0.914858i	−0.0817915	+	0.996649i	$0.526064\pi$
$278$	15.6776	+	15.6776i	0.940278	+	0.940278i
$279$	5.54552			0.332002
$280$		0			0
$281$	−5.64885			−0.336982			−0.168491	−	0.985703i	$-0.553889\pi$
$281$	−5.64885			−0.336982			−0.168491	+	0.985703i	$0.553889\pi$
$282$	−3.91170	−	3.91170i	−0.232938	−	0.232938i
$283$	−2.07075	−	2.07075i	−0.123093	−	0.123093i	0.642876	−	0.765970i	$-0.277741\pi$
$283$	−2.07075	−	2.07075i	−0.123093	−	0.123093i	−0.765970	+	0.642876i	$0.777741\pi$
$284$		−	16.0173i		−	0.950450i
$285$	−1.84591	−	4.61397i	−0.109342	−	0.273308i
$286$		−	2.15986i		−	0.127715i
$287$		0			0
$288$	1.14571	−	1.14571i	0.0675116	−	0.0675116i
$289$		−	26.0354i		−	1.53149i
$290$	20.1201	−	8.04942i	1.18149	−	0.472678i
$291$	5.26076			0.308391
$292$	6.25834	−	6.25834i	0.366242	−	0.366242i
$293$	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
$296$	−2.67114			−0.155257
$297$	2.85154	−	2.85154i	0.165463	−	0.165463i
$298$	−2.78767	+	2.78767i	−0.161485	+	0.161485i
$299$	−15.3804			−0.889471
$300$	−5.87135	−	0.142505i	−0.338982	−	0.00822751i
$301$		0			0
$302$	14.1035	+	14.1035i	0.811564	+	0.811564i
$303$	−9.28724	+	9.28724i	−0.533538	+	0.533538i
$304$	1.89205			0.108517
$305$	5.34906	−	12.4832i	0.306287	−	0.714786i
$306$			10.6293i			0.607634i
$307$	−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	$0.339718\pi$
$308$		0			0
$309$		−	2.84982i		−	0.162121i
$310$	7.10556	−	2.84271i	0.403569	−	0.161455i
$311$		−	0.126019i		−	0.00714589i	−0.999994	−	0.00357294i	$-0.998863\pi$
$311$		−	0.126019i		−	0.00714589i	0.999994	−	0.00357294i	$-0.00113731\pi$
$312$	2.41421	+	2.41421i	0.136678	+	0.136678i
$313$	8.26887	+	8.26887i	0.467384	+	0.467384i	0.901066	−	0.433682i	$-0.142786\pi$
$313$	8.26887	+	8.26887i	0.467384	+	0.467384i	−0.433682	+	0.901066i	$0.642786\pi$
$314$	−7.46334			−0.421181
$315$		0			0
$316$	−6.58284			−0.370314
$317$	−7.74013	−	7.74013i	−0.434729	−	0.434729i	0.455505	−	0.890233i	$-0.349459\pi$
$317$	−7.74013	−	7.74013i	−0.434729	−	0.434729i	−0.890233	+	0.455505i	$0.849459\pi$
$318$	−4.14102	−	4.14102i	−0.232217	−	0.232217i
$319$			7.20137i			0.403199i
$320$	0.880708	−	2.05532i	0.0492331	−	0.114896i
$321$		−	7.80001i		−	0.435354i
$322$		0			0
$323$	−8.77670	+	8.77670i	−0.488349	+	0.488349i
$324$			1.51386i			0.0841031i
$325$	−0.352638	+	14.5291i	−0.0195608	+	0.805927i
$326$	−12.1665			−0.673843
$327$	7.44238	−	7.44238i	0.411565	−	0.411565i
$328$	−0.578200	−	0.578200i	−0.0319258	−	0.0319258i
$329$		0			0
$330$	0.768703	−	1.79393i	0.0423157	−	0.0987528i
$331$	−5.46038			−0.300129			−0.150065	−	0.988676i	$-0.547948\pi$
$331$	−5.46038			−0.300129			−0.150065	+	0.988676i	$0.547948\pi$
$332$	−9.23519	+	9.23519i	−0.506847	+	0.506847i
$333$	−3.06036	+	3.06036i	−0.167706	+	0.167706i
$334$	−2.05859			−0.112641
$335$	−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	$0.460625\pi$
$338$	−3.21825	+	3.21825i	−0.175050	+	0.175050i
$339$	0.511288			0.0277694
$340$	5.44871	+	13.6194i	0.295498	+	0.738617i
$341$			2.54322i			0.137723i
$342$	2.16775	−	2.16775i	0.117218	−	0.117218i
$343$		0			0
$344$		−	2.25693i		−	0.121685i
$345$	−12.7746	−	5.47394i	−0.687762	−	0.294707i
$346$			9.40807i			0.505781i
$347$	−15.2296	−	15.2296i	−0.817567	−	0.817567i	0.168188	−	0.985755i	$-0.446209\pi$
$347$	−15.2296	−	15.2296i	−0.817567	−	0.817567i	−0.985755	+	0.168188i	$0.946209\pi$
$348$	−8.04942	−	8.04942i	−0.431494	−	0.431494i
$349$	12.5744			0.673093			0.336546	−	0.941667i	$-0.390741\pi$
$349$	12.5744			0.673093			0.336546	+	0.941667i	$0.390741\pi$
$350$		0			0
$351$	15.7746			0.841987
$352$	0.525431	+	0.525431i	0.0280056	+	0.0280056i
$353$	0.487554	+	0.487554i	0.0259499	+	0.0259499i	0.719963	−	0.694013i	$-0.244159\pi$
$353$	0.487554	+	0.487554i	0.0259499	+	0.0259499i	−0.694013	+	0.719963i	$0.744159\pi$
$354$		−	2.99497i		−	0.159181i
$355$	−32.9206	−	14.1065i	−1.74725	−	0.748697i
$356$		−	6.03207i		−	0.319699i
$357$		0			0
$358$	3.18020	−	3.18020i	0.168079	−	0.168079i
$359$			22.0988i			1.16633i	0.812354	+	0.583165i	$0.198186\pi$
$359$			22.0988i			1.16633i	−0.812354	+	0.583165i	$0.801814\pi$
$360$	−1.34577	−	3.36384i	−0.0709282	−	0.177290i
$361$	−15.4201			−0.811586
$362$	−12.6466	+	12.6466i	−0.664691	+	0.664691i
$363$	−8.67775	−	8.67775i	−0.455464	−	0.455464i
$364$		0			0
$365$	−7.35115	−	18.3747i	−0.384777	−	0.961775i
$366$	−7.13414			−0.372907
$367$	−9.48295	+	9.48295i	−0.495006	+	0.495006i	−0.909879	−	0.414873i	$-0.863826\pi$
$367$	−9.48295	+	9.48295i	−0.495006	+	0.495006i	0.414873	+	0.909879i	$0.363826\pi$
$368$	3.74160	−	3.74160i	0.195044	−	0.195044i
$369$	−1.32490			−0.0689715
$370$	−2.35250	+	5.49006i	−0.122300	+	0.285415i
$371$		0			0
$372$	−2.84271	−	2.84271i	−0.147388	−	0.147388i
$373$	−10.5828	+	10.5828i	−0.547959	+	0.547959i	−0.925850	−	0.377891i	$-0.876649\pi$
$373$	−10.5828	+	10.5828i	−0.547959	+	0.547959i	0.377891	+	0.925850i	$0.376649\pi$
$374$	−4.87465			−0.252062
$375$	−5.46384	+	11.9420i	−0.282151	+	0.616683i
$376$		−	4.70961i		−	0.242880i
