LMFDB - Embedded newform 1210.3.d.c.241.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1210,3,Mod(241,1210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1210, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1210.241"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 1210 = 2 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1210.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$32.9701119876$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 92 x^{14} - 504 x^{13} + 3078 x^{12} - 12280 x^{11} + 49836 x^{10} - 147672 x^{9} + \cdots + 339856 $ x^16 - 8x^15 + 92x^14 - 504x^13 + 3078x^12 - 12280x^11 + 49836x^10 - 147672x^9 + 423553x^8 - 924384x^7 + 1876224x^6 - 2898272x^5 + 3947928x^4 - 3906048x^3 + 3026408x^2 - 1437952*x + 339856
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			241.2
Root			$0.500000 + 3.59455i$ of defining polynomial
Character	$\chi$	$=$	1210.241
Dual form			1210.3.d.c.241.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} -5.33478 q^{3} -2.00000 q^{4} +2.23607 q^{5} +7.54452i q^{6} -8.94509i q^{7} +2.82843i q^{8} +19.4599 q^{9} -3.16228i q^{10} +10.6696 q^{12} +15.5829i q^{13} -12.6503 q^{14} -11.9289 q^{15} +4.00000 q^{16} +9.36447i q^{17} -27.5204i q^{18} -25.9807i q^{19} -4.47214 q^{20} +47.7201i q^{21} +1.85528 q^{23} -15.0890i q^{24} +5.00000 q^{25} +22.0375 q^{26} -55.8012 q^{27} +17.8902i q^{28} -14.2031i q^{29} +16.8701i q^{30} -40.1533 q^{31} -5.65685i q^{32} +13.2434 q^{34} -20.0018i q^{35} -38.9198 q^{36} -30.0873 q^{37} -36.7423 q^{38} -83.1312i q^{39} +6.32456i q^{40} +55.9700i q^{41} +67.4864 q^{42} +38.9779i q^{43} +43.5136 q^{45} -2.62376i q^{46} -65.8830 q^{47} -21.3391 q^{48} -31.0146 q^{49} -7.07107i q^{50} -49.9574i q^{51} -31.1658i q^{52} -91.2982 q^{53} +78.9148i q^{54} +25.3005 q^{56} +138.602i q^{57} -20.0863 q^{58} +20.4895 q^{59} +23.8579 q^{60} -47.9471i q^{61} +56.7854i q^{62} -174.070i q^{63} -8.00000 q^{64} +34.8444i q^{65} +70.6355 q^{67} -18.7289i q^{68} -9.89751 q^{69} -28.2869 q^{70} +100.504 q^{71} +55.0409i q^{72} +49.3326i q^{73} +42.5499i q^{74} -26.6739 q^{75} +51.9615i q^{76} -117.565 q^{78} -25.4652i q^{79} +8.94427 q^{80} +122.548 q^{81} +79.1535 q^{82} +45.5564i q^{83} -95.4402i q^{84} +20.9396i q^{85} +55.1231 q^{86} +75.7706i q^{87} +139.002 q^{89} -61.5376i q^{90} +139.390 q^{91} -3.71056 q^{92} +214.209 q^{93} +93.1727i q^{94} -58.0947i q^{95} +30.1781i q^{96} +101.737 q^{97} +43.8613i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} - 32 q^{4} + 40 q^{9} + 32 q^{12} + 16 q^{14} + 40 q^{15} + 64 q^{16} + 108 q^{23} + 80 q^{25} - 292 q^{27} - 268 q^{31} - 16 q^{34} - 80 q^{36} + 44 q^{37} - 280 q^{38} - 16 q^{42} - 476 q^{47}+ \cdots + 296 q^{97}+O(q^{100}) $ 16 * q - 16 * q^3 - 32 * q^4 + 40 * q^9 + 32 * q^12 + 16 * q^14 + 40 * q^15 + 64 * q^16 + 108 * q^23 + 80 * q^25 - 292 * q^27 - 268 * q^31 - 16 * q^34 - 80 * q^36 + 44 * q^37 - 280 * q^38 - 16 * q^42 - 476 * q^47 - 64 * q^48 - 644 * q^49 - 396 * q^53 - 32 * q^56 + 192 * q^58 - 180 * q^59 - 80 * q^60 - 128 * q^64 + 188 * q^67 - 416 * q^69 + 308 * q^71 - 80 * q^75 + 8 * q^78 + 536 * q^81 + 16 * q^82 + 304 * q^86 - 176 * q^89 + 80 * q^91 - 216 * q^92 + 436 * q^93 + 296 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1210\mathbb{Z}\right)^\times$.

$n$	$727$	$1091$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.41421i	− 0.707107i
$2$	− 1.41421i	− 0.707107i
$3$	−5.33478	−1.77826	−0.889130	−	0.457654i	$-0.848690\pi$
$3$	−5.33478	−1.77826	−0.889130	+	0.457654i	$0.848690\pi$
$4$	−2.00000	−0.500000
$5$	2.23607	0.447214
$5$	2.23607	0.447214
$6$	7.54452i	1.25742i
$7$	− 8.94509i	− 1.27787i	−0.769261	−	0.638935i	$-0.779375\pi$
$7$	− 8.94509i	− 1.27787i	0.769261	−	0.638935i	$-0.220625\pi$
$8$	2.82843i	0.353553i
$9$	19.4599	2.16221
$10$	− 3.16228i	− 0.316228i
$11$	0	0
$11$	0	0
$12$	10.6696	0.889130
$13$	15.5829i	1.19868i	0.800493	+	0.599341i	$0.204571\pi$
$13$	15.5829i	1.19868i	−0.800493	+	0.599341i	$0.795429\pi$
$14$	−12.6503	−0.903590
$15$	−11.9289	−0.795262
$16$	4.00000	0.250000
$17$	9.36447i	0.550851i	0.961322	+	0.275426i	$0.0888188\pi$
$17$	9.36447i	0.550851i	−0.961322	+	0.275426i	$0.911181\pi$
$18$	− 27.5204i	− 1.52891i
$19$	− 25.9807i	− 1.36741i	−0.729760	−	0.683704i	$-0.760368\pi$
$19$	− 25.9807i	− 1.36741i	0.729760	−	0.683704i	$-0.239632\pi$
$20$	−4.47214	−0.223607
$21$	47.7201i	2.27239i
$22$	0	0
$23$	1.85528	0.0806643	0.0403322	−	0.999186i	$-0.487158\pi$
$23$	1.85528	0.0806643	0.0403322	+	0.999186i	$0.487158\pi$
$24$	− 15.0890i	− 0.628710i
$25$	5.00000	0.200000
$26$	22.0375	0.847597
$27$	−55.8012	−2.06671
$28$	17.8902i	0.638935i
$29$	− 14.2031i	− 0.489763i	−0.969553	−	0.244881i	$-0.921251\pi$
$29$	− 14.2031i	− 0.489763i	0.969553	−	0.244881i	$-0.0787490\pi$
$30$	16.8701i	0.562335i
$31$	−40.1533	−1.29527	−0.647634	−	0.761951i	$-0.724242\pi$
$31$	−40.1533	−1.29527	−0.647634	+	0.761951i	$0.724242\pi$
$32$	− 5.65685i	− 0.176777i
$33$	0	0
$34$	13.2434	0.389511
$35$	− 20.0018i	− 0.571481i
$36$	−38.9198	−1.08111
$37$	−30.0873	−0.813171	−0.406585	−	0.913613i	$-0.633281\pi$
$37$	−30.0873	−0.813171	−0.406585	+	0.913613i	$0.633281\pi$
$38$	−36.7423	−0.966903
$39$	− 83.1312i	− 2.13157i
$40$	6.32456i	0.158114i
$41$	55.9700i	1.36512i	0.730829	+	0.682561i	$0.239134\pi$
$41$	55.9700i	1.36512i	−0.730829	+	0.682561i	$0.760866\pi$
$42$	67.4864	1.60682
$43$	38.9779i	0.906463i	0.891393	+	0.453231i	$0.149729\pi$
$43$	38.9779i	0.906463i	−0.891393	+	0.453231i	$0.850271\pi$
$44$	0	0
$45$	43.5136	0.966970
$46$	− 2.62376i	− 0.0570383i
$47$	−65.8830	−1.40177	−0.700883	−	0.713276i	$-0.747211\pi$
$47$	−65.8830	−1.40177	−0.700883	+	0.713276i	$0.747211\pi$
$48$	−21.3391	−0.444565
$49$	−31.0146	−0.632951
$50$	− 7.07107i	− 0.141421i
$51$	− 49.9574i	− 0.979557i
$52$	− 31.1658i	− 0.599341i
