LMFDB - Embedded newform 275.4.b.e.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,4,Mod(199,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("275.199");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	275.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.2255252516$
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} + 51x^{6} + 835x^{4} + 4881x^{2} + 9216 $ x^8 + 51x^6 + 835x^4 + 4881*x^2 + 9216
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.6
Root			$2.30365i$ of defining polynomial
Character	$\chi$	$=$	275.199
Dual form			275.4.b.e.199.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30365i q^{2} -6.23583i q^{3} +2.69320 q^{4} +14.3652 q^{6} +13.1506i q^{7} +24.6334i q^{8} -11.8856 q^{9} +O(q^{10})$	\(q+2.30365i q^{2} -6.23583i q^{3} +2.69320 q^{4} +14.3652 q^{6} +13.1506i q^{7} +24.6334i q^{8} -11.8856 q^{9} +11.0000 q^{11} -16.7944i q^{12} +59.5317i q^{13} -30.2943 q^{14} -35.2010 q^{16} -0.315106i q^{17} -27.3803i q^{18} -32.8179 q^{19} +82.0048 q^{21} +25.3401i q^{22} +72.2810i q^{23} +153.610 q^{24} -137.140 q^{26} -94.2508i q^{27} +35.4172i q^{28} +261.137 q^{29} +155.691 q^{31} +115.976i q^{32} -68.5942i q^{33} +0.725893 q^{34} -32.0103 q^{36} +151.261i q^{37} -75.6010i q^{38} +371.230 q^{39} +209.059 q^{41} +188.910i q^{42} -111.040i q^{43} +29.6252 q^{44} -166.510 q^{46} +633.073i q^{47} +219.508i q^{48} +170.062 q^{49} -1.96495 q^{51} +160.331i q^{52} -331.397i q^{53} +217.121 q^{54} -323.943 q^{56} +204.647i q^{57} +601.569i q^{58} -814.568 q^{59} -263.071 q^{61} +358.657i q^{62} -156.302i q^{63} -548.777 q^{64} +158.017 q^{66} -661.609i q^{67} -0.848644i q^{68} +450.732 q^{69} +15.2662 q^{71} -292.783i q^{72} -785.036i q^{73} -348.453 q^{74} -88.3853 q^{76} +144.656i q^{77} +855.183i q^{78} +1075.89 q^{79} -908.644 q^{81} +481.599i q^{82} +1187.89i q^{83} +220.855 q^{84} +255.797 q^{86} -1628.41i q^{87} +270.967i q^{88} -403.471 q^{89} -782.876 q^{91} +194.667i q^{92} -970.863i q^{93} -1458.38 q^{94} +723.208 q^{96} -304.398i q^{97} +391.764i q^{98} -130.742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 38 q^{4} - 38 q^{6} - 98 q^{9}+O(q^{10}) $ 8 * q - 38 * q^4 - 38 * q^6 - 98 * q^9	$ 8 q - 38 q^{4} - 38 q^{6} - 98 q^{9} + 88 q^{11} + 98 q^{14} - 74 q^{16} + 410 q^{19} - 362 q^{21} + 774 q^{24} - 172 q^{26} + 158 q^{29} + 98 q^{31} + 1878 q^{34} + 224 q^{36} + 52 q^{39} + 1472 q^{41} - 418 q^{44} - 668 q^{46} - 74 q^{49} + 826 q^{51} + 2978 q^{54} - 514 q^{56} + 1684 q^{59} - 2194 q^{61} + 330 q^{64} - 418 q^{66} + 116 q^{69} - 1042 q^{71} - 6514 q^{74} - 5650 q^{76} + 2236 q^{79} + 368 q^{81} + 1210 q^{84} + 6904 q^{86} + 362 q^{89} - 4380 q^{91} - 2068 q^{94} + 7962 q^{96} - 1078 q^{99}+O(q^{100}) $ 8 * q - 38 * q^4 - 38 * q^6 - 98 * q^9 + 88 * q^11 + 98 * q^14 - 74 * q^16 + 410 * q^19 - 362 * q^21 + 774 * q^24 - 172 * q^26 + 158 * q^29 + 98 * q^31 + 1878 * q^34 + 224 * q^36 + 52 * q^39 + 1472 * q^41 - 418 * q^44 - 668 * q^46 - 74 * q^49 + 826 * q^51 + 2978 * q^54 - 514 * q^56 + 1684 * q^59 - 2194 * q^61 + 330 * q^64 - 418 * q^66 + 116 * q^69 - 1042 * q^71 - 6514 * q^74 - 5650 * q^76 + 2236 * q^79 + 368 * q^81 + 1210 * q^84 + 6904 * q^86 + 362 * q^89 - 4380 * q^91 - 2068 * q^94 + 7962 * q^96 - 1078 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.30365i	0.814463i	0.913325	+	0.407231i	$0.133506\pi$
$2$	2.30365i	0.814463i	−0.913325	+	0.407231i	$0.866494\pi$
$3$	− 6.23583i	− 1.20009i	−0.799968	−	0.600043i	$-0.795150\pi$
$3$	− 6.23583i	− 1.20009i	0.799968	−	0.600043i	$-0.204850\pi$
$4$	2.69320	0.336650
$5$	0	0
$5$	0	0
$6$	14.3652	0.977426
$7$	13.1506i	0.710064i	0.934854	+	0.355032i	$0.115530\pi$
$7$	13.1506i	0.710064i	−0.934854	+	0.355032i	$0.884470\pi$
$8$	24.6334i	1.08865i
$9$	−11.8856	−0.440208
$10$	0	0
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	− 16.7944i	− 0.404009i
$13$	59.5317i	1.27009i	0.772476	+	0.635044i	$0.219018\pi$
$13$	59.5317i	1.27009i	−0.772476	+	0.635044i	$0.780982\pi$
$14$	−30.2943	−0.578321
$15$	0	0
$16$	−35.2010	−0.550016
$17$	− 0.315106i	− 0.00449555i	−0.999997	−	0.00224778i	$-0.999285\pi$
$17$	− 0.315106i	− 0.00449555i	0.999997	−	0.00224778i	$-0.000715490\pi$
$18$	− 27.3803i	− 0.358533i
$19$	−32.8179	−0.396261	−0.198130	−	0.980176i	$-0.563487\pi$
$19$	−32.8179	−0.396261	−0.198130	+	0.980176i	$0.563487\pi$
$20$	0	0
$21$	82.0048	0.852138
$22$	25.3401i	0.245570i
$23$	72.2810i	0.655288i	0.944801	+	0.327644i	$0.106255\pi$
$23$	72.2810i	0.655288i	−0.944801	+	0.327644i	$0.893745\pi$
$24$	153.610	1.30648
$25$	0	0
$26$	−137.140	−1.03444
$27$	− 94.2508i	− 0.671799i
$28$	35.4172i	0.239043i
$29$	261.137	1.67214	0.836069	−	0.548625i	$-0.184848\pi$
$29$	261.137	1.67214	0.836069	+	0.548625i	$0.184848\pi$
$30$	0	0
$31$	155.691	0.902030	0.451015	−	0.892516i	$-0.351062\pi$
$31$	155.691	0.902030	0.451015	+	0.892516i	$0.351062\pi$
$32$	115.976i	0.640684i
$33$	− 68.5942i	− 0.361840i
$34$	0.725893	0.00366146
$35$	0	0
$36$	−32.0103	−0.148196
$37$	151.261i	0.672087i	0.941846	+	0.336044i	$0.109089\pi$
$37$	151.261i	0.672087i	−0.941846	+	0.336044i	$0.890911\pi$
$38$	− 75.6010i	− 0.322740i
$39$	371.230	1.52421
$40$	0	0
$41$	209.059	0.796331	0.398165	−	0.917314i	$-0.369647\pi$
$41$	209.059	0.796331	0.398165	+	0.917314i	$0.369647\pi$
$42$	188.910i	0.694035i
$43$	− 111.040i	− 0.393801i	−0.980423	−	0.196901i	$-0.936912\pi$
$43$	− 111.040i	− 0.393801i	0.980423	−	0.196901i	$-0.0630876\pi$
$44$	29.6252	0.101504
$45$	0	0
$46$	−166.510	−0.533708
$47$	633.073i	1.96475i	0.186923	+	0.982375i	$0.440148\pi$
$47$	633.073i	1.96475i	−0.186923	+	0.982375i	$0.559852\pi$
$48$	219.508i	0.660067i
$49$	170.062	0.495809
$50$	0	0
$51$	−1.96495	−0.00539505
$52$	160.331i	0.427575i
