LMFDB - Embedded newform 841.4.a.h.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,4,Mod(1,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	841.a (trivial)

Newform invariants

comment:select newform

sage:traces = [21,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$49.6206063148$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 29)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	841.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.89852 q^{2} +4.45749 q^{3} +0.401406 q^{4} -3.28305 q^{5} -12.9201 q^{6} -34.7925 q^{7} +22.0247 q^{8} -7.13078 q^{9} +9.51599 q^{10} -6.91603 q^{11} +1.78926 q^{12} -52.4886 q^{13} +100.847 q^{14} -14.6342 q^{15} -67.0501 q^{16} -43.9870 q^{17} +20.6687 q^{18} +72.5657 q^{19} -1.31784 q^{20} -155.087 q^{21} +20.0462 q^{22} -66.1265 q^{23} +98.1747 q^{24} -114.222 q^{25} +152.139 q^{26} -152.138 q^{27} -13.9659 q^{28} +42.4174 q^{30} -64.1840 q^{31} +18.1487 q^{32} -30.8281 q^{33} +127.497 q^{34} +114.226 q^{35} -2.86234 q^{36} +119.933 q^{37} -210.333 q^{38} -233.968 q^{39} -72.3082 q^{40} -377.848 q^{41} +449.524 q^{42} +108.081 q^{43} -2.77613 q^{44} +23.4107 q^{45} +191.669 q^{46} +238.804 q^{47} -298.875 q^{48} +867.521 q^{49} +331.073 q^{50} -196.072 q^{51} -21.0692 q^{52} -544.106 q^{53} +440.974 q^{54} +22.7057 q^{55} -766.294 q^{56} +323.461 q^{57} -350.082 q^{59} -5.87425 q^{60} +780.765 q^{61} +186.038 q^{62} +248.098 q^{63} +483.797 q^{64} +172.323 q^{65} +89.3559 q^{66} +301.306 q^{67} -17.6566 q^{68} -294.758 q^{69} -331.086 q^{70} +993.619 q^{71} -157.053 q^{72} +396.506 q^{73} -347.628 q^{74} -509.141 q^{75} +29.1283 q^{76} +240.626 q^{77} +678.159 q^{78} -1344.36 q^{79} +220.129 q^{80} -485.621 q^{81} +1095.20 q^{82} -775.934 q^{83} -62.2530 q^{84} +144.412 q^{85} -313.275 q^{86} -152.323 q^{88} +83.7886 q^{89} -67.8565 q^{90} +1826.21 q^{91} -26.5436 q^{92} -286.099 q^{93} -692.177 q^{94} -238.237 q^{95} +80.8976 q^{96} -141.626 q^{97} -2514.53 q^{98} +49.3167 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 6 q^{2} + q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} - 51 q^{8} + 188 q^{9} - 37 q^{10} + 7 q^{11} + 68 q^{12} + 97 q^{13} + 68 q^{14} + 330 q^{15} + 310 q^{16} - 70 q^{17} - 305 q^{18} + 73 q^{19}+ \cdots - 8702 q^{99}+O(q^{100}) $ 21 * q - 6 * q^2 + q^3 + 90 * q^4 + 35 * q^5 + 26 * q^6 + 37 * q^7 - 51 * q^8 + 188 * q^9 - 37 * q^10 + 7 * q^11 + 68 * q^12 + 97 * q^13 + 68 * q^14 + 330 * q^15 + 310 * q^16 - 70 * q^17 - 305 * q^18 + 73 * q^19 + 408 * q^20 - 169 * q^21 + 705 * q^22 + 375 * q^23 + 641 * q^24 + 402 * q^25 - 1144 * q^26 - 14 * q^27 + 178 * q^28 + 1087 * q^30 + 693 * q^31 - 449 * q^32 + 820 * q^33 + 53 * q^34 + 886 * q^35 + 1464 * q^36 + 243 * q^37 + 914 * q^38 - 244 * q^39 - 275 * q^40 + 552 * q^41 - 373 * q^42 - 1151 * q^43 + 1502 * q^44 + 1139 * q^45 - 2992 * q^46 + 403 * q^47 + 3329 * q^48 + 1078 * q^49 - 1317 * q^50 + 2272 * q^51 - 1267 * q^52 + 1505 * q^53 + 140 * q^54 - 588 * q^55 + 2549 * q^56 + 859 * q^57 + 3086 * q^59 + 4371 * q^60 + 39 * q^61 + 1356 * q^62 + 1527 * q^63 - 1993 * q^64 + 1132 * q^65 + 980 * q^66 + 413 * q^67 + 919 * q^68 - 6116 * q^69 - 6779 * q^70 + 4015 * q^71 - 5524 * q^72 + 2667 * q^73 + 3844 * q^74 - 3734 * q^75 - 438 * q^76 + 5252 * q^77 - 4128 * q^78 - 1441 * q^79 + 6887 * q^80 - 371 * q^81 + 3401 * q^82 + 2505 * q^83 + 140 * q^84 + 3340 * q^85 + 3412 * q^86 + 8149 * q^88 + 2757 * q^89 + 1740 * q^90 + 4824 * q^91 + 3957 * q^92 - 4278 * q^93 + 1507 * q^94 + 2496 * q^95 + 3663 * q^96 + 1223 * q^97 - 10921 * q^98 - 8702 * 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 $

$2$	−2.89852	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$2$	−2.89852	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$3$	4.45749	0.857844	0.428922	−	0.903341i	$-0.358893\pi$
$3$	4.45749	0.857844	0.428922	+	0.903341i	$0.358893\pi$
$4$	0.401406	0.0501757
$5$	−3.28305	−0.293645	−0.146823	−	0.989163i	$-0.546905\pi$
$5$	−3.28305	−0.293645	−0.146823	+	0.989163i	$0.546905\pi$
$6$	−12.9201	−0.879102
$7$	−34.7925	−1.87862	−0.939311	−	0.343068i	$-0.888534\pi$
$7$	−34.7925	−1.87862	−0.939311	+	0.343068i	$0.888534\pi$
$8$	22.0247	0.973362
$9$	−7.13078	−0.264103
$10$	9.51599	0.300922
$11$	−6.91603	−0.189569	−0.0947846	−	0.995498i	$-0.530216\pi$
$11$	−6.91603	−0.189569	−0.0947846	+	0.995498i	$0.530216\pi$
$12$	1.78926	0.0430430
$13$	−52.4886	−1.11983	−0.559913	−	0.828552i	$-0.689165\pi$
$13$	−52.4886	−1.11983	−0.559913	+	0.828552i	$0.689165\pi$
$14$	100.847	1.92517
$15$	−14.6342	−0.251902
$16$	−67.0501	−1.04766
$17$	−43.9870	−0.627554	−0.313777	−	0.949497i	$-0.601594\pi$
$17$	−43.9870	−0.627554	−0.313777	+	0.949497i	$0.601594\pi$
$18$	20.6687	0.270648
$19$	72.5657	0.876196	0.438098	−	0.898927i	$-0.355652\pi$
$19$	72.5657	0.876196	0.438098	+	0.898927i	$0.355652\pi$
$20$	−1.31784	−0.0147339
$21$	−155.087	−1.61156
$22$	20.0462	0.194267
$23$	−66.1265	−0.599493	−0.299746	−	0.954019i	$-0.596902\pi$
$23$	−66.1265	−0.599493	−0.299746	+	0.954019i	$0.596902\pi$
$24$	98.1747	0.834993
$25$	−114.222	−0.913772
$26$	152.139	1.14758
$27$	−152.138	−1.08440
$28$	−13.9659	−0.0942612
$29$	0	0
$29$	0	0
$30$	42.4174	0.258144
$31$	−64.1840	−0.371864	−0.185932	−	0.982563i	$-0.559530\pi$
$31$	−64.1840	−0.371864	−0.185932	+	0.982563i	$0.559530\pi$
$32$	18.1487	0.100258
$33$	−30.8281	−0.162621
$34$	127.497	0.643105
$35$	114.226	0.551648
$36$	−2.86234	−0.0132516
$37$	119.933	0.532888	0.266444	−	0.963850i	$-0.414151\pi$
$37$	119.933	0.532888	0.266444	+	0.963850i	$0.414151\pi$
$38$	−210.333	−0.897909
$39$	−233.968	−0.960636
$40$	−72.3082	−0.285823
$41$	−377.848	−1.43927	−0.719633	−	0.694355i	$-0.755690\pi$
$41$	−377.848	−1.43927	−0.719633	+	0.694355i	$0.755690\pi$
$42$	449.524	1.65150
$43$	108.081	0.383307	0.191653	−	0.981463i	$-0.438615\pi$
$43$	108.081	0.383307	0.191653	+	0.981463i	$0.438615\pi$
$44$	−2.77613	−0.00951177
$45$	23.4107	0.0775526
