LMFDB - Embedded newform 260.2.r.b.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(177,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("260.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.r (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			177.2
Root			$-1.61803i$ of defining polynomial
Character	$\chi$	$=$	260.177
Dual form			260.2.r.b.213.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.61803 - 1.61803i) q^{3} +2.23607 q^{5} -2.23607i q^{9} +O(q^{10})$	\(q+(1.61803 - 1.61803i) q^{3} +2.23607 q^{5} -2.23607i q^{9} +(-0.381966 + 0.381966i) q^{11} +(-3.00000 + 2.00000i) q^{13} +(3.61803 - 3.61803i) q^{15} +(-2.23607 + 2.23607i) q^{17} +(0.854102 - 0.854102i) q^{19} +(-5.61803 - 5.61803i) q^{23} +5.00000 q^{25} +(1.23607 + 1.23607i) q^{27} -0.763932i q^{29} +(-0.854102 - 0.854102i) q^{31} +1.23607i q^{33} -3.70820 q^{37} +(-1.61803 + 8.09017i) q^{39} +(8.23607 + 8.23607i) q^{41} +(-2.85410 - 2.85410i) q^{43} -5.00000i q^{45} +8.94427 q^{47} -7.00000 q^{49} +7.23607i q^{51} +(-7.47214 + 7.47214i) q^{53} +(-0.854102 + 0.854102i) q^{55} -2.76393i q^{57} +(5.61803 + 5.61803i) q^{59} -7.70820 q^{61} +(-6.70820 + 4.47214i) q^{65} -13.7082i q^{67} -18.1803 q^{69} +(0.381966 + 0.381966i) q^{71} +1.70820i q^{73} +(8.09017 - 8.09017i) q^{75} +9.70820i q^{79} +10.7082 q^{81} -1.52786 q^{83} +(-5.00000 + 5.00000i) q^{85} +(-1.23607 - 1.23607i) q^{87} +(-2.23607 - 2.23607i) q^{89} -2.76393 q^{93} +(1.90983 - 1.90983i) q^{95} -11.4164i q^{97} +(0.854102 + 0.854102i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3}+O(q^{10}) $ 4 * q + 2 * q^3	$ 4 q + 2 q^{3} - 6 q^{11} - 12 q^{13} + 10 q^{15} - 10 q^{19} - 18 q^{23} + 20 q^{25} - 4 q^{27} + 10 q^{31} + 12 q^{37} - 2 q^{39} + 24 q^{41} + 2 q^{43} - 28 q^{49} - 12 q^{53} + 10 q^{55} + 18 q^{59} - 4 q^{61} - 28 q^{69} + 6 q^{71} + 10 q^{75} + 16 q^{81} - 24 q^{83} - 20 q^{85} + 4 q^{87} - 20 q^{93} + 30 q^{95} - 10 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^11 - 12 * q^13 + 10 * q^15 - 10 * q^19 - 18 * q^23 + 20 * q^25 - 4 * q^27 + 10 * q^31 + 12 * q^37 - 2 * q^39 + 24 * q^41 + 2 * q^43 - 28 * q^49 - 12 * q^53 + 10 * q^55 + 18 * q^59 - 4 * q^61 - 28 * q^69 + 6 * q^71 + 10 * q^75 + 16 * q^81 - 24 * q^83 - 20 * q^85 + 4 * q^87 - 20 * q^93 + 30 * q^95 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.61803	−	1.61803i	0.934172	−	0.934172i	−0.0637909	−	0.997963i	$-0.520319\pi$
$3$	1.61803	−	1.61803i	0.934172	−	0.934172i	0.997963	+	0.0637909i	$0.0203191\pi$
$4$		0			0
$5$	2.23607			1.00000
$5$	2.23607			1.00000
$6$		0			0
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$		0			0
$9$		−	2.23607i		−	0.745356i
$10$		0			0
$11$	−0.381966	+	0.381966i	−0.115167	+	0.115167i	−0.762342	−	0.647175i	$-0.775950\pi$
$11$	−0.381966	+	0.381966i	−0.115167	+	0.115167i	0.647175	+	0.762342i	$0.275950\pi$
$12$		0			0
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$13$	−3.00000	+	2.00000i	−0.832050	+	0.554700i
$14$		0			0
$15$	3.61803	−	3.61803i	0.934172	−	0.934172i
$16$		0			0
$17$	−2.23607	+	2.23607i	−0.542326	+	0.542326i	−0.924210	−	0.381884i	$-0.875275\pi$
$17$	−2.23607	+	2.23607i	−0.542326	+	0.542326i	0.381884	+	0.924210i	$0.375275\pi$
$18$		0			0
$19$	0.854102	−	0.854102i	0.195944	−	0.195944i	−0.602314	−	0.798259i	$-0.705755\pi$
$19$	0.854102	−	0.854102i	0.195944	−	0.195944i	0.798259	+	0.602314i	$0.205755\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.61803	−	5.61803i	−1.17144	−	1.17144i	−0.981866	−	0.189575i	$-0.939289\pi$
$23$	−5.61803	−	5.61803i	−1.17144	−	1.17144i	−0.189575	−	0.981866i	$-0.560711\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	1.23607	+	1.23607i	0.237881	+	0.237881i
$28$		0			0
$29$		−	0.763932i		−	0.141859i	−0.997481	−	0.0709293i	$-0.977404\pi$
$29$		−	0.763932i		−	0.141859i	0.997481	−	0.0709293i	$-0.0225965\pi$
$30$		0			0
$31$	−0.854102	−	0.854102i	−0.153401	−	0.153401i	0.626234	−	0.779635i	$-0.284595\pi$
$31$	−0.854102	−	0.854102i	−0.153401	−	0.153401i	−0.779635	+	0.626234i	$0.784595\pi$
$32$		0			0
$33$			1.23607i			0.215172i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.70820			−0.609625			−0.304812	−	0.952412i	$-0.598594\pi$
$37$	−3.70820			−0.609625			−0.304812	+	0.952412i	$0.598594\pi$
$38$		0			0
$39$	−1.61803	+	8.09017i	−0.259093	+	1.29546i
$40$		0			0
$41$	8.23607	+	8.23607i	1.28626	+	1.28626i	0.937043	+	0.349215i	$0.113552\pi$
$41$	8.23607	+	8.23607i	1.28626	+	1.28626i	0.349215	+	0.937043i	$0.386448\pi$
$42$		0			0
$43$	−2.85410	−	2.85410i	−0.435246	−	0.435246i	0.455162	−	0.890409i	$-0.349581\pi$
$43$	−2.85410	−	2.85410i	−0.435246	−	0.435246i	−0.890409	+	0.455162i	$0.849581\pi$
$44$		0			0
$45$		−	5.00000i		−	0.745356i
$46$		0			0
$47$	8.94427			1.30466			0.652328	−	0.757937i	$-0.273792\pi$
$47$	8.94427			1.30466			0.652328	+	0.757937i	$0.273792\pi$
$48$		0			0
$49$	−7.00000			−1.00000
$50$		0			0
$51$			7.23607i			1.01325i
$52$		0			0
$53$	−7.47214	+	7.47214i	−1.02638	+	1.02638i	−0.0267342	+	0.999643i	$0.508511\pi$
$53$	−7.47214	+	7.47214i	−1.02638	+	1.02638i	−0.999643	+	0.0267342i	$0.991489\pi$
$54$		0			0
$55$	−0.854102	+	0.854102i	−0.115167	+	0.115167i
$56$		0			0
$57$		−	2.76393i		−	0.366092i
$58$		0			0
$59$	5.61803	+	5.61803i	0.731406	+	0.731406i	0.970898	−	0.239492i	$-0.0769810\pi$
$59$	5.61803	+	5.61803i	0.731406	+	0.731406i	−0.239492	+	0.970898i	$0.576981\pi$
$60$		0			0
$61$	−7.70820			−0.986934			−0.493467	−	0.869764i	$-0.664271\pi$
$61$	−7.70820			−0.986934			−0.493467	+	0.869764i	$0.664271\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.70820	+	4.47214i	−0.832050	+	0.554700i
$66$		0			0
$67$		−	13.7082i		−	1.67472i	−0.546649	−	0.837362i	$-0.684097\pi$
$67$		−	13.7082i		−	1.67472i	0.546649	−	0.837362i	$-0.315903\pi$
$68$		0			0
$69$	−18.1803			−2.18866
$70$		0			0
$71$	0.381966	+	0.381966i	0.0453310	+	0.0453310i	0.729409	−	0.684078i	$-0.239795\pi$
$71$	0.381966	+	0.381966i	0.0453310	+	0.0453310i	−0.684078	+	0.729409i	$0.739795\pi$
$72$		0			0
$73$			1.70820i			0.199930i	0.994991	+	0.0999651i	$0.0318731\pi$
