LMFDB - Embedded newform 1849.4.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.23595 q^{2} -2.93512 q^{3} +19.4152 q^{4} +0.131108 q^{5} +15.3681 q^{6} -16.0025 q^{7} -59.7695 q^{8} -18.3851 q^{9} +O(q^{10})$	\(q-5.23595 q^{2} -2.93512 q^{3} +19.4152 q^{4} +0.131108 q^{5} +15.3681 q^{6} -16.0025 q^{7} -59.7695 q^{8} -18.3851 q^{9} -0.686473 q^{10} -45.7909 q^{11} -56.9859 q^{12} +65.8136 q^{13} +83.7883 q^{14} -0.384816 q^{15} +157.628 q^{16} +75.4240 q^{17} +96.2634 q^{18} -1.35794 q^{19} +2.54548 q^{20} +46.9692 q^{21} +239.759 q^{22} +132.000 q^{23} +175.430 q^{24} -124.983 q^{25} -344.597 q^{26} +133.211 q^{27} -310.692 q^{28} +28.6913 q^{29} +2.01488 q^{30} +285.553 q^{31} -347.180 q^{32} +134.402 q^{33} -394.917 q^{34} -2.09805 q^{35} -356.950 q^{36} -434.994 q^{37} +7.11011 q^{38} -193.171 q^{39} -7.83623 q^{40} -197.797 q^{41} -245.929 q^{42} -889.041 q^{44} -2.41042 q^{45} -691.147 q^{46} -234.527 q^{47} -462.658 q^{48} -86.9202 q^{49} +654.404 q^{50} -221.378 q^{51} +1277.78 q^{52} +610.331 q^{53} -697.484 q^{54} -6.00354 q^{55} +956.461 q^{56} +3.98572 q^{57} -150.227 q^{58} +396.213 q^{59} -7.47128 q^{60} -421.005 q^{61} -1495.14 q^{62} +294.207 q^{63} +556.788 q^{64} +8.62866 q^{65} -703.722 q^{66} -451.231 q^{67} +1464.37 q^{68} -387.436 q^{69} +10.9853 q^{70} -376.254 q^{71} +1098.87 q^{72} +470.723 q^{73} +2277.61 q^{74} +366.839 q^{75} -26.3647 q^{76} +732.769 q^{77} +1011.43 q^{78} -643.475 q^{79} +20.6663 q^{80} +105.409 q^{81} +1035.65 q^{82} -960.687 q^{83} +911.917 q^{84} +9.88866 q^{85} -84.2125 q^{87} +2736.90 q^{88} +424.475 q^{89} +12.6209 q^{90} -1053.18 q^{91} +2562.81 q^{92} -838.133 q^{93} +1227.97 q^{94} -0.178036 q^{95} +1019.01 q^{96} -1126.25 q^{97} +455.110 q^{98} +841.870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	$ 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) $ 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * 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 $

$2$	−5.23595	−1.85119	−0.925594	−	0.378517i	$-0.876434\pi$
$2$	−5.23595	−1.85119	−0.925594	+	0.378517i	$0.876434\pi$
$3$	−2.93512	−0.564864	−0.282432	−	0.959287i	$-0.591141\pi$
$3$	−2.93512	−0.564864	−0.282432	+	0.959287i	$0.591141\pi$
$4$	19.4152	2.42690
$5$	0.131108	0.0117266	0.00586331	−	0.999983i	$-0.498134\pi$
$5$	0.131108	0.0117266	0.00586331	+	0.999983i	$0.498134\pi$
$6$	15.3681	1.04567
$7$	−16.0025	−0.864054	−0.432027	−	0.901861i	$-0.642201\pi$
$7$	−16.0025	−0.864054	−0.432027	+	0.901861i	$0.642201\pi$
$8$	−59.7695	−2.64146
$9$	−18.3851	−0.680929
$10$	−0.686473	−0.0217082
$11$	−45.7909	−1.25514	−0.627568	−	0.778562i	$-0.715949\pi$
$11$	−45.7909	−1.25514	−0.627568	+	0.778562i	$0.715949\pi$
$12$	−56.9859	−1.37087
$13$	65.8136	1.40411	0.702054	−	0.712124i	$-0.252267\pi$
$13$	65.8136	1.40411	0.702054	+	0.712124i	$0.252267\pi$
$14$	83.7883	1.59953
$15$	−0.384816	−0.00662394
$16$	157.628	2.46295
$17$	75.4240	1.07606	0.538030	−	0.842926i	$-0.319169\pi$
$17$	75.4240	1.07606	0.538030	+	0.842926i	$0.319169\pi$
$18$	96.2634	1.26053
$19$	−1.35794	−0.0163965	−0.00819824	−	0.999966i	$-0.502610\pi$
$19$	−1.35794	−0.0163965	−0.00819824	+	0.999966i	$0.502610\pi$
$20$	2.54548	0.0284593
$21$	46.9692	0.488072
$22$	239.759	2.32349
$23$	132.000	1.19669	0.598346	−	0.801238i	$-0.295825\pi$
$23$	132.000	1.19669	0.598346	+	0.801238i	$0.295825\pi$
$24$	175.430	1.49207
$25$	−124.983	−0.999862
$26$	−344.597	−2.59927
$27$	133.211	0.949496
$28$	−310.692	−2.09697
$29$	28.6913	0.183719	0.0918594	−	0.995772i	$-0.470719\pi$
$29$	28.6913	0.183719	0.0918594	+	0.995772i	$0.470719\pi$
$30$	2.01488	0.0122622
$31$	285.553	1.65442	0.827208	−	0.561895i	$-0.189928\pi$
$31$	285.553	1.65442	0.827208	+	0.561895i	$0.189928\pi$
$32$	−347.180	−1.91791
$33$	134.402	0.708980
$34$	−394.917	−1.99199
$35$	−2.09805	−0.0101324
$36$	−356.950	−1.65255
$37$	−434.994	−1.93277	−0.966386	−	0.257094i	$-0.917235\pi$
$37$	−434.994	−1.93277	−0.966386	+	0.257094i	$0.917235\pi$
$38$	7.11011	0.0303530
$39$	−193.171	−0.793129
$40$	−7.83623	−0.0309754
$41$	−197.797	−0.753430	−0.376715	−	0.926329i	$-0.622946\pi$
$41$	−197.797	−0.753430	−0.376715	+	0.926329i	$0.622946\pi$
$42$	−245.929	−0.903514
$43$	0	0
$43$	0	0
$44$	−889.041	−3.04609
$45$	−2.41042	−0.00798499
$46$	−691.147	−2.21530
$47$	−234.527	−0.727858	−0.363929	−	0.931427i	$-0.618565\pi$
$47$	−234.527	−0.727858	−0.363929	+	0.931427i	$0.618565\pi$
$48$	−462.658	−1.39123
$49$	−86.9202	−0.253412
$50$	654.404	1.85093
$51$	−221.378	−0.607827
$52$	1277.78	3.40763
$53$	610.331	1.58180	0.790901	−	0.611945i	$-0.209612\pi$
$53$	610.331	1.58180	0.790901	+	0.611945i	$0.209612\pi$
$54$	−697.484	−1.75770
$55$	−6.00354	−0.0147185
$56$	956.461	2.28236
$57$	3.98572	0.00926177
$58$	−150.227	−0.340098
$59$	396.213	0.874281	0.437141	−	0.899393i	$-0.355991\pi$
$59$	396.213	0.874281	0.437141	+	0.899393i	$0.355991\pi$
$60$	−7.47128	−0.0160756
$61$	−421.005	−0.883674	−0.441837	−	0.897095i	$-0.645673\pi$
$61$	−421.005	−0.883674	−0.441837	+	0.897095i	$0.645673\pi$
$62$	−1495.14	−3.06264
$63$	294.207	0.588359
$64$	556.788	1.08748
$65$	8.62866	0.0164654
$66$	−703.722	−1.31246
$67$	−451.231	−0.822785	−0.411393	−	0.911458i	$-0.634957\pi$
$67$	−451.231	−0.822785	−0.411393	+	0.911458i	$0.634957\pi$
$68$	1464.37	2.61149
$69$	−387.436	−0.675968
$70$	10.9853	0.0187570
$71$	−376.254	−0.628917	−0.314458	−	0.949271i	$-0.601823\pi$
$71$	−376.254	−0.628917	−0.314458	+	0.949271i	$0.601823\pi$
$72$	1098.87	1.79865
$73$	470.723	0.754711	0.377356	−	0.926068i	$-0.376833\pi$
$73$	470.723	0.754711	0.377356	+	0.926068i	$0.376833\pi$
$74$	2277.61	3.57793
