LMFDB - Embedded newform 2023.4.a.g.1.6

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			1.6
Root			$-2.93035$ 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)

$f(q)$	$=$	\(q+3.93035 q^{2} -9.43251 q^{3} +7.44766 q^{4} +8.85857 q^{5} -37.0731 q^{6} +7.00000 q^{7} -2.17089 q^{8} +61.9722 q^{9} +34.8173 q^{10} -22.3403 q^{11} -70.2501 q^{12} +26.4397 q^{13} +27.5125 q^{14} -83.5585 q^{15} -68.1136 q^{16} +243.572 q^{18} -70.7543 q^{19} +65.9756 q^{20} -66.0275 q^{21} -87.8051 q^{22} +138.445 q^{23} +20.4769 q^{24} -46.5257 q^{25} +103.917 q^{26} -329.875 q^{27} +52.1336 q^{28} -17.3234 q^{29} -328.414 q^{30} +194.239 q^{31} -250.343 q^{32} +210.725 q^{33} +62.0100 q^{35} +461.548 q^{36} -341.475 q^{37} -278.089 q^{38} -249.392 q^{39} -19.2309 q^{40} -284.332 q^{41} -259.511 q^{42} +532.685 q^{43} -166.383 q^{44} +548.985 q^{45} +544.138 q^{46} -328.545 q^{47} +642.482 q^{48} +49.0000 q^{49} -182.863 q^{50} +196.914 q^{52} -71.9054 q^{53} -1296.52 q^{54} -197.903 q^{55} -15.1962 q^{56} +667.390 q^{57} -68.0872 q^{58} +469.717 q^{59} -622.315 q^{60} -33.4619 q^{61} +763.428 q^{62} +433.805 q^{63} -439.029 q^{64} +234.218 q^{65} +828.222 q^{66} +893.096 q^{67} -1305.88 q^{69} +243.721 q^{70} -833.641 q^{71} -134.534 q^{72} +1153.84 q^{73} -1342.12 q^{74} +438.854 q^{75} -526.954 q^{76} -156.382 q^{77} -980.200 q^{78} -270.921 q^{79} -603.389 q^{80} +1438.30 q^{81} -1117.52 q^{82} -588.633 q^{83} -491.751 q^{84} +2093.64 q^{86} +163.403 q^{87} +48.4982 q^{88} +136.078 q^{89} +2157.70 q^{90} +185.078 q^{91} +1031.09 q^{92} -1832.16 q^{93} -1291.30 q^{94} -626.782 q^{95} +2361.37 q^{96} -668.732 q^{97} +192.587 q^{98} -1384.47 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	3.93035	1.38959	0.694795	−	0.719208i	$-0.255495\pi$
$2$	3.93035	1.38959	0.694795	+	0.719208i	$0.255495\pi$
$3$	−9.43251	−1.81529	−0.907643	−	0.419742i	$-0.862120\pi$
$3$	−9.43251	−1.81529	−0.907643	+	0.419742i	$0.862120\pi$
$4$	7.44766	0.930958
$5$	8.85857	0.792335	0.396167	−	0.918178i	$-0.370340\pi$
$5$	8.85857	0.792335	0.396167	+	0.918178i	$0.370340\pi$
$6$	−37.0731	−2.52250
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−2.17089	−0.0959405
$9$	61.9722	2.29527
$10$	34.8173	1.10102
$11$	−22.3403	−0.612349	−0.306175	−	0.951975i	$-0.599049\pi$
$11$	−22.3403	−0.612349	−0.306175	+	0.951975i	$0.599049\pi$
$12$	−70.2501	−1.68995
$13$	26.4397	0.564081	0.282040	−	0.959403i	$-0.408989\pi$
$13$	26.4397	0.564081	0.282040	+	0.959403i	$0.408989\pi$
$14$	27.5125	0.525215
$15$	−83.5585	−1.43831
$16$	−68.1136	−1.06428
$17$	0	0
$17$	0	0
$18$	243.572	3.18948
$19$	−70.7543	−0.854324	−0.427162	−	0.904175i	$-0.640487\pi$
$19$	−70.7543	−0.854324	−0.427162	+	0.904175i	$0.640487\pi$
$20$	65.9756	0.737630
$21$	−66.0275	−0.686114
$22$	−87.8051	−0.850914
$23$	138.445	1.25512	0.627561	−	0.778568i	$-0.284053\pi$
$23$	138.445	1.25512	0.627561	+	0.778568i	$0.284053\pi$
$24$	20.4769	0.174159
$25$	−46.5257	−0.372206
$26$	103.917	0.783840
$27$	−329.875	−2.35128
$28$	52.1336	0.351869
$29$	−17.3234	−0.110927	−0.0554635	−	0.998461i	$-0.517664\pi$
$29$	−17.3234	−0.110927	−0.0554635	+	0.998461i	$0.517664\pi$
$30$	−328.414	−1.99867
$31$	194.239	1.12537	0.562684	−	0.826672i	$-0.309769\pi$
$31$	194.239	1.12537	0.562684	+	0.826672i	$0.309769\pi$
$32$	−250.343	−1.38297
$33$	210.725	1.11159
$34$	0	0
$35$	62.0100	0.299474
$36$	461.548	2.13679
$37$	−341.475	−1.51725	−0.758623	−	0.651530i	$-0.774127\pi$
$37$	−341.475	−1.51725	−0.758623	+	0.651530i	$0.774127\pi$
$38$	−278.089	−1.18716
$39$	−249.392	−1.02397
$40$	−19.2309	−0.0760170
$41$	−284.332	−1.08305	−0.541527	−	0.840683i	$-0.682154\pi$
$41$	−284.332	−1.08305	−0.541527	+	0.840683i	$0.682154\pi$
$42$	−259.511	−0.953416
$43$	532.685	1.88916	0.944579	−	0.328285i	$-0.106471\pi$
$43$	532.685	1.88916	0.944579	+	0.328285i	$0.106471\pi$
$44$	−166.383	−0.570071
$45$	548.985	1.81862
$46$	544.138	1.74410
$47$	−328.545	−1.01964	−0.509821	−	0.860281i	$-0.670288\pi$
$47$	−328.545	−1.01964	−0.509821	+	0.860281i	$0.670288\pi$
$48$	642.482	1.93196
$49$	49.0000	0.142857
$50$	−182.863	−0.517213
$51$	0	0
$52$	196.914	0.525135
$53$	−71.9054	−0.186358	−0.0931789	−	0.995649i	$-0.529703\pi$
$53$	−71.9054	−0.186358	−0.0931789	+	0.995649i	$0.529703\pi$
$54$	−1296.52	−3.26731
$55$	−197.903	−0.485186
$56$	−15.1962	−0.0362621
$57$	667.390	1.55084
$58$	−68.0872	−0.154143
$59$	469.717	1.03647	0.518237	−	0.855237i	$-0.326589\pi$
$59$	469.717	1.03647	0.518237	+	0.855237i	$0.326589\pi$
$60$	−622.315	−1.33901
$61$	−33.4619	−0.0702354	−0.0351177	−	0.999383i	$-0.511181\pi$
$61$	−33.4619	−0.0702354	−0.0351177	+	0.999383i	$0.511181\pi$
$62$	763.428	1.56380
$63$	433.805	0.867529
$64$	−439.029	−0.857478
$65$	234.218	0.446941
$66$	828.222	1.54465
$67$	893.096	1.62849	0.814246	−	0.580520i	$-0.197151\pi$
$67$	893.096	1.62849	0.814246	+	0.580520i	$0.197151\pi$
$68$	0	0
$69$	−1305.88	−2.27840
$70$	243.721	0.416146
$71$	−833.641	−1.39345	−0.696726	−	0.717338i	$-0.745360\pi$
$71$	−833.641	−1.39345	−0.696726	+	0.717338i	$0.745360\pi$
$72$	−134.534	−0.220209
$73$	1153.84	1.84995	0.924976	−	0.380025i	$-0.124085\pi$
$73$	1153.84	1.84995	0.924976	+	0.380025i	$0.124085\pi$
$74$	−1342.12	−2.10835
$75$	438.854	0.675661
$76$	−526.954	−0.795339
$77$	−156.382	−0.231446
$78$	−980.200	−1.42289
$79$	−270.921	−0.385835	−0.192917	−	0.981215i	$-0.561795\pi$
$79$	−270.921	−0.385835	−0.192917	+	0.981215i	$0.561795\pi$