$377$	−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	$0.985952\pi$
$380$	1.66635	−	3.88878i	0.0854818	−	0.199490i
$381$		−	18.5755i		−	0.951653i
$382$	1.96256	+	1.96256i	0.100413	+	0.100413i
$383$	7.39499	+	7.39499i	0.377866	+	0.377866i	0.870332	−	0.492465i	$-0.163904\pi$
$383$	7.39499	+	7.39499i	0.377866	+	0.377866i	−0.492465	+	0.870332i	$0.663904\pi$
$384$	−1.17462			−0.0599418
$385$		0			0
$386$	5.14005			0.261622
$387$	−2.58579	−	2.58579i	−0.131443	−	0.131443i
$388$	3.16693	+	3.16693i	0.160776	+	0.160776i
$389$		−	21.7717i		−	1.10387i	−0.833888	−	0.551934i	$-0.813890\pi$
$389$		−	21.7717i		−	1.10387i	0.833888	−	0.551934i	$-0.186110\pi$
$390$	7.08821	−	2.83577i	0.358925	−	0.143595i
$391$			34.7124i			1.75548i
$392$		0			0
$393$	−7.96759	+	7.96759i	−0.401912	+	0.401912i
$394$		−	1.89566i		−	0.0955019i
$395$	−5.79756	+	13.5299i	−0.291707	+	0.680762i
$396$	1.20398			0.0605025
$397$	−22.4145	+	22.4145i	−1.12495	+	1.12495i	−0.133965	+	0.990986i	$0.542771\pi$
$397$	−22.4145	+	22.4145i	−1.12495	+	1.12495i	−0.990986	+	0.133965i	$0.957229\pi$
$398$	−10.2551	−	10.2551i	−0.514043	−	0.514043i
$399$		0			0
$400$	−3.44871	−	3.62028i	−0.172435	−	0.181014i
$401$	13.9706			0.697657			0.348828	−	0.937187i	$-0.386580\pi$
$401$	13.9706			0.697657			0.348828	+	0.937187i	$0.386580\pi$
$402$	−11.3717	+	11.3717i	−0.567171	+	0.567171i
$403$	−7.03449	+	7.03449i	−0.350413	+	0.350413i
$404$	−11.1817			−0.556308
$405$	3.11146	+	1.33327i	0.154610	+	0.0662505i
$406$		0			0
$407$	−1.40350	−	1.40350i	−0.0695690	−	0.0695690i
$408$	5.44871	−	5.44871i	0.269751	−	0.269751i
$409$	−18.7392			−0.926594			−0.463297	−	0.886203i	$-0.653334\pi$
$409$	−18.7392			−0.926594			−0.463297	+	0.886203i	$0.653334\pi$
$410$	−1.69761	+	0.679163i	−0.0838392	+	0.0335415i
$411$			10.9351i			0.539390i
$412$	1.71557	−	1.71557i	0.0845198	−	0.0845198i
$413$		0			0
$414$		−	8.57358i		−	0.421369i
$415$	10.8478	+	27.1148i	0.532497	+	1.33101i
$416$			2.90667i			0.142511i
$417$	−18.4151	−	18.4151i	−0.901792	−	0.901792i
$418$	0.994144	+	0.994144i	0.0486252	+	0.0486252i
$419$	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	$0.607171\pi$
$422$	−7.09399	−	7.09399i	−0.345330	−	0.345330i
$423$	−5.39585	−	5.39585i	−0.262355	−	0.262355i
$424$		−	4.98571i		−	0.242128i
$425$	32.7910	+	0.795878i	1.59060	+	0.0386058i
$426$			18.8141i			0.911547i
$427$		0			0
$428$	4.69553	−	4.69553i	0.226967	−	0.226967i
$429$			2.53701i			0.122488i
$430$	−4.63872	−	1.98769i	−0.223699	−	0.0958552i
$431$	13.2704			0.639210			0.319605	−	0.947551i	$-0.396450\pi$
$431$	13.2704			0.639210			0.319605	+	0.947551i	$0.396450\pi$
$432$	−3.83750	+	3.83750i	−0.184632	+	0.184632i
$433$	−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	$0.884329\pi$
$434$		0			0
$435$	−23.6334	+	9.45497i	−1.13313	+	0.453331i
$436$	8.96048			0.429129
$437$	7.07931	−	7.07931i	0.338649	−	0.338649i
$438$	−7.35115	+	7.35115i	−0.351251	+	0.351251i
$439$	35.0476			1.67273			0.836366	−	0.548172i	$-0.184676\pi$
$439$	35.0476			1.67273			0.836366	+	0.548172i	$0.184676\pi$
$440$	1.54268	−	0.617179i	0.0735445	−	0.0294229i
$441$		0			0
$442$	−13.4832	−	13.4832i	−0.641330	−	0.641330i
$443$	−0.0445958	+	0.0445958i	−0.00211881	+	0.00211881i	−0.708165	−	0.706047i	$-0.750477\pi$
$443$	−0.0445958	+	0.0445958i	−0.00211881	+	0.00211881i	0.706047	+	0.708165i	$0.250477\pi$
$444$	3.13756			0.148902
$445$	−12.3978	−	5.31249i	−0.587714	−	0.251836i
$446$			4.43718i			0.210107i
$447$	3.27444	−	3.27444i	0.154876	−	0.154876i
$448$		0			0
$449$		−	24.5207i		−	1.15720i	−0.815611	−	0.578601i	$-0.803599\pi$
$449$		−	24.5207i		−	1.15720i	0.815611	−	0.578601i	$-0.196401\pi$
$450$	−8.09901	−	0.196573i	−0.381791	−	0.00926653i
$451$		−	0.607609i		−	0.0286112i
$452$	0.307790	+	0.307790i	0.0144772	+	0.0144772i
$453$	−16.5662	−	16.5662i	−0.778346	−	0.778346i
$454$	0.670872			0.0314856
$455$		0			0
$456$	−2.22244			−0.104075
$457$	14.1939	+	14.1939i	0.663961	+	0.663961i	0.956311	−	0.292350i	$-0.0944374\pi$
$457$	14.1939	+	14.1939i	0.663961	+	0.663961i	−0.292350	+	0.956311i	$0.594437\pi$
$458$	−9.33616	−	9.33616i	−0.436250	−	0.436250i
$459$		−	35.6022i		−	1.66177i
$460$	−4.39494	−	10.9855i	−0.204915	−	0.512199i
$461$		−	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	$0.220961\pi$
$464$		−	9.69135i		−	0.449910i
$465$	−8.34630	+	3.33910i	−0.387050	+	0.154847i
$466$	8.65894			0.401117
$467$	−14.7933	+	14.7933i	−0.684552	+	0.684552i	−0.961022	−	0.276470i	$-0.910835\pi$
$467$	−14.7933	+	14.7933i	−0.684552	+	0.684552i	0.276470	+	0.961022i	$0.410835\pi$
$468$	3.33020	+	3.33020i	0.153938	+	0.153938i
$469$		0			0
$470$	−9.67977	−	4.14779i	−0.446495	−	0.191323i
$471$	8.76655			0.403941
$472$	1.80295	−	1.80295i	0.0829873	−	0.0829873i
$473$	1.18586	−	1.18586i	0.0545259	−	0.0545259i
$474$	7.73231			0.355157
$475$	−6.52514	−	6.84976i	−0.299394	−	0.314289i
$476$		0			0
$477$	−5.71218	−	5.71218i	−0.261543	−	0.261543i
$478$	2.83051	−	2.83051i	0.129464	−	0.129464i
$479$	−24.2837			−1.10955			−0.554775	−	0.832000i	$-0.687196\pi$