$46$	191.669	0.614349
$47$	238.804	0.741130	0.370565	−	0.928807i	$-0.379164\pi$
$47$	238.804	0.741130	0.370565	+	0.928807i	$0.379164\pi$
$48$	−298.875	−0.898728
$49$	867.521	2.52922
$50$	331.073	0.936416
$51$	−196.072	−0.538343
$52$	−21.0692	−0.0561880
$53$	−544.106	−1.41017	−0.705083	−	0.709125i	$-0.749090\pi$
$53$	−544.106	−1.41017	−0.705083	+	0.709125i	$0.749090\pi$
$54$	440.974	1.11128
$55$	22.7057	0.0556661
$56$	−766.294	−1.82858
$57$	323.461	0.751640
$58$	0	0
$59$	−350.082	−0.772488	−0.386244	−	0.922397i	$-0.626228\pi$
$59$	−350.082	−0.772488	−0.386244	+	0.922397i	$0.626228\pi$
$60$	−5.87425	−0.0126394
$61$	780.765	1.63880	0.819399	−	0.573223i	$-0.194307\pi$
$61$	780.765	1.63880	0.819399	+	0.573223i	$0.194307\pi$
$62$	186.038	0.381079
$63$	248.098	0.496149
$64$	483.797	0.944915
$65$	172.323	0.328832
$66$	89.3559	0.166651
$67$	301.306	0.549408	0.274704	−	0.961529i	$-0.411420\pi$
$67$	301.306	0.549408	0.274704	+	0.961529i	$0.411420\pi$
$68$	−17.6566	−0.0314880
$69$	−294.758	−0.514271
$70$	−331.086	−0.565319
$71$	993.619	1.66086	0.830429	−	0.557125i	$-0.188096\pi$
$71$	993.619	1.66086	0.830429	+	0.557125i	$0.188096\pi$
$72$	−157.053	−0.257068
$73$	396.506	0.635719	0.317859	−	0.948138i	$-0.397036\pi$
$73$	396.506	0.635719	0.317859	+	0.948138i	$0.397036\pi$
$74$	−347.628	−0.546094
$75$	−509.141	−0.783875
$76$	29.1283	0.0439638
$77$	240.626	0.356129
$78$	678.159	0.984441
$79$	−1344.36	−1.91459	−0.957293	−	0.289121i	$-0.906637\pi$
$79$	−1344.36	−1.91459	−0.957293	+	0.289121i	$0.906637\pi$
$80$	220.129	0.307640
$81$	−485.621	−0.666147
$82$	1095.20	1.47493
$83$	−775.934	−1.02614	−0.513071	−	0.858346i	$-0.671492\pi$
$83$	−775.934	−1.02614	−0.513071	+	0.858346i	$0.671492\pi$
$84$	−62.2530	−0.0808614
$85$	144.412	0.184278
$86$	−313.275	−0.392805
$87$	0	0
$88$	−152.323	−0.184519
$89$	83.7886	0.0997930	0.0498965	−	0.998754i	$-0.484111\pi$
$89$	83.7886	0.0997930	0.0498965	+	0.998754i	$0.484111\pi$
$90$	−67.8565	−0.0794744
$91$	1826.21	2.10373
$92$	−26.5436	−0.0300800
$93$	−286.099	−0.319001
$94$	−692.177	−0.759495
$95$	−238.237	−0.257291
$96$	80.8976	0.0860060
$97$	−141.626	−0.148247	−0.0741235	−	0.997249i	$-0.523616\pi$
$97$	−141.626	−0.148247	−0.0741235	+	0.997249i	$0.523616\pi$
$98$	−2514.53	−2.59189
$99$	49.3167	0.0500658
$100$	−45.8492	−0.0458492
$101$	1365.75	1.34551	0.672756	−	0.739864i	$-0.265110\pi$
$101$	1365.75	1.34551	0.672756	+	0.739864i	$0.265110\pi$
$102$	568.317	0.551684
$103$	−1602.75	−1.53324	−0.766619	−	0.642102i	$-0.778063\pi$
$103$	−1602.75	−1.53324	−0.766619	+	0.642102i	$0.778063\pi$
$104$	−1156.04	−1.09000
$105$	509.161	0.473228
$106$	1577.10	1.44511
$107$	−808.713	−0.730666	−0.365333	−	0.930877i	$-0.619045\pi$
$107$	−808.713	−0.730666	−0.365333	+	0.930877i	$0.619045\pi$
$108$	−61.0689	−0.0544107
$109$	744.458	0.654185	0.327093	−	0.944992i	$-0.393931\pi$
$109$	744.458	0.654185	0.327093	+	0.944992i	$0.393931\pi$
$110$	−65.8129	−0.0570456
$111$	534.600	0.457135
$112$	2332.84	1.96815
$113$	37.8473	0.0315077	0.0157539	−	0.999876i	$-0.494985\pi$
$113$	37.8473	0.0315077	0.0157539	+	0.999876i	$0.494985\pi$
$114$	−937.558	−0.770266
$115$	217.097	0.176038
$116$	0	0
$117$	374.285	0.295749
$118$	1014.72	0.791630
$119$	1530.42	1.17894
$120$	−322.313	−0.245192
$121$	−1283.17	−0.964063
$122$	−2263.06	−1.67941
$123$	−1684.25	−1.23467
$124$	−25.7638	−0.0186585
$125$	785.377	0.561970
$126$	−719.117	−0.508444
$127$	−117.904	−0.0823805	−0.0411903	−	0.999151i	$-0.513115\pi$
$127$	−117.904	−0.0823805	−0.0411903	+	0.999151i	$0.513115\pi$
$128$	−1547.48	−1.06859
$129$	481.770	0.328818
$130$	−499.482	−0.336980
$131$	299.782	0.199939	0.0999697	−	0.994990i	$-0.468125\pi$
$131$	299.782	0.199939	0.0999697	+	0.994990i	$0.468125\pi$
$132$	−12.3746	−0.00815962
$133$	−2524.75	−1.64604
$134$	−873.340	−0.563023
$135$	499.476	0.318430
$136$	−968.799	−0.610837
$137$	2248.81	1.40240	0.701201	−	0.712964i	$-0.252648\pi$
$137$	2248.81	1.40240	0.701201	+	0.712964i	$0.252648\pi$
$138$	854.362	0.527016
$139$	−541.475	−0.330412	−0.165206	−	0.986259i	$-0.552829\pi$
$139$	−541.475	−0.330412	−0.165206	+	0.986259i	$0.552829\pi$
$140$	45.8509	0.0276793
$141$	1064.46	0.635774
$142$	−2880.02	−1.70201
$143$	363.013	0.212285
$144$	478.120	0.276690
$145$	0	0
$146$	−1149.28	−0.651473
$147$	3866.97	2.16967
$148$	48.1418	0.0267380
$149$	2104.33	1.15700	0.578502	−	0.815681i	$-0.303638\pi$
$149$	2104.33	1.15700	0.578502	+	0.815681i	$0.303638\pi$
$150$	1475.76	0.803300
$151$	1800.21	0.970192	0.485096	−	0.874461i	$-0.338785\pi$
$151$	1800.21	0.970192	0.485096	+	0.874461i	$0.338785\pi$
$152$	1598.24	0.852856
$153$	313.662	0.165739
$154$	−697.460	−0.364954
$155$	210.720	0.109196
$156$	−93.9159	−0.0482006
$157$	369.755	0.187960	0.0939799	−	0.995574i	$-0.470041\pi$
$157$	369.755	0.187960	0.0939799	+	0.995574i	$0.470041\pi$
$158$	3896.65	1.96203
$159$	−2425.35	−1.20970
$160$	−59.5831	−0.0294404
$161$	2300.71	1.12622
$162$	1407.58	0.682654
$163$	−1391.28	−0.668551	−0.334275	−	0.942475i	$-0.608492\pi$
$163$	−1391.28	−0.668551	−0.334275	+	0.942475i	$0.608492\pi$
$164$	−151.670	−0.0722162
$165$	101.210	0.0477529
$166$	2249.06	1.05157
$167$	2009.34	0.931063	0.465531	−	0.885031i	$-0.345863\pi$
$167$	2009.34	0.931063	0.465531	+	0.885031i	$0.345863\pi$
$168$	−3415.75	−1.56864
$169$	558.058	0.254009
$170$	−418.580	−0.188845
$171$	−517.450	−0.231406
$172$	43.3843	0.0192327
$173$	−1303.20	−0.572720	−0.286360	−	0.958122i	$-0.592445\pi$
$173$	−1303.20	−0.572720	−0.286360	+	0.958122i	$0.592445\pi$
$174$	0	0
$175$	3974.06	1.71663
$176$	463.721	0.198604
$177$	−1560.49	−0.662674
$178$	−242.863	−0.102266
$179$	−2153.92	−0.899395	−0.449698	−	0.893181i	$-0.648468\pi$
$179$	−2153.92	−0.899395	−0.449698	+	0.893181i	$0.648468\pi$
$180$	9.39721	0.00389126
$181$	3542.77	1.45487	0.727437	−	0.686174i	$-0.240711\pi$
$181$	3542.77	1.45487	0.727437	+	0.686174i	$0.240711\pi$
