LMFDB - Embedded newform 490.4.a.u.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,4,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("490.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	490.a (trivial)

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:	yes
Analytic conductor:	$28.9109359028$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{177}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 44 $ x^2 - x - 44
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-6.15207$ of defining polynomial
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +9.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} -18.3041 q^{6} -8.00000 q^{8} +56.7603 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +9.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} -18.3041 q^{6} -8.00000 q^{8} +56.7603 q^{9} -10.0000 q^{10} -35.7603 q^{11} +36.6083 q^{12} +67.4562 q^{13} +45.7603 q^{15} +16.0000 q^{16} -19.1521 q^{17} -113.521 q^{18} -86.6083 q^{19} +20.0000 q^{20} +71.5207 q^{22} +195.041 q^{23} -73.2165 q^{24} +25.0000 q^{25} -134.912 q^{26} +272.369 q^{27} +272.802 q^{29} -91.5207 q^{30} +21.6959 q^{31} -32.0000 q^{32} -327.281 q^{33} +38.3041 q^{34} +227.041 q^{36} +132.562 q^{37} +173.217 q^{38} +617.364 q^{39} -40.0000 q^{40} -67.7786 q^{41} -107.521 q^{43} -143.041 q^{44} +283.802 q^{45} -390.083 q^{46} +609.622 q^{47} +146.433 q^{48} -50.0000 q^{50} -175.281 q^{51} +269.825 q^{52} -645.041 q^{53} -544.737 q^{54} -178.802 q^{55} -792.645 q^{57} -545.603 q^{58} +140.526 q^{59} +183.041 q^{60} -834.036 q^{61} -43.3917 q^{62} +64.0000 q^{64} +337.281 q^{65} +654.562 q^{66} +491.521 q^{67} -76.6083 q^{68} +1785.03 q^{69} -479.207 q^{71} -454.083 q^{72} -610.119 q^{73} -265.124 q^{74} +228.802 q^{75} -346.433 q^{76} -1234.73 q^{78} -153.364 q^{79} +80.0000 q^{80} +960.207 q^{81} +135.557 q^{82} +1015.09 q^{83} -95.7603 q^{85} +215.041 q^{86} +2496.70 q^{87} +286.083 q^{88} -784.331 q^{89} -567.603 q^{90} +780.165 q^{92} +198.562 q^{93} -1219.24 q^{94} -433.041 q^{95} -292.866 q^{96} -227.926 q^{97} -2029.77 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9}+O(q^{10}) $ 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9} - 20 q^{10} - 5 q^{11} + 20 q^{12} + 95 q^{13} + 25 q^{15} + 32 q^{16} - 25 q^{17} - 94 q^{18} - 120 q^{19} + 40 q^{20} + 10 q^{22} + 124 q^{23} - 40 q^{24} + 50 q^{25} - 190 q^{26} + 425 q^{27} + 213 q^{29} - 50 q^{30} + 70 q^{31} - 64 q^{32} - 455 q^{33} + 50 q^{34} + 188 q^{36} - 134 q^{37} + 240 q^{38} + 503 q^{39} - 80 q^{40} + 370 q^{41} - 82 q^{43} - 20 q^{44} + 235 q^{45} - 248 q^{46} + 115 q^{47} + 80 q^{48} - 100 q^{50} - 151 q^{51} + 380 q^{52} - 1024 q^{53} - 850 q^{54} - 25 q^{55} - 654 q^{57} - 426 q^{58} + 760 q^{59} + 100 q^{60} - 790 q^{61} - 140 q^{62} + 128 q^{64} + 475 q^{65} + 910 q^{66} + 850 q^{67} - 100 q^{68} + 2080 q^{69} + 372 q^{71} - 376 q^{72} + 190 q^{73} + 268 q^{74} + 125 q^{75} - 480 q^{76} - 1006 q^{78} + 425 q^{79} + 160 q^{80} + 590 q^{81} - 740 q^{82} + 2110 q^{83} - 125 q^{85} + 164 q^{86} + 2745 q^{87} + 40 q^{88} + 560 q^{89} - 470 q^{90} + 496 q^{92} - 2 q^{93} - 230 q^{94} - 600 q^{95} - 160 q^{96} + 675 q^{97} - 2330 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9 - 20 * q^10 - 5 * q^11 + 20 * q^12 + 95 * q^13 + 25 * q^15 + 32 * q^16 - 25 * q^17 - 94 * q^18 - 120 * q^19 + 40 * q^20 + 10 * q^22 + 124 * q^23 - 40 * q^24 + 50 * q^25 - 190 * q^26 + 425 * q^27 + 213 * q^29 - 50 * q^30 + 70 * q^31 - 64 * q^32 - 455 * q^33 + 50 * q^34 + 188 * q^36 - 134 * q^37 + 240 * q^38 + 503 * q^39 - 80 * q^40 + 370 * q^41 - 82 * q^43 - 20 * q^44 + 235 * q^45 - 248 * q^46 + 115 * q^47 + 80 * q^48 - 100 * q^50 - 151 * q^51 + 380 * q^52 - 1024 * q^53 - 850 * q^54 - 25 * q^55 - 654 * q^57 - 426 * q^58 + 760 * q^59 + 100 * q^60 - 790 * q^61 - 140 * q^62 + 128 * q^64 + 475 * q^65 + 910 * q^66 + 850 * q^67 - 100 * q^68 + 2080 * q^69 + 372 * q^71 - 376 * q^72 + 190 * q^73 + 268 * q^74 + 125 * q^75 - 480 * q^76 - 1006 * q^78 + 425 * q^79 + 160 * q^80 + 590 * q^81 - 740 * q^82 + 2110 * q^83 - 125 * q^85 + 164 * q^86 + 2745 * q^87 + 40 * q^88 + 560 * q^89 - 470 * q^90 + 496 * q^92 - 2 * q^93 - 230 * q^94 - 600 * q^95 - 160 * q^96 + 675 * q^97 - 2330 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	9.15207	1.76132	0.880658	−	0.473752i	$-0.157101\pi$
$3$	9.15207	1.76132	0.880658	+	0.473752i	$0.157101\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−18.3041	−1.24544
$7$	0	0
$7$	0	0
$8$	−8.00000	−0.353553
$9$	56.7603	2.10223
$10$	−10.0000	−0.316228
$11$	−35.7603	−0.980195	−0.490098	−	0.871668i	$-0.663039\pi$
$11$	−35.7603	−0.980195	−0.490098	+	0.871668i	$0.663039\pi$
$12$	36.6083	0.880658
$13$	67.4562	1.43915	0.719576	−	0.694413i	$-0.244336\pi$
$13$	67.4562	1.43915	0.719576	+	0.694413i	$0.244336\pi$
$14$	0	0
$15$	45.7603	0.787685
$16$	16.0000	0.250000
$17$	−19.1521	−0.273239	−0.136619	−	0.990624i	$-0.543624\pi$
$17$	−19.1521	−0.273239	−0.136619	+	0.990624i	$0.543624\pi$
$18$	−113.521	−1.48650
$19$	−86.6083	−1.04575	−0.522876	−	0.852409i	$-0.675141\pi$
$19$	−86.6083	−1.04575	−0.522876	+	0.852409i	$0.675141\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	71.5207	0.693103
$23$	195.041	1.76821	0.884107	−	0.467284i	$-0.154767\pi$
$23$	195.041	1.76821	0.884107	+	0.467284i	$0.154767\pi$
$24$	−73.2165	−0.622719
$25$	25.0000	0.200000
$26$	−134.912	−1.01763
$27$	272.369	1.94138
$28$	0	0
$29$	272.802	1.74683	0.873414	−	0.486979i	$-0.161901\pi$
$29$	272.802	1.74683	0.873414	+	0.486979i	$0.161901\pi$
$30$	−91.5207	−0.556977
$31$	21.6959	0.125700	0.0628499	−	0.998023i	$-0.479981\pi$
$31$	21.6959	0.125700	0.0628499	+	0.998023i	$0.479981\pi$
$32$	−32.0000	−0.176777
$33$	−327.281	−1.72643
$34$	38.3041	0.193209
$35$	0	0
$36$	227.041	1.05112
$37$	132.562	0.589002	0.294501	−	0.955651i	$-0.404847\pi$
