LMFDB - Embedded newform 1450.2.b.j.349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(349,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1450.349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.b (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:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.14077504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} + 33x^{2} + 16 $ x^6 + 11x^4 + 33x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			349.5
Root			$2.16425i$ of defining polynomial
Character	$\chi$	$=$	1450.349
Dual form			1450.2.b.j.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -0.683969i q^{3} -1.00000 q^{4} +0.683969 q^{6} +2.16425i q^{7} -1.00000i q^{8} +2.53219 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -0.683969i q^{3} -1.00000 q^{4} +0.683969 q^{6} +2.16425i q^{7} -1.00000i q^{8} +2.53219 q^{9} -4.32850 q^{11} +0.683969i q^{12} -5.64453i q^{13} -2.16425 q^{14} +1.00000 q^{16} -4.16425i q^{17} +2.53219i q^{18} +1.36794 q^{19} +1.48028 q^{21} -4.32850i q^{22} +0.683969i q^{23} -0.683969 q^{24} +5.64453 q^{26} -3.78384i q^{27} -2.16425i q^{28} -1.00000 q^{29} +7.86068 q^{31} +1.00000i q^{32} +2.96056i q^{33} +4.16425 q^{34} -2.53219 q^{36} -6.32850i q^{37} +1.36794i q^{38} -3.86068 q^{39} -2.32850 q^{41} +1.48028i q^{42} +10.8212i q^{43} +4.32850 q^{44} -0.683969 q^{46} -8.00000i q^{47} -0.683969i q^{48} +2.31603 q^{49} -2.84822 q^{51} +5.64453i q^{52} -8.49274i q^{53} +3.78384 q^{54} +2.16425 q^{56} -0.935628i q^{57} -1.00000i q^{58} -2.27659 q^{59} +2.68397 q^{61} +7.86068i q^{62} +5.48028i q^{63} -1.00000 q^{64} -2.96056 q^{66} -2.73588i q^{67} +4.16425i q^{68} +0.467814 q^{69} +2.73588 q^{71} -2.53219i q^{72} -15.2286i q^{73} +6.32850 q^{74} -1.36794 q^{76} -9.36794i q^{77} -3.86068i q^{78} +15.0374 q^{79} +5.00853 q^{81} -2.32850i q^{82} +6.63206i q^{83} -1.48028 q^{84} -10.8212 q^{86} +0.683969i q^{87} +4.32850i q^{88} +5.28905 q^{89} +12.2162 q^{91} -0.683969i q^{92} -5.37646i q^{93} +8.00000 q^{94} +0.683969 q^{96} +0.987535i q^{97} +2.31603i q^{98} -10.9606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	$ 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$1$	$-1$

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
$3$	− 0.683969i	− 0.394890i	−0.980314	−	0.197445i	$-0.936736\pi$
$3$	− 0.683969i	− 0.394890i	0.980314	−	0.197445i	$-0.0632643\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0.683969	0.279229
$7$	2.16425i	0.818009i	0.912532	+	0.409004i	$0.134124\pi$
$7$	2.16425i	0.818009i	−0.912532	+	0.409004i	$0.865876\pi$
$8$	− 1.00000i	− 0.353553i
$9$	2.53219	0.844062
$10$	0	0
$11$	−4.32850	−1.30509	−0.652545	−	0.757750i	$-0.726299\pi$
$11$	−4.32850	−1.30509	−0.652545	+	0.757750i	$0.726299\pi$
$12$	0.683969i	0.197445i
$13$	− 5.64453i	− 1.56551i	−0.622330	−	0.782755i	$-0.713814\pi$
$13$	− 5.64453i	− 1.56551i	0.622330	−	0.782755i	$-0.286186\pi$
$14$	−2.16425	−0.578420
$15$	0	0
$16$	1.00000	0.250000
$17$	− 4.16425i	− 1.00998i	−0.863126	−	0.504989i	$-0.831496\pi$
$17$	− 4.16425i	− 1.00998i	0.863126	−	0.504989i	$-0.168504\pi$
$18$	2.53219i	0.596842i
$19$	1.36794	0.313827	0.156913	−	0.987612i	$-0.449846\pi$
$19$	1.36794	0.313827	0.156913	+	0.987612i	$0.449846\pi$
$20$	0	0
$21$	1.48028	0.323023
$22$	− 4.32850i	− 0.922838i
$23$	0.683969i	0.142617i	0.997454	+	0.0713087i	$0.0227175\pi$
$23$	0.683969i	0.142617i	−0.997454	+	0.0713087i	$0.977282\pi$
$24$	−0.683969	−0.139615
$25$	0	0
$26$	5.64453	1.10698
$27$	− 3.78384i	− 0.728201i
$28$	− 2.16425i	− 0.409004i
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0	0
$31$	7.86068	1.41182	0.705910	−	0.708301i	$-0.250538\pi$
$31$	7.86068	1.41182	0.705910	+	0.708301i	$0.250538\pi$
$32$	1.00000i	0.176777i
$33$	2.96056i	0.515367i
$34$	4.16425	0.714163
$35$	0	0
$36$	−2.53219	−0.422031
$37$	− 6.32850i	− 1.04040i	−0.854045	−	0.520199i	$-0.825858\pi$
$37$	− 6.32850i	− 1.04040i	0.854045	−	0.520199i	$-0.174142\pi$
$38$	1.36794i	0.221909i
$39$	−3.86068	−0.618204
$40$	0	0
$41$	−2.32850	−0.363650	−0.181825	−	0.983331i	$-0.558200\pi$
$41$	−2.32850	−0.363650	−0.181825	+	0.983331i	$0.558200\pi$
$42$	1.48028i	0.228412i
$43$	10.8212i	1.65022i	0.564969	+	0.825112i	$0.308888\pi$
$43$	10.8212i	1.65022i	−0.564969	+	0.825112i	$0.691112\pi$
$44$	4.32850	0.652545
$45$	0	0
$46$	−0.683969	−0.100846
$47$	− 8.00000i	− 1.16692i	−0.812142	−	0.583460i	$-0.801699\pi$
$47$	− 8.00000i	− 1.16692i	0.812142	−	0.583460i	$-0.198301\pi$
$48$	− 0.683969i	− 0.0987224i
$49$	2.31603	0.330862
$50$	0	0
$51$	−2.84822	−0.398830
$52$	5.64453i	0.782755i
$53$	− 8.49274i	− 1.16657i	−0.812268	−	0.583284i	$-0.801767\pi$
$53$	− 8.49274i	− 1.16657i	0.812268	−	0.583284i	$-0.198233\pi$
$54$	3.78384	0.514916
$55$	0	0
$56$	2.16425	0.289210
$57$	− 0.935628i	− 0.123927i
$58$	− 1.00000i	− 0.131306i
$59$	−2.27659	−0.296387	−0.148193	−	0.988958i	$-0.547346\pi$
$59$	−2.27659	−0.296387	−0.148193	+	0.988958i	$0.547346\pi$
$60$	0	0
$61$	2.68397	0.343647	0.171824	−	0.985128i	$-0.445034\pi$
$61$	2.68397	0.343647	0.171824	+	0.985128i	$0.445034\pi$
$62$	7.86068i	0.998308i
$63$	5.48028i	0.690450i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.96056	−0.364419
$67$	− 2.73588i	− 0.334241i	−0.985937	−	0.167120i	$-0.946553\pi$
$67$	− 2.73588i	− 0.334241i	0.985937	−	0.167120i	$-0.0534468\pi$
$68$	4.16425i	0.504989i
$69$	0.467814	0.0563182
$70$	0	0
$71$	2.73588	0.324689	0.162344	−	0.986734i	$-0.448094\pi$
$71$	2.73588	0.324689	0.162344	+	0.986734i	$0.448094\pi$
$72$	− 2.53219i	− 0.298421i
$73$	− 15.2286i	− 1.78238i	−0.453635	−	0.891188i	$-0.649873\pi$
