LMFDB - Embedded newform 525.4.d.o.274.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,4,Mod(274,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	525.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.9760027530$
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} + 40x^{6} + 488x^{4} + 1945x^{2} + 1936 $ x^8 + 40x^6 + 488x^4 + 1945*x^2 + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.8
Root			$4.56826i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.o.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.56826i q^{2} -3.00000i q^{3} -23.0055 q^{4} +16.7048 q^{6} -7.00000i q^{7} -83.5546i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+5.56826i q^{2} -3.00000i q^{3} -23.0055 q^{4} +16.7048 q^{6} -7.00000i q^{7} -83.5546i q^{8} -9.00000 q^{9} +23.2885 q^{11} +69.0165i q^{12} +46.5366i q^{13} +38.9778 q^{14} +281.210 q^{16} +76.0316i q^{17} -50.1143i q^{18} +114.605 q^{19} -21.0000 q^{21} +129.677i q^{22} -113.880i q^{23} -250.664 q^{24} -259.128 q^{26} +27.0000i q^{27} +161.039i q^{28} -120.470 q^{29} -182.048 q^{31} +897.411i q^{32} -69.8656i q^{33} -423.363 q^{34} +207.050 q^{36} -322.477i q^{37} +638.151i q^{38} +139.610 q^{39} -93.0481 q^{41} -116.933i q^{42} +452.579i q^{43} -535.765 q^{44} +634.113 q^{46} +402.565i q^{47} -843.629i q^{48} -49.0000 q^{49} +228.095 q^{51} -1070.60i q^{52} +495.787i q^{53} -150.343 q^{54} -584.882 q^{56} -343.815i q^{57} -670.808i q^{58} -496.707 q^{59} -265.742 q^{61} -1013.69i q^{62} +63.0000i q^{63} -2747.34 q^{64} +389.030 q^{66} +594.240i q^{67} -1749.14i q^{68} -341.640 q^{69} -510.099 q^{71} +751.991i q^{72} -470.181i q^{73} +1795.63 q^{74} -2636.55 q^{76} -163.020i q^{77} +777.383i q^{78} +487.916 q^{79} +81.0000 q^{81} -518.116i q^{82} +1250.53i q^{83} +483.116 q^{84} -2520.08 q^{86} +361.410i q^{87} -1945.86i q^{88} +1561.98 q^{89} +325.756 q^{91} +2619.87i q^{92} +546.145i q^{93} -2241.59 q^{94} +2692.23 q^{96} +21.5118i q^{97} -272.845i q^{98} -209.597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	$ 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) $ 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	5.56826i	1.96868i	0.176289	+	0.984339i	$0.443591\pi$
$2$	5.56826i	1.96868i	−0.176289	+	0.984339i	$0.556409\pi$
$3$	− 3.00000i	− 0.577350i
$3$	− 3.00000i	− 0.577350i
$4$	−23.0055	−2.87569
$5$	0	0
$5$	0	0
$6$	16.7048	1.13662
$7$	− 7.00000i	− 0.377964i
$7$	− 7.00000i	− 0.377964i
$8$	− 83.5546i	− 3.69263i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	23.2885	0.638342	0.319171	−	0.947697i	$-0.396596\pi$
$11$	23.2885	0.638342	0.319171	+	0.947697i	$0.396596\pi$
$12$	69.0165i	1.66028i
$13$	46.5366i	0.992840i	0.868082	+	0.496420i	$0.165352\pi$
$13$	46.5366i	0.992840i	−0.868082	+	0.496420i	$0.834648\pi$
$14$	38.9778	0.744090
$15$	0	0
$16$	281.210	4.39390
$17$	76.0316i	1.08473i	0.840144	+	0.542364i	$0.182470\pi$
$17$	76.0316i	1.08473i	−0.840144	+	0.542364i	$0.817530\pi$
$18$	− 50.1143i	− 0.656226i
$19$	114.605	1.38380	0.691901	−	0.721993i	$-0.256774\pi$
$19$	114.605	1.38380	0.691901	+	0.721993i	$0.256774\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	129.677i	1.25669i
$23$	− 113.880i	− 1.03242i	−0.856463	−	0.516209i	$-0.827343\pi$
$23$	− 113.880i	− 1.03242i	0.856463	−	0.516209i	$-0.172657\pi$
$24$	−250.664	−2.13194
$25$	0	0
$26$	−259.128	−1.95458
$27$	27.0000i	0.192450i
$28$	161.039i	1.08691i
$29$	−120.470	−0.771404	−0.385702	−	0.922623i	$-0.626041\pi$
$29$	−120.470	−0.771404	−0.385702	+	0.922623i	$0.626041\pi$
$30$	0	0
$31$	−182.048	−1.05474	−0.527369	−	0.849637i	$-0.676821\pi$
$31$	−182.048	−1.05474	−0.527369	+	0.849637i	$0.676821\pi$
$32$	897.411i	4.95754i
$33$	− 69.8656i	− 0.368547i
$34$	−423.363	−2.13548
$35$	0	0
$36$	207.050	0.958563
$37$	− 322.477i	− 1.43283i	−0.697673	−	0.716417i	$-0.745781\pi$
$37$	− 322.477i	− 1.43283i	0.697673	−	0.716417i	$-0.254219\pi$
$38$	638.151i	2.72426i
$39$	139.610	0.573217
$40$	0	0
$41$	−93.0481	−0.354431	−0.177215	−	0.984172i	$-0.556709\pi$
$41$	−93.0481	−0.354431	−0.177215	+	0.984172i	$0.556709\pi$
$42$	− 116.933i	− 0.429601i
$43$	452.579i	1.60506i	0.596612	+	0.802530i	$0.296513\pi$
$43$	452.579i	1.60506i	−0.596612	+	0.802530i	$0.703487\pi$
$44$	−535.765	−1.83567
$45$	0	0
$46$	634.113	2.03250
$47$	402.565i	1.24937i	0.780879	+	0.624683i	$0.214772\pi$
$47$	402.565i	1.24937i	−0.780879	+	0.624683i	$0.785228\pi$
$48$	− 843.629i	− 2.53682i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	228.095	0.626267
$52$	− 1070.60i	− 2.85510i
$53$	495.787i	1.28494i	0.766313	+	0.642468i	$0.222089\pi$
$53$	495.787i	1.28494i	−0.766313	+	0.642468i	$0.777911\pi$
$54$	−150.343	−0.378872
$55$	0	0
$56$	−584.882	−1.39568
$57$	− 343.815i	− 0.798938i
$58$	− 670.808i	− 1.51865i
$59$	−496.707	−1.09603	−0.548015	−	0.836468i	$-0.684616\pi$
$59$	−496.707	−1.09603	−0.548015	+	0.836468i	$0.684616\pi$
$60$	0	0
$61$	−265.742	−0.557783	−0.278891	−	0.960323i	$-0.589967\pi$
$61$	−265.742	−0.557783	−0.278891	+	0.960323i	$0.589967\pi$
$62$	− 1013.69i	− 2.07644i
$63$	63.0000i	0.125988i
$64$	−2747.34	−5.36590
$65$	0	0
$66$	389.030	0.725550
$67$	594.240i	1.08355i	0.840523	+	0.541776i	$0.182248\pi$
$67$	594.240i	1.08355i	−0.840523	+	0.541776i	$0.817752\pi$
$68$	− 1749.14i	− 3.11934i
$69$	−341.640	−0.596066
$70$	0	0
$71$	−510.099	−0.852642	−0.426321	−	0.904572i	$-0.640191\pi$
$71$	−510.099	−0.852642	−0.426321	+	0.904572i	$0.640191\pi$
$72$	751.991i	1.23088i
$73$	− 470.181i	− 0.753843i	−0.926245	−	0.376921i	$-0.876983\pi$