$53$	− 331.397i	− 0.858884i	−0.903094	−	0.429442i	$-0.858710\pi$
$53$	− 331.397i	− 0.858884i	0.903094	−	0.429442i	$-0.141290\pi$
$54$	217.121	0.547156
$55$	0	0
$56$	−323.943	−0.773013
$57$	204.647i	0.475547i
$58$	601.569i	1.36189i
$59$	−814.568	−1.79742	−0.898709	−	0.438545i	$-0.855494\pi$
$59$	−814.568	−1.79742	−0.898709	+	0.438545i	$0.855494\pi$
$60$	0	0
$61$	−263.071	−0.552178	−0.276089	−	0.961132i	$-0.589038\pi$
$61$	−263.071	−0.552178	−0.276089	+	0.961132i	$0.589038\pi$
$62$	358.657i	0.734670i
$63$	− 156.302i	− 0.312576i
$64$	−548.777	−1.07183
$65$	0	0
$66$	158.017	0.294705
$67$	− 661.609i	− 1.20639i	−0.797592	−	0.603197i	$-0.793893\pi$
$67$	− 661.609i	− 1.20639i	0.797592	−	0.603197i	$-0.206107\pi$
$68$	− 0.848644i	− 0.00151343i
$69$	450.732	0.786402
$70$	0	0
$71$	15.2662	0.0255178	0.0127589	−	0.999919i	$-0.495939\pi$
$71$	15.2662	0.0255178	0.0127589	+	0.999919i	$0.495939\pi$
$72$	− 292.783i	− 0.479233i
$73$	− 785.036i	− 1.25865i	−0.777142	−	0.629325i	$-0.783331\pi$
$73$	− 785.036i	− 1.25865i	0.777142	−	0.629325i	$-0.216669\pi$
$74$	−348.453	−0.547390
$75$	0	0
$76$	−88.3853	−0.133401
$77$	144.656i	0.214092i
$78$	855.183i	1.24142i
$79$	1075.89	1.53224	0.766122	−	0.642696i	$-0.222184\pi$
$79$	1075.89	1.53224	0.766122	+	0.642696i	$0.222184\pi$
$80$	0	0
$81$	−908.644	−1.24642
$82$	481.599i	0.648582i
$83$	1187.89i	1.57094i	0.618899	+	0.785471i	$0.287579\pi$
$83$	1187.89i	1.57094i	−0.618899	+	0.785471i	$0.712421\pi$
$84$	220.855	0.286873
$85$	0	0
$86$	255.797	0.320736
$87$	− 1628.41i	− 2.00671i
$88$	270.967i	0.328241i
$89$	−403.471	−0.480538	−0.240269	−	0.970706i	$-0.577236\pi$
$89$	−403.471	−0.480538	−0.240269	+	0.970706i	$0.577236\pi$
$90$	0	0
$91$	−782.876	−0.901843
$92$	194.667i	0.220603i
$93$	− 970.863i	− 1.08251i
$94$	−1458.38	−1.60022
$95$	0	0
$96$	723.208	0.768876
$97$	− 304.398i	− 0.318628i	−0.987228	−	0.159314i	$-0.949072\pi$
$97$	− 304.398i	− 0.318628i	0.987228	−	0.159314i	$-0.0509282\pi$
$98$	391.764i	0.403818i
$99$	−130.742	−0.132728
$100$	0	0
$101$	186.726	0.183959	0.0919797	−	0.995761i	$-0.470681\pi$
$101$	186.726	0.183959	0.0919797	+	0.995761i	$0.470681\pi$
$102$	− 4.52655i	− 0.00439407i
$103$	453.907i	0.434221i	0.976147	+	0.217110i	$0.0696632\pi$
$103$	453.907i	0.434221i	−0.976147	+	0.217110i	$0.930337\pi$
$104$	−1466.47	−1.38268
$105$	0	0
$106$	763.422	0.699529
$107$	759.577i	0.686271i	0.939286	+	0.343136i	$0.111489\pi$
$107$	759.577i	0.686271i	−0.939286	+	0.343136i	$0.888511\pi$
$108$	− 253.837i	− 0.226161i
$109$	854.771	0.751121	0.375560	−	0.926798i	$-0.377450\pi$
$109$	854.771	0.751121	0.375560	+	0.926798i	$0.377450\pi$
$110$	0	0
$111$	943.241	0.806563
$112$	− 462.914i	− 0.390547i
$113$	− 1614.53i	− 1.34409i	−0.740511	−	0.672044i	$-0.765417\pi$
$113$	− 1614.53i	− 1.34409i	0.740511	−	0.672044i	$-0.234583\pi$
$114$	−471.435	−0.387315
$115$	0	0
$116$	703.296	0.562926
$117$	− 707.571i	− 0.559102i
$118$	− 1876.48i	− 1.46393i
$119$	4.14382	0.00319213
$120$	0	0
$121$	121.000	0.0909091
$122$	− 606.024i	− 0.449728i
$123$	− 1303.66i	− 0.955666i
$124$	419.307	0.303669
$125$	0	0
$126$	360.066	0.254581
$127$	− 2379.56i	− 1.66261i	−0.555816	−	0.831306i	$-0.687594\pi$
$127$	− 2379.56i	− 1.66261i	0.555816	−	0.831306i	$-0.312406\pi$
$128$	− 336.379i	− 0.232281i
$129$	−692.427	−0.472595
$130$	0	0
$131$	−1229.50	−0.820012	−0.410006	−	0.912083i	$-0.634473\pi$
$131$	−1229.50	−0.820012	−0.410006	+	0.912083i	$0.634473\pi$
$132$	− 184.738i	− 0.121813i
$133$	− 431.575i	− 0.281370i
$134$	1524.12	0.982564
$135$	0	0
$136$	7.76212	0.00489409
$137$	− 1452.18i	− 0.905604i	−0.891611	−	0.452802i	$-0.850424\pi$
$137$	− 1452.18i	− 0.905604i	0.891611	−	0.452802i	$-0.149576\pi$
$138$	1038.33i	0.640495i
$139$	1659.52	1.01265	0.506325	−	0.862343i	$-0.331004\pi$
$139$	1659.52	1.01265	0.506325	+	0.862343i	$0.331004\pi$
$140$	0	0
$141$	3947.74	2.35787
$142$	35.1680i	0.0207833i
$143$	654.849i	0.382946i
$144$	418.386	0.242121
$145$	0	0
$146$	1808.45	1.02512
$147$	− 1060.48i	− 0.595014i
$148$	407.378i	0.226258i
$149$	−1881.39	−1.03442	−0.517212	−	0.855857i	$-0.673030\pi$
$149$	−1881.39	−1.03442	−0.517212	+	0.855857i	$0.673030\pi$
$150$	0	0
$151$	−3322.65	−1.79068	−0.895342	−	0.445379i	$-0.853069\pi$
$151$	−3322.65	−1.79068	−0.895342	+	0.445379i	$0.853069\pi$
$152$	− 808.417i	− 0.431390i
$153$	3.74522i	0.00197898i
$154$	−333.237	−0.174370
$155$	0	0
$156$	999.797	0.513127
$157$	3062.06i	1.55655i	0.627922	+	0.778276i	$0.283905\pi$
$157$	3062.06i	1.55655i	−0.627922	+	0.778276i	$0.716095\pi$
$158$	2478.48i	1.24796i
$159$	−2066.53	−1.03073
$160$	0	0
$161$	−950.536	−0.465296
$162$	− 2093.20i	− 1.01517i
$163$	− 3278.90i	− 1.57560i	−0.615930	−	0.787801i	$-0.711219\pi$
$163$	− 3278.90i	− 1.57560i	0.615930	−	0.787801i	$-0.288781\pi$
$164$	563.039	0.268085
$165$	0	0
$166$	−2736.49	−1.27947
$167$	− 419.454i	− 0.194361i	−0.995267	−	0.0971805i	$-0.969018\pi$
$167$	− 419.454i	− 0.194361i	0.995267	−	0.0971805i	$-0.0309824\pi$
$168$	2020.05i	0.927682i
$169$	−1347.03	−0.613121
$170$	0	0
$171$	390.061	0.174437
$172$	− 299.053i	− 0.132573i
$173$	1374.15i	0.603901i	0.953324	+	0.301950i	$0.0976377\pi$
$173$	1374.15i	0.603901i	−0.953324	+	0.301950i	$0.902362\pi$
$174$	3751.28	1.63439
$175$	0	0
$176$	−387.211	−0.165836
$177$	5079.51i	2.15706i
$178$	− 929.456i	− 0.391380i
$179$	−3296.73	−1.37659	−0.688295	−	0.725431i	$-0.741640\pi$
$179$	−3296.73	−1.37659	−0.688295	+	0.725431i	$0.741640\pi$
$180$	0	0
$181$	−2288.22	−0.939680	−0.469840	−	0.882752i	$-0.655688\pi$
$181$	−2288.22	−0.939680	−0.469840	+	0.882752i	$0.655688\pi$
$182$	− 1803.47i	− 0.734518i
$183$	1640.47i	0.662661i
$184$	−1780.52	−0.713381
$185$	0	0
$186$	2236.53	0.881668
$187$	− 3.46616i	− 0.00135546i
$188$	1704.99i	0.661433i
$189$	1239.45	0.477021
