LMFDB - Embedded newform 525.4.d.a.274.2

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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	525.274
Dual form			525.4.d.a.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} -15.0000 q^{6} +7.00000i q^{7} -45.0000i q^{8} -9.00000 q^{9} +O(q^{10})$	\(q+5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} -15.0000 q^{6} +7.00000i q^{7} -45.0000i q^{8} -9.00000 q^{9} +12.0000 q^{11} -51.0000i q^{12} -30.0000i q^{13} -35.0000 q^{14} +89.0000 q^{16} -134.000i q^{17} -45.0000i q^{18} +92.0000 q^{19} -21.0000 q^{21} +60.0000i q^{22} -112.000i q^{23} +135.000 q^{24} +150.000 q^{26} -27.0000i q^{27} -119.000i q^{28} +58.0000 q^{29} -224.000 q^{31} +85.0000i q^{32} +36.0000i q^{33} +670.000 q^{34} +153.000 q^{36} -146.000i q^{37} +460.000i q^{38} +90.0000 q^{39} +18.0000 q^{41} -105.000i q^{42} -340.000i q^{43} -204.000 q^{44} +560.000 q^{46} +208.000i q^{47} +267.000i q^{48} -49.0000 q^{49} +402.000 q^{51} +510.000i q^{52} +754.000i q^{53} +135.000 q^{54} +315.000 q^{56} +276.000i q^{57} +290.000i q^{58} -380.000 q^{59} +718.000 q^{61} -1120.00i q^{62} -63.0000i q^{63} +287.000 q^{64} -180.000 q^{66} +412.000i q^{67} +2278.00i q^{68} +336.000 q^{69} -960.000 q^{71} +405.000i q^{72} -1066.00i q^{73} +730.000 q^{74} -1564.00 q^{76} +84.0000i q^{77} +450.000i q^{78} -896.000 q^{79} +81.0000 q^{81} +90.0000i q^{82} -436.000i q^{83} +357.000 q^{84} +1700.00 q^{86} +174.000i q^{87} -540.000i q^{88} +1038.00 q^{89} +210.000 q^{91} +1904.00i q^{92} -672.000i q^{93} -1040.00 q^{94} -255.000 q^{96} -702.000i q^{97} -245.000i q^{98} -108.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 34 q^{4} - 30 q^{6} - 18 q^{9}+O(q^{10}) $ 2 * q - 34 * q^4 - 30 * q^6 - 18 * q^9	$ 2 q - 34 q^{4} - 30 q^{6} - 18 q^{9} + 24 q^{11} - 70 q^{14} + 178 q^{16} + 184 q^{19} - 42 q^{21} + 270 q^{24} + 300 q^{26} + 116 q^{29} - 448 q^{31} + 1340 q^{34} + 306 q^{36} + 180 q^{39} + 36 q^{41} - 408 q^{44} + 1120 q^{46} - 98 q^{49} + 804 q^{51} + 270 q^{54} + 630 q^{56} - 760 q^{59} + 1436 q^{61} + 574 q^{64} - 360 q^{66} + 672 q^{69} - 1920 q^{71} + 1460 q^{74} - 3128 q^{76} - 1792 q^{79} + 162 q^{81} + 714 q^{84} + 3400 q^{86} + 2076 q^{89} + 420 q^{91} - 2080 q^{94} - 510 q^{96} - 216 q^{99}+O(q^{100}) $ 2 * q - 34 * q^4 - 30 * q^6 - 18 * q^9 + 24 * q^11 - 70 * q^14 + 178 * q^16 + 184 * q^19 - 42 * q^21 + 270 * q^24 + 300 * q^26 + 116 * q^29 - 448 * q^31 + 1340 * q^34 + 306 * q^36 + 180 * q^39 + 36 * q^41 - 408 * q^44 + 1120 * q^46 - 98 * q^49 + 804 * q^51 + 270 * q^54 + 630 * q^56 - 760 * q^59 + 1436 * q^61 + 574 * q^64 - 360 * q^66 + 672 * q^69 - 1920 * q^71 + 1460 * q^74 - 3128 * q^76 - 1792 * q^79 + 162 * q^81 + 714 * q^84 + 3400 * q^86 + 2076 * q^89 + 420 * q^91 - 2080 * q^94 - 510 * q^96 - 216 * 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 $

$2$	5.00000i	1.76777i	0.467707	+	0.883883i	$0.345080\pi$
$2$	5.00000i	1.76777i	−0.467707	+	0.883883i	$0.654920\pi$
$3$	3.00000i	0.577350i
$3$	3.00000i	0.577350i
$4$	−17.0000	−2.12500
$5$	0	0
$5$	0	0
$6$	−15.0000	−1.02062
$7$	7.00000i	0.377964i
$7$	7.00000i	0.377964i
$8$	− 45.0000i	− 1.98874i
$9$	−9.00000	−0.333333
$10$	0	0
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	− 51.0000i	− 1.22687i
$13$	− 30.0000i	− 0.640039i	−0.947411	−	0.320019i	$-0.896311\pi$
$13$	− 30.0000i	− 0.640039i	0.947411	−	0.320019i	$-0.103689\pi$
$14$	−35.0000	−0.668153
$15$	0	0
$16$	89.0000	1.39062
$17$	− 134.000i	− 1.91175i	−0.293771	−	0.955876i	$-0.594910\pi$
$17$	− 134.000i	− 1.91175i	0.293771	−	0.955876i	$-0.405090\pi$
$18$	− 45.0000i	− 0.589256i
$19$	92.0000	1.11086	0.555428	−	0.831565i	$-0.312555\pi$
$19$	92.0000	1.11086	0.555428	+	0.831565i	$0.312555\pi$
$20$	0	0
$21$	−21.0000	−0.218218
$22$	60.0000i	0.581456i
$23$	− 112.000i	− 1.01537i	−0.861541	−	0.507687i	$-0.830501\pi$
$23$	− 112.000i	− 1.01537i	0.861541	−	0.507687i	$-0.169499\pi$
$24$	135.000	1.14820
$25$	0	0
$26$	150.000	1.13144
$27$	− 27.0000i	− 0.192450i
$28$	− 119.000i	− 0.803175i
$29$	58.0000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−224.000	−1.29779	−0.648897	−	0.760877i	$-0.724769\pi$
$31$	−224.000	−1.29779	−0.648897	+	0.760877i	$0.724769\pi$
$32$	85.0000i	0.469563i
$33$	36.0000i	0.189903i
$34$	670.000	3.37953
$35$	0	0
$36$	153.000	0.708333
$37$	− 146.000i	− 0.648710i	−0.945936	−	0.324355i	$-0.894853\pi$
$37$	− 146.000i	− 0.648710i	0.945936	−	0.324355i	$-0.105147\pi$
$38$	460.000i	1.96373i
$39$	90.0000	0.369527
$40$	0	0
$41$	18.0000	0.0685641	0.0342820	−	0.999412i	$-0.489086\pi$
$41$	18.0000	0.0685641	0.0342820	+	0.999412i	$0.489086\pi$
$42$	− 105.000i	− 0.385758i
$43$	− 340.000i	− 1.20580i	−0.797816	−	0.602901i	$-0.794011\pi$
$43$	− 340.000i	− 1.20580i	0.797816	−	0.602901i	$-0.205989\pi$
$44$	−204.000	−0.698958
$45$	0	0
$46$	560.000	1.79495
$47$	208.000i	0.645530i	0.946479	+	0.322765i	$0.104612\pi$
$47$	208.000i	0.645530i	−0.946479	+	0.322765i	$0.895388\pi$
$48$	267.000i	0.802878i
$49$	−49.0000	−0.142857
$50$	0	0
$51$	402.000	1.10375
$52$	510.000i	1.36008i
$53$	754.000i	1.95415i	0.212899	+	0.977074i	$0.431709\pi$
$53$	754.000i	1.95415i	−0.212899	+	0.977074i	$0.568291\pi$
$54$	135.000	0.340207
$55$	0	0
$56$	315.000	0.751672
$57$	276.000i	0.641353i
$58$	290.000i	0.656532i
$59$	−380.000	−0.838505	−0.419252	−	0.907870i	$-0.637708\pi$
$59$	−380.000	−0.838505	−0.419252	+	0.907870i	$0.637708\pi$
$60$	0	0
$61$	718.000	1.50706	0.753529	−	0.657415i	$-0.228350\pi$
$61$	718.000	1.50706	0.753529	+	0.657415i	$0.228350\pi$
$62$	− 1120.00i	− 2.29420i
$63$	− 63.0000i	− 0.125988i
$64$	287.000	0.560547
$65$	0	0
