LMFDB - Embedded newform 1849.4.a.m.1.12

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			1.12
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)

$f(q)$	$=$	$q-4.78359 q^{2} +8.84041 q^{3} +14.8827 q^{4} +13.5668 q^{5} -42.2888 q^{6} +6.63547 q^{7} -32.9240 q^{8} +51.1528 q^{9} +O(q^{10})$	\(q-4.78359 q^{2} +8.84041 q^{3} +14.8827 q^{4} +13.5668 q^{5} -42.2888 q^{6} +6.63547 q^{7} -32.9240 q^{8} +51.1528 q^{9} -64.8979 q^{10} -70.0463 q^{11} +131.569 q^{12} +41.7562 q^{13} -31.7413 q^{14} +119.936 q^{15} +38.4332 q^{16} -43.1782 q^{17} -244.694 q^{18} +77.3658 q^{19} +201.910 q^{20} +58.6603 q^{21} +335.072 q^{22} +55.4463 q^{23} -291.061 q^{24} +59.0577 q^{25} -199.744 q^{26} +213.520 q^{27} +98.7537 q^{28} +209.615 q^{29} -573.724 q^{30} -219.037 q^{31} +79.5436 q^{32} -619.237 q^{33} +206.547 q^{34} +90.0220 q^{35} +761.291 q^{36} +166.834 q^{37} -370.086 q^{38} +369.142 q^{39} -446.673 q^{40} -86.8098 q^{41} -280.606 q^{42} -1042.48 q^{44} +693.979 q^{45} -265.232 q^{46} +245.390 q^{47} +339.765 q^{48} -298.971 q^{49} -282.508 q^{50} -381.713 q^{51} +621.445 q^{52} +446.617 q^{53} -1021.39 q^{54} -950.303 q^{55} -218.466 q^{56} +683.945 q^{57} -1002.71 q^{58} +512.244 q^{59} +1784.97 q^{60} -139.120 q^{61} +1047.78 q^{62} +339.423 q^{63} -687.969 q^{64} +566.498 q^{65} +2962.18 q^{66} -279.324 q^{67} -642.609 q^{68} +490.168 q^{69} -430.628 q^{70} +147.165 q^{71} -1684.15 q^{72} -164.295 q^{73} -798.066 q^{74} +522.094 q^{75} +1151.41 q^{76} -464.790 q^{77} -1765.82 q^{78} +253.550 q^{79} +521.414 q^{80} +506.482 q^{81} +415.262 q^{82} +893.764 q^{83} +873.023 q^{84} -585.790 q^{85} +1853.08 q^{87} +2306.20 q^{88} +605.500 q^{89} -3319.71 q^{90} +277.072 q^{91} +825.191 q^{92} -1936.38 q^{93} -1173.84 q^{94} +1049.61 q^{95} +703.198 q^{96} +182.538 q^{97} +1430.15 q^{98} -3583.06 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.78359	−1.69125	−0.845627	−	0.533775i	$-0.820773\pi$
$2$	−4.78359	−1.69125	−0.845627	+	0.533775i	$0.820773\pi$
$3$	8.84041	1.70134	0.850668	−	0.525703i	$-0.176198\pi$
$3$	8.84041	1.70134	0.850668	+	0.525703i	$0.176198\pi$
$4$	14.8827	1.86034
$5$	13.5668	1.21345	0.606725	−	0.794912i	$-0.292483\pi$
$5$	13.5668	1.21345	0.606725	+	0.794912i	$0.292483\pi$
$6$	−42.2888	−2.87739
$7$	6.63547	0.358282	0.179141	−	0.983823i	$-0.442668\pi$
$7$	6.63547	0.358282	0.179141	+	0.983823i	$0.442668\pi$
$8$	−32.9240	−1.45505
$9$	51.1528	1.89455
$10$	−64.8979	−2.05225
$11$	−70.0463	−1.91998	−0.959988	−	0.280040i	$-0.909652\pi$
$11$	−70.0463	−1.91998	−0.959988	+	0.280040i	$0.909652\pi$
$12$	131.569	3.16506
$13$	41.7562	0.890853	0.445427	−	0.895318i	$-0.353052\pi$
$13$	41.7562	0.890853	0.445427	+	0.895318i	$0.353052\pi$
$14$	−31.7413	−0.605945
$15$	119.936	2.06449
$16$	38.4332	0.600518
$17$	−43.1782	−0.616016	−0.308008	−	0.951384i	$-0.599662\pi$
$17$	−43.1782	−0.616016	−0.308008	+	0.951384i	$0.599662\pi$
$18$	−244.694	−3.20416
$19$	77.3658	0.934154	0.467077	−	0.884217i	$-0.345307\pi$
$19$	77.3658	0.934154	0.467077	+	0.884217i	$0.345307\pi$
$20$	201.910	2.25743
$21$	58.6603	0.609558
$22$	335.072	3.24717
$23$	55.4463	0.502667	0.251334	−	0.967900i	$-0.419131\pi$
$23$	55.4463	0.502667	0.251334	+	0.967900i	$0.419131\pi$
$24$	−291.061	−2.47553
$25$	59.0577	0.472461
$26$	−199.744	−1.50666
$27$	213.520	1.52193
$28$	98.7537	0.666525
$29$	209.615	1.34223	0.671113	−	0.741355i	$-0.265816\pi$
$29$	209.615	1.34223	0.671113	+	0.741355i	$0.265816\pi$
$30$	−573.724	−3.49157
$31$	−219.037	−1.26904	−0.634520	−	0.772906i	$-0.718802\pi$
$31$	−219.037	−1.26904	−0.634520	+	0.772906i	$0.718802\pi$
$32$	79.5436	0.439420
$33$	−619.237	−3.26653
$34$	206.547	1.04184
$35$	90.0220	0.434757
$36$	761.291	3.52450
$37$	166.834	0.741280	0.370640	−	0.928777i	$-0.379138\pi$
$37$	166.834	0.741280	0.370640	+	0.928777i	$0.379138\pi$
$38$	−370.086	−1.57989
$39$	369.142	1.51564
$40$	−446.673	−1.76563
$41$	−86.8098	−0.330669	−0.165334	−	0.986238i	$-0.552870\pi$
$41$	−86.8098	−0.330669	−0.165334	+	0.986238i	$0.552870\pi$
$42$	−280.606	−1.03092
$43$	0	0
$43$	0	0
$44$	−1042.48	−3.57180
$45$	693.979	2.29894
$46$	−265.232	−0.850138
$47$	245.390	0.761571	0.380785	−	0.924663i	$-0.375654\pi$
$47$	245.390	0.761571	0.380785	+	0.924663i	$0.375654\pi$
$48$	339.765	1.02168
$49$	−298.971	−0.871634
$50$	−282.508	−0.799052
$51$	−381.713	−1.04805
$52$	621.445	1.65729
$53$	446.617	1.15750	0.578750	−	0.815505i	$-0.303541\pi$
$53$	446.617	1.15750	0.578750	+	0.815505i	$0.303541\pi$
$54$	−1021.39	−2.57396
$55$	−950.303	−2.32980
$56$	−218.466	−0.521317
$57$	683.945	1.58931
$58$	−1002.71	−2.27004
$59$	512.244	1.13031	0.565157	−	0.824983i	$-0.308816\pi$
$59$	512.244	1.13031	0.565157	+	0.824983i	$0.308816\pi$
$60$	1784.97	3.84064
$61$	−139.120	−0.292009	−0.146004	−	0.989284i	$-0.546641\pi$
$61$	−139.120	−0.292009	−0.146004	+	0.989284i	$0.546641\pi$
$62$	1047.78	2.14627
$63$	339.423	0.678782
$64$	−687.969	−1.34369
$65$	566.498	1.08101
$66$	2962.18	5.52453
$67$	−279.324	−0.509325	−0.254663	−	0.967030i	$-0.581964\pi$
$67$	−279.324	−0.509325	−0.254663	+	0.967030i	$0.581964\pi$
$68$	−642.609	−1.14600
$69$	490.168	0.855207
$70$	−430.628	−0.735284
$71$	147.165	0.245989	0.122995	−	0.992407i	$-0.460750\pi$
$71$	147.165	0.245989	0.122995	+	0.992407i	$0.460750\pi$
$72$	−1684.15	−2.75666
$73$	−164.295	−0.263414	−0.131707	−	0.991289i	$-0.542046\pi$
$73$	−164.295	−0.263414	−0.131707	+	0.991289i	$0.542046\pi$
$74$	−798.066	−1.25369
