LMFDB - Embedded newform 1275.2.b.d.1174.1

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			1174.1
Root			$-2.56155i$ of defining polynomial
Character	$\chi$	$=$	1275.1174
Dual form			1275.2.b.d.1174.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.56155i q^{2} +1.00000i q^{3} -4.56155 q^{4} +2.56155 q^{6} +6.56155i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.56155i q^{2} +1.00000i q^{3} -4.56155 q^{4} +2.56155 q^{6} +6.56155i q^{8} -1.00000 q^{9} +1.56155 q^{11} -4.56155i q^{12} -0.438447i q^{13} +7.68466 q^{16} +1.00000i q^{17} +2.56155i q^{18} +4.68466 q^{19} -4.00000i q^{22} +2.43845i q^{23} -6.56155 q^{24} -1.12311 q^{26} -1.00000i q^{27} +8.24621 q^{29} +3.12311 q^{31} -6.56155i q^{32} +1.56155i q^{33} +2.56155 q^{34} +4.56155 q^{36} -5.12311i q^{37} -12.0000i q^{38} +0.438447 q^{39} -3.56155 q^{41} -4.68466i q^{43} -7.12311 q^{44} +6.24621 q^{46} -11.1231i q^{47} +7.68466i q^{48} +7.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -12.2462i q^{53} -2.56155 q^{54} +4.68466i q^{57} -21.1231i q^{58} -7.12311 q^{59} +9.12311 q^{61} -8.00000i q^{62} -1.43845 q^{64} +4.00000 q^{66} +4.00000i q^{67} -4.56155i q^{68} -2.43845 q^{69} -6.24621 q^{71} -6.56155i q^{72} +12.2462i q^{73} -13.1231 q^{74} -21.3693 q^{76} -1.12311i q^{78} +9.36932 q^{79} +1.00000 q^{81} +9.12311i q^{82} +0.876894i q^{83} -12.0000 q^{86} +8.24621i q^{87} +10.2462i q^{88} +1.12311 q^{89} -11.1231i q^{92} +3.12311i q^{93} -28.4924 q^{94} +6.56155 q^{96} -2.87689i q^{97} -17.9309i q^{98} -1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 2.56155i	− 1.81129i	−0.424035	−	0.905646i	$-0.639387\pi$
$2$	− 2.56155i	− 1.81129i	0.424035	−	0.905646i	$-0.360613\pi$
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−4.56155	−2.28078
$5$	0	0
$5$	0	0
$6$	2.56155	1.04575
$7$	0	0	1.00000			$0$
$7$	0	0	−1.00000			$\pi$
$8$	6.56155i	2.31986i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	1.56155	0.470826	0.235413	−	0.971895i	$-0.424356\pi$
$11$	1.56155	0.470826	0.235413	+	0.971895i	$0.424356\pi$
$12$	− 4.56155i	− 1.31681i
$13$	− 0.438447i	− 0.121603i	−0.998150	−	0.0608017i	$-0.980634\pi$
$13$	− 0.438447i	− 0.121603i	0.998150	−	0.0608017i	$-0.0193657\pi$
$14$	0	0
$15$	0	0
$16$	7.68466	1.92116
$17$	1.00000i	0.242536i
$17$	1.00000i	0.242536i
$18$	2.56155i	0.603764i
$19$	4.68466	1.07473	0.537367	−	0.843348i	$-0.319419\pi$
$19$	4.68466	1.07473	0.537367	+	0.843348i	$0.319419\pi$
$20$	0	0
$21$	0	0
$22$	− 4.00000i	− 0.852803i
$23$	2.43845i	0.508451i	0.967145	+	0.254226i	$0.0818206\pi$
$23$	2.43845i	0.508451i	−0.967145	+	0.254226i	$0.918179\pi$
$24$	−6.56155	−1.33937
$25$	0	0
$26$	−1.12311	−0.220259
$27$	− 1.00000i	− 0.192450i
$28$	0	0
$29$	8.24621	1.53128	0.765641	−	0.643268i	$-0.222422\pi$
$29$	8.24621	1.53128	0.765641	+	0.643268i	$0.222422\pi$
$30$	0	0
$31$	3.12311	0.560926	0.280463	−	0.959865i	$-0.409512\pi$
$31$	3.12311	0.560926	0.280463	+	0.959865i	$0.409512\pi$
$32$	− 6.56155i	− 1.15993i
$33$	1.56155i	0.271831i
$34$	2.56155	0.439303
$35$	0	0
$36$	4.56155	0.760259
$37$	− 5.12311i	− 0.842233i	−0.907006	−	0.421117i	$-0.861638\pi$
$37$	− 5.12311i	− 0.842233i	0.907006	−	0.421117i	$-0.138362\pi$
$38$	− 12.0000i	− 1.94666i
$39$	0.438447	0.0702077
$40$	0	0
$41$	−3.56155	−0.556221	−0.278111	−	0.960549i	$-0.589708\pi$
$41$	−3.56155	−0.556221	−0.278111	+	0.960549i	$0.589708\pi$
$42$	0	0
$43$	− 4.68466i	− 0.714404i	−0.934027	−	0.357202i	$-0.883731\pi$
$43$	− 4.68466i	− 0.714404i	0.934027	−	0.357202i	$-0.116269\pi$
$44$	−7.12311	−1.07385
$45$	0	0
$46$	6.24621	0.920954
$47$	− 11.1231i	− 1.62247i	−0.584719	−	0.811236i	$-0.698795\pi$
$47$	− 11.1231i	− 1.62247i	0.584719	−	0.811236i	$-0.301205\pi$
$48$	7.68466i	1.10918i
$49$	7.00000	1.00000
$50$	0	0
$51$	−1.00000	−0.140028
$52$	2.00000i	0.277350i
$53$	− 12.2462i	− 1.68215i	−0.540921	−	0.841073i	$-0.681924\pi$
$53$	− 12.2462i	− 1.68215i	0.540921	−	0.841073i	$-0.318076\pi$
$54$	−2.56155	−0.348583
$55$	0	0
$56$	0	0
$57$	4.68466i	0.620498i
$58$	− 21.1231i	− 2.77360i
$59$	−7.12311	−0.927349	−0.463675	−	0.886006i	$-0.653469\pi$
$59$	−7.12311	−0.927349	−0.463675	+	0.886006i	$0.653469\pi$
$60$	0	0
$61$	9.12311	1.16809	0.584047	−	0.811720i	$-0.301468\pi$
$61$	9.12311	1.16809	0.584047	+	0.811720i	$0.301468\pi$
$62$	− 8.00000i	− 1.01600i
$63$	0	0
$64$	−1.43845	−0.179806
$65$	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	$0.921429\pi$
$68$	− 4.56155i	− 0.553170i
$69$	−2.43845	−0.293555
$70$	0	0
$71$	−6.24621	−0.741289	−0.370644	−	0.928775i	$-0.620863\pi$
$71$	−6.24621	−0.741289	−0.370644	+	0.928775i	$0.620863\pi$
$72$	− 6.56155i	− 0.773286i
$73$	12.2462i	1.43331i	0.697428	+	0.716655i	$0.254328\pi$
$73$	12.2462i	1.43331i	−0.697428	+	0.716655i	$0.745672\pi$
$74$	−13.1231	−1.52553
$75$	0	0
$76$	−21.3693	−2.45123
$77$	0	0
$78$	− 1.12311i	− 0.127167i
$79$	9.36932	1.05413	0.527065	−	0.849825i	$-0.323292\pi$
$79$	9.36932	1.05413	0.527065	+	0.849825i	$0.323292\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	9.12311i	1.00748i
$83$	0.876894i	0.0962517i	0.998841	+	0.0481258i	$0.0153248\pi$
$83$	0.876894i	0.0962517i	−0.998841	+	0.0481258i	$0.984675\pi$
$84$	0	0
$85$	0	0
$86$	−12.0000	−1.29399