$66$	−180.000	−0.335704
$67$	412.000i	0.751251i	0.926772	+	0.375625i	$0.122572\pi$
$67$	412.000i	0.751251i	−0.926772	+	0.375625i	$0.877428\pi$
$68$	2278.00i	4.06247i
$69$	336.000	0.586227
$70$	0	0
$71$	−960.000	−1.60466	−0.802331	−	0.596879i	$-0.796407\pi$
$71$	−960.000	−1.60466	−0.802331	+	0.596879i	$0.796407\pi$
$72$	405.000i	0.662913i
$73$	− 1066.00i	− 1.70912i	−0.519352	−	0.854561i	$-0.673826\pi$
$73$	− 1066.00i	− 1.70912i	0.519352	−	0.854561i	$-0.326174\pi$
$74$	730.000	1.14677
$75$	0	0
$76$	−1564.00	−2.36057
$77$	84.0000i	0.124321i
$78$	450.000i	0.653237i
$79$	−896.000	−1.27605	−0.638025	−	0.770016i	$-0.720248\pi$
$79$	−896.000	−1.27605	−0.638025	+	0.770016i	$0.720248\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	90.0000i	0.121205i
$83$	− 436.000i	− 0.576593i	−0.957541	−	0.288296i	$-0.906911\pi$
$83$	− 436.000i	− 0.576593i	0.957541	−	0.288296i	$-0.0930889\pi$
$84$	357.000	0.463713
$85$	0	0
$86$	1700.00	2.13158
$87$	174.000i	0.214423i
$88$	− 540.000i	− 0.654139i
$89$	1038.00	1.23627	0.618134	−	0.786073i	$-0.287889\pi$
$89$	1038.00	1.23627	0.618134	+	0.786073i	$0.287889\pi$
$90$	0	0
$91$	210.000	0.241912
$92$	1904.00i	2.15767i
$93$	− 672.000i	− 0.749281i
$94$	−1040.00	−1.14115
$95$	0	0
$96$	−255.000	−0.271102
$97$	− 702.000i	− 0.734818i	−0.930060	−	0.367409i	$-0.880245\pi$
$97$	− 702.000i	− 0.734818i	0.930060	−	0.367409i	$-0.119755\pi$
$98$	− 245.000i	− 0.252538i
$99$	−108.000	−0.109640
$100$	0	0
$101$	46.0000	0.0453185	0.0226593	−	0.999743i	$-0.492787\pi$
$101$	46.0000	0.0453185	0.0226593	+	0.999743i	$0.492787\pi$
$102$	2010.00i	1.95117i
$103$	− 1880.00i	− 1.79847i	−0.437471	−	0.899233i	$-0.644126\pi$
$103$	− 1880.00i	− 1.79847i	0.437471	−	0.899233i	$-0.355874\pi$
$104$	−1350.00	−1.27287
$105$	0	0
$106$	−3770.00	−3.45448
$107$	732.000i	0.661356i	0.943744	+	0.330678i	$0.107277\pi$
$107$	732.000i	0.661356i	−0.943744	+	0.330678i	$0.892723\pi$
$108$	459.000i	0.408956i
$109$	378.000	0.332164	0.166082	−	0.986112i	$-0.446888\pi$
$109$	378.000	0.332164	0.166082	+	0.986112i	$0.446888\pi$
$110$	0	0
$111$	438.000	0.374533
$112$	623.000i	0.525607i
$113$	− 1458.00i	− 1.21378i	−0.794786	−	0.606890i	$-0.792417\pi$
$113$	− 1458.00i	− 1.21378i	0.794786	−	0.606890i	$-0.207583\pi$
$114$	−1380.00	−1.13376
$115$	0	0
$116$	−986.000	−0.789205
$117$	270.000i	0.213346i
$118$	− 1900.00i	− 1.48228i
$119$	938.000	0.722574
$120$	0	0
$121$	−1187.00	−0.891811
$122$	3590.00i	2.66413i
$123$	54.0000i	0.0395855i
$124$	3808.00	2.75781
$125$	0	0
$126$	315.000	0.222718
$127$	608.000i	0.424813i	0.977181	+	0.212407i	$0.0681301\pi$
$127$	608.000i	0.424813i	−0.977181	+	0.212407i	$0.931870\pi$
$128$	2115.00i	1.46048i
$129$	1020.00	0.696170
$130$	0	0
$131$	−956.000	−0.637604	−0.318802	−	0.947821i	$-0.603280\pi$
$131$	−956.000	−0.637604	−0.318802	+	0.947821i	$0.603280\pi$
$132$	− 612.000i	− 0.403544i
$133$	644.000i	0.419864i
$134$	−2060.00	−1.32804
$135$	0	0
$136$	−6030.00	−3.80197
$137$	− 374.000i	− 0.233233i	−0.993177	−	0.116617i	$-0.962795\pi$
$137$	− 374.000i	− 0.233233i	0.993177	−	0.116617i	$-0.0372049\pi$
$138$	1680.00i	1.03631i
$139$	−396.000	−0.241642	−0.120821	−	0.992674i	$-0.538553\pi$
$139$	−396.000	−0.241642	−0.120821	+	0.992674i	$0.538553\pi$
$140$	0	0
$141$	−624.000	−0.372697
$142$	− 4800.00i	− 2.83667i
$143$	− 360.000i	− 0.210522i
$144$	−801.000	−0.463542
$145$	0	0
$146$	5330.00	3.02133
$147$	− 147.000i	− 0.0824786i
$148$	2482.00i	1.37851i
$149$	1874.00	1.03036	0.515181	−	0.857081i	$-0.327725\pi$
$149$	1874.00	1.03036	0.515181	+	0.857081i	$0.327725\pi$
$150$	0	0
$151$	−1096.00	−0.590670	−0.295335	−	0.955394i	$-0.595431\pi$
$151$	−1096.00	−0.590670	−0.295335	+	0.955394i	$0.595431\pi$
$152$	− 4140.00i	− 2.20920i
$153$	1206.00i	0.637250i
$154$	−420.000	−0.219770
$155$	0	0
$156$	−1530.00	−0.785244
$157$	1918.00i	0.974988i	0.873126	+	0.487494i	$0.162089\pi$
$157$	1918.00i	0.974988i	−0.873126	+	0.487494i	$0.837911\pi$
$158$	− 4480.00i	− 2.25576i
$159$	−2262.00	−1.12823
$160$	0	0
$161$	784.000	0.383776
$162$	405.000i	0.196419i
$163$	− 2316.00i	− 1.11290i	−0.830880	−	0.556451i	$-0.812163\pi$
$163$	− 2316.00i	− 1.11290i	0.830880	−	0.556451i	$-0.187837\pi$
$164$	−306.000	−0.145699
$165$	0	0
$166$	2180.00	1.01928
$167$	− 1736.00i	− 0.804405i	−0.915551	−	0.402203i	$-0.868245\pi$
$167$	− 1736.00i	− 0.804405i	0.915551	−	0.402203i	$-0.131755\pi$
$168$	945.000i	0.433978i
$169$	1297.00	0.590350
$170$	0	0
$171$	−828.000	−0.370285
$172$	5780.00i	2.56233i
$173$	2442.00i	1.07319i	0.843840	+	0.536595i	$0.180290\pi$
$173$	2442.00i	1.07319i	−0.843840	+	0.536595i	$0.819710\pi$
$174$	−870.000	−0.379049
$175$	0	0
$176$	1068.00	0.457406
$177$	− 1140.00i	− 0.484111i
$178$	5190.00i	2.18543i
$179$	4092.00	1.70866	0.854331	−	0.519730i	$-0.173967\pi$
$179$	4092.00	1.70866	0.854331	+	0.519730i	$0.173967\pi$
$180$	0	0
$181$	1270.00	0.521538	0.260769	−	0.965401i	$-0.416024\pi$
$181$	1270.00	0.521538	0.260769	+	0.965401i	$0.416024\pi$
$182$	1050.00i	0.427644i
$183$	2154.00i	0.870100i
$184$	−5040.00	−2.01931
$185$	0	0
$186$	3360.00	1.32455
$187$	− 1608.00i	− 0.628816i
$188$	− 3536.00i	− 1.37175i
$189$	189.000	0.0727393
$190$	0	0
$191$	4904.00	1.85781	0.928903	−	0.370323i	$-0.120753\pi$
$191$	4904.00	1.85781	0.928903	+	0.370323i	$0.120753\pi$
$192$	861.000i	0.323632i
$193$	− 2178.00i	− 0.812310i	−0.913804	−	0.406155i	$-0.866869\pi$
$193$	− 2178.00i	− 0.812310i	0.913804	−	0.406155i	$-0.133131\pi$
$194$	3510.00	1.29899
$195$	0	0
$196$	833.000	0.303571
$197$	− 2850.00i	− 1.03073i	−0.856970	−	0.515366i	$-0.827656\pi$
$197$	− 2850.00i	− 1.03073i	0.856970	−	0.515366i	$-0.172344\pi$