$479$	−24.2837			−1.10955			−0.554775	+	0.832000i	$0.687196\pi$
$480$	−1.03449	+	2.41421i	−0.0472179	+	0.110193i
$481$		−	7.76412i		−	0.354013i
$482$	−12.2507	+	12.2507i	−0.558005	+	0.558005i
$483$		0			0
$484$		−	10.4478i		−	0.474902i
$485$	9.29820	−	3.71992i	0.422210	−	0.168913i
$486$			14.5030i			0.657867i
$487$	1.80736	+	1.80736i	0.0818993	+	0.0818993i	0.746870	−	0.664970i	$-0.231556\pi$
$487$	1.80736	+	1.80736i	0.0818993	+	0.0818993i	−0.664970	+	0.746870i	$0.731556\pi$
$488$	−4.29468	−	4.29468i	−0.194411	−	0.194411i
$489$	14.2910			0.646262
$490$		0			0
$491$	14.5668			0.657391			0.328695	−	0.944436i	$-0.393391\pi$
$491$	14.5668			0.657391			0.328695	+	0.944436i	$0.393391\pi$
$492$	0.679163	+	0.679163i	0.0306190	+	0.0306190i
$493$	44.9554	+	44.9554i	2.02469	+	2.02469i
$494$			5.49957i			0.247437i
$495$	1.06036	−	2.47458i	0.0476596	−	0.111224i
$496$		−	3.42257i		−	0.153678i
$497$		0			0
$498$	10.8478	−	10.8478i	0.486101	−	0.486101i
$499$		−	30.0875i		−	1.34690i	−0.739233	−	0.673450i	$-0.764812\pi$
$499$		−	30.0875i		−	1.34690i	0.739233	−	0.673450i	$-0.235188\pi$
$500$	−10.4781	+	3.89980i	−0.468597	+	0.174404i
$501$	2.41805			0.108030
$502$	3.88865	−	3.88865i	0.173559	−	0.173559i
$503$	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
$506$	3.93191			0.174795
$507$	3.78021	−	3.78021i	0.167885	−	0.167885i
$508$	11.1823	−	11.1823i	0.496134	−	0.496134i
$509$	12.4504			0.551855			0.275927	−	0.961178i	$-0.411015\pi$
$509$	12.4504			0.551855			0.275927	+	0.961178i	$0.411015\pi$
$510$	−6.40013	−	15.9976i	−0.283403	−	0.708384i
$511$		0			0
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−7.26076	+	7.26076i	−0.320571	+	0.320571i
$514$	−16.5099			−0.728219
$515$	−2.01513	−	5.03695i	−0.0887972	−	0.221955i
$516$			2.65102i			0.116705i
$517$	2.47458	−	2.47458i	0.108832	−	0.108832i
$518$		0			0
$519$		−	11.0509i		−	0.485079i
$520$	5.97414	+	2.55992i	0.261983	+	0.112260i
$521$			35.3351i			1.54806i	0.633149	+	0.774030i	$0.281762\pi$
$521$			35.3351i			1.54806i	−0.633149	+	0.774030i	$0.718238\pi$
$522$	−11.1035	−	11.1035i	−0.485986	−	0.485986i
$523$	11.6252	+	11.6252i	0.508336	+	0.508336i	0.914015	−	0.405680i	$-0.132965\pi$
$523$	11.6252	+	11.6252i	0.508336	+	0.508336i	−0.405680	+	0.914015i	$0.632965\pi$
$524$	−9.59282			−0.419064
$525$		0			0
$526$	9.86084			0.429953
$527$	15.8763	+	15.8763i	0.691584	+	0.691584i
$528$	−0.617179	−	0.617179i	−0.0268593	−	0.0268593i
$529$		−	4.99914i		−	0.217354i
$530$	−10.2473	−	4.39096i	−0.445112	−	0.190731i
$531$		−	4.13131i		−	0.179283i
$532$		0			0
$533$	1.68063	−	1.68063i	0.0727964	−	0.0727964i
$534$			7.08536i			0.306613i
$535$	−5.51544	−	13.7862i	−0.238453	−	0.596031i
$536$	−13.6913			−0.591376
$537$	−3.73552	+	3.73552i	−0.161199	+	0.161199i
$538$	−6.33457	−	6.33457i	−0.273103	−	0.273103i
$539$		0			0
$540$	4.50759	+	11.2670i	0.193976	+	0.484856i
$541$	−26.5143			−1.13994			−0.569970	−	0.821665i	$-0.693045\pi$
$541$	−26.5143			−1.13994			−0.569970	+	0.821665i	$0.693045\pi$
$542$	16.1576	−	16.1576i	0.694027	−	0.694027i
$543$	14.8549	−	14.8549i	0.637485	−	0.637485i
$544$	6.56014			0.281264
$545$	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	$0.760338\pi$
$548$	−6.58284	+	6.58284i	−0.281205	+	0.281205i
$549$	−9.84092			−0.420000
$550$	0.0901497	−	3.71427i	0.00384400	−	0.158377i
$551$		−	18.3366i		−	0.781163i
$552$	−4.39494	+	4.39494i	−0.187061	+	0.187061i
$553$		0			0
$554$		−	21.5332i		−	0.914858i
$555$	2.76328	−	6.44871i	0.117295	−	0.273732i
$556$		−	22.1714i		−	0.940278i
$557$	10.9914	+	10.9914i	0.465721	+	0.465721i	0.900525	−	0.434804i	$-0.143182\pi$
$557$	10.9914	+	10.9914i	0.465721	+	0.465721i	−0.434804	+	0.900525i	$0.643182\pi$
$558$	−3.92128	−	3.92128i	−0.166001	−	0.166001i
$559$	6.56014			0.277464
$560$		0			0
$561$	5.72584			0.241745
$562$	3.99434	+	3.99434i	0.168491	+	0.168491i
$563$	−19.4073	−	19.4073i	−0.817919	−	0.817919i	0.167887	−	0.985806i	$-0.446305\pi$
$563$	−19.4073	−	19.4073i	−0.817919	−	0.817919i	−0.985806	+	0.167887i	$0.946305\pi$
$564$			5.53198i			0.232938i
$565$	0.903682	−	0.361535i	0.0380182	−	0.0152099i
$566$			2.92849i			0.123093i
$567$		0			0
$568$	−11.3259	+	11.3259i	−0.475225	+	0.475225i
$569$			6.75739i			0.283284i	0.989918	+	0.141642i	$0.0452383\pi$
$569$			6.75739i			0.283284i	−0.989918	+	0.141642i	$0.954762\pi$
$570$	−1.95732	+	4.56782i	−0.0819830	+	0.191325i
$571$	11.7544			0.491907			0.245953	−	0.969282i	$-0.420899\pi$
$571$	11.7544			0.491907			0.245953	+	0.969282i	$0.420899\pi$
$572$	−1.52725	+	1.52725i	−0.0638576	+	0.0638576i
$573$	−2.30526	−	2.30526i	−0.0963034	−	0.0963034i
$574$		0			0
$575$	−26.4493	−	0.641957i	−1.10301	−	0.0267715i
$576$	−1.62028			−0.0675116
$577$	−1.59488	+	1.59488i	−0.0663958	+	0.0663958i	−0.739525	−	0.673129i	$-0.764950\pi$
$577$	−1.59488	+	1.59488i	−0.0663958	+	0.0663958i	0.673129	+	0.739525i	$0.264950\pi$
$578$	−18.4098	+	18.4098i	−0.765747	+	0.765747i
$579$	−6.03758			−0.250913
$580$	−19.9189	−	8.53525i	−0.827085	−	0.354407i
$581$		0			0
$582$	−3.71992	−	3.71992i	−0.154196	−	0.154196i
