LMFDB - Embedded newform 121.4.a.g.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,4,Mod(1,121)] 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("121.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,4,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$7.13923111069$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{5}, \sqrt{37})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 21x^{2} + 64 $ x^4 - 21*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.92335$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.923347 q^{2} -1.54138 q^{3} -7.14743 q^{4} +8.72550 q^{5} +1.42323 q^{6} +0.775116 q^{7} +13.9863 q^{8} -24.6241 q^{9} -8.05666 q^{10} +11.0169 q^{12} +64.6023 q^{13} -0.715701 q^{14} -13.4493 q^{15} +44.2652 q^{16} +70.1252 q^{17} +22.7366 q^{18} +129.616 q^{19} -62.3649 q^{20} -1.19475 q^{21} +103.308 q^{23} -21.5583 q^{24} -48.8657 q^{25} -59.6503 q^{26} +79.5725 q^{27} -5.54008 q^{28} -68.7573 q^{29} +12.4184 q^{30} +5.72719 q^{31} -152.763 q^{32} -64.7499 q^{34} +6.76327 q^{35} +175.999 q^{36} +172.293 q^{37} -119.681 q^{38} -99.5768 q^{39} +122.038 q^{40} -211.423 q^{41} +1.10317 q^{42} +300.793 q^{43} -214.858 q^{45} -95.3890 q^{46} -191.018 q^{47} -68.2295 q^{48} -342.399 q^{49} +45.1200 q^{50} -108.090 q^{51} -461.740 q^{52} +641.603 q^{53} -73.4730 q^{54} +10.8410 q^{56} -199.788 q^{57} +63.4869 q^{58} +52.0026 q^{59} +96.1281 q^{60} -492.775 q^{61} -5.28819 q^{62} -19.0866 q^{63} -213.068 q^{64} +563.687 q^{65} -320.988 q^{67} -501.215 q^{68} -159.237 q^{69} -6.24485 q^{70} -182.613 q^{71} -344.402 q^{72} -207.923 q^{73} -159.087 q^{74} +75.3207 q^{75} -926.421 q^{76} +91.9439 q^{78} +652.867 q^{79} +386.236 q^{80} +542.200 q^{81} +195.216 q^{82} +1202.37 q^{83} +8.53938 q^{84} +611.877 q^{85} -277.736 q^{86} +105.981 q^{87} +716.942 q^{89} +198.388 q^{90} +50.0742 q^{91} -738.385 q^{92} -8.82778 q^{93} +176.376 q^{94} +1130.96 q^{95} +235.466 q^{96} -628.369 q^{97} +316.153 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 11 q^{5} + 43 q^{6} + 25 q^{7} + 66 q^{8} - 62 q^{9} + 20 q^{10} + 95 q^{12} + 25 q^{13} + 132 q^{14} + 2 q^{15} + 34 q^{16} + 232 q^{17} + 49 q^{18} + 154 q^{19} - 254 q^{20}+ \cdots + 1370 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 11 * q^5 + 43 * q^6 + 25 * q^7 + 66 * q^8 - 62 * q^9 + 20 * q^10 + 95 * q^12 + 25 * q^13 + 132 * q^14 + 2 * q^15 + 34 * q^16 + 232 * q^17 + 49 * q^18 + 154 * q^19 - 254 * q^20 + 167 * q^21 - 6 * q^23 + 99 * q^24 - 13 * q^25 - 200 * q^26 - 144 * q^27 + 24 * q^28 + 363 * q^29 - 192 * q^30 + 37 * q^31 + 162 * q^32 - 149 * q^34 + 356 * q^35 + 5 * q^36 + 93 * q^37 + 379 * q^38 - 240 * q^39 - 814 * q^40 + 152 * q^41 + 420 * q^42 - 325 * q^43 + 226 * q^45 - 1258 * q^46 - 869 * q^47 + 347 * q^48 - 245 * q^49 - 1016 * q^50 + 52 * q^51 - 1010 * q^52 + 811 * q^53 - 1550 * q^54 - 780 * q^56 + 231 * q^57 + 956 * q^58 + 178 * q^59 - 566 * q^60 - 105 * q^61 - 342 * q^62 + q^63 + 818 * q^64 + 895 * q^65 + 43 * q^67 - 135 * q^68 - 1156 * q^69 - 22 * q^70 + 629 * q^71 - 1023 * q^72 - 270 * q^73 + 202 * q^74 - 815 * q^75 - 121 * q^76 - 670 * q^78 + 977 * q^79 + 122 * q^80 + 52 * q^81 + 789 * q^82 + 1686 * q^83 + 258 * q^84 - 721 * q^85 - 277 * q^86 + 1155 * q^87 + 1891 * q^89 - 976 * q^90 - 80 * q^91 - 3450 * q^92 - 666 * q^93 + 756 * q^94 + 1804 * q^95 + 1131 * q^96 - 1772 * q^97 + 1370 * q^98

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 $

$2$	−0.923347	−0.326453	−0.163226	−	0.986589i	$-0.552190\pi$
$2$	−0.923347	−0.326453	−0.163226	+	0.986589i	$0.552190\pi$
$3$	−1.54138	−0.296639	−0.148319	−	0.988939i	$-0.547386\pi$
$3$	−1.54138	−0.296639	−0.148319	+	0.988939i	$0.547386\pi$
$4$	−7.14743	−0.893429
$5$	8.72550	0.780432	0.390216	−	0.920723i	$-0.372400\pi$
$5$	8.72550	0.780432	0.390216	+	0.920723i	$0.372400\pi$
$6$	1.42323	0.0968385
$7$	0.775116	0.0418523	0.0209262	−	0.999781i	$-0.493339\pi$
$7$	0.775116	0.0418523	0.0209262	+	0.999781i	$0.493339\pi$
$8$	13.9863	0.618115
$9$	−24.6241	−0.912005
$10$	−8.05666	−0.254774
$11$	0	0
$11$	0	0
$12$	11.0169	0.265026
$13$	64.6023	1.37827	0.689133	−	0.724635i	$-0.257992\pi$
$13$	64.6023	1.37827	0.689133	+	0.724635i	$0.257992\pi$
$14$	−0.715701	−0.0136628
$15$	−13.4493	−0.231507
$16$	44.2652	0.691644
$17$	70.1252	1.00046	0.500231	−	0.865892i	$-0.333248\pi$
$17$	70.1252	1.00046	0.500231	+	0.865892i	$0.333248\pi$
$18$	22.7366	0.297726
$19$	129.616	1.56505	0.782525	−	0.622620i	$-0.213932\pi$
$19$	129.616	1.56505	0.782525	+	0.622620i	$0.213932\pi$
$20$	−62.3649	−0.697261
$21$	−1.19475	−0.0124150
$22$	0	0
$23$	103.308	0.936572	0.468286	−	0.883577i	$-0.344872\pi$
$23$	103.308	0.936572	0.468286	+	0.883577i	$0.344872\pi$
$24$	−21.5583	−0.183357
$25$	−48.8657	−0.390926
$26$	−59.6503	−0.449938
$27$	79.5725	0.567175
$28$	−5.54008	−0.0373921
$29$	−68.7573	−0.440273	−0.220136	−	0.975469i	$-0.570650\pi$
$29$	−68.7573	−0.440273	−0.220136	+	0.975469i	$0.570650\pi$
$30$	12.4184	0.0755759
$31$	5.72719	0.0331817	0.0165909	−	0.999862i	$-0.494719\pi$
$31$	5.72719	0.0331817	0.0165909	+	0.999862i	$0.494719\pi$
$32$	−152.763	−0.843903
$33$	0	0
$34$	−64.7499	−0.326604
$35$	6.76327	0.0326629
$36$	175.999	0.814812
$37$	172.293	0.765537	0.382768	−	0.923844i	$-0.374971\pi$
$37$	172.293	0.765537	0.382768	+	0.923844i	$0.374971\pi$
$38$	−119.681	−0.510914
$39$	−99.5768	−0.408847
$40$	122.038	0.482397
$41$	−211.423	−0.805333	−0.402667	−	0.915347i	$-0.631917\pi$
$41$	−211.423	−0.805333	−0.402667	+	0.915347i	$0.631917\pi$
$42$	1.10317	0.00405292
$43$	300.793	1.06676	0.533378	−	0.845877i	$-0.320922\pi$
$43$	300.793	1.06676	0.533378	+	0.845877i	$0.320922\pi$
$44$	0	0
$45$	−214.858	−0.711758
$46$	−95.3890	−0.305746
$47$	−191.018	−0.592825	−0.296413	−	0.955060i	$-0.595790\pi$
$47$	−191.018	−0.592825	−0.296413	+	0.955060i	$0.595790\pi$
$48$	−68.2295	−0.205168
$49$	−342.399	−0.998248