$37$	132.562	0.589002	0.294501	+	0.955651i	$0.404847\pi$
$38$	173.217	0.739459
$39$	617.364	2.53480
$40$	−40.0000	−0.158114
$41$	−67.7786	−0.258176	−0.129088	−	0.991633i	$-0.541205\pi$
$41$	−67.7786	−0.258176	−0.129088	+	0.991633i	$0.541205\pi$
$42$	0	0
$43$	−107.521	−0.381320	−0.190660	−	0.981656i	$-0.561063\pi$
$43$	−107.521	−0.381320	−0.190660	+	0.981656i	$0.561063\pi$
$44$	−143.041	−0.490098
$45$	283.802	0.940148
$46$	−390.083	−1.25032
$47$	609.622	1.89197	0.945983	−	0.324215i	$-0.105100\pi$
$47$	609.622	1.89197	0.945983	+	0.324215i	$0.105100\pi$
$48$	146.433	0.440329
$49$	0	0
$50$	−50.0000	−0.141421
$51$	−175.281	−0.481260
$52$	269.825	0.719576
$53$	−645.041	−1.67176	−0.835880	−	0.548913i	$-0.815042\pi$
$53$	−645.041	−1.67176	−0.835880	+	0.548913i	$0.815042\pi$
$54$	−544.737	−1.37277
$55$	−178.802	−0.438357
$56$	0	0
$57$	−792.645	−1.84190
$58$	−545.603	−1.23519
$59$	140.526	0.310083	0.155041	−	0.987908i	$-0.450449\pi$
$59$	140.526	0.310083	0.155041	+	0.987908i	$0.450449\pi$
$60$	183.041	0.393842
$61$	−834.036	−1.75061	−0.875307	−	0.483568i	$-0.839341\pi$
$61$	−834.036	−1.75061	−0.875307	+	0.483568i	$0.839341\pi$
$62$	−43.3917	−0.0888831
$63$	0	0
$64$	64.0000	0.125000
$65$	337.281	0.643609
$66$	654.562	1.22077
$67$	491.521	0.896251	0.448125	−	0.893971i	$-0.352092\pi$
$67$	491.521	0.896251	0.448125	+	0.893971i	$0.352092\pi$
$68$	−76.6083	−0.136619
$69$	1785.03	3.11438
$70$	0	0
$71$	−479.207	−0.801005	−0.400503	−	0.916296i	$-0.631164\pi$
$71$	−479.207	−0.801005	−0.400503	+	0.916296i	$0.631164\pi$
$72$	−454.083	−0.743252
$73$	−610.119	−0.978206	−0.489103	−	0.872226i	$-0.662676\pi$
$73$	−610.119	−0.978206	−0.489103	+	0.872226i	$0.662676\pi$
$74$	−265.124	−0.416487
$75$	228.802	0.352263
$76$	−346.433	−0.522876
$77$	0	0
$78$	−1234.73	−1.79238
$79$	−153.364	−0.218415	−0.109207	−	0.994019i	$-0.534831\pi$
$79$	−153.364	−0.218415	−0.109207	+	0.994019i	$0.534831\pi$
$80$	80.0000	0.111803
$81$	960.207	1.31716
$82$	135.557	0.182558
$83$	1015.09	1.34241	0.671207	−	0.741270i	$-0.265776\pi$
$83$	1015.09	1.34241	0.671207	+	0.741270i	$0.265776\pi$
$84$	0	0
$85$	−95.7603	−0.122196
$86$	215.041	0.269634
$87$	2496.70	3.07672
$88$	286.083	0.346551
$89$	−784.331	−0.934145	−0.467072	−	0.884219i	$-0.654691\pi$
$89$	−784.331	−0.934145	−0.467072	+	0.884219i	$0.654691\pi$
$90$	−567.603	−0.664785
$91$	0	0
$92$	780.165	0.884107
$93$	198.562	0.221397
$94$	−1219.24	−1.33782
$95$	−433.041	−0.467675
$96$	−292.866	−0.311360
$97$	−227.926	−0.238581	−0.119290	−	0.992859i	$-0.538062\pi$
$97$	−227.926	−0.238581	−0.119290	+	0.992859i	$0.538062\pi$
$98$	0	0
$99$	−2029.77	−2.06060
$100$	100.000	0.100000
$101$	703.217	0.692799	0.346399	−	0.938087i	$-0.387404\pi$
$101$	703.217	0.692799	0.346399	+	0.938087i	$0.387404\pi$
$102$	350.562	0.340302
$103$	464.590	0.444441	0.222220	−	0.974996i	$-0.428670\pi$
$103$	464.590	0.444441	0.222220	+	0.974996i	$0.428670\pi$
$104$	−539.650	−0.508817
$105$	0	0
$106$	1290.08	1.18211
$107$	−1955.85	−1.76710	−0.883548	−	0.468340i	$-0.844852\pi$
$107$	−1955.85	−1.76710	−0.883548	+	0.468340i	$0.844852\pi$
$108$	1089.47	0.970692
$109$	−712.008	−0.625670	−0.312835	−	0.949807i	$-0.601279\pi$
$109$	−712.008	−0.625670	−0.312835	+	0.949807i	$0.601279\pi$
$110$	357.603	0.309965
$111$	1213.22	1.03742
$112$	0	0
$113$	2303.14	1.91736	0.958678	−	0.284493i	$-0.0918252\pi$
$113$	2303.14	1.91736	0.958678	+	0.284493i	$0.0918252\pi$
$114$	1585.29	1.30242
$115$	975.207	0.790770
$116$	1091.21	0.873414
$117$	3828.84	3.02544
$118$	−281.051	−0.219261
$119$	0	0
$120$	−366.083	−0.278489
$121$	−52.1983	−0.0392174
$122$	1668.07	1.23787
$123$	−620.314	−0.454730
$124$	86.7835	0.0628499
$125$	125.000	0.0894427
$126$	0	0
$127$	1060.81	0.741194	0.370597	−	0.928794i	$-0.379153\pi$
$127$	1060.81	0.741194	0.370597	+	0.928794i	$0.379153\pi$
$128$	−128.000	−0.0883883
$129$	−984.036	−0.671625
$130$	−674.562	−0.455100
$131$	2020.82	1.34779	0.673893	−	0.738829i	$-0.264621\pi$
$131$	2020.82	1.34779	0.673893	+	0.738829i	$0.264621\pi$
$132$	−1309.12	−0.863217
$133$	0	0
$134$	−983.041	−0.633745
$135$	1361.84	0.868213
$136$	153.217	0.0966045
$137$	−1047.93	−0.653511	−0.326756	−	0.945109i	$-0.605955\pi$
$137$	−1047.93	−0.653511	−0.326756	+	0.945109i	$0.605955\pi$
$138$	−3570.06	−2.20220
$139$	1655.68	1.01031	0.505153	−	0.863030i	$-0.331436\pi$
$139$	1655.68	1.01031	0.505153	+	0.863030i	$0.331436\pi$
$140$	0	0
$141$	5579.30	3.33235
$142$	958.413	0.566396
$143$	−2412.26	−1.41065
$144$	908.165	0.525559
$145$	1364.01	0.781205
$146$	1220.24	0.691696
$147$	0	0
$148$	530.248	0.294501
$149$	135.289	0.0743848	0.0371924	−	0.999308i	$-0.488159\pi$
$149$	135.289	0.0743848	0.0371924	+	0.999308i	$0.488159\pi$
$150$	−457.603	−0.249088
$151$	−782.653	−0.421797	−0.210899	−	0.977508i	$-0.567639\pi$
$151$	−782.653	−0.421797	−0.210899	+	0.977508i	$0.567639\pi$
$152$	692.866	0.369729
$153$	−1087.08	−0.574412
$154$	0	0
$155$	108.479	0.0562146
$156$	2469.45	1.26740
$157$	−869.411	−0.441953	−0.220976	−	0.975279i	$-0.570924\pi$
$157$	−869.411	−0.441953	−0.220976	+	0.975279i	$0.570924\pi$
$158$	306.727	0.154443
$159$	−5903.46	−2.94450
$160$	−160.000	−0.0790569
$161$	0	0
$162$	−1920.41	−0.931370
$163$	−831.207	−0.399418	−0.199709	−	0.979855i	$-0.564000\pi$
$163$	−831.207	−0.399418	−0.199709	+	0.979855i	$0.564000\pi$
$164$	−271.114	−0.129088
$165$	−1636.41	−0.772085
$166$	−2030.18	−0.949230
$167$	−2553.55	−1.18323	−0.591615	−	0.806221i	$-0.701509\pi$
$167$	−2553.55	−1.18323	−0.591615	+	0.806221i	$0.701509\pi$
$168$	0	0
$169$	2353.34	1.07116
$170$	191.521	0.0864057
$171$	−4915.91	−2.19842
$172$	−430.083	−0.190660
$173$	810.203	0.356061	0.178031	−	0.984025i	$-0.443027\pi$
$173$	810.203	0.356061	0.178031	+	0.984025i	$0.443027\pi$
$174$	−4993.40	−2.17557
$175$	0	0
$176$	−572.165	−0.245049
$177$	1286.10	0.546153
$178$	1568.66	0.660540