$182$	−5293.31	−2.15586
$183$	3480.25	1.40583
$184$	−1456.41	−0.583523
$185$	−393.747	−0.156480
$186$	829.264	0.326907
$187$	304.215	0.118965
$188$	95.8571	0.0371867
$189$	5293.26	2.03718
$190$	690.535	0.263667
$191$	2097.93	0.794768	0.397384	−	0.917652i	$-0.369918\pi$
$191$	2097.93	0.794768	0.397384	+	0.917652i	$0.369918\pi$
$192$	2156.52	0.810590
$193$	324.877	0.121166	0.0605832	−	0.998163i	$-0.480704\pi$
$193$	324.877	0.121166	0.0605832	+	0.998163i	$0.480704\pi$
$194$	410.506	0.151921
$195$	768.128	0.282086
$196$	348.228	0.126905
$197$	−1475.86	−0.533760	−0.266880	−	0.963730i	$-0.585993\pi$
$197$	−1475.86	−0.533760	−0.266880	+	0.963730i	$0.585993\pi$
$198$	−142.945	−0.0513065
$199$	1468.57	0.523137	0.261569	−	0.965185i	$-0.415760\pi$
$199$	1468.57	0.523137	0.261569	+	0.965185i	$0.415760\pi$
$200$	−2515.69	−0.889431
$201$	1343.07	0.471307
$202$	−3958.64	−1.37886
$203$	0	0
$204$	−78.7043	−0.0270118
$205$	1240.49	0.422634
$206$	4645.60	1.57123
$207$	471.534	0.158328
$208$	3519.37	1.17319
$209$	−501.867	−0.166100
$210$	−1475.81	−0.484955
$211$	5862.62	1.91279	0.956396	−	0.292073i	$-0.0943451\pi$
$211$	5862.62	1.91279	0.956396	+	0.292073i	$0.0943451\pi$
$212$	−218.407	−0.0707561
$213$	4429.05	1.42476
$214$	2344.07	0.748772
$215$	−354.836	−0.112556
$216$	−3350.78	−1.05552
$217$	2233.12	0.698591
$218$	−2157.83	−0.670396
$219$	1767.42	0.545348
$220$	9.11420	0.00279309
$221$	2308.82	0.702751
$222$	−1549.55	−0.468463
$223$	2024.94	0.608071	0.304036	−	0.952661i	$-0.401666\pi$
$223$	2024.94	0.608071	0.304036	+	0.952661i	$0.401666\pi$
$224$	−631.439	−0.188347
$225$	814.489	0.241330
$226$	−109.701	−0.0322885
$227$	4417.82	1.29172	0.645861	−	0.763455i	$-0.276498\pi$
$227$	4417.82	1.29172	0.645861	+	0.763455i	$0.276498\pi$
$228$	129.839	0.0377141
$229$	177.751	0.0512931	0.0256466	−	0.999671i	$-0.491836\pi$
$229$	177.751	0.0512931	0.0256466	+	0.999671i	$0.491836\pi$
$230$	−629.259	−0.180401
$231$	1072.59	0.305503
$232$	0	0
$233$	3219.30	0.905164	0.452582	−	0.891723i	$-0.350503\pi$
$233$	3219.30	0.905164	0.452582	+	0.891723i	$0.350503\pi$
$234$	−1084.87	−0.303078
$235$	−784.005	−0.217629
$236$	−140.525	−0.0387601
$237$	−5992.47	−1.64242
$238$	−4435.95	−1.20815
$239$	−2800.82	−0.758032	−0.379016	−	0.925390i	$-0.623737\pi$
$239$	−2800.82	−0.758032	−0.379016	+	0.925390i	$0.623737\pi$
$240$	981.224	0.263907
$241$	−4873.54	−1.30262	−0.651312	−	0.758810i	$-0.725781\pi$
$241$	−4873.54	−1.30262	−0.651312	+	0.758810i	$0.725781\pi$
$242$	3719.29	0.987954
$243$	1943.07	0.512954
$244$	313.404	0.0822279
$245$	−2848.12	−0.742693
$246$	4881.83	1.26526
$247$	−3808.88	−0.981186
$248$	−1413.63	−0.361958
$249$	−3458.72	−0.880270
$250$	−2276.43	−0.575896
$251$	2615.86	0.657816	0.328908	−	0.944362i	$-0.393319\pi$
$251$	2615.86	0.657816	0.328908	+	0.944362i	$0.393319\pi$
$252$	99.5880	0.0248947
$253$	457.333	0.113645
$254$	341.748	0.0844220
$255$	643.714	0.158082
$256$	615.033	0.150155
$257$	−5809.30	−1.41002	−0.705008	−	0.709199i	$-0.749057\pi$
$257$	−5809.30	−1.41002	−0.705008	+	0.709199i	$0.749057\pi$
$258$	−1396.42	−0.336966
$259$	−4172.77	−1.00109
$260$	69.1715	0.0164994
$261$	0	0
$262$	−868.923	−0.204894
$263$	−2725.55	−0.639029	−0.319514	−	0.947581i	$-0.603520\pi$
$263$	−2725.55	−0.639029	−0.319514	+	0.947581i	$0.603520\pi$
$264$	−678.979	−0.158289
$265$	1786.33	0.414089
$266$	7318.02	1.68683
$267$	373.487	0.0856069
$268$	120.946	0.0275670
$269$	1564.87	0.354691	0.177346	−	0.984149i	$-0.443249\pi$
$269$	1564.87	0.354691	0.177346	+	0.984149i	$0.443249\pi$
$270$	−1447.74	−0.326321
$271$	−4324.63	−0.969383	−0.484692	−	0.874685i	$-0.661068\pi$
$271$	−4324.63	−0.969383	−0.484692	+	0.874685i	$0.661068\pi$
$272$	2949.33	0.657462
$273$	8140.33	1.80467
$274$	−6518.22	−1.43715
$275$	789.960	0.173223
$276$	−118.318	−0.0258039
$277$	1051.60	0.228102	0.114051	−	0.993475i	$-0.463617\pi$
$277$	1051.60	0.228102	0.114051	+	0.993475i	$0.463617\pi$
$278$	1569.47	0.338600
$279$	457.682	0.0982104
$280$	2515.79	0.536953
$281$	−4842.35	−1.02801	−0.514004	−	0.857788i	$-0.671838\pi$
$281$	−4842.35	−1.02801	−0.514004	+	0.857788i	$0.671838\pi$
$282$	−3085.37	−0.651529
$283$	−4944.27	−1.03854	−0.519269	−	0.854611i	$-0.673796\pi$
$283$	−4944.27	−1.03854	−0.519269	+	0.854611i	$0.673796\pi$
$284$	398.844	0.0833347
$285$	−1061.94	−0.220716
$286$	−1052.20	−0.217545
$287$	13146.3	2.70383
$288$	−129.414	−0.0264785
$289$	−2978.14	−0.606176
$290$	0	0
$291$	−631.297	−0.127173
$292$	159.160	0.0318977
$293$	−6806.76	−1.35719	−0.678593	−	0.734515i	$-0.737410\pi$
$293$	−6806.76	−1.35719	−0.678593	+	0.734515i	$0.737410\pi$
$294$	−11208.5	−2.22344
$295$	1149.34	0.226837
$296$	2641.48	0.518693
$297$	1052.19	0.205570
$298$	−6099.44	−1.18567
$299$	3470.89	0.671327
$300$	−204.372	−0.0393315
$301$	−3760.41	−0.720088
$302$	−5217.94	−0.994234
$303$	6087.80	1.15424
$304$	−4865.54	−0.917954
$305$	−2563.29	−0.481226
$306$	−909.154	−0.169846
$307$	1047.99	0.194828	0.0974139	−	0.995244i	$-0.468943\pi$
$307$	1047.99	0.194828	0.0974139	+	0.995244i	$0.468943\pi$
$308$	96.5888	0.0178690
$309$	−7144.24	−1.31528
$310$	−610.774	−0.111902
$311$	−2493.86	−0.454707	−0.227353	−	0.973812i	$-0.573007\pi$
$311$	−2493.86	−0.454707	−0.227353	+	0.973812i	$0.573007\pi$
$312$	−5153.06	−0.935046
$313$	3490.12	0.630266	0.315133	−	0.949047i	$-0.397951\pi$
$313$	3490.12	0.630266	0.315133	+	0.949047i	$0.397951\pi$
$314$	−1071.74	−0.192618
$315$	−814.519	−0.145692
$316$	−539.633	−0.0960657
$317$	5935.04	1.05156	0.525781	−	0.850620i	$-0.323773\pi$
$317$	5935.04	1.05156	0.525781	+	0.850620i	$0.323773\pi$
$318$	7029.92	1.23968
$319$	0	0
$320$	−1588.33	−0.277470
$321$	−3604.83	−0.626797
$322$	−6668.65	−1.15413
$323$	−3191.95	−0.549860
$324$	−194.931	−0.0334244
$325$	5995.33	1.02327
$326$	4032.66	0.685118
$327$	3318.42	0.561189
$328$	−8321.97	−1.40093
$329$	−8308.59	−1.39230
$330$	−293.360	−0.0489362
$331$	−7078.74	−1.17548	−0.587739	−	0.809051i	$-0.699982\pi$
