LMFDB - Embedded newform 825.4.c.p.199.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,4,Mod(199,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("825.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	825.c (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:	$48.6765757547$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 54x^{6} + 913x^{4} + 5292x^{2} + 8464 $ x^8 + 54x^6 + 913x^4 + 5292*x^2 + 8464
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.7
Root			$5.20196i$ of defining polynomial
Character	$\chi$	$=$	825.199
Dual form			825.4.c.p.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.20196i q^{2} +3.00000i q^{3} -9.65650 q^{4} -12.6059 q^{6} -15.3793i q^{7} -6.96057i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+4.20196i q^{2} +3.00000i q^{3} -9.65650 q^{4} -12.6059 q^{6} -15.3793i q^{7} -6.96057i q^{8} -9.00000 q^{9} -11.0000 q^{11} -28.9695i q^{12} +24.4926i q^{13} +64.6233 q^{14} -48.0040 q^{16} +54.9072i q^{17} -37.8177i q^{18} -119.454 q^{19} +46.1379 q^{21} -46.2216i q^{22} -191.351i q^{23} +20.8817 q^{24} -102.917 q^{26} -27.0000i q^{27} +148.510i q^{28} -225.140 q^{29} +303.901 q^{31} -257.395i q^{32} -33.0000i q^{33} -230.718 q^{34} +86.9085 q^{36} -109.382i q^{37} -501.939i q^{38} -73.4778 q^{39} +348.133 q^{41} +193.870i q^{42} +92.7623i q^{43} +106.222 q^{44} +804.051 q^{46} -306.728i q^{47} -144.012i q^{48} +106.477 q^{49} -164.722 q^{51} -236.513i q^{52} -216.854i q^{53} +113.453 q^{54} -107.049 q^{56} -358.361i q^{57} -946.029i q^{58} +692.952 q^{59} -152.661 q^{61} +1276.98i q^{62} +138.414i q^{63} +697.535 q^{64} +138.665 q^{66} +62.9772i q^{67} -530.211i q^{68} +574.054 q^{69} +554.295 q^{71} +62.6452i q^{72} +122.911i q^{73} +459.619 q^{74} +1153.50 q^{76} +169.172i q^{77} -308.751i q^{78} -476.528 q^{79} +81.0000 q^{81} +1462.84i q^{82} -913.360i q^{83} -445.531 q^{84} -389.784 q^{86} -675.419i q^{87} +76.5663i q^{88} -1603.65 q^{89} +376.679 q^{91} +1847.78i q^{92} +911.704i q^{93} +1288.86 q^{94} +772.186 q^{96} +498.916i q^{97} +447.412i q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9	$ 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9} - 88 q^{11} + 104 q^{14} + 132 q^{16} - 272 q^{19} + 204 q^{21} - 288 q^{24} - 640 q^{26} - 104 q^{29} + 984 q^{31} - 488 q^{34} + 468 q^{36} - 12 q^{39} + 536 q^{41} + 572 q^{44} + 736 q^{46} + 992 q^{49} + 444 q^{51} - 216 q^{54} - 1704 q^{56} + 2064 q^{59} + 232 q^{61} + 1836 q^{64} - 264 q^{66} + 384 q^{69} - 1840 q^{71} + 5712 q^{74} + 3144 q^{76} - 2304 q^{79} + 648 q^{81} + 120 q^{84} + 472 q^{86} + 2128 q^{89} + 5560 q^{91} + 2864 q^{94} + 1248 q^{96} + 792 q^{99}+O(q^{100}) $ 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9 - 88 * q^11 + 104 * q^14 + 132 * q^16 - 272 * q^19 + 204 * q^21 - 288 * q^24 - 640 * q^26 - 104 * q^29 + 984 * q^31 - 488 * q^34 + 468 * q^36 - 12 * q^39 + 536 * q^41 + 572 * q^44 + 736 * q^46 + 992 * q^49 + 444 * q^51 - 216 * q^54 - 1704 * q^56 + 2064 * q^59 + 232 * q^61 + 1836 * q^64 - 264 * q^66 + 384 * q^69 - 1840 * q^71 + 5712 * q^74 + 3144 * q^76 - 2304 * q^79 + 648 * q^81 + 120 * q^84 + 472 * q^86 + 2128 * q^89 + 5560 * q^91 + 2864 * q^94 + 1248 * q^96 + 792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	4.20196i	1.48562i	0.669503	+	0.742809i	$0.266507\pi$
$2$	4.20196i	1.48562i	−0.669503	+	0.742809i	$0.733493\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−9.65650	−1.20706
$5$	0	0
$5$	0	0
$6$	−12.6059	−0.857722
$7$	− 15.3793i	− 0.830404i	−0.909729	−	0.415202i	$-0.863711\pi$
$7$	− 15.3793i	− 0.830404i	0.909729	−	0.415202i	$-0.136289\pi$
$8$	− 6.96057i	− 0.307617i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	− 28.9695i	− 0.696898i
$13$	24.4926i	0.522540i	0.965266	+	0.261270i	$0.0841413\pi$
$13$	24.4926i	0.522540i	−0.965266	+	0.261270i	$0.915859\pi$
$14$	64.6233	1.23366
$15$	0	0
$16$	−48.0040	−0.750062
$17$	54.9072i	0.783350i	0.920104	+	0.391675i	$0.128104\pi$
$17$	54.9072i	0.783350i	−0.920104	+	0.391675i	$0.871896\pi$
$18$	− 37.8177i	− 0.495206i
$19$	−119.454	−1.44234	−0.721172	−	0.692757i	$-0.756396\pi$
$19$	−119.454	−1.44234	−0.721172	+	0.692757i	$0.756396\pi$
$20$	0	0
$21$	46.1379	0.479434
$22$	− 46.2216i	− 0.447931i
$23$	− 191.351i	− 1.73476i	−0.497646	−	0.867380i	$-0.665802\pi$
$23$	− 191.351i	− 1.73476i	0.497646	−	0.867380i	$-0.334198\pi$
$24$	20.8817	0.177603
$25$	0	0
$26$	−102.917	−0.776296
$27$	− 27.0000i	− 0.192450i
$28$	148.510i	1.00235i
$29$	−225.140	−1.44163	−0.720817	−	0.693125i	$-0.756233\pi$
$29$	−225.140	−1.44163	−0.720817	+	0.693125i	$0.756233\pi$
$30$	0	0
$31$	303.901	1.76072	0.880359	−	0.474307i	$-0.157301\pi$
$31$	303.901	1.76072	0.880359	+	0.474307i	$0.157301\pi$
$32$	− 257.395i	− 1.42192i
$33$	− 33.0000i	− 0.174078i
$34$	−230.718	−1.16376
$35$	0	0
$36$	86.9085	0.402354
$37$	− 109.382i	− 0.486008i	−0.970025	−	0.243004i	$-0.921867\pi$
$37$	− 109.382i	− 0.486008i	0.970025	−	0.243004i	$-0.0781328\pi$
$38$	− 501.939i	− 2.14277i
$39$	−73.4778	−0.301689
$40$	0	0
$41$	348.133	1.32608	0.663040	−	0.748584i	$-0.269266\pi$
$41$	348.133	1.32608	0.663040	+	0.748584i	$0.269266\pi$
$42$	193.870i	0.712256i
$43$	92.7623i	0.328979i	0.986379	+	0.164490i	$0.0525977\pi$
$43$	92.7623i	0.328979i	−0.986379	+	0.164490i	$0.947402\pi$
$44$	106.222	0.363943
$45$	0	0
$46$	804.051	2.57719
$47$	− 306.728i	− 0.951932i	−0.879464	−	0.475966i	$-0.842099\pi$
$47$	− 306.728i	− 0.951932i	0.879464	−	0.475966i	$-0.157901\pi$
$48$	− 144.012i	− 0.433048i
$49$	106.477	0.310429
$50$	0	0
$51$	−164.722	−0.452267
$52$	− 236.513i	− 0.630739i
$53$	− 216.854i	− 0.562021i	−0.959705	−	0.281011i	$-0.909330\pi$