$73$	− 470.181i	− 0.753843i	0.926245	−	0.376921i	$-0.123017\pi$
$74$	1795.63	2.82079
$75$	0	0
$76$	−2636.55	−3.97938
$77$	− 163.020i	− 0.241271i
$78$	777.383i	1.12848i
$79$	487.916	0.694871	0.347435	−	0.937704i	$-0.387053\pi$
$79$	487.916	0.694871	0.347435	+	0.937704i	$0.387053\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	− 518.116i	− 0.697760i
$83$	1250.53i	1.65378i	0.562362	+	0.826891i	$0.309893\pi$
$83$	1250.53i	1.65378i	−0.562362	+	0.826891i	$0.690107\pi$
$84$	483.116	0.627527
$85$	0	0
$86$	−2520.08	−3.15985
$87$	361.410i	0.445370i
$88$	− 1945.86i	− 2.35716i
$89$	1561.98	1.86033	0.930164	−	0.367145i	$-0.119665\pi$
$89$	1561.98	1.86033	0.930164	+	0.367145i	$0.119665\pi$
$90$	0	0
$91$	325.756	0.375258
$92$	2619.87i	2.96891i
$93$	546.145i	0.608953i
$94$	−2241.59	−2.45960
$95$	0	0
$96$	2692.23	2.86224
$97$	21.5118i	0.0225175i	0.999937	+	0.0112587i	$0.00358384\pi$
$97$	21.5118i	0.0225175i	−0.999937	+	0.0112587i	$0.996416\pi$
$98$	− 272.845i	− 0.281240i
$99$	−209.597	−0.212781
$100$	0	0
$101$	211.353	0.208222	0.104111	−	0.994566i	$-0.466800\pi$
$101$	211.353	0.208222	0.104111	+	0.994566i	$0.466800\pi$
$102$	1270.09i	1.23292i
$103$	1180.82i	1.12961i	0.825224	+	0.564806i	$0.191049\pi$
$103$	1180.82i	1.12961i	−0.825224	+	0.564806i	$0.808951\pi$
$104$	3888.35	3.66619
$105$	0	0
$106$	−2760.67	−2.52962
$107$	1114.80i	1.00721i	0.863933	+	0.503607i	$0.167994\pi$
$107$	1114.80i	1.00721i	−0.863933	+	0.503607i	$0.832006\pi$
$108$	− 621.149i	− 0.553427i
$109$	−970.519	−0.852834	−0.426417	−	0.904527i	$-0.640224\pi$
$109$	−970.519	−0.852834	−0.426417	+	0.904527i	$0.640224\pi$
$110$	0	0
$111$	−967.430	−0.827247
$112$	− 1968.47i	− 1.66074i
$113$	− 800.030i	− 0.666022i	−0.942923	−	0.333011i	$-0.891935\pi$
$113$	− 800.030i	− 0.666022i	0.942923	−	0.333011i	$-0.108065\pi$
$114$	1914.45	1.57285
$115$	0	0
$116$	2771.47	2.21832
$117$	− 418.829i	− 0.330947i
$118$	− 2765.79i	− 2.15773i
$119$	532.221	0.409988
$120$	0	0
$121$	−788.644	−0.592520
$122$	− 1479.72i	− 1.09809i
$123$	279.144i	0.204631i
$124$	4188.12	3.03310
$125$	0	0
$126$	−350.800	−0.248030
$127$	526.685i	0.367998i	0.982926	+	0.183999i	$0.0589043\pi$
$127$	526.685i	0.367998i	−0.982926	+	0.183999i	$0.941096\pi$
$128$	− 8118.62i	− 5.60618i
$129$	1357.74	0.926682
$130$	0	0
$131$	827.813	0.552110	0.276055	−	0.961142i	$-0.410973\pi$
$131$	827.813	0.552110	0.276055	+	0.961142i	$0.410973\pi$
$132$	1607.29i	1.05983i
$133$	− 802.236i	− 0.523028i
$134$	−3308.88	−2.13316
$135$	0	0
$136$	6352.79	4.00549
$137$	1636.01i	1.02025i	0.860101	+	0.510124i	$0.170401\pi$
$137$	1636.01i	1.02025i	−0.860101	+	0.510124i	$0.829599\pi$
$138$	− 1902.34i	− 1.17346i
$139$	1463.08	0.892783	0.446391	−	0.894838i	$-0.352709\pi$
$139$	1463.08	0.892783	0.446391	+	0.894838i	$0.352709\pi$
$140$	0	0
$141$	1207.70	0.721321
$142$	− 2840.36i	− 1.67858i
$143$	1083.77i	0.633772i
$144$	−2530.89	−1.46463
$145$	0	0
$146$	2618.09	1.48407
$147$	147.000i	0.0824786i
$148$	7418.74i	4.12038i
$149$	−330.833	−0.181898	−0.0909492	−	0.995856i	$-0.528990\pi$
$149$	−330.833	−0.181898	−0.0909492	+	0.995856i	$0.528990\pi$
$150$	0	0
$151$	−1139.90	−0.614327	−0.307164	−	0.951657i	$-0.599380\pi$
$151$	−1139.90	−0.614327	−0.307164	+	0.951657i	$0.599380\pi$
$152$	− 9575.79i	− 5.10986i
$153$	− 684.284i	− 0.361576i
$154$	907.737	0.474984
$155$	0	0
$156$	−3211.79	−1.64839
$157$	3297.93i	1.67645i	0.545322	+	0.838227i	$0.316408\pi$
$157$	3297.93i	1.67645i	−0.545322	+	0.838227i	$0.683592\pi$
$158$	2716.84i	1.36798i
$159$	1487.36	0.741858
$160$	0	0
$161$	−797.159	−0.390217
$162$	451.029i	0.218742i
$163$	− 2569.02i	− 1.23449i	−0.786773	−	0.617243i	$-0.788250\pi$
$163$	− 2569.02i	− 1.23449i	0.786773	−	0.617243i	$-0.211750\pi$
$164$	2140.62	1.01923
$165$	0	0
$166$	−6963.30	−3.25576
$167$	1034.90i	0.479540i	0.970830	+	0.239770i	$0.0770720\pi$
$167$	1034.90i	0.479540i	−0.970830	+	0.239770i	$0.922928\pi$
$168$	1754.65i	0.805797i
$169$	31.3467	0.0142679
$170$	0	0
$171$	−1031.45	−0.461267
$172$	− 10411.8i	− 4.61565i
$173$	− 244.188i	− 0.107314i	−0.998559	−	0.0536568i	$-0.982912\pi$
$173$	− 244.188i	− 0.107314i	0.998559	−	0.0536568i	$-0.0170877\pi$
$174$	−2012.42	−0.876790
$175$	0	0
$176$	6548.96	2.80481
$177$	1490.12i	0.632793i
$178$	8697.49i	3.66238i
$179$	−1523.83	−0.636294	−0.318147	−	0.948041i	$-0.603061\pi$
$179$	−1523.83	−0.636294	−0.318147	+	0.948041i	$0.603061\pi$
$180$	0	0
$181$	−3144.63	−1.29137	−0.645687	−	0.763602i	$-0.723429\pi$
$181$	−3144.63	−1.29137	−0.645687	+	0.763602i	$0.723429\pi$
$182$	1813.89i	0.738763i
$183$	797.225i	0.322036i
$184$	−9515.19	−3.81233
$185$	0	0
$186$	−3041.08	−1.19883
$187$	1770.66i	0.692427i
$188$	− 9261.22i	− 3.59279i
$189$	189.000	0.0727393
$190$	0	0
$191$	−734.675	−0.278320	−0.139160	−	0.990270i	$-0.544440\pi$
$191$	−734.675	−0.278320	−0.139160	+	0.990270i	$0.544440\pi$
$192$	8242.02i	3.09800i
$193$	3248.41i	1.21153i	0.795643	+	0.605765i	$0.207133\pi$
$193$	3248.41i	1.21153i	−0.795643	+	0.605765i	$0.792867\pi$
$194$	−119.783	−0.0443297
$195$	0	0
$196$	1127.27	0.410813
$197$	2915.78i	1.05452i	0.849703	+	0.527261i	$0.176781\pi$
$197$	2915.78i	1.05452i	−0.849703	+	0.527261i	$0.823219\pi$
$198$	− 1167.09i	− 0.418896i
$199$	1397.88	0.497955	0.248977	−	0.968509i	$-0.419905\pi$
$199$	1397.88	0.497955	0.248977	+	0.968509i	$0.419905\pi$
$200$	0	0
$201$	1782.72	0.625589
$202$	1176.87i	0.409923i
$203$	843.290i	0.291563i
$204$	−5247.43	−1.80095
$205$	0	0
$206$	−6575.14	−2.22384
$207$	1024.92i	0.344139i
$208$	13086.5i	4.36244i
$209$	2668.99	0.883338
$210$	0	0