$53$	−91.2982	−1.72261	−0.861304	−	0.508091i	$-0.830351\pi$
$53$	−91.2982	−1.72261	−0.861304	+	0.508091i	$0.830351\pi$
$54$	78.9148i	1.46139i
$55$	0	0
$56$	25.3005	0.451795
$57$	138.602i	2.43161i
$58$	−20.0863	−0.346315
$59$	20.4895	0.347280	0.173640	−	0.984809i	$-0.444447\pi$
$59$	20.4895	0.347280	0.173640	+	0.984809i	$0.444447\pi$
$60$	23.8579	0.397631
$61$	− 47.9471i	− 0.786018i	−0.919535	−	0.393009i	$-0.871434\pi$
$61$	− 47.9471i	− 0.786018i	0.919535	−	0.393009i	$-0.128566\pi$
$62$	56.7854i	0.915893i
$63$	− 174.070i	− 2.76302i
$64$	−8.00000	−0.125000
$65$	34.8444i	0.536067i
$66$	0	0
$67$	70.6355	1.05426	0.527131	−	0.849784i	$-0.323268\pi$
$67$	70.6355	1.05426	0.527131	+	0.849784i	$0.323268\pi$
$68$	− 18.7289i	− 0.275426i
$69$	−9.89751	−0.143442
$70$	−28.2869	−0.404098
$71$	100.504	1.41555	0.707774	−	0.706439i	$-0.249700\pi$
$71$	100.504	1.41555	0.707774	+	0.706439i	$0.249700\pi$
$72$	55.0409i	0.764457i
$73$	49.3326i	0.675788i	0.941184	+	0.337894i	$0.109715\pi$
$73$	49.3326i	0.675788i	−0.941184	+	0.337894i	$0.890285\pi$
$74$	42.5499i	0.574998i
$75$	−26.6739	−0.355652
$76$	51.9615i	0.683704i
$77$	0	0
$78$	−117.565	−1.50725
$79$	− 25.4652i	− 0.322344i	−0.986926	−	0.161172i	$-0.948473\pi$
$79$	− 25.4652i	− 0.322344i	0.986926	−	0.161172i	$-0.0515274\pi$
$80$	8.94427	0.111803
$81$	122.548	1.51294
$82$	79.1535	0.965287
$83$	45.5564i	0.548872i	0.961605	+	0.274436i	$0.0884911\pi$
$83$	45.5564i	0.548872i	−0.961605	+	0.274436i	$0.911509\pi$
$84$	− 95.4402i	− 1.13619i
$85$	20.9396i	0.246348i
$86$	55.1231	0.640966
$87$	75.7706i	0.870926i
$88$	0	0
$89$	139.002	1.56182	0.780911	−	0.624642i	$-0.214755\pi$
$89$	139.002	1.56182	0.780911	+	0.624642i	$0.214755\pi$
$90$	− 61.5376i	− 0.683751i
$91$	139.390	1.53176
$92$	−3.71056	−0.0403322
$93$	214.209	2.30333
$94$	93.1727i	0.991199i
$95$	− 58.0947i	− 0.611523i
$96$	30.1781i	0.314355i
$97$	101.737	1.04883	0.524415	−	0.851463i	$-0.324284\pi$
$97$	101.737	1.04883	0.524415	+	0.851463i	$0.324284\pi$
$98$	43.8613i	0.447564i
$99$	0	0
$100$	−10.0000	−0.100000
$101$	145.354i	1.43915i	0.694414	+	0.719576i	$0.255664\pi$
$101$	145.354i	1.43915i	−0.694414	+	0.719576i	$0.744336\pi$
$102$	−70.6505	−0.692652
$103$	−1.50658	−0.0146270	−0.00731348	−	0.999973i	$-0.502328\pi$
$103$	−1.50658	−0.0146270	−0.00731348	+	0.999973i	$0.502328\pi$
$104$	−44.0750	−0.423798
$105$	106.705i	1.01624i
$106$	129.115i	1.21807i
$107$	179.793i	1.68031i	0.542345	+	0.840156i	$0.317536\pi$
$107$	179.793i	1.68031i	−0.542345	+	0.840156i	$0.682464\pi$
$108$	111.602	1.03336
$109$	− 75.4374i	− 0.692086i	−0.938219	−	0.346043i	$-0.887525\pi$
$109$	− 75.4374i	− 0.692086i	0.938219	−	0.346043i	$-0.112475\pi$
$110$	0	0
$111$	160.509	1.44603
$112$	− 35.7804i	− 0.319467i
$113$	16.5575	0.146526	0.0732631	−	0.997313i	$-0.476659\pi$
$113$	16.5575	0.146526	0.0732631	+	0.997313i	$0.476659\pi$
$114$	196.012	1.71941
$115$	4.14853	0.0360742
$116$	28.4062i	0.244881i
$117$	303.241i	2.59180i
$118$	− 28.9766i	− 0.245564i
$119$	83.7661	0.703916
$120$	− 33.7401i	− 0.281168i
$121$	0	0
$122$	−67.8074	−0.555798
$123$	− 298.588i	− 2.42754i
$124$	80.3067	0.647634
$125$	11.1803	0.0894427
$126$	−246.173	−1.95375
$127$	22.5096i	0.177241i	0.996065	+	0.0886206i	$0.0282459\pi$
$127$	22.5096i	0.177241i	−0.996065	+	0.0886206i	$0.971754\pi$
$128$	11.3137i	0.0883883i
$129$	− 207.939i	− 1.61193i
$130$	49.2774	0.379057
$131$	96.9601i	0.740153i	0.929001	+	0.370077i	$0.120669\pi$
$131$	96.9601i	0.740153i	−0.929001	+	0.370077i	$0.879331\pi$
$132$	0	0
$133$	−232.400	−1.74737
$134$	− 99.8938i	− 0.745476i
$135$	−124.775	−0.924262
$136$	−26.4867	−0.194755
$137$	−130.070	−0.949414	−0.474707	−	0.880144i	$-0.657446\pi$
$137$	−130.070	−0.949414	−0.474707	+	0.880144i	$0.657446\pi$
$138$	13.9972i	0.101429i
$139$	122.264i	0.879598i	0.898096	+	0.439799i	$0.144950\pi$
$139$	122.264i	0.879598i	−0.898096	+	0.439799i	$0.855050\pi$
$140$	40.0037i	0.285740i
$141$	351.472	2.49271
$142$	− 142.134i	− 1.00094i
$143$	0	0
$144$	77.8396	0.540553
$145$	− 31.7592i	− 0.219029i
$146$	69.7668	0.477855
$147$	165.456	1.12555
$148$	60.1746	0.406585
$149$	− 35.7217i	− 0.239743i	−0.992789	−	0.119872i	$-0.961752\pi$
$149$	− 35.7217i	− 0.239743i	0.992789	−	0.119872i	$-0.0382483\pi$
$150$	37.7226i	0.251484i
$151$	− 139.405i	− 0.923212i	−0.887085	−	0.461606i	$-0.847273\pi$
$151$	− 139.405i	− 0.923212i	0.887085	−	0.461606i	$-0.152727\pi$
$152$	73.4846	0.483452
$153$	182.232i	1.19106i
$154$	0	0
$155$	−89.7856	−0.579262
$156$	166.262i	1.06579i
$157$	184.955	1.17806	0.589029	−	0.808112i	$-0.299511\pi$
$157$	184.955	1.17806	0.589029	+	0.808112i	$0.299511\pi$
$158$	−36.0132	−0.227932
$159$	487.056	3.06324
$160$	− 12.6491i	− 0.0790569i
$161$	− 16.5956i	− 0.103079i
$162$	− 173.309i	− 1.06981i
$163$	−181.246	−1.11194	−0.555970	−	0.831202i	$-0.687653\pi$
$163$	−181.246	−1.11194	−0.555970	+	0.831202i	$0.687653\pi$
$164$	− 111.940i	− 0.682561i
$165$	0	0
$166$	64.4264	0.388111
$167$	− 40.4998i	− 0.242514i	−0.992621	−	0.121257i	$-0.961308\pi$
$167$	− 40.4998i	− 0.242514i	0.992621	−	0.121257i	$-0.0386925\pi$
$168$	−134.973	−0.803410
$169$	−73.8261	−0.436841
$170$	29.6131	0.174195
$171$	− 505.582i	− 2.95662i
$172$	− 77.9558i	− 0.453231i
$173$	38.7844i	0.224187i	0.993698	+	0.112094i	$0.0357556\pi$
$173$	38.7844i	0.224187i	−0.993698	+	0.112094i	$0.964244\pi$
$174$	107.156	0.615838
$175$	− 44.7254i	− 0.255574i
$176$	0	0
$177$	−109.307	−0.617554
$178$	− 196.579i	− 1.10438i
$179$	26.2522	0.146660	0.0733301	−	0.997308i	$-0.476637\pi$
$179$	26.2522	0.146660	0.0733301	+	0.997308i	$0.476637\pi$
$180$	−87.0273	−0.483485
$181$	−142.784	−0.788860	−0.394430	−	0.918926i	$-0.629058\pi$
$181$	−142.784	−0.788860	−0.394430	+	0.918926i	$0.629058\pi$
$182$	− 197.128i	− 1.08312i
$183$	255.787i	1.39774i
$184$	5.24752i	0.0285191i
$185$	−67.2773	−0.363661
$186$	− 302.938i	− 1.62870i
$187$	0	0