$50$	45.1200	0.127619
$51$	−108.090	−0.296776
$52$	−461.740	−1.23138
$53$	641.603	1.66285	0.831424	−	0.555638i	$-0.187526\pi$
$53$	641.603	1.66285	0.831424	+	0.555638i	$0.187526\pi$
$54$	−73.4730	−0.185156
$55$	0	0
$56$	10.8410	0.0258695
$57$	−199.788	−0.464255
$58$	63.4869	0.143728
$59$	52.0026	0.114748	0.0573742	−	0.998353i	$-0.481727\pi$
$59$	52.0026	0.114748	0.0573742	+	0.998353i	$0.481727\pi$
$60$	96.1281	0.206835
$61$	−492.775	−1.03432	−0.517158	−	0.855890i	$-0.673010\pi$
$61$	−492.775	−1.03432	−0.517158	+	0.855890i	$0.673010\pi$
$62$	−5.28819	−0.0108323
$63$	−19.0866	−0.0381695
$64$	−213.068	−0.416149
$65$	563.687	1.07564
$66$	0	0
$67$	−320.988	−0.585298	−0.292649	−	0.956220i	$-0.594537\pi$
$67$	−320.988	−0.585298	−0.292649	+	0.956220i	$0.594537\pi$
$68$	−501.215	−0.893842
$69$	−159.237	−0.277824
$70$	−6.24485	−0.0106629
$71$	−182.613	−0.305241	−0.152621	−	0.988285i	$-0.548771\pi$
$71$	−182.613	−0.305241	−0.152621	+	0.988285i	$0.548771\pi$
$72$	−344.402	−0.563724
$73$	−207.923	−0.333363	−0.166681	−	0.986011i	$-0.553305\pi$
$73$	−207.923	−0.333363	−0.166681	+	0.986011i	$0.553305\pi$
$74$	−159.087	−0.249911
$75$	75.3207	0.115964
$76$	−926.421	−1.39826
$77$	0	0
$78$	91.9439	0.133469
$79$	652.867	0.929788	0.464894	−	0.885366i	$-0.346092\pi$
$79$	652.867	0.929788	0.464894	+	0.885366i	$0.346092\pi$
$80$	386.236	0.539781
$81$	542.200	0.743759
$82$	195.216	0.262903
$83$	1202.37	1.59009	0.795045	−	0.606550i	$-0.207447\pi$
$83$	1202.37	1.59009	0.795045	+	0.606550i	$0.207447\pi$
$84$	8.53938	0.0110919
$85$	611.877	0.780793
$86$	−277.736	−0.348245
$87$	105.981	0.130602
$88$	0	0
$89$	716.942	0.853885	0.426942	−	0.904279i	$-0.359591\pi$
$89$	716.942	0.853885	0.426942	+	0.904279i	$0.359591\pi$
$90$	198.388	0.232355
$91$	50.0742	0.0576836
$92$	−738.385	−0.836761
$93$	−8.82778	−0.00984299
$94$	176.376	0.193529
$95$	1130.96	1.22141
$96$	235.466	0.250335
$97$	−628.369	−0.657744	−0.328872	−	0.944375i	$-0.606668\pi$
$97$	−628.369	−0.657744	−0.328872	+	0.944375i	$0.606668\pi$
$98$	316.153	0.325881
$99$	0	0
$100$	349.264	0.349264
$101$	509.211	0.501667	0.250833	−	0.968030i	$-0.419295\pi$
$101$	509.211	0.501667	0.250833	+	0.968030i	$0.419295\pi$
$102$	99.8043	0.0968833
$103$	−174.927	−0.167341	−0.0836703	−	0.996493i	$-0.526664\pi$
$103$	−174.927	−0.167341	−0.0836703	+	0.996493i	$0.526664\pi$
$104$	903.549	0.851926
$105$	−10.4248	−0.00968908
$106$	−592.422	−0.542841
$107$	1769.33	1.59858	0.799288	−	0.600949i	$-0.205210\pi$
$107$	1769.33	1.59858	0.799288	+	0.600949i	$0.205210\pi$
$108$	−568.739	−0.506731
$109$	−823.593	−0.723724	−0.361862	−	0.932232i	$-0.617859\pi$
$109$	−823.593	−0.723724	−0.361862	+	0.932232i	$0.617859\pi$
$110$	0	0
$111$	−265.570	−0.227088
$112$	34.3106	0.0289469
$113$	−1088.91	−0.906514	−0.453257	−	0.891380i	$-0.649738\pi$
$113$	−1088.91	−0.906514	−0.453257	+	0.891380i	$0.649738\pi$
$114$	184.473	0.151557
$115$	901.412	0.730931
$116$	491.438	0.393352
$117$	−1590.78	−1.25699
$118$	−48.0164	−0.0374599
$119$	54.3551	0.0418717
$120$	−188.107	−0.143098
$121$	0	0
$122$	455.002	0.337655
$123$	325.883	0.238893
$124$	−40.9347	−0.0296455
$125$	−1517.06	−1.08552
$126$	17.6235	0.0124605
$127$	−1255.25	−0.877053	−0.438526	−	0.898718i	$-0.644499\pi$
$127$	−1255.25	−0.877053	−0.438526	+	0.898718i	$0.644499\pi$
$128$	1418.84	0.979756
$129$	−463.637	−0.316441
$130$	−520.479	−0.351146
$131$	1401.18	0.934519	0.467259	−	0.884120i	$-0.345241\pi$
$131$	1401.18	0.934519	0.467259	+	0.884120i	$0.345241\pi$
$132$	0	0
$133$	100.467	0.0655009
$134$	296.384	0.191072
$135$	694.310	0.442642
$136$	980.795	0.618400
$137$	−409.334	−0.255268	−0.127634	−	0.991821i	$-0.540738\pi$
$137$	−409.334	−0.255268	−0.127634	+	0.991821i	$0.540738\pi$
$138$	147.031	0.0906963
$139$	595.380	0.363305	0.181653	−	0.983363i	$-0.441855\pi$
$139$	595.380	0.363305	0.181653	+	0.983363i	$0.441855\pi$
$140$	−48.3400	−0.0291820
$141$	294.431	0.175855
$142$	168.615	0.0996468
$143$	0	0
$144$	−1089.99	−0.630783
$145$	−599.942	−0.343603
$146$	191.985	0.108827
$147$	527.768	0.296119
$148$	−1231.46	−0.683953
$149$	2170.08	1.19316	0.596578	−	0.802555i	$-0.296527\pi$
$149$	2170.08	1.19316	0.596578	+	0.802555i	$0.296527\pi$
$150$	−69.5471	−0.0378567
$151$	−1798.76	−0.969410	−0.484705	−	0.874678i	$-0.661073\pi$
$151$	−1798.76	−0.969410	−0.484705	+	0.874678i	$0.661073\pi$
$152$	1812.85	0.967380
$153$	−1726.77	−0.912427
$154$	0	0
$155$	49.9726	0.0258961
$156$	711.718	0.365276
$157$	−78.4137	−0.0398605	−0.0199302	−	0.999801i	$-0.506344\pi$
$157$	−78.4137	−0.0398605	−0.0199302	+	0.999801i	$0.506344\pi$
$158$	−602.823	−0.303532
$159$	−988.955	−0.493266
$160$	−1332.93	−0.658609
$161$	80.0755	0.0391977
$162$	−500.639	−0.242802
$163$	328.833	0.158014	0.0790068	−	0.996874i	$-0.474825\pi$
$163$	328.833	0.158014	0.0790068	+	0.996874i	$0.474825\pi$
$164$	1511.13	0.719508
$165$	0	0
$166$	−1110.21	−0.519089
$167$	−3523.75	−1.63279	−0.816394	−	0.577495i	$-0.804030\pi$
$167$	−3523.75	−1.63279	−0.816394	+	0.577495i	$0.804030\pi$
$168$	−16.7102	−0.00767391
$169$	1976.46	0.899616
$170$	−564.975	−0.254892
$171$	−3191.68	−1.42733
$172$	−2149.90	−0.953071
$173$	−2707.22	−1.18975	−0.594874	−	0.803819i	$-0.702798\pi$
$173$	−2707.22	−1.18975	−0.594874	+	0.803819i	$0.702798\pi$
$174$	−97.8575	−0.0426354
$175$	−37.8766	−0.0163611
$176$	0	0
$177$	−80.1558	−0.0340389
$178$	−661.987	−0.278753
$179$	1473.17	0.615139	0.307569	−	0.951526i	$-0.400484\pi$
$179$	1473.17	0.615139	0.307569	+	0.951526i	$0.400484\pi$
$180$	1535.68	0.635905
$181$	−492.121	−0.202094	−0.101047	−	0.994882i	$-0.532219\pi$
$181$	−492.121	−0.202094	−0.101047	+	0.994882i	$0.532219\pi$
$182$	−46.2359	−0.0188310
$183$	759.554	0.306819
$184$	1444.90	0.578909
$185$	1503.35	0.597450
$186$	8.15111	0.00321327
$187$	0	0
$188$	1365.29	0.529647
$189$	61.6779	0.0237376
$190$	−1044.27	−0.398734
$191$	−1293.92	−0.490183	−0.245091	−	0.969500i	$-0.578818\pi$