$211$	−998.781	−0.325872	−0.162936	−	0.986637i	$-0.552096\pi$
$211$	−998.781	−0.325872	−0.162936	+	0.986637i	$0.552096\pi$
$212$	− 11405.8i	− 3.69508i
$213$	1530.30i	0.492273i
$214$	−6207.50	−1.98288
$215$	0	0
$216$	2255.97	0.710646
$217$	1274.34i	0.398653i
$218$	− 5404.10i	− 1.67895i
$219$	−1410.54	−0.435231
$220$	0	0
$221$	−3538.25	−1.07696
$222$	− 5386.90i	− 1.62858i
$223$	− 2820.52i	− 0.846979i	−0.905901	−	0.423489i	$-0.860805\pi$
$223$	− 2820.52i	− 0.846979i	0.905901	−	0.423489i	$-0.139195\pi$
$224$	6281.88	1.87377
$225$	0	0
$226$	4454.78	1.31118
$227$	− 1420.92i	− 0.415460i	−0.978186	−	0.207730i	$-0.933392\pi$
$227$	− 1420.92i	− 0.415460i	0.978186	−	0.207730i	$-0.0666076\pi$
$228$	7909.65i	2.29750i
$229$	87.4506	0.0252354	0.0126177	−	0.999920i	$-0.495984\pi$
$229$	87.4506	0.0252354	0.0126177	+	0.999920i	$0.495984\pi$
$230$	0	0
$231$	−489.059	−0.139298
$232$	10065.8i	2.84851i
$233$	4719.66i	1.32702i	0.748169	+	0.663509i	$0.230933\pi$
$233$	4719.66i	1.32702i	−0.748169	+	0.663509i	$0.769067\pi$
$234$	2332.15	0.651527
$235$	0	0
$236$	11427.0	3.15184
$237$	− 1463.75i	− 0.401184i
$238$	2963.54i	0.807135i
$239$	850.656	0.230227	0.115114	−	0.993352i	$-0.463277\pi$
$239$	850.656	0.230227	0.115114	+	0.993352i	$0.463277\pi$
$240$	0	0
$241$	4036.74	1.07896	0.539480	−	0.841999i	$-0.318621\pi$
$241$	4036.74	1.07896	0.539480	+	0.841999i	$0.318621\pi$
$242$	− 4391.37i	− 1.16648i
$243$	− 243.000i	− 0.0641500i
$244$	6113.52	1.60401
$245$	0	0
$246$	−1554.35	−0.402852
$247$	5333.33i	1.37389i
$248$	15211.0i	3.89475i
$249$	3751.60	0.954812
$250$	0	0
$251$	4659.33	1.17169	0.585845	−	0.810423i	$-0.300763\pi$
$251$	4659.33	1.17169	0.585845	+	0.810423i	$0.300763\pi$
$252$	− 1449.35i	− 0.362303i
$253$	− 2652.10i	− 0.659035i
$254$	−2932.72	−0.724469
$255$	0	0
$256$	23227.9	5.67086
$257$	− 1160.22i	− 0.281605i	−0.990038	−	0.140802i	$-0.955032\pi$
$257$	− 1160.22i	− 0.281605i	0.990038	−	0.140802i	$-0.0449682\pi$
$258$	7560.23i	1.82434i
$259$	−2257.34	−0.541560
$260$	0	0
$261$	1084.23	0.257135
$262$	4609.48i	1.08693i
$263$	− 1589.53i	− 0.372680i	−0.982485	−	0.186340i	$-0.940337\pi$
$263$	− 1589.53i	− 0.372680i	0.982485	−	0.186340i	$-0.0596625\pi$
$264$	−5837.59	−1.36091
$265$	0	0
$266$	4467.06	1.02967
$267$	− 4685.93i	− 1.07406i
$268$	− 13670.8i	− 3.11596i
$269$	−4568.96	−1.03559	−0.517796	−	0.855504i	$-0.673247\pi$
$269$	−4568.96	−1.03559	−0.517796	+	0.855504i	$0.673247\pi$
$270$	0	0
$271$	−6520.72	−1.46164	−0.730822	−	0.682569i	$-0.760863\pi$
$271$	−6520.72	−1.46164	−0.730822	+	0.682569i	$0.760863\pi$
$272$	21380.8i	4.76618i
$273$	− 977.268i	− 0.216656i
$274$	−9109.75	−2.00854
$275$	0	0
$276$	7859.60	1.71410
$277$	− 4921.65i	− 1.06756i	−0.845624	−	0.533779i	$-0.820771\pi$
$277$	− 4921.65i	− 1.06756i	0.845624	−	0.533779i	$-0.179229\pi$
$278$	8146.81i	1.75760i
$279$	1638.44	0.351579
$280$	0	0
$281$	2378.08	0.504856	0.252428	−	0.967616i	$-0.418771\pi$
$281$	2378.08	0.504856	0.252428	+	0.967616i	$0.418771\pi$
$282$	6724.76i	1.42005i
$283$	− 8673.45i	− 1.82185i	−0.412574	−	0.910924i	$-0.635370\pi$
$283$	− 8673.45i	− 1.82185i	0.412574	−	0.910924i	$-0.364630\pi$
$284$	11735.1	2.45193
$285$	0	0
$286$	−6034.71	−1.24769
$287$	651.337i	0.133962i
$288$	− 8076.70i	− 1.65251i
$289$	−867.797	−0.176633
$290$	0	0
$291$	64.5355	0.0130005
$292$	10816.8i	2.16782i
$293$	− 4334.99i	− 0.864344i	−0.901791	−	0.432172i	$-0.857747\pi$
$293$	− 4334.99i	− 0.864344i	0.901791	−	0.432172i	$-0.142253\pi$
$294$	−818.534	−0.162374
$295$	0	0
$296$	−26944.4	−5.29092
$297$	628.791i	0.122849i
$298$	− 1842.16i	− 0.358099i
$299$	5299.58	1.02503
$300$	0	0
$301$	3168.05	0.606656
$302$	− 6347.24i	− 1.20941i
$303$	− 634.060i	− 0.120217i
$304$	32228.1	6.08028
$305$	0	0
$306$	3810.27	0.711826
$307$	5849.36i	1.08743i	0.839270	+	0.543715i	$0.182983\pi$
$307$	5849.36i	1.08743i	−0.839270	+	0.543715i	$0.817017\pi$
$308$	3750.35i	0.693819i
$309$	3542.47	0.652182
$310$	0	0
$311$	−5005.00	−0.912564	−0.456282	−	0.889835i	$-0.650819\pi$
$311$	−5005.00	−0.912564	−0.456282	+	0.889835i	$0.650819\pi$
$312$	− 11665.0i	− 2.11667i
$313$	− 7362.05i	− 1.32948i	−0.747074	−	0.664741i	$-0.768542\pi$
$313$	− 7362.05i	− 1.32948i	0.747074	−	0.664741i	$-0.231458\pi$
$314$	−18363.7	−3.30040
$315$	0	0
$316$	−11224.7	−1.99823
$317$	7869.89i	1.39438i	0.716889	+	0.697188i	$0.245566\pi$
$317$	7869.89i	1.39438i	−0.716889	+	0.697188i	$0.754434\pi$
$318$	8282.01i	1.46048i
$319$	−2805.57	−0.492419
$320$	0	0
$321$	3344.40	0.581515
$322$	− 4438.79i	− 0.768211i
$323$	8713.61i	1.50105i
$324$	−1863.45	−0.319521
$325$	0	0
$326$	14305.0	2.43030
$327$	2911.56i	0.492384i
$328$	7774.60i	1.30878i
$329$	2817.96	0.472216
$330$	0	0
$331$	−2608.54	−0.433167	−0.216584	−	0.976264i	$-0.569491\pi$
$331$	−2608.54	−0.433167	−0.216584	+	0.976264i	$0.569491\pi$
$332$	− 28769.2i	− 4.75576i
$333$	2902.29i	0.477611i
$334$	−5762.61	−0.944059
$335$	0	0
$336$	−5905.40	−0.958827
$337$	− 5355.89i	− 0.865739i	−0.901457	−	0.432870i	$-0.857501\pi$
$337$	− 5355.89i	− 0.865739i	0.901457	−	0.432870i	$-0.142499\pi$
$338$	174.546i	0.0280890i
$339$	−2400.09	−0.384528
$340$	0	0
$341$	−4239.64	−0.673283
$342$	− 5743.36i	− 0.908086i
$343$	343.000i	0.0539949i
$344$	37815.0	5.92689
$345$	0	0
$346$	1359.70	0.211266
$347$	10607.0i	1.64097i	0.571670	+	0.820484i	$0.306296\pi$
$347$	10607.0i	1.64097i	−0.571670	+	0.820484i	$0.693704\pi$
$348$	− 8314.42i	− 1.28075i
$349$	1896.78	0.290923	0.145462	−	0.989364i	$-0.453533\pi$
$349$	1896.78	0.290923	0.145462	+	0.989364i	$0.453533\pi$
$350$	0	0
$351$	−1256.49	−0.191072
