LMFDB - Embedded newform 121.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,4,Mod(1,121)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$7.13923111069$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ 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)

$f(q)$	$=$	\(q-2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} +1.32051 q^{6} +28.2487 q^{7} +24.4641 q^{8} -26.7128 q^{9} +3.78461 q^{10} +1.03332 q^{12} -68.4641 q^{13} -69.6077 q^{14} +0.823085 q^{15} -44.8564 q^{16} -55.3538 q^{17} +65.8231 q^{18} +55.1769 q^{19} +2.96152 q^{20} -15.1384 q^{21} -178.315 q^{23} -13.1103 q^{24} -122.641 q^{25} +168.703 q^{26} +28.7846 q^{27} -54.4693 q^{28} -113.172 q^{29} -2.02817 q^{30} +70.8128 q^{31} -85.1821 q^{32} +136.397 q^{34} -43.3872 q^{35} +51.5077 q^{36} -210.664 q^{37} -135.962 q^{38} +36.6898 q^{39} -37.5744 q^{40} -191.928 q^{41} +37.3027 q^{42} +208.210 q^{43} +41.0282 q^{45} +439.387 q^{46} +512.515 q^{47} +24.0385 q^{48} +454.990 q^{49} +302.200 q^{50} +29.6640 q^{51} +132.013 q^{52} -375.449 q^{53} -70.9282 q^{54} +691.079 q^{56} -29.5692 q^{57} +278.867 q^{58} -506.508 q^{59} -1.58708 q^{60} +468.697 q^{61} -174.490 q^{62} -754.603 q^{63} +568.749 q^{64} +105.154 q^{65} -289.895 q^{67} +106.733 q^{68} +95.5589 q^{69} +106.910 q^{70} -394.010 q^{71} -653.505 q^{72} -289.538 q^{73} +519.098 q^{74} +65.7231 q^{75} -106.392 q^{76} -90.4074 q^{78} +169.587 q^{79} +68.8949 q^{80} +705.820 q^{81} +472.931 q^{82} +303.331 q^{83} +29.1900 q^{84} +85.0179 q^{85} -513.051 q^{86} +60.6486 q^{87} -1146.68 q^{89} -101.098 q^{90} -1934.02 q^{91} +343.828 q^{92} -37.9485 q^{93} -1262.89 q^{94} -84.7461 q^{95} +45.6489 q^{96} +641.600 q^{97} -1121.14 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} + 2 q^{9} - 34 q^{10} - 88 q^{12} - 130 q^{13} - 160 q^{14} + 64 q^{15} - 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} - 98 q^{20}+ \cdots - 822 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 + 2 * q^9 - 34 * q^10 - 88 * q^12 - 130 * q^13 - 160 * q^14 + 64 * q^15 - 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 - 98 * q^20 + 136 * q^21 - 128 * q^23 - 144 * q^24 - 176 * q^25 - 106 * q^26 + 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 - 184 * q^31 - 302 * q^32 + 446 * q^34 + 128 * q^35 + 394 * q^36 + 126 * q^37 - 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 + 712 * q^42 + 264 * q^43 - 202 * q^45 + 664 * q^46 + 256 * q^47 + 152 * q^48 + 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 - 162 * q^53 - 128 * q^54 + 336 * q^56 + 24 * q^57 + 918 * q^58 - 1304 * q^59 + 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 - 262 * q^64 + 626 * q^65 - 656 * q^67 + 934 * q^68 - 280 * q^69 + 872 * q^70 - 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 + 464 * q^75 - 192 * q^76 + 1960 * q^78 - 416 * q^79 + 214 * q^80 + 26 * q^81 - 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 - 264 * q^86 - 1008 * q^87 - 1074 * q^89 - 1186 * q^90 - 688 * q^91 + 944 * q^92 + 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 - 338 * q^97 - 822 * 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 $