$73$			1.70820i			0.199930i	−0.994991	+	0.0999651i	$0.968127\pi$
$74$		0			0
$75$	8.09017	−	8.09017i	0.934172	−	0.934172i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			9.70820i			1.09226i	0.837701	+	0.546129i	$0.183899\pi$
$79$			9.70820i			1.09226i	−0.837701	+	0.546129i	$0.816101\pi$
$80$		0			0
$81$	10.7082			1.18980
$82$		0			0
$83$	−1.52786			−0.167705			−0.0838524	−	0.996478i	$-0.526722\pi$
$83$	−1.52786			−0.167705			−0.0838524	+	0.996478i	$0.526722\pi$
$84$		0			0
$85$	−5.00000	+	5.00000i	−0.542326	+	0.542326i
$86$		0			0
$87$	−1.23607	−	1.23607i	−0.132520	−	0.132520i
$88$		0			0
$89$	−2.23607	−	2.23607i	−0.237023	−	0.237023i	0.578593	−	0.815616i	$-0.303602\pi$
$89$	−2.23607	−	2.23607i	−0.237023	−	0.237023i	−0.815616	+	0.578593i	$0.803602\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−2.76393			−0.286606
$94$		0			0
$95$	1.90983	−	1.90983i	0.195944	−	0.195944i
$96$		0			0
$97$		−	11.4164i		−	1.15916i	−0.814915	−	0.579580i	$-0.803217\pi$
$97$		−	11.4164i		−	1.15916i	0.814915	−	0.579580i	$-0.196783\pi$
$98$		0			0
$99$	0.854102	+	0.854102i	0.0858405	+	0.0858405i
$100$		0			0
$101$			10.4721i			1.04202i	0.853552	+	0.521008i	$0.174444\pi$
$101$			10.4721i			1.04202i	−0.853552	+	0.521008i	$0.825556\pi$
$102$		0			0
$103$	−2.85410	−	2.85410i	−0.281223	−	0.281223i	0.552374	−	0.833597i	$-0.313722\pi$
$103$	−2.85410	−	2.85410i	−0.281223	−	0.281223i	−0.833597	+	0.552374i	$0.813722\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.381966	−	0.381966i	−0.0369260	−	0.0369260i	0.688403	−	0.725329i	$-0.258312\pi$
$107$	−0.381966	−	0.381966i	−0.0369260	−	0.0369260i	−0.725329	+	0.688403i	$0.758312\pi$
$108$		0			0
$109$	8.70820	−	8.70820i	0.834095	−	0.834095i	−0.153979	−	0.988074i	$-0.549209\pi$
$109$	8.70820	−	8.70820i	0.834095	−	0.834095i	0.988074	+	0.153979i	$0.0492089\pi$
$110$		0			0
$111$	−6.00000	+	6.00000i	−0.569495	+	0.569495i
$112$		0			0
$113$	5.94427	−	5.94427i	0.559190	−	0.559190i	−0.369887	−	0.929077i	$-0.620604\pi$
$113$	5.94427	−	5.94427i	0.559190	−	0.559190i	0.929077	+	0.369887i	$0.120604\pi$
$114$		0			0
$115$	−12.5623	−	12.5623i	−1.17144	−	1.17144i
$116$		0			0
$117$	4.47214	+	6.70820i	0.413449	+	0.620174i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			10.7082i			0.973473i
$122$		0			0
$123$	26.6525			2.40317
$124$		0			0
$125$	11.1803			1.00000
$126$		0			0
$127$	6.85410	−	6.85410i	0.608203	−	0.608203i	−0.334273	−	0.942476i	$-0.608491\pi$
$127$	6.85410	−	6.85410i	0.608203	−	0.608203i	0.942476	+	0.334273i	$0.108491\pi$
$128$		0			0
$129$	−9.23607			−0.813190
$130$		0			0
$131$	19.4164			1.69642			0.848210	−	0.529661i	$-0.177681\pi$
$131$	19.4164			1.69642			0.848210	+	0.529661i	$0.177681\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.76393	+	2.76393i	0.237881	+	0.237881i
$136$		0			0
$137$	7.52786			0.643149			0.321574	−	0.946884i	$-0.395788\pi$
$137$	7.52786			0.643149			0.321574	+	0.946884i	$0.395788\pi$
$138$		0			0
$139$		−	17.1246i		−	1.45249i	−0.687436	−	0.726245i	$-0.741264\pi$
$139$		−	17.1246i		−	1.45249i	0.687436	−	0.726245i	$-0.258736\pi$
$140$		0			0
$141$	14.4721	−	14.4721i	1.21877	−	1.21877i
$142$		0			0
$143$	0.381966	−	1.90983i	0.0319416	−	0.159708i
$144$		0			0
$145$		−	1.70820i		−	0.141859i
$146$		0			0
$147$	−11.3262	+	11.3262i	−0.934172	+	0.934172i
$148$		0			0
$149$	11.9443	−	11.9443i	0.978513	−	0.978513i	−0.0212611	−	0.999774i	$-0.506768\pi$
$149$	11.9443	−	11.9443i	0.978513	−	0.978513i	0.999774	+	0.0212611i	$0.00676812\pi$
$150$		0			0
$151$	−6.85410	+	6.85410i	−0.557779	+	0.557779i	−0.928675	−	0.370896i	$-0.879051\pi$
$151$	−6.85410	+	6.85410i	−0.557779	+	0.557779i	0.370896	+	0.928675i	$0.379051\pi$
$152$		0			0
$153$	5.00000	+	5.00000i	0.404226	+	0.404226i
$154$		0			0
$155$	−1.90983	−	1.90983i	−0.153401	−	0.153401i
$156$		0			0
$157$	−5.00000	−	5.00000i	−0.399043	−	0.399043i	0.478852	−	0.877896i	$-0.341053\pi$
$157$	−5.00000	−	5.00000i	−0.399043	−	0.399043i	−0.877896	+	0.478852i	$0.841053\pi$
$158$		0			0
$159$			24.1803i			1.91763i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	17.7082i		−	1.38701i	−0.720450	−	0.693507i	$-0.756065\pi$
$163$		−	17.7082i		−	1.38701i	0.720450	−	0.693507i	$-0.243935\pi$
$164$		0			0
$165$			2.76393i			0.215172i
$166$		0			0
$167$	−22.4721			−1.73895			−0.869473	−	0.493980i	$-0.835541\pi$
$167$	−22.4721			−1.73895			−0.869473	+	0.493980i	$0.835541\pi$
$168$		0			0
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$		0			0
$171$	−1.90983	−	1.90983i	−0.146048	−	0.146048i
$172$		0			0
$173$	−5.18034	−	5.18034i	−0.393854	−	0.393854i	0.482205	−	0.876059i	$-0.339836\pi$
$173$	−5.18034	−	5.18034i	−0.393854	−	0.393854i	−0.876059	+	0.482205i	$0.839836\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	18.1803			1.36652
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$		−	21.7082i		−	1.61356i	−0.590853	−	0.806779i	$-0.701209\pi$
$181$		−	21.7082i		−	1.61356i	0.590853	−	0.806779i	$-0.298791\pi$
$182$		0			0
$183$	−12.4721	+	12.4721i	−0.921967	+	0.921967i
$184$		0			0
$185$	−8.29180			−0.609625
$186$		0			0
$187$		−	1.70820i		−	0.124916i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−19.4164			−1.40492			−0.702461	−	0.711722i	$-0.747915\pi$
$191$	−19.4164			−1.40492			−0.702461	+	0.711722i	$0.747915\pi$
$192$		0			0
$193$			23.4164i			1.68555i	0.538266	+	0.842775i	$0.319080\pi$
$193$			23.4164i			1.68555i	−0.538266	+	0.842775i	$0.680920\pi$
$194$		0			0
$195$	−3.61803	+	18.0902i	−0.259093	+	1.29546i
$196$		0			0
$197$			12.0000i			0.854965i	0.904024	+	0.427482i	$0.140599\pi$
$197$			12.0000i			0.854965i	−0.904024	+	0.427482i	$0.859401\pi$
$198$		0			0
$199$	−15.4164			−1.09284			−0.546420	−	0.837511i	$-0.684010\pi$
$199$	−15.4164			−1.09284			−0.546420	+	0.837511i	$0.684010\pi$
$200$		0			0
$201$	−22.1803	−	22.1803i	−1.56448	−	1.56448i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	18.4164	+	18.4164i	1.28626	+	1.28626i
$206$		0			0
$207$	−12.5623	+	12.5623i	−0.873141	+	0.873141i