$87$	8.24621i	0.884087i
$88$	10.2462i	1.09225i
$89$	1.12311	0.119049	0.0595245	−	0.998227i	$-0.481042\pi$
$89$	1.12311	0.119049	0.0595245	+	0.998227i	$0.481042\pi$
$90$	0	0
$91$	0	0
$92$	− 11.1231i	− 1.15966i
$93$	3.12311i	0.323851i
$94$	−28.4924	−2.93877
$95$	0	0
$96$	6.56155	0.669686
$97$	− 2.87689i	− 0.292104i	−0.989277	−	0.146052i	$-0.953343\pi$
$97$	− 2.87689i	− 0.292104i	0.989277	−	0.146052i	$-0.0466567\pi$
$98$	− 17.9309i	− 1.81129i
$99$	−1.56155	−0.156942
$100$	0	0
$101$	10.8769	1.08229	0.541146	−	0.840929i	$-0.317991\pi$
$101$	10.8769	1.08229	0.541146	+	0.840929i	$0.317991\pi$
$102$	2.56155i	0.253632i
$103$	− 16.6847i	− 1.64399i	−0.569496	−	0.821994i	$-0.692862\pi$
$103$	− 16.6847i	− 1.64399i	0.569496	−	0.821994i	$-0.307138\pi$
$104$	2.87689	0.282103
$105$	0	0
$106$	−31.3693	−3.04686
$107$	− 4.68466i	− 0.452883i	−0.974025	−	0.226442i	$-0.927291\pi$
$107$	− 4.68466i	− 0.452883i	0.974025	−	0.226442i	$-0.0727092\pi$
$108$	4.56155i	0.438936i
$109$	6.87689	0.658687	0.329344	−	0.944210i	$-0.393173\pi$
$109$	6.87689	0.658687	0.329344	+	0.944210i	$0.393173\pi$
$110$	0	0
$111$	5.12311	0.486264
$112$	0	0
$113$	0.438447i	0.0412456i	0.999787	+	0.0206228i	$0.00656491\pi$
$113$	0.438447i	0.0412456i	−0.999787	+	0.0206228i	$0.993435\pi$
$114$	12.0000	1.12390
$115$	0	0
$116$	−37.6155	−3.49251
$117$	0.438447i	0.0405345i
$118$	18.2462i	1.67970i
$119$	0	0
$120$	0	0
$121$	−8.56155	−0.778323
$122$	− 23.3693i	− 2.11576i
$123$	− 3.56155i	− 0.321134i
$124$	−14.2462	−1.27935
$125$	0	0
$126$	0	0
$127$	19.8078i	1.75765i	0.477140	+	0.878827i	$0.341674\pi$
$127$	19.8078i	1.75765i	−0.477140	+	0.878827i	$0.658326\pi$
$128$	− 9.43845i	− 0.834249i
$129$	4.68466	0.412461
$130$	0	0
$131$	14.4384	1.26149	0.630746	−	0.775989i	$-0.282749\pi$
$131$	14.4384	1.26149	0.630746	+	0.775989i	$0.282749\pi$
$132$	− 7.12311i	− 0.619987i
$133$	0	0
$134$	10.2462	0.885138
$135$	0	0
$136$	−6.56155	−0.562649
$137$	0.246211i	0.0210352i	0.999945	+	0.0105176i	$0.00334793\pi$
$137$	0.246211i	0.0210352i	−0.999945	+	0.0105176i	$0.996652\pi$
$138$	6.24621i	0.531713i
$139$	0.876894	0.0743772	0.0371886	−	0.999308i	$-0.488160\pi$
$139$	0.876894	0.0743772	0.0371886	+	0.999308i	$0.488160\pi$
$140$	0	0
$141$	11.1231	0.936734
$142$	16.0000i	1.34269i
$143$	− 0.684658i	− 0.0572540i
$144$	−7.68466	−0.640388
$145$	0	0
$146$	31.3693	2.59614
$147$	7.00000i	0.577350i
$148$	23.3693i	1.92095i
$149$	−12.2462	−1.00325	−0.501624	−	0.865086i	$-0.667264\pi$
$149$	−12.2462	−1.00325	−0.501624	+	0.865086i	$0.667264\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	30.7386i	2.49323i
$153$	− 1.00000i	− 0.0808452i
$154$	0	0
$155$	0	0
$156$	−2.00000	−0.160128
$157$	6.68466i	0.533494i	0.963767	+	0.266747i	$0.0859488\pi$
$157$	6.68466i	0.533494i	−0.963767	+	0.266747i	$0.914051\pi$
$158$	− 24.0000i	− 1.90934i
$159$	12.2462	0.971188
$160$	0	0
$161$	0	0
$162$	− 2.56155i	− 0.201255i
$163$	15.1231i	1.18453i	0.805742	+	0.592267i	$0.201767\pi$
$163$	15.1231i	1.18453i	−0.805742	+	0.592267i	$0.798233\pi$
$164$	16.2462	1.26862
$165$	0	0
$166$	2.24621	0.174340
$167$	19.8078i	1.53277i	0.642381	+	0.766385i	$0.277947\pi$
$167$	19.8078i	1.53277i	−0.642381	+	0.766385i	$0.722053\pi$
$168$	0	0
$169$	12.8078	0.985213
$170$	0	0
$171$	−4.68466	−0.358245
$172$	21.3693i	1.62940i
$173$	− 1.80776i	− 0.137442i	−0.997636	−	0.0687209i	$-0.978108\pi$
$173$	− 1.80776i	− 0.137442i	0.997636	−	0.0687209i	$-0.0218918\pi$
$174$	21.1231	1.60134
$175$	0	0
$176$	12.0000	0.904534
$177$	− 7.12311i	− 0.535405i
$178$	− 2.87689i	− 0.215632i
$179$	0.876894	0.0655422	0.0327711	−	0.999463i	$-0.489567\pi$
$179$	0.876894	0.0655422	0.0327711	+	0.999463i	$0.489567\pi$
$180$	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
$183$	9.12311i	0.674399i
$184$	−16.0000	−1.17954
$185$	0	0
$186$	8.00000	0.586588
$187$	1.56155i	0.114192i
$188$	50.7386i	3.70050i
$189$	0	0
$190$	0	0
$191$	−4.87689	−0.352880	−0.176440	−	0.984311i	$-0.556458\pi$
$191$	−4.87689	−0.352880	−0.176440	+	0.984311i	$0.556458\pi$
$192$	− 1.43845i	− 0.103811i
$193$	7.75379i	0.558130i	0.960272	+	0.279065i	$0.0900245\pi$
$193$	7.75379i	0.558130i	−0.960272	+	0.279065i	$0.909976\pi$
$194$	−7.36932	−0.529086
$195$	0	0
$196$	−31.9309	−2.28078
$197$	− 8.93087i	− 0.636298i	−0.948041	−	0.318149i	$-0.896939\pi$
$197$	− 8.93087i	− 0.636298i	0.948041	−	0.318149i	$-0.103061\pi$
$198$	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
$202$	− 27.8617i	− 1.96035i
$203$	0	0
$204$	4.56155	0.319373
$205$	0	0
$206$	−42.7386	−2.97774
$207$	− 2.43845i	− 0.169484i
$208$	− 3.36932i	− 0.233620i
$209$	7.31534	0.506013
$210$	0	0
$211$	13.3693	0.920382	0.460191	−	0.887820i	$-0.347781\pi$
$211$	13.3693	0.920382	0.460191	+	0.887820i	$0.347781\pi$
$212$	55.8617i	3.83660i
$213$	− 6.24621i	− 0.427983i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	6.56155	0.446457
$217$	0	0
$218$	− 17.6155i	− 1.19307i
$219$	−12.2462	−0.827522
$220$	0	0
$221$	0.438447	0.0294931
$222$	− 13.1231i	− 0.880765i
$223$	14.9309i	0.999845i	0.866070	+	0.499922i	$0.166638\pi$
$223$	14.9309i	0.999845i	−0.866070	+	0.499922i	$0.833362\pi$
$224$	0	0
$225$	0	0
$226$	1.12311	0.0747079
