LMFDB - Embedded newform 1275.2.b.d.1174.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1275,2,Mod(1174,1275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1275, 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("1275.1174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1275 = 3 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1275.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:	$10.1809262577$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1174.3
Root			$1.56155i$ of defining polynomial
Character	$\chi$	$=$	1275.1174
Dual form			1275.2.b.d.1174.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56155i q^{2} +1.00000i q^{3} -0.438447 q^{4} -1.56155 q^{6} +2.43845i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.56155i q^{2} +1.00000i q^{3} -0.438447 q^{4} -1.56155 q^{6} +2.43845i q^{8} -1.00000 q^{9} -2.56155 q^{11} -0.438447i q^{12} -4.56155i q^{13} -4.68466 q^{16} +1.00000i q^{17} -1.56155i q^{18} -7.68466 q^{19} -4.00000i q^{22} +6.56155i q^{23} -2.43845 q^{24} +7.12311 q^{26} -1.00000i q^{27} -8.24621 q^{29} -5.12311 q^{31} -2.43845i q^{32} -2.56155i q^{33} -1.56155 q^{34} +0.438447 q^{36} +3.12311i q^{37} -12.0000i q^{38} +4.56155 q^{39} +0.561553 q^{41} +7.68466i q^{43} +1.12311 q^{44} -10.2462 q^{46} -2.87689i q^{47} -4.68466i q^{48} +7.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} +4.24621i q^{53} +1.56155 q^{54} -7.68466i q^{57} -12.8769i q^{58} +1.12311 q^{59} +0.876894 q^{61} -8.00000i q^{62} -5.56155 q^{64} +4.00000 q^{66} +4.00000i q^{67} -0.438447i q^{68} -6.56155 q^{69} +10.2462 q^{71} -2.43845i q^{72} -4.24621i q^{73} -4.87689 q^{74} +3.36932 q^{76} +7.12311i q^{78} -15.3693 q^{79} +1.00000 q^{81} +0.876894i q^{82} +9.12311i q^{83} -12.0000 q^{86} -8.24621i q^{87} -6.24621i q^{88} -7.12311 q^{89} -2.87689i q^{92} -5.12311i q^{93} +4.49242 q^{94} +2.43845 q^{96} -11.1231i q^{97} +10.9309i q^{98} +2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) $ 4 * q - 10 * q^4 + 2 * q^6 - 4 * q^9	$ 4 q - 10 q^{4} + 2 q^{6} - 4 q^{9} - 2 q^{11} + 6 q^{16} - 6 q^{19} - 18 q^{24} + 12 q^{26} - 4 q^{31} + 2 q^{34} + 10 q^{36} + 10 q^{39} - 6 q^{41} - 12 q^{44} - 8 q^{46} + 28 q^{49} - 4 q^{51} - 2 q^{54} - 12 q^{59} + 20 q^{61} - 14 q^{64} + 16 q^{66} - 18 q^{69} + 8 q^{71} - 36 q^{74} - 36 q^{76} - 12 q^{79} + 4 q^{81} - 48 q^{86} - 12 q^{89} - 48 q^{94} + 18 q^{96} + 2 q^{99}+O(q^{100}) $ 4 * q - 10 * q^4 + 2 * q^6 - 4 * q^9 - 2 * q^11 + 6 * q^16 - 6 * q^19 - 18 * q^24 + 12 * q^26 - 4 * q^31 + 2 * q^34 + 10 * q^36 + 10 * q^39 - 6 * q^41 - 12 * q^44 - 8 * q^46 + 28 * q^49 - 4 * q^51 - 2 * q^54 - 12 * q^59 + 20 * q^61 - 14 * q^64 + 16 * q^66 - 18 * q^69 + 8 * q^71 - 36 * q^74 - 36 * q^76 - 12 * q^79 + 4 * q^81 - 48 * q^86 - 12 * q^89 - 48 * q^94 + 18 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1275\mathbb{Z}\right)^\times$.

$n$	$52$	$751$	$851$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	1.56155i	1.10418i	0.833783	+	0.552092i	$0.186170\pi$
$2$	1.56155i	1.10418i	−0.833783	+	0.552092i	$0.813830\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−0.438447	−0.219224
$5$	0	0
$5$	0	0
$6$	−1.56155	−0.637501
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	2.43845i	0.862121i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−2.56155	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$11$	−2.56155	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$12$	− 0.438447i	− 0.126569i
$13$	− 4.56155i	− 1.26515i	−0.774500	−	0.632574i	$-0.781999\pi$
$13$	− 4.56155i	− 1.26515i	0.774500	−	0.632574i	$-0.218001\pi$
$14$	0	0
$15$	0	0
$16$	−4.68466	−1.17116
$17$	1.00000i	0.242536i
$17$	1.00000i	0.242536i
$18$	− 1.56155i	− 0.368062i
$19$	−7.68466	−1.76298	−0.881491	−	0.472201i	$-0.843460\pi$
$19$	−7.68466	−1.76298	−0.881491	+	0.472201i	$0.843460\pi$
$20$	0	0
$21$	0	0
$22$	− 4.00000i	− 0.852803i
$23$	6.56155i	1.36818i	0.729398	+	0.684089i	$0.239800\pi$
$23$	6.56155i	1.36818i	−0.729398	+	0.684089i	$0.760200\pi$
$24$	−2.43845	−0.497746
$25$	0	0
$26$	7.12311	1.39696
$27$	− 1.00000i	− 0.192450i
$28$	0	0
$29$	−8.24621	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$30$	0	0
$31$	−5.12311	−0.920137	−0.460068	−	0.887883i	$-0.652175\pi$
$31$	−5.12311	−0.920137	−0.460068	+	0.887883i	$0.652175\pi$
$32$	− 2.43845i	− 0.431061i
$33$	− 2.56155i	− 0.445909i
$34$	−1.56155	−0.267804
$35$	0	0
$36$	0.438447	0.0730745
$37$	3.12311i	0.513435i	0.966486	+	0.256718i	$0.0826411\pi$
$37$	3.12311i	0.513435i	−0.966486	+	0.256718i	$0.917359\pi$
$38$	− 12.0000i	− 1.94666i
$39$	4.56155	0.730433
$40$	0	0
$41$	0.561553	0.0876998	0.0438499	−	0.999038i	$-0.486038\pi$
$41$	0.561553	0.0876998	0.0438499	+	0.999038i	$0.486038\pi$
$42$	0	0
$43$	7.68466i	1.17190i	0.810347	+	0.585950i	$0.199278\pi$
$43$	7.68466i	1.17190i	−0.810347	+	0.585950i	$0.800722\pi$
$44$	1.12311	0.169315
$45$	0	0
$46$	−10.2462	−1.51072
$47$	− 2.87689i	− 0.419638i	−0.977740	−	0.209819i	$-0.932712\pi$
$47$	− 2.87689i	− 0.419638i	0.977740	−	0.209819i	$-0.0672875\pi$
$48$	− 4.68466i	− 0.676172i
$49$	7.00000	1.00000
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000i	0.277350i
$53$	4.24621i	0.583262i	0.956531	+	0.291631i	$0.0941979\pi$
$53$	4.24621i	0.583262i	−0.956531	+	0.291631i	$0.905802\pi$
$54$	1.56155	0.212500
$55$	0	0
$56$	0	0
$57$	− 7.68466i	− 1.01786i
$58$	− 12.8769i	− 1.69082i
$59$	1.12311	0.146216	0.0731079	−	0.997324i	$-0.476708\pi$
$59$	1.12311	0.146216	0.0731079	+	0.997324i	$0.476708\pi$
$60$	0	0
$61$	0.876894	0.112275	0.0561374	−	0.998423i	$-0.482122\pi$