$352$	20899.4i	3.16461i
$353$	4040.68i	0.609245i	0.952473	+	0.304622i	$0.0985303\pi$
$353$	4040.68i	0.609245i	−0.952473	+	0.304622i	$0.901470\pi$
$354$	−8297.38	−1.24577
$355$	0	0
$356$	−35934.1	−5.34972
$357$	− 1596.66i	− 0.236707i
$358$	− 8485.09i	− 1.25266i
$359$	2054.91	0.302100	0.151050	−	0.988526i	$-0.451734\pi$
$359$	2054.91	0.302100	0.151050	+	0.988526i	$0.451734\pi$
$360$	0	0
$361$	6275.34	0.914906
$362$	− 17510.1i	− 2.54230i
$363$	2365.93i	0.342091i
$364$	−7494.19	−1.07913
$365$	0	0
$366$	−4439.16	−0.633985
$367$	− 9866.34i	− 1.40332i	−0.712511	−	0.701661i	$-0.752442\pi$
$367$	− 9866.34i	− 1.40332i	0.712511	−	0.701661i	$-0.247558\pi$
$368$	− 32024.1i	− 4.53634i
$369$	837.433	0.118144
$370$	0	0
$371$	3470.51	0.485660
$372$	− 12564.3i	− 1.75116i
$373$	− 4420.36i	− 0.613613i	−0.951772	−	0.306806i	$-0.900740\pi$
$373$	− 4420.36i	− 0.613613i	0.951772	−	0.306806i	$-0.0992604\pi$
$374$	−9859.52	−1.36316
$375$	0	0
$376$	33636.2	4.61344
$377$	− 5606.26i	− 0.765881i
$378$	1052.40i	0.143200i
$379$	13.7935	0.00186945	0.000934727	−	1.00000i	$-0.499702\pi$
$379$	13.7935	0.00186945	0.000934727		1.00000i	$0.499702\pi$
$380$	0	0
$381$	1580.06	0.212464
$382$	− 4090.86i	− 0.547923i
$383$	1229.76i	0.164067i	0.996630	+	0.0820335i	$0.0261415\pi$
$383$	1229.76i	0.164067i	−0.996630	+	0.0820335i	$0.973859\pi$
$384$	−24355.9	−3.23673
$385$	0	0
$386$	−18088.0	−2.38511
$387$	− 4073.21i	− 0.535020i
$388$	− 494.891i	− 0.0647533i
$389$	2827.48	0.368532	0.184266	−	0.982876i	$-0.441009\pi$
$389$	2827.48	0.368532	0.184266	+	0.982876i	$0.441009\pi$
$390$	0	0
$391$	8658.47	1.11989
$392$	4094.18i	0.527518i
$393$	− 2483.44i	− 0.318761i
$394$	−16235.8	−2.07601
$395$	0	0
$396$	4821.88	0.611891
$397$	1322.12i	0.167142i	0.996502	+	0.0835711i	$0.0266326\pi$
$397$	1322.12i	0.167142i	−0.996502	+	0.0835711i	$0.973367\pi$
$398$	7783.76i	0.980313i
$399$	−2406.71	−0.301970
$400$	0	0
$401$	7112.69	0.885762	0.442881	−	0.896580i	$-0.353956\pi$
$401$	7112.69	0.885762	0.442881	+	0.896580i	$0.353956\pi$
$402$	9926.65i	1.23158i
$403$	− 8471.91i	− 1.04719i
$404$	−4862.30	−0.598783
$405$	0	0
$406$	−4695.66	−0.573994
$407$	− 7510.01i	− 0.914637i
$408$	− 19058.4i	− 2.31257i
$409$	−5986.22	−0.723715	−0.361858	−	0.932233i	$-0.617857\pi$
$409$	−5986.22	−0.723715	−0.361858	+	0.932233i	$0.617857\pi$
$410$	0	0
$411$	4908.04	0.589041
$412$	− 27165.5i	− 3.24841i
$413$	3476.95i	0.414260i
$414$	−5707.02	−0.677499
$415$	0	0
$416$	−41762.4	−4.92205
$417$	− 4389.24i	− 0.515448i
$418$	14861.6i	1.73901i
$419$	64.5704	0.00752857	0.00376428	−	0.999993i	$-0.498802\pi$
$419$	64.5704	0.00752857	0.00376428	+	0.999993i	$0.498802\pi$
$420$	0	0
$421$	−4482.13	−0.518874	−0.259437	−	0.965760i	$-0.583537\pi$
$421$	−4482.13	−0.518874	−0.259437	+	0.965760i	$0.583537\pi$
$422$	− 5561.47i	− 0.641536i
$423$	− 3623.09i	− 0.416455i
$424$	41425.3	4.74479
$425$	0	0
$426$	−8521.08	−0.969126
$427$	1860.19i	0.210822i
$428$	− 25646.6i	− 2.89643i
$429$	3251.31	0.365908
$430$	0	0
$431$	10161.5	1.13564	0.567821	−	0.823152i	$-0.307787\pi$
$431$	10161.5	1.13564	0.567821	+	0.823152i	$0.307787\pi$
$432$	7592.66i	0.845606i
$433$	− 2027.12i	− 0.224982i	−0.993653	−	0.112491i	$-0.964117\pi$
$433$	− 2027.12i	− 0.224982i	0.993653	−	0.112491i	$-0.0358830\pi$
$434$	−7095.85	−0.784819
$435$	0	0
$436$	22327.3	2.45249
$437$	− 13051.2i	− 1.42866i
$438$	− 7854.27i	− 0.856830i
$439$	9366.44	1.01830	0.509152	−	0.860676i	$-0.329959\pi$
$439$	9366.44	1.01830	0.509152	+	0.860676i	$0.329959\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 19701.9i	− 2.12019i
$443$	− 7341.52i	− 0.787373i	−0.919245	−	0.393686i	$-0.871200\pi$
$443$	− 7341.52i	− 0.787373i	0.919245	−	0.393686i	$-0.128800\pi$
$444$	22256.2	2.37890
$445$	0	0
$446$	15705.4	1.66743
$447$	992.498i	0.105019i
$448$	19231.4i	2.02812i
$449$	4667.02	0.490535	0.245267	−	0.969455i	$-0.421124\pi$
$449$	4667.02	0.490535	0.245267	+	0.969455i	$0.421124\pi$
$450$	0	0
$451$	−2166.95	−0.226248
$452$	18405.1i	1.91527i
$453$	3419.69i	0.354682i
$454$	7912.03	0.817907
$455$	0	0
$456$	−28727.4	−2.95018
$457$	9648.38i	0.987598i	0.869576	+	0.493799i	$0.164392\pi$
$457$	9648.38i	0.987598i	−0.869576	+	0.493799i	$0.835608\pi$
$458$	486.948i	0.0496803i
$459$	−2052.85	−0.208756
$460$	0	0
$461$	16097.6	1.62634	0.813168	−	0.582028i	$-0.197741\pi$
$461$	16097.6	1.62634	0.813168	+	0.582028i	$0.197741\pi$
$462$	− 2723.21i	− 0.274232i
$463$	− 11024.6i	− 1.10661i	−0.832980	−	0.553303i	$-0.813367\pi$
$463$	− 11024.6i	− 1.10661i	0.832980	−	0.553303i	$-0.186633\pi$
$464$	−33877.3	−3.38947
$465$	0	0
$466$	−26280.3	−2.61247
$467$	15275.8i	1.51366i	0.653613	+	0.756829i	$0.273252\pi$
$467$	15275.8i	1.51366i	−0.653613	+	0.756829i	$0.726748\pi$
$468$	9635.38i	0.951700i
$469$	4159.68	0.409544
$470$	0	0
$471$	9893.78	0.967901
$472$	41502.2i	4.04723i
$473$	10539.9i	1.02458i
$474$	8150.52	0.789801
$475$	0	0
$476$	−12244.0	−1.17900
$477$	− 4462.08i	− 0.428312i
$478$	4736.67i	0.453243i
$479$	6247.49	0.595939	0.297970	−	0.954575i	$-0.403691\pi$
$479$	6247.49	0.595939	0.297970	+	0.954575i	$0.403691\pi$
$480$	0	0
$481$	15007.0	1.42257
$482$	22477.6i	2.12412i
$483$	2391.48i	0.225292i
$484$	18143.2	1.70390
$485$	0	0
$486$	1353.09	0.126291
$487$	15579.8i	1.44967i	0.688922	+	0.724835i	$0.258084\pi$
$487$	15579.8i	1.44967i	−0.688922	+	0.724835i	$0.741916\pi$
$488$	22203.9i	2.05968i
$489$	−7707.06	−0.712730
$490$	0	0
$491$	5604.60	0.515137	0.257568	−	0.966260i	$-0.417079\pi$
$491$	5604.60	0.515137	0.257568	+	0.966260i	$0.417079\pi$