$75$	522.094	0.803816
$76$	1151.41	1.73784
$77$	−464.790	−0.687893
$78$	−1765.82	−2.56333
$79$	253.550	0.361096	0.180548	−	0.983566i	$-0.442213\pi$
$79$	253.550	0.361096	0.180548	+	0.983566i	$0.442213\pi$
$80$	521.414	0.728699
$81$	506.482	0.694762
$82$	415.262	0.559244
$83$	893.764	1.18197	0.590984	−	0.806683i	$-0.298740\pi$
$83$	893.764	1.18197	0.590984	+	0.806683i	$0.298740\pi$
$84$	873.023	1.13398
$85$	−585.790	−0.747504
$86$	0	0
$87$	1853.08	2.28358
$88$	2306.20	2.79366
$89$	605.500	0.721156	0.360578	−	0.932729i	$-0.382579\pi$
$89$	605.500	0.721156	0.360578	+	0.932729i	$0.382579\pi$
$90$	−3319.71	−3.88809
$91$	277.072	0.319176
$92$	825.191	0.935131
$93$	−1936.38	−2.15907
$94$	−1173.84	−1.28801
$95$	1049.61	1.13355
$96$	703.198	0.747602
$97$	182.538	0.191072	0.0955359	−	0.995426i	$-0.469544\pi$
$97$	182.538	0.191072	0.0955359	+	0.995426i	$0.469544\pi$
$98$	1430.15	1.47415
$99$	−3583.06	−3.63749
$100$	878.938	0.878938
$101$	572.349	0.563870	0.281935	−	0.959434i	$-0.409024\pi$
$101$	572.349	0.563870	0.281935	+	0.959434i	$0.409024\pi$
$102$	1825.96	1.77252
$103$	1938.03	1.85398	0.926990	−	0.375087i	$-0.122387\pi$
$103$	1938.03	1.85398	0.926990	+	0.375087i	$0.122387\pi$
$104$	−1374.78	−1.29623
$105$	795.831	0.739668
$106$	−2136.43	−1.95763
$107$	1560.41	1.40981	0.704907	−	0.709300i	$-0.250989\pi$
$107$	1560.41	1.40981	0.704907	+	0.709300i	$0.250989\pi$
$108$	3177.76	2.83130
$109$	−667.880	−0.586893	−0.293447	−	0.955975i	$-0.594802\pi$
$109$	−667.880	−0.586893	−0.293447	+	0.955975i	$0.594802\pi$
$110$	4545.86	3.94028
$111$	1474.88	1.26117
$112$	255.022	0.215155
$113$	1840.24	1.53199	0.765995	−	0.642846i	$-0.222247\pi$
$113$	1840.24	1.53199	0.765995	+	0.642846i	$0.222247\pi$
$114$	−3271.71	−2.68793
$115$	752.228	0.609962
$116$	3119.64	2.49699
$117$	2135.95	1.68776
$118$	−2450.37	−1.91165
$119$	−286.508	−0.220707
$120$	−3948.77	−3.00393
$121$	3575.48	2.68631
$122$	665.494	0.493860
$123$	−767.434	−0.562579
$124$	−3259.87	−2.36084
$125$	−894.625	−0.640142
$126$	−1623.66	−1.14799
$127$	335.724	0.234572	0.117286	−	0.993098i	$-0.462581\pi$
$127$	335.724	0.234572	0.117286	+	0.993098i	$0.462581\pi$
$128$	2654.61	1.83310
$129$	0	0
$130$	−2709.89	−1.82825
$131$	−559.869	−0.373405	−0.186702	−	0.982417i	$-0.559780\pi$
$131$	−559.869	−0.373405	−0.186702	+	0.982417i	$0.559780\pi$
$132$	−9215.93	−6.07684
$133$	513.359	0.334690
$134$	1336.17	0.861398
$135$	2896.78	1.84678
$136$	1421.60	0.896333
$137$	−571.747	−0.356552	−0.178276	−	0.983981i	$-0.557052\pi$
$137$	−571.747	−0.356552	−0.178276	+	0.983981i	$0.557052\pi$
$138$	−2344.76	−1.44637
$139$	−187.746	−0.114564	−0.0572820	−	0.998358i	$-0.518243\pi$
$139$	−187.746	−0.114564	−0.0572820	+	0.998358i	$0.518243\pi$
$140$	1339.77	0.808795
$141$	2169.35	1.29569
$142$	−703.975	−0.416030
$143$	−2924.87	−1.71042
$144$	1965.96	1.13771
$145$	2843.80	1.62872
$146$	785.917	0.445500
$147$	−2643.02	−1.48294
$148$	2482.94	1.37903
$149$	3167.45	1.74153	0.870763	−	0.491702i	$-0.163625\pi$
$149$	3167.45	1.74153	0.870763	+	0.491702i	$0.163625\pi$
$150$	−2497.48	−1.35946
$151$	−322.788	−0.173961	−0.0869805	−	0.996210i	$-0.527722\pi$
$151$	−322.788	−0.173961	−0.0869805	+	0.996210i	$0.527722\pi$
$152$	−2547.19	−1.35924
$153$	−2208.69	−1.16707
$154$	2223.36	1.16340
$155$	−2971.63	−1.53992
$156$	5493.83	2.81960
$157$	338.761	0.172204	0.0861021	−	0.996286i	$-0.472559\pi$
$157$	338.761	0.172204	0.0861021	+	0.996286i	$0.472559\pi$
$158$	−1212.88	−0.610704
$159$	3948.27	1.96930
$160$	1079.15	0.533215
$161$	367.912	0.180097
$162$	−2422.80	−1.17502
$163$	1683.99	0.809202	0.404601	−	0.914493i	$-0.367410\pi$
$163$	1683.99	0.809202	0.404601	+	0.914493i	$0.367410\pi$
$164$	−1291.96	−0.615155
$165$	−8401.06	−3.96377
$166$	−4275.40	−1.99901
$167$	130.423	0.0604337	0.0302169	−	0.999543i	$-0.490380\pi$
$167$	130.423	0.0604337	0.0302169	+	0.999543i	$0.490380\pi$
$168$	−1931.33	−0.886936
$169$	−453.418	−0.206381
$170$	2802.18	1.26422
$171$	3957.48	1.76980
$172$	0	0
$173$	−366.990	−0.161282	−0.0806408	−	0.996743i	$-0.525697\pi$
$173$	−366.990	−0.161282	−0.0806408	+	0.996743i	$0.525697\pi$
$174$	−8864.38	−3.86211
$175$	391.875	0.169274
$176$	−2692.10	−1.15298
$177$	4528.45	1.92305
$178$	−2896.46	−1.21966
$179$	−1391.41	−0.581000	−0.290500	−	0.956875i	$-0.593822\pi$
$179$	−1391.41	−0.581000	−0.290500	+	0.956875i	$0.593822\pi$
$180$	10328.3	4.27680
$181$	−3208.62	−1.31765	−0.658825	−	0.752296i	$-0.728946\pi$
$181$	−3208.62	−1.31765	−0.658825	+	0.752296i	$0.728946\pi$
$182$	−1325.40	−0.539808
$183$	−1229.88	−0.496805
$184$	−1825.51	−0.731406
$185$	2263.40	0.899507
$186$	9262.83	3.65153
$187$	3024.48	1.18274
$188$	3652.07	1.41678
$189$	1416.81	0.545278
$190$	−5020.88	−1.91712
$191$	−59.1616	−0.0224125	−0.0112062	−	0.999937i	$-0.503567\pi$
$191$	−59.1616	−0.0224125	−0.0112062	+	0.999937i	$0.503567\pi$
$192$	−6081.92	−2.28607
$193$	2336.09	0.871272	0.435636	−	0.900123i	$-0.356523\pi$
$193$	2336.09	0.871272	0.435636	+	0.900123i	$0.356523\pi$
$194$	−873.188	−0.323151
$195$	5008.07	1.83916
$196$	−4449.49	−1.62153
$197$	236.575	0.0855597	0.0427799	−	0.999085i	$-0.486379\pi$
$197$	236.575	0.0855597	0.0427799	+	0.999085i	$0.486379\pi$
$198$	17139.9	6.15191
$199$	−3392.43	−1.20846	−0.604229	−	0.796810i	$-0.706519\pi$
$199$	−3392.43	−1.20846	−0.604229	+	0.796810i	$0.706519\pi$
$200$	−1944.41	−0.687454
$201$	−2469.33	−0.866534
$202$	−2737.88	−0.953647
$203$	1390.90	0.480895