$53$	− 216.854i	− 0.562021i	0.959705	−	0.281011i	$-0.0906696\pi$
$54$	113.453	0.285907
$55$	0	0
$56$	−107.049	−0.255446
$57$	− 358.361i	− 0.832737i
$58$	− 946.029i	− 2.14172i
$59$	692.952	1.52906	0.764532	−	0.644586i	$-0.222970\pi$
$59$	692.952	1.52906	0.764532	+	0.644586i	$0.222970\pi$
$60$	0	0
$61$	−152.661	−0.320431	−0.160215	−	0.987082i	$-0.551219\pi$
$61$	−152.661	−0.320431	−0.160215	+	0.987082i	$0.551219\pi$
$62$	1276.98i	2.61576i
$63$	138.414i	0.276801i
$64$	697.535	1.36237
$65$	0	0
$66$	138.665	0.258613
$67$	62.9772i	0.114834i	0.998350	+	0.0574170i	$0.0182865\pi$
$67$	62.9772i	0.114834i	−0.998350	+	0.0574170i	$0.981714\pi$
$68$	− 530.211i	− 0.945553i
$69$	574.054	1.00156
$70$	0	0
$71$	554.295	0.926518	0.463259	−	0.886223i	$-0.346680\pi$
$71$	554.295	0.926518	0.463259	+	0.886223i	$0.346680\pi$
$72$	62.6452i	0.102539i
$73$	122.911i	0.197063i	0.995134	+	0.0985314i	$0.0314145\pi$
$73$	122.911i	0.197063i	−0.995134	+	0.0985314i	$0.968586\pi$
$74$	459.619	0.722022
$75$	0	0
$76$	1153.50	1.74100
$77$	169.172i	0.250376i
$78$	− 308.751i	− 0.448195i
$79$	−476.528	−0.678653	−0.339326	−	0.940669i	$-0.610199\pi$
$79$	−476.528	−0.678653	−0.339326	+	0.940669i	$0.610199\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	1462.84i	1.97005i
$83$	− 913.360i	− 1.20788i	−0.797029	−	0.603941i	$-0.793596\pi$
$83$	− 913.360i	− 1.20788i	0.797029	−	0.603941i	$-0.206404\pi$
$84$	−445.531	−0.578707
$85$	0	0
$86$	−389.784	−0.488738
$87$	− 675.419i	− 0.832328i
$88$	76.5663i	0.0927500i
$89$	−1603.65	−1.90996	−0.954980	−	0.296669i	$-0.904124\pi$
$89$	−1603.65	−1.90996	−0.954980	+	0.296669i	$0.904124\pi$
$90$	0	0
$91$	376.679	0.433920
$92$	1847.78i	2.09397i
$93$	911.704i	1.01655i
$94$	1288.86	1.41421
$95$	0	0
$96$	772.186	0.820947
$97$	498.916i	0.522239i	0.965306	+	0.261120i	$0.0840917\pi$
$97$	498.916i	0.522239i	−0.965306	+	0.261120i	$0.915908\pi$
$98$	447.412i	0.461178i
$99$	99.0000	0.100504
$100$	0	0
$101$	−570.956	−0.562497	−0.281248	−	0.959635i	$-0.590749\pi$
$101$	−570.956	−0.562497	−0.281248	+	0.959635i	$0.590749\pi$
$102$	− 692.154i	− 0.671897i
$103$	− 1050.64i	− 1.00507i	−0.864556	−	0.502537i	$-0.832400\pi$
$103$	− 1050.64i	− 1.00507i	0.864556	−	0.502537i	$-0.167600\pi$
$104$	170.483	0.160742
$105$	0	0
$106$	911.211	0.834949
$107$	− 1870.49i	− 1.68997i	−0.534791	−	0.844985i	$-0.679609\pi$
$107$	− 1870.49i	− 1.68997i	0.534791	−	0.844985i	$-0.320391\pi$
$108$	260.726i	0.232299i
$109$	657.285	0.577583	0.288791	−	0.957392i	$-0.406747\pi$
$109$	657.285	0.577583	0.288791	+	0.957392i	$0.406747\pi$
$110$	0	0
$111$	328.146	0.280597
$112$	738.267i	0.622855i
$113$	− 1144.38i	− 0.952691i	−0.879258	−	0.476345i	$-0.841961\pi$
$113$	− 1144.38i	− 0.952691i	0.879258	−	0.476345i	$-0.158039\pi$
$114$	1505.82	1.23713
$115$	0	0
$116$	2174.06	1.74014
$117$	− 220.433i	− 0.174180i
$118$	2911.76i	2.27160i
$119$	844.434	0.650497
$120$	0	0
$121$	121.000	0.0909091
$122$	− 641.477i	− 0.476038i
$123$	1044.40i	0.765612i
$124$	−2934.62	−2.12530
$125$	0	0
$126$	−581.610	−0.411221
$127$	85.1754i	0.0595126i	0.999557	+	0.0297563i	$0.00947312\pi$
$127$	85.1754i	0.0595126i	−0.999557	+	0.0297563i	$0.990527\pi$
$128$	871.854i	0.602045i
$129$	−278.287	−0.189936
$130$	0	0
$131$	−541.509	−0.361159	−0.180580	−	0.983560i	$-0.557797\pi$
$131$	−541.509	−0.361159	−0.180580	+	0.983560i	$0.557797\pi$
$132$	318.665i	0.210123i
$133$	1837.11i	1.19773i
$134$	−264.628	−0.170600
$135$	0	0
$136$	382.185	0.240972
$137$	35.7727i	0.0223085i	0.999938	+	0.0111543i	$0.00355059\pi$
$137$	35.7727i	0.0223085i	−0.999938	+	0.0111543i	$0.996449\pi$
$138$	2412.15i	1.48794i
$139$	1479.11	0.902563	0.451281	−	0.892382i	$-0.350967\pi$
$139$	1479.11	0.902563	0.451281	+	0.892382i	$0.350967\pi$
$140$	0	0
$141$	920.183	0.549598
$142$	2329.13i	1.37645i
$143$	− 269.419i	− 0.157552i
$144$	432.036	0.250021
$145$	0	0
$146$	−516.466	−0.292760
$147$	319.431i	0.179226i
$148$	1056.25i	0.586642i
$149$	−1779.29	−0.978287	−0.489143	−	0.872203i	$-0.662691\pi$
$149$	−1779.29	−0.978287	−0.489143	+	0.872203i	$0.662691\pi$
$150$	0	0
$151$	−182.059	−0.0981173	−0.0490587	−	0.998796i	$-0.515622\pi$
$151$	−182.059	−0.0981173	−0.0490587	+	0.998796i	$0.515622\pi$
$152$	831.465i	0.443689i
$153$	− 494.165i	− 0.261117i
$154$	−710.856	−0.371964
$155$	0	0
$156$	709.539	0.364157
$157$	1579.89i	0.803114i	0.915834	+	0.401557i	$0.131531\pi$
$157$	1579.89i	0.803114i	−0.915834	+	0.401557i	$0.868469\pi$
$158$	− 2002.35i	− 1.00822i
$159$	650.561	0.324483
$160$	0	0
$161$	−2942.85	−1.44055
$162$	340.359i	0.165069i
$163$	− 1958.49i	− 0.941109i	−0.882371	−	0.470554i	$-0.844054\pi$
$163$	− 1958.49i	− 0.941109i	0.882371	−	0.470554i	$-0.155946\pi$
$164$	−3361.75	−1.60066
$165$	0	0
$166$	3837.90	1.79445
$167$	443.726i	0.205608i	0.994702	+	0.102804i	$0.0327814\pi$
$167$	443.726i	0.205608i	−0.994702	+	0.102804i	$0.967219\pi$
$168$	− 321.146i	− 0.147482i
$169$	1597.11	0.726952
$170$	0	0
$171$	1075.08	0.480781
$172$	− 895.760i	− 0.397099i
$173$	809.958i	0.355954i	0.984035	+	0.177977i	$0.0569552\pi$
$173$	809.958i	0.355954i	−0.984035	+	0.177977i	$0.943045\pi$
$174$	2838.09	1.23652
$175$	0	0
$176$	528.043	0.226152
$177$	2078.86i	0.882805i
$178$	− 6738.48i	− 2.83747i
$179$	−413.043	−0.172471	−0.0862355	−	0.996275i	$-0.527484\pi$
$179$	−413.043	−0.172471	−0.0862355	+	0.996275i	$0.527484\pi$
$180$	0	0
$181$	−3558.89	−1.46149	−0.730746	−	0.682649i	$-0.760828\pi$
$181$	−3558.89	−1.46149	−0.730746	+	0.682649i	$0.760828\pi$
$182$	1582.79i	0.644639i
$183$	− 457.984i	− 0.185001i
$184$	−1331.91	−0.533641
$185$	0	0
$186$	−3830.95	−1.51021
$187$	− 603.979i	− 0.236189i
$188$	2961.92i	1.14904i
$189$	−415.241	−0.159811
$190$	0	0
$191$	−2899.55	−1.09845	−0.549225	−	0.835675i	$-0.685077\pi$