$492$	− 6421.86i	− 0.588455i
$493$	− 9159.52i	− 0.836763i
$494$	−29697.4	−2.70475
$495$	0	0
$496$	−51193.7	−4.63441
$497$	3570.69i	0.322268i
$498$	20889.9i	1.87972i
$499$	−18016.9	−1.61633	−0.808163	−	0.588958i	$-0.799538\pi$
$499$	−18016.9	−1.61633	−0.808163	+	0.588958i	$0.799538\pi$
$500$	0	0
$501$	3104.71	0.276862
$502$	25944.4i	2.30668i
$503$	− 3405.38i	− 0.301865i	−0.988544	−	0.150933i	$-0.951772\pi$
$503$	− 3405.38i	− 0.301865i	0.988544	−	0.150933i	$-0.0482276\pi$
$504$	5263.94	0.465227
$505$	0	0
$506$	14767.6	1.29743
$507$	− 94.0400i	− 0.00823760i
$508$	− 12116.7i	− 1.05825i
$509$	3669.88	0.319577	0.159788	−	0.987151i	$-0.448919\pi$
$509$	3669.88	0.319577	0.159788	+	0.987151i	$0.448919\pi$
$510$	0	0
$511$	−3291.27	−0.284926
$512$	64389.7i	5.55791i
$513$	3094.34i	0.266313i
$514$	6460.40	0.554389
$515$	0	0
$516$	−31235.4	−2.66485
$517$	9375.16i	0.797522i
$518$	− 12569.4i	− 1.06616i
$519$	−732.563	−0.0619576
$520$	0	0
$521$	12171.2	1.02347	0.511736	−	0.859143i	$-0.329003\pi$
$521$	12171.2	1.02347	0.511736	+	0.859143i	$0.329003\pi$
$522$	6037.27i	0.506215i
$523$	− 15624.1i	− 1.30630i	−0.757230	−	0.653148i	$-0.773448\pi$
$523$	− 15624.1i	− 1.30630i	0.757230	−	0.653148i	$-0.226552\pi$
$524$	−19044.3	−1.58770
$525$	0	0
$526$	8850.93	0.733686
$527$	− 13841.4i	− 1.14410i
$528$	− 19646.9i	− 1.61936i
$529$	−801.633	−0.0658858
$530$	0	0
$531$	4470.37	0.365343
$532$	18455.9i	1.50407i
$533$	− 4330.14i	− 0.351893i
$534$	26092.5	2.11448
$535$	0	0
$536$	49651.5	4.00115
$537$	4571.50i	0.367364i
$538$	− 25441.2i	− 2.03875i
$539$	−1141.14	−0.0911917
$540$	0	0
$541$	10905.8	0.866688	0.433344	−	0.901229i	$-0.357334\pi$
$541$	10905.8	0.866688	0.433344	+	0.901229i	$0.357334\pi$
$542$	− 36309.0i	− 2.87750i
$543$	9433.89i	0.745575i
$544$	−68231.5	−5.37758
$545$	0	0
$546$	5441.68	0.426525
$547$	− 9430.33i	− 0.737133i	−0.929601	−	0.368566i	$-0.879849\pi$
$547$	− 9430.33i	− 0.737133i	0.929601	−	0.368566i	$-0.120151\pi$
$548$	− 37637.3i	− 2.93392i
$549$	2391.68	0.185928
$550$	0	0
$551$	−13806.5	−1.06747
$552$	28545.6i	2.20105i
$553$	− 3415.41i	− 0.262636i
$554$	27405.0	2.10168
$555$	0	0
$556$	−33658.9	−2.56737
$557$	− 12304.7i	− 0.936029i	−0.883721	−	0.468015i	$-0.844969\pi$
$557$	− 12304.7i	− 0.936029i	0.883721	−	0.468015i	$-0.155031\pi$
$558$	9123.23i	0.692146i
$559$	−21061.5	−1.59357
$560$	0	0
$561$	5311.99	0.399773
$562$	13241.8i	0.993899i
$563$	15768.1i	1.18037i	0.807268	+	0.590184i	$0.200945\pi$
$563$	15768.1i	1.18037i	−0.807268	+	0.590184i	$0.799055\pi$
$564$	−27783.7	−2.07430
$565$	0	0
$566$	48296.0	3.58663
$567$	− 567.000i	− 0.0419961i
$568$	42621.1i	3.14849i
$569$	−243.490	−0.0179396	−0.00896981	−	0.999960i	$-0.502855\pi$
$569$	−243.490	−0.0179396	−0.00896981	+	0.999960i	$0.502855\pi$
$570$	0	0
$571$	−26619.7	−1.95096	−0.975480	−	0.220090i	$-0.929365\pi$
$571$	−26619.7	−1.95096	−0.975480	+	0.220090i	$0.929365\pi$
$572$	− 24932.7i	− 1.82253i
$573$	2204.02i	0.160688i
$574$	−3626.81	−0.263729
$575$	0	0
$576$	24726.1	1.78863
$577$	4868.88i	0.351290i	0.984454	+	0.175645i	$0.0562011\pi$
$577$	4868.88i	0.351290i	−0.984454	+	0.175645i	$0.943799\pi$
$578$	− 4832.12i	− 0.347733i
$579$	9745.22	0.699478
$580$	0	0
$581$	8753.74	0.625071
$582$	359.350i	0.0255937i
$583$	11546.2i	0.820228i
$584$	−39285.8	−2.78366
$585$	0	0
$586$	24138.4	1.70161
$587$	12698.7i	0.892898i	0.894809	+	0.446449i	$0.147312\pi$
$587$	12698.7i	0.892898i	−0.894809	+	0.446449i	$0.852688\pi$
$588$	− 3381.81i	− 0.237183i
$589$	−20863.7	−1.45955
$590$	0	0
$591$	8747.35	0.608829
$592$	− 90683.5i	− 6.29573i
$593$	− 22043.0i	− 1.52647i	−0.646119	−	0.763237i	$-0.723609\pi$
$593$	− 22043.0i	− 1.52647i	0.646119	−	0.763237i	$-0.276391\pi$
$594$	−3501.27	−0.241850
$595$	0	0
$596$	7610.97	0.523083
$597$	− 4193.64i	− 0.287494i
$598$	29509.4i	2.01794i
$599$	15180.6	1.03550	0.517750	−	0.855532i	$-0.326770\pi$
$599$	15180.6	1.03550	0.517750	+	0.855532i	$0.326770\pi$
$600$	0	0
$601$	415.176	0.0281787	0.0140893	−	0.999901i	$-0.495515\pi$
$601$	415.176	0.0281787	0.0140893	+	0.999901i	$0.495515\pi$
$602$	17640.5i	1.19431i
$603$	− 5348.16i	− 0.361184i
$604$	26223.9	1.76661
$605$	0	0
$606$	3530.61	0.236669
$607$	− 23973.2i	− 1.60303i	−0.597973	−	0.801516i	$-0.704027\pi$
$607$	− 23973.2i	− 1.60303i	0.597973	−	0.801516i	$-0.295973\pi$
$608$	102848.i	6.86025i
$609$	2529.87	0.168334
$610$	0	0
$611$	−18734.0	−1.24042
$612$	15742.3i	1.03978i
$613$	5616.87i	0.370087i	0.982730	+	0.185043i	$0.0592426\pi$
$613$	5616.87i	0.370087i	−0.982730	+	0.185043i	$0.940757\pi$
$614$	−32570.8	−2.14080
$615$	0	0
$616$	−13621.1	−0.890922
$617$	− 15690.3i	− 1.02377i	−0.859053	−	0.511886i	$-0.828947\pi$
$617$	− 15690.3i	− 1.02377i	0.859053	−	0.511886i	$-0.171053\pi$
$618$	19725.4i	1.28394i
$619$	−7832.79	−0.508605	−0.254302	−	0.967125i	$-0.581846\pi$
$619$	−7832.79	−0.508605	−0.254302	+	0.967125i	$0.581846\pi$
$620$	0	0
$621$	3074.76	0.198689
$622$	− 27869.1i	− 1.79654i
$623$	− 10933.8i	− 0.703138i
$624$	39259.6	2.51866
$625$	0	0
$626$	40993.8	2.61732
$627$	− 8006.96i	− 0.509996i
$628$	− 75870.5i	− 4.82096i
$629$	24518.4	1.55423
$630$	0	0
$631$	−16365.7	−1.03250	−0.516250	−	0.856438i	$-0.672673\pi$
$631$	−16365.7	−1.03250	−0.516250	+	0.856438i	$0.672673\pi$
$632$	− 40767.6i	− 2.56590i
$633$	2996.34i	0.188142i
$634$	−43821.6	−2.74507
$635$	0	0
$636$	−34217.5	−2.13335
$637$	− 2280.29i	− 0.141834i
$638$	− 15622.1i	− 0.969415i
$639$	4590.89	0.284214
$640$	0	0
$641$	−8208.10	−0.505773	−0.252886	−	0.967496i	$-0.581380\pi$
$641$	−8208.10	−0.505773	−0.252886	+	0.967496i	$0.581380\pi$