$73$	− 15.2286i	− 1.78238i	0.453635	−	0.891188i	$-0.350127\pi$
$74$	6.32850	0.735673
$75$	0	0
$76$	−1.36794	−0.156913
$77$	− 9.36794i	− 1.06758i
$78$	− 3.86068i	− 0.437136i
$79$	15.0374	1.69184	0.845920	−	0.533311i	$-0.179052\pi$
$79$	15.0374	1.69184	0.845920	+	0.533311i	$0.179052\pi$
$80$	0	0
$81$	5.00853	0.556503
$82$	− 2.32850i	− 0.257139i
$83$	6.63206i	0.727963i	0.931406	+	0.363982i	$0.118583\pi$
$83$	6.63206i	0.727963i	−0.931406	+	0.363982i	$0.881417\pi$
$84$	−1.48028	−0.161512
$85$	0	0
$86$	−10.8212	−1.16688
$87$	0.683969i	0.0733292i
$88$	4.32850i	0.461419i
$89$	5.28905	0.560639	0.280319	−	0.959907i	$-0.409560\pi$
$89$	5.28905	0.560639	0.280319	+	0.959907i	$0.409560\pi$
$90$	0	0
$91$	12.2162	1.28060
$92$	− 0.683969i	− 0.0713087i
$93$	− 5.37646i	− 0.557513i
$94$	8.00000	0.825137
$95$	0	0
$96$	0.683969	0.0698073
$97$	0.987535i	0.100269i	0.998742	+	0.0501345i	$0.0159650\pi$
$97$	0.987535i	0.100269i	−0.998742	+	0.0501345i	$0.984035\pi$
$98$	2.31603i	0.233954i
$99$	−10.9606	−1.10158
$100$	0	0
$101$	12.7089	1.26458	0.632291	−	0.774731i	$-0.282115\pi$
$101$	12.7089	1.26458	0.632291	+	0.774731i	$0.282115\pi$
$102$	− 2.84822i	− 0.282016i
$103$	− 9.92112i	− 0.977557i	−0.872408	−	0.488778i	$-0.837443\pi$
$103$	− 9.92112i	− 0.977557i	0.872408	−	0.488778i	$-0.162557\pi$
$104$	−5.64453	−0.553491
$105$	0	0
$106$	8.49274	0.824888
$107$	− 12.1038i	− 1.17012i	−0.810990	−	0.585060i	$-0.801071\pi$
$107$	− 12.1038i	− 1.17012i	0.810990	−	0.585060i	$-0.198929\pi$
$108$	3.78384i	0.364101i
$109$	−18.9855	−1.81848	−0.909240	−	0.416272i	$-0.863336\pi$
$109$	−18.9855	−1.81848	−0.909240	+	0.416272i	$0.863336\pi$
$110$	0	0
$111$	−4.32850	−0.410843
$112$	2.16425i	0.204502i
$113$	− 3.72341i	− 0.350269i	−0.984545	−	0.175135i	$-0.943964\pi$
$113$	− 3.72341i	− 0.350269i	0.984545	−	0.175135i	$-0.0560360\pi$
$114$	0.935628	0.0876296
$115$	0	0
$116$	1.00000	0.0928477
$117$	− 14.2930i	− 1.32139i
$118$	− 2.27659i	− 0.209577i
$119$	9.01247	0.826171
$120$	0	0
$121$	7.73588	0.703262
$122$	2.68397i	0.242995i
$123$	1.59262i	0.143602i
$124$	−7.86068	−0.705910
$125$	0	0
$126$	−5.48028	−0.488222
$127$	2.73588i	0.242770i	0.992606	+	0.121385i	$0.0387335\pi$
$127$	2.73588i	0.242770i	−0.992606	+	0.121385i	$0.961266\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	7.40139	0.651656
$130$	0	0
$131$	16.4323	1.43570	0.717849	−	0.696199i	$-0.245127\pi$
$131$	16.4323	1.43570	0.717849	+	0.696199i	$0.245127\pi$
$132$	− 2.96056i	− 0.257683i
$133$	2.96056i	0.256713i
$134$	2.73588	0.236344
$135$	0	0
$136$	−4.16425	−0.357081
$137$	4.38040i	0.374243i	0.982337	+	0.187122i	$0.0599158\pi$
$137$	4.38040i	0.374243i	−0.982337	+	0.187122i	$0.940084\pi$
$138$	0.467814i	0.0398230i
$139$	2.38893	0.202626	0.101313	−	0.994855i	$-0.467696\pi$
$139$	2.38893	0.202626	0.101313	+	0.994855i	$0.467696\pi$
$140$	0	0
$141$	−5.47175	−0.460805
$142$	2.73588i	0.229590i
$143$	24.4323i	2.04313i
$144$	2.53219	0.211016
$145$	0	0
$146$	15.2286	1.26033
$147$	− 1.58409i	− 0.130654i
$148$	6.32850i	0.520199i
$149$	−18.1038	−1.48312	−0.741561	−	0.670885i	$-0.765914\pi$
$149$	−18.1038	−1.48312	−0.741561	+	0.670885i	$0.765914\pi$
$150$	0	0
$151$	0.710947	0.0578560	0.0289280	−	0.999581i	$-0.490791\pi$
$151$	0.710947	0.0578560	0.0289280	+	0.999581i	$0.490791\pi$
$152$	− 1.36794i	− 0.110954i
$153$	− 10.5447i	− 0.852485i
$154$	9.36794	0.754890
$155$	0	0
$156$	3.86068	0.309102
$157$	22.6570i	1.80822i	0.427295	+	0.904112i	$0.359467\pi$
$157$	22.6570i	1.80822i	−0.427295	+	0.904112i	$0.640533\pi$
$158$	15.0374i	1.19631i
$159$	−5.80877	−0.460666
$160$	0	0
$161$	−1.48028	−0.116662
$162$	5.00853i	0.393507i
$163$	− 18.5781i	− 1.45515i	−0.686028	−	0.727575i	$-0.740647\pi$
$163$	− 18.5781i	− 1.45515i	0.686028	−	0.727575i	$-0.259353\pi$
$164$	2.32850	0.181825
$165$	0	0
$166$	−6.63206	−0.514748
$167$	− 5.83575i	− 0.451584i	−0.974176	−	0.225792i	$-0.927503\pi$
$167$	− 5.83575i	− 0.451584i	0.974176	−	0.225792i	$-0.0724970\pi$
$168$	− 1.48028i	− 0.114206i
$169$	−18.8607	−1.45082
$170$	0	0
$171$	3.46387	0.264889
$172$	− 10.8212i	− 0.825112i
$173$	18.3015i	1.39144i	0.718314	+	0.695719i	$0.244914\pi$
$173$	18.3015i	1.39144i	−0.718314	+	0.695719i	$0.755086\pi$
$174$	−0.683969	−0.0518516
$175$	0	0
$176$	−4.32850	−0.326273
$177$	1.55712i	0.117040i
$178$	5.28905i	0.396431i
$179$	−23.0374	−1.72190	−0.860948	−	0.508693i	$-0.830129\pi$
$179$	−23.0374	−1.72190	−0.860948	+	0.508693i	$0.830129\pi$
$180$	0	0
$181$	−26.3784	−1.96069	−0.980344	−	0.197296i	$-0.936784\pi$
$181$	−26.3784	−1.96069	−0.980344	+	0.197296i	$0.936784\pi$
$182$	12.2162i	0.905522i
$183$	− 1.83575i	− 0.135703i
$184$	0.683969	0.0504229
$185$	0	0
$186$	5.37646	0.394221
$187$	18.0249i	1.31811i
$188$	8.00000i	0.583460i
$189$	8.18918	0.595675
$190$	0	0
$191$	1.45330	0.105157	0.0525786	−	0.998617i	$-0.483256\pi$
$191$	1.45330	0.105157	0.0525786	+	0.998617i	$0.483256\pi$
$192$	0.683969i	0.0493612i
$193$	11.5656i	0.832513i	0.909247	+	0.416257i	$0.136658\pi$
$193$	11.5656i	0.832513i	−0.909247	+	0.416257i	$0.863342\pi$
$194$	−0.987535	−0.0709009
$195$	0	0
$196$	−2.31603	−0.165431
$197$	13.9645i	0.994929i	0.867484	+	0.497465i	$0.165736\pi$
$197$	13.9645i	0.994929i	−0.867484	+	0.497465i	$0.834264\pi$
$198$	− 10.9606i	− 0.778933i
$199$	12.3285	0.873944	0.436972	−	0.899475i	$-0.356051\pi$
$199$	12.3285	0.873944	0.436972	+	0.899475i	$0.356051\pi$
$200$	0	0
$201$	−1.87126	−0.131988
$202$	12.7089i	0.894195i
$203$	− 2.16425i	− 0.151900i
$204$	2.84822	0.199415
$205$	0	0
$206$	9.92112	0.691237
$207$	1.73194i	0.120378i