$190$	0	0
$191$	−4115.73	−1.55918	−0.779590	−	0.626290i	$-0.784573\pi$
$191$	−4115.73	−1.55918	−0.779590	+	0.626290i	$0.784573\pi$
$192$	3422.08i	1.28629i
$193$	− 3659.72i	− 1.36493i	−0.730916	−	0.682467i	$-0.760907\pi$
$193$	− 3659.72i	− 1.36493i	0.730916	−	0.682467i	$-0.239093\pi$
$194$	701.225	0.259510
$195$	0	0
$196$	458.013	0.166914
$197$	2404.37i	0.869566i	0.900535	+	0.434783i	$0.143175\pi$
$197$	2404.37i	0.869566i	−0.900535	+	0.434783i	$0.856825\pi$
$198$	− 301.183i	− 0.108102i
$199$	1370.55	0.488221	0.244111	−	0.969747i	$-0.421504\pi$
$199$	1370.55	0.488221	0.244111	+	0.969747i	$0.421504\pi$
$200$	0	0
$201$	−4125.68	−1.44778
$202$	430.150i	0.149828i
$203$	3434.11i	1.18733i
$204$	−5.29200	−0.00181625
$205$	0	0
$206$	−1045.64	−0.353657
$207$	− 859.103i	− 0.288463i
$208$	− 2095.58i	− 0.698569i
$209$	−360.997	−0.119477
$210$	0	0
$211$	934.820	0.305003	0.152502	−	0.988303i	$-0.451267\pi$
$211$	934.820	0.305003	0.152502	+	0.988303i	$0.451267\pi$
$212$	− 892.519i	− 0.289144i
$213$	− 95.1976i	− 0.0306236i
$214$	−1749.80	−0.558943
$215$	0	0
$216$	2321.72	0.731356
$217$	2047.43i	0.640499i
$218$	1969.09i	0.611760i
$219$	−4895.35	−1.51049
$220$	0	0
$221$	18.7588	0.00570974
$222$	2172.90i	0.656915i
$223$	− 2151.48i	− 0.646071i	−0.946387	−	0.323035i	$-0.895297\pi$
$223$	− 2151.48i	− 0.646071i	0.946387	−	0.323035i	$-0.104703\pi$
$224$	−1525.15	−0.454927
$225$	0	0
$226$	3719.30	1.09471
$227$	2697.19i	0.788628i	0.918976	+	0.394314i	$0.129018\pi$
$227$	2697.19i	0.788628i	−0.918976	+	0.394314i	$0.870982\pi$
$228$	551.156i	0.160093i
$229$	6218.07	1.79433	0.897166	−	0.441694i	$-0.145622\pi$
$229$	6218.07	1.79433	0.897166	+	0.441694i	$0.145622\pi$
$230$	0	0
$231$	902.052	0.256929
$232$	6432.70i	1.82038i
$233$	− 3082.76i	− 0.866774i	−0.901208	−	0.433387i	$-0.857318\pi$
$233$	− 3082.76i	− 0.866774i	0.901208	−	0.433387i	$-0.142682\pi$
$234$	1629.99	0.455368
$235$	0	0
$236$	−2193.80	−0.605101
$237$	− 6709.08i	− 1.83882i
$238$	9.54591i	0.00259987i
$239$	−168.639	−0.0456418	−0.0228209	−	0.999740i	$-0.507265\pi$
$239$	−168.639	−0.0456418	−0.0228209	+	0.999740i	$0.507265\pi$
$240$	0	0
$241$	2588.87	0.691965	0.345982	−	0.938241i	$-0.387546\pi$
$241$	2588.87	0.691965	0.345982	+	0.938241i	$0.387546\pi$
$242$	278.742i	0.0740421i
$243$	3121.38i	0.824018i
$244$	−708.504	−0.185891
$245$	0	0
$246$	3003.17	0.778354
$247$	− 1953.71i	− 0.503285i
$248$	3835.20i	0.981997i
$249$	7407.50	1.88527
$250$	0	0
$251$	−1117.67	−0.281061	−0.140531	−	0.990076i	$-0.544881\pi$
$251$	−1117.67	−0.281061	−0.140531	+	0.990076i	$0.544881\pi$
$252$	− 420.954i	− 0.105229i
$253$	795.091i	0.197577i
$254$	5481.67	1.35413
$255$	0	0
$256$	−3615.31	−0.882645
$257$	3833.21i	0.930384i	0.885210	+	0.465192i	$0.154015\pi$
$257$	3833.21i	0.930384i	−0.885210	+	0.465192i	$0.845985\pi$
$258$	− 1595.11i	− 0.384911i
$259$	−1989.17	−0.477225
$260$	0	0
$261$	−3103.78	−0.736088
$262$	− 2832.33i	− 0.667870i
$263$	− 3099.11i	− 0.726614i	−0.931670	−	0.363307i	$-0.881648\pi$
$263$	− 3099.11i	− 0.726614i	0.931670	−	0.363307i	$-0.118352\pi$
$264$	1689.71	0.393917
$265$	0	0
$266$	994.196	0.229166
$267$	2515.98i	0.576687i
$268$	− 1781.85i	− 0.406133i
$269$	6221.46	1.41015	0.705073	−	0.709135i	$-0.250914\pi$
$269$	6221.46	1.41015	0.705073	+	0.709135i	$0.250914\pi$
$270$	0	0
$271$	1180.29	0.264567	0.132283	−	0.991212i	$-0.457769\pi$
$271$	1180.29	0.264567	0.132283	+	0.991212i	$0.457769\pi$
$272$	11.0921i	0.00247263i
$273$	4881.89i	1.08229i
$274$	3345.30	0.737581
$275$	0	0
$276$	1213.91	0.264743
$277$	− 4624.95i	− 1.00320i	−0.865100	−	0.501600i	$-0.832745\pi$
$277$	− 4624.95i	− 1.00320i	0.865100	−	0.501600i	$-0.167255\pi$
$278$	3822.94i	0.824766i
$279$	−1850.48	−0.397080
$280$	0	0
$281$	7501.11	1.59245	0.796225	−	0.605000i	$-0.206827\pi$
$281$	7501.11	1.59245	0.796225	+	0.605000i	$0.206827\pi$
$282$	9094.20i	1.92040i
$283$	540.526i	0.113537i	0.998387	+	0.0567685i	$0.0180797\pi$
$283$	540.526i	0.113537i	−0.998387	+	0.0567685i	$0.981920\pi$
$284$	41.1150	0.00859059
$285$	0	0
$286$	−1508.54	−0.311895
$287$	2749.25i	0.565446i
$288$	− 1378.45i	− 0.282034i
$289$	4912.90	0.999980
$290$	0	0
$291$	−1898.17	−0.382381
$292$	− 2114.26i	− 0.423725i
$293$	3385.58i	0.675044i	0.941318	+	0.337522i	$0.109589\pi$
$293$	3385.58i	0.675044i	−0.941318	+	0.337522i	$0.890411\pi$
$294$	2442.98	0.484616
$295$	0	0
$296$	−3726.08	−0.731669
$297$	− 1036.76i	− 0.202555i
$298$	− 4334.05i	− 0.842500i
$299$	−4303.01	−0.832273
$300$	0	0
$301$	1460.24	0.279624
$302$	− 7654.21i	− 1.45845i
$303$	− 1164.39i	− 0.220767i
$304$	1155.23	0.217950
$305$	0	0
$306$	−8.62768	−0.00161180
$307$	− 32.5963i	− 0.00605984i	−0.999995	−	0.00302992i	$-0.999036\pi$
$307$	− 32.5963i	− 0.00605984i	0.999995	−	0.00302992i	$-0.000964454\pi$
$308$	389.589i	0.0720743i
$309$	2830.49	0.521103
$310$	0	0
$311$	−1071.50	−0.195367	−0.0976836	−	0.995218i	$-0.531143\pi$
$311$	−1071.50	−0.195367	−0.0976836	+	0.995218i	$0.531143\pi$
$312$	9144.65i	1.65934i
$313$	− 4808.89i	− 0.868417i	−0.900812	−	0.434208i	$-0.857028\pi$
$313$	− 4808.89i	− 0.868417i	0.900812	−	0.434208i	$-0.142972\pi$
$314$	−7053.90	−1.26775
$315$	0	0
$316$	2897.59	0.515830
$317$	− 5615.88i	− 0.995014i	−0.867460	−	0.497507i	$-0.834249\pi$
$317$	− 5615.88i	− 0.995014i	0.867460	−	0.497507i	$-0.165751\pi$
$318$	− 4760.57i	− 0.839495i
$319$	2872.51	0.504168
$320$	0	0
$321$	4736.59	0.823585
$322$	− 2189.70i	− 0.378967i
$323$	10.3411i	0.00178141i
$324$	−2447.16	−0.419609
$325$	0	0
$326$	7553.43	1.28327
$327$	− 5330.21i	− 0.901410i
$328$	5149.84i	0.866927i
$329$	−8325.27	−1.39510
$330$	0	0
$331$	−1355.05	−0.225015	−0.112508	−	0.993651i	$-0.535888\pi$
$331$	−1355.05	−0.225015	−0.112508	+	0.993651i	$0.535888\pi$
$332$	3199.24i	0.528858i