$642$	18622.5i	1.14482i
$643$	− 13351.5i	− 0.818868i	−0.912340	−	0.409434i	$-0.865726\pi$
$643$	− 13351.5i	− 0.818868i	0.912340	−	0.409434i	$-0.134274\pi$
$644$	18339.1	1.12214
$645$	0	0
$646$	−48519.6	−2.95508
$647$	23313.9i	1.41663i	0.705894	+	0.708317i	$0.250545\pi$
$647$	23313.9i	1.41663i	−0.705894	+	0.708317i	$0.749455\pi$
$648$	− 6767.92i	− 0.410292i
$649$	−11567.6	−0.699642
$650$	0	0
$651$	3823.02	0.230162
$652$	59101.6i	3.55000i
$653$	21077.4i	1.26313i	0.775323	+	0.631565i	$0.217587\pi$
$653$	21077.4i	1.26313i	−0.775323	+	0.631565i	$0.782413\pi$
$654$	−16212.3	−0.969345
$655$	0	0
$656$	−26166.0	−1.55733
$657$	4231.63i	0.251281i
$658$	15691.1i	0.929640i
$659$	−31971.5	−1.88988	−0.944940	−	0.327243i	$-0.893881\pi$
$659$	−31971.5	−1.88988	−0.944940	+	0.327243i	$0.893881\pi$
$660$	0	0
$661$	482.048	0.0283654	0.0141827	−	0.999899i	$-0.495485\pi$
$661$	482.048	0.0283654	0.0141827	+	0.999899i	$0.495485\pi$
$662$	− 14525.0i	− 0.852766i
$663$	10614.7i	0.621784i
$664$	104488.	6.10680
$665$	0	0
$666$	−16160.7	−0.940262
$667$	13719.1i	0.796411i
$668$	− 23808.5i	− 1.37901i
$669$	−8461.57	−0.489003
$670$	0	0
$671$	−6188.74	−0.356056
$672$	− 18845.6i	− 1.08182i
$673$	22561.8i	1.29226i	0.763225	+	0.646132i	$0.223615\pi$
$673$	22561.8i	1.29226i	−0.763225	+	0.646132i	$0.776385\pi$
$674$	29823.0	1.70436
$675$	0	0
$676$	−721.146	−0.0410302
$677$	1449.65i	0.0822962i	0.999153	+	0.0411481i	$0.0131015\pi$
$677$	1449.65i	0.0822962i	−0.999153	+	0.0411481i	$0.986898\pi$
$678$	− 13364.3i	− 0.757012i
$679$	150.583	0.00851081
$680$	0	0
$681$	−4262.75	−0.239866
$682$	− 23607.4i	− 1.32548i
$683$	10176.4i	0.570114i	0.958511	+	0.285057i	$0.0920125\pi$
$683$	10176.4i	0.570114i	−0.958511	+	0.285057i	$0.907987\pi$
$684$	23729.0	1.32646
$685$	0	0
$686$	−1909.91	−0.106299
$687$	− 262.352i	− 0.0145696i
$688$	127269.i	7.05247i
$689$	−23072.2	−1.27574
$690$	0	0
$691$	23323.3	1.28402	0.642011	−	0.766695i	$-0.278100\pi$
$691$	23323.3	1.28402	0.642011	+	0.766695i	$0.278100\pi$
$692$	5617.67i	0.308601i
$693$	1467.18i	0.0804235i
$694$	−59062.7	−3.23053
$695$	0	0
$696$	30197.5	1.64459
$697$	− 7074.59i	− 0.384461i
$698$	10561.8i	0.572734i
$699$	14159.0	0.766154
$700$	0	0
$701$	−15221.7	−0.820138	−0.410069	−	0.912055i	$-0.634495\pi$
$701$	−15221.7	−0.820138	−0.410069	+	0.912055i	$0.634495\pi$
$702$	− 6996.45i	− 0.376159i
$703$	− 36957.5i	− 1.98276i
$704$	−63981.6	−3.42528
$705$	0	0
$706$	−22499.5	−1.19941
$707$	− 1479.47i	− 0.0787006i
$708$	− 34281.0i	− 1.81972i
$709$	13088.0	0.693274	0.346637	−	0.937999i	$-0.387324\pi$
$709$	13088.0	0.693274	0.346637	+	0.937999i	$0.387324\pi$
$710$	0	0
$711$	−4391.24	−0.231624
$712$	− 130510.i	− 6.86949i
$713$	20731.6i	1.08893i
$714$	8890.63	0.465999
$715$	0	0
$716$	35056.5	1.82978
$717$	− 2551.97i	− 0.132922i
$718$	11442.3i	0.594738i
$719$	13845.7	0.718160	0.359080	−	0.933307i	$-0.383091\pi$
$719$	13845.7	0.718160	0.359080	+	0.933307i	$0.383091\pi$
$720$	0	0
$721$	8265.77	0.426953
$722$	34942.7i	1.80115i
$723$	− 12110.2i	− 0.622937i
$724$	72343.9	3.71359
$725$	0	0
$726$	−13174.1	−0.673468
$727$	2691.12i	0.137287i	0.997641	+	0.0686437i	$0.0218672\pi$
$727$	2691.12i	0.137287i	−0.997641	+	0.0686437i	$0.978133\pi$
$728$	− 27218.4i	− 1.38569i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−34410.3	−1.74105
$732$	− 18340.6i	− 0.926075i
$733$	− 765.975i	− 0.0385975i	−0.999814	−	0.0192987i	$-0.993857\pi$
$733$	− 765.975i	− 0.0385975i	0.999814	−	0.0192987i	$-0.00614336\pi$
$734$	54938.4	2.76269
$735$	0	0
$736$	102197.	5.11825
$737$	13839.0i	0.691676i
$738$	4663.04i	0.232587i
$739$	20961.2	1.04340	0.521698	−	0.853130i	$-0.325299\pi$
$739$	20961.2	1.04340	0.521698	+	0.853130i	$0.325299\pi$
$740$	0	0
$741$	16000.0	0.793218
$742$	19324.7i	0.956108i
$743$	28175.2i	1.39118i	0.718439	+	0.695590i	$0.244857\pi$
$743$	28175.2i	1.39118i	−0.718439	+	0.695590i	$0.755143\pi$
$744$	45632.9	2.24863
$745$	0	0
$746$	24613.7	1.20801
$747$	− 11254.8i	− 0.551261i
$748$	− 40735.0i	− 1.99120i
$749$	7803.60	0.380691
$750$	0	0
$751$	10303.4	0.500636	0.250318	−	0.968164i	$-0.419465\pi$
$751$	10303.4	0.500636	0.250318	+	0.968164i	$0.419465\pi$
$752$	113205.i	5.48959i
$753$	− 13978.0i	− 0.676476i
$754$	31217.1	1.50777
$755$	0	0
$756$	−4348.04	−0.209176
$757$	− 38444.4i	− 1.84582i	−0.385019	−	0.922909i	$-0.625805\pi$
$757$	− 38444.4i	− 1.84582i	0.385019	−	0.922909i	$-0.374195\pi$
$758$	76.8057i	0.00368035i
$759$	−7956.29	−0.380494
$760$	0	0
$761$	−7765.25	−0.369895	−0.184947	−	0.982748i	$-0.559211\pi$
$761$	−7765.25	−0.369895	−0.184947	+	0.982748i	$0.559211\pi$
$762$	8798.16i	0.418272i
$763$	6793.64i	0.322341i
$764$	16901.6	0.800363
$765$	0	0
$766$	−6847.61	−0.322995
$767$	− 23115.1i	− 1.08818i
$768$	− 69683.6i	− 3.27407i
$769$	10320.1	0.483945	0.241972	−	0.970283i	$-0.422206\pi$
$769$	10320.1	0.483945	0.241972	+	0.970283i	$0.422206\pi$
$770$	0	0
$771$	−3480.65	−0.162585
$772$	− 74731.3i	− 3.48399i
$773$	167.975i	0.00781584i	0.999992	+	0.00390792i	$0.00124393\pi$
$773$	167.975i	0.00781584i	−0.999992	+	0.00390792i	$0.998756\pi$
$774$	22680.7	1.05328
$775$	0	0
$776$	1797.41	0.0831487
$777$	6772.01i	0.312670i
$778$	15744.1i	0.725520i
$779$	−10663.8	−0.490462
$780$	0	0
$781$	−11879.5	−0.544277
$782$	48212.6i	2.20470i
$783$	− 3252.69i	− 0.148457i
$784$	−13779.3	−0.627700
$785$	0	0
$786$	13828.4	0.627537
$787$	− 12700.6i	− 0.575256i	−0.957742	−	0.287628i	$-0.907133\pi$
$787$	− 12700.6i	− 0.575256i	0.957742	−	0.287628i	$-0.0928666\pi$
$788$	− 67079.1i	− 3.03248i