$61$	0.876894	0.112275	0.0561374	+	0.998423i	$0.482122\pi$
$62$	− 8.00000i	− 1.01600i
$63$	0	0
$64$	−5.56155	−0.695194
$65$	0	0
$66$	4.00000	0.492366
$67$	4.00000i	0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$	4.00000i	0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$	− 0.438447i	− 0.0531695i
$69$	−6.56155	−0.789918
$70$	0	0
$71$	10.2462	1.21600	0.608001	−	0.793936i	$-0.291972\pi$
$71$	10.2462	1.21600	0.608001	+	0.793936i	$0.291972\pi$
$72$	− 2.43845i	− 0.287374i
$73$	− 4.24621i	− 0.496981i	−0.968634	−	0.248491i	$-0.920065\pi$
$73$	− 4.24621i	− 0.496981i	0.968634	−	0.248491i	$-0.0799345\pi$
$74$	−4.87689	−0.566927
$75$	0	0
$76$	3.36932	0.386487
$77$	0	0
$78$	7.12311i	0.806533i
$79$	−15.3693	−1.72918	−0.864592	−	0.502475i	$-0.832423\pi$
$79$	−15.3693	−1.72918	−0.864592	+	0.502475i	$0.832423\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0.876894i	0.0968368i
$83$	9.12311i	1.00139i	0.865624	+	0.500695i	$0.166922\pi$
$83$	9.12311i	1.00139i	−0.865624	+	0.500695i	$0.833078\pi$
$84$	0	0
$85$	0	0
$86$	−12.0000	−1.29399
$87$	− 8.24621i	− 0.884087i
$88$	− 6.24621i	− 0.665848i
$89$	−7.12311	−0.755048	−0.377524	−	0.926000i	$-0.623224\pi$
$89$	−7.12311	−0.755048	−0.377524	+	0.926000i	$0.623224\pi$
$90$	0	0
$91$	0	0
$92$	− 2.87689i	− 0.299937i
$93$	− 5.12311i	− 0.531241i
$94$	4.49242	0.463358
$95$	0	0
$96$	2.43845	0.248873
$97$	− 11.1231i	− 1.12938i	−0.825303	−	0.564690i	$-0.808996\pi$
$97$	− 11.1231i	− 1.12938i	0.825303	−	0.564690i	$-0.191004\pi$
$98$	10.9309i	1.10418i
$99$	2.56155	0.257446
$100$	0	0
$101$	19.1231	1.90282	0.951410	−	0.307927i	$-0.0996352\pi$
$101$	19.1231	1.90282	0.951410	+	0.307927i	$0.0996352\pi$
$102$	− 1.56155i	− 0.154617i
$103$	− 4.31534i	− 0.425203i	−0.977139	−	0.212602i	$-0.931806\pi$
$103$	− 4.31534i	− 0.425203i	0.977139	−	0.212602i	$-0.0681937\pi$
$104$	11.1231	1.09071
$105$	0	0
$106$	−6.63068	−0.644029
$107$	7.68466i	0.742904i	0.928452	+	0.371452i	$0.121140\pi$
$107$	7.68466i	0.742904i	−0.928452	+	0.371452i	$0.878860\pi$
$108$	0.438447i	0.0421896i
$109$	15.1231	1.44853	0.724265	−	0.689521i	$-0.242179\pi$
$109$	15.1231	1.44853	0.724265	+	0.689521i	$0.242179\pi$
$110$	0	0
$111$	−3.12311	−0.296432
$112$	0	0
$113$	4.56155i	0.429115i	0.976711	+	0.214557i	$0.0688309\pi$
$113$	4.56155i	0.429115i	−0.976711	+	0.214557i	$0.931169\pi$
$114$	12.0000	1.12390
$115$	0	0
$116$	3.61553	0.335693
$117$	4.56155i	0.421716i
$118$	1.75379i	0.161449i
$119$	0	0
$120$	0	0
$121$	−4.43845	−0.403495
$122$	1.36932i	0.123972i
$123$	0.561553i	0.0506335i
$124$	2.24621	0.201716
$125$	0	0
$126$	0	0
$127$	− 0.807764i	− 0.0716775i	−0.999358	−	0.0358387i	$-0.988590\pi$
$127$	− 0.807764i	− 0.0716775i	0.999358	−	0.0358387i	$-0.0114103\pi$
$128$	− 13.5616i	− 1.19868i
$129$	−7.68466	−0.676596
$130$	0	0
$131$	18.5616	1.62173	0.810865	−	0.585233i	$-0.198997\pi$
$131$	18.5616	1.62173	0.810865	+	0.585233i	$0.198997\pi$
$132$	1.12311i	0.0977538i
$133$	0	0
$134$	−6.24621	−0.539590
$135$	0	0
$136$	−2.43845	−0.209095
$137$	− 16.2462i	− 1.38801i	−0.719971	−	0.694004i	$-0.755845\pi$
$137$	− 16.2462i	− 1.38801i	0.719971	−	0.694004i	$-0.244155\pi$
$138$	− 10.2462i	− 0.872215i
$139$	9.12311	0.773812	0.386906	−	0.922119i	$-0.373544\pi$
$139$	9.12311	0.773812	0.386906	+	0.922119i	$0.373544\pi$
$140$	0	0
$141$	2.87689	0.242278
$142$	16.0000i	1.34269i
$143$	11.6847i	0.977120i
$144$	4.68466	0.390388
$145$	0	0
$146$	6.63068	0.548759
$147$	7.00000i	0.577350i
$148$	− 1.36932i	− 0.112557i
$149$	4.24621	0.347863	0.173932	−	0.984758i	$-0.444353\pi$
$149$	4.24621	0.347863	0.173932	+	0.984758i	$0.444353\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	− 18.7386i	− 1.51990i
$153$	− 1.00000i	− 0.0808452i
$154$	0	0
$155$	0	0
$156$	−2.00000	−0.160128
$157$	− 5.68466i	− 0.453685i	−0.973931	−	0.226843i	$-0.927160\pi$
$157$	− 5.68466i	− 0.453685i	0.973931	−	0.226843i	$-0.0728403\pi$
$158$	− 24.0000i	− 1.90934i
$159$	−4.24621	−0.336746
$160$	0	0
$161$	0	0
$162$	1.56155i	0.122687i
$163$	6.87689i	0.538640i	0.963051	+	0.269320i	$0.0867989\pi$
$163$	6.87689i	0.538640i	−0.963051	+	0.269320i	$0.913201\pi$
$164$	−0.246211	−0.0192259
$165$	0	0
$166$	−14.2462	−1.10572
$167$	− 0.807764i	− 0.0625067i	−0.999511	−	0.0312533i	$-0.990050\pi$
$167$	− 0.807764i	− 0.0625067i	0.999511	−	0.0312533i	$-0.00994986\pi$
$168$	0	0
$169$	−7.80776	−0.600597
$170$	0	0
$171$	7.68466	0.587661
$172$	− 3.36932i	− 0.256908i
$173$	18.8078i	1.42993i	0.699161	+	0.714964i	$0.253557\pi$
$173$	18.8078i	1.42993i	−0.699161	+	0.714964i	$0.746443\pi$
$174$	12.8769	0.976195
$175$	0	0
$176$	12.0000	0.904534
$177$	1.12311i	0.0844178i
$178$	− 11.1231i	− 0.833712i
$179$	9.12311	0.681893	0.340946	−	0.940083i	$-0.389253\pi$
$179$	9.12311	0.681893	0.340946	+	0.940083i	$0.389253\pi$
$180$	0	0
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	0	0
$183$	0.876894i	0.0648219i
$184$	−16.0000	−1.17954
$185$	0	0
$186$	8.00000	0.586588
$187$	− 2.56155i	− 0.187319i
$188$	1.26137i	0.0919946i
$189$	0	0
$190$	0	0
$191$	−13.1231	−0.949555	−0.474777	−	0.880106i	$-0.657471\pi$
$191$	−13.1231	−0.949555	−0.474777	+	0.880106i	$0.657471\pi$
$192$	− 5.56155i	− 0.401371i
$193$	24.2462i	1.74528i	0.488364	+	0.872640i	$0.337594\pi$
$193$	24.2462i	1.74528i	−0.488364	+	0.872640i	$0.662406\pi$
$194$	17.3693	1.24704
$195$	0	0
$196$	−3.06913	−0.219224
$197$	19.9309i	1.42002i	0.704194	+	0.710008i	$0.251309\pi$
$197$	19.9309i	1.42002i	−0.704194	+	0.710008i	$0.748691\pi$
$198$	4.00000i	0.284268i
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	29.8617i	2.10106i