$208$	− 5.64453i	− 0.391378i
$209$	−5.92112	−0.409572
$210$	0	0
$211$	4.32850	0.297986	0.148993	−	0.988838i	$-0.452397\pi$
$211$	4.32850	0.297986	0.148993	+	0.988838i	$0.452397\pi$
$212$	8.49274i	0.583284i
$213$	− 1.87126i	− 0.128216i
$214$	12.1038	0.827400
$215$	0	0
$216$	−3.78384	−0.257458
$217$	17.0125i	1.15488i
$218$	− 18.9855i	− 1.28586i
$219$	−10.4159	−0.703842
$220$	0	0
$221$	−23.5052	−1.58113
$222$	− 4.32850i	− 0.290510i
$223$	11.4198i	0.764729i	0.924011	+	0.382365i	$0.124890\pi$
$223$	11.4198i	0.764729i	−0.924011	+	0.382365i	$0.875110\pi$
$224$	−2.16425	−0.144605
$225$	0	0
$226$	3.72341	0.247678
$227$	− 28.2745i	− 1.87665i	−0.345758	−	0.938324i	$-0.612378\pi$
$227$	− 28.2745i	− 1.87665i	0.345758	−	0.938324i	$-0.387622\pi$
$228$	0.935628i	0.0619634i
$229$	−11.4533	−0.756855	−0.378428	−	0.925631i	$-0.623535\pi$
$229$	−11.4533	−0.756855	−0.378428	+	0.925631i	$0.623535\pi$
$230$	0	0
$231$	−6.40738	−0.421575
$232$	1.00000i	0.0656532i
$233$	0.0788848i	0.00516792i	0.999997	+	0.00258396i	$0.000822500\pi$
$233$	0.0788848i	0.00516792i	−0.999997	+	0.00258396i	$0.999177\pi$
$234$	14.2930	0.934362
$235$	0	0
$236$	2.27659	0.148193
$237$	− 10.2851i	− 0.668090i
$238$	9.01247i	0.584191i
$239$	−10.9606	−0.708980	−0.354490	−	0.935060i	$-0.615345\pi$
$239$	−10.9606	−0.708980	−0.354490	+	0.935060i	$0.615345\pi$
$240$	0	0
$241$	17.3659	1.11864	0.559318	−	0.828953i	$-0.311063\pi$
$241$	17.3659	1.11864	0.559318	+	0.828953i	$0.311063\pi$
$242$	7.73588i	0.497281i
$243$	− 14.7772i	− 0.947959i
$244$	−2.68397	−0.171824
$245$	0	0
$246$	−1.59262	−0.101542
$247$	− 7.72136i	− 0.491299i
$248$	− 7.86068i	− 0.499154i
$249$	4.53613	0.287465
$250$	0	0
$251$	−26.0249	−1.64268	−0.821340	−	0.570440i	$-0.806773\pi$
$251$	−26.0249	−1.64268	−0.821340	+	0.570440i	$0.806773\pi$
$252$	− 5.48028i	− 0.345225i
$253$	− 2.96056i	− 0.186129i
$254$	−2.73588	−0.171664
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 10.3285i	− 0.644274i	−0.946693	−	0.322137i	$-0.895599\pi$
$257$	− 10.3285i	− 0.644274i	0.946693	−	0.322137i	$-0.104401\pi$
$258$	7.40139i	0.460791i
$259$	13.6964	0.851055
$260$	0	0
$261$	−2.53219	−0.156738
$262$	16.4323i	1.01519i
$263$	16.0000i	0.986602i	0.869859	+	0.493301i	$0.164210\pi$
$263$	16.0000i	0.986602i	−0.869859	+	0.493301i	$0.835790\pi$
$264$	2.96056	0.182210
$265$	0	0
$266$	−2.96056	−0.181523
$267$	− 3.61755i	− 0.221390i
$268$	2.73588i	0.167120i
$269$	13.8607	0.845101	0.422550	−	0.906339i	$-0.361135\pi$
$269$	13.8607	0.845101	0.422550	+	0.906339i	$0.361135\pi$
$270$	0	0
$271$	6.73588	0.409175	0.204588	−	0.978848i	$-0.434415\pi$
$271$	6.73588	0.409175	0.204588	+	0.978848i	$0.434415\pi$
$272$	− 4.16425i	− 0.252495i
$273$	− 8.35547i	− 0.505696i
$274$	−4.38040	−0.264630
$275$	0	0
$276$	−0.467814	−0.0281591
$277$	17.3929i	1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$277$	17.3929i	1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$278$	2.38893i	0.143278i
$279$	19.9047	1.19166
$280$	0	0
$281$	−11.9396	−0.712255	−0.356127	−	0.934437i	$-0.615903\pi$
$281$	−11.9396	−0.712255	−0.356127	+	0.934437i	$0.615903\pi$
$282$	− 5.47175i	− 0.325838i
$283$	23.4967i	1.39673i	0.715740	+	0.698366i	$0.246089\pi$
$283$	23.4967i	1.39673i	−0.715740	+	0.698366i	$0.753911\pi$
$284$	−2.73588	−0.162344
$285$	0	0
$286$	−24.4323	−1.44471
$287$	− 5.03944i	− 0.297469i
$288$	2.53219i	0.149211i
$289$	−0.340961	−0.0200565
$290$	0	0
$291$	0.675443	0.0395952
$292$	15.2286i	0.891188i
$293$	− 5.51373i	− 0.322116i	−0.986945	−	0.161058i	$-0.948509\pi$
$293$	− 5.51373i	− 0.322116i	0.986945	−	0.161058i	$-0.0514906\pi$
$294$	1.58409	0.0923862
$295$	0	0
$296$	−6.32850	−0.367836
$297$	16.3784i	0.950369i
$298$	− 18.1038i	− 1.04873i
$299$	3.86068	0.223269
$300$	0	0
$301$	−23.4198	−1.34990
$302$	0.710947i	0.0409104i
$303$	− 8.69249i	− 0.499371i
$304$	1.36794	0.0784566
$305$	0	0
$306$	10.5447	0.602798
$307$	− 4.65699i	− 0.265789i	−0.991130	−	0.132894i	$-0.957573\pi$
$307$	− 4.65699i	− 0.265789i	0.991130	−	0.132894i	$-0.0424271\pi$
$308$	9.36794i	0.533788i
$309$	−6.78574	−0.386027
$310$	0	0
$311$	−4.35547	−0.246976	−0.123488	−	0.992346i	$-0.539408\pi$
$311$	−4.35547	−0.246976	−0.123488	+	0.992346i	$0.539408\pi$
$312$	3.86068i	0.218568i
$313$	− 1.34301i	− 0.0759113i	−0.999279	−	0.0379557i	$-0.987915\pi$
$313$	− 1.34301i	− 0.0759113i	0.999279	−	0.0379557i	$-0.0120846\pi$
$314$	−22.6570	−1.27861
$315$	0	0
$316$	−15.0374	−0.845920
$317$	− 11.3679i	− 0.638487i	−0.947673	−	0.319244i	$-0.896571\pi$
$317$	− 11.3679i	− 0.638487i	0.947673	−	0.319244i	$-0.103429\pi$
$318$	− 5.80877i	− 0.325740i
$319$	4.32850	0.242349
$320$	0	0
$321$	−8.27864	−0.462068
$322$	− 1.48028i	− 0.0824927i
$323$	− 5.69643i	− 0.316958i
$324$	−5.00853	−0.278251
$325$	0	0
$326$	18.5781	1.02895
$327$	12.9855i	0.718099i
$328$	2.32850i	0.128570i
$329$	17.3140	0.954551
$330$	0	0
$331$	12.3285	0.677635	0.338818	−	0.940852i	$-0.389973\pi$
$331$	12.3285	0.677635	0.338818	+	0.940852i	$0.389973\pi$
$332$	− 6.63206i	− 0.363982i
$333$	− 16.0249i	− 0.878161i
$334$	5.83575	0.319318
$335$	0	0
$336$	1.48028	0.0807558
$337$	− 17.8067i	− 0.969994i	−0.874516	−	0.484997i	$-0.838821\pi$
$337$	− 17.8067i	− 0.969994i	0.874516	−	0.484997i	$-0.161179\pi$
$338$	− 18.8607i	− 1.02589i
$339$	−2.54670	−0.138318
$340$	0	0
$341$	−34.0249	−1.84255
$342$	3.46387i	0.187305i
$343$	20.1622i	1.08866i
$344$	10.8212	0.583442
$345$	0	0
$346$	−18.3015	−0.983896
$347$	23.2891i	1.25022i	0.780536	+	0.625111i	$0.214946\pi$
$347$	23.2891i	1.25022i	−0.780536	+	0.625111i	$0.785054\pi$
$348$	− 0.683969i	− 0.0366646i
