LMFDB - Embedded newform 1849.4.a.e.1.8

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 62x^{8} + 1289x^{6} - 11252x^{4} + 39376x^{2} - 35688 $ x^10 - 62x^8 + 1289x^6 - 11252x^4 + 39376x^2 - 35688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$3.05512$ of defining polynomial
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)

$f(q)$	$=$	$q+3.05512 q^{2} +4.99167 q^{3} +1.33374 q^{4} -15.7813 q^{5} +15.2501 q^{6} +15.1156 q^{7} -20.3662 q^{8} -2.08325 q^{9} +O(q^{10})$	\(q+3.05512 q^{2} +4.99167 q^{3} +1.33374 q^{4} -15.7813 q^{5} +15.2501 q^{6} +15.1156 q^{7} -20.3662 q^{8} -2.08325 q^{9} -48.2136 q^{10} -21.4756 q^{11} +6.65759 q^{12} +59.1204 q^{13} +46.1801 q^{14} -78.7748 q^{15} -72.8911 q^{16} -89.2363 q^{17} -6.36458 q^{18} -3.71618 q^{19} -21.0481 q^{20} +75.4523 q^{21} -65.6104 q^{22} +132.040 q^{23} -101.661 q^{24} +124.048 q^{25} +180.620 q^{26} -145.174 q^{27} +20.1603 q^{28} +220.497 q^{29} -240.666 q^{30} -173.787 q^{31} -59.7611 q^{32} -107.199 q^{33} -272.627 q^{34} -238.544 q^{35} -2.77852 q^{36} +341.140 q^{37} -11.3534 q^{38} +295.109 q^{39} +321.404 q^{40} +334.536 q^{41} +230.515 q^{42} -28.6428 q^{44} +32.8763 q^{45} +403.397 q^{46} +182.605 q^{47} -363.848 q^{48} -114.517 q^{49} +378.981 q^{50} -445.438 q^{51} +78.8513 q^{52} +296.886 q^{53} -443.523 q^{54} +338.911 q^{55} -307.848 q^{56} -18.5499 q^{57} +673.646 q^{58} +668.255 q^{59} -105.065 q^{60} -461.669 q^{61} -530.940 q^{62} -31.4897 q^{63} +400.551 q^{64} -932.994 q^{65} -327.505 q^{66} +485.027 q^{67} -119.018 q^{68} +659.099 q^{69} -728.779 q^{70} +358.344 q^{71} +42.4279 q^{72} -136.162 q^{73} +1042.22 q^{74} +619.206 q^{75} -4.95642 q^{76} -324.617 q^{77} +901.594 q^{78} -590.322 q^{79} +1150.31 q^{80} -668.412 q^{81} +1022.05 q^{82} -45.5071 q^{83} +100.634 q^{84} +1408.26 q^{85} +1100.65 q^{87} +437.376 q^{88} +1615.18 q^{89} +100.441 q^{90} +893.643 q^{91} +176.107 q^{92} -867.487 q^{93} +557.880 q^{94} +58.6460 q^{95} -298.308 q^{96} +1569.66 q^{97} -349.864 q^{98} +44.7390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	$ 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) $ 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * 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 $

$2$	3.05512	1.08015	0.540074	−	0.841618i	$-0.318396\pi$
$2$	3.05512	1.08015	0.540074	+	0.841618i	$0.318396\pi$
$3$	4.99167	0.960647	0.480323	−	0.877091i	$-0.340519\pi$
$3$	4.99167	0.960647	0.480323	+	0.877091i	$0.340519\pi$
$4$	1.33374	0.166718
$5$	−15.7813	−1.41152	−0.705759	−	0.708452i	$-0.749394\pi$
$5$	−15.7813	−1.41152	−0.705759	+	0.708452i	$0.749394\pi$
$6$	15.2501	1.03764
$7$	15.1156	0.816168	0.408084	−	0.912944i	$-0.366197\pi$
$7$	15.1156	0.816168	0.408084	+	0.912944i	$0.366197\pi$
$8$	−20.3662	−0.900068
$9$	−2.08325	−0.0771575
$10$	−48.2136	−1.52465
$11$	−21.4756	−0.588648	−0.294324	−	0.955706i	$-0.595094\pi$
$11$	−21.4756	−0.588648	−0.294324	+	0.955706i	$0.595094\pi$
$12$	6.65759	0.160157
$13$	59.1204	1.26131	0.630656	−	0.776063i	$-0.282786\pi$
$13$	59.1204	1.26131	0.630656	+	0.776063i	$0.282786\pi$
$14$	46.1801	0.881581
$15$	−78.7748	−1.35597
$16$	−72.8911	−1.13892
$17$	−89.2363	−1.27312	−0.636558	−	0.771228i	$-0.719643\pi$
$17$	−89.2363	−1.27312	−0.636558	+	0.771228i	$0.719643\pi$
$18$	−6.36458	−0.0833414
$19$	−3.71618	−0.0448711	−0.0224355	−	0.999748i	$-0.507142\pi$
$19$	−3.71618	−0.0448711	−0.0224355	+	0.999748i	$0.507142\pi$
$20$	−21.0481	−0.235325
$21$	75.4523	0.784049
$22$	−65.6104	−0.635827
$23$	132.040	1.19705	0.598526	−	0.801103i	$-0.295753\pi$
$23$	132.040	1.19705	0.598526	+	0.801103i	$0.295753\pi$
$24$	−101.661	−0.864647
$25$	124.048	0.992384
$26$	180.620	1.36240
$27$	−145.174	−1.03477
$28$	20.1603	0.136070
$29$	220.497	1.41191	0.705954	−	0.708257i	$-0.250518\pi$
$29$	220.497	1.41191	0.705954	+	0.708257i	$0.250518\pi$
$30$	−240.666	−1.46465
$31$	−173.787	−1.00687	−0.503437	−	0.864032i	$-0.667931\pi$
$31$	−173.787	−1.00687	−0.503437	+	0.864032i	$0.667931\pi$
$32$	−59.7611	−0.330137
$33$	−107.199	−0.565483
$34$	−272.627	−1.37515
$35$	−238.544	−1.15204
$36$	−2.77852	−0.0128635
$37$	341.140	1.51576	0.757880	−	0.652394i	$-0.226235\pi$
$37$	341.140	1.51576	0.757880	+	0.652394i	$0.226235\pi$
$38$	−11.3534	−0.0484674
$39$	295.109	1.21167
$40$	321.404	1.27046
$41$	334.536	1.27429	0.637144	−	0.770745i	$-0.280116\pi$
$41$	334.536	1.27429	0.637144	+	0.770745i	$0.280116\pi$
$42$	230.515	0.846888
$43$	0	0
$43$	0	0
$44$	−28.6428	−0.0981380
$45$	32.8763	0.108909
$46$	403.397	1.29299
$47$	182.605	0.566717	0.283358	−	0.959014i	$-0.408551\pi$
$47$	182.605	0.566717	0.283358	+	0.959014i	$0.408551\pi$
$48$	−363.848	−1.09410
$49$	−114.517	−0.333870
$50$	378.981	1.07192
$51$	−445.438	−1.22302
$52$	78.8513	0.210283
$53$	296.886	0.769442	0.384721	−	0.923033i	$-0.374298\pi$
$53$	296.886	0.769442	0.384721	+	0.923033i	$0.374298\pi$
$54$	−443.523	−1.11770
$55$	338.911	0.830888
$56$	−307.848	−0.734606
$57$	−18.5499	−0.0431053
$58$	673.646	1.52507
$59$	668.255	1.47457	0.737283	−	0.675584i	$-0.236109\pi$
$59$	668.255	1.47457	0.737283	+	0.675584i	$0.236109\pi$
$60$	−105.065	−0.226064
$61$	−461.669	−0.969026	−0.484513	−	0.874784i	$-0.661003\pi$
$61$	−461.669	−0.969026	−0.484513	+	0.874784i	$0.661003\pi$
$62$	−530.940	−1.08757
$63$	−31.4897	−0.0629735
$64$	400.551	0.782327
$65$	−932.994	−1.78036
$66$	−327.505	−0.610805
$67$	485.027	0.884411	0.442205	−	0.896914i	$-0.354196\pi$
$67$	485.027	0.884411	0.442205	+	0.896914i	$0.354196\pi$
$68$	−119.018	−0.212251
$69$	659.099	1.14994
$70$	−728.779	−1.24437
$71$	358.344	0.598981	0.299490	−	0.954099i	$-0.403183\pi$
$71$	358.344	0.598981	0.299490	+	0.954099i	$0.403183\pi$
$72$	42.4279	0.0694470