$191$	−1293.92	−0.490183	−0.245091	+	0.969500i	$0.578818\pi$
$192$	328.420	0.123446
$193$	−524.138	−0.195483	−0.0977417	−	0.995212i	$-0.531162\pi$
$193$	−524.138	−0.195483	−0.0977417	+	0.995212i	$0.531162\pi$
$194$	580.202	0.214722
$195$	−868.857	−0.319078
$196$	2447.27	0.891864
$197$	−1177.35	−0.425801	−0.212900	−	0.977074i	$-0.568291\pi$
$197$	−1177.35	−0.425801	−0.212900	+	0.977074i	$0.568291\pi$
$198$	0	0
$199$	−3054.83	−1.08820	−0.544098	−	0.839022i	$-0.683128\pi$
$199$	−3054.83	−1.08820	−0.544098	+	0.839022i	$0.683128\pi$
$200$	−683.452	−0.241637
$201$	494.765	0.173622
$202$	−470.178	−0.163770
$203$	−53.2949	−0.0184264
$204$	772.563	0.265148
$205$	−1844.77	−0.628508
$206$	161.519	0.0546288
$207$	−2543.87	−0.854159
$208$	2859.63	0.953269
$209$	0	0
$210$	9.62569	0.00316303
$211$	1704.64	0.556172	0.278086	−	0.960556i	$-0.410300\pi$
$211$	1704.64	0.556172	0.278086	+	0.960556i	$0.410300\pi$
$212$	−4585.81	−1.48564
$213$	281.476	0.0905465
$214$	−1633.71	−0.521859
$215$	2624.57	0.832531
$216$	1112.93	0.350579
$217$	4.43923	0.00138873
$218$	760.463	0.236262
$219$	320.488	0.0988884
$220$	0	0
$221$	4530.25	1.37890
$222$	245.213	0.0741335
$223$	4602.52	1.38210	0.691049	−	0.722808i	$-0.257149\pi$
$223$	4602.52	1.38210	0.691049	+	0.722808i	$0.257149\pi$
$224$	−118.409	−0.0353193
$225$	1203.28	0.356526
$226$	1005.44	0.295934
$227$	3287.46	0.961216	0.480608	−	0.876936i	$-0.340416\pi$
$227$	3287.46	0.961216	0.480608	+	0.876936i	$0.340416\pi$
$228$	1427.97	0.414778
$229$	−2950.99	−0.851558	−0.425779	−	0.904827i	$-0.640000\pi$
$229$	−2950.99	−0.851558	−0.425779	+	0.904827i	$0.640000\pi$
$230$	−832.316	−0.238614
$231$	0	0
$232$	−961.663	−0.272139
$233$	2822.70	0.793654	0.396827	−	0.917893i	$-0.370111\pi$
$233$	2822.70	0.793654	0.396827	+	0.917893i	$0.370111\pi$
$234$	1468.84	0.410346
$235$	−1666.72	−0.462660
$236$	−371.685	−0.102520
$237$	−1006.32	−0.275811
$238$	−50.1887	−0.0136691
$239$	2061.17	0.557848	0.278924	−	0.960313i	$-0.410022\pi$
$239$	2061.17	0.557848	0.278924	+	0.960313i	$0.410022\pi$
$240$	−595.337	−0.160120
$241$	−3089.45	−0.825763	−0.412881	−	0.910785i	$-0.635478\pi$
$241$	−3089.45	−0.825763	−0.412881	+	0.910785i	$0.635478\pi$
$242$	0	0
$243$	−2984.19	−0.787803
$244$	3522.07	0.924088
$245$	−2987.60	−0.779065
$246$	−300.903	−0.0779873
$247$	8373.49	2.15705
$248$	80.1024	0.0205101
$249$	−1853.31	−0.471683
$250$	1400.78	0.354372
$251$	−4029.16	−1.01322	−0.506610	−	0.862176i	$-0.669101\pi$
$251$	−4029.16	−1.01322	−0.506610	+	0.862176i	$0.669101\pi$
$252$	136.420	0.0341017
$253$	0	0
$254$	1159.03	0.286316
$255$	−943.136	−0.231614
$256$	394.466	0.0963052
$257$	−4397.47	−1.06734	−0.533671	−	0.845692i	$-0.679188\pi$
$257$	−4397.47	−1.06734	−0.533671	+	0.845692i	$0.679188\pi$
$258$	428.098	0.103303
$259$	133.547	0.0320395
$260$	−4028.91	−0.961010
$261$	1693.09	0.401531
$262$	−1293.78	−0.305076
$263$	−914.661	−0.214450	−0.107225	−	0.994235i	$-0.534197\pi$
$263$	−914.661	−0.214450	−0.107225	+	0.994235i	$0.534197\pi$
$264$	0	0
$265$	5598.31	1.29774
$266$	−92.7662	−0.0213829
$267$	−1105.08	−0.253296
$268$	2294.24	0.522922
$269$	−1768.78	−0.400908	−0.200454	−	0.979703i	$-0.564242\pi$
$269$	−1768.78	−0.400908	−0.200454	+	0.979703i	$0.564242\pi$
$270$	−641.089	−0.144502
$271$	4018.54	0.900771	0.450385	−	0.892834i	$-0.351287\pi$
$271$	4018.54	0.900771	0.450385	+	0.892834i	$0.351287\pi$
$272$	3104.11	0.691963
$273$	−77.1835	−0.0171112
$274$	377.957	0.0833330
$275$	0	0
$276$	1138.13	0.248216
$277$	−6645.80	−1.44154	−0.720772	−	0.693173i	$-0.756212\pi$
$277$	−6645.80	−1.44154	−0.720772	+	0.693173i	$0.756212\pi$
$278$	−549.742	−0.118602
$279$	−141.027	−0.0302619
$280$	94.5934	0.0201894
$281$	4383.05	0.930502	0.465251	−	0.885179i	$-0.345964\pi$
$281$	4383.05	0.930502	0.465251	+	0.885179i	$0.345964\pi$
$282$	−271.862	−0.0574084
$283$	3734.87	0.784504	0.392252	−	0.919858i	$-0.371696\pi$
$283$	3734.87	0.784504	0.392252	+	0.919858i	$0.371696\pi$
$284$	1305.21	0.272711
$285$	−1743.25	−0.362319
$286$	0	0
$287$	−163.877	−0.0337050
$288$	3761.65	0.769644
$289$	4.54474	0.000925043 0
$290$	553.955	0.112170
$291$	968.556	0.195113
$292$	1486.11	0.297836
$293$	−2235.17	−0.445665	−0.222833	−	0.974857i	$-0.571530\pi$
$293$	−2235.17	−0.445665	−0.222833	+	0.974857i	$0.571530\pi$
$294$	−487.313	−0.0966689
$295$	453.748	0.0895534
$296$	2409.75	0.473190
$297$	0	0
$298$	−2003.74	−0.389509
$299$	6673.92	1.29085
$300$	−538.349	−0.103605
$301$	233.149	0.0446462
$302$	1660.88	0.316466
$303$	−784.888	−0.148814
$304$	5737.47	1.08246
$305$	−4299.70	−0.807214
$306$	1594.41	0.297864
$307$	1022.51	0.190090	0.0950451	−	0.995473i	$-0.469700\pi$
$307$	1022.51	0.190090	0.0950451	+	0.995473i	$0.469700\pi$
$308$	0	0
$309$	269.629	0.0496398
$310$	−46.1420	−0.00845385
$311$	5319.39	0.969886	0.484943	−	0.874546i	$-0.338840\pi$
$311$	5319.39	0.969886	0.484943	+	0.874546i	$0.338840\pi$
$312$	−1392.71	−0.252714
$313$	−6993.46	−1.26292	−0.631460	−	0.775409i	$-0.717544\pi$
$313$	−6993.46	−1.26292	−0.631460	+	0.775409i	$0.717544\pi$
$314$	72.4030	0.0130125
$315$	−166.540	−0.0297887
$316$	−4666.32	−0.830699
$317$	4314.67	0.764468	0.382234	−	0.924066i	$-0.375155\pi$
$317$	4314.67	0.764468	0.382234	+	0.924066i	$0.375155\pi$
$318$	913.149	0.161028
$319$	0	0
$320$	−1859.13	−0.324776
$321$	−2727.21	−0.474200
$322$	−73.9375	−0.0127962
$323$	9089.34	1.56577
$324$	−3875.34	−0.664496
$325$	−3156.84	−0.538799
$326$	−303.627	−0.0515839
$327$	1269.47	0.214685
$328$	−2957.03	−0.497788
$329$	−148.061	−0.0248111
$330$	0	0
$331$	−3886.73	−0.645420	−0.322710	−	0.946498i	$-0.604594\pi$
$331$	−3886.73	−0.645420	−0.322710	+	0.946498i	$0.604594\pi$
$332$	−8593.87	−1.42063
$333$	−4242.58	−0.698174
$334$	3253.64	0.533028
$335$	−2800.78	−0.456785
$336$	−52.8858	−0.00858677
$337$	−9102.10	−1.47129	−0.735643	−	0.677370i	$-0.763120\pi$
