LMFDB - Embedded newform 3450.2.d.z.2899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.d (of order $2$, degree $1$, not 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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{57})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 29x^{2} + 196 $ x^4 + 29*x^2 + 196
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.1
Root			$3.27492i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.z.2899.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.27492 q^{11} -1.00000i q^{12} +3.27492i q^{13} -3.00000 q^{14} +1.00000 q^{16} +2.27492i q^{17} +1.00000i q^{18} -3.27492 q^{19} +3.00000 q^{21} +1.27492i q^{22} -1.00000i q^{23} -1.00000 q^{24} +3.27492 q^{26} -1.00000i q^{27} +3.00000i q^{28} +9.54983 q^{29} +6.00000 q^{31} -1.00000i q^{32} -1.27492i q^{33} +2.27492 q^{34} +1.00000 q^{36} -10.8248i q^{37} +3.27492i q^{38} -3.27492 q^{39} -2.72508 q^{41} -3.00000i q^{42} +7.27492i q^{43} +1.27492 q^{44} -1.00000 q^{46} -8.27492i q^{47} +1.00000i q^{48} -2.00000 q^{49} -2.27492 q^{51} -3.27492i q^{52} -10.5498i q^{53} -1.00000 q^{54} +3.00000 q^{56} -3.27492i q^{57} -9.54983i q^{58} -12.5498 q^{59} +0.549834 q^{61} -6.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} -1.27492 q^{66} +4.54983i q^{67} -2.27492i q^{68} +1.00000 q^{69} -8.82475 q^{71} -1.00000i q^{72} -15.5498i q^{73} -10.8248 q^{74} +3.27492 q^{76} +3.82475i q^{77} +3.27492i q^{78} +11.8248 q^{79} +1.00000 q^{81} +2.72508i q^{82} -2.45017i q^{83} -3.00000 q^{84} +7.27492 q^{86} +9.54983i q^{87} -1.27492i q^{88} -8.27492 q^{89} +9.82475 q^{91} +1.00000i q^{92} +6.00000i q^{93} -8.27492 q^{94} +1.00000 q^{96} -14.0000i q^{97} +2.00000i q^{98} +1.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	$ 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 10 q^{11} - 12 q^{14} + 4 q^{16} + 2 q^{19} + 12 q^{21} - 4 q^{24} - 2 q^{26} + 8 q^{29} + 24 q^{31} - 6 q^{34} + 4 q^{36} + 2 q^{39} - 26 q^{41} - 10 q^{44} - 4 q^{46} - 8 q^{49} + 6 q^{51} - 4 q^{54} + 12 q^{56} - 20 q^{59} - 28 q^{61} - 4 q^{64} + 10 q^{66} + 4 q^{69} + 10 q^{71} + 2 q^{74} - 2 q^{76} + 2 q^{79} + 4 q^{81} - 12 q^{84} + 14 q^{86} - 18 q^{89} - 6 q^{91} - 18 q^{94} + 4 q^{96} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 10 * q^11 - 12 * q^14 + 4 * q^16 + 2 * q^19 + 12 * q^21 - 4 * q^24 - 2 * q^26 + 8 * q^29 + 24 * q^31 - 6 * q^34 + 4 * q^36 + 2 * q^39 - 26 * q^41 - 10 * q^44 - 4 * q^46 - 8 * q^49 + 6 * q^51 - 4 * q^54 + 12 * q^56 - 20 * q^59 - 28 * q^61 - 4 * q^64 + 10 * q^66 + 4 * q^69 + 10 * q^71 + 2 * q^74 - 2 * q^76 + 2 * q^79 + 4 * q^81 - 12 * q^84 + 14 * q^86 - 18 * q^89 - 6 * q^91 - 18 * q^94 + 4 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	− 3.00000i	− 1.13389i	−0.823754	−	0.566947i	$-0.808125\pi$
$7$	− 3.00000i	− 1.13389i	0.823754	−	0.566947i	$-0.191875\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−1.27492	−0.384402	−0.192201	−	0.981356i	$-0.561563\pi$
$11$	−1.27492	−0.384402	−0.192201	+	0.981356i	$0.561563\pi$
$12$	− 1.00000i	− 0.288675i
$13$	3.27492i	0.908299i	0.890926	+	0.454149i	$0.150057\pi$
$13$	3.27492i	0.908299i	−0.890926	+	0.454149i	$0.849943\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	2.27492i	0.551748i	0.961194	+	0.275874i	$0.0889673\pi$
$17$	2.27492i	0.551748i	−0.961194	+	0.275874i	$0.911033\pi$
$18$	1.00000i	0.235702i
$19$	−3.27492	−0.751318	−0.375659	−	0.926758i	$-0.622584\pi$
$19$	−3.27492	−0.751318	−0.375659	+	0.926758i	$0.622584\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	1.27492i	0.271813i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	−1.00000	−0.204124
$25$	0	0
$26$	3.27492	0.642264
$27$	− 1.00000i	− 0.192450i
$28$	3.00000i	0.566947i
$29$	9.54983	1.77336	0.886680	−	0.462384i	$-0.153006\pi$
$29$	9.54983	1.77336	0.886680	+	0.462384i	$0.153006\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 1.27492i	− 0.221935i
$34$	2.27492	0.390145
$35$	0	0
$36$	1.00000	0.166667
$37$	− 10.8248i	− 1.77958i	−0.456372	−	0.889789i	$-0.650851\pi$
$37$	− 10.8248i	− 1.77958i	0.456372	−	0.889789i	$-0.349149\pi$
$38$	3.27492i	0.531262i
$39$	−3.27492	−0.524406
$40$	0	0
$41$	−2.72508	−0.425586	−0.212793	−	0.977097i	$-0.568256\pi$
$41$	−2.72508	−0.425586	−0.212793	+	0.977097i	$0.568256\pi$
$42$	− 3.00000i	− 0.462910i
$43$	7.27492i	1.10941i	0.832046	+	0.554707i	$0.187170\pi$
$43$	7.27492i	1.10941i	−0.832046	+	0.554707i	$0.812830\pi$
$44$	1.27492	0.192201
$45$	0	0
$46$	−1.00000	−0.147442
$47$	− 8.27492i	− 1.20702i	−0.797355	−	0.603510i	$-0.793768\pi$
$47$	− 8.27492i	− 1.20702i	0.797355	−	0.603510i	$-0.206232\pi$
$48$	1.00000i	0.144338i
$49$	−2.00000	−0.285714
$50$	0	0
$51$	−2.27492	−0.318552
$52$	− 3.27492i	− 0.454149i
$53$	− 10.5498i	− 1.44913i	−0.689206	−	0.724566i	$-0.742040\pi$
$53$	− 10.5498i	− 1.44913i	0.689206	−	0.724566i	$-0.257960\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	3.00000	0.400892
$57$	− 3.27492i	− 0.433773i
$58$	− 9.54983i	− 1.25395i
$59$	−12.5498	−1.63385	−0.816925	−	0.576744i	$-0.804323\pi$
$59$	−12.5498	−1.63385	−0.816925	+	0.576744i	$0.804323\pi$
$60$	0	0
$61$	0.549834	0.0703991	0.0351995	−	0.999380i	$-0.488793\pi$
$61$	0.549834	0.0703991	0.0351995	+	0.999380i	$0.488793\pi$
$62$	− 6.00000i	− 0.762001i
$63$	3.00000i	0.377964i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−1.27492	−0.156931
$67$	4.54983i	0.555851i	0.960603	+	0.277925i	$0.0896468\pi$
$67$	4.54983i	0.555851i	−0.960603	+	0.277925i	$0.910353\pi$
$68$	− 2.27492i	− 0.275874i