$198$	− 540.000i	− 0.193819i
$199$	1144.00	0.407518	0.203759	−	0.979021i	$-0.434684\pi$
$199$	1144.00	0.407518	0.203759	+	0.979021i	$0.434684\pi$
$200$	0	0
$201$	−1236.00	−0.433735
$202$	230.000i	0.0801126i
$203$	406.000i	0.140372i
$204$	−6834.00	−2.34547
$205$	0	0
$206$	9400.00	3.17927
$207$	1008.00i	0.338458i
$208$	− 2670.00i	− 0.890054i
$209$	1104.00	0.365384
$210$	0	0
$211$	412.000	0.134423	0.0672115	−	0.997739i	$-0.478590\pi$
$211$	412.000	0.134423	0.0672115	+	0.997739i	$0.478590\pi$
$212$	− 12818.0i	− 4.15257i
$213$	− 2880.00i	− 0.926452i
$214$	−3660.00	−1.16912
$215$	0	0
$216$	−1215.00	−0.382733
$217$	− 1568.00i	− 0.490520i
$218$	1890.00i	0.587188i
$219$	3198.00	0.986762
$220$	0	0
$221$	−4020.00	−1.22359
$222$	2190.00i	0.662086i
$223$	1632.00i	0.490075i	0.969514	+	0.245038i	$0.0788003\pi$
$223$	1632.00i	0.490075i	−0.969514	+	0.245038i	$0.921200\pi$
$224$	−595.000	−0.177478
$225$	0	0
$226$	7290.00	2.14568
$227$	4084.00i	1.19412i	0.802198	+	0.597059i	$0.203664\pi$
$227$	4084.00i	1.19412i	−0.802198	+	0.597059i	$0.796336\pi$
$228$	− 4692.00i	− 1.36287i
$229$	3386.00	0.977088	0.488544	−	0.872539i	$-0.337528\pi$
$229$	3386.00	0.977088	0.488544	+	0.872539i	$0.337528\pi$
$230$	0	0
$231$	−252.000	−0.0717765
$232$	− 2610.00i	− 0.738599i
$233$	− 5322.00i	− 1.49638i	−0.663486	−	0.748188i	$-0.730924\pi$
$233$	− 5322.00i	− 1.49638i	0.663486	−	0.748188i	$-0.269076\pi$
$234$	−1350.00	−0.377146
$235$	0	0
$236$	6460.00	1.78182
$237$	− 2688.00i	− 0.736727i
$238$	4690.00i	1.27734i
$239$	−3736.00	−1.01114	−0.505569	−	0.862786i	$-0.668717\pi$
$239$	−3736.00	−1.01114	−0.505569	+	0.862786i	$0.668717\pi$
$240$	0	0
$241$	210.000	0.0561298	0.0280649	−	0.999606i	$-0.491065\pi$
$241$	210.000	0.0561298	0.0280649	+	0.999606i	$0.491065\pi$
$242$	− 5935.00i	− 1.57651i
$243$	243.000i	0.0641500i
$244$	−12206.0	−3.20250
$245$	0	0
$246$	−270.000	−0.0699779
$247$	− 2760.00i	− 0.710990i
$248$	10080.0i	2.58097i
$249$	1308.00	0.332896
$250$	0	0
$251$	−4212.00	−1.05920	−0.529600	−	0.848248i	$-0.677658\pi$
$251$	−4212.00	−1.05920	−0.529600	+	0.848248i	$0.677658\pi$
$252$	1071.00i	0.267725i
$253$	− 1344.00i	− 0.333978i
$254$	−3040.00	−0.750971
$255$	0	0
$256$	−8279.00	−2.02124
$257$	5130.00i	1.24514i	0.782565	+	0.622569i	$0.213911\pi$
$257$	5130.00i	1.24514i	−0.782565	+	0.622569i	$0.786089\pi$
$258$	5100.00i	1.23067i
$259$	1022.00	0.245189
$260$	0	0
$261$	−522.000	−0.123797
$262$	− 4780.00i	− 1.12714i
$263$	− 848.000i	− 0.198821i	−0.995047	−	0.0994105i	$-0.968304\pi$
$263$	− 848.000i	− 0.198821i	0.995047	−	0.0994105i	$-0.0316957\pi$
$264$	1620.00	0.377667
$265$	0	0
$266$	−3220.00	−0.742221
$267$	3114.00i	0.713759i
$268$	− 7004.00i	− 1.59641i
$269$	1274.00	0.288763	0.144381	−	0.989522i	$-0.453881\pi$
$269$	1274.00	0.288763	0.144381	+	0.989522i	$0.453881\pi$
$270$	0	0
$271$	864.000	0.193669	0.0968344	−	0.995301i	$-0.469128\pi$
$271$	864.000	0.193669	0.0968344	+	0.995301i	$0.469128\pi$
$272$	− 11926.0i	− 2.65853i
$273$	630.000i	0.139668i
$274$	1870.00	0.412302
$275$	0	0
$276$	−5712.00	−1.24573
$277$	− 8530.00i	− 1.85025i	−0.379668	−	0.925123i	$-0.623962\pi$
$277$	− 8530.00i	− 1.85025i	0.379668	−	0.925123i	$-0.376038\pi$
$278$	− 1980.00i	− 0.427167i
$279$	2016.00	0.432598
$280$	0	0
$281$	−5382.00	−1.14257	−0.571287	−	0.820750i	$-0.693556\pi$
$281$	−5382.00	−1.14257	−0.571287	+	0.820750i	$0.693556\pi$
$282$	− 3120.00i	− 0.658841i
$283$	− 6236.00i	− 1.30986i	−0.755687	−	0.654932i	$-0.772697\pi$
$283$	− 6236.00i	− 1.30986i	0.755687	−	0.654932i	$-0.227303\pi$
$284$	16320.0	3.40991
$285$	0	0
$286$	1800.00	0.372155
$287$	126.000i	0.0259148i
$288$	− 765.000i	− 0.156521i
$289$	−13043.0	−2.65479
$290$	0	0
$291$	2106.00	0.424247
$292$	18122.0i	3.63188i
$293$	818.000i	0.163099i	0.996669	+	0.0815496i	$0.0259869\pi$
$293$	818.000i	0.163099i	−0.996669	+	0.0815496i	$0.974013\pi$
$294$	735.000	0.145803
$295$	0	0
$296$	−6570.00	−1.29011
$297$	− 324.000i	− 0.0633010i
$298$	9370.00i	1.82144i
$299$	−3360.00	−0.649879
$300$	0	0
$301$	2380.00	0.455751
$302$	− 5480.00i	− 1.04417i
$303$	138.000i	0.0261647i
$304$	8188.00	1.54478
$305$	0	0
$306$	−6030.00	−1.12651
$307$	− 2268.00i	− 0.421634i	−0.977526	−	0.210817i	$-0.932388\pi$
$307$	− 2268.00i	− 0.421634i	0.977526	−	0.210817i	$-0.0676124\pi$
$308$	− 1428.00i	− 0.264181i
$309$	5640.00	1.03834
$310$	0	0
$311$	6648.00	1.21213	0.606067	−	0.795414i	$-0.292746\pi$
$311$	6648.00	1.21213	0.606067	+	0.795414i	$0.292746\pi$
$312$	− 4050.00i	− 0.734891i
$313$	− 9818.00i	− 1.77299i	−0.462737	−	0.886495i	$-0.653133\pi$
$313$	− 9818.00i	− 1.77299i	0.462737	−	0.886495i	$-0.346867\pi$
$314$	−9590.00	−1.72355
$315$	0	0
$316$	15232.0	2.71160
$317$	934.000i	0.165485i	0.996571	+	0.0827424i	$0.0263679\pi$
$317$	934.000i	0.165485i	−0.996571	+	0.0827424i	$0.973632\pi$
$318$	− 11310.0i	− 1.99444i
$319$	696.000	0.122158
$320$	0	0
$321$	−2196.00	−0.381834
$322$	3920.00i	0.678426i
$323$	− 12328.0i	− 2.12368i
$324$	−1377.00	−0.236111
$325$	0	0
$326$	11580.0	1.96735
$327$	1134.00i	0.191775i
$328$	− 810.000i	− 0.136356i
$329$	−1456.00	−0.243987
$330$	0	0
$331$	2292.00	0.380603	0.190302	−	0.981726i	$-0.439053\pi$
$331$	2292.00	0.380603	0.190302	+	0.981726i	$0.439053\pi$
$332$	7412.00i	1.22526i
$333$	1314.00i	0.216237i
$334$	8680.00	1.42200
$335$	0	0
$336$	−1869.00	−0.303459
$337$	− 6062.00i	− 0.979876i	−0.871757	−	0.489938i	$-0.837019\pi$
$337$	− 6062.00i	− 0.979876i	0.871757	−	0.489938i	$-0.162981\pi$
$338$	6485.00i	1.04360i
$339$	4374.00	0.700776
$340$	0	0
$341$	−2688.00	−0.426872
$342$	− 4140.00i	− 0.654578i
$343$	− 343.000i	− 0.0539949i
$344$	−15300.0	−2.39803