$80$	−603.389	−0.843262
$81$	1438.30	1.97298
$82$	−1117.52	−1.50500
$83$	−588.633	−0.778444	−0.389222	−	0.921144i	$-0.627256\pi$
$83$	−588.633	−0.778444	−0.389222	+	0.921144i	$0.627256\pi$
$84$	−491.751	−0.638743
$85$	0	0
$86$	2093.64	2.62515
$87$	163.403	0.201364
$88$	48.4982	0.0587491
$89$	136.078	0.162070	0.0810351	−	0.996711i	$-0.474177\pi$
$89$	136.078	0.162070	0.0810351	+	0.996711i	$0.474177\pi$
$90$	2157.70	2.52713
$91$	185.078	0.213202
$92$	1031.09	1.16846
$93$	−1832.16	−2.04286
$94$	−1291.30	−1.41688
$95$	−626.782	−0.676910
$96$	2361.37	2.51048
$97$	−668.732	−0.699994	−0.349997	−	0.936751i	$-0.613817\pi$
$97$	−668.732	−0.699994	−0.349997	+	0.936751i	$0.613817\pi$
$98$	192.587	0.198513
$99$	−1384.47	−1.40550
$100$	−346.508	−0.346508
$101$	−597.682	−0.588828	−0.294414	−	0.955678i	$-0.595124\pi$
$101$	−597.682	−0.588828	−0.294414	+	0.955678i	$0.595124\pi$
$102$	0	0
$103$	−900.623	−0.861563	−0.430782	−	0.902456i	$-0.641762\pi$
$103$	−900.623	−0.861563	−0.430782	+	0.902456i	$0.641762\pi$
$104$	−57.3975	−0.0541182
$105$	−584.910	−0.543632
$106$	−282.613	−0.258961
$107$	−1109.98	−1.00285	−0.501427	−	0.865200i	$-0.667191\pi$
$107$	−1109.98	−1.00285	−0.501427	+	0.865200i	$0.667191\pi$
$108$	−2456.80	−2.18894
$109$	−1663.55	−1.46183	−0.730914	−	0.682470i	$-0.760906\pi$
$109$	−1663.55	−1.46183	−0.730914	+	0.682470i	$0.760906\pi$
$110$	−777.827	−0.674208
$111$	3220.96	2.75424
$112$	−476.795	−0.402258
$113$	179.217	0.149198	0.0745989	−	0.997214i	$-0.476232\pi$
$113$	179.217	0.149198	0.0745989	+	0.997214i	$0.476232\pi$
$114$	2623.08	2.15503
$115$	1226.42	0.994476
$116$	−129.019	−0.103268
$117$	1638.52	1.29471
$118$	1846.15	1.44027
$119$	0	0
$120$	181.396	0.137993
$121$	−831.913	−0.625028
$122$	−131.517	−0.0975984
$123$	2681.96	1.96605
$124$	1446.63	1.04767
$125$	−1519.47	−1.08725
$126$	1705.01	1.20551
$127$	−2012.00	−1.40580	−0.702898	−	0.711291i	$-0.748111\pi$
$127$	−2012.00	−1.40580	−0.702898	+	0.711291i	$0.748111\pi$
$128$	277.211	0.191424
$129$	−5024.56	−3.42936
$130$	920.558	0.621064
$131$	844.055	0.562943	0.281471	−	0.959570i	$-0.409178\pi$
$131$	844.055	0.562943	0.281471	+	0.959570i	$0.409178\pi$
$132$	1569.41	1.03484
$133$	−495.280	−0.322904
$134$	3510.18	2.26294
$135$	−2922.22	−1.86300
$136$	0	0
$137$	−98.9558	−0.0617107	−0.0308553	−	0.999524i	$-0.509823\pi$
$137$	−98.9558	−0.0617107	−0.0308553	+	0.999524i	$0.509823\pi$
$138$	−5132.58	−3.16605
$139$	1615.31	0.985675	0.492837	−	0.870121i	$-0.335960\pi$
$139$	1615.31	0.985675	0.492837	+	0.870121i	$0.335960\pi$
$140$	461.829	0.278798
$141$	3099.00	1.85094
$142$	−3276.50	−1.93632
$143$	−590.670	−0.345414
$144$	−4221.15	−2.44279
$145$	−153.461	−0.0878912
$146$	4534.99	2.57067
$147$	−462.193	−0.259327
$148$	−2543.19	−1.41249
$149$	−3466.07	−1.90571	−0.952857	−	0.303420i	$-0.901871\pi$
$149$	−3466.07	−1.90571	−0.952857	+	0.303420i	$0.901871\pi$
$150$	1724.85	0.938890
$151$	573.024	0.308822	0.154411	−	0.988007i	$-0.450652\pi$
$151$	573.024	0.308822	0.154411	+	0.988007i	$0.450652\pi$
$152$	153.600	0.0819643
$153$	0	0
$154$	−614.636	−0.321615
$155$	1720.68	0.891667
$156$	−1857.39	−0.953271
$157$	907.161	0.461142	0.230571	−	0.973055i	$-0.425941\pi$
$157$	907.161	0.461142	0.230571	+	0.973055i	$0.425941\pi$
$158$	−1064.81	−0.536152
$159$	678.248	0.338293
$160$	−2217.68	−1.09577
$161$	969.115	0.474391
$162$	5653.02	2.74163
$163$	−1014.46	−0.487478	−0.243739	−	0.969841i	$-0.578374\pi$
$163$	−1014.46	−0.487478	−0.243739	+	0.969841i	$0.578374\pi$
$164$	−2117.61	−1.00828
$165$	1866.72	0.880751
$166$	−2313.54	−1.08172
$167$	1444.73	0.669440	0.334720	−	0.942318i	$-0.391358\pi$
$167$	1444.73	0.669440	0.334720	+	0.942318i	$0.391358\pi$
$168$	143.338	0.0658261
$169$	−1497.94	−0.681813
$170$	0	0
$171$	−4384.80	−1.96090
$172$	3967.26	1.75873
$173$	4238.03	1.86249	0.931247	−	0.364388i	$-0.118722\pi$
$173$	4238.03	1.86249	0.931247	+	0.364388i	$0.118722\pi$
$174$	642.233	0.279813
$175$	−325.680	−0.140681
$176$	1521.68	0.651708
$177$	−4430.61	−1.88150
$178$	534.835	0.225211
$179$	−4270.64	−1.78326	−0.891628	−	0.452768i	$-0.850436\pi$
$179$	−4270.64	−1.78326	−0.891628	+	0.452768i	$0.850436\pi$
$180$	4088.65	1.69306
$181$	−2752.81	−1.13047	−0.565235	−	0.824930i	$-0.691214\pi$
$181$	−2752.81	−1.13047	−0.565235	+	0.824930i	$0.691214\pi$
$182$	727.421	0.296264
$183$	315.630	0.127497
$184$	−300.548	−0.120417
$185$	−3024.98	−1.20217
$186$	−7201.04	−2.83874
$187$	0	0
$188$	−2446.89	−0.949243
$189$	−2309.13	−0.888699
$190$	−2463.47	−0.940627
$191$	−2324.42	−0.880573	−0.440286	−	0.897857i	$-0.645123\pi$
$191$	−2324.42	−0.880573	−0.440286	+	0.897857i	$0.645123\pi$
$192$	4141.14	1.55657
$193$	−4082.15	−1.52249	−0.761243	−	0.648467i	$-0.775410\pi$
$193$	−4082.15	−1.52249	−0.761243	+	0.648467i	$0.775410\pi$
$194$	−2628.35	−0.972704
$195$	−2209.26	−0.811325
$196$	364.935	0.132994
$197$	1556.21	0.562818	0.281409	−	0.959588i	$-0.409198\pi$
$197$	1556.21	0.562818	0.281409	+	0.959588i	$0.409198\pi$
$198$	−5441.47	−1.95307
$199$	1588.11	0.565718	0.282859	−	0.959161i	$-0.408717\pi$
$199$	1588.11	0.565718	0.282859	+	0.959161i	$0.408717\pi$
$200$	101.002	0.0357096
$201$	−8424.13	−2.95618
$202$	−2349.10	−0.818229
$203$	−121.264	−0.0419264
$204$	0	0
$205$	−2518.77	−0.858141
$206$	−3539.76	−1.19722
$207$	8579.74	2.88084
$208$	−1800.90	−0.600337
$209$	1580.67	0.523145
$210$	−2298.90	−0.755425
$211$	−3817.62	−1.24557	−0.622786	−	0.782393i	$-0.713999\pi$