$69$	1.00000	0.120386
$70$	0	0
$71$	−8.82475	−1.04731	−0.523653	−	0.851932i	$-0.675431\pi$
$71$	−8.82475	−1.04731	−0.523653	+	0.851932i	$0.675431\pi$
$72$	− 1.00000i	− 0.117851i
$73$	− 15.5498i	− 1.81997i	−0.414641	−	0.909985i	$-0.636093\pi$
$73$	− 15.5498i	− 1.81997i	0.414641	−	0.909985i	$-0.363907\pi$
$74$	−10.8248	−1.25835
$75$	0	0
$76$	3.27492	0.375659
$77$	3.82475i	0.435871i
$78$	3.27492i	0.370811i
$79$	11.8248	1.33039	0.665194	−	0.746670i	$-0.268349\pi$
$79$	11.8248	1.33039	0.665194	+	0.746670i	$0.268349\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	2.72508i	0.300935i
$83$	− 2.45017i	− 0.268941i	−0.990918	−	0.134470i	$-0.957067\pi$
$83$	− 2.45017i	− 0.268941i	0.990918	−	0.134470i	$-0.0429333\pi$
$84$	−3.00000	−0.327327
$85$	0	0
$86$	7.27492	0.784474
$87$	9.54983i	1.02385i
$88$	− 1.27492i	− 0.135907i
$89$	−8.27492	−0.877139	−0.438570	−	0.898697i	$-0.644515\pi$
$89$	−8.27492	−0.877139	−0.438570	+	0.898697i	$0.644515\pi$
$90$	0	0
$91$	9.82475	1.02991
$92$	1.00000i	0.104257i
$93$	6.00000i	0.622171i
$94$	−8.27492	−0.853493
$95$	0	0
$96$	1.00000	0.102062
$97$	− 14.0000i	− 1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$	− 14.0000i	− 1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$	2.00000i	0.202031i
$99$	1.27492	0.128134
$100$	0	0
$101$	8.27492	0.823385	0.411693	−	0.911323i	$-0.364938\pi$
$101$	8.27492	0.823385	0.411693	+	0.911323i	$0.364938\pi$
$102$	2.27492i	0.225250i
$103$	− 3.00000i	− 0.295599i	−0.989017	−	0.147799i	$-0.952781\pi$
$103$	− 3.00000i	− 0.295599i	0.989017	−	0.147799i	$-0.0472190\pi$
$104$	−3.27492	−0.321132
$105$	0	0
$106$	−10.5498	−1.02469
$107$	12.0000i	1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$	12.0000i	1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$	1.00000i	0.0962250i
$109$	−2.82475	−0.270562	−0.135281	−	0.990807i	$-0.543194\pi$
$109$	−2.82475	−0.270562	−0.135281	+	0.990807i	$0.543194\pi$
$110$	0	0
$111$	10.8248	1.02744
$112$	− 3.00000i	− 0.283473i
$113$	− 3.72508i	− 0.350426i	−0.984531	−	0.175213i	$-0.943939\pi$
$113$	− 3.72508i	− 0.350426i	0.984531	−	0.175213i	$-0.0560615\pi$
$114$	−3.27492	−0.306724
$115$	0	0
$116$	−9.54983	−0.886680
$117$	− 3.27492i	− 0.302766i
$118$	12.5498i	1.15531i
$119$	6.82475	0.625624
$120$	0	0
$121$	−9.37459	−0.852235
$122$	− 0.549834i	− 0.0497797i
$123$	− 2.72508i	− 0.245712i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	3.00000	0.267261
$127$	− 8.00000i	− 0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$	− 8.00000i	− 0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	1.00000i	0.0883883i
$129$	−7.27492	−0.640521
$130$	0	0
$131$	6.54983	0.572262	0.286131	−	0.958191i	$-0.407631\pi$
$131$	6.54983	0.572262	0.286131	+	0.958191i	$0.407631\pi$
$132$	1.27492i	0.110967i
$133$	9.82475i	0.851914i
$134$	4.54983	0.393046
$135$	0	0
$136$	−2.27492	−0.195073
$137$	− 8.82475i	− 0.753949i	−0.926224	−	0.376975i	$-0.876964\pi$
$137$	− 8.82475i	− 0.753949i	0.926224	−	0.376975i	$-0.123036\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	−6.27492	−0.532232	−0.266116	−	0.963941i	$-0.585740\pi$
$139$	−6.27492	−0.532232	−0.266116	+	0.963941i	$0.585740\pi$
$140$	0	0
$141$	8.27492	0.696874
$142$	8.82475i	0.740557i
$143$	− 4.17525i	− 0.349152i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−15.5498	−1.28691
$147$	− 2.00000i	− 0.164957i
$148$	10.8248i	0.889789i
$149$	2.54983	0.208891	0.104445	−	0.994531i	$-0.466693\pi$
$149$	2.54983	0.208891	0.104445	+	0.994531i	$0.466693\pi$
$150$	0	0
$151$	−2.54983	−0.207503	−0.103751	−	0.994603i	$-0.533085\pi$
$151$	−2.54983	−0.207503	−0.103751	+	0.994603i	$0.533085\pi$
$152$	− 3.27492i	− 0.265631i
$153$	− 2.27492i	− 0.183916i
$154$	3.82475	0.308207
$155$	0	0
$156$	3.27492	0.262203
$157$	− 14.0000i	− 1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$	− 14.0000i	− 1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$	− 11.8248i	− 0.940727i
$159$	10.5498	0.836656
$160$	0	0
$161$	−3.00000	−0.236433
$162$	− 1.00000i	− 0.0785674i
$163$	− 23.6495i	− 1.85237i	−0.377067	−	0.926186i	$-0.623067\pi$
$163$	− 23.6495i	− 1.85237i	0.377067	−	0.926186i	$-0.376933\pi$
$164$	2.72508	0.212793
$165$	0	0
$166$	−2.45017	−0.190170
$167$	12.2749i	0.949862i	0.880023	+	0.474931i	$0.157527\pi$
$167$	12.2749i	0.949862i	−0.880023	+	0.474931i	$0.842473\pi$
$168$	3.00000i	0.231455i
$169$	2.27492	0.174994
$170$	0	0
$171$	3.27492	0.250439
$172$	− 7.27492i	− 0.554707i
$173$	− 15.2749i	− 1.16133i	−0.814142	−	0.580665i	$-0.802793\pi$
$173$	− 15.2749i	− 1.16133i	0.814142	−	0.580665i	$-0.197207\pi$
$174$	9.54983	0.723971
$175$	0	0
$176$	−1.27492	−0.0961005
$177$	− 12.5498i	− 0.943303i
$178$	8.27492i	0.620231i
$179$	−26.5498	−1.98443	−0.992214	−	0.124545i	$-0.960253\pi$
$179$	−26.5498	−1.98443	−0.992214	+	0.124545i	$0.960253\pi$
$180$	0	0
$181$	1.72508	0.128224	0.0641122	−	0.997943i	$-0.479578\pi$
$181$	1.72508	0.128224	0.0641122	+	0.997943i	$0.479578\pi$
$182$	− 9.82475i	− 0.728259i
$183$	0.549834i	0.0406449i
$184$	1.00000	0.0737210
$185$	0	0
$186$	6.00000	0.439941
$187$	− 2.90033i	− 0.212093i
$188$	8.27492i	0.603510i
$189$	−3.00000	−0.218218
$190$	0	0
$191$	23.2749	1.68411	0.842057	−	0.539389i	$-0.181345\pi$
$191$	23.2749	1.68411	0.842057	+	0.539389i	$0.181345\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 7.72508i	− 0.556064i	−0.960572	−	0.278032i	$-0.910318\pi$
$193$	− 7.72508i	− 0.556064i	0.960572	−	0.278032i	$-0.0896821\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	4.45017i	0.317061i	0.987354	+	0.158531i	$0.0506756\pi$