$227$	− 14.0540i	− 0.932795i	−0.884575	−	0.466398i	$-0.845552\pi$
$227$	− 14.0540i	− 0.932795i	0.884575	−	0.466398i	$-0.154448\pi$
$228$	− 21.3693i	− 1.41522i
$229$	−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
$232$	54.1080i	3.55236i
$233$	3.56155i	0.233325i	0.993172	+	0.116663i	$0.0372196\pi$
$233$	3.56155i	0.233325i	−0.993172	+	0.116663i	$0.962780\pi$
$234$	1.12311	0.0734197
$235$	0	0
$236$	32.4924	2.11508
$237$	9.36932i	0.608603i
$238$	0	0
$239$	6.24621	0.404034	0.202017	−	0.979382i	$-0.435250\pi$
$239$	6.24621	0.404034	0.202017	+	0.979382i	$0.435250\pi$
$240$	0	0
$241$	3.36932	0.217037	0.108518	−	0.994094i	$-0.465389\pi$
$241$	3.36932	0.217037	0.108518	+	0.994094i	$0.465389\pi$
$242$	21.9309i	1.40977i
$243$	1.00000i	0.0641500i
$244$	−41.6155	−2.66416
$245$	0	0
$246$	−9.12311	−0.581668
$247$	− 2.05398i	− 0.130691i
$248$	20.4924i	1.30127i
$249$	−0.876894	−0.0555709
$250$	0	0
$251$	8.49242	0.536037	0.268018	−	0.963414i	$-0.413631\pi$
$251$	8.49242	0.536037	0.268018	+	0.963414i	$0.413631\pi$
$252$	0	0
$253$	3.80776i	0.239392i
$254$	50.7386	3.18363
$255$	0	0
$256$	−27.0540	−1.69087
$257$	− 15.3693i	− 0.958712i	−0.877621	−	0.479356i	$-0.840870\pi$
$257$	− 15.3693i	− 0.958712i	0.877621	−	0.479356i	$-0.159130\pi$
$258$	− 12.0000i	− 0.747087i
$259$	0	0
$260$	0	0
$261$	−8.24621	−0.510428
$262$	− 36.9848i	− 2.28493i
$263$	20.4924i	1.26362i	0.775125	+	0.631808i	$0.217687\pi$
$263$	20.4924i	1.26362i	−0.775125	+	0.631808i	$0.782313\pi$
$264$	−10.2462	−0.630611
$265$	0	0
$266$	0	0
$267$	1.12311i	0.0687329i
$268$	− 18.2462i	− 1.11456i
$269$	−16.4384	−1.00227	−0.501135	−	0.865369i	$-0.667084\pi$
$269$	−16.4384	−1.00227	−0.501135	+	0.865369i	$0.667084\pi$
$270$	0	0
$271$	19.8078	1.20324	0.601618	−	0.798784i	$-0.294523\pi$
$271$	19.8078	1.20324	0.601618	+	0.798784i	$0.294523\pi$
$272$	7.68466i	0.465951i
$273$	0	0
$274$	0.630683	0.0381010
$275$	0	0
$276$	11.1231	0.669532
$277$	6.00000i	0.360505i	0.983620	+	0.180253i	$0.0576915\pi$
$277$	6.00000i	0.360505i	−0.983620	+	0.180253i	$0.942309\pi$
$278$	− 2.24621i	− 0.134719i
$279$	−3.12311	−0.186975
$280$	0	0
$281$	−10.8769	−0.648861	−0.324431	−	0.945910i	$-0.605173\pi$
$281$	−10.8769	−0.648861	−0.324431	+	0.945910i	$0.605173\pi$
$282$	− 28.4924i	− 1.69670i
$283$	− 21.3693i	− 1.27027i	−0.772399	−	0.635137i	$-0.780944\pi$
$283$	− 21.3693i	− 1.27027i	0.772399	−	0.635137i	$-0.219056\pi$
$284$	28.4924	1.69071
$285$	0	0
$286$	−1.75379	−0.103704
$287$	0	0
$288$	6.56155i	0.386643i
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	2.87689	0.168647
$292$	− 55.8617i	− 3.26906i
$293$	− 1.12311i	− 0.0656125i	−0.999462	−	0.0328063i	$-0.989556\pi$
$293$	− 1.12311i	− 0.0656125i	0.999462	−	0.0328063i	$-0.0104444\pi$
$294$	17.9309	1.04575
$295$	0	0
$296$	33.6155	1.95386
$297$	− 1.56155i	− 0.0906105i
$298$	31.3693i	1.81718i
$299$	1.06913	0.0618294
$300$	0	0
$301$	0	0
$302$	− 20.4924i	− 1.17921i
$303$	10.8769i	0.624861i
$304$	36.0000	2.06474
$305$	0	0
$306$	−2.56155	−0.146434
$307$	32.4924i	1.85444i	0.374516	+	0.927220i	$0.377809\pi$
$307$	32.4924i	1.85444i	−0.374516	+	0.927220i	$0.622191\pi$
$308$	0	0
$309$	16.6847	0.949157
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	2.87689i	0.162872i
$313$	− 33.6155i	− 1.90006i	−0.312156	−	0.950031i	$-0.601051\pi$
$313$	− 33.6155i	− 1.90006i	0.312156	−	0.950031i	$-0.398949\pi$
$314$	17.1231	0.966313
$315$	0	0
$316$	−42.7386	−2.40424
$317$	− 18.0000i	− 1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$	− 18.0000i	− 1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$	− 31.3693i	− 1.75910i
$319$	12.8769	0.720968
$320$	0	0
$321$	4.68466	0.261472
$322$	0	0
$323$	4.68466i	0.260661i
$324$	−4.56155	−0.253420
$325$	0	0
$326$	38.7386	2.14553
$327$	6.87689i	0.380293i
$328$	− 23.3693i	− 1.29035i
$329$	0	0
$330$	0	0
$331$	−34.9309	−1.91997	−0.959987	−	0.280044i	$-0.909651\pi$
$331$	−34.9309	−1.91997	−0.959987	+	0.280044i	$0.909651\pi$
$332$	− 4.00000i	− 0.219529i
$333$	5.12311i	0.280744i
$334$	50.7386	2.77629
$335$	0	0
$336$	0	0
$337$	− 16.7386i	− 0.911811i	−0.890028	−	0.455906i	$-0.849315\pi$
$337$	− 16.7386i	− 0.911811i	0.890028	−	0.455906i	$-0.150685\pi$
$338$	− 32.8078i	− 1.78451i
$339$	−0.438447	−0.0238132
$340$	0	0
$341$	4.87689	0.264099
$342$	12.0000i	0.648886i
$343$	0	0
$344$	30.7386	1.65732
$345$	0	0
$346$	−4.63068	−0.248947
$347$	− 8.49242i	− 0.455897i	−0.973673	−	0.227949i	$-0.926798\pi$
$347$	− 8.49242i	− 0.455897i	0.973673	−	0.227949i	$-0.0732018\pi$
$348$	− 37.6155i	− 2.01640i
$349$	−11.5616	−0.618876	−0.309438	−	0.950920i	$-0.600141\pi$
$349$	−11.5616	−0.618876	−0.309438	+	0.950920i	$0.600141\pi$
$350$	0	0
$351$	−0.438447	−0.0234026
$352$	− 10.2462i	− 0.546125i
$353$	10.4924i	0.558455i	0.960225	+	0.279228i	$0.0900784\pi$
$353$	10.4924i	0.558455i	−0.960225	+	0.279228i	$0.909922\pi$
$354$	−18.2462	−0.969775
$355$	0	0
$356$	−5.12311	−0.271524
$357$	0	0
$358$	− 2.24621i	− 0.118716i
$359$	−14.2462	−0.751886	−0.375943	−	0.926643i	$-0.622681\pi$
$359$	−14.2462	−0.751886	−0.375943	+	0.926643i	$0.622681\pi$
$360$	0	0
$361$	2.94602	0.155054
$362$	− 15.3693i	− 0.807793i
$363$	− 8.56155i	− 0.449365i
$364$	0	0
$365$	0	0
$366$	23.3693	1.22153