$337$	−9102.10	−1.47129	−0.735643	+	0.677370i	$0.763120\pi$
$338$	−1824.96	−0.293682
$339$	1678.43	0.268907
$340$	−4373.35	−0.697583
$341$	0	0
$342$	2947.03	0.465957
$343$	−531.264	−0.0836313
$344$	4206.99	0.659378
$345$	−1389.42	−0.216823
$346$	2499.71	0.388396
$347$	−10152.7	−1.57068	−0.785340	−	0.619064i	$-0.787512\pi$
$347$	−10152.7	−1.57068	−0.785340	+	0.619064i	$0.787512\pi$
$348$	−757.493	−0.116684
$349$	−10672.1	−1.63687	−0.818434	−	0.574601i	$-0.805157\pi$
$349$	−10672.1	−1.63687	−0.818434	+	0.574601i	$0.805157\pi$
$350$	34.9732	0.00534113
$351$	5140.56	0.781718
$352$	0	0
$353$	−9301.69	−1.40249	−0.701245	−	0.712920i	$-0.747372\pi$
$353$	−9301.69	−1.40249	−0.701245	+	0.712920i	$0.747372\pi$
$354$	74.0116	0.0111121
$355$	−1593.39	−0.238220
$356$	−5124.30	−0.762885
$357$	−83.7820	−0.0124208
$358$	−1360.25	−0.200814
$359$	8397.40	1.23453	0.617267	−	0.786754i	$-0.288240\pi$
$359$	8397.40	1.23453	0.617267	+	0.786754i	$0.288240\pi$
$360$	−3005.08	−0.439948
$361$	9941.29	1.44938
$362$	454.398	0.0659742
$363$	0	0
$364$	−357.902	−0.0515362
$365$	−1814.23	−0.260167
$366$	−701.332	−0.100162
$367$	−9367.96	−1.33243	−0.666217	−	0.745758i	$-0.732088\pi$
$367$	−9367.96	−1.33243	−0.666217	+	0.745758i	$0.732088\pi$
$368$	4572.94	0.647774
$369$	5206.10	0.734468
$370$	−1388.11	−0.195039
$371$	497.316	0.0695940
$372$	63.0960	0.00879401
$373$	2639.31	0.366376	0.183188	−	0.983078i	$-0.441358\pi$
$373$	2639.31	0.366376	0.183188	+	0.983078i	$0.441358\pi$
$374$	0	0
$375$	2338.38	0.322008
$376$	−2671.64	−0.366434
$377$	−4441.88	−0.606813
$378$	−56.9501	−0.00774920
$379$	−7366.52	−0.998398	−0.499199	−	0.866488i	$-0.666372\pi$
$379$	−7366.52	−0.998398	−0.499199	+	0.866488i	$0.666372\pi$
$380$	−8083.48	−1.09125
$381$	1934.82	0.260168
$382$	1194.74	0.160021
$383$	−3220.38	−0.429644	−0.214822	−	0.976653i	$-0.568917\pi$
$383$	−3220.38	−0.429644	−0.214822	+	0.976653i	$0.568917\pi$
$384$	−2186.97	−0.290634
$385$	0	0
$386$	483.962	0.0638160
$387$	−7406.77	−0.972887
$388$	4491.22	0.587647
$389$	12228.0	1.59379	0.796893	−	0.604121i	$-0.206476\pi$
$389$	12228.0	1.59379	0.796893	+	0.604121i	$0.206476\pi$
$390$	802.256	0.104164
$391$	7244.48	0.937005
$392$	−4788.91	−0.617032
$393$	−2159.76	−0.277215
$394$	1087.10	0.139004
$395$	5696.59	0.725636
$396$	0	0
$397$	8381.55	1.05959	0.529796	−	0.848125i	$-0.322269\pi$
$397$	8381.55	1.05959	0.529796	+	0.848125i	$0.322269\pi$
$398$	2820.67	0.355244
$399$	−154.858	−0.0194301
$400$	−2163.05	−0.270381
$401$	−4330.35	−0.539270	−0.269635	−	0.962963i	$-0.586903\pi$
$401$	−4330.35	−0.539270	−0.269635	+	0.962963i	$0.586903\pi$
$402$	−456.840	−0.0566794
$403$	369.990	0.0457332
$404$	−3639.55	−0.448204
$405$	4730.97	0.580454
$406$	49.2097	0.00601536
$407$	0	0
$408$	−1511.78	−0.183442
$409$	11937.9	1.44325	0.721627	−	0.692282i	$-0.243395\pi$
$409$	11937.9	1.44325	0.721627	+	0.692282i	$0.243395\pi$
$410$	1703.36	0.205178
$411$	630.940	0.0757225
$412$	1250.28	0.149507
$413$	40.3080	0.00480249
$414$	2348.87	0.278842
$415$	10491.3	1.24096
$416$	−9868.83	−1.16312
$417$	−917.707	−0.107770
$418$	0	0
$419$	−11888.5	−1.38614	−0.693070	−	0.720870i	$-0.743743\pi$
$419$	−11888.5	−1.38614	−0.693070	+	0.720870i	$0.743743\pi$
$420$	74.5103	0.00865651
$421$	−8485.46	−0.982318	−0.491159	−	0.871070i	$-0.663427\pi$
$421$	−8485.46	−0.982318	−0.491159	+	0.871070i	$0.663427\pi$
$422$	−1573.98	−0.181564
$423$	4703.65	0.540660
$424$	8973.68	1.02783
$425$	−3426.72	−0.391106
$426$	−259.900	−0.0295591
$427$	−381.957	−0.0432885
$428$	−12646.2	−1.42821
$429$	0	0
$430$	−2423.39	−0.271782
$431$	11460.7	1.28084	0.640422	−	0.768023i	$-0.278759\pi$
$431$	11460.7	1.28084	0.640422	+	0.768023i	$0.278759\pi$
$432$	3522.29	0.392283
$433$	3298.08	0.366041	0.183020	−	0.983109i	$-0.441413\pi$
$433$	3298.08	0.366041	0.183020	+	0.983109i	$0.441413\pi$
$434$	−4.09895	−0.000453355 0
$435$	924.739	0.101926
$436$	5886.57	0.646596
$437$	13390.3	1.46578
$438$	−295.922	−0.0322824
$439$	5549.93	0.603380	0.301690	−	0.953406i	$-0.402449\pi$
$439$	5549.93	0.603380	0.301690	+	0.953406i	$0.402449\pi$
$440$	0	0
$441$	8431.29	0.910408
$442$	−4182.99	−0.450146
$443$	10880.8	1.16696	0.583481	−	0.812127i	$-0.301690\pi$
$443$	10880.8	1.16696	0.583481	+	0.812127i	$0.301690\pi$
$444$	1898.14	0.202887
$445$	6255.68	0.666399
$446$	−4249.73	−0.451189
$447$	−3344.93	−0.353937
$448$	−165.153	−0.0174168
$449$	−7545.71	−0.793105	−0.396553	−	0.918012i	$-0.629794\pi$
$449$	−7545.71	−0.793105	−0.396553	+	0.918012i	$0.629794\pi$
$450$	−1111.04	−0.116389
$451$	0	0
$452$	7782.91	0.809906
$453$	2772.57	0.287565
$454$	−3035.46	−0.313791
$455$	436.923	0.0450181
$456$	−2794.30	−0.286963
$457$	−3239.25	−0.331566	−0.165783	−	0.986162i	$-0.553015\pi$
$457$	−3239.25	−0.331566	−0.165783	+	0.986162i	$0.553015\pi$
$458$	2724.79	0.277993
$459$	5580.04	0.567438
$460$	−6442.78	−0.653035
$461$	−4837.43	−0.488724	−0.244362	−	0.969684i	$-0.578578\pi$
$461$	−4837.43	−0.488724	−0.244362	+	0.969684i	$0.578578\pi$
$462$	0	0
$463$	14089.7	1.41427	0.707133	−	0.707081i	$-0.249988\pi$
$463$	14089.7	1.41427	0.707133	+	0.707081i	$0.249988\pi$
$464$	−3043.56	−0.304512
$465$	−77.0268	−0.00768179
$466$	−2606.34	−0.259090
$467$	14545.3	1.44128	0.720639	−	0.693311i	$-0.243849\pi$
$467$	14545.3	1.44128	0.720639	+	0.693311i	$0.243849\pi$
$468$	11370.0	1.12303
$469$	−248.803	−0.0244961
$470$	1538.97	0.151037
$471$	120.865	0.0118242
$472$	727.326	0.0709277
$473$	0	0
$474$	929.179	0.0900393
$475$	−6333.77	−0.611818
$476$	−388.500	−0.0374093
$477$	−15798.9	−1.51653
$478$	−1903.17	−0.182111
$479$	2830.07	0.269957	0.134978	−	0.990849i	$-0.456904\pi$
$479$	2830.07	0.269957	0.134978	+	0.990849i	$0.456904\pi$
$480$	2054.56	0.195369
$481$	11130.5	1.05511
$482$	2852.63	0.269572
$483$	−123.427	−0.0116276
$484$	0	0
$485$	−5482.83	−0.513325
$486$	2755.45	0.257180
$487$	−19134.5	−1.78043	−0.890214	−	0.455542i	$-0.849445\pi$
