LMFDB - Embedded newform 2023.4.a.g.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2023,4,Mod(1,2023)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2023, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2023.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,4,-5,52,-35,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 49x^{5} + 69x^{4} + 753x^{3} - 122x^{2} - 3621x - 2536 $ x^7 - 3x^6 - 49x^5 + 69x^4 + 753x^3 - 122x^2 - 3621x - 2536
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.77278$ of defining polynomial
Character	$\chi$	$=$	2023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.77278 q^{2} -4.49237 q^{3} +6.23387 q^{4} -19.9390 q^{5} -16.9487 q^{6} +7.00000 q^{7} -6.66322 q^{8} -6.81863 q^{9} -75.2256 q^{10} +49.7349 q^{11} -28.0048 q^{12} -13.4357 q^{13} +26.4095 q^{14} +89.5735 q^{15} -75.0098 q^{16} -25.7252 q^{18} +154.140 q^{19} -124.297 q^{20} -31.4466 q^{21} +187.639 q^{22} -119.649 q^{23} +29.9336 q^{24} +272.565 q^{25} -50.6900 q^{26} +151.926 q^{27} +43.6371 q^{28} +48.3446 q^{29} +337.941 q^{30} +333.947 q^{31} -229.690 q^{32} -223.427 q^{33} -139.573 q^{35} -42.5065 q^{36} -79.6128 q^{37} +581.537 q^{38} +60.3582 q^{39} +132.858 q^{40} -276.450 q^{41} -118.641 q^{42} -340.827 q^{43} +310.041 q^{44} +135.957 q^{45} -451.411 q^{46} +593.644 q^{47} +336.972 q^{48} +49.0000 q^{49} +1028.33 q^{50} -83.7566 q^{52} +32.9719 q^{53} +573.182 q^{54} -991.666 q^{55} -46.6426 q^{56} -692.454 q^{57} +182.394 q^{58} -581.381 q^{59} +558.389 q^{60} -481.579 q^{61} +1259.91 q^{62} -47.7304 q^{63} -266.490 q^{64} +267.896 q^{65} -842.942 q^{66} -7.95468 q^{67} +537.509 q^{69} -526.579 q^{70} -400.666 q^{71} +45.4341 q^{72} -139.914 q^{73} -300.362 q^{74} -1224.46 q^{75} +960.890 q^{76} +348.144 q^{77} +227.718 q^{78} -0.461637 q^{79} +1495.62 q^{80} -498.403 q^{81} -1042.99 q^{82} -194.258 q^{83} -196.034 q^{84} -1285.86 q^{86} -217.182 q^{87} -331.395 q^{88} -823.811 q^{89} +512.936 q^{90} -94.0501 q^{91} -745.879 q^{92} -1500.21 q^{93} +2239.69 q^{94} -3073.41 q^{95} +1031.85 q^{96} +765.429 q^{97} +184.866 q^{98} -339.124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} - 5 q^{3} + 52 q^{4} - 35 q^{5} - 51 q^{6} + 49 q^{7} - 6 q^{8} + 128 q^{9} - 18 q^{10} - 48 q^{11} + 16 q^{12} + 84 q^{13} + 28 q^{14} - 54 q^{15} + 256 q^{16} + 196 q^{18} + 156 q^{19} - 317 q^{20}+ \cdots - 7572 q^{99}+O(q^{100}) $ 7 * q + 4 * q^2 - 5 * q^3 + 52 * q^4 - 35 * q^5 - 51 * q^6 + 49 * q^7 - 6 * q^8 + 128 * q^9 - 18 * q^10 - 48 * q^11 + 16 * q^12 + 84 * q^13 + 28 * q^14 - 54 * q^15 + 256 * q^16 + 196 * q^18 + 156 * q^19 - 317 * q^20 - 35 * q^21 - 244 * q^22 - 290 * q^23 - 818 * q^24 + 94 * q^25 - 246 * q^26 + 10 * q^27 + 364 * q^28 - 1074 * q^29 - 23 * q^30 + 291 * q^31 - 779 * q^32 + 26 * q^33 - 245 * q^35 - 679 * q^36 - 596 * q^37 - 1294 * q^38 + 824 * q^39 + 1159 * q^40 - 649 * q^41 - 357 * q^42 + 257 * q^43 + 196 * q^44 - 720 * q^45 - 1044 * q^46 - 1108 * q^47 + 2655 * q^48 + 343 * q^49 - 23 * q^50 + 768 * q^52 + 321 * q^53 + 1497 * q^54 + 152 * q^55 - 42 * q^56 - 398 * q^57 + 1166 * q^58 - 1176 * q^59 - 1495 * q^60 - 1345 * q^61 + 2824 * q^62 + 896 * q^63 + 4888 * q^64 + 1334 * q^65 - 2280 * q^66 + 1379 * q^67 - 1152 * q^69 - 126 * q^70 - 2000 * q^71 - 3375 * q^72 - 367 * q^73 + 114 * q^74 - 888 * q^75 - 1836 * q^76 - 336 * q^77 - 2362 * q^78 - 704 * q^79 - 4112 * q^80 + 4903 * q^81 + 1421 * q^82 - 16 * q^83 + 112 * q^84 - 2785 * q^86 - 1050 * q^87 - 2840 * q^88 + 1070 * q^89 + 3787 * q^90 + 588 * q^91 + 2700 * q^92 - 1976 * q^93 + 4446 * q^94 - 3950 * q^95 + 1420 * q^96 + 39 * q^97 + 196 * q^98 - 7572 * q^99

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 $

$2$	3.77278	1.33388	0.666940	−	0.745112i	$-0.267604\pi$
$2$	3.77278	1.33388	0.666940	+	0.745112i	$0.267604\pi$
$3$	−4.49237	−0.864557	−0.432278	−	0.901740i	$-0.642290\pi$
$3$	−4.49237	−0.864557	−0.432278	+	0.901740i	$0.642290\pi$
$4$	6.23387	0.779234
$5$	−19.9390	−1.78340	−0.891701	−	0.452625i	$-0.850488\pi$
$5$	−19.9390	−1.78340	−0.891701	+	0.452625i	$0.850488\pi$
$6$	−16.9487	−1.15321
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−6.66322	−0.294476
$9$	−6.81863	−0.252542
$10$	−75.2256	−2.37884
$11$	49.7349	1.36324	0.681620	−	0.731707i	$-0.261276\pi$
$11$	49.7349	1.36324	0.681620	+	0.731707i	$0.261276\pi$
$12$	−28.0048	−0.673692
$13$	−13.4357	−0.286646	−0.143323	−	0.989676i	$-0.545779\pi$
$13$	−13.4357	−0.286646	−0.143323	+	0.989676i	$0.545779\pi$
$14$	26.4095	0.504159
$15$	89.5735	1.54185
$16$	−75.0098	−1.17203
$17$	0	0
$17$	0	0
$18$	−25.7252	−0.336860
$19$	154.140	1.86117	0.930584	−	0.366080i	$-0.119300\pi$
$19$	154.140	1.86117	0.930584	+	0.366080i	$0.119300\pi$
$20$	−124.297	−1.38969
$21$	−31.4466	−0.326772
$22$	187.639	1.81840
$23$	−119.649	−1.08472	−0.542361	−	0.840145i	$-0.682470\pi$
$23$	−119.649	−1.08472	−0.542361	+	0.840145i	$0.682470\pi$
$24$	29.9336	0.254591
$25$	272.565	2.18052
$26$	−50.6900	−0.382351
$27$	151.926	1.08289
$28$	43.6371	0.294523
$29$	48.3446	0.309565	0.154782	−	0.987949i	$-0.450532\pi$
$29$	48.3446	0.309565	0.154782	+	0.987949i	$0.450532\pi$
$30$	337.941	2.05664
$31$	333.947	1.93479	0.967396	−	0.253267i	$-0.0815052\pi$
$31$	333.947	1.93479	0.967396	+	0.253267i	$0.0815052\pi$
$32$	−229.690	−1.26887
$33$	−223.427	−1.17860
$34$	0	0
$35$	−139.573	−0.674063
$36$	−42.5065	−0.196789
$37$	−79.6128	−0.353737	−0.176869	−	0.984234i	$-0.556597\pi$
$37$	−79.6128	−0.353737	−0.176869	+	0.984234i	$0.556597\pi$
$38$	581.537	2.48257
$39$	60.3582	0.247822
$40$	132.858	0.525168
$41$	−276.450	−1.05303	−0.526515	−	0.850166i	$-0.676502\pi$
$41$	−276.450	−1.05303	−0.526515	+	0.850166i	$0.676502\pi$
$42$	−118.641	−0.435874
$43$	−340.827	−1.20873	−0.604367	−	0.796706i	$-0.706574\pi$
$43$	−340.827	−1.20873	−0.604367	+	0.796706i	$0.706574\pi$
$44$	310.041	1.06228