$197$	4.45017i	0.317061i	−0.987354	+	0.158531i	$0.949324\pi$
$198$	− 1.27492i	− 0.0906044i
$199$	−11.0000	−0.779769	−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000	−0.779769	−0.389885	+	0.920864i	$0.627485\pi$
$200$	0	0
$201$	−4.54983	−0.320921
$202$	− 8.27492i	− 0.582221i
$203$	− 28.6495i	− 2.01080i
$204$	2.27492	0.159276
$205$	0	0
$206$	−3.00000	−0.209020
$207$	1.00000i	0.0695048i
$208$	3.27492i	0.227075i
$209$	4.17525	0.288808
$210$	0	0
$211$	−20.8248	−1.43364	−0.716818	−	0.697261i	$-0.754402\pi$
$211$	−20.8248	−1.43364	−0.716818	+	0.697261i	$0.754402\pi$
$212$	10.5498i	0.724566i
$213$	− 8.82475i	− 0.604662i
$214$	12.0000	0.820303
$215$	0	0
$216$	1.00000	0.0680414
$217$	− 18.0000i	− 1.22192i
$218$	2.82475i	0.191316i
$219$	15.5498	1.05076
$220$	0	0
$221$	−7.45017	−0.501152
$222$	− 10.8248i	− 0.726510i
$223$	− 14.0000i	− 0.937509i	−0.883328	−	0.468755i	$-0.844703\pi$
$223$	− 14.0000i	− 0.937509i	0.883328	−	0.468755i	$-0.155297\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	−3.72508	−0.247789
$227$	10.2749i	0.681970i	0.940069	+	0.340985i	$0.110761\pi$
$227$	10.2749i	0.681970i	−0.940069	+	0.340985i	$0.889239\pi$
$228$	3.27492i	0.216887i
$229$	19.0997	1.26214	0.631071	−	0.775725i	$-0.282616\pi$
$229$	19.0997	1.26214	0.631071	+	0.775725i	$0.282616\pi$
$230$	0	0
$231$	−3.82475	−0.251650
$232$	9.54983i	0.626977i
$233$	14.3746i	0.941710i	0.882210	+	0.470855i	$0.156055\pi$
$233$	14.3746i	0.941710i	−0.882210	+	0.470855i	$0.843945\pi$
$234$	−3.27492	−0.214088
$235$	0	0
$236$	12.5498	0.816925
$237$	11.8248i	0.768100i
$238$	− 6.82475i	− 0.442383i
$239$	−12.2749	−0.793998	−0.396999	−	0.917819i	$-0.629948\pi$
$239$	−12.2749	−0.793998	−0.396999	+	0.917819i	$0.629948\pi$
$240$	0	0
$241$	10.5498	0.679575	0.339787	−	0.940502i	$-0.389645\pi$
$241$	10.5498	0.679575	0.339787	+	0.940502i	$0.389645\pi$
$242$	9.37459i	0.602621i
$243$	1.00000i	0.0641500i
$244$	−0.549834	−0.0351995
$245$	0	0
$246$	−2.72508	−0.173745
$247$	− 10.7251i	− 0.682421i
$248$	6.00000i	0.381000i
$249$	2.45017	0.155273
$250$	0	0
$251$	26.8248	1.69316	0.846582	−	0.532259i	$-0.178657\pi$
$251$	26.8248	1.69316	0.846582	+	0.532259i	$0.178657\pi$
$252$	− 3.00000i	− 0.188982i
$253$	1.27492i	0.0801534i
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000i	0.124757i	0.998053	+	0.0623783i	$0.0198685\pi$
$257$	2.00000i	0.124757i	−0.998053	+	0.0623783i	$0.980131\pi$
$258$	7.27492i	0.452917i
$259$	−32.4743	−2.01785
$260$	0	0
$261$	−9.54983	−0.591120
$262$	− 6.54983i	− 0.404650i
$263$	− 4.54983i	− 0.280555i	−0.990112	−	0.140277i	$-0.955201\pi$
$263$	− 4.54983i	− 0.280555i	0.990112	−	0.140277i	$-0.0447994\pi$
$264$	1.27492	0.0784657
$265$	0	0
$266$	9.82475	0.602394
$267$	− 8.27492i	− 0.506417i
$268$	− 4.54983i	− 0.277925i
$269$	3.27492	0.199675	0.0998376	−	0.995004i	$-0.468168\pi$
$269$	3.27492	0.199675	0.0998376	+	0.995004i	$0.468168\pi$
$270$	0	0
$271$	1.45017	0.0880913	0.0440456	−	0.999030i	$-0.485975\pi$
$271$	1.45017	0.0880913	0.0440456	+	0.999030i	$0.485975\pi$
$272$	2.27492i	0.137937i
$273$	9.82475i	0.594621i
$274$	−8.82475	−0.533123
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	− 5.82475i	− 0.349975i	−0.984571	−	0.174988i	$-0.944011\pi$
$277$	− 5.82475i	− 0.349975i	0.984571	−	0.174988i	$-0.0559886\pi$
$278$	6.27492i	0.376345i
$279$	−6.00000	−0.359211
$280$	0	0
$281$	5.37459	0.320621	0.160310	−	0.987067i	$-0.448750\pi$
$281$	5.37459	0.320621	0.160310	+	0.987067i	$0.448750\pi$
$282$	− 8.27492i	− 0.492764i
$283$	− 16.0000i	− 0.951101i	−0.879688	−	0.475551i	$-0.842249\pi$
$283$	− 16.0000i	− 0.951101i	0.879688	−	0.475551i	$-0.157751\pi$
$284$	8.82475	0.523653
$285$	0	0
$286$	−4.17525	−0.246888
$287$	8.17525i	0.482570i
$288$	1.00000i	0.0589256i
$289$	11.8248	0.695574
$290$	0	0
$291$	14.0000	0.820695
$292$	15.5498i	0.909985i
$293$	− 21.6495i	− 1.26478i	−0.774651	−	0.632389i	$-0.782075\pi$
$293$	− 21.6495i	− 1.26478i	0.774651	−	0.632389i	$-0.217925\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	10.8248	0.629176
$297$	1.27492i	0.0739782i
$298$	− 2.54983i	− 0.147708i
$299$	3.27492	0.189393
$300$	0	0
$301$	21.8248	1.25796
$302$	2.54983i	0.146726i
$303$	8.27492i	0.475382i
$304$	−3.27492	−0.187829
$305$	0	0
$306$	−2.27492	−0.130048
$307$	− 6.27492i	− 0.358128i	−0.983837	−	0.179064i	$-0.942693\pi$
$307$	− 6.27492i	− 0.358128i	0.983837	−	0.179064i	$-0.0573070\pi$
$308$	− 3.82475i	− 0.217935i
$309$	3.00000	0.170664
$310$	0	0
$311$	−10.8248	−0.613815	−0.306908	−	0.951739i	$-0.599294\pi$
$311$	−10.8248	−0.613815	−0.306908	+	0.951739i	$0.599294\pi$
$312$	− 3.27492i	− 0.185406i
$313$	− 32.0000i	− 1.80875i	−0.426742	−	0.904373i	$-0.640339\pi$
$313$	− 32.0000i	− 1.80875i	0.426742	−	0.904373i	$-0.359661\pi$
$314$	−14.0000	−0.790066
$315$	0	0
$316$	−11.8248	−0.665194
$317$	13.5498i	0.761035i	0.924774	+	0.380517i	$0.124254\pi$
$317$	13.5498i	0.761035i	−0.924774	+	0.380517i	$0.875746\pi$
$318$	− 10.5498i	− 0.591605i
$319$	−12.1752	−0.681683
$320$	0	0
$321$	−12.0000	−0.669775
$322$	3.00000i	0.167183i
$323$	− 7.45017i	− 0.414538i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−23.6495	−1.30982
$327$	− 2.82475i	− 0.156209i
$328$	− 2.72508i	− 0.150468i
$329$	−24.8248	−1.36863
$330$	0	0
$331$	16.8248	0.924772	0.462386	−	0.886679i	$-0.346993\pi$
$331$	16.8248	0.924772	0.462386	+	0.886679i	$0.346993\pi$
$332$	2.45017i	0.134470i
$333$	10.8248i	0.593193i
$334$	12.2749	0.671654
$335$	0	0
$336$	3.00000	0.163663
$337$	− 9.45017i	− 0.514783i	−0.966307	−	0.257392i	$-0.917137\pi$