$333$	− 1797.83i	− 0.295858i
$334$	966.274	0.158300
$335$	0	0
$336$	−2886.65	−0.468690
$337$	− 4072.44i	− 0.658278i	−0.944281	−	0.329139i	$-0.893241\pi$
$337$	− 4072.44i	− 0.658278i	0.944281	−	0.329139i	$-0.106759\pi$
$338$	− 3103.08i	− 0.499364i
$339$	−10067.9	−1.61302
$340$	0	0
$341$	1712.60	0.271972
$342$	898.564i	0.142072i
$343$	6747.06i	1.06212i
$344$	2735.29	0.428712
$345$	0	0
$346$	−3165.56	−0.491855
$347$	− 5212.03i	− 0.806329i	−0.915128	−	0.403165i	$-0.867910\pi$
$347$	− 5212.03i	− 0.806329i	0.915128	−	0.403165i	$-0.132090\pi$
$348$	− 4385.63i	− 0.675559i
$349$	−8528.85	−1.30813	−0.654067	−	0.756436i	$-0.726939\pi$
$349$	−8528.85	−1.30813	−0.654067	+	0.756436i	$0.726939\pi$
$350$	0	0
$351$	5610.92	0.853244
$352$	1275.74i	0.193174i
$353$	9548.25i	1.43967i	0.694147	+	0.719833i	$0.255782\pi$
$353$	9548.25i	1.43967i	−0.694147	+	0.719833i	$0.744218\pi$
$354$	−11701.4	−1.75684
$355$	0	0
$356$	−1086.63	−0.161773
$357$	− 25.8402i	− 0.00383083i
$358$	− 7594.52i	− 1.12118i
$359$	−1150.37	−0.169121	−0.0845604	−	0.996418i	$-0.526949\pi$
$359$	−1150.37	−0.169121	−0.0845604	+	0.996418i	$0.526949\pi$
$360$	0	0
$361$	−5781.98	−0.842978
$362$	− 5271.26i	− 0.765335i
$363$	− 754.536i	− 0.109099i
$364$	−2108.44	−0.303606
$365$	0	0
$366$	−3779.06	−0.539713
$367$	− 10086.2i	− 1.43459i	−0.696772	−	0.717293i	$-0.745381\pi$
$367$	− 10086.2i	− 1.43459i	0.696772	−	0.717293i	$-0.254619\pi$
$368$	− 2544.37i	− 0.360419i
$369$	−2484.80	−0.350551
$370$	0	0
$371$	4358.06	0.609863
$372$	− 2614.73i	− 0.364429i
$373$	− 192.336i	− 0.0266991i	−0.999911	−	0.0133495i	$-0.995751\pi$
$373$	− 192.336i	− 0.0266991i	0.999911	−	0.0133495i	$-0.00424942\pi$
$374$	7.98482	0.00110397
$375$	0	0
$376$	−15594.7	−2.13893
$377$	15546.0i	2.12376i
$378$	2855.26i	0.388516i
$379$	−5563.29	−0.754003	−0.377002	−	0.926213i	$-0.623045\pi$
$379$	−5563.29	−0.754003	−0.377002	+	0.926213i	$0.623045\pi$
$380$	0	0
$381$	−14838.5	−1.99528
$382$	− 9481.19i	− 1.26989i
$383$	− 441.480i	− 0.0588997i	−0.999566	−	0.0294498i	$-0.990624\pi$
$383$	− 441.480i	− 0.0588997i	0.999566	−	0.0294498i	$-0.00937553\pi$
$384$	−2097.60	−0.278758
$385$	0	0
$386$	8430.71	1.11169
$387$	1319.78i	0.173354i
$388$	− 819.804i	− 0.107266i
$389$	11903.2	1.55145	0.775726	−	0.631070i	$-0.217384\pi$
$389$	11903.2	1.55145	0.775726	+	0.631070i	$0.217384\pi$
$390$	0	0
$391$	22.7762	0.00294588
$392$	4189.21i	0.539763i
$393$	7666.94i	0.984086i
$394$	−5538.83	−0.708229
$395$	0	0
$396$	−352.114	−0.0446828
$397$	9182.52i	1.16085i	0.814314	+	0.580425i	$0.197114\pi$
$397$	9182.52i	1.16085i	−0.814314	+	0.580425i	$0.802886\pi$
$398$	3157.27i	0.397638i
$399$	−2691.23	−0.337669
$400$	0	0
$401$	14020.6	1.74602	0.873010	−	0.487703i	$-0.162165\pi$
$401$	14020.6	1.74602	0.873010	+	0.487703i	$0.162165\pi$
$402$	− 9504.13i	− 1.17916i
$403$	9268.56i	1.14566i
$404$	502.890	0.0619300
$405$	0	0
$406$	−7910.97	−0.967032
$407$	1663.88i	0.202642i
$408$	− 48.4033i	− 0.00587333i
$409$	14457.1	1.74782	0.873909	−	0.486089i	$-0.161577\pi$
$409$	14457.1	1.74782	0.873909	+	0.486089i	$0.161577\pi$
$410$	0	0
$411$	−9055.53	−1.08680
$412$	1222.46i	0.146181i
$413$	− 10712.0i	− 1.27628i
$414$	1979.07	0.234942
$415$	0	0
$416$	−6904.27	−0.813725
$417$	− 10348.5i	− 1.21527i
$418$	− 831.611i	− 0.0973096i
$419$	9808.29	1.14360	0.571798	−	0.820395i	$-0.306246\pi$
$419$	9808.29	1.14360	0.571798	+	0.820395i	$0.306246\pi$
$420$	0	0
$421$	2119.58	0.245373	0.122687	−	0.992445i	$-0.460849\pi$
$421$	2119.58	0.245373	0.122687	+	0.992445i	$0.460849\pi$
$422$	2153.50i	0.248414i
$423$	− 7524.46i	− 0.864897i
$424$	8163.42	0.935026
$425$	0	0
$426$	219.302	0.0249418
$427$	− 3459.54i	− 0.392081i
$428$	2045.69i	0.231033i
$429$	4083.53	0.459568
$430$	0	0
$431$	15401.4	1.72125	0.860627	−	0.509236i	$-0.170072\pi$
$431$	15401.4	1.72125	0.860627	+	0.509236i	$0.170072\pi$
$432$	3317.73i	0.369501i
$433$	− 12399.3i	− 1.37614i	−0.725642	−	0.688072i	$-0.758457\pi$
$433$	− 12399.3i	− 1.37614i	0.725642	−	0.688072i	$-0.241543\pi$
$434$	−4716.55	−0.521663
$435$	0	0
$436$	2302.07	0.252865
$437$	− 2372.11i	− 0.259665i
$438$	− 11277.2i	− 1.23024i
$439$	−16988.5	−1.84696	−0.923480	−	0.383647i	$-0.874668\pi$
$439$	−16988.5	−1.84696	−0.923480	+	0.383647i	$0.874668\pi$
$440$	0	0
$441$	−2021.29	−0.218259
$442$	43.2137i	0.00465037i
$443$	− 9276.05i	− 0.994850i	−0.867507	−	0.497425i	$-0.834279\pi$
$443$	− 9276.05i	− 0.994850i	0.867507	−	0.497425i	$-0.165721\pi$
$444$	2540.34	0.271530
$445$	0	0
$446$	4956.25	0.526201
$447$	11732.0i	1.24140i
$448$	− 7216.73i	− 0.761068i
$449$	−14861.9	−1.56209	−0.781043	−	0.624478i	$-0.785312\pi$
$449$	−14861.9	−1.56209	−0.781043	+	0.624478i	$0.785312\pi$
$450$	0	0
$451$	2299.65	0.240103
$452$	− 4348.25i	− 0.452488i
$453$	20719.5i	2.14898i
$454$	−6213.37	−0.642308
$455$	0	0
$456$	−5041.15	−0.517705
$457$	8738.15i	0.894428i	0.894427	+	0.447214i	$0.147584\pi$
$457$	8738.15i	0.894428i	−0.894427	+	0.447214i	$0.852416\pi$
$458$	14324.3i	1.46142i
$459$	−29.6990	−0.00302011
$460$	0	0
$461$	−13.0828	−0.00132175	−0.000660874	−	1.00000i	$-0.500210\pi$
$461$	−13.0828	−0.00132175	−0.000660874		1.00000i	$0.500210\pi$
$462$	2078.01i	0.209259i
$463$	− 12934.7i	− 1.29833i	−0.760647	−	0.649166i	$-0.775118\pi$
$463$	− 12934.7i	− 1.29833i	0.760647	−	0.649166i	$-0.224882\pi$
$464$	−9192.31	−0.919703
$465$	0	0
$466$	7101.60	0.705955
$467$	− 11982.9i	− 1.18737i	−0.804698	−	0.593684i	$-0.797673\pi$
$467$	− 11982.9i	− 1.18737i	0.804698	−	0.593684i	$-0.202327\pi$
$468$	− 1905.63i	− 0.188222i
$469$	8700.54	0.856618
$470$	0	0
$471$	19094.5	1.86800
$472$	− 20065.6i	− 1.95676i
$473$	− 1221.44i	− 0.118735i
$474$	15455.4	1.49765
$475$	0	0
$476$	11.1602	0.00107463
$477$	3938.85i	0.378087i
$478$	− 388.486i	− 0.0371735i