$45$	135.957	0.450384
$46$	−451.411	−1.44689
$47$	593.644	1.84238	0.921190	−	0.389114i	$-0.127219\pi$
$47$	593.644	1.84238	0.921190	+	0.389114i	$0.127219\pi$
$48$	336.972	1.01328
$49$	49.0000	0.142857
$50$	1028.33	2.90855
$51$	0	0
$52$	−83.7566	−0.223364
$53$	32.9719	0.0854536	0.0427268	−	0.999087i	$-0.486395\pi$
$53$	32.9719	0.0854536	0.0427268	+	0.999087i	$0.486395\pi$
$54$	573.182	1.44445
$55$	−991.666	−2.43120
$56$	−46.6426	−0.111301
$57$	−692.454	−1.60908
$58$	182.394	0.412922
$59$	−581.381	−1.28287	−0.641435	−	0.767177i	$-0.721661\pi$
$59$	−581.381	−1.28287	−0.641435	+	0.767177i	$0.721661\pi$
$60$	558.389	1.20146
$61$	−481.579	−1.01082	−0.505409	−	0.862880i	$-0.668658\pi$
$61$	−481.579	−1.01082	−0.505409	+	0.862880i	$0.668658\pi$
$62$	1259.91	2.58078
$63$	−47.7304	−0.0954519
$64$	−266.490	−0.520489
$65$	267.896	0.511205
$66$	−842.942	−1.57211
$67$	−7.95468	−0.0145048	−0.00725238	−	0.999974i	$-0.502309\pi$
$67$	−7.95468	−0.0145048	−0.00725238	+	0.999974i	$0.502309\pi$
$68$	0	0
$69$	537.509	0.937804
$70$	−526.579	−0.899118
$71$	−400.666	−0.669722	−0.334861	−	0.942268i	$-0.608689\pi$
$71$	−400.666	−0.669722	−0.334861	+	0.942268i	$0.608689\pi$
$72$	45.4341	0.0743674
$73$	−139.914	−0.224324	−0.112162	−	0.993690i	$-0.535778\pi$
$73$	−139.914	−0.224324	−0.112162	+	0.993690i	$0.535778\pi$
$74$	−300.362	−0.471842
$75$	−1224.46	−1.88518
$76$	960.890	1.45028
$77$	348.144	0.515256
$78$	227.718	0.330564
$79$	−0.461637	−0.000657445 0	−0.000328723	−	1.00000i	$-0.500105\pi$
$79$	−0.461637	−0.000657445 0	−0.000328723		1.00000i	$0.500105\pi$
$80$	1495.62	2.09020
$81$	−498.403	−0.683681
$82$	−1042.99	−1.40462
$83$	−194.258	−0.256898	−0.128449	−	0.991716i	$-0.541000\pi$
$83$	−194.258	−0.256898	−0.128449	+	0.991716i	$0.541000\pi$
$84$	−196.034	−0.254631
$85$	0	0
$86$	−1285.86	−1.61231
$87$	−217.182	−0.267636
$88$	−331.395	−0.401441
$89$	−823.811	−0.981166	−0.490583	−	0.871394i	$-0.663216\pi$
$89$	−823.811	−0.981166	−0.490583	+	0.871394i	$0.663216\pi$
$90$	512.936	0.600758
$91$	−94.0501	−0.108342
$92$	−745.879	−0.845253
$93$	−1500.21	−1.67274
$94$	2239.69	2.45751
$95$	−3073.41	−3.31921
$96$	1031.85	1.09701
$97$	765.429	0.801212	0.400606	−	0.916250i	$-0.368800\pi$
$97$	765.429	0.801212	0.400606	+	0.916250i	$0.368800\pi$
$98$	184.866	0.190554
$99$	−339.124	−0.344275
$100$	1699.14	1.69914
$101$	1330.69	1.31098	0.655489	−	0.755205i	$-0.272463\pi$
$101$	1330.69	1.31098	0.655489	+	0.755205i	$0.272463\pi$
$102$	0	0
$103$	−369.346	−0.353327	−0.176664	−	0.984271i	$-0.556530\pi$
$103$	−369.346	−0.353327	−0.176664	+	0.984271i	$0.556530\pi$
$104$	89.5252	0.0844103
$105$	627.014	0.582765
$106$	124.396	0.113985
$107$	1286.08	1.16196	0.580981	−	0.813917i	$-0.302669\pi$
$107$	1286.08	1.16196	0.580981	+	0.813917i	$0.302669\pi$
$108$	947.085	0.843827
$109$	−685.643	−0.602502	−0.301251	−	0.953545i	$-0.597404\pi$
$109$	−685.643	−0.602502	−0.301251	+	0.953545i	$0.597404\pi$
$110$	−3741.34	−3.24293
$111$	357.650	0.305826
$112$	−525.069	−0.442985
$113$	−1720.74	−1.43251	−0.716254	−	0.697839i	$-0.754145\pi$
$113$	−1720.74	−1.43251	−0.716254	+	0.697839i	$0.754145\pi$
$114$	−2612.48	−2.14632
$115$	2385.69	1.93450
$116$	301.374	0.241223
$117$	91.6133	0.0723902
$118$	−2193.42	−1.71119
$119$	0	0
$120$	−596.848	−0.454038
$121$	1142.56	0.858422
$122$	−1816.89	−1.34831
$123$	1241.92	0.910404
$124$	2081.78	1.50766
$125$	−2942.31	−2.10535
$126$	−180.076	−0.127321
$127$	774.769	0.541336	0.270668	−	0.962673i	$-0.412755\pi$
$127$	774.769	0.541336	0.270668	+	0.962673i	$0.412755\pi$
$128$	832.108	0.574599
$129$	1531.12	1.04502
$130$	1010.71	0.681886
$131$	94.1724	0.0628082	0.0314041	−	0.999507i	$-0.490002\pi$
$131$	94.1724	0.0628082	0.0314041	+	0.999507i	$0.490002\pi$
$132$	−1392.82	−0.918403
$133$	1078.98	0.703455
$134$	−30.0113	−0.0193476
$135$	−3029.25	−1.93123
$136$	0	0
$137$	−138.820	−0.0865705	−0.0432852	−	0.999063i	$-0.513782\pi$
$137$	−138.820	−0.0865705	−0.0432852	+	0.999063i	$0.513782\pi$
$138$	2027.90	1.25092
$139$	63.0237	0.0384576	0.0192288	−	0.999815i	$-0.493879\pi$
$139$	63.0237	0.0384576	0.0192288	+	0.999815i	$0.493879\pi$
$140$	−870.082	−0.525252
$141$	−2666.87	−1.59284
$142$	−1511.62	−0.893328
$143$	−668.224	−0.390767
$144$	511.464	0.295986
$145$	−963.946	−0.552078
$146$	−527.864	−0.299222
$147$	−220.126	−0.123508
$148$	−496.296	−0.275644
$149$	−841.625	−0.462743	−0.231371	−	0.972866i	$-0.574321\pi$
$149$	−841.625	−0.462743	−0.231371	+	0.972866i	$0.574321\pi$
$150$	−4619.63	−2.51461
$151$	−558.778	−0.301144	−0.150572	−	0.988599i	$-0.548111\pi$
$151$	−558.778	−0.301144	−0.150572	+	0.988599i	$0.548111\pi$
$152$	−1027.07	−0.548068
$153$	0	0
$154$	1313.47	0.687289
$155$	−6658.57	−3.45051
$156$	376.265	0.193111
$157$	1779.36	0.904514	0.452257	−	0.891888i	$-0.350619\pi$
$157$	1779.36	0.904514	0.452257	+	0.891888i	$0.350619\pi$
$158$	−1.74165	−0.000876953 0
$159$	−148.122	−0.0738795
$160$	4579.79	2.26290
$161$	−837.546	−0.409987
$162$	−1880.37	−0.911947
$163$	−597.601	−0.287164	−0.143582	−	0.989638i	$-0.545862\pi$
$163$	−597.601	−0.287164	−0.143582	+	0.989638i	$0.545862\pi$
$164$	−1723.35	−0.820557
$165$	4454.93	2.10191
$166$	−732.891	−0.342671
$167$	−1864.25	−0.863830	−0.431915	−	0.901914i	$-0.642162\pi$
$167$	−1864.25	−0.863830	−0.431915	+	0.901914i	$0.642162\pi$
$168$	209.536	0.0962263
$169$	−2016.48	−0.917834
$170$	0	0
$171$	−1051.02	−0.470023
$172$	−2124.67	−0.941887
$173$	−864.071	−0.379735	−0.189867	−	0.981810i	$-0.560806\pi$
$173$	−864.071	−0.379735	−0.189867	+	0.981810i	$0.560806\pi$
$174$	−819.380	−0.356994
$175$	1907.96	0.824160
$176$	−3730.61	−1.59776
$177$	2611.78	1.10911
$178$	−3108.06	−1.30876
$179$	−1422.09	−0.593812	−0.296906	−	0.954907i	$-0.595955\pi$
$179$	−1422.09	−0.593812	−0.296906	+	0.954907i	$0.595955\pi$
$180$	847.538	0.350954
$181$	1003.74	0.412194	0.206097	−	0.978532i	$-0.433924\pi$