$73$	−136.162	−0.218309	−0.109155	−	0.994025i	$-0.534814\pi$
$73$	−136.162	−0.218309	−0.109155	+	0.994025i	$0.534814\pi$
$74$	1042.22	1.63724
$75$	619.206	0.953330
$76$	−4.95642	−0.00748080
$77$	−324.617	−0.480436
$78$	901.594	1.30879
$79$	−590.322	−0.840713	−0.420357	−	0.907359i	$-0.638095\pi$
$79$	−590.322	−0.840713	−0.420357	+	0.907359i	$0.638095\pi$
$80$	1150.31	1.60761
$81$	−668.412	−0.916889
$82$	1022.05	1.37642
$83$	−45.5071	−0.0601814	−0.0300907	−	0.999547i	$-0.509580\pi$
$83$	−45.5071	−0.0601814	−0.0300907	+	0.999547i	$0.509580\pi$
$84$	100.634	0.130715
$85$	1408.26	1.79703
$86$	0	0
$87$	1100.65	1.35635
$88$	437.376	0.529823
$89$	1615.18	1.92369	0.961847	−	0.273589i	$-0.0882109\pi$
$89$	1615.18	1.92369	0.961847	+	0.273589i	$0.0882109\pi$
$90$	100.441	0.117638
$91$	893.643	1.02944
$92$	176.107	0.199570
$93$	−867.487	−0.967250
$94$	557.880	0.612137
$95$	58.6460	0.0633363
$96$	−298.308	−0.317145
$97$	1569.66	1.64303	0.821517	−	0.570184i	$-0.193128\pi$
$97$	1569.66	1.64303	0.821517	+	0.570184i	$0.193128\pi$
$98$	−349.864	−0.360629
$99$	44.7390	0.0454186
$100$	165.448	0.165448
$101$	−1985.34	−1.95593	−0.977965	−	0.208771i	$-0.933054\pi$
$101$	−1985.34	−1.95593	−0.977965	+	0.208771i	$0.933054\pi$
$102$	−1360.87	−1.32104
$103$	119.966	0.114763	0.0573815	−	0.998352i	$-0.481725\pi$
$103$	119.966	0.114763	0.0573815	+	0.998352i	$0.481725\pi$
$104$	−1204.06	−1.13527
$105$	−1190.73	−1.10670
$106$	907.021	0.831110
$107$	−684.291	−0.618252	−0.309126	−	0.951021i	$-0.600036\pi$
$107$	−684.291	−0.618252	−0.309126	+	0.951021i	$0.600036\pi$
$108$	−193.624	−0.172514
$109$	−880.341	−0.773590	−0.386795	−	0.922166i	$-0.626418\pi$
$109$	−880.341	−0.773590	−0.386795	+	0.922166i	$0.626418\pi$
$110$	1035.41	0.897481
$111$	1702.86	1.45611
$112$	−1101.80	−0.929552
$113$	1051.95	0.875747	0.437874	−	0.899037i	$-0.355732\pi$
$113$	1051.95	0.875747	0.437874	+	0.899037i	$0.355732\pi$
$114$	−56.6723	−0.0465600
$115$	−2083.75	−1.68966
$116$	294.086	0.235390
$117$	−123.163	−0.0973196
$118$	2041.60	1.59275
$119$	−1348.86	−1.03908
$120$	1604.34	1.22047
$121$	−869.800	−0.653493
$122$	−1410.45	−1.04669
$123$	1669.89	1.22414
$124$	−231.787	−0.167864
$125$	15.0243	0.0107505
$126$	−96.2047	−0.0680206
$127$	−594.064	−0.415076	−0.207538	−	0.978227i	$-0.566545\pi$
$127$	−594.064	−0.415076	−0.207538	+	0.978227i	$0.566545\pi$
$128$	1701.82	1.17516
$129$	0	0
$130$	−2850.41	−1.92305
$131$	1980.10	1.32063	0.660313	−	0.750990i	$-0.270424\pi$
$131$	1980.10	1.32063	0.660313	+	0.750990i	$0.270424\pi$
$132$	−142.976	−0.0942760
$133$	−56.1725	−0.0366223
$134$	1481.82	0.955294
$135$	2291.03	1.46059
$136$	1817.41	1.14589
$137$	−692.962	−0.432144	−0.216072	−	0.976377i	$-0.569325\pi$
$137$	−692.962	−0.432144	−0.216072	+	0.976377i	$0.569325\pi$
$138$	2013.62	1.24211
$139$	2752.84	1.67981	0.839903	−	0.542737i	$-0.182612\pi$
$139$	2752.84	1.67981	0.839903	+	0.542737i	$0.182612\pi$
$140$	−318.155	−0.192065
$141$	911.504	0.544415
$142$	1094.78	0.646987
$143$	−1269.64	−0.742469
$144$	151.850	0.0878764
$145$	−3479.73	−1.99293
$146$	−415.991	−0.235806
$147$	−571.633	−0.320731
$148$	454.993	0.252704
$149$	−800.322	−0.440033	−0.220016	−	0.975496i	$-0.570611\pi$
$149$	−800.322	−0.440033	−0.220016	+	0.975496i	$0.570611\pi$
$150$	1891.75	1.02974
$151$	−1188.66	−0.640606	−0.320303	−	0.947315i	$-0.603785\pi$
$151$	−1188.66	−0.640606	−0.320303	+	0.947315i	$0.603785\pi$
$152$	75.6845	0.0403870
$153$	185.902	0.0982305
$154$	−991.743	−0.518941
$155$	2742.58	1.42122
$156$	393.599	0.202007
$157$	−127.963	−0.0650483	−0.0325242	−	0.999471i	$-0.510355\pi$
$157$	−127.963	−0.0650483	−0.0325242	+	0.999471i	$0.510355\pi$
$158$	−1803.50	−0.908094
$159$	1481.96	0.739162
$160$	943.105	0.465994
$161$	1995.87	0.976995
$162$	−2042.08	−0.990375
$163$	3889.35	1.86894	0.934470	−	0.356043i	$-0.115874\pi$
$163$	3889.35	1.86894	0.934470	+	0.356043i	$0.115874\pi$
$164$	446.184	0.212446
$165$	1691.73	0.798190
$166$	−139.030	−0.0650047
$167$	2043.08	0.946695	0.473348	−	0.880876i	$-0.343045\pi$
$167$	2043.08	0.946695	0.473348	+	0.880876i	$0.343045\pi$
$168$	−1536.68	−0.705697
$169$	1298.22	0.590906
$170$	4302.40	1.94105
$171$	7.74174	0.00346214
$172$	0	0
$173$	−2540.34	−1.11641	−0.558203	−	0.829704i	$-0.688509\pi$
$173$	−2540.34	−1.11641	−0.558203	+	0.829704i	$0.688509\pi$
$174$	3362.62	1.46505
$175$	1875.06	0.809952
$176$	1565.38	0.670425
$177$	3335.71	1.41654
$178$	4934.56	2.07787
$179$	−3910.87	−1.63303	−0.816514	−	0.577325i	$-0.804096\pi$
$179$	−3910.87	−1.63303	−0.816514	+	0.577325i	$0.804096\pi$
$180$	43.8485	0.0181571
$181$	570.165	0.234144	0.117072	−	0.993123i	$-0.462649\pi$
$181$	570.165	0.234144	0.117072	+	0.993123i	$0.462649\pi$
$182$	2730.18	1.11195
$183$	−2304.50	−0.930892
$184$	−2689.15	−1.07743
$185$	−5383.62	−2.13952
$186$	−2650.28	−1.04477
$187$	1916.40	0.749418
$188$	243.548	0.0944816
$189$	−2194.40	−0.844544
$190$	179.170	0.0684126
$191$	2303.16	0.872518	0.436259	−	0.899821i	$-0.356303\pi$
$191$	2303.16	0.872518	0.436259	+	0.899821i	$0.356303\pi$
$192$	1999.42	0.751540
$193$	2322.35	0.866147	0.433074	−	0.901359i	$-0.357429\pi$
$193$	2322.35	0.866147	0.433074	+	0.901359i	$0.357429\pi$
$194$	4795.48	1.77472
$195$	−4657.20	−1.71030
$196$	−152.737	−0.0556620
$197$	3293.02	1.19095	0.595476	−	0.803373i	$-0.296963\pi$
$197$	3293.02	1.19095	0.595476	+	0.803373i	$0.296963\pi$
$198$	136.683	0.0490588
$199$	3266.88	1.16373	0.581866	−	0.813284i	$-0.302323\pi$
$199$	3266.88	1.16373	0.581866	+	0.813284i	$0.302323\pi$
$200$	−2526.39	−0.893212
$201$	2421.10	0.849607
$202$	−6065.45	−2.11269
$203$	3332.96	1.15235
$204$	−594.099	−0.203898
$205$	−5279.40	−1.79868
$206$	366.510	0.123961
$207$	−275.072	−0.0923615
$208$	−4309.35	−1.43654