$487$	−19134.5	−1.78043	−0.890214	+	0.455542i	$0.849445\pi$
$488$	−6892.11	−0.639326
$489$	−506.857	−0.0468730
$490$	2758.60	0.254328
$491$	−11293.7	−1.03804	−0.519020	−	0.854762i	$-0.673703\pi$
$491$	−11293.7	−1.03804	−0.519020	+	0.854762i	$0.673703\pi$
$492$	−2329.22	−0.213434
$493$	−4821.62	−0.440476
$494$	−7731.64	−0.704176
$495$	0	0
$496$	253.515	0.0229499
$497$	−141.546	−0.0127751
$498$	1711.25	0.153982
$499$	866.184	0.0777068	0.0388534	−	0.999245i	$-0.487629\pi$
$499$	866.184	0.0777068	0.0388534	+	0.999245i	$0.487629\pi$
$500$	10843.1	0.969838
$501$	5431.44	0.484349
$502$	3720.31	0.330768
$503$	−5983.51	−0.530401	−0.265200	−	0.964193i	$-0.585438\pi$
$503$	−5983.51	−0.530401	−0.265200	+	0.964193i	$0.585438\pi$
$504$	−266.951	−0.0235931
$505$	4443.12	0.391517
$506$	0	0
$507$	−3046.47	−0.266861
$508$	8971.83	0.783584
$509$	11067.1	0.963734	0.481867	−	0.876244i	$-0.339959\pi$
$509$	11067.1	0.963734	0.481867	+	0.876244i	$0.339959\pi$
$510$	870.842	0.0756109
$511$	−161.164	−0.0139520
$512$	−11714.9	−1.01120
$513$	10313.9	0.887657
$514$	4060.39	0.348436
$515$	−1526.33	−0.130598
$516$	3313.81	0.282718
$517$	0	0
$518$	−123.311	−0.0104594
$519$	4172.86	0.352925
$520$	7883.92	0.664871
$521$	14902.8	1.25318	0.626588	−	0.779351i	$-0.284451\pi$
$521$	14902.8	1.25318	0.626588	+	0.779351i	$0.284451\pi$
$522$	−1563.31	−0.131081
$523$	−1489.44	−0.124529	−0.0622645	−	0.998060i	$-0.519832\pi$
$523$	−1489.44	−0.124529	−0.0622645	+	0.998060i	$0.519832\pi$
$524$	−10014.9	−0.834926
$525$	58.3822	0.00485335
$526$	844.550	0.0700078
$527$	401.620	0.0331971
$528$	0	0
$529$	−1494.50	−0.122832
$530$	−5169.18	−0.423651
$531$	−1280.52	−0.104651
$532$	−718.083	−0.0585204
$533$	−13658.4	−1.10996
$534$	1020.37	0.0826890
$535$	15438.3	1.24758
$536$	−4489.45	−0.361781
$537$	−2270.72	−0.182474
$538$	1633.19	0.130877
$539$	0	0
$540$	−4962.53	−0.395469
$541$	533.528	0.0423996	0.0211998	−	0.999775i	$-0.493251\pi$
$541$	533.528	0.0423996	0.0211998	+	0.999775i	$0.493251\pi$
$542$	−3710.51	−0.294059
$543$	758.546	0.0599490
$544$	−10712.5	−0.844294
$545$	−7186.26	−0.564818
$546$	71.2672	0.00558599
$547$	−18499.2	−1.44601	−0.723006	−	0.690842i	$-0.757240\pi$
$547$	−18499.2	−1.44601	−0.723006	+	0.690842i	$0.757240\pi$
$548$	2925.69	0.228064
$549$	12134.2	0.943302
$550$	0	0
$551$	−8912.04	−0.689049
$552$	−2227.14	−0.171727
$553$	506.047	0.0389138
$554$	6136.38	0.470596
$555$	−2317.23	−0.177227
$556$	−4255.43	−0.324587
$557$	−15743.8	−1.19764	−0.598819	−	0.800884i	$-0.704363\pi$
$557$	−15743.8	−1.19764	−0.598819	+	0.800884i	$0.704363\pi$
$558$	130.217	0.00987908
$559$	19431.9	1.47027
$560$	299.377	0.0225911
$561$	0	0
$562$	−4047.08	−0.303765
$563$	6032.14	0.451553	0.225777	−	0.974179i	$-0.427508\pi$
$563$	6032.14	0.451553	0.225777	+	0.974179i	$0.427508\pi$
$564$	−2104.43	−0.157114
$565$	−9501.28	−0.707473
$566$	−3448.58	−0.256103
$567$	420.268	0.0311280
$568$	−2554.08	−0.188674
$569$	−15629.6	−1.15154	−0.575770	−	0.817612i	$-0.695298\pi$
$569$	−15629.6	−1.15154	−0.575770	+	0.817612i	$0.695298\pi$
$570$	1609.62	0.118280
$571$	−7252.67	−0.531550	−0.265775	−	0.964035i	$-0.585628\pi$
$571$	−7252.67	−0.531550	−0.265775	+	0.964035i	$0.585628\pi$
$572$	0	0
$573$	1994.43	0.145407
$574$	151.315	0.0110031
$575$	−5048.21	−0.366130
$576$	5246.63	0.379530
$577$	12997.7	0.937783	0.468892	−	0.883256i	$-0.344653\pi$
$577$	12997.7	0.937783	0.468892	+	0.883256i	$0.344653\pi$
$578$	−4.19637	−0.000301983 0
$579$	807.897	0.0579880
$580$	4288.04	0.306985
$581$	931.978	0.0665490
$582$	−894.313	−0.0636950
$583$	0	0
$584$	−2908.08	−0.206057
$585$	−13880.3	−0.980992
$586$	2063.84	0.145489
$587$	10132.7	0.712474	0.356237	−	0.934396i	$-0.384060\pi$
$587$	10132.7	0.712474	0.356237	+	0.934396i	$0.384060\pi$
$588$	−3772.18	−0.264562
$589$	742.335	0.0519310
$590$	−418.967	−0.0292349
$591$	1814.75	0.126309
$592$	7626.60	0.529479
$593$	−838.751	−0.0580833	−0.0290416	−	0.999578i	$-0.509246\pi$
$593$	−838.751	−0.0580833	−0.0290416	+	0.999578i	$0.509246\pi$
$594$	0	0
$595$	474.276	0.0326780
$596$	−15510.5	−1.06600
$597$	4708.65	0.322801
$598$	−6162.35	−0.421400
$599$	−25712.4	−1.75389	−0.876944	−	0.480592i	$-0.840422\pi$
$599$	−25712.4	−1.75389	−0.876944	+	0.480592i	$0.840422\pi$
$600$	1053.46	0.0716789
$601$	−1423.48	−0.0966140	−0.0483070	−	0.998833i	$-0.515383\pi$
$601$	−1423.48	−0.0966140	−0.0483070	+	0.998833i	$0.515383\pi$
$602$	−215.278	−0.0145749
$603$	7904.06	0.533795
$604$	12856.5	0.866098
$605$	0	0
$606$	724.724	0.0485807
$607$	−25571.7	−1.70993	−0.854963	−	0.518689i	$-0.826420\pi$
$607$	−25571.7	−1.70993	−0.854963	+	0.518689i	$0.826420\pi$
$608$	−19800.5	−1.32075
$609$	82.1477	0.00546600
$610$	3970.12	0.263517
$611$	−12340.2	−0.817071
$612$	12342.0	0.815189
$613$	−4851.98	−0.319690	−0.159845	−	0.987142i	$-0.551099\pi$
$613$	−4851.98	−0.319690	−0.159845	+	0.987142i	$0.551099\pi$
$614$	−944.131	−0.0620554
$615$	2843.49	0.186440
$616$	0	0
$617$	3850.99	0.251272	0.125636	−	0.992076i	$-0.459903\pi$
$617$	3850.99	0.251272	0.125636	+	0.992076i	$0.459903\pi$
$618$	−248.962	−0.0162050
$619$	24087.4	1.56407	0.782033	−	0.623238i	$-0.214183\pi$
$619$	24087.4	1.56407	0.782033	+	0.623238i	$0.214183\pi$
$620$	−357.176	−0.0231363
$621$	8220.46	0.531201
$622$	−4911.64	−0.316622
$623$	555.713	0.0357370
$624$	−4407.78	−0.282777
$625$	−7128.93	−0.456252
$626$	6457.39	0.412283
$627$	0	0
$628$	560.456	0.0356125
$629$	12082.1	0.765891
$630$	153.774	0.00972461
$631$	−2912.36	−0.183739	−0.0918695	−	0.995771i	$-0.529284\pi$
$631$	−2912.36	−0.183739	−0.0918695	+	0.995771i	$0.529284\pi$
$632$	9131.21	0.574715
$633$	−2627.50	−0.164982
$634$	−3983.94	−0.249562
$635$	−10952.7	−0.684480
$636$	7068.49	0.440698
$637$	−22119.8	−1.37585
$638$	0	0
$639$	4496.68	0.278382
$640$	12380.1	0.764633
$641$	6150.64	0.378995	0.189497	−	0.981881i	$-0.439314\pi$
$641$	6150.64	0.378995	0.189497	+	0.981881i	$0.439314\pi$