$479$	4569.04	0.435835	0.217917	−	0.975967i	$-0.430074\pi$
$479$	4569.04	0.435835	0.217917	+	0.975967i	$0.430074\pi$
$480$	0	0
$481$	−9004.86	−0.853609
$482$	5963.84i	0.563580i
$483$	5927.38i	0.558396i
$484$	325.877	0.0306046
$485$	0	0
$486$	−7190.56	−0.671132
$487$	194.834i	0.0181289i	0.999959	+	0.00906443i	$0.00288534\pi$
$487$	194.834i	0.0181289i	−0.999959	+	0.00906443i	$0.997115\pi$
$488$	− 6480.34i	− 0.601129i
$489$	−20446.7	−1.89086
$490$	0	0
$491$	−2362.26	−0.217123	−0.108561	−	0.994090i	$-0.534624\pi$
$491$	−2362.26	−0.217123	−0.108561	+	0.994090i	$0.534624\pi$
$492$	− 3511.02i	− 0.321725i
$493$	− 82.2859i	− 0.00751718i
$494$	4500.66	0.409907
$495$	0	0
$496$	−5480.49	−0.496131
$497$	200.759i	0.0181193i
$498$	17064.3i	1.53548i
$499$	10071.4	0.903524	0.451762	−	0.892139i	$-0.350796\pi$
$499$	10071.4	0.903524	0.451762	+	0.892139i	$0.350796\pi$
$500$	0	0
$501$	−2615.64	−0.233250
$502$	− 2574.71i	− 0.228914i
$503$	− 12093.0i	− 1.07197i	−0.844229	−	0.535983i	$-0.819941\pi$
$503$	− 12093.0i	− 1.07197i	0.844229	−	0.535983i	$-0.180059\pi$
$504$	3850.26	0.340286
$505$	0	0
$506$	−1831.61	−0.160919
$507$	8399.84i	0.735798i
$508$	− 6408.63i	− 0.559719i
$509$	11545.7	1.00541	0.502707	−	0.864457i	$-0.332337\pi$
$509$	11545.7	1.00541	0.502707	+	0.864457i	$0.332337\pi$
$510$	0	0
$511$	10323.7	0.893722
$512$	− 11019.4i	− 0.951163i
$513$	3093.12i	0.266208i
$514$	−8830.36	−0.757764
$515$	0	0
$516$	−1864.85	−0.159099
$517$	6963.80i	0.592394i
$518$	− 4582.36i	− 0.388682i
$519$	8568.98	0.724733
$520$	0	0
$521$	7278.47	0.612045	0.306023	−	0.952024i	$-0.401002\pi$
$521$	7278.47	0.612045	0.306023	+	0.952024i	$0.401002\pi$
$522$	− 7150.01i	− 0.599516i
$523$	− 11961.3i	− 1.00006i	−0.866007	−	0.500032i	$-0.833322\pi$
$523$	− 11961.3i	− 1.00006i	0.866007	−	0.500032i	$-0.166678\pi$
$524$	−3311.28	−0.276057
$525$	0	0
$526$	7139.26	0.591800
$527$	− 49.0591i	− 0.00405512i
$528$	2414.59i	0.199018i
$529$	6942.46	0.570598
$530$	0	0
$531$	9681.63	0.791237
$532$	− 1162.32i	− 0.0947234i
$533$	12445.7i	1.01141i
$534$	−5795.93	−0.469690
$535$	0	0
$536$	16297.7	1.31334
$537$	20557.9i	1.65203i
$538$	14332.1i	1.14851i
$539$	1870.69	0.149492
$540$	0	0
$541$	−13421.1	−1.06658	−0.533288	−	0.845934i	$-0.679044\pi$
$541$	−13421.1	−1.06658	−0.533288	+	0.845934i	$0.679044\pi$
$542$	2718.98i	0.215480i
$543$	14269.0i	1.12770i
$544$	36.5448	0.00288023
$545$	0	0
$546$	−11246.1	−0.881485
$547$	4928.89i	0.385273i	0.981270	+	0.192636i	$0.0617038\pi$
$547$	4928.89i	0.385273i	−0.981270	+	0.192636i	$0.938296\pi$
$548$	− 3911.00i	− 0.304872i
$549$	3126.76	0.243073
$550$	0	0
$551$	−8569.99	−0.662602
$552$	11103.1i	0.856118i
$553$	14148.6i	1.08799i
$554$	10654.3	0.817069
$555$	0	0
$556$	4469.41	0.340909
$557$	21545.6i	1.63899i	0.573089	+	0.819493i	$0.305745\pi$
$557$	21545.6i	1.63899i	−0.573089	+	0.819493i	$0.694255\pi$
$558$	− 4262.86i	− 0.323407i
$559$	6610.41	0.500162
$560$	0	0
$561$	−21.6144	−0.00162667
$562$	17279.9i	1.29699i
$563$	− 4151.42i	− 0.310766i	−0.987854	−	0.155383i	$-0.950339\pi$
$563$	− 4151.42i	− 0.310766i	0.987854	−	0.155383i	$-0.0496612\pi$
$564$	10632.1	0.793777
$565$	0	0
$566$	−1245.18	−0.0924716
$567$	− 11949.2i	− 0.885042i
$568$	376.059i	0.0277800i
$569$	−3669.56	−0.270362	−0.135181	−	0.990821i	$-0.543162\pi$
$569$	−3669.56	−0.270362	−0.135181	+	0.990821i	$0.543162\pi$
$570$	0	0
$571$	−14356.6	−1.05220	−0.526101	−	0.850422i	$-0.676346\pi$
$571$	−14356.6	−1.05220	−0.526101	+	0.850422i	$0.676346\pi$
$572$	1763.64i	0.128919i
$573$	25665.0i	1.87115i
$574$	−6333.30	−0.460535
$575$	0	0
$576$	6522.54	0.471828
$577$	− 10064.1i	− 0.726125i	−0.931765	−	0.363063i	$-0.881731\pi$
$577$	− 10064.1i	− 0.726125i	0.931765	−	0.363063i	$-0.118269\pi$
$578$	11317.6i	0.814446i
$579$	−22821.4	−1.63804
$580$	0	0
$581$	−15621.5	−1.11547
$582$	− 4372.72i	− 0.311435i
$583$	− 3645.36i	− 0.258963i
$584$	19338.1	1.37023
$585$	0	0
$586$	−7799.20	−0.549799
$587$	− 6069.76i	− 0.426790i	−0.976966	−	0.213395i	$-0.931548\pi$
$587$	− 6069.76i	− 0.426790i	0.976966	−	0.213395i	$-0.0684521\pi$
$588$	− 2856.09i	− 0.200311i
$589$	−5109.46	−0.357439
$590$	0	0
$591$	14993.3	1.04355
$592$	− 5324.56i	− 0.369659i
$593$	10565.2i	0.731637i	0.930686	+	0.365819i	$0.119211\pi$
$593$	10565.2i	0.731637i	−0.930686	+	0.365819i	$0.880789\pi$
$594$	2388.33	0.164974
$595$	0	0
$596$	−5066.95	−0.348239
$597$	− 8546.54i	− 0.585908i
$598$	− 9912.63i	− 0.677855i
$599$	4810.98	0.328166	0.164083	−	0.986447i	$-0.447534\pi$
$599$	4810.98	0.328166	0.164083	+	0.986447i	$0.447534\pi$
$600$	0	0
$601$	6860.33	0.465622	0.232811	−	0.972522i	$-0.425208\pi$
$601$	6860.33	0.465622	0.232811	+	0.972522i	$0.425208\pi$
$602$	3363.88i	0.227743i
$603$	7863.63i	0.531064i
$604$	−8948.56	−0.602834
$605$	0	0
$606$	2682.34	0.179807
$607$	− 13571.4i	− 0.907490i	−0.891132	−	0.453745i	$-0.850088\pi$
$607$	− 13571.4i	− 0.907490i	0.891132	−	0.453745i	$-0.149912\pi$
$608$	− 3806.10i	− 0.253878i
$609$	21414.5	1.42489
$610$	0	0
$611$	−37687.9	−2.49540
$612$	10.0866i	0 0.000666223i
$613$	1406.62i	0.0926803i	0.998926	+	0.0463402i	$0.0147558\pi$
$613$	1406.62i	0.0926803i	−0.998926	+	0.0463402i	$0.985244\pi$
$614$	75.0904	0.00493551
$615$	0	0
$616$	−3563.37	−0.233072
$617$	7788.23i	0.508172i	0.967182	+	0.254086i	$0.0817747\pi$
$617$	7788.23i	0.508172i	−0.967182	+	0.254086i	$0.918225\pi$
$618$	6520.45i	0.424419i
$619$	7131.66	0.463079	0.231539	−	0.972826i	$-0.425624\pi$
$619$	7131.66	0.463079	0.231539	+	0.972826i	$0.425624\pi$
$620$	0	0
$621$	6812.54	0.440222
$622$	− 2468.36i	− 0.159119i
$623$	− 5305.88i	− 0.341213i
$624$	−13067.7	−0.838343
$625$	0	0
$626$	11078.0	0.707293
$627$	2251.12i	0.143383i
$628$	8246.73i	0.524014i
$629$	47.6634	0.00302140
$630$	0	0