$181$	1003.74	0.412194	0.206097	+	0.978532i	$0.433924\pi$
$182$	−354.830	−0.144515
$183$	2163.43	0.873909
$184$	797.251	0.319424
$185$	1587.40	0.630855
$186$	−5659.97	−2.23123
$187$	0	0
$188$	3700.70	1.43564
$189$	1063.48	0.409295
$190$	−11595.3	−4.42742
$191$	−3874.54	−1.46781	−0.733906	−	0.679251i	$-0.762305\pi$
$191$	−3874.54	−1.46781	−0.733906	+	0.679251i	$0.762305\pi$
$192$	1197.17	0.449992
$193$	−26.9598	−0.0100550	−0.00502748	−	0.999987i	$-0.501600\pi$
$193$	−26.9598	−0.0100550	−0.00502748	+	0.999987i	$0.501600\pi$
$194$	2887.80	1.06872
$195$	−1203.49	−0.441966
$196$	305.460	0.111319
$197$	−77.1287	−0.0278944	−0.0139472	−	0.999903i	$-0.504440\pi$
$197$	−77.1287	−0.0278944	−0.0139472	+	0.999903i	$0.504440\pi$
$198$	−1279.44	−0.459221
$199$	3338.51	1.18925	0.594625	−	0.804003i	$-0.297300\pi$
$199$	3338.51	1.18925	0.594625	+	0.804003i	$0.297300\pi$
$200$	−1816.16	−0.642111
$201$	35.7354	0.0125402
$202$	5020.41	1.74869
$203$	338.413	0.117004
$204$	0	0
$205$	5512.15	1.87798
$206$	−1393.46	−0.471296
$207$	815.845	0.273938
$208$	1007.81	0.335958
$209$	7666.14	2.53722
$210$	2365.59	0.777338
$211$	−4891.79	−1.59604	−0.798021	−	0.602629i	$-0.794120\pi$
$211$	−4891.79	−1.59604	−0.798021	+	0.602629i	$0.794120\pi$
$212$	205.543	0.0665883
$213$	1799.94	0.579012
$214$	4852.09	1.54992
$215$	6795.76	2.15566
$216$	−1012.31	−0.318886
$217$	2337.63	0.731283
$218$	−2586.78	−0.803664
$219$	628.545	0.193941
$220$	−6181.92	−1.89448
$221$	0	0
$222$	1349.34	0.407934
$223$	4338.34	1.30276	0.651382	−	0.758750i	$-0.274189\pi$
$223$	4338.34	1.30276	0.651382	+	0.758750i	$0.274189\pi$
$224$	−1607.83	−0.479587
$225$	−1858.52	−0.550673
$226$	−6491.97	−1.91079
$227$	−1351.98	−0.395304	−0.197652	−	0.980272i	$-0.563332\pi$
$227$	−1351.98	−0.395304	−0.197652	+	0.980272i	$0.563332\pi$
$228$	−4316.67	−1.25385
$229$	886.201	0.255728	0.127864	−	0.991792i	$-0.459188\pi$
$229$	886.201	0.255728	0.127864	+	0.991792i	$0.459188\pi$
$230$	9000.70	2.58039
$231$	−1563.99	−0.445468
$232$	−322.131	−0.0911592
$233$	886.333	0.249209	0.124604	−	0.992207i	$-0.460234\pi$
$233$	886.333	0.249209	0.124604	+	0.992207i	$0.460234\pi$
$234$	345.637	0.0965598
$235$	−11836.7	−3.28570
$236$	−3624.25	−0.999656
$237$	2.07384	0.000568399 0
$238$	0	0
$239$	−4776.49	−1.29274	−0.646372	−	0.763023i	$-0.723714\pi$
$239$	−4776.49	−1.29274	−0.646372	+	0.763023i	$0.723714\pi$
$240$	−6718.89	−1.80709
$241$	−1627.74	−0.435071	−0.217536	−	0.976052i	$-0.569802\pi$
$241$	−1627.74	−0.435071	−0.217536	+	0.976052i	$0.569802\pi$
$242$	4310.62	1.14503
$243$	−1862.98	−0.491813
$244$	−3002.10	−0.787663
$245$	−977.013	−0.254772
$246$	4685.47	1.21437
$247$	−2070.99	−0.533496
$248$	−2225.16	−0.569749
$249$	872.676	0.222103
$250$	−11100.7	−2.80828
$251$	−2179.33	−0.548039	−0.274019	−	0.961724i	$-0.588353\pi$
$251$	−2179.33	−0.548039	−0.274019	+	0.961724i	$0.588353\pi$
$252$	−297.545	−0.0743793
$253$	−5950.75	−1.47874
$254$	2923.03	0.722076
$255$	0	0
$256$	5271.29	1.28694
$257$	2021.55	0.490665	0.245333	−	0.969439i	$-0.421103\pi$
$257$	2021.55	0.490665	0.245333	+	0.969439i	$0.421103\pi$
$258$	5776.57	1.39393
$259$	−557.290	−0.133700
$260$	1670.03	0.398348
$261$	−329.644	−0.0781781
$262$	355.292	0.0837786
$263$	−5855.38	−1.37285	−0.686423	−	0.727202i	$-0.740820\pi$
$263$	−5855.38	−1.37285	−0.686423	+	0.727202i	$0.740820\pi$
$264$	1488.75	0.347068
$265$	−657.428	−0.152398
$266$	4070.76	0.938324
$267$	3700.86	0.848274
$268$	−49.5884	−0.0113026
$269$	1230.97	0.279011	0.139505	−	0.990221i	$-0.455449\pi$
$269$	1230.97	0.279011	0.139505	+	0.990221i	$0.455449\pi$
$270$	−11428.7	−2.57603
$271$	−8087.41	−1.81282	−0.906411	−	0.422396i	$-0.861189\pi$
$271$	−8087.41	−1.81282	−0.906411	+	0.422396i	$0.861189\pi$
$272$	0	0
$273$	422.508	0.0936679
$274$	−523.736	−0.115475
$275$	13556.0	2.97257
$276$	3350.76	0.730769
$277$	−2212.82	−0.479985	−0.239992	−	0.970775i	$-0.577145\pi$
$277$	−2212.82	−0.479985	−0.239992	+	0.970775i	$0.577145\pi$
$278$	237.775	0.0512977
$279$	−2277.06	−0.488616
$280$	930.008	0.198495
$281$	6275.18	1.33219	0.666096	−	0.745866i	$-0.267964\pi$
$281$	6275.18	1.33219	0.666096	+	0.745866i	$0.267964\pi$
$282$	−10061.5	−2.12466
$283$	−3278.83	−0.688714	−0.344357	−	0.938839i	$-0.611903\pi$
$283$	−3278.83	−0.688714	−0.344357	+	0.938839i	$0.611903\pi$
$284$	−2497.70	−0.521870
$285$	13806.9	2.86964
$286$	−2521.06	−0.521236
$287$	−1935.15	−0.398008
$288$	1566.17	0.320443
$289$	0	0
$290$	−3636.76	−0.736406
$291$	−3438.59	−0.692693
$292$	−872.205	−0.174801
$293$	−6378.66	−1.27183	−0.635913	−	0.771761i	$-0.719376\pi$
$293$	−6378.66	−1.27183	−0.635913	+	0.771761i	$0.719376\pi$
$294$	−830.487	−0.164745
$295$	11592.2	2.28787
$296$	530.478	0.104167
$297$	7556.01	1.47624
$298$	−3175.27	−0.617243
$299$	1607.58	0.310932
$300$	−7633.15	−1.46900
$301$	−2385.79	−0.456859
$302$	−2108.15	−0.401689
$303$	−5977.96	−1.13341
$304$	−11562.0	−2.18134
$305$	9602.22	1.80269
$306$	0	0
$307$	−6646.87	−1.23569	−0.617845	−	0.786300i	$-0.711994\pi$
$307$	−6646.87	−1.23569	−0.617845	+	0.786300i	$0.711994\pi$
$308$	2170.29	0.401505
$309$	1659.24	0.305471
$310$	−25121.3	−4.60257
$311$	7483.33	1.36444	0.682220	−	0.731147i	$-0.261015\pi$
$311$	7483.33	1.36444	0.682220	+	0.731147i	$0.261015\pi$
$312$	−402.180	−0.0729775
$313$	1464.16	0.264407	0.132203	−	0.991223i	$-0.457795\pi$
$313$	1464.16	0.264407	0.132203	+	0.991223i	$0.457795\pi$
$314$	6713.15	1.20651
$315$	951.699	0.170229
$316$	−2.87778	−0.000512304 0
$317$	−761.092	−0.134849	−0.0674245	−	0.997724i	$-0.521478\pi$
$317$	−761.092	−0.134849	−0.0674245	+	0.997724i	$0.521478\pi$
$318$	−558.832	−0.0985463
$319$	2404.42	0.422011
$320$	5313.56	0.928241
$321$	−5777.54	−1.00458
$322$	−3159.88	−0.546873
$323$	0	0
$324$	−3106.98	−0.532747
$325$	−3662.11	−0.625038
$326$	−2254.62	−0.383042
$327$	3080.16	0.520897
$328$	1842.05	0.310092