$75$	366.839	0.564786
$76$	−26.3647	−0.0397926
$77$	732.769	1.08450
$78$	1011.43	1.46823
$79$	−643.475	−0.916412	−0.458206	−	0.888846i	$-0.651508\pi$
$79$	−643.475	−0.916412	−0.458206	+	0.888846i	$0.651508\pi$
$80$	20.6663	0.0288820
$81$	105.409	0.144593
$82$	1035.65	1.39474
$83$	−960.687	−1.27047	−0.635236	−	0.772318i	$-0.719097\pi$
$83$	−960.687	−1.27047	−0.635236	+	0.772318i	$0.719097\pi$
$84$	911.917	1.18450
$85$	9.88866	0.0126185
$86$	0	0
$87$	−84.2125	−0.103776
$88$	2736.90	3.31539
$89$	424.475	0.505553	0.252777	−	0.967525i	$-0.418656\pi$
$89$	424.475	0.505553	0.252777	+	0.967525i	$0.418656\pi$
$90$	12.6209	0.0147817
$91$	−1053.18	−1.21322
$92$	2562.81	2.90425
$93$	−838.133	−0.934520
$94$	1227.97	1.34740
$95$	−0.178036	−0.000192275 0
$96$	1019.01	1.08336
$97$	−1126.25	−1.17890	−0.589450	−	0.807805i	$-0.700656\pi$
$97$	−1126.25	−1.17890	−0.589450	+	0.807805i	$0.700656\pi$
$98$	455.110	0.469113
$99$	841.870	0.854658
$100$	−2426.57	−2.42657
$101$	1380.17	1.35972	0.679860	−	0.733342i	$-0.262041\pi$
$101$	1380.17	1.35972	0.679860	+	0.733342i	$0.262041\pi$
$102$	1159.13	1.12520
$103$	288.601	0.276085	0.138042	−	0.990426i	$-0.455919\pi$
$103$	288.601	0.276085	0.138042	+	0.990426i	$0.455919\pi$
$104$	−3933.64	−3.70890
$105$	6.15802	0.00572344
$106$	−3195.67	−2.92821
$107$	499.855	0.451615	0.225808	−	0.974172i	$-0.427498\pi$
$107$	499.855	0.451615	0.225808	+	0.974172i	$0.427498\pi$
$108$	2586.31	2.30433
$109$	−1695.33	−1.48976	−0.744878	−	0.667200i	$-0.767492\pi$
$109$	−1695.33	−1.48976	−0.744878	+	0.667200i	$0.767492\pi$
$110$	31.4343	0.0272467
$111$	1276.76	1.09175
$112$	−2522.45	−2.12812
$113$	140.413	0.116893	0.0584467	−	0.998291i	$-0.481385\pi$
$113$	140.413	0.116893	0.0584467	+	0.998291i	$0.481385\pi$
$114$	−20.8690	−0.0171453
$115$	17.3062	0.0140332
$116$	557.048	0.445867
$117$	−1209.99	−0.956098
$118$	−2074.55	−1.61846
$119$	−1206.97	−0.929773
$120$	23.0003	0.0174969
$121$	765.811	0.575365
$122$	2204.36	1.63585
$123$	580.556	0.425585
$124$	5544.08	4.01510
$125$	−32.7746	−0.0234516
$126$	−1540.46	−1.08916
$127$	208.242	0.145500	0.0727501	−	0.997350i	$-0.476822\pi$
$127$	208.242	0.145500	0.0727501	+	0.997350i	$0.476822\pi$
$128$	−137.880	−0.0952107
$129$	0	0
$130$	−45.1792	−0.0304806
$131$	340.841	0.227324	0.113662	−	0.993519i	$-0.463742\pi$
$131$	340.841	0.227324	0.113662	+	0.993519i	$0.463742\pi$
$132$	2609.44	1.72062
$133$	21.7304	0.0141674
$134$	2362.62	1.52313
$135$	17.4649	0.0111344
$136$	−4508.06	−2.84237
$137$	−2047.79	−1.27704	−0.638521	−	0.769604i	$-0.720454\pi$
$137$	−2047.79	−1.27704	−0.638521	+	0.769604i	$0.720454\pi$
$138$	2028.60	1.25134
$139$	−229.269	−0.139902	−0.0699509	−	0.997550i	$-0.522284\pi$
$139$	−229.269	−0.139902	−0.0699509	+	0.997550i	$0.522284\pi$
$140$	−40.7340	−0.0245904
$141$	688.365	0.411140
$142$	1970.05	1.16424
$143$	−3013.67	−1.76235
$144$	−2898.01	−1.67709
$145$	3.76165	0.00215440
$146$	−2464.68	−1.39711
$147$	255.121	0.143143
$148$	−8445.50	−4.69065
$149$	1462.16	0.803926	0.401963	−	0.915656i	$-0.368328\pi$
$149$	1462.16	0.803926	0.401963	+	0.915656i	$0.368328\pi$
$150$	−1920.75	−1.04553
$151$	−484.483	−0.261104	−0.130552	−	0.991441i	$-0.541675\pi$
$151$	−484.483	−0.261104	−0.130552	+	0.991441i	$0.541675\pi$
$152$	81.1634	0.0433107
$153$	−1386.68	−0.732720
$154$	−3836.75	−2.00762
$155$	37.4382	0.0194007
$156$	−3750.45	−1.92485
$157$	2475.68	1.25847	0.629237	−	0.777213i	$-0.283367\pi$
$157$	2475.68	1.25847	0.629237	+	0.777213i	$0.283367\pi$
$158$	3369.20	1.69645
$159$	−1791.39	−0.893502
$160$	−45.5179	−0.0224906
$161$	−2112.33	−1.03401
$162$	−551.914	−0.267670
$163$	−4066.74	−1.95418	−0.977090	−	0.212826i	$-0.931733\pi$
$163$	−4066.74	−1.95418	−0.977090	+	0.212826i	$0.931733\pi$
$164$	−3840.26	−1.82850
$165$	17.6211	0.00831394
$166$	5030.11	2.35188
$167$	−3453.41	−1.60020	−0.800100	−	0.599867i	$-0.795220\pi$
$167$	−3453.41	−1.60020	−0.800100	+	0.599867i	$0.795220\pi$
$168$	−2807.32	−1.28922
$169$	2134.42	0.971518
$170$	−51.7766	−0.0233593
$171$	24.9659	0.0111648
$172$	0	0
$173$	−390.887	−0.171784	−0.0858918	−	0.996304i	$-0.527374\pi$
$173$	−390.887	−0.171784	−0.0858918	+	0.996304i	$0.527374\pi$
$174$	440.932	0.192109
$175$	2000.04	0.863935
$176$	−7217.96	−3.09133
$177$	−1162.93	−0.493850
$178$	−2222.53	−0.935874
$179$	1591.08	0.664375	0.332188	−	0.943213i	$-0.392213\pi$
$179$	1591.08	0.664375	0.332188	+	0.943213i	$0.392213\pi$
$180$	−46.7989	−0.0193788
$181$	−2207.02	−0.906335	−0.453167	−	0.891425i	$-0.649706\pi$
$181$	−2207.02	−0.906335	−0.453167	+	0.891425i	$0.649706\pi$
$182$	5514.41	2.24591
$183$	1235.70	0.499155
$184$	−7889.58	−3.16102
$185$	−57.0310	−0.0226649
$186$	4388.43	1.72997
$187$	−3453.74	−1.35060
$188$	−4553.39	−1.76644
$189$	−2131.70	−0.820415
$190$	0.932190	0.000355938 0
$191$	−616.480	−0.233544	−0.116772	−	0.993159i	$-0.537255\pi$
$191$	−616.480	−0.233544	−0.116772	+	0.993159i	$0.537255\pi$
$192$	−1634.24	−0.614276
$193$	−1316.79	−0.491113	−0.245556	−	0.969382i	$-0.578971\pi$
$193$	−1316.79	−0.491113	−0.245556	+	0.969382i	$0.578971\pi$
$194$	5896.99	2.18237
$195$	−25.3261	−0.00930072
$196$	−1687.57	−0.615005
$197$	−3396.37	−1.22833	−0.614165	−	0.789177i	$-0.710507\pi$
$197$	−3396.37	−1.22833	−0.614165	+	0.789177i	$0.710507\pi$
$198$	−4407.99	−1.58213
$199$	3835.38	1.36625	0.683123	−	0.730303i	$-0.260621\pi$
$199$	3835.38	1.36625	0.683123	+	0.730303i	$0.260621\pi$
$200$	7470.16	2.64110
$201$	1324.42	0.464762
$202$	−7226.48	−2.51710
$203$	−459.133	−0.158743
$204$	−4298.11	−1.47514
$205$	−25.9326	−0.00883519
$206$	−1511.10	−0.511085
$207$	−2426.83	−0.814863