$349$	23.6964	1.26844	0.634221	−	0.773152i	$-0.281321\pi$
$349$	23.6964	1.26844	0.634221	+	0.773152i	$0.281321\pi$
$350$	0	0
$351$	−21.3580	−1.14001
$352$	− 4.32850i	− 0.230710i
$353$	6.43231i	0.342357i	0.985240	+	0.171179i	$0.0547575\pi$
$353$	6.43231i	0.342357i	−0.985240	+	0.171179i	$0.945242\pi$
$354$	−1.55712	−0.0827598
$355$	0	0
$356$	−5.28905	−0.280319
$357$	− 6.16425i	− 0.326247i
$358$	− 23.0374i	− 1.21756i
$359$	12.3555	0.652097	0.326048	−	0.945353i	$-0.394283\pi$
$359$	12.3555	0.652097	0.326048	+	0.945353i	$0.394283\pi$
$360$	0	0
$361$	−17.1287	−0.901513
$362$	− 26.3784i	− 1.38642i
$363$	− 5.29110i	− 0.277711i
$364$	−12.2162	−0.640301
$365$	0	0
$366$	1.83575	0.0959563
$367$	18.4743i	0.964350i	0.876075	+	0.482175i	$0.160153\pi$
$367$	18.4743i	0.964350i	−0.876075	+	0.482175i	$0.839847\pi$
$368$	0.683969i	0.0356544i
$369$	−5.89619	−0.306943
$370$	0	0
$371$	18.3804	0.954263
$372$	5.37646i	0.278757i
$373$	− 2.57163i	− 0.133154i	−0.997781	−	0.0665769i	$-0.978792\pi$
$373$	− 2.57163i	− 0.133154i	0.997781	−	0.0665769i	$-0.0212078\pi$
$374$	−18.0249	−0.932047
$375$	0	0
$376$	−8.00000	−0.412568
$377$	5.64453i	0.290708i
$378$	8.18918i	0.421206i
$379$	−23.7214	−1.21848	−0.609242	−	0.792984i	$-0.708526\pi$
$379$	−23.7214	−1.21848	−0.609242	+	0.792984i	$0.708526\pi$
$380$	0	0
$381$	1.87126	0.0958673
$382$	1.45330i	0.0743574i
$383$	− 5.55712i	− 0.283955i	−0.989870	−	0.141978i	$-0.954654\pi$
$383$	− 5.55712i	− 0.283955i	0.989870	−	0.141978i	$-0.0453461\pi$
$384$	−0.683969	−0.0349037
$385$	0	0
$386$	−11.5656	−0.588676
$387$	27.4014i	1.39289i
$388$	− 0.987535i	− 0.0501345i
$389$	−27.4718	−1.39287	−0.696437	−	0.717618i	$-0.745232\pi$
$389$	−27.4718	−1.39287	−0.696437	+	0.717618i	$0.745232\pi$
$390$	0	0
$391$	2.84822	0.144041
$392$	− 2.31603i	− 0.116977i
$393$	− 11.2392i	− 0.566942i
$394$	−13.9645	−0.703521
$395$	0	0
$396$	10.9606	0.550789
$397$	− 14.5716i	− 0.731329i	−0.930747	−	0.365665i	$-0.880842\pi$
$397$	− 14.5716i	− 0.731329i	0.930747	−	0.365665i	$-0.119158\pi$
$398$	12.3285i	0.617972i
$399$	2.02493	0.101373
$400$	0	0
$401$	−10.0270	−0.500723	−0.250362	−	0.968152i	$-0.580550\pi$
$401$	−10.0270	−0.500723	−0.250362	+	0.968152i	$0.580550\pi$
$402$	− 1.87126i	− 0.0933297i
$403$	− 44.3698i	− 2.21022i
$404$	−12.7089	−0.632291
$405$	0	0
$406$	2.16425	0.107410
$407$	27.3929i	1.35781i
$408$	2.84822i	0.141008i
$409$	39.0893	1.93284	0.966421	−	0.256965i	$-0.0827224\pi$
$409$	39.0893	1.93284	0.966421	+	0.256965i	$0.0827224\pi$
$410$	0	0
$411$	2.99606	0.147785
$412$	9.92112i	0.488778i
$413$	− 4.92710i	− 0.242447i
$414$	−1.73194	−0.0851201
$415$	0	0
$416$	5.64453	0.276746
$417$	− 1.63395i	− 0.0800151i
$418$	− 5.92112i	− 0.289611i
$419$	−31.8607	−1.55650	−0.778248	−	0.627957i	$-0.783891\pi$
$419$	−31.8607	−1.55650	−0.778248	+	0.627957i	$0.783891\pi$
$420$	0	0
$421$	36.1287	1.76081	0.880404	−	0.474225i	$-0.157272\pi$
$421$	36.1287	1.76081	0.880404	+	0.474225i	$0.157272\pi$
$422$	4.32850i	0.210708i
$423$	− 20.2575i	− 0.984953i
$424$	−8.49274	−0.412444
$425$	0	0
$426$	1.87126	0.0906626
$427$	5.80877i	0.281106i
$428$	12.1038i	0.585060i
$429$	16.7109	0.806812
$430$	0	0
$431$	−9.36794	−0.451238	−0.225619	−	0.974216i	$-0.572440\pi$
$431$	−9.36794	−0.451238	−0.225619	+	0.974216i	$0.572440\pi$
$432$	− 3.78384i	− 0.182050i
$433$	10.8148i	0.519724i	0.965646	+	0.259862i	$0.0836771\pi$
$433$	10.8148i	0.519724i	−0.965646	+	0.259862i	$0.916323\pi$
$434$	−17.0125	−0.816624
$435$	0	0
$436$	18.9855	0.909240
$437$	0.935628i	0.0447571i
$438$	− 10.4159i	− 0.497691i
$439$	−29.6964	−1.41733	−0.708667	−	0.705543i	$-0.750703\pi$
$439$	−29.6964	−1.41733	−0.708667	+	0.705543i	$0.750703\pi$
$440$	0	0
$441$	5.86462	0.279268
$442$	− 23.5052i	− 1.11803i
$443$	23.2621i	1.10521i	0.833442	+	0.552607i	$0.186367\pi$
$443$	23.2621i	1.10521i	−0.833442	+	0.552607i	$0.813633\pi$
$444$	4.32850	0.205421
$445$	0	0
$446$	−11.4198	−0.540745
$447$	12.3825i	0.585670i
$448$	− 2.16425i	− 0.102251i
$449$	5.72136	0.270008	0.135004	−	0.990845i	$-0.456895\pi$
$449$	5.72136	0.270008	0.135004	+	0.990845i	$0.456895\pi$
$450$	0	0
$451$	10.0789	0.474596
$452$	3.72341i	0.175135i
$453$	− 0.486265i	− 0.0228467i
$454$	28.2745	1.32699
$455$	0	0
$456$	−0.935628	−0.0438148
$457$	− 31.9710i	− 1.49554i	−0.663958	−	0.747770i	$-0.731125\pi$
$457$	− 31.9710i	− 1.49554i	0.663958	−	0.747770i	$-0.268875\pi$
$458$	− 11.4533i	− 0.535178i
$459$	−15.7569	−0.735468
$460$	0	0
$461$	6.18918	0.288259	0.144129	−	0.989559i	$-0.453962\pi$
$461$	6.18918	0.288259	0.144129	+	0.989559i	$0.453962\pi$
$462$	− 6.40738i	− 0.298098i
$463$	12.0000i	0.557687i	0.960337	+	0.278844i	$0.0899511\pi$
$463$	12.0000i	0.557687i	−0.960337	+	0.278844i	$0.910049\pi$
$464$	−1.00000	−0.0464238
$465$	0	0
$466$	−0.0788848	−0.00365427
$467$	− 15.4284i	− 0.713940i	−0.934116	−	0.356970i	$-0.883810\pi$
$467$	− 15.4284i	− 0.713940i	0.934116	−	0.356970i	$-0.116190\pi$
$468$	14.2930i	0.660694i
$469$	5.92112	0.273412
$470$	0	0
$471$	15.4967	0.714049
$472$	2.27659i	0.104788i
$473$	− 46.8397i	− 2.15369i
$474$	10.2851	0.472411
$475$	0	0
$476$	−9.01247	−0.413086
$477$	− 21.5052i	− 0.984656i
$478$	− 10.9606i	− 0.501324i
$479$	−32.0314	−1.46355	−0.731776	−	0.681545i	$-0.761308\pi$
$479$	−32.0314	−1.46355	−0.731776	+	0.681545i	$0.761308\pi$
$480$	0	0
$481$	−35.7214	−1.62875
$482$	17.3659i	0.790995i
$483$	1.01247i	0.0460688i
$484$	−7.73588	−0.351631
$485$	0	0
$486$	14.7772	0.670308
$487$	24.8916i	1.12795i	0.825793	+	0.563973i	$0.190728\pi$
$487$	24.8916i	1.12795i	−0.825793	+	0.563973i	$0.809272\pi$
$488$	− 2.68397i	− 0.121498i