$345$	0	0
$346$	−12210.0	−1.89715
$347$	1484.00i	0.229583i	0.993390	+	0.114791i	$0.0366200\pi$
$347$	1484.00i	0.229583i	−0.993390	+	0.114791i	$0.963380\pi$
$348$	− 2958.00i	− 0.455648i
$349$	−254.000	−0.0389579	−0.0194790	−	0.999810i	$-0.506201\pi$
$349$	−254.000	−0.0389579	−0.0194790	+	0.999810i	$0.506201\pi$
$350$	0	0
$351$	−810.000	−0.123176
$352$	1020.00i	0.154449i
$353$	10950.0i	1.65102i	0.564388	+	0.825509i	$0.309112\pi$
$353$	10950.0i	1.65102i	−0.564388	+	0.825509i	$0.690888\pi$
$354$	5700.00	0.855795
$355$	0	0
$356$	−17646.0	−2.62707
$357$	2814.00i	0.417178i
$358$	20460.0i	3.02052i
$359$	−11376.0	−1.67243	−0.836215	−	0.548402i	$-0.815236\pi$
$359$	−11376.0	−1.67243	−0.836215	+	0.548402i	$0.815236\pi$
$360$	0	0
$361$	1605.00	0.233999
$362$	6350.00i	0.921957i
$363$	− 3561.00i	− 0.514887i
$364$	−3570.00	−0.514063
$365$	0	0
$366$	−10770.0	−1.53813
$367$	− 1136.00i	− 0.161577i	−0.996731	−	0.0807884i	$-0.974256\pi$
$367$	− 1136.00i	− 0.161577i	0.996731	−	0.0807884i	$-0.0257438\pi$
$368$	− 9968.00i	− 1.41201i
$369$	−162.000	−0.0228547
$370$	0	0
$371$	−5278.00	−0.738599
$372$	11424.0i	1.59222i
$373$	8242.00i	1.14411i	0.820214	+	0.572057i	$0.193854\pi$
$373$	8242.00i	1.14411i	−0.820214	+	0.572057i	$0.806146\pi$
$374$	8040.00	1.11160
$375$	0	0
$376$	9360.00	1.28379
$377$	− 1740.00i	− 0.237704i
$378$	945.000i	0.128586i
$379$	−3620.00	−0.490625	−0.245313	−	0.969444i	$-0.578891\pi$
$379$	−3620.00	−0.490625	−0.245313	+	0.969444i	$0.578891\pi$
$380$	0	0
$381$	−1824.00	−0.245266
$382$	24520.0i	3.28417i
$383$	8464.00i	1.12922i	0.825359	+	0.564609i	$0.190973\pi$
$383$	8464.00i	1.12922i	−0.825359	+	0.564609i	$0.809027\pi$
$384$	−6345.00	−0.843208
$385$	0	0
$386$	10890.0	1.43598
$387$	3060.00i	0.401934i
$388$	11934.0i	1.56149i
$389$	−3678.00	−0.479388	−0.239694	−	0.970848i	$-0.577047\pi$
$389$	−3678.00	−0.479388	−0.239694	+	0.970848i	$0.577047\pi$
$390$	0	0
$391$	−15008.0	−1.94114
$392$	2205.00i	0.284105i
$393$	− 2868.00i	− 0.368121i
$394$	14250.0	1.82209
$395$	0	0
$396$	1836.00	0.232986
$397$	12590.0i	1.59162i	0.605545	+	0.795811i	$0.292955\pi$
$397$	12590.0i	1.59162i	−0.605545	+	0.795811i	$0.707045\pi$
$398$	5720.00i	0.720396i
$399$	−1932.00	−0.242408
$400$	0	0
$401$	2850.00	0.354918	0.177459	−	0.984128i	$-0.443212\pi$
$401$	2850.00	0.354918	0.177459	+	0.984128i	$0.443212\pi$
$402$	− 6180.00i	− 0.766742i
$403$	6720.00i	0.830638i
$404$	−782.000	−0.0963019
$405$	0	0
$406$	−2030.00	−0.248146
$407$	− 1752.00i	− 0.213374i
$408$	− 18090.0i	− 2.19507i
$409$	−1226.00	−0.148220	−0.0741098	−	0.997250i	$-0.523612\pi$
$409$	−1226.00	−0.148220	−0.0741098	+	0.997250i	$0.523612\pi$
$410$	0	0
$411$	1122.00	0.134657
$412$	31960.0i	3.82174i
$413$	− 2660.00i	− 0.316925i
$414$	−5040.00	−0.598315
$415$	0	0
$416$	2550.00	0.300539
$417$	− 1188.00i	− 0.139512i
$418$	5520.00i	0.645914i
$419$	−612.000	−0.0713560	−0.0356780	−	0.999363i	$-0.511359\pi$
$419$	−612.000	−0.0713560	−0.0356780	+	0.999363i	$0.511359\pi$
$420$	0	0
$421$	5182.00	0.599894	0.299947	−	0.953956i	$-0.403031\pi$
$421$	5182.00	0.599894	0.299947	+	0.953956i	$0.403031\pi$
$422$	2060.00i	0.237629i
$423$	− 1872.00i	− 0.215177i
$424$	33930.0	3.88629
$425$	0	0
$426$	14400.0	1.63775
$427$	5026.00i	0.569614i
$428$	− 12444.0i	− 1.40538i
$429$	1080.00	0.121545
$430$	0	0
$431$	−4984.00	−0.557009	−0.278504	−	0.960435i	$-0.589839\pi$
$431$	−4984.00	−0.557009	−0.278504	+	0.960435i	$0.589839\pi$
$432$	− 2403.00i	− 0.267626i
$433$	1694.00i	0.188010i	0.995572	+	0.0940051i	$0.0299670\pi$
$433$	1694.00i	0.188010i	−0.995572	+	0.0940051i	$0.970033\pi$
$434$	7840.00	0.867125
$435$	0	0
$436$	−6426.00	−0.705848
$437$	− 10304.0i	− 1.12793i
$438$	15990.0i	1.74436i
$439$	−13864.0	−1.50727	−0.753636	−	0.657292i	$-0.771702\pi$
$439$	−13864.0	−1.50727	−0.753636	+	0.657292i	$0.771702\pi$
$440$	0	0
$441$	441.000	0.0476190
$442$	− 20100.0i	− 2.16303i
$443$	4644.00i	0.498066i	0.968495	+	0.249033i	$0.0801127\pi$
$443$	4644.00i	0.498066i	−0.968495	+	0.249033i	$0.919887\pi$
$444$	−7446.00	−0.795882
$445$	0	0
$446$	−8160.00	−0.866339
$447$	5622.00i	0.594880i
$448$	2009.00i	0.211867i
$449$	4926.00	0.517756	0.258878	−	0.965910i	$-0.416647\pi$
$449$	4926.00	0.517756	0.258878	+	0.965910i	$0.416647\pi$
$450$	0	0
$451$	216.000	0.0225522
$452$	24786.0i	2.57928i
$453$	− 3288.00i	− 0.341024i
$454$	−20420.0	−2.11092
$455$	0	0
$456$	12420.0	1.27548
$457$	− 14694.0i	− 1.50406i	−0.659128	−	0.752031i	$-0.729074\pi$
$457$	− 14694.0i	− 1.50406i	0.659128	−	0.752031i	$-0.270926\pi$
$458$	16930.0i	1.72726i
$459$	−3618.00	−0.367917
$460$	0	0
$461$	2006.00	0.202665	0.101333	−	0.994853i	$-0.467689\pi$
$461$	2006.00	0.202665	0.101333	+	0.994853i	$0.467689\pi$
$462$	− 1260.00i	− 0.126884i
$463$	− 4896.00i	− 0.491439i	−0.969341	−	0.245720i	$-0.920976\pi$
$463$	− 4896.00i	− 0.491439i	0.969341	−	0.245720i	$-0.0790243\pi$
$464$	5162.00	0.516465
$465$	0	0
$466$	26610.0	2.64525
$467$	2660.00i	0.263576i	0.991278	+	0.131788i	$0.0420719\pi$
$467$	2660.00i	0.263576i	−0.991278	+	0.131788i	$0.957928\pi$
$468$	− 4590.00i	− 0.453361i
$469$	−2884.00	−0.283946
$470$	0	0
$471$	−5754.00	−0.562909
$472$	17100.0i	1.66757i
$473$	− 4080.00i	− 0.396614i
$474$	13440.0	1.30236
$475$	0	0
$476$	−15946.0	−1.53547
$477$	− 6786.00i	− 0.651383i
$478$	− 18680.0i	− 1.78745i
$479$	5600.00	0.534176	0.267088	−	0.963672i	$-0.413938\pi$
$479$	5600.00	0.534176	0.267088	+	0.963672i	$0.413938\pi$
$480$	0	0
$481$	−4380.00	−0.415199
$482$	1050.00i	0.0992245i
$483$	2352.00i	0.221573i
$484$	20179.0	1.89510
$485$	0	0
$486$	−1215.00	−0.113402
$487$	− 6424.00i	− 0.597740i	−0.954294	−	0.298870i	$-0.903390\pi$