$208$	10374.1	3.45824
$209$	62.1814	0.0205798
$210$	−32.2431	−0.0105952
$211$	2804.24	0.914939	0.457469	−	0.889225i	$-0.348756\pi$
$211$	2804.24	0.914939	0.457469	+	0.889225i	$0.348756\pi$
$212$	11849.7	3.83887
$213$	1104.35	0.355252
$214$	−2617.22	−0.836025
$215$	0	0
$216$	−7961.92	−2.50806
$217$	−4569.57	−1.42950
$218$	8876.69	2.75782
$219$	−1381.63	−0.426309
$220$	−116.560	−0.0357203
$221$	4963.93	1.51090
$222$	−6685.05	−2.02104
$223$	4948.34	1.48594	0.742972	−	0.669323i	$-0.233416\pi$
$223$	4948.34	1.48594	0.742972	+	0.669323i	$0.233416\pi$
$224$	5555.74	1.65718
$225$	2297.82	0.680835
$226$	−735.197	−0.216392
$227$	−2686.06	−0.785375	−0.392687	−	0.919672i	$-0.628455\pi$
$227$	−2686.06	−0.785375	−0.392687	+	0.919672i	$0.628455\pi$
$228$	77.3835	0.0224774
$229$	1084.22	0.312871	0.156436	−	0.987688i	$-0.450000\pi$
$229$	1084.22	0.312871	0.156436	+	0.987688i	$0.450000\pi$
$230$	−90.6145	−0.0259780
$231$	−2150.76	−0.612597
$232$	−1714.87	−0.485287
$233$	1900.24	0.534286	0.267143	−	0.963657i	$-0.413920\pi$
$233$	1900.24	0.534286	0.267143	+	0.963657i	$0.413920\pi$
$234$	6335.44	1.76992
$235$	−30.7483	−0.00853531
$236$	7692.56	2.12179
$237$	1888.67	0.517648
$238$	6319.65	1.72119
$239$	−525.653	−0.142266	−0.0711331	−	0.997467i	$-0.522662\pi$
$239$	−525.653	−0.142266	−0.0711331	+	0.997467i	$0.522662\pi$
$240$	−60.6580	−0.0163144
$241$	2848.06	0.761244	0.380622	−	0.924731i	$-0.375710\pi$
$241$	2848.06	0.761244	0.380622	+	0.924731i	$0.375710\pi$
$242$	−4009.75	−1.06511
$243$	−3906.07	−1.03117
$244$	−8173.89	−2.14459
$245$	−11.3959	−0.00297166
$246$	−3039.77	−0.787839
$247$	−89.3709	−0.0230224
$248$	−17067.4	−4.37008
$249$	2819.73	0.717643
$250$	171.606	0.0434134
$251$	1879.52	0.472647	0.236324	−	0.971674i	$-0.424057\pi$
$251$	1879.52	0.472647	0.236324	+	0.971674i	$0.424057\pi$
$252$	5712.09	1.42789
$253$	−6044.41	−1.50201
$254$	−1090.35	−0.269348
$255$	−29.0244	−0.00712776
$256$	−3732.37	−0.911224
$257$	203.687	0.0494382	0.0247191	−	0.999694i	$-0.492131\pi$
$257$	203.687	0.0494382	0.0247191	+	0.999694i	$0.492131\pi$
$258$	0	0
$259$	6960.99	1.67002
$260$	167.527	0.0399600
$261$	−527.493	−0.125100
$262$	−1784.63	−0.420819
$263$	3153.35	0.739330	0.369665	−	0.929165i	$-0.379473\pi$
$263$	3153.35	0.739330	0.369665	+	0.929165i	$0.379473\pi$
$264$	−8033.12	−1.87274
$265$	80.0191	0.0185492
$266$	−113.780	−0.0262266
$267$	−1245.88	−0.285569
$268$	−8760.74	−1.99682
$269$	2506.79	0.568184	0.284092	−	0.958797i	$-0.408308\pi$
$269$	2506.79	0.568184	0.284092	+	0.958797i	$0.408308\pi$
$270$	−91.4455	−0.0206118
$271$	3503.35	0.785289	0.392645	−	0.919690i	$-0.371560\pi$
$271$	3503.35	0.785289	0.392645	+	0.919690i	$0.371560\pi$
$272$	11889.0	2.65028
$273$	3091.21	0.685306
$274$	10722.2	2.36405
$275$	5723.08	1.25496
$276$	−7522.15	−1.64051
$277$	−3504.16	−0.760089	−0.380045	−	0.924968i	$-0.624091\pi$
$277$	−3504.16	−0.760089	−0.380045	+	0.924968i	$0.624091\pi$
$278$	1200.44	0.258985
$279$	−5249.92	−1.12654
$280$	125.399	0.0267644
$281$	−69.8996	−0.0148394	−0.00741968	−	0.999972i	$-0.502362\pi$
$281$	−69.8996	−0.0148394	−0.00741968	+	0.999972i	$0.502362\pi$
$282$	−3604.25	−0.761098
$283$	2594.19	0.544907	0.272453	−	0.962169i	$-0.412165\pi$
$283$	2594.19	0.544907	0.272453	+	0.962169i	$0.412165\pi$
$284$	−7305.04	−1.52632
$285$	0.522558	0.000108609 0
$286$	15779.4	3.26243
$287$	3165.24	0.651004
$288$	6382.93	1.30596
$289$	775.787	0.157905
$290$	−19.6958	−0.00398820
$291$	3305.67	0.665918
$292$	9139.18	1.83161
$293$	5944.70	1.18530	0.592650	−	0.805460i	$-0.298082\pi$
$293$	5944.70	1.18530	0.592650	+	0.805460i	$0.298082\pi$
$294$	−1335.80	−0.264985
$295$	51.9466	0.0102524
$296$	25999.4	5.10535
$297$	−6099.84	−1.19175
$298$	−7655.81	−1.48822
$299$	8687.40	1.68029
$300$	7122.26	1.37068
$301$	0	0
$302$	2536.73	0.483352
$303$	−4050.95	−0.768056
$304$	−214.050	−0.0403836
$305$	−55.1969	−0.0103625
$306$	7260.58	1.35640
$307$	4331.15	0.805184	0.402592	−	0.915379i	$-0.368109\pi$
$307$	4331.15	0.805184	0.402592	+	0.915379i	$0.368109\pi$
$308$	14226.9	2.63198
$309$	−847.078	−0.155950
$310$	−196.025	−0.0359144
$311$	4569.52	0.833162	0.416581	−	0.909099i	$-0.363228\pi$
$311$	4569.52	0.833162	0.416581	+	0.909099i	$0.363228\pi$
$312$	11545.7	2.09502
$313$	1089.81	0.196804	0.0984020	−	0.995147i	$-0.468627\pi$
$313$	1089.81	0.196804	0.0984020	+	0.995147i	$0.468627\pi$
$314$	−12962.5	−2.32967
$315$	38.5728	0.00689946
$316$	−12493.2	−2.22404
$317$	−330.095	−0.0584857	−0.0292428	−	0.999572i	$-0.509310\pi$
$317$	−330.095	−0.0584857	−0.0292428	+	0.999572i	$0.509310\pi$
$318$	9379.66	1.65404
$319$	−1313.80	−0.230592
$320$	72.9991	0.0127524
$321$	−1467.13	−0.255101
$322$	11060.1	1.91414
$323$	−102.421	−0.0176436
$324$	2046.53	0.350914
$325$	−8225.56	−1.40391
$326$	21293.2	3.61756
$327$	4976.00	0.841509
$328$	11822.2	1.99016
$329$	3753.02	0.628908
$330$	−92.2632	−0.0153907
$331$	−4587.68	−0.761818	−0.380909	−	0.924613i	$-0.624389\pi$
$331$	−4587.68	−0.761818	−0.380909	+	0.924613i	$0.624389\pi$
$332$	−18651.9	−3.08331
$333$	7997.40	1.31608
$334$	18081.9	2.96227
$335$	−59.1598	−0.00964849
$336$	7403.68	1.20210
$337$	−7916.40	−1.27963	−0.639813	−	0.768531i	$-0.720988\pi$
$337$	−7916.40	−1.27963	−0.639813	+	0.768531i	$0.720988\pi$
$338$	−11175.7	−1.79846
$339$	−412.129	−0.0660289
$340$	191.990	0.0306239
$341$	−13075.8	−2.07652
$342$	−130.720	−0.0206682
$343$	6879.80	1.08301
$344$	0	0
$345$	−50.7958	−0.00792682
$346$	2046.66	0.318004
$347$	−9728.52	−1.50506	−0.752528	−	0.658560i	$-0.771166\pi$
$347$	−9728.52	−1.50506	−0.752528	+	0.658560i	$0.771166\pi$
$348$	−1635.00	−0.251854