$188$	131.766	0.700883
$189$	499.147i	2.64099i
$190$	−82.1583	−0.432412
$191$	295.343	1.54630	0.773148	−	0.634226i	$-0.218681\pi$
$191$	295.343	1.54630	0.773148	+	0.634226i	$0.218681\pi$
$192$	42.6782	0.222283
$193$	81.5399i	0.422487i	0.977433	+	0.211243i	$0.0677513\pi$
$193$	81.5399i	0.422487i	−0.977433	+	0.211243i	$0.932249\pi$
$194$	− 143.877i	− 0.741635i
$195$	− 185.887i	− 0.953267i
$196$	62.0292	0.316476
$197$	136.444i	0.692611i	0.938122	+	0.346305i	$0.112564\pi$
$197$	136.444i	0.692611i	−0.938122	+	0.346305i	$0.887436\pi$
$198$	0	0
$199$	287.505	1.44475	0.722376	−	0.691501i	$-0.243050\pi$
$199$	287.505	1.44475	0.722376	+	0.691501i	$0.243050\pi$
$200$	14.1421i	0.0707107i
$201$	−376.825	−1.87475
$202$	205.562	1.01763
$203$	−127.048	−0.625853
$204$	99.9148i	0.489779i
$205$	125.153i	0.610501i
$206$	2.13062i	0.0103428i
$207$	36.1035	0.174413
$208$	62.3315i	0.299671i
$209$	0	0
$210$	150.904	0.718591
$211$	298.363i	1.41404i	0.707192	+	0.707022i	$0.249962\pi$
$211$	298.363i	1.41404i	−0.707192	+	0.707022i	$0.750038\pi$
$212$	182.596	0.861304
$213$	−536.166	−2.51721
$214$	254.266	1.18816
$215$	87.1572i	0.405382i
$216$	− 157.830i	− 0.730693i
$217$	359.175i	1.65519i
$218$	−106.685	−0.489379
$219$	− 263.178i	− 1.20173i
$220$	0	0
$221$	−145.925	−0.660296
$222$	− 226.994i	− 1.02250i
$223$	−60.9490	−0.273314	−0.136657	−	0.990618i	$-0.543636\pi$
$223$	−60.9490	−0.273314	−0.136657	+	0.990618i	$0.543636\pi$
$224$	−50.6011	−0.225898
$225$	97.2995	0.432442
$226$	− 23.4158i	− 0.103610i
$227$	20.9025i	0.0920817i	0.998940	+	0.0460408i	$0.0146604\pi$
$227$	20.9025i	0.0920817i	−0.998940	+	0.0460408i	$0.985340\pi$
$228$	− 277.203i	− 1.21580i
$229$	−134.110	−0.585635	−0.292817	−	0.956168i	$-0.594593\pi$
$229$	−134.110	−0.585635	−0.292817	+	0.956168i	$0.594593\pi$
$230$	− 5.86691i	− 0.0255083i
$231$	0	0
$232$	40.1725	0.173157
$233$	− 47.4302i	− 0.203563i	−0.994807	−	0.101781i	$-0.967546\pi$
$233$	− 47.4302i	− 0.203563i	0.994807	−	0.101781i	$-0.0324543\pi$
$234$	428.848	1.83268
$235$	−147.319	−0.626889
$236$	−40.9790	−0.173640
$237$	135.851i	0.573212i
$238$	− 118.463i	− 0.497744i
$239$	91.4419i	0.382602i	0.981531	+	0.191301i	$0.0612707\pi$
$239$	91.4419i	0.382602i	−0.981531	+	0.191301i	$0.938729\pi$
$240$	−47.7157	−0.198816
$241$	309.598i	1.28464i	0.766437	+	0.642319i	$0.222028\pi$
$241$	309.598i	1.28464i	−0.766437	+	0.642319i	$0.777972\pi$
$242$	0	0
$243$	−151.557	−0.623693
$244$	95.8942i	0.393009i
$245$	−69.3508	−0.283064
$246$	−422.267	−1.71653
$247$	404.855	1.63909
$248$	− 113.571i	− 0.457947i
$249$	− 243.033i	− 0.976037i
$250$	− 15.8114i	− 0.0632456i
$251$	−220.416	−0.878153	−0.439076	−	0.898450i	$-0.644694\pi$
$251$	−220.416	−0.878153	−0.439076	+	0.898450i	$0.644694\pi$
$252$	348.141i	1.38151i
$253$	0	0
$254$	31.8334	0.125328
$255$	− 111.708i	− 0.438071i
$256$	16.0000	0.0625000
$257$	231.513	0.900830	0.450415	−	0.892819i	$-0.351276\pi$
$257$	231.513	0.900830	0.450415	+	0.892819i	$0.351276\pi$
$258$	−294.070	−1.13980
$259$	269.134i	1.03913i
$260$	− 69.6888i	− 0.268034i
$261$	− 276.391i	− 1.05897i
$262$	137.122	0.523367
$263$	− 279.651i	− 1.06331i	−0.846961	−	0.531655i	$-0.821570\pi$
$263$	− 279.651i	− 1.06331i	0.846961	−	0.531655i	$-0.178430\pi$
$264$	0	0
$265$	−204.149	−0.770373
$266$	328.663i	1.23558i
$267$	−741.546	−2.77733
$268$	−141.271	−0.527131
$269$	−259.795	−0.965781	−0.482891	−	0.875681i	$-0.660413\pi$
$269$	−259.795	−0.965781	−0.482891	+	0.875681i	$0.660413\pi$
$270$	176.459i	0.653552i
$271$	− 40.8713i	− 0.150816i	−0.997153	−	0.0754082i	$-0.975974\pi$
$271$	− 40.8713i	− 0.150816i	0.997153	−	0.0754082i	$-0.0240260\pi$
$272$	37.4579i	0.137713i
$273$	−743.616	−2.72387
$274$	183.946i	0.671337i
$275$	0	0
$276$	19.7950	0.0717211
$277$	− 225.216i	− 0.813053i	−0.913639	−	0.406526i	$-0.866740\pi$
$277$	− 225.216i	− 0.813053i	0.913639	−	0.406526i	$-0.133260\pi$
$278$	172.908	0.621970
$279$	−781.379	−2.80064
$280$	56.5737	0.202049
$281$	− 129.664i	− 0.461437i	−0.973021	−	0.230719i	$-0.925892\pi$
$281$	− 129.664i	− 0.461437i	0.973021	−	0.230719i	$-0.0741077\pi$
$282$	− 497.056i	− 1.76261i
$283$	469.324i	1.65839i	0.558959	+	0.829195i	$0.311201\pi$
$283$	469.324i	1.65839i	−0.558959	+	0.829195i	$0.688799\pi$
$284$	−201.008	−0.707774
$285$	309.923i	1.08745i
$286$	0	0
$287$	500.657	1.74445
$288$	− 110.082i	− 0.382228i
$289$	201.307	0.696563
$290$	−44.9142	−0.154877
$291$	−542.742	−1.86509
$292$	− 98.6651i	− 0.337894i
$293$	164.259i	0.560612i	0.959911	+	0.280306i	$0.0904359\pi$
$293$	164.259i	0.560612i	−0.959911	+	0.280306i	$0.909564\pi$
$294$	− 233.990i	− 0.795886i
$295$	45.8160	0.155308
$296$	− 85.0998i	− 0.287499i
$297$	0	0
$298$	−50.5182	−0.169524
$299$	28.9106i	0.0966909i
$300$	53.3478	0.177826
$301$	348.661	1.15834
$302$	−197.148	−0.652809
$303$	− 775.434i	− 2.55919i
$304$	− 103.923i	− 0.341852i
$305$	− 107.213i	− 0.351518i
$306$	257.714	0.842204
$307$	− 253.409i	− 0.825438i	−0.910858	−	0.412719i	$-0.864579\pi$
$307$	− 253.409i	− 0.825438i	0.910858	−	0.412719i	$-0.135421\pi$
$308$	0	0
$309$	8.03726	0.0260105
$310$	126.976i	0.409600i
$311$	−370.459	−1.19119	−0.595593	−	0.803286i	$-0.703083\pi$
$311$	−370.459	−1.19119	−0.595593	+	0.803286i	$0.703083\pi$
$312$	235.131	0.753624
$313$	364.418	1.16427	0.582137	−	0.813090i	$-0.302217\pi$
$313$	364.418	1.16427	0.582137	+	0.813090i	$0.302217\pi$
$314$	− 261.566i	− 0.833012i
$315$	− 389.233i	− 1.23566i
$316$	50.9304i	0.161172i
$317$	177.054	0.558531	0.279265	−	0.960214i	$-0.409909\pi$
$317$	177.054	0.558531	0.279265	+	0.960214i	$0.409909\pi$
$318$	− 688.801i	− 2.16604i
$319$	0	0
$320$	−17.8885	−0.0559017
$321$	− 959.158i	− 2.98803i
$322$	−23.4698	−0.0728875
$323$	243.296	0.753238
$324$	−245.097	−0.756471
$325$	77.9144i	0.239737i
$326$	256.321i	0.786261i
$327$	402.442i	1.23071i
$328$	−158.307	−0.482644
$329$	589.330i	1.79128i