$211$	−3817.62	−1.24557	−0.622786	+	0.782393i	$0.713999\pi$
$212$	−535.527	−0.173491
$213$	7863.33	2.52951
$214$	−4362.59	−1.39355
$215$	4718.83	1.49684
$216$	716.121	0.225583
$217$	1359.67	0.425349
$218$	−6538.33	−2.03134
$219$	−10883.6	−3.35819
$220$	−1473.91	−0.451687
$221$	0	0
$222$	12659.5	3.82725
$223$	−2007.16	−0.602731	−0.301366	−	0.953509i	$-0.597442\pi$
$223$	−2007.16	−0.602731	−0.301366	+	0.953509i	$0.597442\pi$
$224$	−1752.40	−0.522712
$225$	−2883.30	−0.854311
$226$	704.388	0.207324
$227$	−3538.83	−1.03471	−0.517357	−	0.855769i	$-0.673084\pi$
$227$	−3538.83	−1.03471	−0.517357	+	0.855769i	$0.673084\pi$
$228$	4970.50	1.44377
$229$	2724.21	0.786117	0.393058	−	0.919514i	$-0.371417\pi$
$229$	2724.21	0.786117	0.393058	+	0.919514i	$0.371417\pi$
$230$	4820.28	1.38191
$231$	1475.07	0.420141
$232$	37.6072	0.0106424
$233$	−5172.45	−1.45433	−0.727164	−	0.686463i	$-0.759162\pi$
$233$	−5172.45	−1.45433	−0.727164	+	0.686463i	$0.759162\pi$
$234$	6439.98	1.79912
$235$	−2910.44	−0.807898
$236$	3498.29	0.964913
$237$	2555.46	0.700401
$238$	0	0
$239$	−1423.64	−0.385305	−0.192652	−	0.981267i	$-0.561709\pi$
$239$	−1423.64	−0.385305	−0.192652	+	0.981267i	$0.561709\pi$
$240$	5691.47	1.53076
$241$	−4759.79	−1.27222	−0.636110	−	0.771598i	$-0.719458\pi$
$241$	−4759.79	−1.27222	−0.636110	+	0.771598i	$0.719458\pi$
$242$	−3269.71	−0.868532
$243$	−4660.15	−1.23024
$244$	−249.213	−0.0653862
$245$	434.070	0.113191
$246$	10541.1	2.73201
$247$	−1870.72	−0.481908
$248$	−421.671	−0.107968
$249$	5552.29	1.41310
$250$	−5972.06	−1.51083
$251$	1644.01	0.413421	0.206711	−	0.978402i	$-0.433724\pi$
$251$	1644.01	0.413421	0.206711	+	0.978402i	$0.433724\pi$
$252$	3230.83	0.807632
$253$	−3092.90	−0.768573
$254$	−7907.87	−1.95348
$255$	0	0
$256$	4601.76	1.12348
$257$	−6166.93	−1.49682	−0.748410	−	0.663236i	$-0.769182\pi$
$257$	−6166.93	−1.49682	−0.748410	+	0.663236i	$0.769182\pi$
$258$	−19748.3	−4.76540
$259$	−2390.32	−0.573465
$260$	1744.37	0.416083
$261$	−1073.57	−0.254607
$262$	3317.43	0.782259
$263$	−1068.30	−0.250472	−0.125236	−	0.992127i	$-0.539969\pi$
$263$	−1068.30	−0.250472	−0.125236	+	0.992127i	$0.539969\pi$
$264$	−457.459	−0.106646
$265$	−636.979	−0.147658
$266$	−1946.63	−0.448704
$267$	−1283.56	−0.294204
$268$	6651.47	1.51606
$269$	−2342.64	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$269$	−2342.64	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$270$	−11485.4	−2.58880
$271$	3281.52	0.735564	0.367782	−	0.929912i	$-0.380117\pi$
$271$	3281.52	0.735564	0.367782	+	0.929912i	$0.380117\pi$
$272$	0	0
$273$	−1745.75	−0.387024
$274$	−388.931	−0.0857525
$275$	1039.40	0.227920
$276$	−9725.78	−2.12110
$277$	−6980.15	−1.51407	−0.757033	−	0.653376i	$-0.773352\pi$
$277$	−6980.15	−1.51407	−0.757033	+	0.653376i	$0.773352\pi$
$278$	6348.74	1.36968
$279$	12037.4	2.58302
$280$	−134.617	−0.0287317
$281$	−2256.65	−0.479077	−0.239538	−	0.970887i	$-0.576996\pi$
$281$	−2256.65	−0.479077	−0.239538	+	0.970887i	$0.576996\pi$
$282$	12180.2	2.57205
$283$	5009.33	1.05220	0.526102	−	0.850421i	$-0.323653\pi$
$283$	5009.33	1.05220	0.526102	+	0.850421i	$0.323653\pi$
$284$	−6208.68	−1.29724
$285$	5912.12	1.22879
$286$	−2321.54	−0.479984
$287$	−1990.32	−0.409356
$288$	−15514.3	−3.17427
$289$	0	0
$290$	−603.155	−0.122133
$291$	6307.82	1.27069
$292$	8593.39	1.72223
$293$	−4319.30	−0.861215	−0.430608	−	0.902539i	$-0.641701\pi$
$293$	−4319.30	−0.861215	−0.430608	+	0.902539i	$0.641701\pi$
$294$	−1816.58	−0.360357
$295$	4161.02	0.821234
$296$	741.302	0.145565
$297$	7369.50	1.43980
$298$	−13622.9	−2.64816
$299$	3660.44	0.707990
$300$	3268.44	0.629011
$301$	3728.80	0.714034
$302$	2252.19	0.429135
$303$	5637.64	1.06889
$304$	4819.33	0.909236
$305$	−296.425	−0.0556500
$306$	0	0
$307$	9601.85	1.78504	0.892518	−	0.451011i	$-0.148937\pi$
$307$	9601.85	1.78504	0.892518	+	0.451011i	$0.148937\pi$
$308$	−1164.68	−0.215467
$309$	8495.13	1.56398
$310$	6762.88	1.23905
$311$	1010.42	0.184230	0.0921148	−	0.995748i	$-0.470637\pi$
$311$	1010.42	0.184230	0.0921148	+	0.995748i	$0.470637\pi$
$312$	541.403	0.0982400
$313$	−3636.85	−0.656763	−0.328381	−	0.944545i	$-0.606503\pi$
$313$	−3636.85	−0.656763	−0.328381	+	0.944545i	$0.606503\pi$
$314$	3565.46	0.640798
$315$	3842.89	0.687373
$316$	−2017.72	−0.359196
$317$	8639.17	1.53068	0.765338	−	0.643629i	$-0.222572\pi$
$317$	8639.17	1.53068	0.765338	+	0.643629i	$0.222572\pi$
$318$	2665.75	0.470088
$319$	387.010	0.0679260
$320$	−3889.16	−0.679409
$321$	10469.8	1.82047
$322$	3808.96	0.659209
$323$	0	0
$324$	10712.0	1.83676
$325$	−1230.13	−0.209954
$326$	−3987.20	−0.677394
$327$	15691.4	2.65364
$328$	617.252	0.103909
$329$	−2299.81	−0.385388
$330$	7336.86	1.22388
$331$	−2084.40	−0.346131	−0.173065	−	0.984910i	$-0.555367\pi$
$331$	−2084.40	−0.346131	−0.173065	+	0.984910i	$0.555367\pi$
$332$	−4383.94	−0.724699
$333$	−21161.9	−3.48248
$334$	5678.29	0.930246
$335$	7911.55	1.29031
$336$	4497.38	0.730214
$337$	6271.39	1.01372	0.506861	−	0.862028i	$-0.330806\pi$
$337$	6271.39	1.01372	0.506861	+	0.862028i	$0.330806\pi$
$338$	−5887.44	−0.947440
$339$	−1690.47	−0.270837
$340$	0	0
$341$	−4339.35	−0.689118
$342$	−17233.8	−2.72484
$343$	343.000	0.0539949
$344$	−1156.40	−0.181247
$345$	−11568.3	−1.80526
$346$	16656.9	2.58810
$347$	−6748.32	−1.04400	−0.522001	−	0.852945i	$-0.674814\pi$
$347$	−6748.32	−1.04400	−0.522001	+	0.852945i	$0.674814\pi$
$348$	1216.97	0.187461