$331$	−7078.74	−1.17548	−0.587739	+	0.809051i	$0.699982\pi$
$332$	−311.464	−0.0514874
$333$	−855.216	−0.140737
$334$	−5824.11	−0.954135
$335$	−989.203	−0.161331
$336$	10398.6	1.68837
$337$	2205.74	0.356541	0.178271	−	0.983982i	$-0.442950\pi$
$337$	2205.74	0.356541	0.178271	+	0.983982i	$0.442950\pi$
$338$	−1617.54	−0.260303
$339$	168.704	0.0270287
$340$	57.9677	0.00924629
$341$	443.898	0.0704940
$342$	1499.84	0.237140
$343$	−18249.4	−2.87282
$344$	2380.45	0.373096
$345$	967.708	0.151013
$346$	3777.35	0.586912
$347$	6318.41	0.977493	0.488746	−	0.872426i	$-0.337454\pi$
$347$	6318.41	0.977493	0.488746	+	0.872426i	$0.337454\pi$
$348$	0	0
$349$	−4618.78	−0.708417	−0.354208	−	0.935167i	$-0.615250\pi$
$349$	−4618.78	−0.708417	−0.354208	+	0.935167i	$0.615250\pi$
$350$	−11518.9	−1.75917
$351$	7985.50	1.21434
$352$	−125.517	−0.0190059
$353$	−7078.84	−1.06733	−0.533667	−	0.845695i	$-0.679186\pi$
$353$	−7078.84	−1.06733	−0.533667	+	0.845695i	$0.679186\pi$
$354$	4523.10	0.679096
$355$	−3262.11	−0.487703
$356$	33.6332	0.00500719
$357$	6821.83	1.01134
$358$	6243.18	0.921683
$359$	10670.6	1.56872	0.784361	−	0.620305i	$-0.212991\pi$
$359$	10670.6	1.56872	0.784361	+	0.620305i	$0.212991\pi$
$360$	515.614	0.0754867
$361$	−1593.21	−0.232281
$362$	−10268.8	−1.49093
$363$	−5719.71	−0.827016
$364$	733.053	0.105556
$365$	−1301.75	−0.186676
$366$	−10087.6	−1.44067
$367$	−9102.82	−1.29472	−0.647361	−	0.762183i	$-0.724127\pi$
$367$	−9102.82	−1.29472	−0.647361	+	0.762183i	$0.724127\pi$
$368$	4433.79	0.628063
$369$	2694.35	0.380114
$370$	1141.28	0.160358
$371$	18930.9	2.64917
$372$	−114.842	−0.0160061
$373$	−3650.08	−0.506687	−0.253343	−	0.967376i	$-0.581530\pi$
$373$	−3650.08	−0.506687	−0.253343	+	0.967376i	$0.581530\pi$
$374$	−881.774	−0.121913
$375$	3500.81	0.482083
$376$	5259.57	0.721387
$377$	0	0
$378$	−15342.6	−2.08767
$379$	−2299.72	−0.311685	−0.155843	−	0.987782i	$-0.549809\pi$
$379$	−2299.72	−0.311685	−0.155843	+	0.987782i	$0.549809\pi$
$380$	−95.6298	−0.0129098
$381$	−525.558	−0.0706697
$382$	−6080.88	−0.814463
$383$	1012.28	0.135053	0.0675265	−	0.997717i	$-0.478489\pi$
$383$	1012.28	0.135053	0.0675265	+	0.997717i	$0.478489\pi$
$384$	−6897.89	−0.916683
$385$	−789.990	−0.104576
$386$	−941.660	−0.124169
$387$	−770.702	−0.101232
$388$	−56.8496	−0.00743840
$389$	7379.62	0.961855	0.480928	−	0.876760i	$-0.340300\pi$
$389$	7379.62	0.961855	0.480928	+	0.876760i	$0.340300\pi$
$390$	−2226.43	−0.289077
$391$	2908.71	0.376214
$392$	19106.9	2.46184
$393$	1336.27	0.171517
$394$	4277.81	0.546987
$395$	4413.60	0.562209
$396$	19.7960	0.00251209
$397$	7990.41	1.01014	0.505072	−	0.863077i	$-0.331466\pi$
$397$	7990.41	1.01014	0.505072	+	0.863077i	$0.331466\pi$
$398$	−4256.68	−0.536101
$399$	−11254.0	−1.41205
$400$	7658.57	0.957321
$401$	−7743.98	−0.964379	−0.482190	−	0.876067i	$-0.660158\pi$
$401$	−7743.98	−0.964379	−0.482190	+	0.876067i	$0.660158\pi$
$402$	−3892.90	−0.482986
$403$	3368.93	0.416423
$404$	548.218	0.0675121
$405$	1594.32	0.195611
$406$	0	0
$407$	−829.460	−0.101019
$408$	−4318.41	−0.524003
$409$	−7076.84	−0.855567	−0.427784	−	0.903881i	$-0.640706\pi$
$409$	−7076.84	−0.855567	−0.427784	+	0.903881i	$0.640706\pi$
$410$	−3595.60	−0.433107
$411$	10024.1	1.20304
$412$	−643.353	−0.0769314
$413$	12180.2	1.45121
$414$	−1366.75	−0.162251
$415$	2547.43	0.301322
$416$	−952.599	−0.112272
$417$	−2413.62	−0.283442
$418$	1454.67	0.170216
$419$	−3078.66	−0.358955	−0.179478	−	0.983762i	$-0.557441\pi$
$419$	−3078.66	−0.358955	−0.179478	+	0.983762i	$0.557441\pi$
$420$	204.380	0.0237446
$421$	−9755.18	−1.12931	−0.564654	−	0.825328i	$-0.690990\pi$
$421$	−9755.18	−1.12931	−0.564654	+	0.825328i	$0.690990\pi$
$422$	−16992.9	−1.96019
$423$	−1702.86	−0.195735
$424$	−11983.8	−1.37260
$425$	5024.26	0.573441
$426$	−12837.7	−1.46006
$427$	−27164.8	−3.07868
$428$	−324.622	−0.0366617
$429$	1618.13	0.182107
$430$	1028.50	0.115345
$431$	−1533.99	−0.171438	−0.0857191	−	0.996319i	$-0.527319\pi$
$431$	−1533.99	−0.171438	−0.0857191	+	0.996319i	$0.527319\pi$
$432$	10200.8	1.13608
$433$	1352.29	0.150086	0.0750428	−	0.997180i	$-0.476091\pi$
$433$	1352.29	0.150086	0.0750428	+	0.997180i	$0.476091\pi$
$434$	−6472.75	−0.715903
$435$	0	0
$436$	298.830	0.0328242
$437$	−4798.52	−0.525273
$438$	−5122.90	−0.558862
$439$	14450.1	1.57099	0.785494	−	0.618870i	$-0.212409\pi$
$439$	14450.1	1.57099	0.785494	+	0.618870i	$0.212409\pi$
$440$	500.086	0.0541833
$441$	−6186.11	−0.667974
$442$	−6692.15	−0.720165
$443$	8009.20	0.858981	0.429491	−	0.903071i	$-0.358693\pi$
$443$	8009.20	0.858981	0.429491	+	0.903071i	$0.358693\pi$
$444$	214.592	0.0229371
$445$	−275.083	−0.0293038
$446$	−5869.32	−0.623140
$447$	9380.03	0.992529
$448$	−16832.5	−1.77514
$449$	−10099.0	−1.06147	−0.530735	−	0.847538i	$-0.678084\pi$
$449$	−10099.0	−1.06147	−0.530735	+	0.847538i	$0.678084\pi$
$450$	−2360.81	−0.247310
$451$	2613.21	0.272841
$452$	15.1921	0.00158092
$453$	8024.42	0.832274
$454$	−12805.1	−1.32373
$455$	−5995.56	−0.617750
$456$	7124.12	0.731617
$457$	−981.643	−0.100480	−0.0502400	−	0.998737i	$-0.515999\pi$
$457$	−981.643	−0.100480	−0.0502400	+	0.998737i	$0.515999\pi$
$458$	−515.215	−0.0525642
$459$	6692.08	0.680522
$460$	87.1440	0.00883284
$461$	−10537.5	−1.06460	−0.532298	−	0.846557i	$-0.678671\pi$
$461$	−10537.5	−1.06460	−0.532298	+	0.846557i	$0.678671\pi$
$462$	−3108.92	−0.313074
$463$	−4266.69	−0.428271	−0.214136	−	0.976804i	$-0.568693\pi$
$463$	−4266.69	−0.428271	−0.214136	+	0.976804i	$0.568693\pi$
$464$	0	0
$465$	939.280	0.0936733
$466$	−9331.19	−0.927595
$467$	−14724.5	−1.45903	−0.729514	−	0.683966i	$-0.760254\pi$
$467$	−14724.5	−1.45903	−0.729514	+	0.683966i	$0.760254\pi$
$468$	150.240	0.0148394
$469$	−10483.2	−1.03213
$470$	2272.45	0.223022
$471$	1648.18	0.161240
$472$	−7710.43	−0.751910
$473$	−747.491	−0.0726632
$474$	17369.3	1.68312
$475$	−8288.57	−0.800644
$476$	614.319	0.0591539
