LMFDB - Embedded newform 260.2.bg.a.147.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{12}]$

Embedding invariants

Embedding label			147.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	260.147
Dual form			260.2.bg.a.23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-3.00000 + 1.00000i) q^{10} +(1.59808 + 3.23205i) q^{13} +(2.00000 - 3.46410i) q^{16} +(0.0358984 - 0.133975i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.46410 - 3.73205i) q^{20} +(-4.96410 + 0.598076i) q^{25} +(-3.83013 + 3.36603i) q^{26} +(9.23205 + 5.33013i) q^{29} +(5.46410 + 1.46410i) q^{32} +0.196152 q^{34} +(3.00000 - 5.19615i) q^{36} +(-2.86603 - 10.6962i) q^{37} +(4.19615 - 4.73205i) q^{40} +(10.3301 + 5.96410i) q^{41} +(-3.69615 - 5.59808i) q^{45} +(6.06218 + 3.50000i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(-6.00000 - 4.00000i) q^{52} +(5.29423 - 5.29423i) q^{53} +(-3.90192 + 14.5622i) q^{58} +(1.33013 + 2.30385i) q^{61} +8.00000i q^{64} +(-7.00000 + 4.00000i) q^{65} +(0.0717968 + 0.267949i) q^{68} +(8.19615 + 2.19615i) q^{72} +(-1.16987 - 1.16987i) q^{73} +(13.5622 - 7.83013i) q^{74} +(8.00000 + 4.00000i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.36603 + 16.2942i) q^{82} +(0.303848 + 0.0621778i) q^{85} +(-5.00000 + 8.66025i) q^{89} +(6.29423 - 7.09808i) q^{90} +(-17.7583 - 4.75833i) q^{97} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8	$ 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8 - 12 * q^10 - 4 * q^13 + 8 * q^16 + 14 * q^17 - 12 * q^18 + 4 * q^20 - 6 * q^25 + 2 * q^26 + 30 * q^29 + 8 * q^32 - 20 * q^34 + 12 * q^36 - 8 * q^37 - 4 * q^40 + 24 * q^41 + 6 * q^45 - 14 * q^50 - 24 * q^52 - 10 * q^53 - 26 * q^58 - 12 * q^61 - 28 * q^65 + 28 * q^68 + 12 * q^72 - 22 * q^73 + 30 * q^74 + 32 * q^80 + 18 * q^81 - 14 * q^82 + 22 * q^85 - 20 * q^89 - 6 * q^90 - 26 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$3$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$7$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	−2.59808	+	1.50000i	−0.866025	+	0.500000i
$10$	−3.00000	+	1.00000i	−0.948683	+	0.316228i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$13$	1.59808	+	3.23205i	0.443227	+	0.896410i
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	0.0358984	−	0.133975i	0.00870664	−	0.0324936i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	0.0358984	−	0.133975i	0.00870664	−	0.0324936i	0.970143	+	0.242536i	$0.0779791\pi$
$18$	−3.00000	−	3.00000i	−0.707107	−	0.707107i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−2.46410	−	3.73205i	−0.550990	−	0.834512i
$21$		0			0
$22$		0			0
$23$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$23$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−3.83013	+	3.36603i	−0.751150	+	0.660132i
$27$		0			0
$28$		0			0
$29$	9.23205	+	5.33013i	1.71435	+	0.989780i	0.928477	+	0.371391i	$0.121119\pi$
$29$	9.23205	+	5.33013i	1.71435	+	0.989780i	0.785872	+	0.618389i	$0.212214\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$		0			0
$34$	0.196152			0.0336399
$35$		0			0
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	−2.86603	−	10.6962i	−0.471172	−	1.75844i	−0.635571	−	0.772043i	$-0.719235\pi$
$37$	−2.86603	−	10.6962i	−0.471172	−	1.75844i	0.164399	−	0.986394i	$-0.447432\pi$
$38$		0			0
$39$		0			0
$40$	4.19615	−	4.73205i	0.663470	−	0.748203i
$41$	10.3301	+	5.96410i	1.61329	+	0.931436i	0.988600	+	0.150567i	$0.0481100\pi$
$41$	10.3301	+	5.96410i	1.61329	+	0.931436i	0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$43$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$44$		0			0
$45$	−3.69615	−	5.59808i	−0.550990	−	0.834512i
$46$		0			0
$47$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$47$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$48$		0			0
$49$	6.06218	+	3.50000i	0.866025	+	0.500000i
$50$	−2.63397	−	6.56218i	−0.372500	−	0.928032i
$51$		0			0
$52$	−6.00000	−	4.00000i	−0.832050	−	0.554700i
$53$	5.29423	−	5.29423i	0.727218	−	0.727218i	−0.242846	−	0.970065i	$-0.578081\pi$
$53$	5.29423	−	5.29423i	0.727218	−	0.727218i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−3.90192	+	14.5622i	−0.512348	+	1.91211i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$		0			0
$61$	1.33013	+	2.30385i	0.170305	+	0.294977i	0.938527	−	0.345207i	$-0.112191\pi$
$61$	1.33013	+	2.30385i	0.170305	+	0.294977i	−0.768221	+	0.640184i	$0.778858\pi$
$62$		0			0
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−7.00000	+	4.00000i	−0.868243	+	0.496139i
$66$		0			0
$67$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$67$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$68$	0.0717968	+	0.267949i	0.00870664	+	0.0324936i
$69$		0			0
$70$		0			0
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	8.19615	+	2.19615i	0.965926	+	0.258819i
$73$	−1.16987	−	1.16987i	−0.136923	−	0.136923i	0.635323	−	0.772246i	$-0.280867\pi$
$73$	−1.16987	−	1.16987i	−0.136923	−	0.136923i	−0.772246	+	0.635323i	$0.780867\pi$