$329$	4155.51	0.696354
$330$	16807.5	2.80370
$331$	7077.08	1.17520	0.587600	−	0.809151i	$-0.300073\pi$
$331$	7077.08	1.17520	0.587600	+	0.809151i	$0.300073\pi$
$332$	−1210.98	−0.200184
$333$	542.851	0.0893334
$334$	−7033.39	−1.15225
$335$	158.609	0.0258678
$336$	2358.80	0.382986
$337$	−1725.65	−0.278938	−0.139469	−	0.990226i	$-0.544540\pi$
$337$	−1725.65	−0.278938	−0.139469	+	0.990226i	$0.544540\pi$
$338$	−7607.74	−1.22428
$339$	7730.19	1.23848
$340$	0	0
$341$	16608.8	2.63759
$342$	−3965.29	−0.626954
$343$	343.000	0.0539949
$344$	2271.00	0.355943
$345$	−10717.4	−1.67248
$346$	−3259.95	−0.506520
$347$	−1118.99	−0.173113	−0.0865566	−	0.996247i	$-0.527586\pi$
$347$	−1118.99	−0.173113	−0.0865566	+	0.996247i	$0.527586\pi$
$348$	−1353.88	−0.208551
$349$	−1726.31	−0.264777	−0.132388	−	0.991198i	$-0.542265\pi$
$349$	−1726.31	−0.264777	−0.132388	+	0.991198i	$0.542265\pi$
$350$	7198.30	1.09933
$351$	−2041.23	−0.310407
$352$	−11423.6	−1.72977
$353$	1783.51	0.268914	0.134457	−	0.990919i	$-0.457071\pi$
$353$	1783.51	0.268914	0.134457	+	0.990919i	$0.457071\pi$
$354$	9853.66	1.47942
$355$	7988.89	1.19438
$356$	−5135.53	−0.764558
$357$	0	0
$358$	−5365.25	−0.792073
$359$	−1288.16	−0.189378	−0.0946888	−	0.995507i	$-0.530186\pi$
$359$	−1288.16	−0.189378	−0.0946888	+	0.995507i	$0.530186\pi$
$360$	−905.912	−0.132627
$361$	16900.2	2.46394
$362$	3786.88	0.549817
$363$	−5132.80	−0.742154
$364$	−586.296	−0.0844238
$365$	2789.75	0.400061
$366$	8162.15	1.16569
$367$	8660.62	1.23183	0.615914	−	0.787813i	$-0.288787\pi$
$367$	8660.62	1.23183	0.615914	+	0.787813i	$0.288787\pi$
$368$	8974.88	1.27133
$369$	1885.01	0.265934
$370$	5988.92	0.841485
$371$	230.803	0.0322984
$372$	−9352.12	−1.30345
$373$	8322.88	1.15534	0.577671	−	0.816270i	$-0.303962\pi$
$373$	8322.88	1.15534	0.577671	+	0.816270i	$0.303962\pi$
$374$	0	0
$375$	13217.9	1.82019
$376$	−3955.58	−0.542536
$377$	−649.546	−0.0887355
$378$	4012.28	0.545950
$379$	5250.99	0.711676	0.355838	−	0.934548i	$-0.384196\pi$
$379$	5250.99	0.711676	0.355838	+	0.934548i	$0.384196\pi$
$380$	−19159.2	−2.58644
$381$	−3480.55	−0.468015
$382$	−14617.8	−1.95788
$383$	−7076.87	−0.944155	−0.472077	−	0.881557i	$-0.656496\pi$
$383$	−7076.87	−0.944155	−0.472077	+	0.881557i	$0.656496\pi$
$384$	−3738.14	−0.496773
$385$	−6941.66	−0.918909
$386$	−101.713	−0.0134121
$387$	2323.97	0.305256
$388$	4771.59	0.624332
$389$	−5565.98	−0.725466	−0.362733	−	0.931893i	$-0.618156\pi$
$389$	−5565.98	−0.725466	−0.362733	+	0.931893i	$0.618156\pi$
$390$	−4540.48	−0.589529
$391$	0	0
$392$	−326.498	−0.0420679
$393$	−423.057	−0.0543013
$394$	−290.990	−0.0372077
$395$	9.20459	0.00117249
$396$	−2114.05	−0.268271
$397$	−3419.46	−0.432287	−0.216143	−	0.976362i	$-0.569348\pi$
$397$	−3419.46	−0.432287	−0.216143	+	0.976362i	$0.569348\pi$
$398$	12595.5	1.58632
$399$	−4847.18	−0.608177
$400$	−20445.1	−2.55563
$401$	−4833.39	−0.601915	−0.300957	−	0.953638i	$-0.597306\pi$
$401$	−4833.39	−0.601915	−0.300957	+	0.953638i	$0.597306\pi$
$402$	134.822	0.0167271
$403$	−4486.82	−0.554601
$404$	8295.36	1.02156
$405$	9937.68	1.21928
$406$	1276.76	0.156070
$407$	−3959.54	−0.482228
$408$	0	0
$409$	−5691.17	−0.688044	−0.344022	−	0.938962i	$-0.611789\pi$
$409$	−5691.17	−0.688044	−0.344022	+	0.938962i	$0.611789\pi$
$410$	20796.1	2.50499
$411$	623.628	0.0748451
$412$	−2302.45	−0.275324
$413$	−4069.67	−0.484879
$414$	3078.01	0.365400
$415$	3873.31	0.458152
$416$	3086.05	0.363716
$417$	−283.126	−0.0332487
$418$	28922.7	3.38434
$419$	7050.92	0.822100	0.411050	−	0.911613i	$-0.365162\pi$
$419$	7050.92	0.822100	0.411050	+	0.911613i	$0.365162\pi$
$420$	3908.73	0.454110
$421$	7427.11	0.859799	0.429900	−	0.902877i	$-0.358549\pi$
$421$	7427.11	0.859799	0.429900	+	0.902877i	$0.358549\pi$
$422$	−18455.7	−2.12893
$423$	−4047.84	−0.465278
$424$	−219.699	−0.0251640
$425$	0	0
$426$	6790.77	0.772333
$427$	−3371.05	−0.382053
$428$	8017.24	0.905440
$429$	3001.91	0.337841
$430$	25638.9	2.87539
$431$	−5373.17	−0.600503	−0.300251	−	0.953860i	$-0.597071\pi$
$431$	−5373.17	−0.600503	−0.300251	+	0.953860i	$0.597071\pi$
$432$	−11395.9	−1.26918
$433$	−5398.75	−0.599186	−0.299593	−	0.954067i	$-0.596851\pi$
$433$	−5398.75	−0.599186	−0.299593	+	0.954067i	$0.596851\pi$
$434$	8819.35	0.975443
$435$	4330.40	0.477303
$436$	−4274.21	−0.469490
$437$	−18442.8	−2.01885
$438$	2371.36	0.258694
$439$	1390.40	0.151162	0.0755812	−	0.997140i	$-0.475919\pi$
$439$	1390.40	0.151162	0.0755812	+	0.997140i	$0.475919\pi$
$440$	6607.69	0.715930
$441$	−334.113	−0.0360774
$442$	0	0
$443$	−16501.1	−1.76973	−0.884865	−	0.465848i	$-0.845749\pi$
$443$	−16501.1	−1.76973	−0.884865	+	0.465848i	$0.845749\pi$
$444$	2229.54	0.238310
$445$	16426.0	1.74981
$446$	16367.6	1.73773
$447$	3780.89	0.400067
$448$	−1865.43	−0.196726
$449$	13745.9	1.44479	0.722393	−	0.691482i	$-0.243042\pi$
$449$	13745.9	1.44479	0.722393	+	0.691482i	$0.243042\pi$
$450$	−7011.80	−0.734532
$451$	−13749.2	−1.43553
$452$	−10726.9	−1.11626
$453$	2510.24	0.260356
$454$	−5100.72	−0.527288
$455$	1875.27	0.193217
$456$	4613.98	0.473836
$457$	4248.42	0.434864	0.217432	−	0.976076i	$-0.430232\pi$
$457$	4248.42	0.434864	0.217432	+	0.976076i	$0.430232\pi$
$458$	3343.44	0.341111
$459$	0	0
$460$	14872.1	1.50743
$461$	−9621.73	−0.972079	−0.486040	−	0.873937i	$-0.661559\pi$
$461$	−9621.73	−0.972079	−0.486040	+	0.873937i	$0.661559\pi$
$462$	−5900.60	−0.594201
$463$	−4867.75	−0.488603	−0.244302	−	0.969699i	$-0.578559\pi$
$463$	−4867.75	−0.488603	−0.244302	+	0.969699i	$0.578559\pi$
$464$	−3626.32	−0.362819
$465$	29912.8	2.98316
$466$	3343.94	0.332414
$467$	6984.80	0.692115	0.346058	−	0.938213i	$-0.387520\pi$
$467$	6984.80	0.692115	0.346058	+	0.938213i	$0.387520\pi$
$468$	571.105	0.0564089
$469$	−55.6828	−0.00548228
$470$	−44657.2	−4.38273
$471$	−7993.55	−0.782003
$472$	3873.87	0.377774
$473$	−16951.0	−1.64779