$367$	− 1.75379i	− 0.0915470i	−0.998952	−	0.0457735i	$-0.985425\pi$
$367$	− 1.75379i	− 0.0915470i	0.998952	−	0.0457735i	$-0.0145753\pi$
$368$	18.7386i	0.976819i
$369$	3.56155	0.185407
$370$	0	0
$371$	0	0
$372$	− 14.2462i	− 0.738632i
$373$	0.246211i	0.0127483i	0.999980	+	0.00637417i	$0.00202897\pi$
$373$	0.246211i	0.0127483i	−0.999980	+	0.00637417i	$0.997971\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	72.9848	3.76391
$377$	− 3.61553i	− 0.186209i
$378$	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
$381$	−19.8078	−1.01478
$382$	12.4924i	0.639168i
$383$	− 6.24621i	− 0.319166i	−0.987184	−	0.159583i	$-0.948985\pi$
$383$	− 6.24621i	− 0.319166i	0.987184	−	0.159583i	$-0.0510150\pi$
$384$	9.43845	0.481654
$385$	0	0
$386$	19.8617	1.01094
$387$	4.68466i	0.238135i
$388$	13.1231i	0.666225i
$389$	−35.8617	−1.81826	−0.909131	−	0.416510i	$-0.863253\pi$
$389$	−35.8617	−1.81826	−0.909131	+	0.416510i	$0.863253\pi$
$390$	0	0
$391$	−2.43845	−0.123318
$392$	45.9309i	2.31986i
$393$	14.4384i	0.728323i
$394$	−22.8769	−1.15252
$395$	0	0
$396$	7.12311	0.357950
$397$	− 19.3693i	− 0.972118i	−0.873926	−	0.486059i	$-0.838434\pi$
$397$	− 19.3693i	− 0.972118i	0.873926	−	0.486059i	$-0.161566\pi$
$398$	40.9848i	2.05438i
$399$	0	0
$400$	0	0
$401$	39.1771	1.95641	0.978205	−	0.207641i	$-0.0665787\pi$
$401$	39.1771	1.95641	0.978205	+	0.207641i	$0.0665787\pi$
$402$	10.2462i	0.511035i
$403$	− 1.36932i	− 0.0682105i
$404$	−49.6155	−2.46846
$405$	0	0
$406$	0	0
$407$	− 8.00000i	− 0.396545i
$408$	− 6.56155i	− 0.324845i
$409$	14.6847	0.726110	0.363055	−	0.931768i	$-0.381734\pi$
$409$	14.6847	0.726110	0.363055	+	0.931768i	$0.381734\pi$
$410$	0	0
$411$	−0.246211	−0.0121447
$412$	76.1080i	3.74957i
$413$	0	0
$414$	−6.24621	−0.306985
$415$	0	0
$416$	−2.87689	−0.141051
$417$	0.876894i	0.0429417i
$418$	− 18.7386i	− 0.916537i
$419$	0.492423	0.0240564	0.0120282	−	0.999928i	$-0.496171\pi$
$419$	0.492423	0.0240564	0.0120282	+	0.999928i	$0.496171\pi$
$420$	0	0
$421$	24.4384	1.19106	0.595529	−	0.803334i	$-0.296943\pi$
$421$	24.4384	1.19106	0.595529	+	0.803334i	$0.296943\pi$
$422$	− 34.2462i	− 1.66708i
$423$	11.1231i	0.540824i
$424$	80.3542	3.90234
$425$	0	0
$426$	−16.0000	−0.775203
$427$	0	0
$428$	21.3693i	1.03292i
$429$	0.684658	0.0330556
$430$	0	0
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	− 7.68466i	− 0.369728i
$433$	− 26.6847i	− 1.28238i	−0.767381	−	0.641191i	$-0.778440\pi$
$433$	− 26.6847i	− 1.28238i	0.767381	−	0.641191i	$-0.221560\pi$
$434$	0	0
$435$	0	0
$436$	−31.3693	−1.50232
$437$	11.4233i	0.546450i
$438$	31.3693i	1.49888i
$439$	22.2462	1.06175	0.530877	−	0.847449i	$-0.321863\pi$
$439$	22.2462	1.06175	0.530877	+	0.847449i	$0.321863\pi$
$440$	0	0
$441$	−7.00000	−0.333333
$442$	− 1.12311i	− 0.0534207i
$443$	31.1231i	1.47870i	0.673319	+	0.739352i	$0.264868\pi$
$443$	31.1231i	1.47870i	−0.673319	+	0.739352i	$0.735132\pi$
$444$	−23.3693	−1.10906
$445$	0	0
$446$	38.2462	1.81101
$447$	− 12.2462i	− 0.579226i
$448$	0	0
$449$	−36.7386	−1.73380	−0.866902	−	0.498479i	$-0.833892\pi$
$449$	−36.7386	−1.73380	−0.866902	+	0.498479i	$0.833892\pi$
$450$	0	0
$451$	−5.56155	−0.261883
$452$	− 2.00000i	− 0.0940721i
$453$	8.00000i	0.375873i
$454$	−36.0000	−1.68956
$455$	0	0
$456$	−30.7386	−1.43947
$457$	13.8078i	0.645900i	0.946416	+	0.322950i	$0.104675\pi$
$457$	13.8078i	0.645900i	−0.946416	+	0.322950i	$0.895325\pi$
$458$	15.3693i	0.718161i
$459$	1.00000	0.0466760
$460$	0	0
$461$	−8.24621	−0.384064	−0.192032	−	0.981389i	$-0.561508\pi$
$461$	−8.24621	−0.384064	−0.192032	+	0.981389i	$0.561508\pi$
$462$	0	0
$463$	40.9848i	1.90473i	0.304965	+	0.952364i	$0.401355\pi$
$463$	40.9848i	1.90473i	−0.304965	+	0.952364i	$0.598645\pi$
$464$	63.3693	2.94185
$465$	0	0
$466$	9.12311	0.422620
$467$	21.3693i	0.988854i	0.869219	+	0.494427i	$0.164622\pi$
$467$	21.3693i	0.988854i	−0.869219	+	0.494427i	$0.835378\pi$
$468$	− 2.00000i	− 0.0924500i
$469$	0	0
$470$	0	0
$471$	−6.68466	−0.308013
$472$	− 46.7386i	− 2.15132i
$473$	− 7.31534i	− 0.336360i
$474$	24.0000	1.10236
$475$	0	0
$476$	0	0
$477$	12.2462i	0.560715i
$478$	− 16.0000i	− 0.731823i
$479$	−24.3002	−1.11030	−0.555152	−	0.831749i	$-0.687340\pi$
$479$	−24.3002	−1.11030	−0.555152	+	0.831749i	$0.687340\pi$
$480$	0	0
$481$	−2.24621	−0.102418
$482$	− 8.63068i	− 0.393117i
$483$	0	0
$484$	39.0540	1.77518
$485$	0	0
$486$	2.56155	0.116194
$487$	17.3693i	0.787079i	0.919308	+	0.393539i	$0.128750\pi$
$487$	17.3693i	0.787079i	−0.919308	+	0.393539i	$0.871250\pi$
$488$	59.8617i	2.70981i
$489$	−15.1231	−0.683890
$490$	0	0
$491$	−21.3693	−0.964384	−0.482192	−	0.876066i	$-0.660159\pi$
$491$	−21.3693	−0.964384	−0.482192	+	0.876066i	$0.660159\pi$
$492$	16.2462i	0.732436i
$493$	8.24621i	0.371391i
$494$	−5.26137	−0.236720
$495$	0	0
$496$	24.0000	1.07763
$497$	0	0
$498$	2.24621i	0.100655i
$499$	−13.3693	−0.598493	−0.299246	−	0.954176i	$-0.596735\pi$
$499$	−13.3693	−0.598493	−0.299246	+	0.954176i	$0.596735\pi$
$500$	0	0
$501$	−19.8078	−0.884946
$502$	− 21.7538i	− 0.970919i
$503$	29.5616i	1.31808i	0.752106	+	0.659042i	$0.229038\pi$
$503$	29.5616i	1.31808i	−0.752106	+	0.659042i	$0.770962\pi$
$504$	0	0
$505$	0	0
$506$	9.75379	0.433609
$507$	12.8078i	0.568813i