$209$	79.8071	0.0264133
$210$	−3637.82	−1.19540
$211$	−2236.86	−0.729819	−0.364909	−	0.931043i	$-0.618900\pi$
$211$	−2236.86	−0.729819	−0.364909	+	0.931043i	$0.618900\pi$
$212$	395.969	0.128279
$213$	1788.73	0.575409
$214$	−2090.59	−0.667803
$215$	0	0
$216$	2956.64	0.931361
$217$	−2626.90	−0.821778
$218$	−2689.54	−0.835591
$219$	−679.676	−0.209718
$220$	452.020	0.138524
$221$	−5275.69	−1.60580
$222$	5202.44	1.57281
$223$	−5277.70	−1.58485	−0.792423	−	0.609972i	$-0.791181\pi$
$223$	−5277.70	−1.58485	−0.792423	+	0.609972i	$0.791181\pi$
$224$	−903.327	−0.269447
$225$	−258.423	−0.0765698
$226$	3213.84	0.945936
$227$	5243.93	1.53327	0.766635	−	0.642084i	$-0.221930\pi$
$227$	5243.93	1.53327	0.766635	+	0.642084i	$0.221930\pi$
$228$	−24.7408	−0.00718641
$229$	1658.73	0.478655	0.239328	−	0.970939i	$-0.423073\pi$
$229$	1658.73	0.478655	0.239328	+	0.970939i	$0.423073\pi$
$230$	−6366.11	−1.82508
$231$	−1620.38	−0.461529
$232$	−4490.70	−1.27081
$233$	290.160	0.0815837	0.0407919	−	0.999168i	$-0.487012\pi$
$233$	290.160	0.0815837	0.0407919	+	0.999168i	$0.487012\pi$
$234$	−376.277	−0.105120
$235$	−2881.74	−0.799931
$236$	891.278	0.245836
$237$	−2946.69	−0.807629
$238$	−4120.94	−1.12236
$239$	5851.40	1.58366	0.791832	−	0.610739i	$-0.209128\pi$
$239$	5851.40	1.58366	0.791832	+	0.610739i	$0.209128\pi$
$240$	5741.98	1.54435
$241$	1736.35	0.464100	0.232050	−	0.972704i	$-0.425457\pi$
$241$	1736.35	0.464100	0.232050	+	0.972704i	$0.425457\pi$
$242$	−2657.34	−0.705869
$243$	583.204	0.153961
$244$	−615.746	−0.161554
$245$	1807.23	0.471264
$246$	5101.72	1.32225
$247$	−219.702	−0.0565964
$248$	3539.38	0.906254
$249$	−227.156	−0.0578130
$250$	45.9011	0.0116122
$251$	−6882.85	−1.73084	−0.865421	−	0.501045i	$-0.832949\pi$
$251$	−6882.85	−1.73084	−0.865421	+	0.501045i	$0.832949\pi$
$252$	−41.9991	−0.0104988
$253$	−2835.63	−0.704642
$254$	−1814.93	−0.448343
$255$	7029.57	1.72631
$256$	1994.85	0.487024
$257$	−1572.19	−0.381598	−0.190799	−	0.981629i	$-0.561108\pi$
$257$	−1572.19	−0.381598	−0.190799	+	0.981629i	$0.561108\pi$
$258$	0	0
$259$	5156.56	1.23711
$260$	−1244.37	−0.296818
$261$	−459.352	−0.108939
$262$	6049.43	1.42647
$263$	−3425.31	−0.803095	−0.401547	−	0.915838i	$-0.631527\pi$
$263$	−3425.31	−0.803095	−0.401547	+	0.915838i	$0.631527\pi$
$264$	2183.24	0.508973
$265$	−4685.23	−1.08608
$266$	−171.613	−0.0395575
$267$	8062.44	1.84799
$268$	646.901	0.147447
$269$	3907.21	0.885601	0.442801	−	0.896620i	$-0.353985\pi$
$269$	3907.21	0.885601	0.442801	+	0.896620i	$0.353985\pi$
$270$	6999.35	1.57766
$271$	2862.10	0.641551	0.320775	−	0.947155i	$-0.396057\pi$
$271$	2862.10	0.641551	0.320775	+	0.947155i	$0.396057\pi$
$272$	6504.53	1.44998
$273$	4460.77	0.988930
$274$	−2117.08	−0.466779
$275$	−2664.00	−0.584165
$276$	879.066	0.191716
$277$	1361.01	0.295218	0.147609	−	0.989046i	$-0.452842\pi$
$277$	1361.01	0.295218	0.147609	+	0.989046i	$0.452842\pi$
$278$	8410.26	1.81444
$279$	362.042	0.0776879
$280$	4858.23	1.03691
$281$	3455.07	0.733494	0.366747	−	0.930321i	$-0.380471\pi$
$281$	3455.07	0.733494	0.366747	+	0.930321i	$0.380471\pi$
$282$	2784.75	0.588048
$283$	−547.918	−0.115090	−0.0575448	−	0.998343i	$-0.518327\pi$
$283$	−547.918	−0.115090	−0.0575448	+	0.998343i	$0.518327\pi$
$284$	477.938	0.0998606
$285$	292.741	0.0608439
$286$	−3878.91	−0.801975
$287$	5056.73	1.04003
$288$	124.497	0.0254725
$289$	3050.12	0.620827
$290$	−10631.0	−2.15266
$291$	7835.20	1.57838
$292$	−181.605	−0.0363960
$293$	4349.89	0.867315	0.433657	−	0.901078i	$-0.357223\pi$
$293$	4349.89	0.867315	0.433657	+	0.901078i	$0.357223\pi$
$294$	−1746.41	−0.346437
$295$	−10545.9	−2.08138
$296$	−6947.73	−1.36429
$297$	3117.69	0.609114
$298$	−2445.08	−0.475300
$299$	7806.24	1.50985
$300$	825.860	0.158937
$301$	0	0
$302$	−3631.49	−0.691949
$303$	−9910.16	−1.87896
$304$	270.876	0.0511047
$305$	7285.71	1.36780
$306$	567.952	0.106103
$307$	4215.70	0.783723	0.391861	−	0.920024i	$-0.371831\pi$
$307$	4215.70	0.783723	0.391861	+	0.920024i	$0.371831\pi$
$308$	−432.955	−0.0800971
$309$	598.829	0.110247
$310$	8378.90	1.53513
$311$	3421.26	0.623801	0.311900	−	0.950115i	$-0.399034\pi$
$311$	3421.26	0.623801	0.311900	+	0.950115i	$0.399034\pi$
$312$	−6010.26	−1.09059
$313$	−5650.32	−1.02037	−0.510184	−	0.860065i	$-0.670423\pi$
$313$	−5650.32	−1.02037	−0.510184	+	0.860065i	$0.670423\pi$
$314$	−390.943	−0.0702617
$315$	496.947	0.0888882
$316$	−787.336	−0.140162
$317$	−2209.08	−0.391402	−0.195701	−	0.980664i	$-0.562698\pi$
$317$	−2209.08	−0.391402	−0.195701	+	0.980664i	$0.562698\pi$
$318$	4527.55	0.798404
$319$	−4735.31	−0.831117
$320$	−6321.20	−1.10427
$321$	−3415.75	−0.593921
$322$	6097.60	1.05530
$323$	331.618	0.0571261
$324$	−891.489	−0.152862
$325$	7333.76	1.25170
$326$	11882.4	2.01873
$327$	−4394.37	−0.743147
$328$	−6813.23	−1.14694
$329$	2760.19	0.462536
$330$	5168.44	0.862162
$331$	−5378.50	−0.893140	−0.446570	−	0.894749i	$-0.647355\pi$
$331$	−5378.50	−0.893140	−0.446570	+	0.894749i	$0.647355\pi$
$332$	−60.6947	−0.0100333
$333$	−710.682	−0.116952
$334$	6241.84	1.02257
$335$	−7654.34	−1.24836
$336$	−5499.80	−0.892971
$337$	−3423.39	−0.553365	−0.276683	−	0.960961i	$-0.589235\pi$
$337$	−3423.39	−0.553365	−0.276683	+	0.960961i	$0.589235\pi$
$338$	3966.22	0.638266
$339$	5251.00	0.841284
$340$	1878.25	0.299596
$341$	3732.18	0.592694
$342$	23.6519	0.00373962
$343$	−6915.67	−1.08866
$344$	0	0
$345$	−10401.4	−1.62317
$346$	−7761.03	−1.20588
$347$	−2323.39	−0.359441	−0.179720	−	0.983718i	$-0.557519\pi$
$347$	−2323.39	−0.359441	−0.179720	+	0.983718i	$0.557519\pi$
$348$	1467.98	0.226127
$349$	−11472.1	−1.75956	−0.879782	−	0.475378i	$-0.842311\pi$
$349$	−11472.1	−1.75956	−0.879782	+	0.475378i	$0.842311\pi$
$350$	5728.54	0.874867