$337$	− 9.45017i	− 0.514783i	0.966307	−	0.257392i	$-0.0828630\pi$
$338$	− 2.27492i	− 0.123739i
$339$	3.72508	0.202319
$340$	0	0
$341$	−7.64950	−0.414244
$342$	− 3.27492i	− 0.177087i
$343$	− 15.0000i	− 0.809924i
$344$	−7.27492	−0.392237
$345$	0	0
$346$	−15.2749	−0.821185
$347$	19.4502i	1.04414i	0.852903	+	0.522070i	$0.174840\pi$
$347$	19.4502i	1.04414i	−0.852903	+	0.522070i	$0.825160\pi$
$348$	− 9.54983i	− 0.511925i
$349$	27.2749	1.45999	0.729996	−	0.683451i	$-0.239522\pi$
$349$	27.2749	1.45999	0.729996	+	0.683451i	$0.239522\pi$
$350$	0	0
$351$	3.27492	0.174802
$352$	1.27492i	0.0679533i
$353$	24.3746i	1.29733i	0.761075	+	0.648664i	$0.224672\pi$
$353$	24.3746i	1.29733i	−0.761075	+	0.648664i	$0.775328\pi$
$354$	−12.5498	−0.667016
$355$	0	0
$356$	8.27492	0.438570
$357$	6.82475i	0.361204i
$358$	26.5498i	1.40320i
$359$	28.9244	1.52657	0.763286	−	0.646060i	$-0.223585\pi$
$359$	28.9244	1.52657	0.763286	+	0.646060i	$0.223585\pi$
$360$	0	0
$361$	−8.27492	−0.435522
$362$	− 1.72508i	− 0.0906683i
$363$	− 9.37459i	− 0.492038i
$364$	−9.82475	−0.514957
$365$	0	0
$366$	0.549834	0.0287403
$367$	− 9.27492i	− 0.484147i	−0.970258	−	0.242073i	$-0.922173\pi$
$367$	− 9.27492i	− 0.484147i	0.970258	−	0.242073i	$-0.0778275\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	2.72508	0.141862
$370$	0	0
$371$	−31.6495	−1.64316
$372$	− 6.00000i	− 0.311086i
$373$	− 23.3746i	− 1.21029i	−0.796115	−	0.605145i	$-0.793115\pi$
$373$	− 23.3746i	− 1.21029i	0.796115	−	0.605145i	$-0.206885\pi$
$374$	−2.90033	−0.149973
$375$	0	0
$376$	8.27492	0.426746
$377$	31.2749i	1.61074i
$378$	3.00000i	0.154303i
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	0	0
$381$	8.00000	0.409852
$382$	− 23.2749i	− 1.19085i
$383$	0.175248i	0.00895477i	0.999990	+	0.00447739i	$0.00142520\pi$
$383$	0.175248i	0.00895477i	−0.999990	+	0.00447739i	$0.998575\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−7.72508	−0.393196
$387$	− 7.27492i	− 0.369805i
$388$	14.0000i	0.710742i
$389$	−23.0997	−1.17120	−0.585600	−	0.810600i	$-0.699141\pi$
$389$	−23.0997	−1.17120	−0.585600	+	0.810600i	$0.699141\pi$
$390$	0	0
$391$	2.27492	0.115048
$392$	− 2.00000i	− 0.101015i
$393$	6.54983i	0.330395i
$394$	4.45017	0.224196
$395$	0	0
$396$	−1.27492	−0.0640670
$397$	21.4502i	1.07655i	0.842768	+	0.538276i	$0.180924\pi$
$397$	21.4502i	1.07655i	−0.842768	+	0.538276i	$0.819076\pi$
$398$	11.0000i	0.551380i
$399$	−9.82475	−0.491853
$400$	0	0
$401$	−9.64950	−0.481873	−0.240937	−	0.970541i	$-0.577455\pi$
$401$	−9.64950	−0.481873	−0.240937	+	0.970541i	$0.577455\pi$
$402$	4.54983i	0.226925i
$403$	19.6495i	0.978811i
$404$	−8.27492	−0.411693
$405$	0	0
$406$	−28.6495	−1.42185
$407$	13.8007i	0.684073i
$408$	− 2.27492i	− 0.112625i
$409$	7.00000	0.346128	0.173064	−	0.984911i	$-0.444633\pi$
$409$	7.00000	0.346128	0.173064	+	0.984911i	$0.444633\pi$
$410$	0	0
$411$	8.82475	0.435293
$412$	3.00000i	0.147799i
$413$	37.6495i	1.85261i
$414$	1.00000	0.0491473
$415$	0	0
$416$	3.27492	0.160566
$417$	− 6.27492i	− 0.307284i
$418$	− 4.17525i	− 0.204218i
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	0	0
$421$	31.0997	1.51571	0.757853	−	0.652426i	$-0.226249\pi$
$421$	31.0997	1.51571	0.757853	+	0.652426i	$0.226249\pi$
$422$	20.8248i	1.01373i
$423$	8.27492i	0.402340i
$424$	10.5498	0.512345
$425$	0	0
$426$	−8.82475	−0.427561
$427$	− 1.64950i	− 0.0798251i
$428$	− 12.0000i	− 0.580042i
$429$	4.17525	0.201583
$430$	0	0
$431$	−12.5498	−0.604504	−0.302252	−	0.953228i	$-0.597738\pi$
$431$	−12.5498	−0.604504	−0.302252	+	0.953228i	$0.597738\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	17.6495i	0.848181i	0.905620	+	0.424091i	$0.139406\pi$
$433$	17.6495i	0.848181i	−0.905620	+	0.424091i	$0.860594\pi$
$434$	−18.0000	−0.864028
$435$	0	0
$436$	2.82475	0.135281
$437$	3.27492i	0.156661i
$438$	− 15.5498i	− 0.743000i
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	2.00000	0.0952381
$442$	7.45017i	0.354368i
$443$	15.6495i	0.743530i	0.928327	+	0.371765i	$0.121247\pi$
$443$	15.6495i	0.743530i	−0.928327	+	0.371765i	$0.878753\pi$
$444$	−10.8248	−0.513720
$445$	0	0
$446$	−14.0000	−0.662919
$447$	2.54983i	0.120603i
$448$	3.00000i	0.141737i
$449$	−15.0997	−0.712597	−0.356299	−	0.934372i	$-0.615961\pi$
$449$	−15.0997	−0.712597	−0.356299	+	0.934372i	$0.615961\pi$
$450$	0	0
$451$	3.47425	0.163596
$452$	3.72508i	0.175213i
$453$	− 2.54983i	− 0.119802i
$454$	10.2749	0.482226
$455$	0	0
$456$	3.27492	0.153362
$457$	39.6495i	1.85473i	0.374163	+	0.927363i	$0.377930\pi$
$457$	39.6495i	1.85473i	−0.374163	+	0.927363i	$0.622070\pi$
$458$	− 19.0997i	− 0.892469i
$459$	2.27492	0.106184
$460$	0	0
$461$	0.0996689	0.00464204	0.00232102	−	0.999997i	$-0.499261\pi$
$461$	0.0996689	0.00464204	0.00232102	+	0.999997i	$0.499261\pi$
$462$	3.82475i	0.177944i
$463$	− 29.0997i	− 1.35238i	−0.736729	−	0.676188i	$-0.763631\pi$
$463$	− 29.0997i	− 1.35238i	0.736729	−	0.676188i	$-0.236369\pi$
$464$	9.54983	0.443340
$465$	0	0
$466$	14.3746	0.665890
$467$	21.0000i	0.971764i	0.874024	+	0.485882i	$0.161502\pi$
$467$	21.0000i	0.971764i	−0.874024	+	0.485882i	$0.838498\pi$
$468$	3.27492i	0.151383i
$469$	13.6495	0.630276
$470$	0	0
$471$	14.0000	0.645086
$472$	− 12.5498i	− 0.577653i
$473$	− 9.27492i	− 0.426461i
$474$	11.8248	0.543129
$475$	0	0
$476$	−6.82475	−0.312812
$477$	10.5498i	0.483044i
$478$	12.2749i	0.561442i
$479$	−7.27492	−0.332399	−0.166200	−	0.986092i	$-0.553150\pi$
$479$	−7.27492	−0.332399	−0.166200	+	0.986092i	$0.553150\pi$
$480$	0	0