$477$	3879.90	0.372429
$478$	8118.21	0.776817
$479$	−9083.72	−0.866483	−0.433242	−	0.901278i	$-0.642630\pi$
$479$	−9083.72	−0.866483	−0.433242	+	0.901278i	$0.642630\pi$
$480$	−265.591	−0.0252553
$481$	−6295.12	−0.596742
$482$	14126.1	1.33491
$483$	10255.4	0.966121
$484$	−515.071	−0.0483726
$485$	464.966	0.0435320
$486$	−5632.01	−0.525665
$487$	782.150	0.0727774	0.0363887	−	0.999338i	$-0.488415\pi$
$487$	782.150	0.0727774	0.0363887	+	0.999338i	$0.488415\pi$
$488$	17196.1	1.59514
$489$	−6201.64	−0.573513
$490$	8255.33	0.761097
$491$	3228.96	0.296784	0.148392	−	0.988929i	$-0.452590\pi$
$491$	3228.96	0.296784	0.148392	+	0.988929i	$0.452590\pi$
$492$	−676.068	−0.0619502
$493$	0	0
$494$	11040.1	1.00550
$495$	−161.909	−0.0147016
$496$	4303.54	0.389586
$497$	−34570.5	−3.12012
$498$	10025.2	0.902084
$499$	−6626.01	−0.594431	−0.297215	−	0.954810i	$-0.596058\pi$
$499$	−6626.01	−0.594431	−0.297215	+	0.954810i	$0.596058\pi$
$500$	315.255	0.0281973
$501$	8956.62	0.798707
$502$	−7582.13	−0.674117
$503$	−12530.9	−1.11079	−0.555393	−	0.831588i	$-0.687432\pi$
$503$	−12530.9	−1.11079	−0.555393	+	0.831588i	$0.687432\pi$
$504$	5464.28	0.482933
$505$	−4483.82	−0.395104
$506$	−1325.59	−0.116462
$507$	2487.54	0.217900
$508$	−47.3275	−0.00413350
$509$	19121.0	1.66507	0.832537	−	0.553970i	$-0.186888\pi$
$509$	19121.0	1.66507	0.832537	+	0.553970i	$0.186888\pi$
$510$	−1865.82	−0.161999
$511$	−13795.4	−1.19427
$512$	10597.2	0.914714
$513$	−11040.0	−0.950150
$514$	16838.4	1.44496
$515$	5261.91	0.450228
$516$	193.385	0.0164987
$517$	−1651.57	−0.140495
$518$	12094.9	1.02590
$519$	−5809.01	−0.491305
$520$	3795.36	0.320072
$521$	7261.51	0.610619	0.305310	−	0.952253i	$-0.401240\pi$
$521$	7261.51	0.610619	0.305310	+	0.952253i	$0.401240\pi$
$522$	0	0
$523$	1886.78	0.157750	0.0788749	−	0.996885i	$-0.474867\pi$
$523$	1886.78	0.157750	0.0788749	+	0.996885i	$0.474867\pi$
$524$	120.334	0.0100321
$525$	17714.3	1.47260
$526$	7900.06	0.654865
$527$	2823.26	0.233365
$528$	2067.03	0.170371
$529$	−7794.28	−0.640609
$530$	−5177.71	−0.424350
$531$	2496.36	0.204016
$532$	−1013.45	−0.0825912
$533$	19832.7	1.61173
$534$	−1082.56	−0.0877283
$535$	2655.05	0.214557
$536$	6636.16	0.534773
$537$	−9601.09	−0.771541
$538$	−4535.81	−0.363481
$539$	−5999.81	−0.479462
$540$	200.493	0.0159775
$541$	−2306.54	−0.183301	−0.0916507	−	0.995791i	$-0.529214\pi$
$541$	−2306.54	−0.183301	−0.0916507	+	0.995791i	$0.529214\pi$
$542$	12535.0	0.993405
$543$	15791.9	1.24806
$544$	−798.306	−0.0629174
$545$	−2444.10	−0.192098
$546$	−23594.9	−1.84939
$547$	309.663	0.0242052	0.0121026	−	0.999927i	$-0.496148\pi$
$547$	309.663	0.0242052	0.0121026	+	0.999927i	$0.496148\pi$
$548$	902.686	0.0703665
$549$	−5567.46	−0.432812
$550$	−2289.71	−0.177516
$551$	0	0
$552$	−6491.95	−0.500572
$553$	46773.7	3.59678
$554$	−3048.07	−0.233755
$555$	−1755.12	−0.134236
$556$	−217.351	−0.0165787
$557$	−12306.2	−0.936140	−0.468070	−	0.883691i	$-0.655050\pi$
$557$	−12306.2	−0.936140	−0.468070	+	0.883691i	$0.655050\pi$
$558$	−1326.60	−0.100644
$559$	−5673.02	−0.429237
$560$	−7658.86	−0.577939
$561$	1356.04	0.102053
$562$	14035.6	1.05348
$563$	2558.68	0.191537	0.0957685	−	0.995404i	$-0.469469\pi$
$563$	2558.68	0.191537	0.0957685	+	0.995404i	$0.469469\pi$
$564$	427.282	0.0319004
$565$	−124.255	−0.00925210
$566$	14331.1	1.06427
$567$	16896.0	1.25144
$568$	21884.1	1.61662
$569$	8601.85	0.633758	0.316879	−	0.948466i	$-0.397365\pi$
$569$	8601.85	0.633758	0.316879	+	0.948466i	$0.397365\pi$
$570$	3078.05	0.226185
$571$	7867.60	0.576618	0.288309	−	0.957537i	$-0.406907\pi$
$571$	7867.60	0.576618	0.288309	+	0.957537i	$0.406907\pi$
$572$	145.716	0.0106515
$573$	9351.49	0.681787
$574$	−38104.7	−2.77084
$575$	7553.07	0.547800
$576$	−3449.85	−0.249555
$577$	−978.513	−0.0705997	−0.0352998	−	0.999377i	$-0.511239\pi$
$577$	−978.513	−0.0705997	−0.0352998	+	0.999377i	$0.511239\pi$
$578$	8632.20	0.621198
$579$	1448.13	0.103942
$580$	0	0
$581$	26996.7	1.92773
$582$	1829.83	0.130324
$583$	3763.06	0.267324
$584$	8732.90	0.618784
$585$	−1228.80	−0.0868454
$586$	19729.5	1.39082
$587$	17958.7	1.26275	0.631374	−	0.775478i	$-0.282491\pi$
$587$	17958.7	1.26275	0.631374	+	0.775478i	$0.282491\pi$
$588$	1552.22	0.108865
$589$	−4657.56	−0.325826
$590$	−3331.38	−0.232459
$591$	−6578.63	−0.457883
$592$	−8041.52	−0.558285
$593$	1749.15	0.121128	0.0605640	−	0.998164i	$-0.480710\pi$
$593$	1749.15	0.121128	0.0605640	+	0.998164i	$0.480710\pi$
$594$	−3049.79	−0.210664
$595$	−5024.45	−0.346189
$596$	844.690	0.0580535
$597$	6546.15	0.448770
$598$	−10060.4	−0.687963
$599$	−18932.1	−1.29140	−0.645698	−	0.763593i	$-0.723434\pi$
$599$	−18932.1	−1.29140	−0.645698	+	0.763593i	$0.723434\pi$
$600$	−11213.7	−0.762993
$601$	15333.4	1.04070	0.520352	−	0.853952i	$-0.325801\pi$
$601$	15333.4	1.04070	0.520352	+	0.853952i	$0.325801\pi$
$602$	10899.6	0.737933
$603$	−2148.55	−0.145100
$604$	722.615	0.0486801
$605$	4212.71	0.283093
$606$	−17645.6	−1.18284
$607$	−8597.83	−0.574918	−0.287459	−	0.957793i	$-0.592811\pi$
$607$	−8597.83	−0.574918	−0.287459	+	0.957793i	$0.592811\pi$
$608$	1316.97	0.0878459
$609$	0	0
$610$	7429.75	0.493151
$611$	−12534.5	−0.829936
$612$	125.906	0.00831606
$613$	14218.4	0.936830	0.468415	−	0.883509i	$-0.344825\pi$
$613$	14218.4	0.936830	0.468415	+	0.883509i	$0.344825\pi$
$614$	−3037.63	−0.199656
$615$	5529.49	0.362554
$616$	5299.71	0.346642
$617$	−17355.2	−1.13240	−0.566202	−	0.824266i	$-0.691588\pi$
$617$	−17355.2	−1.13240	−0.566202	+	0.824266i	$0.691588\pi$
$618$	20707.7	1.34787
$619$	−1358.21	−0.0881921	−0.0440961	−	0.999027i	$-0.514041\pi$
$619$	−1358.21	−0.0881921	−0.0440961	+	0.999027i	$0.514041\pi$
$620$	84.5840	0.00547899
$621$	10060.3	0.650092
$622$	7228.50	0.465975
$623$	−2915.22	−0.187473
$624$	15687.6	1.00642
$625$	11699.3	0.748752
$626$	−10116.2	−0.645885
$627$	−2237.07	−0.142488
$628$	148.422	0.00943102
$629$	−5275.49	−0.334416
$630$	2360.90	0.149302