$74$	13.5622	−	7.83013i	1.57657	−	0.910234i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	8.00000	+	4.00000i	0.894427	+	0.447214i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−4.36603	+	16.2942i	−0.482147	+	1.79940i
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$		0			0
$85$	0.303848	+	0.0621778i	0.0329569	+	0.00674413i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$	6.29423	−	7.09808i	0.663470	−	0.748203i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−17.7583	−	4.75833i	−1.80309	−	0.483135i	−0.808632	−	0.588315i	$-0.799792\pi$
$97$	−17.7583	−	4.75833i	−1.80309	−	0.483135i	−0.994453	+	0.105180i	$0.966458\pi$
$98$	−2.56218	+	9.56218i	−0.258819	+	0.965926i
$99$		0			0
$100$	8.00000	−	6.00000i	0.800000	−	0.600000i
$101$	9.16025	−	15.8660i	0.911479	−	1.57873i	0.0995037	−	0.995037i	$-0.468274\pi$
$101$	9.16025	−	15.8660i	0.911479	−	1.57873i	0.811976	−	0.583691i	$-0.198392\pi$
$102$		0			0
$103$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$103$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$104$	3.26795	−	9.66025i	0.320449	−	0.947266i
$105$		0			0
$106$	9.16987	+	5.29423i	0.890657	+	0.514221i
$107$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$107$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$108$		0			0
$109$	−20.0000			−1.91565			−0.957826	−	0.287348i	$-0.907226\pi$
$109$	−20.0000			−1.91565			−0.957826	+	0.287348i	$0.907226\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.06218	−	2.42820i	−0.852498	−	0.228426i	−0.193993	−	0.981003i	$-0.562144\pi$
$113$	−9.06218	−	2.42820i	−0.852498	−	0.228426i	−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$		0			0
$116$	−21.3205			−1.97956
$117$	−9.00000	−	6.00000i	−0.832050	−	0.554700i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$	−2.66025	+	2.66025i	−0.240848	+	0.240848i
$123$		0			0
$124$		0			0
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$127$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$		0			0
$130$	−8.02628	−	8.09808i	−0.703951	−	0.710248i
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.339746	+	0.196152i	−0.0291330	+	0.0168199i
$137$	12.9641	+	3.47372i	1.10760	+	0.296780i	0.765855	−	0.643013i	$-0.222316\pi$
$137$	12.9641	+	3.47372i	1.10760	+	0.296780i	0.341743	+	0.939793i	$0.388983\pi$
$138$		0			0
$139$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$139$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$			12.0000i			1.00000i
$145$	−10.6603	+	21.3205i	−0.885286	+	1.77057i
$146$	1.16987	−	2.02628i	0.0968194	−	0.167696i
$147$		0			0
$148$	15.6603	+	15.6603i	1.28726	+	1.28726i
$149$	−11.0622	−	19.1603i	−0.906249	−	1.56967i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−11.0622	−	19.1603i	−0.906249	−	1.56967i	−0.0870170	−	0.996207i	$-0.527733\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$	0.107695	+	0.401924i	0.00870664	+	0.0324936i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−17.2224	−	17.2224i	−1.37450	−	1.37450i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	−17.2224	−	17.2224i	−1.37450	−	1.37450i	−0.520854	−	0.853646i	$-0.674386\pi$
$158$		0			0
$159$		0			0
$160$	−2.53590	+	12.3923i	−0.200480	+	0.979698i
$161$		0			0
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$163$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$164$	−23.8564			−1.86287
$165$		0			0
$166$		0			0
$167$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$167$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$168$		0			0
$169$	−7.89230	+	10.3301i	−0.607100	+	0.794625i
$170$	0.0262794	+	0.437822i	0.00201554	+	0.0335794i
$171$		0			0
$172$		0			0
$173$	20.4904	+	5.49038i	1.55785	+	0.417426i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	20.4904	+	5.49038i	1.55785	+	0.417426i	0.625871	+	0.779926i	$0.284744\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−13.6603	−	3.66025i	−1.02388	−	0.274348i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	12.0000	+	6.00000i	0.894427	+	0.447214i
$181$	8.32051			0.618458			0.309229	−	0.950988i	$-0.399929\pi$
$181$	8.32051			0.618458			0.309229	+	0.950988i	$0.399929\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	23.4904	−	7.83013i	1.72705	−	0.575682i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$		0			0
$193$	7.06218	−	1.89230i	0.508347	−	0.136211i	0.00447566	−	0.999990i	$-0.498575\pi$
$193$	7.06218	−	1.89230i	0.508347	−	0.136211i	0.503871	+	0.863779i	$0.331909\pi$
$194$		−	26.0000i		−	1.86669i
$195$		0			0
$196$	−14.0000			−1.00000
$197$	4.75833	+	17.7583i	0.339017	+	1.26523i	0.899448	+	0.437028i	$0.143969\pi$
$197$	4.75833	+	17.7583i	0.339017	+	1.26523i	−0.560431	+	0.828201i	$0.689365\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	11.1244	+	8.73205i	0.786611	+	0.617449i
$201$		0			0
$202$	25.0263	+	6.70577i	1.76084	+	0.471816i
$203$		0			0
$204$		0			0
$205$	−11.9282	+	23.8564i	−0.833102	+	1.66620i