$642$	2518.16	0.154804
$643$	−9755.36	−0.598311	−0.299155	−	0.954204i	$-0.596705\pi$
$643$	−9755.36	−0.598311	−0.299155	+	0.954204i	$0.596705\pi$
$644$	−572.334	−0.0350204
$645$	−4045.46	−0.246961
$646$	−8392.62	−0.511151
$647$	−1821.66	−0.110691	−0.0553454	−	0.998467i	$-0.517626\pi$
$647$	−1821.66	−0.110691	−0.0553454	+	0.998467i	$0.517626\pi$
$648$	7583.40	0.459728
$649$	0	0
$650$	2914.86	0.175892
$651$	−6.84255	−0.000411952 0
$652$	−2350.31	−0.141174
$653$	6381.35	0.382422	0.191211	−	0.981549i	$-0.438759\pi$
$653$	6381.35	0.382422	0.191211	+	0.981549i	$0.438759\pi$
$654$	−1172.16	−0.0700844
$655$	12226.0	0.729328
$656$	−9358.66	−0.557004
$657$	5119.91	0.304029
$658$	136.712	0.00809965
$659$	−27285.6	−1.61289	−0.806445	−	0.591309i	$-0.798611\pi$
$659$	−27285.6	−1.61289	−0.806445	+	0.591309i	$0.798611\pi$
$660$	0	0
$661$	−23925.0	−1.40783	−0.703913	−	0.710286i	$-0.748566\pi$
$661$	−23925.0	−1.40783	−0.703913	+	0.710286i	$0.748566\pi$
$662$	3588.80	0.210699
$663$	−6982.84	−0.409036
$664$	16816.8	0.982859
$665$	876.627	0.0511190
$666$	3917.37	0.227921
$667$	−7103.16	−0.412347
$668$	25185.7	1.45878
$669$	−7094.24	−0.409984
$670$	2586.10	0.149119
$671$	0	0
$672$	182.513	0.0104771
$673$	−8336.73	−0.477500	−0.238750	−	0.971081i	$-0.576738\pi$
$673$	−8336.73	−0.477500	−0.238750	+	0.971081i	$0.576738\pi$
$674$	8404.40	0.480305
$675$	−3888.37	−0.221723
$676$	−14126.6	−0.803743
$677$	−1110.30	−0.0630315	−0.0315157	−	0.999503i	$-0.510033\pi$
$677$	−1110.30	−0.0630315	−0.0315157	+	0.999503i	$0.510033\pi$
$678$	−1549.77	−0.0877855
$679$	−487.058	−0.0275281
$680$	8557.92	0.482620
$681$	−5067.22	−0.285134
$682$	0	0
$683$	8337.88	0.467116	0.233558	−	0.972343i	$-0.424963\pi$
$683$	8337.88	0.467116	0.233558	+	0.972343i	$0.424963\pi$
$684$	22812.3	1.27522
$685$	−3571.64	−0.199220
$686$	490.541	0.0273017
$687$	4548.60	0.252605
$688$	13314.7	0.737815
$689$	41449.0	2.29185
$690$	1282.92	0.0707823
$691$	−33371.9	−1.83723	−0.918617	−	0.395150i	$-0.870693\pi$
$691$	−33371.9	−1.83723	−0.918617	+	0.395150i	$0.870693\pi$
$692$	19349.7	1.06295
$693$	0	0
$694$	9374.48	0.512753
$695$	5194.98	0.283535
$696$	1482.29	0.0807271
$697$	−14826.1	−0.805706
$698$	9854.09	0.534359
$699$	−4350.86	−0.235429
$700$	270.720	0.0146175
$701$	7808.86	0.420737	0.210368	−	0.977622i	$-0.432534\pi$
$701$	7808.86	0.420737	0.210368	+	0.977622i	$0.432534\pi$
$702$	−4746.53	−0.255194
$703$	22332.0	1.19810
$704$	0	0
$705$	2569.06	0.137243
$706$	8588.69	0.457847
$707$	394.697	0.0209959
$708$	572.908	0.0304113
$709$	27952.0	1.48062	0.740311	−	0.672265i	$-0.234678\pi$
$709$	27952.0	1.48062	0.740311	+	0.672265i	$0.234678\pi$
$710$	1471.25	0.0777676
$711$	−16076.3	−0.847971
$712$	10027.4	0.527799
$713$	591.663	0.0310771
$714$	77.3599	0.00405479
$715$	0	0
$716$	−10529.4	−0.549583
$717$	−3177.04	−0.165479
$718$	−7753.72	−0.403017
$719$	−24982.9	−1.29583	−0.647917	−	0.761711i	$-0.724360\pi$
$719$	−24982.9	−1.29583	−0.647917	+	0.761711i	$0.724360\pi$
$720$	−9510.73	−0.492283
$721$	−135.589	−0.00700359
$722$	−9179.27	−0.473154
$723$	4762.02	0.244953
$724$	3517.40	0.180557
$725$	3359.87	0.172114
$726$	0	0
$727$	31671.2	1.61571	0.807855	−	0.589381i	$-0.200628\pi$
$727$	31671.2	1.61571	0.807855	+	0.589381i	$0.200628\pi$
$728$	700.355	0.0356551
$729$	−10039.6	−0.510066
$730$	1675.16	0.0849322
$731$	21093.2	1.06725
$732$	−5428.86	−0.274121
$733$	11831.8	0.596203	0.298102	−	0.954534i	$-0.403647\pi$
$733$	11831.8	0.596203	0.298102	+	0.954534i	$0.403647\pi$
$734$	8649.88	0.434977
$735$	4605.04	0.231101
$736$	−15781.6	−0.790377
$737$	0	0
$738$	−4807.04	−0.239769
$739$	5550.14	0.276272	0.138136	−	0.990413i	$-0.455889\pi$
$739$	5550.14	0.276272	0.138136	+	0.990413i	$0.455889\pi$
$740$	−10745.1	−0.533779
$741$	−12906.7	−0.639866
$742$	−459.196	−0.0227191
$743$	37299.7	1.84172	0.920858	−	0.389898i	$-0.127490\pi$
$743$	37299.7	1.84172	0.920858	+	0.389898i	$0.127490\pi$
$744$	−123.468	−0.00608410
$745$	18935.1	0.931177
$746$	−2437.00	−0.119604
$747$	−29607.4	−1.45017
$748$	0	0
$749$	1371.43	0.0669041
$750$	−2159.13	−0.105120
$751$	−5199.27	−0.252628	−0.126314	−	0.991990i	$-0.540315\pi$
$751$	−5199.27	−0.252628	−0.126314	+	0.991990i	$0.540315\pi$
$752$	−8455.44	−0.410024
$753$	6210.46	0.300560
$754$	4101.40	0.198096
$755$	−15695.1	−0.756558
$756$	−440.838	−0.0212078
$757$	158.061	0.00758895	0.00379448	−	0.999993i	$-0.498792\pi$
$757$	158.061	0.00758895	0.00379448	+	0.999993i	$0.498792\pi$
$758$	6801.86	0.325929
$759$	0	0
$760$	15818.0	0.754974
$761$	6653.76	0.316949	0.158475	−	0.987363i	$-0.449342\pi$
$761$	6653.76	0.316949	0.158475	+	0.987363i	$0.449342\pi$
$762$	−1786.51	−0.0849325
$763$	−638.380	−0.0302895
$764$	9248.22	0.437944
$765$	−15067.0	−0.712087
$766$	2973.53	0.140258
$767$	3359.49	0.158154
$768$	−608.022	−0.0285679
$769$	5519.26	0.258816	0.129408	−	0.991591i	$-0.458692\pi$
$769$	5519.26	0.258816	0.129408	+	0.991591i	$0.458692\pi$
$770$	0	0
$771$	6778.18	0.316615
$772$	3746.24	0.174650
$773$	30874.4	1.43658	0.718289	−	0.695744i	$-0.244925\pi$
$773$	30874.4	1.43658	0.718289	+	0.695744i	$0.244925\pi$
$774$	6839.02	0.317602
$775$	−279.863	−0.0129716
$776$	−8788.58	−0.406561
$777$	−205.847	−0.00950416
$778$	−11290.7	−0.520295
$779$	−27403.7	−1.26039
$780$	6210.09	0.285073
$781$	0	0
$782$	−6689.17	−0.305888
$783$	−5471.19	−0.249712
$784$	−15156.4	−0.690432
$785$	−684.198	−0.0311084
$786$	1994.21	0.0904974
$787$	−24993.7	−1.13206	−0.566030	−	0.824385i	$-0.691521\pi$
$787$	−24993.7	−1.13206	−0.566030	+	0.824385i	$0.691521\pi$
$788$	8415.03	0.380423
$789$	1409.84	0.0636143
$790$	−5259.93	−0.236886
$791$	−844.031	−0.0379397
$792$	0	0
$793$	−31834.4	−1.42556
$794$	−7739.08	−0.345906
$795$	−8629.12	−0.384960
$796$	21834.2	0.972225
$797$	−20473.4	−0.909920	−0.454960	−	0.890512i	$-0.650346\pi$
$797$	−20473.4	−0.909920	−0.454960	+	0.890512i	$0.650346\pi$