$204$	−5680.92	−1.94973
$205$	−1177.73	−0.401250
$206$	−9270.74	−3.13555
$207$	2836.23	0.952327
$208$	1604.82	0.534973
$209$	−5419.19	−1.79355
$210$	−3806.93	−1.25097
$211$	3426.45	1.11794	0.558972	−	0.829186i	$-0.311196\pi$
$211$	3426.45	1.11794	0.558972	+	0.829186i	$0.311196\pi$
$212$	6646.86	2.15334
$213$	1301.00	0.418511
$214$	−7464.34	−2.38435
$215$	0	0
$216$	−7029.94	−2.21448
$217$	−1453.42	−0.454674
$218$	3194.86	0.992585
$219$	−1452.43	−0.448156
$220$	−14143.1	−4.33421
$221$	−1802.96	−0.548779
$222$	−7055.22	−2.13295
$223$	−2951.11	−0.886193	−0.443096	−	0.896474i	$-0.646120\pi$
$223$	−2951.11	−0.886193	−0.443096	+	0.896474i	$0.646120\pi$
$224$	527.809	0.157436
$225$	3020.96	0.895101
$226$	−8802.93	−2.59098
$227$	−6814.60	−1.99251	−0.996257	−	0.0864423i	$-0.972450\pi$
$227$	−6814.60	−1.99251	−0.996257	+	0.0864423i	$0.972450\pi$
$228$	10179.0	2.95666
$229$	−5072.03	−1.46362	−0.731811	−	0.681508i	$-0.761325\pi$
$229$	−5072.03	−1.46362	−0.731811	+	0.681508i	$0.761325\pi$
$230$	−3598.35	−1.03160
$231$	−4108.93	−1.17034
$232$	−6901.37	−1.95300
$233$	884.469	0.248685	0.124342	−	0.992239i	$-0.460318\pi$
$233$	884.469	0.248685	0.124342	+	0.992239i	$0.460318\pi$
$234$	−10217.5	−2.85444
$235$	3329.15	0.924128
$236$	7623.58	2.10277
$237$	2241.48	0.614346
$238$	1370.54	0.373272
$239$	1854.58	0.501937	0.250969	−	0.967995i	$-0.419251\pi$
$239$	1854.58	0.501937	0.250969	+	0.967995i	$0.419251\pi$
$240$	4609.52	1.23976
$241$	−1668.84	−0.446056	−0.223028	−	0.974812i	$-0.571594\pi$
$241$	−1668.84	−0.446056	−0.223028	+	0.974812i	$0.571594\pi$
$242$	−17103.6	−4.54323
$243$	−1287.55	−0.339902
$244$	−2070.48	−0.543234
$245$	−4056.07	−1.05768
$246$	3671.09	0.951463
$247$	3230.50	0.832194
$248$	7211.58	1.84652
$249$	7901.23	2.01093
$250$	4279.52	1.08264
$251$	−4283.12	−1.07709	−0.538543	−	0.842598i	$-0.681025\pi$
$251$	−4283.12	−1.07709	−0.538543	+	0.842598i	$0.681025\pi$
$252$	5051.53	1.26276
$253$	−3883.81	−0.965110
$254$	−1605.96	−0.396721
$255$	−5178.62	−1.27176
$256$	−7194.81	−1.75654
$257$	4776.83	1.15942	0.579708	−	0.814824i	$-0.303166\pi$
$257$	4776.83	1.15942	0.579708	+	0.814824i	$0.303166\pi$
$258$	0	0
$259$	1107.02	0.265587
$260$	8431.01	2.01104
$261$	10722.4	2.54291
$262$	2678.18	0.631522
$263$	−5313.06	−1.24569	−0.622846	−	0.782344i	$-0.714024\pi$
$263$	−5313.06	−1.24569	−0.622846	+	0.782344i	$0.714024\pi$
$264$	20387.8	4.75296
$265$	6059.16	1.40457
$266$	−2455.69	−0.566046
$267$	5352.87	1.22693
$268$	−4157.09	−0.947517
$269$	−7228.76	−1.63846	−0.819229	−	0.573466i	$-0.805598\pi$
$269$	−7228.76	−1.63846	−0.819229	+	0.573466i	$0.805598\pi$
$270$	−13857.0	−3.12338
$271$	3191.00	0.715275	0.357637	−	0.933861i	$-0.383582\pi$
$271$	3191.00	0.715275	0.357637	+	0.933861i	$0.383582\pi$
$272$	−1659.48	−0.369928
$273$	2449.43	0.543027
$274$	2735.00	0.603020
$275$	−4136.77	−0.907115
$276$	7295.02	1.59097
$277$	−1752.37	−0.380106	−0.190053	−	0.981774i	$-0.560866\pi$
$277$	−1752.37	−0.380106	−0.190053	+	0.981774i	$0.560866\pi$
$278$	898.099	0.193757
$279$	−11204.4	−2.40426
$280$	−2963.88	−0.632593
$281$	−1124.41	−0.238707	−0.119354	−	0.992852i	$-0.538082\pi$
$281$	−1124.41	−0.238707	−0.119354	+	0.992852i	$0.538082\pi$
$282$	−10377.3	−2.19134
$283$	7663.63	1.60974	0.804868	−	0.593454i	$-0.202236\pi$
$283$	7663.63	1.60974	0.804868	+	0.593454i	$0.202236\pi$
$284$	2190.21	0.457623
$285$	9278.94	1.92855
$286$	13991.4	2.89275
$287$	−576.024	−0.118473
$288$	4068.87	0.832503
$289$	−3048.64	−0.620525
$290$	−13603.6	−2.75459
$291$	1613.71	0.325078
$292$	−2445.15	−0.490039
$293$	−6405.78	−1.27724	−0.638618	−	0.769524i	$-0.720493\pi$
$293$	−6405.78	−1.27724	−0.638618	+	0.769524i	$0.720493\pi$
$294$	12643.1	2.50803
$295$	6949.51	1.37158
$296$	−5492.85	−1.07860
$297$	−14956.3	−2.92206
$298$	−15151.8	−2.94536
$299$	2315.23	0.447803
$300$	7770.17	1.49537
$301$	0	0
$302$	1544.08	0.294212
$303$	5059.80	0.959333
$304$	2973.41	0.560977
$305$	−1887.41	−0.354338
$306$	10565.4	1.97381
$307$	−607.141	−0.112871	−0.0564354	−	0.998406i	$-0.517974\pi$
$307$	−607.141	−0.112871	−0.0564354	+	0.998406i	$0.517974\pi$
$308$	−6917.33	−1.27971
$309$	17133.0	3.15424
$310$	14215.1	2.60439
$311$	8528.36	1.55498	0.777490	−	0.628895i	$-0.216492\pi$
$311$	8528.36	1.55498	0.777490	+	0.628895i	$0.216492\pi$
$312$	−12153.6	−2.20533
$313$	4444.49	0.802612	0.401306	−	0.915944i	$-0.368556\pi$
$313$	4444.49	0.802612	0.401306	+	0.915944i	$0.368556\pi$
$314$	−1620.49	−0.291241
$315$	4604.88	0.823668
$316$	3773.50	0.671760
$317$	7541.20	1.33614	0.668069	−	0.744099i	$-0.267121\pi$
$317$	7541.20	1.33614	0.668069	+	0.744099i	$0.267121\pi$
$318$	−18886.9	−3.33058
$319$	−14682.8	−2.57704
$320$	−9333.53	−1.63050
$321$	13794.6	2.39857
$322$	−1759.94	−0.304589
$323$	−3340.52	−0.575454
$324$	7537.81	1.29249
$325$	2466.03	0.420894
$326$	−8055.49	−1.36857
$327$	−5904.33	−0.998503
$328$	2858.12	0.481139
$329$	1628.28	0.272857
$330$	40187.2	6.70374
$331$	10755.8	1.78608	0.893040	−	0.449978i	$-0.148568\pi$
$331$	10755.8	1.78608	0.893040	+	0.449978i	$0.148568\pi$
$332$	13301.6	2.19886
$333$	8534.03	1.40439
$334$	−623.889	−0.102209
$335$	−3789.52	−0.618041
$336$	2254.50	0.366051
$337$	2511.16	0.405910	0.202955	−	0.979188i	$-0.434945\pi$
$337$	2511.16	0.405910	0.202955	+	0.979188i	$0.434945\pi$
$338$	2168.97	0.349042
$339$	16268.4	2.60643
$340$	−8718.14	−1.39061
$341$	15342.7	2.43653
$342$	−18930.9	−2.99318
$343$	−4259.78	−0.670572
$344$	0	0