$179$	−2350.58	−0.981511	−0.490756	−	0.871297i	$-0.663279\pi$
$179$	−2350.58	−0.981511	−0.490756	+	0.871297i	$0.663279\pi$
$180$	1135.21	0.470074
$181$	−1827.31	−0.750402	−0.375201	−	0.926943i	$-0.622426\pi$
$181$	−1827.31	−0.750402	−0.375201	+	0.926943i	$0.622426\pi$
$182$	0	0
$183$	−7633.16	−3.08338
$184$	−1560.33	−0.625158
$185$	662.810	0.263410
$186$	−397.124	−0.156551
$187$	684.884	0.267827
$188$	2438.49	0.945983
$189$	0	0
$190$	866.083	0.330696
$191$	−815.629	−0.308989	−0.154494	−	0.987994i	$-0.549375\pi$
$191$	−815.629	−0.308989	−0.154494	+	0.987994i	$0.549375\pi$
$192$	585.732	0.220165
$193$	−3749.06	−1.39825	−0.699127	−	0.714997i	$-0.746428\pi$
$193$	−3749.06	−1.39825	−0.699127	+	0.714997i	$0.746428\pi$
$194$	455.851	0.168702
$195$	3086.82	1.13360
$196$	0	0
$197$	−2862.00	−1.03507	−0.517536	−	0.855662i	$-0.673151\pi$
$197$	−2862.00	−1.03507	−0.517536	+	0.855662i	$0.673151\pi$
$198$	4059.54	1.45706
$199$	−246.251	−0.0877199	−0.0438600	−	0.999038i	$-0.513966\pi$
$199$	−246.251	−0.0877199	−0.0438600	+	0.999038i	$0.513966\pi$
$200$	−200.000	−0.0707107
$201$	4498.43	1.57858
$202$	−1406.43	−0.489883
$203$	0	0
$204$	−701.124	−0.240630
$205$	−338.893	−0.115460
$206$	−929.180	−0.314267
$207$	11070.6	3.71720
$208$	1079.30	0.359788
$209$	3097.14	1.02504
$210$	0	0
$211$	2895.26	0.944636	0.472318	−	0.881428i	$-0.343417\pi$
$211$	2895.26	0.944636	0.472318	+	0.881428i	$0.343417\pi$
$212$	−2580.17	−0.835880
$213$	−4385.73	−1.41082
$214$	3911.70	1.24953
$215$	−537.603	−0.170531
$216$	−2178.95	−0.686383
$217$	0	0
$218$	1424.02	0.442416
$219$	−5583.85	−1.72293
$220$	−715.207	−0.219178
$221$	−1291.93	−0.393232
$222$	−2426.43	−0.733565
$223$	−5183.72	−1.55663	−0.778313	−	0.627876i	$-0.783924\pi$
$223$	−5183.72	−1.55663	−0.778313	+	0.627876i	$0.783924\pi$
$224$	0	0
$225$	1419.01	0.420447
$226$	−4606.28	−1.35578
$227$	−535.641	−0.156616	−0.0783078	−	0.996929i	$-0.524952\pi$
$227$	−535.641	−0.156616	−0.0783078	+	0.996929i	$0.524952\pi$
$228$	−3170.58	−0.920951
$229$	1403.92	0.405124	0.202562	−	0.979269i	$-0.435073\pi$
$229$	1403.92	0.405124	0.202562	+	0.979269i	$0.435073\pi$
$230$	−1950.41	−0.559159
$231$	0	0
$232$	−2182.41	−0.617597
$233$	−1261.06	−0.354569	−0.177285	−	0.984160i	$-0.556731\pi$
$233$	−1261.06	−0.354569	−0.177285	+	0.984160i	$0.556731\pi$
$234$	−7657.67	−2.13931
$235$	3048.11	0.846113
$236$	562.102	0.155041
$237$	−1403.59	−0.384697
$238$	0	0
$239$	−2747.15	−0.743508	−0.371754	−	0.928331i	$-0.621243\pi$
$239$	−2747.15	−0.743508	−0.371754	+	0.928331i	$0.621243\pi$
$240$	732.165	0.196921
$241$	−5493.22	−1.46825	−0.734127	−	0.679012i	$-0.762408\pi$
$241$	−5493.22	−1.46825	−0.734127	+	0.679012i	$0.762408\pi$
$242$	104.397	0.0277309
$243$	1433.92	0.378544
$244$	−3336.15	−0.875307
$245$	0	0
$246$	1240.63	0.321543
$247$	−5842.26	−1.50500
$248$	−173.567	−0.0444416
$249$	9290.15	2.36442
$250$	−250.000	−0.0632456
$251$	6078.02	1.52845	0.764225	−	0.644950i	$-0.223122\pi$
$251$	6078.02	1.52845	0.764225	+	0.644950i	$0.223122\pi$
$252$	0	0
$253$	−6974.74	−1.73320
$254$	−2121.62	−0.524104
$255$	−876.405	−0.215226
$256$	256.000	0.0625000
$257$	−3245.80	−0.787812	−0.393906	−	0.919151i	$-0.628876\pi$
$257$	−3245.80	−0.787812	−0.393906	+	0.919151i	$0.628876\pi$
$258$	1968.07	0.474910
$259$	0	0
$260$	1349.12	0.321804
$261$	15484.3	3.67224
$262$	−4041.64	−0.953028
$263$	−1018.07	−0.238694	−0.119347	−	0.992853i	$-0.538080\pi$
$263$	−1018.07	−0.238694	−0.119347	+	0.992853i	$0.538080\pi$
$264$	2618.25	0.610386
$265$	−3225.21	−0.747633
$266$	0	0
$267$	−7178.25	−1.64532
$268$	1966.08	0.448125
$269$	4572.65	1.03643	0.518214	−	0.855251i	$-0.326597\pi$
$269$	4572.65	1.03643	0.518214	+	0.855251i	$0.326597\pi$
$270$	−2723.69	−0.613919
$271$	−3691.35	−0.827431	−0.413715	−	0.910406i	$-0.635769\pi$
$271$	−3691.35	−0.827431	−0.413715	+	0.910406i	$0.635769\pi$
$272$	−306.433	−0.0683097
$273$	0	0
$274$	2095.87	0.462102
$275$	−894.008	−0.196039
$276$	7140.13	1.55719
$277$	−5126.22	−1.11193	−0.555965	−	0.831206i	$-0.687651\pi$
$277$	−5126.22	−1.11193	−0.555965	+	0.831206i	$0.687651\pi$
$278$	−3311.35	−0.714395
$279$	1231.46	0.264250
$280$	0	0
$281$	6967.68	1.47921	0.739603	−	0.673044i	$-0.235013\pi$
$281$	6967.68	1.47921	0.739603	+	0.673044i	$0.235013\pi$
$282$	−11158.6	−2.35633
$283$	−3288.23	−0.690688	−0.345344	−	0.938476i	$-0.612238\pi$
$283$	−3288.23	−0.690688	−0.345344	+	0.938476i	$0.612238\pi$
$284$	−1916.83	−0.400503
$285$	−3963.22	−0.823723
$286$	4824.51	0.997481
$287$	0	0
$288$	−1816.33	−0.371626
$289$	−4546.20	−0.925341
$290$	−2728.02	−0.552395
$291$	−2085.99	−0.420216
$292$	−2440.48	−0.489103
$293$	−2338.46	−0.466260	−0.233130	−	0.972446i	$-0.574897\pi$
$293$	−2338.46	−0.466260	−0.233130	+	0.972446i	$0.574897\pi$
$294$	0	0
$295$	702.628	0.138673
$296$	−1060.50	−0.208244
$297$	−9739.99	−1.90294
$298$	−270.579	−0.0525980
$299$	13156.7	2.54473
$300$	915.207	0.176132
$301$	0	0
$302$	1565.31	0.298256
$303$	6435.89	1.22024
$304$	−1385.73	−0.261438
$305$	−4170.18	−0.782898
$306$	2174.16	0.406171
$307$	1689.57	0.314101	0.157050	−	0.987591i	$-0.449801\pi$
$307$	1689.57	0.314101	0.157050	+	0.987591i	$0.449801\pi$
$308$	0	0
$309$	4251.96	0.782801
$310$	−216.959	−0.0397498
$311$	6093.16	1.11097	0.555485	−	0.831527i	$-0.312533\pi$
$311$	6093.16	1.11097	0.555485	+	0.831527i	$0.312533\pi$
$312$	−4938.91	−0.896188
$313$	7883.26	1.42360	0.711802	−	0.702380i	$-0.247879\pi$
$313$	7883.26	1.42360	0.711802	+	0.702380i	$0.247879\pi$
$314$	1738.82	0.312508
$315$	0	0
$316$	−613.455	−0.109207
$317$	5997.57	1.06264	0.531320	−	0.847171i	$-0.321696\pi$
$317$	5997.57	1.06264	0.531320	+	0.847171i	$0.321696\pi$
$318$	11806.9	2.08207
$319$	−9755.48	−1.71223
$320$	320.000	0.0559017
$321$	−17900.1	−3.11242
$322$	0	0
$323$	1658.73	0.285740
$324$	3840.83	0.658578
$325$	1686.41	0.287831
$326$	1662.41	0.282431
$327$	−6516.35	−1.10200
$328$	542.228	0.0912791