$208$		0			0
$209$			0.652476i			0.0451327i
$210$		0			0
$211$	−23.4164			−1.61205			−0.806026	−	0.591880i	$-0.798386\pi$
$211$	−23.4164			−1.61205			−0.806026	+	0.591880i	$0.798386\pi$
$212$		0			0
$213$	1.23607			0.0846940
$214$		0			0
$215$	−6.38197	−	6.38197i	−0.435246	−	0.435246i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.76393	+	2.76393i	0.186769	+	0.186769i
$220$		0			0
$221$	2.23607	−	11.1803i	0.150414	−	0.752071i
$222$		0			0
$223$	−19.4164			−1.30022			−0.650109	−	0.759841i	$-0.725277\pi$
$223$	−19.4164			−1.30022			−0.650109	+	0.759841i	$0.725277\pi$
$224$		0			0
$225$		−	11.1803i		−	0.745356i
$226$		0			0
$227$			21.7082i			1.44082i	0.693546	+	0.720412i	$0.256047\pi$
$227$			21.7082i			1.44082i	−0.693546	+	0.720412i	$0.743953\pi$
$228$		0			0
$229$	18.4164	+	18.4164i	1.21699	+	1.21699i	0.968681	+	0.248310i	$0.0798751\pi$
$229$	18.4164	+	18.4164i	1.21699	+	1.21699i	0.248310	+	0.968681i	$0.420125\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.47214	−	1.47214i	−0.0964428	−	0.0964428i	0.657239	−	0.753682i	$-0.271724\pi$
$233$	−1.47214	−	1.47214i	−0.0964428	−	0.0964428i	−0.753682	+	0.657239i	$0.771724\pi$
$234$		0			0
$235$	20.0000			1.30466
$236$		0			0
$237$	15.7082	+	15.7082i	1.02036	+	1.02036i
$238$		0			0
$239$	6.38197	−	6.38197i	0.412815	−	0.412815i	−0.469903	−	0.882718i	$-0.655711\pi$
$239$	6.38197	−	6.38197i	0.412815	−	0.412815i	0.882718	+	0.469903i	$0.155711\pi$
$240$		0			0
$241$	10.7082	−	10.7082i	0.689776	−	0.689776i	−0.272406	−	0.962182i	$-0.587819\pi$
$241$	10.7082	−	10.7082i	0.689776	−	0.689776i	0.962182	+	0.272406i	$0.0878195\pi$
$242$		0			0
$243$	13.6180	−	13.6180i	0.873597	−	0.873597i
$244$		0			0
$245$	−15.6525			−1.00000
$246$		0			0
$247$	−0.854102	+	4.27051i	−0.0543452	+	0.271726i
$248$		0			0
$249$	−2.47214	+	2.47214i	−0.156665	+	0.156665i
$250$		0			0
$251$		−	3.81966i		−	0.241095i	−0.992708	−	0.120547i	$-0.961535\pi$
$251$		−	3.81966i		−	0.241095i	0.992708	−	0.120547i	$-0.0384650\pi$
$252$		0			0
$253$	4.29180			0.269823
$254$		0			0
$255$			16.1803i			1.01325i
$256$		0			0
$257$	5.18034	−	5.18034i	0.323141	−	0.323141i	−0.526830	−	0.849971i	$-0.676620\pi$
$257$	5.18034	−	5.18034i	0.323141	−	0.323141i	0.849971	+	0.526830i	$0.176620\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.70820			−0.105735
$262$		0			0
$263$	−7.03444	+	7.03444i	−0.433762	+	0.433762i	−0.889906	−	0.456144i	$-0.849230\pi$
$263$	−7.03444	+	7.03444i	−0.433762	+	0.433762i	0.456144	+	0.889906i	$0.349230\pi$
$264$		0			0
$265$	−16.7082	+	16.7082i	−1.02638	+	1.02638i
$266$		0			0
$267$	−7.23607			−0.442840
$268$		0			0
$269$		−	22.4721i		−	1.37015i	−0.728472	−	0.685075i	$-0.759769\pi$
$269$		−	22.4721i		−	1.37015i	0.728472	−	0.685075i	$-0.240231\pi$
$270$		0			0
$271$	12.5623	−	12.5623i	0.763106	−	0.763106i	−0.213777	−	0.976883i	$-0.568577\pi$
$271$	12.5623	−	12.5623i	0.763106	−	0.763106i	0.976883	+	0.213777i	$0.0685765\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.90983	+	1.90983i	−0.115167	+	0.115167i
$276$		0			0
$277$	−10.7082	+	10.7082i	−0.643394	+	0.643394i	−0.951388	−	0.307995i	$-0.900342\pi$
$277$	−10.7082	+	10.7082i	−0.643394	+	0.643394i	0.307995	+	0.951388i	$0.400342\pi$
$278$		0			0
$279$	−1.90983	+	1.90983i	−0.114339	+	0.114339i
$280$		0			0
$281$	−2.23607	+	2.23607i	−0.133393	+	0.133393i	−0.770651	−	0.637258i	$-0.780069\pi$
$281$	−2.23607	+	2.23607i	−0.133393	+	0.133393i	0.637258	+	0.770651i	$0.280069\pi$
$282$		0			0
$283$	9.14590	+	9.14590i	0.543667	+	0.543667i	0.924602	−	0.380935i	$-0.124398\pi$
$283$	9.14590	+	9.14590i	0.543667	+	0.543667i	−0.380935	+	0.924602i	$0.624398\pi$
$284$		0			0
$285$		−	6.18034i		−	0.366092i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			7.00000i			0.411765i
$290$		0			0
$291$	−18.4721	−	18.4721i	−1.08286	−	1.08286i
$292$		0			0
$293$		−	14.2918i		−	0.834936i	−0.908692	−	0.417468i	$-0.862918\pi$
$293$		−	14.2918i		−	0.834936i	0.908692	−	0.417468i	$-0.137082\pi$
$294$		0			0
$295$	12.5623	+	12.5623i	0.731406	+	0.731406i
$296$		0			0
$297$	−0.944272			−0.0547922
$298$		0			0
$299$	28.0902	+	5.61803i	1.62450	+	0.324899i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	16.9443	+	16.9443i	0.973423	+	0.973423i
$304$		0			0
$305$	−17.2361			−0.986934
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$	−9.23607			−0.525422
$310$		0			0
$311$			20.1803i			1.14432i	0.820141	+	0.572161i	$0.193895\pi$
$311$			20.1803i			1.14432i	−0.820141	+	0.572161i	$0.806105\pi$
$312$		0			0
$313$	−1.29180	+	1.29180i	−0.0730166	+	0.0730166i	−0.742672	−	0.669655i	$-0.766442\pi$
$313$	−1.29180	+	1.29180i	−0.0730166	+	0.0730166i	0.669655	+	0.742672i	$0.266442\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			9.70820i			0.545267i	0.962118	+	0.272634i	$0.0878947\pi$
$317$			9.70820i			0.545267i	−0.962118	+	0.272634i	$0.912105\pi$
$318$		0			0
$319$	0.291796	+	0.291796i	0.0163374	+	0.0163374i
$320$		0			0
$321$	−1.23607			−0.0689906
$322$		0			0
$323$			3.81966i			0.212532i
$324$		0			0
$325$	−15.0000	+	10.0000i	−0.832050	+	0.554700i
$326$		0			0
$327$		−	28.1803i		−	1.55838i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−9.14590	−	9.14590i	−0.502704	−	0.502704i	0.409573	−	0.912277i	$-0.365678\pi$
$331$	−9.14590	−	9.14590i	−0.502704	−	0.502704i	−0.912277	+	0.409573i	$0.865678\pi$
$332$		0			0
$333$			8.29180i			0.454388i
$334$		0			0
$335$		−	30.6525i		−	1.67472i
$336$		0			0
$337$	12.4164	−	12.4164i	0.676365	−	0.676365i	−0.282811	−	0.959176i	$-0.591267\pi$
$337$	12.4164	−	12.4164i	0.676365	−	0.676365i	0.959176	+	0.282811i	$0.0912669\pi$
$338$		0			0
$339$		−	19.2361i		−	1.04476i
$340$		0			0
$341$	0.652476			0.0353335
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−40.6525			−2.18866
$346$		0			0
$347$	−4.09017	−	4.09017i	−0.219572	−	0.219572i	0.588746	−	0.808318i	$-0.299622\pi$
$347$	−4.09017	−	4.09017i	−0.219572	−	0.219572i	−0.808318	+	0.588746i	$0.799622\pi$
$348$		0			0
$349$	−3.29180	−	3.29180i	−0.176206	−	0.176206i	0.613494	−	0.789700i	$-0.289764\pi$