$798$	142.988	0.00634301
$799$	−13395.2	−0.593100
$800$	7464.86	0.329903
$801$	−17654.1	−0.778748
$802$	3998.41	0.176046
$803$	0	0
$804$	−3536.30	−0.155119
$805$	698.698	0.0305912
$806$	−341.629	−0.0149297
$807$	2726.36	0.118925
$808$	7121.99	0.310088
$809$	14674.6	0.637738	0.318869	−	0.947799i	$-0.396697\pi$
$809$	14674.6	0.637738	0.318869	+	0.947799i	$0.396697\pi$
$810$	−4368.33	−0.189491
$811$	4724.23	0.204550	0.102275	−	0.994756i	$-0.467388\pi$
$811$	4724.23	0.204550	0.102275	+	0.994756i	$0.467388\pi$
$812$	380.921	0.0164627
$813$	−6194.10	−0.267204
$814$	0	0
$815$	2869.23	0.123319
$816$	−4784.61	−0.205263
$817$	38987.6	1.66953
$818$	−11022.8	−0.471154
$819$	−1233.04	−0.0526077
$820$	13185.3	0.561527
$821$	44921.6	1.90959	0.954796	−	0.297261i	$-0.0960731\pi$
$821$	44921.6	1.90959	0.954796	+	0.297261i	$0.0960731\pi$
$822$	−582.576	−0.0247198
$823$	39557.5	1.67544	0.837721	−	0.546099i	$-0.183888\pi$
$823$	39557.5	1.67544	0.837721	+	0.546099i	$0.183888\pi$
$824$	−2446.59	−0.103436
$825$	0	0
$826$	−37.2183	−0.00156778
$827$	15762.7	0.662784	0.331392	−	0.943493i	$-0.392482\pi$
$827$	15762.7	0.662784	0.331392	+	0.943493i	$0.392482\pi$
$828$	18182.1	0.763130
$829$	22580.6	0.946029	0.473014	−	0.881055i	$-0.343166\pi$
$829$	22580.6	0.946029	0.473014	+	0.881055i	$0.343166\pi$
$830$	−9687.11	−0.405114
$831$	10243.7	0.427618
$832$	−13764.7	−0.573564
$833$	−24010.8	−0.998710
$834$	847.362	0.0351820
$835$	−30746.4	−1.27428
$836$	0	0
$837$	455.727	0.0188199
$838$	10977.2	0.452509
$839$	−23447.7	−0.964844	−0.482422	−	0.875939i	$-0.660243\pi$
$839$	−23447.7	−0.964844	−0.482422	+	0.875939i	$0.660243\pi$
$840$	−145.804	−0.00598897
$841$	−19661.4	−0.806160
$842$	7835.02	0.320680
$843$	−6755.96	−0.276023
$844$	−12183.8	−0.496900
$845$	17245.6	0.702089
$846$	−4343.10	−0.176500
$847$	0	0
$848$	28400.7	1.15010
$849$	−5756.85	−0.232715
$850$	3164.05	0.127678
$851$	17799.3	0.716981
$852$	−2011.83	−0.0808968
$853$	−14996.8	−0.601970	−0.300985	−	0.953629i	$-0.597315\pi$
$853$	−14996.8	−0.601970	−0.300985	+	0.953629i	$0.597315\pi$
$854$	352.679	0.0141317
$855$	−27849.0	−1.11394
$856$	24746.4	0.988103
$857$	46121.7	1.83838	0.919188	−	0.393819i	$-0.128846\pi$
$857$	46121.7	1.83838	0.919188	+	0.393819i	$0.128846\pi$
$858$	0	0
$859$	−17398.7	−0.691080	−0.345540	−	0.938404i	$-0.612304\pi$
$859$	−17398.7	−0.691080	−0.345540	+	0.938404i	$0.612304\pi$
$860$	−18758.9	−0.743807
$861$	252.597	0.00999823
$862$	−10582.2	−0.418135
$863$	−11111.7	−0.438293	−0.219147	−	0.975692i	$-0.570327\pi$
$863$	−11111.7	−0.438293	−0.219147	+	0.975692i	$0.570327\pi$
$864$	−12155.7	−0.478641
$865$	−23621.9	−0.928517
$866$	−3045.27	−0.119495
$867$	−7.00517	−0.000274404 0
$868$	−31.7291	−0.00124073
$869$	0	0
$870$	−853.855	−0.0332740
$871$	−20736.6	−0.806696
$872$	−11519.1	−0.447344
$873$	15473.0	0.599866
$874$	−12363.9	−0.478508
$875$	−1175.90	−0.0454316
$876$	−2290.67	−0.0883498
$877$	1596.62	0.0614756	0.0307378	−	0.999527i	$-0.490214\pi$
$877$	1596.62	0.0614756	0.0307378	+	0.999527i	$0.490214\pi$
$878$	−5124.51	−0.196975
$879$	3445.25	0.132202
$880$	0	0
$881$	4924.45	0.188319	0.0941594	−	0.995557i	$-0.469984\pi$
$881$	4924.45	0.188319	0.0941594	+	0.995557i	$0.469984\pi$
$882$	−7785.01	−0.297205
$883$	−21571.2	−0.822116	−0.411058	−	0.911609i	$-0.634841\pi$
$883$	−21571.2	−0.822116	−0.411058	+	0.911609i	$0.634841\pi$
$884$	−32379.6	−1.23195
$885$	−699.399	−0.0265650
$886$	−10046.8	−0.380958
$887$	22123.9	0.837485	0.418742	−	0.908105i	$-0.362471\pi$
$887$	22123.9	0.837485	0.418742	+	0.908105i	$0.362471\pi$
$888$	−3714.35	−0.140366
$889$	−972.966	−0.0367067
$890$	−5776.16	−0.217548
$891$	0	0
$892$	−32896.2	−1.23481
$893$	−24758.9	−0.927801
$894$	3088.53	0.115543
$895$	12854.1	0.480074
$896$	1099.76	0.0410051
$897$	−10287.1	−0.382915
$898$	6967.31	0.258911
$899$	−393.786	−0.0146090
$900$	−8600.33	−0.318531
$901$	44992.5	1.66362
$902$	0	0
$903$	−359.372	−0.0132438
$904$	−15229.9	−0.560330
$905$	−4294.00	−0.157721
$906$	−2560.05	−0.0938762
$907$	−2037.82	−0.0746027	−0.0373013	−	0.999304i	$-0.511876\pi$
$907$	−2037.82	−0.0746027	−0.0373013	+	0.999304i	$0.511876\pi$
$908$	−23496.9	−0.858778
$909$	−12538.9	−0.457523
$910$	−403.431	−0.0146963
$911$	43481.7	1.58135	0.790676	−	0.612235i	$-0.209729\pi$
$911$	43481.7	1.58135	0.790676	+	0.612235i	$0.209729\pi$
$912$	−8843.64	−0.321099
$913$	0	0
$914$	2990.95	0.108241
$915$	6627.48	0.239451
$916$	21092.0	0.760806
$917$	1086.08	0.0391118
$918$	−5152.31	−0.185241
$919$	−9636.79	−0.345907	−0.172953	−	0.984930i	$-0.555331\pi$
$919$	−9636.79	−0.345907	−0.172953	+	0.984930i	$0.555331\pi$
$920$	12607.4	0.451799
$921$	−1576.08	−0.0563882
$922$	4466.63	0.159545
$923$	−11797.2	−0.420704
$924$	0	0
$925$	−8419.24	−0.299268
$926$	−13009.7	−0.461691
$927$	4307.43	0.152616
$928$	10503.6	0.371548
$929$	6285.75	0.221990	0.110995	−	0.993821i	$-0.464596\pi$
$929$	6285.75	0.221990	0.110995	+	0.993821i	$0.464596\pi$
$930$	71.1225	0.00250774
$931$	−44380.4	−1.56231
$932$	−20175.1	−0.709074
$933$	−8199.20	−0.287706
$934$	−13430.4	−0.470509
$935$	0	0
$936$	−22249.1	−0.776961
$937$	24613.7	0.858159	0.429080	−	0.903267i	$-0.358838\pi$
$937$	24613.7	0.858159	0.429080	+	0.903267i	$0.358838\pi$
$938$	229.732	0.00799680
$939$	10779.6	0.374631
$940$	11912.8	0.413354
$941$	19651.0	0.680769	0.340384	−	0.940286i	$-0.389443\pi$
$941$	19651.0	0.680769	0.340384	+	0.940286i	$0.389443\pi$
$942$	−111.601	−0.00386003
$943$	−21841.6	−0.754253
$944$	2301.90	0.0793650
$945$	538.170	0.0185256
$946$	0	0
$947$	3025.82	0.103829	0.0519144	−	0.998652i	$-0.483468\pi$
$947$	3025.82	0.103829	0.0519144	+	0.998652i	$0.483468\pi$
$948$	7192.58	0.246418
$949$	−13432.3	−0.459463
$950$	5848.27	0.199729
$951$	−6650.56	−0.226771
$952$	760.229	0.0258815
$953$	−11707.3	−0.397941	−0.198971	−	0.980005i	$-0.563760\pi$
$953$	−11707.3	−0.397941	−0.198971	+	0.980005i	$0.563760\pi$