$329$	0	0
$330$	3272.81	0.545946
$331$	6454.58	1.07183	0.535915	−	0.844272i	$-0.319967\pi$
$331$	6454.58	1.07183	0.535915	+	0.844272i	$0.319967\pi$
$332$	4060.35	0.671207
$333$	7524.26	1.23822
$334$	5107.09	0.836670
$335$	2457.60	0.400816
$336$	0	0
$337$	−5806.78	−0.938621	−0.469310	−	0.883033i	$-0.655497\pi$
$337$	−5806.78	−0.938621	−0.469310	+	0.883033i	$0.655497\pi$
$338$	−4706.68	−0.757425
$339$	21078.5	3.37707
$340$	−383.041	−0.0610980
$341$	−775.851	−0.123210
$342$	9831.83	1.55452
$343$	0	0
$344$	860.165	0.134817
$345$	8925.16	1.39280
$346$	−1620.41	−0.251773
$347$	6583.50	1.01850	0.509252	−	0.860617i	$-0.329922\pi$
$347$	6583.50	1.01850	0.509252	+	0.860617i	$0.329922\pi$
$348$	9986.80	1.53836
$349$	−7951.40	−1.21957	−0.609783	−	0.792568i	$-0.708744\pi$
$349$	−7951.40	−1.21957	−0.609783	+	0.792568i	$0.708744\pi$
$350$	0	0
$351$	18373.0	2.79395
$352$	1144.33	0.173276
$353$	−5874.13	−0.885690	−0.442845	−	0.896598i	$-0.646031\pi$
$353$	−5874.13	−0.885690	−0.442845	+	0.896598i	$0.646031\pi$
$354$	−2572.20	−0.386189
$355$	−2396.03	−0.358220
$356$	−3137.32	−0.467072
$357$	0	0
$358$	4701.16	0.694033
$359$	2395.57	0.352182	0.176091	−	0.984374i	$-0.443655\pi$
$359$	2395.57	0.352182	0.176091	+	0.984374i	$0.443655\pi$
$360$	−2270.41	−0.332392
$361$	641.992	0.0935985
$362$	3654.62	0.530615
$363$	−477.723	−0.0690742
$364$	0	0
$365$	−3050.60	−0.437467
$366$	15266.3	2.18028
$367$	819.895	0.116616	0.0583081	−	0.998299i	$-0.481429\pi$
$367$	819.895	0.116616	0.0583081	+	0.998299i	$0.481429\pi$
$368$	3120.66	0.442054
$369$	−3847.13	−0.542747
$370$	−1325.62	−0.186259
$371$	0	0
$372$	794.248	0.110699
$373$	−7314.35	−1.01534	−0.507671	−	0.861551i	$-0.669493\pi$
$373$	−7314.35	−1.01534	−0.507671	+	0.861551i	$0.669493\pi$
$374$	−1369.77	−0.189383
$375$	1144.01	0.157537
$376$	−4876.97	−0.668911
$377$	18402.2	2.51395
$378$	0	0
$379$	−11854.0	−1.60659	−0.803294	−	0.595583i	$-0.796921\pi$
$379$	−11854.0	−1.60659	−0.803294	+	0.595583i	$0.796921\pi$
$380$	−1732.17	−0.233837
$381$	9708.61	1.30548
$382$	1631.26	0.218488
$383$	−1988.30	−0.265267	−0.132633	−	0.991165i	$-0.542343\pi$
$383$	−1988.30	−0.265267	−0.132633	+	0.991165i	$0.542343\pi$
$384$	−1171.46	−0.155680
$385$	0	0
$386$	7498.12	0.988715
$387$	−6102.91	−0.801624
$388$	−911.703	−0.119290
$389$	−7570.29	−0.986707	−0.493353	−	0.869829i	$-0.664229\pi$
$389$	−7570.29	−0.986707	−0.493353	+	0.869829i	$0.664229\pi$
$390$	−6173.64	−0.801575
$391$	−3735.45	−0.483145
$392$	0	0
$393$	18494.7	2.37388
$394$	5724.00	0.731906
$395$	−766.819	−0.0976780
$396$	−8119.08	−1.03030
$397$	−13833.2	−1.74879	−0.874395	−	0.485216i	$-0.838741\pi$
$397$	−13833.2	−1.74879	−0.874395	+	0.485216i	$0.838741\pi$
$398$	492.502	0.0620273
$399$	0	0
$400$	400.000	0.0500000
$401$	−3068.57	−0.382138	−0.191069	−	0.981577i	$-0.561195\pi$
$401$	−3068.57	−0.382138	−0.191069	+	0.981577i	$0.561195\pi$
$402$	−8996.86	−1.11623
$403$	1463.52	0.180901
$404$	2812.87	0.346399
$405$	4801.03	0.589050
$406$	0	0
$407$	−4740.46	−0.577337
$408$	1402.25	0.170151
$409$	8359.02	1.01058	0.505290	−	0.862950i	$-0.331386\pi$
$409$	8359.02	1.01058	0.505290	+	0.862950i	$0.331386\pi$
$410$	677.786	0.0816425
$411$	−9590.76	−1.15104
$412$	1858.36	0.222220
$413$	0	0
$414$	−22141.2	−2.62846
$415$	5075.44	0.600346
$416$	−2158.60	−0.254409
$417$	15152.9	1.77947
$418$	−6194.28	−0.724814
$419$	7642.74	0.891103	0.445552	−	0.895256i	$-0.353008\pi$
$419$	7642.74	0.891103	0.445552	+	0.895256i	$0.353008\pi$
$420$	0	0
$421$	−3505.20	−0.405779	−0.202890	−	0.979202i	$-0.565033\pi$
$421$	−3505.20	−0.405779	−0.202890	+	0.979202i	$0.565033\pi$
$422$	−5790.53	−0.667959
$423$	34602.3	3.97736
$424$	5160.33	0.591056
$425$	−478.802	−0.0546477
$426$	8771.46	0.997603
$427$	0	0
$428$	−7823.41	−0.883548
$429$	−22077.1	−2.48460
$430$	1075.21	0.120584
$431$	−7862.80	−0.878742	−0.439371	−	0.898306i	$-0.644799\pi$
$431$	−7862.80	−0.878742	−0.439371	+	0.898306i	$0.644799\pi$
$432$	4357.90	0.485346
$433$	−7253.27	−0.805012	−0.402506	−	0.915417i	$-0.631861\pi$
$433$	−7253.27	−0.805012	−0.402506	+	0.915417i	$0.631861\pi$
$434$	0	0
$435$	12483.5	1.37595
$436$	−2848.03	−0.312835
$437$	−16892.2	−1.84911
$438$	11167.7	1.21830
$439$	3422.37	0.372075	0.186037	−	0.982543i	$-0.440435\pi$
$439$	3422.37	0.372075	0.186037	+	0.982543i	$0.440435\pi$
$440$	1430.41	0.154982
$441$	0	0
$442$	2583.85	0.278057
$443$	−9385.60	−1.00660	−0.503300	−	0.864112i	$-0.667881\pi$
$443$	−9385.60	−1.00660	−0.503300	+	0.864112i	$0.667881\pi$
$444$	4852.87	0.518709
$445$	−3921.65	−0.417762
$446$	10367.4	1.10070
$447$	1238.18	0.131015
$448$	0	0
$449$	−3115.07	−0.327414	−0.163707	−	0.986509i	$-0.552345\pi$
$449$	−3115.07	−0.327414	−0.163707	+	0.986509i	$0.552345\pi$
$450$	−2838.02	−0.297301
$451$	2423.78	0.253063
$452$	9212.56	0.958678
$453$	−7162.89	−0.742919
$454$	1071.28	0.110744
$455$	0	0
$456$	6341.16	0.651210
$457$	136.214	0.0139428	0.00697138	−	0.999976i	$-0.497781\pi$
$457$	136.214	0.0139428	0.00697138	+	0.999976i	$0.497781\pi$
$458$	−2807.83	−0.286466
$459$	−5216.42	−0.530461
$460$	3900.83	0.395385
$461$	10306.6	1.04127	0.520633	−	0.853780i	$-0.325696\pi$
$461$	10306.6	1.04127	0.520633	+	0.853780i	$0.325696\pi$
$462$	0	0
$463$	5319.01	0.533899	0.266950	−	0.963711i	$-0.413984\pi$
$463$	5319.01	0.533899	0.266950	+	0.963711i	$0.413984\pi$
$464$	4364.83	0.436707
$465$	992.810	0.0990118
$466$	2522.12	0.250718
$467$	402.901	0.0399230	0.0199615	−	0.999801i	$-0.493646\pi$
$467$	402.901	0.0399230	0.0199615	+	0.999801i	$0.493646\pi$
$468$	15315.3	1.51272
$469$	0	0
$470$	−6096.22	−0.598292
$471$	−7956.91	−0.778418
$472$	−1124.20	−0.109631
$473$	3844.98	0.373768
$474$	2807.19	0.272022
$475$	−2165.21	−0.209151
$476$	0	0
$477$	−36612.8	−3.51443
$478$	5494.30	0.525739
$479$	5314.04	0.506899	0.253450	−	0.967349i	$-0.418435\pi$
$479$	5314.04	0.506899	0.253450	+	0.967349i	$0.418435\pi$