$349$	−6988.60	−1.07189	−0.535947	−	0.844251i	$-0.680045\pi$
$349$	−6988.60	−1.07189	−0.535947	+	0.844251i	$0.680045\pi$
$350$	−10472.1	−1.59931
$351$	8767.06	1.33319
$352$	15897.7	2.40724
$353$	−6365.68	−0.959804	−0.479902	−	0.877322i	$-0.659328\pi$
$353$	−6365.68	−0.959804	−0.479902	+	0.877322i	$0.659328\pi$
$354$	6089.06	0.914209
$355$	−49.3297	−0.00737506
$356$	8241.26	1.22693
$357$	3542.61	0.525195
$358$	−8330.84	−1.22988
$359$	1747.38	0.256889	0.128445	−	0.991717i	$-0.459002\pi$
$359$	1747.38	0.256889	0.128445	+	0.991717i	$0.459002\pi$
$360$	144.070	0.0210921
$361$	−6857.16	−0.999731
$362$	11555.9	1.67780
$363$	−2247.74	−0.325003
$364$	−20447.7	−2.94437
$365$	61.7153	0.00885021
$366$	−6470.06	−0.924031
$367$	−7177.64	−1.02090	−0.510449	−	0.859908i	$-0.670521\pi$
$367$	−7177.64	−1.02090	−0.510449	+	0.859908i	$0.670521\pi$
$368$	20807.0	2.94739
$369$	3636.51	0.513033
$370$	298.612	0.0419570
$371$	−9766.82	−1.36676
$372$	−16272.5	−2.26799
$373$	−9491.92	−1.31762	−0.658811	−	0.752309i	$-0.728940\pi$
$373$	−9491.92	−1.31762	−0.658811	+	0.752309i	$0.728940\pi$
$374$	18083.6	2.50022
$375$	96.1974	0.0132470
$376$	14017.6	1.92261
$377$	1888.28	0.257961
$378$	11161.5	1.51874
$379$	2235.11	0.302928	0.151464	−	0.988463i	$-0.451601\pi$
$379$	2235.11	0.302928	0.151464	+	0.988463i	$0.451601\pi$
$380$	−3.45661	−0.000466633 0
$381$	−611.216	−0.0821877
$382$	3227.86	0.432334
$383$	12537.8	1.67272	0.836360	−	0.548180i	$-0.184679\pi$
$383$	12537.8	1.67272	0.836360	+	0.548180i	$0.184679\pi$
$384$	404.693	0.0537810
$385$	96.0716	0.0127176
$386$	6894.66	0.909143
$387$	0	0
$388$	−21866.4	−2.86107
$389$	−596.353	−0.0777283	−0.0388641	−	0.999245i	$-0.512374\pi$
$389$	−596.353	−0.0777283	−0.0388641	+	0.999245i	$0.512374\pi$
$390$	132.606	0.0172174
$391$	9955.99	1.28771
$392$	5195.17	0.669377
$393$	−1000.41	−0.128407
$394$	17783.2	2.27387
$395$	−84.3644	−0.0107464
$396$	16345.1	2.07417
$397$	−12929.6	−1.63455	−0.817275	−	0.576249i	$-0.804516\pi$
$397$	−12929.6	−1.63455	−0.817275	+	0.576249i	$0.804516\pi$
$398$	−20081.9	−2.52918
$399$	−63.7814	−0.00800267
$400$	−19700.9	−2.46261
$401$	14655.3	1.82506	0.912529	−	0.409011i	$-0.134126\pi$
$401$	14655.3	1.82506	0.912529	+	0.409011i	$0.134126\pi$
$402$	−6934.58	−0.860361
$403$	18793.3	2.32298
$404$	26796.2	3.29990
$405$	13.8199	0.00169559
$406$	2404.00	0.293863
$407$	19918.8	2.42589
$408$	13231.7	1.60555
$409$	−6388.16	−0.772309	−0.386154	−	0.922434i	$-0.626197\pi$
$409$	−6388.16	−0.772309	−0.386154	+	0.922434i	$0.626197\pi$
$410$	135.782	0.0163556
$411$	6010.52	0.721355
$412$	5603.25	0.670030
$413$	−6340.40	−0.755426
$414$	12706.8	1.50846
$415$	−125.953	−0.0148983
$416$	−22849.1	−2.69296
$417$	672.932	0.0790255
$418$	−325.579	−0.0380971
$419$	9158.65	1.06785	0.533925	−	0.845532i	$-0.320716\pi$
$419$	9158.65	1.06785	0.533925	+	0.845532i	$0.320716\pi$
$420$	119.559	0.0138902
$421$	12160.9	1.40781	0.703903	−	0.710296i	$-0.251439\pi$
$421$	12160.9	1.40781	0.703903	+	0.710296i	$0.251439\pi$
$422$	−14682.9	−1.69372
$423$	4311.80	0.495619
$424$	−36479.2	−4.17827
$425$	−9426.71	−1.07591
$426$	−5782.32	−0.657639
$427$	6737.13	0.763542
$428$	9704.79	1.09603
$429$	8845.46	0.995485
$430$	0	0
$431$	3887.23	0.434435	0.217217	−	0.976123i	$-0.430302\pi$
$431$	3887.23	0.434435	0.217217	+	0.976123i	$0.430302\pi$
$432$	20997.8	2.33856
$433$	8805.99	0.977341	0.488671	−	0.872468i	$-0.337482\pi$
$433$	8805.99	0.977341	0.488671	+	0.872468i	$0.337482\pi$
$434$	23926.0	2.64628
$435$	−11.0409	−0.00121694
$436$	−32915.2	−3.61549
$437$	−179.248	−0.0196215
$438$	7234.13	0.789178
$439$	−1493.90	−0.162415	−0.0812074	−	0.996697i	$-0.525878\pi$
$439$	−1493.90	−0.162415	−0.0812074	+	0.996697i	$0.525878\pi$
$440$	358.828	0.0388783
$441$	1598.03	0.172555
$442$	−25990.9	−2.79697
$443$	14119.7	1.51433	0.757163	−	0.653226i	$-0.226585\pi$
$443$	14119.7	1.51433	0.757163	+	0.653226i	$0.226585\pi$
$444$	24788.5	2.64958
$445$	55.6519	0.00592843
$446$	−25909.3	−2.75076
$447$	−4291.62	−0.454109
$448$	−8910.00	−0.939638
$449$	−13589.1	−1.42830	−0.714152	−	0.699991i	$-0.753187\pi$
$449$	−13589.1	−1.42830	−0.714152	+	0.699991i	$0.753187\pi$
$450$	−12031.3	−1.26035
$451$	9057.29	0.945657
$452$	2726.15	0.283689
$453$	1422.01	0.147488
$454$	14064.1	1.45388
$455$	−138.080	−0.0142270
$456$	−238.224	−0.0244646
$457$	18821.4	1.92654	0.963269	−	0.268539i	$-0.0865407\pi$
$457$	18821.4	1.92654	0.963269	+	0.268539i	$0.0865407\pi$
$458$	−5676.94	−0.579183
$459$	10047.3	1.02171
$460$	336.004	0.0340571
$461$	5712.32	0.577113	0.288557	−	0.957463i	$-0.406825\pi$
$461$	5712.32	0.577113	0.288557	+	0.957463i	$0.406825\pi$
$462$	11261.3	1.13403
$463$	−815.875	−0.0818940	−0.0409470	−	0.999161i	$-0.513037\pi$
$463$	−815.875	−0.0818940	−0.0409470	+	0.999161i	$0.513037\pi$
$464$	4522.57	0.452490
$465$	−109.886	−0.0109588
$466$	−9949.55	−0.989064
$467$	−13614.1	−1.34901	−0.674503	−	0.738272i	$-0.735642\pi$
$467$	−13614.1	−1.34901	−0.674503	+	0.738272i	$0.735642\pi$
$468$	−23492.2	−2.32035
$469$	7220.82	0.710931
$470$	160.997	0.0158005
$471$	−7266.40	−0.710866
$472$	−23681.5	−2.30938
$473$	0	0
$474$	−9889.01	−0.958264
$475$	169.719	0.0163942
$476$	−23433.6	−2.25647
$477$	−11221.0	−1.07709
$478$	2752.29	0.263362
$479$	11863.3	1.13162	0.565812	−	0.824534i	$-0.308563\pi$
$479$	11863.3	1.13162	0.565812	+	0.824534i	$0.308563\pi$
$480$	133.600	0.0127042
$481$	−28628.5	−2.71382
$482$	−14912.3	−1.40921
$483$	6199.94	0.584073
$484$	14868.4	1.39635
$485$	−147.660	−0.0138245
$486$	20452.0	1.90889
$487$	10310.8	0.959400	0.479700	−	0.877432i	$-0.340745\pi$
$487$	10310.8	0.959400	0.479700	+	0.877432i	$0.340745\pi$