$481$	35.4502	1.61639
$482$	− 10.5498i	− 0.480532i
$483$	− 3.00000i	− 0.136505i
$484$	9.37459	0.426118
$485$	0	0
$486$	1.00000	0.0453609
$487$	6.54983i	0.296801i	0.988927	+	0.148401i	$0.0474125\pi$
$487$	6.54983i	0.296801i	−0.988927	+	0.148401i	$0.952587\pi$
$488$	0.549834i	0.0248898i
$489$	23.6495	1.06947
$490$	0	0
$491$	−8.54983	−0.385849	−0.192924	−	0.981214i	$-0.561797\pi$
$491$	−8.54983	−0.385849	−0.192924	+	0.981214i	$0.561797\pi$
$492$	2.72508i	0.122856i
$493$	21.7251i	0.978449i
$494$	−10.7251	−0.482544
$495$	0	0
$496$	6.00000	0.269408
$497$	26.4743i	1.18753i
$498$	− 2.45017i	− 0.109795i
$499$	−11.7251	−0.524887	−0.262443	−	0.964947i	$-0.584528\pi$
$499$	−11.7251	−0.524887	−0.262443	+	0.964947i	$0.584528\pi$
$500$	0	0
$501$	−12.2749	−0.548403
$502$	− 26.8248i	− 1.19725i
$503$	− 18.3746i	− 0.819282i	−0.912247	−	0.409641i	$-0.865654\pi$
$503$	− 18.3746i	− 0.819282i	0.912247	−	0.409641i	$-0.134346\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	1.27492	0.0566770
$507$	2.27492i	0.101033i
$508$	8.00000i	0.354943i
$509$	30.4743	1.35075	0.675374	−	0.737476i	$-0.263982\pi$
$509$	30.4743	1.35075	0.675374	+	0.737476i	$0.263982\pi$
$510$	0	0
$511$	−46.6495	−2.06365
$512$	− 1.00000i	− 0.0441942i
$513$	3.27492i	0.144591i
$514$	2.00000	0.0882162
$515$	0	0
$516$	7.27492	0.320260
$517$	10.5498i	0.463981i
$518$	32.4743i	1.42684i
$519$	15.2749	0.670494
$520$	0	0
$521$	3.37459	0.147843	0.0739217	−	0.997264i	$-0.476449\pi$
$521$	3.37459	0.147843	0.0739217	+	0.997264i	$0.476449\pi$
$522$	9.54983i	0.417985i
$523$	26.3746i	1.15328i	0.816998	+	0.576640i	$0.195636\pi$
$523$	26.3746i	1.15328i	−0.816998	+	0.576640i	$0.804364\pi$
$524$	−6.54983	−0.286131
$525$	0	0
$526$	−4.54983	−0.198382
$527$	13.6495i	0.594582i
$528$	− 1.27492i	− 0.0554837i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	12.5498	0.544616
$532$	− 9.82475i	− 0.425957i
$533$	− 8.92442i	− 0.386560i
$534$	−8.27492	−0.358091
$535$	0	0
$536$	−4.54983	−0.196523
$537$	− 26.5498i	− 1.14571i
$538$	− 3.27492i	− 0.141192i
$539$	2.54983	0.109829
$540$	0	0
$541$	−31.8248	−1.36825	−0.684126	−	0.729363i	$-0.739816\pi$
$541$	−31.8248	−1.36825	−0.684126	+	0.729363i	$0.739816\pi$
$542$	− 1.45017i	− 0.0622899i
$543$	1.72508i	0.0740304i
$544$	2.27492	0.0975363
$545$	0	0
$546$	9.82475	0.420461
$547$	44.8248i	1.91657i	0.285818	+	0.958284i	$0.407735\pi$
$547$	44.8248i	1.91657i	−0.285818	+	0.958284i	$0.592265\pi$
$548$	8.82475i	0.376975i
$549$	−0.549834	−0.0234664
$550$	0	0
$551$	−31.2749	−1.33236
$552$	1.00000i	0.0425628i
$553$	− 35.4743i	− 1.50852i
$554$	−5.82475	−0.247470
$555$	0	0
$556$	6.27492	0.266116
$557$	20.5498i	0.870724i	0.900255	+	0.435362i	$0.143380\pi$
$557$	20.5498i	0.870724i	−0.900255	+	0.435362i	$0.856620\pi$
$558$	6.00000i	0.254000i
$559$	−23.8248	−1.00768
$560$	0	0
$561$	2.90033	0.122452
$562$	− 5.37459i	− 0.226713i
$563$	6.72508i	0.283428i	0.989908	+	0.141714i	$0.0452614\pi$
$563$	6.72508i	0.283428i	−0.989908	+	0.141714i	$0.954739\pi$
$564$	−8.27492	−0.348437
$565$	0	0
$566$	−16.0000	−0.672530
$567$	− 3.00000i	− 0.125988i
$568$	− 8.82475i	− 0.370278i
$569$	7.45017	0.312327	0.156164	−	0.987731i	$-0.450087\pi$
$569$	7.45017	0.312327	0.156164	+	0.987731i	$0.450087\pi$
$570$	0	0
$571$	−32.5498	−1.36217	−0.681084	−	0.732205i	$-0.738491\pi$
$571$	−32.5498	−1.36217	−0.681084	+	0.732205i	$0.738491\pi$
$572$	4.17525i	0.174576i
$573$	23.2749i	0.972324i
$574$	8.17525	0.341228
$575$	0	0
$576$	1.00000	0.0416667
$577$	1.82475i	0.0759654i	0.999278	+	0.0379827i	$0.0120932\pi$
$577$	1.82475i	0.0759654i	−0.999278	+	0.0379827i	$0.987907\pi$
$578$	− 11.8248i	− 0.491845i
$579$	7.72508	0.321043
$580$	0	0
$581$	−7.35050	−0.304950
$582$	− 14.0000i	− 0.580319i
$583$	13.4502i	0.557049i
$584$	15.5498	0.643457
$585$	0	0
$586$	−21.6495	−0.894333
$587$	41.0997i	1.69636i	0.529704	+	0.848182i	$0.322303\pi$
$587$	41.0997i	1.69636i	−0.529704	+	0.848182i	$0.677697\pi$
$588$	2.00000i	0.0824786i
$589$	−19.6495	−0.809644
$590$	0	0
$591$	−4.45017	−0.183055
$592$	− 10.8248i	− 0.444895i
$593$	8.17525i	0.335717i	0.985811	+	0.167859i	$0.0536852\pi$
$593$	8.17525i	0.335717i	−0.985811	+	0.167859i	$0.946315\pi$
$594$	1.27492	0.0523105
$595$	0	0
$596$	−2.54983	−0.104445
$597$	− 11.0000i	− 0.450200i
$598$	− 3.27492i	− 0.133921i
$599$	−36.7492	−1.50153	−0.750765	−	0.660569i	$-0.770315\pi$
$599$	−36.7492	−1.50153	−0.750765	+	0.660569i	$0.770315\pi$
$600$	0	0
$601$	19.7251	0.804603	0.402301	−	0.915507i	$-0.368210\pi$
$601$	19.7251	0.804603	0.402301	+	0.915507i	$0.368210\pi$
$602$	− 21.8248i	− 0.889510i
$603$	− 4.54983i	− 0.185284i
$604$	2.54983	0.103751
$605$	0	0
$606$	8.27492	0.336146
$607$	− 35.0997i	− 1.42465i	−0.701849	−	0.712326i	$-0.747642\pi$
$607$	− 35.0997i	− 1.42465i	0.701849	−	0.712326i	$-0.252358\pi$
$608$	3.27492i	0.132815i
$609$	28.6495	1.16094
$610$	0	0
$611$	27.0997	1.09634
$612$	2.27492i	0.0919581i
$613$	26.2749i	1.06123i	0.847612	+	0.530617i	$0.178040\pi$
$613$	26.2749i	1.06123i	−0.847612	+	0.530617i	$0.821960\pi$
$614$	−6.27492	−0.253235
$615$	0	0
$616$	−3.82475	−0.154104
$617$	− 37.6495i	− 1.51571i	−0.652422	−	0.757856i	$-0.726247\pi$
$617$	− 37.6495i	− 1.51571i	0.652422	−	0.757856i	$-0.273753\pi$
$618$	− 3.00000i	− 0.120678i
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	10.8248i	0.434033i
$623$	24.8248i	0.994583i
$624$	−3.27492	−0.131102
$625$	0	0
$626$	−32.0000	−1.27898
$627$	4.17525i	0.166743i
$628$	14.0000i	0.558661i
$629$	24.6254	0.981880
$630$	0	0