$583$	2.61965	−	2.61965i	0.108495	−	0.108495i
$584$	−8.85064			−0.366242
$585$	9.77756	−	3.91170i	0.404253	−	0.161729i
$586$		−	15.2558i		−	0.630212i
$587$	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
$590$	−2.11777	−	5.29350i	−0.0871871	−	0.217930i
$591$			2.22667i			0.0915929i
$592$	1.88878	+	1.88878i	0.0776285	+	0.0776285i
$593$	−25.7074	−	25.7074i	−1.05568	−	1.05568i	−0.998356	−	0.0573221i	$-0.981744\pi$
$593$	−25.7074	−	25.7074i	−1.05568	−	1.05568i	−0.0573221	−	0.998356i	$-0.518256\pi$
$594$	−4.03269			−0.165463
$595$		0			0
$596$	3.94236			0.161485
$597$	12.0458	+	12.0458i	0.493003	+	0.493003i
$598$	10.8756	+	10.8756i	0.444736	+	0.444736i
$599$			35.7717i			1.46159i	0.682596	+	0.730796i	$0.260851\pi$
$599$			35.7717i			1.46159i	−0.682596	+	0.730796i	$0.739149\pi$
$600$	4.05090	+	4.25243i	0.165377	+	0.173605i
$601$			45.6631i			1.86264i	0.364204	+	0.931319i	$0.381341\pi$
$601$			45.6631i			1.86264i	−0.364204	+	0.931319i	$0.618659\pi$
$602$		0			0
$603$	−15.6863	+	15.6863i	−0.638796	+	0.638796i
$604$		−	19.9453i		−	0.811564i
$605$	−21.4737	−	9.20150i	−0.873030	−	0.374094i
$606$	13.1341			0.533538
$607$	−0.828325	+	0.828325i	−0.0336207	+	0.0336207i	−0.723717	−	0.690097i	$-0.757568\pi$
$607$	−0.828325	+	0.828325i	−0.0336207	+	0.0336207i	0.690097	+	0.723717i	$0.257568\pi$
$608$	−1.33788	−	1.33788i	−0.0542584	−	0.0542584i
$609$		0			0
$610$	−12.6093	+	5.04460i	−0.510536	+	0.204250i
$611$	13.6893			0.553808
$612$	7.51602	−	7.51602i	0.303817	−	0.303817i
$613$	−9.85551	+	9.85551i	−0.398060	+	0.398060i	−0.877548	−	0.479488i	$-0.840822\pi$
$613$	−9.85551	+	9.85551i	−0.398060	+	0.398060i	0.479488	+	0.877548i	$0.340822\pi$
$614$	9.74677			0.393348
$615$	1.99404	−	0.797755i	0.0804076	−	0.0321686i
$616$		0			0
$617$	22.7725	+	22.7725i	0.916788	+	0.916788i	0.996794	−	0.0800065i	$-0.0254941\pi$
$617$	22.7725	+	22.7725i	0.916788	+	0.916788i	−0.0800065	+	0.996794i	$0.525494\pi$
$618$	−2.01513	+	2.01513i	−0.0810604	+	0.0810604i
$619$	22.6773			0.911476			0.455738	−	0.890114i	$-0.349375\pi$
$619$	22.6773			0.911476			0.455738	+	0.890114i	$0.349375\pi$
$620$	−7.03449	−	3.01429i	−0.282512	−	0.121057i
$621$			28.7168i			1.15237i
$622$	−0.0891090	+	0.0891090i	−0.00357294	+	0.00357294i
$623$		0			0
$624$		−	3.41421i		−	0.136678i
$625$	−1.21285	+	24.9706i	−0.0485138	+	0.998823i
$626$		−	11.6940i		−	0.467384i
$627$	−1.16774	−	1.16774i	−0.0466349	−	0.0466349i
$628$	5.27738	+	5.27738i	0.210590	+	0.210590i
$629$	−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	$0.276720\pi$
$632$	4.65477	+	4.65477i	0.185157	+	0.185157i
$633$	8.33270	+	8.33270i	0.331195	+	0.331195i
$634$			10.9462i			0.434729i
$635$	−13.1349	−	32.8315i	−0.521242	−	1.30288i
$636$			5.85629i			0.232217i
$637$		0			0
$638$	5.09214	−	5.09214i	0.201600	−	0.201600i
$639$			25.9524i			1.02666i
$640$	−2.07609	+	0.830578i	−0.0820646	+	0.0328315i
$641$	−0.856140			−0.0338155			−0.0169077	−	0.999857i	$-0.505382\pi$
$641$	−0.856140			−0.0338155			−0.0169077	+	0.999857i	$0.505382\pi$
$642$	−5.51544	+	5.51544i	−0.217677	+	0.217677i
$643$	−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	$0.901445\pi$
$644$		0			0
$645$	5.44871	+	2.33478i	0.214543	+	0.0919317i
$646$	12.4121			0.488349
$647$	33.5510	−	33.5510i	1.31903	−	1.31903i	0.404482	−	0.914546i	$-0.367452\pi$
$647$	33.5510	−	33.5510i	1.31903	−	1.31903i	0.914546	−	0.404482i	$-0.132548\pi$
$648$	1.07046	−	1.07046i	0.0420516	−	0.0420516i
$649$	1.89465			0.0743714
$650$	10.5229	−	10.0242i	0.412744	−	0.393183i
$651$		0			0
$652$	8.60305	+	8.60305i	0.336921	+	0.336921i
$653$	18.5780	−	18.5780i	0.727015	−	0.727015i	−0.243009	−	0.970024i	$-0.578134\pi$
$653$	18.5780	−	18.5780i	0.727015	−	0.727015i	0.970024	+	0.243009i	$0.0781344\pi$
$654$	−10.5251			−0.411565
$655$	−8.44848	+	19.7163i	−0.330109	+	0.770381i
$656$			0.817699i			0.0319258i
$657$	−10.1403	+	10.1403i	−0.395609	+	0.395609i
$658$		0			0
$659$			26.2355i			1.02199i	0.859583	+	0.510996i	$0.170723\pi$
$659$			26.2355i			1.02199i	−0.859583	+	0.510996i	$0.829277\pi$
$660$	−1.81206	+	0.724948i	−0.0705343	+	0.0282186i
$661$		−	14.5719i		−	0.566782i	−0.959004	−	0.283391i	$-0.908541\pi$
$661$		−	14.5719i		−	0.566782i	0.959004	−	0.283391i	$-0.0914595\pi$
$662$	3.86107	+	3.86107i	0.150065	+	0.150065i
$663$	15.8376	+	15.8376i	0.615080	+	0.615080i
$664$	13.0605			0.506847
$665$		0			0
$666$	4.32800			0.167706
$667$	−36.2611	−	36.2611i	−1.40404	−	1.40404i
$668$	1.45564	+	1.45564i	0.0563205	+	0.0563205i
$669$		−	5.21198i		−	0.201507i
$670$	−12.0581	+	28.1401i	−0.465844	+	1.08715i
$671$		−	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	$0.397708\pi$
$674$		−	28.9664i		−	1.11574i
$675$	27.1273	+	0.658412i	1.04413	+	0.0253423i
$676$	4.55129			0.175050
$677$	−16.0965	+	16.0965i	−0.618638	+	0.618638i	−0.945182	−	0.326544i	$-0.894116\pi$
$677$	−16.0965	+	16.0965i	−0.618638	+	0.618638i	0.326544	+	0.945182i	$0.394116\pi$
$678$	−0.361535	−	0.361535i	−0.0138847	−	0.0138847i
$679$		0			0
$680$	5.77756	−	13.4832i	0.221559	−	0.517057i