$330$	0	0
$331$	−45.6020	−0.137770	−0.0688851	−	0.997625i	$-0.521944\pi$
$331$	−45.6020	−0.137770	−0.0688851	+	0.997625i	$0.521944\pi$
$332$	− 91.1127i	− 0.274436i
$333$	−585.496	−1.75825
$334$	−57.2754	−0.171483
$335$	157.946	0.471480
$336$	190.880i	0.568096i
$337$	155.659i	0.461896i	0.972966	+	0.230948i	$0.0741827\pi$
$337$	155.659i	0.461896i	−0.972966	+	0.230948i	$0.925817\pi$
$338$	104.406i	0.308893i
$339$	−88.3305	−0.260562
$340$	− 41.8792i	− 0.123174i
$341$	0	0
$342$	−715.001	−2.09065
$343$	− 160.881i	− 0.469040i
$344$	−110.246	−0.320483
$345$	−22.1315	−0.0641493
$346$	54.8494	0.158524
$347$	76.2388i	0.219708i	0.993948	+	0.109854i	$0.0350384\pi$
$347$	76.2388i	0.219708i	−0.993948	+	0.109854i	$0.964962\pi$
$348$	− 151.541i	− 0.435463i
$349$	594.286i	1.70283i	0.524496	+	0.851413i	$0.324254\pi$
$349$	594.286i	1.70283i	−0.524496	+	0.851413i	$0.675746\pi$
$350$	−63.2513	−0.180718
$351$	− 869.544i	− 2.47733i
$352$	0	0
$353$	−251.283	−0.711850	−0.355925	−	0.934515i	$-0.615834\pi$
$353$	−251.283	−0.711850	−0.355925	+	0.934515i	$0.615834\pi$
$354$	154.584i	0.436677i
$355$	224.734	0.633052
$356$	−278.004	−0.780911
$357$	−446.874	−1.25175
$358$	− 37.1262i	− 0.103704i
$359$	110.177i	0.306899i	0.988157	+	0.153449i	$0.0490382\pi$
$359$	110.177i	0.306899i	−0.988157	+	0.153449i	$0.950962\pi$
$360$	123.075i	0.341875i
$361$	−313.999	−0.869803
$362$	201.927i	0.557808i
$363$	0	0
$364$	−278.780	−0.765880
$365$	110.311i	0.302222i
$366$	361.738	0.988354
$367$	−467.613	−1.27415	−0.637075	−	0.770802i	$-0.719856\pi$
$367$	−467.613	−1.27415	−0.637075	+	0.770802i	$0.719856\pi$
$368$	7.42112	0.0201661
$369$	1089.17i	2.95168i
$370$	95.1444i	0.257147i
$371$	816.670i	2.20127i
$372$	−428.419	−1.15166
$373$	189.436i	0.507871i	0.967221	+	0.253936i	$0.0817252\pi$
$373$	189.436i	0.507871i	−0.967221	+	0.253936i	$0.918275\pi$
$374$	0	0
$375$	−59.6447	−0.159052
$376$	− 186.345i	− 0.495599i
$377$	221.326	0.587070
$378$	705.900	1.86746
$379$	−458.268	−1.20915	−0.604576	−	0.796548i	$-0.706657\pi$
$379$	−458.268	−1.20915	−0.604576	+	0.796548i	$0.706657\pi$
$380$	116.189i	0.305762i
$381$	− 120.084i	− 0.315181i
$382$	− 417.677i	− 1.09340i
$383$	361.655	0.944268	0.472134	−	0.881527i	$-0.343484\pi$
$383$	361.655	0.944268	0.472134	+	0.881527i	$0.343484\pi$
$384$	− 60.3562i	− 0.157177i
$385$	0	0
$386$	115.315	0.298743
$387$	758.506i	1.95996i
$388$	−203.473	−0.524415
$389$	−7.38627	−0.0189878	−0.00949392	−	0.999955i	$-0.503022\pi$
$389$	−7.38627	−0.0189878	−0.00949392	+	0.999955i	$0.503022\pi$
$390$	−262.884	−0.674062
$391$	17.3737i	0.0444341i
$392$	− 87.7226i	− 0.223782i
$393$	− 517.261i	− 1.31619i
$394$	192.961	0.489750
$395$	− 56.9419i	− 0.144157i
$396$	0	0
$397$	−561.028	−1.41317	−0.706585	−	0.707628i	$-0.749765\pi$
$397$	−561.028	−1.41317	−0.706585	+	0.707628i	$0.749765\pi$
$398$	− 406.594i	− 1.02159i
$399$	1239.80	3.10728
$400$	20.0000	0.0500000
$401$	489.003	1.21946	0.609729	−	0.792610i	$-0.291278\pi$
$401$	489.003	1.21946	0.609729	+	0.792610i	$0.291278\pi$
$402$	532.911i	1.32565i
$403$	− 625.705i	− 1.55262i
$404$	− 290.709i	− 0.719576i
$405$	274.026	0.676608
$406$	179.673i	0.442545i
$407$	0	0
$408$	141.301	0.346326
$409$	745.082i	1.82172i	0.412721	+	0.910858i	$0.364579\pi$
$409$	745.082i	1.82172i	−0.412721	+	0.910858i	$0.635421\pi$
$410$	176.993	0.431690
$411$	693.894	1.68831
$412$	3.01315	0.00731348
$413$	− 183.281i	− 0.443779i
$414$	− 51.0581i	− 0.123329i
$415$	101.867i	0.245463i
$416$	88.1501	0.211899
$417$	− 652.253i	− 1.56415i
$418$	0	0
$419$	531.657	1.26887	0.634436	−	0.772975i	$-0.281232\pi$
$419$	531.657	1.26887	0.634436	+	0.772975i	$0.281232\pi$
$420$	− 213.411i	− 0.508121i
$421$	687.099	1.63206	0.816032	−	0.578007i	$-0.196169\pi$
$421$	687.099	1.63206	0.816032	+	0.578007i	$0.196169\pi$
$422$	421.949	0.999879
$423$	−1282.08	−3.03091
$424$	− 258.230i	− 0.609034i
$425$	46.8224i	0.110170i
$426$	758.254i	1.77994i
$427$	−428.891	−1.00443
$428$	− 359.587i	− 0.840156i
$429$	0	0
$430$	123.259	0.286649
$431$	135.133i	0.313533i	0.987636	+	0.156766i	$0.0501070\pi$
$431$	135.133i	0.313533i	−0.987636	+	0.156766i	$0.949893\pi$
$432$	−223.205	−0.516678
$433$	501.410	1.15799	0.578995	−	0.815331i	$-0.303445\pi$
$433$	501.410	1.15799	0.578995	+	0.815331i	$0.303445\pi$
$434$	507.950	1.17039
$435$	169.428i	0.389490i
$436$	150.875i	0.346043i
$437$	− 48.2015i	− 0.110301i
$438$	−372.190	−0.849750
$439$	− 94.1832i	− 0.214540i	−0.994230	−	0.107270i	$-0.965789\pi$
$439$	− 94.1832i	− 0.214540i	0.994230	−	0.107270i	$-0.0342110\pi$
$440$	0	0
$441$	−603.541	−1.36857
$442$	206.370i	0.466900i
$443$	773.143	1.74524	0.872621	−	0.488397i	$-0.162418\pi$
$443$	773.143	1.74524	0.872621	+	0.488397i	$0.162418\pi$
$444$	−321.018	−0.723015
$445$	310.818	0.698468
$446$	86.1949i	0.193262i
$447$	190.568i	0.426326i
$448$	71.5607i	0.159734i
$449$	105.544	0.235064	0.117532	−	0.993069i	$-0.462502\pi$
$449$	105.544	0.235064	0.117532	+	0.993069i	$0.462502\pi$
$450$	− 137.602i	− 0.305783i
$451$	0	0
$452$	−33.1149	−0.0732631
$453$	743.695i	1.64171i
$454$	29.5607	0.0651116
$455$	311.686	0.685024
$456$	−392.024	−0.859703
$457$	187.760i	0.410853i	0.978673	+	0.205427i	$0.0658582\pi$
$457$	187.760i	0.410853i	−0.978673	+	0.205427i	$0.934142\pi$
$458$	189.661i	0.414106i
$459$	− 522.549i	− 1.13845i
$460$	−8.29706	−0.0180371
$461$	− 268.745i	− 0.582961i	−0.956577	−	0.291481i	$-0.905852\pi$
$461$	− 268.745i	− 0.582961i	0.956577	−	0.291481i	$-0.0941479\pi$
$462$	0	0
$463$	−339.060	−0.732310	−0.366155	−	0.930554i	$-0.619326\pi$
$463$	−339.060	−0.732310	−0.366155	+	0.930554i	$0.619326\pi$
$464$	− 56.8125i	− 0.122441i
$465$	478.986	1.03008
$466$	−67.0764	−0.143941
$467$	−135.885	−0.290973	−0.145487	−	0.989360i	$-0.546475\pi$
$467$	−135.885	−0.290973	−0.145487	+	0.989360i	$0.546475\pi$
$468$	− 606.482i	− 1.29590i