$191$	−2899.55	−1.09845	−0.549225	+	0.835675i	$0.685077\pi$
$192$	2092.61i	0.786567i
$193$	− 1391.37i	− 0.518929i	−0.965753	−	0.259464i	$-0.916454\pi$
$193$	− 1391.37i	− 0.518929i	0.965753	−	0.259464i	$-0.0835460\pi$
$194$	−2096.43	−0.775848
$195$	0	0
$196$	−1028.20	−0.374707
$197$	− 171.519i	− 0.0620316i	−0.999519	−	0.0310158i	$-0.990126\pi$
$197$	− 171.519i	− 0.0620316i	0.999519	−	0.0310158i	$-0.00987423\pi$
$198$	415.994i	0.149310i
$199$	−3602.86	−1.28342	−0.641709	−	0.766948i	$-0.721774\pi$
$199$	−3602.86	−1.28342	−0.641709	+	0.766948i	$0.721774\pi$
$200$	0	0
$201$	−188.931	−0.0662995
$202$	− 2399.13i	− 0.835656i
$203$	3462.49i	1.19714i
$204$	1590.63	0.545915
$205$	0	0
$206$	4414.75	1.49316
$207$	1722.16i	0.578253i
$208$	− 1175.74i	− 0.391937i
$209$	1313.99	0.434883
$210$	0	0
$211$	3185.02	1.03918	0.519588	−	0.854417i	$-0.326086\pi$
$211$	3185.02	1.03918	0.519588	+	0.854417i	$0.326086\pi$
$212$	2094.05i	0.678395i
$213$	1662.89i	0.534925i
$214$	7859.72	2.51065
$215$	0	0
$216$	−187.936	−0.0592009
$217$	− 4673.79i	− 1.46211i
$218$	2761.89i	0.858068i
$219$	−368.732	−0.113774
$220$	0	0
$221$	−1344.82	−0.409332
$222$	1378.86i	0.416860i
$223$	5396.94i	1.62065i	0.585978	+	0.810327i	$0.300711\pi$
$223$	5396.94i	1.62065i	−0.585978	+	0.810327i	$0.699289\pi$
$224$	−3958.56	−1.18077
$225$	0	0
$226$	4808.64	1.41534
$227$	6799.75i	1.98817i	0.108593	+	0.994086i	$0.465366\pi$
$227$	6799.75i	1.98817i	−0.108593	+	0.994086i	$0.534634\pi$
$228$	3460.51i	1.00517i
$229$	4596.19	1.32631	0.663154	−	0.748483i	$-0.269217\pi$
$229$	4596.19	1.32631	0.663154	+	0.748483i	$0.269217\pi$
$230$	0	0
$231$	−507.517	−0.144555
$232$	1567.10i	0.443471i
$233$	− 5745.30i	− 1.61540i	−0.589597	−	0.807698i	$-0.700713\pi$
$233$	− 5745.30i	− 1.61540i	0.589597	−	0.807698i	$-0.299287\pi$
$234$	926.253	0.258765
$235$	0	0
$236$	−6691.50	−1.84568
$237$	− 1429.58i	− 0.391820i
$238$	3548.28i	0.966391i
$239$	1.65110	0.000446865 0	0.000223432	−	1.00000i	$-0.499929\pi$
$239$	1.65110	0.000446865 0	0.000223432		1.00000i	$0.499929\pi$
$240$	0	0
$241$	−6300.83	−1.68412	−0.842058	−	0.539387i	$-0.818656\pi$
$241$	−6300.83	−1.68412	−0.842058	+	0.539387i	$0.818656\pi$
$242$	508.438i	0.135056i
$243$	243.000i	0.0641500i
$244$	1474.17	0.386780
$245$	0	0
$246$	−4388.53	−1.13741
$247$	− 2925.73i	− 0.753682i
$248$	− 2115.33i	− 0.541627i
$249$	2740.08	0.697371
$250$	0	0
$251$	6949.86	1.74769	0.873847	−	0.486201i	$-0.161618\pi$
$251$	6949.86	1.74769	0.873847	+	0.486201i	$0.161618\pi$
$252$	− 1336.59i	− 0.334117i
$253$	2104.86i	0.523050i
$254$	−357.904	−0.0884130
$255$	0	0
$256$	1916.78	0.467965
$257$	− 2795.78i	− 0.678584i	−0.940681	−	0.339292i	$-0.889812\pi$
$257$	− 2795.78i	− 0.678584i	0.940681	−	0.339292i	$-0.110188\pi$
$258$	− 1169.35i	− 0.282173i
$259$	−1682.22	−0.403583
$260$	0	0
$261$	2026.26	0.480545
$262$	− 2275.40i	− 0.536545i
$263$	− 4185.49i	− 0.981325i	−0.871350	−	0.490662i	$-0.836755\pi$
$263$	− 4185.49i	− 0.981325i	0.871350	−	0.490662i	$-0.163245\pi$
$264$	−229.699	−0.0535492
$265$	0	0
$266$	−7719.48	−1.77937
$267$	− 4810.95i	− 1.10272i
$268$	− 608.139i	− 0.138612i
$269$	1924.32	0.436164	0.218082	−	0.975930i	$-0.430020\pi$
$269$	1924.32	0.436164	0.218082	+	0.975930i	$0.430020\pi$
$270$	0	0
$271$	2472.36	0.554190	0.277095	−	0.960843i	$-0.410628\pi$
$271$	2472.36	0.554190	0.277095	+	0.960843i	$0.410628\pi$
$272$	− 2635.76i	− 0.587561i
$273$	1130.04i	0.250524i
$274$	−150.316	−0.0331420
$275$	0	0
$276$	−5543.35	−1.20895
$277$	− 1462.93i	− 0.317324i	−0.987333	−	0.158662i	$-0.949282\pi$
$277$	− 1462.93i	− 0.317324i	0.987333	−	0.158662i	$-0.0507181\pi$
$278$	6215.16i	1.34086i
$279$	−2735.11	−0.586906
$280$	0	0
$281$	−3956.44	−0.839934	−0.419967	−	0.907539i	$-0.637958\pi$
$281$	−3956.44	−0.839934	−0.419967	+	0.907539i	$0.637958\pi$
$282$	3866.57i	0.816493i
$283$	− 4179.28i	− 0.877854i	−0.898523	−	0.438927i	$-0.855359\pi$
$283$	− 4179.28i	− 0.877854i	0.898523	−	0.438927i	$-0.144641\pi$
$284$	−5352.56	−1.11837
$285$	0	0
$286$	1132.09	0.234062
$287$	− 5354.04i	− 1.10118i
$288$	2316.56i	0.473974i
$289$	1898.20	0.386363
$290$	0	0
$291$	−1496.75	−0.301515
$292$	− 1186.89i	− 0.237867i
$293$	5677.09i	1.13194i	0.824425	+	0.565971i	$0.191499\pi$
$293$	5677.09i	1.13194i	−0.824425	+	0.565971i	$0.808501\pi$
$294$	−1342.24	−0.266261
$295$	0	0
$296$	−761.362	−0.149504
$297$	297.000i	0.0580259i
$298$	− 7476.49i	− 1.45336i
$299$	4686.69	0.906482
$300$	0	0
$301$	1426.62	0.273186
$302$	− 765.003i	− 0.145765i
$303$	− 1712.87i	− 0.324758i
$304$	5734.24	1.08185
$305$	0	0
$306$	2076.46	0.387920
$307$	1020.96i	0.189801i	0.995487	+	0.0949007i	$0.0302534\pi$
$307$	1020.96i	0.189801i	−0.995487	+	0.0949007i	$0.969747\pi$
$308$	− 1633.61i	− 0.302220i
$309$	3151.92	0.580280
$310$	0	0
$311$	−8338.99	−1.52045	−0.760227	−	0.649658i	$-0.774912\pi$
$311$	−8338.99	−1.52045	−0.760227	+	0.649658i	$0.774912\pi$
$312$	511.448i	0.0928045i
$313$	− 5245.08i	− 0.947186i	−0.880744	−	0.473593i	$-0.842957\pi$
$313$	− 5245.08i	− 0.947186i	0.880744	−	0.473593i	$-0.157043\pi$
$314$	−6638.64	−1.19312
$315$	0	0
$316$	4601.59	0.819177
$317$	− 1076.71i	− 0.190770i	−0.995440	−	0.0953849i	$-0.969592\pi$
$317$	− 1076.71i	− 0.190770i	0.995440	−	0.0953849i	$-0.0304082\pi$
$318$	2733.63i	0.482058i
$319$	2476.54	0.434669
$320$	0	0
$321$	5611.46	0.975704
$322$	− 12365.7i	− 2.14011i
$323$	− 6558.86i	− 1.12986i
$324$	−782.177	−0.134118
$325$	0	0
$326$	8229.50	1.39813
$327$	1971.86i	0.333468i
$328$	− 2423.21i	− 0.407924i
$329$	−4717.26	−0.790489
$330$	0	0
$331$	−1678.48	−0.278723	−0.139362	−	0.990242i	$-0.544505\pi$
$331$	−1678.48	−0.278723	−0.139362	+	0.990242i	$0.544505\pi$