$349$	−3.29180	−	3.29180i	−0.176206	−	0.176206i	−0.789700	+	0.613494i	$0.789764\pi$
$350$		0			0
$351$	−6.18034	−	1.23607i	−0.329882	−	0.0659764i
$352$		0			0
$353$	−17.2361			−0.917383			−0.458692	−	0.888595i	$-0.651682\pi$
$353$	−17.2361			−0.917383			−0.458692	+	0.888595i	$0.651682\pi$
$354$		0			0
$355$	0.854102	+	0.854102i	0.0453310	+	0.0453310i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.90983	+	1.90983i	0.100797	+	0.100797i	0.755707	−	0.654910i	$-0.227293\pi$
$359$	1.90983	+	1.90983i	0.100797	+	0.100797i	−0.654910	+	0.755707i	$0.727293\pi$
$360$		0			0
$361$			17.5410i			0.923212i
$362$		0			0
$363$	17.3262	+	17.3262i	0.909392	+	0.909392i
$364$		0			0
$365$			3.81966i			0.199930i
$366$		0			0
$367$	5.14590	+	5.14590i	0.268614	+	0.268614i	0.828541	−	0.559928i	$-0.189171\pi$
$367$	5.14590	+	5.14590i	0.268614	+	0.268614i	−0.559928	+	0.828541i	$0.689171\pi$
$368$		0			0
$369$	18.4164	−	18.4164i	0.958720	−	0.958720i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	26.4164	−	26.4164i	1.36779	−	1.36779i	0.504207	−	0.863583i	$-0.331785\pi$
$373$	26.4164	−	26.4164i	1.36779	−	1.36779i	0.863583	−	0.504207i	$-0.168215\pi$
$374$		0			0
$375$	18.0902	−	18.0902i	0.934172	−	0.934172i
$376$		0			0
$377$	1.52786	+	2.29180i	0.0786890	+	0.118034i
$378$		0			0
$379$	−2.85410	+	2.85410i	−0.146605	+	0.146605i	−0.776600	−	0.629994i	$-0.783057\pi$
$379$	−2.85410	+	2.85410i	−0.146605	+	0.146605i	0.629994	+	0.776600i	$0.283057\pi$
$380$		0			0
$381$		−	22.1803i		−	1.13633i
$382$		0			0
$383$	17.8885			0.914062			0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885			0.914062			0.457031	+	0.889451i	$0.348913\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.38197	+	6.38197i	−0.324414	+	0.324414i
$388$		0			0
$389$	−1.41641			−0.0718147			−0.0359074	−	0.999355i	$-0.511432\pi$
$389$	−1.41641			−0.0718147			−0.0359074	+	0.999355i	$0.511432\pi$
$390$		0			0
$391$	25.1246			1.27061
$392$		0			0
$393$	31.4164	−	31.4164i	1.58475	−	1.58475i
$394$		0			0
$395$			21.7082i			1.09226i
$396$		0			0
$397$	35.1246			1.76285			0.881427	−	0.472321i	$-0.156584\pi$
$397$	35.1246			1.76285			0.881427	+	0.472321i	$0.156584\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.23607	+	2.23607i	−0.111664	+	0.111664i	−0.760731	−	0.649067i	$-0.775159\pi$
$401$	−2.23607	+	2.23607i	−0.111664	+	0.111664i	0.649067	+	0.760731i	$0.275159\pi$
$402$		0			0
$403$	4.27051	+	0.854102i	0.212729	+	0.0425458i
$404$		0			0
$405$	23.9443			1.18980
$406$		0			0
$407$	1.41641	−	1.41641i	0.0702087	−	0.0702087i
$408$		0			0
$409$	−16.7082	+	16.7082i	−0.826168	+	0.826168i	−0.986984	−	0.160817i	$-0.948587\pi$
$409$	−16.7082	+	16.7082i	−0.826168	+	0.826168i	0.160817	+	0.986984i	$0.448587\pi$
$410$		0			0
$411$	12.1803	−	12.1803i	0.600812	−	0.600812i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−3.41641			−0.167705
$416$		0			0
$417$	−27.7082	−	27.7082i	−1.35688	−	1.35688i
$418$		0			0
$419$		−	27.5967i		−	1.34819i	−0.738645	−	0.674095i	$-0.764534\pi$
$419$		−	27.5967i		−	1.34819i	0.738645	−	0.674095i	$-0.235466\pi$
$420$		0			0
$421$	16.7082	+	16.7082i	0.814308	+	0.814308i	0.985277	−	0.170968i	$-0.0546896\pi$
$421$	16.7082	+	16.7082i	0.814308	+	0.814308i	−0.170968	+	0.985277i	$0.554690\pi$
$422$		0			0
$423$		−	20.0000i		−	0.972433i
$424$		0			0
$425$	−11.1803	+	11.1803i	−0.542326	+	0.542326i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.47214	−	3.70820i	−0.119356	−	0.179034i
$430$		0			0
$431$	28.0902	+	28.0902i	1.35306	+	1.35306i	0.882222	+	0.470834i	$0.156047\pi$
$431$	28.0902	+	28.0902i	1.35306	+	1.35306i	0.470834	+	0.882222i	$0.343953\pi$
$432$		0			0
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	0.985668	−	0.168700i	$-0.0539568\pi$
$433$	17.0000	+	17.0000i	0.816968	+	0.816968i	−0.168700	+	0.985668i	$0.553957\pi$
$434$		0			0
$435$	−2.76393	−	2.76393i	−0.132520	−	0.132520i
$436$		0			0
$437$	−9.59675			−0.459075
$438$		0			0
$439$	−20.0000			−0.954548			−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000			−0.954548			−0.477274	+	0.878755i	$0.658375\pi$
$440$		0			0
$441$			15.6525i			0.745356i
$442$		0			0
$443$	−15.3262	+	15.3262i	−0.728172	+	0.728172i	−0.970255	−	0.242084i	$-0.922169\pi$
$443$	−15.3262	+	15.3262i	−0.728172	+	0.728172i	0.242084	+	0.970255i	$0.422169\pi$
$444$		0			0
$445$	−5.00000	−	5.00000i	−0.237023	−	0.237023i
$446$		0			0
$447$		−	38.6525i		−	1.82820i
$448$		0			0
$449$	19.4721	+	19.4721i	0.918947	+	0.918947i	0.996953	−	0.0780060i	$-0.0248553\pi$
$449$	19.4721	+	19.4721i	0.918947	+	0.918947i	−0.0780060	+	0.996953i	$0.524855\pi$
$450$		0			0
$451$	−6.29180			−0.296269
$452$		0			0
$453$			22.1803i			1.04212i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			3.41641i			0.159813i	0.996802	+	0.0799064i	$0.0254621\pi$
$457$			3.41641i			0.159813i	−0.996802	+	0.0799064i	$0.974538\pi$
$458$		0			0
$459$	−5.52786			−0.258019
$460$		0			0
$461$	−5.18034	−	5.18034i	−0.241272	−	0.241272i	0.576104	−	0.817376i	$-0.304572\pi$
$461$	−5.18034	−	5.18034i	−0.241272	−	0.241272i	−0.817376	+	0.576104i	$0.804572\pi$
$462$		0			0
$463$		−	17.7082i		−	0.822970i	−0.911417	−	0.411485i	$-0.865010\pi$
$463$		−	17.7082i		−	0.822970i	0.911417	−	0.411485i	$-0.134990\pi$
$464$		0			0
$465$	−6.18034			−0.286606
$466$		0			0
$467$	13.0344	−	13.0344i	0.603162	−	0.603162i	−0.337988	−	0.941150i	$-0.609746\pi$
$467$	13.0344	−	13.0344i	0.603162	−	0.603162i	0.941150	+	0.337988i	$0.109746\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−16.1803			−0.745551
$472$		0			0
$473$	2.18034			0.100252
$474$		0			0
$475$	4.27051	−	4.27051i	0.195944	−	0.195944i
$476$		0			0
$477$	16.7082	+	16.7082i	0.765016	+	0.765016i
$478$		0			0
$479$	16.7426	+	16.7426i	0.764991	+	0.764991i	0.977220	−	0.212229i	$-0.0680723\pi$
$479$	16.7426	+	16.7426i	0.764991	+	0.764991i	−0.212229	+	0.977220i	$0.568072\pi$
$480$		0			0
$481$	11.1246	−	7.41641i	0.507239	−	0.338159i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	25.5279i		−	1.15916i
$486$		0			0