$489$	−12.7069	−0.574624
$490$	0	0
$491$	16.0000	0.722070	0.361035	−	0.932552i	$-0.382424\pi$
$491$	16.0000	0.722070	0.361035	+	0.932552i	$0.382424\pi$
$492$	− 1.59262i	− 0.0718008i
$493$	4.16425i	0.187548i
$494$	7.72136	0.347401
$495$	0	0
$496$	7.86068	0.352955
$497$	5.92112i	0.265598i
$498$	4.53613i	0.203269i
$499$	24.8547	1.11265	0.556324	−	0.830965i	$-0.312211\pi$
$499$	24.8547	1.11265	0.556324	+	0.830965i	$0.312211\pi$
$500$	0	0
$501$	−3.99147	−0.178326
$502$	− 26.0249i	− 1.16155i
$503$	19.3929i	0.864685i	0.901709	+	0.432343i	$0.142313\pi$
$503$	19.3929i	0.864685i	−0.901709	+	0.432343i	$0.857687\pi$
$504$	5.48028	0.244111
$505$	0	0
$506$	2.96056	0.131613
$507$	12.9001i	0.572915i
$508$	− 2.73588i	− 0.121385i
$509$	−17.6715	−0.783276	−0.391638	−	0.920119i	$-0.628091\pi$
$509$	−17.6715	−0.783276	−0.391638	+	0.920119i	$0.628091\pi$
$510$	0	0
$511$	32.9585	1.45800
$512$	1.00000i	0.0441942i
$513$	− 5.17607i	− 0.228529i
$514$	10.3285	0.455570
$515$	0	0
$516$	−7.40139	−0.325828
$517$	34.6280i	1.52294i
$518$	13.6964i	0.601787i
$519$	12.5177	0.549465
$520$	0	0
$521$	−2.31004	−0.101205	−0.0506024	−	0.998719i	$-0.516114\pi$
$521$	−2.31004	−0.101205	−0.0506024	+	0.998719i	$0.516114\pi$
$522$	− 2.53219i	− 0.110831i
$523$	1.36794i	0.0598158i	0.999553	+	0.0299079i	$0.00952139\pi$
$523$	1.36794i	0.0598158i	−0.999553	+	0.0299079i	$0.990479\pi$
$524$	−16.4323	−0.717849
$525$	0	0
$526$	−16.0000	−0.697633
$527$	− 32.7338i	− 1.42591i
$528$	2.96056i	0.128842i
$529$	22.5322	0.979660
$530$	0	0
$531$	−5.76475	−0.250169
$532$	− 2.96056i	− 0.128356i
$533$	13.1433i	0.569298i
$534$	3.61755	0.156547
$535$	0	0
$536$	−2.73588	−0.118172
$537$	15.7569i	0.679959i
$538$	13.8607i	0.597576i
$539$	−10.0249	−0.431804
$540$	0	0
$541$	0.717425	0.0308445	0.0154223	−	0.999881i	$-0.495091\pi$
$541$	0.717425	0.0308445	0.0154223	+	0.999881i	$0.495091\pi$
$542$	6.73588i	0.289331i
$543$	18.0420i	0.774256i
$544$	4.16425	0.178541
$545$	0	0
$546$	8.35547	0.357581
$547$	31.9460i	1.36591i	0.730458	+	0.682957i	$0.239306\pi$
$547$	31.9460i	1.36591i	−0.730458	+	0.682957i	$0.760694\pi$
$548$	− 4.38040i	− 0.187122i
$549$	6.79631	0.290059
$550$	0	0
$551$	−1.36794	−0.0582761
$552$	− 0.467814i	− 0.0199115i
$553$	32.5447i	1.38394i
$554$	−17.3929	−0.738952
$555$	0	0
$556$	−2.38893	−0.101313
$557$	− 3.72341i	− 0.157766i	−0.996884	−	0.0788830i	$-0.974865\pi$
$557$	− 3.72341i	− 0.157766i	0.996884	−	0.0788830i	$-0.0251354\pi$
$558$	19.9047i	0.842634i
$559$	61.0808	2.58344
$560$	0	0
$561$	12.3285	0.520510
$562$	− 11.9396i	− 0.503640i
$563$	− 23.2621i	− 0.980380i	−0.871616	−	0.490190i	$-0.836927\pi$
$563$	− 23.2621i	− 0.980380i	0.871616	−	0.490190i	$-0.163073\pi$
$564$	5.47175	0.230402
$565$	0	0
$566$	−23.4967	−0.987639
$567$	10.8397i	0.455224i
$568$	− 2.73588i	− 0.114795i
$569$	−14.2745	−0.598420	−0.299210	−	0.954187i	$-0.596723\pi$
$569$	−14.2745	−0.598420	−0.299210	+	0.954187i	$0.596723\pi$
$570$	0	0
$571$	6.82977	0.285817	0.142908	−	0.989736i	$-0.454355\pi$
$571$	6.82977	0.285817	0.142908	+	0.989736i	$0.454355\pi$
$572$	− 24.4323i	− 1.02157i
$573$	− 0.994013i	− 0.0415255i
$574$	5.03944	0.210342
$575$	0	0
$576$	−2.53219	−0.105508
$577$	− 42.9500i	− 1.78803i	−0.448036	−	0.894016i	$-0.647876\pi$
$577$	− 42.9500i	− 1.78803i	0.448036	−	0.894016i	$-0.352124\pi$
$578$	− 0.340961i	− 0.0141821i
$579$	7.91054	0.328751
$580$	0	0
$581$	−14.3534	−0.595480
$582$	0.675443i	0.0279980i
$583$	36.7608i	1.52248i
$584$	−15.2286	−0.630165
$585$	0	0
$586$	5.51373	0.227770
$587$	− 1.08930i	− 0.0449603i	−0.999747	−	0.0224802i	$-0.992844\pi$
$587$	− 1.08930i	− 0.0449603i	0.999747	−	0.0224802i	$-0.00715626\pi$
$588$	1.58409i	0.0653269i
$589$	10.7529	0.443067
$590$	0	0
$591$	9.55128	0.392887
$592$	− 6.32850i	− 0.260100i
$593$	− 7.21017i	− 0.296086i	−0.988981	−	0.148043i	$-0.952703\pi$
$593$	− 7.21017i	− 0.296086i	0.988981	−	0.148043i	$-0.0472974\pi$
$594$	−16.3784	−0.672012
$595$	0	0
$596$	18.1038	0.741561
$597$	− 8.43231i	− 0.345112i
$598$	3.86068i	0.157875i
$599$	42.3179	1.72906	0.864532	−	0.502578i	$-0.167615\pi$
$599$	42.3179	1.72906	0.864532	+	0.502578i	$0.167615\pi$
$600$	0	0
$601$	−16.6819	−0.680470	−0.340235	−	0.940340i	$-0.610507\pi$
$601$	−16.6819	−0.680470	−0.340235	+	0.940340i	$0.610507\pi$
$602$	− 23.4198i	− 0.954522i
$603$	− 6.92775i	− 0.282120i
$604$	−0.710947	−0.0289280
$605$	0	0
$606$	8.69249	0.353108
$607$	− 8.00000i	− 0.324710i	−0.986732	−	0.162355i	$-0.948091\pi$
$607$	− 8.00000i	− 0.324710i	0.986732	−	0.162355i	$-0.0519090\pi$
$608$	1.36794i	0.0554772i
$609$	−1.48028	−0.0599839
$610$	0	0
$611$	−45.1562	−1.82682
$612$	10.5447i	0.426242i
$613$	− 37.1996i	− 1.50248i	−0.660031	−	0.751239i	$-0.729457\pi$
$613$	− 37.1996i	− 1.50248i	0.660031	−	0.751239i	$-0.270543\pi$
$614$	4.65699	0.187941
$615$	0	0
$616$	−9.36794	−0.377445
$617$	4.77138i	0.192089i	0.995377	+	0.0960443i	$0.0306190\pi$
$617$	4.77138i	0.192089i	−0.995377	+	0.0960443i	$0.969381\pi$
$618$	− 6.78574i	− 0.272962i
$619$	−6.80279	−0.273427	−0.136714	−	0.990611i	$-0.543654\pi$
$619$	−6.80279	−0.273427	−0.136714	+	0.990611i	$0.543654\pi$
$620$	0	0
$621$	2.58803	0.103854
$622$	− 4.35547i	− 0.174639i
$623$	11.4468i	0.458607i
$624$	−3.86068	−0.154551
$625$	0	0
$626$	1.34301	0.0536774
$627$	4.04986i	0.161736i
$628$	− 22.6570i	− 0.904112i
$629$	−26.3534	−1.05078
$630$	0	0
$631$	17.0893	0.680314	0.340157	−	0.940369i	$-0.389520\pi$
$631$	17.0893	0.680314	0.340157	+	0.940369i	$0.389520\pi$
$632$	− 15.0374i	− 0.598155i
$633$	− 2.96056i	− 0.117672i
$634$	11.3679	0.451479
$635$	0	0
