LMFDB - Embedded newform 2031.4.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2031,4,Mod(1,2031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2031.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2031 = 3 \cdot 677 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$119.832879222$
Analytic rank:	$0$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	2031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.55506 q^{2} +3.00000 q^{3} +12.7486 q^{4} +8.74592 q^{5} -13.6652 q^{6} +18.2953 q^{7} -21.6301 q^{8} +9.00000 q^{9} -39.8382 q^{10} +12.7063 q^{11} +38.2457 q^{12} +9.77175 q^{13} -83.3363 q^{14} +26.2378 q^{15} -3.46229 q^{16} +34.5355 q^{17} -40.9956 q^{18} +121.100 q^{19} +111.498 q^{20} +54.8859 q^{21} -57.8780 q^{22} +34.1060 q^{23} -64.8903 q^{24} -48.5088 q^{25} -44.5109 q^{26} +27.0000 q^{27} +233.239 q^{28} -31.4056 q^{29} -119.515 q^{30} +58.3665 q^{31} +188.812 q^{32} +38.1189 q^{33} -157.311 q^{34} +160.009 q^{35} +114.737 q^{36} -327.799 q^{37} -551.619 q^{38} +29.3153 q^{39} -189.175 q^{40} +245.245 q^{41} -250.009 q^{42} +110.450 q^{43} +161.987 q^{44} +78.7133 q^{45} -155.355 q^{46} +95.6811 q^{47} -10.3869 q^{48} -8.28164 q^{49} +220.961 q^{50} +103.607 q^{51} +124.576 q^{52} -440.957 q^{53} -122.987 q^{54} +111.128 q^{55} -395.729 q^{56} +363.301 q^{57} +143.054 q^{58} +406.828 q^{59} +334.494 q^{60} +623.637 q^{61} -265.863 q^{62} +164.658 q^{63} -832.350 q^{64} +85.4630 q^{65} -173.634 q^{66} +256.362 q^{67} +440.279 q^{68} +102.318 q^{69} -728.852 q^{70} +221.706 q^{71} -194.671 q^{72} -132.371 q^{73} +1493.15 q^{74} -145.526 q^{75} +1543.86 q^{76} +232.466 q^{77} -133.533 q^{78} +621.010 q^{79} -30.2809 q^{80} +81.0000 q^{81} -1117.10 q^{82} +514.471 q^{83} +699.718 q^{84} +302.045 q^{85} -503.107 q^{86} -94.2167 q^{87} -274.839 q^{88} -128.152 q^{89} -358.544 q^{90} +178.777 q^{91} +434.803 q^{92} +175.100 q^{93} -435.833 q^{94} +1059.13 q^{95} +566.435 q^{96} -1515.99 q^{97} +37.7234 q^{98} +114.357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q + 19 q^{2} + 282 q^{3} + 409 q^{4} + 84 q^{5} + 57 q^{6} + 39 q^{7} + 228 q^{8} + 846 q^{9} + 145 q^{10} + 357 q^{11} + 1227 q^{12} + 271 q^{13} + 366 q^{14} + 252 q^{15} + 1865 q^{16} + 690 q^{17}+ \cdots + 3213 q^{99}+O(q^{100}) $ 94 * q + 19 * q^2 + 282 * q^3 + 409 * q^4 + 84 * q^5 + 57 * q^6 + 39 * q^7 + 228 * q^8 + 846 * q^9 + 145 * q^10 + 357 * q^11 + 1227 * q^12 + 271 * q^13 + 366 * q^14 + 252 * q^15 + 1865 * q^16 + 690 * q^17 + 171 * q^18 + 345 * q^19 + 939 * q^20 + 117 * q^21 + 148 * q^22 + 1135 * q^23 + 684 * q^24 + 3280 * q^25 + 1261 * q^26 + 2538 * q^27 + 214 * q^28 + 1396 * q^29 + 435 * q^30 + 889 * q^31 + 2048 * q^32 + 1071 * q^33 + 1590 * q^34 + 2104 * q^35 + 3681 * q^36 + 711 * q^37 + 2075 * q^38 + 813 * q^39 + 1675 * q^40 + 2931 * q^41 + 1098 * q^42 + 585 * q^43 + 4058 * q^44 + 756 * q^45 + 1148 * q^46 + 2733 * q^47 + 5595 * q^48 + 8415 * q^49 + 2640 * q^50 + 2070 * q^51 + 2174 * q^52 + 3430 * q^53 + 513 * q^54 + 2458 * q^55 + 4034 * q^56 + 1035 * q^57 + 259 * q^58 + 5376 * q^59 + 2817 * q^60 + 2064 * q^61 + 3610 * q^62 + 351 * q^63 + 10194 * q^64 + 5442 * q^65 + 444 * q^66 + 1429 * q^67 + 6932 * q^68 + 3405 * q^69 + 3888 * q^70 + 5336 * q^71 + 2052 * q^72 + 2412 * q^73 + 5911 * q^74 + 9840 * q^75 + 5988 * q^76 + 7100 * q^77 + 3783 * q^78 + 2018 * q^79 + 8054 * q^80 + 7614 * q^81 + 3546 * q^82 + 6229 * q^83 + 642 * q^84 + 2728 * q^85 + 6619 * q^86 + 4188 * q^87 + 3679 * q^88 + 11972 * q^89 + 1305 * q^90 + 5586 * q^91 + 15073 * q^92 + 2667 * q^93 + 3650 * q^94 + 8168 * q^95 + 6144 * q^96 + 5859 * q^97 + 8121 * q^98 + 3213 * 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 $

$2$	−4.55506	−1.61046	−0.805229	−	0.592964i	$-0.797957\pi$
$2$	−4.55506	−1.61046	−0.805229	+	0.592964i	$0.797957\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	12.7486	1.59357
$5$	8.74592	0.782259	0.391130	−	0.920336i	$-0.372084\pi$
$5$	8.74592	0.782259	0.391130	+	0.920336i	$0.372084\pi$
$6$	−13.6652	−0.929798
$7$	18.2953	0.987854	0.493927	−	0.869503i	$-0.335561\pi$
$7$	18.2953	0.987854	0.493927	+	0.869503i	$0.335561\pi$
$8$	−21.6301	−0.955924
$9$	9.00000	0.333333
$10$	−39.8382	−1.25979
$11$	12.7063	0.348282	0.174141	−	0.984721i	$-0.444285\pi$
$11$	12.7063	0.348282	0.174141	+	0.984721i	$0.444285\pi$
$12$	38.2457	0.920050
$13$	9.77175	0.208477	0.104238	−	0.994552i	$-0.466760\pi$
$13$	9.77175	0.208477	0.104238	+	0.994552i	$0.466760\pi$
$14$	−83.3363	−1.59090
$15$	26.2378	0.451638
$16$	−3.46229	−0.0540983
$17$	34.5355	0.492712	0.246356	−	0.969179i	$-0.420767\pi$
$17$	34.5355	0.492712	0.246356	+	0.969179i	$0.420767\pi$
$18$	−40.9956	−0.536819
$19$	121.100	1.46223	0.731114	−	0.682256i	$-0.239001\pi$
$19$	121.100	1.46223	0.731114	+	0.682256i	$0.239001\pi$
$20$	111.498	1.24659
$21$	54.8859	0.570338
$22$	−57.8780	−0.560893
$23$	34.1060	0.309200	0.154600	−	0.987977i	$-0.450591\pi$
$23$	34.1060	0.309200	0.154600	+	0.987977i	$0.450591\pi$
$24$	−64.8903	−0.551903
$25$	−48.5088	−0.388071
$26$	−44.5109	−0.335743
$27$	27.0000	0.192450
$28$	233.239	1.57422
$29$	−31.4056	−0.201099	−0.100549	−	0.994932i	$-0.532060\pi$
$29$	−31.4056	−0.201099	−0.100549	+	0.994932i	$0.532060\pi$
$30$	−119.515	−0.727343
$31$	58.3665	0.338159	0.169080	−	0.985602i	$-0.445920\pi$
$31$	58.3665	0.338159	0.169080	+	0.985602i	$0.445920\pi$
$32$	188.812	1.04305
$33$	38.1189	0.201080
$34$	−157.311	−0.793491
$35$	160.009	0.772758
$36$	114.737	0.531191
$37$	−327.799	−1.45648	−0.728242	−	0.685320i	$-0.759662\pi$
$37$	−327.799	−1.45648	−0.728242	+	0.685320i	$0.759662\pi$
$38$	−551.619	−2.35485
$39$	29.3153	0.120364
$40$	−189.175	−0.747780
$41$	245.245	0.934165	0.467083	−	0.884214i	$-0.345305\pi$
$41$	245.245	0.934165	0.467083	+	0.884214i	$0.345305\pi$
$42$	−250.009	−0.918505
$43$	110.450	0.391709	0.195855	−	0.980633i	$-0.437252\pi$
$43$	110.450	0.391709	0.195855	+	0.980633i	$0.437252\pi$
$44$	161.987	0.555012