$345$	6650.00	1.03775
$346$	1755.53	0.272768
$347$	11246.2	1.73985	0.869925	−	0.493185i	$-0.164167\pi$
$347$	11246.2	1.73985	0.869925	+	0.493185i	$0.164167\pi$
$348$	27578.9	4.24823
$349$	−2505.35	−0.384265	−0.192133	−	0.981369i	$-0.561540\pi$
$349$	−2505.35	−0.384265	−0.192133	+	0.981369i	$0.561540\pi$
$350$	−1874.57	−0.286286
$351$	8915.80	1.35581
$352$	−5571.73	−0.843677
$353$	915.699	0.138067	0.0690336	−	0.997614i	$-0.478008\pi$
$353$	915.699	0.138067	0.0690336	+	0.997614i	$0.478008\pi$
$354$	−21662.2	−3.25236
$355$	1996.55	0.298496
$356$	9011.48	1.34159
$357$	−2532.85	−0.375497
$358$	6655.93	0.982617
$359$	−2250.47	−0.330850	−0.165425	−	0.986222i	$-0.552900\pi$
$359$	−2250.47	−0.330850	−0.165425	+	0.986222i	$0.552900\pi$
$360$	−22848.6	−3.34507
$361$	−873.532	−0.127356
$362$	15348.7	2.22848
$363$	31608.7	4.57032
$364$	4123.58	0.593776
$365$	−2228.95	−0.319640
$366$	5883.23	0.840223
$367$	−4847.02	−0.689407	−0.344703	−	0.938712i	$-0.612020\pi$
$367$	−4847.02	−0.689407	−0.344703	+	0.938712i	$0.612020\pi$
$368$	2130.98	0.301861
$369$	−4440.56	−0.626467
$370$	−10827.2	−1.52129
$371$	2963.51	0.414711
$372$	−28818.5	−4.01659
$373$	−1543.22	−0.214223	−0.107111	−	0.994247i	$-0.534160\pi$
$373$	−1543.22	−0.214223	−0.107111	+	0.994247i	$0.534160\pi$
$374$	−14467.8	−2.00031
$375$	−7908.85	−1.08910
$376$	−8079.22	−1.10812
$377$	8752.74	1.19573
$378$	−6777.42	−0.922204
$379$	−13033.9	−1.76651	−0.883256	−	0.468892i	$-0.844653\pi$
$379$	−13033.9	−1.76651	−0.883256	+	0.468892i	$0.844653\pi$
$380$	15621.0	2.10879
$381$	2967.93	0.399086
$382$	283.005	0.0379052
$383$	7084.06	0.945113	0.472557	−	0.881300i	$-0.343331\pi$
$383$	7084.06	0.945113	0.472557	+	0.881300i	$0.343331\pi$
$384$	23467.8	3.11872
$385$	−6305.71	−0.834723
$386$	−11174.9	−1.47354
$387$	0	0
$388$	2716.67	0.355458
$389$	−4681.84	−0.610228	−0.305114	−	0.952316i	$-0.598695\pi$
$389$	−4681.84	−0.610228	−0.305114	+	0.952316i	$0.598695\pi$
$390$	−23956.5	−3.11048
$391$	−2394.07	−0.309651
$392$	9843.30	1.26827
$393$	−4949.47	−0.635287
$394$	−1131.68	−0.144703
$395$	3439.85	0.438172
$396$	−53325.6	−6.76695
$397$	−903.717	−0.114247	−0.0571237	−	0.998367i	$-0.518193\pi$
$397$	−903.717	−0.114247	−0.0571237	+	0.998367i	$0.518193\pi$
$398$	16228.0	2.04381
$399$	4538.30	0.569421
$400$	2269.77	0.283722
$401$	−8123.03	−1.01158	−0.505791	−	0.862656i	$-0.668799\pi$
$401$	−8123.03	−1.01158	−0.505791	+	0.862656i	$0.668799\pi$
$402$	11812.3	1.46553
$403$	−9146.17	−1.13053
$404$	8518.10	1.04899
$405$	6871.33	0.843059
$406$	−6653.47	−0.813315
$407$	−11686.1	−1.42324
$408$	12567.5	1.52496
$409$	−11124.3	−1.34490	−0.672448	−	0.740144i	$-0.734757\pi$
$409$	−11124.3	−1.34490	−0.672448	+	0.740144i	$0.734757\pi$
$410$	5633.77	0.678615
$411$	−5054.48	−0.606615
$412$	28843.1	3.44903
$413$	3398.98	0.404971
$414$	−13567.4	−1.61063
$415$	12125.5	1.43426
$416$	3321.44	0.391459
$417$	−1659.75	−0.194912
$418$	25923.1	3.03336
$419$	−5143.54	−0.599710	−0.299855	−	0.953985i	$-0.596938\pi$
$419$	−5143.54	−0.599710	−0.299855	+	0.953985i	$0.596938\pi$
$420$	11844.1	1.37603
$421$	3561.04	0.412244	0.206122	−	0.978526i	$-0.433916\pi$
$421$	3561.04	0.412244	0.206122	+	0.978526i	$0.433916\pi$
$422$	−16390.7	−1.89073
$423$	12552.4	1.44283
$424$	−14704.4	−1.68422
$425$	−2550.01	−0.291044
$426$	−6223.43	−0.707807
$427$	−923.128	−0.104621
$428$	23223.1	2.62273
$429$	−25857.0	−2.91000
$430$	0	0
$431$	11456.0	1.28031	0.640156	−	0.768245i	$-0.278870\pi$
$431$	11456.0	1.28031	0.640156	+	0.768245i	$0.278870\pi$
$432$	8206.26	0.913944
$433$	−9936.08	−1.10277	−0.551383	−	0.834252i	$-0.685900\pi$
$433$	−9936.08	−1.10277	−0.551383	+	0.834252i	$0.685900\pi$
$434$	6952.54	0.768969
$435$	25140.4	2.77101
$436$	−9939.86	−1.09182
$437$	4289.65	0.469569
$438$	6947.83	0.757945
$439$	−11032.3	−1.19942	−0.599709	−	0.800218i	$-0.704717\pi$
$439$	−11032.3	−1.19942	−0.599709	+	0.800218i	$0.704717\pi$
$440$	31287.8	3.38997
$441$	−15293.2	−1.65135
$442$	8624.62	0.928125
$443$	16387.7	1.75757	0.878784	−	0.477220i	$-0.158356\pi$
$443$	16387.7	1.75757	0.878784	+	0.477220i	$0.158356\pi$
$444$	21950.2	2.34620
$445$	8214.69	0.875087
$446$	14116.9	1.49878
$447$	28001.5	2.96292
$448$	−4565.00	−0.481419
$449$	−18861.4	−1.98246	−0.991231	−	0.132140i	$-0.957815\pi$
$449$	−18861.4	−1.98246	−0.991231	+	0.132140i	$0.957815\pi$
$450$	−14451.0	−1.51384
$451$	6080.70	0.634876
$452$	27387.7	2.85002
$453$	−2853.58	−0.295966
$454$	32598.2	3.36985
$455$	3758.98	0.387305
$456$	−22518.2	−2.31253
$457$	−1518.90	−0.155473	−0.0777364	−	0.996974i	$-0.524769\pi$
$457$	−1518.90	−0.155473	−0.0777364	+	0.996974i	$0.524769\pi$
$458$	24262.5	2.47535
$459$	−9219.43	−0.937530
$460$	11195.2	1.13474
$461$	−18024.8	−1.82104	−0.910520	−	0.413465i	$-0.864318\pi$
$461$	−18024.8	−1.82104	−0.910520	+	0.413465i	$0.864318\pi$
$462$	19655.4	1.97934
$463$	142.990	0.0143527	0.00717636	−	0.999974i	$-0.497716\pi$
$463$	142.990	0.0143527	0.00717636	+	0.999974i	$0.497716\pi$
$464$	8056.17	0.806031
$465$	−26270.4	−2.61992
$466$	−4230.93	−0.420588
$467$	3530.63	0.349846	0.174923	−	0.984582i	$-0.444032\pi$
$467$	3530.63	0.349846	0.174923	+	0.984582i	$0.444032\pi$
$468$	31788.7	3.13981
$469$	−1853.44	−0.182482
$470$	−15925.3	−1.56293
$471$	2994.78	0.292977
$472$	−16865.1	−1.64466
$473$	0	0
$474$	−10722.3	−1.03901
$475$	4569.04	0.441352
$476$	−4264.01	−0.410590
$477$	22845.7	2.19294
$478$	−8871.56	−0.848903
$479$	13225.9	1.26160	0.630799	−	0.775946i	$-0.282727\pi$