$636$	5.80877	0.230333
$637$	− 13.0729i	− 0.517967i
$638$	4.32850i	0.171367i
$639$	6.92775	0.274058
$640$	0	0
$641$	11.1433	0.440132	0.220066	−	0.975485i	$-0.429373\pi$
$641$	11.1433	0.440132	0.220066	+	0.975485i	$0.429373\pi$
$642$	− 8.27864i	− 0.326732i
$643$	24.9356i	0.983365i	0.870775	+	0.491683i	$0.163618\pi$
$643$	24.9356i	0.983365i	−0.870775	+	0.491683i	$0.836382\pi$
$644$	1.48028	0.0583312
$645$	0	0
$646$	5.69643	0.224123
$647$	0.814761i	0.0320316i	0.999872	+	0.0160158i	$0.00509820\pi$
$647$	0.814761i	0.0320316i	−0.999872	+	0.0160158i	$0.994902\pi$
$648$	− 5.00853i	− 0.196753i
$649$	9.85420	0.386811
$650$	0	0
$651$	11.6360	0.456051
$652$	18.5781i	0.727575i
$653$	29.9959i	1.17383i	0.809648	+	0.586915i	$0.199658\pi$
$653$	29.9959i	1.17383i	−0.809648	+	0.586915i	$0.800342\pi$
$654$	−12.9855	−0.507773
$655$	0	0
$656$	−2.32850	−0.0909125
$657$	− 38.5617i	− 1.50444i
$658$	17.3140i	0.674969i
$659$	−27.6715	−1.07793	−0.538964	−	0.842329i	$-0.681184\pi$
$659$	−27.6715	−1.07793	−0.538964	+	0.842329i	$0.681184\pi$
$660$	0	0
$661$	−6.55318	−0.254889	−0.127445	−	0.991846i	$-0.540677\pi$
$661$	−6.55318	−0.254889	−0.127445	+	0.991846i	$0.540677\pi$
$662$	12.3285i	0.479161i
$663$	16.0768i	0.624373i
$664$	6.63206	0.257374
$665$	0	0
$666$	16.0249	0.620953
$667$	− 0.683969i	− 0.0264834i
$668$	5.83575i	0.225792i
$669$	7.81082	0.301984
$670$	0	0
$671$	−11.6175	−0.448491
$672$	1.48028i	0.0571030i
$673$	18.9855i	0.731837i	0.930647	+	0.365918i	$0.119245\pi$
$673$	18.9855i	0.731837i	−0.930647	+	0.365918i	$0.880755\pi$
$674$	17.8067	0.685890
$675$	0	0
$676$	18.8607	0.725411
$677$	33.6175i	1.29203i	0.763326	+	0.646014i	$0.223565\pi$
$677$	33.6175i	1.29203i	−0.763326	+	0.646014i	$0.776435\pi$
$678$	− 2.54670i	− 0.0978054i
$679$	−2.13727	−0.0820209
$680$	0	0
$681$	−19.3389	−0.741069
$682$	− 34.0249i	− 1.30288i
$683$	18.6819i	0.714844i	0.933943	+	0.357422i	$0.116344\pi$
$683$	18.6819i	0.714844i	−0.933943	+	0.357422i	$0.883656\pi$
$684$	−3.46387	−0.132445
$685$	0	0
$686$	−20.1622	−0.769796
$687$	7.83370i	0.298874i
$688$	10.8212i	0.412556i
$689$	−47.9375	−1.82627
$690$	0	0
$691$	38.7174	1.47288	0.736440	−	0.676503i	$-0.236505\pi$
$691$	38.7174	1.47288	0.736440	+	0.676503i	$0.236505\pi$
$692$	− 18.3015i	− 0.695719i
$693$	− 23.7214i	− 0.901100i
$694$	−23.2891	−0.884040
$695$	0	0
$696$	0.683969	0.0259258
$697$	9.69643i	0.367279i
$698$	23.6964i	0.896923i
$699$	0.0539548	0.00204076
$700$	0	0
$701$	28.7318	1.08518	0.542592	−	0.839996i	$-0.317443\pi$
$701$	28.7318	1.08518	0.542592	+	0.839996i	$0.317443\pi$
$702$	− 21.3580i	− 0.806106i
$703$	− 8.65699i	− 0.326505i
$704$	4.32850	0.163136
$705$	0	0
$706$	−6.43231	−0.242083
$707$	27.5052i	1.03444i
$708$	− 1.55712i	− 0.0585200i
$709$	47.2102	1.77302	0.886508	−	0.462714i	$-0.153124\pi$
$709$	47.2102	1.77302	0.886508	+	0.462714i	$0.153124\pi$
$710$	0	0
$711$	38.0775	1.42802
$712$	− 5.28905i	− 0.198216i
$713$	5.37646i	0.201350i
$714$	6.16425	0.230691
$715$	0	0
$716$	23.0374	0.860948
$717$	7.49668i	0.279969i
$718$	12.3555i	0.461102i
$719$	14.6321	0.545684	0.272842	−	0.962059i	$-0.412036\pi$
$719$	14.6321	0.545684	0.272842	+	0.962059i	$0.412036\pi$
$720$	0	0
$721$	21.4718	0.799650
$722$	− 17.1287i	− 0.637466i
$723$	− 11.8777i	− 0.441738i
$724$	26.3784	0.980344
$725$	0	0
$726$	5.29110	0.196371
$727$	− 1.59262i	− 0.0590670i	−0.999564	−	0.0295335i	$-0.990598\pi$
$727$	− 1.59262i	− 0.0590670i	0.999564	−	0.0295335i	$-0.00940217\pi$
$728$	− 12.2162i	− 0.452761i
$729$	4.91842	0.182164
$730$	0	0
$731$	45.0623	1.66669
$732$	1.83575i	0.0678513i
$733$	12.3036i	0.454443i	0.973843	+	0.227221i	$0.0729641\pi$
$733$	12.3036i	0.454443i	−0.973843	+	0.227221i	$0.927036\pi$
$734$	−18.4743	−0.681899
$735$	0	0
$736$	−0.683969	−0.0252114
$737$	11.8422i	0.436214i
$738$	− 5.89619i	− 0.217042i
$739$	25.3140	0.931190	0.465595	−	0.884998i	$-0.345840\pi$
$739$	25.3140	0.931190	0.465595	+	0.884998i	$0.345840\pi$
$740$	0	0
$741$	−5.28117	−0.194009
$742$	18.3804i	0.674766i
$743$	16.6570i	0.611086i	0.952178	+	0.305543i	$0.0988379\pi$
$743$	16.6570i	0.611086i	−0.952178	+	0.305543i	$0.901162\pi$
$744$	−5.37646	−0.197111
$745$	0	0
$746$	2.57163	0.0941540
$747$	16.7936i	0.614446i
$748$	− 18.0249i	− 0.659057i
$749$	26.1957	0.957168
$750$	0	0
$751$	−13.3140	−0.485834	−0.242917	−	0.970047i	$-0.578104\pi$
$751$	−13.3140	−0.485834	−0.242917	+	0.970047i	$0.578104\pi$
$752$	− 8.00000i	− 0.291730i
$753$	17.8002i	0.648677i
$754$	−5.64453	−0.205562
$755$	0	0
$756$	−8.18918	−0.297838
$757$	− 20.4572i	− 0.743531i	−0.928327	−	0.371766i	$-0.878753\pi$
$757$	− 20.4572i	− 0.743531i	0.928327	−	0.371766i	$-0.121247\pi$
$758$	− 23.7214i	− 0.861599i
$759$	−2.02493	−0.0735003
$760$	0	0
$761$	30.9670	1.12255	0.561277	−	0.827628i	$-0.310310\pi$
$761$	30.9670	1.12255	0.561277	+	0.827628i	$0.310310\pi$
$762$	1.87126i	0.0677884i
$763$	− 41.0893i	− 1.48753i
$764$	−1.45330	−0.0525786
$765$	0	0
$766$	5.55712	0.200787
$767$	12.8503i	0.463996i
$768$	− 0.683969i	− 0.0246806i
$769$	4.18270	0.150832	0.0754160	−	0.997152i	$-0.475972\pi$
$769$	4.18270	0.150832	0.0754160	+	0.997152i	$0.475972\pi$
$770$	0	0
$771$	−7.06437	−0.254417
$772$	− 11.5656i	− 0.416257i
$773$	− 42.0499i	− 1.51243i	−0.654324	−	0.756214i	$-0.727047\pi$
$773$	− 42.0499i	− 1.51243i	0.654324	−	0.756214i	$-0.272953\pi$
$774$	−27.4014	−0.984923
$775$	0	0
$776$	0.987535	0.0354504
$777$	− 9.36794i	− 0.336073i
$778$	− 27.4718i	− 0.984910i
$779$	−3.18524	−0.114123
$780$	0	0
$781$	−11.8422	−0.423748
$782$	2.84822i	0.101852i
$783$	3.78384i	0.135224i
$784$	2.31603	0.0827154
$785$	0	0