$45$	78.7133	0.260753
$46$	−155.355	−0.497953
$47$	95.6811	0.296947	0.148474	−	0.988916i	$-0.452564\pi$
$47$	95.6811	0.296947	0.148474	+	0.988916i	$0.452564\pi$
$48$	−10.3869	−0.0312337
$49$	−8.28164	−0.0241447
$50$	220.961	0.624971
$51$	103.607	0.284467
$52$	124.576	0.332223
$53$	−440.957	−1.14283	−0.571416	−	0.820660i	$-0.693606\pi$
$53$	−440.957	−1.14283	−0.571416	+	0.820660i	$0.693606\pi$
$54$	−122.987	−0.309933
$55$	111.128	0.272446
$56$	−395.729	−0.944313
$57$	363.301	0.844217
$58$	143.054	0.323861
$59$	406.828	0.897703	0.448852	−	0.893606i	$-0.351833\pi$
$59$	406.828	0.897703	0.448852	+	0.893606i	$0.351833\pi$
$60$	334.494	0.719717
$61$	623.637	1.30899	0.654496	−	0.756065i	$-0.272881\pi$
$61$	623.637	1.30899	0.654496	+	0.756065i	$0.272881\pi$
$62$	−265.863	−0.544591
$63$	164.658	0.329285
$64$	−832.350	−1.62568
$65$	85.4630	0.163083
$66$	−173.634	−0.323832
$67$	256.362	0.467457	0.233728	−	0.972302i	$-0.424907\pi$
$67$	256.362	0.467457	0.233728	+	0.972302i	$0.424907\pi$
$68$	440.279	0.785172
$69$	102.318	0.178517
$70$	−728.852	−1.24449
$71$	221.706	0.370586	0.185293	−	0.982683i	$-0.440677\pi$
$71$	221.706	0.370586	0.185293	+	0.982683i	$0.440677\pi$
$72$	−194.671	−0.318641
$73$	−132.371	−0.212230	−0.106115	−	0.994354i	$-0.533841\pi$
$73$	−132.371	−0.212230	−0.106115	+	0.994354i	$0.533841\pi$
$74$	1493.15	2.34560
$75$	−145.526	−0.224053
$76$	1543.86	2.33017
$77$	232.466	0.344051
$78$	−133.533	−0.193841
$79$	621.010	0.884419	0.442209	−	0.896912i	$-0.354195\pi$
$79$	621.010	0.884419	0.442209	+	0.896912i	$0.354195\pi$
$80$	−30.2809	−0.0423189
$81$	81.0000	0.111111
$82$	−1117.10	−1.50443
$83$	514.471	0.680367	0.340184	−	0.940359i	$-0.389511\pi$
$83$	514.471	0.680367	0.340184	+	0.940359i	$0.389511\pi$
$84$	699.718	0.908875
$85$	302.045	0.385428
$86$	−503.107	−0.630831
$87$	−94.2167	−0.116104
$88$	−274.839	−0.332931
$89$	−128.152	−0.152630	−0.0763151	−	0.997084i	$-0.524315\pi$
$89$	−128.152	−0.152630	−0.0763151	+	0.997084i	$0.524315\pi$
$90$	−358.544	−0.419932
$91$	178.777	0.205945
$92$	434.803	0.492732
$93$	175.100	0.195236
$94$	−435.833	−0.478221
$95$	1059.13	1.14384
$96$	566.435	0.602203
$97$	−1515.99	−1.58686	−0.793431	−	0.608660i	$-0.791707\pi$
$97$	−1515.99	−1.58686	−0.793431	+	0.608660i	$0.791707\pi$
$98$	37.7234	0.0388841
$99$	114.357	0.116094
$100$	−618.419	−0.618419
$101$	893.235	0.880002	0.440001	−	0.897997i	$-0.354978\pi$
$101$	893.235	0.880002	0.440001	+	0.897997i	$0.354978\pi$
$102$	−471.934	−0.458122
$103$	−592.477	−0.566781	−0.283391	−	0.959005i	$-0.591459\pi$
$103$	−592.477	−0.566781	−0.283391	+	0.959005i	$0.591459\pi$
$104$	−211.364	−0.199288
$105$	480.028	0.446152
$106$	2008.59	1.84048
$107$	1683.62	1.52114	0.760569	−	0.649257i	$-0.224920\pi$
$107$	1683.62	1.52114	0.760569	+	0.649257i	$0.224920\pi$
$108$	344.212	0.306683
$109$	1023.66	0.899534	0.449767	−	0.893146i	$-0.351507\pi$
$109$	1023.66	0.899534	0.449767	+	0.893146i	$0.351507\pi$
$110$	−506.197	−0.438763
$111$	−983.398	−0.840901
$112$	−63.3437	−0.0534412
$113$	1004.92	0.836589	0.418295	−	0.908311i	$-0.362628\pi$
$113$	1004.92	0.836589	0.418295	+	0.908311i	$0.362628\pi$
$114$	−1654.86	−1.35958
$115$	298.289	0.241874
$116$	−400.376	−0.320466
$117$	87.9458	0.0694922
$118$	−1853.13	−1.44571
$119$	631.838	0.486727
$120$	−567.525	−0.431731
$121$	−1169.55	−0.878700
$122$	−2840.70	−2.10808
$123$	735.734	0.539341
$124$	744.091	0.538882
$125$	−1517.49	−1.08583
$126$	−750.026	−0.530299
$127$	86.9016	0.0607187	0.0303593	−	0.999539i	$-0.490335\pi$
$127$	86.9016	0.0607187	0.0303593	+	0.999539i	$0.490335\pi$
$128$	2280.91	1.57505
$129$	331.351	0.226153
$130$	−389.289	−0.262638
$131$	1730.20	1.15396	0.576978	−	0.816760i	$-0.304232\pi$
$131$	1730.20	1.15396	0.576978	+	0.816760i	$0.304232\pi$
$132$	485.962	0.320436
$133$	2215.57	1.44447
$134$	−1167.74	−0.752819
$135$	236.140	0.150546
$136$	−747.007	−0.470995
$137$	−2136.04	−1.33207	−0.666036	−	0.745919i	$-0.732010\pi$
$137$	−2136.04	−1.33207	−0.666036	+	0.745919i	$0.732010\pi$
$138$	−466.065	−0.287493
$139$	1265.25	0.772066	0.386033	−	0.922485i	$-0.373845\pi$
$139$	1265.25	0.772066	0.386033	+	0.922485i	$0.373845\pi$
$140$	2039.89	1.23145
$141$	287.043	0.171443
$142$	−1009.88	−0.596813
$143$	124.163	0.0726086
$144$	−31.1606	−0.0180328
$145$	−274.671	−0.157311
$146$	602.956	0.341788
$147$	−24.8449	−0.0139400
$148$	−4178.98	−2.32101
$149$	984.115	0.541086	0.270543	−	0.962708i	$-0.412797\pi$
$149$	984.115	0.541086	0.270543	+	0.962708i	$0.412797\pi$
$150$	662.882	0.360827
$151$	−3537.60	−1.90653	−0.953265	−	0.302135i	$-0.902301\pi$
$151$	−3537.60	−1.90653	−0.953265	+	0.302135i	$0.902301\pi$
$152$	−2619.41	−1.39778
$153$	310.820	0.164237
$154$	−1058.90	−0.554080
$155$	510.469	0.264528
$156$	373.728	0.191809
$157$	3060.67	1.55585	0.777923	−	0.628359i	$-0.216273\pi$
$157$	3060.67	1.55585	0.777923	+	0.628359i	$0.216273\pi$
$158$	−2828.74	−1.42432
$159$	−1322.87	−0.659815
$160$	1651.33	0.815933
$161$	623.980	0.305444
$162$	−368.960	−0.178940
$163$	3839.28	1.84488	0.922441	−	0.386138i	$-0.126191\pi$
$163$	3839.28	1.84488	0.922441	+	0.386138i	$0.126191\pi$
$164$	3126.52	1.48866
$165$	333.385	0.157297
$166$	−2343.44	−1.09570
$167$	2304.59	1.06787	0.533936	−	0.845525i	$-0.320712\pi$
$167$	2304.59	1.06787	0.533936	+	0.845525i	$0.320712\pi$
$168$	−1187.19	−0.545199
$169$	−2101.51	−0.956537
$170$	−1375.83	−0.620716
$171$	1089.90	0.487409
$172$	1408.08	0.624217
$173$	−2285.84	−1.00456	−0.502280	−	0.864705i	$-0.667505\pi$
$173$	−2285.84	−1.00456	−0.502280	+	0.864705i	$0.667505\pi$
$174$	429.163	0.186981
$175$	−887.484	−0.383357
$176$	−43.9930	−0.0188415
$177$	1220.48	0.518289
$178$	583.740	0.245804
$179$	−1946.89	−0.812944	−0.406472	−	0.913663i	$-0.633241\pi$
$179$	−1946.89	−0.812944	−0.406472	+	0.913663i	$0.633241\pi$
$180$	1003.48	0.415529
$181$	−3902.46	−1.60258	−0.801291	−	0.598275i	$-0.795853\pi$
$181$	−3902.46	−1.60258	−0.801291	+	0.598275i	$0.795853\pi$