$487$			25.1246i			1.13850i	0.822163	+	0.569252i	$0.192767\pi$
$487$			25.1246i			1.13850i	−0.822163	+	0.569252i	$0.807233\pi$
$488$		0			0
$489$	−28.6525	−	28.6525i	−1.29571	−	1.29571i
$490$		0			0
$491$		−	6.65248i		−	0.300222i	−0.988669	−	0.150111i	$-0.952037\pi$
$491$		−	6.65248i		−	0.300222i	0.988669	−	0.150111i	$-0.0479631\pi$
$492$		0			0
$493$	1.70820	+	1.70820i	0.0769336	+	0.0769336i
$494$		0			0
$495$	1.90983	+	1.90983i	0.0858405	+	0.0858405i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−25.9787	+	25.9787i	−1.16297	+	1.16297i	−0.179144	+	0.983823i	$0.557333\pi$
$499$	−25.9787	+	25.9787i	−1.16297	+	1.16297i	−0.983823	+	0.179144i	$0.942667\pi$
$500$		0			0
$501$	−36.3607	+	36.3607i	−1.62448	+	1.62448i
$502$		0			0
$503$	−27.3262	+	27.3262i	−1.21842	+	1.21842i	−0.250230	+	0.968186i	$0.580506\pi$
$503$	−27.3262	+	27.3262i	−1.21842	+	1.21842i	−0.968186	+	0.250230i	$0.919494\pi$
$504$		0			0
$505$			23.4164i			1.04202i
$506$		0			0
$507$	−11.3262	−	27.5066i	−0.503016	−	1.22161i
$508$		0			0
$509$	14.2361	−	14.2361i	0.631003	−	0.631003i	−0.317317	−	0.948320i	$-0.602782\pi$
$509$	14.2361	−	14.2361i	0.631003	−	0.631003i	0.948320	+	0.317317i	$0.102782\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.11146			0.0932231
$514$		0			0
$515$	−6.38197	−	6.38197i	−0.281223	−	0.281223i
$516$		0			0
$517$	−3.41641	+	3.41641i	−0.150253	+	0.150253i
$518$		0			0
$519$	−16.7639			−0.735855
$520$		0			0
$521$	0.875388			0.0383515			0.0191757	−	0.999816i	$-0.493896\pi$
$521$	0.875388			0.0383515			0.0191757	+	0.999816i	$0.493896\pi$
$522$		0			0
$523$	−8.27051	+	8.27051i	−0.361644	+	0.361644i	−0.864418	−	0.502774i	$-0.832313\pi$
$523$	−8.27051	+	8.27051i	−0.361644	+	0.361644i	0.502774	+	0.864418i	$0.332313\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.81966			0.166387
$528$		0			0
$529$			40.1246i			1.74455i
$530$		0			0
$531$	12.5623	−	12.5623i	0.545158	−	0.545158i
$532$		0			0
$533$	−41.1803	−	8.23607i	−1.78372	−	0.356744i
$534$		0			0
$535$	−0.854102	−	0.854102i	−0.0369260	−	0.0369260i
$536$		0			0
$537$	19.4164	−	19.4164i	0.837880	−	0.837880i
$538$		0			0
$539$	2.67376	−	2.67376i	0.115167	−	0.115167i
$540$		0			0
$541$	−12.4164	+	12.4164i	−0.533823	+	0.533823i	−0.921708	−	0.387885i	$-0.873206\pi$
$541$	−12.4164	+	12.4164i	−0.533823	+	0.533823i	0.387885	+	0.921708i	$0.373206\pi$
$542$		0			0
$543$	−35.1246	−	35.1246i	−1.50734	−	1.50734i
$544$		0			0
$545$	19.4721	−	19.4721i	0.834095	−	0.834095i
$546$		0			0
$547$	12.5623	+	12.5623i	0.537125	+	0.537125i	0.922684	−	0.385558i	$-0.125991\pi$
$547$	12.5623	+	12.5623i	0.537125	+	0.537125i	−0.385558	+	0.922684i	$0.625991\pi$
$548$		0			0
$549$			17.2361i			0.735617i
$550$		0			0
$551$	−0.652476	−	0.652476i	−0.0277964	−	0.0277964i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−13.4164	+	13.4164i	−0.569495	+	0.569495i
$556$		0			0
$557$	−30.7639			−1.30351			−0.651755	−	0.758430i	$-0.725967\pi$
$557$	−30.7639			−1.30351			−0.651755	+	0.758430i	$0.725967\pi$
$558$		0			0
$559$	14.2705	+	2.85410i	0.603578	+	0.120716i
$560$		0			0
$561$	−2.76393	−	2.76393i	−0.116693	−	0.116693i
$562$		0			0
$563$	10.0902	+	10.0902i	0.425250	+	0.425250i	0.887007	−	0.461757i	$-0.152781\pi$
$563$	10.0902	+	10.0902i	0.425250	+	0.425250i	−0.461757	+	0.887007i	$0.652781\pi$
$564$		0			0
$565$	13.2918	−	13.2918i	0.559190	−	0.559190i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.1246			−0.969434			−0.484717	−	0.874671i	$-0.661077\pi$
$569$	−23.1246			−0.969434			−0.484717	+	0.874671i	$0.661077\pi$
$570$		0			0
$571$		−	21.7082i		−	0.908460i	−0.890884	−	0.454230i	$-0.849914\pi$
$571$		−	21.7082i		−	0.908460i	0.890884	−	0.454230i	$-0.150086\pi$
$572$		0			0
$573$	−31.4164	+	31.4164i	−1.31244	+	1.31244i
$574$		0			0
$575$	−28.0902	−	28.0902i	−1.17144	−	1.17144i
$576$		0			0
$577$			13.1246i			0.546385i	0.961959	+	0.273192i	$0.0880796\pi$
$577$			13.1246i			0.546385i	−0.961959	+	0.273192i	$0.911920\pi$
$578$		0			0
$579$	37.8885	+	37.8885i	1.57459	+	1.57459i
$580$		0			0
$581$		0			0
$582$		0			0
$583$		−	5.70820i		−	0.236410i
$584$		0			0
$585$	10.0000	+	15.0000i	0.413449	+	0.620174i
$586$		0			0
$587$			17.1246i			0.706808i	0.935471	+	0.353404i	$0.114976\pi$
$587$			17.1246i			0.706808i	−0.935471	+	0.353404i	$0.885024\pi$
$588$		0			0
$589$	−1.45898			−0.0601162
$590$		0			0
$591$	19.4164	+	19.4164i	0.798684	+	0.798684i
$592$		0			0
$593$		−	43.4164i		−	1.78290i	−0.453121	−	0.891449i	$-0.649689\pi$
$593$		−	43.4164i		−	1.78290i	0.453121	−	0.891449i	$-0.350311\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−24.9443	+	24.9443i	−1.02090	+	1.02090i
$598$		0			0
$599$		−	35.0132i		−	1.43060i	−0.698818	−	0.715299i	$-0.746290\pi$
$599$		−	35.0132i		−	1.43060i	0.698818	−	0.715299i	$-0.253710\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$	−30.6525			−1.24827
$604$		0			0
$605$			23.9443i			0.973473i
$606$		0			0
$607$	4.27051	+	4.27051i	0.173335	+	0.173335i	0.788443	−	0.615108i	$-0.210888\pi$
$607$	4.27051	+	4.27051i	0.173335	+	0.173335i	−0.615108	+	0.788443i	$0.710888\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−26.8328	+	17.8885i	−1.08554	+	0.723693i
$612$		0			0
$613$	−13.4164			−0.541884			−0.270942	−	0.962596i	$-0.587335\pi$
$613$	−13.4164			−0.541884			−0.270942	+	0.962596i	$0.587335\pi$
$614$		0			0
$615$	59.5967			2.40317
$616$		0			0
$617$			31.4164i			1.26478i	0.774651	+	0.632388i	$0.217925\pi$
$617$			31.4164i			1.26478i	−0.774651	+	0.632388i	$0.782075\pi$
$618$		0			0
$619$	−16.2705	−	16.2705i	−0.653967	−	0.653967i	0.299979	−	0.953946i	$-0.403020\pi$
$619$	−16.2705	−	16.2705i	−0.653967	−	0.653967i	−0.953946	+	0.299979i	$0.903020\pi$
$620$		0			0
$621$		−	13.8885i		−	0.557328i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	1.05573	+	1.05573i	0.0421617	+	0.0421617i
$628$		0			0
$629$	8.29180	−	8.29180i	0.330616	−	0.330616i
$630$		0			0
$631$	4.27051	−	4.27051i	0.170006	−	0.170006i	−0.616976	−	0.786982i	$-0.711642\pi$
$631$	4.27051	−	4.27051i	0.170006	−	0.170006i	0.786982	+	0.616976i	$0.211642\pi$