$487$	− 6424.00i	− 0.597740i	0.954294	−	0.298870i	$-0.0966096\pi$
$488$	− 32310.0i	− 2.99714i
$489$	6948.00	0.642535
$490$	0	0
$491$	−18900.0	−1.73716	−0.868579	−	0.495550i	$-0.834967\pi$
$491$	−18900.0	−1.73716	−0.868579	+	0.495550i	$0.834967\pi$
$492$	− 918.000i	− 0.0841192i
$493$	− 7772.00i	− 0.710007i
$494$	13800.0	1.25687
$495$	0	0
$496$	−19936.0	−1.80474
$497$	− 6720.00i	− 0.606505i
$498$	6540.00i	0.588483i
$499$	15364.0	1.37833	0.689165	−	0.724604i	$-0.257977\pi$
$499$	15364.0	1.37833	0.689165	+	0.724604i	$0.257977\pi$
$500$	0	0
$501$	5208.00	0.464424
$502$	− 21060.0i	− 1.87242i
$503$	− 2216.00i	− 0.196435i	−0.995165	−	0.0982173i	$-0.968686\pi$
$503$	− 2216.00i	− 0.196435i	0.995165	−	0.0982173i	$-0.0313140\pi$
$504$	−2835.00	−0.250557
$505$	0	0
$506$	6720.00	0.590396
$507$	3891.00i	0.340839i
$508$	− 10336.0i	− 0.902728i
$509$	3754.00	0.326902	0.163451	−	0.986551i	$-0.447737\pi$
$509$	3754.00	0.326902	0.163451	+	0.986551i	$0.447737\pi$
$510$	0	0
$511$	7462.00	0.645987
$512$	− 24475.0i	− 2.11260i
$513$	− 2484.00i	− 0.213784i
$514$	−25650.0	−2.20111
$515$	0	0
$516$	−17340.0	−1.47936
$517$	2496.00i	0.212329i
$518$	5110.00i	0.433437i
$519$	−7326.00	−0.619606
$520$	0	0
$521$	−4702.00	−0.395390	−0.197695	−	0.980264i	$-0.563346\pi$
$521$	−4702.00	−0.395390	−0.197695	+	0.980264i	$0.563346\pi$
$522$	− 2610.00i	− 0.218844i
$523$	22660.0i	1.89456i	0.320413	+	0.947278i	$0.396178\pi$
$523$	22660.0i	1.89456i	−0.320413	+	0.947278i	$0.603822\pi$
$524$	16252.0	1.35491
$525$	0	0
$526$	4240.00	0.351469
$527$	30016.0i	2.48106i
$528$	3204.00i	0.264084i
$529$	−377.000	−0.0309855
$530$	0	0
$531$	3420.00	0.279502
$532$	− 10948.0i	− 0.892211i
$533$	− 540.000i	− 0.0438837i
$534$	−15570.0	−1.26176
$535$	0	0
$536$	18540.0	1.49404
$537$	12276.0i	0.986496i
$538$	6370.00i	0.510465i
$539$	−588.000	−0.0469888
$540$	0	0
$541$	−8634.00	−0.686145	−0.343073	−	0.939309i	$-0.611468\pi$
$541$	−8634.00	−0.686145	−0.343073	+	0.939309i	$0.611468\pi$
$542$	4320.00i	0.342361i
$543$	3810.00i	0.301110i
$544$	11390.0	0.897688
$545$	0	0
$546$	−3150.00	−0.246900
$547$	− 19284.0i	− 1.50736i	−0.657243	−	0.753679i	$-0.728278\pi$
$547$	− 19284.0i	− 1.50736i	0.657243	−	0.753679i	$-0.271722\pi$
$548$	6358.00i	0.495621i
$549$	−6462.00	−0.502352
$550$	0	0
$551$	5336.00	0.412561
$552$	− 15120.0i	− 1.16585i
$553$	− 6272.00i	− 0.482301i
$554$	42650.0	3.27080
$555$	0	0
$556$	6732.00	0.513490
$557$	− 19658.0i	− 1.49540i	−0.664038	−	0.747699i	$-0.731159\pi$
$557$	− 19658.0i	− 1.49540i	0.664038	−	0.747699i	$-0.268841\pi$
$558$	10080.0i	0.764732i
$559$	−10200.0	−0.771760
$560$	0	0
$561$	4824.00	0.363047
$562$	− 26910.0i	− 2.01980i
$563$	25612.0i	1.91726i	0.284656	+	0.958630i	$0.408121\pi$
$563$	25612.0i	1.91726i	−0.284656	+	0.958630i	$0.591879\pi$
$564$	10608.0	0.791981
$565$	0	0
$566$	31180.0	2.31554
$567$	567.000i	0.0419961i
$568$	43200.0i	3.19125i
$569$	−7002.00	−0.515886	−0.257943	−	0.966160i	$-0.583045\pi$
$569$	−7002.00	−0.515886	−0.257943	+	0.966160i	$0.583045\pi$
$570$	0	0
$571$	−4524.00	−0.331565	−0.165782	−	0.986162i	$-0.553015\pi$
$571$	−4524.00	−0.331565	−0.165782	+	0.986162i	$0.553015\pi$
$572$	6120.00i	0.447360i
$573$	14712.0i	1.07260i
$574$	−630.000	−0.0458113
$575$	0	0
$576$	−2583.00	−0.186849
$577$	− 6014.00i	− 0.433910i	−0.976182	−	0.216955i	$-0.930388\pi$
$577$	− 6014.00i	− 0.433910i	0.976182	−	0.216955i	$-0.0696125\pi$
$578$	− 65215.0i	− 4.69306i
$579$	6534.00	0.468988
$580$	0	0
$581$	3052.00	0.217932
$582$	10530.0i	0.749970i
$583$	9048.00i	0.642761i
$584$	−47970.0	−3.39899
$585$	0	0
$586$	−4090.00	−0.288321
$587$	− 11748.0i	− 0.826051i	−0.910719	−	0.413025i	$-0.864472\pi$
$587$	− 11748.0i	− 0.826051i	0.910719	−	0.413025i	$-0.135528\pi$
$588$	2499.00i	0.175267i
$589$	−20608.0	−1.44166
$590$	0	0
$591$	8550.00	0.595093
$592$	− 12994.0i	− 0.902112i
$593$	9462.00i	0.655241i	0.944809	+	0.327620i	$0.106247\pi$
$593$	9462.00i	0.655241i	−0.944809	+	0.327620i	$0.893753\pi$
$594$	1620.00	0.111901
$595$	0	0
$596$	−31858.0	−2.18952
$597$	3432.00i	0.235280i
$598$	− 16800.0i	− 1.14883i
$599$	−2320.00	−0.158251	−0.0791257	−	0.996865i	$-0.525213\pi$
$599$	−2320.00	−0.158251	−0.0791257	+	0.996865i	$0.525213\pi$
$600$	0	0
$601$	4650.00	0.315603	0.157802	−	0.987471i	$-0.449559\pi$
$601$	4650.00	0.315603	0.157802	+	0.987471i	$0.449559\pi$
$602$	11900.0i	0.805661i
$603$	− 3708.00i	− 0.250417i
$604$	18632.0	1.25517
$605$	0	0
$606$	−690.000	−0.0462530
$607$	− 14656.0i	− 0.980014i	−0.871718	−	0.490007i	$-0.836994\pi$
$607$	− 14656.0i	− 0.980014i	0.871718	−	0.490007i	$-0.163006\pi$
$608$	7820.00i	0.521617i
$609$	−1218.00	−0.0810441
$610$	0	0
$611$	6240.00	0.413164
$612$	− 20502.0i	− 1.35416i
$613$	− 29166.0i	− 1.92170i	−0.277065	−	0.960851i	$-0.589362\pi$
$613$	− 29166.0i	− 1.92170i	0.277065	−	0.960851i	$-0.410638\pi$
$614$	11340.0	0.745350
$615$	0	0
$616$	3780.00	0.247241
$617$	28554.0i	1.86311i	0.363597	+	0.931557i	$0.381549\pi$
$617$	28554.0i	1.86311i	−0.363597	+	0.931557i	$0.618451\pi$
$618$	28200.0i	1.83555i
$619$	3876.00	0.251679	0.125840	−	0.992051i	$-0.459837\pi$
$619$	3876.00	0.251679	0.125840	+	0.992051i	$0.459837\pi$
$620$	0	0
$621$	−3024.00	−0.195409
$622$	33240.0i	2.14277i
$623$	7266.00i	0.467265i
$624$	8010.00	0.513873
$625$	0	0
$626$	49090.0	3.13423
$627$	3312.00i	0.210955i
$628$	− 32606.0i	− 2.07185i
$629$	−19564.0	−1.24017
$630$	0	0
$631$	2904.00	0.183211	0.0916057	−	0.995795i	$-0.470800\pi$
$631$	2904.00	0.183211	0.0916057	+	0.995795i	$0.470800\pi$
$632$	40320.0i	2.53773i
$633$	1236.00i	0.0776091i
$634$	−4670.00	−0.292538
$635$	0	0
$636$	38454.0	2.39748
$637$	1470.00i	0.0914341i