$182$	−814.341	−0.331665
$183$	1870.91	0.755747
$184$	−737.716	−0.295571
$185$	−2866.91	−1.13935
$186$	−797.589	−0.314420
$187$	438.819	0.171602
$188$	1219.80	0.473207
$189$	493.973	0.190113
$190$	−4824.42	−1.84211
$191$	−4278.96	−1.62102	−0.810509	−	0.585726i	$-0.800810\pi$
$191$	−4278.96	−1.62102	−0.810509	+	0.585726i	$0.800810\pi$
$192$	−2497.05	−0.938589
$193$	−3463.46	−1.29174	−0.645869	−	0.763448i	$-0.723505\pi$
$193$	−3463.46	−1.29174	−0.645869	+	0.763448i	$0.723505\pi$
$194$	6905.43	2.55557
$195$	256.389	0.0941559
$196$	−105.579	−0.0384764
$197$	155.996	0.0564175	0.0282087	−	0.999602i	$-0.491020\pi$
$197$	155.996	0.0564175	0.0282087	+	0.999602i	$0.491020\pi$
$198$	−520.902	−0.186964
$199$	−1443.49	−0.514201	−0.257101	−	0.966385i	$-0.582767\pi$
$199$	−1443.49	−0.514201	−0.257101	+	0.966385i	$0.582767\pi$
$200$	1049.25	0.370966
$201$	769.086	0.269886
$202$	−4068.74	−1.41721
$203$	−574.574	−0.198656
$204$	1320.84	0.453319
$205$	2144.89	0.730759
$206$	2698.77	0.912777
$207$	306.954	0.103067
$208$	−33.8327	−0.0112782
$209$	1538.74	0.509267
$210$	−2186.56	−0.718509
$211$	−466.361	−0.152159	−0.0760796	−	0.997102i	$-0.524240\pi$
$211$	−466.361	−0.152159	−0.0760796	+	0.997102i	$0.524240\pi$
$212$	−5621.58	−1.82119
$213$	665.117	0.213958
$214$	−7668.99	−2.44973
$215$	965.989	0.306418
$216$	−584.012	−0.183968
$217$	1067.83	0.334052
$218$	−4662.85	−1.44866
$219$	−397.112	−0.122531
$220$	1416.73	0.434163
$221$	337.473	0.102719
$222$	4479.44	1.35424
$223$	265.929	0.0798560	0.0399280	−	0.999203i	$-0.487287\pi$
$223$	265.929	0.0798560	0.0399280	+	0.999203i	$0.487287\pi$
$224$	3454.37	1.03038
$225$	−436.579	−0.129357
$226$	−4577.46	−1.34729
$227$	3760.42	1.09951	0.549753	−	0.835327i	$-0.314722\pi$
$227$	3760.42	1.09951	0.549753	+	0.835327i	$0.314722\pi$
$228$	4631.57	1.34532
$229$	−6670.93	−1.92501	−0.962505	−	0.271263i	$-0.912559\pi$
$229$	−6670.93	−1.92501	−0.962505	+	0.271263i	$0.912559\pi$
$230$	−1358.72	−0.389528
$231$	697.398	0.198638
$232$	679.305	0.192235
$233$	933.360	0.262431	0.131216	−	0.991354i	$-0.458112\pi$
$233$	933.360	0.262431	0.131216	+	0.991354i	$0.458112\pi$
$234$	−400.598	−0.111914
$235$	836.820	0.232290
$236$	5186.48	1.43056
$237$	1863.03	0.510619
$238$	−2878.06	−0.783853
$239$	151.421	0.0409816	0.0204908	−	0.999790i	$-0.493477\pi$
$239$	151.421	0.0409816	0.0204908	+	0.999790i	$0.493477\pi$
$240$	−90.8428	−0.0244328
$241$	2827.74	0.755812	0.377906	−	0.925844i	$-0.376644\pi$
$241$	2827.74	0.755812	0.377906	+	0.925844i	$0.376644\pi$
$242$	5327.37	1.41511
$243$	243.000	0.0641500
$244$	7950.49	2.08597
$245$	−72.4306	−0.0188874
$246$	−3351.31	−0.868585
$247$	1183.36	0.304840
$248$	−1262.47	−0.323255
$249$	1543.41	0.392810
$250$	6912.28	1.74868
$251$	2324.37	0.584514	0.292257	−	0.956340i	$-0.405594\pi$
$251$	2324.37	0.584514	0.292257	+	0.956340i	$0.405594\pi$
$252$	2099.15	0.524739
$253$	433.362	0.107689
$254$	−395.842	−0.0977848
$255$	906.135	0.222527
$256$	−3730.90	−0.910864
$257$	−2139.85	−0.519377	−0.259689	−	0.965692i	$-0.583620\pi$
$257$	−2139.85	−0.519377	−0.259689	+	0.965692i	$0.583620\pi$
$258$	−1509.32	−0.364210
$259$	−5997.19	−1.43879
$260$	1089.53	0.259884
$261$	−282.650	−0.0670329
$262$	−7881.16	−1.85840
$263$	272.073	0.0637899	0.0318949	−	0.999491i	$-0.489846\pi$
$263$	272.073	0.0637899	0.0318949	+	0.999491i	$0.489846\pi$
$264$	−824.516	−0.192218
$265$	−3856.58	−0.893991
$266$	−10092.0	−2.32625
$267$	−384.456	−0.0881211
$268$	3268.25	0.744926
$269$	1324.60	0.300233	0.150116	−	0.988668i	$-0.452035\pi$
$269$	1324.60	0.300233	0.150116	+	0.988668i	$0.452035\pi$
$270$	−1075.63	−0.242448
$271$	−10.0506	−0.00225289	−0.00112644	−	0.999999i	$-0.500359\pi$
$271$	−10.0506	−0.00225289	−0.00112644	+	0.999999i	$0.500359\pi$
$272$	−119.572	−0.0266549
$273$	536.332	0.118902
$274$	9729.78	2.14525
$275$	−616.368	−0.135158
$276$	1304.41	0.284479
$277$	−8637.85	−1.87364	−0.936820	−	0.349813i	$-0.886245\pi$
$277$	−8637.85	−1.87364	−0.936820	+	0.349813i	$0.886245\pi$
$278$	−5763.29	−1.24338
$279$	525.299	0.112720
$280$	−3461.02	−0.738698
$281$	−765.126	−0.162433	−0.0812164	−	0.996696i	$-0.525880\pi$
$281$	−765.126	−0.162433	−0.0812164	+	0.996696i	$0.525880\pi$
$282$	−1307.50	−0.276101
$283$	−4264.69	−0.895793	−0.447896	−	0.894085i	$-0.647827\pi$
$283$	−4264.69	−0.895793	−0.447896	+	0.894085i	$0.647827\pi$
$284$	2826.43	0.590556
$285$	3177.40	0.660397
$286$	−565.570	−0.116933
$287$	4486.83	0.922819
$288$	1699.30	0.347682
$289$	−3720.30	−0.757235
$290$	1251.14	0.253343
$291$	−4547.97	−0.916175
$292$	−1687.54	−0.338204
$293$	7618.43	1.51902	0.759511	−	0.650495i	$-0.225438\pi$
$293$	7618.43	1.51902	0.759511	+	0.650495i	$0.225438\pi$
$294$	113.170	0.0224497
$295$	3558.09	0.702237
$296$	7090.33	1.39229
$297$	343.070	0.0670268
$298$	−4482.71	−0.871397
$299$	333.276	0.0644610
$300$	−1855.26	−0.357044
$301$	2020.72	0.386951
$302$	16114.0	3.07039
$303$	2679.71	0.508070
$304$	−419.285	−0.0791041
$305$	5454.28	1.02397
$306$	−1415.80	−0.264497
$307$	5610.25	1.04298	0.521488	−	0.853258i	$-0.325377\pi$
$307$	5610.25	1.04298	0.521488	+	0.853258i	$0.325377\pi$
$308$	2963.61	0.548271
$309$	−1777.43	−0.327231
$310$	−2325.22	−0.426011
$311$	−7103.21	−1.29513	−0.647566	−	0.762009i	$-0.724213\pi$
$311$	−7103.21	−1.29513	−0.647566	+	0.762009i	$0.724213\pi$
$312$	−634.092	−0.115059
$313$	2508.52	0.453003	0.226502	−	0.974011i	$-0.427271\pi$
$313$	2508.52	0.453003	0.226502	+	0.974011i	$0.427271\pi$
$314$	−13941.5	−2.50562
$315$	1440.08	0.257586
$316$	7917.00	1.40939
$317$	−3416.84	−0.605390	−0.302695	−	0.953087i	$-0.597886\pi$
$317$	−3416.84	−0.605390	−0.302695	+	0.953087i	$0.597886\pi$
$318$	6025.76	1.06260
$319$	−399.049	−0.0700390
$320$	−7279.67	−1.27171
$321$	5050.86	0.878229
$322$	−2842.27	−0.491905
$323$	4182.26	0.720456
$324$	1032.64	0.177064
$325$	−474.016	−0.0809037
$326$	−17488.2	−2.97110
$327$	3070.99	0.519346
$328$	−5304.66	−0.892991
$329$	1750.52	0.293341