$632$		0			0
$633$	−37.8885	+	37.8885i	−1.50593	+	1.50593i
$634$		0			0
$635$	15.3262	−	15.3262i	0.608203	−	0.608203i
$636$		0			0
$637$	21.0000	−	14.0000i	0.832050	−	0.554700i
$638$		0			0
$639$	0.854102	−	0.854102i	0.0337878	−	0.0337878i
$640$		0			0
$641$			15.0557i			0.594666i	0.954774	+	0.297333i	$0.0960971\pi$
$641$			15.0557i			0.594666i	−0.954774	+	0.297333i	$0.903903\pi$
$642$		0			0
$643$	16.5836			0.653993			0.326997	−	0.945026i	$-0.393963\pi$
$643$	16.5836			0.653993			0.326997	+	0.945026i	$0.393963\pi$
$644$		0			0
$645$	−20.6525			−0.813190
$646$		0			0
$647$	−10.0902	+	10.0902i	−0.396686	+	0.396686i	−0.877062	−	0.480377i	$-0.840500\pi$
$647$	−10.0902	+	10.0902i	−0.396686	+	0.396686i	0.480377	+	0.877062i	$0.340500\pi$
$648$		0			0
$649$	−4.29180			−0.168468
$650$		0			0
$651$		0			0
$652$		0			0
$653$	29.0689	−	29.0689i	1.13755	−	1.13755i	0.148666	−	0.988887i	$-0.452502\pi$
$653$	29.0689	−	29.0689i	1.13755	−	1.13755i	0.988887	−	0.148666i	$-0.0474979\pi$
$654$		0			0
$655$	43.4164			1.69642
$656$		0			0
$657$	3.81966			0.149019
$658$		0			0
$659$			26.0689i			1.01550i	0.861505	+	0.507750i	$0.169523\pi$
$659$			26.0689i			1.01550i	−0.861505	+	0.507750i	$0.830477\pi$
$660$		0			0
$661$	−2.70820	+	2.70820i	−0.105337	+	0.105337i	−0.757811	−	0.652474i	$-0.773731\pi$
$661$	−2.70820	+	2.70820i	−0.105337	+	0.105337i	0.652474	+	0.757811i	$0.273731\pi$
$662$		0			0
$663$	−14.4721	−	21.7082i	−0.562051	−	0.843077i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.29180	+	4.29180i	−0.166179	+	0.166179i
$668$		0			0
$669$	−31.4164	+	31.4164i	−1.21463	+	1.21463i
$670$		0			0
$671$	2.94427	−	2.94427i	0.113662	−	0.113662i
$672$		0			0
$673$	10.1246	+	10.1246i	0.390275	+	0.390275i	0.874786	−	0.484510i	$-0.161002\pi$
$673$	10.1246	+	10.1246i	0.390275	+	0.390275i	−0.484510	+	0.874786i	$0.661002\pi$
$674$		0			0
$675$	6.18034	+	6.18034i	0.237881	+	0.237881i
$676$		0			0
$677$	−17.9443	−	17.9443i	−0.689654	−	0.689654i	0.272501	−	0.962155i	$-0.412149\pi$
$677$	−17.9443	−	17.9443i	−0.689654	−	0.689654i	−0.962155	+	0.272501i	$0.912149\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	35.1246	+	35.1246i	1.34598	+	1.34598i
$682$		0			0
$683$			5.12461i			0.196088i	0.995182	+	0.0980439i	$0.0312586\pi$
$683$			5.12461i			0.196088i	−0.995182	+	0.0980439i	$0.968741\pi$
$684$		0			0
$685$	16.8328			0.643149
$686$		0			0
$687$	59.5967			2.27376
$688$		0			0
$689$	7.47214	−	37.3607i	0.284666	−	1.42333i
$690$		0			0
$691$	−11.9787	−	11.9787i	−0.455692	−	0.455692i	0.441547	−	0.897238i	$-0.354430\pi$
$691$	−11.9787	−	11.9787i	−0.455692	−	0.455692i	−0.897238	+	0.441547i	$0.854430\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	38.2918i		−	1.45249i
$696$		0			0
$697$	−36.8328			−1.39514
$698$		0			0
$699$	−4.76393			−0.180188
$700$		0			0
$701$		−	16.3607i		−	0.617934i	−0.951073	−	0.308967i	$-0.900017\pi$
$701$		−	16.3607i		−	0.617934i	0.951073	−	0.308967i	$-0.0999833\pi$
$702$		0			0
$703$	−3.16718	+	3.16718i	−0.119453	+	0.119453i
$704$		0			0
$705$	32.3607	−	32.3607i	1.21877	−	1.21877i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−8.41641	−	8.41641i	−0.316085	−	0.316085i	0.531176	−	0.847261i	$-0.321750\pi$
$709$	−8.41641	−	8.41641i	−0.316085	−	0.316085i	−0.847261	+	0.531176i	$0.821750\pi$
$710$		0			0
$711$	21.7082			0.814121
$712$		0			0
$713$			9.59675i			0.359401i
$714$		0			0
$715$	0.854102	−	4.27051i	0.0319416	−	0.159708i
$716$		0			0
$717$		−	20.6525i		−	0.771281i
$718$		0			0
$719$	−4.58359			−0.170939			−0.0854696	−	0.996341i	$-0.527239\pi$
$719$	−4.58359			−0.170939			−0.0854696	+	0.996341i	$0.527239\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		−	34.6525i		−	1.28874i
$724$		0			0
$725$		−	3.81966i		−	0.141859i
$726$		0			0
$727$	15.1459	−	15.1459i	0.561730	−	0.561730i	−0.368068	−	0.929799i	$-0.619981\pi$
$727$	15.1459	−	15.1459i	0.561730	−	0.561730i	0.929799	+	0.368068i	$0.119981\pi$
$728$		0			0
$729$		−	11.9443i		−	0.442380i
$730$		0			0
$731$	12.7639			0.472091
$732$		0			0
$733$	−30.0000			−1.10808			−0.554038	−	0.832492i	$-0.686914\pi$
$733$	−30.0000			−1.10808			−0.554038	+	0.832492i	$0.686914\pi$
$734$		0			0
$735$	−25.3262	+	25.3262i	−0.934172	+	0.934172i
$736$		0			0
$737$	5.23607	+	5.23607i	0.192873	+	0.192873i
$738$		0			0
$739$	−12.5623	−	12.5623i	−0.462112	−	0.462112i	0.437235	−	0.899347i	$-0.355958\pi$
$739$	−12.5623	−	12.5623i	−0.462112	−	0.462112i	−0.899347	+	0.437235i	$0.855958\pi$
$740$		0			0
$741$	5.52786	+	8.29180i	0.203071	+	0.304607i
$742$		0			0
$743$	25.3050			0.928349			0.464174	−	0.885744i	$-0.346351\pi$
$743$	25.3050			0.928349			0.464174	+	0.885744i	$0.346351\pi$
$744$		0			0
$745$	26.7082	−	26.7082i	0.978513	−	0.978513i
$746$		0			0
$747$			3.41641i			0.125000i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			29.1246i			1.06277i	0.847130	+	0.531386i	$0.178329\pi$
$751$			29.1246i			1.06277i	−0.847130	+	0.531386i	$0.821671\pi$
$752$		0			0
$753$	−6.18034	−	6.18034i	−0.225224	−	0.225224i
$754$		0			0
$755$	−15.3262	+	15.3262i	−0.557779	+	0.557779i
$756$		0			0
$757$	−26.7082	−	26.7082i	−0.970726	−	0.970726i	0.0288574	−	0.999584i	$-0.490813\pi$
$757$	−26.7082	−	26.7082i	−0.970726	−	0.970726i	−0.999584	+	0.0288574i	$0.990813\pi$
$758$		0			0
$759$	6.94427	−	6.94427i	0.252061	−	0.252061i
$760$		0			0
$761$	−16.5279	+	16.5279i	−0.599135	+	0.599135i	−0.940082	−	0.340948i	$-0.889252\pi$
$761$	−16.5279	+	16.5279i	−0.599135	+	0.599135i	0.340948	+	0.940082i	$0.389252\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.1803	+	11.1803i	0.404226	+	0.404226i
$766$		0			0
$767$	−28.0902	−	5.61803i	−1.01428	−	0.202855i
$768$		0			0
$769$	5.00000	−	5.00000i	0.180305	−	0.180305i	−0.611184	−	0.791489i	$-0.709306\pi$
$769$	5.00000	−	5.00000i	0.180305	−	0.180305i	0.791489	+	0.611184i	$0.209306\pi$
$770$		0			0
$771$		−	16.7639i		−	0.603738i
$772$		0			0
$773$	−0.652476			−0.0234679			−0.0117340	−	0.999931i	$-0.503735\pi$