$480$	−1464.33	−0.139244
$481$	8942.13	0.847663
$482$	10986.4	1.03821
$483$	0	0
$484$	−208.793	−0.0196087
$485$	−1139.63	−0.106697
$486$	−2867.85	−0.267671
$487$	−8283.74	−0.770784	−0.385392	−	0.922753i	$-0.625934\pi$
$487$	−8283.74	−0.770784	−0.385392	+	0.922753i	$0.625934\pi$
$488$	6672.29	0.618935
$489$	−7607.26	−0.703501
$490$	0	0
$491$	−12400.1	−1.13974	−0.569868	−	0.821736i	$-0.693006\pi$
$491$	−12400.1	−1.13974	−0.569868	+	0.821736i	$0.693006\pi$
$492$	−2481.26	−0.227365
$493$	−5224.72	−0.477301
$494$	11684.5	1.06419
$495$	−10148.8	−0.921528
$496$	347.134	0.0314249
$497$	0	0
$498$	−18580.3	−1.67189
$499$	4250.69	0.381336	0.190668	−	0.981655i	$-0.438935\pi$
$499$	4250.69	0.381336	0.190668	+	0.981655i	$0.438935\pi$
$500$	500.000	0.0447214
$501$	−23370.2	−2.08404
$502$	−12156.0	−1.08078
$503$	15514.1	1.37523	0.687615	−	0.726076i	$-0.258658\pi$
$503$	15514.1	1.37523	0.687615	+	0.726076i	$0.258658\pi$
$504$	0	0
$505$	3516.08	0.309829
$506$	13949.5	1.22555
$507$	21537.9	1.88665
$508$	4243.24	0.370597
$509$	4255.68	0.370588	0.185294	−	0.982683i	$-0.440676\pi$
$509$	4255.68	0.370588	0.185294	+	0.982683i	$0.440676\pi$
$510$	1752.81	0.152188
$511$	0	0
$512$	−512.000	−0.0441942
$513$	−23589.4	−2.03021
$514$	6491.60	0.557067
$515$	2322.95	0.198760
$516$	−3936.15	−0.335812
$517$	−21800.3	−1.85450
$518$	0	0
$519$	7415.03	0.627137
$520$	−2698.25	−0.227550
$521$	1635.88	0.137561	0.0687804	−	0.997632i	$-0.478089\pi$
$521$	1635.88	0.137561	0.0687804	+	0.997632i	$0.478089\pi$
$522$	−30968.6	−2.59667
$523$	−5211.93	−0.435759	−0.217880	−	0.975976i	$-0.569914\pi$
$523$	−5211.93	−0.435759	−0.217880	+	0.975976i	$0.569914\pi$
$524$	8083.28	0.673893
$525$	0	0
$526$	2036.13	0.168782
$527$	−415.521	−0.0343460
$528$	−5236.50	−0.431608
$529$	25874.1	2.12658
$530$	6450.41	0.528657
$531$	7976.28	0.651866
$532$	0	0
$533$	−4572.08	−0.371555
$534$	14356.5	1.16342
$535$	−9779.26	−0.790269
$536$	−3932.17	−0.316873
$537$	−21512.7	−1.72875
$538$	−9145.30	−0.732866
$539$	0	0
$540$	5447.37	0.434107
$541$	950.719	0.0755538	0.0377769	−	0.999286i	$-0.487972\pi$
$541$	950.719	0.0755538	0.0377769	+	0.999286i	$0.487972\pi$
$542$	7382.71	0.585082
$543$	−16723.7	−1.32170
$544$	612.866	0.0483022
$545$	−3560.04	−0.279808
$546$	0	0
$547$	4188.13	0.327371	0.163685	−	0.986513i	$-0.447662\pi$
$547$	4188.13	0.327371	0.163685	+	0.986513i	$0.447662\pi$
$548$	−4191.74	−0.326756
$549$	−47340.2	−3.68020
$550$	1788.02	0.138621
$551$	−23626.9	−1.82675
$552$	−14280.3	−1.10110
$553$	0	0
$554$	10252.4	0.786253
$555$	6066.08	0.463948
$556$	6622.71	0.505153
$557$	2076.69	0.157975	0.0789877	−	0.996876i	$-0.474831\pi$
$557$	2076.69	0.157975	0.0789877	+	0.996876i	$0.474831\pi$
$558$	−2462.93	−0.186853
$559$	−7252.94	−0.548777
$560$	0	0
$561$	6268.11	0.471729
$562$	−13935.4	−1.04596
$563$	−18676.6	−1.39809	−0.699047	−	0.715076i	$-0.746392\pi$
$563$	−18676.6	−1.39809	−0.699047	+	0.715076i	$0.746392\pi$
$564$	22317.2	1.66618
$565$	11515.7	0.857468
$566$	6576.45	0.488390
$567$	0	0
$568$	3833.65	0.283198
$569$	−2948.74	−0.217254	−0.108627	−	0.994083i	$-0.534645\pi$
$569$	−2948.74	−0.217254	−0.108627	+	0.994083i	$0.534645\pi$
$570$	7926.45	0.582460
$571$	−6710.58	−0.491820	−0.245910	−	0.969293i	$-0.579087\pi$
$571$	−6710.58	−0.491820	−0.245910	+	0.969293i	$0.579087\pi$
$572$	−9649.03	−0.705325
$573$	−7464.69	−0.544227
$574$	0	0
$575$	4876.03	0.353643
$576$	3632.66	0.262779
$577$	17264.0	1.24560	0.622798	−	0.782382i	$-0.285996\pi$
$577$	17264.0	1.24560	0.622798	+	0.782382i	$0.285996\pi$
$578$	9092.40	0.654315
$579$	−34311.6	−2.46277
$580$	5456.03	0.390603
$581$	0	0
$582$	4171.98	0.297138
$583$	23066.9	1.63865
$584$	4880.95	0.345848
$585$	19144.2	1.35302
$586$	4676.92	0.329696
$587$	−4130.21	−0.290412	−0.145206	−	0.989401i	$-0.546385\pi$
$587$	−4130.21	−0.290412	−0.145206	+	0.989401i	$0.546385\pi$
$588$	0	0
$589$	−1879.04	−0.131451
$590$	−1405.26	−0.0980567
$591$	−26193.2	−1.82309
$592$	2120.99	0.147250
$593$	7813.76	0.541100	0.270550	−	0.962706i	$-0.412794\pi$
$593$	7813.76	0.541100	0.270550	+	0.962706i	$0.412794\pi$
$594$	19480.0	1.34558
$595$	0	0
$596$	541.158	0.0371924
$597$	−2253.70	−0.154502
$598$	−26313.5	−1.79940
$599$	1024.11	0.0698563	0.0349281	−	0.999390i	$-0.488880\pi$
$599$	1024.11	0.0698563	0.0349281	+	0.999390i	$0.488880\pi$
$600$	−1830.41	−0.124544
$601$	4999.87	0.339350	0.169675	−	0.985500i	$-0.445728\pi$
$601$	4999.87	0.339350	0.169675	+	0.985500i	$0.445728\pi$
$602$	0	0
$603$	27898.9	1.88413
$604$	−3130.61	−0.210899
$605$	−260.992	−0.0175385
$606$	−12871.8	−0.862838
$607$	25477.6	1.70363	0.851814	−	0.523844i	$-0.175502\pi$
$607$	25477.6	1.70363	0.851814	+	0.523844i	$0.175502\pi$
$608$	2771.46	0.184865
$609$	0	0
$610$	8340.36	0.553593
$611$	41122.8	2.72283
$612$	−4348.31	−0.287206
$613$	−10349.6	−0.681917	−0.340959	−	0.940078i	$-0.610752\pi$
$613$	−10349.6	−0.681917	−0.340959	+	0.940078i	$0.610752\pi$
$614$	−3379.15	−0.222103
$615$	−3101.57	−0.203362
$616$	0	0
$617$	−350.675	−0.0228811	−0.0114406	−	0.999935i	$-0.503642\pi$
$617$	−350.675	−0.0228811	−0.0114406	+	0.999935i	$0.503642\pi$
$618$	−8503.92	−0.553524
$619$	13709.1	0.890171	0.445086	−	0.895488i	$-0.353173\pi$
$619$	13709.1	0.890171	0.445086	+	0.895488i	$0.353173\pi$
$620$	433.917	0.0281073
$621$	53123.1	3.43278
$622$	−12186.3	−0.785574
$623$	0	0
$624$	9877.82	0.633701
$625$	625.000	0.0400000
$626$	−15766.5	−1.00664
$627$	28345.2	1.80542
$628$	−3477.65	−0.220976
$629$	−2538.84	−0.160938
$630$	0	0
$631$	14458.7	0.912191	0.456096	−	0.889931i	$-0.349248\pi$
$631$	14458.7	0.912191	0.456096	+	0.889931i	$0.349248\pi$
$632$	1226.91	0.0772213
$633$	26497.7	1.66380
$634$	−11995.1	−0.751401
$635$	5304.05	0.331472
$636$	−23613.8	−1.47225
$637$	0	0
$638$	19511.0	1.21073
$639$	−27199.9	−1.68390
$640$	−640.000	−0.0395285
$641$	3740.68	0.230496	0.115248	−	0.993337i	$-0.463234\pi$