$351$	−8582.74	−1.30516
$352$	1283.40	0.194334
$353$	−7136.51	−1.07603	−0.538014	−	0.842936i	$-0.680825\pi$
$353$	−7136.51	−1.07603	−0.538014	+	0.842936i	$0.680825\pi$
$354$	10191.0	1.53007
$355$	−5655.12	−0.845472
$356$	2154.23	0.320713
$357$	−6733.08	−0.998186
$358$	−11948.2	−1.76391
$359$	−3801.33	−0.558848	−0.279424	−	0.960168i	$-0.590144\pi$
$359$	−3801.33	−0.558848	−0.279424	+	0.960168i	$0.590144\pi$
$360$	−669.566	−0.0980257
$361$	−6845.19	−0.997987
$362$	1741.92	0.252910
$363$	−4341.75	−0.627776
$364$	1191.89	0.171626
$365$	2148.81	0.308147
$366$	−7040.51	−1.00550
$367$	−970.263	−0.138004	−0.0690018	−	0.997617i	$-0.521981\pi$
$367$	−970.263	−0.138004	−0.0690018	+	0.997617i	$0.521981\pi$
$368$	−9624.52	−1.36335
$369$	−696.923	−0.0983208
$370$	−16447.6	−2.31100
$371$	4487.62	0.627994
$372$	−1157.00	−0.161258
$373$	−4565.98	−0.633827	−0.316913	−	0.948454i	$-0.602646\pi$
$373$	−4565.98	−0.633827	−0.316913	+	0.948454i	$0.602646\pi$
$374$	5854.83	0.809481
$375$	74.9965	0.0103275
$376$	−3718.97	−0.510083
$377$	13035.9	1.78086
$378$	−6704.14	−0.912232
$379$	1211.00	0.164129	0.0820643	−	0.996627i	$-0.473849\pi$
$379$	1211.00	0.164129	0.0820643	+	0.996627i	$0.473849\pi$
$380$	78.2186	0.0105593
$381$	−2965.37	−0.398741
$382$	7036.43	0.942447
$383$	−4576.99	−0.610635	−0.305317	−	0.952251i	$-0.598763\pi$
$383$	−4576.99	−0.610635	−0.305317	+	0.952251i	$0.598763\pi$
$384$	8494.92	1.12892
$385$	5122.86	0.678144
$386$	7095.05	0.935566
$387$	0	0
$388$	2093.51	0.273923
$389$	−1490.12	−0.194221	−0.0971105	−	0.995274i	$-0.530960\pi$
$389$	−1490.12	−0.194221	−0.0971105	+	0.995274i	$0.530960\pi$
$390$	−14228.3	−1.84738
$391$	−11782.7	−1.52399
$392$	2332.28	0.300506
$393$	9884.00	1.26866
$394$	10060.5	1.28640
$395$	9316.01	1.18668
$396$	59.6703	0.00757208
$397$	3177.79	0.401734	0.200867	−	0.979618i	$-0.435624\pi$
$397$	3177.79	0.401734	0.200867	+	0.979618i	$0.435624\pi$
$398$	9980.69	1.25700
$399$	−280.394	−0.0351811
$400$	−9041.99	−1.13025
$401$	−7617.68	−0.948651	−0.474325	−	0.880350i	$-0.657308\pi$
$401$	−7617.68	−0.948651	−0.474325	+	0.880350i	$0.657308\pi$
$402$	7396.73	0.917700
$403$	−10274.4	−1.26998
$404$	−2647.93	−0.326088
$405$	10548.4	1.29421
$406$	10182.6	1.24471
$407$	−7326.19	−0.892249
$408$	9071.88	1.10080
$409$	1427.26	0.172551	0.0862753	−	0.996271i	$-0.472504\pi$
$409$	1427.26	0.172551	0.0862753	+	0.996271i	$0.472504\pi$
$410$	−16129.2	−1.94284
$411$	−3459.04	−0.415138
$412$	160.003	0.0191330
$413$	10101.1	1.20349
$414$	−840.378	−0.0997640
$415$	718.159	0.0849471
$416$	−3533.10	−0.416405
$417$	13741.3	1.61370
$418$	243.820	0.0285302
$419$	−8478.74	−0.988576	−0.494288	−	0.869298i	$-0.664571\pi$
$419$	−8478.74	−0.988576	−0.494288	+	0.869298i	$0.664571\pi$
$420$	−1588.13	−0.184506
$421$	6824.96	0.790091	0.395045	−	0.918662i	$-0.370729\pi$
$421$	6824.96	0.790091	0.395045	+	0.918662i	$0.370729\pi$
$422$	−6833.87	−0.788312
$423$	−380.412	−0.0437264
$424$	−6046.44	−0.692550
$425$	−11069.6	−1.26342
$426$	5464.79	0.621526
$427$	−6978.42	−0.790888
$428$	−912.667	−0.103073
$429$	−6337.64	−0.713250
$430$	0	0
$431$	5594.86	0.625279	0.312639	−	0.949872i	$-0.398787\pi$
$431$	5594.86	0.625279	0.312639	+	0.949872i	$0.398787\pi$
$432$	10581.9	1.17852
$433$	6469.41	0.718014	0.359007	−	0.933335i	$-0.383115\pi$
$433$	6469.41	0.718014	0.359007	+	0.933335i	$0.383115\pi$
$434$	−8025.50	−0.887641
$435$	−17369.6	−1.91451
$436$	−1174.15	−0.128971
$437$	−490.684	−0.0537130
$438$	−2076.49	−0.226526
$439$	−5772.38	−0.627564	−0.313782	−	0.949495i	$-0.601596\pi$
$439$	−5772.38	−0.627564	−0.313782	+	0.949495i	$0.601596\pi$
$440$	−6902.34	−0.747855
$441$	238.569	0.0257606
$442$	−16117.8	−1.73450
$443$	12893.5	1.38282	0.691409	−	0.722463i	$-0.256990\pi$
$443$	12893.5	1.38282	0.691409	+	0.722463i	$0.256990\pi$
$444$	2271.17	0.242759
$445$	−25489.6	−2.71533
$446$	−16124.0	−1.71187
$447$	−3994.94	−0.422716
$448$	6054.59	0.638510
$449$	5360.01	0.563373	0.281687	−	0.959506i	$-0.409106\pi$
$449$	5360.01	0.563373	0.281687	+	0.959506i	$0.409106\pi$
$450$	−789.513	−0.0827067
$451$	−7184.36	−0.750107
$452$	1403.03	0.146002
$453$	−5933.38	−0.615396
$454$	16020.8	1.65616
$455$	−14102.8	−1.45308
$456$	377.792	0.0387976
$457$	327.885	0.0335620	0.0167810	−	0.999859i	$-0.494658\pi$
$457$	327.885	0.0335620	0.0167810	+	0.999859i	$0.494658\pi$
$458$	5067.62	0.517018
$459$	12954.8	1.31738
$460$	−2779.19	−0.281696
$461$	10444.8	1.05524	0.527618	−	0.849482i	$-0.323085\pi$
$461$	10444.8	1.05524	0.527618	+	0.849482i	$0.323085\pi$
$462$	−4950.45	−0.498519
$463$	−11801.3	−1.18456	−0.592282	−	0.805731i	$-0.701773\pi$
$463$	−11801.3	−1.18456	−0.592282	+	0.805731i	$0.701773\pi$
$464$	−16072.3	−1.60806
$465$	13690.0	1.36529
$466$	886.473	0.0881224
$467$	−8957.03	−0.887541	−0.443771	−	0.896140i	$-0.646359\pi$
$467$	−8957.03	−0.887541	−0.443771	+	0.896140i	$0.646359\pi$
$468$	−164.267	−0.0162249
$469$	7331.50	0.721828
$470$	−8804.04	−0.864043
$471$	−638.750	−0.0624885
$472$	−13609.8	−1.32721
$473$	0	0
$474$	−9002.48	−0.872358
$475$	−460.985	−0.0445293
$476$	−1799.03	−0.173232
$477$	−618.488	−0.0593682
$478$	17876.7	1.71059
$479$	777.002	0.0741172	0.0370586	−	0.999313i	$-0.488201\pi$
$479$	777.002	0.0741172	0.0370586	+	0.999313i	$0.488201\pi$
$480$	4707.67	0.447655
$481$	20168.4	1.91185
$482$	5304.76	0.501297
$483$	9962.70	0.938547
$484$	−1160.09	−0.108949
$485$	−24771.1	−2.31917
$486$	1781.76	0.166301
$487$	14184.9	1.31988	0.659938	−	0.751320i	$-0.270583\pi$
$487$	14184.9	1.31988	0.659938	+	0.751320i	$0.270583\pi$
$488$	9402.44	0.872189
$489$	19414.3	1.79539
$490$	5521.29	0.509034
$491$	−2677.72	−0.246117	−0.123059	−	0.992399i	$-0.539270\pi$
$491$	−2677.72	−0.246117	−0.123059	+	0.992399i	$0.539270\pi$