$681$	−0.788016			−0.0301968
$682$	1.79833	−	1.79833i	0.0688615	−	0.0688615i
$683$	21.6661	−	21.6661i	0.829030	−	0.829030i	−0.158353	−	0.987383i	$-0.550618\pi$
$683$	21.6661	−	21.6661i	0.829030	−	0.829030i	0.987383	+	0.158353i	$0.0506183\pi$
$684$	−3.06566			−0.117218
$685$	7.73231	+	19.3274i	0.295436	+	0.738463i
$686$		0			0
$687$	10.9664	+	10.9664i	0.418394	+	0.418394i
$688$	−1.59589	+	1.59589i	−0.0608427	+	0.0608427i
$689$	14.4918			0.552094
$690$	5.16236	+	12.9037i	0.196528	+	0.491235i
$691$		−	32.0180i		−	1.21802i	−0.793161	−	0.609012i	$-0.791566\pi$
$691$		−	32.0180i		−	1.21802i	0.793161	−	0.609012i	$-0.208434\pi$
$692$	6.65251	−	6.65251i	0.252891	−	0.252891i
$693$		0			0
$694$			21.5379i			0.817567i
$695$	−45.5694	−	19.5266i	−1.72855	−	0.740684i
$696$			11.3836i			0.431494i
$697$	−3.79307	−	3.79307i	−0.143673	−	0.143673i
$698$	−8.89145	−	8.89145i	−0.336546	−	0.336546i
$699$	−10.1709			−0.384699
$700$		0			0
$701$	−18.5294			−0.699844			−0.349922	−	0.936779i	$-0.613792\pi$
$701$	−18.5294			−0.699844			−0.349922	+	0.936779i	$0.613792\pi$
$702$	−11.1543	−	11.1543i	−0.420993	−	0.420993i
$703$	3.57368	+	3.57368i	0.134784	+	0.134784i
$704$		−	0.743072i		−	0.0280056i
$705$	11.3700	+	4.87206i	0.428219	+	0.183492i
$706$		−	0.689506i		−	0.0259499i
$707$		0			0
$708$	−2.11777	+	2.11777i	−0.0795905	+	0.0795905i
$709$			26.6822i			1.00207i	0.865427	+	0.501035i	$0.167047\pi$
$709$			26.6822i			1.00207i	−0.865427	+	0.501035i	$0.832953\pi$
$710$	13.3036	+	33.2532i	0.499275	+	1.24797i
$711$	10.6660			0.400008
$712$	−4.26531	+	4.26531i	−0.159849	+	0.159849i
$713$	−12.8059	−	12.8059i	−0.479585	−	0.479585i
$714$		0			0
$715$	1.79393	+	4.48406i	0.0670893	+	0.167694i
$716$	−4.49749			−0.168079
$717$	−3.32476	+	3.32476i	−0.124165	+	0.124165i
$718$	15.6262	−	15.6262i	0.583165	−	0.583165i
$719$	31.9779			1.19258			0.596288	−	0.802771i	$-0.296642\pi$
$719$	31.9779			1.19258			0.596288	+	0.802771i	$0.296642\pi$
$720$	−1.42699	+	3.33020i	−0.0531809	+	0.124109i
$721$		0			0
$722$	10.9037	+	10.9037i	0.405793	+	0.405793i
$723$	14.3899	−	14.3899i	0.535165	−	0.535165i
$724$	17.8850			0.664691
$725$	−35.0854	+	33.4226i	−1.30304	+	1.24128i
$726$			12.2722i			0.455464i
$727$	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	$0.0597885\pi$
$728$		0			0
$729$		−	21.5770i		−	0.799146i
$730$	−7.79483	+	18.1909i	−0.288499	+	0.673276i
$731$		−	14.8058i		−	0.547611i
$732$	5.04460	+	5.04460i	0.186454	+	0.186454i
$733$	9.20125	+	9.20125i	0.339856	+	0.339856i	0.856313	−	0.516457i	$-0.172749\pi$
$733$	9.20125	+	9.20125i	0.339856	+	0.339856i	−0.516457	+	0.856313i	$0.672749\pi$
$734$	13.4109			0.495006
$735$		0			0
$736$	−5.29142			−0.195044
$737$	−7.19386	−	7.19386i	−0.264989	−	0.264989i
$738$	0.936846	+	0.936846i	0.0344858	+	0.0344858i
$739$		−	3.60424i		−	0.132584i	−0.997800	−	0.0662920i	$-0.978883\pi$
$739$		−	3.60424i		−	0.132584i	0.997800	−	0.0662920i	$-0.0211169\pi$
$740$	5.54552	−	2.21859i	0.203858	−	0.0815571i
$741$		−	6.45988i		−	0.237309i
$742$		0			0
$743$	31.1070	−	31.1070i	1.14121	−	1.14121i	0.152977	−	0.988230i	$-0.451114\pi$
$743$	31.1070	−	31.1070i	1.14121	−	1.14121i	0.988230	−	0.152977i	$-0.0488859\pi$
$744$			4.02021i			0.147388i
$745$	3.47207	−	8.10282i	0.127207	−	0.296864i
$746$	14.9664			0.547959
$747$	14.9636	−	14.9636i	0.547489	−	0.547489i
$748$	3.44690	+	3.44690i	0.126031	+	0.126031i
$749$		0			0
$750$	12.3078	−	4.58076i	0.449417	−	0.167266i
$751$	−51.0282			−1.86205			−0.931023	−	0.364960i	$-0.881083\pi$
$751$	−51.0282			−1.86205			−0.931023	+	0.364960i	$0.881083\pi$
$752$	−3.33020	+	3.33020i	−0.121440	+	0.121440i
$753$	−4.56766	+	4.56766i	−0.166455	+	0.166455i
$754$	28.1695			1.02587
$755$	−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	$0.507993\pi$
$758$	1.21470	−	1.21470i	0.0441198	−	0.0441198i
$759$	−4.61848			−0.167640
$760$	−3.92807	+	1.57150i	−0.142486	+	0.0570043i
$761$			29.8782i			1.08309i	0.840673	+	0.541543i	$0.182160\pi$
$761$			29.8782i			1.08309i	−0.840673	+	0.541543i	$0.817840\pi$
$762$	−13.1349	+	13.1349i	−0.475827	+	0.475827i
$763$		0			0
$764$		−	2.77548i		−	0.100413i
$765$	−8.82843	−	22.0673i	−0.319192	−	0.797844i
$766$		−	10.4581i		−	0.377866i
$767$	5.24056	+	5.24056i	0.189226	+	0.189226i
$768$	0.830578	+	0.830578i	0.0299709	+	0.0299709i
$769$	44.7341			1.61315			0.806576	−	0.591130i	$-0.201318\pi$
$769$	44.7341			1.61315			0.806576	+	0.591130i	$0.201318\pi$
$770$		0			0
$771$	19.3927			0.698413
$772$	−3.63457	−	3.63457i	−0.130811	−	0.130811i
$773$	−17.0808	−	17.0808i	−0.614355	−	0.614355i	0.329723	−	0.944078i	$-0.393045\pi$
$773$	−17.0808	−	17.0808i	−0.614355	−	0.614355i	−0.944078	+	0.329723i	$0.893045\pi$
$774$			3.65685i			0.131443i
$775$	−12.3907	+	11.8034i	−0.445086	+	0.423992i
$776$		−	4.47871i		−	0.160776i
$777$		0			0
$778$	−15.3949	+	15.3949i	−0.551934	+	0.551934i
$779$			1.54713i			0.0554317i
$780$	−7.01731	−	3.00693i	−0.251260	−	0.107665i
$781$	−11.9020			−0.425886
$782$	24.5454	−	24.5454i	0.877742	−	0.877742i