$469$	− 631.841i	− 1.34721i
$470$	208.340i	0.443278i
$471$	−986.694	−2.09489
$472$	57.9531i	0.122782i
$473$	0	0
$474$	192.123	0.405322
$475$	− 129.904i	− 0.273481i
$476$	−167.532	−0.351958
$477$	−1776.65	−3.72464
$478$	129.318	0.270541
$479$	− 534.169i	− 1.11518i	−0.830118	−	0.557588i	$-0.811727\pi$
$479$	− 534.169i	− 1.11518i	0.830118	−	0.557588i	$-0.188273\pi$
$480$	67.4802i	0.140584i
$481$	− 468.847i	− 0.974734i
$482$	437.837	0.908376
$483$	88.5341i	0.183300i
$484$	0	0
$485$	227.490	0.469051
$486$	214.335i	0.441018i
$487$	39.8099	0.0817451	0.0408726	−	0.999164i	$-0.486986\pi$
$487$	39.8099	0.0817451	0.0408726	+	0.999164i	$0.486986\pi$
$488$	135.615	0.277899
$489$	966.909	1.97732
$490$	98.0768i	0.200157i
$491$	− 59.2775i	− 0.120728i	−0.998176	−	0.0603641i	$-0.980774\pi$
$491$	− 59.2775i	− 0.120728i	0.998176	−	0.0603641i	$-0.0192262\pi$
$492$	597.176i	1.21377i
$493$	133.005	0.269787
$494$	− 572.551i	− 1.15901i
$495$	0	0
$496$	−160.613	−0.323817
$497$	− 899.016i	− 1.80889i
$498$	−343.701	−0.690162
$499$	−184.415	−0.369570	−0.184785	−	0.982779i	$-0.559159\pi$
$499$	−184.415	−0.369570	−0.184785	+	0.982779i	$0.559159\pi$
$500$	−22.3607	−0.0447214
$501$	216.058i	0.431253i
$502$	311.716i	0.620948i
$503$	124.818i	0.248147i	0.992273	+	0.124073i	$0.0395958\pi$
$503$	124.818i	0.248147i	−0.992273	+	0.124073i	$0.960404\pi$
$504$	492.346	0.976876
$505$	325.022i	0.643608i
$506$	0	0
$507$	393.846	0.776817
$508$	− 45.0193i	− 0.0886206i
$509$	201.980	0.396817	0.198408	−	0.980119i	$-0.436423\pi$
$509$	201.980	0.396817	0.198408	+	0.980119i	$0.436423\pi$
$510$	−157.979	−0.309763
$511$	441.284	0.863570
$512$	− 22.6274i	− 0.0441942i
$513$	1449.76i	2.82604i
$514$	− 327.409i	− 0.636983i
$515$	−3.36881	−0.00654138
$516$	415.877i	0.805963i
$517$	0	0
$518$	380.613	0.734773
$519$	− 206.906i	− 0.398663i
$520$	−98.5548	−0.189528
$521$	805.784	1.54661	0.773305	−	0.634034i	$-0.218602\pi$
$521$	805.784	1.54661	0.773305	+	0.634034i	$0.218602\pi$
$522$	−390.876	−0.748805
$523$	729.656i	1.39514i	0.716518	+	0.697568i	$0.245735\pi$
$523$	729.656i	1.39514i	−0.716518	+	0.697568i	$0.754265\pi$
$524$	− 193.920i	− 0.370077i
$525$	238.600i	0.454477i
$526$	−395.486	−0.751874
$527$	− 376.015i	− 0.713501i
$528$	0	0
$529$	−525.558	−0.993493
$530$	288.710i	0.544736i
$531$	398.724	0.750892
$532$	464.800	0.873684
$533$	−872.174	−1.63635
$534$	1048.70i	1.96387i
$535$	402.030i	0.751458i
$536$	199.788i	0.372738i
$537$	−140.050	−0.260800
$538$	367.406i	0.682910i
$539$	0	0
$540$	249.551	0.462131
$541$	− 566.169i	− 1.04652i	−0.852172	−	0.523261i	$-0.824715\pi$
$541$	− 566.169i	− 1.04652i	0.852172	−	0.523261i	$-0.175285\pi$
$542$	−57.8007	−0.106643
$543$	761.720	1.40280
$544$	52.9735	0.0973777
$545$	− 168.683i	− 0.309510i
$546$	1051.63i	1.92607i
$547$	− 1074.11i	− 1.96364i	−0.189809	−	0.981821i	$-0.560787\pi$
$547$	− 1074.11i	− 1.96364i	0.189809	−	0.981821i	$-0.439213\pi$
$548$	260.140	0.474707
$549$	− 933.045i	− 1.69954i
$550$	0	0
$551$	−369.008	−0.669705
$552$	− 27.9944i	− 0.0507145i
$553$	−227.788	−0.411914
$554$	−318.503	−0.574915
$555$	358.910	0.646684
$556$	− 244.528i	− 0.439799i
$557$	450.657i	0.809078i	0.914521	+	0.404539i	$0.132568\pi$
$557$	450.657i	0.809078i	−0.914521	+	0.404539i	$0.867432\pi$
$558$	1105.04i	1.98035i
$559$	−607.388	−1.08656
$560$	− 80.0073i	− 0.142870i
$561$	0	0
$562$	−183.372	−0.326285
$563$	982.354i	1.74486i	0.488743	+	0.872428i	$0.337456\pi$
$563$	982.354i	1.74486i	−0.488743	+	0.872428i	$0.662544\pi$
$564$	−702.943	−1.24635
$565$	37.0236	0.0655285
$566$	663.725	1.17266
$567$	− 1096.21i	− 1.93334i
$568$	284.268i	0.500472i
$569$	418.272i	0.735101i	0.930004	+	0.367550i	$0.119803\pi$
$569$	418.272i	0.735101i	−0.930004	+	0.367550i	$0.880197\pi$
$570$	438.297	0.768941
$571$	997.234i	1.74647i	0.487300	+	0.873234i	$0.337982\pi$
$571$	997.234i	1.74647i	−0.487300	+	0.873234i	$0.662018\pi$
$572$	0	0
$573$	−1575.59	−2.74972
$574$	− 708.036i	− 1.23351i
$575$	9.27640	0.0161329
$576$	−155.679	−0.270276
$577$	−542.954	−0.940995	−0.470497	−	0.882401i	$-0.655925\pi$
$577$	−542.954	−0.940995	−0.470497	+	0.882401i	$0.655925\pi$
$578$	− 284.691i	− 0.492544i
$579$	− 434.998i	− 0.751291i
$580$	63.5183i	0.109514i
$581$	407.506	0.701387
$582$	767.553i	1.31882i
$583$	0	0
$584$	−139.534	−0.238927
$585$	678.068i	1.15909i
$586$	232.298	0.396412
$587$	684.464	1.16604	0.583019	−	0.812459i	$-0.301871\pi$
$587$	684.464	1.16604	0.583019	+	0.812459i	$0.301871\pi$
$588$	−330.912	−0.562776
$589$	1043.21i	1.77116i
$590$	− 64.7935i	− 0.109820i
$591$	− 727.901i	− 1.23164i
$592$	−120.349	−0.203293
$593$	− 227.090i	− 0.382950i	−0.981497	−	0.191475i	$-0.938673\pi$
$593$	− 227.090i	− 0.382950i	0.981497	−	0.191475i	$-0.0613272\pi$
$594$	0	0
$595$	187.307	0.314801
$596$	71.4435i	0.119872i
$597$	−1533.78	−2.56914
$598$	40.8858	0.0683708
$599$	774.572	1.29311	0.646554	−	0.762868i	$-0.276209\pi$
$599$	774.572	1.29311	0.646554	+	0.762868i	$0.276209\pi$
$600$	− 75.4452i	− 0.125742i
$601$	− 295.829i	− 0.492228i	−0.969241	−	0.246114i	$-0.920846\pi$
$601$	− 295.829i	− 0.492228i	0.969241	−	0.246114i	$-0.0791538\pi$
$602$	− 493.081i	− 0.819071i
$603$	1374.56	2.27954
$604$	278.810i	0.461606i
$605$	0	0
$606$	−1096.63	−1.80962
$607$	− 101.479i	− 0.167182i	−0.996500	−	0.0835909i	$-0.973361\pi$
$607$	− 101.479i	− 0.167182i	0.996500	−	0.0835909i	$-0.0266389\pi$
$608$	−146.969	−0.241726
$609$	677.774	1.11293
$610$	−151.622	−0.248561
$611$	− 1026.65i	− 1.68027i
$612$	− 364.463i	− 0.595528i
$613$	388.428i	0.633652i	0.948484	+	0.316826i	$0.102617\pi$
$613$	388.428i	0.633652i	−0.948484	+	0.316826i	$0.897383\pi$
$614$	−358.375	−0.583673
$615$	− 667.663i	− 1.08563i
$616$	0	0
$617$	60.0091	0.0972595	0.0486297	−	0.998817i	$-0.484515\pi$
$617$	60.0091	0.0972595	0.0486297	+	0.998817i	$0.484515\pi$
$618$	− 11.3664i	− 0.0183922i