$508$	− 90.3542i	− 4.00882i
$509$	−25.1231	−1.11356	−0.556781	−	0.830659i	$-0.687964\pi$
$509$	−25.1231	−1.11356	−0.556781	+	0.830659i	$0.687964\pi$
$510$	0	0
$511$	0	0
$512$	50.4233i	2.22842i
$513$	− 4.68466i	− 0.206833i
$514$	−39.3693	−1.73651
$515$	0	0
$516$	−21.3693	−0.940732
$517$	− 17.3693i	− 0.763902i
$518$	0	0
$519$	1.80776	0.0793520
$520$	0	0
$521$	−35.5616	−1.55798	−0.778990	−	0.627036i	$-0.784268\pi$
$521$	−35.5616	−1.55798	−0.778990	+	0.627036i	$0.784268\pi$
$522$	21.1231i	0.924533i
$523$	20.0000i	0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$	20.0000i	0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	−65.8617	−2.87718
$525$	0	0
$526$	52.4924	2.28878
$527$	3.12311i	0.136045i
$528$	12.0000i	0.522233i
$529$	17.0540	0.741477
$530$	0	0
$531$	7.12311	0.309116
$532$	0	0
$533$	1.56155i	0.0676384i
$534$	2.87689	0.124495
$535$	0	0
$536$	−26.2462	−1.13366
$537$	0.876894i	0.0378408i
$538$	42.1080i	1.81540i
$539$	10.9309	0.470826
$540$	0	0
$541$	34.1080	1.46642	0.733208	−	0.680005i	$-0.238022\pi$
$541$	34.1080	1.46642	0.733208	+	0.680005i	$0.238022\pi$
$542$	− 50.7386i	− 2.17941i
$543$	6.00000i	0.257485i
$544$	6.56155	0.281324
$545$	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	$0.795725\pi$
$548$	− 1.12311i	− 0.0479767i
$549$	−9.12311	−0.389365
$550$	0	0
$551$	38.6307	1.64572
$552$	− 16.0000i	− 0.681005i
$553$	0	0
$554$	15.3693	0.652980
$555$	0	0
$556$	−4.00000	−0.169638
$557$	26.4924i	1.12252i	0.827640	+	0.561260i	$0.189683\pi$
$557$	26.4924i	1.12252i	−0.827640	+	0.561260i	$0.810317\pi$
$558$	8.00000i	0.338667i
$559$	−2.05398	−0.0868739
$560$	0	0
$561$	−1.56155	−0.0659288
$562$	27.8617i	1.17528i
$563$	− 31.1231i	− 1.31168i	−0.754899	−	0.655841i	$-0.772314\pi$
$563$	− 31.1231i	− 1.31168i	0.754899	−	0.655841i	$-0.227686\pi$
$564$	−50.7386	−2.13648
$565$	0	0
$566$	−54.7386	−2.30084
$567$	0	0
$568$	− 40.9848i	− 1.71969i
$569$	−21.1231	−0.885527	−0.442763	−	0.896639i	$-0.646002\pi$
$569$	−21.1231	−0.885527	−0.442763	+	0.896639i	$0.646002\pi$
$570$	0	0
$571$	−30.7386	−1.28637	−0.643186	−	0.765710i	$-0.722388\pi$
$571$	−30.7386	−1.28637	−0.643186	+	0.765710i	$0.722388\pi$
$572$	3.12311i	0.130584i
$573$	− 4.87689i	− 0.203735i
$574$	0	0
$575$	0	0
$576$	1.43845	0.0599353
$577$	− 3.94602i	− 0.164275i	−0.996621	−	0.0821376i	$-0.973825\pi$
$577$	− 3.94602i	− 0.164275i	0.996621	−	0.0821376i	$-0.0261747\pi$
$578$	2.56155i	0.106547i
$579$	−7.75379	−0.322236
$580$	0	0
$581$	0	0
$582$	− 7.36932i	− 0.305468i
$583$	− 19.1231i	− 0.791998i
$584$	−80.3542	−3.32508
$585$	0	0
$586$	−2.87689	−0.118843
$587$	− 28.9848i	− 1.19633i	−0.801372	−	0.598166i	$-0.795896\pi$
$587$	− 28.9848i	− 1.19633i	0.801372	−	0.598166i	$-0.204104\pi$
$588$	− 31.9309i	− 1.31681i
$589$	14.6307	0.602847
$590$	0	0
$591$	8.93087	0.367367
$592$	− 39.3693i	− 1.61807i
$593$	− 27.7538i	− 1.13971i	−0.821745	−	0.569856i	$-0.806999\pi$
$593$	− 27.7538i	− 1.13971i	0.821745	−	0.569856i	$-0.193001\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	55.8617	2.28819
$597$	− 16.0000i	− 0.654836i
$598$	− 2.73863i	− 0.111991i
$599$	0.384472	0.0157091	0.00785455	−	0.999969i	$-0.497500\pi$
$599$	0.384472	0.0157091	0.00785455	+	0.999969i	$0.497500\pi$
$600$	0	0
$601$	−30.9848	−1.26390	−0.631949	−	0.775010i	$-0.717745\pi$
$601$	−30.9848	−1.26390	−0.631949	+	0.775010i	$0.717745\pi$
$602$	0	0
$603$	− 4.00000i	− 0.162893i
$604$	−36.4924	−1.48486
$605$	0	0
$606$	27.8617	1.13181
$607$	− 9.36932i	− 0.380289i	−0.981756	−	0.190144i	$-0.939104\pi$
$607$	− 9.36932i	− 0.380289i	0.981756	−	0.190144i	$-0.0608956\pi$
$608$	− 30.7386i	− 1.24662i
$609$	0	0
$610$	0	0
$611$	−4.87689	−0.197298
$612$	4.56155i	0.184390i
$613$	− 14.6847i	− 0.593108i	−0.955016	−	0.296554i	$-0.904163\pi$
$613$	− 14.6847i	− 0.593108i	0.955016	−	0.296554i	$-0.0958374\pi$
$614$	83.2311	3.35893
$615$	0	0
$616$	0	0
$617$	− 44.2462i	− 1.78129i	−0.454704	−	0.890643i	$-0.650255\pi$
$617$	− 44.2462i	− 1.78129i	0.454704	−	0.890643i	$-0.349745\pi$
$618$	− 42.7386i	− 1.71920i
$619$	−5.36932	−0.215811	−0.107906	−	0.994161i	$-0.534414\pi$
$619$	−5.36932	−0.215811	−0.107906	+	0.994161i	$0.534414\pi$
$620$	0	0
$621$	2.43845	0.0978515
$622$	0	0
$623$	0	0
$624$	3.36932	0.134881
$625$	0	0
$626$	−86.1080	−3.44157
$627$	7.31534i	0.292147i
$628$	− 30.4924i	− 1.21678i
$629$	5.12311	0.204272
$630$	0	0
$631$	−0.684658	−0.0272558	−0.0136279	−	0.999907i	$-0.504338\pi$
$631$	−0.684658	−0.0272558	−0.0136279	+	0.999907i	$0.504338\pi$
$632$	61.4773i	2.44543i
$633$	13.3693i	0.531383i
$634$	−46.1080	−1.83118
$635$	0	0
$636$	−55.8617	−2.21506
$637$	− 3.06913i	− 0.121603i
$638$	− 32.9848i	− 1.30588i
$639$	6.24621	0.247096
$640$	0	0
$641$	−28.9309	−1.14270	−0.571350	−	0.820706i	$-0.693580\pi$
$641$	−28.9309	−1.14270	−0.571350	+	0.820706i	$0.693580\pi$
$642$	− 12.0000i	− 0.473602i
$643$	13.7538i	0.542396i	0.962524	+	0.271198i	$0.0874199\pi$
$643$	13.7538i	0.542396i	−0.962524	+	0.271198i	$0.912580\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	− 9.36932i	− 0.368346i	−0.982894	−	0.184173i	$-0.941039\pi$
$647$	− 9.36932i	− 0.368346i	0.982894	−	0.184173i	$-0.0589606\pi$
$648$	6.56155i	0.257762i
$649$	−11.1231	−0.436620
$650$	0	0