$474$	7.82415	0.000758175 0
$475$	42013.3	4.05832
$476$	0	0
$477$	−224.823	−0.0215806
$478$	−18020.7	−1.72436
$479$	−7637.78	−0.728557	−0.364279	−	0.931290i	$-0.618684\pi$
$479$	−7637.78	−0.728557	−0.364279	+	0.931290i	$0.618684\pi$
$480$	−20574.1	−1.95641
$481$	1069.66	0.101397
$482$	−6141.12	−0.580332
$483$	3762.56	0.354457
$484$	7122.56	0.668911
$485$	−15261.9	−1.42888
$486$	−7028.63	−0.656019
$487$	−5410.89	−0.503472	−0.251736	−	0.967796i	$-0.581001\pi$
$487$	−5410.89	−0.503472	−0.251736	+	0.967796i	$0.581001\pi$
$488$	3208.87	0.297661
$489$	2684.64	0.248269
$490$	−3686.05	−0.339835
$491$	17932.7	1.64825	0.824126	−	0.566407i	$-0.191667\pi$
$491$	17932.7	1.64825	0.824126	+	0.566407i	$0.191667\pi$
$492$	7741.94	0.709418
$493$	0	0
$494$	−7813.37	−0.711620
$495$	6761.81	0.613981
$496$	−25049.3	−2.26763
$497$	−2804.66	−0.253131
$498$	3292.42	0.296258
$499$	−9787.43	−0.878047	−0.439024	−	0.898475i	$-0.644676\pi$
$499$	−9787.43	−0.878047	−0.439024	+	0.898475i	$0.644676\pi$
$500$	−18342.0	−1.64056
$501$	8374.88	0.746830
$502$	−8222.11	−0.731018
$503$	−17088.8	−1.51481	−0.757407	−	0.652943i	$-0.773534\pi$
$503$	−17088.8	−1.51481	−0.757407	+	0.652943i	$0.773534\pi$
$504$	318.038	0.0281082
$505$	−26532.7	−2.33800
$506$	−22450.9	−1.97246
$507$	9058.78	0.793519
$508$	4829.81	0.421827
$509$	−1917.08	−0.166941	−0.0834705	−	0.996510i	$-0.526600\pi$
$509$	−1917.08	−0.166941	−0.0834705	+	0.996510i	$0.526600\pi$
$510$	0	0
$511$	−979.397	−0.0847867
$512$	13230.5	1.14202
$513$	23417.9	2.01545
$514$	7626.88	0.654488
$515$	7364.39	0.630124
$516$	9544.79	0.814314
$517$	29524.8	2.51160
$518$	−2102.53	−0.178340
$519$	3881.72	0.328302
$520$	−1785.05	−0.150538
$521$	5844.92	0.491499	0.245749	−	0.969333i	$-0.420966\pi$
$521$	5844.92	0.491499	0.245749	+	0.969333i	$0.420966\pi$
$522$	−1243.68	−0.104280
$523$	−8752.93	−0.731815	−0.365907	−	0.930651i	$-0.619241\pi$
$523$	−8752.93	−0.731815	−0.365907	+	0.930651i	$0.619241\pi$
$524$	587.058	0.0489423
$525$	−8571.24	−0.712533
$526$	−22091.1	−1.83121
$527$	0	0
$528$	16759.3	1.38135
$529$	2148.98	0.176624
$530$	−2480.33	−0.203281
$531$	3964.22	0.323979
$532$	6726.23	0.548156
$533$	3714.31	0.301847
$534$	13962.5	1.13149
$535$	−25643.2	−2.07224
$536$	53.0038	0.00427130
$537$	6388.57	0.513384
$538$	4644.20	0.372166
$539$	2437.01	0.194748
$540$	−18884.0	−1.50488
$541$	6930.52	0.550770	0.275385	−	0.961334i	$-0.411195\pi$
$541$	6930.52	0.550770	0.275385	+	0.961334i	$0.411195\pi$
$542$	−30512.0	−2.41809
$543$	−4509.15	−0.356365
$544$	0	0
$545$	13671.1	1.07450
$546$	1594.03	0.124942
$547$	10626.2	0.830612	0.415306	−	0.909682i	$-0.363674\pi$
$547$	10626.2	0.830612	0.415306	+	0.909682i	$0.363674\pi$
$548$	−865.383	−0.0674586
$549$	3283.71	0.255274
$550$	51143.8	3.96505
$551$	7451.85	0.576152
$552$	−3581.54	−0.276160
$553$	−3.23146	−0.000248491 0
$554$	−8348.50	−0.640242
$555$	−7131.20	−0.545410
$556$	392.882	0.0299674
$557$	−21690.1	−1.64998	−0.824991	−	0.565145i	$-0.808820\pi$
$557$	−21690.1	−1.64998	−0.824991	+	0.565145i	$0.808820\pi$
$558$	−8590.84	−0.651755
$559$	4579.25	0.346479
$560$	10469.4	0.790021
$561$	0	0
$562$	23674.9	1.77698
$563$	4332.97	0.324357	0.162179	−	0.986761i	$-0.448148\pi$
$563$	4332.97	0.324357	0.162179	+	0.986761i	$0.448148\pi$
$564$	−16624.9	−1.24120
$565$	34309.9	2.55474
$566$	−12370.3	−0.918662
$567$	−3488.82	−0.258407
$568$	2669.72	0.197217
$569$	23267.4	1.71427	0.857136	−	0.515090i	$-0.172241\pi$
$569$	23267.4	1.71427	0.857136	+	0.515090i	$0.172241\pi$
$570$	52090.3	3.82776
$571$	−18899.0	−1.38511	−0.692557	−	0.721363i	$-0.743516\pi$
$571$	−18899.0	−1.38511	−0.692557	+	0.721363i	$0.743516\pi$
$572$	−4165.62	−0.304499
$573$	17405.9	1.26901
$574$	−7300.90	−0.530895
$575$	−32612.3	−2.36526
$576$	1817.10	0.131445
$577$	−2353.02	−0.169770	−0.0848851	−	0.996391i	$-0.527052\pi$
$577$	−2353.02	−0.169770	−0.0848851	+	0.996391i	$0.527052\pi$
$578$	0	0
$579$	121.113	0.00869309
$580$	−6009.11	−0.430198
$581$	−1359.80	−0.0970983
$582$	−12973.0	−0.923969
$583$	1639.85	0.116494
$584$	932.277	0.0660581
$585$	−1826.68	−0.129101
$586$	−24065.3	−1.69646
$587$	−13490.3	−0.948558	−0.474279	−	0.880375i	$-0.657291\pi$
$587$	−13490.3	−0.948558	−0.474279	+	0.880375i	$0.657291\pi$
$588$	−1372.24	−0.0962417
$589$	51474.6	3.60097
$590$	43734.7	3.05175
$591$	346.490	0.0241163
$592$	5971.75	0.414590
$593$	−15267.2	−1.05725	−0.528626	−	0.848855i	$-0.677293\pi$
$593$	−15267.2	−1.05725	−0.528626	+	0.848855i	$0.677293\pi$
$594$	28507.2	1.96913
$595$	0	0
$596$	−5246.58	−0.360585
$597$	−14997.8	−1.02817
$598$	6065.03	0.414745
$599$	−8040.64	−0.548467	−0.274233	−	0.961663i	$-0.588424\pi$
$599$	−8040.64	−0.548467	−0.274233	+	0.961663i	$0.588424\pi$
$600$	8158.87	0.555141
$601$	−17415.6	−1.18203	−0.591013	−	0.806662i	$-0.701272\pi$
$601$	−17415.6	−1.18203	−0.591013	+	0.806662i	$0.701272\pi$
$602$	−9001.05	−0.609394
$603$	54.2401	0.00366306
$604$	−3483.35	−0.234661
$605$	−22781.5	−1.53091
$606$	−22553.5	−1.51184
$607$	−9575.20	−0.640272	−0.320136	−	0.947372i	$-0.603729\pi$
$607$	−9575.20	−0.640272	−0.320136	+	0.947372i	$0.603729\pi$
$608$	−35404.4	−2.36158
$609$	−1520.27	−0.101157
$610$	36227.1	2.40458
$611$	−7976.04	−0.528111
$612$	0	0
$613$	−15777.3	−1.03954	−0.519770	−	0.854306i	$-0.673982\pi$
$613$	−15777.3	−1.03954	−0.519770	+	0.854306i	$0.673982\pi$
$614$	−25077.2	−1.64826
$615$	−24762.6	−1.62362
$616$	−2319.76	−0.151730
$617$	−2368.44	−0.154538	−0.0772688	−	0.997010i	$-0.524620\pi$
$617$	−2368.44	−0.154538	−0.0772688	+	0.997010i	$0.524620\pi$
$618$	6259.93	0.407462
$619$	−17179.1	−1.11549	−0.557743	−	0.830014i	$-0.688333\pi$
$619$	−17179.1	−1.11549	−0.557743	+	0.830014i	$0.688333\pi$
$620$	−41508.7	−2.68876
$621$	−18177.8	−1.17464
$622$	28233.0	1.82000
$623$	−5766.68	−0.370846
$624$	−4527.46	−0.290454
$625$	24596.2	1.57415
$626$	5523.95	0.352686