$2$	−2.46410	−0.871191	−0.435596	−	0.900142i	$-0.643462\pi$
$2$	−2.46410	−0.871191	−0.435596	+	0.900142i	$0.643462\pi$
$3$	−0.535898	−0.103134	−0.0515668	−	0.998670i	$-0.516422\pi$
$3$	−0.535898	−0.103134	−0.0515668	+	0.998670i	$0.516422\pi$
$4$	−1.92820	−0.241025
$5$	−1.53590	−0.137375	−0.0686875	−	0.997638i	$-0.521881\pi$
$5$	−1.53590	−0.137375	−0.0686875	+	0.997638i	$0.521881\pi$
$6$	1.32051	0.0898492
$7$	28.2487	1.52529	0.762644	−	0.646819i	$-0.223901\pi$
$7$	28.2487	1.52529	0.762644	+	0.646819i	$0.223901\pi$
$8$	24.4641	1.08117
$9$	−26.7128	−0.989363
$10$	3.78461	0.119680
$11$	0	0
$11$	0	0
$12$	1.03332	0.0248578
$13$	−68.4641	−1.46066	−0.730328	−	0.683097i	$-0.760633\pi$
$13$	−68.4641	−1.46066	−0.730328	+	0.683097i	$0.760633\pi$
$14$	−69.6077	−1.32882
$15$	0.823085	0.0141680
$16$	−44.8564	−0.700881
$17$	−55.3538	−0.789722	−0.394861	−	0.918741i	$-0.629207\pi$
$17$	−55.3538	−0.789722	−0.394861	+	0.918741i	$0.629207\pi$
$18$	65.8231	0.861925
$19$	55.1769	0.666234	0.333117	−	0.942885i	$-0.391900\pi$
$19$	55.1769	0.666234	0.333117	+	0.942885i	$0.391900\pi$
$20$	2.96152	0.0331108
$21$	−15.1384	−0.157308
$22$	0	0
$23$	−178.315	−1.61658	−0.808290	−	0.588785i	$-0.799606\pi$
$23$	−178.315	−1.61658	−0.808290	+	0.588785i	$0.799606\pi$
$24$	−13.1103	−0.111505
$25$	−122.641	−0.981128
$26$	168.703	1.27251
$27$	28.7846	0.205170
$28$	−54.4693	−0.367633
$29$	−113.172	−0.724671	−0.362336	−	0.932048i	$-0.618021\pi$
$29$	−113.172	−0.724671	−0.362336	+	0.932048i	$0.618021\pi$
$30$	−2.02817	−0.0123430
$31$	70.8128	0.410269	0.205135	−	0.978734i	$-0.434237\pi$
$31$	70.8128	0.410269	0.205135	+	0.978734i	$0.434237\pi$
$32$	−85.1821	−0.470569
$33$	0	0
$34$	136.397	0.687999
$35$	−43.3872	−0.209536
$36$	51.5077	0.238462
$37$	−210.664	−0.936026	−0.468013	−	0.883722i	$-0.655030\pi$
$37$	−210.664	−0.936026	−0.468013	+	0.883722i	$0.655030\pi$
$38$	−135.962	−0.580418
$39$	36.6898	0.150643
$40$	−37.5744	−0.148526
$41$	−191.928	−0.731077	−0.365538	−	0.930796i	$-0.619115\pi$
$41$	−191.928	−0.731077	−0.365538	+	0.930796i	$0.619115\pi$
$42$	37.3027	0.137046
$43$	208.210	0.738413	0.369207	−	0.929347i	$-0.379629\pi$
$43$	208.210	0.738413	0.369207	+	0.929347i	$0.379629\pi$
$44$	0	0
$45$	41.0282	0.135914
$46$	439.387	1.40835
$47$	512.515	1.59060	0.795298	−	0.606218i	$-0.207314\pi$
$47$	512.515	1.59060	0.795298	+	0.606218i	$0.207314\pi$
$48$	24.0385	0.0722845
$49$	454.990	1.32650
$50$	302.200	0.854750
$51$	29.6640	0.0814470
$52$	132.013	0.352055
$53$	−375.449	−0.973054	−0.486527	−	0.873666i	$-0.661736\pi$
$53$	−375.449	−0.973054	−0.486527	+	0.873666i	$0.661736\pi$
$54$	−70.9282	−0.178743
$55$	0	0
$56$	691.079	1.64910
$57$	−29.5692	−0.0687112
$58$	278.867	0.631327
$59$	−506.508	−1.11766	−0.558828	−	0.829284i	$-0.688749\pi$
$59$	−506.508	−1.11766	−0.558828	+	0.829284i	$0.688749\pi$
$60$	−1.58708	−0.00341484