$783$	37.1906	+	37.1906i	1.32908	+	1.32908i
$784$		0			0
$785$	15.4945	−	6.19889i	0.553024	−	0.221248i
$786$	11.2679			0.401912
$787$	−8.97996	+	8.97996i	−0.320101	+	0.320101i	−0.848806	−	0.528705i	$-0.822678\pi$
$787$	−8.97996	+	8.97996i	−0.320101	+	0.320101i	0.528705	+	0.848806i	$0.322678\pi$
$788$	−1.34043	+	1.34043i	−0.0477510	+	0.0477510i
$789$	−11.5827			−0.412355
$790$	13.6666	−	5.46757i	0.486234	−	0.194527i
$791$		0			0
$792$	−0.851345	−	0.851345i	−0.0302512	−	0.0302512i
$793$	12.4832	−	12.4832i	0.443291	−	0.443291i
$794$	31.6989			1.12495
$795$	12.0366	+	5.15768i	0.426893	+	0.182924i
$796$			14.5030i			0.514043i
$797$	−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
$800$	−0.121320	+	4.99853i	−0.00428932	+	0.176725i
$801$			9.77363i			0.345334i
$802$	−9.87868	−	9.87868i	−0.348828	−	0.348828i
$803$	−4.65040	−	4.65040i	−0.164109	−	0.164109i
$804$	16.0821			0.567171
$805$		0			0
$806$	9.94828			0.350413
$807$	7.44069	+	7.44069i	0.261925	+	0.261925i
$808$	7.90662	+	7.90662i	0.278154	+	0.278154i
$809$			27.4567i			0.965326i	0.875806	+	0.482663i	$0.160330\pi$
$809$			27.4567i			0.965326i	−0.875806	+	0.482663i	$0.839670\pi$
$810$	−1.25738	−	3.14290i	−0.0441797	−	0.110430i
$811$			12.7335i			0.447132i	0.974689	+	0.223566i	$0.0717699\pi$
$811$			12.7335i			0.447132i	−0.974689	+	0.223566i	$0.928230\pi$
$812$		0			0
$813$	−18.9789	+	18.9789i	−0.665620	+	0.665620i
$814$			1.98485i			0.0695690i
$815$	25.2588	−	10.1053i	0.884778	−	0.353972i
$816$	−7.70563			−0.269751
$817$	−3.01951	+	3.01951i	−0.105639	+	0.105639i
$818$	13.2506	+	13.2506i	0.463297	+	0.463297i
$819$		0			0
$820$	1.68063	+	0.720154i	0.0586903	+	0.0251489i
$821$	30.3414			1.05892			0.529461	−	0.848334i	$-0.322394\pi$
$821$	30.3414			1.05892			0.529461	+	0.848334i	$0.322394\pi$
$822$	7.73231	−	7.73231i	0.269695	−	0.269695i
$823$	7.19388	−	7.19388i	0.250763	−	0.250763i	−0.570520	−	0.821283i	$-0.693258\pi$
$823$	7.19388	−	7.19388i	0.250763	−	0.250763i	0.821283	+	0.570520i	$0.193258\pi$
$824$	−2.42618			−0.0845198
$825$	−0.105891	+	4.36283i	−0.00368666	+	0.151894i
$826$		0			0
$827$	−15.9794	−	15.9794i	−0.555660	−	0.555660i	0.372409	−	0.928069i	$-0.378532\pi$
$827$	−15.9794	−	15.9794i	−0.555660	−	0.555660i	−0.928069	+	0.372409i	$0.878532\pi$
$828$	−6.06244	+	6.06244i	−0.210684	+	0.210684i
$829$	−6.34895			−0.220508			−0.110254	−	0.993903i	$-0.535166\pi$
$829$	−6.34895			−0.220508			−0.110254	+	0.993903i	$0.535166\pi$
$830$	11.5025	−	26.8436i	0.399258	−	0.931755i
$831$			25.2932i			0.877412i
$832$	2.05532	−	2.05532i	0.0712555	−	0.0712555i
$833$		0			0
$834$			26.0429i			0.901792i
$835$	4.27381	−	1.70982i	0.147901	−	0.0591707i
$836$		−	1.40593i		−	0.0486252i
$837$	13.1341	+	13.1341i	0.453982	+	0.453982i
$838$	−22.3265	−	22.3265i	−0.771255	−	0.771255i
$839$	−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
$842$	9.58616	+	9.58616i	0.330361	+	0.330361i
$843$	−4.69182	−	4.69182i	−0.161595	−	0.161595i
$844$			10.0324i			0.345330i
$845$	4.00836	−	9.35438i	0.137892	−	0.321800i
$846$			7.63089i			0.262355i
$847$		0			0
$848$	−3.52543	+	3.52543i	−0.121064	+	0.121064i
$849$		−	3.43984i		−	0.118055i
$850$	−22.6240	−	23.7495i	−0.775996	−	0.814602i
$851$	14.1341			0.484512
$852$	13.3036	−	13.3036i	0.455773	−	0.455773i
$853$	−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	$0.886252\pi$
$854$		0			0
$855$	−2.69995	+	6.30091i	−0.0923363	+	0.215487i
$856$	−6.64048			−0.226967
$857$	−11.9087	+	11.9087i	−0.406795	+	0.406795i	−0.880619	−	0.473824i	$-0.842873\pi$
$857$	−11.9087	+	11.9087i	−0.406795	+	0.406795i	0.473824	+	0.880619i	$0.342873\pi$
$858$	1.79393	−	1.79393i	0.0612439	−	0.0612439i
$859$	−30.8690			−1.05324			−0.526619	−	0.850102i	$-0.676540\pi$
$859$	−30.8690			−1.05324			−0.526619	+	0.850102i	$0.676540\pi$
$860$	1.87456	+	4.68558i	0.0639218	+	0.159777i
$861$		0			0
$862$	−9.38356	−	9.38356i	−0.319605	−	0.319605i
$863$	−0.914392	+	0.914392i	−0.0311263	+	0.0311263i	−0.722499	−	0.691372i	$-0.757006\pi$
$863$	−0.914392	+	0.914392i	−0.0311263	+	0.0311263i	0.691372	+	0.722499i	$0.257006\pi$
$864$	5.42705			0.184632
$865$	−7.81414	−	19.5320i	−0.265689	−	0.664107i
$866$			17.0462i			0.579252i
$867$	21.6244	−	21.6244i	0.734404	−	0.734404i
$868$		0			0
$869$			4.89152i			0.165934i
$870$	23.3970	+	10.0256i	0.793232	+	0.339901i
$871$		−	39.7962i		−	1.34844i
$872$	−6.33602	−	6.33602i	−0.214565	−	0.214565i
$873$	−5.13131	−	5.13131i	−0.173669	−	0.173669i
$874$	−10.0117			−0.338649
$875$		0			0
$876$	10.3961			0.351251
$877$	6.86229	+	6.86229i	0.231723	+	0.231723i	0.813412	−	0.581689i	$-0.197608\pi$
$877$	6.86229	+	6.86229i	0.231723	+	0.231723i	−0.581689	+	0.813412i	$0.697608\pi$
$878$	−24.7824	−	24.7824i	−0.836366	−	0.836366i
$879$			17.9197i			0.604416i
$880$	−1.52725	−	0.654429i	−0.0514837	−	0.0220608i
$881$		−	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	$0.0587913\pi$
$884$			19.0681i			0.641330i
$885$	2.48756	+	6.21783i	0.0836184	+	0.209010i
$886$	0.0630679			0.00211881
$887$	27.4700	−	27.4700i	0.922352	−	0.922352i	−0.0748434	−	0.997195i	$-0.523846\pi$