$627$	−34439.1	−2.19357
$628$	11092.3	0.704828
$629$	0	0
$630$	3590.55	0.227065
$631$	17802.6	1.12316	0.561578	−	0.827424i	$-0.310194\pi$
$631$	17802.6	1.12316	0.561578	+	0.827424i	$0.310194\pi$
$632$	3.07599	0.000193602 0
$633$	21975.7	1.37987
$634$	−2871.43	−0.179872
$635$	−15448.2	−0.965419
$636$	−923.373	−0.0575694
$637$	−658.351	−0.0409495
$638$	9071.33	0.562911
$639$	2731.99	0.169133
$640$	−16591.4	−1.02474
$641$	21616.0	1.33195	0.665974	−	0.745975i	$-0.268016\pi$
$641$	21616.0	1.33195	0.665974	+	0.745975i	$0.268016\pi$
$642$	−21797.4	−1.33999
$643$	25331.0	1.55359	0.776794	−	0.629755i	$-0.216845\pi$
$643$	25331.0	1.55359	0.776794	+	0.629755i	$0.216845\pi$
$644$	−5221.15	−0.319475
$645$	−30529.0	−1.86369
$646$	0	0
$647$	−8177.66	−0.496904	−0.248452	−	0.968644i	$-0.579922\pi$
$647$	−8177.66	−0.496904	−0.248452	+	0.968644i	$0.579922\pi$
$648$	3320.97	0.201327
$649$	−28914.9	−1.74886
$650$	−13816.3	−0.833726
$651$	−10501.5	−0.632235
$652$	−3725.37	−0.223768
$653$	−3747.71	−0.224593	−0.112296	−	0.993675i	$-0.535821\pi$
$653$	−3747.71	−0.224593	−0.112296	+	0.993675i	$0.535821\pi$
$654$	11620.8	0.694813
$655$	−1877.71	−0.112012
$656$	20736.5	1.23418
$657$	954.021	0.0566513
$658$	15677.8	0.928852
$659$	11994.5	0.709012	0.354506	−	0.935054i	$-0.384649\pi$
$659$	11994.5	0.709012	0.354506	+	0.935054i	$0.384649\pi$
$660$	27771.4	1.63788
$661$	15094.2	0.888196	0.444098	−	0.895978i	$-0.353524\pi$
$661$	15094.2	0.888196	0.444098	+	0.895978i	$0.353524\pi$
$662$	26700.3	1.56758
$663$	0	0
$664$	1294.38	0.0756502
$665$	−21513.8	−1.25454
$666$	2048.06	0.119160
$667$	−5784.41	−0.335792
$668$	−11621.5	−0.673126
$669$	−19489.4	−1.12631
$670$	598.396	0.0345045
$671$	−23951.3	−1.37799
$672$	7222.96	0.414630
$673$	−31175.1	−1.78561	−0.892803	−	0.450447i	$-0.851265\pi$
$673$	−31175.1	−1.78561	−0.892803	+	0.450447i	$0.851265\pi$
$674$	−6510.50	−0.372070
$675$	41409.7	2.36127
$676$	−12570.5	−0.715207
$677$	14385.2	0.816645	0.408322	−	0.912838i	$-0.366114\pi$
$677$	14385.2	0.816645	0.408322	+	0.912838i	$0.366114\pi$
$678$	29164.3	1.65199
$679$	5358.01	0.302830
$680$	0	0
$681$	6073.59	0.341763
$682$	62661.3	3.51822
$683$	9627.72	0.539377	0.269688	−	0.962948i	$-0.413079\pi$
$683$	9627.72	0.539377	0.269688	+	0.962948i	$0.413079\pi$
$684$	−6551.95	−0.366258
$685$	2767.93	0.154390
$686$	1294.06	0.0720227
$687$	−3981.14	−0.221092
$688$	25565.3	1.41667
$689$	−443.002	−0.0244950
$690$	−40434.5	−2.23089
$691$	28261.2	1.55587	0.777936	−	0.628343i	$-0.216267\pi$
$691$	28261.2	1.55587	0.777936	+	0.628343i	$0.216267\pi$
$692$	−5386.51	−0.295902
$693$	−2373.87	−0.130124
$694$	−4221.69	−0.230912
$695$	−1256.63	−0.0685853
$696$	1447.13	0.0788123
$697$	0	0
$698$	−6512.98	−0.353180
$699$	−3981.73	−0.215455
$700$	11894.0	0.642213
$701$	−3919.95	−0.211205	−0.105602	−	0.994408i	$-0.533677\pi$
$701$	−3919.95	−0.211205	−0.105602	+	0.994408i	$0.533677\pi$
$702$	−7701.12	−0.414046
$703$	−12271.5	−0.658364
$704$	−13253.9	−0.709551
$705$	53174.7	2.84068
$706$	6728.78	0.358698
$707$	9314.84	0.495503
$708$	16281.5	0.864259
$709$	3491.48	0.184944	0.0924720	−	0.995715i	$-0.470523\pi$
$709$	3491.48	0.184944	0.0924720	+	0.995715i	$0.470523\pi$
$710$	30140.3	1.59316
$711$	3.14773	0.000166033 0
$712$	5489.24	0.288930
$713$	−39956.5	−2.09871
$714$	0	0
$715$	13323.8	0.696895
$716$	−8865.15	−0.462718
$717$	21457.8	1.11765
$718$	−4859.95	−0.252607
$719$	−31534.6	−1.63566	−0.817831	−	0.575459i	$-0.804823\pi$
$719$	−31534.6	−1.63566	−0.817831	+	0.575459i	$0.804823\pi$
$720$	−10198.1	−0.527863
$721$	−2585.42	−0.133545
$722$	63760.7	3.28660
$723$	7312.42	0.376144
$724$	6257.16	0.321195
$725$	13177.1	0.675013
$726$	−19364.9	−0.989944
$727$	13535.2	0.690501	0.345251	−	0.938511i	$-0.387794\pi$
$727$	13535.2	0.690501	0.345251	+	0.938511i	$0.387794\pi$
$728$	626.677	0.0319041
$729$	21826.1	1.10888
$730$	10525.1	0.533632
$731$	0	0
$732$	13486.5	0.680979
$733$	11366.9	0.572777	0.286388	−	0.958114i	$-0.407545\pi$
$733$	11366.9	0.572777	0.286388	+	0.958114i	$0.407545\pi$
$734$	32674.6	1.64311
$735$	4389.10	0.220265
$736$	27482.3	1.37637
$737$	−395.625	−0.0197735
$738$	7111.73	0.354724
$739$	15687.1	0.780866	0.390433	−	0.920631i	$-0.372325\pi$
$739$	15687.1	0.780866	0.390433	+	0.920631i	$0.372325\pi$
$740$	9895.67	0.491584
$741$	9303.63	0.461238
$742$	870.771	0.0430822
$743$	−20784.3	−1.02625	−0.513124	−	0.858314i	$-0.671512\pi$
$743$	−20784.3	−1.02625	−0.513124	+	0.858314i	$0.671512\pi$
$744$	9996.24	0.492580
$745$	16781.2	0.825256
$746$	31400.4	1.54109
$747$	1324.57	0.0648775
$748$	0	0
$749$	9002.55	0.439180
$750$	49868.4	2.42791
$751$	−3383.71	−0.164412	−0.0822059	−	0.996615i	$-0.526196\pi$
$751$	−3383.71	−0.164412	−0.0822059	+	0.996615i	$0.526196\pi$
$752$	−44529.1	−2.15932
$753$	9790.33	0.473811
$754$	−2450.59	−0.118362
$755$	11141.5	0.537060
$756$	6629.60	0.318937
$757$	−22133.0	−1.06266	−0.531332	−	0.847164i	$-0.678308\pi$
$757$	−22133.0	−1.06266	−0.531332	+	0.847164i	$0.678308\pi$
$758$	19810.8	0.949290
$759$	26733.0	1.27845
$760$	20478.8	0.977426
$761$	9887.67	0.470996	0.235498	−	0.971875i	$-0.424328\pi$
$761$	9887.67	0.470996	0.235498	+	0.971875i	$0.424328\pi$
$762$	−13131.3	−0.624276
$763$	−4799.50	−0.227724
$764$	−24153.4	−1.14377
$765$	0	0
$766$	−26699.5	−1.25939
$767$	7811.28	0.367730
$768$	−23680.6	−1.11263
$769$	41534.8	1.94770	0.973852	−	0.227185i	$-0.0729523\pi$
$769$	41534.8	1.94770	0.973852	+	0.227185i	$0.0729523\pi$
$770$	−26189.4	−1.22571
$771$	−9081.56	−0.424208
$772$	−168.064	−0.00783517
$773$	−24660.5	−1.14744	−0.573722	−	0.819050i	$-0.694501\pi$
$773$	−24660.5	−1.14744	−0.573722	+	0.819050i	$0.694501\pi$
$774$	8767.83	0.407175
$775$	91022.2	4.21886
$776$	−5100.23	−0.235937
$777$	2503.55	0.115591
$778$	−20999.2	−0.967684
$779$	−42612.0	−1.95987
$780$	−7502.37	−0.344395
$781$	−19927.1	−0.912991
$782$	0	0
$783$	7344.80	0.335226