$651$	0	0
$652$	− 68.9848i	− 2.70166i
$653$	32.9309i	1.28868i	0.764737	+	0.644342i	$0.222869\pi$
$653$	32.9309i	1.28868i	−0.764737	+	0.644342i	$0.777131\pi$
$654$	17.6155	0.688822
$655$	0	0
$656$	−27.3693	−1.06859
$657$	− 12.2462i	− 0.477770i
$658$	0	0
$659$	9.86174	0.384159	0.192079	−	0.981379i	$-0.438477\pi$
$659$	9.86174	0.384159	0.192079	+	0.981379i	$0.438477\pi$
$660$	0	0
$661$	13.3153	0.517907	0.258953	−	0.965890i	$-0.416622\pi$
$661$	13.3153	0.517907	0.258953	+	0.965890i	$0.416622\pi$
$662$	89.4773i	3.47763i
$663$	0.438447i	0.0170279i
$664$	−5.75379	−0.223290
$665$	0	0
$666$	13.1231	0.508510
$667$	20.1080i	0.778583i
$668$	− 90.3542i	− 3.49591i
$669$	−14.9309	−0.577261
$670$	0	0
$671$	14.2462	0.549969
$672$	0	0
$673$	0.738634i	0.0284722i	0.999899	+	0.0142361i	$0.00453165\pi$
$673$	0.738634i	0.0284722i	−0.999899	+	0.0142361i	$0.995468\pi$
$674$	−42.8769	−1.65156
$675$	0	0
$676$	−58.4233	−2.24705
$677$	− 1.31534i	− 0.0505527i	−0.999681	−	0.0252763i	$-0.991953\pi$
$677$	− 1.31534i	− 0.0505527i	0.999681	−	0.0252763i	$-0.00804657\pi$
$678$	1.12311i	0.0431326i
$679$	0	0
$680$	0	0
$681$	14.0540	0.538550
$682$	− 12.4924i	− 0.478360i
$683$	9.56155i	0.365863i	0.983126	+	0.182931i	$0.0585586\pi$
$683$	9.56155i	0.365863i	−0.983126	+	0.182931i	$0.941441\pi$
$684$	21.3693	0.817076
$685$	0	0
$686$	0	0
$687$	− 6.00000i	− 0.228914i
$688$	− 36.0000i	− 1.37249i
$689$	−5.36932	−0.204555
$690$	0	0
$691$	−28.9848	−1.10264	−0.551318	−	0.834295i	$-0.685875\pi$
$691$	−28.9848	−1.10264	−0.551318	+	0.834295i	$0.685875\pi$
$692$	8.24621i	0.313474i
$693$	0	0
$694$	−21.7538	−0.825763
$695$	0	0
$696$	−54.1080	−2.05096
$697$	− 3.56155i	− 0.134903i
$698$	29.6155i	1.12096i
$699$	−3.56155	−0.134710
$700$	0	0
$701$	15.3693	0.580491	0.290246	−	0.956952i	$-0.406263\pi$
$701$	15.3693	0.580491	0.290246	+	0.956952i	$0.406263\pi$
$702$	1.12311i	0.0423889i
$703$	− 24.0000i	− 0.905177i
$704$	−2.24621	−0.0846573
$705$	0	0
$706$	26.8769	1.01153
$707$	0	0
$708$	32.4924i	1.22114i
$709$	44.7386	1.68019	0.840097	−	0.542436i	$-0.182498\pi$
$709$	44.7386	1.68019	0.840097	+	0.542436i	$0.182498\pi$
$710$	0	0
$711$	−9.36932	−0.351377
$712$	7.36932i	0.276177i
$713$	7.61553i	0.285204i
$714$	0	0
$715$	0	0
$716$	−4.00000	−0.149487
$717$	6.24621i	0.233269i
$718$	36.4924i	1.36189i
$719$	11.8078	0.440355	0.220178	−	0.975460i	$-0.429336\pi$
$719$	11.8078	0.440355	0.220178	+	0.975460i	$0.429336\pi$
$720$	0	0
$721$	0	0
$722$	− 7.54640i	− 0.280848i
$723$	3.36932i	0.125306i
$724$	−27.3693	−1.01717
$725$	0	0
$726$	−21.9309	−0.813931
$727$	− 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
$731$	4.68466	0.173268
$732$	− 41.6155i	− 1.53815i
$733$	11.7538i	0.434136i	0.976156	+	0.217068i	$0.0696494\pi$
$733$	11.7538i	0.434136i	−0.976156	+	0.217068i	$0.930351\pi$
$734$	−4.49242	−0.165818
$735$	0	0
$736$	16.0000	0.589768
$737$	6.24621i	0.230082i
$738$	− 9.12311i	− 0.335826i
$739$	20.6847	0.760897	0.380449	−	0.924802i	$-0.375770\pi$
$739$	20.6847	0.760897	0.380449	+	0.924802i	$0.375770\pi$
$740$	0	0
$741$	2.05398	0.0754547
$742$	0	0
$743$	− 28.4924i	− 1.04529i	−0.852552	−	0.522643i	$-0.824946\pi$
$743$	− 28.4924i	− 1.04529i	0.852552	−	0.522643i	$-0.175054\pi$
$744$	−20.4924	−0.751289
$745$	0	0
$746$	0.630683	0.0230909
$747$	− 0.876894i	− 0.0320839i
$748$	− 7.12311i	− 0.260447i
$749$	0	0
$750$	0	0
$751$	−25.3693	−0.925740	−0.462870	−	0.886426i	$-0.653180\pi$
$751$	−25.3693	−0.925740	−0.462870	+	0.886426i	$0.653180\pi$
$752$	− 85.4773i	− 3.11704i
$753$	8.49242i	0.309481i
$754$	−9.26137	−0.337279
$755$	0	0
$756$	0	0
$757$	16.0540i	0.583492i	0.956496	+	0.291746i	$0.0942361\pi$
$757$	16.0540i	0.583492i	−0.956496	+	0.291746i	$0.905764\pi$
$758$	− 30.7386i	− 1.11648i
$759$	−3.80776	−0.138213
$760$	0	0
$761$	−15.7538	−0.571074	−0.285537	−	0.958368i	$-0.592172\pi$
$761$	−15.7538	−0.571074	−0.285537	+	0.958368i	$0.592172\pi$
$762$	50.7386i	1.83807i
$763$	0	0
$764$	22.2462	0.804840
$765$	0	0
$766$	−16.0000	−0.578103
$767$	3.12311i	0.112769i
$768$	− 27.0540i	− 0.976226i
$769$	−40.5464	−1.46214	−0.731070	−	0.682302i	$-0.760979\pi$
$769$	−40.5464	−1.46214	−0.731070	+	0.682302i	$0.760979\pi$
$770$	0	0
$771$	15.3693	0.553512
$772$	− 35.3693i	− 1.27297i
$773$	8.63068i	0.310424i	0.987881	+	0.155212i	$0.0496061\pi$
$773$	8.63068i	0.310424i	−0.987881	+	0.155212i	$0.950394\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	18.8769	0.677641
$777$	0	0
$778$	91.8617i	3.29340i
$779$	−16.6847	−0.597790
$780$	0	0
$781$	−9.75379	−0.349018
$782$	6.24621i	0.223364i
$783$	− 8.24621i	− 0.294696i
$784$	53.7926	1.92116
$785$	0	0
$786$	36.9848	1.31921
$787$	− 10.2462i	− 0.365238i	−0.983184	−	0.182619i	$-0.941543\pi$
$787$	− 10.2462i	− 0.365238i	0.983184	−	0.182619i	$-0.0584575\pi$
$788$	40.7386i	1.45125i
$789$	−20.4924	−0.729550
$790$	0	0
$791$	0	0
$792$	− 10.2462i	− 0.364083i
$793$	− 4.00000i	− 0.142044i
$794$	−49.6155	−1.76079
$795$	0	0
$796$	72.9848	2.58688
$797$	− 9.61553i	− 0.340599i	−0.985392	−	0.170300i	$-0.945526\pi$
$797$	− 9.61553i	− 0.340599i	0.985392	−	0.170300i	$-0.0544736\pi$
$798$	0	0
$799$	11.1231	0.393507
$800$	0	0
$801$	−1.12311	−0.0396830
$802$	− 100.354i	− 3.54363i