$330$	−1518.59	−0.253320
$331$	3066.97	0.509292	0.254646	−	0.967034i	$-0.418041\pi$
$331$	3066.97	0.509292	0.254646	+	0.967034i	$0.418041\pi$
$332$	6558.77	1.08421
$333$	−2950.19	−0.485494
$334$	−10497.5	−1.71976
$335$	2242.12	0.365672
$336$	−190.031	−0.0308543
$337$	−11316.0	−1.82914	−0.914572	−	0.404423i	$-0.867472\pi$
$337$	−11316.0	−1.82914	−0.914572	+	0.404423i	$0.867472\pi$
$338$	9572.52	1.54046
$339$	3014.75	0.483005
$340$	3850.65	0.614208
$341$	741.623	0.117775
$342$	−4964.57	−0.784952
$343$	−6426.81	−1.01171
$344$	−2389.05	−0.374444
$345$	894.866	0.139646
$346$	10412.1	1.61780
$347$	−6755.02	−1.04504	−0.522519	−	0.852627i	$-0.675008\pi$
$347$	−6755.02	−1.04504	−0.522519	+	0.852627i	$0.675008\pi$
$348$	−1201.13	−0.185021
$349$	−4316.66	−0.662078	−0.331039	−	0.943617i	$-0.607399\pi$
$349$	−4316.66	−0.662078	−0.331039	+	0.943617i	$0.607399\pi$
$350$	4042.54	0.617380
$351$	263.837	0.0401214
$352$	2399.10	0.363274
$353$	9568.66	1.44274	0.721372	−	0.692548i	$-0.243512\pi$
$353$	9568.66	1.44274	0.721372	+	0.692548i	$0.243512\pi$
$354$	−5559.38	−0.834683
$355$	1939.02	0.289894
$356$	−1633.76	−0.243227
$357$	1895.52	0.281012
$358$	8868.18	1.30921
$359$	6482.94	0.953082	0.476541	−	0.879152i	$-0.341890\pi$
$359$	6482.94	0.953082	0.476541	+	0.879152i	$0.341890\pi$
$360$	−1702.58	−0.249260
$361$	7806.29	1.13811
$362$	17775.9	2.58089
$363$	−3508.65	−0.507318
$364$	2279.16	0.328188
$365$	−1157.70	−0.166019
$366$	−8522.11	−1.21710
$367$	2710.76	0.385560	0.192780	−	0.981242i	$-0.438250\pi$
$367$	2710.76	0.385560	0.192780	+	0.981242i	$0.438250\pi$
$368$	−118.085	−0.0167272
$369$	2207.20	0.311388
$370$	13058.9	1.83487
$371$	−8067.45	−1.12895
$372$	2232.27	0.311123
$373$	3503.90	0.486394	0.243197	−	0.969977i	$-0.421804\pi$
$373$	3503.90	0.486394	0.243197	+	0.969977i	$0.421804\pi$
$374$	−1998.85	−0.276358
$375$	−4552.48	−0.626905
$376$	−2069.59	−0.283859
$377$	−306.887	−0.0419244
$378$	−2250.08	−0.306168
$379$	13016.2	1.76411	0.882053	−	0.471151i	$-0.156161\pi$
$379$	13016.2	1.76411	0.882053	+	0.471151i	$0.156161\pi$
$380$	13502.5	1.82279
$381$	260.705	0.0350559
$382$	19490.9	2.61058
$383$	12611.8	1.68259	0.841293	−	0.540579i	$-0.181795\pi$
$383$	12611.8	1.68259	0.841293	+	0.540579i	$0.181795\pi$
$384$	6842.74	0.909354
$385$	2033.13	0.269137
$386$	15776.3	2.08029
$387$	994.052	0.130570
$388$	−19326.7	−2.52878
$389$	8644.84	1.12676	0.563382	−	0.826197i	$-0.309500\pi$
$389$	8644.84	1.12676	0.563382	+	0.826197i	$0.309500\pi$
$390$	−1167.87	−0.151634
$391$	1177.87	0.152346
$392$	179.133	0.0230805
$393$	5190.60	0.666237
$394$	−710.571	−0.0908580
$395$	5431.31	0.691845
$396$	1457.89	0.185004
$397$	−13068.5	−1.65212	−0.826058	−	0.563585i	$-0.809422\pi$
$397$	−13068.5	−1.65212	−0.826058	+	0.563585i	$0.809422\pi$
$398$	6575.17	0.828099
$399$	6646.70	0.833963
$400$	167.952	0.0209940
$401$	11123.0	1.38518	0.692589	−	0.721333i	$-0.256470\pi$
$401$	11123.0	1.38518	0.692589	+	0.721333i	$0.256470\pi$
$402$	−3503.23	−0.434640
$403$	570.343	0.0704983
$404$	11387.5	1.40235
$405$	708.420	0.0869177
$406$	2617.22	0.319927
$407$	−4165.12	−0.507266
$408$	−2241.02	−0.271929
$409$	10348.6	1.25112	0.625558	−	0.780178i	$-0.284871\pi$
$409$	10348.6	1.25112	0.625558	+	0.780178i	$0.284871\pi$
$410$	−9770.11	−1.17686
$411$	−6408.11	−0.769072
$412$	−7553.24	−0.903207
$413$	7443.05	0.886800
$414$	−1398.19	−0.165984
$415$	4499.52	0.532223
$416$	1845.02	0.217451
$417$	3795.75	0.445752
$418$	−7009.05	−0.820153
$419$	10772.2	1.25598	0.627991	−	0.778220i	$-0.283877\pi$
$419$	10772.2	1.25598	0.627991	+	0.778220i	$0.283877\pi$
$420$	6119.68	0.710976
$421$	8150.55	0.943548	0.471774	−	0.881720i	$-0.343614\pi$
$421$	8150.55	0.943548	0.471774	+	0.881720i	$0.343614\pi$
$422$	2124.30	0.245046
$423$	861.130	0.0989825
$424$	9537.95	1.09246
$425$	−1675.28	−0.191207
$426$	−3029.65	−0.344570
$427$	11409.6	1.29309
$428$	21463.8	2.42404
$429$	372.489	0.0419206
$430$	−4400.14	−0.493473
$431$	10897.6	1.21791	0.608955	−	0.793204i	$-0.291589\pi$
$431$	10897.6	1.21791	0.608955	+	0.793204i	$0.291589\pi$
$432$	−93.4819	−0.0104112
$433$	2835.54	0.314705	0.157352	−	0.987543i	$-0.449704\pi$
$433$	2835.54	0.314705	0.157352	+	0.987543i	$0.449704\pi$
$434$	−4864.05	−0.537977
$435$	−824.012	−0.0908238
$436$	13050.3	1.43347
$437$	4130.25	0.452120
$438$	1808.87	0.197331
$439$	−17519.5	−1.90469	−0.952346	−	0.305021i	$-0.901337\pi$
$439$	−17519.5	−1.90469	−0.952346	+	0.305021i	$0.901337\pi$
$440$	−2403.72	−0.260438
$441$	−74.5348	−0.00804824
$442$	−1537.21	−0.165424
$443$	1782.71	0.191195	0.0955974	−	0.995420i	$-0.469524\pi$
$443$	1782.71	0.191195	0.0955974	+	0.995420i	$0.469524\pi$
$444$	−12536.9	−1.34004
$445$	−1120.81	−0.119396
$446$	−1211.32	−0.128605
$447$	2952.35	0.312396
$448$	−15228.1	−1.60594
$449$	6378.38	0.670411	0.335205	−	0.942145i	$-0.391194\pi$
$449$	6378.38	0.670411	0.335205	+	0.942145i	$0.391194\pi$
$450$	1988.65	0.208324
$451$	3116.15	0.325353
$452$	12811.3	1.33317
$453$	−10612.8	−1.10074
$454$	−17128.9	−1.77071
$455$	1563.57	0.161102
$456$	−7858.23	−0.807008
$457$	5904.09	0.604336	0.302168	−	0.953255i	$-0.402290\pi$
$457$	5904.09	0.604336	0.302168	+	0.953255i	$0.402290\pi$
$458$	30386.5	3.10015
$459$	932.460	0.0948224
$460$	3802.76	0.385444
$461$	329.915	0.0333311	0.0166656	−	0.999861i	$-0.494695\pi$
$461$	329.915	0.0333311	0.0166656	+	0.999861i	$0.494695\pi$
$462$	−3176.69	−0.319898
$463$	−162.404	−0.0163014	−0.00815072	−	0.999967i	$-0.502594\pi$
$463$	−162.404	−0.0163014	−0.00815072	+	0.999967i	$0.502594\pi$
$464$	108.735	0.0108791
$465$	1531.41	0.152725
$466$	−4251.51	−0.422634
$467$	−4935.39	−0.489042	−0.244521	−	0.969644i	$-0.578631\pi$
$467$	−4935.39	−0.489042	−0.244521	+	0.969644i	$0.578631\pi$
$468$	1121.18	0.110741
$469$	4690.22	0.461779
$470$	−3811.77	−0.374093
$471$	9182.01	0.898269
$472$	−8799.73	−0.858136
$473$	1403.41	0.136425
$474$	−8486.22	−0.822331
$475$	−5874.44	−0.567448
$476$	8055.04	0.775635