$332$	8819.86i	1.45799i
$333$	984.438i	0.162003i
$334$	−1864.52	−0.305455
$335$	0	0
$336$	−2214.80	−0.359605
$337$	− 6953.49i	− 1.12398i	−0.827145	−	0.561989i	$-0.810036\pi$
$337$	− 6953.49i	− 1.12398i	0.827145	−	0.561989i	$-0.189964\pi$
$338$	6711.01i	1.07997i
$339$	3433.14	0.550036
$340$	0	0
$341$	−3342.91	−0.530877
$342$	4517.45i	0.714257i
$343$	− 6912.64i	− 1.08819i
$344$	645.679	0.101200
$345$	0	0
$346$	−3403.41	−0.528811
$347$	− 5160.09i	− 0.798294i	−0.916887	−	0.399147i	$-0.869306\pi$
$347$	− 5160.09i	− 0.798294i	0.916887	−	0.399147i	$-0.130694\pi$
$348$	6522.19i	1.00467i
$349$	9631.12	1.47720	0.738599	−	0.674145i	$-0.235488\pi$
$349$	9631.12	1.47720	0.738599	+	0.674145i	$0.235488\pi$
$350$	0	0
$351$	661.300	0.100563
$352$	2831.35i	0.428726i
$353$	− 7054.97i	− 1.06373i	−0.846828	−	0.531867i	$-0.821491\pi$
$353$	− 7054.97i	− 1.06373i	0.846828	−	0.531867i	$-0.178509\pi$
$354$	−8735.28	−1.31151
$355$	0	0
$356$	15485.6	2.30544
$357$	2533.30i	0.375565i
$358$	− 1735.59i	− 0.256226i
$359$	−13176.9	−1.93719	−0.968596	−	0.248640i	$-0.920016\pi$
$359$	−13176.9	−1.93719	−0.968596	+	0.248640i	$0.920016\pi$
$360$	0	0
$361$	7410.14	1.08035
$362$	− 14954.3i	− 2.17122i
$363$	363.000i	0.0524864i
$364$	−3637.40	−0.523769
$365$	0	0
$366$	1924.43	0.274841
$367$	− 652.403i	− 0.0927934i	−0.998923	−	0.0463967i	$-0.985226\pi$
$367$	− 652.403i	− 0.0927934i	0.998923	−	0.0463967i	$-0.0147738\pi$
$368$	9185.62i	1.30118i
$369$	−3133.20	−0.442026
$370$	0	0
$371$	−3335.06	−0.466705
$372$	− 8803.87i	− 1.22704i
$373$	− 8214.36i	− 1.14028i	−0.821548	−	0.570139i	$-0.806889\pi$
$373$	− 8214.36i	− 1.14028i	0.821548	−	0.570139i	$-0.193111\pi$
$374$	2537.90	0.350887
$375$	0	0
$376$	−2135.00	−0.292830
$377$	− 5514.26i	− 0.753312i
$378$	− 1744.83i	− 0.237419i
$379$	−12437.6	−1.68569	−0.842845	−	0.538157i	$-0.819121\pi$
$379$	−12437.6	−1.68569	−0.842845	+	0.538157i	$0.819121\pi$
$380$	0	0
$381$	−255.526	−0.0343596
$382$	− 12183.8i	− 1.63188i
$383$	3966.13i	0.529137i	0.964367	+	0.264569i	$0.0852296\pi$
$383$	3966.13i	0.529137i	−0.964367	+	0.264569i	$0.914770\pi$
$384$	−2615.56	−0.347591
$385$	0	0
$386$	5846.50	0.770930
$387$	− 834.861i	− 0.109660i
$388$	− 4817.78i	− 0.630376i
$389$	7656.45	0.997937	0.498969	−	0.866620i	$-0.333712\pi$
$389$	7656.45	0.997937	0.498969	+	0.866620i	$0.333712\pi$
$390$	0	0
$391$	10506.6	1.35892
$392$	− 741.141i	− 0.0954930i
$393$	− 1624.53i	− 0.208515i
$394$	720.717	0.0921554
$395$	0	0
$396$	−955.994	−0.121314
$397$	5023.47i	0.635065i	0.948247	+	0.317533i	$0.102854\pi$
$397$	5023.47i	0.635065i	−0.948247	+	0.317533i	$0.897146\pi$
$398$	− 15139.1i	− 1.90667i
$399$	−5511.34	−0.691509
$400$	0	0
$401$	−10128.4	−1.26132	−0.630659	−	0.776060i	$-0.717216\pi$
$401$	−10128.4	−1.26132	−0.630659	+	0.776060i	$0.717216\pi$
$402$	− 793.883i	− 0.0984958i
$403$	7443.33i	0.920046i
$404$	5513.43	0.678969
$405$	0	0
$406$	−14549.3	−1.77849
$407$	1203.20i	0.146537i
$408$	1146.56i	0.139125i
$409$	−11872.6	−1.43536	−0.717680	−	0.696373i	$-0.754796\pi$
$409$	−11872.6	−1.43536	−0.717680	+	0.696373i	$0.754796\pi$
$410$	0	0
$411$	−107.318	−0.0128798
$412$	10145.5i	1.21319i
$413$	− 10657.1i	− 1.26974i
$414$	−7236.46	−0.859064
$415$	0	0
$416$	6304.28	0.743012
$417$	4437.32i	0.521095i
$418$	5521.33i	0.646070i
$419$	−12257.3	−1.42914	−0.714571	−	0.699563i	$-0.753378\pi$
$419$	−12257.3	−1.42914	−0.714571	+	0.699563i	$0.753378\pi$
$420$	0	0
$421$	6571.84	0.760789	0.380394	−	0.924824i	$-0.375788\pi$
$421$	6571.84	0.760789	0.380394	+	0.924824i	$0.375788\pi$
$422$	13383.4i	1.54382i
$423$	2760.55i	0.317311i
$424$	−1509.43	−0.172887
$425$	0	0
$426$	−6987.39	−0.794695
$427$	2347.82i	0.266087i
$428$	18062.4i	2.03990i
$429$	808.256	0.0909626
$430$	0	0
$431$	6413.42	0.716760	0.358380	−	0.933576i	$-0.383329\pi$
$431$	6413.42	0.716760	0.358380	+	0.933576i	$0.383329\pi$
$432$	1296.11i	0.144349i
$433$	− 10320.0i	− 1.14537i	−0.819775	−	0.572685i	$-0.805902\pi$
$433$	− 10320.0i	− 1.14537i	0.819775	−	0.572685i	$-0.194098\pi$
$434$	19639.1	2.17214
$435$	0	0
$436$	−6347.08	−0.697179
$437$	22857.6i	2.50212i
$438$	− 1549.40i	− 0.169025i
$439$	−5316.31	−0.577981	−0.288991	−	0.957332i	$-0.593320\pi$
$439$	−5316.31	−0.577981	−0.288991	+	0.957332i	$0.593320\pi$
$440$	0	0
$441$	−958.293	−0.103476
$442$	− 5650.88i	− 0.608111i
$443$	− 6180.96i	− 0.662904i	−0.943472	−	0.331452i	$-0.892462\pi$
$443$	− 6180.96i	− 0.662904i	0.943472	−	0.331452i	$-0.107538\pi$
$444$	−3168.74	−0.338698
$445$	0	0
$446$	−22677.8	−2.40767
$447$	− 5337.86i	− 0.564814i
$448$	− 10727.6i	− 1.13132i
$449$	8468.27	0.890072	0.445036	−	0.895513i	$-0.353191\pi$
$449$	8468.27	0.890072	0.445036	+	0.895513i	$0.353191\pi$
$450$	0	0
$451$	−3829.46	−0.399828
$452$	11050.7i	1.14996i
$453$	− 546.176i	− 0.0566481i
$454$	−28572.3	−2.95367
$455$	0	0
$456$	−2494.40	−0.256164
$457$	− 11707.1i	− 1.19833i	−0.800627	−	0.599163i	$-0.795500\pi$
$457$	− 11707.1i	− 1.19833i	0.800627	−	0.599163i	$-0.204500\pi$
$458$	19313.0i	1.97039i
$459$	1482.49	0.150756
$460$	0	0
$461$	−16533.1	−1.67034	−0.835169	−	0.549994i	$-0.814630\pi$
$461$	−16533.1	−1.67034	−0.835169	+	0.549994i	$0.814630\pi$
$462$	− 2132.57i	− 0.214753i
$463$	− 15065.7i	− 1.51223i	−0.654436	−	0.756117i	$-0.727094\pi$
$463$	− 15065.7i	− 1.51223i	0.654436	−	0.756117i	$-0.272906\pi$
$464$	10807.6	1.08132
$465$	0	0
$466$	24141.6	2.39986
$467$	− 17843.1i	− 1.76806i	−0.467433	−	0.884028i	$-0.654821\pi$
$467$	− 17843.1i	− 1.76806i	0.467433	−	0.884028i	$-0.345179\pi$
$468$	2128.62i	0.210246i
$469$	968.545	0.0953587
$470$	0	0
$471$	−4739.67	−0.463678
$472$	− 4823.35i	− 0.470366i
$473$	− 1020.39i	− 0.0991910i
$474$	6007.06	0.582096
$475$	0	0