$61$	468.697	0.983779	0.491890	−	0.870658i	$-0.336306\pi$
$61$	468.697	0.983779	0.491890	+	0.870658i	$0.336306\pi$
$62$	−174.490	−0.357423
$63$	−754.603	−1.50906
$64$	568.749	1.11084
$65$	105.154	0.200657
$66$	0	0
$67$	−289.895	−0.528601	−0.264301	−	0.964440i	$-0.585141\pi$
$67$	−289.895	−0.528601	−0.264301	+	0.964440i	$0.585141\pi$
$68$	106.733	0.190343
$69$	95.5589	0.166724
$70$	106.910	0.182546
$71$	−394.010	−0.658597	−0.329299	−	0.944226i	$-0.606812\pi$
$71$	−394.010	−0.658597	−0.329299	+	0.944226i	$0.606812\pi$
$72$	−653.505	−1.06967
$73$	−289.538	−0.464218	−0.232109	−	0.972690i	$-0.574563\pi$
$73$	−289.538	−0.464218	−0.232109	+	0.972690i	$0.574563\pi$
$74$	519.098	0.815458
$75$	65.7231	0.101187
$76$	−106.392	−0.160579
$77$	0	0
$78$	−90.4074	−0.131239
$79$	169.587	0.241519	0.120760	−	0.992682i	$-0.461467\pi$
$79$	169.587	0.241519	0.120760	+	0.992682i	$0.461467\pi$
$80$	68.8949	0.0962835
$81$	705.820	0.968203
$82$	472.931	0.636908
$83$	303.331	0.401143	0.200572	−	0.979679i	$-0.435720\pi$
$83$	303.331	0.401143	0.200572	+	0.979679i	$0.435720\pi$
$84$	29.1900	0.0379153
$85$	85.0179	0.108488
$86$	−513.051	−0.643299
$87$	60.6486	0.0747380
$88$	0	0
$89$	−1146.68	−1.36571	−0.682854	−	0.730555i	$-0.739262\pi$
$89$	−1146.68	−1.36571	−0.682854	+	0.730555i	$0.739262\pi$
$90$	−101.098	−0.118407
$91$	−1934.02	−2.22792
$92$	343.828	0.389637
$93$	−37.9485	−0.0423126
$94$	−1262.89	−1.38571
$95$	−84.7461	−0.0915239
$96$	45.6489	0.0485315
$97$	641.600	0.671594	0.335797	−	0.941934i	$-0.390994\pi$
$97$	641.600	0.671594	0.335797	+	0.941934i	$0.390994\pi$
$98$	−1121.14	−1.15564
$99$	0	0
$100$	236.477	0.236477
$101$	−1107.57	−1.09116	−0.545580	−	0.838058i	$-0.683691\pi$
$101$	−1107.57	−1.09116	−0.545580	+	0.838058i	$0.683691\pi$
$102$	−73.0952	−0.0709559
$103$	−298.297	−0.285360	−0.142680	−	0.989769i	$-0.545572\pi$
$103$	−298.297	−0.285360	−0.142680	+	0.989769i	$0.545572\pi$
$104$	−1674.91	−1.57922
$105$	23.2511	0.0216102
$106$	925.144	0.847716
$107$	598.126	0.540402	0.270201	−	0.962804i	$-0.412910\pi$
$107$	598.126	0.540402	0.270201	+	0.962804i	$0.412910\pi$
$108$	−55.5026	−0.0494513
$109$	1530.16	1.34461	0.672305	−	0.740275i	$-0.265305\pi$
$109$	1530.16	1.34461	0.672305	+	0.740275i	$0.265305\pi$
$110$	0	0
$111$	112.895	0.0965358
$112$	−1267.14	−1.06905
$113$	−151.010	−0.125716	−0.0628578	−	0.998022i	$-0.520021\pi$
$113$	−151.010	−0.125716	−0.0628578	+	0.998022i	$0.520021\pi$
$114$	72.8616	0.0598606
$115$	273.874	0.222077
$116$	218.218	0.174664
$117$	1828.87	1.44512
$118$	1248.09	0.973692
$119$	−1563.67	−1.20455
$120$	20.1360	0.0153180
$121$	0	0
$122$	−1154.92	−0.857060
$123$	102.854	0.0753987
$124$	−136.541	−0.0988853
$125$	380.351	0.272157
$126$	1859.42	1.31468
$127$	695.749	0.486124	0.243062	−	0.970011i	$-0.421848\pi$
$127$	695.749	0.486124	0.243062	+	0.970011i	$0.421848\pi$
$128$	−719.998	−0.497183
$129$	−111.580	−0.0761553
$130$	−259.110	−0.174811
$131$	−1665.68	−1.11093	−0.555463	−	0.831541i	$-0.687459\pi$
$131$	−1665.68	−1.11093	−0.555463	+	0.831541i	$0.687459\pi$