$488$	25163.2	2.33419
$489$	11936.3	1.10385
$490$	59.6683	0.00550110
$491$	14420.9	1.32547	0.662736	−	0.748853i	$-0.269395\pi$
$491$	14420.9	1.32547	0.662736	+	0.748853i	$0.269395\pi$
$492$	11271.6	1.03285
$493$	2164.02	0.197693
$494$	467.942	0.0426188
$495$	110.376	0.0100222
$496$	45011.4	4.07474
$497$	6021.00	0.543418
$498$	−14764.0	−1.32849
$499$	8154.61	0.731564	0.365782	−	0.930700i	$-0.380802\pi$
$499$	8154.61	0.731564	0.365782	+	0.930700i	$0.380802\pi$
$500$	−636.326	−0.0569148
$501$	10136.2	0.903894
$502$	−9841.10	−0.874959
$503$	−8208.06	−0.727593	−0.363797	−	0.931478i	$-0.618520\pi$
$503$	−8208.06	−0.727593	−0.363797	+	0.931478i	$0.618520\pi$
$504$	−17584.6	−1.55413
$505$	180.950	0.0159449
$506$	31648.3	2.78051
$507$	−6264.79	−0.548775
$508$	4043.07	0.353114
$509$	−17919.3	−1.56043	−0.780216	−	0.625510i	$-0.784891\pi$
$509$	−17919.3	−1.56043	−0.780216	+	0.625510i	$0.784891\pi$
$510$	151.970	0.0131948
$511$	−7532.74	−0.652111
$512$	20645.6	1.78206
$513$	−180.892	−0.0155684
$514$	−1066.49	−0.0915194
$515$	37.8378	0.00323754
$516$	0	0
$517$	10739.2	0.913560
$518$	−36447.4	−3.09152
$519$	1147.30	0.0970343
$520$	−515.730	−0.0434928
$521$	−1205.14	−0.101340	−0.0506702	−	0.998715i	$-0.516136\pi$
$521$	−1205.14	−0.101340	−0.0506702	+	0.998715i	$0.516136\pi$
$522$	2761.93	0.231583
$523$	13397.8	1.12016	0.560081	−	0.828438i	$-0.310770\pi$
$523$	13397.8	1.12016	0.560081	+	0.828438i	$0.310770\pi$
$524$	6617.50	0.551692
$525$	−5870.34	−0.488005
$526$	−16510.8	−1.36864
$527$	21537.6	1.78025
$528$	21185.6	1.74618
$529$	5257.04	0.432073
$530$	−418.976	−0.0343380
$531$	−7284.42	−0.595323
$532$	421.901	0.0343829
$533$	−13017.7	−1.05790
$534$	6523.39	0.528641
$535$	65.5348	0.00529592
$536$	26969.8	2.17336
$537$	−4670.02	−0.375282
$538$	−13125.4	−1.05182
$539$	3980.16	0.318066
$540$	339.085	0.0270220
$541$	5227.97	0.415468	0.207734	−	0.978185i	$-0.433391\pi$
$541$	5227.97	0.415468	0.207734	+	0.978185i	$0.433391\pi$
$542$	−18343.4	−1.45372
$543$	6477.87	0.511956
$544$	−26185.7	−2.06379
$545$	−222.271	−0.0174698
$546$	−16185.4	−1.26863
$547$	−7178.68	−0.561130	−0.280565	−	0.959835i	$-0.590522\pi$
$547$	−7178.68	−0.561130	−0.280565	+	0.959835i	$0.590522\pi$
$548$	−39758.3	−3.09926
$549$	7740.21	0.601719
$550$	−29965.8	−2.32317
$551$	−38.9611	−0.00301234
$552$	23156.8	1.78554
$553$	10297.2	0.791829
$554$	18347.6	1.40707
$555$	167.393	0.0128026
$556$	−4451.31	−0.339528
$557$	12436.4	0.946045	0.473023	−	0.881050i	$-0.343163\pi$
$557$	12436.4	0.946045	0.473023	+	0.881050i	$0.343163\pi$
$558$	27488.4	2.08544
$559$	0	0
$560$	−330.712	−0.0249556
$561$	10137.1	0.762905
$562$	365.991	0.0274705
$563$	−9263.21	−0.693424	−0.346712	−	0.937972i	$-0.612702\pi$
$563$	−9263.21	−0.693424	−0.346712	+	0.937972i	$0.612702\pi$
$564$	13364.7	0.997797
$565$	18.4092	0.00137076
$566$	−13583.1	−1.00873
$567$	−1686.80	−0.124936
$568$	22488.5	1.66126
$569$	12658.0	0.932600	0.466300	−	0.884627i	$-0.345587\pi$
$569$	12658.0	0.932600	0.466300	+	0.884627i	$0.345587\pi$
$570$	−2.73609	−0.000201056 0
$571$	4639.82	0.340053	0.170027	−	0.985439i	$-0.445615\pi$
$571$	4639.82	0.340053	0.170027	+	0.985439i	$0.445615\pi$
$572$	−58510.9	−4.27704
$573$	1809.44	0.131921
$574$	−16573.0	−1.20513
$575$	−16497.7	−1.19653
$576$	−10236.6	−0.740495
$577$	−1301.07	−0.0938720	−0.0469360	−	0.998898i	$-0.514946\pi$
$577$	−1301.07	−0.0938720	−0.0469360	+	0.998898i	$0.514946\pi$
$578$	−4061.98	−0.292312
$579$	3864.94	0.277412
$580$	73.0332	0.00522852
$581$	15373.4	1.09775
$582$	−17308.4	−1.23274
$583$	−27947.7	−1.98537
$584$	−28134.8	−1.99354
$585$	−158.639	−0.0112118
$586$	−31126.2	−2.19421
$587$	27587.0	1.93975	0.969877	−	0.243594i	$-0.0783266\pi$
$587$	27587.0	1.93975	0.969877	+	0.243594i	$0.0783266\pi$
$588$	4953.22	0.347394
$589$	−387.765	−0.0271266
$590$	−271.990	−0.0189791
$591$	9968.74	0.693839
$592$	−68567.5	−4.76031
$593$	13496.3	0.934613	0.467306	−	0.884095i	$-0.345224\pi$
$593$	13496.3	0.934613	0.467306	+	0.884095i	$0.345224\pi$
$594$	31938.5	2.20615
$595$	−158.243	−0.0109031
$596$	28388.2	1.95105
$597$	−11257.3	−0.771743
$598$	−45486.8	−3.11053
$599$	−6323.45	−0.431334	−0.215667	−	0.976467i	$-0.569193\pi$
$599$	−6323.45	−0.431334	−0.215667	+	0.976467i	$0.569193\pi$
$600$	−21925.8	−1.49186
$601$	−447.577	−0.0303778	−0.0151889	−	0.999885i	$-0.504835\pi$
$601$	−447.577	−0.0303778	−0.0151889	+	0.999885i	$0.504835\pi$
$602$	0	0
$603$	8295.92	0.560258
$604$	−9406.34	−0.633673
$605$	100.404	0.00674708
$606$	21210.6	1.42182
$607$	−14391.9	−0.962352	−0.481176	−	0.876624i	$-0.659790\pi$
$607$	−14391.9	−0.962352	−0.481176	+	0.876624i	$0.659790\pi$
$608$	471.449	0.0314470
$609$	1347.61	0.0896681
$610$	289.008	0.0191830
$611$	−15435.1	−1.02199
$612$	−26922.6	−1.77824
$613$	−1934.52	−0.127463	−0.0637314	−	0.997967i	$-0.520300\pi$
$613$	−1934.52	−0.127463	−0.0637314	+	0.997967i	$0.520300\pi$
$614$	−22677.7	−1.49055
$615$	76.1153	0.00499068
$616$	−43797.2	−2.86468
$617$	−637.638	−0.0416051	−0.0208025	−	0.999784i	$-0.506622\pi$
$617$	−637.638	−0.0416051	−0.0208025	+	0.999784i	$0.506622\pi$
$618$	4435.26	0.288693
$619$	−12531.1	−0.813680	−0.406840	−	0.913500i	$-0.633369\pi$
$619$	−12531.1	−0.813680	−0.406840	+	0.913500i	$0.633369\pi$
$620$	726.871	0.0470836
$621$	17583.8	1.13625
$622$	−23925.8	−1.54234
$623$	−6792.66	−0.436825
$624$	−30449.2	−1.95343
$625$	15618.6	0.999587
$626$	−5706.19	−0.364321
$627$	−182.510	−0.0116248
$628$	48065.7	3.05419
$629$	−32809.0	−2.07978
$630$	−201.965	−0.0127722
$631$	27309.6	1.72294	0.861471	−	0.507806i	$-0.169543\pi$