$638$	3480.00i	0.215948i
$639$	8640.00	0.534888
$640$	0	0
$641$	9330.00	0.574903	0.287452	−	0.957795i	$-0.407192\pi$
$641$	9330.00	0.574903	0.287452	+	0.957795i	$0.407192\pi$
$642$	− 10980.0i	− 0.674994i
$643$	18332.0i	1.12433i	0.827025	+	0.562164i	$0.190031\pi$
$643$	18332.0i	1.12433i	−0.827025	+	0.562164i	$0.809969\pi$
$644$	−13328.0	−0.815523
$645$	0	0
$646$	61640.0	3.75417
$647$	− 2088.00i	− 0.126874i	−0.997986	−	0.0634372i	$-0.979794\pi$
$647$	− 2088.00i	− 0.126874i	0.997986	−	0.0634372i	$-0.0202063\pi$
$648$	− 3645.00i	− 0.220971i
$649$	−4560.00	−0.275802
$650$	0	0
$651$	4704.00	0.283202
$652$	39372.0i	2.36492i
$653$	− 22.0000i	− 0.00131842i	−1.00000		0.000659209i	$-0.999790\pi$
$653$	− 22.0000i	− 0.00131842i	1.00000		0.000659209i	$-0.000209833\pi$
$654$	−5670.00	−0.339013
$655$	0	0
$656$	1602.00	0.0953469
$657$	9594.00i	0.569707i
$658$	− 7280.00i	− 0.431313i
$659$	−16260.0	−0.961153	−0.480576	−	0.876953i	$-0.659573\pi$
$659$	−16260.0	−0.961153	−0.480576	+	0.876953i	$0.659573\pi$
$660$	0	0
$661$	−23818.0	−1.40153	−0.700766	−	0.713391i	$-0.747158\pi$
$661$	−23818.0	−1.40153	−0.700766	+	0.713391i	$0.747158\pi$
$662$	11460.0i	0.672818i
$663$	− 12060.0i	− 0.706443i
$664$	−19620.0	−1.14669
$665$	0	0
$666$	−6570.00	−0.382256
$667$	− 6496.00i	− 0.377101i
$668$	29512.0i	1.70936i
$669$	−4896.00	−0.282945
$670$	0	0
$671$	8616.00	0.495703
$672$	− 1785.00i	− 0.102467i
$673$	− 31106.0i	− 1.78165i	−0.454350	−	0.890823i	$-0.650128\pi$
$673$	− 31106.0i	− 1.78165i	0.454350	−	0.890823i	$-0.349872\pi$
$674$	30310.0	1.73219
$675$	0	0
$676$	−22049.0	−1.25449
$677$	− 1090.00i	− 0.0618790i	−0.999521	−	0.0309395i	$-0.990150\pi$
$677$	− 1090.00i	− 0.0618790i	0.999521	−	0.0309395i	$-0.00984993\pi$
$678$	21870.0i	1.23881i
$679$	4914.00	0.277735
$680$	0	0
$681$	−12252.0	−0.689424
$682$	− 13440.0i	− 0.754610i
$683$	12372.0i	0.693121i	0.938028	+	0.346560i	$0.112650\pi$
$683$	12372.0i	0.693121i	−0.938028	+	0.346560i	$0.887350\pi$
$684$	14076.0	0.786856
$685$	0	0
$686$	1715.00	0.0954504
$687$	10158.0i	0.564122i
$688$	− 30260.0i	− 1.67682i
$689$	22620.0	1.25073
$690$	0	0
$691$	3252.00	0.179033	0.0895166	−	0.995985i	$-0.471468\pi$
$691$	3252.00	0.179033	0.0895166	+	0.995985i	$0.471468\pi$
$692$	− 41514.0i	− 2.28053i
$693$	− 756.000i	− 0.0414402i
$694$	−7420.00	−0.405849
$695$	0	0
$696$	7830.00	0.426430
$697$	− 2412.00i	− 0.131077i
$698$	− 1270.00i	− 0.0688685i
$699$	15966.0	0.863934
$700$	0	0
$701$	−5434.00	−0.292781	−0.146390	−	0.989227i	$-0.546766\pi$
$701$	−5434.00	−0.292781	−0.146390	+	0.989227i	$0.546766\pi$
$702$	− 4050.00i	− 0.217746i
$703$	− 13432.0i	− 0.720622i
$704$	3444.00	0.184376
$705$	0	0
$706$	−54750.0	−2.91862
$707$	322.000i	0.0171288i
$708$	19380.0i	1.02874i
$709$	5330.00	0.282331	0.141165	−	0.989986i	$-0.454915\pi$
$709$	5330.00	0.282331	0.141165	+	0.989986i	$0.454915\pi$
$710$	0	0
$711$	8064.00	0.425350
$712$	− 46710.0i	− 2.45861i
$713$	25088.0i	1.31775i
$714$	−14070.0	−0.737474
$715$	0	0
$716$	−69564.0	−3.63091
$717$	− 11208.0i	− 0.583780i
$718$	− 56880.0i	− 2.95647i
$719$	7520.00	0.390054	0.195027	−	0.980798i	$-0.437521\pi$
$719$	7520.00	0.390054	0.195027	+	0.980798i	$0.437521\pi$
$720$	0	0
$721$	13160.0	0.679756
$722$	8025.00i	0.413656i
$723$	630.000i	0.0324066i
$724$	−21590.0	−1.10827
$725$	0	0
$726$	17805.0	0.910200
$727$	19336.0i	0.986427i	0.869908	+	0.493214i	$0.164178\pi$
$727$	19336.0i	0.986427i	−0.869908	+	0.493214i	$0.835822\pi$
$728$	− 9450.00i	− 0.481099i
$729$	−729.000	−0.0370370
$730$	0	0
$731$	−45560.0	−2.30519
$732$	− 36618.0i	− 1.84896i
$733$	22498.0i	1.13367i	0.823830	+	0.566837i	$0.191833\pi$
$733$	22498.0i	1.13367i	−0.823830	+	0.566837i	$0.808167\pi$
$734$	5680.00	0.285630
$735$	0	0
$736$	9520.00	0.476782
$737$	4944.00i	0.247103i
$738$	− 810.000i	− 0.0404018i
$739$	18292.0	0.910531	0.455265	−	0.890356i	$-0.349544\pi$
$739$	18292.0	0.910531	0.455265	+	0.890356i	$0.349544\pi$
$740$	0	0
$741$	8280.00	0.410490
$742$	− 26390.0i	− 1.30567i
$743$	− 17904.0i	− 0.884030i	−0.897008	−	0.442015i	$-0.854264\pi$
$743$	− 17904.0i	− 0.884030i	0.897008	−	0.442015i	$-0.145736\pi$
$744$	−30240.0	−1.49012
$745$	0	0
$746$	−41210.0	−2.02253
$747$	3924.00i	0.192198i
$748$	27336.0i	1.33623i
$749$	−5124.00	−0.249969
$750$	0	0
$751$	5408.00	0.262771	0.131385	−	0.991331i	$-0.458057\pi$
$751$	5408.00	0.262771	0.131385	+	0.991331i	$0.458057\pi$
$752$	18512.0i	0.897690i
$753$	− 12636.0i	− 0.611529i
$754$	8700.00	0.420206
$755$	0	0
$756$	−3213.00	−0.154571
$757$	8318.00i	0.399370i	0.979860	+	0.199685i	$0.0639918\pi$
$757$	8318.00i	0.399370i	−0.979860	+	0.199685i	$0.936008\pi$
$758$	− 18100.0i	− 0.867311i
$759$	4032.00	0.192823
$760$	0	0
$761$	6690.00	0.318676	0.159338	−	0.987224i	$-0.449064\pi$
$761$	6690.00	0.318676	0.159338	+	0.987224i	$0.449064\pi$
$762$	− 9120.00i	− 0.433573i
$763$	2646.00i	0.125546i
$764$	−83368.0	−3.94784
$765$	0	0
$766$	−42320.0	−1.99619
$767$	11400.0i	0.536676i
$768$	− 24837.0i	− 1.16696i
$769$	−9266.00	−0.434513	−0.217257	−	0.976115i	$-0.569711\pi$
$769$	−9266.00	−0.434513	−0.217257	+	0.976115i	$0.569711\pi$
$770$	0	0
$771$	−15390.0	−0.718881
$772$	37026.0i	1.72616i
$773$	− 9678.00i	− 0.450315i	−0.974322	−	0.225157i	$-0.927710\pi$
$773$	− 9678.00i	− 0.450315i	0.974322	−	0.225157i	$-0.0722897\pi$
$774$	−15300.0	−0.710526
$775$	0	0
$776$	−31590.0	−1.46136
$777$	3066.00i	0.141560i
$778$	− 18390.0i	− 0.847447i
$779$	1656.00	0.0761648
$780$	0	0
$781$	−11520.0	−0.527808
$782$	− 75040.0i	− 3.43149i
$783$	− 1566.00i	− 0.0714742i
$784$	−4361.00	−0.198661
$785$	0	0
$786$	14340.0	0.650752