$631$	16959.5	1.06997	0.534983	−	0.844863i	$-0.320318\pi$
$631$	16959.5	1.06997	0.534983	+	0.844863i	$0.320318\pi$
$632$	−29609.1	−1.86358
$633$	26132.6	1.64088
$634$	−17202.8	−1.07762
$635$	387.087	0.0241907
$636$	−973.549	−0.0606977
$637$	−45535.0	−2.83228
$638$	0	0
$639$	−7085.28	−0.438637
$640$	5080.47	0.313786
$641$	−466.812	−0.0287644	−0.0143822	−	0.999897i	$-0.504578\pi$
$641$	−466.812	−0.0287644	−0.0143822	+	0.999897i	$0.504578\pi$
$642$	10448.7	0.642330
$643$	−4041.33	−0.247861	−0.123930	−	0.992291i	$-0.539550\pi$
$643$	−4041.33	−0.247861	−0.123930	+	0.992291i	$0.539550\pi$
$644$	923.518	0.0565089
$645$	−1581.68	−0.0965557
$646$	9251.92	0.563486
$647$	150.558	0.00914844	0.00457422	−	0.999990i	$-0.498544\pi$
$647$	150.558	0.00914844	0.00457422	+	0.999990i	$0.498544\pi$
$648$	−10695.6	−0.648402
$649$	2421.18	0.146440
$650$	−17377.6	−1.04862
$651$	9954.13	0.599283
$652$	−558.470	−0.0335450
$653$	21849.5	1.30940	0.654700	−	0.755889i	$-0.272795\pi$
$653$	21849.5	1.30940	0.654700	+	0.755889i	$0.272795\pi$
$654$	−9618.49	−0.575096
$655$	−984.200	−0.0587113
$656$	25334.7	1.50786
$657$	−2827.39	−0.167895
$658$	24082.6	1.42680
$659$	−2858.89	−0.168993	−0.0844966	−	0.996424i	$-0.526928\pi$
$659$	−2858.89	−0.168993	−0.0844966	+	0.996424i	$0.526928\pi$
$660$	40.6265	0.00239604
$661$	7204.91	0.423961	0.211981	−	0.977274i	$-0.432009\pi$
$661$	7204.91	0.423961	0.211981	+	0.977274i	$0.432009\pi$
$662$	20517.9	1.20461
$663$	10291.5	0.602851
$664$	−17089.7	−0.998807
$665$	8288.88	0.483352
$666$	2478.86	0.144225
$667$	0	0
$668$	806.561	0.0467167
$669$	9026.14	0.521631
$670$	2867.22	0.165329
$671$	−5399.80	−0.310666
$672$	−2814.63	−0.161573
$673$	−16504.0	−0.945295	−0.472648	−	0.881251i	$-0.656702\pi$
$673$	−16504.0	−0.945295	−0.472648	+	0.881251i	$0.656702\pi$
$674$	−6393.38	−0.365377
$675$	17377.4	0.990898
$676$	224.007	0.0127451
$677$	33702.2	1.91327	0.956633	−	0.291297i	$-0.0940866\pi$
$677$	33702.2	1.91327	0.956633	+	0.291297i	$0.0940866\pi$
$678$	−488.992	−0.0276985
$679$	4927.54	0.278500
$680$	3180.62	0.179369
$681$	19692.4	1.10810
$682$	−1286.65	−0.0722409
$683$	−12477.9	−0.699051	−0.349526	−	0.936927i	$-0.613657\pi$
$683$	−12477.9	−0.699051	−0.349526	+	0.936927i	$0.613657\pi$
$684$	−207.708	−0.0116110
$685$	−7382.98	−0.411809
$686$	52896.3	2.94401
$687$	792.324	0.0440015
$688$	−7246.84	−0.401574
$689$	28559.4	1.57914
$690$	−2804.92	−0.154756
$691$	−12346.2	−0.679697	−0.339849	−	0.940480i	$-0.610376\pi$
$691$	−12346.2	−0.679697	−0.339849	+	0.940480i	$0.610376\pi$
$692$	−523.112	−0.0287366
$693$	−1715.85	−0.0940547
$694$	−18314.0	−1.00172
$695$	1777.69	0.0970240
$696$	0	0
$697$	16620.4	0.903216
$698$	13387.6	0.725972
$699$	14350.0	0.776490
$700$	1595.21	0.0861332
$701$	5760.03	0.310347	0.155173	−	0.987887i	$-0.450406\pi$
$701$	5760.03	0.310347	0.155173	+	0.987887i	$0.450406\pi$
$702$	−23146.1	−1.24444
$703$	8703.03	0.466914
$704$	−3345.95	−0.179127
$705$	−3494.70	−0.186692
$706$	20518.1	1.09378
$707$	−47517.8	−2.52771
$708$	−626.388	−0.0332501
$709$	14317.5	0.758401	0.379201	−	0.925315i	$-0.376199\pi$
$709$	14317.5	0.758401	0.379201	+	0.925315i	$0.376199\pi$
$710$	9455.27	0.499789
$711$	9586.33	0.505648
$712$	1845.42	0.0971347
$713$	4244.26	0.222930
$714$	−19773.2	−1.03641
$715$	−1191.79	−0.0623364
$716$	−864.597	−0.0451278
$717$	−12484.6	−0.650274
$718$	−30928.8	−1.60760
$719$	26651.8	1.38240	0.691198	−	0.722665i	$-0.257083\pi$
$719$	26651.8	1.38240	0.691198	+	0.722665i	$0.257083\pi$
$720$	−1569.69	−0.0812486
$721$	55763.7	2.88037
$722$	4617.96	0.238037
$723$	−21723.8	−1.11745
$724$	1422.09	0.0729994
$725$	0	0
$726$	16578.7	0.847511
$727$	11378.5	0.580475	0.290237	−	0.956955i	$-0.406266\pi$
$727$	11378.5	0.580475	0.290237	+	0.956955i	$0.406266\pi$
$728$	40221.7	2.04769
$729$	21773.0	1.10618
$730$	3773.15	0.191302
$731$	−4754.16	−0.240546
$732$	1396.99	0.0705387
$733$	7154.35	0.360507	0.180254	−	0.983620i	$-0.442308\pi$
$733$	7154.35	0.360507	0.180254	+	0.983620i	$0.442308\pi$
$734$	26384.7	1.32681
$735$	−12695.5	−0.637115
$736$	−1200.11	−0.0601041
$737$	−2083.84	−0.104151
$738$	−7809.62	−0.389534
$739$	7654.00	0.380997	0.190499	−	0.981687i	$-0.438990\pi$
$739$	7654.00	0.380997	0.190499	+	0.981687i	$0.438990\pi$
$740$	−158.052	−0.00785150
$741$	−16978.0	−0.841705
$742$	−54871.4	−2.71482
$743$	24833.6	1.22619	0.613093	−	0.790011i	$-0.289925\pi$
$743$	24833.6	1.22619	0.613093	+	0.790011i	$0.289925\pi$
$744$	−6301.24	−0.310504
$745$	−6908.63	−0.339749
$746$	10579.8	0.519243
$747$	5533.01	0.271007
$748$	122.114	0.00596915
$749$	28137.2	1.37264
$750$	−10147.2	−0.494030
$751$	−30438.4	−1.47898	−0.739491	−	0.673167i	$-0.764934\pi$
$751$	−30438.4	−1.47898	−0.739491	+	0.673167i	$0.764934\pi$
$752$	−16011.8	−0.776450
$753$	11660.2	0.564304
$754$	0	0
$755$	−5910.19	−0.284892
$756$	2124.74	0.102217
$757$	−23768.5	−1.14119	−0.570596	−	0.821231i	$-0.693288\pi$
$757$	−23768.5	−1.14119	−0.570596	+	0.821231i	$0.693288\pi$
$758$	6665.78	0.319409
$759$	2038.56	0.0974901
$760$	−5247.10	−0.250437
$761$	−27539.0	−1.31181	−0.655905	−	0.754843i	$-0.727713\pi$
$761$	−27539.0	−1.31181	−0.655905	+	0.754843i	$0.727713\pi$
$762$	1523.34	0.0724209
$763$	−25901.6	−1.22897
$764$	842.120	0.0398781
$765$	−1029.77	−0.0486684
$766$	−2934.12	−0.138400
$767$	18375.3	0.865051
$768$	2741.50	0.128809
$769$	−29142.6	−1.36659	−0.683297	−	0.730141i	$-0.739454\pi$
$769$	−29142.6	−1.36659	−0.683297	+	0.730141i	$0.739454\pi$
$770$	2289.80	0.107167
$771$	−25894.9	−1.20957
$772$	130.407	0.00607961
$773$	−16314.8	−0.759123	−0.379561	−	0.925167i	$-0.623925\pi$
$773$	−16314.8	−0.759123	−0.379561	+	0.925167i	$0.623925\pi$
$774$	2233.89	0.103741
$775$	7331.19	0.339799
$776$	−3119.27	−0.144298
$777$	−18600.1	−0.858784
$778$	−21390.0	−0.985691
$779$	−27418.8	−1.26108
$780$	308.331	0.0141539
$781$	−6871.90	−0.314848
$782$	−8430.94	−0.385537
$783$	0	0
$784$	−58167.4	−2.64975