$349$	5436.30	0.833806	0.416903	−	0.908951i	$-0.363115\pi$
$349$	5436.30	0.833806	0.416903	+	0.908951i	$0.363115\pi$
$350$	−1280.04	−0.195488
$351$	−8721.79	−1.32631
$352$	5592.74	0.846858
$353$	−2470.44	−0.372489	−0.186244	−	0.982503i	$-0.559632\pi$
$353$	−2470.44	−0.372489	−0.186244	+	0.982503i	$0.559632\pi$
$354$	−17413.9	−2.61451
$355$	−7384.87	−1.10408
$356$	1013.46	0.150881
$357$	0	0
$358$	−16785.1	−2.47799
$359$	−3608.58	−0.530512	−0.265256	−	0.964178i	$-0.585456\pi$
$359$	−3608.58	−0.530512	−0.265256	+	0.964178i	$0.585456\pi$
$360$	−1191.78	−0.174479
$361$	−1852.83	−0.270131
$362$	−10819.5	−1.57089
$363$	7847.02	1.13461
$364$	1378.40	0.198482
$365$	10221.4	1.46578
$366$	1240.54	0.177169
$367$	5029.56	0.715370	0.357685	−	0.933842i	$-0.383566\pi$
$367$	5029.56	0.715370	0.357685	+	0.933842i	$0.383566\pi$
$368$	−9429.99	−1.33579
$369$	−17620.7	−2.48590
$370$	−11889.2	−1.67052
$371$	−503.338	−0.0704366
$372$	−13645.3	−1.90182
$373$	8843.15	1.22756	0.613781	−	0.789476i	$-0.289648\pi$
$373$	8843.15	1.22756	0.613781	+	0.789476i	$0.289648\pi$
$374$	0	0
$375$	14332.4	1.97366
$376$	713.233	0.0978250
$377$	−458.026	−0.0625717
$378$	−9075.67	−1.23493
$379$	12892.4	1.74733	0.873667	−	0.486525i	$-0.161736\pi$
$379$	12892.4	1.74733	0.873667	+	0.486525i	$0.161736\pi$
$380$	−4668.06	−0.630175
$381$	18978.2	2.55192
$382$	−9135.80	−1.22363
$383$	−5211.84	−0.695333	−0.347666	−	0.937618i	$-0.613026\pi$
$383$	−5211.84	−0.695333	−0.347666	+	0.937618i	$0.613026\pi$
$384$	−2614.80	−0.347489
$385$	−1385.32	−0.183383
$386$	−16044.3	−2.11563
$387$	33011.7	4.33612
$388$	−4980.49	−0.651665
$389$	−4139.68	−0.539563	−0.269781	−	0.962922i	$-0.586951\pi$
$389$	−4139.68	−0.539563	−0.269781	+	0.962922i	$0.586951\pi$
$390$	−8683.17	−1.12741
$391$	0	0
$392$	−106.373	−0.0137058
$393$	−7961.56	−1.02190
$394$	6116.44	0.782085
$395$	−2399.97	−0.305710
$396$	−10311.1	−1.30846
$397$	−12133.5	−1.53391	−0.766953	−	0.641703i	$-0.778228\pi$
$397$	−12133.5	−1.53391	−0.766953	+	0.641703i	$0.778228\pi$
$398$	6241.82	0.786116
$399$	4671.73	0.586163
$400$	3169.04	0.396130
$401$	2192.48	0.273035	0.136518	−	0.990638i	$-0.456409\pi$
$401$	2192.48	0.273035	0.136518	+	0.990638i	$0.456409\pi$
$402$	−33109.8	−4.10788
$403$	5135.62	0.634798
$404$	−4451.33	−0.548174
$405$	12741.3	1.56326
$406$	−476.610	−0.0582605
$407$	7628.63	0.929084
$408$	0	0
$409$	−13267.8	−1.60404	−0.802019	−	0.597299i	$-0.796241\pi$
$409$	−13267.8	−1.60404	−0.802019	+	0.597299i	$0.796241\pi$
$410$	−9899.67	−1.19246
$411$	933.401	0.112023
$412$	−6707.53	−0.802079
$413$	3288.02	0.391750
$414$	33721.4	4.00318
$415$	−5214.45	−0.616788
$416$	−6619.00	−0.780104
$417$	−15236.4	−1.78928
$418$	6212.59	0.726956
$419$	−2475.03	−0.288576	−0.144288	−	0.989536i	$-0.546089\pi$
$419$	−2475.03	−0.288576	−0.144288	+	0.989536i	$0.546089\pi$
$420$	−4356.21	−0.506098
$421$	12506.8	1.44785	0.723925	−	0.689879i	$-0.242336\pi$
$421$	12506.8	1.44785	0.723925	+	0.689879i	$0.242336\pi$
$422$	−15004.6	−1.73083
$423$	−20360.6	−2.34035
$424$	156.098	0.0178793
$425$	0	0
$426$	30905.6	3.51498
$427$	−234.234	−0.0265465
$428$	−8266.72	−0.933614
$429$	5571.49	0.627026
$430$	18546.7	2.08000
$431$	−5659.14	−0.632462	−0.316231	−	0.948682i	$-0.602417\pi$
$431$	−5659.14	−0.632462	−0.316231	+	0.948682i	$0.602417\pi$
$432$	22469.0	2.50241
$433$	−14602.7	−1.62069	−0.810347	−	0.585950i	$-0.800721\pi$
$433$	−14602.7	−1.62069	−0.810347	+	0.585950i	$0.800721\pi$
$434$	5344.00	0.591060
$435$	1447.52	0.159548
$436$	−12389.6	−1.36090
$437$	−9795.58	−1.07228
$438$	−42776.3	−4.66651
$439$	2832.32	0.307925	0.153963	−	0.988077i	$-0.450796\pi$
$439$	2832.32	0.307925	0.153963	+	0.988077i	$0.450796\pi$
$440$	429.624	0.0465489
$441$	3036.64	0.327895
$442$	0	0
$443$	−689.867	−0.0739877	−0.0369939	−	0.999315i	$-0.511778\pi$
$443$	−689.867	−0.0739877	−0.0369939	+	0.999315i	$0.511778\pi$
$444$	23988.6	2.56408
$445$	1205.46	0.128414
$446$	−7888.83	−0.837549
$447$	32693.7	3.45942
$448$	−3073.20	−0.324096
$449$	3658.88	0.384573	0.192286	−	0.981339i	$-0.438410\pi$
$449$	3658.88	0.384573	0.192286	+	0.981339i	$0.438410\pi$
$450$	−11332.4	−1.18714
$451$	6352.05	0.663207
$452$	1334.75	0.138897
$453$	−5405.06	−0.560600
$454$	−13908.8	−1.43783
$455$	1639.52	0.168928
$456$	−1448.83	−0.148789
$457$	4852.75	0.496723	0.248361	−	0.968667i	$-0.420108\pi$
$457$	4852.75	0.496723	0.248361	+	0.968667i	$0.420108\pi$
$458$	10707.1	1.09238
$459$	0	0
$460$	9134.00	0.925815
$461$	14413.7	1.45621	0.728105	−	0.685466i	$-0.240402\pi$
$461$	14413.7	1.45621	0.728105	+	0.685466i	$0.240402\pi$
$462$	5797.55	0.583824
$463$	2377.15	0.238608	0.119304	−	0.992858i	$-0.461934\pi$
$463$	2377.15	0.238608	0.119304	+	0.992858i	$0.461934\pi$
$464$	1179.96	0.118057
$465$	−16230.3	−1.61863
$466$	−20329.6	−2.02092
$467$	−3789.21	−0.375468	−0.187734	−	0.982220i	$-0.560114\pi$
$467$	−3789.21	−0.375468	−0.187734	+	0.982220i	$0.560114\pi$
$468$	12203.2	1.20532
$469$	6251.67	0.615512
$470$	−11439.0	−1.12265
$471$	−8556.80	−0.837105
$472$	−1019.70	−0.0994398
$473$	−11900.3	−1.15682
$474$	10043.9	0.973269
$475$	3291.90	0.317984
$476$	0	0
$477$	−4456.13	−0.427741
$478$	−5595.42	−0.535415
$479$	6696.56	0.638776	0.319388	−	0.947624i	$-0.396523\pi$
$479$	6696.56	0.638776	0.319388	+	0.947624i	$0.396523\pi$
$480$	20918.3	1.98914
$481$	−9028.48	−0.855849
$482$	−18707.6	−1.76786
$483$	−9141.18	−0.861156
$484$	−6195.80	−0.581875
$485$	−5924.01	−0.554630
$486$	−18316.0	−1.70953