$619$	−636.089	−1.02761	−0.513804	−	0.857908i	$-0.671764\pi$
$619$	−636.089	−1.02761	−0.513804	+	0.857908i	$0.671764\pi$
$620$	179.571	0.289631
$621$	−103.527	−0.166710
$622$	523.908i	0.842296i
$623$	− 1243.39i	− 1.99581i
$624$	− 332.525i	− 0.532893i
$625$	25.0000	0.0400000
$626$	− 515.365i	− 0.823267i
$627$	0	0
$628$	−369.910	−0.589029
$629$	− 281.752i	− 0.447936i
$630$	−550.459	−0.873745
$631$	−1020.59	−1.61741	−0.808707	−	0.588212i	$-0.799832\pi$
$631$	−1020.59	−1.61741	−0.808707	+	0.588212i	$0.799832\pi$
$632$	72.0265	0.113966
$633$	− 1591.70i	− 2.51454i
$634$	− 250.392i	− 0.394941i
$635$	50.3331i	0.0792647i
$636$	−974.112	−1.53162
$637$	− 483.297i	− 0.758708i
$638$	0	0
$639$	1955.79	3.06071
$640$	25.2982i	0.0395285i
$641$	−708.695	−1.10561	−0.552804	−	0.833311i	$-0.686442\pi$
$641$	−708.695	−1.10561	−0.552804	+	0.833311i	$0.686442\pi$
$642$	−1356.45	−2.11286
$643$	−1110.52	−1.72709	−0.863546	−	0.504270i	$-0.831762\pi$
$643$	−1110.52	−1.72709	−0.863546	+	0.504270i	$0.831762\pi$
$644$	33.1913i	0.0515393i
$645$	− 464.965i	− 0.720876i
$646$	− 344.072i	− 0.532620i
$647$	209.581	0.323928	0.161964	−	0.986797i	$-0.448217\pi$
$647$	209.581	0.323928	0.161964	+	0.986797i	$0.448217\pi$
$648$	346.619i	0.534906i
$649$	0	0
$650$	110.188	0.169519
$651$	− 1916.12i	− 2.94335i
$652$	362.493	0.555970
$653$	−180.567	−0.276520	−0.138260	−	0.990396i	$-0.544151\pi$
$653$	−180.567	−0.276520	−0.138260	+	0.990396i	$0.544151\pi$
$654$	569.139	0.870243
$655$	216.809i	0.331007i
$656$	223.880i	0.341281i
$657$	960.006i	1.46120i
$658$	833.438	1.26662
$659$	452.544i	0.686714i	0.939205	+	0.343357i	$0.111564\pi$
$659$	452.544i	0.686714i	−0.939205	+	0.343357i	$0.888436\pi$
$660$	0	0
$661$	834.204	1.26203	0.631016	−	0.775770i	$-0.282638\pi$
$661$	834.204	1.26203	0.631016	+	0.775770i	$0.282638\pi$
$662$	64.4909i	0.0974183i
$663$	778.480	1.17418
$664$	−128.853	−0.194055
$665$	−519.662	−0.781447
$666$	828.016i	1.24327i
$667$	− 26.3508i	− 0.0395064i
$668$	80.9996i	0.121257i
$669$	325.150	0.486023
$670$	− 223.369i	− 0.333387i
$671$	0	0
$672$	269.946	0.401705
$673$	− 167.470i	− 0.248842i	−0.992230	−	0.124421i	$-0.960293\pi$
$673$	− 167.470i	− 0.248842i	0.992230	−	0.124421i	$-0.0397073\pi$
$674$	220.135	0.326610
$675$	−279.006	−0.413342
$676$	147.652	0.218420
$677$	373.522i	0.551731i	0.961196	+	0.275866i	$0.0889645\pi$
$677$	373.522i	0.551731i	−0.961196	+	0.275866i	$0.911036\pi$
$678$	124.918i	0.184245i
$679$	− 910.042i	− 1.34027i
$680$	−59.2261	−0.0870973
$681$	− 111.510i	− 0.163745i
$682$	0	0
$683$	522.625	0.765190	0.382595	−	0.923916i	$-0.375031\pi$
$683$	522.625	0.765190	0.382595	+	0.923916i	$0.375031\pi$
$684$	1011.16i	1.47831i
$685$	−290.845	−0.424591
$686$	−227.520	−0.331662
$687$	715.449	1.04141
$688$	155.912i	0.226616i
$689$	− 1422.69i	− 2.06486i
$690$	31.2987i	0.0453604i
$691$	−517.184	−0.748457	−0.374229	−	0.927336i	$-0.622092\pi$
$691$	−517.184	−0.748457	−0.374229	+	0.927336i	$0.622092\pi$
$692$	− 77.5687i	− 0.112094i
$693$	0	0
$694$	107.818	0.155357
$695$	273.391i	0.393368i
$696$	−214.312	−0.307919
$697$	−524.130	−0.751979
$698$	840.448	1.20408
$699$	253.030i	0.361988i
$700$	89.4509i	0.127787i
$701$	− 1007.50i	− 1.43724i	−0.695405	−	0.718618i	$-0.744775\pi$
$701$	− 1007.50i	− 1.43724i	0.695405	−	0.718618i	$-0.255225\pi$
$702$	−1229.72	−1.75174
$703$	781.691i	1.11194i
$704$	0	0
$705$	785.914	1.11477
$706$	355.368i	0.503354i
$707$	1300.21	1.83905
$708$	218.614	0.308777
$709$	−399.704	−0.563757	−0.281879	−	0.959450i	$-0.590958\pi$
$709$	−399.704	−0.563757	−0.281879	+	0.959450i	$0.590958\pi$
$710$	− 317.821i	− 0.447636i
$711$	− 495.550i	− 0.696976i
$712$	393.158i	0.552188i
$713$	−74.4957	−0.104482
$714$	631.975i	0.885119i
$715$	0	0
$716$	−52.5044	−0.0733301
$717$	− 487.823i	− 0.680366i
$718$	155.813	0.217010
$719$	−327.211	−0.455092	−0.227546	−	0.973767i	$-0.573070\pi$
$719$	−327.211	−0.455092	−0.227546	+	0.973767i	$0.573070\pi$
$720$	174.055	0.241742
$721$	13.4765i	0.0186914i
$722$	444.062i	0.615044i
$723$	− 1651.64i	− 2.28442i
$724$	285.567	0.394430
$725$	− 71.0156i	− 0.0979526i
$726$	0	0
$727$	−502.859	−0.691691	−0.345845	−	0.938291i	$-0.612408\pi$
$727$	−502.859	−0.691691	−0.345845	+	0.938291i	$0.612408\pi$
$728$	394.255i	0.541559i
$729$	−294.409	−0.403853
$730$	156.003	0.213703
$731$	−365.008	−0.499326
$732$	− 511.574i	− 0.698872i
$733$	1413.85i	1.92885i	0.264351	+	0.964426i	$0.414842\pi$
$733$	1413.85i	1.92885i	−0.264351	+	0.964426i	$0.585158\pi$
$734$	661.305i	0.900961i
$735$	369.971	0.503362
$736$	− 10.4950i	− 0.0142596i
$737$	0	0
$738$	1540.32	2.08715
$739$	− 548.081i	− 0.741653i	−0.928702	−	0.370826i	$-0.879074\pi$
$739$	− 548.081i	− 0.741653i	0.928702	−	0.370826i	$-0.120926\pi$
$740$	134.555	0.181830
$741$	−2159.81	−2.91473
$742$	1154.95	1.55653
$743$	− 1033.42i	− 1.39087i	−0.718589	−	0.695435i	$-0.755212\pi$
$743$	− 1033.42i	− 1.39087i	0.718589	−	0.695435i	$-0.244788\pi$
$744$	605.875i	0.814348i
$745$	− 79.8762i	− 0.107216i
$746$	267.903	0.359119
$747$	886.522i	1.18678i
$748$	0	0
$749$	1608.27	2.14722
$750$	84.3503i	0.112467i
$751$	−792.835	−1.05571	−0.527853	−	0.849336i	$-0.677003\pi$
$751$	−792.835	−1.05571	−0.527853	+	0.849336i	$0.677003\pi$
$752$	−263.532	−0.350442
$753$	1175.87	1.56158
$754$	− 313.002i	− 0.415122i
$755$	− 311.719i	− 0.412873i
$756$	− 998.294i	− 1.32049i
$757$	170.002	0.224574	0.112287	−	0.993676i	$-0.464182\pi$
$757$	170.002	0.224574	0.112287	+	0.993676i	$0.464182\pi$
$758$	648.089i	0.854999i
$759$	0	0
$760$	164.317	0.216206
$761$	− 343.012i	− 0.450738i	−0.974273	−	0.225369i	$-0.927641\pi$
$761$	− 343.012i	− 0.450738i	0.974273	−	0.225369i	$-0.0723588\pi$
$762$	−169.824	−0.222867
$763$	−674.794	−0.884396
$764$	−590.685	−0.773148
$765$	407.482i	0.532657i
$766$	− 511.457i	− 0.667698i
$767$	319.286i	0.416279i
$768$	−85.3565	−0.111141