$477$	−3968.62	−0.380944
$478$	−689.731	−0.0659991
$479$	14755.4	1.40750	0.703751	−	0.710447i	$-0.251507\pi$
$479$	14755.4	1.40750	0.703751	+	0.710447i	$0.251507\pi$
$480$	4954.00	0.471079
$481$	−3203.18	−0.303643
$482$	−12880.5	−1.21720
$483$	1871.94	0.176348
$484$	−14910.1	−1.40027
$485$	−13258.7	−1.24134
$486$	−1106.88	−0.103311
$487$	11238.4	1.04571	0.522854	−	0.852422i	$-0.324867\pi$
$487$	11238.4	1.04571	0.522854	+	0.852422i	$0.324867\pi$
$488$	−13489.3	−1.25130
$489$	11517.8	1.06514
$490$	329.926	0.0304174
$491$	−20283.5	−1.86433	−0.932163	−	0.362040i	$-0.882080\pi$
$491$	−20283.5	−1.86433	−0.932163	+	0.362040i	$0.882080\pi$
$492$	9379.56	0.859478
$493$	−1084.61	−0.0990837
$494$	−5390.29	−0.490932
$495$	1000.16	0.0908155
$496$	−202.082	−0.0182939
$497$	4056.17	0.366085
$498$	−7030.33	−0.632604
$499$	4542.60	0.407525	0.203762	−	0.979020i	$-0.434683\pi$
$499$	4542.60	0.407525	0.203762	+	0.979020i	$0.434683\pi$
$500$	−19345.9	−1.73035
$501$	6913.77	0.616536
$502$	−10587.7	−0.941335
$503$	−5811.95	−0.515193	−0.257596	−	0.966253i	$-0.582930\pi$
$503$	−5811.95	−0.515193	−0.257596	+	0.966253i	$0.582930\pi$
$504$	−3561.56	−0.314771
$505$	7812.17	0.688390
$506$	−1973.99	−0.173428
$507$	−6304.54	−0.552257
$508$	1107.87	0.0967596
$509$	10952.8	0.953780	0.476890	−	0.878963i	$-0.341764\pi$
$509$	10952.8	0.953780	0.476890	+	0.878963i	$0.341764\pi$
$510$	−4127.50	−0.358370
$511$	−2421.76	−0.209653
$512$	−1252.84	−0.108141
$513$	3269.71	0.281406
$514$	9747.13	0.836435
$515$	−5181.76	−0.443370
$516$	4224.25	0.360392
$517$	1215.75	0.103421
$518$	27317.6	2.31711
$519$	−6857.51	−0.579983
$520$	−1848.57	−0.155895
$521$	−19312.4	−1.62398	−0.811990	−	0.583672i	$-0.801616\pi$
$521$	−19312.4	−1.62398	−0.811990	+	0.583672i	$0.801616\pi$
$522$	1287.49	0.107954
$523$	9730.02	0.813507	0.406753	−	0.913538i	$-0.366661\pi$
$523$	9730.02	0.813507	0.406753	+	0.913538i	$0.366661\pi$
$524$	22057.6	1.83891
$525$	−2662.45	−0.221331
$526$	−1239.31	−0.102731
$527$	2015.72	0.166615
$528$	−131.979	−0.0108781
$529$	−11003.8	−0.904395
$530$	17567.0	1.43974
$531$	3661.45	0.299234
$532$	28245.4	2.30186
$533$	2396.47	0.194752
$534$	1751.22	0.141915
$535$	14724.8	1.18992
$536$	−5545.13	−0.446853
$537$	−5840.66	−0.469354
$538$	−6033.65	−0.483512
$539$	−105.229	−0.00840916
$540$	3010.45	0.239906
$541$	8759.35	0.696107	0.348053	−	0.937475i	$-0.386843\pi$
$541$	8759.35	0.696107	0.348053	+	0.937475i	$0.386843\pi$
$542$	45.7813	0.00362818
$543$	−11707.4	−0.925251
$544$	6520.71	0.513921
$545$	8952.88	0.703669
$546$	−2443.02	−0.191487
$547$	5909.21	0.461901	0.230950	−	0.972966i	$-0.425816\pi$
$547$	5909.21	0.461901	0.230950	+	0.972966i	$0.425816\pi$
$548$	−27231.4	−2.12275
$549$	5612.73	0.436331
$550$	2807.60	0.217666
$551$	−3803.22	−0.294052
$552$	−2213.15	−0.170648
$553$	11361.6	0.873677
$554$	39345.9	3.01742
$555$	−8600.72	−0.657803
$556$	16130.1	1.23034
$557$	−15368.8	−1.16912	−0.584558	−	0.811352i	$-0.698732\pi$
$557$	−15368.8	−1.16912	−0.584558	+	0.811352i	$0.698732\pi$
$558$	−2392.77	−0.181530
$559$	1079.29	0.0816622
$560$	−553.999	−0.0418049
$561$	1316.46	0.0990747
$562$	3485.20	0.261591
$563$	−24500.9	−1.83408	−0.917041	−	0.398793i	$-0.869429\pi$
$563$	−24500.9	−1.83408	−0.917041	+	0.398793i	$0.869429\pi$
$564$	3659.40	0.273206
$565$	8788.92	0.654430
$566$	19425.9	1.44264
$567$	1481.92	0.109762
$568$	−4795.51	−0.354252
$569$	21985.1	1.61980	0.809899	−	0.586570i	$-0.199522\pi$
$569$	21985.1	1.61980	0.809899	+	0.586570i	$0.199522\pi$
$570$	−14473.3	−1.06354
$571$	21934.5	1.60758	0.803790	−	0.594913i	$-0.202813\pi$
$571$	21934.5	1.60758	0.803790	+	0.594913i	$0.202813\pi$
$572$	1582.90	0.115707
$573$	−12836.9	−0.935895
$574$	−20437.8	−1.48616
$575$	−1654.44	−0.119991
$576$	−7491.15	−0.541895
$577$	4510.06	0.325401	0.162700	−	0.986676i	$-0.447980\pi$
$577$	4510.06	0.325401	0.162700	+	0.986676i	$0.447980\pi$
$578$	16946.2	1.21950
$579$	−10390.4	−0.745785
$580$	−3501.66	−0.250687
$581$	9412.40	0.672103
$582$	20716.3	1.47546
$583$	−5602.94	−0.398028
$584$	2863.19	0.202876
$585$	769.167	0.0543609
$586$	−34702.4	−2.44632
$587$	15348.9	1.07925	0.539623	−	0.841907i	$-0.318567\pi$
$587$	15348.9	1.07925	0.539623	+	0.841907i	$0.318567\pi$
$588$	−316.738	−0.0222143
$589$	7068.21	0.494466
$590$	−16207.3	−1.13092
$591$	467.988	0.0325727
$592$	1134.94	0.0787933
$593$	−10515.1	−0.728165	−0.364082	−	0.931367i	$-0.618617\pi$
$593$	−10515.1	−0.728165	−0.364082	+	0.931367i	$0.618617\pi$
$594$	−1562.71	−0.107944
$595$	5526.01	0.380747
$596$	12546.1	0.862261
$597$	−4330.46	−0.296874
$598$	−1518.09	−0.103812
$599$	4526.71	0.308775	0.154388	−	0.988010i	$-0.450660\pi$
$599$	4526.71	0.308775	0.154388	+	0.988010i	$0.450660\pi$
$600$	3147.75	0.214177
$601$	−2187.26	−0.148453	−0.0742265	−	0.997241i	$-0.523649\pi$
$601$	−2187.26	−0.148453	−0.0742265	+	0.997241i	$0.523649\pi$
$602$	−9204.51	−0.623169
$603$	2307.26	0.155819
$604$	−45099.4	−3.03819
$605$	−10228.8	−0.687371
$606$	−12206.2	−0.818225
$607$	12060.3	0.806443	0.403221	−	0.915102i	$-0.367890\pi$
$607$	12060.3	0.806443	0.403221	+	0.915102i	$0.367890\pi$
$608$	22865.2	1.52517
$609$	−1723.72	−0.114694
$610$	−24844.6	−1.64906
$611$	934.973	0.0619066
$612$	3962.51	0.261724
$613$	−13459.4	−0.886820	−0.443410	−	0.896319i	$-0.646232\pi$
$613$	−13459.4	−0.886820	−0.443410	+	0.896319i	$0.646232\pi$
$614$	−25555.0	−1.67967
$615$	6434.67	0.421904
$616$	−5028.26	−0.328887
$617$	10467.2	0.682970	0.341485	−	0.939887i	$-0.389070\pi$
$617$	10467.2	0.682970	0.341485	+	0.939887i	$0.389070\pi$
$618$	8096.30	0.526992
$619$	5187.90	0.336865	0.168432	−	0.985713i	$-0.446130\pi$
$619$	5187.90	0.336865	0.168432	+	0.985713i	$0.446130\pi$
$620$	6507.76	0.421545
$621$	920.862	0.0595055
$622$	32355.6	2.08575
$623$	−2344.58	−0.150776
$624$	−101.498	−0.00651150
$625$	−7208.29	−0.461331
$626$	−11426.5	−0.729543
$627$	4616.22	0.294025
$628$	39019.2	2.47936
$629$	−11320.7	−0.717626