$492$	2227.20	0.204086
$493$	−19676.4	−1.79752
$494$	−671.216	−0.0611324
$495$	−706.038	−0.0641092
$496$	12667.5	1.14675
$497$	5416.60	0.488869
$498$	−693.989	−0.0624466
$499$	−11775.2	−1.05638	−0.528188	−	0.849127i	$-0.677129\pi$
$499$	−11775.2	−1.05638	−0.528188	+	0.849127i	$0.677129\pi$
$500$	20.0386	0.00179230
$501$	10198.4	0.909440
$502$	−21027.9	−1.86956
$503$	−1095.68	−0.0971248	−0.0485624	−	0.998820i	$-0.515464\pi$
$503$	−1095.68	−0.0971248	−0.0485624	+	0.998820i	$0.515464\pi$
$504$	641.326	0.0566804
$505$	31331.2	2.76083
$506$	−8663.18	−0.761117
$507$	6480.29	0.567652
$508$	−792.327	−0.0692005
$509$	2497.55	0.217489	0.108744	−	0.994070i	$-0.465317\pi$
$509$	2497.55	0.217489	0.108744	+	0.994070i	$0.465317\pi$
$510$	21476.2	1.86467
$511$	−2058.18	−0.178177
$512$	−7520.06	−0.649107
$513$	539.493	0.0464312
$514$	−4803.23	−0.412182
$515$	−1893.21	−0.161990
$516$	0	0
$517$	−3921.55	−0.333597
$518$	15753.9	1.33627
$519$	−12680.5	−1.07247
$520$	19001.5	1.60245
$521$	−9002.64	−0.757030	−0.378515	−	0.925595i	$-0.623565\pi$
$521$	−9002.64	−0.757030	−0.378515	+	0.925595i	$0.623565\pi$
$522$	−1403.37	−0.117671
$523$	11093.0	0.927465	0.463732	−	0.885975i	$-0.346510\pi$
$523$	11093.0	0.927465	0.463732	+	0.885975i	$0.346510\pi$
$524$	2640.94	0.220172
$525$	9359.70	0.778078
$526$	−10464.7	−0.867460
$527$	15508.1	1.28187
$528$	7813.84	0.644041
$529$	5267.49	0.432933
$530$	−14313.9	−1.17313
$531$	−1392.14	−0.113774
$532$	−74.9195	−0.00610559
$533$	19777.9	1.60727
$534$	24631.7	1.99610
$535$	10799.0	0.872673
$536$	−9878.17	−0.796030
$537$	−19521.8	−1.56876
$538$	11937.0	0.956579
$539$	2459.33	0.196532
$540$	3055.64	0.243507
$541$	14140.7	1.12376	0.561881	−	0.827218i	$-0.310078\pi$
$541$	14140.7	1.12376	0.561881	+	0.827218i	$0.310078\pi$
$542$	8744.05	0.692969
$543$	2846.08	0.224930
$544$	5332.86	0.420302
$545$	13892.9	1.09194
$546$	13628.2	1.06819
$547$	8289.93	0.647992	0.323996	−	0.946058i	$-0.394974\pi$
$547$	8289.93	0.647992	0.323996	+	0.946058i	$0.394974\pi$
$548$	−924.231	−0.0720460
$549$	961.772	0.0747677
$550$	−8138.84	−0.630984
$551$	−819.409	−0.0633539
$552$	−13423.3	−1.03503
$553$	−8923.09	−0.686163
$554$	4158.05	0.318878
$555$	−26873.3	−2.05533
$556$	3671.58	0.280053
$557$	−8299.84	−0.631374	−0.315687	−	0.948863i	$-0.602235\pi$
$557$	−8299.84	−0.631374	−0.315687	+	0.948863i	$0.602235\pi$
$558$	1106.08	0.0839143
$559$	0	0
$560$	17387.7	1.31208
$561$	9566.04	0.719926
$562$	10555.6	0.792282
$563$	22079.4	1.65282	0.826408	−	0.563071i	$-0.190380\pi$
$563$	22079.4	1.65282	0.826408	+	0.563071i	$0.190380\pi$
$564$	1215.71	0.0907635
$565$	−16601.1	−1.23613
$566$	−1673.96	−0.124314
$567$	−10103.5	−0.748336
$568$	−7298.11	−0.539123
$569$	6483.18	0.477661	0.238831	−	0.971061i	$-0.423236\pi$
$569$	6483.18	0.477661	0.238831	+	0.971061i	$0.423236\pi$
$570$	894.359	0.0657203
$571$	−8403.34	−0.615882	−0.307941	−	0.951405i	$-0.599640\pi$
$571$	−8403.34	−0.615882	−0.307941	+	0.951405i	$0.599640\pi$
$572$	−1693.38	−0.123783
$573$	11496.6	0.838181
$574$	15448.9	1.12339
$575$	16379.3	1.18793
$576$	−834.450	−0.0603624
$577$	−3579.80	−0.258282	−0.129141	−	0.991626i	$-0.541222\pi$
$577$	−3579.80	−0.258282	−0.129141	+	0.991626i	$0.541222\pi$
$578$	9318.48	0.670584
$579$	11592.4	0.832062
$580$	−4641.05	−0.332257
$581$	−687.869	−0.0491181
$582$	23937.4	1.70488
$583$	−6375.80	−0.452931
$584$	2773.10	0.196493
$585$	1943.66	0.137368
$586$	13289.4	0.936827
$587$	10896.7	0.766191	0.383096	−	0.923709i	$-0.374858\pi$
$587$	10896.7	0.766191	0.383096	+	0.923709i	$0.374858\pi$
$588$	−762.410	−0.0534715
$589$	645.824	0.0451795
$590$	−32218.9	−2.24819
$591$	16437.6	1.14408
$592$	−24866.1	−1.72633
$593$	−1858.08	−0.128672	−0.0643358	−	0.997928i	$-0.520493\pi$
$593$	−1858.08	−0.128672	−0.0643358	+	0.997928i	$0.520493\pi$
$594$	9524.92	0.657933
$595$	21286.8	1.46668
$596$	−1067.42	−0.0733612
$597$	16307.2	1.11794
$598$	23849.0	1.63087
$599$	5459.07	0.372373	0.186186	−	0.982514i	$-0.440387\pi$
$599$	5459.07	0.372373	0.186186	+	0.982514i	$0.440387\pi$
$600$	−12610.9	−0.858062
$601$	7307.36	0.495962	0.247981	−	0.968765i	$-0.420233\pi$
$601$	7307.36	0.495962	0.247981	+	0.968765i	$0.420233\pi$
$602$	0	0
$603$	−1010.43	−0.0682389
$604$	−1585.36	−0.106800
$605$	13726.5	0.922418
$606$	−30276.7	−2.02955
$607$	−548.992	−0.0367099	−0.0183550	−	0.999832i	$-0.505843\pi$
$607$	−548.992	−0.0367099	−0.0183550	+	0.999832i	$0.505843\pi$
$608$	222.083	0.0148136
$609$	16637.0	1.10701
$610$	22258.7	1.47742
$611$	10795.7	0.714806
$612$	247.945	0.0163768
$613$	−20952.2	−1.38051	−0.690255	−	0.723566i	$-0.742502\pi$
$613$	−20952.2	−1.38051	−0.690255	+	0.723566i	$0.742502\pi$
$614$	12879.5	0.846536
$615$	−26353.0	−1.72790
$616$	6611.22	0.432425
$617$	15844.2	1.03381	0.516907	−	0.856042i	$-0.327083\pi$
$617$	15844.2	1.03381	0.516907	+	0.856042i	$0.327083\pi$
$618$	1829.49	0.119083
$619$	879.578	0.0571135	0.0285567	−	0.999592i	$-0.490909\pi$
$619$	879.578	0.0571135	0.0285567	+	0.999592i	$0.490909\pi$
$620$	3657.89	0.236942
$621$	−19168.7	−1.23867
$622$	10452.4	0.673797
$623$	24414.5	1.57006
$624$	−21510.8	−1.38000
$625$	−15743.1	−1.00756
$626$	−17262.4	−1.10215
$627$	398.371	0.0253738
$628$	−170.670	−0.0108447
$629$	−30442.1	−1.92974
$630$	1518.23	0.0960123
$631$	−20975.5	−1.32333	−0.661667	−	0.749798i	$-0.730151\pi$
$631$	−20975.5	−1.32333	−0.661667	+	0.749798i	$0.730151\pi$
$632$	12022.6	0.756699
$633$	−11165.7	−0.701098
$634$	−6749.01	−0.422772
$635$	9375.07	0.585887
$636$	1976.54	0.123231
$637$	−6770.31	−0.421114
$638$	−14466.9	−0.897729
$639$	−746.521	−0.0462158
$640$	−26856.9	−1.65877
$641$	24275.9	1.49585	0.747925	−	0.663784i	$-0.231050\pi$
$641$	24275.9	1.49585	0.747925	+	0.663784i	$0.231050\pi$