$631$	−1.90033	−0.0756510	−0.0378255	−	0.999284i	$-0.512043\pi$
$631$	−1.90033	−0.0756510	−0.0378255	+	0.999284i	$0.512043\pi$
$632$	11.8248i	0.470363i
$633$	− 20.8248i	− 0.827710i
$634$	13.5498	0.538133
$635$	0	0
$636$	−10.5498	−0.418328
$637$	− 6.54983i	− 0.259514i
$638$	12.1752i	0.482023i
$639$	8.82475	0.349102
$640$	0	0
$641$	8.62541	0.340683	0.170342	−	0.985385i	$-0.445513\pi$
$641$	8.62541	0.340683	0.170342	+	0.985385i	$0.445513\pi$
$642$	12.0000i	0.473602i
$643$	7.27492i	0.286895i	0.989658	+	0.143447i	$0.0458188\pi$
$643$	7.27492i	0.286895i	−0.989658	+	0.143447i	$0.954181\pi$
$644$	3.00000	0.118217
$645$	0	0
$646$	−7.45017	−0.293123
$647$	15.1752i	0.596601i	0.954472	+	0.298300i	$0.0964197\pi$
$647$	15.1752i	0.596601i	−0.954472	+	0.298300i	$0.903580\pi$
$648$	1.00000i	0.0392837i
$649$	16.0000	0.628055
$650$	0	0
$651$	18.0000	0.705476
$652$	23.6495i	0.926186i
$653$	38.0997i	1.49096i	0.666531	+	0.745478i	$0.267779\pi$
$653$	38.0997i	1.49096i	−0.666531	+	0.745478i	$0.732221\pi$
$654$	−2.82475	−0.110457
$655$	0	0
$656$	−2.72508	−0.106397
$657$	15.5498i	0.606657i
$658$	24.8248i	0.967770i
$659$	26.0997	1.01670	0.508349	−	0.861151i	$-0.330256\pi$
$659$	26.0997	1.01670	0.508349	+	0.861151i	$0.330256\pi$
$660$	0	0
$661$	40.8248	1.58790	0.793949	−	0.607984i	$-0.208021\pi$
$661$	40.8248	1.58790	0.793949	+	0.607984i	$0.208021\pi$
$662$	− 16.8248i	− 0.653913i
$663$	− 7.45017i	− 0.289340i
$664$	2.45017	0.0950849
$665$	0	0
$666$	10.8248	0.419451
$667$	− 9.54983i	− 0.369771i
$668$	− 12.2749i	− 0.474931i
$669$	14.0000	0.541271
$670$	0	0
$671$	−0.700993	−0.0270615
$672$	− 3.00000i	− 0.115728i
$673$	6.45017i	0.248636i	0.992242	+	0.124318i	$0.0396742\pi$
$673$	6.45017i	0.248636i	−0.992242	+	0.124318i	$0.960326\pi$
$674$	−9.45017	−0.364007
$675$	0	0
$676$	−2.27492	−0.0874968
$677$	− 17.0997i	− 0.657194i	−0.944470	−	0.328597i	$-0.893424\pi$
$677$	− 17.0997i	− 0.657194i	0.944470	−	0.328597i	$-0.106576\pi$
$678$	− 3.72508i	− 0.143061i
$679$	−42.0000	−1.61181
$680$	0	0
$681$	−10.2749	−0.393736
$682$	7.64950i	0.292915i
$683$	− 22.5498i	− 0.862845i	−0.902150	−	0.431423i	$-0.858012\pi$
$683$	− 22.5498i	− 0.862845i	0.902150	−	0.431423i	$-0.141988\pi$
$684$	−3.27492	−0.125220
$685$	0	0
$686$	−15.0000	−0.572703
$687$	19.0997i	0.728698i
$688$	7.27492i	0.277354i
$689$	34.5498	1.31624
$690$	0	0
$691$	17.7251	0.674294	0.337147	−	0.941452i	$-0.390538\pi$
$691$	17.7251	0.674294	0.337147	+	0.941452i	$0.390538\pi$
$692$	15.2749i	0.580665i
$693$	− 3.82475i	− 0.145290i
$694$	19.4502	0.738318
$695$	0	0
$696$	−9.54983	−0.361986
$697$	− 6.19934i	− 0.234817i
$698$	− 27.2749i	− 1.03237i
$699$	−14.3746	−0.543697
$700$	0	0
$701$	17.6495	0.666613	0.333306	−	0.942819i	$-0.391836\pi$
$701$	17.6495	0.666613	0.333306	+	0.942819i	$0.391836\pi$
$702$	− 3.27492i	− 0.123604i
$703$	35.4502i	1.33703i
$704$	1.27492	0.0480503
$705$	0	0
$706$	24.3746	0.917350
$707$	− 24.8248i	− 0.933631i
$708$	12.5498i	0.471652i
$709$	27.1752	1.02059	0.510294	−	0.860000i	$-0.329537\pi$
$709$	27.1752	1.02059	0.510294	+	0.860000i	$0.329537\pi$
$710$	0	0
$711$	−11.8248	−0.443463
$712$	− 8.27492i	− 0.310116i
$713$	− 6.00000i	− 0.224702i
$714$	6.82475	0.255410
$715$	0	0
$716$	26.5498	0.992214
$717$	− 12.2749i	− 0.458415i
$718$	− 28.9244i	− 1.07945i
$719$	−15.3746	−0.573375	−0.286688	−	0.958024i	$-0.592554\pi$
$719$	−15.3746	−0.573375	−0.286688	+	0.958024i	$0.592554\pi$
$720$	0	0
$721$	−9.00000	−0.335178
$722$	8.27492i	0.307961i
$723$	10.5498i	0.392353i
$724$	−1.72508	−0.0641122
$725$	0	0
$726$	−9.37459	−0.347924
$727$	− 34.1993i	− 1.26838i	−0.773176	−	0.634192i	$-0.781333\pi$
$727$	− 34.1993i	− 1.26838i	0.773176	−	0.634192i	$-0.218667\pi$
$728$	9.82475i	0.364130i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−16.5498	−0.612118
$732$	− 0.549834i	− 0.0203225i
$733$	33.9244i	1.25303i	0.779411	+	0.626514i	$0.215519\pi$
$733$	33.9244i	1.25303i	−0.779411	+	0.626514i	$0.784481\pi$
$734$	−9.27492	−0.342343
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	− 5.80066i	− 0.213670i
$738$	− 2.72508i	− 0.100312i
$739$	33.9244	1.24793	0.623965	−	0.781452i	$-0.285521\pi$
$739$	33.9244	1.24793	0.623965	+	0.781452i	$0.285521\pi$
$740$	0	0
$741$	10.7251	0.393996
$742$	31.6495i	1.16189i
$743$	21.8248i	0.800672i	0.916368	+	0.400336i	$0.131107\pi$
$743$	21.8248i	0.800672i	−0.916368	+	0.400336i	$0.868893\pi$
$744$	−6.00000	−0.219971
$745$	0	0
$746$	−23.3746	−0.855804
$747$	2.45017i	0.0896469i
$748$	2.90033i	0.106047i
$749$	36.0000	1.31541
$750$	0	0
$751$	−8.64950	−0.315625	−0.157812	−	0.987469i	$-0.550444\pi$
$751$	−8.64950	−0.315625	−0.157812	+	0.987469i	$0.550444\pi$
$752$	− 8.27492i	− 0.301755i
$753$	26.8248i	0.977548i
$754$	31.2749	1.13897
$755$	0	0
$756$	3.00000	0.109109
$757$	− 21.7251i	− 0.789612i	−0.918765	−	0.394806i	$-0.870812\pi$
$757$	− 21.7251i	− 0.789612i	0.918765	−	0.394806i	$-0.129188\pi$
$758$	12.0000i	0.435860i
$759$	−1.27492	−0.0462766
$760$	0	0
$761$	−13.8248	−0.501147	−0.250573	−	0.968098i	$-0.580619\pi$
$761$	−13.8248	−0.501147	−0.250573	+	0.968098i	$0.580619\pi$
$762$	− 8.00000i	− 0.289809i
$763$	8.47425i	0.306789i
$764$	−23.2749	−0.842057
$765$	0	0
$766$	0.175248	0.00633198
$767$	− 41.0997i	− 1.48402i
$768$	1.00000i	0.0360844i
$769$	−8.54983	−0.308315	−0.154157	−	0.988046i	$-0.549266\pi$
$769$	−8.54983	−0.308315	−0.154157	+	0.988046i	$0.549266\pi$
$770$	0	0
$771$	−2.00000	−0.0720282
$772$	7.72508i	0.278032i
$773$	− 46.7492i	− 1.68145i	−0.541462	−	0.840725i	$-0.682129\pi$
$773$	− 46.7492i	− 1.68145i	0.541462	−	0.840725i	$-0.317871\pi$