$203$	0	0
$204$	0.438447	0.0306974
$205$	0	0
$206$	6.73863	0.469503
$207$	− 6.56155i	− 0.456059i
$208$	21.3693i	1.48170i
$209$	19.6847	1.36162
$210$	0	0
$211$	−11.3693	−0.782696	−0.391348	−	0.920243i	$-0.627991\pi$
$211$	−11.3693	−0.782696	−0.391348	+	0.920243i	$0.627991\pi$
$212$	− 1.86174i	− 0.127865i
$213$	10.2462i	0.702059i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	2.43845	0.165915
$217$	0	0
$218$	23.6155i	1.59945i
$219$	4.24621	0.286932
$220$	0	0
$221$	4.56155	0.306843
$222$	− 4.87689i	− 0.327316i
$223$	− 13.9309i	− 0.932880i	−0.884553	−	0.466440i	$-0.845536\pi$
$223$	− 13.9309i	− 0.932880i	0.884553	−	0.466440i	$-0.154464\pi$
$224$	0	0
$225$	0	0
$226$	−7.12311	−0.473822
$227$	23.0540i	1.53015i	0.643944	+	0.765073i	$0.277297\pi$
$227$	23.0540i	1.53015i	−0.643944	+	0.765073i	$0.722703\pi$
$228$	3.36932i	0.223138i
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	0	0
$231$	0	0
$232$	− 20.1080i	− 1.32015i
$233$	− 0.561553i	− 0.0367885i	−0.999831	−	0.0183943i	$-0.994145\pi$
$233$	− 0.561553i	− 0.0367885i	0.999831	−	0.0183943i	$-0.00585541\pi$
$234$	−7.12311	−0.465652
$235$	0	0
$236$	−0.492423	−0.0320540
$237$	− 15.3693i	− 0.998344i
$238$	0	0
$239$	−10.2462	−0.662772	−0.331386	−	0.943495i	$-0.607516\pi$
$239$	−10.2462	−0.662772	−0.331386	+	0.943495i	$0.607516\pi$
$240$	0	0
$241$	−21.3693	−1.37652	−0.688259	−	0.725465i	$-0.741625\pi$
$241$	−21.3693	−1.37652	−0.688259	+	0.725465i	$0.741625\pi$
$242$	− 6.93087i	− 0.445533i
$243$	1.00000i	0.0641500i
$244$	−0.384472	−0.0246133
$245$	0	0
$246$	−0.876894	−0.0559087
$247$	35.0540i	2.23043i
$248$	− 12.4924i	− 0.793270i
$249$	−9.12311	−0.578153
$250$	0	0
$251$	−24.4924	−1.54595	−0.772974	−	0.634438i	$-0.781232\pi$
$251$	−24.4924	−1.54595	−0.772974	+	0.634438i	$0.781232\pi$
$252$	0	0
$253$	− 16.8078i	− 1.05670i
$254$	1.26137	0.0791452
$255$	0	0
$256$	10.0540	0.628373
$257$	9.36932i	0.584442i	0.956351	+	0.292221i	$0.0943943\pi$
$257$	9.36932i	0.584442i	−0.956351	+	0.292221i	$0.905606\pi$
$258$	− 12.0000i	− 0.747087i
$259$	0	0
$260$	0	0
$261$	8.24621	0.510428
$262$	28.9848i	1.79069i
$263$	− 12.4924i	− 0.770316i	−0.922851	−	0.385158i	$-0.874147\pi$
$263$	− 12.4924i	− 0.770316i	0.922851	−	0.385158i	$-0.125853\pi$
$264$	6.24621	0.384428
$265$	0	0
$266$	0	0
$267$	− 7.12311i	− 0.435927i
$268$	− 1.75379i	− 0.107130i
$269$	−20.5616	−1.25366	−0.626830	−	0.779156i	$-0.715648\pi$
$269$	−20.5616	−1.25366	−0.626830	+	0.779156i	$0.715648\pi$
$270$	0	0
$271$	−0.807764	−0.0490682	−0.0245341	−	0.999699i	$-0.507810\pi$
$271$	−0.807764	−0.0490682	−0.0245341	+	0.999699i	$0.507810\pi$
$272$	− 4.68466i	− 0.284049i
$273$	0	0
$274$	25.3693	1.53262
$275$	0	0
$276$	2.87689	0.173169
$277$	6.00000i	0.360505i	0.983620	+	0.180253i	$0.0576915\pi$
$277$	6.00000i	0.360505i	−0.983620	+	0.180253i	$0.942309\pi$
$278$	14.2462i	0.854431i
$279$	5.12311	0.306712
$280$	0	0
$281$	−19.1231	−1.14079	−0.570394	−	0.821371i	$-0.693210\pi$
$281$	−19.1231	−1.14079	−0.570394	+	0.821371i	$0.693210\pi$
$282$	4.49242i	0.267520i
$283$	3.36932i	0.200285i	0.994973	+	0.100143i	$0.0319299\pi$
$283$	3.36932i	0.200285i	−0.994973	+	0.100143i	$0.968070\pi$
$284$	−4.49242	−0.266576
$285$	0	0
$286$	−18.2462	−1.07892
$287$	0	0
$288$	2.43845i	0.143687i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	11.1231	0.652048
$292$	1.86174i	0.108950i
$293$	7.12311i	0.416136i	0.978114	+	0.208068i	$0.0667176\pi$
$293$	7.12311i	0.416136i	−0.978114	+	0.208068i	$0.933282\pi$
$294$	−10.9309	−0.637501
$295$	0	0
$296$	−7.61553	−0.442644
$297$	2.56155i	0.148636i
$298$	6.63068i	0.384105i
$299$	29.9309	1.73095
$300$	0	0
$301$	0	0
$302$	12.4924i	0.718858i
$303$	19.1231i	1.09859i
$304$	36.0000	2.06474
$305$	0	0
$306$	1.56155	0.0892680
$307$	− 0.492423i	− 0.0281040i	−0.999901	−	0.0140520i	$-0.995527\pi$
$307$	− 0.492423i	− 0.0281040i	0.999901	−	0.0140520i	$-0.00447304\pi$
$308$	0	0
$309$	4.31534	0.245491
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	11.1231i	0.629722i
$313$	7.61553i	0.430455i	0.976564	+	0.215228i	$0.0690493\pi$
$313$	7.61553i	0.430455i	−0.976564	+	0.215228i	$0.930951\pi$
$314$	8.87689	0.500952
$315$	0	0
$316$	6.73863	0.379078
$317$	− 18.0000i	− 1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$	− 18.0000i	− 1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	− 6.63068i	− 0.371830i
$319$	21.1231	1.18267
$320$	0	0
$321$	−7.68466	−0.428916
$322$	0	0
$323$	− 7.68466i	− 0.427586i
$324$	−0.438447	−0.0243582
$325$	0	0
$326$	−10.7386	−0.594758
$327$	15.1231i	0.836310i
$328$	1.36932i	0.0756079i
$329$	0	0
$330$	0	0
$331$	−6.06913	−0.333590	−0.166795	−	0.985992i	$-0.553342\pi$
$331$	−6.06913	−0.333590	−0.166795	+	0.985992i	$0.553342\pi$
$332$	− 4.00000i	− 0.219529i
$333$	− 3.12311i	− 0.171145i
$334$	1.26137	0.0690189
$335$	0	0
$336$	0	0
$337$	32.7386i	1.78339i	0.452640	+	0.891694i	$0.350482\pi$
$337$	32.7386i	1.78339i	−0.452640	+	0.891694i	$0.649518\pi$
$338$	− 12.1922i	− 0.663170i
$339$	−4.56155	−0.247750
$340$	0	0
$341$	13.1231	0.710656
$342$	12.0000i	0.648886i
$343$	0	0
$344$	−18.7386	−1.01032
$345$	0	0
$346$	−29.3693	−1.57890
$347$	24.4924i	1.31482i	0.753532	+	0.657411i	$0.228348\pi$
$347$	24.4924i	1.31482i	−0.753532	+	0.657411i	$0.771652\pi$
$348$	3.61553i	0.193813i
$349$	−7.43845	−0.398171	−0.199085	−	0.979982i	$-0.563797\pi$
$349$	−7.43845	−0.398171	−0.199085	+	0.979982i	$0.563797\pi$
$350$	0	0
$351$	−4.56155	−0.243478
$352$	6.24621i	0.332924i
$353$	− 22.4924i	− 1.19715i	−0.801066	−	0.598575i	$-0.795734\pi$