$631$	27309.6	1.72294	0.861471	+	0.507806i	$0.169543\pi$
$632$	38460.1	2.42067
$633$	−8230.79	−0.516816
$634$	1728.36	0.108268
$635$	27.3021	0.00170622
$636$	−34780.3	−2.16844
$637$	−5720.52	−0.355817
$638$	6879.01	0.426870
$639$	6917.45	0.428248
$640$	−18.0771	−0.00111650
$641$	13151.6	0.810384	0.405192	−	0.914232i	$-0.367205\pi$
$641$	13151.6	0.810384	0.405192	+	0.914232i	$0.367205\pi$
$642$	7681.85	0.472240
$643$	19475.3	1.19445	0.597224	−	0.802074i	$-0.296270\pi$
$643$	19475.3	1.19445	0.597224	+	0.802074i	$0.296270\pi$
$644$	−41011.3	−2.50943
$645$	0	0
$646$	536.274	0.0326616
$647$	−11582.1	−0.703769	−0.351884	−	0.936043i	$-0.614459\pi$
$647$	−11582.1	−0.703769	−0.351884	+	0.936043i	$0.614459\pi$
$648$	−6300.21	−0.381938
$649$	−18143.0	−1.09734
$650$	43068.7	2.59891
$651$	13412.2	0.807475
$652$	−78956.5	−4.74260
$653$	13564.9	0.812918	0.406459	−	0.913669i	$-0.366763\pi$
$653$	13564.9	0.812918	0.406459	+	0.913669i	$0.366763\pi$
$654$	−26054.1	−1.55779
$655$	44.6868	0.00266574
$656$	−31178.4	−1.85566
$657$	−8654.28	−0.513905
$658$	−19650.6	−1.16423
$659$	−3888.78	−0.229872	−0.114936	−	0.993373i	$-0.536666\pi$
$659$	−3888.78	−0.229872	−0.114936	+	0.993373i	$0.536666\pi$
$660$	342.117	0.0201771
$661$	−10866.6	−0.639429	−0.319715	−	0.947514i	$-0.603587\pi$
$661$	−10866.6	−0.639429	−0.319715	+	0.947514i	$0.603587\pi$
$662$	24020.9	1.41027
$663$	−14569.7	−0.853455
$664$	57419.7	3.35590
$665$	2.84903	0.000166136 0
$666$	−41874.0	−2.43631
$667$	3787.26	0.219855
$668$	−67048.7	−3.88352
$669$	−14524.0	−0.839356
$670$	309.758	0.0178612
$671$	19278.2	1.10913
$672$	−16306.8	−0.936081
$673$	−8663.98	−0.496243	−0.248122	−	0.968729i	$-0.579813\pi$
$673$	−8663.98	−0.496243	−0.248122	+	0.968729i	$0.579813\pi$
$674$	41449.9	2.36883
$675$	−16649.0	−0.949365
$676$	41440.3	2.35778
$677$	−17819.1	−1.01159	−0.505794	−	0.862654i	$-0.668801\pi$
$677$	−17819.1	−1.01159	−0.505794	+	0.862654i	$0.668801\pi$
$678$	2157.89	0.122232
$679$	18022.8	1.01863
$680$	−591.040	−0.0333314
$681$	7883.90	0.443630
$682$	68464.1	3.84403
$683$	−4580.11	−0.256593	−0.128296	−	0.991736i	$-0.540951\pi$
$683$	−4580.11	−0.256593	−0.128296	+	0.991736i	$0.540951\pi$
$684$	484.717	0.0270959
$685$	−268.481	−0.0149754
$686$	−36022.3	−2.00486
$687$	−3182.32	−0.176729
$688$	0	0
$689$	40168.1	2.22102
$690$	265.964	0.0146740
$691$	24468.4	1.34707	0.673533	−	0.739158i	$-0.264776\pi$
$691$	24468.4	1.34707	0.673533	+	0.739158i	$0.264776\pi$
$692$	−7589.14	−0.416902
$693$	−13472.0	−0.738470
$694$	50938.1	2.78614
$695$	−30.0589	−0.00164058
$696$	5033.33	0.274121
$697$	−14918.6	−0.810736
$698$	36592.0	1.98428
$699$	−5577.42	−0.301799
$700$	38831.1	2.09668
$701$	21220.6	1.14335	0.571677	−	0.820479i	$-0.306293\pi$
$701$	21220.6	1.14335	0.571677	+	0.820479i	$0.306293\pi$
$702$	−45903.9	−2.46799
$703$	590.696	0.0316907
$704$	−25495.9	−1.36493
$705$	90.2499	0.00482129
$706$	33330.4	1.77678
$707$	−22086.1	−1.17487
$708$	−22578.6	−1.19852
$709$	8386.23	0.444219	0.222110	−	0.975022i	$-0.428706\pi$
$709$	8386.23	0.444219	0.222110	+	0.975022i	$0.428706\pi$
$710$	258.288	0.0136526
$711$	11830.3	0.624012
$712$	−25370.6	−1.33540
$713$	37693.1	1.97983
$714$	−18548.9	−0.972236
$715$	−395.114	−0.0206663
$716$	30891.2	1.61237
$717$	1542.85	0.0803611
$718$	−9149.20	−0.475550
$719$	11985.5	0.621676	0.310838	−	0.950463i	$-0.399390\pi$
$719$	11985.5	0.621676	0.310838	+	0.950463i	$0.399390\pi$
$720$	−379.951	−0.0196666
$721$	−4618.34	−0.238552
$722$	35903.7	1.85069
$723$	−8359.39	−0.429999
$724$	−42849.8	−2.19958
$725$	−3585.92	−0.183694
$726$	11769.1	0.601642
$727$	−1242.16	−0.0633690	−0.0316845	−	0.999498i	$-0.510087\pi$
$727$	−1242.16	−0.0633690	−0.0316845	+	0.999498i	$0.510087\pi$
$728$	62948.1	3.20469
$729$	8618.75	0.437878
$730$	−323.138	−0.0163834
$731$	0	0
$732$	23991.3	1.21140
$733$	−14423.5	−0.726800	−0.363400	−	0.931633i	$-0.618384\pi$
$733$	−14423.5	−0.726800	−0.363400	+	0.931633i	$0.618384\pi$
$734$	37581.8	1.88988
$735$	33.4483	0.00167858
$736$	−45827.8	−2.29515
$737$	20662.3	1.03271
$738$	−19040.6	−0.949720
$739$	29711.6	1.47897	0.739486	−	0.673172i	$-0.235069\pi$
$739$	29711.6	1.47897	0.739486	+	0.673172i	$0.235069\pi$
$740$	−1107.27	−0.0550054
$741$	262.314	0.0130045
$742$	51138.6	2.53013
$743$	−7957.09	−0.392890	−0.196445	−	0.980515i	$-0.562940\pi$
$743$	−7957.09	−0.392890	−0.196445	+	0.980515i	$0.562940\pi$
$744$	50094.8	2.46850
$745$	191.701	0.00942733
$746$	49699.2	2.43917
$747$	17662.3	0.865101
$748$	−67055.0	−3.27777
$749$	−7998.93	−0.390220
$750$	−503.685	−0.0245226
$751$	−2023.18	−0.0983047	−0.0491523	−	0.998791i	$-0.515652\pi$
$751$	−2023.18	−0.0983047	−0.0491523	+	0.998791i	$0.515652\pi$
$752$	−36968.2	−1.79267
$753$	−5516.62	−0.266981
$754$	−9886.94	−0.477535
$755$	−63.5194	−0.00306186
$756$	−41387.4	−1.99107
$757$	−4885.83	−0.234582	−0.117291	−	0.993098i	$-0.537421\pi$
$757$	−4885.83	−0.234582	−0.117291	+	0.993098i	$0.537421\pi$
$758$	−11702.9	−0.560777
$759$	17741.1	0.848432
$760$	10.6411	0.000507888 0
$761$	−22688.2	−1.08074	−0.540372	−	0.841426i	$-0.681716\pi$
$761$	−22688.2	−1.08074	−0.540372	+	0.841426i	$0.681716\pi$
$762$	3200.30	0.152145
$763$	27129.6	1.28723
$764$	−11969.1	−0.566788
$765$	−181.804	−0.00859233
$766$	−65647.4	−3.09652
$767$	26076.2	1.22758
$768$	10955.0	0.514717
$769$	−32911.5	−1.54333	−0.771664	−	0.636031i	$-0.780575\pi$
$769$	−32911.5	−1.54333	−0.771664	+	0.636031i	$0.780575\pi$
$770$	−503.026	−0.0235426
$771$	−597.844	−0.0279258
$772$	−25565.8	−1.19188
$773$	9788.24	0.455445	0.227722	−	0.973726i	$-0.426872\pi$
$773$	9788.24	0.455445	0.227722	+	0.973726i	$0.426872\pi$