$631$	28826.0	1.81862	0.909308	−	0.416124i	$-0.136612\pi$
$631$	28826.0	1.81862	0.909308	+	0.416124i	$0.136612\pi$
$632$	26502.8i	1.66808i
$633$	− 5829.38i	− 0.366030i
$634$	12937.0	0.810402
$635$	0	0
$636$	−5565.60	−0.346997
$637$	10124.1i	0.629720i
$638$	6617.26i	0.410627i
$639$	−181.448	−0.0112331
$640$	0	0
$641$	11535.8	0.710821	0.355410	−	0.934710i	$-0.384341\pi$
$641$	11535.8	0.710821	0.355410	+	0.934710i	$0.384341\pi$
$642$	10911.4i	0.670779i
$643$	− 1123.87i	− 0.0689283i	−0.999406	−	0.0344642i	$-0.989028\pi$
$643$	− 1123.87i	− 0.0689283i	0.999406	−	0.0344642i	$-0.0109725\pi$
$644$	−2559.99	−0.156642
$645$	0	0
$646$	−23.8223	−0.00145089
$647$	4567.53i	0.277539i	0.990325	+	0.138770i	$0.0443148\pi$
$647$	4567.53i	0.277539i	−0.990325	+	0.138770i	$0.955685\pi$
$648$	− 22383.0i	− 1.35692i
$649$	−8960.24	−0.541942
$650$	0	0
$651$	12767.4	0.768654
$652$	− 8830.74i	− 0.530427i
$653$	− 19663.0i	− 1.17836i	−0.808001	−	0.589181i	$-0.799450\pi$
$653$	− 19663.0i	− 1.17836i	0.808001	−	0.589181i	$-0.200550\pi$
$654$	12278.9	0.734165
$655$	0	0
$656$	−7359.10	−0.437995
$657$	9330.62i	0.554067i
$658$	− 19178.5i	− 1.13626i
$659$	5440.78	0.321612	0.160806	−	0.986986i	$-0.448591\pi$
$659$	5440.78	0.321612	0.160806	+	0.986986i	$0.448591\pi$
$660$	0	0
$661$	−14661.0	−0.862703	−0.431351	−	0.902184i	$-0.641963\pi$
$661$	−14661.0	−0.862703	−0.431351	+	0.902184i	$0.641963\pi$
$662$	− 3121.55i	− 0.183267i
$663$	− 116.977i	− 0.00685218i
$664$	−29261.8	−1.71021
$665$	0	0
$666$	4141.58	0.240965
$667$	18875.3i	1.09573i
$668$	− 1129.67i	− 0.0654317i
$669$	−13416.3	−0.775341
$670$	0	0
$671$	−2893.78	−0.166488
$672$	9510.60i	0.545952i
$673$	− 7054.34i	− 0.404049i	−0.979380	−	0.202024i	$-0.935248\pi$
$673$	− 7054.34i	− 0.404049i	0.979380	−	0.202024i	$-0.0647520\pi$
$674$	9381.46	0.536143
$675$	0	0
$676$	−3627.82	−0.206407
$677$	16034.4i	0.910271i	0.890422	+	0.455136i	$0.150409\pi$
$677$	16034.4i	0.910271i	−0.890422	+	0.455136i	$0.849591\pi$
$678$	− 23193.0i	− 1.31375i
$679$	4003.00	0.226246
$680$	0	0
$681$	16819.2	0.946422
$682$	3945.23i	0.221511i
$683$	11575.3i	0.648486i	0.945974	+	0.324243i	$0.105110\pi$
$683$	11575.3i	0.648486i	−0.945974	+	0.324243i	$0.894890\pi$
$684$	1050.51	0.0587242
$685$	0	0
$686$	−15542.9	−0.865057
$687$	− 38774.9i	− 2.15335i
$688$	3908.73i	0.216597i
$689$	19728.6	1.09086
$690$	0	0
$691$	−14758.9	−0.812525	−0.406262	−	0.913756i	$-0.633168\pi$
$691$	−14758.9	−0.812525	−0.406262	+	0.913756i	$0.633168\pi$
$692$	3700.87i	0.203303i
$693$	− 1719.33i	− 0.0942451i
$694$	12006.7	0.656725
$695$	0	0
$696$	40113.2	2.18461
$697$	− 65.8758i	− 0.00357995i
$698$	− 19647.5i	− 1.06543i
$699$	−19223.6	−1.04020
$700$	0	0
$701$	−14332.4	−0.772224	−0.386112	−	0.922452i	$-0.626182\pi$
$701$	−14332.4	−0.772224	−0.386112	+	0.922452i	$0.626182\pi$
$702$	12925.6i	0.694935i
$703$	− 4964.09i	− 0.266322i
$704$	−6036.55	−0.323169
$705$	0	0
$706$	−21995.8	−1.17255
$707$	2455.55i	0.130623i
$708$	13680.1i	0.726174i
$709$	14159.3	0.750020	0.375010	−	0.927021i	$-0.377639\pi$
$709$	14159.3	0.750020	0.375010	+	0.927021i	$0.377639\pi$
$710$	0	0
$711$	−12787.6	−0.674505
$712$	− 9938.86i	− 0.523138i
$713$	11253.5i	0.591089i
$714$	59.5267	0.00312007
$715$	0	0
$716$	−8878.77	−0.463429
$717$	1051.61i	0.0547741i
$718$	− 2650.05i	− 0.137743i
$719$	−2750.64	−0.142672	−0.0713362	−	0.997452i	$-0.522726\pi$
$719$	−2750.64	−0.142672	−0.0713362	+	0.997452i	$0.522726\pi$
$720$	0	0
$721$	−5969.13	−0.308325
$722$	− 13319.7i	− 0.686574i
$723$	− 16143.7i	− 0.830418i
$724$	−6162.64	−0.316344
$725$	0	0
$726$	1738.19	0.0888569
$727$	17477.0i	0.891591i	0.895135	+	0.445795i	$0.147079\pi$
$727$	17477.0i	0.891591i	−0.895135	+	0.445795i	$0.852921\pi$
$728$	− 19284.9i	− 0.981794i
$729$	−5069.00	−0.257532
$730$	0	0
$731$	−34.9894	−0.00177035
$732$	4418.11i	0.223085i
$733$	34334.1i	1.73010i	0.501690	+	0.865048i	$0.332712\pi$
$733$	34334.1i	1.73010i	−0.501690	+	0.865048i	$0.667288\pi$
$734$	23235.0	1.16842
$735$	0	0
$736$	−8382.87	−0.419833
$737$	− 7277.70i	− 0.363742i
$738$	− 5724.10i	− 0.285511i
$739$	−2372.52	−0.118098	−0.0590491	−	0.998255i	$-0.518807\pi$
$739$	−2372.52	−0.118098	−0.0590491	+	0.998255i	$0.518807\pi$
$740$	0	0
$741$	−12183.0	−0.603986
$742$	10039.4i	0.496710i
$743$	24756.2i	1.22236i	0.791490	+	0.611182i	$0.209306\pi$
$743$	24756.2i	1.22236i	−0.791490	+	0.611182i	$0.790694\pi$
$744$	23915.6	1.17848
$745$	0	0
$746$	443.073	0.0217454
$747$	− 14118.8i	− 0.691540i
$748$	− 9.33508i	0 0.000456316i
$749$	−9988.87	−0.487297
$750$	0	0
$751$	3961.78	0.192500	0.0962500	−	0.995357i	$-0.469315\pi$
$751$	3961.78	0.192500	0.0962500	+	0.995357i	$0.469315\pi$
$752$	− 22284.8i	− 1.08064i
$753$	6969.57i	0.337298i
$754$	−35812.4	−1.72972
$755$	0	0
$756$	3338.10	0.160589
$757$	− 6139.00i	− 0.294750i	−0.989081	−	0.147375i	$-0.952918\pi$
$757$	− 6139.00i	− 0.294750i	0.989081	−	0.147375i	$-0.0470825\pi$
$758$	− 12815.9i	− 0.614108i
$759$	4958.05	0.237109
$760$	0	0
$761$	9191.35	0.437827	0.218913	−	0.975744i	$-0.429749\pi$
$761$	9191.35	0.437827	0.218913	+	0.975744i	$0.429749\pi$
$762$	− 34182.7i	− 1.62508i
$763$	11240.7i	0.533344i
$764$	−11084.5	−0.524899
$765$	0	0
$766$	1017.02	0.0479716
$767$	− 48492.6i	− 2.28288i
$768$	22544.5i	1.05925i
$769$	2314.79	0.108548	0.0542741	−	0.998526i	$-0.482716\pi$
$769$	2314.79	0.108548	0.0542741	+	0.998526i	$0.482716\pi$
$770$	0	0
$771$	23903.2	1.11654
$772$	− 9856.36i	− 0.459505i
$773$	− 7953.06i	− 0.370054i	−0.982733	−	0.185027i	$-0.940763\pi$
$773$	− 7953.06i	− 0.370054i	0.982733	−	0.185027i	$-0.0592372\pi$
$774$	−3040.30	−0.141191
$775$	0	0
$776$	7498.34	0.346875
$777$	12404.2i	0.572711i
$778$	27420.7i	1.26360i
$779$	−6860.89	−0.315555
$780$	0	0
$781$	167.928	0.00769392
$782$	52.4683i	0.00239931i