$784$	−3675.48	−0.167433
$785$	−35478.8	−1.61311
$786$	−1596.10	−0.0724313
$787$	−19161.0	−0.867872	−0.433936	−	0.900944i	$-0.642876\pi$
$787$	−19161.0	−0.867872	−0.433936	+	0.900944i	$0.642876\pi$
$788$	−480.810	−0.0217362
$789$	26304.5	1.18690
$790$	34.7269	0.00156396
$791$	−12045.2	−0.541437
$792$	2259.66	0.101381
$793$	6470.36	0.289747
$794$	−12900.9	−0.576618
$795$	2953.41	0.131757
$796$	20811.9	0.926704
$797$	22511.6	1.00051	0.500253	−	0.865879i	$-0.333240\pi$
$797$	22511.6	1.00051	0.500253	+	0.865879i	$0.333240\pi$
$798$	−18287.3	−0.811234
$799$	0	0
$800$	−62605.5	−2.76680
$801$	5617.26	0.247786
$802$	−18235.3	−0.802882
$803$	−6958.60	−0.305808
$804$	222.770	0.00977174
$805$	16699.9	0.731171
$806$	−16927.8	−0.739771
$807$	−5529.99	−0.241220
$808$	−8866.69	−0.386051
$809$	−18382.1	−0.798863	−0.399431	−	0.916763i	$-0.630792\pi$
$809$	−18382.1	−0.798863	−0.399431	+	0.916763i	$0.630792\pi$
$810$	37492.7	1.62637
$811$	−39981.9	−1.73114	−0.865570	−	0.500788i	$-0.833044\pi$
$811$	−39981.9	−1.73114	−0.865570	+	0.500788i	$0.833044\pi$
$812$	2109.62	0.0911738
$813$	36331.6	1.56729
$814$	−14938.5	−0.643234
$815$	11915.6	0.512129
$816$	0	0
$817$	−52535.1	−2.24966
$818$	−21471.5	−0.917768
$819$	641.293	0.0273609
$820$	34362.0	1.46338
$821$	−35660.6	−1.51591	−0.757956	−	0.652306i	$-0.773802\pi$
$821$	−35660.6	−1.51591	−0.757956	+	0.652306i	$0.773802\pi$
$822$	2352.81	0.0998343
$823$	−31669.5	−1.34135	−0.670673	−	0.741753i	$-0.733995\pi$
$823$	−31669.5	−1.34135	−0.670673	+	0.741753i	$0.733995\pi$
$824$	2461.03	0.104046
$825$	−60898.6	−2.56996
$826$	−15354.0	−0.646770
$827$	12830.7	0.539501	0.269750	−	0.962930i	$-0.413059\pi$
$827$	12830.7	0.539501	0.269750	+	0.962930i	$0.413059\pi$
$828$	5085.87	0.213462
$829$	−16343.9	−0.684738	−0.342369	−	0.939566i	$-0.611229\pi$
$829$	−16343.9	−0.684738	−0.342369	+	0.939566i	$0.611229\pi$
$830$	14613.1	0.611120
$831$	9940.82	0.414974
$832$	3580.49	0.149196
$833$	0	0
$834$	−1068.17	−0.0443498
$835$	37171.3	1.54056
$836$	47789.7	1.97708
$837$	50735.1	2.09517
$838$	26601.6	1.09658
$839$	29502.4	1.21399	0.606994	−	0.794706i	$-0.292375\pi$
$839$	29502.4	1.21399	0.606994	+	0.794706i	$0.292375\pi$
$840$	−4177.94	−0.171610
$841$	−22051.8	−0.904170
$842$	28020.9	1.14687
$843$	−28190.4	−1.15176
$844$	−30494.8	−1.24369
$845$	40206.7	1.63687
$846$	−15271.6	−0.620625
$847$	7997.91	0.324453
$848$	−2473.22	−0.100154
$849$	14729.7	0.595433
$850$	0	0
$851$	9525.63	0.383707
$852$	11220.6	0.451186
$853$	−21444.5	−0.860782	−0.430391	−	0.902643i	$-0.641624\pi$
$853$	−21444.5	−0.860782	−0.430391	+	0.902643i	$0.641624\pi$
$854$	−12718.2	−0.509613
$855$	20956.4	0.838239
$856$	−8569.43	−0.342169
$857$	−33131.2	−1.32058	−0.660292	−	0.751009i	$-0.729567\pi$
$857$	−33131.2	−1.32058	−0.660292	+	0.751009i	$0.729567\pi$
$858$	11325.5	0.450638
$859$	−19063.9	−0.757222	−0.378611	−	0.925556i	$-0.623598\pi$
$859$	−19063.9	−0.757222	−0.378611	+	0.925556i	$0.623598\pi$
$860$	42363.9	1.67976
$861$	8693.41	0.344100
$862$	−20271.8	−0.800998
$863$	−30934.6	−1.22019	−0.610096	−	0.792327i	$-0.708869\pi$
$863$	−30934.6	−1.22019	−0.610096	+	0.792327i	$0.708869\pi$
$864$	−34895.8	−1.37405
$865$	17228.7	0.677219
$866$	−20368.3	−0.799242
$867$	0	0
$868$	14572.5	0.569840
$869$	−22.9594	−0.000896255 0
$870$	16337.6	0.636664
$871$	106.877	0.00415773
$872$	4568.59	0.177422
$873$	−5219.18	−0.202340
$874$	−69580.5	−2.69290
$875$	−20596.2	−0.795746
$876$	3918.27	0.151125
$877$	−6769.89	−0.260665	−0.130332	−	0.991470i	$-0.541604\pi$
$877$	−6769.89	−0.260665	−0.130332	+	0.991470i	$0.541604\pi$
$878$	5245.68	0.201632
$879$	28655.3	1.09957
$880$	74384.7	2.84944
$881$	−2253.05	−0.0861603	−0.0430802	−	0.999072i	$-0.513717\pi$
$881$	−2253.05	−0.0861603	−0.0430802	+	0.999072i	$0.513717\pi$
$882$	−1260.53	−0.0481229
$883$	−5039.29	−0.192056	−0.0960281	−	0.995379i	$-0.530614\pi$
$883$	−5039.29	−0.192056	−0.0960281	+	0.995379i	$0.530614\pi$
$884$	0	0
$885$	−52076.3	−1.97800
$886$	−62254.9	−2.36060
$887$	23459.1	0.888025	0.444013	−	0.896021i	$-0.353555\pi$
$887$	23459.1	0.888025	0.444013	+	0.896021i	$0.353555\pi$
$888$	−2383.10	−0.0900582
$889$	5423.38	0.204606
$890$	61971.7	2.33404
$891$	−24788.0	−0.932020
$892$	27044.6	1.01516
$893$	91504.3	3.42898
$894$	14264.5	0.533641
$895$	28355.2	1.05901
$896$	5824.76	0.217178
$897$	−7221.83	−0.268818
$898$	51860.3	1.92717
$899$	16144.5	0.598943
$900$	−11585.8	−0.429103
$901$	0	0
$902$	−51872.8	−1.91483
$903$	10717.8	0.394980
$904$	11465.7	0.421839
$905$	−20013.5	−0.735108
$906$	9470.56	0.347283
$907$	−38192.8	−1.39820	−0.699101	−	0.715023i	$-0.746416\pi$
$907$	−38192.8	−1.39820	−0.699101	+	0.715023i	$0.746416\pi$
$908$	−8428.06	−0.308034
$909$	−9073.50	−0.331077
$910$	7074.98	0.257729
$911$	16467.6	0.598899	0.299450	−	0.954112i	$-0.403197\pi$
$911$	16467.6	0.598899	0.299450	+	0.954112i	$0.403197\pi$
$912$	51940.9	1.88589
$913$	−9661.38	−0.350214
$914$	16028.4	0.580055
$915$	−43136.7	−1.55853
$916$	5524.46	0.199272
$917$	659.207	0.0237393
$918$	0	0
$919$	−8376.08	−0.300654	−0.150327	−	0.988636i	$-0.548033\pi$
$919$	−8376.08	−0.300654	−0.150327	+	0.988636i	$0.548033\pi$
$920$	−15896.4	−0.569662
$921$	29860.2	1.06832
$922$	−36300.7	−1.29664
$923$	5383.23	0.191973
$924$	−9749.72	−0.347124
$925$	−21699.7	−0.771331
$926$	−18364.9	−0.651738
$927$	2518.43	0.0892299
$928$	−11104.3	−0.392797
$929$	−16875.6	−0.595986	−0.297993	−	0.954568i	$-0.596317\pi$
$929$	−16875.6	−0.595986	−0.297993	+	0.954568i	$0.596317\pi$
$930$	112854.	3.97918
$931$	7552.87	0.265881
$932$	5525.28	0.194192
$933$	−33617.9	−1.17964
$934$	26352.1	0.923198
$935$	0	0
$936$	−610.440	−0.0213171
$937$	−21226.7	−0.740071	−0.370035	−	0.929018i	$-0.620654\pi$
$937$	−21226.7	−0.740071	−0.370035	+	0.929018i	$0.620654\pi$
$938$	−210.079	−0.00731271
$939$	−6577.55	−0.228594
$940$	−73788.4	−2.56033