$642$	−10435.5	−0.641523
$643$	19783.9	1.21338	0.606688	−	0.794940i	$-0.292498\pi$
$643$	19783.9	1.21338	0.606688	+	0.794940i	$0.292498\pi$
$644$	2661.97	0.162882
$645$	0	0
$646$	1013.13	0.0617046
$647$	7539.98	0.458157	0.229078	−	0.973408i	$-0.426429\pi$
$647$	7539.98	0.458157	0.229078	+	0.973408i	$0.426429\pi$
$648$	13613.0	0.825262
$649$	−14351.2	−0.868000
$650$	22405.5	1.35203
$651$	−13112.6	−0.789438
$652$	5187.38	0.311585
$653$	−1288.35	−0.0772081	−0.0386041	−	0.999255i	$-0.512291\pi$
$653$	−1288.35	−0.0772081	−0.0386041	+	0.999255i	$0.512291\pi$
$654$	−13425.3	−0.802708
$655$	−31248.4	−1.86409
$656$	−24384.7	−1.45131
$657$	283.660	0.0168442
$658$	8432.71	0.499607
$659$	13574.7	0.802420	0.401210	−	0.915986i	$-0.368590\pi$
$659$	13574.7	0.802420	0.401210	+	0.915986i	$0.368590\pi$
$660$	2256.33	0.133072
$661$	14332.4	0.843368	0.421684	−	0.906743i	$-0.361439\pi$
$661$	14332.4	0.843368	0.421684	+	0.906743i	$0.361439\pi$
$662$	−16432.0	−0.964722
$663$	−26334.5	−1.54260
$664$	926.807	0.0541673
$665$	886.472	0.0516931
$666$	−2171.22	−0.126326
$667$	29114.4	1.69013
$668$	2724.94	0.157831
$669$	−26344.5	−1.52248
$670$	−23384.9	−1.34841
$671$	9914.60	0.570416
$672$	−4509.11	−0.258843
$673$	−8301.11	−0.475460	−0.237730	−	0.971331i	$-0.576403\pi$
$673$	−8301.11	−0.475460	−0.237730	+	0.971331i	$0.576403\pi$
$674$	−10458.9	−0.597716
$675$	−18008.5	−1.02689
$676$	1731.49	0.0985145
$677$	11712.0	0.664888	0.332444	−	0.943123i	$-0.392127\pi$
$677$	11712.0	0.664888	0.332444	+	0.943123i	$0.392127\pi$
$678$	16042.4	0.908710
$679$	23726.3	1.34099
$680$	−28680.9	−1.61745
$681$	26176.0	1.47293
$682$	11402.2	0.640197
$683$	30661.5	1.71776	0.858881	−	0.512175i	$-0.171160\pi$
$683$	30661.5	1.71776	0.858881	+	0.512175i	$0.171160\pi$
$684$	10.3255	0.000577200 0
$685$	10935.8	0.609979
$686$	−21128.2	−1.17591
$687$	8279.84	0.459819
$688$	0	0
$689$	17552.0	0.970506
$690$	−31777.5	−1.75326
$691$	−2530.11	−0.139291	−0.0696454	−	0.997572i	$-0.522187\pi$
$691$	−2530.11	−0.139291	−0.0696454	+	0.997572i	$0.522187\pi$
$692$	−3388.15	−0.186125
$693$	676.259	0.0370692
$694$	−7098.21	−0.388249
$695$	−43443.3	−2.37108
$696$	−22416.1	−1.22080
$697$	−29852.8	−1.62232
$698$	−35048.6	−1.90059
$699$	1448.38	0.0783732
$700$	2500.85	0.135033
$701$	29878.4	1.60983	0.804915	−	0.593390i	$-0.202211\pi$
$701$	29878.4	1.60983	0.804915	+	0.593390i	$0.202211\pi$
$702$	−26221.3	−1.40977
$703$	−1267.74	−0.0680138
$704$	−8602.07	−0.460515
$705$	−14384.7	−0.768451
$706$	−21802.9	−1.16227
$707$	−30009.7	−1.59637
$708$	4448.97	0.236162
$709$	−1455.09	−0.0770765	−0.0385382	−	0.999257i	$-0.512270\pi$
$709$	−1455.09	−0.0770765	−0.0385382	+	0.999257i	$0.512270\pi$
$710$	−17277.0	−0.913234
$711$	1229.79	0.0648673
$712$	−32895.1	−1.73145
$713$	−22946.8	−1.20528
$714$	−20570.4	−1.07819
$715$	20036.6	1.04801
$716$	−5216.08	−0.272255
$717$	29208.3	1.52134
$718$	−11613.5	−0.603638
$719$	2748.33	0.142553	0.0712765	−	0.997457i	$-0.477293\pi$
$719$	2748.33	0.142553	0.0712765	+	0.997457i	$0.477293\pi$
$720$	−2396.39	−0.124039
$721$	1813.36	0.0936658
$722$	−20912.9	−1.07797
$723$	8667.29	0.445837
$724$	760.453	0.0390359
$725$	27352.3	1.40116
$726$	−13264.6	−0.678091
$727$	−29119.3	−1.48552	−0.742761	−	0.669556i	$-0.766484\pi$
$727$	−29119.3	−1.48552	−0.742761	+	0.669556i	$0.766484\pi$
$728$	−18200.1	−0.926567
$729$	20958.3	1.06479
$730$	6564.86	0.332844
$731$	0	0
$732$	−3073.60	−0.155196
$733$	22990.6	1.15850	0.579248	−	0.815151i	$-0.303346\pi$
$733$	22990.6	1.15850	0.579248	+	0.815151i	$0.303346\pi$
$734$	−2964.27	−0.149064
$735$	9021.08	0.452718
$736$	−7890.84	−0.395191
$737$	−10416.2	−0.520607
$738$	−2129.18	−0.106201
$739$	−12574.0	−0.625905	−0.312952	−	0.949769i	$-0.601318\pi$
$739$	−12574.0	−0.625905	−0.312952	+	0.949769i	$0.601318\pi$
$740$	−7180.36	−0.356696
$741$	−1096.68	−0.0543692
$742$	13710.2	0.678326
$743$	36672.3	1.81073	0.905367	−	0.424631i	$-0.139596\pi$
$743$	36672.3	1.81073	0.905367	+	0.424631i	$0.139596\pi$
$744$	17667.4	0.870590
$745$	12630.1	0.621115
$746$	−13949.6	−0.684626
$747$	94.8028	0.00464344
$748$	2555.98	0.124941
$749$	−10343.5	−0.504597
$750$	229.123	0.0111552
$751$	14516.0	0.705322	0.352661	−	0.935751i	$-0.385277\pi$
$751$	14516.0	0.705322	0.352661	+	0.935751i	$0.385277\pi$
$752$	−13310.3	−0.645446
$753$	−34356.9	−1.66273
$754$	39826.2	1.92359
$755$	18758.5	0.904227
$756$	−2926.76	−0.140800
$757$	25899.1	1.24348	0.621742	−	0.783222i	$-0.286425\pi$
$757$	25899.1	1.24348	0.621742	+	0.783222i	$0.286425\pi$
$758$	3699.74	0.177283
$759$	−14154.5	−0.676912
$760$	−1194.40	−0.0570070
$761$	−18599.9	−0.886002	−0.443001	−	0.896521i	$-0.646086\pi$
$761$	−18599.9	−0.886002	−0.443001	+	0.896521i	$0.646086\pi$
$762$	−9059.55	−0.430699
$763$	−13306.9	−0.631380
$764$	3071.82	0.145464
$765$	−2933.76	−0.138654
$766$	−13983.2	−0.659575
$767$	39507.5	1.85989
$768$	9957.62	0.467858
$769$	24888.9	1.16712	0.583560	−	0.812070i	$-0.301659\pi$
$769$	24888.9	1.16712	0.583560	+	0.812070i	$0.301659\pi$
$770$	15651.0	0.732495
$771$	−7847.87	−0.366581
$772$	3097.41	0.144402
$773$	41420.2	1.92727	0.963636	−	0.267217i	$-0.0861042\pi$
$773$	41420.2	1.92727	0.963636	+	0.267217i	$0.0861042\pi$
$774$	0	0
$775$	−21557.9	−0.999205
$776$	−31967.9	−1.47884
$777$	25739.8	1.18843
$778$	−4552.48	−0.209787
$779$	−1243.20	−0.0571786
$780$	−6211.49	−0.285137
$781$	−7695.64	−0.352589
$782$	−35997.7	−1.64613
$783$	−32010.5	−1.46100
$784$	8347.29	0.380252
$785$	2019.42	0.0918169
$786$	30196.8	1.37033
$787$	−9546.36	−0.432390	−0.216195	−	0.976350i	$-0.569365\pi$
$787$	−9546.36	−0.432390	−0.216195	+	0.976350i	$0.569365\pi$
$788$	4392.03	0.198553
$789$	−17098.0	−0.771491
$790$	28461.5	1.28179