$774$	0	0
$775$	−35689.3	−1.65419
$776$	67315.3	3.11402
$777$	−20431.3	−0.943333
$778$	3122.48	0.143890
$779$	268.596	0.0123536
$780$	−491.712	−0.0225719
$781$	17229.0	0.789376
$782$	−52129.1	−2.38380
$783$	3821.99	0.174440
$784$	−13701.1	−0.624139
$785$	324.580	0.0147576
$786$	5238.09	0.237706
$787$	25810.4	1.16905	0.584524	−	0.811376i	$-0.301281\pi$
$787$	25810.4	1.16905	0.584524	+	0.811376i	$0.301281\pi$
$788$	−65941.2	−2.98104
$789$	−9255.44	−0.417620
$790$	441.728	0.0198936
$791$	−2246.96	−0.101002
$792$	−50318.1	−2.25755
$793$	−27707.8	−1.24077
$794$	67698.6	3.02586
$795$	−234.865	−0.0104778
$796$	74464.7	3.31574
$797$	−25430.4	−1.13023	−0.565115	−	0.825012i	$-0.691168\pi$
$797$	−25430.4	−1.13023	−0.565115	+	0.825012i	$0.691168\pi$
$798$	333.956	0.0148144
$799$	−17689.0	−0.783218
$800$	43391.5	1.91765
$801$	−7804.00	−0.344246
$802$	−76734.2	−3.37853
$803$	−21554.8	−0.947265
$804$	25713.8	1.12793
$805$	−276.943	−0.0121254
$806$	−98400.8	−4.30027
$807$	−7357.71	−0.320946
$808$	−82491.8	−3.59165
$809$	7901.93	0.343408	0.171704	−	0.985149i	$-0.445073\pi$
$809$	7901.93	0.343408	0.171704	+	0.985149i	$0.445073\pi$
$810$	−72.3601	−0.00313886
$811$	9854.97	0.426701	0.213351	−	0.976976i	$-0.431562\pi$
$811$	9854.97	0.426701	0.213351	+	0.976976i	$0.431562\pi$
$812$	−8914.16	−0.385253
$813$	−10282.7	−0.443581
$814$	−104294.	−4.49078
$815$	−533.180	−0.0229159
$816$	−34895.6	−1.49704
$817$	0	0
$818$	33448.1	1.42969
$819$	19362.8	0.826119
$820$	−503.487	−0.0214421
$821$	10968.8	0.466277	0.233138	−	0.972444i	$-0.425101\pi$
$821$	10968.8	0.466277	0.233138	+	0.972444i	$0.425101\pi$
$822$	−31470.8	−1.33536
$823$	22357.6	0.946948	0.473474	−	0.880808i	$-0.343000\pi$
$823$	22357.6	0.946948	0.473474	+	0.880808i	$0.343000\pi$
$824$	−17249.5	−0.729267
$825$	−16797.9	−0.708883
$826$	33198.0	1.39844
$827$	455.048	0.0191337	0.00956686	−	0.999954i	$-0.496955\pi$
$827$	455.048	0.0191337	0.00956686	+	0.999954i	$0.496955\pi$
$828$	−47117.5	−1.97759
$829$	2638.12	0.110526	0.0552628	−	0.998472i	$-0.482400\pi$
$829$	2638.12	0.110526	0.0552628	+	0.998472i	$0.482400\pi$
$830$	659.486	0.0275796
$831$	10285.1	0.429347
$832$	36644.2	1.52693
$833$	−6555.87	−0.272686
$834$	−3523.44	−0.146291
$835$	−452.769	−0.0187649
$836$	1207.26	0.0499451
$837$	38038.7	1.57086
$838$	−47954.2	−1.97679
$839$	−26143.8	−1.07578	−0.537892	−	0.843014i	$-0.680779\pi$
$839$	−26143.8	−1.07578	−0.537892	+	0.843014i	$0.680779\pi$
$840$	−368.061	−0.0151182
$841$	−23565.8	−0.966247
$842$	−63674.0	−2.60612
$843$	205.164	0.00838222
$844$	54445.0	2.22047
$845$	279.839	0.0113926
$846$	−22576.4	−0.917485
$847$	−12254.9	−0.497146
$848$	96205.6	3.89589
$849$	−7614.25	−0.307798
$850$	49357.8	1.99172
$851$	−57419.3	−2.31293
$852$	21441.1	0.862162
$853$	2909.28	0.116778	0.0583892	−	0.998294i	$-0.481404\pi$
$853$	2909.28	0.116778	0.0583892	+	0.998294i	$0.481404\pi$
$854$	−35275.3	−1.41346
$855$	3.27321	0.000130926 0
$856$	−29876.1	−1.19292
$857$	45185.5	1.80106	0.900528	−	0.434797i	$-0.143180\pi$
$857$	45185.5	1.80106	0.900528	+	0.434797i	$0.143180\pi$
$858$	−46314.4	−1.84283
$859$	7103.90	0.282168	0.141084	−	0.989998i	$-0.454941\pi$
$859$	7103.90	0.282168	0.141084	+	0.989998i	$0.454941\pi$
$860$	0	0
$861$	−9290.35	−0.367729
$862$	−20353.4	−0.804220
$863$	−36520.3	−1.44052	−0.720259	−	0.693705i	$-0.755977\pi$
$863$	−36520.3	−1.44052	−0.720259	+	0.693705i	$0.755977\pi$
$864$	−46248.0	−1.82105
$865$	−51.2482	−0.00201444
$866$	−46107.7	−1.80924
$867$	−2277.03	−0.0891948
$868$	−88719.1	−3.46927
$869$	29465.3	1.15022
$870$	57.8096	0.00225279
$871$	−29697.1	−1.15528
$872$	101329.	3.93514
$873$	20706.2	0.802747
$874$	938.536	0.0363232
$875$	524.476	0.0202635
$876$	−26824.6	−1.03461
$877$	9600.27	0.369644	0.184822	−	0.982772i	$-0.440829\pi$
$877$	9600.27	0.369644	0.184822	+	0.982772i	$0.440829\pi$
$878$	7822.00	0.300660
$879$	−17448.4	−0.669533
$880$	−946.329	−0.0362508
$881$	32330.3	1.23636	0.618181	−	0.786036i	$-0.287870\pi$
$881$	32330.3	1.23636	0.618181	+	0.786036i	$0.287870\pi$
$882$	−8367.23	−0.319432
$883$	−8346.59	−0.318103	−0.159052	−	0.987270i	$-0.550844\pi$
$883$	−8346.59	−0.318103	−0.159052	+	0.987270i	$0.550844\pi$
$884$	96375.6	3.66681
$885$	−152.469	−0.00579119
$886$	−73930.0	−2.80330
$887$	38617.7	1.46184	0.730922	−	0.682461i	$-0.239090\pi$
$887$	38617.7	1.46184	0.730922	+	0.682461i	$0.239090\pi$
$888$	−76311.2	−2.88382
$889$	−3332.40	−0.125720
$890$	−291.390	−0.0109746
$891$	−4826.76	−0.181484
$892$	96073.1	3.60624
$893$	318.474	0.0119343
$894$	22470.7	0.840641
$895$	208.603	0.00779088
$896$	2206.42	0.0822671
$897$	−25498.5	−0.949132
$898$	71151.8	2.64406
$899$	8192.91	0.303948
$900$	44612.6	1.65232
$901$	46033.7	1.70211
$902$	−47423.6	−1.75059
$903$	0	0
$904$	−8392.42	−0.308770
$905$	−289.357	−0.0106282
$906$	−7445.60	−0.273028
$907$	548.846	0.0200928	0.0100464	−	0.999950i	$-0.496802\pi$
$907$	548.846	0.0200928	0.0100464	+	0.999950i	$0.496802\pi$
$908$	−52150.4	−1.90603
$909$	−25374.5	−0.925872
$910$	722.981	0.0263369
$911$	−45421.8	−1.65191	−0.825956	−	0.563735i	$-0.809364\pi$
$911$	−45421.8	−1.65191	−0.825956	+	0.563735i	$0.809364\pi$
$912$	628.262	0.0228112
$913$	43990.8	1.59461
$914$	−98547.9	−3.56639
$915$	162.009	0.00585341
$916$	21050.4	0.759307
$917$	−5454.31	−0.196420
$918$	−52607.1	−1.89139
$919$	−22601.1	−0.811254	−0.405627	−	0.914039i	$-0.632947\pi$
$919$	−22601.1	−0.811254	−0.405627	+	0.914039i	$0.632947\pi$
$920$	−1034.38	−0.0370681
$921$	−12712.4	−0.454819
$922$	−29909.4	−1.06835
$923$	−24762.6	−0.883067
$924$	−41757.5	−1.48671
$925$	54366.8	1.93251
$926$	4271.88	0.151601