$641$	3740.68	0.230496	0.115248	+	0.993337i	$0.463234\pi$
$642$	35800.2	2.20081
$643$	−6702.89	−0.411098	−0.205549	−	0.978647i	$-0.565898\pi$
$643$	−6702.89	−0.411098	−0.205549	+	0.978647i	$0.565898\pi$
$644$	0	0
$645$	−4920.18	−0.300360
$646$	−3317.45	−0.202049
$647$	13882.8	0.843567	0.421783	−	0.906697i	$-0.361404\pi$
$647$	13882.8	0.843567	0.421783	+	0.906697i	$0.361404\pi$
$648$	−7681.65	−0.465685
$649$	−5025.24	−0.303941
$650$	−3372.81	−0.203527
$651$	0	0
$652$	−3324.83	−0.199709
$653$	27279.9	1.63483	0.817415	−	0.576049i	$-0.195406\pi$
$653$	27279.9	1.63483	0.817415	+	0.576049i	$0.195406\pi$
$654$	13032.7	0.779234
$655$	10104.1	0.602748
$656$	−1084.46	−0.0645441
$657$	−34630.6	−2.05642
$658$	0	0
$659$	19618.4	1.15967	0.579835	−	0.814734i	$-0.303117\pi$
$659$	19618.4	1.15967	0.579835	+	0.814734i	$0.303117\pi$
$660$	−6545.62	−0.386042
$661$	26282.3	1.54654	0.773270	−	0.634077i	$-0.218620\pi$
$661$	26282.3	1.54654	0.773270	+	0.634077i	$0.218620\pi$
$662$	−12909.2	−0.757898
$663$	−11823.8	−0.692606
$664$	−8120.70	−0.474615
$665$	0	0
$666$	−15048.5	−0.875554
$667$	53207.6	3.08877
$668$	−10214.2	−0.591615
$669$	−47441.8	−2.74171
$670$	−4915.21	−0.283419
$671$	29825.4	1.71594
$672$	0	0
$673$	−23248.4	−1.33159	−0.665796	−	0.746134i	$-0.731908\pi$
$673$	−23248.4	−1.33159	−0.665796	+	0.746134i	$0.731908\pi$
$674$	11613.6	0.663705
$675$	6809.22	0.388277
$676$	9413.36	0.535580
$677$	25830.6	1.46640	0.733199	−	0.680014i	$-0.238026\pi$
$677$	25830.6	1.46640	0.733199	+	0.680014i	$0.238026\pi$
$678$	−42157.0	−2.38795
$679$	0	0
$680$	766.083	0.0432028
$681$	−4902.22	−0.275850
$682$	1551.70	0.0871228
$683$	1259.01	0.0705338	0.0352669	−	0.999378i	$-0.488772\pi$
$683$	1259.01	0.0705338	0.0352669	+	0.999378i	$0.488772\pi$
$684$	−19663.7	−1.09921
$685$	−5239.67	−0.292259
$686$	0	0
$687$	12848.7	0.713552
$688$	−1720.33	−0.0953299
$689$	−43512.0	−2.40592
$690$	−17850.3	−0.984855
$691$	−26686.8	−1.46919	−0.734596	−	0.678504i	$-0.762628\pi$
$691$	−26686.8	−1.46919	−0.734596	+	0.678504i	$0.762628\pi$
$692$	3240.81	0.178031
$693$	0	0
$694$	−13167.0	−0.720191
$695$	8278.38	0.451823
$696$	−19973.6	−1.08778
$697$	1298.10	0.0705438
$698$	15902.8	0.862364
$699$	−11541.3	−0.624509
$700$	0	0
$701$	−15022.0	−0.809377	−0.404689	−	0.914455i	$-0.632620\pi$
$701$	−15022.0	−0.809377	−0.404689	+	0.914455i	$0.632620\pi$
$702$	−36745.9	−1.97562
$703$	−11481.0	−0.615950
$704$	−2288.66	−0.122524
$705$	27896.5	1.49027
$706$	11748.3	0.626278
$707$	0	0
$708$	5144.40	0.273077
$709$	22722.9	1.20363	0.601817	−	0.798634i	$-0.294443\pi$
$709$	22722.9	1.20363	0.601817	+	0.798634i	$0.294443\pi$
$710$	4792.07	0.253300
$711$	−8704.98	−0.459159
$712$	6274.65	0.330270
$713$	4231.59	0.222264
$714$	0	0
$715$	−12061.3	−0.630862
$716$	−9402.32	−0.490756
$717$	−25142.1	−1.30955
$718$	−4791.14	−0.249030
$719$	27585.5	1.43083	0.715415	−	0.698700i	$-0.246238\pi$
$719$	27585.5	1.43083	0.715415	+	0.698700i	$0.246238\pi$
$720$	4540.83	0.235037
$721$	0	0
$722$	−1283.98	−0.0661842
$723$	−50274.3	−2.58606
$724$	−7309.24	−0.375201
$725$	6820.04	0.349366
$726$	955.445	0.0488428
$727$	21917.7	1.11813	0.559066	−	0.829123i	$-0.311160\pi$
$727$	21917.7	1.11813	0.559066	+	0.829123i	$0.311160\pi$
$728$	0	0
$729$	−12802.2	−0.650420
$730$	6101.19	0.309336
$731$	2059.24	0.104191
$732$	−30532.6	−1.54169
$733$	−29998.2	−1.51161	−0.755805	−	0.654797i	$-0.772754\pi$
$733$	−29998.2	−1.51161	−0.755805	+	0.654797i	$0.772754\pi$
$734$	−1639.79	−0.0824601
$735$	0	0
$736$	−6241.32	−0.312579
$737$	−17576.9	−0.878501
$738$	7694.27	0.383780
$739$	−1146.47	−0.0570685	−0.0285342	−	0.999593i	$-0.509084\pi$
$739$	−1146.47	−0.0570685	−0.0285342	+	0.999593i	$0.509084\pi$
$740$	2651.24	0.131705
$741$	−53468.8	−2.65078
$742$	0	0
$743$	12817.9	0.632900	0.316450	−	0.948609i	$-0.397509\pi$
$743$	12817.9	0.632900	0.316450	+	0.948609i	$0.397509\pi$
$744$	−1588.50	−0.0782757
$745$	676.447	0.0332659
$746$	14628.7	0.717955
$747$	57616.7	2.82207
$748$	2739.54	0.133914
$749$	0	0
$750$	−2288.02	−0.111395
$751$	−12077.6	−0.586841	−0.293421	−	0.955983i	$-0.594794\pi$
$751$	−12077.6	−0.586841	−0.293421	+	0.955983i	$0.594794\pi$
$752$	9753.95	0.472992
$753$	55626.4	2.69208
$754$	−36804.3	−1.77763
$755$	−3913.27	−0.188634
$756$	0	0
$757$	−10645.3	−0.511108	−0.255554	−	0.966795i	$-0.582258\pi$
$757$	−10645.3	−0.511108	−0.255554	+	0.966795i	$0.582258\pi$
$758$	23707.9	1.13603
$759$	−63833.3	−3.05270
$760$	3464.33	0.165348
$761$	8383.14	0.399328	0.199664	−	0.979864i	$-0.436015\pi$
$761$	8383.14	0.399328	0.199664	+	0.979864i	$0.436015\pi$
$762$	−19417.2	−0.923112
$763$	0	0
$764$	−3262.51	−0.154494
$765$	−5435.39	−0.256885
$766$	3976.59	0.187572
$767$	9479.32	0.446256
$768$	2342.93	0.110082
$769$	−20190.1	−0.946781	−0.473391	−	0.880853i	$-0.656970\pi$
$769$	−20190.1	−0.946781	−0.473391	+	0.880853i	$0.656970\pi$
$770$	0	0
$771$	−29705.8	−1.38759
$772$	−14996.2	−0.699127
$773$	−36336.3	−1.69072	−0.845360	−	0.534197i	$-0.820614\pi$
$773$	−36336.3	−1.69072	−0.845360	+	0.534197i	$0.820614\pi$
$774$	12205.8	0.566833
$775$	542.397	0.0251400
$776$	1823.41	0.0843511
$777$	0	0
$778$	15140.6	0.697707
$779$	5870.18	0.269989
$780$	12347.3	0.566799
$781$	17136.6	0.785142
$782$	7470.89	0.341635
$783$	74302.6	3.39126
$784$	0	0
$785$	−4347.06	−0.197647
$786$	−36989.4	−1.67858
$787$	38228.0	1.73149	0.865745	−	0.500486i	$-0.166845\pi$
$787$	38228.0	1.73149	0.865745	+	0.500486i	$0.166845\pi$
$788$	−11448.0	−0.517536
$789$	−9317.41	−0.420416
$790$	1533.64	0.0690688
$791$	0	0
$792$	16238.2	0.728532
$793$	−56260.9	−2.51940
$794$	27666.4	1.23658
$795$	−29517.3	−1.31682
$796$	−985.003	−0.0438600
$797$	26666.6	1.18517	0.592585	−	0.805508i	$-0.298107\pi$
$797$	26666.6	1.18517	0.592585	+	0.805508i	$0.298107\pi$
$798$	0	0
$799$	−11675.5	−0.516959
$800$	−800.000	−0.0353553
$801$	−44518.9	−1.96379