$479$	13225.9	1.26160	0.630799	+	0.775946i	$0.282727\pi$
$480$	9540.13	0.907178
$481$	6966.36	0.660372
$482$	7983.05	0.754394
$483$	3252.49	0.306405
$484$	53212.8	4.99745
$485$	2476.46	0.231856
$486$	6159.09	0.574860
$487$	−5830.54	−0.542520	−0.271260	−	0.962506i	$-0.587440\pi$
$487$	−5830.54	−0.542520	−0.271260	+	0.962506i	$0.587440\pi$
$488$	4580.39	0.424887
$489$	14887.1	1.37673
$490$	19402.6	1.78881
$491$	19045.4	1.75052	0.875259	−	0.483654i	$-0.160691\pi$
$491$	19045.4	1.75052	0.875259	+	0.483654i	$0.160691\pi$
$492$	−11421.5	−1.04659
$493$	−9050.82	−0.826832
$494$	−15453.4	−1.40745
$495$	−48610.6	−4.41391
$496$	−8418.30	−0.762082
$497$	976.507	0.0881335
$498$	−37796.2	−3.40098
$499$	5878.42	0.527363	0.263681	−	0.964610i	$-0.415063\pi$
$499$	5878.42	0.527363	0.263681	+	0.964610i	$0.415063\pi$
$500$	−13314.4	−1.19088
$501$	1152.99	0.102818
$502$	20488.7	1.82162
$503$	18193.3	1.61272	0.806360	−	0.591425i	$-0.201434\pi$
$503$	18193.3	1.61272	0.806360	+	0.591425i	$0.201434\pi$
$504$	−11175.2	−0.987660
$505$	7764.94	0.684228
$506$	18578.5	1.63225
$507$	−4008.40	−0.351123
$508$	4996.48	0.436383
$509$	−11107.5	−0.967253	−0.483627	−	0.875274i	$-0.660681\pi$
$509$	−11107.5	−0.967253	−0.483627	+	0.875274i	$0.660681\pi$
$510$	24772.4	2.15086
$511$	−1090.17	−0.0943764
$512$	13180.1	1.13766
$513$	16519.2	1.42171
$514$	−22850.4	−1.96087
$515$	26292.9	2.24971
$516$	0	0
$517$	−17188.7	−1.46220
$518$	−5295.54	−0.449175
$519$	−3244.34	−0.274394
$520$	−18651.4	−1.57292
$521$	−20080.9	−1.68860	−0.844300	−	0.535871i	$-0.819983\pi$
$521$	−20080.9	−1.68860	−0.844300	+	0.535871i	$0.819983\pi$
$522$	−51291.5	−4.30071
$523$	10381.4	0.867966	0.433983	−	0.900921i	$-0.357108\pi$
$523$	10381.4	0.867966	0.433983	+	0.900921i	$0.357108\pi$
$524$	−8332.37	−0.694659
$525$	3464.34	0.287993
$526$	25415.5	2.10678
$527$	9457.65	0.781749
$528$	−23799.3	−1.96161
$529$	−9092.71	−0.747325
$530$	−28984.5	−2.37548
$531$	26202.7	2.14143
$532$	7640.16	0.622637
$533$	−3624.85	−0.294577
$534$	−25605.9	−2.07505
$535$	21169.7	1.71074
$536$	9196.45	0.741093
$537$	−12300.6	−0.988476
$538$	34579.4	2.77105
$539$	20941.8	1.67352
$540$	43112.0	3.43564
$541$	−6009.38	−0.477567	−0.238783	−	0.971073i	$-0.576749\pi$
$541$	−6009.38	−0.477567	−0.238783	+	0.971073i	$0.576749\pi$
$542$	−15264.4	−1.20971
$543$	−28365.5	−2.24177
$544$	−3434.55	−0.270690
$545$	−9060.99	−0.712166
$546$	−11717.1	−0.918396
$547$	−8555.81	−0.668775	−0.334387	−	0.942436i	$-0.608529\pi$
$547$	−8555.81	−0.668775	−0.334387	+	0.942436i	$0.608529\pi$
$548$	−8509.14	−0.663307
$549$	−7116.39	−0.553224
$550$	19788.6	1.53416
$551$	16217.0	1.25385
$552$	−16138.3	−1.24437
$553$	1682.42	0.129374
$554$	8382.59	0.642856
$555$	20009.4	1.53036
$556$	−2794.17	−0.213128
$557$	5784.93	0.440063	0.220032	−	0.975493i	$-0.429384\pi$
$557$	5784.93	0.440063	0.220032	+	0.975493i	$0.429384\pi$
$558$	53597.0	4.06621
$559$	0	0
$560$	3459.83	0.261079
$561$	26737.6	2.01223
$562$	5378.71	0.403714
$563$	2848.60	0.213240	0.106620	−	0.994300i	$-0.465997\pi$
$563$	2848.60	0.213240	0.106620	+	0.994300i	$0.465997\pi$
$564$	32285.7	2.41042
$565$	24966.1	1.85899
$566$	−36659.6	−2.72247
$567$	3360.74	0.248921
$568$	−4845.25	−0.357926
$569$	−19361.2	−1.42648	−0.713239	−	0.700921i	$-0.752772\pi$
$569$	−19361.2	−1.42648	−0.713239	+	0.700921i	$0.752772\pi$
$570$	−44386.6	−3.26167
$571$	18464.9	1.35329	0.676647	−	0.736307i	$-0.263432\pi$
$571$	18464.9	1.35329	0.676647	+	0.736307i	$0.263432\pi$
$572$	−43529.9	−3.18195
$573$	−523.012	−0.0381312
$574$	2755.46	0.200367
$575$	3274.53	0.237491
$576$	−35191.5	−2.54568
$577$	−1517.98	−0.109523	−0.0547613	−	0.998499i	$-0.517440\pi$
$577$	−1517.98	−0.109523	−0.0547613	+	0.998499i	$0.517440\pi$
$578$	14583.4	1.04946
$579$	20652.0	1.48233
$580$	42323.5	3.02998
$581$	5930.54	0.423477
$582$	−7719.34	−0.549789
$583$	−31283.8	−2.22237
$584$	5409.23	0.383280
$585$	28977.9	2.04802
$586$	30642.6	2.16013
$587$	−2080.81	−0.146311	−0.0731553	−	0.997321i	$-0.523307\pi$
$587$	−2080.81	−0.146311	−0.0731553	+	0.997321i	$0.523307\pi$
$588$	−39335.3	−2.75878
$589$	−16946.0	−1.18548
$590$	−33243.6	−2.31969
$591$	2091.42	0.145566
$592$	6411.96	0.445152
$593$	−8787.01	−0.608498	−0.304249	−	0.952593i	$-0.598405\pi$
$593$	−8787.01	−0.608498	−0.304249	+	0.952593i	$0.598405\pi$
$594$	71544.8	4.94195
$595$	−3886.99	−0.267817
$596$	47140.2	3.23983
$597$	−29990.5	−2.05600
$598$	−11075.1	−0.757348
$599$	−23528.5	−1.60492	−0.802461	−	0.596705i	$-0.796476\pi$
$599$	−23528.5	−1.60492	−0.802461	+	0.596705i	$0.796476\pi$
$600$	−17189.4	−1.16959
$601$	1317.37	0.0894120	0.0447060	−	0.999000i	$-0.485765\pi$
$601$	1317.37	0.0894120	0.0447060	+	0.999000i	$0.485765\pi$
$602$	0	0
$603$	−14288.2	−0.964941
$604$	−4803.96	−0.323626
$605$	48507.8	3.25970
$606$	−24204.0	−1.62247
$607$	−12575.8	−0.840918	−0.420459	−	0.907312i	$-0.638131\pi$
$607$	−12575.8	−0.840918	−0.420459	+	0.907312i	$0.638131\pi$
$608$	6153.95	0.410486
$609$	12296.1	0.818165
$610$	9028.61	0.599275
$611$	10246.6	0.678448
$612$	−32871.2	−2.17115
$613$	22645.1	1.49205	0.746024	−	0.665919i	$-0.231960\pi$
$613$	22645.1	1.49205	0.746024	+	0.665919i	$0.231960\pi$
$614$	2904.31	0.190893
$615$	−10411.6	−0.682661
$616$	15302.7	1.00092
$617$	19191.4	1.25221	0.626107	−	0.779737i	$-0.284647\pi$
$617$	19191.4	1.25221	0.626107	+	0.779737i	$0.284647\pi$
$618$	−81957.1	−5.33462
$619$	1860.59	0.120813	0.0604066	−	0.998174i	$-0.480760\pi$