$630$	−6559.67	−0.414831
$631$	−22233.6	−1.40270	−0.701351	−	0.712816i	$-0.747419\pi$
$631$	−22233.6	−1.40270	−0.701351	+	0.712816i	$0.747419\pi$
$632$	−13432.5	−0.845437
$633$	−1399.08	−0.0878492
$634$	15563.9	0.974955
$635$	760.035	0.0474977
$636$	−16864.7	−1.05146
$637$	−80.9262	−0.00503361
$638$	1817.69	0.112795
$639$	1995.35	0.123529
$640$	19948.7	1.23210
$641$	6468.10	0.398556	0.199278	−	0.979943i	$-0.436140\pi$
$641$	6468.10	0.398556	0.199278	+	0.979943i	$0.436140\pi$
$642$	−23007.0	−1.41435
$643$	1197.51	0.0734448	0.0367224	−	0.999326i	$-0.488308\pi$
$643$	1197.51	0.0734448	0.0367224	+	0.999326i	$0.488308\pi$
$644$	7954.86	0.486748
$645$	2897.97	0.176911
$646$	−19050.5	−1.16026
$647$	−13534.0	−0.822377	−0.411189	−	0.911550i	$-0.634886\pi$
$647$	−13534.0	−0.822377	−0.411189	+	0.911550i	$0.634886\pi$
$648$	−1752.04	−0.106214
$649$	5169.29	0.312654
$650$	2159.17	0.130292
$651$	3203.50	0.192865
$652$	48945.4	2.93995
$653$	−10606.3	−0.635614	−0.317807	−	0.948155i	$-0.602946\pi$
$653$	−10606.3	−0.635614	−0.317807	+	0.948155i	$0.602946\pi$
$654$	−13988.6	−0.836385
$655$	15132.2	0.902692
$656$	−849.109	−0.0505368
$657$	−1191.34	−0.0707434
$658$	−7973.71	−0.472413
$659$	4859.49	0.287252	0.143626	−	0.989632i	$-0.454124\pi$
$659$	4859.49	0.287252	0.143626	+	0.989632i	$0.454124\pi$
$660$	4250.19	0.250664
$661$	12050.0	0.709062	0.354531	−	0.935044i	$-0.384641\pi$
$661$	12050.0	0.709062	0.354531	+	0.935044i	$0.384641\pi$
$662$	−13970.2	−0.820193
$663$	1012.42	0.0593048
$664$	−11128.0	−0.650379
$665$	19377.2	1.12995
$666$	13438.3	0.781868
$667$	−1071.12	−0.0621797
$668$	29380.2	1.70173
$669$	797.786	0.0461049
$670$	−10213.0	−0.588900
$671$	7924.13	0.455898
$672$	10363.1	0.594889
$673$	−31642.7	−1.81238	−0.906192	−	0.422866i	$-0.861024\pi$
$673$	−31642.7	−1.81238	−0.906192	+	0.422866i	$0.861024\pi$
$674$	51545.1	2.94576
$675$	−1309.74	−0.0746842
$676$	−26791.3	−1.52431
$677$	677.000	0.0384331
$677$	677.000	0.0384331
$678$	−13732.4	−0.777859
$679$	−27735.5	−1.56759
$680$	−6533.26	−0.368440
$681$	11281.3	0.634800
$682$	−3378.14	−0.189671
$683$	519.835	0.0291229	0.0145614	−	0.999894i	$-0.495365\pi$
$683$	519.835	0.0291229	0.0145614	+	0.999894i	$0.495365\pi$
$684$	13894.7	0.776722
$685$	−18681.6	−1.04203
$686$	29274.5	1.62931
$687$	−20012.8	−1.11141
$688$	−382.411	−0.0211908
$689$	−4308.93	−0.238254
$690$	−4076.17	−0.224894
$691$	11836.5	0.651637	0.325818	−	0.945432i	$-0.394360\pi$
$691$	11836.5	0.651637	0.325818	+	0.945432i	$0.394360\pi$
$692$	−29141.2	−1.60084
$693$	2092.19	0.114684
$694$	30769.5	1.68299
$695$	11065.8	0.603955
$696$	2037.91	0.110987
$697$	8469.65	0.460274
$698$	19662.6	1.06625
$699$	2800.08	0.151515
$700$	−11314.2	−0.610907
$701$	−923.652	−0.0497659	−0.0248829	−	0.999690i	$-0.507921\pi$
$701$	−923.652	−0.0497659	−0.0248829	+	0.999690i	$0.507921\pi$
$702$	−1201.80	−0.0646137
$703$	−39696.6	−2.12971
$704$	−10576.1	−0.566196
$705$	2510.46	0.134113
$706$	−43585.8	−2.32348
$707$	16342.0	0.869314
$708$	15559.4	0.825932
$709$	−21364.5	−1.13168	−0.565838	−	0.824516i	$-0.691447\pi$
$709$	−21364.5	−1.13168	−0.565838	+	0.824516i	$0.691447\pi$
$710$	−8832.36	−0.466863
$711$	5589.09	0.294806
$712$	2771.94	0.145903
$713$	1990.65	0.104559
$714$	−8634.19	−0.452558
$715$	1085.92	0.0567987
$716$	−24820.0	−1.29549
$717$	454.262	0.0236607
$718$	−29530.2	−1.53490
$719$	−18900.2	−0.980332	−0.490166	−	0.871629i	$-0.663064\pi$
$719$	−18900.2	−0.980332	−0.490166	+	0.871629i	$0.663064\pi$
$720$	−272.529	−0.0141063
$721$	−10839.5	−0.559897
$722$	−35558.1	−1.83288
$723$	8483.22	0.436369
$724$	−49750.8	−2.55383
$725$	1523.45	0.0780405
$726$	15982.1	0.817013
$727$	10283.8	0.524631	0.262315	−	0.964982i	$-0.415514\pi$
$727$	10283.8	0.524631	0.262315	+	0.964982i	$0.415514\pi$
$728$	−3866.97	−0.196867
$729$	729.000	0.0370370
$730$	5273.41	0.267367
$731$	3814.46	0.193000
$732$	23851.5	1.20434
$733$	−2905.05	−0.146385	−0.0731926	−	0.997318i	$-0.523319\pi$
$733$	−2905.05	−0.146385	−0.0731926	+	0.997318i	$0.523319\pi$
$734$	−12347.7	−0.620928
$735$	−217.292	−0.0109047
$736$	6439.61	0.322510
$737$	3257.42	0.162807
$738$	−10053.9	−0.501478
$739$	−11422.4	−0.568577	−0.284289	−	0.958739i	$-0.591757\pi$
$739$	−11422.4	−0.568577	−0.284289	+	0.958739i	$0.591757\pi$
$740$	−36549.0	−1.81563
$741$	3550.09	0.176000
$742$	36747.7	1.81813
$743$	−15000.2	−0.740652	−0.370326	−	0.928902i	$-0.620754\pi$
$743$	−15000.2	−0.740652	−0.370326	+	0.928902i	$0.620754\pi$
$744$	−3787.42	−0.186631
$745$	8607.00	0.423270
$746$	−15960.5	−0.783318
$747$	4630.23	0.226789
$748$	5594.33	0.273461
$749$	30802.4	1.50266
$750$	20736.8	1.00960
$751$	3796.45	0.184467	0.0922334	−	0.995737i	$-0.470599\pi$
$751$	3796.45	0.184467	0.0922334	+	0.995737i	$0.470599\pi$
$752$	−331.276	−0.0160644
$753$	6973.11	0.337469
$754$	1397.89	0.0675175
$755$	−30939.6	−1.49140
$756$	6297.46	0.302958
$757$	−14402.1	−0.691484	−0.345742	−	0.938330i	$-0.612373\pi$
$757$	−14402.1	−0.691484	−0.345742	+	0.938330i	$0.612373\pi$
$758$	−59289.5	−2.84102
$759$	1300.09	0.0621740
$760$	−22909.2	−1.09342
$761$	−24730.9	−1.17805	−0.589023	−	0.808116i	$-0.700487\pi$
$761$	−24730.9	−1.17805	−0.589023	+	0.808116i	$0.700487\pi$
$762$	−1187.53	−0.0564561
$763$	18728.2	0.888608
$764$	−54550.7	−2.58321
$765$	2718.41	0.128476
$766$	−57447.3	−2.70973
$767$	3975.42	0.187150
$768$	−11192.7	−0.525887
$769$	24729.4	1.15964	0.579822	−	0.814743i	$-0.303122\pi$
$769$	24729.4	1.15964	0.579822	+	0.814743i	$0.303122\pi$
$770$	−9261.03	−0.433434
$771$	−6419.54	−0.299863
$772$	−44154.2	−2.05848
$773$	−31978.2	−1.48794	−0.743968	−	0.668215i	$-0.767059\pi$
$773$	−31978.2	−1.48794	−0.743968	+	0.668215i	$0.767059\pi$
$774$	−4527.97	−0.210277
$775$	−2831.29	−0.131230
$776$	32791.0	1.51692
$777$	−17991.6	−0.830687
$778$	−39377.8	−1.81460
$779$	29699.2	1.36596
$780$	3268.60	0.150044
$781$	2817.06	0.129068
$782$	−5365.27	−0.245347
$783$	−847.950	−0.0387015
$784$	28.6735	0.00130619