$476$	−8154.28	−0.785191
$477$	1951.68i	0.187340i
$478$	6.93786i	0 0.000663871i
$479$	6103.98	0.582250	0.291125	−	0.956685i	$-0.405970\pi$
$479$	6103.98	0.582250	0.291125	+	0.956685i	$0.405970\pi$
$480$	0	0
$481$	2679.05	0.253959
$482$	− 26475.8i	− 2.50195i
$483$	− 8828.55i	− 0.831703i
$484$	−1168.44	−0.109733
$485$	0	0
$486$	−1021.08	−0.0953025
$487$	487.182i	0.0453313i	0.999743	+	0.0226656i	$0.00721531\pi$
$487$	487.182i	0.0453313i	−0.999743	+	0.0226656i	$0.992785\pi$
$488$	1062.61i	0.0985699i
$489$	5875.47	0.543350
$490$	0	0
$491$	−12160.8	−1.11774	−0.558870	−	0.829256i	$-0.688765\pi$
$491$	−12160.8	−1.11774	−0.558870	+	0.829256i	$0.688765\pi$
$492$	− 10085.2i	− 0.924142i
$493$	− 12361.8i	− 1.12930i
$494$	12293.8	1.11968
$495$	0	0
$496$	−14588.5	−1.32065
$497$	− 8524.68i	− 0.769384i
$498$	11513.7i	1.03603i
$499$	−12827.4	−1.15076	−0.575382	−	0.817885i	$-0.695147\pi$
$499$	−12827.4	−1.15076	−0.575382	+	0.817885i	$0.695147\pi$
$500$	0	0
$501$	−1331.18	−0.118708
$502$	29203.1i	2.59641i
$503$	10573.7i	0.937289i	0.883387	+	0.468644i	$0.155257\pi$
$503$	10573.7i	0.937289i	−0.883387	+	0.468644i	$0.844743\pi$
$504$	963.439	0.0851488
$505$	0	0
$506$	−8844.56	−0.777053
$507$	4791.34i	0.419706i
$508$	− 822.497i	− 0.0718354i
$509$	6591.24	0.573971	0.286986	−	0.957935i	$-0.407347\pi$
$509$	6591.24	0.573971	0.286986	+	0.957935i	$0.407347\pi$
$510$	0	0
$511$	1890.28	0.163642
$512$	15029.1i	1.29726i
$513$	3225.25i	0.277579i
$514$	11747.8	1.00812
$515$	0	0
$516$	2687.28	0.229265
$517$	3374.00i	0.287018i
$518$	− 7068.63i	− 0.599571i
$519$	−2429.87	−0.205510
$520$	0	0
$521$	−12331.0	−1.03691	−0.518454	−	0.855105i	$-0.673492\pi$
$521$	−12331.0	−1.03691	−0.518454	+	0.855105i	$0.673492\pi$
$522$	8514.26i	0.713907i
$523$	17902.2i	1.49677i	0.663265	+	0.748385i	$0.269170\pi$
$523$	17902.2i	1.49677i	−0.663265	+	0.748385i	$0.730830\pi$
$524$	5229.08	0.435942
$525$	0	0
$526$	17587.3	1.45787
$527$	16686.4i	1.37926i
$528$	1584.13i	0.130569i
$529$	−24448.3	−2.00939
$530$	0	0
$531$	−6236.57	−0.509688
$532$	− 17740.1i	− 1.44573i
$533$	8526.68i	0.692930i
$534$	20215.4	1.63822
$535$	0	0
$536$	438.357	0.0353249
$537$	− 1239.13i	− 0.0995762i
$538$	8085.93i	0.647973i
$539$	−1171.25	−0.0935977
$540$	0	0
$541$	−7506.67	−0.596556	−0.298278	−	0.954479i	$-0.596412\pi$
$541$	−7506.67	−0.596556	−0.298278	+	0.954479i	$0.596412\pi$
$542$	10388.8i	0.823315i
$543$	− 10676.7i	− 0.843793i
$544$	14132.9	1.11386
$545$	0	0
$546$	−4748.38	−0.372183
$547$	4579.71i	0.357978i	0.983851	+	0.178989i	$0.0572827\pi$
$547$	4579.71i	0.357978i	−0.983851	+	0.178989i	$0.942717\pi$
$548$	− 345.439i	− 0.0269278i
$549$	1373.95	0.106810
$550$	0	0
$551$	26893.7	2.07933
$552$	− 3995.74i	− 0.308098i
$553$	7328.67i	0.563556i
$554$	6147.17	0.471423
$555$	0	0
$556$	−14283.0	−1.08945
$557$	1839.13i	0.139904i	0.997550	+	0.0699519i	$0.0222846\pi$
$557$	1839.13i	0.139904i	−0.997550	+	0.0699519i	$0.977715\pi$
$558$	− 11492.8i	− 0.871919i
$559$	−2271.99	−0.171905
$560$	0	0
$561$	1811.94	0.136364
$562$	− 16624.8i	− 1.24782i
$563$	− 1870.00i	− 0.139984i	−0.997548	−	0.0699921i	$-0.977703\pi$
$563$	− 1870.00i	− 0.139984i	0.997548	−	0.0699921i	$-0.0222974\pi$
$564$	−8885.75	−0.663400
$565$	0	0
$566$	17561.2	1.30416
$567$	− 1245.72i	− 0.0922672i
$568$	− 3858.21i	− 0.285012i
$569$	6673.53	0.491685	0.245843	−	0.969310i	$-0.420935\pi$
$569$	6673.53	0.491685	0.245843	+	0.969310i	$0.420935\pi$
$570$	0	0
$571$	15176.4	1.11228	0.556140	−	0.831088i	$-0.312282\pi$
$571$	15176.4	1.11228	0.556140	+	0.831088i	$0.312282\pi$
$572$	2601.64i	0.190175i
$573$	− 8698.64i	− 0.634190i
$574$	22497.5	1.63594
$575$	0	0
$576$	−6277.82	−0.454124
$577$	13861.6i	1.00011i	0.865993	+	0.500056i	$0.166687\pi$
$577$	13861.6i	1.00011i	−0.865993	+	0.500056i	$0.833313\pi$
$578$	7976.18i	0.573988i
$579$	4174.12	0.299604
$580$	0	0
$581$	−14046.8	−1.00303
$582$	− 6289.28i	− 0.447936i
$583$	2385.39i	0.169456i
$584$	855.528	0.0606198
$585$	0	0
$586$	−23854.9	−1.68163
$587$	− 26717.1i	− 1.87859i	−0.343113	−	0.939294i	$-0.611482\pi$
$587$	− 26717.1i	− 1.87859i	0.343113	−	0.939294i	$-0.388518\pi$
$588$	− 3084.59i	− 0.216337i
$589$	−36302.1	−2.53956
$590$	0	0
$591$	514.557	0.0358140
$592$	5250.77i	0.364536i
$593$	13459.5i	0.932066i	0.884767	+	0.466033i	$0.154317\pi$
$593$	13459.5i	0.932066i	−0.884767	+	0.466033i	$0.845683\pi$
$594$	−1247.98	−0.0862043
$595$	0	0
$596$	17181.7	1.18085
$597$	− 10808.6i	− 0.740982i
$598$	19693.3i	1.34669i
$599$	8052.34	0.549265	0.274632	−	0.961549i	$-0.411444\pi$
$599$	8052.34	0.549265	0.274632	+	0.961549i	$0.411444\pi$
$600$	0	0
$601$	−11113.5	−0.754292	−0.377146	−	0.926154i	$-0.623094\pi$
$601$	−11113.5	−0.754292	−0.377146	+	0.926154i	$0.623094\pi$
$602$	5994.60i	0.405850i
$603$	− 566.794i	− 0.0382780i
$604$	1758.05	0.118434
$605$	0	0
$606$	7197.40	0.482466
$607$	27871.8i	1.86372i	0.362813	+	0.931862i	$0.381816\pi$
$607$	27871.8i	1.86372i	−0.362813	+	0.931862i	$0.618184\pi$
$608$	30746.8i	2.05090i
$609$	−10387.5	−0.691169
$610$	0	0
$611$	7512.55	0.497423
$612$	4771.90i	0.315184i
$613$	1266.99i	0.0834798i	0.999129	+	0.0417399i	$0.0132901\pi$
$613$	1266.99i	0.0834798i	−0.999129	+	0.0417399i	$0.986710\pi$
$614$	−4290.02	−0.281973
$615$	0	0
$616$	1177.54	0.0770200
$617$	− 23103.8i	− 1.50750i	−0.657164	−	0.753748i	$-0.728244\pi$
$617$	− 23103.8i	− 1.50750i	0.657164	−	0.753748i	$-0.271756\pi$
$618$	13244.3i	0.862075i
$619$	23151.2	1.50327	0.751636	−	0.659578i	$-0.229265\pi$
$619$	23151.2	1.50327	0.751636	+	0.659578i	$0.229265\pi$
$620$	0	0
$621$	−5166.48	−0.333855
$622$	− 35040.2i	− 2.25881i
$623$	24663.0i	1.58604i
$624$	3527.22	0.226285
$625$	0	0
$626$	22039.6	1.40716
$627$	3941.97i	0.251080i