$787$	− 6860.00i	− 0.310715i	−0.987858	−	0.155357i	$-0.950347\pi$
$787$	− 6860.00i	− 0.310715i	0.987858	−	0.155357i	$-0.0496529\pi$
$788$	48450.0i	2.19030i
$789$	2544.00	0.114789
$790$	0	0
$791$	10206.0	0.458766
$792$	4860.00i	0.218046i
$793$	− 21540.0i	− 0.964575i
$794$	−62950.0	−2.81362
$795$	0	0
$796$	−19448.0	−0.865975
$797$	10950.0i	0.486661i	0.969943	+	0.243331i	$0.0782400\pi$
$797$	10950.0i	0.486661i	−0.969943	+	0.243331i	$0.921760\pi$
$798$	− 9660.00i	− 0.428522i
$799$	27872.0	1.23409
$800$	0	0
$801$	−9342.00	−0.412089
$802$	14250.0i	0.627413i
$803$	− 12792.0i	− 0.562167i
$804$	21012.0	0.921687
$805$	0	0
$806$	−33600.0	−1.46837
$807$	3822.00i	0.166717i
$808$	− 2070.00i	− 0.0901267i
$809$	−26010.0	−1.13036	−0.565181	−	0.824967i	$-0.691194\pi$
$809$	−26010.0	−1.13036	−0.565181	+	0.824967i	$0.691194\pi$
$810$	0	0
$811$	−14628.0	−0.633364	−0.316682	−	0.948532i	$-0.602569\pi$
$811$	−14628.0	−0.633364	−0.316682	+	0.948532i	$0.602569\pi$
$812$	− 6902.00i	− 0.298292i
$813$	2592.00i	0.111815i
$814$	8760.00	0.377196
$815$	0	0
$816$	35778.0	1.53490
$817$	− 31280.0i	− 1.33947i
$818$	− 6130.00i	− 0.262018i
$819$	−1890.00	−0.0806373
$820$	0	0
$821$	8718.00	0.370597	0.185299	−	0.982682i	$-0.440675\pi$
$821$	8718.00	0.370597	0.185299	+	0.982682i	$0.440675\pi$
$822$	5610.00i	0.238043i
$823$	7432.00i	0.314779i	0.987537	+	0.157390i	$0.0503078\pi$
$823$	7432.00i	0.314779i	−0.987537	+	0.157390i	$0.949692\pi$
$824$	−84600.0	−3.57668
$825$	0	0
$826$	13300.0	0.560250
$827$	17388.0i	0.731125i	0.930787	+	0.365562i	$0.119123\pi$
$827$	17388.0i	0.731125i	−0.930787	+	0.365562i	$0.880877\pi$
$828$	− 17136.0i	− 0.719224i
$829$	−7902.00	−0.331059	−0.165529	−	0.986205i	$-0.552933\pi$
$829$	−7902.00	−0.331059	−0.165529	+	0.986205i	$0.552933\pi$
$830$	0	0
$831$	25590.0	1.06824
$832$	− 8610.00i	− 0.358772i
$833$	6566.00i	0.273107i
$834$	5940.00	0.246625
$835$	0	0
$836$	−18768.0	−0.776441
$837$	6048.00i	0.249760i
$838$	− 3060.00i	− 0.126141i
$839$	31848.0	1.31051	0.655253	−	0.755409i	$-0.272562\pi$
$839$	31848.0	1.31051	0.655253	+	0.755409i	$0.272562\pi$
$840$	0	0
$841$	−21025.0	−0.862069
$842$	25910.0i	1.06047i
$843$	− 16146.0i	− 0.659665i
$844$	−7004.00	−0.285649
$845$	0	0
$846$	9360.00	0.380382
$847$	− 8309.00i	− 0.337073i
$848$	67106.0i	2.71749i
$849$	18708.0	0.756251
$850$	0	0
$851$	−16352.0	−0.658683
$852$	48960.0i	1.96871i
$853$	− 30150.0i	− 1.21022i	−0.796142	−	0.605109i	$-0.793129\pi$
$853$	− 30150.0i	− 1.21022i	0.796142	−	0.605109i	$-0.206871\pi$
$854$	−25130.0	−1.00694
$855$	0	0
$856$	32940.0	1.31526
$857$	− 4350.00i	− 0.173388i	−0.996235	−	0.0866938i	$-0.972370\pi$
$857$	− 4350.00i	− 0.173388i	0.996235	−	0.0866938i	$-0.0276302\pi$
$858$	5400.00i	0.214864i
$859$	30676.0	1.21845	0.609227	−	0.792996i	$-0.291480\pi$
$859$	30676.0	1.21845	0.609227	+	0.792996i	$0.291480\pi$
$860$	0	0
$861$	−378.000	−0.0149619
$862$	− 24920.0i	− 0.984662i
$863$	23688.0i	0.934356i	0.884163	+	0.467178i	$0.154729\pi$
$863$	23688.0i	0.934356i	−0.884163	+	0.467178i	$0.845271\pi$
$864$	2295.00	0.0903675
$865$	0	0
$866$	−8470.00	−0.332358
$867$	− 39129.0i	− 1.53275i
$868$	26656.0i	1.04235i
$869$	−10752.0	−0.419720
$870$	0	0
$871$	12360.0	0.480830
$872$	− 17010.0i	− 0.660586i
$873$	6318.00i	0.244939i
$874$	51520.0	1.99392
$875$	0	0
$876$	−54366.0	−2.09687
$877$	31910.0i	1.22865i	0.789054	+	0.614324i	$0.210571\pi$
$877$	31910.0i	1.22865i	−0.789054	+	0.614324i	$0.789429\pi$
$878$	− 69320.0i	− 2.66451i
$879$	−2454.00	−0.0941654
$880$	0	0
$881$	50250.0	1.92164	0.960820	−	0.277172i	$-0.0893971\pi$
$881$	50250.0	1.92164	0.960820	+	0.277172i	$0.0893971\pi$
$882$	2205.00i	0.0841794i
$883$	− 5980.00i	− 0.227908i	−0.993486	−	0.113954i	$-0.963648\pi$
$883$	− 5980.00i	− 0.227908i	0.993486	−	0.113954i	$-0.0363517\pi$
$884$	68340.0	2.60014
$885$	0	0
$886$	−23220.0	−0.880464
$887$	− 24568.0i	− 0.930003i	−0.885310	−	0.465002i	$-0.846054\pi$
$887$	− 24568.0i	− 0.930003i	0.885310	−	0.465002i	$-0.153946\pi$
$888$	− 19710.0i	− 0.744847i
$889$	−4256.00	−0.160564
$890$	0	0
$891$	972.000	0.0365468
$892$	− 27744.0i	− 1.04141i
$893$	19136.0i	0.717091i
$894$	−28110.0	−1.05161
$895$	0	0
$896$	−14805.0	−0.552009
$897$	− 10080.0i	− 0.375208i
$898$	24630.0i	0.915271i
$899$	−12992.0	−0.481988
$900$	0	0
$901$	101036.	3.73585
$902$	1080.00i	0.0398670i
$903$	7140.00i	0.263128i
$904$	−65610.0	−2.41389
$905$	0	0
$906$	16440.0	0.602850
$907$	13252.0i	0.485144i	0.970133	+	0.242572i	$0.0779910\pi$
$907$	13252.0i	0.485144i	−0.970133	+	0.242572i	$0.922009\pi$
$908$	− 69428.0i	− 2.53750i
$909$	−414.000	−0.0151062
$910$	0	0
$911$	−6744.00	−0.245267	−0.122634	−	0.992452i	$-0.539134\pi$
$911$	−6744.00	−0.245267	−0.122634	+	0.992452i	$0.539134\pi$
$912$	24564.0i	0.891881i
$913$	− 5232.00i	− 0.189654i
$914$	73470.0	2.65883
$915$	0	0
$916$	−57562.0	−2.07631
$917$	− 6692.00i	− 0.240992i
$918$	− 18090.0i	− 0.650391i
$919$	45336.0	1.62731	0.813654	−	0.581349i	$-0.197475\pi$
$919$	45336.0	1.62731	0.813654	+	0.581349i	$0.197475\pi$
$920$	0	0
$921$	6804.00	0.243430
$922$	10030.0i	0.358265i
$923$	28800.0i	1.02705i
$924$	4284.00	0.152525
$925$	0	0
$926$	24480.0	0.868750
$927$	16920.0i	0.599488i
$928$	4930.00i	0.174391i
$929$	−30074.0	−1.06211	−0.531053	−	0.847339i	$-0.678203\pi$
$929$	−30074.0	−1.06211	−0.531053	+	0.847339i	$0.678203\pi$
$930$	0	0
$931$	−4508.00	−0.158694
$932$	90474.0i	3.17980i
$933$	19944.0i	0.699826i
$934$	−13300.0	−0.465941
$935$	0	0
$936$	12150.0	0.424290
$937$	21754.0i	0.758455i	0.925303	+	0.379227i	$0.123810\pi$
$937$	21754.0i	0.758455i	−0.925303	+	0.379227i	$0.876190\pi$
$938$	− 14420.0i	− 0.501951i
$939$	29454.0	1.02364
$940$	0	0