$785$	26768.4	1.21708
$786$	−23643.5	−1.07295
$787$	34827.5	1.57747	0.788733	−	0.614736i	$-0.210737\pi$
$787$	34827.5	1.57747	0.788733	+	0.614736i	$0.210737\pi$
$788$	1988.73	0.0899054
$789$	816.219	0.0368291
$790$	−24739.9	−1.11419
$791$	18385.3	0.826428
$792$	−2473.55	−0.110977
$793$	6094.03	0.272894
$794$	59527.9	2.66066
$795$	−11569.7	−0.516146
$796$	−18402.4	−0.819417
$797$	29580.6	1.31468	0.657340	−	0.753594i	$-0.271682\pi$
$797$	29580.6	1.31468	0.657340	+	0.753594i	$0.271682\pi$
$798$	−30276.1	−1.34306
$799$	3304.40	0.146309
$800$	−9159.03	−0.404776
$801$	−1153.37	−0.0508767
$802$	−50666.0	−2.23077
$803$	−1681.94	−0.0739159
$804$	9804.76	0.430083
$805$	5457.28	0.238937
$806$	−2597.95	−0.113535
$807$	3973.81	0.173339
$808$	−19320.8	−0.841215
$809$	−25380.6	−1.10301	−0.551505	−	0.834172i	$-0.685946\pi$
$809$	−25380.6	−1.10301	−0.551505	+	0.834172i	$0.685946\pi$
$810$	−3226.90	−0.139977
$811$	7885.35	0.341421	0.170710	−	0.985321i	$-0.445394\pi$
$811$	7885.35	0.341421	0.170710	+	0.985321i	$0.445394\pi$
$812$	−7325.01	−0.316573
$813$	−30.1519	−0.00130071
$814$	18972.4	0.816931
$815$	33578.1	1.44318
$816$	−358.716	−0.0153892
$817$	13375.6	0.572768
$818$	−47138.6	−2.01487
$819$	1609.00	0.0686482
$820$	27344.3	1.16452
$821$	261.584	0.0111198	0.00555990	−	0.999985i	$-0.498230\pi$
$821$	261.584	0.0111198	0.00555990	+	0.999985i	$0.498230\pi$
$822$	29189.3	1.23856
$823$	−13226.4	−0.560198	−0.280099	−	0.959971i	$-0.590367\pi$
$823$	−13226.4	−0.560198	−0.280099	+	0.959971i	$0.590367\pi$
$824$	12815.3	0.541800
$825$	−1849.11	−0.0780334
$826$	−33903.5	−1.42815
$827$	34863.5	1.46593	0.732964	−	0.680268i	$-0.238136\pi$
$827$	34863.5	1.46593	0.732964	+	0.680268i	$0.238136\pi$
$828$	3913.23	0.164244
$829$	−7156.22	−0.299814	−0.149907	−	0.988700i	$-0.547897\pi$
$829$	−7156.22	−0.299814	−0.149907	+	0.988700i	$0.547897\pi$
$830$	−20495.6	−0.857123
$831$	−25913.5	−1.08175
$832$	−8133.52	−0.338917
$833$	−286.011	−0.0118964
$834$	−17289.9	−0.717865
$835$	20155.8	0.835352
$836$	19616.7	0.811554
$837$	1575.90	0.0650788
$838$	−49068.1	−2.02271
$839$	−33918.3	−1.39570	−0.697849	−	0.716245i	$-0.745859\pi$
$839$	−33918.3	−1.39570	−0.697849	+	0.716245i	$0.745859\pi$
$840$	−10383.0	−0.426487
$841$	−23402.7	−0.959559
$842$	−37126.3	−1.51954
$843$	−2295.38	−0.0937806
$844$	−5945.44	−0.242477
$845$	−18379.7	−0.748260
$846$	−3922.50	−0.159407
$847$	−21397.3	−0.868027
$848$	1526.72	0.0618253
$849$	−12794.1	−0.517186
$850$	7631.00	0.307931
$851$	−11179.9	−0.450344
$852$	8479.30	0.340958
$853$	11362.1	0.456072	0.228036	−	0.973653i	$-0.426770\pi$
$853$	11362.1	0.456072	0.228036	+	0.973653i	$0.426770\pi$
$854$	−51971.6	−2.08247
$855$	9532.21	0.381280
$856$	−36416.9	−1.45409
$857$	923.026	0.0367911	0.0183956	−	0.999831i	$-0.494144\pi$
$857$	923.026	0.0367911	0.0183956	+	0.999831i	$0.494144\pi$
$858$	−1696.71	−0.0675113
$859$	−16783.2	−0.666631	−0.333316	−	0.942815i	$-0.608167\pi$
$859$	−16783.2	−0.666631	−0.333316	+	0.942815i	$0.608167\pi$
$860$	12315.0	0.488300
$861$	13460.5	0.532790
$862$	−49639.3	−1.96139
$863$	−30425.3	−1.20010	−0.600052	−	0.799961i	$-0.704853\pi$
$863$	−30425.3	−1.20010	−0.600052	+	0.799961i	$0.704853\pi$
$864$	5097.91	0.200734
$865$	−19991.8	−0.785827
$866$	−12916.0	−0.506819
$867$	−11160.9	−0.437190
$868$	13613.4	0.532336
$869$	7890.75	0.308027
$870$	3753.42	0.146268
$871$	2505.11	0.0974538
$872$	−22141.9	−0.859886
$873$	−13643.9	−0.528954
$874$	−18813.5	−0.728121
$875$	−27763.0	−1.07264
$876$	−5062.61	−0.195262
$877$	16904.1	0.650869	0.325434	−	0.945565i	$-0.394489\pi$
$877$	16904.1	0.650869	0.325434	+	0.945565i	$0.394489\pi$
$878$	79802.3	3.06742
$879$	22855.3	0.877008
$880$	−384.759	−0.0147389
$881$	27928.6	1.06803	0.534017	−	0.845474i	$-0.320682\pi$
$881$	27928.6	1.06803	0.534017	+	0.845474i	$0.320682\pi$
$882$	339.510	0.0129614
$883$	18997.5	0.724029	0.362014	−	0.932173i	$-0.382089\pi$
$883$	18997.5	0.724029	0.362014	+	0.932173i	$0.382089\pi$
$884$	4302.30	0.163690
$885$	10674.3	0.405437
$886$	−8120.37	−0.307911
$887$	29581.5	1.11978	0.559892	−	0.828566i	$-0.310843\pi$
$887$	29581.5	1.11978	0.559892	+	0.828566i	$0.310843\pi$
$888$	21271.0	0.803837
$889$	1589.89	0.0599812
$890$	5105.35	0.192283
$891$	1029.21	0.0386980
$892$	3390.21	0.127256
$893$	11587.0	0.434205
$894$	−13448.1	−0.503101
$895$	−17027.3	−0.635933
$896$	41730.0	1.55592
$897$	999.827	0.0372166
$898$	−29053.9	−1.07967
$899$	−1833.03	−0.0680034
$900$	−5565.77	−0.206140
$901$	−15228.7	−0.563087
$902$	−14194.3	−0.523966
$903$	6062.16	0.223407
$904$	−21736.4	−0.799716
$905$	−34130.6	−1.25363
$906$	48342.0	1.77269
$907$	−16670.8	−0.610303	−0.305152	−	0.952304i	$-0.598707\pi$
$907$	−16670.8	−0.610303	−0.305152	+	0.952304i	$0.598707\pi$
$908$	47940.0	1.75214
$909$	8039.12	0.293334
$910$	−7122.17	−0.259448
$911$	23493.9	0.854434	0.427217	−	0.904149i	$-0.359494\pi$
$911$	23493.9	0.854434	0.427217	+	0.904149i	$0.359494\pi$
$912$	−1257.85	−0.0456707
$913$	6537.02	0.236959
$914$	−26893.5	−0.973258
$915$	16362.8	0.591190
$916$	−85044.9	−3.06764
$917$	31654.5	1.13994
$918$	−4247.41	−0.152707
$919$	29701.6	1.06612	0.533060	−	0.846077i	$-0.321042\pi$
$919$	29701.6	1.06612	0.533060	+	0.846077i	$0.321042\pi$
$920$	−6452.01	−0.231213
$921$	16830.7	0.602163
$922$	−1502.78	−0.0536784
$923$	2166.45	0.0772586
$924$	8890.83	0.316544
$925$	15901.2	0.565218
$926$	739.762	0.0262528
$927$	−5332.29	−0.188927
$928$	−5929.74	−0.209755
$929$	−2709.20	−0.0956793	−0.0478397	−	0.998855i	$-0.515234\pi$
$929$	−2709.20	−0.0956793	−0.0478397	+	0.998855i	$0.515234\pi$
$930$	−6975.66	−0.245958
$931$	−1002.91	−0.0353051
$932$	11899.0	0.418203
$933$	−21309.6	−0.747745
$934$	22481.0	0.787581
$935$	3837.88	0.134238
$936$	−1902.28	−0.0664293
$937$	−31513.7	−1.09873	−0.549364	−	0.835583i	$-0.685130\pi$
$937$	−31513.7	−1.09873	−0.549364	+	0.835583i	$0.685130\pi$
$938$	−21364.2	−0.743675
$939$	7525.57	0.261542
$940$	10668.3	0.370171