$789$	−4768.60	−0.215167
$790$	0	0
$791$	−5600.21	−0.251733
$792$	17512.8i	0.785719i
$793$	− 12366.7i	− 0.553789i
$794$	−7361.93	−0.329049
$795$	0	0
$796$	−32158.9	−1.43196
$797$	7995.40i	0.355347i	0.984089	+	0.177674i	$0.0568571\pi$
$797$	7995.40i	0.355347i	−0.984089	+	0.177674i	$0.943143\pi$
$798$	− 13401.2i	− 0.594482i
$799$	−30607.7	−1.35522
$800$	0	0
$801$	−14057.8	−0.620109
$802$	39605.3i	1.74378i
$803$	− 10949.8i	− 0.481209i
$804$	−41012.4	−1.79900
$805$	0	0
$806$	47173.8	2.06157
$807$	13706.9i	0.597900i
$808$	− 17659.6i	− 0.768887i
$809$	−7248.83	−0.315025	−0.157513	−	0.987517i	$-0.550348\pi$
$809$	−7248.83	−0.315025	−0.157513	+	0.987517i	$0.550348\pi$
$810$	0	0
$811$	12097.4	0.523793	0.261896	−	0.965096i	$-0.415652\pi$
$811$	12097.4	0.523793	0.261896	+	0.965096i	$0.415652\pi$
$812$	− 19400.3i	− 0.838445i
$813$	19562.1i	0.843880i
$814$	41817.7	1.80063
$815$	0	0
$816$	64142.4	2.75176
$817$	51867.8i	2.22108i
$818$	− 33332.8i	− 1.42476i
$819$	−2931.80	−0.125086
$820$	0	0
$821$	4821.38	0.204954	0.102477	−	0.994735i	$-0.467323\pi$
$821$	4821.38	0.204954	0.102477	+	0.994735i	$0.467323\pi$
$822$	27329.2i	1.15963i
$823$	3733.51i	0.158131i	0.996869	+	0.0790657i	$0.0251937\pi$
$823$	3733.51i	0.158131i	−0.996869	+	0.0790657i	$0.974806\pi$
$824$	98663.3	4.17124
$825$	0	0
$826$	−19360.6	−0.815545
$827$	− 1160.78i	− 0.0488079i	−0.999702	−	0.0244040i	$-0.992231\pi$
$827$	− 1160.78i	− 0.0488079i	0.999702	−	0.0244040i	$-0.00776879\pi$
$828$	− 23578.8i	− 0.989637i
$829$	−18627.0	−0.780389	−0.390195	−	0.920732i	$-0.627592\pi$
$829$	−18627.0	−0.780389	−0.390195	+	0.920732i	$0.627592\pi$
$830$	0	0
$831$	−14765.0	−0.616355
$832$	− 127852.i	− 5.32748i
$833$	− 3725.55i	− 0.154961i
$834$	24440.4	1.01475
$835$	0	0
$836$	−61401.4	−2.54021
$837$	− 4915.31i	− 0.202984i
$838$	359.545i	0.0148213i
$839$	−4213.40	−0.173376	−0.0866881	−	0.996236i	$-0.527628\pi$
$839$	−4213.40	−0.173376	−0.0866881	+	0.996236i	$0.527628\pi$
$840$	0	0
$841$	−9875.99	−0.404936
$842$	− 24957.7i	− 1.02150i
$843$	− 7134.25i	− 0.291479i
$844$	22977.5	0.937106
$845$	0	0
$846$	20174.3	0.819866
$847$	5520.51i	0.223951i
$848$	139420.i	5.64588i
$849$	−26020.4	−1.05184
$850$	0	0
$851$	−36723.6	−1.47928
$852$	− 35205.2i	− 1.41562i
$853$	3940.85i	0.158185i	0.996867	+	0.0790926i	$0.0252023\pi$
$853$	3940.85i	0.158185i	−0.996867	+	0.0790926i	$0.974798\pi$
$854$	−10358.0	−0.415040
$855$	0	0
$856$	93146.7	3.71926
$857$	− 38267.2i	− 1.52530i	−0.646811	−	0.762650i	$-0.723898\pi$
$857$	− 38267.2i	− 1.52530i	0.646811	−	0.762650i	$-0.276102\pi$
$858$	18104.1i	0.720355i
$859$	−10145.2	−0.402969	−0.201484	−	0.979492i	$-0.564577\pi$
$859$	−10145.2	−0.402969	−0.201484	+	0.979492i	$0.564577\pi$
$860$	0	0
$861$	1954.01	0.0773432
$862$	56581.8i	2.23571i
$863$	− 17608.5i	− 0.694553i	−0.937763	−	0.347277i	$-0.887106\pi$
$863$	− 17608.5i	− 0.694553i	0.937763	−	0.347277i	$-0.112894\pi$
$864$	−24230.1	−0.954079
$865$	0	0
$866$	11287.5	0.442917
$867$	2603.39i	0.101979i
$868$	− 29316.8i	− 1.14640i
$869$	11362.8	0.443565
$870$	0	0
$871$	−27653.9	−1.07579
$872$	81091.3i	3.14920i
$873$	− 193.607i	− 0.00750583i
$874$	72672.6	2.81257
$875$	0	0
$876$	32450.3	1.25159
$877$	23555.5i	0.906972i	0.891263	+	0.453486i	$0.149820\pi$
$877$	23555.5i	0.906972i	−0.891263	+	0.453486i	$0.850180\pi$
$878$	52154.8i	2.00471i
$879$	−13005.0	−0.499029
$880$	0	0
$881$	−43719.7	−1.67191	−0.835955	−	0.548797i	$-0.815086\pi$
$881$	−43719.7	−1.67191	−0.835955	+	0.548797i	$0.815086\pi$
$882$	2455.60i	0.0937465i
$883$	31393.4i	1.19646i	0.801325	+	0.598229i	$0.204129\pi$
$883$	31393.4i	1.19646i	−0.801325	+	0.598229i	$0.795871\pi$
$884$	81399.2	3.09700
$885$	0	0
$886$	40879.5	1.55008
$887$	40021.9i	1.51500i	0.652836	+	0.757499i	$0.273579\pi$
$887$	40021.9i	1.51500i	−0.652836	+	0.757499i	$0.726421\pi$
$888$	80833.2i	3.05471i
$889$	3686.80	0.139090
$890$	0	0
$891$	1886.37	0.0709269
$892$	64887.6i	2.43565i
$893$	46136.0i	1.72887i
$894$	−5526.48	−0.206749
$895$	0	0
$896$	−56830.3	−2.11894
$897$	− 15898.7i	− 0.591799i
$898$	25987.2i	0.965705i
$899$	21931.4	0.813628
$900$	0	0
$901$	−37695.5	−1.39380
$902$	− 12066.2i	− 0.445409i
$903$	− 9504.15i	− 0.350253i
$904$	−66846.2	−2.45937
$905$	0	0
$906$	−19041.7	−0.698254
$907$	2729.28i	0.0999165i	0.998751	+	0.0499583i	$0.0159088\pi$
$907$	2729.28i	0.0999165i	−0.998751	+	0.0499583i	$0.984091\pi$
$908$	32688.9i	1.19473i
$909$	−1902.18	−0.0694074
$910$	0	0
$911$	−20874.8	−0.759181	−0.379590	−	0.925155i	$-0.623935\pi$
$911$	−20874.8	−0.759181	−0.379590	+	0.925155i	$0.623935\pi$
$912$	− 96684.2i	− 3.51045i
$913$	29123.1i	1.05568i
$914$	−53724.7	−1.94426
$915$	0	0
$916$	−2011.85	−0.0725691
$917$	− 5794.69i	− 0.208678i
$918$	− 11430.8i	− 0.410973i
$919$	−12339.8	−0.442931	−0.221466	−	0.975168i	$-0.571084\pi$
$919$	−12339.8	−0.442931	−0.221466	+	0.975168i	$0.571084\pi$
$920$	0	0
$921$	17548.1	0.627827
$922$	89635.8i	3.20173i
$923$	− 23738.2i	− 0.846537i
$924$	11251.1	0.400577
$925$	0	0
$926$	61388.1	2.17855
$927$	− 10627.4i	− 0.376538i
$928$	− 108111.i	− 3.82427i
$929$	51868.3	1.83180	0.915900	−	0.401407i	$-0.131479\pi$
$929$	51868.3	1.83180	0.915900	+	0.401407i	$0.131479\pi$
$930$	0	0
$931$	−5615.65	−0.197686
$932$	− 108578.i	− 3.81609i
$933$	15015.0i	0.526869i
$934$	−85059.5	−2.97990
$935$	0	0
$936$	−34995.1	−1.22206
$937$	− 47757.7i	− 1.66508i	−0.553967	−	0.832538i	$-0.686887\pi$
$937$	− 47757.7i	− 1.66508i	0.553967	−	0.832538i	$-0.313113\pi$
$938$	23162.2i	0.806260i
$939$	−22086.2	−0.767577
$940$	0	0