$619$	1860.59	0.120813	0.0604066	+	0.998174i	$0.480760\pi$
$620$	−44225.9	−2.86477
$621$	11838.9	0.765023
$622$	−40796.2	−2.62987
$623$	4017.78	0.258377
$624$	14187.3	0.910170
$625$	−19519.4	−1.24924
$626$	−21260.6	−1.35742
$627$	−47907.8	−3.05144
$628$	5041.68	0.320358
$629$	−7203.61	−0.456640
$630$	−22027.8	−1.39303
$631$	−18340.5	−1.15709	−0.578545	−	0.815651i	$-0.696379\pi$
$631$	−18340.5	−1.15709	−0.578545	+	0.815651i	$0.696379\pi$
$632$	−8347.87	−0.525412
$633$	30291.2	1.90200
$634$	−36074.0	−2.25975
$635$	4554.69	0.284642
$636$	58761.0	3.66356
$637$	−12483.9	−0.776498
$638$	70236.3	4.35843
$639$	7527.88	0.466038
$640$	36014.5	2.22437
$641$	−27939.1	−1.72157	−0.860785	−	0.508968i	$-0.830027\pi$
$641$	−27939.1	−1.72157	−0.860785	+	0.508968i	$0.830027\pi$
$642$	−65987.8	−4.05659
$643$	4170.73	0.255797	0.127899	−	0.991787i	$-0.459177\pi$
$643$	4170.73	0.255797	0.127899	+	0.991787i	$0.459177\pi$
$644$	5475.53	0.335040
$645$	0	0
$646$	15979.7	0.973238
$647$	−13630.9	−0.828262	−0.414131	−	0.910217i	$-0.635914\pi$
$647$	−13630.9	−0.828262	−0.414131	+	0.910217i	$0.635914\pi$
$648$	−16675.4	−1.01091
$649$	−35880.8	−2.17018
$650$	−11796.4	−0.711838
$651$	−12848.8	−0.773554
$652$	25062.2	1.50539
$653$	−10379.1	−0.621998	−0.310999	−	0.950410i	$-0.600664\pi$
$653$	−10379.1	−0.621998	−0.310999	+	0.950410i	$0.600664\pi$
$654$	28243.9	1.68872
$655$	−7595.63	−0.453108
$656$	−3336.37	−0.198572
$657$	−8404.12	−0.499050
$658$	−7789.01	−0.461470
$659$	979.439	0.0578961	0.0289480	−	0.999581i	$-0.490784\pi$
$659$	979.439	0.0578961	0.0289480	+	0.999581i	$0.490784\pi$
$660$	−125030.	−7.37395
$661$	−2864.62	−0.168564	−0.0842820	−	0.996442i	$-0.526860\pi$
$661$	−2864.62	−0.168564	−0.0842820	+	0.996442i	$0.526860\pi$
$662$	−51451.3	−3.02071
$663$	−15938.9	−0.933659
$664$	−29426.3	−1.71982
$665$	6964.63	0.406130
$666$	−40823.3	−2.37518
$667$	11622.4	0.674693
$668$	1941.05	0.112427
$669$	−26089.0	−1.50771
$670$	18127.5	1.04526
$671$	9744.85	0.560650
$672$	4666.05	0.267852
$673$	20909.0	1.19760	0.598798	−	0.800900i	$-0.295645\pi$
$673$	20909.0	1.19760	0.598798	+	0.800900i	$0.295645\pi$
$674$	−12012.4	−0.686497
$675$	12610.0	0.719051
$676$	−6748.09	−0.383938
$677$	18448.0	1.04729	0.523643	−	0.851938i	$-0.324573\pi$
$677$	18448.0	1.04729	0.523643	+	0.851938i	$0.324573\pi$
$678$	−77821.5	−4.40814
$679$	1211.23	0.0684576
$680$	19286.5	1.08765
$681$	−60243.8	−3.38994
$682$	−73393.3	−4.12079
$683$	−22023.4	−1.23382	−0.616912	−	0.787032i	$-0.711617\pi$
$683$	−22023.4	−1.23382	−0.616912	+	0.787032i	$0.711617\pi$
$684$	58897.9	3.29242
$685$	−7756.77	−0.432658
$686$	20377.0	1.13411
$687$	−44838.8	−2.49011
$688$	0	0
$689$	18649.0	1.03116
$690$	−31810.9	−1.75510
$691$	−16084.4	−0.885499	−0.442749	−	0.896645i	$-0.645997\pi$
$691$	−16084.4	−0.885499	−0.442749	+	0.896645i	$0.645997\pi$
$692$	−5461.80	−0.300038
$693$	−23775.3	−1.30325
$694$	−53797.2	−2.94253
$695$	−2547.11	−0.139018
$696$	−61010.9	−3.32272
$697$	3748.29	0.203697
$698$	11984.6	0.649890
$699$	7819.07	0.423096
$700$	5832.17	0.314907
$701$	10025.7	0.540177	0.270088	−	0.962836i	$-0.412947\pi$
$701$	10025.7	0.540177	0.270088	+	0.962836i	$0.412947\pi$
$702$	−42649.5	−2.29302
$703$	12907.3	0.692470
$704$	48189.7	2.57985
$705$	29431.1	1.57225
$706$	−4380.33	−0.233507
$707$	3797.80	0.202024
$708$	67395.6	3.57751
$709$	−27204.6	−1.44103	−0.720516	−	0.693438i	$-0.756095\pi$
$709$	−27204.6	−1.44103	−0.720516	+	0.693438i	$0.756095\pi$
$710$	−9550.68	−0.504832
$711$	12969.8	0.684113
$712$	−19935.5	−1.04932
$713$	−12144.8	−0.637905
$714$	12116.1	0.635061
$715$	−39681.0	−2.07551
$716$	−20707.9	−1.08086
$717$	16395.3	0.853965
$718$	10765.3	0.559551
$719$	12238.9	0.634820	0.317410	−	0.948288i	$-0.397187\pi$
$719$	12238.9	0.634820	0.317410	+	0.948288i	$0.397187\pi$
$720$	26671.8	1.38055
$721$	12859.7	0.664247
$722$	4178.62	0.215391
$723$	−14753.2	−0.758892
$724$	−47752.9	−2.45127
$725$	12379.4	0.634150
$726$	−151203.	−7.72957
$727$	12512.2	0.638309	0.319155	−	0.947703i	$-0.396601\pi$
$727$	12512.2	0.638309	0.319155	+	0.947703i	$0.396601\pi$
$728$	−9122.32	−0.464417
$729$	−25057.4	−1.27305
$730$	10662.4	0.540592
$731$	0	0
$732$	−18303.9	−0.924225
$733$	−10526.6	−0.530436	−0.265218	−	0.964189i	$-0.585444\pi$
$733$	−10526.6	−0.530436	−0.265218	+	0.964189i	$0.585444\pi$
$734$	23186.1	1.16596
$735$	−35857.3	−1.79948
$736$	4410.40	0.220882
$737$	19565.6	0.977893
$738$	21241.8	1.05951
$739$	21359.0	1.06320	0.531600	−	0.846995i	$-0.321591\pi$
$739$	21359.0	1.06320	0.531600	+	0.846995i	$0.321591\pi$
$740$	33685.6	1.67339
$741$	28559.0	1.41584
$742$	−14176.2	−0.701382
$743$	−34361.4	−1.69663	−0.848315	−	0.529491i	$-0.822383\pi$
$743$	−34361.4	−1.69663	−0.848315	+	0.529491i	$0.822383\pi$
$744$	63753.3	3.14155
$745$	42972.1	2.11326
$746$	7382.14	0.362305
$747$	45718.5	2.23929
$748$	45012.4	2.20029
$749$	10354.0	0.505111
$750$	37832.7	1.84194
$751$	−3582.74	−0.174083	−0.0870413	−	0.996205i	$-0.527741\pi$
$751$	−3582.74	−0.174083	−0.0870413	+	0.996205i	$0.527741\pi$
$752$	9431.11	0.457337
$753$	−37864.6	−1.83249
$754$	−41869.5	−2.02228
$755$	−4379.20	−0.211093
$756$	21085.9	1.01440
$757$	12956.7	0.622085	0.311043	−	0.950396i	$-0.399322\pi$
$757$	12956.7	0.622085	0.311043	+	0.950396i	$0.399322\pi$
$758$	62348.9	2.98762
$759$	−34334.4	−1.64198
$760$	−34557.2	−1.64937
$761$	−21423.8	−1.02052	−0.510258	−	0.860021i	$-0.670450\pi$
$761$	−21423.8	−1.02052	−0.510258	+	0.860021i	$0.670450\pi$