$487$	157.846	0.0146872	0.00734362	−	0.999973i	$-0.497662\pi$
$487$	157.846	0.0146872	0.00734362	+	0.999973i	$0.497662\pi$
$488$	72.6420	0.00673842
$489$	9568.94	0.884913
$490$	1706.05	0.157288
$491$	13786.7	1.26718	0.633591	−	0.773668i	$-0.281580\pi$
$491$	13786.7	1.26718	0.633591	+	0.773668i	$0.281580\pi$
$492$	19974.4	1.83031
$493$	0	0
$494$	−7352.59	−0.669653
$495$	−12264.5	−1.11363
$496$	−13230.3	−1.19770
$497$	−5835.49	−0.526675
$498$	21822.4	1.96363
$499$	16222.9	1.45539	0.727693	−	0.685903i	$-0.240592\pi$
$499$	16222.9	1.45539	0.727693	+	0.685903i	$0.240592\pi$
$500$	−11316.5	−1.01218
$501$	−13627.4	−1.21523
$502$	6461.52	0.574486
$503$	9374.24	0.830968	0.415484	−	0.909601i	$-0.363612\pi$
$503$	9374.24	0.830968	0.415484	+	0.909601i	$0.363612\pi$
$504$	−941.741	−0.0832311
$505$	−5294.61	−0.466549
$506$	−12156.2	−1.06800
$507$	14129.4	1.23769
$508$	−14984.7	−1.30874
$509$	2374.04	0.206734	0.103367	−	0.994643i	$-0.467038\pi$
$509$	2374.04	0.206734	0.103367	+	0.994643i	$0.467038\pi$
$510$	0	0
$511$	8076.87	0.699216
$512$	15868.9	1.36975
$513$	23340.1	2.00875
$514$	−24238.2	−2.07997
$515$	−7978.23	−0.682646
$516$	−37421.2	−3.19259
$517$	7339.78	0.624377
$518$	−9394.81	−0.796880
$519$	−39975.2	−3.38096
$520$	−508.460	−0.0428797
$521$	−3619.07	−0.304327	−0.152164	−	0.988355i	$-0.548624\pi$
$521$	−3619.07	−0.304327	−0.152164	+	0.988355i	$0.548624\pi$
$522$	−4219.51	−0.353799
$523$	1960.92	0.163949	0.0819743	−	0.996634i	$-0.473877\pi$
$523$	1960.92	0.163949	0.0819743	+	0.996634i	$0.473877\pi$
$524$	6286.24	0.524076
$525$	3071.98	0.255376
$526$	−4198.79	−0.348053
$527$	0	0
$528$	−14353.2	−1.18304
$529$	7000.03	0.575329
$530$	−2503.55	−0.205184
$531$	29109.4	2.37898
$532$	−3688.68	−0.300610
$533$	−7517.65	−0.610930
$534$	−5044.83	−0.408823
$535$	−9832.79	−0.794596
$536$	−1938.81	−0.156238
$537$	40282.9	3.23712
$538$	−9207.40	−0.737842
$539$	−1094.67	−0.0874785
$540$	−21763.7	−1.73437
$541$	−12020.5	−0.955272	−0.477636	−	0.878558i	$-0.658506\pi$
$541$	−12020.5	−0.955272	−0.477636	+	0.878558i	$0.658506\pi$
$542$	12897.5	1.02213
$543$	25965.9	2.05213
$544$	0	0
$545$	−14736.7	−1.15826
$546$	−6861.40	−0.537804
$547$	−16516.4	−1.29102	−0.645512	−	0.763750i	$-0.723356\pi$
$547$	−16516.4	−1.29102	−0.645512	+	0.763750i	$0.723356\pi$
$548$	−736.989	−0.0574500
$549$	−2073.71	−0.161209
$550$	4085.20	0.316715
$551$	1225.71	0.0947675
$552$	2834.92	0.218591
$553$	−1896.44	−0.145832
$554$	−27434.4	−2.10393
$555$	28533.1	2.18228
$556$	12030.3	0.917622
$557$	−2504.68	−0.190533	−0.0952665	−	0.995452i	$-0.530370\pi$
$557$	−2504.68	−0.190533	−0.0952665	+	0.995452i	$0.530370\pi$
$558$	47311.3	3.58933
$559$	14084.0	1.06564
$560$	−4223.73	−0.318723
$561$	0	0
$562$	−8869.44	−0.665720
$563$	−3051.24	−0.228410	−0.114205	−	0.993457i	$-0.536432\pi$
$563$	−3051.24	−0.228410	−0.114205	+	0.993457i	$0.536432\pi$
$564$	23080.3	1.72315
$565$	1587.61	0.118215
$566$	19688.4	1.46213
$567$	10068.1	0.745715
$568$	1809.74	0.133688
$569$	−641.900	−0.0472932	−0.0236466	−	0.999720i	$-0.507528\pi$
$569$	−641.900	−0.0472932	−0.0236466	+	0.999720i	$0.507528\pi$
$570$	23236.7	1.70751
$571$	9690.89	0.710248	0.355124	−	0.934819i	$-0.384439\pi$
$571$	9690.89	0.710248	0.355124	+	0.934819i	$0.384439\pi$
$572$	−4399.11	−0.321566
$573$	21925.1	1.59849
$574$	−7822.67	−0.568836
$575$	−6441.26	−0.467164
$576$	−27207.5	−1.96814
$577$	22461.3	1.62058	0.810292	−	0.586026i	$-0.199308\pi$
$577$	22461.3	1.62058	0.810292	+	0.586026i	$0.199308\pi$
$578$	0	0
$579$	38504.9	2.76375
$580$	−1142.92	−0.0818230
$581$	−4120.43	−0.294224
$582$	24791.9	1.76574
$583$	1606.39	0.114116
$584$	−2504.85	−0.177485
$585$	14515.0	1.02585
$586$	−16976.4	−1.19674
$587$	2755.77	0.193770	0.0968849	−	0.995296i	$-0.469112\pi$
$587$	2755.77	0.193770	0.0968849	+	0.995296i	$0.469112\pi$
$588$	−3442.26	−0.241422
$589$	−13743.3	−0.961428
$590$	16354.3	1.14118
$591$	−14678.9	−1.02168
$592$	23259.1	1.61477
$593$	18946.4	1.31203	0.656015	−	0.754747i	$-0.272241\pi$
$593$	18946.4	1.31203	0.656015	+	0.754747i	$0.272241\pi$
$594$	28964.7	2.00073
$595$	0	0
$596$	−25814.1	−1.77414
$597$	−14979.8	−1.02694
$598$	14386.8	0.983814
$599$	17975.5	1.22614	0.613070	−	0.790029i	$-0.289934\pi$
$599$	17975.5	1.22614	0.613070	+	0.790029i	$0.289934\pi$
$600$	−952.703	−0.0648232
$601$	−8801.27	−0.597357	−0.298678	−	0.954354i	$-0.596546\pi$
$601$	−8801.27	−0.597357	−0.298678	+	0.954354i	$0.596546\pi$
$602$	14655.5	0.992214
$603$	55347.1	3.73782
$604$	4267.69	0.287500
$605$	−7369.56	−0.495231
$606$	22157.9	1.48532
$607$	−10986.3	−0.734631	−0.367315	−	0.930096i	$-0.619723\pi$
$607$	−10986.3	−0.734631	−0.367315	+	0.930096i	$0.619723\pi$
$608$	17712.9	1.18150
$609$	1143.82	0.0761085
$610$	−1165.05	−0.0773306
$611$	−8686.62	−0.575160
$612$	0	0
$613$	−4473.68	−0.294764	−0.147382	−	0.989080i	$-0.547085\pi$
$613$	−4473.68	−0.294764	−0.147382	+	0.989080i	$0.547085\pi$
$614$	37738.6	2.48047
$615$	23758.4	1.55777
$616$	339.487	0.0222051
$617$	6126.50	0.399746	0.199873	−	0.979822i	$-0.435947\pi$
$617$	6126.50	0.399746	0.199873	+	0.979822i	$0.435947\pi$
$618$	33388.8	2.17329
$619$	1433.55	0.0930844	0.0465422	−	0.998916i	$-0.485180\pi$
$619$	1433.55	0.0930844	0.0465422	+	0.998916i	$0.485180\pi$
$620$	12815.1	0.830105
$621$	−45669.6	−2.95114
$622$	3971.29	0.256003
$623$	952.547	0.0612568
$624$	16987.0	1.08978
$625$	−7644.64	−0.489257
$626$	−14294.1	−0.912631
$627$	−14909.7	−0.949657