$628$	− 15256.2i	− 0.969410i
$629$	6005.86	0.380714
$630$	0	0
$631$	17741.1	1.11927	0.559636	−	0.828738i	$-0.310941\pi$
$631$	17741.1	1.11927	0.559636	+	0.828738i	$0.310941\pi$
$632$	3316.91i	0.208765i
$633$	9555.07i	0.599968i
$634$	4524.30	0.283411
$635$	0	0
$636$	−6282.14	−0.391672
$637$	2607.90i	0.162211i
$638$	10406.3i	0.645753i
$639$	−4988.66	−0.308839
$640$	0	0
$641$	11428.1	0.704187	0.352094	−	0.935965i	$-0.385470\pi$
$641$	11428.1	0.704187	0.352094	+	0.935965i	$0.385470\pi$
$642$	23579.1i	1.44952i
$643$	27018.9i	1.65711i	0.559909	+	0.828554i	$0.310836\pi$
$643$	27018.9i	1.65711i	−0.559909	+	0.828554i	$0.689164\pi$
$644$	28417.6	1.73884
$645$	0	0
$646$	27560.1	1.67854
$647$	− 8637.82i	− 0.524865i	−0.964950	−	0.262433i	$-0.915475\pi$
$647$	− 8637.82i	− 0.524865i	0.964950	−	0.262433i	$-0.0845247\pi$
$648$	− 563.807i	− 0.0341796i
$649$	−7622.48	−0.461030
$650$	0	0
$651$	14021.4	0.844149
$652$	18912.2i	1.13598i
$653$	− 2186.14i	− 0.131011i	−0.997852	−	0.0655055i	$-0.979134\pi$
$653$	− 2186.14i	− 0.131011i	0.997852	−	0.0655055i	$-0.0208660\pi$
$654$	−8285.67	−0.495406
$655$	0	0
$656$	−16711.8	−0.994641
$657$	− 1106.19i	− 0.0656876i
$658$	− 19821.7i	− 1.17436i
$659$	−32361.9	−1.91296	−0.956479	−	0.291800i	$-0.905746\pi$
$659$	−32361.9	−1.91296	−0.956479	+	0.291800i	$0.905746\pi$
$660$	0	0
$661$	6029.07	0.354771	0.177385	−	0.984141i	$-0.443236\pi$
$661$	6029.07	0.354771	0.177385	+	0.984141i	$0.443236\pi$
$662$	− 7052.90i	− 0.414076i
$663$	− 4034.46i	− 0.236328i
$664$	−6357.51	−0.371565
$665$	0	0
$666$	−4136.57	−0.240674
$667$	43080.8i	2.50089i
$668$	− 4284.84i	− 0.248182i
$669$	−16190.8	−0.935685
$670$	0	0
$671$	1679.27	0.0966135
$672$	− 11875.7i	− 0.681718i
$673$	7367.28i	0.421973i	0.977489	+	0.210986i	$0.0676676\pi$
$673$	7367.28i	0.421973i	−0.977489	+	0.210986i	$0.932332\pi$
$674$	29218.3	1.66980
$675$	0	0
$676$	−15422.5	−0.877477
$677$	7017.15i	0.398362i	0.979963	+	0.199181i	$0.0638282\pi$
$677$	7017.15i	0.398362i	−0.979963	+	0.199181i	$0.936172\pi$
$678$	14425.9i	0.817144i
$679$	7672.97	0.433670
$680$	0	0
$681$	−20399.2	−1.14787
$682$	− 14046.8i	− 0.788680i
$683$	16608.1i	0.930442i	0.885195	+	0.465221i	$0.154025\pi$
$683$	16608.1i	0.930442i	−0.885195	+	0.465221i	$0.845975\pi$
$684$	−10381.5	−0.580333
$685$	0	0
$686$	29046.7	1.61663
$687$	13788.6i	0.765745i
$688$	− 4452.96i	− 0.246755i
$689$	5311.31	0.293679
$690$	0	0
$691$	3349.66	0.184409	0.0922047	−	0.995740i	$-0.470609\pi$
$691$	3349.66	0.184409	0.0922047	+	0.995740i	$0.470609\pi$
$692$	− 7821.36i	− 0.429658i
$693$	− 1522.55i	− 0.0834588i
$694$	21682.5	1.18596
$695$	0	0
$696$	−4701.31	−0.256038
$697$	19115.0i	1.03878i
$698$	40469.6i	2.19455i
$699$	17235.9	0.932649
$700$	0	0
$701$	14755.7	0.795030	0.397515	−	0.917596i	$-0.369873\pi$
$701$	14755.7	0.795030	0.397515	+	0.917596i	$0.369873\pi$
$702$	2778.76i	0.149398i
$703$	13066.1i	0.700990i
$704$	−7672.89	−0.410771
$705$	0	0
$706$	29644.7	1.58030
$707$	8780.90i	0.467100i
$708$	− 20074.5i	− 1.06560i
$709$	−27937.6	−1.47985	−0.739927	−	0.672687i	$-0.765140\pi$
$709$	−27937.6	−1.47985	−0.739927	+	0.672687i	$0.765140\pi$
$710$	0	0
$711$	4288.75	0.226218
$712$	11162.3i	0.587536i
$713$	− 58151.9i	− 3.05442i
$714$	−10644.8	−0.557946
$715$	0	0
$716$	3988.56	0.208183
$717$	4.95329i	0 0.000257997i
$718$	− 55369.0i	− 2.87793i
$719$	23650.0	1.22670	0.613349	−	0.789812i	$-0.289822\pi$
$719$	23650.0	1.22670	0.613349	+	0.789812i	$0.289822\pi$
$720$	0	0
$721$	−16158.1	−0.834618
$722$	31137.2i	1.60499i
$723$	− 18902.5i	− 0.972325i
$724$	34366.4	1.76411
$725$	0	0
$726$	−1525.31	−0.0779748
$727$	9880.21i	0.504039i	0.967722	+	0.252020i	$0.0810948\pi$
$727$	9880.21i	0.504039i	−0.967722	+	0.252020i	$0.918905\pi$
$728$	− 2621.90i	− 0.133481i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−5093.32	−0.257706
$732$	4422.52i	0.223308i
$733$	− 7315.37i	− 0.368621i	−0.982868	−	0.184311i	$-0.940995\pi$
$733$	− 7315.37i	− 0.368621i	0.982868	−	0.184311i	$-0.0590052\pi$
$734$	2741.38	0.137856
$735$	0	0
$736$	−49252.9	−2.46670
$737$	− 692.749i	− 0.0346238i
$738$	− 13165.6i	− 0.656683i
$739$	−18857.1	−0.938661	−0.469331	−	0.883022i	$-0.655505\pi$
$739$	−18857.1	−0.938661	−0.469331	+	0.883022i	$0.655505\pi$
$740$	0	0
$741$	8777.18	0.435139
$742$	− 14013.8i	− 0.693346i
$743$	18305.4i	0.903851i	0.892056	+	0.451925i	$0.149263\pi$
$743$	18305.4i	0.903851i	−0.892056	+	0.451925i	$0.850737\pi$
$744$	6345.98	0.312708
$745$	0	0
$746$	34516.5	1.69402
$747$	8220.24i	0.402627i
$748$	5832.33i	0.285095i
$749$	−28766.8	−1.40336
$750$	0	0
$751$	−8697.79	−0.422619	−0.211310	−	0.977419i	$-0.567773\pi$
$751$	−8697.79	−0.422619	−0.211310	+	0.977419i	$0.567773\pi$
$752$	14724.1i	0.714008i
$753$	20849.6i	1.00903i
$754$	23170.7	1.11913
$755$	0	0
$756$	4009.78	0.192902
$757$	1545.04i	0.0741814i	0.999312	+	0.0370907i	$0.0118090\pi$
$757$	1545.04i	0.0741814i	−0.999312	+	0.0370907i	$0.988191\pi$
$758$	− 52262.3i	− 2.50429i
$759$	−6314.59	−0.301983
$760$	0	0
$761$	10359.5	0.493472	0.246736	−	0.969083i	$-0.420642\pi$
$761$	10359.5	0.493472	0.246736	+	0.969083i	$0.420642\pi$
$762$	− 1073.71i	− 0.0510452i
$763$	− 10108.6i	− 0.479627i
$764$	27999.5	1.32590
$765$	0	0
$766$	−16665.5	−0.786096
$767$	16972.2i	0.798997i
$768$	5750.35i	0.270179i
$769$	35625.3	1.67059	0.835293	−	0.549806i	$-0.185298\pi$
$769$	35625.3	1.67059	0.835293	+	0.549806i	$0.185298\pi$
$770$	0	0
$771$	8387.35	0.391781
$772$	13435.8i	0.626380i
$773$	− 290.303i	− 0.0135077i	−0.999977	−	0.00675387i	$-0.997850\pi$
$773$	− 290.303i	− 0.0135077i	0.999977	−	0.00675387i	$-0.00214984\pi$
$774$	3508.05	0.162913
$775$	0	0
$776$	3472.74	0.160650
$777$	− 5046.66i	− 0.233009i