$803$	19.1231i	0.674840i
$804$	18.2462	0.643494
$805$	0	0
$806$	−3.50758	−0.123549
$807$	− 16.4384i	− 0.578661i
$808$	71.3693i	2.51076i
$809$	−15.9460	−0.560632	−0.280316	−	0.959908i	$-0.590439\pi$
$809$	−15.9460	−0.560632	−0.280316	+	0.959908i	$0.590439\pi$
$810$	0	0
$811$	−45.3693	−1.59313	−0.796566	−	0.604551i	$-0.793352\pi$
$811$	−45.3693	−1.59313	−0.796566	+	0.604551i	$0.793352\pi$
$812$	0	0
$813$	19.8078i	0.694689i
$814$	−20.4924	−0.718259
$815$	0	0
$816$	−7.68466	−0.269017
$817$	− 21.9460i	− 0.767794i
$818$	− 37.6155i	− 1.31520i
$819$	0	0
$820$	0	0
$821$	−12.4384	−0.434105	−0.217052	−	0.976160i	$-0.569644\pi$
$821$	−12.4384	−0.434105	−0.217052	+	0.976160i	$0.569644\pi$
$822$	0.630683i	0.0219976i
$823$	− 3.50758i	− 0.122266i	−0.998130	−	0.0611332i	$-0.980529\pi$
$823$	− 3.50758i	− 0.122266i	0.998130	−	0.0611332i	$-0.0194715\pi$
$824$	109.477	3.81382
$825$	0	0
$826$	0	0
$827$	47.4233i	1.64907i	0.565811	+	0.824535i	$0.308563\pi$
$827$	47.4233i	1.64907i	−0.565811	+	0.824535i	$0.691437\pi$
$828$	11.1231i	0.386555i
$829$	−17.5076	−0.608063	−0.304032	−	0.952662i	$-0.598333\pi$
$829$	−17.5076	−0.608063	−0.304032	+	0.952662i	$0.598333\pi$
$830$	0	0
$831$	−6.00000	−0.208138
$832$	0.630683i	0.0218650i
$833$	7.00000i	0.242536i
$834$	2.24621	0.0777799
$835$	0	0
$836$	−33.3693	−1.15410
$837$	− 3.12311i	− 0.107950i
$838$	− 1.26137i	− 0.0435732i
$839$	26.0540	0.899483	0.449742	−	0.893159i	$-0.351516\pi$
$839$	26.0540	0.899483	0.449742	+	0.893159i	$0.351516\pi$
$840$	0	0
$841$	39.0000	1.34483
$842$	− 62.6004i	− 2.15735i
$843$	− 10.8769i	− 0.374620i
$844$	−60.9848	−2.09918
$845$	0	0
$846$	28.4924	0.979590
$847$	0	0
$848$	− 94.1080i	− 3.23168i
$849$	21.3693	0.733393
$850$	0	0
$851$	12.4924	0.428235
$852$	28.4924i	0.976134i
$853$	28.7386i	0.983992i	0.870597	+	0.491996i	$0.163733\pi$
$853$	28.7386i	0.983992i	−0.870597	+	0.491996i	$0.836267\pi$
$854$	0	0
$855$	0	0
$856$	30.7386	1.05062
$857$	− 6.00000i	− 0.204956i	−0.994735	−	0.102478i	$-0.967323\pi$
$857$	− 6.00000i	− 0.204956i	0.994735	−	0.102478i	$-0.0326771\pi$
$858$	− 1.75379i	− 0.0598734i
$859$	−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
$862$	61.4773i	2.09392i
$863$	9.75379i	0.332023i	0.986124	+	0.166011i	$0.0530889\pi$
$863$	9.75379i	0.332023i	−0.986124	+	0.166011i	$0.946911\pi$
$864$	−6.56155	−0.223229
$865$	0	0
$866$	−68.3542	−2.32277
$867$	− 1.00000i	− 0.0339618i
$868$	0	0
$869$	14.6307	0.496312
$870$	0	0
$871$	1.75379	0.0594249
$872$	45.1231i	1.52806i
$873$	2.87689i	0.0973681i
$874$	29.2614	0.989780
$875$	0	0
$876$	55.8617	1.88739
$877$	− 34.0000i	− 1.14810i	−0.818821	−	0.574049i	$-0.805372\pi$
$877$	− 34.0000i	− 1.14810i	0.818821	−	0.574049i	$-0.194628\pi$
$878$	− 56.9848i	− 1.92315i
$879$	1.12311	0.0378814
$880$	0	0
$881$	40.2462	1.35593	0.677965	−	0.735095i	$-0.262862\pi$
$881$	40.2462	1.35593	0.677965	+	0.735095i	$0.262862\pi$
$882$	17.9309i	0.603764i
$883$	23.4233i	0.788257i	0.919055	+	0.394128i	$0.128953\pi$
$883$	23.4233i	0.788257i	−0.919055	+	0.394128i	$0.871047\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	79.7235	2.67836
$887$	18.4384i	0.619102i	0.950883	+	0.309551i	$0.100179\pi$
$887$	18.4384i	0.619102i	−0.950883	+	0.309551i	$0.899821\pi$
$888$	33.6155i	1.12806i
$889$	0	0
$890$	0	0
$891$	1.56155	0.0523140
$892$	− 68.1080i	− 2.28042i
$893$	− 52.1080i	− 1.74373i
$894$	−31.3693	−1.04915
$895$	0	0
$896$	0	0
$897$	1.06913i	0.0356972i
$898$	94.1080i	3.14042i
$899$	25.7538	0.858937
$900$	0	0
$901$	12.2462	0.407980
$902$	14.2462i	0.474347i
$903$	0	0
$904$	−2.87689	−0.0956841
$905$	0	0
$906$	20.4924	0.680815
$907$	− 9.86174i	− 0.327454i	−0.986506	−	0.163727i	$-0.947648\pi$
$907$	− 9.86174i	− 0.327454i	0.986506	−	0.163727i	$-0.0523516\pi$
$908$	64.1080i	2.12750i
$909$	−10.8769	−0.360764
$910$	0	0
$911$	24.3002	0.805101	0.402551	−	0.915398i	$-0.368124\pi$
$911$	24.3002	0.805101	0.402551	+	0.915398i	$0.368124\pi$
$912$	36.0000i	1.19208i
$913$	1.36932i	0.0453178i
$914$	35.3693	1.16991
$915$	0	0
$916$	27.3693	0.904308
$917$	0	0
$918$	− 2.56155i	− 0.0845438i
$919$	16.6847	0.550376	0.275188	−	0.961390i	$-0.411260\pi$
$919$	16.6847	0.550376	0.275188	+	0.961390i	$0.411260\pi$
$920$	0	0
$921$	−32.4924	−1.07066
$922$	21.1231i	0.695652i
$923$	2.73863i	0.0901432i
$924$	0	0
$925$	0	0
$926$	104.985	3.45002
$927$	16.6847i	0.547996i
$928$	− 54.1080i	− 1.77618i
$929$	−3.06913	−0.100695	−0.0503474	−	0.998732i	$-0.516033\pi$
$929$	−3.06913	−0.100695	−0.0503474	+	0.998732i	$0.516033\pi$
$930$	0	0
$931$	32.7926	1.07473
$932$	− 16.2462i	− 0.532162i
$933$	0	0
$934$	54.7386	1.79110
$935$	0	0
$936$	−2.87689	−0.0940342
$937$	− 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
$939$	33.6155	1.09700
$940$	0	0
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	17.1231i	0.557901i
$943$	− 8.68466i	− 0.282811i
$944$	−54.7386	−1.78159
$945$	0	0
$946$	−18.7386	−0.609246
$947$	12.0000i	0.389948i	0.980808	+	0.194974i	$0.0624622\pi$
$947$	12.0000i	0.389948i	−0.980808	+	0.194974i	$0.937538\pi$
$948$	− 42.7386i	− 1.38809i
$949$	5.36932	0.174295
$950$	0	0
$951$	18.0000	0.583690
$952$	0	0
$953$	− 36.3542i	− 1.17763i	−0.808269	−	0.588813i	$-0.799595\pi$