$353$	− 22.4924i	− 1.19715i	0.801066	−	0.598575i	$-0.204266\pi$
$354$	−1.75379	−0.0932128
$355$	0	0
$356$	3.12311	0.165524
$357$	0	0
$358$	14.2462i	0.752936i
$359$	2.24621	0.118550	0.0592752	−	0.998242i	$-0.481121\pi$
$359$	2.24621	0.118550	0.0592752	+	0.998242i	$0.481121\pi$
$360$	0	0
$361$	40.0540	2.10810
$362$	9.36932i	0.492440i
$363$	− 4.43845i	− 0.232958i
$364$	0	0
$365$	0	0
$366$	−1.36932	−0.0715753
$367$	− 18.2462i	− 0.952444i	−0.879325	−	0.476222i	$-0.842006\pi$
$367$	− 18.2462i	− 0.952444i	0.879325	−	0.476222i	$-0.157994\pi$
$368$	− 30.7386i	− 1.60236i
$369$	−0.561553	−0.0292333
$370$	0	0
$371$	0	0
$372$	2.24621i	0.116461i
$373$	− 16.2462i	− 0.841197i	−0.907247	−	0.420598i	$-0.861820\pi$
$373$	− 16.2462i	− 0.841197i	0.907247	−	0.420598i	$-0.138180\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	7.01515	0.361779
$377$	37.6155i	1.93730i
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0.807764	0.0413830
$382$	− 20.4924i	− 1.04848i
$383$	10.2462i	0.523557i	0.965128	+	0.261778i	$0.0843090\pi$
$383$	10.2462i	0.523557i	−0.965128	+	0.261778i	$0.915691\pi$
$384$	13.5616	0.692060
$385$	0	0
$386$	−37.8617	−1.92711
$387$	− 7.68466i	− 0.390633i
$388$	4.87689i	0.247587i
$389$	21.8617	1.10843	0.554217	−	0.832372i	$-0.313018\pi$
$389$	21.8617	1.10843	0.554217	+	0.832372i	$0.313018\pi$
$390$	0	0
$391$	−6.56155	−0.331832
$392$	17.0691i	0.862121i
$393$	18.5616i	0.936306i
$394$	−31.1231	−1.56796
$395$	0	0
$396$	−1.12311	−0.0564382
$397$	5.36932i	0.269478i	0.990881	+	0.134739i	$0.0430196\pi$
$397$	5.36932i	0.269478i	−0.990881	+	0.134739i	$0.956980\pi$
$398$	− 24.9848i	− 1.25238i
$399$	0	0
$400$	0	0
$401$	−6.17708	−0.308469	−0.154234	−	0.988034i	$-0.549291\pi$
$401$	−6.17708	−0.308469	−0.154234	+	0.988034i	$0.549291\pi$
$402$	− 6.24621i	− 0.311533i
$403$	23.3693i	1.16411i
$404$	−8.38447	−0.417143
$405$	0	0
$406$	0	0
$407$	− 8.00000i	− 0.396545i
$408$	− 2.43845i	− 0.120721i
$409$	2.31534	0.114486	0.0572431	−	0.998360i	$-0.481769\pi$
$409$	2.31534	0.114486	0.0572431	+	0.998360i	$0.481769\pi$
$410$	0	0
$411$	16.2462	0.801367
$412$	1.89205i	0.0932146i
$413$	0	0
$414$	10.2462	0.503574
$415$	0	0
$416$	−11.1231	−0.545355
$417$	9.12311i	0.446760i
$418$	30.7386i	1.50348i
$419$	−32.4924	−1.58736	−0.793679	−	0.608336i	$-0.791837\pi$
$419$	−32.4924	−1.58736	−0.793679	+	0.608336i	$0.791837\pi$
$420$	0	0
$421$	28.5616	1.39200	0.696002	−	0.718039i	$-0.254960\pi$
$421$	28.5616	1.39200	0.696002	+	0.718039i	$0.254960\pi$
$422$	− 17.7538i	− 0.864241i
$423$	2.87689i	0.139879i
$424$	−10.3542	−0.502843
$425$	0	0
$426$	−16.0000	−0.775203
$427$	0	0
$428$	− 3.36932i	− 0.162862i
$429$	−11.6847	−0.564141
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	4.68466i	0.225391i
$433$	− 14.3153i	− 0.687951i	−0.938979	−	0.343976i	$-0.888226\pi$
$433$	− 14.3153i	− 0.687951i	0.938979	−	0.343976i	$-0.111774\pi$
$434$	0	0
$435$	0	0
$436$	−6.63068	−0.317552
$437$	− 50.4233i	− 2.41207i
$438$	6.63068i	0.316826i
$439$	5.75379	0.274613	0.137307	−	0.990529i	$-0.456155\pi$
$439$	5.75379	0.274613	0.137307	+	0.990529i	$0.456155\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	7.12311i	0.338812i
$443$	22.8769i	1.08691i	0.839437	+	0.543457i	$0.182885\pi$
$443$	22.8769i	1.08691i	−0.839437	+	0.543457i	$0.817115\pi$
$444$	1.36932	0.0649849
$445$	0	0
$446$	21.7538	1.03007
$447$	4.24621i	0.200839i
$448$	0	0
$449$	12.7386	0.601173	0.300587	−	0.953755i	$-0.402818\pi$
$449$	12.7386	0.601173	0.300587	+	0.953755i	$0.402818\pi$
$450$	0	0
$451$	−1.43845	−0.0677338
$452$	− 2.00000i	− 0.0940721i
$453$	8.00000i	0.375873i
$454$	−36.0000	−1.68956
$455$	0	0
$456$	18.7386	0.877517
$457$	− 6.80776i	− 0.318454i	−0.987242	−	0.159227i	$-0.949100\pi$
$457$	− 6.80776i	− 0.318454i	0.987242	−	0.159227i	$-0.0509001\pi$
$458$	− 9.36932i	− 0.437799i
$459$	1.00000	0.0466760
$460$	0	0
$461$	8.24621	0.384064	0.192032	−	0.981389i	$-0.438492\pi$
$461$	8.24621	0.384064	0.192032	+	0.981389i	$0.438492\pi$
$462$	0	0
$463$	− 24.9848i	− 1.16114i	−0.814209	−	0.580572i	$-0.802829\pi$
$463$	− 24.9848i	− 1.16114i	0.814209	−	0.580572i	$-0.197171\pi$
$464$	38.6307	1.79338
$465$	0	0
$466$	0.876894	0.0406213
$467$	− 3.36932i	− 0.155913i	−0.996957	−	0.0779567i	$-0.975160\pi$
$467$	− 3.36932i	− 0.155913i	0.996957	−	0.0779567i	$-0.0248396\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	0	0
$470$	0	0
$471$	5.68466	0.261935
$472$	2.73863i	0.126056i
$473$	− 19.6847i	− 0.905102i
$474$	24.0000	1.10236
$475$	0	0
$476$	0	0
$477$	− 4.24621i	− 0.194421i
$478$	− 16.0000i	− 0.731823i
$479$	29.3002	1.33876	0.669380	−	0.742920i	$-0.266560\pi$
$479$	29.3002	1.33876	0.669380	+	0.742920i	$0.266560\pi$
$480$	0	0
$481$	14.2462	0.649571
$482$	− 33.3693i	− 1.51993i
$483$	0	0
$484$	1.94602	0.0884557
$485$	0	0
$486$	−1.56155	−0.0708335
$487$	− 7.36932i	− 0.333936i	−0.985962	−	0.166968i	$-0.946602\pi$
$487$	− 7.36932i	− 0.333936i	0.985962	−	0.166968i	$-0.0533976\pi$
$488$	2.13826i	0.0967945i
$489$	−6.87689	−0.310984
$490$	0	0
$491$	3.36932	0.152055	0.0760276	−	0.997106i	$-0.475776\pi$
$491$	3.36932	0.152055	0.0760276	+	0.997106i	$0.475776\pi$
$492$	− 0.246211i	− 0.0111001i
$493$	− 8.24621i	− 0.371391i
$494$	−54.7386	−2.46281
$495$	0	0
$496$	24.0000	1.07763
$497$	0	0
$498$	− 14.2462i	− 0.638388i
$499$	11.3693	0.508961	0.254480	−	0.967078i	$-0.418096\pi$
$499$	11.3693	0.508961	0.254480	+	0.967078i	$0.418096\pi$
$500$	0	0
$501$	0.807764	0.0360882
$502$	− 38.2462i	− 1.70701i
$503$	25.4384i	1.13424i	0.823634	+	0.567122i	$0.191943\pi$
$503$	25.4384i	1.13424i	−0.823634	+	0.567122i	$0.808057\pi$