$783$	− 24612.4i	− 1.12334i
$784$	−5986.38	−0.272703
$785$	0	0
$786$	−17661.9	−0.801501
$787$	− 11035.5i	− 0.499841i	−0.968266	−	0.249920i	$-0.919596\pi$
$787$	− 11035.5i	− 0.499841i	0.968266	−	0.249920i	$-0.0804045\pi$
$788$	6475.46i	0.292740i
$789$	−19325.5	−0.871999
$790$	0	0
$791$	21232.0	0.954389
$792$	− 3220.61i	− 0.144494i
$793$	− 15661.1i	− 0.701314i
$794$	−21153.3	−0.945470
$795$	0	0
$796$	3691.18	0.164360
$797$	− 18269.9i	− 0.811984i	−0.913877	−	0.405992i	$-0.866926\pi$
$797$	− 18269.9i	− 0.811984i	0.913877	−	0.405992i	$-0.133074\pi$
$798$	− 6199.64i	− 0.275019i
$799$	199.485	0.00883263
$800$	0	0
$801$	4795.50	0.211536
$802$	32298.5i	1.42207i
$803$	− 8635.39i	− 0.379497i
$804$	−11111.3	−0.487395
$805$	0	0
$806$	−21351.5	−0.933095
$807$	− 38796.0i	− 1.69230i
$808$	4599.68i	0.200268i
$809$	−26864.0	−1.16747	−0.583737	−	0.811943i	$-0.698410\pi$
$809$	−26864.0	−1.16747	−0.583737	+	0.811943i	$0.698410\pi$
$810$	0	0
$811$	−18456.1	−0.799114	−0.399557	−	0.916708i	$-0.630836\pi$
$811$	−18456.1	−0.799114	−0.399557	+	0.916708i	$0.630836\pi$
$812$	9248.74i	0.399713i
$813$	− 7360.10i	− 0.317503i
$814$	−3832.99	−0.165044
$815$	0	0
$816$	69.1682	0.00296737
$817$	3644.11i	0.156048i
$818$	33304.1i	1.42353i
$819$	9304.96	0.396998
$820$	0	0
$821$	32876.4	1.39756	0.698779	−	0.715337i	$-0.253727\pi$
$821$	32876.4	1.39756	0.698779	+	0.715337i	$0.253727\pi$
$822$	− 20860.8i	− 0.885161i
$823$	15535.6i	0.658004i	0.944329	+	0.329002i	$0.106712\pi$
$823$	15535.6i	0.658004i	−0.944329	+	0.329002i	$0.893288\pi$
$824$	−11181.3	−0.472716
$825$	0	0
$826$	24676.8	1.03948
$827$	− 7730.74i	− 0.325059i	−0.986704	−	0.162530i	$-0.948035\pi$
$827$	− 7730.74i	− 0.325059i	0.986704	−	0.162530i	$-0.0519653\pi$
$828$	− 2313.74i	− 0.0971111i
$829$	−44577.2	−1.86759	−0.933794	−	0.357810i	$-0.883524\pi$
$829$	−44577.2	−1.86759	−0.933794	+	0.357810i	$0.883524\pi$
$830$	0	0
$831$	−28840.4	−1.20393
$832$	− 32669.6i	− 1.36132i
$833$	− 53.5877i	− 0.00222893i
$834$	23839.2	0.989790
$835$	0	0
$836$	−972.239	−0.0402220
$837$	− 14674.0i	− 0.605983i
$838$	22594.9i	0.931416i
$839$	−20585.6	−0.847073	−0.423537	−	0.905879i	$-0.639211\pi$
$839$	−20585.6	−0.847073	−0.423537	+	0.905879i	$0.639211\pi$
$840$	0	0
$841$	43803.7	1.79604
$842$	4882.77i	0.199847i
$843$	− 46775.7i	− 1.91108i
$844$	2517.66	0.102679
$845$	0	0
$846$	17333.7	0.704427
$847$	1591.22i	0.0645513i
$848$	11665.5i	0.472400i
$849$	3370.63	0.136254
$850$	0	0
$851$	−10933.3	−0.440411
$852$	− 256.386i	− 0.0103094i
$853$	− 35960.9i	− 1.44347i	−0.692170	−	0.721735i	$-0.743345\pi$
$853$	− 35960.9i	− 1.44347i	0.692170	−	0.721735i	$-0.256655\pi$
$854$	7969.56	0.319336
$855$	0	0
$856$	−18710.9	−0.747111
$857$	10177.0i	0.405646i	0.979215	+	0.202823i	$0.0650115\pi$
$857$	10177.0i	0.405646i	−0.979215	+	0.202823i	$0.934988\pi$
$858$	9407.02i	0.374301i
$859$	−37146.9	−1.47548	−0.737740	−	0.675085i	$-0.764107\pi$
$859$	−37146.9	−1.47548	−0.737740	+	0.675085i	$0.764107\pi$
$860$	0	0
$861$	17143.9	0.678584
$862$	35479.5i	1.40190i
$863$	− 176.455i	− 0.00696015i	−0.999994	−	0.00348007i	$-0.998892\pi$
$863$	− 176.455i	− 0.00696015i	0.999994	−	0.00348007i	$-0.00110774\pi$
$864$	10930.9	0.430411
$865$	0	0
$866$	28563.5	1.12082
$867$	− 30636.0i	− 1.20006i
$868$	5514.13i	0.215624i
$869$	11834.8	0.461989
$870$	0	0
$871$	39386.7	1.53223
$872$	21055.9i	0.817709i
$873$	3617.95i	0.140262i
$874$	5464.51	0.211487
$875$	0	0
$876$	−13184.2	−0.508507
$877$	3639.38i	0.140129i	0.997542	+	0.0700644i	$0.0223205\pi$
$877$	3639.38i	0.140129i	−0.997542	+	0.0700644i	$0.977680\pi$
$878$	− 39135.5i	− 1.50428i
$879$	21111.9	0.810112
$880$	0	0
$881$	−31931.9	−1.22113	−0.610565	−	0.791967i	$-0.709057\pi$
$881$	−31931.9	−1.22113	−0.610565	+	0.791967i	$0.709057\pi$
$882$	− 4656.35i	− 0.177764i
$883$	− 5974.79i	− 0.227710i	−0.993497	−	0.113855i	$-0.963680\pi$
$883$	− 5974.79i	− 0.227710i	0.993497	−	0.113855i	$-0.0363199\pi$
$884$	50.5212	0.00192219
$885$	0	0
$886$	21368.8	0.810268
$887$	7750.43i	0.293387i	0.989182	+	0.146693i	$0.0468630\pi$
$887$	7750.43i	0.293387i	−0.989182	+	0.146693i	$0.953137\pi$
$888$	23235.2i	0.878066i
$889$	31292.5	1.18056
$890$	0	0
$891$	−9995.08	−0.375811
$892$	− 5794.37i	− 0.217500i
$893$	− 20776.2i	− 0.778553i
$894$	−27026.4	−1.01107
$895$	0	0
$896$	4423.58	0.164935
$897$	26832.9i	0.998799i
$898$	− 34236.6i	− 1.27226i
$899$	40656.7	1.50832
$900$	0	0
$901$	−104.425	−0.00386116
$902$	5297.59i	0.195555i
$903$	− 9105.81i	− 0.335573i
$904$	39771.3	1.46324
$905$	0	0
$906$	−47730.4	−1.75026
$907$	25477.1i	0.932693i	0.884602	+	0.466346i	$0.154430\pi$
$907$	25477.1i	0.932693i	−0.884602	+	0.466346i	$0.845570\pi$
$908$	7264.07i	0.265492i
$909$	−2219.35	−0.0809803
$910$	0	0
$911$	−19229.5	−0.699342	−0.349671	−	0.936873i	$-0.613707\pi$
$911$	−19229.5	−0.699342	−0.349671	+	0.936873i	$0.613707\pi$
$912$	− 7203.79i	− 0.261559i
$913$	13066.8i	0.473657i
$914$	−20129.6	−0.728478
$915$	0	0
$916$	16746.5	0.604062
$917$	− 16168.6i	− 0.582261i
$918$	− 68.4160i	− 0.00245977i
$919$	3232.39	0.116025	0.0580124	−	0.998316i	$-0.481524\pi$
$919$	3232.39	0.116025	0.0580124	+	0.998316i	$0.481524\pi$
$920$	0	0
$921$	−203.265	−0.00727233
$922$	− 30.1381i	− 0.00107651i
$923$	908.824i	0.0324099i
$924$	2429.41	0.0864954
$925$	0	0
$926$	29797.0	1.05744
$927$	− 5394.96i	− 0.191147i
$928$	30285.7i	1.07131i
$929$	−41921.6	−1.48052	−0.740260	−	0.672321i	$-0.765298\pi$
$929$	−41921.6	−1.48052	−0.740260	+	0.672321i	$0.765298\pi$
$930$	0	0
$931$	−5581.10	−0.196470
$932$	− 8302.50i	− 0.291800i
$933$	6681.70i	0.234458i
$934$	27604.3	0.967067
$935$	0	0
$936$	17429.9	0.608667
$937$	34983.9i	1.21972i	0.792511	+	0.609858i	$0.208773\pi$
$937$	34983.9i	1.21972i	−0.792511	+	0.609858i	$0.791227\pi$