$206$		0			0
$207$		0			0
$208$	14.3923	+	0.928203i	0.997927	+	0.0643593i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	−3.87564	+	14.4641i	−0.266180	+	0.993399i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−7.32051	−	27.3205i	−0.495807	−	1.85038i
$219$		0			0
$220$		0			0
$221$	0.490381	−	0.0980762i	0.0329866	−	0.00659732i
$222$		0			0
$223$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$223$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$224$		0			0
$225$	12.0000	−	9.00000i	0.800000	−	0.600000i
$226$		−	13.2679i		−	0.882571i
$227$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$227$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$228$		0			0
$229$	30.0000			1.98246			0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000			1.98246			0.991228	+	0.132164i	$0.0421925\pi$
$230$		0			0
$231$		0			0
$232$	−7.80385	−	29.1244i	−0.512348	−	1.91211i
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$	4.90192	−	14.4904i	0.320449	−	0.947266i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$	−18.9904	+	10.9641i	−1.22328	+	0.706260i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−18.9904	+	10.9641i	−1.22328	+	0.706260i	−0.257663	+	0.966235i	$0.582952\pi$
$242$	−11.0000	+	11.0000i	−0.707107	+	0.707107i
$243$		0			0
$244$	−4.60770	−	2.66025i	−0.294977	−	0.170305i
$245$	−7.00000	+	14.0000i	−0.447214	+	0.894427i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	14.2942	−	6.75833i	0.904046	−	0.427434i
$251$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$251$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	30.3564	−	8.13397i	1.89358	−	0.507383i	0.895528	−	0.445005i	$-0.146798\pi$
$257$	30.3564	−	8.13397i	1.89358	−	0.507383i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$		0			0
$259$		0			0
$260$	8.12436	−	13.9282i	0.503851	−	0.863790i
$261$	−31.9808			−1.97956
$262$		0			0
$263$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$263$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$264$		0			0
$265$	12.5263	+	11.1077i	0.769483	+	0.682340i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	22.5167	−	13.0000i	1.37287	−	0.792624i	0.381577	−	0.924337i	$-0.375381\pi$
$269$	22.5167	−	13.0000i	1.37287	−	0.792624i	0.991288	+	0.131713i	$0.0420477\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−0.392305	−	0.392305i	−0.0237870	−	0.0237870i
$273$		0			0
$274$			18.9808i			1.14667i
$275$		0			0
$276$		0			0
$277$	8.20577	−	30.6244i	0.493037	−	1.84004i	−0.0477206	−	0.998861i	$-0.515196\pi$
$277$	8.20577	−	30.6244i	0.493037	−	1.84004i	0.540758	−	0.841178i	$-0.318138\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			22.7128i			1.35493i	0.735554	+	0.677466i	$0.236922\pi$
$281$			22.7128i			1.35493i	−0.735554	+	0.677466i	$0.763078\pi$
$282$		0			0
$283$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$283$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−16.3923	+	4.39230i	−0.965926	+	0.258819i
$289$	14.7058	+	8.49038i	0.865045	+	0.499434i
$290$	−33.0263	−	6.75833i	−1.93937	−	0.396863i
$291$		0			0
$292$	3.19615	+	0.856406i	0.187041	+	0.0501174i
$293$	8.23205	−	30.7224i	0.480922	−	1.79482i	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	8.23205	−	30.7224i	0.480922	−	1.79482i	0.597763	−	0.801673i	$-0.296056\pi$
$294$		0			0
$295$		0			0
$296$	−15.6603	+	27.1244i	−0.910234	+	1.57657i
$297$		0			0
$298$	22.1244	−	22.1244i	1.28163	−	1.28163i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.96410	+	3.27757i	−0.284244	+	0.187673i
$306$	−0.509619	+	0.294229i	−0.0291330	+	0.0168199i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	25.0000	−	25.0000i	1.41308	−	1.41308i	0.678280	−	0.734803i	$-0.262726\pi$
$313$	25.0000	−	25.0000i	1.41308	−	1.41308i	0.734803	−	0.678280i	$-0.237274\pi$
$314$	17.2224	−	29.8301i	0.971918	−	1.68341i
$315$		0			0
$316$		0			0
$317$	−20.1506	+	20.1506i	−1.13177	+	1.13177i	−0.141890	+	0.989882i	$0.545318\pi$
$317$	−20.1506	+	20.1506i	−1.13177	+	1.13177i	−0.989882	+	0.141890i	$0.954682\pi$
$318$		0			0
$319$		0			0
$320$	−17.8564	+	1.07180i	−0.998203	+	0.0599153i
$321$		0			0
$322$		0			0
$323$		0			0
$324$			18.0000i			1.00000i
$325$	−9.86603	−	15.0885i	−0.547269	−	0.836957i
$326$		0			0
$327$		0			0
$328$	−8.73205	−	32.5885i	−0.482147	−	1.79940i
$329$		0			0
$330$		0			0
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$		0			0
$333$	23.4904	+	23.4904i	1.28726	+	1.28726i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	18.5622	+	18.5622i	1.01115	+	1.01115i	0.999937	+	0.0112091i	$0.00356804\pi$
$337$	18.5622	+	18.5622i	1.01115	+	1.01115i	0.0112091	+	0.999937i	$0.496432\pi$
$338$	−17.0000	−	7.00000i	−0.924678	−	0.380750i
$339$		0			0
$340$	−0.588457	+	0.196152i	−0.0319136	+	0.0106379i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$			30.0000i			1.61281i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−35.7224	+	9.57180i	−1.90131	+	0.509455i	−0.904819	+	0.425797i	$0.859994\pi$