$769$	820.759i	1.06731i	0.845703	+	0.533654i	$0.179181\pi$
$769$	820.759i	1.06731i	−0.845703	+	0.533654i	$0.820819\pi$
$770$	0	0
$771$	−1235.07	−1.60191
$772$	− 163.080i	− 0.211243i
$773$	−307.514	−0.397818	−0.198909	−	0.980018i	$-0.563740\pi$
$773$	−307.514	−0.397818	−0.198909	+	0.980018i	$0.563740\pi$
$774$	1072.69	1.38590
$775$	−200.767	−0.259054
$776$	287.754i	0.370817i
$777$	− 1435.77i	− 1.84784i
$778$	10.4458i	0.0134264i
$779$	1454.14	1.86668
$780$	371.774i	0.476634i
$781$	0	0
$782$	24.5701	0.0314196
$783$	792.552i	1.01220i
$784$	−124.058	−0.158238
$785$	413.572	0.526843
$786$	−731.517	−0.930683
$787$	− 295.549i	− 0.375539i	−0.982213	−	0.187770i	$-0.939874\pi$
$787$	− 295.549i	− 0.375539i	0.982213	−	0.187770i	$-0.0601258\pi$
$788$	− 272.889i	− 0.346305i
$789$	1491.88i	1.89084i
$790$	−80.5280	−0.101934
$791$	− 148.108i	− 0.187241i
$792$	0	0
$793$	747.154	0.942186
$794$	793.414i	0.999262i
$795$	1089.09	1.36992
$796$	−575.011	−0.722376
$797$	544.028	0.682595	0.341297	−	0.939955i	$-0.389134\pi$
$797$	544.028	0.682595	0.341297	+	0.939955i	$0.389134\pi$
$798$	− 1753.35i	− 2.19718i
$799$	− 616.960i	− 0.772165i
$800$	− 28.2843i	− 0.0353553i
$801$	2704.97	3.37699
$802$	− 691.555i	− 0.862287i
$803$	0	0
$804$	753.650	0.937376
$805$	− 37.1090i	− 0.0460981i
$806$	−884.880	−1.09787
$807$	1385.95	1.71741
$808$	−411.124	−0.508817
$809$	803.416i	0.993097i	0.868009	+	0.496549i	$0.165400\pi$
$809$	803.416i	0.993097i	−0.868009	+	0.496549i	$0.834600\pi$
$810$	− 387.532i	− 0.478434i
$811$	21.3033i	0.0262679i	0.999914	+	0.0131340i	$0.00418079\pi$
$811$	21.3033i	0.0262679i	−0.999914	+	0.0131340i	$0.995819\pi$
$812$	254.096	0.312927
$813$	218.039i	0.268191i
$814$	0	0
$815$	−405.279	−0.497275
$816$	− 199.830i	− 0.244889i
$817$	1012.67	1.23950
$818$	1053.70	1.28815
$819$	2712.52	3.31199
$820$	− 250.305i	− 0.305251i
$821$	619.666i	0.754770i	0.926057	+	0.377385i	$0.123177\pi$
$821$	619.666i	0.754770i	−0.926057	+	0.377385i	$0.876823\pi$
$822$	− 981.314i	− 1.19381i
$823$	−1003.87	−1.21977	−0.609887	−	0.792489i	$-0.708785\pi$
$823$	−1003.87	−1.21977	−0.609887	+	0.792489i	$0.708785\pi$
$824$	− 4.26124i	− 0.00517141i
$825$	0	0
$826$	−259.198	−0.313799
$827$	436.941i	0.528345i	0.964475	+	0.264172i	$0.0850988\pi$
$827$	436.941i	0.528345i	−0.964475	+	0.264172i	$0.914901\pi$
$828$	−72.2071	−0.0872066
$829$	204.942	0.247215	0.123608	−	0.992331i	$-0.460554\pi$
$829$	204.942	0.247215	0.123608	+	0.992331i	$0.460554\pi$
$830$	144.062	0.173568
$831$	1201.48i	1.44582i
$832$	− 124.663i	− 0.149835i
$833$	− 290.436i	− 0.348662i
$834$	−922.424	−1.10602
$835$	− 90.5603i	− 0.108455i
$836$	0	0
$837$	2240.61	2.67695
$838$	− 751.877i	− 0.897228i
$839$	−246.587	−0.293905	−0.146953	−	0.989144i	$-0.546947\pi$
$839$	−246.587	−0.293905	−0.146953	+	0.989144i	$0.546947\pi$
$840$	−301.808	−0.359296
$841$	639.271	0.760132
$842$	− 971.705i	− 1.15404i
$843$	691.728i	0.820556i
$844$	− 596.726i	− 0.707022i
$845$	−165.080	−0.195361
$846$	1813.13i	2.14318i
$847$	0	0
$848$	−365.193	−0.430652
$849$	− 2503.74i	− 2.94905i
$850$	66.2168	0.0779022
$851$	−55.8204	−0.0655939
$852$	1072.33	1.25861
$853$	− 358.945i	− 0.420803i	−0.977615	−	0.210402i	$-0.932523\pi$
$853$	− 358.945i	− 0.420803i	0.977615	−	0.210402i	$-0.0674771\pi$
$854$	606.543i	0.710238i
$855$	− 1130.52i	− 1.32224i
$856$	−508.532	−0.594080
$857$	688.891i	0.803840i	0.915675	+	0.401920i	$0.131657\pi$
$857$	688.891i	0.803840i	−0.915675	+	0.401920i	$0.868343\pi$
$858$	0	0
$859$	−896.881	−1.04410	−0.522049	−	0.852915i	$-0.674832\pi$
$859$	−896.881	−1.04410	−0.522049	+	0.852915i	$0.674832\pi$
$860$	− 174.314i	− 0.202691i
$861$	−2670.89	−3.10208
$862$	191.106	0.221701
$863$	−1278.88	−1.48189	−0.740947	−	0.671563i	$-0.765623\pi$
$863$	−1278.88	−1.48189	−0.740947	+	0.671563i	$0.765623\pi$
$864$	315.659i	0.365347i
$865$	86.7245i	0.100259i
$866$	− 709.100i	− 0.818823i
$867$	−1073.93	−1.23867
$868$	− 718.350i	− 0.827593i
$869$	0	0
$870$	239.608	0.275411
$871$	1100.71i	1.26373i
$872$	213.369	0.244689
$873$	1979.78	2.26779
$874$	−68.1673	−0.0779946
$875$	− 100.009i	− 0.114296i
$876$	526.357i	0.600864i
$877$	940.916i	1.07288i	0.843938	+	0.536440i	$0.180231\pi$
$877$	940.916i	1.07288i	−0.843938	+	0.536440i	$0.819769\pi$
$878$	−133.195	−0.151703
$879$	− 876.287i	− 0.996913i
$880$	0	0
$881$	457.191	0.518945	0.259473	−	0.965750i	$-0.416451\pi$
$881$	457.191	0.518945	0.259473	+	0.965750i	$0.416451\pi$
$882$	853.536i	0.967728i
$883$	−600.865	−0.680482	−0.340241	−	0.940338i	$-0.610509\pi$
$883$	−600.865	−0.680482	−0.340241	+	0.940338i	$0.610509\pi$
$884$	291.851	0.330148
$885$	−244.418	−0.276179
$886$	− 1093.39i	− 1.23407i
$887$	456.006i	0.514099i	0.966398	+	0.257049i	$0.0827503\pi$
$887$	456.006i	0.514099i	−0.966398	+	0.257049i	$0.917250\pi$
$888$	453.989i	0.511248i
$889$	201.351	0.226491
$890$	− 439.564i	− 0.493892i
$891$	0	0
$892$	121.898	0.136657
$893$	1711.69i	1.91679i
$894$	269.503	0.301458
$895$	58.7017	0.0655885
$896$	101.202	0.112949
$897$	− 154.232i	− 0.171942i
$898$	− 149.261i	− 0.166215i
$899$	570.303i	0.634375i
$900$	−194.599	−0.216221
$901$	− 854.959i	− 0.948901i
$902$	0	0
$903$	−1860.03	−2.05983
$904$	46.8316i	0.0518049i
$905$	−319.274	−0.352789
$906$	1051.74	1.16087
$907$	−675.509	−0.744773	−0.372386	−	0.928078i	$-0.621460\pi$
$907$	−675.509	−0.744773	−0.372386	+	0.928078i	$0.621460\pi$
$908$	− 41.8051i	− 0.0460408i
$909$	2828.58i	3.11175i
$910$	− 440.791i	− 0.484385i
$911$	−664.631	−0.729562	−0.364781	−	0.931093i	$-0.618856\pi$
$911$	−664.631	−0.729562	−0.364781	+	0.931093i	$0.618856\pi$
$912$	554.406i	0.607902i
$913$	0	0
$914$	265.533	0.290517
$915$	571.958i	0.625090i
$916$	268.221	0.292817
$917$	867.316	0.945819
$918$	−738.996	−0.805007
$919$	− 838.215i	− 0.912095i	−0.889955	−	0.456047i	$-0.849265\pi$
$919$	− 838.215i	− 0.912095i	0.889955	−	0.456047i	$-0.150735\pi$