$802$	6137.14	0.270212
$803$	21818.1	0.958833
$804$	17993.7	0.789291
$805$	0	0
$806$	−2927.04	−0.127916
$807$	41849.2	1.82548
$808$	−5625.73	−0.244941
$809$	−14610.3	−0.634943	−0.317472	−	0.948268i	$-0.602834\pi$
$809$	−14610.3	−0.634943	−0.317472	+	0.948268i	$0.602834\pi$
$810$	−9602.07	−0.416521
$811$	−14217.3	−0.615583	−0.307792	−	0.951454i	$-0.599590\pi$
$811$	−14217.3	−0.615583	−0.307792	+	0.951454i	$0.599590\pi$
$812$	0	0
$813$	−33783.5	−1.45737
$814$	9480.92	0.408239
$815$	−4156.03	−0.178625
$816$	−2804.50	−0.120315
$817$	9312.18	0.398766
$818$	−16718.0	−0.714587
$819$	0	0
$820$	−1355.57	−0.0577300
$821$	−14714.9	−0.625520	−0.312760	−	0.949832i	$-0.601254\pi$
$821$	−14714.9	−0.625520	−0.312760	+	0.949832i	$0.601254\pi$
$822$	19181.5	0.813908
$823$	43481.2	1.84163	0.920813	−	0.390004i	$-0.127526\pi$
$823$	43481.2	1.84163	0.920813	+	0.390004i	$0.127526\pi$
$824$	−3716.72	−0.157134
$825$	−8182.03	−0.345287
$826$	0	0
$827$	−41511.8	−1.74547	−0.872737	−	0.488191i	$-0.837657\pi$
$827$	−41511.8	−1.74547	−0.872737	+	0.488191i	$0.837657\pi$
$828$	44282.5	1.85860
$829$	2803.06	0.117436	0.0587180	−	0.998275i	$-0.481299\pi$
$829$	2803.06	0.117436	0.0587180	+	0.998275i	$0.481299\pi$
$830$	−10150.9	−0.424508
$831$	−46915.5	−1.95846
$832$	4317.20	0.179894
$833$	0	0
$834$	−30305.7	−1.25827
$835$	−12767.7	−0.529156
$836$	12388.6	0.512521
$837$	5909.27	0.244031
$838$	−15285.5	−0.630105
$839$	4235.16	0.174272	0.0871359	−	0.996196i	$-0.472229\pi$
$839$	4235.16	0.174272	0.0871359	+	0.996196i	$0.472229\pi$
$840$	0	0
$841$	50031.8	2.05141
$842$	7010.40	0.286929
$843$	63768.7	2.60535
$844$	11581.1	0.472318
$845$	11766.7	0.479037
$846$	−69204.7	−2.81242
$847$	0	0
$848$	−10320.7	−0.417940
$849$	−30094.1	−1.21652
$850$	957.603	0.0386418
$851$	25855.1	1.04148
$852$	−17542.9	−0.705412
$853$	8330.22	0.334374	0.167187	−	0.985925i	$-0.446532\pi$
$853$	8330.22	0.334374	0.167187	+	0.985925i	$0.446532\pi$
$854$	0	0
$855$	−24579.6	−0.983162
$856$	15646.8	0.624763
$857$	−28427.5	−1.13310	−0.566548	−	0.824029i	$-0.691721\pi$
$857$	−28427.5	−1.13310	−0.566548	+	0.824029i	$0.691721\pi$
$858$	44154.3	1.75688
$859$	40374.9	1.60370	0.801848	−	0.597528i	$-0.203850\pi$
$859$	40374.9	1.60370	0.801848	+	0.597528i	$0.203850\pi$
$860$	−2150.41	−0.0852657
$861$	0	0
$862$	15725.6	0.621364
$863$	16397.5	0.646787	0.323394	−	0.946265i	$-0.395176\pi$
$863$	16397.5	0.646787	0.323394	+	0.946265i	$0.395176\pi$
$864$	−8715.80	−0.343191
$865$	4051.02	0.159235
$866$	14506.5	0.569229
$867$	−41607.1	−1.62982
$868$	0	0
$869$	5484.34	0.214089
$870$	−24967.0	−0.972943
$871$	33156.1	1.28984
$872$	5696.07	0.221208
$873$	−12937.1	−0.501553
$874$	33784.4	1.30752
$875$	0	0
$876$	−22335.4	−0.861465
$877$	32573.0	1.25418	0.627088	−	0.778948i	$-0.284247\pi$
$877$	32573.0	1.25418	0.627088	+	0.778948i	$0.284247\pi$
$878$	−6844.74	−0.263096
$879$	−21401.7	−0.821231
$880$	−2860.83	−0.109589
$881$	38088.9	1.45658	0.728290	−	0.685269i	$-0.240315\pi$
$881$	38088.9	1.45658	0.728290	+	0.685269i	$0.240315\pi$
$882$	0	0
$883$	8477.98	0.323111	0.161555	−	0.986864i	$-0.448349\pi$
$883$	8477.98	0.323111	0.161555	+	0.986864i	$0.448349\pi$
$884$	−5167.70	−0.196616
$885$	6430.50	0.244247
$886$	18771.2	0.711773
$887$	32152.1	1.21709	0.608547	−	0.793518i	$-0.291753\pi$
$887$	32152.1	1.21709	0.608547	+	0.793518i	$0.291753\pi$
$888$	−9705.73	−0.366783
$889$	0	0
$890$	7843.31	0.295403
$891$	−34337.3	−1.29107
$892$	−20734.9	−0.778313
$893$	−52798.3	−1.97853
$894$	−2476.36	−0.0926418
$895$	−11752.9	−0.438945
$896$	0	0
$897$	120411.	4.48207
$898$	6230.13	0.231517
$899$	5918.67	0.219576
$900$	5676.03	0.210223
$901$	12353.9	0.456789
$902$	−4847.57	−0.178943
$903$	0	0
$904$	−18425.1	−0.677888
$905$	−9136.55	−0.335590
$906$	14325.8	0.525323
$907$	−22134.9	−0.810339	−0.405170	−	0.914242i	$-0.632788\pi$
$907$	−22134.9	−0.810339	−0.405170	+	0.914242i	$0.632788\pi$
$908$	−2142.56	−0.0783078
$909$	39914.8	1.45643
$910$	0	0
$911$	−24814.1	−0.902445	−0.451222	−	0.892412i	$-0.649012\pi$
$911$	−24814.1	−0.902445	−0.451222	+	0.892412i	$0.649012\pi$
$912$	−12682.3	−0.460475
$913$	−36299.9	−1.31583
$914$	−272.429	−0.00985902
$915$	−38165.8	−1.37893
$916$	5615.67	0.202562
$917$	0	0
$918$	10432.8	0.375093
$919$	−10935.2	−0.392512	−0.196256	−	0.980553i	$-0.562878\pi$
$919$	−10935.2	−0.392512	−0.196256	+	0.980553i	$0.562878\pi$
$920$	−7801.65	−0.279579
$921$	15463.1	0.553231
$922$	−20613.1	−0.736287
$923$	−32325.5	−1.15277
$924$	0	0
$925$	3314.05	0.117800
$926$	−10638.0	−0.377524
$927$	26370.3	0.934319
$928$	−8729.65	−0.308798
$929$	−36214.3	−1.27896	−0.639479	−	0.768809i	$-0.720850\pi$
$929$	−36214.3	−1.27896	−0.639479	+	0.768809i	$0.720850\pi$
$930$	−1985.62	−0.0700119
$931$	0	0
$932$	−5044.23	−0.177285
$933$	55765.0	1.95677
$934$	−805.802	−0.0282298
$935$	3424.42	0.119776
$936$	−30630.7	−1.06965
$937$	42925.7	1.49661	0.748304	−	0.663356i	$-0.230868\pi$
$937$	42925.7	1.49661	0.748304	+	0.663356i	$0.230868\pi$
$938$	0	0
$939$	72148.1	2.50742
$940$	12192.4	0.423057
$941$	37124.9	1.28612	0.643060	−	0.765816i	$-0.277665\pi$
$941$	37124.9	1.28612	0.643060	+	0.765816i	$0.277665\pi$
$942$	15913.8	0.550425
$943$	−13219.6	−0.456511
$944$	2248.41	0.0775206
$945$	0	0
$946$	−7689.95	−0.264294
$947$	−13149.9	−0.451228	−0.225614	−	0.974217i	$-0.572439\pi$
$947$	−13149.9	−0.451228	−0.225614	+	0.974217i	$0.572439\pi$
$948$	−5614.38	−0.192349
$949$	−41156.3	−1.40779
$950$	4330.41	0.147892
$951$	54890.2	1.87165
$952$	0	0
$953$	−9082.99	−0.308738	−0.154369	−	0.988013i	$-0.549334\pi$
$953$	−9082.99	−0.308738	−0.154369	+	0.988013i	$0.549334\pi$
$954$	73225.5	2.48508
$955$	−4078.14	−0.138184
$956$	−10988.6	−0.371754
$957$	−89282.8	−3.01578
$958$	−10628.1	−0.358432
$959$	0	0
$960$	2928.66	0.0984606
$961$	−29320.3	−0.984200
$962$	−17884.3	−0.599388
$963$	−111015.	−3.71485
$964$	−21972.9	−0.734127