$353$	−35.7224	+	9.57180i	−1.90131	+	0.509455i	−0.996495	+	0.0836583i	$0.973340\pi$
$354$		0			0
$355$		0			0
$356$		−	20.0000i		−	1.06000i
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−3.80385	+	18.5885i	−0.200480	+	0.979698i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	3.04552	+	11.3660i	0.160069	+	0.597385i
$363$		0			0
$364$		0			0
$365$	2.45448	−	2.76795i	0.128473	−	0.144881i
$366$		0			0
$367$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$367$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$368$		0			0
$369$	−35.7846			−1.86287
$370$	19.2942	+	29.2224i	1.00306	+	1.51920i
$371$		0			0
$372$		0			0
$373$	−30.0885	−	8.06218i	−1.55792	−	0.417444i	−0.625917	−	0.779890i	$-0.715275\pi$
$373$	−30.0885	−	8.06218i	−1.55792	−	0.417444i	−0.932005	+	0.362446i	$0.881942\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.47372	+	38.3564i	−0.127403	+	1.97546i
$378$		0			0
$379$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$379$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$383$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$384$		0			0
$385$		0			0
$386$	5.16987	+	8.95448i	0.263140	+	0.455771i
$387$		0			0
$388$	35.5167	−	9.51666i	1.80309	−	0.483135i
$389$			34.3205i			1.74012i	0.492947	+	0.870059i	$0.335920\pi$
$389$			34.3205i			1.74012i	−0.492947	+	0.870059i	$0.664080\pi$
$390$		0			0
$391$		0			0
$392$	−5.12436	−	19.1244i	−0.258819	−	0.965926i
$393$		0			0
$394$	−22.5167	+	13.0000i	−1.13437	+	0.654931i
$395$		0			0
$396$		0			0
$397$	17.7583	+	4.75833i	0.891265	+	0.238814i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	17.7583	+	4.75833i	0.891265	+	0.238814i	0.216004	+	0.976392i	$0.430698\pi$
$398$		0			0
$399$		0			0
$400$	−7.85641	+	18.3923i	−0.392820	+	0.919615i
$401$	−18.8205	−	10.8660i	−0.939851	−	0.542623i	−0.0499376	−	0.998752i	$-0.515902\pi$
$401$	−18.8205	−	10.8660i	−0.939851	−	0.542623i	−0.889914	+	0.456129i	$0.849236\pi$
$402$		0			0
$403$		0			0
$404$			36.6410i			1.82296i
$405$	18.0000	+	9.00000i	0.894427	+	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−12.5981	−	21.8205i	−0.622935	−	1.07895i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−12.5981	−	21.8205i	−0.622935	−	1.07895i	0.366002	−	0.930614i	$-0.380726\pi$
$410$	−36.9545	−	7.56218i	−1.82505	−	0.373469i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	4.00000	+	20.0000i	0.196116	+	0.980581i
$417$		0			0
$418$		0			0
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$		0			0
$421$		−	9.24871i		−	0.450755i	−0.974272	−	0.225377i	$-0.927639\pi$
$421$		−	9.24871i		−	0.450755i	0.974272	−	0.225377i	$-0.0723615\pi$
$422$		0			0
$423$		0			0
$424$	−21.1769			−1.02844
$425$	−0.0980762	+	0.686533i	−0.00475740	+	0.0333018i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	−30.8923	−	8.27757i	−1.48459	−	0.397795i	−0.576683	−	0.816968i	$-0.695653\pi$
$433$	−30.8923	−	8.27757i	−1.48459	−	0.397795i	−0.907906	+	0.419173i	$0.862320\pi$
$434$		0			0
$435$		0			0
$436$	34.6410	−	20.0000i	1.65900	−	0.957826i
$437$		0			0
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−21.0000			−1.00000
$442$	0.313467	+	0.633975i	0.0149101	+	0.0301551i
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−20.0000	−	10.0000i	−0.948091	−	0.474045i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−20.0000	−	34.6410i	−0.943858	−	1.63481i	−0.758021	−	0.652230i	$-0.773834\pi$
$449$	−20.0000	−	34.6410i	−0.943858	−	1.63481i	−0.185837	−	0.982581i	$-0.559500\pi$
$450$	16.6865	+	13.0981i	0.786611	+	0.617449i
$451$		0			0
$452$	18.1244	−	4.85641i	0.852498	−	0.228426i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.81347	−	17.9641i	−0.225164	−	0.840325i	−0.982339	−	0.187112i	$-0.940087\pi$
$457$	−4.81347	−	17.9641i	−0.225164	−	0.840325i	0.757174	−	0.653213i	$-0.226579\pi$
$458$	10.9808	+	40.9808i	0.513097	+	1.91491i
$459$		0			0
$460$		0			0
$461$	19.8397	−	11.4545i	0.924029	−	0.533488i	0.0391109	−	0.999235i	$-0.487547\pi$
$461$	19.8397	−	11.4545i	0.924029	−	0.533488i	0.884918	+	0.465746i	$0.154214\pi$
$462$		0			0
$463$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$463$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$464$	36.9282	−	21.3205i	1.71435	−	0.989780i
$465$		0			0
$466$	−8.66025	−	5.00000i	−0.401179	−	0.231621i
$467$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$	21.5885	+	1.39230i	0.997927	+	0.0643593i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.81347	+	21.6962i	−0.266180	+	0.993399i
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	29.9904	−	26.3564i	1.36744	−	1.20175i
$482$	−21.9282	−	21.9282i	−0.998802	−	0.998802i
$483$		0			0
$484$	−19.0526	−	11.0000i	−0.866025	−	0.500000i
$485$	8.24167	−	40.2750i	0.374235	−	1.82879i
$486$		0			0
$487$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$487$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$488$	1.94744	−	7.26795i	0.0881565	−	0.329005i