$785$	−1213.93	−0.0551935
$786$	−3873.22	−0.175767
$787$	15125.1	0.685070	0.342535	−	0.939505i	$-0.388714\pi$
$787$	15125.1	0.685070	0.342535	+	0.939505i	$0.388714\pi$
$788$	−592.419	−0.0267818
$789$	−12149.1	−0.548187
$790$	−12792.9	−0.576141
$791$	−1316.80	−0.0591911
$792$	1086.18	0.0487321
$793$	−40981.3	−1.83517
$794$	−23160.3	−1.03518
$795$	7962.55	0.355224
$796$	589.493	0.0262488
$797$	−18301.4	−0.813387	−0.406693	−	0.913565i	$-0.633318\pi$
$797$	−18301.4	−0.813387	−0.406693	+	0.913565i	$0.633318\pi$
$798$	32620.0	1.44704
$799$	−10504.3	−0.465099
$800$	−2072.97	−0.0916132
$801$	−597.478	−0.0263556
$802$	22446.1	0.988278
$803$	−2742.25	−0.120513
$804$	539.115	0.0236482
$805$	−7553.36	−0.330709
$806$	−9764.90	−0.426742
$807$	6975.41	0.304270
$808$	30080.1	1.30967
$809$	24890.7	1.08172	0.540859	−	0.841113i	$-0.318099\pi$
$809$	24890.7	1.08172	0.540859	+	0.841113i	$0.318099\pi$
$810$	−4621.16	−0.200458
$811$	19933.7	0.863093	0.431546	−	0.902091i	$-0.357968\pi$
$811$	19933.7	0.863093	0.431546	+	0.902091i	$0.357968\pi$
$812$	0	0
$813$	−19277.0	−0.831580
$814$	2404.21	0.103523
$815$	4567.66	0.196317
$816$	13146.6	0.564000
$817$	7842.97	0.335852
$818$	20512.3	0.876769
$819$	−13022.3	−0.555601
$820$	497.942	0.0212059
$821$	38903.6	1.65377	0.826885	−	0.562371i	$-0.190111\pi$
$821$	38903.6	1.65377	0.826885	+	0.562371i	$0.190111\pi$
$822$	−29054.9	−1.23285
$823$	−40479.3	−1.71448	−0.857242	−	0.514914i	$-0.827824\pi$
$823$	−40479.3	−1.71448	−0.857242	+	0.514914i	$0.827824\pi$
$824$	−35300.0	−1.49240
$825$	3521.24	0.148599
$826$	−35304.6	−1.48717
$827$	−1318.15	−0.0554253	−0.0277126	−	0.999616i	$-0.508822\pi$
$827$	−1318.15	−0.0554253	−0.0277126	+	0.999616i	$0.508822\pi$
$828$	189.276	0.00794421
$829$	15446.1	0.647125	0.323563	−	0.946207i	$-0.395119\pi$
$829$	15446.1	0.647125	0.323563	+	0.946207i	$0.395119\pi$
$830$	−7383.78	−0.308789
$831$	4687.48	0.195676
$832$	−25393.8	−1.05814
$833$	−38159.7	−1.58722
$834$	6995.91	0.290466
$835$	−6596.78	−0.273402
$836$	−201.452	−0.00833418
$837$	9764.80	0.403251
$838$	8923.55	0.367851
$839$	32339.6	1.33074	0.665369	−	0.746515i	$-0.268274\pi$
$839$	32339.6	1.33074	0.665369	+	0.746515i	$0.268274\pi$
$840$	11214.1	0.460622
$841$	0	0
$842$	28275.6	1.15729
$843$	−21584.7	−0.881871
$844$	2353.29	0.0959757
$845$	−1832.13	−0.0745885
$846$	4935.76	0.200585
$847$	44644.7	1.81111
$848$	36482.4	1.47737
$849$	−22039.0	−0.890905
$850$	−14562.9	−0.587652
$851$	−7930.75	−0.319463
$852$	1777.84	0.0714882
$853$	−6726.56	−0.270003	−0.135002	−	0.990845i	$-0.543104\pi$
$853$	−6726.56	−0.270003	−0.135002	+	0.990845i	$0.543104\pi$
$854$	78737.7	3.15497
$855$	1698.82	0.0679513
$856$	−17811.6	−0.711202
$857$	−17643.8	−0.703267	−0.351633	−	0.936138i	$-0.614374\pi$
$857$	−17643.8	−0.703267	−0.351633	+	0.936138i	$0.614374\pi$
$858$	−4690.17	−0.186620
$859$	−11080.5	−0.440118	−0.220059	−	0.975487i	$-0.570625\pi$
$859$	−11080.5	−0.440118	−0.220059	+	0.975487i	$0.570625\pi$
$860$	−142.433	−0.00564759
$861$	58599.4	2.31947
$862$	4446.31	0.175687
$863$	−4923.23	−0.194193	−0.0970966	−	0.995275i	$-0.530956\pi$
$863$	−4923.23	−0.194193	−0.0970966	+	0.995275i	$0.530956\pi$
$864$	−2761.10	−0.108720
$865$	4278.48	0.168177
$866$	−3919.64	−0.153805
$867$	−13275.0	−0.520005
$868$	896.389	0.0350523
$869$	9297.63	0.362947
$870$	0	0
$871$	−15815.1	−0.615241
$872$	16396.4	0.636759
$873$	1009.91	0.0391525
$874$	13908.6	0.538290
$875$	−27325.3	−1.05573
$876$	709.453	0.0273632
$877$	−1195.41	−0.0460276	−0.0230138	−	0.999735i	$-0.507326\pi$
$877$	−1195.41	−0.0460276	−0.0230138	+	0.999735i	$0.507326\pi$
$878$	−41883.7	−1.60992
$879$	−30341.1	−1.16425
$880$	−1522.42	−0.0583191
$881$	−937.102	−0.0358363	−0.0179181	−	0.999839i	$-0.505704\pi$
$881$	−937.102	−0.0358363	−0.0179181	+	0.999839i	$0.505704\pi$
$882$	17930.5	0.684527
$883$	−18133.8	−0.691112	−0.345556	−	0.938398i	$-0.612310\pi$
$883$	−18133.8	−0.691112	−0.345556	+	0.938398i	$0.612310\pi$
$884$	926.773	0.0352610
$885$	5123.16	0.194591
$886$	−23214.8	−0.880268
$887$	26591.9	1.00662	0.503309	−	0.864106i	$-0.332116\pi$
$887$	26591.9	1.00662	0.503309	+	0.864106i	$0.332116\pi$
$888$	11774.4	0.444958
$889$	4102.20	0.154762
$890$	797.332	0.0300299
$891$	3358.57	0.126281
$892$	812.822	0.0305104
$893$	17329.0	0.649375
$894$	−27188.2	−1.01712
$895$	7071.45	0.264103
$896$	53840.9	2.00747
$897$	15471.5	0.575894
$898$	29272.1	1.08777
$899$	0	0
$900$	326.940	0.0121089
$901$	23933.6	0.884955
$902$	−7574.42	−0.279602
$903$	−16762.0	−0.617724
$904$	833.574	0.0306684
$905$	−11631.1	−0.427217
$906$	−23258.9	−0.852898
$907$	352.360	0.0128996	0.00644979	−	0.999979i	$-0.497947\pi$
$907$	352.360	0.0128996	0.00644979	+	0.999979i	$0.497947\pi$
$908$	1773.34	0.0648131
$909$	−9738.83	−0.355354
$910$	17378.2	0.633058
$911$	−51218.5	−1.86273	−0.931363	−	0.364091i	$-0.881380\pi$
$911$	−51218.5	−1.86273	−0.931363	+	0.364091i	$0.881380\pi$
$912$	−21688.1	−0.787461
$913$	5366.38	0.194525
$914$	2845.31	0.102970
$915$	−11425.9	−0.412817
$916$	71.3503	0.00257367
$917$	−10430.2	−0.375610
$918$	−19397.1	−0.697385
$919$	44262.9	1.58879	0.794395	−	0.607401i	$-0.207788\pi$
$919$	44262.9	1.58879	0.794395	+	0.607401i	$0.207788\pi$
$920$	4781.49	0.171349
$921$	4671.42	0.167132
$922$	30543.0	1.09098
$923$	−52153.7	−1.85987
$924$	430.544	0.0153288
$925$	−13698.9	−0.486939
$926$	12367.1	0.438884
$927$	11428.9	0.404933
$928$	0	0
$929$	−15097.5	−0.533189	−0.266595	−	0.963809i	$-0.585898\pi$
$929$	−15097.5	−0.533189	−0.266595	+	0.963809i	$0.585898\pi$
$930$	−2722.52	−0.0959946
$931$	62952.3	2.21609
$932$	1292.24	0.0454173
$933$	−11116.4	−0.390068
$934$	42679.1	1.49518
$935$	−998.756	−0.0349335
$936$	8243.50	0.287871
$937$	44931.7	1.56655	0.783274	−	0.621677i	$-0.213548\pi$
$937$	44931.7	1.56655	0.783274	+	0.621677i	$0.213548\pi$
$938$	30385.7	1.05771
$939$	15557.2	0.540670
$940$	−314.704	−0.0109197
$941$	18872.4	0.653797	0.326898	−	0.945059i	$-0.393996\pi$