$887$	27.4700	−	27.4700i	0.922352	−	0.922352i	0.997195	+	0.0748434i	$0.0238457\pi$
$888$	−2.21859	−	2.21859i	−0.0744511	−	0.0744511i
$889$		0			0
$890$	5.01010	+	12.5231i	0.167939	+	0.419775i
$891$	1.12490			0.0376857
$892$	3.13756	−	3.13756i	0.105053	−	0.105053i
$893$	−6.30091	+	6.30091i	−0.210852	+	0.210852i
$894$	−4.63075			−0.154876
$895$	−3.96097	+	9.24379i	−0.132401	+	0.308986i
$896$		0			0
$897$	−12.7746	−	12.7746i	−0.426532	−	0.426532i
$898$	−17.3387	+	17.3387i	−0.578601	+	0.578601i
$899$	−33.1693			−1.10626
$900$	5.58787	+	5.86586i	0.186262	+	0.195529i
$901$		−	32.7070i		−	1.08963i
$902$	−0.429644	+	0.429644i	−0.0143056	+	0.0143056i
$903$		0			0
$904$		−	0.435281i		−	0.0144772i
$905$	15.7515	−	36.7595i	0.523597	−	1.22193i
$906$			23.4281i			0.778346i
$907$	24.5269	+	24.5269i	0.814403	+	0.814403i	0.985291	−	0.170887i	$-0.0546634\pi$
$907$	24.5269	+	24.5269i	0.814403	+	0.814403i	−0.170887	+	0.985291i	$0.554663\pi$
$908$	−0.474378	−	0.474378i	−0.0157428	−	0.0157428i
$909$	18.1174			0.600916
$910$		0			0
$911$	48.1523			1.59536			0.797678	−	0.603083i	$-0.206061\pi$
$911$	48.1523			1.59536			0.797678	+	0.603083i	$0.206061\pi$
$912$	1.57150	+	1.57150i	0.0520375	+	0.0520375i
$913$	6.86241	+	6.86241i	0.227113	+	0.227113i
$914$		−	20.0731i		−	0.663961i
$915$	14.8111	−	5.92546i	0.489640	−	0.195890i
$916$			13.2033i			0.436250i
$917$		0			0
$918$	−25.1745	+	25.1745i	−0.830884	+	0.830884i
$919$		−	17.8103i		−	0.587508i	−0.955881	−	0.293754i	$-0.905095\pi$
$919$		−	17.8103i		−	0.587508i	0.955881	−	0.293754i	$-0.0949046\pi$
$920$	−4.66020	+	10.8756i	−0.153642	+	0.358557i
$921$	−11.4487			−0.377248
$922$	−8.26887	+	8.26887i	−0.272321	+	0.272321i
$923$	−32.9206	−	32.9206i	−1.08360	−	1.08360i
$924$		0			0
$925$	0.324064	−	13.3518i	0.0106552	−	0.439004i
$926$	−3.92056			−0.128838
$927$	−2.77970	+	2.77970i	−0.0912972	+	0.0912972i
$928$	−6.85282	+	6.85282i	−0.224955	+	0.224955i
$929$	−32.2651			−1.05858			−0.529292	−	0.848440i	$-0.677542\pi$
$929$	−32.2651			−1.05858			−0.529292	+	0.848440i	$0.677542\pi$
$930$	8.26282	+	3.54063i	0.270949	+	0.116102i
$931$		0			0
$932$	−6.12279	−	6.12279i	−0.200559	−	0.200559i
$933$	0.104669	−	0.104669i	0.00342670	−	0.00342670i
$934$	20.9209			0.684552
$935$	10.1202	−	4.04878i	0.330966	−	0.132409i
$936$		−	4.70961i		−	0.153938i
$937$	−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	$0.483318\pi$
$938$		0			0
$939$			13.7359i			0.448254i
$940$	3.91170	+	9.77756i	0.127586	+	0.318909i
$941$			35.6375i			1.16175i	0.813993	+	0.580874i	$0.197289\pi$
$941$			35.6375i			1.16175i	−0.813993	+	0.580874i	$0.802711\pi$
$942$	−6.19889	−	6.19889i	−0.201971	−	0.201971i
$943$	3.05950	+	3.05950i	0.0996310	+	0.0996310i
$944$	−2.54975			−0.0829873
$945$		0			0
$946$	−1.67706			−0.0545259
$947$	9.86678	+	9.86678i	0.320627	+	0.320627i	0.849008	−	0.528381i	$-0.177201\pi$
$947$	9.86678	+	9.86678i	0.320627	+	0.320627i	−0.528381	+	0.849008i	$0.677201\pi$
$948$	−5.46757	−	5.46757i	−0.177578	−	0.177578i
$949$		−	25.7258i		−	0.835096i
$950$	−0.229545	+	9.45748i	−0.00744741	+	0.306841i
$951$		−	12.8576i		−	0.416935i
$952$		0			0
$953$	25.4475	−	25.4475i	0.824326	−	0.824326i	−0.162399	−	0.986725i	$-0.551923\pi$
$953$	25.4475	−	25.4475i	0.824326	−	0.824326i	0.986725	+	0.162399i	$0.0519232\pi$
$954$			8.07825i			0.261543i
$955$	−5.70451	−	2.44439i	−0.184594	−	0.0790986i
$956$	−4.00294			−0.129464
$957$	−5.98130	+	5.98130i	−0.193348	+	0.193348i
$958$	17.1712	+	17.1712i	0.554775	+	0.554775i
$959$		0			0
$960$	2.43860	−	0.975610i	0.0787056	−	0.0314877i
$961$	19.2860			0.622129
$962$	−5.49006	+	5.49006i	−0.177007	+	0.177007i
$963$	−7.60807	+	7.60807i	−0.245167	+	0.245167i
$964$	17.3251			0.558005
$965$	−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	$-0.532149\pi$
$968$	−7.38774	+	7.38774i	−0.237451	+	0.237451i
$969$	−14.5795			−0.468360
$970$	−9.20520	−	3.94444i	−0.295561	−	0.126648i
$971$		−	4.70594i		−	0.151021i	−0.997145	−	0.0755105i	$-0.975941\pi$
$971$		−	4.70594i		−	0.151021i	0.997145	−	0.0755105i	$-0.0240586\pi$
$972$	10.2551	−	10.2551i	0.328934	−	0.328934i
$973$		0			0
$974$		−	2.55599i		−	0.0818993i
$975$	−12.3604	+	11.7746i	−0.395850	+	0.377090i
$976$			6.07359i			0.194411i
$977$	−19.4618	−	19.4618i	−0.622638	−	0.622638i	0.323567	−	0.946205i	$-0.395118\pi$
$977$	−19.4618	−	19.4618i	−0.622638	−	0.622638i	−0.946205	+	0.323567i	$0.895118\pi$
$978$	−10.1053	−	10.1053i	−0.323131	−	0.323131i
$979$	−4.48226			−0.143254
$980$		0			0
$981$	−14.5185			−0.463539
$982$	−10.3003	−	10.3003i	−0.328695	−	0.328695i
$983$	31.7618	+	31.7618i	1.01304	+	1.01304i	0.999914	+	0.0131290i	$0.00417920\pi$
$983$	31.7618	+	31.7618i	1.01304	+	1.01304i	0.0131290	+	0.999914i	$0.495821\pi$
$984$		−	0.960481i		−	0.0306190i
$985$	1.57449	+	3.93555i	0.0501675	+	0.125397i
$986$		−	63.5766i		−	2.02469i
$987$		0			0
$988$	3.88878	−	3.88878i	0.123719	−	0.123719i
$989$			11.9424i			0.379745i
$990$	−2.49958	+	1.00000i	−0.0794418	+	0.0317822i