$774$	−7.27492	−0.261491
$775$	0	0
$776$	14.0000	0.502571
$777$	− 32.4743i	− 1.16501i
$778$	23.0997i	0.828163i
$779$	8.92442	0.319751
$780$	0	0
$781$	11.2508	0.402586
$782$	− 2.27492i	− 0.0813509i
$783$	− 9.54983i	− 0.341283i
$784$	−2.00000	−0.0714286
$785$	0	0
$786$	6.54983	0.233625
$787$	23.8248i	0.849261i	0.905367	+	0.424630i	$0.139596\pi$
$787$	23.8248i	0.849261i	−0.905367	+	0.424630i	$0.860404\pi$
$788$	− 4.45017i	− 0.158531i
$789$	4.54983	0.161978
$790$	0	0
$791$	−11.1752	−0.397346
$792$	1.27492i	0.0453022i
$793$	1.80066i	0.0639434i
$794$	21.4502	0.761238
$795$	0	0
$796$	11.0000	0.389885
$797$	− 12.5498i	− 0.444538i	−0.974985	−	0.222269i	$-0.928654\pi$
$797$	− 12.5498i	− 0.444538i	0.974985	−	0.222269i	$-0.0713463\pi$
$798$	9.82475i	0.347792i
$799$	18.8248	0.665972
$800$	0	0
$801$	8.27492	0.292380
$802$	9.64950i	0.340736i
$803$	19.8248i	0.699600i
$804$	4.54983	0.160460
$805$	0	0
$806$	19.6495	0.692124
$807$	3.27492i	0.115283i
$808$	8.27492i	0.291111i
$809$	−13.4743	−0.473730	−0.236865	−	0.971543i	$-0.576120\pi$
$809$	−13.4743	−0.473730	−0.236865	+	0.971543i	$0.576120\pi$
$810$	0	0
$811$	−41.0997	−1.44320	−0.721602	−	0.692308i	$-0.756594\pi$
$811$	−41.0997	−1.44320	−0.721602	+	0.692308i	$0.756594\pi$
$812$	28.6495i	1.00540i
$813$	1.45017i	0.0508595i
$814$	13.8007	0.483713
$815$	0	0
$816$	−2.27492	−0.0796380
$817$	− 23.8248i	− 0.833523i
$818$	− 7.00000i	− 0.244749i
$819$	−9.82475	−0.343305
$820$	0	0
$821$	−52.0241	−1.81565	−0.907827	−	0.419346i	$-0.862260\pi$
$821$	−52.0241	−1.81565	−0.907827	+	0.419346i	$0.862260\pi$
$822$	− 8.82475i	− 0.307799i
$823$	− 16.0000i	− 0.557725i	−0.960331	−	0.278862i	$-0.910043\pi$
$823$	− 16.0000i	− 0.557725i	0.960331	−	0.278862i	$-0.0899574\pi$
$824$	3.00000	0.104510
$825$	0	0
$826$	37.6495	1.30999
$827$	− 48.0997i	− 1.67259i	−0.548280	−	0.836295i	$-0.684717\pi$
$827$	− 48.0997i	− 1.67259i	0.548280	−	0.836295i	$-0.315283\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	4.37459	0.151936	0.0759678	−	0.997110i	$-0.475795\pi$
$829$	4.37459	0.151936	0.0759678	+	0.997110i	$0.475795\pi$
$830$	0	0
$831$	5.82475	0.202058
$832$	− 3.27492i	− 0.113537i
$833$	− 4.54983i	− 0.157642i
$834$	−6.27492	−0.217283
$835$	0	0
$836$	−4.17525	−0.144404
$837$	− 6.00000i	− 0.207390i
$838$	3.00000i	0.103633i
$839$	−3.82475	−0.132045	−0.0660225	−	0.997818i	$-0.521031\pi$
$839$	−3.82475	−0.132045	−0.0660225	+	0.997818i	$0.521031\pi$
$840$	0	0
$841$	62.1993	2.14480
$842$	− 31.0997i	− 1.07177i
$843$	5.37459i	0.185111i
$844$	20.8248	0.716818
$845$	0	0
$846$	8.27492	0.284498
$847$	28.1238i	0.966344i
$848$	− 10.5498i	− 0.362283i
$849$	16.0000	0.549119
$850$	0	0
$851$	−10.8248	−0.371068
$852$	8.82475i	0.302331i
$853$	18.7251i	0.641135i	0.947226	+	0.320567i	$0.103874\pi$
$853$	18.7251i	0.641135i	−0.947226	+	0.320567i	$0.896126\pi$
$854$	−1.64950	−0.0564448
$855$	0	0
$856$	−12.0000	−0.410152
$857$	3.09967i	0.105883i	0.998598	+	0.0529413i	$0.0168596\pi$
$857$	3.09967i	0.105883i	−0.998598	+	0.0529413i	$0.983140\pi$
$858$	− 4.17525i	− 0.142541i
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	0	0
$861$	−8.17525	−0.278612
$862$	12.5498i	0.427449i
$863$	− 53.9244i	− 1.83561i	−0.397033	−	0.917804i	$-0.629960\pi$
$863$	− 53.9244i	− 1.83561i	0.397033	−	0.917804i	$-0.370040\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	17.6495	0.599755
$867$	11.8248i	0.401590i
$868$	18.0000i	0.610960i
$869$	−15.0756	−0.511404
$870$	0	0
$871$	−14.9003	−0.504878
$872$	− 2.82475i	− 0.0956582i
$873$	14.0000i	0.473828i
$874$	3.27492	0.110776
$875$	0	0
$876$	−15.5498	−0.525380
$877$	− 0.900331i	− 0.0304020i	−0.999884	−	0.0152010i	$-0.995161\pi$
$877$	− 0.900331i	− 0.0304020i	0.999884	−	0.0152010i	$-0.00483882\pi$
$878$	− 20.0000i	− 0.674967i
$879$	21.6495	0.730220
$880$	0	0
$881$	−30.7492	−1.03597	−0.517983	−	0.855391i	$-0.673317\pi$
$881$	−30.7492	−1.03597	−0.517983	+	0.855391i	$0.673317\pi$
$882$	− 2.00000i	− 0.0673435i
$883$	− 30.2749i	− 1.01883i	−0.860520	−	0.509416i	$-0.829861\pi$
$883$	− 30.2749i	− 1.01883i	0.860520	−	0.509416i	$-0.170139\pi$
$884$	7.45017	0.250576
$885$	0	0
$886$	15.6495	0.525755
$887$	47.3746i	1.59068i	0.606162	+	0.795341i	$0.292708\pi$
$887$	47.3746i	1.59068i	−0.606162	+	0.795341i	$0.707292\pi$
$888$	10.8248i	0.363255i
$889$	−24.0000	−0.804934
$890$	0	0
$891$	−1.27492	−0.0427113
$892$	14.0000i	0.468755i
$893$	27.0997i	0.906856i
$894$	2.54983	0.0852792
$895$	0	0
$896$	3.00000	0.100223
$897$	3.27492i	0.109346i
$898$	15.0997i	0.503882i
$899$	57.2990	1.91103
$900$	0	0
$901$	24.0000	0.799556
$902$	− 3.47425i	− 0.115680i
$903$	21.8248i	0.726282i
$904$	3.72508	0.123894
$905$	0	0
$906$	−2.54983	−0.0847126
$907$	0.374586i	0.0124379i	0.999981	+	0.00621896i	$0.00197957\pi$
$907$	0.374586i	0.0124379i	−0.999981	+	0.00621896i	$0.998020\pi$
$908$	− 10.2749i	− 0.340985i
$909$	−8.27492	−0.274462
$910$	0	0
$911$	−43.8248	−1.45198	−0.725989	−	0.687706i	$-0.758618\pi$
$911$	−43.8248	−1.45198	−0.725989	+	0.687706i	$0.758618\pi$
$912$	− 3.27492i	− 0.108443i
$913$	3.12376i	0.103381i
$914$	39.6495	1.31149
$915$	0	0
$916$	−19.0997	−0.631071
$917$	− 19.6495i	− 0.648884i
$918$	− 2.27492i	− 0.0750835i
$919$	−48.4743	−1.59902	−0.799509	−	0.600654i	$-0.794907\pi$
$919$	−48.4743	−1.59902	−0.799509	+	0.600654i	$0.794907\pi$
$920$	0	0
$921$	6.27492	0.206766
$922$	− 0.0996689i	− 0.00328242i
$923$	− 28.9003i	− 0.951266i
$924$	3.82475	0.125825
$925$	0	0
$926$	−29.0997	−0.956274
$927$	3.00000i	0.0985329i