$628$	6756.23	0.429304
$629$	0	0
$630$	15103.9	0.955166
$631$	−387.780	−0.0244648	−0.0122324	−	0.999925i	$-0.503894\pi$
$631$	−387.780	−0.0244648	−0.0122324	+	0.999925i	$0.503894\pi$
$632$	588.138	0.0370172
$633$	36009.7	2.26107
$634$	33955.0	2.12701
$635$	−17823.4	−1.11386
$636$	5051.36	0.314936
$637$	1295.54	0.0805830
$638$	1521.09	0.0943893
$639$	−51662.6	−3.19834
$640$	2455.69	0.151672
$641$	2957.71	0.182251	0.0911253	−	0.995839i	$-0.470954\pi$
$641$	2957.71	0.182251	0.0911253	+	0.995839i	$0.470954\pi$
$642$	41150.2	2.52970
$643$	−12435.4	−0.762679	−0.381339	−	0.924435i	$-0.624537\pi$
$643$	−12435.4	−0.762679	−0.381339	+	0.924435i	$0.624537\pi$
$644$	7217.64	0.441638
$645$	−44510.4	−2.71720
$646$	0	0
$647$	−13556.5	−0.823743	−0.411872	−	0.911242i	$-0.635125\pi$
$647$	−13556.5	−0.823743	−0.411872	+	0.911242i	$0.635125\pi$
$648$	−3122.39	−0.189288
$649$	−10493.6	−0.634684
$650$	−4834.83	−0.291750
$651$	−12825.1	−0.772130
$652$	−7555.38	−0.453822
$653$	14638.4	0.877254	0.438627	−	0.898669i	$-0.355465\pi$
$653$	14638.4	0.877254	0.438627	+	0.898669i	$0.355465\pi$
$654$	61672.9	3.68746
$655$	7477.12	0.446039
$656$	19366.9	1.15267
$657$	71505.8	4.24613
$658$	−9039.07	−0.535532
$659$	6764.02	0.399831	0.199916	−	0.979813i	$-0.435933\pi$
$659$	6764.02	0.399831	0.199916	+	0.979813i	$0.435933\pi$
$660$	13902.7	0.819942
$661$	−13961.6	−0.821549	−0.410774	−	0.911737i	$-0.634742\pi$
$661$	−13961.6	−0.821549	−0.410774	+	0.911737i	$0.634742\pi$
$662$	−8192.44	−0.480979
$663$	0	0
$664$	1277.86	0.0746843
$665$	−4387.47	−0.255848
$666$	−83173.8	−4.83922
$667$	−2398.34	−0.139227
$668$	10759.8	0.623220
$669$	18932.5	1.09413
$670$	31095.2	1.79300
$671$	747.548	0.0430086
$672$	16529.6	0.948871
$673$	−9308.34	−0.533151	−0.266575	−	0.963814i	$-0.585892\pi$
$673$	−9308.34	−0.533151	−0.266575	+	0.963814i	$0.585892\pi$
$674$	24648.8	1.40866
$675$	15347.7	0.875160
$676$	−11156.2	−0.634739
$677$	10440.6	0.592709	0.296354	−	0.955078i	$-0.404229\pi$
$677$	10440.6	0.592709	0.296354	+	0.955078i	$0.404229\pi$
$678$	−6644.14	−0.376352
$679$	−4681.12	−0.264573
$680$	0	0
$681$	33380.0	1.87830
$682$	−17055.2	−0.957591
$683$	14822.6	0.830412	0.415206	−	0.909727i	$-0.363710\pi$
$683$	14822.6	0.830412	0.415206	+	0.909727i	$0.363710\pi$
$684$	−32656.5	−1.82551
$685$	−876.607	−0.0488955
$686$	1348.11	0.0750308
$687$	−25696.1	−1.42703
$688$	−36283.1	−2.01058
$689$	−1901.16	−0.105121
$690$	−45467.3	−2.50857
$691$	10908.5	0.600547	0.300274	−	0.953853i	$-0.402922\pi$
$691$	10908.5	0.600547	0.300274	+	0.953853i	$0.402922\pi$
$692$	31563.4	1.73390
$693$	−9691.32	−0.531231
$694$	−26523.3	−1.45073
$695$	14309.3	0.780984
$696$	−354.730	−0.0193190
$697$	0	0
$698$	21366.6	1.15865
$699$	48789.2	2.64002
$700$	−2425.56	−0.130968
$701$	10608.7	0.571592	0.285796	−	0.958291i	$-0.407742\pi$
$701$	10608.7	0.571592	0.285796	+	0.958291i	$0.407742\pi$
$702$	−34279.7	−1.84303
$703$	24160.8	1.29622
$704$	9808.01	0.525076
$705$	27452.7	1.46657
$706$	−9709.71	−0.517606
$707$	−4183.78	−0.222556
$708$	−32997.7	−1.75159
$709$	−32294.4	−1.71064	−0.855318	−	0.518103i	$-0.826638\pi$
$709$	−32294.4	−1.71064	−0.855318	+	0.518103i	$0.826638\pi$
$710$	−29025.1	−1.53422
$711$	−16789.5	−0.885593
$712$	−295.410	−0.0155491
$713$	26891.4	1.41247
$714$	0	0
$715$	−5232.49	−0.273684
$716$	−31806.3	−1.66014
$717$	13428.5	0.699439
$718$	−14183.0	−0.737193
$719$	29131.4	1.51101	0.755505	−	0.655142i	$-0.227391\pi$
$719$	29131.4	1.51101	0.755505	+	0.655142i	$0.227391\pi$
$720$	−37393.3	−1.93551
$721$	−6304.36	−0.325640
$722$	−7282.26	−0.375371
$723$	44896.7	2.30944
$724$	−20502.0	−1.05242
$725$	805.986	0.0412877
$726$	30841.5	1.57664
$727$	27738.0	1.41506	0.707528	−	0.706685i	$-0.249810\pi$
$727$	27738.0	1.41506	0.707528	+	0.706685i	$0.249810\pi$
$728$	−401.783	−0.0204548
$729$	5122.76	0.260263
$730$	40173.5	2.03683
$731$	0	0
$732$	2350.70	0.118695
$733$	−5036.56	−0.253792	−0.126896	−	0.991916i	$-0.540501\pi$
$733$	−5036.56	−0.253792	−0.126896	+	0.991916i	$0.540501\pi$
$734$	19767.9	0.994070
$735$	−4094.37	−0.205473
$736$	−34658.8	−1.73579
$737$	−19952.0	−0.997206
$738$	−69255.4	−3.45437
$739$	−8573.21	−0.426753	−0.213376	−	0.976970i	$-0.568446\pi$
$739$	−8573.21	−0.426753	−0.213376	+	0.976970i	$0.568446\pi$
$740$	−22529.0	−1.11917
$741$	17645.6	0.874800
$742$	−1978.29	−0.0978780
$743$	39607.6	1.95567	0.977835	−	0.209377i	$-0.0671435\pi$
$743$	39607.6	1.95567	0.977835	+	0.209377i	$0.0671435\pi$
$744$	3977.41	0.195993
$745$	−30704.4	−1.50996
$746$	34756.7	1.70581
$747$	−36478.9	−1.78674
$748$	0	0
$749$	−7769.83	−0.379043
$750$	56331.5	2.74258
$751$	745.217	0.0362095	0.0181048	−	0.999836i	$-0.494237\pi$
$751$	745.217	0.0362095	0.0181048	+	0.999836i	$0.494237\pi$
$752$	22378.4	1.08518
$753$	−15507.1	−0.750478
$754$	−1800.20	−0.0869490
$755$	5076.18	0.244690
$756$	−17197.6	−0.827341
$757$	−30762.6	−1.47699	−0.738497	−	0.674257i	$-0.764464\pi$
$757$	−30762.6	−1.47699	−0.738497	+	0.674257i	$0.764464\pi$
$758$	50671.8	2.42808
$759$	29173.8	1.39518
$760$	1360.67	0.0649431
$761$	−29341.3	−1.39766	−0.698831	−	0.715287i	$-0.746296\pi$
$761$	−29341.3	−1.39766	−0.698831	+	0.715287i	$0.746296\pi$
$762$	74591.0	3.54612
$763$	−11644.8	−0.552519
$764$	−17311.5	−0.819776
$765$	0	0
$766$	−20484.4	−0.966227
$767$	12419.2	0.584655
$768$	−43406.2	−2.03943
$769$	2295.12	0.107626	0.0538128	−	0.998551i	$-0.482863\pi$
$769$	2295.12	0.107626	0.0538128	+	0.998551i	$0.482863\pi$