$504$	0	0
$505$	0	0
$506$	26.2462	1.16679
$507$	− 7.80776i	− 0.346755i
$508$	0.354162i	0.0157134i
$509$	−16.8769	−0.748055	−0.374028	−	0.927418i	$-0.622023\pi$
$509$	−16.8769	−0.748055	−0.374028	+	0.927418i	$0.622023\pi$
$510$	0	0
$511$	0	0
$512$	− 11.4233i	− 0.504843i
$513$	7.68466i	0.339286i
$514$	−14.6307	−0.645332
$515$	0	0
$516$	3.36932	0.148326
$517$	7.36932i	0.324102i
$518$	0	0
$519$	−18.8078	−0.825569
$520$	0	0
$521$	−31.4384	−1.37734	−0.688672	−	0.725073i	$-0.741806\pi$
$521$	−31.4384	−1.37734	−0.688672	+	0.725073i	$0.741806\pi$
$522$	12.8769i	0.563606i
$523$	20.0000i	0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$	20.0000i	0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−8.13826	−0.355522
$525$	0	0
$526$	19.5076	0.850571
$527$	− 5.12311i	− 0.223166i
$528$	12.0000i	0.522233i
$529$	−20.0540	−0.871912
$530$	0	0
$531$	−1.12311	−0.0487386
$532$	0	0
$533$	− 2.56155i	− 0.110953i
$534$	11.1231	0.481344
$535$	0	0
$536$	−9.75379	−0.421300
$537$	9.12311i	0.393691i
$538$	− 32.1080i	− 1.38427i
$539$	−17.9309	−0.772337
$540$	0	0
$541$	−40.1080	−1.72438	−0.862188	−	0.506589i	$-0.830906\pi$
$541$	−40.1080	−1.72438	−0.862188	+	0.506589i	$0.830906\pi$
$542$	− 1.26137i	− 0.0541803i
$543$	6.00000i	0.257485i
$544$	2.43845	0.104548
$545$	0	0
$546$	0	0
$547$	28.0000i	1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$	28.0000i	1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$	7.12311i	0.304284i
$549$	−0.876894	−0.0374249
$550$	0	0
$551$	63.3693	2.69962
$552$	− 16.0000i	− 0.681005i
$553$	0	0
$554$	−9.36932	−0.398064
$555$	0	0
$556$	−4.00000	−0.169638
$557$	− 6.49242i	− 0.275093i	−0.990495	−	0.137546i	$-0.956078\pi$
$557$	− 6.49242i	− 0.275093i	0.990495	−	0.137546i	$-0.0439216\pi$
$558$	8.00000i	0.338667i
$559$	35.0540	1.48263
$560$	0	0
$561$	2.56155	0.108149
$562$	− 29.8617i	− 1.25964i
$563$	− 22.8769i	− 0.964146i	−0.876131	−	0.482073i	$-0.839884\pi$
$563$	− 22.8769i	− 0.964146i	0.876131	−	0.482073i	$-0.160116\pi$
$564$	−1.26137	−0.0531131
$565$	0	0
$566$	−5.26137	−0.221152
$567$	0	0
$568$	24.9848i	1.04834i
$569$	−12.8769	−0.539827	−0.269914	−	0.962885i	$-0.586995\pi$
$569$	−12.8769	−0.539827	−0.269914	+	0.962885i	$0.586995\pi$
$570$	0	0
$571$	18.7386	0.784187	0.392094	−	0.919925i	$-0.371751\pi$
$571$	18.7386	0.784187	0.392094	+	0.919925i	$0.371751\pi$
$572$	− 5.12311i	− 0.214208i
$573$	− 13.1231i	− 0.548226i
$574$	0	0
$575$	0	0
$576$	5.56155	0.231731
$577$	− 41.0540i	− 1.70910i	−0.519370	−	0.854550i	$-0.673833\pi$
$577$	− 41.0540i	− 1.70910i	0.519370	−	0.854550i	$-0.326167\pi$
$578$	− 1.56155i	− 0.0649520i
$579$	−24.2462	−1.00764
$580$	0	0
$581$	0	0
$582$	17.3693i	0.719981i
$583$	− 10.8769i	− 0.450475i
$584$	10.3542	0.428458
$585$	0	0
$586$	−11.1231	−0.459491
$587$	36.9848i	1.52653i	0.646087	+	0.763264i	$0.276404\pi$
$587$	36.9848i	1.52653i	−0.646087	+	0.763264i	$0.723596\pi$
$588$	− 3.06913i	− 0.126569i
$589$	39.3693	1.62218
$590$	0	0
$591$	−19.9309	−0.819846
$592$	− 14.6307i	− 0.601317i
$593$	− 44.2462i	− 1.81697i	−0.417913	−	0.908487i	$-0.637238\pi$
$593$	− 44.2462i	− 1.81697i	0.417913	−	0.908487i	$-0.362762\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	−1.86174	−0.0762598
$597$	− 16.0000i	− 0.654836i
$598$	46.7386i	1.91128i
$599$	41.6155	1.70036	0.850182	−	0.526489i	$-0.176492\pi$
$599$	41.6155	1.70036	0.850182	+	0.526489i	$0.176492\pi$
$600$	0	0
$601$	34.9848	1.42706	0.713531	−	0.700624i	$-0.247095\pi$
$601$	34.9848	1.42706	0.713531	+	0.700624i	$0.247095\pi$
$602$	0	0
$603$	− 4.00000i	− 0.162893i
$604$	−3.50758	−0.142721
$605$	0	0
$606$	−29.8617	−1.21305
$607$	15.3693i	0.623821i	0.950111	+	0.311911i	$0.100969\pi$
$607$	15.3693i	0.623821i	−0.950111	+	0.311911i	$0.899031\pi$
$608$	18.7386i	0.759952i
$609$	0	0
$610$	0	0
$611$	−13.1231	−0.530904
$612$	0.438447i	0.0177232i
$613$	− 2.31534i	− 0.0935158i	−0.998906	−	0.0467579i	$-0.985111\pi$
$613$	− 2.31534i	− 0.0935158i	0.998906	−	0.0467579i	$-0.0148889\pi$
$614$	0.768944	0.0310320
$615$	0	0
$616$	0	0
$617$	− 27.7538i	− 1.11733i	−0.829395	−	0.558663i	$-0.811315\pi$
$617$	− 27.7538i	− 1.11733i	0.829395	−	0.558663i	$-0.188685\pi$
$618$	6.73863i	0.271068i
$619$	19.3693	0.778519	0.389259	−	0.921128i	$-0.372731\pi$
$619$	19.3693	0.778519	0.389259	+	0.921128i	$0.372731\pi$
$620$	0	0
$621$	6.56155	0.263306
$622$	0	0
$623$	0	0
$624$	−21.3693	−0.855457
$625$	0	0
$626$	−11.8920	−0.475302
$627$	19.6847i	0.786130i
$628$	2.49242i	0.0994585i
$629$	−3.12311	−0.124526
$630$	0	0
$631$	11.6847	0.465159	0.232579	−	0.972577i	$-0.425283\pi$
$631$	11.6847	0.465159	0.232579	+	0.972577i	$0.425283\pi$
$632$	− 37.4773i	− 1.49077i
$633$	− 11.3693i	− 0.451890i
$634$	28.1080	1.11631
$635$	0	0
$636$	1.86174	0.0738228
$637$	− 31.9309i	− 1.26515i
$638$	32.9848i	1.30588i
$639$	−10.2462	−0.405334
$640$	0	0
$641$	−0.0691303	−0.00273048	−0.00136524	−	0.999999i	$-0.500435\pi$
$641$	−0.0691303	−0.00273048	−0.00136524	+	0.999999i	$0.500435\pi$
$642$	− 12.0000i	− 0.473602i
$643$	30.2462i	1.19279i	0.802690	+	0.596397i	$0.203402\pi$
$643$	30.2462i	1.19279i	−0.802690	+	0.596397i	$0.796598\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	15.3693i	0.604230i	0.953271	+	0.302115i	$0.0976927\pi$
$647$	15.3693i	0.604230i	−0.953271	+	0.302115i	$0.902307\pi$
$648$	2.43845i	0.0957913i
$649$	−2.87689	−0.112928
$650$	0	0
$651$	0	0
$652$	− 3.01515i	− 0.118083i
$653$	4.06913i	0.159237i	0.996825	+	0.0796187i	$0.0253703\pi$
$653$	4.06913i	0.159237i	−0.996825	+	0.0796187i	$0.974630\pi$
$654$	−23.6155	−0.923440
$655$	0	0