$791$	15900.9	0.714757
$792$	−911.165	−0.0408798
$793$	−27294.0	−1.22224
$794$	9708.51	0.433932
$795$	−23387.1	−1.04334
$796$	4357.17	0.194015
$797$	1574.59	0.0699808	0.0349904	−	0.999388i	$-0.488860\pi$
$797$	1574.59	0.0699808	0.0349904	+	0.999388i	$0.488860\pi$
$798$	−856.637	−0.0380008
$799$	−16295.0	−0.721496
$800$	−7413.24	−0.327622
$801$	−3364.83	−0.148427
$802$	−23272.9	−1.02468
$803$	2924.16	0.128507
$804$	3229.11	0.141644
$805$	−31497.3	−1.37905
$806$	−31389.4	−1.37177
$807$	19503.5	0.850750
$808$	40433.9	1.76047
$809$	−2642.40	−0.114835	−0.0574176	−	0.998350i	$-0.518287\pi$
$809$	−2642.40	−0.114835	−0.0574176	+	0.998350i	$0.518287\pi$
$810$	32226.5	1.39793
$811$	−8604.81	−0.372572	−0.186286	−	0.982496i	$-0.559645\pi$
$811$	−8604.81	−0.372572	−0.186286	+	0.982496i	$0.559645\pi$
$812$	4445.30	0.192118
$813$	14286.7	0.616304
$814$	−22382.4	−0.963761
$815$	−61378.8	−2.63804
$816$	32468.5	1.39292
$817$	0	0
$818$	4360.43	0.186380
$819$	−1861.68	−0.0794292
$820$	−7041.35	−0.299871
$821$	−13653.9	−0.580417	−0.290209	−	0.956963i	$-0.593725\pi$
$821$	−13653.9	−0.580417	−0.290209	+	0.956963i	$0.593725\pi$
$822$	−10567.8	−0.448410
$823$	−35324.1	−1.49614	−0.748068	−	0.663622i	$-0.769018\pi$
$823$	−35324.1	−1.49614	−0.748068	+	0.663622i	$0.769018\pi$
$824$	−2443.25	−0.103294
$825$	−13297.8	−0.561176
$826$	30860.0	1.29995
$827$	36897.8	1.55147	0.775733	−	0.631061i	$-0.217380\pi$
$827$	36897.8	1.55147	0.775733	+	0.631061i	$0.217380\pi$
$828$	−366.875	−0.0153983
$829$	−25449.6	−1.06623	−0.533113	−	0.846044i	$-0.678978\pi$
$829$	−25449.6	−1.06623	−0.533113	+	0.846044i	$0.678978\pi$
$830$	2194.06	0.0917553
$831$	6793.72	0.283600
$832$	23680.8	0.986758
$833$	10219.1	0.425056
$834$	41981.2	1.74303
$835$	−32242.3	−1.33628
$836$	106.442	0.00440356
$837$	25229.4	1.04188
$838$	−25903.5	−1.06781
$839$	−11708.4	−0.481789	−0.240894	−	0.970551i	$-0.577441\pi$
$839$	−11708.4	−0.481789	−0.240894	+	0.970551i	$0.577441\pi$
$840$	24250.7	0.996104
$841$	24230.1	0.993486
$842$	20851.1	0.853414
$843$	17246.5	0.704629
$844$	−2983.39	−0.121674
$845$	−20487.6	−0.834075
$846$	−1162.20	−0.0472310
$847$	−13147.6	−0.533360
$848$	−21640.3	−0.876335
$849$	−2735.03	−0.110561
$850$	−33818.9	−1.36468
$851$	45044.1	1.81444
$852$	2385.71	0.0959308
$853$	−30324.8	−1.21723	−0.608617	−	0.793464i	$-0.708275\pi$
$853$	−30324.8	−1.21723	−0.608617	+	0.793464i	$0.708275\pi$
$854$	−21319.9	−0.854276
$855$	−122.174	−0.00488687
$856$	13936.4	0.556468
$857$	−13821.8	−0.550924	−0.275462	−	0.961312i	$-0.588831\pi$
$857$	−13821.8	−0.550924	−0.275462	+	0.961312i	$0.588831\pi$
$858$	−19362.2	−0.770415
$859$	−43930.5	−1.74493	−0.872463	−	0.488681i	$-0.837478\pi$
$859$	−43930.5	−1.74493	−0.872463	+	0.488681i	$0.837478\pi$
$860$	0	0
$861$	25241.5	0.999104
$862$	17093.0	0.675393
$863$	−644.396	−0.0254177	−0.0127089	−	0.999919i	$-0.504045\pi$
$863$	−644.396	−0.0254177	−0.0127089	+	0.999919i	$0.504045\pi$
$864$	8675.75	0.341615
$865$	40089.7	1.57583
$866$	19764.8	0.775561
$867$	15225.2	0.596395
$868$	−3503.61	−0.137005
$869$	12677.5	0.494884
$870$	−53066.3	−2.06795
$871$	28675.0	1.11552
$872$	17929.2	0.696284
$873$	−3269.99	−0.126772
$874$	−1499.10	−0.0580179
$875$	227.102	0.00877424
$876$	−906.511	−0.0349637
$877$	21633.7	0.832975	0.416488	−	0.909141i	$-0.363261\pi$
$877$	21633.7	0.832975	0.416488	+	0.909141i	$0.363261\pi$
$878$	−17635.3	−0.677862
$879$	21713.2	0.833183
$880$	−24703.6	−0.946317
$881$	−23264.2	−0.889661	−0.444830	−	0.895615i	$-0.646736\pi$
$881$	−23264.2	−0.889661	−0.444830	+	0.895615i	$0.646736\pi$
$882$	728.855	0.0278252
$883$	7201.01	0.274443	0.137222	−	0.990540i	$-0.456183\pi$
$883$	7201.01	0.274443	0.137222	+	0.990540i	$0.456183\pi$
$884$	−7036.40	−0.267715
$885$	−52641.6	−1.99947
$886$	39391.2	1.49365
$887$	−34582.1	−1.30908	−0.654540	−	0.756027i	$-0.727138\pi$
$887$	−34582.1	−1.30908	−0.654540	+	0.756027i	$0.727138\pi$
$888$	−34680.8	−1.31060
$889$	−8979.66	−0.338772
$890$	−77873.6	−2.93295
$891$	14354.5	0.539725
$892$	−7039.08	−0.264222
$893$	−678.593	−0.0254292
$894$	−12205.0	−0.456596
$895$	61718.4	2.30505
$896$	25724.1	0.959132
$897$	38966.2	1.45044
$898$	16375.5	0.608526
$899$	−38319.6	−1.42161
$900$	−344.670	−0.0127655
$901$	−26493.0	−0.979589
$902$	−21949.0	−0.810226
$903$	0	0
$904$	−21424.3	−0.788231
$905$	−8997.92	−0.330498
$906$	−18127.2	−0.664718
$907$	−38466.5	−1.40822	−0.704111	−	0.710090i	$-0.748654\pi$
$907$	−38466.5	−1.40822	−0.704111	+	0.710090i	$0.748654\pi$
$908$	6994.05	0.255623
$909$	4135.97	0.150915
$910$	−43085.7	−1.56954
$911$	−40167.6	−1.46083	−0.730413	−	0.683005i	$-0.760673\pi$
$911$	−40167.6	−1.46083	−0.730413	+	0.683005i	$0.760673\pi$
$912$	1352.13	0.0490936
$913$	977.291	0.0354256
$914$	1001.73	0.0362519
$915$	36367.8	1.31397
$916$	2212.32	0.0798002
$917$	29930.5	1.07785
$918$	39578.4	1.42296
$919$	11458.8	0.411305	0.205653	−	0.978625i	$-0.434068\pi$
$919$	11458.8	0.411305	0.205653	+	0.978625i	$0.434068\pi$
$920$	42438.1	1.52081
$921$	21043.4	0.752881
$922$	31910.1	1.13981
$923$	21185.4	0.755501
$924$	−2161.17	−0.0769450
$925$	42317.8	1.50422
$926$	−36054.4	−1.27950
$927$	−249.919	−0.00885482
$928$	−13177.2	−0.466123
$929$	6550.23	0.231330	0.115665	−	0.993288i	$-0.463100\pi$
$929$	6550.23	0.231330	0.115665	+	0.993288i	$0.463100\pi$
$930$	41824.7	1.47472
$931$	425.567	0.0149811
$932$	386.998	0.0136014
$933$	17077.8	0.599252
$934$	−27364.8	−0.958675
$935$	−30243.2	−1.05782
$936$	2508.36	0.0875942
$937$	−6402.67	−0.223230	−0.111615	−	0.993752i	$-0.535602\pi$
$937$	−6402.67	−0.223230	−0.111615	+	0.993752i	$0.535602\pi$
$938$	22398.6	0.779680
$939$	−28204.5	−0.980214
$940$	−3843.49	−0.133363
$941$	21377.3	0.740573	0.370286	−	0.928918i	$-0.379260\pi$