$953$	− 36.3542i	− 1.17763i	0.808269	−	0.588813i	$-0.200405\pi$
$954$	31.3693	1.01562
$955$	0	0
$956$	−28.4924	−0.921511
$957$	12.8769i	0.416251i
$958$	62.2462i	2.01108i
$959$	0	0
$960$	0	0
$961$	−21.2462	−0.685362
$962$	5.75379i	0.185510i
$963$	4.68466i	0.150961i
$964$	−15.3693	−0.495012
$965$	0	0
$966$	0	0
$967$	42.4384i	1.36473i	0.731012	+	0.682364i	$0.239048\pi$
$967$	42.4384i	1.36473i	−0.731012	+	0.682364i	$0.760952\pi$
$968$	− 56.1771i	− 1.80560i
$969$	−4.68466	−0.150493
$970$	0	0
$971$	−43.6155	−1.39969	−0.699844	−	0.714295i	$-0.746747\pi$
$971$	−43.6155	−1.39969	−0.699844	+	0.714295i	$0.746747\pi$
$972$	− 4.56155i	− 0.146312i
$973$	0	0
$974$	44.4924	1.42563
$975$	0	0
$976$	70.1080	2.24410
$977$	8.24621i	0.263820i	0.991262	+	0.131910i	$0.0421109\pi$
$977$	8.24621i	0.263820i	−0.991262	+	0.131910i	$0.957889\pi$
$978$	38.7386i	1.23872i
$979$	1.75379	0.0560513
$980$	0	0
$981$	−6.87689	−0.219562
$982$	54.7386i	1.74678i
$983$	− 30.9309i	− 0.986542i	−0.869876	−	0.493271i	$-0.835801\pi$
$983$	− 30.9309i	− 0.986542i	0.869876	−	0.493271i	$-0.164199\pi$
$984$	23.3693	0.744987
$985$	0	0
$986$	21.1231	0.672697
$987$	0	0
$988$	9.36932i	0.298078i
$989$	11.4233	0.363240
$990$	0	0
$991$	42.7386	1.35764	0.678819	−	0.734306i	$-0.262492\pi$
$991$	42.7386	1.35764	0.678819	+	0.734306i	$0.262492\pi$
$992$	− 20.4924i	− 0.650635i
$993$	− 34.9309i	− 1.10850i
$994$	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	$-0.0506179\pi$
$998$	34.2462i	1.08404i
$999$	−5.12311	−0.162088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1275.2.b.d.1174.1		4
5.2	odd	4		1275.2.a.n.1.2		2
5.3	odd	4		51.2.a.b.1.1	✓	2
5.4	even	2	inner	1275.2.b.d.1174.4		4
15.2	even	4		3825.2.a.s.1.1		2
15.8	even	4		153.2.a.e.1.2		2
20.3	even	4		816.2.a.m.1.2		2
35.13	even	4		2499.2.a.o.1.1		2
40.3	even	4		3264.2.a.bg.1.1		2
40.13	odd	4		3264.2.a.bl.1.1		2
55.43	even	4		6171.2.a.p.1.2		2
60.23	odd	4		2448.2.a.v.1.1		2
65.38	odd	4		8619.2.a.q.1.2		2
85.3	even	16		867.2.h.j.757.1		16
85.8	odd	8		867.2.e.f.829.4		8
85.13	odd	4		867.2.d.c.577.3		4
85.23	even	16		867.2.h.j.733.1		16
85.28	even	16		867.2.h.j.733.2		16
85.33	odd	4		867.2.a.f.1.1		2
85.38	odd	4		867.2.d.c.577.4		4
85.43	odd	8		867.2.e.f.829.3		8
85.48	even	16		867.2.h.j.757.2		16
85.53	odd	8		867.2.e.f.616.1		8
85.58	even	16		867.2.h.j.712.4		16
85.63	even	16		867.2.h.j.688.3		16
85.73	even	16		867.2.h.j.688.4		16
85.78	even	16		867.2.h.j.712.3		16
85.83	odd	8		867.2.e.f.616.2		8
105.83	odd	4		7497.2.a.v.1.2		2
120.53	even	4		9792.2.a.cy.1.2		2
120.83	odd	4		9792.2.a.cz.1.2		2
255.203	even	4		2601.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.1	✓	2	5.3	odd	4
153.2.a.e.1.2		2	15.8	even	4
816.2.a.m.1.2		2	20.3	even	4
867.2.a.f.1.1		2	85.33	odd	4
867.2.d.c.577.3		4	85.13	odd	4
867.2.d.c.577.4		4	85.38	odd	4
867.2.e.f.616.1		8	85.53	odd	8
867.2.e.f.616.2		8	85.83	odd	8
867.2.e.f.829.3		8	85.43	odd	8
867.2.e.f.829.4		8	85.8	odd	8
867.2.h.j.688.3		16	85.63	even	16
867.2.h.j.688.4		16	85.73	even	16
867.2.h.j.712.3		16	85.78	even	16
867.2.h.j.712.4		16	85.58	even	16
867.2.h.j.733.1		16	85.23	even	16
867.2.h.j.733.2		16	85.28	even	16
867.2.h.j.757.1		16	85.3	even	16
867.2.h.j.757.2		16	85.48	even	16
1275.2.a.n.1.2		2	5.2	odd	4
1275.2.b.d.1174.1		4	1.1	even	1	trivial
1275.2.b.d.1174.4		4	5.4	even	2	inner
2448.2.a.v.1.1		2	60.23	odd	4
2499.2.a.o.1.1		2	35.13	even	4
2601.2.a.t.1.2		2	255.203	even	4
3264.2.a.bg.1.1		2	40.3	even	4
3264.2.a.bl.1.1		2	40.13	odd	4
3825.2.a.s.1.1		2	15.2	even	4
6171.2.a.p.1.2		2	55.43	even	4
7497.2.a.v.1.2		2	105.83	odd	4
8619.2.a.q.1.2		2	65.38	odd	4
9792.2.a.cy.1.2		2	120.53	even	4
9792.2.a.cz.1.2		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)

\(f(q)\)	\(=\)	\(q-2.56155i q^{2} +1.00000i q^{3} -4.56155 q^{4} +2.56155 q^{6} +6.56155i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.56155i q^{2} +1.00000i q^{3} -4.56155 q^{4} +2.56155 q^{6} +6.56155i q^{8} -1.00000 q^{9} +1.56155 q^{11} -4.56155i q^{12} -0.438447i q^{13} +7.68466 q^{16} +1.00000i q^{17} +2.56155i q^{18} +4.68466 q^{19} -4.00000i q^{22} +2.43845i q^{23} -6.56155 q^{24} -1.12311 q^{26} -1.00000i q^{27} +8.24621 q^{29} +3.12311 q^{31} -6.56155i q^{32} +1.56155i q^{33} +2.56155 q^{34} +4.56155 q^{36} -5.12311i q^{37} -12.0000i q^{38} +0.438447 q^{39} -3.56155 q^{41} -4.68466i q^{43} -7.12311 q^{44} +6.24621 q^{46} -11.1231i q^{47} +7.68466i q^{48} +7.00000 q^{49} -1.00000 q^{51} +2.00000i q^{52} -12.2462i q^{53} -2.56155 q^{54} +4.68466i q^{57} -21.1231i q^{58} -7.12311 q^{59} +9.12311 q^{61} -8.00000i q^{62} -1.43845 q^{64} +4.00000 q^{66} +4.00000i q^{67} -4.56155i q^{68} -2.43845 q^{69} -6.24621 q^{71} -6.56155i q^{72} +12.2462i q^{73} -13.1231 q^{74} -21.3693 q^{76} -1.12311i q^{78} +9.36932 q^{79} +1.00000 q^{81} +9.12311i q^{82} +0.876894i q^{83} -12.0000 q^{86} +8.24621i q^{87} +10.2462i q^{88} +1.12311 q^{89} -11.1231i q^{92} +3.12311i q^{93} -28.4924 q^{94} +6.56155 q^{96} -2.87689i q^{97} -17.9309i q^{98} -1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{4} + 2 q^{6} - 4 q^{9}+O(q^{10}) \) 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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