$941$	−41845.5	−1.44966	−0.724828	−	0.688930i	$-0.758081\pi$
$941$	−41845.5	−1.44966	−0.724828	+	0.688930i	$0.758081\pi$
$942$	55091.1i	1.90548i
$943$	10596.3i	0.365921i
$944$	−139679.	−4.81585
$945$	0	0
$946$	−58688.9	−2.01706
$947$	14121.8i	0.484580i	0.970204	+	0.242290i	$0.0778985\pi$
$947$	14121.8i	0.484580i	−0.970204	+	0.242290i	$0.922101\pi$
$948$	33674.2i	1.15368i
$949$	21880.6	0.748445
$950$	0	0
$951$	23609.7	0.805043
$952$	− 44469.5i	− 1.51393i
$953$	31178.0i	1.05976i	0.848071	+	0.529882i	$0.177764\pi$
$953$	31178.0i	1.05976i	−0.848071	+	0.529882i	$0.822236\pi$
$954$	24846.0	0.843208
$955$	0	0
$956$	−19569.8	−0.662062
$957$	8416.71i	0.284298i
$958$	34787.6i	1.17321i
$959$	11452.1	0.385618
$960$	0	0
$961$	3350.60	0.112470
$962$	83562.6i	2.80059i
$963$	− 10033.2i	− 0.335738i
$964$	−92867.2	−3.10275
$965$	0	0
$966$	−13316.4	−0.443527
$967$	− 34789.7i	− 1.15694i	−0.815704	−	0.578470i	$-0.803650\pi$
$967$	− 34789.7i	− 1.15694i	0.815704	−	0.578470i	$-0.196350\pi$
$968$	65894.8i	2.18795i
$969$	26140.8	0.866630
$970$	0	0
$971$	20481.9	0.676926	0.338463	−	0.940980i	$-0.390093\pi$
$971$	20481.9	0.676926	0.338463	+	0.940980i	$0.390093\pi$
$972$	5590.34i	0.184476i
$973$	− 10241.6i	− 0.337440i
$974$	−86752.6	−2.85393
$975$	0	0
$976$	−74729.1	−2.45084
$977$	5605.71i	0.183565i	0.995779	+	0.0917823i	$0.0292564\pi$
$977$	5605.71i	0.183565i	−0.995779	+	0.0917823i	$0.970744\pi$
$978$	− 42914.9i	− 1.40314i
$979$	36376.1	1.18752
$980$	0	0
$981$	8734.67	0.284278
$982$	31207.9i	1.01414i
$983$	− 34728.1i	− 1.12681i	−0.826180	−	0.563406i	$-0.809491\pi$
$983$	− 34728.1i	− 1.12681i	0.826180	−	0.563406i	$-0.190509\pi$
$984$	23323.8	0.755625
$985$	0	0
$986$	51002.6	1.64732
$987$	− 8453.87i	− 0.272634i
$988$	− 122696.i	− 3.95089i
$989$	51539.6	1.65709
$990$	0	0
$991$	−2145.57	−0.0687753	−0.0343876	−	0.999409i	$-0.510948\pi$
$991$	−2145.57	−0.0687753	−0.0343876	+	0.999409i	$0.510948\pi$
$992$	− 163372.i	− 5.22890i
$993$	7825.62i	0.250089i
$994$	−19882.5	−0.634442
$995$	0	0
$996$	−86307.5	−2.74574
$997$	− 59620.3i	− 1.89388i	−0.321417	−	0.946938i	$-0.604159\pi$
$997$	− 59620.3i	− 1.89388i	0.321417	−	0.946938i	$-0.395841\pi$
$998$	− 100323.i	− 3.18203i
$999$	8706.87	0.275749

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.o.274.8		8
5.2	odd	4		525.4.a.s.1.1	✓	4
5.3	odd	4		525.4.a.v.1.4	yes	4
5.4	even	2	inner	525.4.d.o.274.1		8
15.2	even	4		1575.4.a.bm.1.4		4
15.8	even	4		1575.4.a.bf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.4.a.s.1.1	✓	4	5.2	odd	4
525.4.a.v.1.4	yes	4	5.3	odd	4
525.4.d.o.274.1		8	5.4	even	2	inner
525.4.d.o.274.8		8	1.1	even	1	trivial
1575.4.a.bf.1.1		4	15.8	even	4
1575.4.a.bm.1.4		4	15.2	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	525.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+5.56826i q^{2} -3.00000i q^{3} -23.0055 q^{4} +16.7048 q^{6} -7.00000i q^{7} -83.5546i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+5.56826i q^{2} -3.00000i q^{3} -23.0055 q^{4} +16.7048 q^{6} -7.00000i q^{7} -83.5546i q^{8} -9.00000 q^{9} +23.2885 q^{11} +69.0165i q^{12} +46.5366i q^{13} +38.9778 q^{14} +281.210 q^{16} +76.0316i q^{17} -50.1143i q^{18} +114.605 q^{19} -21.0000 q^{21} +129.677i q^{22} -113.880i q^{23} -250.664 q^{24} -259.128 q^{26} +27.0000i q^{27} +161.039i q^{28} -120.470 q^{29} -182.048 q^{31} +897.411i q^{32} -69.8656i q^{33} -423.363 q^{34} +207.050 q^{36} -322.477i q^{37} +638.151i q^{38} +139.610 q^{39} -93.0481 q^{41} -116.933i q^{42} +452.579i q^{43} -535.765 q^{44} +634.113 q^{46} +402.565i q^{47} -843.629i q^{48} -49.0000 q^{49} +228.095 q^{51} -1070.60i q^{52} +495.787i q^{53} -150.343 q^{54} -584.882 q^{56} -343.815i q^{57} -670.808i q^{58} -496.707 q^{59} -265.742 q^{61} -1013.69i q^{62} +63.0000i q^{63} -2747.34 q^{64} +389.030 q^{66} +594.240i q^{67} -1749.14i q^{68} -341.640 q^{69} -510.099 q^{71} +751.991i q^{72} -470.181i q^{73} +1795.63 q^{74} -2636.55 q^{76} -163.020i q^{77} +777.383i q^{78} +487.916 q^{79} +81.0000 q^{81} -518.116i q^{82} +1250.53i q^{83} +483.116 q^{84} -2520.08 q^{86} +361.410i q^{87} -1945.86i q^{88} +1561.98 q^{89} +325.756 q^{91} +2619.87i q^{92} +546.145i q^{93} -2241.59 q^{94} +2692.23 q^{96} +21.5118i q^{97} -272.845i q^{98} -209.597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9}+O(q^{10}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9	\( 8 q - 32 q^{4} + 36 q^{6} - 72 q^{9} + 114 q^{11} + 84 q^{14} + 432 q^{16} + 24 q^{19} - 168 q^{21} - 558 q^{24} - 162 q^{26} - 756 q^{29} - 186 q^{31} - 1566 q^{34} + 288 q^{36} - 258 q^{39} - 930 q^{41} - 1362 q^{44} + 620 q^{46} - 392 q^{49} + 594 q^{51} - 324 q^{54} - 1302 q^{56} - 462 q^{59} - 2706 q^{61} - 6214 q^{64} - 246 q^{66} - 936 q^{69} - 3450 q^{71} + 3906 q^{74} - 6092 q^{76} - 3258 q^{79} + 648 q^{81} + 672 q^{84} - 9084 q^{86} + 1956 q^{89} - 602 q^{91} - 4960 q^{94} + 4140 q^{96} - 1026 q^{99}+O(q^{100}) \) 8 * q - 32 * q^4 + 36 * q^6 - 72 * q^9 + 114 * q^11 + 84 * q^14 + 432 * q^16 + 24 * q^19 - 168 * q^21 - 558 * q^24 - 162 * q^26 - 756 * q^29 - 186 * q^31 - 1566 * q^34 + 288 * q^36 - 258 * q^39 - 930 * q^41 - 1362 * q^44 + 620 * q^46 - 392 * q^49 + 594 * q^51 - 324 * q^54 - 1302 * q^56 - 462 * q^59 - 2706 * q^61 - 6214 * q^64 - 246 * q^66 - 936 * q^69 - 3450 * q^71 + 3906 * q^74 - 6092 * q^76 - 3258 * q^79 + 648 * q^81 + 672 * q^84 - 9084 * q^86 + 1956 * q^89 - 602 * q^91 - 4960 * q^94 + 4140 * q^96 - 1026 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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