$965$	−18745.3	−0.625318
$966$	0	0
$967$	−17837.3	−0.593185	−0.296593	−	0.955004i	$-0.595850\pi$
$967$	−17837.3	−0.593185	−0.296593	+	0.955004i	$0.595850\pi$
$968$	417.587	0.0138654
$969$	15180.8	0.503279
$970$	2279.26	0.0754459
$971$	−27826.3	−0.919660	−0.459830	−	0.888007i	$-0.652090\pi$
$971$	−27826.3	−0.919660	−0.459830	+	0.888007i	$0.652090\pi$
$972$	5735.70	0.189272
$973$	0	0
$974$	16567.5	0.545027
$975$	15434.1	0.506961
$976$	−13344.6	−0.437653
$977$	29822.3	0.976562	0.488281	−	0.872687i	$-0.337624\pi$
$977$	29822.3	0.976562	0.488281	+	0.872687i	$0.337624\pi$
$978$	15214.5	0.497451
$979$	28047.9	0.915644
$980$	0	0
$981$	−40413.8	−1.31531
$982$	24800.3	0.805915
$983$	−6464.25	−0.209743	−0.104872	−	0.994486i	$-0.533443\pi$
$983$	−6464.25	−0.209743	−0.104872	+	0.994486i	$0.533443\pi$
$984$	4962.51	0.160771
$985$	−14310.0	−0.462898
$986$	10449.4	0.337503
$987$	0	0
$988$	−23369.1	−0.752499
$989$	−20971.0	−0.674255
$990$	20297.7	0.651619
$991$	−1177.29	−0.0377376	−0.0188688	−	0.999822i	$-0.506006\pi$
$991$	−1177.29	−0.0377376	−0.0188688	+	0.999822i	$0.506006\pi$
$992$	−694.268	−0.0222208
$993$	59072.7	1.88783
$994$	0	0
$995$	−1231.25	−0.0392295
$996$	37160.6	1.18221
$997$	−13918.3	−0.442123	−0.221062	−	0.975260i	$-0.570952\pi$
$997$	−13918.3	−0.442123	−0.221062	+	0.975260i	$0.570952\pi$
$998$	−8501.37	−0.269646
$999$	36105.7	1.14348

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.4.a.u.1.2	yes	2
5.4	even	2		2450.4.a.bt.1.1		2
7.2	even	3		490.4.e.t.361.1		4
7.3	odd	6		490.4.e.x.471.2		4
7.4	even	3		490.4.e.t.471.1		4
7.5	odd	6		490.4.e.x.361.2		4
7.6	odd	2		490.4.a.p.1.1	✓	2
35.34	odd	2		2450.4.a.ca.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.4.a.p.1.1	✓	2	7.6	odd	2
490.4.a.u.1.2	yes	2	1.1	even	1	trivial
490.4.e.t.361.1		4	7.2	even	3
490.4.e.t.471.1		4	7.4	even	3
490.4.e.x.361.2		4	7.5	odd	6
490.4.e.x.471.2		4	7.3	odd	6
2450.4.a.bt.1.1		2	5.4	even	2
2450.4.a.ca.1.2		2	35.34	odd	2

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +9.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} -18.3041 q^{6} -8.00000 q^{8} +56.7603 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +9.15207 q^{3} +4.00000 q^{4} +5.00000 q^{5} -18.3041 q^{6} -8.00000 q^{8} +56.7603 q^{9} -10.0000 q^{10} -35.7603 q^{11} +36.6083 q^{12} +67.4562 q^{13} +45.7603 q^{15} +16.0000 q^{16} -19.1521 q^{17} -113.521 q^{18} -86.6083 q^{19} +20.0000 q^{20} +71.5207 q^{22} +195.041 q^{23} -73.2165 q^{24} +25.0000 q^{25} -134.912 q^{26} +272.369 q^{27} +272.802 q^{29} -91.5207 q^{30} +21.6959 q^{31} -32.0000 q^{32} -327.281 q^{33} +38.3041 q^{34} +227.041 q^{36} +132.562 q^{37} +173.217 q^{38} +617.364 q^{39} -40.0000 q^{40} -67.7786 q^{41} -107.521 q^{43} -143.041 q^{44} +283.802 q^{45} -390.083 q^{46} +609.622 q^{47} +146.433 q^{48} -50.0000 q^{50} -175.281 q^{51} +269.825 q^{52} -645.041 q^{53} -544.737 q^{54} -178.802 q^{55} -792.645 q^{57} -545.603 q^{58} +140.526 q^{59} +183.041 q^{60} -834.036 q^{61} -43.3917 q^{62} +64.0000 q^{64} +337.281 q^{65} +654.562 q^{66} +491.521 q^{67} -76.6083 q^{68} +1785.03 q^{69} -479.207 q^{71} -454.083 q^{72} -610.119 q^{73} -265.124 q^{74} +228.802 q^{75} -346.433 q^{76} -1234.73 q^{78} -153.364 q^{79} +80.0000 q^{80} +960.207 q^{81} +135.557 q^{82} +1015.09 q^{83} -95.7603 q^{85} +215.041 q^{86} +2496.70 q^{87} +286.083 q^{88} -784.331 q^{89} -567.603 q^{90} +780.165 q^{92} +198.562 q^{93} -1219.24 q^{94} -433.041 q^{95} -292.866 q^{96} -227.926 q^{97} -2029.77 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9}+O(q^{10}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9	\( 2 q - 4 q^{2} + 5 q^{3} + 8 q^{4} + 10 q^{5} - 10 q^{6} - 16 q^{8} + 47 q^{9} - 20 q^{10} - 5 q^{11} + 20 q^{12} + 95 q^{13} + 25 q^{15} + 32 q^{16} - 25 q^{17} - 94 q^{18} - 120 q^{19} + 40 q^{20} + 10 q^{22} + 124 q^{23} - 40 q^{24} + 50 q^{25} - 190 q^{26} + 425 q^{27} + 213 q^{29} - 50 q^{30} + 70 q^{31} - 64 q^{32} - 455 q^{33} + 50 q^{34} + 188 q^{36} - 134 q^{37} + 240 q^{38} + 503 q^{39} - 80 q^{40} + 370 q^{41} - 82 q^{43} - 20 q^{44} + 235 q^{45} - 248 q^{46} + 115 q^{47} + 80 q^{48} - 100 q^{50} - 151 q^{51} + 380 q^{52} - 1024 q^{53} - 850 q^{54} - 25 q^{55} - 654 q^{57} - 426 q^{58} + 760 q^{59} + 100 q^{60} - 790 q^{61} - 140 q^{62} + 128 q^{64} + 475 q^{65} + 910 q^{66} + 850 q^{67} - 100 q^{68} + 2080 q^{69} + 372 q^{71} - 376 q^{72} + 190 q^{73} + 268 q^{74} + 125 q^{75} - 480 q^{76} - 1006 q^{78} + 425 q^{79} + 160 q^{80} + 590 q^{81} - 740 q^{82} + 2110 q^{83} - 125 q^{85} + 164 q^{86} + 2745 q^{87} + 40 q^{88} + 560 q^{89} - 470 q^{90} + 496 q^{92} - 2 q^{93} - 230 q^{94} - 600 q^{95} - 160 q^{96} + 675 q^{97} - 2330 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 + 5 * q^3 + 8 * q^4 + 10 * q^5 - 10 * q^6 - 16 * q^8 + 47 * q^9 - 20 * q^10 - 5 * q^11 + 20 * q^12 + 95 * q^13 + 25 * q^15 + 32 * q^16 - 25 * q^17 - 94 * q^18 - 120 * q^19 + 40 * q^20 + 10 * q^22 + 124 * q^23 - 40 * q^24 + 50 * q^25 - 190 * q^26 + 425 * q^27 + 213 * q^29 - 50 * q^30 + 70 * q^31 - 64 * q^32 - 455 * q^33 + 50 * q^34 + 188 * q^36 - 134 * q^37 + 240 * q^38 + 503 * q^39 - 80 * q^40 + 370 * q^41 - 82 * q^43 - 20 * q^44 + 235 * q^45 - 248 * q^46 + 115 * q^47 + 80 * q^48 - 100 * q^50 - 151 * q^51 + 380 * q^52 - 1024 * q^53 - 850 * q^54 - 25 * q^55 - 654 * q^57 - 426 * q^58 + 760 * q^59 + 100 * q^60 - 790 * q^61 - 140 * q^62 + 128 * q^64 + 475 * q^65 + 910 * q^66 + 850 * q^67 - 100 * q^68 + 2080 * q^69 + 372 * q^71 - 376 * q^72 + 190 * q^73 + 268 * q^74 + 125 * q^75 - 480 * q^76 - 1006 * q^78 + 425 * q^79 + 160 * q^80 + 590 * q^81 - 740 * q^82 + 2110 * q^83 - 125 * q^85 + 164 * q^86 + 2745 * q^87 + 40 * q^88 + 560 * q^89 - 470 * q^90 + 496 * q^92 - 2 * q^93 - 230 * q^94 - 600 * q^95 - 160 * q^96 + 675 * q^97 - 2330 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more