$927$	−5305.96	−0.187994
$928$	−9961.05	−0.352357
$929$	40360.7	1.42540	0.712698	−	0.701471i	$-0.247473\pi$
$929$	40360.7	1.42540	0.712698	+	0.701471i	$0.247473\pi$
$930$	575.356	0.0202867
$931$	118.032	0.00415506
$932$	36893.5	1.29666
$933$	−13412.1	−0.470623
$934$	71282.9	2.49727
$935$	−452.811	−0.0158380
$936$	72320.3	2.52550
$937$	−31284.2	−1.09072	−0.545362	−	0.838201i	$-0.683608\pi$
$937$	−31284.2	−1.09072	−0.545362	+	0.838201i	$0.683608\pi$
$938$	−37807.9	−1.31607
$939$	−3198.72	−0.111167
$940$	−596.984	−0.0207143
$941$	−5029.28	−0.174229	−0.0871147	−	0.996198i	$-0.527765\pi$
$941$	−5029.28	−0.174229	−0.0871147	+	0.996198i	$0.527765\pi$
$942$	38046.5	1.31595
$943$	−26109.2	−0.901624
$944$	62454.5	2.15331
$945$	−279.482	−0.00962069
$946$	0	0
$947$	−19035.0	−0.653171	−0.326585	−	0.945168i	$-0.605898\pi$
$947$	−19035.0	−0.653171	−0.326585	+	0.945168i	$0.605898\pi$
$948$	36669.0	1.25628
$949$	30979.9	1.05970
$950$	−888.642	−0.0303488
$951$	968.866	0.0330364
$952$	72140.1	2.45596
$953$	20110.7	0.683578	0.341789	−	0.939777i	$-0.388967\pi$
$953$	20110.7	0.683578	0.341789	+	0.939777i	$0.388967\pi$
$954$	58752.6	1.99391
$955$	−80.8252	−0.00273868
$956$	−10205.7	−0.345266
$957$	3856.17	0.130253
$958$	−62115.7	−2.09485
$959$	32769.8	1.10343
$960$	−214.261	−0.00720338
$961$	51749.8	1.73709
$962$	149898.	5.02379
$963$	−9189.88	−0.307518
$964$	55295.7	1.84746
$965$	−172.641	−0.00575909
$966$	−32462.6	−1.08123
$967$	1106.55	0.0367984	0.0183992	−	0.999831i	$-0.494143\pi$
$967$	1106.55	0.0367984	0.0183992	+	0.999831i	$0.494143\pi$
$968$	−45772.1	−1.51980
$969$	300.619	0.00996622
$970$	773.140	0.0255918
$971$	19250.7	0.636235	0.318118	−	0.948051i	$-0.396949\pi$
$971$	19250.7	0.636235	0.318118	+	0.948051i	$0.396949\pi$
$972$	−75837.2	−2.50255
$973$	3668.88	0.120883
$974$	−53987.0	−1.77603
$975$	24143.0	0.793020
$976$	−66362.3	−2.17644
$977$	7468.24	0.244555	0.122277	−	0.992496i	$-0.460980\pi$
$977$	7468.24	0.244555	0.122277	+	0.992496i	$0.460980\pi$
$978$	−62498.2	−2.04343
$979$	−19437.1	−0.634538
$980$	−221.254	−0.00721192
$981$	31168.8	1.01442
$982$	−75507.2	−2.45370
$983$	−34834.7	−1.13027	−0.565135	−	0.824999i	$-0.691176\pi$
$983$	−34834.7	−1.13027	−0.565135	+	0.824999i	$0.691176\pi$
$984$	−34699.5	−1.12417
$985$	−445.289	−0.0144042
$986$	−11330.7	−0.365966
$987$	−11015.6	−0.355247
$988$	−1735.15	−0.0558731
$989$	0	0
$990$	−577.921	−0.0185531
$991$	18102.4	0.580263	0.290132	−	0.956987i	$-0.406301\pi$
$991$	18102.4	0.580263	0.290132	+	0.956987i	$0.406301\pi$
$992$	−99138.3	−3.17303
$993$	13465.4	0.430323
$994$	−31525.6	−1.00597
$995$	502.847	0.0160214
$996$	54745.6	1.74165
$997$	3140.26	0.0997523	0.0498761	−	0.998755i	$-0.484117\pi$
$997$	3140.26	0.0997523	0.0498761	+	0.998755i	$0.484117\pi$
$998$	−42697.2	−1.35426
$999$	−57945.8	−1.83516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.5	✓	110
43.42	odd	2	inner	1849.4.a.m.1.106	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.5	✓	110	1.1	even	1	trivial
1849.4.a.m.1.106	yes	110	43.42	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-5.23595 q^{2} -2.93512 q^{3} +19.4152 q^{4} +0.131108 q^{5} +15.3681 q^{6} -16.0025 q^{7} -59.7695 q^{8} -18.3851 q^{9} +O(q^{10})\)	\(q-5.23595 q^{2} -2.93512 q^{3} +19.4152 q^{4} +0.131108 q^{5} +15.3681 q^{6} -16.0025 q^{7} -59.7695 q^{8} -18.3851 q^{9} -0.686473 q^{10} -45.7909 q^{11} -56.9859 q^{12} +65.8136 q^{13} +83.7883 q^{14} -0.384816 q^{15} +157.628 q^{16} +75.4240 q^{17} +96.2634 q^{18} -1.35794 q^{19} +2.54548 q^{20} +46.9692 q^{21} +239.759 q^{22} +132.000 q^{23} +175.430 q^{24} -124.983 q^{25} -344.597 q^{26} +133.211 q^{27} -310.692 q^{28} +28.6913 q^{29} +2.01488 q^{30} +285.553 q^{31} -347.180 q^{32} +134.402 q^{33} -394.917 q^{34} -2.09805 q^{35} -356.950 q^{36} -434.994 q^{37} +7.11011 q^{38} -193.171 q^{39} -7.83623 q^{40} -197.797 q^{41} -245.929 q^{42} -889.041 q^{44} -2.41042 q^{45} -691.147 q^{46} -234.527 q^{47} -462.658 q^{48} -86.9202 q^{49} +654.404 q^{50} -221.378 q^{51} +1277.78 q^{52} +610.331 q^{53} -697.484 q^{54} -6.00354 q^{55} +956.461 q^{56} +3.98572 q^{57} -150.227 q^{58} +396.213 q^{59} -7.47128 q^{60} -421.005 q^{61} -1495.14 q^{62} +294.207 q^{63} +556.788 q^{64} +8.62866 q^{65} -703.722 q^{66} -451.231 q^{67} +1464.37 q^{68} -387.436 q^{69} +10.9853 q^{70} -376.254 q^{71} +1098.87 q^{72} +470.723 q^{73} +2277.61 q^{74} +366.839 q^{75} -26.3647 q^{76} +732.769 q^{77} +1011.43 q^{78} -643.475 q^{79} +20.6663 q^{80} +105.409 q^{81} +1035.65 q^{82} -960.687 q^{83} +911.917 q^{84} +9.88866 q^{85} -84.2125 q^{87} +2736.90 q^{88} +424.475 q^{89} +12.6209 q^{90} -1053.18 q^{91} +2562.81 q^{92} -838.133 q^{93} +1227.97 q^{94} -0.178036 q^{95} +1019.01 q^{96} -1126.25 q^{97} +455.110 q^{98} +841.870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 110 * q + 492 * q^4 + 102 * q^6 + 1234 * q^9 + 102 * q^10 + 360 * q^11 + 166 * q^13 + 496 * q^14 + 540 * q^15 + 2204 * q^16 + 610 * q^17 + 896 * q^21 + 1508 * q^23 + 1086 * q^24 + 3168 * q^25 + 2312 * q^31 + 2760 * q^35 + 8334 * q^36 + 3626 * q^38 + 1462 * q^40 + 3598 * q^41 + 1596 * q^44 + 4448 * q^47 + 7194 * q^49 + 3620 * q^52 + 3818 * q^53 - 2570 * q^54 - 714 * q^56 + 3236 * q^57 + 3242 * q^58 + 8556 * q^59 + 178 * q^60 + 7308 * q^64 + 4202 * q^66 + 1992 * q^67 + 8994 * q^68 + 8256 * q^74 + 4784 * q^78 + 13752 * q^79 + 19678 * q^81 + 7620 * q^83 + 11390 * q^84 + 6012 * q^87 - 476 * q^90 + 8022 * q^92 + 7392 * q^95 + 16760 * q^96 - 1186 * q^97 + 11068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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