$928$	− 9.54983i	− 0.313489i
$929$	8.37459	0.274761	0.137381	−	0.990518i	$-0.456132\pi$
$929$	8.37459	0.274761	0.137381	+	0.990518i	$0.456132\pi$
$930$	0	0
$931$	6.54983	0.214662
$932$	− 14.3746i	− 0.470855i
$933$	− 10.8248i	− 0.354386i
$934$	21.0000	0.687141
$935$	0	0
$936$	3.27492	0.107044
$937$	− 2.00000i	− 0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$	− 2.00000i	− 0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	− 13.6495i	− 0.445672i
$939$	32.0000	1.04428
$940$	0	0
$941$	−16.1993	−0.528083	−0.264042	−	0.964511i	$-0.585056\pi$
$941$	−16.1993	−0.528083	−0.264042	+	0.964511i	$0.585056\pi$
$942$	− 14.0000i	− 0.456145i
$943$	2.72508i	0.0887409i
$944$	−12.5498	−0.408462
$945$	0	0
$946$	−9.27492	−0.301554
$947$	51.6495i	1.67838i	0.543836	+	0.839192i	$0.316971\pi$
$947$	51.6495i	1.67838i	−0.543836	+	0.839192i	$0.683029\pi$
$948$	− 11.8248i	− 0.384050i
$949$	50.9244	1.65308
$950$	0	0
$951$	−13.5498	−0.439383
$952$	6.82475i	0.221191i
$953$	35.9244i	1.16371i	0.813294	+	0.581853i	$0.197672\pi$
$953$	35.9244i	1.16371i	−0.813294	+	0.581853i	$0.802328\pi$
$954$	10.5498	0.341564
$955$	0	0
$956$	12.2749	0.396999
$957$	− 12.1752i	− 0.393570i
$958$	7.27492i	0.235042i
$959$	−26.4743	−0.854898
$960$	0	0
$961$	5.00000	0.161290
$962$	− 35.4502i	− 1.14296i
$963$	− 12.0000i	− 0.386695i
$964$	−10.5498	−0.339787
$965$	0	0
$966$	−3.00000	−0.0965234
$967$	− 25.6495i	− 0.824832i	−0.910996	−	0.412416i	$-0.864685\pi$
$967$	− 25.6495i	− 0.824832i	0.910996	−	0.412416i	$-0.135315\pi$
$968$	− 9.37459i	− 0.301311i
$969$	7.45017	0.239334
$970$	0	0
$971$	4.09967	0.131565	0.0657823	−	0.997834i	$-0.479046\pi$
$971$	4.09967	0.131565	0.0657823	+	0.997834i	$0.479046\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	18.8248i	0.603494i
$974$	6.54983	0.209870
$975$	0	0
$976$	0.549834	0.0175998
$977$	− 33.9244i	− 1.08534i	−0.839947	−	0.542669i	$-0.817414\pi$
$977$	− 33.9244i	− 1.08534i	0.839947	−	0.542669i	$-0.182586\pi$
$978$	− 23.6495i	− 0.756228i
$979$	10.5498	0.337174
$980$	0	0
$981$	2.82475	0.0901874
$982$	8.54983i	0.272836i
$983$	36.9244i	1.17771i	0.808240	+	0.588853i	$0.200420\pi$
$983$	36.9244i	1.17771i	−0.808240	+	0.588853i	$0.799580\pi$
$984$	2.72508	0.0868725
$985$	0	0
$986$	21.7251	0.691868
$987$	− 24.8248i	− 0.790181i
$988$	10.7251i	0.341210i
$989$	7.27492	0.231329
$990$	0	0
$991$	10.5498	0.335127	0.167563	−	0.985861i	$-0.446410\pi$
$991$	10.5498	0.335127	0.167563	+	0.985861i	$0.446410\pi$
$992$	− 6.00000i	− 0.190500i
$993$	16.8248i	0.533917i
$994$	26.4743	0.839712
$995$	0	0
$996$	−2.45017	−0.0776365
$997$	− 8.72508i	− 0.276326i	−0.990409	−	0.138163i	$-0.955880\pi$
$997$	− 8.72508i	− 0.276326i	0.990409	−	0.138163i	$-0.0441198\pi$
$998$	11.7251i	0.371151i
$999$	−10.8248	−0.342480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.z.2899.1		4
5.2	odd	4		3450.2.a.bm.1.1	yes	2
5.3	odd	4		3450.2.a.bd.1.1	✓	2
5.4	even	2	inner	3450.2.d.z.2899.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bd.1.1	✓	2	5.3	odd	4
3450.2.a.bm.1.1	yes	2	5.2	odd	4
3450.2.d.z.2899.1		4	1.1	even	1	trivial
3450.2.d.z.2899.3		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.00000 q^{6} -3.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -1.27492 q^{11} -1.00000i q^{12} +3.27492i q^{13} -3.00000 q^{14} +1.00000 q^{16} +2.27492i q^{17} +1.00000i q^{18} -3.27492 q^{19} +3.00000 q^{21} +1.27492i q^{22} -1.00000i q^{23} -1.00000 q^{24} +3.27492 q^{26} -1.00000i q^{27} +3.00000i q^{28} +9.54983 q^{29} +6.00000 q^{31} -1.00000i q^{32} -1.27492i q^{33} +2.27492 q^{34} +1.00000 q^{36} -10.8248i q^{37} +3.27492i q^{38} -3.27492 q^{39} -2.72508 q^{41} -3.00000i q^{42} +7.27492i q^{43} +1.27492 q^{44} -1.00000 q^{46} -8.27492i q^{47} +1.00000i q^{48} -2.00000 q^{49} -2.27492 q^{51} -3.27492i q^{52} -10.5498i q^{53} -1.00000 q^{54} +3.00000 q^{56} -3.27492i q^{57} -9.54983i q^{58} -12.5498 q^{59} +0.549834 q^{61} -6.00000i q^{62} +3.00000i q^{63} -1.00000 q^{64} -1.27492 q^{66} +4.54983i q^{67} -2.27492i q^{68} +1.00000 q^{69} -8.82475 q^{71} -1.00000i q^{72} -15.5498i q^{73} -10.8248 q^{74} +3.27492 q^{76} +3.82475i q^{77} +3.27492i q^{78} +11.8248 q^{79} +1.00000 q^{81} +2.72508i q^{82} -2.45017i q^{83} -3.00000 q^{84} +7.27492 q^{86} +9.54983i q^{87} -1.27492i q^{88} -8.27492 q^{89} +9.82475 q^{91} +1.00000i q^{92} +6.00000i q^{93} -8.27492 q^{94} +1.00000 q^{96} -14.0000i q^{97} +2.00000i q^{98} +1.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9	\( 4 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 10 q^{11} - 12 q^{14} + 4 q^{16} + 2 q^{19} + 12 q^{21} - 4 q^{24} - 2 q^{26} + 8 q^{29} + 24 q^{31} - 6 q^{34} + 4 q^{36} + 2 q^{39} - 26 q^{41} - 10 q^{44} - 4 q^{46} - 8 q^{49} + 6 q^{51} - 4 q^{54} + 12 q^{56} - 20 q^{59} - 28 q^{61} - 4 q^{64} + 10 q^{66} + 4 q^{69} + 10 q^{71} + 2 q^{74} - 2 q^{76} + 2 q^{79} + 4 q^{81} - 12 q^{84} + 14 q^{86} - 18 q^{89} - 6 q^{91} - 18 q^{94} + 4 q^{96} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 4 * q^6 - 4 * q^9 + 10 * q^11 - 12 * q^14 + 4 * q^16 + 2 * q^19 + 12 * q^21 - 4 * q^24 - 2 * q^26 + 8 * q^29 + 24 * q^31 - 6 * q^34 + 4 * q^36 + 2 * q^39 - 26 * q^41 - 10 * q^44 - 4 * q^46 - 8 * q^49 + 6 * q^51 - 4 * q^54 + 12 * q^56 - 20 * q^59 - 28 * q^61 - 4 * q^64 + 10 * q^66 + 4 * q^69 + 10 * q^71 + 2 * q^74 - 2 * q^76 + 2 * q^79 + 4 * q^81 - 12 * q^84 + 14 * q^86 - 18 * q^89 - 6 * q^91 - 18 * q^94 + 4 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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