$941$	−28301.2	−0.980439	−0.490220	−	0.871599i	$-0.663083\pi$
$941$	−28301.2	−0.980439	−0.490220	+	0.871599i	$0.663083\pi$
$942$	−30157.9	−1.04310
$943$	33077.1	1.14225
$944$	43609.3	1.50356
$945$	−21204.8	−0.729938
$946$	−63952.3	−2.19796
$947$	4441.24	0.152398	0.0761991	−	0.997093i	$-0.475722\pi$
$947$	4441.24	0.152398	0.0761991	+	0.997093i	$0.475722\pi$
$948$	12.9281	0.000442915 0
$949$	1879.85	0.0643017
$950$	158507.	5.41330
$951$	3419.10	0.116585
$952$	0	0
$953$	−39500.6	−1.34265	−0.671327	−	0.741162i	$-0.734275\pi$
$953$	−39500.6	−1.34265	−0.671327	+	0.741162i	$0.734275\pi$
$954$	−848.209	−0.0287859
$955$	77254.7	2.61770
$956$	−29776.0	−1.00735
$957$	−10801.5	−0.364852
$958$	−28815.7	−0.971808
$959$	−971.737	−0.0327206
$960$	−23870.5	−0.802517
$961$	81729.3	2.74342
$962$	4035.58	0.135252
$963$	−8769.30	−0.293444
$964$	−10147.1	−0.339022
$965$	537.552	0.0179320
$966$	14195.3	0.472802
$967$	6485.44	0.215675	0.107837	−	0.994169i	$-0.465607\pi$
$967$	6485.44	0.215675	0.107837	+	0.994169i	$0.465607\pi$
$968$	−7613.13	−0.252784
$969$	0	0
$970$	−57579.9	−1.90596
$971$	−41476.3	−1.37079	−0.685395	−	0.728172i	$-0.740370\pi$
$971$	−41476.3	−1.37079	−0.685395	+	0.728172i	$0.740370\pi$
$972$	−11613.6	−0.383237
$973$	441.166	0.0145356
$974$	−20414.1	−0.671571
$975$	16451.6	0.540381
$976$	36123.2	1.18471
$977$	−15965.6	−0.522810	−0.261405	−	0.965229i	$-0.584186\pi$
$977$	−15965.6	−0.522810	−0.261405	+	0.965229i	$0.584186\pi$
$978$	10128.6	0.331161
$979$	−40972.2	−1.33756
$980$	−6090.57	−0.198527
$981$	4675.15	0.152157
$982$	67656.1	2.19857
$983$	−8196.83	−0.265960	−0.132980	−	0.991119i	$-0.542455\pi$
$983$	−8196.83	−0.265960	−0.132980	+	0.991119i	$0.542455\pi$
$984$	−8275.16	−0.268092
$985$	1537.87	0.0497469
$986$	0	0
$987$	−18668.1	−0.602037
$988$	−12910.3	−0.415718
$989$	40779.7	1.31114
$990$	25510.8	0.818976
$991$	−50887.6	−1.63118	−0.815590	−	0.578630i	$-0.803587\pi$
$991$	−50887.6	−1.63118	−0.815590	+	0.578630i	$0.803587\pi$
$992$	−76704.1	−2.45500
$993$	−31792.8	−1.01603
$994$	−10581.4	−0.337646
$995$	−66566.7	−2.12091
$996$	5440.15	0.173070
$997$	−18147.3	−0.576459	−0.288230	−	0.957561i	$-0.593067\pi$
$997$	−18147.3	−0.576459	−0.288230	+	0.957561i	$0.593067\pi$
$998$	−36925.8	−1.17121
$999$	−12095.2	−0.383059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.g.1.5		7
17.16	even	2		119.4.a.d.1.5	✓	7
51.50	odd	2		1071.4.a.o.1.3		7
68.67	odd	2		1904.4.a.p.1.3		7
119.118	odd	2		833.4.a.f.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.d.1.5	✓	7	17.16	even	2
833.4.a.f.1.5		7	119.118	odd	2
1071.4.a.o.1.3		7	51.50	odd	2
1904.4.a.p.1.3		7	68.67	odd	2
2023.4.a.g.1.5		7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q+3.77278 q^{2} -4.49237 q^{3} +6.23387 q^{4} -19.9390 q^{5} -16.9487 q^{6} +7.00000 q^{7} -6.66322 q^{8} -6.81863 q^{9} -75.2256 q^{10} +49.7349 q^{11} -28.0048 q^{12} -13.4357 q^{13} +26.4095 q^{14} +89.5735 q^{15} -75.0098 q^{16} -25.7252 q^{18} +154.140 q^{19} -124.297 q^{20} -31.4466 q^{21} +187.639 q^{22} -119.649 q^{23} +29.9336 q^{24} +272.565 q^{25} -50.6900 q^{26} +151.926 q^{27} +43.6371 q^{28} +48.3446 q^{29} +337.941 q^{30} +333.947 q^{31} -229.690 q^{32} -223.427 q^{33} -139.573 q^{35} -42.5065 q^{36} -79.6128 q^{37} +581.537 q^{38} +60.3582 q^{39} +132.858 q^{40} -276.450 q^{41} -118.641 q^{42} -340.827 q^{43} +310.041 q^{44} +135.957 q^{45} -451.411 q^{46} +593.644 q^{47} +336.972 q^{48} +49.0000 q^{49} +1028.33 q^{50} -83.7566 q^{52} +32.9719 q^{53} +573.182 q^{54} -991.666 q^{55} -46.6426 q^{56} -692.454 q^{57} +182.394 q^{58} -581.381 q^{59} +558.389 q^{60} -481.579 q^{61} +1259.91 q^{62} -47.7304 q^{63} -266.490 q^{64} +267.896 q^{65} -842.942 q^{66} -7.95468 q^{67} +537.509 q^{69} -526.579 q^{70} -400.666 q^{71} +45.4341 q^{72} -139.914 q^{73} -300.362 q^{74} -1224.46 q^{75} +960.890 q^{76} +348.144 q^{77} +227.718 q^{78} -0.461637 q^{79} +1495.62 q^{80} -498.403 q^{81} -1042.99 q^{82} -194.258 q^{83} -196.034 q^{84} -1285.86 q^{86} -217.182 q^{87} -331.395 q^{88} -823.811 q^{89} +512.936 q^{90} -94.0501 q^{91} -745.879 q^{92} -1500.21 q^{93} +2239.69 q^{94} -3073.41 q^{95} +1031.85 q^{96} +765.429 q^{97} +184.866 q^{98} -339.124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 5 q^{3} + 52 q^{4} - 35 q^{5} - 51 q^{6} + 49 q^{7} - 6 q^{8} + 128 q^{9} - 18 q^{10} - 48 q^{11} + 16 q^{12} + 84 q^{13} + 28 q^{14} - 54 q^{15} + 256 q^{16} + 196 q^{18} + 156 q^{19} - 317 q^{20}+ \cdots - 7572 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 - 5 * q^3 + 52 * q^4 - 35 * q^5 - 51 * q^6 + 49 * q^7 - 6 * q^8 + 128 * q^9 - 18 * q^10 - 48 * q^11 + 16 * q^12 + 84 * q^13 + 28 * q^14 - 54 * q^15 + 256 * q^16 + 196 * q^18 + 156 * q^19 - 317 * q^20 - 35 * q^21 - 244 * q^22 - 290 * q^23 - 818 * q^24 + 94 * q^25 - 246 * q^26 + 10 * q^27 + 364 * q^28 - 1074 * q^29 - 23 * q^30 + 291 * q^31 - 779 * q^32 + 26 * q^33 - 245 * q^35 - 679 * q^36 - 596 * q^37 - 1294 * q^38 + 824 * q^39 + 1159 * q^40 - 649 * q^41 - 357 * q^42 + 257 * q^43 + 196 * q^44 - 720 * q^45 - 1044 * q^46 - 1108 * q^47 + 2655 * q^48 + 343 * q^49 - 23 * q^50 + 768 * q^52 + 321 * q^53 + 1497 * q^54 + 152 * q^55 - 42 * q^56 - 398 * q^57 + 1166 * q^58 - 1176 * q^59 - 1495 * q^60 - 1345 * q^61 + 2824 * q^62 + 896 * q^63 + 4888 * q^64 + 1334 * q^65 - 2280 * q^66 + 1379 * q^67 - 1152 * q^69 - 126 * q^70 - 2000 * q^71 - 3375 * q^72 - 367 * q^73 + 114 * q^74 - 888 * q^75 - 1836 * q^76 - 336 * q^77 - 2362 * q^78 - 704 * q^79 - 4112 * q^80 + 4903 * q^81 + 1421 * q^82 - 16 * q^83 + 112 * q^84 - 2785 * q^86 - 1050 * q^87 - 2840 * q^88 + 1070 * q^89 + 3787 * q^90 + 588 * q^91 + 2700 * q^92 - 1976 * q^93 + 4446 * q^94 - 3950 * q^95 + 1420 * q^96 + 39 * q^97 + 196 * q^98 - 7572 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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