$489$		0			0
$490$	−21.6865	−	4.43782i	−0.979698	−	0.200480i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$	1.04552	−	1.04552i	0.0470877	−	0.0470877i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	14.4641	+	17.0526i	0.646854	+	0.762614i
$501$		0			0
$502$		0			0
$503$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$503$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$504$		0			0
$505$	36.6410	+	18.3205i	1.63050	+	0.815252i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.5526	−	28.6699i	0.733679	−	1.27077i	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	16.5526	−	28.6699i	0.733679	−	1.27077i	0.955300	−	0.295637i	$-0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	22.2224	+	38.4904i	0.980189	+	1.69774i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	22.0000	+	6.00000i	0.964764	+	0.263117i
$521$	−23.6410			−1.03573			−0.517866	−	0.855462i	$-0.673273\pi$
$521$	−23.6410			−1.03573			−0.517866	+	0.855462i	$0.673273\pi$
$522$	−11.7058	−	43.6865i	−0.512348	−	1.91211i
$523$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$523$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−19.9186	+	11.5000i	−0.866025	+	0.500000i
$530$	−10.5885	+	21.1769i	−0.459933	+	0.919866i
$531$		0			0
$532$		0			0
$533$	−2.76795	+	42.9186i	−0.119893	+	1.85901i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	26.0000	+	26.0000i	1.12094	+	1.12094i
$539$		0			0
$540$		0			0
$541$		−	46.3731i		−	1.99373i	−0.0790969	−	0.996867i	$-0.525204\pi$
$541$		−	46.3731i		−	1.99373i	0.0790969	−	0.996867i	$-0.474796\pi$
$542$		0			0
$543$		0			0
$544$	0.392305	−	0.679492i	0.0168199	−	0.0291330i
$545$	−2.67949	−	44.6410i	−0.114777	−	1.91221i
$546$		0			0
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−25.9282	+	6.94744i	−1.10760	+	0.296780i
$549$	−6.91154	−	3.99038i	−0.294977	−	0.170305i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	44.8372			1.90495
$555$		0			0
$556$		0			0
$557$	7.62436	+	28.4545i	0.323054	+	1.20566i	0.916253	+	0.400599i	$0.131198\pi$
$557$	7.62436	+	28.4545i	0.323054	+	1.20566i	−0.593199	+	0.805056i	$0.702135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−31.0263	+	8.31347i	−1.30876	+	0.350682i
$563$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$563$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$564$		0			0
$565$	4.20577	−	20.5526i	0.176938	−	0.864653i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.5167	+	13.0000i	0.943948	+	0.544988i	0.891196	−	0.453619i	$-0.149867\pi$
$569$	22.5167	+	13.0000i	0.943948	+	0.544988i	0.0527519	+	0.998608i	$0.483201\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−12.0000	−	20.7846i	−0.500000	−	0.866025i
$577$	33.1506	−	33.1506i	1.38008	−	1.38008i	0.535620	−	0.844459i	$-0.320078\pi$
$577$	33.1506	−	33.1506i	1.38008	−	1.38008i	0.844459	−	0.535620i	$-0.179922\pi$
$578$	−6.21539	+	23.1962i	−0.258526	+	0.964833i
$579$		0			0
$580$	−2.85641	−	47.5885i	−0.118606	−	1.97600i
$581$		0			0
$582$		0			0
$583$		0			0
$584$			4.67949i			0.193639i
$585$	12.1865	−	20.8923i	0.503851	−	0.863790i
$586$	44.9808			1.85814
$587$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$587$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−42.7846	−	11.4641i	−1.75844	−	0.471172i
$593$	2.50962	+	2.50962i	0.103058	+	0.103058i	0.756756	−	0.653698i	$-0.226783\pi$
$593$	2.50962	+	2.50962i	0.103058	+	0.103058i	−0.653698	+	0.756756i	$0.726783\pi$
$594$		0			0
$595$		0			0
$596$	38.3205	+	22.1244i	1.56967	+	0.906249i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−7.66987	+	13.2846i	−0.312861	+	0.541891i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$	−7.66987	+	13.2846i	−0.312861	+	0.541891i	0.666120	+	0.745845i	$0.267954\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−20.5263	+	13.5526i	−0.834512	+	0.550990i
$606$		0			0
$607$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$607$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$608$		0			0
$609$		0			0
$610$	−6.29423	−	5.58142i	−0.254846	−	0.225985i
$611$		0			0
$612$	−0.588457	−	0.588457i	−0.0237870	−	0.0237870i
$613$	−42.0885	+	11.2776i	−1.69994	+	0.455497i	−0.972924	−	0.231127i	$-0.925759\pi$
$613$	−42.0885	+	11.2776i	−1.69994	+	0.455497i	−0.727013	+	0.686624i	$0.759092\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−39.3564	−	10.5455i	−1.58443	−	0.424547i	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−39.3564	−	10.5455i	−1.58443	−	0.424547i	−0.940294	+	0.340365i	$0.889449\pi$
$618$		0			0
$619$		0			0		1.00000			$0$
$619$		0			0		−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	43.3013	+	25.0000i	1.73067	+	0.999201i
$627$		0			0
$628$	47.0526	+	12.6077i	1.87760	+	0.503102i
$629$	−1.53590			−0.0612403
$630$		0			0
$631$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$631$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$632$		0			0
$633$		0			0
$634$	−34.9019	−	20.1506i	−1.38613	−	0.800284i