$656$	−2.63068	−0.102711
$657$	4.24621i	0.165660i
$658$	0	0
$659$	−47.8617	−1.86443	−0.932214	−	0.361907i	$-0.882126\pi$
$659$	−47.8617	−1.86443	−0.932214	+	0.361907i	$0.882126\pi$
$660$	0	0
$661$	25.6847	0.999017	0.499509	−	0.866309i	$-0.333514\pi$
$661$	25.6847	0.999017	0.499509	+	0.866309i	$0.333514\pi$
$662$	− 9.47727i	− 0.368344i
$663$	4.56155i	0.177156i
$664$	−22.2462	−0.863320
$665$	0	0
$666$	4.87689	0.188976
$667$	− 54.1080i	− 2.09507i
$668$	0.354162i	0.0137029i
$669$	13.9309	0.538599
$670$	0	0
$671$	−2.24621	−0.0867140
$672$	0	0
$673$	− 48.7386i	− 1.87874i	−0.342910	−	0.939368i	$-0.611413\pi$
$673$	− 48.7386i	− 1.87874i	0.342910	−	0.939368i	$-0.388587\pi$
$674$	−51.1231	−1.96919
$675$	0	0
$676$	3.42329	0.131665
$677$	− 13.6847i	− 0.525944i	−0.964803	−	0.262972i	$-0.915297\pi$
$677$	− 13.6847i	− 0.525944i	0.964803	−	0.262972i	$-0.0847027\pi$
$678$	− 7.12311i	− 0.273561i
$679$	0	0
$680$	0	0
$681$	−23.0540	−0.883430
$682$	20.4924i	0.784695i
$683$	5.43845i	0.208096i	0.994572	+	0.104048i	$0.0331796\pi$
$683$	5.43845i	0.208096i	−0.994572	+	0.104048i	$0.966820\pi$
$684$	−3.36932	−0.128829
$685$	0	0
$686$	0	0
$687$	− 6.00000i	− 0.228914i
$688$	− 36.0000i	− 1.37249i
$689$	19.3693	0.737912
$690$	0	0
$691$	36.9848	1.40697	0.703485	−	0.710710i	$-0.251626\pi$
$691$	36.9848	1.40697	0.703485	+	0.710710i	$0.251626\pi$
$692$	− 8.24621i	− 0.313474i
$693$	0	0
$694$	−38.2462	−1.45181
$695$	0	0
$696$	20.1080	0.762190
$697$	0.561553i	0.0212703i
$698$	− 11.6155i	− 0.439654i
$699$	0.561553	0.0212399
$700$	0	0
$701$	−9.36932	−0.353874	−0.176937	−	0.984222i	$-0.556619\pi$
$701$	−9.36932	−0.353874	−0.176937	+	0.984222i	$0.556619\pi$
$702$	− 7.12311i	− 0.268844i
$703$	− 24.0000i	− 0.905177i
$704$	14.2462	0.536924
$705$	0	0
$706$	35.1231	1.32188
$707$	0	0
$708$	− 0.492423i	− 0.0185064i
$709$	−4.73863	−0.177963	−0.0889816	−	0.996033i	$-0.528361\pi$
$709$	−4.73863	−0.177963	−0.0889816	+	0.996033i	$0.528361\pi$
$710$	0	0
$711$	15.3693	0.576394
$712$	− 17.3693i	− 0.650943i
$713$	− 33.6155i	− 1.25891i
$714$	0	0
$715$	0	0
$716$	−4.00000	−0.149487
$717$	− 10.2462i	− 0.382652i
$718$	3.50758i	0.130902i
$719$	−8.80776	−0.328474	−0.164237	−	0.986421i	$-0.552516\pi$
$719$	−8.80776	−0.328474	−0.164237	+	0.986421i	$0.552516\pi$
$720$	0	0
$721$	0	0
$722$	62.5464i	2.32774i
$723$	− 21.3693i	− 0.794733i
$724$	−2.63068	−0.0977686
$725$	0	0
$726$	6.93087	0.257229
$727$	− 8.00000i	− 0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$	− 8.00000i	− 0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$	0	0
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−7.68466	−0.284227
$732$	− 0.384472i	− 0.0142105i
$733$	28.2462i	1.04330i	0.853160	+	0.521649i	$0.174683\pi$
$733$	28.2462i	1.04330i	−0.853160	+	0.521649i	$0.825317\pi$
$734$	28.4924	1.05167
$735$	0	0
$736$	16.0000	0.589768
$737$	− 10.2462i	− 0.377424i
$738$	− 0.876894i	− 0.0322789i
$739$	8.31534	0.305885	0.152942	−	0.988235i	$-0.451125\pi$
$739$	8.31534	0.305885	0.152942	+	0.988235i	$0.451125\pi$
$740$	0	0
$741$	−35.0540	−1.28774
$742$	0	0
$743$	4.49242i	0.164811i	0.996599	+	0.0824055i	$0.0262603\pi$
$743$	4.49242i	0.164811i	−0.996599	+	0.0824055i	$0.973740\pi$
$744$	12.4924	0.457994
$745$	0	0
$746$	25.3693	0.928837
$747$	− 9.12311i	− 0.333797i
$748$	1.12311i	0.0410648i
$749$	0	0
$750$	0	0
$751$	−0.630683	−0.0230140	−0.0115070	−	0.999934i	$-0.503663\pi$
$751$	−0.630683	−0.0230140	−0.0115070	+	0.999934i	$0.503663\pi$
$752$	13.4773i	0.491465i
$753$	− 24.4924i	− 0.892553i
$754$	−58.7386	−2.13913
$755$	0	0
$756$	0	0
$757$	− 21.0540i	− 0.765220i	−0.923910	−	0.382610i	$-0.875025\pi$
$757$	− 21.0540i	− 0.765220i	0.923910	−	0.382610i	$-0.124975\pi$
$758$	18.7386i	0.680618i
$759$	16.8078	0.610083
$760$	0	0
$761$	−32.2462	−1.16892	−0.584462	−	0.811421i	$-0.698694\pi$
$761$	−32.2462	−1.16892	−0.584462	+	0.811421i	$0.698694\pi$
$762$	1.26137i	0.0456945i
$763$	0	0
$764$	5.75379	0.208165
$765$	0	0
$766$	−16.0000	−0.578103
$767$	− 5.12311i	− 0.184985i
$768$	10.0540i	0.362792i
$769$	29.5464	1.06547	0.532735	−	0.846282i	$-0.321164\pi$
$769$	29.5464	1.06547	0.532735	+	0.846282i	$0.321164\pi$
$770$	0	0
$771$	−9.36932	−0.337428
$772$	− 10.6307i	− 0.382607i
$773$	33.3693i	1.20021i	0.799921	+	0.600105i	$0.204875\pi$
$773$	33.3693i	1.20021i	−0.799921	+	0.600105i	$0.795125\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	27.1231	0.973663
$777$	0	0
$778$	34.1383i	1.22392i
$779$	−4.31534	−0.154613
$780$	0	0
$781$	−26.2462	−0.939163
$782$	− 10.2462i	− 0.366404i
$783$	8.24621i	0.294696i
$784$	−32.7926	−1.17116
$785$	0	0
$786$	−28.9848	−1.03386
$787$	6.24621i	0.222653i	0.993784	+	0.111327i	$0.0355100\pi$
$787$	6.24621i	0.222653i	−0.993784	+	0.111327i	$0.964490\pi$
$788$	− 8.73863i	− 0.311301i
$789$	12.4924	0.444742
$790$	0	0
$791$	0	0
$792$	6.24621i	0.221949i
$793$	− 4.00000i	− 0.142044i
$794$	−8.38447	−0.297554
$795$	0	0
$796$	7.01515	0.248646
$797$	31.6155i	1.11988i	0.828533	+	0.559940i	$0.189176\pi$
$797$	31.6155i	1.11988i	−0.828533	+	0.559940i	$0.810824\pi$
$798$	0	0
$799$	2.87689	0.101777
$800$	0	0
$801$	7.12311	0.251683
$802$	− 9.64584i	− 0.340606i
$803$	10.8769i	0.383837i
$804$	1.75379	0.0618514
$805$	0	0
$806$	−36.4924	−1.28539
$807$	− 20.5616i	− 0.723801i
$808$	46.6307i	1.64046i
$809$	−53.0540	−1.86528	−0.932639	−	0.360810i	$-0.882500\pi$
$809$	−53.0540	−1.86528	−0.932639	+	0.360810i	$0.882500\pi$
$810$	0	0
$811$	−20.6307	−0.724441	−0.362221	−	0.932092i	$-0.617981\pi$
$811$	−20.6307	−0.724441	−0.362221	+	0.932092i	$0.617981\pi$
$812$	0	0
$813$	− 0.807764i	− 0.0283295i