$786$	11.2392	0.400889
$787$	− 33.0524i	− 1.17819i	−0.808063	−	0.589095i	$-0.799484\pi$
$787$	− 33.0524i	− 1.17819i	0.808063	−	0.589095i	$-0.200516\pi$
$788$	− 13.9645i	− 0.497465i
$789$	10.9435	0.389599
$790$	0	0
$791$	8.05839	0.286523
$792$	10.9606i	0.389466i
$793$	− 15.1497i	− 0.537983i
$794$	14.5716	0.517128
$795$	0	0
$796$	−12.3285	−0.436972
$797$	11.9041i	0.421664i	0.977522	+	0.210832i	$0.0676172\pi$
$797$	11.9041i	0.421664i	−0.977522	+	0.210832i	$0.932383\pi$
$798$	2.02493i	0.0716817i
$799$	−33.3140	−1.17856
$800$	0	0
$801$	13.3929	0.473214
$802$	− 10.0270i	− 0.354065i
$803$	65.9170i	2.32616i
$804$	1.87126	0.0659941
$805$	0	0
$806$	44.3698	1.56286
$807$	− 9.48028i	− 0.333722i
$808$	− 12.7089i	− 0.447098i
$809$	53.6674	1.88685	0.943423	−	0.331592i	$-0.107586\pi$
$809$	53.6674	1.88685	0.943423	+	0.331592i	$0.107586\pi$
$810$	0	0
$811$	47.3034	1.66105	0.830524	−	0.556983i	$-0.188041\pi$
$811$	47.3034	1.66105	0.830524	+	0.556983i	$0.188041\pi$
$812$	2.16425i	0.0759502i
$813$	− 4.60713i	− 0.161579i
$814$	−27.3929	−0.960120
$815$	0	0
$816$	−2.84822	−0.0997075
$817$	14.8028i	0.517884i
$818$	39.0893i	1.36673i
$819$	30.9336	1.08091
$820$	0	0
$821$	31.3679	1.09475	0.547374	−	0.836888i	$-0.315627\pi$
$821$	31.3679	1.09475	0.547374	+	0.836888i	$0.315627\pi$
$822$	2.99606i	0.104500i
$823$	23.4598i	0.817757i	0.912589	+	0.408878i	$0.134080\pi$
$823$	23.4598i	0.817757i	−0.912589	+	0.408878i	$0.865920\pi$
$824$	−9.92112	−0.345618
$825$	0	0
$826$	4.92710	0.171436
$827$	− 13.1788i	− 0.458270i	−0.973395	−	0.229135i	$-0.926410\pi$
$827$	− 13.1788i	− 0.458270i	0.973395	−	0.229135i	$-0.0735898\pi$
$828$	− 1.73194i	− 0.0601890i
$829$	20.2312	0.702657	0.351329	−	0.936252i	$-0.385730\pi$
$829$	20.2312	0.702657	0.351329	+	0.936252i	$0.385730\pi$
$830$	0	0
$831$	11.8962	0.412674
$832$	5.64453i	0.195689i
$833$	− 9.64453i	− 0.334163i
$834$	1.63395	0.0565792
$835$	0	0
$836$	5.92112	0.204786
$837$	− 29.7436i	− 1.02809i
$838$	− 31.8607i	− 1.10061i
$839$	33.3638	1.15185	0.575924	−	0.817503i	$-0.304642\pi$
$839$	33.3638	1.15185	0.575924	+	0.817503i	$0.304642\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	36.1287i	1.24508i
$843$	8.16630i	0.281262i
$844$	−4.32850	−0.148993
$845$	0	0
$846$	20.2575	0.696467
$847$	16.7424i	0.575274i
$848$	− 8.49274i	− 0.291642i
$849$	16.0710	0.551556
$850$	0	0
$851$	4.32850	0.148379
$852$	1.87126i	0.0641081i
$853$	55.0852i	1.88608i	0.332677	+	0.943041i	$0.392048\pi$
$853$	55.0852i	1.88608i	−0.332677	+	0.943041i	$0.607952\pi$
$854$	−5.80877	−0.198772
$855$	0	0
$856$	−12.1038	−0.413700
$857$	− 8.02493i	− 0.274126i	−0.990562	−	0.137063i	$-0.956234\pi$
$857$	− 8.02493i	− 0.274126i	0.990562	−	0.137063i	$-0.0437663\pi$
$858$	16.7109i	0.570502i
$859$	30.0748	1.02614	0.513069	−	0.858347i	$-0.328508\pi$
$859$	30.0748	1.02614	0.513069	+	0.858347i	$0.328508\pi$
$860$	0	0
$861$	−3.44682	−0.117467
$862$	− 9.36794i	− 0.319073i
$863$	20.5802i	0.700557i	0.936646	+	0.350278i	$0.113913\pi$
$863$	20.5802i	0.700557i	−0.936646	+	0.350278i	$0.886087\pi$
$864$	3.78384	0.128729
$865$	0	0
$866$	−10.8148	−0.367501
$867$	0.233207i	0.00792012i
$868$	− 17.0125i	− 0.577441i
$869$	−65.0893	−2.20800
$870$	0	0
$871$	−15.4427	−0.523257
$872$	18.9855i	0.642930i
$873$	2.50062i	0.0846332i
$874$	−0.935628	−0.0316481
$875$	0	0
$876$	10.4159	0.351921
$877$	− 19.7234i	− 0.666012i	−0.942925	−	0.333006i	$-0.891937\pi$
$877$	− 19.7234i	− 0.666012i	0.942925	−	0.333006i	$-0.108063\pi$
$878$	− 29.6964i	− 1.00221i
$879$	−3.77122	−0.127200
$880$	0	0
$881$	10.1707	0.342660	0.171330	−	0.985214i	$-0.445193\pi$
$881$	10.1707	0.342660	0.171330	+	0.985214i	$0.445193\pi$
$882$	5.86462i	0.197472i
$883$	13.2102i	0.444558i	0.974983	+	0.222279i	$0.0713495\pi$
$883$	13.2102i	0.444558i	−0.974983	+	0.222279i	$0.928650\pi$
$884$	23.5052	0.790566
$885$	0	0
$886$	−23.2621	−0.781505
$887$	17.5216i	0.588318i	0.955756	+	0.294159i	$0.0950396\pi$
$887$	17.5216i	0.588318i	−0.955756	+	0.294159i	$0.904960\pi$
$888$	4.32850i	0.145255i
$889$	−5.92112	−0.198588
$890$	0	0
$891$	−21.6794	−0.726287
$892$	− 11.4198i	− 0.382365i
$893$	− 10.9435i	− 0.366210i
$894$	−12.3825	−0.414131
$895$	0	0
$896$	2.16425	0.0723024
$897$	− 2.64059i	− 0.0881666i
$898$	5.72136i	0.190924i
$899$	−7.86068	−0.262168
$900$	0	0
$901$	−35.3659	−1.17821
$902$	10.0789i	0.335590i
$903$	16.0185i	0.533061i
$904$	−3.72341	−0.123839
$905$	0	0
$906$	0.486265	0.0161551
$907$	− 25.0210i	− 0.830808i	−0.909637	−	0.415404i	$-0.863640\pi$
$907$	− 25.0210i	− 0.830808i	0.909637	−	0.415404i	$-0.136360\pi$
$908$	28.2745i	0.938324i
$909$	32.1813	1.06739
$910$	0	0
$911$	−49.0623	−1.62551	−0.812754	−	0.582607i	$-0.802033\pi$
$911$	−49.0623	−1.62551	−0.812754	+	0.582607i	$0.802033\pi$
$912$	− 0.935628i	− 0.0309817i
$913$	− 28.7069i	− 0.950058i
$914$	31.9710	1.05751
$915$	0	0
$916$	11.4533	0.378428
$917$	35.5636i	1.17441i
$918$	− 15.7569i	− 0.520054i
$919$	−33.3140	−1.09893	−0.549463	−	0.835518i	$-0.685168\pi$
$919$	−33.3140	−1.09893	−0.549463	+	0.835518i	$0.685168\pi$
$920$	0	0
$921$	−3.18524	−0.104957
$922$	6.18918i	0.203830i
$923$	− 15.4427i	− 0.508304i
$924$	6.40738	0.210787
$925$	0	0
$926$	−12.0000	−0.394344
$927$	− 25.1221i	− 0.825118i
$928$	− 1.00000i	− 0.0328266i
$929$	1.68996	0.0554457	0.0277228	−	0.999616i	$-0.491174\pi$
$929$	1.68996	0.0554457	0.0277228	+	0.999616i	$0.491174\pi$
$930$	0	0
$931$	3.16819	0.103833
$932$	− 0.0788848i	− 0.00258396i
$933$	2.97901i	0.0975284i
$934$	15.4284	0.504832
$935$	0	0
$936$	−14.2930	−0.467181
$937$	23.1931i	0.757686i	0.925461	+	0.378843i	$0.123678\pi$