$938$	20043.0i	0.697683i
$939$	−29987.4	−1.04218
$940$	0	0
$941$	−20711.8	−0.717519	−0.358760	−	0.933430i	$-0.616800\pi$
$941$	−20711.8	−0.717519	−0.358760	+	0.933430i	$0.616800\pi$
$942$	43986.9i	1.52141i
$943$	15111.0i	0.521826i
$944$	28673.6	0.988609
$945$	0	0
$946$	2813.77	0.0967056
$947$	− 23659.4i	− 0.811854i	−0.913905	−	0.405927i	$-0.866949\pi$
$947$	− 23659.4i	− 0.811854i	0.913905	−	0.405927i	$-0.133051\pi$
$948$	− 18068.9i	− 0.619041i
$949$	46734.5	1.59860
$950$	0	0
$951$	−35019.7	−1.19410
$952$	102.076i	0.00347512i
$953$	− 10969.7i	− 0.372869i	−0.982467	−	0.186434i	$-0.940307\pi$
$953$	− 10969.7i	− 0.372869i	0.982467	−	0.186434i	$-0.0596932\pi$
$954$	−9073.73	−0.307938
$955$	0	0
$956$	−454.180	−0.0153653
$957$	− 17912.5i	− 0.605046i
$958$	10525.5i	0.354971i
$959$	19096.9	0.643037
$960$	0	0
$961$	−5551.31	−0.186342
$962$	− 20744.0i	− 0.695233i
$963$	− 9028.03i	− 0.302102i
$964$	6972.34	0.232950
$965$	0	0
$966$	−13654.6	−0.454793
$967$	− 38508.5i	− 1.28061i	−0.768121	−	0.640305i	$-0.778808\pi$
$967$	− 38508.5i	− 1.28061i	0.768121	−	0.640305i	$-0.221192\pi$
$968$	2980.64i	0.0989684i
$969$	64.4855	0.00213785
$970$	0	0
$971$	−57757.1	−1.90887	−0.954436	−	0.298417i	$-0.903541\pi$
$971$	−57757.1	−1.90887	−0.954436	+	0.298417i	$0.903541\pi$
$972$	8406.50i	0.277406i
$973$	21823.6i	0.719046i
$974$	−448.828	−0.0147653
$975$	0	0
$976$	9260.38	0.303707
$977$	22681.9i	0.742742i	0.928485	+	0.371371i	$0.121112\pi$
$977$	22681.9i	0.742742i	−0.928485	+	0.371371i	$0.878888\pi$
$978$	− 47101.9i	− 1.54003i
$979$	−4438.18	−0.144888
$980$	0	0
$981$	−10159.5	−0.330649
$982$	− 5441.82i	− 0.176839i
$983$	− 20920.1i	− 0.678787i	−0.940644	−	0.339394i	$-0.889778\pi$
$983$	− 20920.1i	− 0.678787i	0.940644	−	0.339394i	$-0.110222\pi$
$984$	32113.5	1.04039
$985$	0	0
$986$	189.558	0.00612247
$987$	51915.0i	1.67424i
$988$	− 5261.73i	− 0.169431i
$989$	8026.08	0.258053
$990$	0	0
$991$	10809.1	0.346480	0.173240	−	0.984880i	$-0.444576\pi$
$991$	10809.1	0.346480	0.173240	+	0.984880i	$0.444576\pi$
$992$	18056.5i	0.577916i
$993$	8449.84i	0.270038i
$994$	−462.479	−0.0147575
$995$	0	0
$996$	19949.9	0.634675
$997$	− 26066.0i	− 0.828001i	−0.910277	−	0.414001i	$-0.864131\pi$
$997$	− 26066.0i	− 0.828001i	0.910277	−	0.414001i	$-0.135869\pi$
$998$	23201.0i	0.735886i
$999$	14256.5	0.451508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.4.b.e.199.6		8
5.2	odd	4		275.4.a.e.1.2		4
5.3	odd	4		55.4.a.d.1.3	✓	4
5.4	even	2	inner	275.4.b.e.199.3		8
15.2	even	4		2475.4.a.bc.1.3		4
15.8	even	4		495.4.a.n.1.2		4
20.3	even	4		880.4.a.z.1.2		4
55.43	even	4		605.4.a.j.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.4.a.d.1.3	✓	4	5.3	odd	4
275.4.a.e.1.2		4	5.2	odd	4
275.4.b.e.199.3		8	5.4	even	2	inner
275.4.b.e.199.6		8	1.1	even	1	trivial
495.4.a.n.1.2		4	15.8	even	4
605.4.a.j.1.2		4	55.43	even	4
880.4.a.z.1.2		4	20.3	even	4
2475.4.a.bc.1.3		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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.30365i q^{2} -6.23583i q^{3} +2.69320 q^{4} +14.3652 q^{6} +13.1506i q^{7} +24.6334i q^{8} -11.8856 q^{9} +O(q^{10})\)	\(q+2.30365i q^{2} -6.23583i q^{3} +2.69320 q^{4} +14.3652 q^{6} +13.1506i q^{7} +24.6334i q^{8} -11.8856 q^{9} +11.0000 q^{11} -16.7944i q^{12} +59.5317i q^{13} -30.2943 q^{14} -35.2010 q^{16} -0.315106i q^{17} -27.3803i q^{18} -32.8179 q^{19} +82.0048 q^{21} +25.3401i q^{22} +72.2810i q^{23} +153.610 q^{24} -137.140 q^{26} -94.2508i q^{27} +35.4172i q^{28} +261.137 q^{29} +155.691 q^{31} +115.976i q^{32} -68.5942i q^{33} +0.725893 q^{34} -32.0103 q^{36} +151.261i q^{37} -75.6010i q^{38} +371.230 q^{39} +209.059 q^{41} +188.910i q^{42} -111.040i q^{43} +29.6252 q^{44} -166.510 q^{46} +633.073i q^{47} +219.508i q^{48} +170.062 q^{49} -1.96495 q^{51} +160.331i q^{52} -331.397i q^{53} +217.121 q^{54} -323.943 q^{56} +204.647i q^{57} +601.569i q^{58} -814.568 q^{59} -263.071 q^{61} +358.657i q^{62} -156.302i q^{63} -548.777 q^{64} +158.017 q^{66} -661.609i q^{67} -0.848644i q^{68} +450.732 q^{69} +15.2662 q^{71} -292.783i q^{72} -785.036i q^{73} -348.453 q^{74} -88.3853 q^{76} +144.656i q^{77} +855.183i q^{78} +1075.89 q^{79} -908.644 q^{81} +481.599i q^{82} +1187.89i q^{83} +220.855 q^{84} +255.797 q^{86} -1628.41i q^{87} +270.967i q^{88} -403.471 q^{89} -782.876 q^{91} +194.667i q^{92} -970.863i q^{93} -1458.38 q^{94} +723.208 q^{96} -304.398i q^{97} +391.764i q^{98} -130.742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 38 q^{4} - 38 q^{6} - 98 q^{9}+O(q^{10}) \) 8 * q - 38 * q^4 - 38 * q^6 - 98 * q^9	\( 8 q - 38 q^{4} - 38 q^{6} - 98 q^{9} + 88 q^{11} + 98 q^{14} - 74 q^{16} + 410 q^{19} - 362 q^{21} + 774 q^{24} - 172 q^{26} + 158 q^{29} + 98 q^{31} + 1878 q^{34} + 224 q^{36} + 52 q^{39} + 1472 q^{41} - 418 q^{44} - 668 q^{46} - 74 q^{49} + 826 q^{51} + 2978 q^{54} - 514 q^{56} + 1684 q^{59} - 2194 q^{61} + 330 q^{64} - 418 q^{66} + 116 q^{69} - 1042 q^{71} - 6514 q^{74} - 5650 q^{76} + 2236 q^{79} + 368 q^{81} + 1210 q^{84} + 6904 q^{86} + 362 q^{89} - 4380 q^{91} - 2068 q^{94} + 7962 q^{96} - 1078 q^{99}+O(q^{100}) \) 8 * q - 38 * q^4 - 38 * q^6 - 98 * q^9 + 88 * q^11 + 98 * q^14 - 74 * q^16 + 410 * q^19 - 362 * q^21 + 774 * q^24 - 172 * q^26 + 158 * q^29 + 98 * q^31 + 1878 * q^34 + 224 * q^36 + 52 * q^39 + 1472 * q^41 - 418 * q^44 - 668 * q^46 - 74 * q^49 + 826 * q^51 + 2978 * q^54 - 514 * q^56 + 1684 * q^59 - 2194 * q^61 + 330 * q^64 - 418 * q^66 + 116 * q^69 - 1042 * q^71 - 6514 * q^74 - 5650 * q^76 + 2236 * q^79 + 368 * q^81 + 1210 * q^84 + 6904 * q^86 + 362 * q^89 - 4380 * q^91 - 2068 * q^94 + 7962 * q^96 - 1078 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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