$941$	18872.4	0.653797	0.326898	+	0.945059i	$0.393996\pi$
$942$	−4777.28	−0.165236
$943$	24985.7	0.862829
$944$	23473.0	0.809303
$945$	−17378.0	−0.598209
$946$	2166.62	0.0744638
$947$	12651.5	0.434128	0.217064	−	0.976157i	$-0.430352\pi$
$947$	12651.5	0.434128	0.217064	+	0.976157i	$0.430352\pi$
$948$	−2405.41	−0.0824094
$949$	−20812.0	−0.711894
$950$	24024.6	0.820484
$951$	26455.4	0.902076
$952$	33707.0	1.14753
$953$	−27783.7	−0.944389	−0.472194	−	0.881494i	$-0.656538\pi$
$953$	−27783.7	−0.944389	−0.472194	+	0.881494i	$0.656538\pi$
$954$	−11246.0	−0.381658
$955$	−6887.61	−0.233380
$956$	−1124.26	−0.0380348
$957$	0	0
$958$	26329.3	0.887956
$959$	−78241.9	−2.63458
$960$	−7079.97	−0.238026
$961$	−25671.4	−0.861717
$962$	18246.5	0.611529
$963$	5766.75	0.192971
$964$	−1956.27	−0.0653601
$965$	−1066.59	−0.0355800
$966$	−29725.4	−0.990062
$967$	2625.48	0.0873109	0.0436555	−	0.999047i	$-0.486100\pi$
$967$	2625.48	0.0873109	0.0436555	+	0.999047i	$0.486100\pi$
$968$	−28261.4	−0.938382
$969$	−14228.1	−0.471694
$970$	−1347.71	−0.0446108
$971$	58845.8	1.94485	0.972426	−	0.233210i	$-0.0749229\pi$
$971$	58845.8	1.94485	0.972426	+	0.233210i	$0.0749229\pi$
$972$	779.958	0.0257378
$973$	18839.3	0.620719
$974$	−2267.08	−0.0745809
$975$	26724.1	0.877803
$976$	−52350.4	−1.71690
$977$	−39646.6	−1.29827	−0.649133	−	0.760675i	$-0.724868\pi$
$977$	−39646.6	−1.29827	−0.649133	+	0.760675i	$0.724868\pi$
$978$	17975.6	0.587725
$979$	−579.485	−0.0189177
$980$	−1143.25	−0.0372651
$981$	−5308.57	−0.172772
$982$	−9359.19	−0.304138
$983$	1316.50	0.0427160	0.0213580	−	0.999772i	$-0.493201\pi$
$983$	1316.50	0.0427160	0.0213580	+	0.999772i	$0.493201\pi$
$984$	−37095.1	−1.20178
$985$	4845.33	0.156736
$986$	0	0
$987$	−37035.4	−1.19438
$988$	−1528.91	−0.0492317
$989$	−7147.02	−0.229790
$990$	469.297	0.0150659
$991$	−8398.31	−0.269204	−0.134602	−	0.990900i	$-0.542976\pi$
$991$	−8398.31	−0.269204	−0.134602	+	0.990900i	$0.542976\pi$
$992$	−1164.85	−0.0372824
$993$	−31553.4	−1.00838
$994$	100203.	3.19744
$995$	−4821.40	−0.153617
$996$	−1388.35	−0.0441682
$997$	22199.2	0.705170	0.352585	−	0.935780i	$-0.385303\pi$
$997$	22199.2	0.705170	0.352585	+	0.935780i	$0.385303\pi$
$998$	19205.6	0.609161
$999$	−18246.3	−0.577866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.4.a.h.1.7		21
29.7	even	7		29.4.d.a.20.5	yes	42
29.25	even	7		29.4.d.a.16.5	✓	42
29.28	even	2		841.4.a.i.1.15		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.4.d.a.16.5	✓	42	29.25	even	7
29.4.d.a.20.5	yes	42	29.7	even	7
841.4.a.h.1.7		21	1.1	even	1	trivial
841.4.a.i.1.15		21	29.28	even	2

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	841.a (trivial)

\(f(q)\)	\(=\)	\(q-2.89852 q^{2} +4.45749 q^{3} +0.401406 q^{4} -3.28305 q^{5} -12.9201 q^{6} -34.7925 q^{7} +22.0247 q^{8} -7.13078 q^{9} +9.51599 q^{10} -6.91603 q^{11} +1.78926 q^{12} -52.4886 q^{13} +100.847 q^{14} -14.6342 q^{15} -67.0501 q^{16} -43.9870 q^{17} +20.6687 q^{18} +72.5657 q^{19} -1.31784 q^{20} -155.087 q^{21} +20.0462 q^{22} -66.1265 q^{23} +98.1747 q^{24} -114.222 q^{25} +152.139 q^{26} -152.138 q^{27} -13.9659 q^{28} +42.4174 q^{30} -64.1840 q^{31} +18.1487 q^{32} -30.8281 q^{33} +127.497 q^{34} +114.226 q^{35} -2.86234 q^{36} +119.933 q^{37} -210.333 q^{38} -233.968 q^{39} -72.3082 q^{40} -377.848 q^{41} +449.524 q^{42} +108.081 q^{43} -2.77613 q^{44} +23.4107 q^{45} +191.669 q^{46} +238.804 q^{47} -298.875 q^{48} +867.521 q^{49} +331.073 q^{50} -196.072 q^{51} -21.0692 q^{52} -544.106 q^{53} +440.974 q^{54} +22.7057 q^{55} -766.294 q^{56} +323.461 q^{57} -350.082 q^{59} -5.87425 q^{60} +780.765 q^{61} +186.038 q^{62} +248.098 q^{63} +483.797 q^{64} +172.323 q^{65} +89.3559 q^{66} +301.306 q^{67} -17.6566 q^{68} -294.758 q^{69} -331.086 q^{70} +993.619 q^{71} -157.053 q^{72} +396.506 q^{73} -347.628 q^{74} -509.141 q^{75} +29.1283 q^{76} +240.626 q^{77} +678.159 q^{78} -1344.36 q^{79} +220.129 q^{80} -485.621 q^{81} +1095.20 q^{82} -775.934 q^{83} -62.2530 q^{84} +144.412 q^{85} -313.275 q^{86} -152.323 q^{88} +83.7886 q^{89} -67.8565 q^{90} +1826.21 q^{91} -26.5436 q^{92} -286.099 q^{93} -692.177 q^{94} -238.237 q^{95} +80.8976 q^{96} -141.626 q^{97} -2514.53 q^{98} +49.3167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 6 q^{2} + q^{3} + 90 q^{4} + 35 q^{5} + 26 q^{6} + 37 q^{7} - 51 q^{8} + 188 q^{9} - 37 q^{10} + 7 q^{11} + 68 q^{12} + 97 q^{13} + 68 q^{14} + 330 q^{15} + 310 q^{16} - 70 q^{17} - 305 q^{18} + 73 q^{19}+ \cdots - 8702 q^{99}+O(q^{100}) \) 21 * q - 6 * q^2 + q^3 + 90 * q^4 + 35 * q^5 + 26 * q^6 + 37 * q^7 - 51 * q^8 + 188 * q^9 - 37 * q^10 + 7 * q^11 + 68 * q^12 + 97 * q^13 + 68 * q^14 + 330 * q^15 + 310 * q^16 - 70 * q^17 - 305 * q^18 + 73 * q^19 + 408 * q^20 - 169 * q^21 + 705 * q^22 + 375 * q^23 + 641 * q^24 + 402 * q^25 - 1144 * q^26 - 14 * q^27 + 178 * q^28 + 1087 * q^30 + 693 * q^31 - 449 * q^32 + 820 * q^33 + 53 * q^34 + 886 * q^35 + 1464 * q^36 + 243 * q^37 + 914 * q^38 - 244 * q^39 - 275 * q^40 + 552 * q^41 - 373 * q^42 - 1151 * q^43 + 1502 * q^44 + 1139 * q^45 - 2992 * q^46 + 403 * q^47 + 3329 * q^48 + 1078 * q^49 - 1317 * q^50 + 2272 * q^51 - 1267 * q^52 + 1505 * q^53 + 140 * q^54 - 588 * q^55 + 2549 * q^56 + 859 * q^57 + 3086 * q^59 + 4371 * q^60 + 39 * q^61 + 1356 * q^62 + 1527 * q^63 - 1993 * q^64 + 1132 * q^65 + 980 * q^66 + 413 * q^67 + 919 * q^68 - 6116 * q^69 - 6779 * q^70 + 4015 * q^71 - 5524 * q^72 + 2667 * q^73 + 3844 * q^74 - 3734 * q^75 - 438 * q^76 + 5252 * q^77 - 4128 * q^78 - 1441 * q^79 + 6887 * q^80 - 371 * q^81 + 3401 * q^82 + 2505 * q^83 + 140 * q^84 + 3340 * q^85 + 3412 * q^86 + 8149 * q^88 + 2757 * q^89 + 1740 * q^90 + 4824 * q^91 + 3957 * q^92 - 4278 * q^93 + 1507 * q^94 + 2496 * q^95 + 3663 * q^96 + 1223 * q^97 - 10921 * q^98 - 8702 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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