$814$	12.4924	0.437859
$815$	0	0
$816$	4.68466	0.163996
$817$	− 59.0540i	− 2.06604i
$818$	3.61553i	0.126414i
$819$	0	0
$820$	0	0
$821$	−16.5616	−0.578002	−0.289001	−	0.957329i	$-0.593323\pi$
$821$	−16.5616	−0.578002	−0.289001	+	0.957329i	$0.593323\pi$
$822$	25.3693i	0.884857i
$823$	− 36.4924i	− 1.27205i	−0.771670	−	0.636023i	$-0.780578\pi$
$823$	− 36.4924i	− 1.27205i	0.771670	−	0.636023i	$-0.219422\pi$
$824$	10.5227	0.366577
$825$	0	0
$826$	0	0
$827$	− 14.4233i	− 0.501547i	−0.968046	−	0.250774i	$-0.919315\pi$
$827$	− 14.4233i	− 0.501547i	0.968046	−	0.250774i	$-0.0806849\pi$
$828$	2.87689i	0.0999790i
$829$	−50.4924	−1.75367	−0.876837	−	0.480787i	$-0.840351\pi$
$829$	−50.4924	−1.75367	−0.876837	+	0.480787i	$0.840351\pi$
$830$	0	0
$831$	−6.00000	−0.208138
$832$	25.3693i	0.879523i
$833$	7.00000i	0.242536i
$834$	−14.2462	−0.493306
$835$	0	0
$836$	−8.63068	−0.298498
$837$	5.12311i	0.177080i
$838$	− 50.7386i	− 1.75274i
$839$	−11.0540	−0.381626	−0.190813	−	0.981626i	$-0.561112\pi$
$839$	−11.0540	−0.381626	−0.190813	+	0.981626i	$0.561112\pi$
$840$	0	0
$841$	39.0000	1.34483
$842$	44.6004i	1.53703i
$843$	− 19.1231i	− 0.658635i
$844$	4.98485	0.171585
$845$	0	0
$846$	−4.49242	−0.154453
$847$	0	0
$848$	− 19.8920i	− 0.683096i
$849$	−3.36932	−0.115635
$850$	0	0
$851$	−20.4924	−0.702471
$852$	− 4.49242i	− 0.153908i
$853$	− 20.7386i	− 0.710077i	−0.934852	−	0.355039i	$-0.884468\pi$
$853$	− 20.7386i	− 0.710077i	0.934852	−	0.355039i	$-0.115532\pi$
$854$	0	0
$855$	0	0
$856$	−18.7386	−0.640473
$857$	− 6.00000i	− 0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$	− 6.00000i	− 0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$	− 18.2462i	− 0.622915i
$859$	−12.0000	−0.409435	−0.204717	−	0.978821i	$-0.565628\pi$
$859$	−12.0000	−0.409435	−0.204717	+	0.978821i	$0.565628\pi$
$860$	0	0
$861$	0	0
$862$	− 37.4773i	− 1.27648i
$863$	26.2462i	0.893431i	0.894676	+	0.446716i	$0.147406\pi$
$863$	26.2462i	0.893431i	−0.894676	+	0.446716i	$0.852594\pi$
$864$	−2.43845	−0.0829577
$865$	0	0
$866$	22.3542	0.759625
$867$	− 1.00000i	− 0.0339618i
$868$	0	0
$869$	39.3693	1.33551
$870$	0	0
$871$	18.2462	0.618249
$872$	36.8769i	1.24881i
$873$	11.1231i	0.376460i
$874$	78.7386	2.66337
$875$	0	0
$876$	−1.86174	−0.0629023
$877$	− 34.0000i	− 1.14810i	−0.818821	−	0.574049i	$-0.805372\pi$
$877$	− 34.0000i	− 1.14810i	0.818821	−	0.574049i	$-0.194628\pi$
$878$	8.98485i	0.303224i
$879$	−7.12311	−0.240256
$880$	0	0
$881$	23.7538	0.800285	0.400143	−	0.916453i	$-0.368961\pi$
$881$	23.7538	0.800285	0.400143	+	0.916453i	$0.368961\pi$
$882$	− 10.9309i	− 0.368062i
$883$	− 38.4233i	− 1.29305i	−0.762894	−	0.646523i	$-0.776222\pi$
$883$	− 38.4233i	− 1.29305i	0.762894	−	0.646523i	$-0.223778\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	−35.7235	−1.20015
$887$	22.5616i	0.757543i	0.925490	+	0.378771i	$0.123653\pi$
$887$	22.5616i	0.757543i	−0.925490	+	0.378771i	$0.876347\pi$
$888$	− 7.61553i	− 0.255560i
$889$	0	0
$890$	0	0
$891$	−2.56155	−0.0858152
$892$	6.10795i	0.204509i
$893$	22.1080i	0.739814i
$894$	−6.63068	−0.221763
$895$	0	0
$896$	0	0
$897$	29.9309i	0.999363i
$898$	19.8920i	0.663806i
$899$	42.2462	1.40899
$900$	0	0
$901$	−4.24621	−0.141462
$902$	− 2.24621i	− 0.0747907i
$903$	0	0
$904$	−11.1231	−0.369949
$905$	0	0
$906$	−12.4924	−0.415033
$907$	47.8617i	1.58922i	0.607118	+	0.794611i	$0.292325\pi$
$907$	47.8617i	1.58922i	−0.607118	+	0.794611i	$0.707675\pi$
$908$	− 10.1080i	− 0.335444i
$909$	−19.1231	−0.634273
$910$	0	0
$911$	−29.3002	−0.970758	−0.485379	−	0.874304i	$-0.661318\pi$
$911$	−29.3002	−0.970758	−0.485379	+	0.874304i	$0.661318\pi$
$912$	36.0000i	1.19208i
$913$	− 23.3693i	− 0.773412i
$914$	10.6307	0.351632
$915$	0	0
$916$	2.63068	0.0869202
$917$	0	0
$918$	1.56155i	0.0515389i
$919$	4.31534	0.142350	0.0711750	−	0.997464i	$-0.477325\pi$
$919$	4.31534	0.142350	0.0711750	+	0.997464i	$0.477325\pi$
$920$	0	0
$921$	0.492423	0.0162259
$922$	12.8769i	0.424078i
$923$	− 46.7386i	− 1.53842i
$924$	0	0
$925$	0	0
$926$	39.0152	1.28212
$927$	4.31534i	0.141734i
$928$	20.1080i	0.660076i
$929$	−31.9309	−1.04762	−0.523809	−	0.851836i	$-0.675489\pi$
$929$	−31.9309	−1.04762	−0.523809	+	0.851836i	$0.675489\pi$
$930$	0	0
$931$	−53.7926	−1.76298
$932$	0.246211i	0.00806492i
$933$	0	0
$934$	5.26137	0.172157
$935$	0	0
$936$	−11.1231	−0.363570
$937$	− 22.0000i	− 0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$	− 22.0000i	− 0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$	0	0
$939$	−7.61553	−0.248523
$940$	0	0
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	8.87689i	0.289225i
$943$	3.68466i	0.119989i
$944$	−5.26137	−0.171243
$945$	0	0
$946$	30.7386	0.999399
$947$	12.0000i	0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$	12.0000i	0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$	6.73863i	0.218861i
$949$	−19.3693	−0.628755
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	54.3542i	1.76070i	0.474321	+	0.880352i	$0.342694\pi$
$953$	54.3542i	1.76070i	−0.474321	+	0.880352i	$0.657306\pi$
$954$	6.63068	0.214676
$955$	0	0
$956$	4.49242	0.145295
$957$	21.1231i	0.682813i
$958$	45.7538i	1.47824i
$959$	0	0
$960$	0	0
$961$	−4.75379	−0.153348
$962$	22.2462i	0.717247i
$963$	− 7.68466i	− 0.247635i
$964$	9.36932	0.301765
$965$	0	0
$966$	0	0
$967$	46.5616i	1.49732i	0.662955	+	0.748659i	$0.269302\pi$
$967$	46.5616i	1.49732i	−0.662955	+	0.748659i	$0.730698\pi$
$968$	− 10.8229i	− 0.347862i
$969$	7.68466	0.246867
$970$	0	0
$971$	−2.38447	−0.0765213	−0.0382607	−	0.999268i	$-0.512182\pi$