$941$	−3252.29	−0.112669	−0.0563345	−	0.998412i	$-0.517941\pi$
$941$	−3252.29	−0.112669	−0.0563345	+	0.998412i	$0.517941\pi$
$942$	−41824.6	−1.44662
$943$	8364.32	0.288844
$944$	−1408.56	−0.0485643
$945$	4320.25	0.148717
$946$	−6392.64	−0.219707
$947$	−7433.07	−0.255061	−0.127530	−	0.991835i	$-0.540705\pi$
$947$	−7433.07	−0.255061	−0.127530	+	0.991835i	$0.540705\pi$
$948$	23751.0	0.813709
$949$	−1293.49	−0.0442451
$950$	26758.4	0.913850
$951$	−10250.5	−0.349522
$952$	−13666.7	−0.465274
$953$	−656.194	−0.0223045	−0.0111523	−	0.999938i	$-0.503550\pi$
$953$	−656.194	−0.0223045	−0.0111523	+	0.999938i	$0.503550\pi$
$954$	18077.3	0.613495
$955$	−37423.4	−1.26806
$956$	1930.40	0.0653071
$957$	−1197.15	−0.0404370
$958$	−67212.0	−2.26672
$959$	−39079.4	−1.31589
$960$	−21839.0	−0.734220
$961$	−26384.3	−0.885648
$962$	14590.7	0.489004
$963$	15152.6	0.507046
$964$	36049.7	1.20444
$965$	−30291.2	−1.01047
$966$	−8526.80	−0.284001
$967$	−10705.6	−0.356019	−0.178009	−	0.984029i	$-0.556966\pi$
$967$	−10705.6	−0.356019	−0.178009	+	0.984029i	$0.556966\pi$
$968$	25297.5	0.839970
$969$	12546.8	0.415956
$970$	60394.4	1.99912
$971$	−18902.7	−0.624733	−0.312367	−	0.949962i	$-0.601122\pi$
$971$	−18902.7	−0.624733	−0.312367	+	0.949962i	$0.601122\pi$
$972$	3097.91	0.102228
$973$	23148.1	0.762688
$974$	−51191.5	−1.68407
$975$	−1422.05	−0.0467098
$976$	−2159.21	−0.0708143
$977$	25645.8	0.839797	0.419898	−	0.907571i	$-0.362066\pi$
$977$	25645.8	0.839797	0.419898	+	0.907571i	$0.362066\pi$
$978$	−52464.5	−1.71537
$979$	−1628.34	−0.0531583
$980$	−923.387	−0.0300985
$981$	9212.97	0.299845
$982$	92392.8	3.00242
$983$	49668.3	1.61157	0.805785	−	0.592209i	$-0.201744\pi$
$983$	49668.3	1.61157	0.805785	+	0.592209i	$0.201744\pi$
$984$	−15914.0	−0.515568
$985$	1364.33	0.0441331
$986$	4940.45	0.159570
$987$	5251.55	0.169360
$988$	15086.2	0.485785
$989$	3767.02	0.121116
$990$	−4555.77	−0.146254
$991$	33684.1	1.07973	0.539864	−	0.841752i	$-0.318476\pi$
$991$	33684.1	1.07973	0.539864	+	0.841752i	$0.318476\pi$
$992$	11020.3	0.352716
$993$	9200.90	0.294040
$994$	−18476.1	−0.589564
$995$	−12624.6	−0.402239
$996$	19676.3	0.625972
$997$	32444.2	1.03061	0.515304	−	0.857007i	$-0.327679\pi$
$997$	32444.2	1.03061	0.515304	+	0.857007i	$0.327679\pi$
$998$	−20691.8	−0.656301
$999$	−8850.58	−0.280300

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2031.4.a.d.1.11	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2031.4.a.d.1.11	✓	94	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2031 = 3 \cdot 677 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2031.a (trivial)

\(f(q)\)	\(=\)	\(q-4.55506 q^{2} +3.00000 q^{3} +12.7486 q^{4} +8.74592 q^{5} -13.6652 q^{6} +18.2953 q^{7} -21.6301 q^{8} +9.00000 q^{9} -39.8382 q^{10} +12.7063 q^{11} +38.2457 q^{12} +9.77175 q^{13} -83.3363 q^{14} +26.2378 q^{15} -3.46229 q^{16} +34.5355 q^{17} -40.9956 q^{18} +121.100 q^{19} +111.498 q^{20} +54.8859 q^{21} -57.8780 q^{22} +34.1060 q^{23} -64.8903 q^{24} -48.5088 q^{25} -44.5109 q^{26} +27.0000 q^{27} +233.239 q^{28} -31.4056 q^{29} -119.515 q^{30} +58.3665 q^{31} +188.812 q^{32} +38.1189 q^{33} -157.311 q^{34} +160.009 q^{35} +114.737 q^{36} -327.799 q^{37} -551.619 q^{38} +29.3153 q^{39} -189.175 q^{40} +245.245 q^{41} -250.009 q^{42} +110.450 q^{43} +161.987 q^{44} +78.7133 q^{45} -155.355 q^{46} +95.6811 q^{47} -10.3869 q^{48} -8.28164 q^{49} +220.961 q^{50} +103.607 q^{51} +124.576 q^{52} -440.957 q^{53} -122.987 q^{54} +111.128 q^{55} -395.729 q^{56} +363.301 q^{57} +143.054 q^{58} +406.828 q^{59} +334.494 q^{60} +623.637 q^{61} -265.863 q^{62} +164.658 q^{63} -832.350 q^{64} +85.4630 q^{65} -173.634 q^{66} +256.362 q^{67} +440.279 q^{68} +102.318 q^{69} -728.852 q^{70} +221.706 q^{71} -194.671 q^{72} -132.371 q^{73} +1493.15 q^{74} -145.526 q^{75} +1543.86 q^{76} +232.466 q^{77} -133.533 q^{78} +621.010 q^{79} -30.2809 q^{80} +81.0000 q^{81} -1117.10 q^{82} +514.471 q^{83} +699.718 q^{84} +302.045 q^{85} -503.107 q^{86} -94.2167 q^{87} -274.839 q^{88} -128.152 q^{89} -358.544 q^{90} +178.777 q^{91} +434.803 q^{92} +175.100 q^{93} -435.833 q^{94} +1059.13 q^{95} +566.435 q^{96} -1515.99 q^{97} +37.7234 q^{98} +114.357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q + 19 q^{2} + 282 q^{3} + 409 q^{4} + 84 q^{5} + 57 q^{6} + 39 q^{7} + 228 q^{8} + 846 q^{9} + 145 q^{10} + 357 q^{11} + 1227 q^{12} + 271 q^{13} + 366 q^{14} + 252 q^{15} + 1865 q^{16} + 690 q^{17}+ \cdots + 3213 q^{99}+O(q^{100}) \) 94 * q + 19 * q^2 + 282 * q^3 + 409 * q^4 + 84 * q^5 + 57 * q^6 + 39 * q^7 + 228 * q^8 + 846 * q^9 + 145 * q^10 + 357 * q^11 + 1227 * q^12 + 271 * q^13 + 366 * q^14 + 252 * q^15 + 1865 * q^16 + 690 * q^17 + 171 * q^18 + 345 * q^19 + 939 * q^20 + 117 * q^21 + 148 * q^22 + 1135 * q^23 + 684 * q^24 + 3280 * q^25 + 1261 * q^26 + 2538 * q^27 + 214 * q^28 + 1396 * q^29 + 435 * q^30 + 889 * q^31 + 2048 * q^32 + 1071 * q^33 + 1590 * q^34 + 2104 * q^35 + 3681 * q^36 + 711 * q^37 + 2075 * q^38 + 813 * q^39 + 1675 * q^40 + 2931 * q^41 + 1098 * q^42 + 585 * q^43 + 4058 * q^44 + 756 * q^45 + 1148 * q^46 + 2733 * q^47 + 5595 * q^48 + 8415 * q^49 + 2640 * q^50 + 2070 * q^51 + 2174 * q^52 + 3430 * q^53 + 513 * q^54 + 2458 * q^55 + 4034 * q^56 + 1035 * q^57 + 259 * q^58 + 5376 * q^59 + 2817 * q^60 + 2064 * q^61 + 3610 * q^62 + 351 * q^63 + 10194 * q^64 + 5442 * q^65 + 444 * q^66 + 1429 * q^67 + 6932 * q^68 + 3405 * q^69 + 3888 * q^70 + 5336 * q^71 + 2052 * q^72 + 2412 * q^73 + 5911 * q^74 + 9840 * q^75 + 5988 * q^76 + 7100 * q^77 + 3783 * q^78 + 2018 * q^79 + 8054 * q^80 + 7614 * q^81 + 3546 * q^82 + 6229 * q^83 + 642 * q^84 + 2728 * q^85 + 6619 * q^86 + 4188 * q^87 + 3679 * q^88 + 11972 * q^89 + 1305 * q^90 + 5586 * q^91 + 15073 * q^92 + 2667 * q^93 + 3650 * q^94 + 8168 * q^95 + 6144 * q^96 + 5859 * q^97 + 8121 * q^98 + 3213 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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