$762$	−14197.4	−0.674956
$763$	−4431.70	−0.210273
$764$	−880.484	−0.0416948
$765$	−29964.8	−1.41618
$766$	−33887.2	−1.59843
$767$	21389.4	1.00694
$768$	−63605.0	−2.98847
$769$	19698.7	0.923736	0.461868	−	0.886949i	$-0.347179\pi$
$769$	19698.7	0.923736	0.461868	+	0.886949i	$0.347179\pi$
$770$	30163.9	1.41173
$771$	42229.1	1.97256
$772$	34767.3	1.62086
$773$	−9234.08	−0.429659	−0.214830	−	0.976652i	$-0.568920\pi$
$773$	−9234.08	−0.429659	−0.214830	+	0.976652i	$0.568920\pi$
$774$	0	0
$775$	−12935.8	−0.599573
$776$	−6009.89	−0.278019
$777$	9786.53	0.451853
$778$	22396.0	1.03205
$779$	−6716.11	−0.308896
$780$	74533.6	3.42145
$781$	−10308.3	−0.472294
$782$	11452.3	0.523698
$783$	44757.1	2.04277
$784$	−11490.4	−0.523432
$785$	4595.90	0.208961
$786$	23676.2	1.07443
$787$	19919.3	0.902218	0.451109	−	0.892469i	$-0.351029\pi$
$787$	19919.3	0.902218	0.451109	+	0.892469i	$0.351029\pi$
$788$	3520.87	0.159170
$789$	−46969.6	−2.11934
$790$	−16454.8	−0.741059
$791$	12210.8	0.548884
$792$	117969.	5.29272
$793$	−5809.14	−0.260137
$794$	4323.01	0.193221
$795$	53565.4	2.38965
$796$	−50488.6	−2.24814
$797$	18108.9	0.804829	0.402415	−	0.915458i	$-0.368171\pi$
$797$	18108.9	0.804829	0.402415	+	0.915458i	$0.368171\pi$
$798$	−21709.3	−0.963035
$799$	−10595.5	−0.469139
$800$	4697.66	0.207609
$801$	30973.0	1.36626
$802$	38857.2	1.71084
$803$	11508.2	0.505749
$804$	−36750.3	−1.61205
$805$	4991.39	0.218538
$806$	43751.5	1.91201
$807$	−63905.2	−2.78757
$808$	−18844.0	−0.820458
$809$	34573.9	1.50254	0.751269	−	0.659996i	$-0.229442\pi$
$809$	34573.9	1.50254	0.751269	+	0.659996i	$0.229442\pi$
$810$	−32869.6	−1.42583
$811$	−42629.2	−1.84576	−0.922881	−	0.385085i	$-0.874172\pi$
$811$	−42629.2	−1.84576	−0.922881	+	0.385085i	$0.874172\pi$
$812$	20700.3	0.894627
$813$	28209.7	1.21692
$814$	55901.5	2.40706
$815$	22846.3	0.981926
$816$	−14670.4	−0.629373
$817$	0	0
$818$	53214.2	2.27456
$819$	14173.0	0.604695
$820$	−17527.8	−0.746460
$821$	−1831.97	−0.0778758	−0.0389379	−	0.999242i	$-0.512397\pi$
$821$	−1831.97	−0.0778758	−0.0389379	+	0.999242i	$0.512397\pi$
$822$	24178.5	1.02594
$823$	−37813.5	−1.60158	−0.800788	−	0.598948i	$-0.795586\pi$
$823$	−37813.5	−1.60158	−0.800788	+	0.598948i	$0.795586\pi$
$824$	−63807.7	−2.69763
$825$	−36570.7	−1.54331
$826$	−16259.3	−0.684909
$827$	33423.3	1.40537	0.702686	−	0.711500i	$-0.251984\pi$
$827$	33423.3	1.40537	0.702686	+	0.711500i	$0.251984\pi$
$828$	42210.8	1.77165
$829$	38419.1	1.60959	0.804796	−	0.593552i	$-0.202275\pi$
$829$	38419.1	1.60959	0.804796	+	0.593552i	$0.202275\pi$
$830$	−58003.4	−2.42570
$831$	−15491.6	−0.646689
$832$	−28727.0	−1.19703
$833$	12909.0	0.536940
$834$	7939.56	0.329645
$835$	1769.42	0.0733333
$836$	−80652.1	−3.33662
$837$	−46768.9	−1.93139
$838$	24604.6	1.01426
$839$	1390.56	0.0572200	0.0286100	−	0.999591i	$-0.490892\pi$
$839$	1390.56	0.0572200	0.0286100	+	0.999591i	$0.490892\pi$
$840$	−26201.9	−1.07625
$841$	19549.5	0.801571
$842$	−17034.6	−0.697208
$843$	−9940.24	−0.406121
$844$	50994.8	2.07975
$845$	−6151.43	−0.250433
$846$	−60045.4	−2.44019
$847$	23725.0	0.962456
$848$	17164.9	0.695100
$849$	67749.6	2.73870
$850$	12198.2	0.492228
$851$	9250.34	0.372617
$852$	19362.3	0.778571
$853$	−35150.2	−1.41093	−0.705463	−	0.708747i	$-0.749261\pi$
$853$	−35150.2	−1.41093	−0.705463	+	0.708747i	$0.749261\pi$
$854$	4415.86	0.176941
$855$	53690.2	2.14756
$856$	−51374.8	−2.05135
$857$	19454.4	0.775437	0.387718	−	0.921778i	$-0.373263\pi$
$857$	19454.4	0.775437	0.387718	+	0.921778i	$0.373263\pi$
$858$	123689.	4.92154
$859$	29986.3	1.19106	0.595529	−	0.803334i	$-0.296943\pi$
$859$	29986.3	1.19106	0.595529	+	0.803334i	$0.296943\pi$
$860$	0	0
$861$	−5092.28	−0.201562
$862$	−54800.6	−2.16533
$863$	−27928.6	−1.10162	−0.550812	−	0.834629i	$-0.685682\pi$
$863$	−27928.6	−1.10162	−0.550812	+	0.834629i	$0.685682\pi$
$864$	16984.2	0.668765
$865$	−4978.87	−0.195707
$866$	47530.1	1.86506
$867$	−26951.2	−1.05572
$868$	−21630.7	−0.845847
$869$	−17760.2	−0.693296
$870$	−120261.	−4.68648
$871$	−11663.5	−0.453734
$872$	21989.3	0.853958
$873$	9337.35	0.361995
$874$	−20519.9	−0.794160
$875$	−5936.26	−0.229351
$876$	−21616.1	−0.833721
$877$	−12891.2	−0.496358	−0.248179	−	0.968714i	$-0.579832\pi$
$877$	−12891.2	−0.496358	−0.248179	+	0.968714i	$0.579832\pi$
$878$	52774.1	2.02852
$879$	−56629.7	−2.17301
$880$	−36523.1	−1.39908
$881$	−7612.18	−0.291102	−0.145551	−	0.989351i	$-0.546495\pi$
$881$	−7612.18	−0.291102	−0.145551	+	0.989351i	$0.546495\pi$
$882$	73156.2	2.79285
$883$	6529.70	0.248858	0.124429	−	0.992228i	$-0.460290\pi$
$883$	6529.70	0.248858	0.124429	+	0.992228i	$0.460290\pi$
$884$	−26832.9	−1.02091
$885$	61436.5	2.33352
$886$	−78391.9	−2.97249
$887$	16803.5	0.636083	0.318042	−	0.948077i	$-0.396975\pi$
$887$	16803.5	0.636083	0.318042	+	0.948077i	$0.396975\pi$
$888$	−48559.0	−1.83506
$889$	2227.69	0.0840429
$890$	−39295.7	−1.47999
$891$	−35477.1	−1.33393
$892$	−43920.5	−1.64862
$893$	18984.8	0.711424
$894$	−133948.	−5.01105
$895$	−18877.0	−0.705014
$896$	17614.6	0.656766
$897$	20467.6	0.761864
$898$	90225.2	3.35285
$899$	−45913.5	−1.70334
$900$	44960.1	1.66519
$901$	−19284.1	−0.713038
$902$	−29087.6	−1.07374
$903$	0	0
$904$	−60587.9	−2.22912
$905$	−43530.6	−1.59890
$906$	13650.3	0.500554
$907$	−39881.6	−1.46003	−0.730014	−	0.683432i	$-0.760487\pi$
$907$	−39881.6	−1.46003	−0.730014	+	0.683432i	$0.760487\pi$
$908$	−101420.	−3.70675
$909$	29277.2	1.06828