$971$	−2.38447	−0.0765213	−0.0382607	+	0.999268i	$0.512182\pi$
$972$	− 0.438447i	− 0.0140632i
$973$	0	0
$974$	11.5076	0.368727
$975$	0	0
$976$	−4.10795	−0.131492
$977$	− 8.24621i	− 0.263820i	−0.991262	−	0.131910i	$-0.957889\pi$
$977$	− 8.24621i	− 0.263820i	0.991262	−	0.131910i	$-0.0421109\pi$
$978$	− 10.7386i	− 0.343384i
$979$	18.2462	0.583151
$980$	0	0
$981$	−15.1231	−0.482844
$982$	5.26137i	0.167897i
$983$	− 2.06913i	− 0.0659950i	−0.999455	−	0.0329975i	$-0.989495\pi$
$983$	− 2.06913i	− 0.0659950i	0.999455	−	0.0329975i	$-0.0105053\pi$
$984$	−1.36932	−0.0436522
$985$	0	0
$986$	12.8769	0.410084
$987$	0	0
$988$	− 15.3693i	− 0.488963i
$989$	−50.4233	−1.60337
$990$	0	0
$991$	−6.73863	−0.214060	−0.107030	−	0.994256i	$-0.534134\pi$
$991$	−6.73863	−0.214060	−0.107030	+	0.994256i	$0.534134\pi$
$992$	12.4924i	0.396635i
$993$	− 6.06913i	− 0.192598i
$994$	0	0
$995$	0	0
$996$	4.00000	0.126745
$997$	− 10.0000i	− 0.316703i	−0.987383	−	0.158352i	$-0.949382\pi$
$997$	− 10.0000i	− 0.316703i	0.987383	−	0.158352i	$-0.0506179\pi$
$998$	17.7538i	0.561986i
$999$	3.12311	0.0988107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1275.2.b.d.1174.3		4
5.2	odd	4		1275.2.a.n.1.1		2
5.3	odd	4		51.2.a.b.1.2	✓	2
5.4	even	2	inner	1275.2.b.d.1174.2		4
15.2	even	4		3825.2.a.s.1.2		2
15.8	even	4		153.2.a.e.1.1		2
20.3	even	4		816.2.a.m.1.1		2
35.13	even	4		2499.2.a.o.1.2		2
40.3	even	4		3264.2.a.bg.1.2		2
40.13	odd	4		3264.2.a.bl.1.2		2
55.43	even	4		6171.2.a.p.1.1		2
60.23	odd	4		2448.2.a.v.1.2		2
65.38	odd	4		8619.2.a.q.1.1		2
85.3	even	16		867.2.h.j.757.3		16
85.8	odd	8		867.2.e.f.829.2		8
85.13	odd	4		867.2.d.c.577.1		4
85.23	even	16		867.2.h.j.733.3		16
85.28	even	16		867.2.h.j.733.4		16
85.33	odd	4		867.2.a.f.1.2		2
85.38	odd	4		867.2.d.c.577.2		4
85.43	odd	8		867.2.e.f.829.1		8
85.48	even	16		867.2.h.j.757.4		16
85.53	odd	8		867.2.e.f.616.3		8
85.58	even	16		867.2.h.j.712.2		16
85.63	even	16		867.2.h.j.688.1		16
85.73	even	16		867.2.h.j.688.2		16
85.78	even	16		867.2.h.j.712.1		16
85.83	odd	8		867.2.e.f.616.4		8
105.83	odd	4		7497.2.a.v.1.1		2
120.53	even	4		9792.2.a.cy.1.1		2
120.83	odd	4		9792.2.a.cz.1.1		2
255.203	even	4		2601.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.2	✓	2	5.3	odd	4
153.2.a.e.1.1		2	15.8	even	4
816.2.a.m.1.1		2	20.3	even	4
867.2.a.f.1.2		2	85.33	odd	4
867.2.d.c.577.1		4	85.13	odd	4
867.2.d.c.577.2		4	85.38	odd	4
867.2.e.f.616.3		8	85.53	odd	8
867.2.e.f.616.4		8	85.83	odd	8
867.2.e.f.829.1		8	85.43	odd	8
867.2.e.f.829.2		8	85.8	odd	8
867.2.h.j.688.1		16	85.63	even	16
867.2.h.j.688.2		16	85.73	even	16
867.2.h.j.712.1		16	85.78	even	16
867.2.h.j.712.2		16	85.58	even	16
867.2.h.j.733.3		16	85.23	even	16
867.2.h.j.733.4		16	85.28	even	16
867.2.h.j.757.3		16	85.3	even	16
867.2.h.j.757.4		16	85.48	even	16
1275.2.a.n.1.1		2	5.2	odd	4
1275.2.b.d.1174.2		4	5.4	even	2	inner
1275.2.b.d.1174.3		4	1.1	even	1	trivial
2448.2.a.v.1.2		2	60.23	odd	4
2499.2.a.o.1.2		2	35.13	even	4
2601.2.a.t.1.1		2	255.203	even	4
3264.2.a.bg.1.2		2	40.3	even	4
3264.2.a.bl.1.2		2	40.13	odd	4
3825.2.a.s.1.2		2	15.2	even	4
6171.2.a.p.1.1		2	55.43	even	4
7497.2.a.v.1.1		2	105.83	odd	4
8619.2.a.q.1.1		2	65.38	odd	4
9792.2.a.cy.1.1		2	120.53	even	4
9792.2.a.cz.1.1		2	120.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.56155i q^{2} +1.00000i q^{3} -0.438447 q^{4} -1.56155 q^{6} +2.43845i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.56155i q^{2} +1.00000i q^{3} -0.438447 q^{4} -1.56155 q^{6} +2.43845i q^{8} -1.00000 q^{9} -2.56155 q^{11} -0.438447i q^{12} -4.56155i q^{13} -4.68466 q^{16} +1.00000i q^{17} -1.56155i q^{18} -7.68466 q^{19} -4.00000i q^{22} +6.56155i q^{23} -2.43845 q^{24} +7.12311 q^{26} -1.00000i q^{27} -8.24621 q^{29} -5.12311 q^{31} -2.43845i q^{32} -2.56155i q^{33} -1.56155 q^{34} +0.438447 q^{36} +3.12311i q^{37} -12.0000i q^{38} +4.56155 q^{39} +0.561553 q^{41} +7.68466i q^{43} +1.12311 q^{44} -10.2462 q^{46} -2.87689i q^{47} -4.68466i q^{48} +7.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} +4.24621i q^{53} +1.56155 q^{54} -7.68466i q^{57} -12.8769i q^{58} +1.12311 q^{59} +0.876894 q^{61} -8.00000i q^{62} -5.56155 q^{64} +4.00000 q^{66} +4.00000i q^{67} -0.438447i q^{68} -6.56155 q^{69} +10.2462 q^{71} -2.43845i q^{72} -4.24621i q^{73} -4.87689 q^{74} +3.36932 q^{76} +7.12311i q^{78} -15.3693 q^{79} +1.00000 q^{81} +0.876894i q^{82} +9.12311i q^{83} -12.0000 q^{86} -8.24621i q^{87} -6.24621i q^{88} -7.12311 q^{89} -2.87689i q^{92} -5.12311i q^{93} +4.49242 q^{94} +2.43845 q^{96} -11.1231i q^{97} +10.9309i q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 4 * q - 10 * q^4 + 2 * q^6 - 4 * q^9	\( 4 q - 10 q^{4} + 2 q^{6} - 4 q^{9} - 2 q^{11} + 6 q^{16} - 6 q^{19} - 18 q^{24} + 12 q^{26} - 4 q^{31} + 2 q^{34} + 10 q^{36} + 10 q^{39} - 6 q^{41} - 12 q^{44} - 8 q^{46} + 28 q^{49} - 4 q^{51} - 2 q^{54} - 12 q^{59} + 20 q^{61} - 14 q^{64} + 16 q^{66} - 18 q^{69} + 8 q^{71} - 36 q^{74} - 36 q^{76} - 12 q^{79} + 4 q^{81} - 48 q^{86} - 12 q^{89} - 48 q^{94} + 18 q^{96} + 2 q^{99}+O(q^{100}) \) 4 * q - 10 * q^4 + 2 * q^6 - 4 * q^9 - 2 * q^11 + 6 * q^16 - 6 * q^19 - 18 * q^24 + 12 * q^26 - 4 * q^31 + 2 * q^34 + 10 * q^36 + 10 * q^39 - 6 * q^41 - 12 * q^44 - 8 * q^46 + 28 * q^49 - 4 * q^51 - 2 * q^54 - 12 * q^59 + 20 * q^61 - 14 * q^64 + 16 * q^66 - 18 * q^69 + 8 * q^71 - 36 * q^74 - 36 * q^76 - 12 * q^79 + 4 * q^81 - 48 * q^86 - 12 * q^89 - 48 * q^94 + 18 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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