$773$	−0.652476			−0.0234679			−0.0117340	+	0.999931i	$0.503735\pi$
$774$		0			0
$775$	−4.27051	−	4.27051i	−0.153401	−	0.153401i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.0689			0.504070
$780$		0			0
$781$	−0.291796			−0.0104413
$782$		0			0
$783$	0.944272	−	0.944272i	0.0337455	−	0.0337455i
$784$		0			0
$785$	−11.1803	−	11.1803i	−0.399043	−	0.399043i
$786$		0			0
$787$	43.4164			1.54763			0.773814	−	0.633413i	$-0.218347\pi$
$787$	43.4164			1.54763			0.773814	+	0.633413i	$0.218347\pi$
$788$		0			0
$789$			22.7639i			0.810417i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	23.1246	−	15.4164i	0.821179	−	0.547453i
$794$		0			0
$795$			54.0689i			1.91763i
$796$		0			0
$797$	8.88854	−	8.88854i	0.314848	−	0.314848i	−0.531936	−	0.846784i	$-0.678535\pi$
$797$	8.88854	−	8.88854i	0.314848	−	0.314848i	0.846784	+	0.531936i	$0.178535\pi$
$798$		0			0
$799$	−20.0000	+	20.0000i	−0.707549	+	0.707549i
$800$		0			0
$801$	−5.00000	+	5.00000i	−0.176666	+	0.176666i
$802$		0			0
$803$	−0.652476	−	0.652476i	−0.0230254	−	0.0230254i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−36.3607	−	36.3607i	−1.27996	−	1.27996i
$808$		0			0
$809$			3.81966i			0.134292i	0.997743	+	0.0671460i	$0.0213893\pi$
$809$			3.81966i			0.134292i	−0.997743	+	0.0671460i	$0.978611\pi$
$810$		0			0
$811$	−16.5623	−	16.5623i	−0.581581	−	0.581581i	0.353756	−	0.935338i	$-0.384904\pi$
$811$	−16.5623	−	16.5623i	−0.581581	−	0.581581i	−0.935338	+	0.353756i	$0.884904\pi$
$812$		0			0
$813$		−	40.6525i		−	1.42574i
$814$		0			0
$815$		−	39.5967i		−	1.38701i
$816$		0			0
$817$	−4.87539			−0.170568
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.36068	+	7.36068i	0.256889	+	0.256889i	0.823788	−	0.566898i	$-0.191857\pi$
$821$	7.36068	+	7.36068i	0.256889	+	0.256889i	−0.566898	+	0.823788i	$0.691857\pi$
$822$		0			0
$823$	23.9787	+	23.9787i	0.835845	+	0.835845i	0.988309	−	0.152464i	$-0.0487207\pi$
$823$	23.9787	+	23.9787i	0.835845	+	0.835845i	−0.152464	+	0.988309i	$0.548721\pi$
$824$		0			0
$825$			6.18034i			0.215172i
$826$		0			0
$827$	13.5279			0.470410			0.235205	−	0.971946i	$-0.424424\pi$
$827$	13.5279			0.470410			0.235205	+	0.971946i	$0.424424\pi$
$828$		0			0
$829$	0.291796			0.0101345			0.00506725	−	0.999987i	$-0.498387\pi$
$829$	0.291796			0.0101345			0.00506725	+	0.999987i	$0.498387\pi$
$830$		0			0
$831$			34.6525i			1.20208i
$832$		0			0
$833$	15.6525	−	15.6525i	0.542326	−	0.542326i
$834$		0			0
$835$	−50.2492			−1.73895
$836$		0			0
$837$		−	2.11146i		−	0.0729826i
$838$		0			0
$839$	−1.79837	−	1.79837i	−0.0620868	−	0.0620868i	0.675382	−	0.737468i	$-0.263979\pi$
$839$	−1.79837	−	1.79837i	−0.0620868	−	0.0620868i	−0.737468	+	0.675382i	$0.763979\pi$
$840$		0			0
$841$	28.4164			0.979876
$842$		0			0
$843$			7.23607i			0.249223i
$844$		0			0
$845$	11.1803	−	26.8328i	0.384615	−	0.923077i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	29.5967			1.01576
$850$		0			0
$851$	20.8328	+	20.8328i	0.714140	+	0.714140i
$852$		0			0
$853$			45.1246i			1.54504i	0.634992	+	0.772519i	$0.281003\pi$
$853$			45.1246i			1.54504i	−0.634992	+	0.772519i	$0.718997\pi$
$854$		0			0
$855$	−4.27051	−	4.27051i	−0.146048	−	0.146048i
$856$		0			0
$857$	−21.6525	+	21.6525i	−0.739634	+	0.739634i	−0.972507	−	0.232873i	$-0.925187\pi$
$857$	−21.6525	+	21.6525i	−0.739634	+	0.739634i	0.232873	+	0.972507i	$0.425187\pi$
$858$		0			0
$859$		−	38.2918i		−	1.30650i	−0.757143	−	0.653250i	$-0.773405\pi$
$859$		−	38.2918i		−	1.30650i	0.757143	−	0.653250i	$-0.226595\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.5279			−0.868979			−0.434489	−	0.900677i	$-0.643071\pi$
$863$	−25.5279			−0.868979			−0.434489	+	0.900677i	$0.643071\pi$
$864$		0			0
$865$	−11.5836	−	11.5836i	−0.393854	−	0.393854i
$866$		0			0
$867$	11.3262	+	11.3262i	0.384659	+	0.384659i
$868$		0			0
$869$	−3.70820	−	3.70820i	−0.125792	−	0.125792i
$870$		0			0
$871$	27.4164	+	41.1246i	0.928970	+	1.39345i
$872$		0			0
$873$	−25.5279			−0.863987
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	6.83282i		−	0.230728i	−0.993323	−	0.115364i	$-0.963197\pi$
$877$		−	6.83282i		−	0.230728i	0.993323	−	0.115364i	$-0.0368034\pi$
$878$		0			0
$879$	−23.1246	−	23.1246i	−0.779974	−	0.779974i
$880$		0			0
$881$		−	38.0689i		−	1.28257i	−0.767301	−	0.641287i	$-0.778401\pi$
$881$		−	38.0689i		−	1.28257i	0.767301	−	0.641287i	$-0.221599\pi$
$882$		0			0
$883$	21.1459	+	21.1459i	0.711616	+	0.711616i	0.966873	−	0.255257i	$-0.0821601\pi$
$883$	21.1459	+	21.1459i	0.711616	+	0.711616i	−0.255257	+	0.966873i	$0.582160\pi$
$884$		0			0
$885$	40.6525			1.36652
$886$		0			0
$887$	23.6180	+	23.6180i	0.793016	+	0.793016i	0.981983	−	0.188967i	$-0.0605140\pi$
$887$	23.6180	+	23.6180i	0.793016	+	0.793016i	−0.188967	+	0.981983i	$0.560514\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.09017	+	4.09017i	−0.137026	+	0.137026i
$892$		0			0
$893$	7.63932	−	7.63932i	0.255640	−	0.255640i
$894$		0			0
$895$	26.8328			0.896922
$896$		0			0
$897$	54.5410	−	36.3607i	1.82107	−	1.21405i
$898$		0			0
$899$	−0.652476	+	0.652476i	−0.0217613	+	0.0217613i
$900$		0			0
$901$		−	33.4164i		−	1.11326i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	48.5410i		−	1.61356i
$906$		0			0
$907$	−28.2705	+	28.2705i	−0.938707	+	0.938707i	−0.998227	−	0.0595202i	$-0.981043\pi$
$907$	−28.2705	+	28.2705i	−0.938707	+	0.938707i	0.0595202	+	0.998227i	$0.481043\pi$
$908$		0			0
$909$	23.4164			0.776673
$910$		0			0
$911$	−2.83282			−0.0938554			−0.0469277	−	0.998898i	$-0.514943\pi$
$911$	−2.83282			−0.0938554			−0.0469277	+	0.998898i	$0.514943\pi$
$912$		0			0
$913$	0.583592	−	0.583592i	0.0193141	−	0.0193141i
$914$		0			0
$915$	−27.8885	+	27.8885i	−0.921967	+	0.921967i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			5.12461i			0.169045i	0.996422	+	0.0845227i	$0.0269365\pi$
$919$			5.12461i			0.169045i	−0.996422	+	0.0845227i	$0.973063\pi$
$920$		0			0
$921$	−19.4164	+	19.4164i	−0.639792	+	0.639792i
$922$		0			0
$923$	−1.90983	−	0.381966i	−0.0628628	−	0.0125726i
$924$		0			0
$925$	−18.5410			−0.609625