$937$	23.1931i	0.757686i	−0.925461	+	0.378843i	$0.876322\pi$
$938$	5.92112i	0.193331i
$939$	−0.918576	−0.0299766
$940$	0	0
$941$	53.4598	1.74274	0.871370	−	0.490627i	$-0.163232\pi$
$941$	53.4598	1.74274	0.871370	+	0.490627i	$0.163232\pi$
$942$	15.4967i	0.504909i
$943$	− 1.59262i	− 0.0518628i
$944$	−2.27659	−0.0740966
$945$	0	0
$946$	46.8397	1.52289
$947$	− 17.3949i	− 0.565259i	−0.959229	−	0.282629i	$-0.908793\pi$
$947$	− 17.3949i	− 0.565259i	0.959229	−	0.282629i	$-0.0912067\pi$
$948$	10.2851i	0.334045i
$949$	−85.9584	−2.79033
$950$	0	0
$951$	−7.77532	−0.252132
$952$	− 9.01247i	− 0.292096i
$953$	− 60.1786i	− 1.94938i	−0.223569	−	0.974688i	$-0.571771\pi$
$953$	− 60.1786i	− 1.94938i	0.223569	−	0.974688i	$-0.428229\pi$
$954$	21.5052	0.696257
$955$	0	0
$956$	10.9606	0.354490
$957$	− 2.96056i	− 0.0957012i
$958$	− 32.0314i	− 1.03489i
$959$	−9.48028	−0.306134
$960$	0	0
$961$	30.7903	0.993236
$962$	− 35.7214i	− 1.15170i
$963$	− 30.6491i	− 0.987654i
$964$	−17.3659	−0.559318
$965$	0	0
$966$	−1.01247	−0.0325755
$967$	5.09340i	0.163793i	0.996641	+	0.0818963i	$0.0260976\pi$
$967$	5.09340i	0.163793i	−0.996641	+	0.0818963i	$0.973902\pi$
$968$	− 7.73588i	− 0.248640i
$969$	−3.89619	−0.125164
$970$	0	0
$971$	−11.4468	−0.367346	−0.183673	−	0.982987i	$-0.558799\pi$
$971$	−11.4468	−0.367346	−0.183673	+	0.982987i	$0.558799\pi$
$972$	14.7772i	0.473979i
$973$	5.17023i	0.165750i
$974$	−24.8916	−0.797578
$975$	0	0
$976$	2.68397	0.0859118
$977$	− 41.9959i	− 1.34357i	−0.740747	−	0.671784i	$-0.765528\pi$
$977$	− 41.9959i	− 1.34357i	0.740747	−	0.671784i	$-0.234472\pi$
$978$	− 12.7069i	− 0.406320i
$979$	−22.8936	−0.731684
$980$	0	0
$981$	−48.0748	−1.53491
$982$	16.0000i	0.510581i
$983$	2.75293i	0.0878048i	0.999036	+	0.0439024i	$0.0139791\pi$
$983$	2.75293i	0.0878048i	−0.999036	+	0.0439024i	$0.986021\pi$
$984$	1.59262	0.0507708
$985$	0	0
$986$	−4.16425	−0.132617
$987$	− 11.8422i	− 0.376942i
$988$	7.72136i	0.245649i
$989$	−7.40139	−0.235351
$990$	0	0
$991$	−61.7422	−1.96131	−0.980653	−	0.195755i	$-0.937284\pi$
$991$	−61.7422	−1.96131	−0.980653	+	0.195755i	$0.937284\pi$
$992$	7.86068i	0.249577i
$993$	− 8.43231i	− 0.267591i
$994$	−5.92112	−0.187806
$995$	0	0
$996$	−4.53613	−0.143733
$997$	45.4967i	1.44089i	0.693510	+	0.720447i	$0.256063\pi$
$997$	45.4967i	1.44089i	−0.693510	+	0.720447i	$0.743937\pi$
$998$	24.8547i	0.786762i
$999$	−23.9460	−0.757619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.b.j.349.5		6
5.2	odd	4		1450.2.a.r.1.2		3
5.3	odd	4		290.2.a.d.1.2	✓	3
5.4	even	2	inner	1450.2.b.j.349.2		6
15.8	even	4		2610.2.a.w.1.3		3
20.3	even	4		2320.2.a.q.1.2		3
40.3	even	4		9280.2.a.bn.1.2		3
40.13	odd	4		9280.2.a.bp.1.2		3
145.28	odd	4		8410.2.a.w.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.d.1.2	✓	3	5.3	odd	4
1450.2.a.r.1.2		3	5.2	odd	4
1450.2.b.j.349.2		6	5.4	even	2	inner
1450.2.b.j.349.5		6	1.1	even	1	trivial
2320.2.a.q.1.2		3	20.3	even	4
2610.2.a.w.1.3		3	15.8	even	4
8410.2.a.w.1.2		3	145.28	odd	4
9280.2.a.bn.1.2		3	40.3	even	4
9280.2.a.bp.1.2		3	40.13	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.683969i q^{3} -1.00000 q^{4} +0.683969 q^{6} +2.16425i q^{7} -1.00000i q^{8} +2.53219 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -0.683969i q^{3} -1.00000 q^{4} +0.683969 q^{6} +2.16425i q^{7} -1.00000i q^{8} +2.53219 q^{9} -4.32850 q^{11} +0.683969i q^{12} -5.64453i q^{13} -2.16425 q^{14} +1.00000 q^{16} -4.16425i q^{17} +2.53219i q^{18} +1.36794 q^{19} +1.48028 q^{21} -4.32850i q^{22} +0.683969i q^{23} -0.683969 q^{24} +5.64453 q^{26} -3.78384i q^{27} -2.16425i q^{28} -1.00000 q^{29} +7.86068 q^{31} +1.00000i q^{32} +2.96056i q^{33} +4.16425 q^{34} -2.53219 q^{36} -6.32850i q^{37} +1.36794i q^{38} -3.86068 q^{39} -2.32850 q^{41} +1.48028i q^{42} +10.8212i q^{43} +4.32850 q^{44} -0.683969 q^{46} -8.00000i q^{47} -0.683969i q^{48} +2.31603 q^{49} -2.84822 q^{51} +5.64453i q^{52} -8.49274i q^{53} +3.78384 q^{54} +2.16425 q^{56} -0.935628i q^{57} -1.00000i q^{58} -2.27659 q^{59} +2.68397 q^{61} +7.86068i q^{62} +5.48028i q^{63} -1.00000 q^{64} -2.96056 q^{66} -2.73588i q^{67} +4.16425i q^{68} +0.467814 q^{69} +2.73588 q^{71} -2.53219i q^{72} -15.2286i q^{73} +6.32850 q^{74} -1.36794 q^{76} -9.36794i q^{77} -3.86068i q^{78} +15.0374 q^{79} +5.00853 q^{81} -2.32850i q^{82} +6.63206i q^{83} -1.48028 q^{84} -10.8212 q^{86} +0.683969i q^{87} +4.32850i q^{88} +5.28905 q^{89} +12.2162 q^{91} -0.683969i q^{92} -5.37646i q^{93} +8.00000 q^{94} +0.683969 q^{96} +0.987535i q^{97} +2.31603i q^{98} -10.9606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9	\( 6 q - 6 q^{4} - 2 q^{6} - 12 q^{9} + 4 q^{11} + 2 q^{14} + 6 q^{16} - 4 q^{19} + 2 q^{24} + 10 q^{26} - 6 q^{29} - 10 q^{31} + 10 q^{34} + 12 q^{36} + 34 q^{39} + 16 q^{41} - 4 q^{44} + 2 q^{46} + 20 q^{49} + 4 q^{51} + 56 q^{54} - 2 q^{56} - 2 q^{59} + 10 q^{61} - 6 q^{64} + 30 q^{69} - 8 q^{71} + 8 q^{74} + 4 q^{76} - 18 q^{79} + 70 q^{81} + 10 q^{86} - 16 q^{89} + 40 q^{91} + 48 q^{94} - 2 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 2 * q^6 - 12 * q^9 + 4 * q^11 + 2 * q^14 + 6 * q^16 - 4 * q^19 + 2 * q^24 + 10 * q^26 - 6 * q^29 - 10 * q^31 + 10 * q^34 + 12 * q^36 + 34 * q^39 + 16 * q^41 - 4 * q^44 + 2 * q^46 + 20 * q^49 + 4 * q^51 + 56 * q^54 - 2 * q^56 - 2 * q^59 + 10 * q^61 - 6 * q^64 + 30 * q^69 - 8 * q^71 + 8 * q^74 + 4 * q^76 - 18 * q^79 + 70 * q^81 + 10 * q^86 - 16 * q^89 + 40 * q^91 + 48 * q^94 - 2 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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