$954$	14587.9	0.495074
$955$	−11290.1	−0.382555
$956$	−14732.0	−0.498398
$957$	0	0
$958$	−2613.14	−0.0881281
$959$	−317.281	−0.0106836
$960$	2865.62	0.0963413
$961$	−29758.2	−0.998899
$962$	−10277.4	−0.344444
$963$	−43568.2	−1.45791
$964$	22081.6	0.737760
$965$	−4573.37	−0.152562
$966$	113.966	0.00379585
$967$	12352.3	0.410779	0.205390	−	0.978680i	$-0.434154\pi$
$967$	12352.3	0.410779	0.205390	+	0.978680i	$0.434154\pi$
$968$	0	0
$969$	−14010.1	−0.464469
$970$	5062.56	0.167576
$971$	−16908.7	−0.558832	−0.279416	−	0.960170i	$-0.590141\pi$
$971$	−16908.7	−0.558832	−0.279416	+	0.960170i	$0.590141\pi$
$972$	21329.3	0.703846
$973$	461.488	0.0152052
$974$	17667.8	0.581225
$975$	4865.89	0.159829
$976$	−21812.8	−0.715379
$977$	24696.7	0.808717	0.404359	−	0.914600i	$-0.367495\pi$
$977$	24696.7	0.808717	0.404359	+	0.914600i	$0.367495\pi$
$978$	468.005	0.0153018
$979$	0	0
$980$	21353.7	0.696039
$981$	20280.3	0.660040
$982$	10428.0	0.338871
$983$	−30731.3	−0.997129	−0.498564	−	0.866853i	$-0.666139\pi$
$983$	−30731.3	−0.997129	−0.498564	+	0.866853i	$0.666139\pi$
$984$	4557.91	0.147663
$985$	−10273.0	−0.332309
$986$	4452.03	0.143795
$987$	228.218	0.00735994
$988$	−59848.9	−1.92717
$989$	31074.3	0.999094
$990$	0	0
$991$	40862.5	1.30983	0.654915	−	0.755703i	$-0.272705\pi$
$991$	40862.5	1.30983	0.654915	+	0.755703i	$0.272705\pi$
$992$	−874.902	−0.0280022
$993$	5990.93	0.191457
$994$	130.696	0.00417045
$995$	−26654.9	−0.849263
$996$	13246.4	0.421415
$997$	58038.7	1.84364	0.921818	−	0.387624i	$-0.126704\pi$
$997$	58038.7	1.84364	0.921818	+	0.387624i	$0.126704\pi$
$998$	−799.788	−0.0253676
$999$	13709.8	0.434194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.a.g.1.2		4
3.2	odd	2		1089.4.a.y.1.3		4
4.3	odd	2		1936.4.a.bk.1.4		4
11.2	odd	10		121.4.c.i.81.1		8
11.3	even	5		121.4.c.h.9.1		8
11.4	even	5		121.4.c.h.27.1		8
11.5	even	5		11.4.c.a.3.2	✓	8
11.6	odd	10		121.4.c.i.3.1		8
11.7	odd	10		121.4.c.b.27.2		8
11.8	odd	10		121.4.c.b.9.2		8
11.9	even	5		11.4.c.a.4.2	yes	8
11.10	odd	2		121.4.a.f.1.3		4
33.5	odd	10		99.4.f.c.91.1		8
33.20	odd	10		99.4.f.c.37.1		8
33.32	even	2		1089.4.a.bh.1.2		4
44.27	odd	10		176.4.m.c.113.2		8
44.31	odd	10		176.4.m.c.81.2		8
44.43	even	2		1936.4.a.bl.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.3.2	✓	8	11.5	even	5
11.4.c.a.4.2	yes	8	11.9	even	5
99.4.f.c.37.1		8	33.20	odd	10
99.4.f.c.91.1		8	33.5	odd	10
121.4.a.f.1.3		4	11.10	odd	2
121.4.a.g.1.2		4	1.1	even	1	trivial
121.4.c.b.9.2		8	11.8	odd	10
121.4.c.b.27.2		8	11.7	odd	10
121.4.c.h.9.1		8	11.3	even	5
121.4.c.h.27.1		8	11.4	even	5
121.4.c.i.3.1		8	11.6	odd	10
121.4.c.i.81.1		8	11.2	odd	10
176.4.m.c.81.2		8	44.31	odd	10
176.4.m.c.113.2		8	44.27	odd	10
1089.4.a.y.1.3		4	3.2	odd	2
1089.4.a.bh.1.2		4	33.32	even	2
1936.4.a.bk.1.4		4	4.3	odd	2
1936.4.a.bl.1.4		4	44.43	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q-0.923347 q^{2} -1.54138 q^{3} -7.14743 q^{4} +8.72550 q^{5} +1.42323 q^{6} +0.775116 q^{7} +13.9863 q^{8} -24.6241 q^{9} -8.05666 q^{10} +11.0169 q^{12} +64.6023 q^{13} -0.715701 q^{14} -13.4493 q^{15} +44.2652 q^{16} +70.1252 q^{17} +22.7366 q^{18} +129.616 q^{19} -62.3649 q^{20} -1.19475 q^{21} +103.308 q^{23} -21.5583 q^{24} -48.8657 q^{25} -59.6503 q^{26} +79.5725 q^{27} -5.54008 q^{28} -68.7573 q^{29} +12.4184 q^{30} +5.72719 q^{31} -152.763 q^{32} -64.7499 q^{34} +6.76327 q^{35} +175.999 q^{36} +172.293 q^{37} -119.681 q^{38} -99.5768 q^{39} +122.038 q^{40} -211.423 q^{41} +1.10317 q^{42} +300.793 q^{43} -214.858 q^{45} -95.3890 q^{46} -191.018 q^{47} -68.2295 q^{48} -342.399 q^{49} +45.1200 q^{50} -108.090 q^{51} -461.740 q^{52} +641.603 q^{53} -73.4730 q^{54} +10.8410 q^{56} -199.788 q^{57} +63.4869 q^{58} +52.0026 q^{59} +96.1281 q^{60} -492.775 q^{61} -5.28819 q^{62} -19.0866 q^{63} -213.068 q^{64} +563.687 q^{65} -320.988 q^{67} -501.215 q^{68} -159.237 q^{69} -6.24485 q^{70} -182.613 q^{71} -344.402 q^{72} -207.923 q^{73} -159.087 q^{74} +75.3207 q^{75} -926.421 q^{76} +91.9439 q^{78} +652.867 q^{79} +386.236 q^{80} +542.200 q^{81} +195.216 q^{82} +1202.37 q^{83} +8.53938 q^{84} +611.877 q^{85} -277.736 q^{86} +105.981 q^{87} +716.942 q^{89} +198.388 q^{90} +50.0742 q^{91} -738.385 q^{92} -8.82778 q^{93} +176.376 q^{94} +1130.96 q^{95} +235.466 q^{96} -628.369 q^{97} +316.153 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{3} + 14 q^{4} - 11 q^{5} + 43 q^{6} + 25 q^{7} + 66 q^{8} - 62 q^{9} + 20 q^{10} + 95 q^{12} + 25 q^{13} + 132 q^{14} + 2 q^{15} + 34 q^{16} + 232 q^{17} + 49 q^{18} + 154 q^{19} - 254 q^{20}+ \cdots + 1370 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^3 + 14 * q^4 - 11 * q^5 + 43 * q^6 + 25 * q^7 + 66 * q^8 - 62 * q^9 + 20 * q^10 + 95 * q^12 + 25 * q^13 + 132 * q^14 + 2 * q^15 + 34 * q^16 + 232 * q^17 + 49 * q^18 + 154 * q^19 - 254 * q^20 + 167 * q^21 - 6 * q^23 + 99 * q^24 - 13 * q^25 - 200 * q^26 - 144 * q^27 + 24 * q^28 + 363 * q^29 - 192 * q^30 + 37 * q^31 + 162 * q^32 - 149 * q^34 + 356 * q^35 + 5 * q^36 + 93 * q^37 + 379 * q^38 - 240 * q^39 - 814 * q^40 + 152 * q^41 + 420 * q^42 - 325 * q^43 + 226 * q^45 - 1258 * q^46 - 869 * q^47 + 347 * q^48 - 245 * q^49 - 1016 * q^50 + 52 * q^51 - 1010 * q^52 + 811 * q^53 - 1550 * q^54 - 780 * q^56 + 231 * q^57 + 956 * q^58 + 178 * q^59 - 566 * q^60 - 105 * q^61 - 342 * q^62 + q^63 + 818 * q^64 + 895 * q^65 + 43 * q^67 - 135 * q^68 - 1156 * q^69 - 22 * q^70 + 629 * q^71 - 1023 * q^72 - 270 * q^73 + 202 * q^74 - 815 * q^75 - 121 * q^76 - 670 * q^78 + 977 * q^79 + 122 * q^80 + 52 * q^81 + 789 * q^82 + 1686 * q^83 + 258 * q^84 - 721 * q^85 - 277 * q^86 + 1155 * q^87 + 1891 * q^89 - 976 * q^90 - 80 * q^91 - 3450 * q^92 - 666 * q^93 + 756 * q^94 + 1804 * q^95 + 1131 * q^96 - 1772 * q^97 + 1370 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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