$635$		0			0
$636$		0			0
$637$	−1.62436	+	25.1865i	−0.0643593	+	0.997927i
$638$		0			0
$639$		0			0
$640$	−8.00000	−	24.0000i	−0.316228	−	0.948683i
$641$	19.6506	+	34.0359i	0.776153	+	1.34434i	0.934144	+	0.356897i	$0.116165\pi$
$641$	19.6506	+	34.0359i	0.776153	+	1.34434i	−0.157991	+	0.987441i	$0.550502\pi$
$642$		0			0
$643$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$643$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$647$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$648$	−24.5885	+	6.58846i	−0.965926	+	0.258819i
$649$		0			0
$650$	17.0000	−	19.0000i	0.666795	−	0.745241i
$651$		0			0
$652$		0			0
$653$	12.8109	+	47.8109i	0.501329	+	1.87098i	0.491220	+	0.871036i	$0.336551\pi$
$653$	12.8109	+	47.8109i	0.501329	+	1.87098i	0.0101092	+	0.999949i	$0.496782\pi$
$654$		0			0
$655$		0			0
$656$	41.3205	−	23.8564i	1.61329	−	0.931436i
$657$	4.79423	+	1.28461i	0.187041	+	0.0501174i
$658$		0			0
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−12.6506	−	7.30385i	−0.492053	−	0.284087i	0.233373	−	0.972387i	$-0.425024\pi$
$661$	−12.6506	−	7.30385i	−0.492053	−	0.284087i	−0.725426	+	0.688301i	$0.758357\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−23.4904	+	40.6865i	−0.910234	+	1.57657i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−2.91858	−	10.8923i	−0.112503	−	0.419867i	0.886585	−	0.462566i	$-0.153071\pi$
$673$	−2.91858	−	10.8923i	−0.112503	−	0.419867i	−0.999088	+	0.0426985i	$0.986405\pi$
$674$	−18.5622	+	32.1506i	−0.714988	+	1.23840i
$675$		0			0
$676$	3.33975	−	25.7846i	0.128452	−	0.991716i
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	0.999261	−	0.0384331i	$-0.0122367\pi$
$677$	25.0000	+	25.0000i	0.960828	+	0.960828i	−0.0384331	+	0.999261i	$0.512237\pi$
$678$		0			0
$679$		0			0
$680$	−0.483340	−	0.732051i	−0.0185352	−	0.0280729i
$681$		0			0
$682$		0			0
$683$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$683$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$684$		0			0
$685$	−6.01666	+	29.4019i	−0.229885	+	1.12339i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	25.5718	+	8.65064i	0.974208	+	0.329563i
$690$		0			0
$691$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$691$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$692$	−40.9808	+	10.9808i	−1.55785	+	0.417426i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.16987	−	1.16987i	0.0443121	−	0.0443121i
$698$	13.6603	+	3.66025i	0.517048	+	0.138543i
$699$		0			0
$700$		0			0
$701$	52.0000			1.96401			0.982006	−	0.188847i	$-0.0604752\pi$
$701$	52.0000			1.96401			0.982006	+	0.188847i	$0.0604752\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−26.1506	−	45.2942i	−0.984192	−	1.70467i
$707$		0			0
$708$		0			0
$709$	11.5526	+	20.0096i	0.433865	+	0.751477i	0.997202	−	0.0747503i	$-0.0238160\pi$
$709$	11.5526	+	20.0096i	0.433865	+	0.751477i	−0.563337	+	0.826227i	$0.690483\pi$
$710$		0			0
$711$		0			0
$712$	27.3205	−	7.32051i	1.02388	−	0.274348i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−26.7846	+	1.60770i	−0.998203	+	0.0599153i
$721$		0			0
$722$	−25.9545	−	6.95448i	−0.965926	−	0.258819i
$723$		0			0
$724$	−14.4115	+	8.32051i	−0.535601	+	0.309229i
$725$	−49.0167	−	20.9378i	−1.82043	−	0.777611i
$726$		0			0
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	4.67949	+	2.33975i	0.173196	+	0.0865979i
$731$		0			0
$732$		0			0
$733$	7.15064	+	7.15064i	0.264115	+	0.264115i	0.826723	−	0.562609i	$-0.190202\pi$
$733$	7.15064	+	7.15064i	0.264115	+	0.264115i	−0.562609	+	0.826723i	$0.690202\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−13.0981	−	48.8827i	−0.482147	−	1.79940i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$	−32.8564	+	37.0526i	−1.20783	+	1.36208i
$741$		0			0
$742$		0			0
$743$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$743$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$744$		0			0
$745$	41.2846	−	27.2583i	1.51255	−	0.998668i
$746$		−	44.0526i		−	1.61288i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	−53.3013	+	10.6603i	−1.94112	+	0.388224i
$755$		0			0
$756$		0			0
$757$	−47.8109	+	12.8109i	−1.73772	+	0.465620i	−0.981937	−	0.189207i	$-0.939408\pi$
$757$	−47.8109	+	12.8109i	−1.73772	+	0.465620i	−0.755779	+	0.654827i	$0.772742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−34.6410	+	20.0000i	−1.25574	+	0.724999i	−0.972243	−	0.233975i	$-0.924827\pi$
$761$	−34.6410	+	20.0000i	−1.25574	+	0.724999i	−0.283493	+	0.958974i	$0.591493\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.882686	+	0.294229i	−0.0319136	+	0.0106379i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.825518	−	0.564376i	$-0.190883\pi$
$770$		0			0
$771$		0			0
$772$	−10.3397	+	10.3397i	−0.372136	+	0.372136i
$773$	−14.2750	+	53.2750i	−0.513436	+	1.91617i	−0.133887	+	0.990997i	$0.542746\pi$
$773$	−14.2750	+	53.2750i	−0.513436	+	1.91617i	−0.379549	+	0.925172i	$0.623921\pi$
$774$		0			0
$775$		0			0