$778$	32172.1i	1.48255i
$779$	−41585.7	−1.91266
$780$	0	0
$781$	−6097.25	−0.279356
$782$	44148.2i	2.01884i
$783$	6078.77i	0.277443i
$784$	−5111.32	−0.232841
$785$	0	0
$786$	6826.20	0.309774
$787$	6676.06i	0.302383i	0.988504	+	0.151192i	$0.0483111\pi$
$787$	6676.06i	0.302383i	−0.988504	+	0.151192i	$0.951689\pi$
$788$	1656.28i	0.0748761i
$789$	12556.5	0.566568
$790$	0	0
$791$	−17599.7	−0.791119
$792$	− 689.097i	− 0.0309167i
$793$	− 3739.07i	− 0.167438i
$794$	−21108.4	−0.943465
$795$	0	0
$796$	34791.1	1.54917
$797$	− 22698.2i	− 1.00880i	−0.863471	−	0.504399i	$-0.831714\pi$
$797$	− 22698.2i	− 1.00880i	0.863471	−	0.504399i	$-0.168286\pi$
$798$	− 23158.4i	− 1.02732i
$799$	16841.5	0.745696
$800$	0	0
$801$	14432.8	0.636654
$802$	− 42559.2i	− 1.87384i
$803$	− 1352.02i	− 0.0594167i
$804$	1824.42	0.0800277
$805$	0	0
$806$	−31276.6	−1.36684
$807$	5772.97i	0.251819i
$808$	3974.18i	0.173034i
$809$	−40727.4	−1.76996	−0.884982	−	0.465625i	$-0.845829\pi$
$809$	−40727.4	−1.76996	−0.884982	+	0.465625i	$0.845829\pi$
$810$	0	0
$811$	−10202.3	−0.441740	−0.220870	−	0.975303i	$-0.570890\pi$
$811$	−10202.3	−0.441740	−0.220870	+	0.975303i	$0.570890\pi$
$812$	− 33435.6i	− 1.44502i
$813$	7417.09i	0.319962i
$814$	−5055.81	−0.217698
$815$	0	0
$816$	7907.28	0.339228
$817$	− 11080.8i	− 0.474501i
$818$	− 49888.3i	− 2.13240i
$819$	−3390.11	−0.144640
$820$	0	0
$821$	9771.65	0.415387	0.207694	−	0.978194i	$-0.433404\pi$
$821$	9771.65	0.415387	0.207694	+	0.978194i	$0.433404\pi$
$822$	− 450.947i	− 0.0191345i
$823$	− 43074.7i	− 1.82441i	−0.409736	−	0.912204i	$-0.634379\pi$
$823$	− 43074.7i	− 1.82441i	0.409736	−	0.912204i	$-0.365621\pi$
$824$	−7313.06	−0.309178
$825$	0	0
$826$	44780.9	1.88635
$827$	− 22853.5i	− 0.960937i	−0.877012	−	0.480468i	$-0.840467\pi$
$827$	− 22853.5i	− 0.960937i	0.877012	−	0.480468i	$-0.159533\pi$
$828$	− 16630.1i	− 0.697988i
$829$	4593.74	0.192457	0.0962287	−	0.995359i	$-0.469322\pi$
$829$	4593.74	0.192457	0.0962287	+	0.995359i	$0.469322\pi$
$830$	0	0
$831$	4388.78	0.183207
$832$	17084.4i	0.711895i
$833$	5846.35i	0.243174i
$834$	−18645.5	−0.774148
$835$	0	0
$836$	−12688.5	−0.524931
$837$	− 8205.33i	− 0.338850i
$838$	− 51504.9i	− 2.12316i
$839$	−21907.5	−0.901469	−0.450734	−	0.892658i	$-0.648838\pi$
$839$	−21907.5	−0.901469	−0.450734	+	0.892658i	$0.648838\pi$
$840$	0	0
$841$	26298.9	1.07831
$842$	27614.7i	1.13024i
$843$	− 11869.3i	− 0.484936i
$844$	−30756.2	−1.25435
$845$	0	0
$846$	−11599.7	−0.471403
$847$	− 1860.90i	− 0.0754913i
$848$	10409.8i	0.421551i
$849$	12537.8	0.506829
$850$	0	0
$851$	−20930.4	−0.843107
$852$	− 16057.7i	− 0.645689i
$853$	− 8159.43i	− 0.327519i	−0.986500	−	0.163759i	$-0.947638\pi$
$853$	− 8159.43i	− 0.327519i	0.986500	−	0.163759i	$-0.0523621\pi$
$854$	−9865.47	−0.395304
$855$	0	0
$856$	−13019.7	−0.519863
$857$	− 42705.7i	− 1.70222i	−0.524990	−	0.851108i	$-0.675931\pi$
$857$	− 42705.7i	− 1.70222i	0.524990	−	0.851108i	$-0.324069\pi$
$858$	3396.26i	0.135136i
$859$	27898.2	1.10812	0.554060	−	0.832477i	$-0.313078\pi$
$859$	27898.2	1.10812	0.554060	+	0.832477i	$0.313078\pi$
$860$	0	0
$861$	16062.1	0.635768
$862$	26949.0i	1.06483i
$863$	− 19559.0i	− 0.771492i	−0.922605	−	0.385746i	$-0.873944\pi$
$863$	− 19559.0i	− 0.771492i	0.922605	−	0.385746i	$-0.126056\pi$
$864$	−6949.68	−0.273649
$865$	0	0
$866$	43364.1	1.70158
$867$	5694.61i	0.223067i
$868$	45132.5i	1.76486i
$869$	5241.81	0.204621
$870$	0	0
$871$	−1542.47	−0.0600054
$872$	− 4575.08i	− 0.177674i
$873$	− 4490.24i	− 0.174080i
$874$	−96046.7	−3.71720
$875$	0	0
$876$	3560.66	0.137333
$877$	21973.8i	0.846068i	0.906114	+	0.423034i	$0.139035\pi$
$877$	21973.8i	0.846068i	−0.906114	+	0.423034i	$0.860965\pi$
$878$	− 22339.0i	− 0.858660i
$879$	−17031.3	−0.653527
$880$	0	0
$881$	8425.63	0.322210	0.161105	−	0.986937i	$-0.448494\pi$
$881$	8425.63	0.322210	0.161105	+	0.986937i	$0.448494\pi$
$882$	− 4026.71i	− 0.153726i
$883$	8349.89i	0.318229i	0.987260	+	0.159114i	$0.0508639\pi$
$883$	8349.89i	0.318229i	−0.987260	+	0.159114i	$0.949136\pi$
$884$	12986.3	0.494089
$885$	0	0
$886$	25972.2	0.984823
$887$	40472.6i	1.53206i	0.642805	+	0.766030i	$0.277771\pi$
$887$	40472.6i	1.53206i	−0.642805	+	0.766030i	$0.722229\pi$
$888$	− 2284.08i	− 0.0863163i
$889$	1309.94	0.0494195
$890$	0	0
$891$	−891.000	−0.0335013
$892$	− 52115.6i	− 1.95623i
$893$	36639.7i	1.37301i
$894$	22429.5	0.839099
$895$	0	0
$896$	13408.5	0.499940
$897$	14060.1i	0.523358i
$898$	35583.4i	1.32231i
$899$	−68420.3	−2.53831
$900$	0	0
$901$	11906.8	0.440259
$902$	− 16091.3i	− 0.593992i
$903$	4279.86i	0.157724i
$904$	−7965.53	−0.293064
$905$	0	0
$906$	2295.01	0.0841574
$907$	40036.9i	1.46572i	0.680382	+	0.732858i	$0.261814\pi$
$907$	40036.9i	1.46572i	−0.680382	+	0.732858i	$0.738186\pi$
$908$	− 65661.8i	− 2.39985i
$909$	5138.60	0.187499
$910$	0	0
$911$	−40429.0	−1.47033	−0.735166	−	0.677887i	$-0.762896\pi$
$911$	−40429.0	−1.47033	−0.735166	+	0.677887i	$0.762896\pi$
$912$	17202.7i	0.624604i
$913$	10047.0i	0.364190i
$914$	49192.8	1.78026
$915$	0	0
$916$	−44383.1	−1.60094
$917$	8328.03i	0.299908i
$918$	6229.39i	0.223966i
$919$	42179.2	1.51400	0.756998	−	0.653417i	$-0.226665\pi$
$919$	42179.2	1.51400	0.756998	+	0.653417i	$0.226665\pi$
$920$	0	0
$921$	−3062.87	−0.109582
$922$	− 69471.7i	− 2.48148i
$923$	13576.1i	0.484143i
$924$	4900.84	0.174487
$925$	0	0
$926$	63305.7	2.24660
$927$	9455.76i	0.335025i
$928$	57950.0i	2.04989i
$929$	36655.4	1.29454	0.647269	−	0.762262i	$-0.275911\pi$
$929$	36655.4	1.29454	0.647269	+	0.762262i	$0.275911\pi$
$930$	0	0
$931$	−12719.1	−0.447744
$932$	55479.5i	1.94988i
$933$	− 25017.0i	− 0.877834i
$934$	74976.3	2.62666
$935$	0	0
$936$	−1534.34	−0.0535807