$991$	−6.16995			−0.195995			−0.0979975	−	0.995187i	$-0.531244\pi$
$991$	−6.16995			−0.195995			−0.0979975	+	0.995187i	$0.531244\pi$
$992$	−2.42012	+	2.42012i	−0.0768390	+	0.0768390i
$993$	−4.53527	−	4.53527i	−0.143922	−	0.143922i
$994$		0			0
$995$	29.8083	+	12.7729i	0.944985	+	0.404927i
$996$	−15.3411			−0.486101
$997$	−13.3101	+	13.3101i	−0.421536	+	0.421536i	−0.885732	−	0.464196i	$-0.846343\pi$
$997$	−13.3101	+	13.3101i	−0.421536	+	0.421536i	0.464196	+	0.885732i	$0.346343\pi$
$998$	−21.2751	+	21.2751i	−0.673450	+	0.673450i
$999$	−14.4964			−0.458646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.g.c.97.3		16
5.3	odd	4	inner	490.2.g.c.293.2		16
7.2	even	3		490.2.l.c.227.1		16
7.3	odd	6		490.2.l.c.117.3		16
7.4	even	3		70.2.k.a.47.4	yes	16
7.5	odd	6		70.2.k.a.17.2	yes	16
7.6	odd	2	inner	490.2.g.c.97.2		16
21.5	even	6		630.2.bv.c.577.3		16
21.11	odd	6		630.2.bv.c.397.2		16
28.11	odd	6		560.2.ci.c.257.2		16
28.19	even	6		560.2.ci.c.17.2		16
35.3	even	12		490.2.l.c.313.1		16
35.4	even	6		350.2.o.c.257.1		16
35.12	even	12		350.2.o.c.143.1		16
35.13	even	4	inner	490.2.g.c.293.3		16
35.18	odd	12		70.2.k.a.33.2	yes	16
35.19	odd	6		350.2.o.c.157.3		16
35.23	odd	12		490.2.l.c.423.3		16
35.32	odd	12		350.2.o.c.243.3		16
35.33	even	12		70.2.k.a.3.4	✓	16
105.53	even	12		630.2.bv.c.523.3		16
105.68	odd	12		630.2.bv.c.73.2		16
140.103	odd	12		560.2.ci.c.353.2		16
140.123	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	35.33	even	12
70.2.k.a.17.2	yes	16	7.5	odd	6
70.2.k.a.33.2	yes	16	35.18	odd	12
70.2.k.a.47.4	yes	16	7.4	even	3
350.2.o.c.143.1		16	35.12	even	12
350.2.o.c.157.3		16	35.19	odd	6
350.2.o.c.243.3		16	35.32	odd	12
350.2.o.c.257.1		16	35.4	even	6
490.2.g.c.97.2		16	7.6	odd	2	inner
490.2.g.c.97.3		16	1.1	even	1	trivial
490.2.g.c.293.2		16	5.3	odd	4	inner
490.2.g.c.293.3		16	35.13	even	4	inner
490.2.l.c.117.3		16	7.3	odd	6
490.2.l.c.227.1		16	7.2	even	3
490.2.l.c.313.1		16	35.3	even	12
490.2.l.c.423.3		16	35.23	odd	12
560.2.ci.c.17.2		16	28.19	even	6
560.2.ci.c.33.2		16	140.123	even	12
560.2.ci.c.257.2		16	28.11	odd	6
560.2.ci.c.353.2		16	140.103	odd	12
630.2.bv.c.73.2		16	105.68	odd	12
630.2.bv.c.397.2		16	21.11	odd	6
630.2.bv.c.523.3		16	105.53	even	12
630.2.bv.c.577.3		16	21.5	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.830578 + 0.830578i) q^{3} +1.00000i q^{4} +(2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 - 0.707107i) q^{8} -1.62028i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.830578 + 0.830578i) q^{3} +1.00000i q^{4} +(2.05532 + 0.880708i) q^{5} -1.17462i q^{6} +(0.707107 - 0.707107i) q^{8} -1.62028i q^{9} +(-0.830578 - 2.07609i) q^{10} +0.743072 q^{11} +(-0.830578 + 0.830578i) q^{12} +(2.05532 + 2.05532i) q^{13} +(0.975610 + 2.43860i) q^{15} -1.00000 q^{16} +(4.63872 - 4.63872i) q^{17} +(-1.14571 + 1.14571i) q^{18} -1.89205 q^{19} +(-0.880708 + 2.05532i) q^{20} +(-0.525431 - 0.525431i) q^{22} +(-3.74160 + 3.74160i) q^{23} +1.17462 q^{24} +(3.44871 + 3.62028i) q^{25} -2.90667i q^{26} +(3.83750 - 3.83750i) q^{27} +9.69135i q^{29} +(1.03449 - 2.41421i) q^{30} +3.42257i q^{31} +(0.707107 + 0.707107i) q^{32} +(0.617179 + 0.617179i) q^{33} -6.56014 q^{34} +1.62028 q^{36} +(-1.88878 - 1.88878i) q^{37} +(1.33788 + 1.33788i) q^{38} +3.41421i q^{39} +(2.07609 - 0.830578i) q^{40} -0.817699i q^{41} +(1.59589 - 1.59589i) q^{43} +0.743072i q^{44} +(1.42699 - 3.33020i) q^{45} +5.29142 q^{46} +(3.33020 - 3.33020i) q^{47} +(-0.830578 - 0.830578i) q^{48} +(0.121320 - 4.99853i) q^{50} +7.70563 q^{51} +(-2.05532 + 2.05532i) q^{52} +(3.52543 - 3.52543i) q^{53} -5.42705 q^{54} +(1.52725 + 0.654429i) q^{55} +(-1.57150 - 1.57150i) q^{57} +(6.85282 - 6.85282i) q^{58} +2.54975 q^{59} +(-2.43860 + 0.975610i) q^{60} -6.07359i q^{61} +(2.42012 - 2.42012i) q^{62} -1.00000i q^{64} +(2.41421 + 6.03449i) q^{65} -0.872823i q^{66} +(-9.68124 - 9.68124i) q^{67} +(4.63872 + 4.63872i) q^{68} -6.21538 q^{69} -16.0173 q^{71} +(-1.14571 - 1.14571i) q^{72} +(-6.25834 - 6.25834i) q^{73} +2.67114i q^{74} +(-0.142505 + 5.87135i) q^{75} -1.89205i q^{76} +(2.41421 - 2.41421i) q^{78} +6.58284i q^{79} +(-2.05532 - 0.880708i) q^{80} +1.51386 q^{81} +(-0.578200 + 0.578200i) q^{82} +(9.23519 + 9.23519i) q^{83} +(13.6194 - 5.44871i) q^{85} -2.25693 q^{86} +(-8.04942 + 8.04942i) q^{87} +(0.525431 - 0.525431i) q^{88} -6.03207 q^{89} +(-3.36384 + 1.34577i) q^{90} +(-3.74160 - 3.74160i) q^{92} +(-2.84271 + 2.84271i) q^{93} -4.70961 q^{94} +(-3.88878 - 1.66635i) q^{95} +1.17462i q^{96} +(3.16693 - 3.16693i) q^{97} -1.20398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95}+O(q^{100}) \) 16 * q + 24 * q^11 + 16 * q^15 - 16 * q^16 + 16 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^25 - 40 * q^30 - 8 * q^36 - 8 * q^37 - 8 * q^43 + 16 * q^46 - 32 * q^50 + 32 * q^51 + 56 * q^53 + 8 * q^57 + 64 * q^58 - 16 * q^60 + 16 * q^65 - 64 * q^67 + 16 * q^71 + 16 * q^72 + 16 * q^78 + 24 * q^85 - 24 * q^86 + 8 * q^88 + 8 * q^92 - 56 * q^93 - 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more