$770$	−5444.79	−0.254827
$771$	58169.6	2.71716
$772$	−30402.5	−1.41737
$773$	20671.9	0.961858	0.480929	−	0.876759i	$-0.340299\pi$
$773$	20671.9	0.961858	0.480929	+	0.876759i	$0.340299\pi$
$774$	129747.	6.02542
$775$	−9037.12	−0.418868
$776$	1451.74	0.0671578
$777$	22546.7	1.04100
$778$	−16270.4	−0.749770
$779$	20117.7	0.925279
$780$	−16453.8	−0.755309
$781$	18623.8	0.853279
$782$	0	0
$783$	5714.57	0.260820
$784$	−3337.57	−0.152039
$785$	8036.15	0.365379
$786$	−31291.7	−1.42002
$787$	−13292.8	−0.602079	−0.301040	−	0.953612i	$-0.597334\pi$
$787$	−13292.8	−0.602079	−0.301040	+	0.953612i	$0.597334\pi$
$788$	11590.1	0.523959
$789$	10076.7	0.454678
$790$	−9432.72	−0.424812
$791$	1254.52	0.0563915
$792$	3005.54	0.134845
$793$	−884.723	−0.0396184
$794$	−47688.8	−2.13150
$795$	6008.31	0.268041
$796$	11827.7	0.526660
$797$	−13226.2	−0.587826	−0.293913	−	0.955832i	$-0.594958\pi$
$797$	−13226.2	−0.587826	−0.293913	+	0.955832i	$0.594958\pi$
$798$	18361.6	0.814526
$799$	0	0
$800$	11647.4	0.514748
$801$	8433.05	0.371994
$802$	8617.21	0.379407
$803$	−25777.0	−1.13282
$804$	−62740.1	−2.75208
$805$	8584.97	0.375877
$806$	20184.8	0.882108
$807$	22097.0	0.963878
$808$	1297.50	0.0564924
$809$	−20227.3	−0.879052	−0.439526	−	0.898230i	$-0.644854\pi$
$809$	−20227.3	−0.879052	−0.439526	+	0.898230i	$0.644854\pi$
$810$	50077.7	2.17229
$811$	13696.5	0.593034	0.296517	−	0.955028i	$-0.404175\pi$
$811$	13696.5	0.593034	0.296517	+	0.955028i	$0.404175\pi$
$812$	−903.133	−0.0390317
$813$	−30952.9	−1.33526
$814$	29983.2	1.29105
$815$	−8986.70	−0.386246
$816$	0	0
$817$	−37689.8	−1.61395
$818$	−52147.2	−2.22895
$819$	11469.7	0.489356
$820$	−18759.0	−0.798893
$821$	4423.08	0.188022	0.0940112	−	0.995571i	$-0.470031\pi$
$821$	4423.08	0.188022	0.0940112	+	0.995571i	$0.470031\pi$
$822$	3668.59	0.155665
$823$	−21330.0	−0.903422	−0.451711	−	0.892164i	$-0.649186\pi$
$823$	−21330.0	−0.903422	−0.451711	+	0.892164i	$0.649186\pi$
$824$	1955.15	0.0826588
$825$	−9804.12	−0.413740
$826$	12923.1	0.544372
$827$	4359.67	0.183314	0.0916570	−	0.995791i	$-0.470784\pi$
$827$	4359.67	0.183314	0.0916570	+	0.995791i	$0.470784\pi$
$828$	63899.0	2.68194
$829$	27874.3	1.16781	0.583905	−	0.811822i	$-0.301524\pi$
$829$	27874.3	1.16781	0.583905	+	0.811822i	$0.301524\pi$
$830$	−20494.6	−0.857082
$831$	65840.3	2.74846
$832$	−11607.8	−0.483687
$833$	0	0
$834$	−59884.5	−2.48637
$835$	12798.2	0.530420
$836$	11772.3	0.487025
$837$	−64074.7	−2.64605
$838$	−9727.75	−0.401002
$839$	−40422.6	−1.66334	−0.831670	−	0.555270i	$-0.812615\pi$
$839$	−40422.6	−1.66334	−0.831670	+	0.555270i	$0.812615\pi$
$840$	1269.77	0.0521563
$841$	−24088.9	−0.987695
$842$	49156.2	2.01192
$843$	21285.9	0.869662
$844$	−28432.3	−1.15957
$845$	−13269.6	−0.540224
$846$	−80024.4	−3.25212
$847$	−5823.39	−0.236238
$848$	4897.74	0.198336
$849$	−47250.6	−1.91005
$850$	0	0
$851$	−47275.5	−1.90433
$852$	58563.4	2.35487
$853$	8470.48	0.340004	0.170002	−	0.985444i	$-0.445623\pi$
$853$	8470.48	0.340004	0.170002	+	0.985444i	$0.445623\pi$
$854$	−920.620	−0.0368887
$855$	−38843.0	−1.55369
$856$	2409.63	0.0962143
$857$	−29290.0	−1.16748	−0.583739	−	0.811942i	$-0.698411\pi$
$857$	−29290.0	−1.16748	−0.583739	+	0.811942i	$0.698411\pi$
$858$	21897.9	0.871309
$859$	−38954.3	−1.54727	−0.773635	−	0.633632i	$-0.781563\pi$
$859$	−38954.3	−1.54727	−0.773635	+	0.633632i	$0.781563\pi$
$860$	35144.3	1.39350
$861$	18773.7	0.743098
$862$	−22242.4	−0.878862
$863$	−18804.3	−0.741721	−0.370860	−	0.928689i	$-0.620937\pi$
$863$	−18804.3	−0.741721	−0.370860	+	0.928689i	$0.620937\pi$
$864$	82582.1	3.25173
$865$	37542.9	1.47572
$866$	−57393.7	−2.25210
$867$	0	0
$868$	10126.4	0.395982
$869$	6052.44	0.236266
$870$	5689.26	0.221706
$871$	23613.2	0.918601
$872$	3611.38	0.140248
$873$	−41442.8	−1.60667
$874$	−38500.1	−1.49003
$875$	−10636.3	−0.410940
$876$	−81057.2	−3.12634
$877$	−12939.6	−0.498222	−0.249111	−	0.968475i	$-0.580138\pi$
$877$	−12939.6	−0.498222	−0.249111	+	0.968475i	$0.580138\pi$
$878$	11132.0	0.427889
$879$	40741.8	1.56335
$880$	13479.9	0.516371
$881$	−33770.6	−1.29144	−0.645720	−	0.763574i	$-0.723443\pi$
$881$	−33770.6	−1.29144	−0.645720	+	0.763574i	$0.723443\pi$
$882$	11935.0	0.455639
$883$	−18647.4	−0.710686	−0.355343	−	0.934736i	$-0.615636\pi$
$883$	−18647.4	−0.710686	−0.355343	+	0.934736i	$0.615636\pi$
$884$	0	0
$885$	−39248.9	−1.49078
$886$	−2711.42	−0.102813
$887$	−20404.3	−0.772388	−0.386194	−	0.922418i	$-0.626210\pi$
$887$	−20404.3	−0.772388	−0.386194	+	0.922418i	$0.626210\pi$
$888$	−6992.34	−0.264243
$889$	−14084.0	−0.531341
$890$	4737.87	0.178442
$891$	−32132.0	−1.20815
$892$	−14948.6	−0.561117
$893$	23246.0	0.871104
$894$	128498.	4.80717
$895$	−37831.8	−1.41294
$896$	1940.48	0.0723513
$897$	−34527.1	−1.28520
$898$	14380.7	0.534398
$899$	−3364.89	−0.124834
$900$	−21473.8	−0.795328
$901$	0	0
$902$	24965.8	0.921586
$903$	−35171.9	−1.29618
$904$	−389.061	−0.0143141
$905$	−24386.0	−0.895710
$906$	−21243.8	−0.779003
$907$	36787.9	1.34677	0.673386	−	0.739291i	$-0.264839\pi$
$907$	36787.9	1.34677	0.673386	+	0.739291i	$0.264839\pi$
$908$	−26356.0	−0.963276
$909$	−37039.7	−1.35152
$910$	6443.91	0.234740
$911$	−12593.4	−0.458001	−0.229001	−	0.973426i	$-0.573546\pi$
$911$	−12593.4	−0.458001	−0.229001	+	0.973426i	$0.573546\pi$
$912$	−45458.4	−1.65052
$913$	13150.2	0.476680
$914$	19073.0	0.690240
$915$	2796.03	0.101021
$916$	20289.0	0.731841
$917$	5908.39	0.212772