$937$	− 30247.9i	− 1.05459i	−0.849681	−	0.527297i	$-0.823205\pi$
$937$	− 30247.9i	− 1.05459i	0.849681	−	0.527297i	$-0.176795\pi$
$938$	4069.79i	0.141667i
$939$	15735.2	0.546858
$940$	0	0
$941$	−14708.3	−0.509541	−0.254770	−	0.967002i	$-0.582000\pi$
$941$	−14708.3	−0.509541	−0.254770	+	0.967002i	$0.582000\pi$
$942$	− 19915.9i	− 0.688849i
$943$	− 66615.7i	− 2.30043i
$944$	−33264.5	−1.14689
$945$	0	0
$946$	4287.62	0.147360
$947$	− 14714.8i	− 0.504929i	−0.967606	−	0.252464i	$-0.918759\pi$
$947$	− 14714.8i	− 0.504929i	0.967606	−	0.252464i	$-0.0812410\pi$
$948$	13804.8i	0.472952i
$949$	−3010.40	−0.102973
$950$	0	0
$951$	3230.13	0.110141
$952$	− 5877.75i	− 0.200104i
$953$	− 13658.7i	− 0.464270i	−0.972684	−	0.232135i	$-0.925429\pi$
$953$	− 13658.7i	− 0.464270i	0.972684	−	0.232135i	$-0.0745711\pi$
$954$	−8200.90	−0.278316
$955$	0	0
$956$	−15.9438	−0.000539394 0
$957$	7429.61i	0.250956i
$958$	25648.7i	0.865002i
$959$	550.159	0.0185251
$960$	0	0
$961$	62565.0	2.10013
$962$	11257.3i	0.377286i
$963$	16834.4i	0.563323i
$964$	60844.0	2.03283
$965$	0	0
$966$	37097.2	1.23559
$967$	17355.6i	0.577164i	0.957455	+	0.288582i	$0.0931838\pi$
$967$	17355.6i	0.577164i	−0.957455	+	0.288582i	$0.906816\pi$
$968$	− 842.229i	− 0.0279652i
$969$	19676.6	0.652324
$970$	0	0
$971$	9629.08	0.318241	0.159120	−	0.987259i	$-0.449134\pi$
$971$	9629.08	0.318241	0.159120	+	0.987259i	$0.449134\pi$
$972$	− 2346.53i	− 0.0774331i
$973$	− 22747.6i	− 0.749492i
$974$	−2047.12	−0.0673450
$975$	0	0
$976$	7328.34	0.240343
$977$	16039.2i	0.525221i	0.964902	+	0.262610i	$0.0845834\pi$
$977$	16039.2i	0.525221i	−0.964902	+	0.262610i	$0.915417\pi$
$978$	24688.5i	0.807210i
$979$	17640.1	0.575875
$980$	0	0
$981$	−5915.57	−0.192528
$982$	− 51099.3i	− 1.66053i
$983$	− 56471.0i	− 1.83229i	−0.400843	−	0.916147i	$-0.631283\pi$
$983$	− 56471.0i	− 1.83229i	0.400843	−	0.916147i	$-0.368717\pi$
$984$	7269.62	0.235515
$985$	0	0
$986$	51943.8	1.67772
$987$	− 14151.8i	− 0.456389i
$988$	28252.3i	0.909742i
$989$	17750.2	0.570701
$990$	0	0
$991$	7278.03	0.233294	0.116647	−	0.993173i	$-0.462785\pi$
$991$	7278.03	0.233294	0.116647	+	0.993173i	$0.462785\pi$
$992$	− 78222.8i	− 2.50361i
$993$	− 5035.43i	− 0.160921i
$994$	35820.4	1.14301
$995$	0	0
$996$	−26459.6	−0.841771
$997$	6208.44i	0.197215i	0.995126	+	0.0986075i	$0.0314388\pi$
$997$	6208.44i	0.197215i	−0.995126	+	0.0986075i	$0.968561\pi$
$998$	− 53900.1i	− 1.70960i
$999$	−2953.31	−0.0935323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.4.c.p.199.7		8
5.2	odd	4		165.4.a.h.1.1	✓	4
5.3	odd	4		825.4.a.t.1.4		4
5.4	even	2	inner	825.4.c.p.199.2		8
15.2	even	4		495.4.a.m.1.4		4
15.8	even	4		2475.4.a.be.1.1		4
55.32	even	4		1815.4.a.t.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.h.1.1	✓	4	5.2	odd	4
495.4.a.m.1.4		4	15.2	even	4
825.4.a.t.1.4		4	5.3	odd	4
825.4.c.p.199.2		8	5.4	even	2	inner
825.4.c.p.199.7		8	1.1	even	1	trivial
1815.4.a.t.1.4		4	55.32	even	4
2475.4.a.be.1.1		4	15.8	even	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+4.20196i q^{2} +3.00000i q^{3} -9.65650 q^{4} -12.6059 q^{6} -15.3793i q^{7} -6.96057i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+4.20196i q^{2} +3.00000i q^{3} -9.65650 q^{4} -12.6059 q^{6} -15.3793i q^{7} -6.96057i q^{8} -9.00000 q^{9} -11.0000 q^{11} -28.9695i q^{12} +24.4926i q^{13} +64.6233 q^{14} -48.0040 q^{16} +54.9072i q^{17} -37.8177i q^{18} -119.454 q^{19} +46.1379 q^{21} -46.2216i q^{22} -191.351i q^{23} +20.8817 q^{24} -102.917 q^{26} -27.0000i q^{27} +148.510i q^{28} -225.140 q^{29} +303.901 q^{31} -257.395i q^{32} -33.0000i q^{33} -230.718 q^{34} +86.9085 q^{36} -109.382i q^{37} -501.939i q^{38} -73.4778 q^{39} +348.133 q^{41} +193.870i q^{42} +92.7623i q^{43} +106.222 q^{44} +804.051 q^{46} -306.728i q^{47} -144.012i q^{48} +106.477 q^{49} -164.722 q^{51} -236.513i q^{52} -216.854i q^{53} +113.453 q^{54} -107.049 q^{56} -358.361i q^{57} -946.029i q^{58} +692.952 q^{59} -152.661 q^{61} +1276.98i q^{62} +138.414i q^{63} +697.535 q^{64} +138.665 q^{66} +62.9772i q^{67} -530.211i q^{68} +574.054 q^{69} +554.295 q^{71} +62.6452i q^{72} +122.911i q^{73} +459.619 q^{74} +1153.50 q^{76} +169.172i q^{77} -308.751i q^{78} -476.528 q^{79} +81.0000 q^{81} +1462.84i q^{82} -913.360i q^{83} -445.531 q^{84} -389.784 q^{86} -675.419i q^{87} +76.5663i q^{88} -1603.65 q^{89} +376.679 q^{91} +1847.78i q^{92} +911.704i q^{93} +1288.86 q^{94} +772.186 q^{96} +498.916i q^{97} +447.412i q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9	\( 8 q - 52 q^{4} + 24 q^{6} - 72 q^{9} - 88 q^{11} + 104 q^{14} + 132 q^{16} - 272 q^{19} + 204 q^{21} - 288 q^{24} - 640 q^{26} - 104 q^{29} + 984 q^{31} - 488 q^{34} + 468 q^{36} - 12 q^{39} + 536 q^{41} + 572 q^{44} + 736 q^{46} + 992 q^{49} + 444 q^{51} - 216 q^{54} - 1704 q^{56} + 2064 q^{59} + 232 q^{61} + 1836 q^{64} - 264 q^{66} + 384 q^{69} - 1840 q^{71} + 5712 q^{74} + 3144 q^{76} - 2304 q^{79} + 648 q^{81} + 120 q^{84} + 472 q^{86} + 2128 q^{89} + 5560 q^{91} + 2864 q^{94} + 1248 q^{96} + 792 q^{99}+O(q^{100}) \) 8 * q - 52 * q^4 + 24 * q^6 - 72 * q^9 - 88 * q^11 + 104 * q^14 + 132 * q^16 - 272 * q^19 + 204 * q^21 - 288 * q^24 - 640 * q^26 - 104 * q^29 + 984 * q^31 - 488 * q^34 + 468 * q^36 - 12 * q^39 + 536 * q^41 + 572 * q^44 + 736 * q^46 + 992 * q^49 + 444 * q^51 - 216 * q^54 - 1704 * q^56 + 2064 * q^59 + 232 * q^61 + 1836 * q^64 - 264 * q^66 + 384 * q^69 - 1840 * q^71 + 5712 * q^74 + 3144 * q^76 - 2304 * q^79 + 648 * q^81 + 120 * q^84 + 472 * q^86 + 2128 * q^89 + 5560 * q^91 + 2864 * q^94 + 1248 * q^96 + 792 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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