$941$	14550.0	0.504056	0.252028	−	0.967720i	$-0.418903\pi$
$941$	14550.0	0.504056	0.252028	+	0.967720i	$0.418903\pi$
$942$	− 28770.0i	− 0.995093i
$943$	− 2016.00i	− 0.0696182i
$944$	−33820.0	−1.16605
$945$	0	0
$946$	20400.0	0.701122
$947$	46660.0i	1.60110i	0.599263	+	0.800552i	$0.295460\pi$
$947$	46660.0i	1.60110i	−0.599263	+	0.800552i	$0.704540\pi$
$948$	45696.0i	1.56555i
$949$	−31980.0	−1.09390
$950$	0	0
$951$	−2802.00	−0.0955427
$952$	− 42210.0i	− 1.43701i
$953$	− 20810.0i	− 0.707347i	−0.935369	−	0.353674i	$-0.884932\pi$
$953$	− 20810.0i	− 0.707347i	0.935369	−	0.353674i	$-0.115068\pi$
$954$	33930.0	1.15149
$955$	0	0
$956$	63512.0	2.14867
$957$	2088.00i	0.0705282i
$958$	28000.0i	0.944300i
$959$	2618.00	0.0881539
$960$	0	0
$961$	20385.0	0.684267
$962$	− 21900.0i	− 0.733975i
$963$	− 6588.00i	− 0.220452i
$964$	−3570.00	−0.119276
$965$	0	0
$966$	−11760.0	−0.391689
$967$	2776.00i	0.0923166i	0.998934	+	0.0461583i	$0.0146979\pi$
$967$	2776.00i	0.0923166i	−0.998934	+	0.0461583i	$0.985302\pi$
$968$	53415.0i	1.77358i
$969$	36984.0	1.22611
$970$	0	0
$971$	27292.0	0.902000	0.451000	−	0.892524i	$-0.351067\pi$
$971$	27292.0	0.902000	0.451000	+	0.892524i	$0.351067\pi$
$972$	− 4131.00i	− 0.136319i
$973$	− 2772.00i	− 0.0913322i
$974$	32120.0	1.05666
$975$	0	0
$976$	63902.0	2.09575
$977$	− 62.0000i	− 0.00203025i	−0.999999	−	0.00101513i	$-0.999677\pi$
$977$	− 62.0000i	− 0.00203025i	0.999999	−	0.00101513i	$-0.000323125\pi$
$978$	34740.0i	1.13585i
$979$	12456.0	0.406635
$980$	0	0
$981$	−3402.00	−0.110721
$982$	− 94500.0i	− 3.07089i
$983$	− 37912.0i	− 1.23012i	−0.788481	−	0.615058i	$-0.789132\pi$
$983$	− 37912.0i	− 1.23012i	0.788481	−	0.615058i	$-0.210868\pi$
$984$	2430.00	0.0787252
$985$	0	0
$986$	38860.0	1.25513
$987$	− 4368.00i	− 0.140866i
$988$	46920.0i	1.51085i
$989$	−38080.0	−1.22434
$990$	0	0
$991$	10656.0	0.341573	0.170787	−	0.985308i	$-0.445369\pi$
$991$	10656.0	0.341573	0.170787	+	0.985308i	$0.445369\pi$
$992$	− 19040.0i	− 0.609396i
$993$	6876.00i	0.219741i
$994$	33600.0	1.07216
$995$	0	0
$996$	−22236.0	−0.707404
$997$	− 29434.0i	− 0.934989i	−0.883996	−	0.467495i	$-0.845157\pi$
$997$	− 29434.0i	− 0.934989i	0.883996	−	0.467495i	$-0.154843\pi$
$998$	76820.0i	2.43657i
$999$	−3942.00	−0.124844

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.4.d.a.274.2		2
5.2	odd	4		525.4.a.a.1.1		1
5.3	odd	4		105.4.a.b.1.1	✓	1
5.4	even	2	inner	525.4.d.a.274.1		2
15.2	even	4		1575.4.a.l.1.1		1
15.8	even	4		315.4.a.a.1.1		1
20.3	even	4		1680.4.a.u.1.1		1
35.13	even	4		735.4.a.j.1.1		1
105.83	odd	4		2205.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.b.1.1	✓	1	5.3	odd	4
315.4.a.a.1.1		1	15.8	even	4
525.4.a.a.1.1		1	5.2	odd	4
525.4.d.a.274.1		2	5.4	even	2	inner
525.4.d.a.274.2		2	1.1	even	1	trivial
735.4.a.j.1.1		1	35.13	even	4
1575.4.a.l.1.1		1	15.2	even	4
1680.4.a.u.1.1		1	20.3	even	4
2205.4.a.b.1.1		1	105.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} -15.0000 q^{6} +7.00000i q^{7} -45.0000i q^{8} -9.00000 q^{9} +O(q^{10})\)	\(q+5.00000i q^{2} +3.00000i q^{3} -17.0000 q^{4} -15.0000 q^{6} +7.00000i q^{7} -45.0000i q^{8} -9.00000 q^{9} +12.0000 q^{11} -51.0000i q^{12} -30.0000i q^{13} -35.0000 q^{14} +89.0000 q^{16} -134.000i q^{17} -45.0000i q^{18} +92.0000 q^{19} -21.0000 q^{21} +60.0000i q^{22} -112.000i q^{23} +135.000 q^{24} +150.000 q^{26} -27.0000i q^{27} -119.000i q^{28} +58.0000 q^{29} -224.000 q^{31} +85.0000i q^{32} +36.0000i q^{33} +670.000 q^{34} +153.000 q^{36} -146.000i q^{37} +460.000i q^{38} +90.0000 q^{39} +18.0000 q^{41} -105.000i q^{42} -340.000i q^{43} -204.000 q^{44} +560.000 q^{46} +208.000i q^{47} +267.000i q^{48} -49.0000 q^{49} +402.000 q^{51} +510.000i q^{52} +754.000i q^{53} +135.000 q^{54} +315.000 q^{56} +276.000i q^{57} +290.000i q^{58} -380.000 q^{59} +718.000 q^{61} -1120.00i q^{62} -63.0000i q^{63} +287.000 q^{64} -180.000 q^{66} +412.000i q^{67} +2278.00i q^{68} +336.000 q^{69} -960.000 q^{71} +405.000i q^{72} -1066.00i q^{73} +730.000 q^{74} -1564.00 q^{76} +84.0000i q^{77} +450.000i q^{78} -896.000 q^{79} +81.0000 q^{81} +90.0000i q^{82} -436.000i q^{83} +357.000 q^{84} +1700.00 q^{86} +174.000i q^{87} -540.000i q^{88} +1038.00 q^{89} +210.000 q^{91} +1904.00i q^{92} -672.000i q^{93} -1040.00 q^{94} -255.000 q^{96} -702.000i q^{97} -245.000i q^{98} -108.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 34 q^{4} - 30 q^{6} - 18 q^{9}+O(q^{10}) \) 2 * q - 34 * q^4 - 30 * q^6 - 18 * q^9	\( 2 q - 34 q^{4} - 30 q^{6} - 18 q^{9} + 24 q^{11} - 70 q^{14} + 178 q^{16} + 184 q^{19} - 42 q^{21} + 270 q^{24} + 300 q^{26} + 116 q^{29} - 448 q^{31} + 1340 q^{34} + 306 q^{36} + 180 q^{39} + 36 q^{41} - 408 q^{44} + 1120 q^{46} - 98 q^{49} + 804 q^{51} + 270 q^{54} + 630 q^{56} - 760 q^{59} + 1436 q^{61} + 574 q^{64} - 360 q^{66} + 672 q^{69} - 1920 q^{71} + 1460 q^{74} - 3128 q^{76} - 1792 q^{79} + 162 q^{81} + 714 q^{84} + 3400 q^{86} + 2076 q^{89} + 420 q^{91} - 2080 q^{94} - 510 q^{96} - 216 q^{99}+O(q^{100}) \) 2 * q - 34 * q^4 - 30 * q^6 - 18 * q^9 + 24 * q^11 - 70 * q^14 + 178 * q^16 + 184 * q^19 - 42 * q^21 + 270 * q^24 + 300 * q^26 + 116 * q^29 - 448 * q^31 + 1340 * q^34 + 306 * q^36 + 180 * q^39 + 36 * q^41 - 408 * q^44 + 1120 * q^46 - 98 * q^49 + 804 * q^51 + 270 * q^54 + 630 * q^56 - 760 * q^59 + 1436 * q^61 + 574 * q^64 - 360 * q^66 + 672 * q^69 - 1920 * q^71 + 1460 * q^74 - 3128 * q^76 - 1792 * q^79 + 162 * q^81 + 714 * q^84 + 3400 * q^86 + 2076 * q^89 + 420 * q^91 - 2080 * q^94 - 510 * q^96 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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