$910$	−17981.4	−0.655030
$911$	−28701.9	−1.04384	−0.521918	−	0.852996i	$-0.674783\pi$
$911$	−28701.9	−1.04384	−0.521918	+	0.852996i	$0.674783\pi$
$912$	26286.2	0.954410
$913$	−62604.8	−2.26935
$914$	7265.78	0.262944
$915$	−16685.5	−0.602848
$916$	−75485.5	−2.72283
$917$	−3715.00	−0.133784
$918$	44102.0	1.58560
$919$	40964.2	1.47039	0.735193	−	0.677858i	$-0.237092\pi$
$919$	40964.2	1.47039	0.735193	+	0.677858i	$0.237092\pi$
$920$	−24766.3	−0.887524
$921$	−5367.37	−0.192031
$922$	86223.3	3.07984
$923$	6145.04	0.219140
$924$	−61152.0	−2.17722
$925$	9852.84	0.350226
$926$	−684.005	−0.0242741
$927$	99135.7	3.51245
$928$	16673.5	0.589802
$929$	−23424.7	−0.827277	−0.413638	−	0.910441i	$-0.635742\pi$
$929$	−23424.7	−0.827277	−0.413638	+	0.910441i	$0.635742\pi$
$930$	125667.	4.43095
$931$	−23130.1	−0.814241
$932$	13163.3	0.462637
$933$	75394.2	2.64555
$934$	−16889.1	−0.591678
$935$	41032.4	1.43519
$936$	−70323.9	−2.45578
$937$	−24150.6	−0.842012	−0.421006	−	0.907058i	$-0.638323\pi$
$937$	−24150.6	−0.842012	−0.421006	+	0.907058i	$0.638323\pi$
$938$	8866.10	0.308623
$939$	39291.1	1.36551
$940$	49546.8	1.71919
$941$	22707.0	0.786637	0.393319	−	0.919402i	$-0.371327\pi$
$941$	22707.0	0.786637	0.393319	+	0.919402i	$0.371327\pi$
$942$	−14325.8	−0.495499
$943$	−4813.28	−0.166216
$944$	19687.2	0.678774
$945$	19221.5	0.661668
$946$	0	0
$947$	−28437.6	−0.975817	−0.487909	−	0.872895i	$-0.662240\pi$
$947$	−28437.6	−0.975817	−0.487909	+	0.872895i	$0.662240\pi$
$948$	33359.3	1.14289
$949$	−6860.32	−0.234663
$950$	−21856.4	−0.746438
$951$	66667.3	2.27322
$952$	9432.99	0.321140
$953$	−8428.24	−0.286482	−0.143241	−	0.989688i	$-0.545752\pi$
$953$	−8428.24	−0.286482	−0.143241	+	0.989688i	$0.545752\pi$
$954$	−109284.	−3.70882
$955$	−802.633	−0.0271964
$956$	27601.2	0.933773
$957$	−129802.	−4.38442
$958$	−63267.1	−2.13368
$959$	−3793.81	−0.127746
$960$	−82512.2	−2.77403
$961$	18186.3	0.610464
$962$	−33324.2	−1.11686
$963$	79819.1	2.67096
$964$	−24836.9	−0.829815
$965$	31693.2	1.05725
$966$	−15558.6	−0.518208
$967$	−20737.9	−0.689643	−0.344822	−	0.938668i	$-0.612061\pi$
$967$	−20737.9	−0.689643	−0.344822	+	0.938668i	$0.612061\pi$
$968$	−117719.	−3.90871
$969$	−29531.6	−0.979040
$970$	−11846.4	−0.392128
$971$	7444.44	0.246039	0.123019	−	0.992404i	$-0.460742\pi$
$971$	7444.44	0.246039	0.123019	+	0.992404i	$0.460742\pi$
$972$	−19162.2	−0.632332
$973$	−1245.78	−0.0410462
$974$	27890.9	0.917539
$975$	21800.7	0.716082
$976$	−5346.83	−0.175356
$977$	44274.0	1.44979	0.724897	−	0.688857i	$-0.241887\pi$
$977$	44274.0	1.44979	0.724897	+	0.688857i	$0.241887\pi$
$978$	−71213.8	−2.32839
$979$	−42413.0	−1.38460
$980$	−60365.3	−1.96765
$981$	−34163.9	−1.11190
$982$	−91105.1	−2.96057
$983$	−3147.29	−0.102119	−0.0510595	−	0.998696i	$-0.516260\pi$
$983$	−3147.29	−0.102119	−0.0510595	+	0.998696i	$0.516260\pi$
$984$	25267.0	0.818579
$985$	3209.56	0.103822
$986$	43295.4	1.39838
$987$	14394.6	0.464221
$988$	48078.6	1.54816
$989$	0	0
$990$	232533.	7.46504
$991$	12007.8	0.384906	0.192453	−	0.981306i	$-0.438356\pi$
$991$	12007.8	0.384906	0.192453	+	0.981306i	$0.438356\pi$
$992$	−17423.0	−0.557642
$993$	95085.6	3.03872
$994$	−4671.21	−0.149056
$995$	−46024.4	−1.46640
$996$	117592.	3.74100
$997$	26611.1	0.845318	0.422659	−	0.906289i	$-0.361097\pi$
$997$	26611.1	0.845318	0.422659	+	0.906289i	$0.361097\pi$
$998$	−28119.9	−0.891904
$999$	35622.5	1.12817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.m.1.12	✓	110
43.42	odd	2	inner	1849.4.a.m.1.99	yes	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.4.a.m.1.12	✓	110	1.1	even	1	trivial
1849.4.a.m.1.99	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)

\(f(q)\)	\(=\)	\(q-4.78359 q^{2} +8.84041 q^{3} +14.8827 q^{4} +13.5668 q^{5} -42.2888 q^{6} +6.63547 q^{7} -32.9240 q^{8} +51.1528 q^{9} +O(q^{10})\)	\(q-4.78359 q^{2} +8.84041 q^{3} +14.8827 q^{4} +13.5668 q^{5} -42.2888 q^{6} +6.63547 q^{7} -32.9240 q^{8} +51.1528 q^{9} -64.8979 q^{10} -70.0463 q^{11} +131.569 q^{12} +41.7562 q^{13} -31.7413 q^{14} +119.936 q^{15} +38.4332 q^{16} -43.1782 q^{17} -244.694 q^{18} +77.3658 q^{19} +201.910 q^{20} +58.6603 q^{21} +335.072 q^{22} +55.4463 q^{23} -291.061 q^{24} +59.0577 q^{25} -199.744 q^{26} +213.520 q^{27} +98.7537 q^{28} +209.615 q^{29} -573.724 q^{30} -219.037 q^{31} +79.5436 q^{32} -619.237 q^{33} +206.547 q^{34} +90.0220 q^{35} +761.291 q^{36} +166.834 q^{37} -370.086 q^{38} +369.142 q^{39} -446.673 q^{40} -86.8098 q^{41} -280.606 q^{42} -1042.48 q^{44} +693.979 q^{45} -265.232 q^{46} +245.390 q^{47} +339.765 q^{48} -298.971 q^{49} -282.508 q^{50} -381.713 q^{51} +621.445 q^{52} +446.617 q^{53} -1021.39 q^{54} -950.303 q^{55} -218.466 q^{56} +683.945 q^{57} -1002.71 q^{58} +512.244 q^{59} +1784.97 q^{60} -139.120 q^{61} +1047.78 q^{62} +339.423 q^{63} -687.969 q^{64} +566.498 q^{65} +2962.18 q^{66} -279.324 q^{67} -642.609 q^{68} +490.168 q^{69} -430.628 q^{70} +147.165 q^{71} -1684.15 q^{72} -164.295 q^{73} -798.066 q^{74} +522.094 q^{75} +1151.41 q^{76} -464.790 q^{77} -1765.82 q^{78} +253.550 q^{79} +521.414 q^{80} +506.482 q^{81} +415.262 q^{82} +893.764 q^{83} +873.023 q^{84} -585.790 q^{85} +1853.08 q^{87} +2306.20 q^{88} +605.500 q^{89} -3319.71 q^{90} +277.072 q^{91} +825.191 q^{92} -1936.38 q^{93} -1173.84 q^{94} +1049.61 q^{95} +703.198 q^{96} +182.538 q^{97} +1430.15 q^{98} -3583.06 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more