$918$	0	0
$919$	15168.4	0.544460	0.272230	−	0.962232i	$-0.412239\pi$
$919$	15168.4	0.544460	0.272230	+	0.962232i	$0.412239\pi$
$920$	−2662.43	−0.0954105
$921$	−90569.5	−3.24035
$922$	56650.9	2.02353
$923$	−22041.2	−0.786019
$924$	10985.8	0.391134
$925$	15887.4	0.564728
$926$	9343.01	0.331566
$927$	−55813.5	−1.97752
$928$	4336.81	0.153408
$929$	7327.73	0.258789	0.129395	−	0.991593i	$-0.458697\pi$
$929$	7327.73	0.258789	0.129395	+	0.991593i	$0.458697\pi$
$930$	−63790.9	−2.24923
$931$	−3466.96	−0.122046
$932$	−38522.7	−1.35392
$933$	−9530.75	−0.334430
$934$	−14892.9	−0.521747
$935$	0	0
$936$	−3557.05	−0.124216
$937$	33511.5	1.16838	0.584190	−	0.811617i	$-0.301412\pi$
$937$	33511.5	1.16838	0.584190	+	0.811617i	$0.301412\pi$
$938$	24571.3	0.855309
$939$	34304.6	1.19221
$940$	−21675.9	−0.752118
$941$	−1024.08	−0.0354773	−0.0177387	−	0.999843i	$-0.505647\pi$
$941$	−1024.08	−0.0354773	−0.0177387	+	0.999843i	$0.505647\pi$
$942$	−33631.2	−1.16323
$943$	−39364.4	−1.35936
$944$	−31994.1	−1.10309
$945$	−20455.5	−0.704147
$946$	−46772.5	−1.60751
$947$	3511.72	0.120502	0.0602512	−	0.998183i	$-0.480810\pi$
$947$	3511.72	0.120502	0.0602512	+	0.998183i	$0.480810\pi$
$948$	19032.2	0.652043
$949$	30507.1	1.04352
$950$	12938.3	0.441868
$951$	−81489.0	−2.77862
$952$	0	0
$953$	12692.7	0.431435	0.215718	−	0.976456i	$-0.430791\pi$
$953$	12692.7	0.431435	0.215718	+	0.976456i	$0.430791\pi$
$954$	−17514.2	−0.594384
$955$	−20591.1	−0.697708
$956$	−10602.8	−0.358702
$957$	−3650.47	−0.123305
$958$	26319.8	0.887636
$959$	−692.691	−0.0233244
$960$	36684.6	1.23332
$961$	7937.86	0.266452
$962$	−35485.1	−1.18928
$963$	−68787.6	−2.30182
$964$	−35449.3	−1.18438
$965$	−36162.0	−1.20632
$966$	−35928.1	−1.19665
$967$	14772.8	0.491273	0.245637	−	0.969362i	$-0.421003\pi$
$967$	14772.8	0.491273	0.245637	+	0.969362i	$0.421003\pi$
$968$	1805.99	0.0599655
$969$	0	0
$970$	−23283.4	−0.770707
$971$	−57034.1	−1.88497	−0.942487	−	0.334242i	$-0.891520\pi$
$971$	−57034.1	−1.88497	−0.942487	+	0.334242i	$0.891520\pi$
$972$	−34707.2	−1.14530
$973$	11307.2	0.372550
$974$	620.390	0.0204092
$975$	11603.2	0.381127
$976$	2279.21	0.0747498
$977$	10574.4	0.346270	0.173135	−	0.984898i	$-0.444610\pi$
$977$	10574.4	0.346270	0.173135	+	0.984898i	$0.444610\pi$
$978$	37609.3	1.22966
$979$	−3040.02	−0.0992436
$980$	3232.81	0.105376
$981$	−103094.	−3.35528
$982$	54186.7	1.76086
$983$	−47250.6	−1.53312	−0.766562	−	0.642171i	$-0.778034\pi$
$983$	−47250.6	−1.53312	−0.766562	+	0.642171i	$0.778034\pi$
$984$	−5822.24	−0.188624
$985$	13785.8	0.445940
$986$	0	0
$987$	21693.0	0.699590
$988$	−13932.5	−0.448636
$989$	73747.6	2.37112
$990$	−48203.6	−1.54749
$991$	−5984.02	−0.191815	−0.0959075	−	0.995390i	$-0.530575\pi$
$991$	−5984.02	−0.191815	−0.0959075	+	0.995390i	$0.530575\pi$
$992$	−48626.5	−1.55634
$993$	19661.2	0.628326
$994$	−22935.5	−0.731862
$995$	14068.4	0.448238
$996$	41351.5	1.31554
$997$	−27756.7	−0.881709	−0.440855	−	0.897579i	$-0.645325\pi$
$997$	−27756.7	−0.881709	−0.440855	+	0.897579i	$0.645325\pi$
$998$	63761.8	2.02239
$999$	112644.	3.56746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.g.1.6		7
17.16	even	2		119.4.a.d.1.6	✓	7
51.50	odd	2		1071.4.a.o.1.2		7
68.67	odd	2		1904.4.a.p.1.1		7
119.118	odd	2		833.4.a.f.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.4.a.d.1.6	✓	7	17.16	even	2
833.4.a.f.1.6		7	119.118	odd	2
1071.4.a.o.1.2		7	51.50	odd	2
1904.4.a.p.1.1		7	68.67	odd	2
2023.4.a.g.1.6		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)

\(f(q)\)	\(=\)	\(q+3.93035 q^{2} -9.43251 q^{3} +7.44766 q^{4} +8.85857 q^{5} -37.0731 q^{6} +7.00000 q^{7} -2.17089 q^{8} +61.9722 q^{9} +34.8173 q^{10} -22.3403 q^{11} -70.2501 q^{12} +26.4397 q^{13} +27.5125 q^{14} -83.5585 q^{15} -68.1136 q^{16} +243.572 q^{18} -70.7543 q^{19} +65.9756 q^{20} -66.0275 q^{21} -87.8051 q^{22} +138.445 q^{23} +20.4769 q^{24} -46.5257 q^{25} +103.917 q^{26} -329.875 q^{27} +52.1336 q^{28} -17.3234 q^{29} -328.414 q^{30} +194.239 q^{31} -250.343 q^{32} +210.725 q^{33} +62.0100 q^{35} +461.548 q^{36} -341.475 q^{37} -278.089 q^{38} -249.392 q^{39} -19.2309 q^{40} -284.332 q^{41} -259.511 q^{42} +532.685 q^{43} -166.383 q^{44} +548.985 q^{45} +544.138 q^{46} -328.545 q^{47} +642.482 q^{48} +49.0000 q^{49} -182.863 q^{50} +196.914 q^{52} -71.9054 q^{53} -1296.52 q^{54} -197.903 q^{55} -15.1962 q^{56} +667.390 q^{57} -68.0872 q^{58} +469.717 q^{59} -622.315 q^{60} -33.4619 q^{61} +763.428 q^{62} +433.805 q^{63} -439.029 q^{64} +234.218 q^{65} +828.222 q^{66} +893.096 q^{67} -1305.88 q^{69} +243.721 q^{70} -833.641 q^{71} -134.534 q^{72} +1153.84 q^{73} -1342.12 q^{74} +438.854 q^{75} -526.954 q^{76} -156.382 q^{77} -980.200 q^{78} -270.921 q^{79} -603.389 q^{80} +1438.30 q^{81} -1117.52 q^{82} -588.633 q^{83} -491.751 q^{84} +2093.64 q^{86} +163.403 q^{87} +48.4982 q^{88} +136.078 q^{89} +2157.70 q^{90} +185.078 q^{91} +1031.09 q^{92} -1832.16 q^{93} -1291.30 q^{94} -626.782 q^{95} +2361.37 q^{96} -668.732 q^{97} +192.587 q^{98} -1384.47 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} - 5 q^{3} + 52 q^{4} - 35 q^{5} - 51 q^{6} + 49 q^{7} - 6 q^{8} + 128 q^{9} - 18 q^{10} - 48 q^{11} + 16 q^{12} + 84 q^{13} + 28 q^{14} - 54 q^{15} + 256 q^{16} + 196 q^{18} + 156 q^{19} - 317 q^{20}+ \cdots - 7572 q^{99}+O(q^{100}) \) 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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