$776$	26.0000	+	45.0333i	0.933346	+	1.61660i
$777$		0			0
$778$	−46.8827	+	12.5622i	−1.68083	+	0.450376i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	24.2487	−	14.0000i	0.866025	−	0.500000i
$785$	36.1340	−	40.7487i	1.28968	−	1.45438i
$786$		0			0
$787$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	−26.0000	−	26.0000i	−0.926212	−	0.926212i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−5.32051	+	7.98076i	−0.188937	+	0.283405i
$794$			26.0000i			0.922705i
$795$		0			0
$796$		0			0
$797$	−5.49038	+	20.4904i	−0.194479	+	0.725807i	0.797922	+	0.602761i	$0.205933\pi$
$797$	−5.49038	+	20.4904i	−0.194479	+	0.725807i	−0.992401	+	0.123045i	$0.960734\pi$
$798$		0			0
$799$		0			0
$800$	−28.0000	−	4.00000i	−0.989949	−	0.141421i
$801$		−	30.0000i		−	1.06000i
$802$	7.95448	−	29.6865i	0.280883	−	1.04827i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−50.0526	+	13.4115i	−1.76084	+	0.471816i
$809$	−31.7487	−	18.3301i	−1.11623	−	0.644453i	−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−31.7487	−	18.3301i	−1.11623	−	0.644453i	−0.940435	+	0.339975i	$0.889582\pi$
$810$	−5.70577	+	27.8827i	−0.200480	+	0.979698i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	25.1962	−	25.1962i	0.880963	−	0.880963i
$819$		0			0
$820$	−3.19615	−	53.2487i	−0.111614	−	1.85953i
$821$	−43.3013	−	25.0000i	−1.51122	−	0.872506i	−0.999914	−	0.0131101i	$-0.995827\pi$
$821$	−43.3013	−	25.0000i	−1.51122	−	0.872506i	−0.511311	−	0.859396i	$-0.670840\pi$
$822$		0			0
$823$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$823$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$	38.3827	+	22.1603i	1.33309	+	0.769657i	0.985771	−	0.168091i	$-0.0537604\pi$
$829$	38.3827	+	22.1603i	1.33309	+	0.769657i	0.347314	+	0.937749i	$0.387094\pi$
$830$		0			0
$831$		0			0
$832$	−25.8564	+	12.7846i	−0.896410	+	0.443227i
$833$	0.686533	−	0.686533i	0.0237870	−	0.0237870i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$		0			0
$841$	42.3205	+	73.3013i	1.45933	+	2.52763i
$842$	12.6340	−	3.38526i	0.435396	−	0.116664i
$843$		0			0
$844$		0			0
$845$	−24.1147	−	16.2321i	−0.829572	−	0.558400i
$846$		0			0
$847$		0			0
$848$	−7.75129	−	28.9282i	−0.266180	−	0.993399i
$849$		0			0
$850$	−0.973721	+	0.117314i	−0.0333983	+	0.00402384i
$851$		0			0
$852$		0			0
$853$	−24.8301	−	24.8301i	−0.850167	−	0.850167i	0.139986	−	0.990153i	$-0.455294\pi$
$853$	−24.8301	−	24.8301i	−0.850167	−	0.850167i	−0.990153	+	0.139986i	$0.955294\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.0788	−	41.0788i	−1.40323	−	1.40323i	−0.789584	−	0.613642i	$-0.789704\pi$
$857$	−41.0788	−	41.0788i	−1.40323	−	1.40323i	−0.613642	−	0.789584i	$-0.710296\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$		0			0
$865$	−9.50962	+	46.4711i	−0.323337	+	1.58007i
$866$		−	45.2295i		−	1.53696i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	40.0000	+	40.0000i	1.35457	+	1.35457i
$873$	53.2750	−	14.2750i	1.80309	−	0.483135i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	57.1147	+	15.3038i	1.92863	+	0.516774i	0.979260	+	0.202606i	$0.0649409\pi$
$877$	57.1147	+	15.3038i	1.92863	+	0.516774i	0.949367	+	0.314169i	$0.101726\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.6506	−	23.6436i	0.459902	−	0.796573i	−0.539054	−	0.842271i	$-0.681218\pi$
$881$	13.6506	−	23.6436i	0.459902	−	0.796573i	0.998955	+	0.0456985i	$0.0145514\pi$
$882$	−7.68653	−	28.6865i	−0.258819	−	0.965926i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$	−0.751289	+	0.660254i	−0.0252686	+	0.0222067i
$885$		0			0
$886$		0			0
$887$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$887$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$888$		0			0
$889$		0			0
$890$	6.33975	−	30.9808i	0.212509	−	1.03848i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	40.0000	−	40.0000i	1.33482	−	1.33482i
$899$		0			0
$900$	−11.7846	+	27.5885i	−0.392820	+	0.919615i
$901$	−0.519238	−	0.899346i	−0.0172983	−	0.0299616i
$902$		0			0
$903$		0			0
$904$	13.2679	+	22.9808i	0.441285	+	0.764329i
$905$	1.11474	+	18.5718i	0.0370551	+	0.617347i
$906$		0			0
$907$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$907$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$908$		0			0
$909$			54.9615i			1.82296i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	22.7776	−	13.1506i	0.753415	−	0.434984i
$915$		0			0
$916$	−51.9615	+	30.0000i	−1.71686	+	0.991228i
$917$		0			0
$918$		0			0
$919$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$919$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$		0			0
$922$	22.9090	+	22.9090i	0.754467	+	0.754467i
$923$		0			0
$924$		0			0
$925$	20.6244	+	51.3827i	0.678125	+	1.68945i
$926$		0			0
$927$		0			0
$928$	42.6410	+	42.6410i	1.39976	+	1.39976i
$929$	−9.91858	−	17.1795i	−0.325418	−	0.563641i	0.656179	−	0.754606i	$-0.272172\pi$
$929$	−9.91858	−	17.1795i	−0.325418	−	0.563641i	−0.981597	+	0.190965i	$0.938838\pi$
$930$		0			0
$931$		0			0