$941$	21377.3	0.740573	0.370286	+	0.928918i	$0.379260\pi$
$942$	−1951.46	−0.0674967
$943$	44172.1	1.52539
$944$	−48709.8	−1.67942
$945$	34630.3	1.19209
$946$	0	0
$947$	4062.88	0.139415	0.0697074	−	0.997567i	$-0.477793\pi$
$947$	4062.88	0.139415	0.0697074	+	0.997567i	$0.477793\pi$
$948$	−3930.12	−0.134646
$949$	−8049.95	−0.275356
$950$	−1408.36	−0.0480982
$951$	−11027.0	−0.375999
$952$	27471.2	0.935240
$953$	25971.9	0.882803	0.441402	−	0.897310i	$-0.354481\pi$
$953$	25971.9	0.882803	0.441402	+	0.897310i	$0.354481\pi$
$954$	−1889.55	−0.0641264
$955$	−36346.8	−1.23157
$956$	7804.25	0.264025
$957$	−23637.1	−0.798410
$958$	2373.83	0.0800575
$959$	−10474.6	−0.352702
$960$	−31553.3	−1.06081
$961$	410.955	0.0137946
$962$	61616.7	2.06507
$963$	1425.55	0.0477028
$964$	2315.84	0.0773737
$965$	−36649.6	−1.22258
$966$	30437.2	1.01377
$967$	−30978.6	−1.03020	−0.515100	−	0.857130i	$-0.672245\pi$
$967$	−30978.6	−1.03020	−0.515100	+	0.857130i	$0.672245\pi$
$968$	17714.5	0.588188
$969$	1655.33	0.0548780
$970$	−75678.7	−2.50505
$971$	−15282.5	−0.505085	−0.252543	−	0.967586i	$-0.581267\pi$
$971$	−15282.5	−0.505085	−0.252543	+	0.967586i	$0.581267\pi$
$972$	777.843	0.0256680
$973$	41611.0	1.37100
$974$	43336.6	1.42566
$975$	36607.7	1.20245
$976$	33651.5	1.10365
$977$	19872.6	0.650748	0.325374	−	0.945585i	$-0.394510\pi$
$977$	19872.6	0.650748	0.325374	+	0.945585i	$0.394510\pi$
$978$	59313.0	1.93929
$979$	−34686.9	−1.13238
$980$	2410.37	0.0785679
$981$	1833.97	0.0596883
$982$	−8180.73	−0.265843
$983$	−23591.4	−0.765463	−0.382732	−	0.923860i	$-0.625017\pi$
$983$	−23591.4	−0.765463	−0.382732	+	0.923860i	$0.625017\pi$
$984$	−34009.4	−1.10181
$985$	−51967.9	−1.68105
$986$	−60113.7	−1.94159
$987$	13778.0	0.444334
$988$	−293.026	−0.00943561
$989$	0	0
$990$	−2157.03	−0.0692474
$991$	43277.7	1.38725	0.693624	−	0.720337i	$-0.256013\pi$
$991$	43277.7	1.38725	0.693624	+	0.720337i	$0.256013\pi$
$992$	10385.7	0.332406
$993$	−26847.7	−0.857992
$994$	16548.3	0.528050
$995$	−51555.4	−1.64263
$996$	−302.968	−0.00963845
$997$	−8111.07	−0.257653	−0.128826	−	0.991667i	$-0.541121\pi$
$997$	−8111.07	−0.257653	−0.128826	+	0.991667i	$0.541121\pi$
$998$	−35974.7	−1.14104
$999$	−49524.7	−1.56846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.e.1.8	yes	10
43.42	odd	2	inner	1849.4.a.e.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.e.1.3	✓	10	43.42	odd	2	inner
1849.4.a.e.1.8	yes	10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+3.05512 q^{2} +4.99167 q^{3} +1.33374 q^{4} -15.7813 q^{5} +15.2501 q^{6} +15.1156 q^{7} -20.3662 q^{8} -2.08325 q^{9} +O(q^{10})\)	\(q+3.05512 q^{2} +4.99167 q^{3} +1.33374 q^{4} -15.7813 q^{5} +15.2501 q^{6} +15.1156 q^{7} -20.3662 q^{8} -2.08325 q^{9} -48.2136 q^{10} -21.4756 q^{11} +6.65759 q^{12} +59.1204 q^{13} +46.1801 q^{14} -78.7748 q^{15} -72.8911 q^{16} -89.2363 q^{17} -6.36458 q^{18} -3.71618 q^{19} -21.0481 q^{20} +75.4523 q^{21} -65.6104 q^{22} +132.040 q^{23} -101.661 q^{24} +124.048 q^{25} +180.620 q^{26} -145.174 q^{27} +20.1603 q^{28} +220.497 q^{29} -240.666 q^{30} -173.787 q^{31} -59.7611 q^{32} -107.199 q^{33} -272.627 q^{34} -238.544 q^{35} -2.77852 q^{36} +341.140 q^{37} -11.3534 q^{38} +295.109 q^{39} +321.404 q^{40} +334.536 q^{41} +230.515 q^{42} -28.6428 q^{44} +32.8763 q^{45} +403.397 q^{46} +182.605 q^{47} -363.848 q^{48} -114.517 q^{49} +378.981 q^{50} -445.438 q^{51} +78.8513 q^{52} +296.886 q^{53} -443.523 q^{54} +338.911 q^{55} -307.848 q^{56} -18.5499 q^{57} +673.646 q^{58} +668.255 q^{59} -105.065 q^{60} -461.669 q^{61} -530.940 q^{62} -31.4897 q^{63} +400.551 q^{64} -932.994 q^{65} -327.505 q^{66} +485.027 q^{67} -119.018 q^{68} +659.099 q^{69} -728.779 q^{70} +358.344 q^{71} +42.4279 q^{72} -136.162 q^{73} +1042.22 q^{74} +619.206 q^{75} -4.95642 q^{76} -324.617 q^{77} +901.594 q^{78} -590.322 q^{79} +1150.31 q^{80} -668.412 q^{81} +1022.05 q^{82} -45.5071 q^{83} +100.634 q^{84} +1408.26 q^{85} +1100.65 q^{87} +437.376 q^{88} +1615.18 q^{89} +100.441 q^{90} +893.643 q^{91} +176.107 q^{92} -867.487 q^{93} +557.880 q^{94} +58.6460 q^{95} -298.308 q^{96} +1569.66 q^{97} -349.864 q^{98} +44.7390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9}+O(q^{10}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9	\( 10 q + 44 q^{4} + 30 q^{6} + 80 q^{9} + 118 q^{10} - 18 q^{11} + 166 q^{13} + 120 q^{14} + 120 q^{15} + 196 q^{16} + 356 q^{17} + 28 q^{21} + 436 q^{23} + 498 q^{24} + 532 q^{25} + 176 q^{31} + 320 q^{35} - 1422 q^{36} - 1118 q^{38} + 1178 q^{40} + 868 q^{41} + 1740 q^{44} - 1142 q^{47} + 1234 q^{49} - 1612 q^{52} + 1086 q^{53} - 840 q^{54} + 868 q^{56} - 728 q^{57} - 1966 q^{58} + 356 q^{59} - 288 q^{60} + 5876 q^{64} - 1012 q^{66} + 3054 q^{67} + 350 q^{68} + 962 q^{74} - 1352 q^{78} - 1086 q^{79} - 3478 q^{81} + 6282 q^{83} + 5396 q^{84} - 3658 q^{87} + 2236 q^{90} + 7578 q^{92} + 2838 q^{95} + 9266 q^{96} - 116 q^{97} - 2086 q^{99}+O(q^{100}) \) 10 * q + 44 * q^4 + 30 * q^6 + 80 * q^9 + 118 * q^10 - 18 * q^11 + 166 * q^13 + 120 * q^14 + 120 * q^15 + 196 * q^16 + 356 * q^17 + 28 * q^21 + 436 * q^23 + 498 * q^24 + 532 * q^25 + 176 * q^31 + 320 * q^35 - 1422 * q^36 - 1118 * q^38 + 1178 * q^40 + 868 * q^41 + 1740 * q^44 - 1142 * q^47 + 1234 * q^49 - 1612 * q^52 + 1086 * q^53 - 840 * q^54 + 868 * q^56 - 728 * q^57 - 1966 * q^58 + 356 * q^59 - 288 * q^60 + 5876 * q^64 - 1012 * q^66 + 3054 * q^67 + 350 * q^68 + 962 * q^74 - 1352 * q^78 - 1086 * q^79 - 3478 * q^81 + 6282 * q^83 + 5396 * q^84 - 3658 * q^87 + 2236 * q^90 + 7578 * q^92 + 2838 * q^95 + 9266 * q^96 - 116 * q^97 - 2086 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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