$920$	11.7338i	0.0127541i
$921$	1351.88i	1.46784i
$922$	−380.063	−0.412216
$923$	1566.14i	1.69679i
$924$	0	0
$925$	−150.437	−0.162634
$926$	479.503i	0.517822i
$927$	−29.3178	−0.0316266
$928$	−80.3450	−0.0865787
$929$	−1476.85	−1.58972	−0.794862	−	0.606790i	$-0.792457\pi$
$929$	−1476.85	−1.58972	−0.794862	+	0.606790i	$0.792457\pi$
$930$	− 677.389i	− 0.728375i
$931$	805.783i	0.865502i
$932$	94.8603i	0.101781i
$933$	1976.32	2.11824
$934$	192.170i	0.205749i
$935$	0	0
$936$	−857.695	−0.916341
$937$	− 191.337i	− 0.204202i	−0.994774	−	0.102101i	$-0.967444\pi$
$937$	− 191.337i	− 0.204202i	0.994774	−	0.102101i	$-0.0325564\pi$
$938$	−893.558	−0.952621
$939$	−1944.09	−2.07038
$940$	294.638	0.313445
$941$	400.628i	0.425747i	0.977080	+	0.212873i	$0.0682822\pi$
$941$	400.628i	0.425747i	−0.977080	+	0.212873i	$0.931718\pi$
$942$	1395.40i	1.48131i
$943$	103.840i	0.110117i
$944$	81.9581	0.0868200
$945$	1116.13i	1.18109i
$946$	0	0
$947$	−1075.33	−1.13551	−0.567757	−	0.823196i	$-0.692189\pi$
$947$	−1075.33	−1.13551	−0.567757	+	0.823196i	$0.692189\pi$
$948$	− 271.703i	− 0.286606i
$949$	−768.743	−0.810056
$950$	−183.712	−0.193381
$951$	−944.546	−0.993213
$952$	236.926i	0.248872i
$953$	− 103.620i	− 0.108730i	−0.998521	−	0.0543650i	$-0.982687\pi$
$953$	− 103.620i	− 0.108730i	0.998521	−	0.0543650i	$-0.0173134\pi$
$954$	2512.57i	2.63372i
$955$	660.406	0.691525
$956$	− 182.884i	− 0.191301i
$957$	0	0
$958$	−755.430	−0.788549
$959$	1163.49i	1.21323i
$960$	95.4315	0.0994078
$961$	651.290	0.677721
$962$	−663.050	−0.689241
$963$	3498.76i	3.63319i
$964$	− 619.196i	− 0.642319i
$965$	182.329i	0.188942i
$966$	125.206	0.129613
$967$	1347.62i	1.39361i	0.717262	+	0.696803i	$0.245395\pi$
$967$	1347.62i	1.39361i	−0.717262	+	0.696803i	$0.754605\pi$
$968$	0	0
$969$	−1297.93	−1.33945
$970$	− 321.719i	− 0.331669i
$971$	370.102	0.381155	0.190578	−	0.981672i	$-0.438964\pi$
$971$	370.102	0.381155	0.190578	+	0.981672i	$0.438964\pi$
$972$	303.115	0.311847
$973$	1093.66	1.12401
$974$	− 56.2997i	− 0.0578025i
$975$	− 415.656i	− 0.426314i
$976$	− 191.788i	− 0.196504i
$977$	1553.18	1.58975	0.794874	−	0.606774i	$-0.207537\pi$
$977$	1553.18	1.58975	0.794874	+	0.606774i	$0.207537\pi$
$978$	− 1367.42i	− 1.39818i
$979$	0	0
$980$	138.702	0.141532
$981$	− 1468.00i	− 1.49644i
$982$	−83.8311	−0.0853677
$983$	1272.26	1.29426	0.647131	−	0.762379i	$-0.275969\pi$
$983$	1272.26	1.29426	0.647131	+	0.762379i	$0.275969\pi$
$984$	844.534	0.858266
$985$	305.099i	0.309745i
$986$	− 188.097i	− 0.190768i
$987$	− 3143.94i	− 3.18535i
$988$	−809.709	−0.819544
$989$	72.3149i	0.0731192i
$990$	0	0
$991$	993.904	1.00293	0.501465	−	0.865178i	$-0.332794\pi$
$991$	993.904	1.00293	0.501465	+	0.865178i	$0.332794\pi$
$992$	227.142i	0.228973i
$993$	243.276	0.244991
$994$	−1271.40	−1.27908
$995$	642.882	0.646112
$996$	486.066i	0.488018i
$997$	− 6.07964i	− 0.00609793i	−0.999995	−	0.00304896i	$-0.999029\pi$
$997$	− 6.07964i	− 0.00609793i	0.999995	−	0.00304896i	$-0.000970517\pi$
$998$	260.803i	0.261325i
$999$	1678.91	1.68059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1210.3.d.c.241.2		16
11.2	odd	10		110.3.h.b.51.3	yes	16
11.5	even	5		110.3.h.b.41.3	✓	16
11.10	odd	2	inner	1210.3.d.c.241.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.h.b.41.3	✓	16	11.5	even	5
110.3.h.b.51.3	yes	16	11.2	odd	10
1210.3.d.c.241.2		16	1.1	even	1	trivial
1210.3.d.c.241.10		16	11.10	odd	2	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1210.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} -5.33478 q^{3} -2.00000 q^{4} +2.23607 q^{5} +7.54452i q^{6} -8.94509i q^{7} +2.82843i q^{8} +19.4599 q^{9} -3.16228i q^{10} +10.6696 q^{12} +15.5829i q^{13} -12.6503 q^{14} -11.9289 q^{15} +4.00000 q^{16} +9.36447i q^{17} -27.5204i q^{18} -25.9807i q^{19} -4.47214 q^{20} +47.7201i q^{21} +1.85528 q^{23} -15.0890i q^{24} +5.00000 q^{25} +22.0375 q^{26} -55.8012 q^{27} +17.8902i q^{28} -14.2031i q^{29} +16.8701i q^{30} -40.1533 q^{31} -5.65685i q^{32} +13.2434 q^{34} -20.0018i q^{35} -38.9198 q^{36} -30.0873 q^{37} -36.7423 q^{38} -83.1312i q^{39} +6.32456i q^{40} +55.9700i q^{41} +67.4864 q^{42} +38.9779i q^{43} +43.5136 q^{45} -2.62376i q^{46} -65.8830 q^{47} -21.3391 q^{48} -31.0146 q^{49} -7.07107i q^{50} -49.9574i q^{51} -31.1658i q^{52} -91.2982 q^{53} +78.9148i q^{54} +25.3005 q^{56} +138.602i q^{57} -20.0863 q^{58} +20.4895 q^{59} +23.8579 q^{60} -47.9471i q^{61} +56.7854i q^{62} -174.070i q^{63} -8.00000 q^{64} +34.8444i q^{65} +70.6355 q^{67} -18.7289i q^{68} -9.89751 q^{69} -28.2869 q^{70} +100.504 q^{71} +55.0409i q^{72} +49.3326i q^{73} +42.5499i q^{74} -26.6739 q^{75} +51.9615i q^{76} -117.565 q^{78} -25.4652i q^{79} +8.94427 q^{80} +122.548 q^{81} +79.1535 q^{82} +45.5564i q^{83} -95.4402i q^{84} +20.9396i q^{85} +55.1231 q^{86} +75.7706i q^{87} +139.002 q^{89} -61.5376i q^{90} +139.390 q^{91} -3.71056 q^{92} +214.209 q^{93} +93.1727i q^{94} -58.0947i q^{95} +30.1781i q^{96} +101.737 q^{97} +43.8613i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} - 32 q^{4} + 40 q^{9} + 32 q^{12} + 16 q^{14} + 40 q^{15} + 64 q^{16} + 108 q^{23} + 80 q^{25} - 292 q^{27} - 268 q^{31} - 16 q^{34} - 80 q^{36} + 44 q^{37} - 280 q^{38} - 16 q^{42} - 476 q^{47}+ \cdots + 296 q^{97}+O(q^{100}) \) 16 * q - 16 * q^3 - 32 * q^4 + 40 * q^9 + 32 * q^12 + 16 * q^14 + 40 * q^15 + 64 * q^16 + 108 * q^23 + 80 * q^25 - 292 * q^27 - 268 * q^31 - 16 * q^34 - 80 * q^36 + 44 * q^37 - 280 * q^38 - 16 * q^42 - 476 * q^47 - 64 * q^48 - 644 * q^49 - 396 * q^53 - 32 * q^56 + 192 * q^58 - 180 * q^59 - 80 * q^60 - 128 * q^64 + 188 * q^67 - 416 * q^69 + 308 * q^71 - 80 * q^75 + 8 * q^78 + 536 * q^81 + 16 * q^82 + 304 * q^86 - 176 * q^89 + 80 * q^91 - 216 * q^92 + 436 * q^93 + 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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