$932$	3.66025	−	13.6603i	0.119896	−	0.447456i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	6.00000	+	30.0000i	0.196116	+	0.980581i
$937$	39.7391	+	39.7391i	1.29822	+	1.29822i	0.929567	+	0.368652i	$0.120181\pi$
$937$	39.7391	+	39.7391i	1.29822	+	1.29822i	0.368652	+	0.929567i	$0.379819\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$			20.0000i			0.651981i	0.945373	+	0.325991i	$0.105698\pi$
$941$			20.0000i			0.651981i	−0.945373	+	0.325991i	$0.894302\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$947$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$948$		0			0
$949$	1.91154	−	5.65064i	0.0620513	−	0.183427i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.4904	−	5.49038i	−0.663749	−	0.177851i	−0.0888114	−	0.996048i	$-0.528307\pi$
$953$	−20.4904	−	5.49038i	−0.663749	−	0.177851i	−0.574937	+	0.818198i	$0.694974\pi$
$954$	−31.7654			−1.02844
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	46.9808	+	31.3205i	1.51472	+	1.00981i
$963$		0			0
$964$	21.9282	−	37.9808i	0.706260	−	1.22328i
$965$	5.16987	+	15.5096i	0.166424	+	0.499272i
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	8.05256	−	30.0526i	0.258819	−	0.965926i
$969$		0			0
$970$	58.0333	−	3.48334i	1.86334	−	0.111843i
$971$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$971$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	10.6410			0.340611
$977$	−16.0359	−	59.8468i	−0.513034	−	1.91467i	−0.385063	−	0.922890i	$-0.625820\pi$
$977$	−16.0359	−	59.8468i	−0.513034	−	1.91467i	−0.127971	−	0.991778i	$-0.540847\pi$
$978$		0			0
$979$		0			0
$980$	−1.87564	−	31.2487i	−0.0599153	−	0.998203i
$981$	51.9615	−	30.0000i	1.65900	−	0.957826i
$982$		0			0
$983$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$983$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$984$		0			0
$985$	−39.0000	+	13.0000i	−1.24264	+	0.414214i
$986$	1.81089	+	1.04552i	0.0576705	+	0.0332961i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	16.3038	−	60.8468i	0.516348	−	1.92704i	0.190022	−	0.981780i	$-0.439144\pi$
$997$	16.3038	−	60.8468i	0.516348	−	1.92704i	0.326326	−	0.945257i	$-0.394189\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.a.147.1	yes	4
4.3	odd	2	CM	260.2.bg.a.147.1	yes	4
5.3	odd	4		260.2.bg.b.43.1	yes	4
13.10	even	6		260.2.bg.b.127.1	yes	4
20.3	even	4		260.2.bg.b.43.1	yes	4
52.23	odd	6		260.2.bg.b.127.1	yes	4
65.23	odd	12	inner	260.2.bg.a.23.1	✓	4
260.23	even	12	inner	260.2.bg.a.23.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.a.23.1	✓	4	65.23	odd	12	inner
260.2.bg.a.23.1	✓	4	260.23	even	12	inner
260.2.bg.a.147.1	yes	4	1.1	even	1	trivial
260.2.bg.a.147.1	yes	4	4.3	odd	2	CM
260.2.bg.b.43.1	yes	4	5.3	odd	4
260.2.bg.b.43.1	yes	4	20.3	even	4
260.2.bg.b.127.1	yes	4	13.10	even	6
260.2.bg.b.127.1	yes	4	52.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-3.00000 + 1.00000i) q^{10} +(1.59808 + 3.23205i) q^{13} +(2.00000 - 3.46410i) q^{16} +(0.0358984 - 0.133975i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(-2.46410 - 3.73205i) q^{20} +(-4.96410 + 0.598076i) q^{25} +(-3.83013 + 3.36603i) q^{26} +(9.23205 + 5.33013i) q^{29} +(5.46410 + 1.46410i) q^{32} +0.196152 q^{34} +(3.00000 - 5.19615i) q^{36} +(-2.86603 - 10.6962i) q^{37} +(4.19615 - 4.73205i) q^{40} +(10.3301 + 5.96410i) q^{41} +(-3.69615 - 5.59808i) q^{45} +(6.06218 + 3.50000i) q^{49} +(-2.63397 - 6.56218i) q^{50} +(-6.00000 - 4.00000i) q^{52} +(5.29423 - 5.29423i) q^{53} +(-3.90192 + 14.5622i) q^{58} +(1.33013 + 2.30385i) q^{61} +8.00000i q^{64} +(-7.00000 + 4.00000i) q^{65} +(0.0717968 + 0.267949i) q^{68} +(8.19615 + 2.19615i) q^{72} +(-1.16987 - 1.16987i) q^{73} +(13.5622 - 7.83013i) q^{74} +(8.00000 + 4.00000i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-4.36603 + 16.2942i) q^{82} +(0.303848 + 0.0621778i) q^{85} +(-5.00000 + 8.66025i) q^{89} +(6.29423 - 7.09808i) q^{90} +(-17.7583 - 4.75833i) q^{97} +(-2.56218 + 9.56218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8	\( 4 q - 2 q^{2} + 4 q^{5} - 8 q^{8} - 12 q^{10} - 4 q^{13} + 8 q^{16} + 14 q^{17} - 12 q^{18} + 4 q^{20} - 6 q^{25} + 2 q^{26} + 30 q^{29} + 8 q^{32} - 20 q^{34} + 12 q^{36} - 8 q^{37} - 4 q^{40} + 24 q^{41} + 6 q^{45} - 14 q^{50} - 24 q^{52} - 10 q^{53} - 26 q^{58} - 12 q^{61} - 28 q^{65} + 28 q^{68} + 12 q^{72} - 22 q^{73} + 30 q^{74} + 32 q^{80} + 18 q^{81} - 14 q^{82} + 22 q^{85} - 20 q^{89} - 6 q^{90} - 26 q^{97} + 14 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^5 - 8 * q^8 - 12 * q^10 - 4 * q^13 + 8 * q^16 + 14 * q^17 - 12 * q^18 + 4 * q^20 - 6 * q^25 + 2 * q^26 + 30 * q^29 + 8 * q^32 - 20 * q^34 + 12 * q^36 - 8 * q^37 - 4 * q^40 + 24 * q^41 + 6 * q^45 - 14 * q^50 - 24 * q^52 - 10 * q^53 - 26 * q^58 - 12 * q^61 - 28 * q^65 + 28 * q^68 + 12 * q^72 - 22 * q^73 + 30 * q^74 + 32 * q^80 + 18 * q^81 - 14 * q^82 + 22 * q^85 - 20 * q^89 - 6 * q^90 - 26 * q^97 + 14 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more