$926$		0			0
$927$	−6.38197	+	6.38197i	−0.209611	+	0.209611i
$928$		0			0
$929$	−32.8885	+	32.8885i	−1.07904	+	1.07904i	−0.0824423	+	0.996596i	$0.526272\pi$
$929$	−32.8885	+	32.8885i	−1.07904	+	1.07904i	−0.996596	+	0.0824423i	$0.973728\pi$
$930$		0			0
$931$	−5.97871	+	5.97871i	−0.195944	+	0.195944i
$932$		0			0
$933$	32.6525	+	32.6525i	1.06899	+	1.06899i
$934$		0			0
$935$		−	3.81966i		−	0.124916i
$936$		0			0
$937$	5.58359	+	5.58359i	0.182408	+	0.182408i	0.792404	−	0.609996i	$-0.208829\pi$
$937$	5.58359	+	5.58359i	0.182408	+	0.182408i	−0.609996	+	0.792404i	$0.708829\pi$
$938$		0			0
$939$			4.18034i			0.136420i
$940$		0			0
$941$	31.3607	+	31.3607i	1.02233	+	1.02233i	0.999745	+	0.0225840i	$0.00718932\pi$
$941$	31.3607	+	31.3607i	1.02233	+	1.02233i	0.0225840	+	0.999745i	$0.492811\pi$
$942$		0			0
$943$		−	92.5410i		−	3.01355i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.9443			0.680597			0.340299	−	0.940317i	$-0.389472\pi$
$947$	20.9443			0.680597			0.340299	+	0.940317i	$0.389472\pi$
$948$		0			0
$949$	−3.41641	−	5.12461i	−0.110901	−	0.166352i
$950$		0			0
$951$	15.7082	+	15.7082i	0.509373	+	0.509373i
$952$		0			0
$953$	32.2361	+	32.2361i	1.04423	+	1.04423i	0.998976	+	0.0452531i	$0.0144094\pi$
$953$	32.2361	+	32.2361i	1.04423	+	1.04423i	0.0452531	+	0.998976i	$0.485591\pi$
$954$		0			0
$955$	−43.4164			−1.40492
$956$		0			0
$957$	0.944272			0.0305240
$958$		0			0
$959$		0			0
$960$		0			0
$961$		−	29.5410i		−	0.952936i
$962$		0			0
$963$	−0.854102	+	0.854102i	−0.0275231	+	0.0275231i
$964$		0			0
$965$			52.3607i			1.68555i
$966$		0			0
$967$		−	33.1246i		−	1.06522i	−0.846362	−	0.532608i	$-0.821212\pi$
$967$		−	33.1246i		−	1.06522i	0.846362	−	0.532608i	$-0.178788\pi$
$968$		0			0
$969$	6.18034	+	6.18034i	0.198541	+	0.198541i
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−8.09017	+	40.4508i	−0.259093	+	1.29546i
$976$		0			0
$977$		−	9.70820i		−	0.310593i	−0.987868	−	0.155296i	$-0.950367\pi$
$977$		−	9.70820i		−	0.310593i	0.987868	−	0.155296i	$-0.0496333\pi$
$978$		0			0
$979$	1.70820			0.0545944
$980$		0			0
$981$	−19.4721	−	19.4721i	−0.621697	−	0.621697i
$982$		0			0
$983$			45.7082i			1.45787i	0.684585	+	0.728933i	$0.259983\pi$
$983$			45.7082i			1.45787i	−0.684585	+	0.728933i	$0.740017\pi$
$984$		0			0
$985$			26.8328i			0.854965i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			32.0689i			1.01973i
$990$		0			0
$991$	−47.4164			−1.50623			−0.753116	−	0.657888i	$-0.771450\pi$
$991$	−47.4164			−1.50623			−0.753116	+	0.657888i	$0.771450\pi$
$992$		0			0
$993$	−29.5967			−0.939224
$994$		0			0
$995$	−34.4721			−1.09284
$996$		0			0
$997$	−29.0000	−	29.0000i	−0.918439	−	0.918439i	0.0784767	−	0.996916i	$-0.474994\pi$
$997$	−29.0000	−	29.0000i	−0.918439	−	0.918439i	−0.996916	+	0.0784767i	$0.974994\pi$
$998$		0			0
$999$	−4.58359	−	4.58359i	−0.145018	−	0.145018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.r.b.177.2	yes	4
3.2	odd	2		2340.2.bp.e.1477.1		4
4.3	odd	2		1040.2.cd.j.177.1		4
5.2	odd	4		1300.2.m.b.593.1		4
5.3	odd	4		260.2.m.b.73.2	yes	4
5.4	even	2		1300.2.r.b.957.1		4
13.5	odd	4		260.2.m.b.57.2	✓	4
15.8	even	4		2340.2.u.f.73.1		4
20.3	even	4		1040.2.bg.j.593.1		4
39.5	even	4		2340.2.u.f.577.2		4
52.31	even	4		1040.2.bg.j.577.1		4
65.18	even	4	inner	260.2.r.b.213.2	yes	4
65.44	odd	4		1300.2.m.b.57.1		4
65.57	even	4		1300.2.r.b.993.1		4
195.83	odd	4		2340.2.bp.e.1513.1		4
260.83	odd	4		1040.2.cd.j.993.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.m.b.57.2	✓	4	13.5	odd	4
260.2.m.b.73.2	yes	4	5.3	odd	4
260.2.r.b.177.2	yes	4	1.1	even	1	trivial
260.2.r.b.213.2	yes	4	65.18	even	4	inner
1040.2.bg.j.577.1		4	52.31	even	4
1040.2.bg.j.593.1		4	20.3	even	4
1040.2.cd.j.177.1		4	4.3	odd	2
1040.2.cd.j.993.1		4	260.83	odd	4
1300.2.m.b.57.1		4	65.44	odd	4
1300.2.m.b.593.1		4	5.2	odd	4
1300.2.r.b.957.1		4	5.4	even	2
1300.2.r.b.993.1		4	65.57	even	4
2340.2.u.f.73.1		4	15.8	even	4
2340.2.u.f.577.2		4	39.5	even	4
2340.2.bp.e.1477.1		4	3.2	odd	2
2340.2.bp.e.1513.1		4	195.83	odd	4

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 - 1.61803i) q^{3} +2.23607 q^{5} -2.23607i q^{9} +O(q^{10})\)	\(q+(1.61803 - 1.61803i) q^{3} +2.23607 q^{5} -2.23607i q^{9} +(-0.381966 + 0.381966i) q^{11} +(-3.00000 + 2.00000i) q^{13} +(3.61803 - 3.61803i) q^{15} +(-2.23607 + 2.23607i) q^{17} +(0.854102 - 0.854102i) q^{19} +(-5.61803 - 5.61803i) q^{23} +5.00000 q^{25} +(1.23607 + 1.23607i) q^{27} -0.763932i q^{29} +(-0.854102 - 0.854102i) q^{31} +1.23607i q^{33} -3.70820 q^{37} +(-1.61803 + 8.09017i) q^{39} +(8.23607 + 8.23607i) q^{41} +(-2.85410 - 2.85410i) q^{43} -5.00000i q^{45} +8.94427 q^{47} -7.00000 q^{49} +7.23607i q^{51} +(-7.47214 + 7.47214i) q^{53} +(-0.854102 + 0.854102i) q^{55} -2.76393i q^{57} +(5.61803 + 5.61803i) q^{59} -7.70820 q^{61} +(-6.70820 + 4.47214i) q^{65} -13.7082i q^{67} -18.1803 q^{69} +(0.381966 + 0.381966i) q^{71} +1.70820i q^{73} +(8.09017 - 8.09017i) q^{75} +9.70820i q^{79} +10.7082 q^{81} -1.52786 q^{83} +(-5.00000 + 5.00000i) q^{85} +(-1.23607 - 1.23607i) q^{87} +(-2.23607 - 2.23607i) q^{89} -2.76393 q^{93} +(1.90983 - 1.90983i) q^{95} -11.4164i q^{97} +(0.854102 + 0.854102i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3}+O(q^{10}) \) 4 * q + 2 * q^3	\( 4 q + 2 q^{3} - 6 q^{11} - 12 q^{13} + 10 q^{15} - 10 q^{19} - 18 q^{23} + 20 q^{25} - 4 q^{27} + 10 q^{31} + 12 q^{37} - 2 q^{39} + 24 q^{41} + 2 q^{43} - 28 q^{49} - 12 q^{53} + 10 q^{55} + 18 q^{59} - 4 q^{61} - 28 q^{69} + 6 q^{71} + 10 q^{75} + 16 q^{81} - 24 q^{83} - 20 q^{85} + 4 q^{87} - 20 q^{93} + 30 q^{95} - 10 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^11 - 12 * q^13 + 10 * q^15 - 10 * q^19 - 18 * q^23 + 20 * q^25 - 4 * q^27 + 10 * q^31 + 12 * q^37 - 2 * q^39 + 24 * q^41 + 2 * q^43 - 28 * q^49 - 12 * q^53 + 10 * q^55 + 18 * q^59 - 4 * q^61 - 28 * q^69 + 6 * q^71 + 10 * q^75 + 16 * q^81 - 24 * q^83 - 20 * q^85 + 4 * q^87 - 20 * q^93 + 30 * q^95 - 10 * q^99

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