$132$	0	0
$133$	1558.68	1.01620
$134$	714.330	0.460513
$135$	−44.2102	−0.0281853
$136$	−1354.18	−0.853824
$137$	−1605.48	−1.00121	−0.500603	−	0.865677i	$-0.666888\pi$
$137$	−1605.48	−1.00121	−0.500603	+	0.865677i	$0.666888\pi$
$138$	−235.467	−0.145248
$139$	1069.30	0.652495	0.326248	−	0.945284i	$-0.394216\pi$
$139$	1069.30	0.652495	0.326248	+	0.945284i	$0.394216\pi$
$140$	83.6592	0.0505035
$141$	−274.656	−0.164044
$142$	970.881	0.573765
$143$	0	0
$144$	1198.24	0.693426
$145$	173.820	0.0995517
$146$	713.452	0.404423
$147$	−243.828	−0.136807
$148$	406.203	0.225606
$149$	355.172	0.195281	0.0976403	−	0.995222i	$-0.468871\pi$
$149$	355.172	0.195281	0.0976403	+	0.995222i	$0.468871\pi$
$150$	−161.948	−0.0881536
$151$	−1879.55	−1.01295	−0.506476	−	0.862254i	$-0.669052\pi$
$151$	−1879.55	−1.01295	−0.506476	+	0.862254i	$0.669052\pi$
$152$	1349.85	0.720313
$153$	1478.66	0.781322
$154$	0	0
$155$	−108.761	−0.0563607
$156$	−70.7454	−0.0363087
$157$	2499.99	1.27083	0.635417	−	0.772169i	$-0.280828\pi$
$157$	2499.99	1.27083	0.635417	+	0.772169i	$0.280828\pi$
$158$	−417.880	−0.210410
$159$	201.202	0.100355
$160$	130.831	0.0646444
$161$	−5037.18	−2.46575
$162$	−1739.21	−0.843491
$163$	1863.02	0.895235	0.447617	−	0.894225i	$-0.352273\pi$
$163$	1863.02	0.895235	0.447617	+	0.894225i	$0.352273\pi$
$164$	370.077	0.176208
$165$	0	0
$166$	−747.438	−0.349473
$167$	2647.27	1.22666	0.613328	−	0.789828i	$-0.289830\pi$
$167$	2647.27	1.22666	0.613328	+	0.789828i	$0.289830\pi$
$168$	−370.348	−0.170077
$169$	2490.33	1.13352
$170$	−209.493	−0.0945138
$171$	−1473.93	−0.659148
$172$	−401.472	−0.177976
$173$	2109.38	0.927015	0.463507	−	0.886093i	$-0.346591\pi$
$173$	2109.38	0.927015	0.463507	+	0.886093i	$0.346591\pi$
$174$	−149.444	−0.0651111
$175$	−3464.45	−1.49650
$176$	0	0
$177$	271.437	0.115268
$178$	2825.54	1.18979
$179$	1391.25	0.580931	0.290465	−	0.956886i	$-0.406190\pi$
$179$	1391.25	0.580931	0.290465	+	0.956886i	$0.406190\pi$
$180$	−79.1106	−0.0327587
$181$	3701.40	1.52002	0.760008	−	0.649913i	$-0.225195\pi$
$181$	3701.40	1.52002	0.760008	+	0.649913i	$0.225195\pi$
$182$	4765.63	1.94094
$183$	−251.174	−0.101461
$184$	−4362.32	−1.74780
$185$	323.559	0.128586
$186$	93.5088	0.0368624
$187$	0	0
$188$	−988.234	−0.383374
$189$	813.128	0.312944
$190$	208.823	0.0797348
$191$	−3533.03	−1.33844	−0.669218	−	0.743066i	$-0.733371\pi$
$191$	−3533.03	−1.33844	−0.669218	+	0.743066i	$0.733371\pi$
$192$	−304.791	−0.114565
$193$	−2605.66	−0.971811	−0.485906	−	0.874011i	$-0.661510\pi$
$193$	−2605.66	−0.971811	−0.485906	+	0.874011i	$0.661510\pi$
$194$	−1580.97	−0.585087
$195$	−56.3518	−0.0206945
$196$	−877.313	−0.319720
$197$	719.202	0.260107	0.130053	−	0.991507i	$-0.458485\pi$
$197$	719.202	0.260107	0.130053	+	0.991507i	$0.458485\pi$
$198$	0	0
$199$	1035.15	0.368744	0.184372	−	0.982857i	$-0.440975\pi$
$199$	1035.15	0.368744	0.184372	+	0.982857i	$0.440975\pi$
$200$	−3000.30	−1.06077
$201$	155.354	0.0545166
$202$	2729.16	0.950610
$203$	−3196.96	−1.10533
$204$	−57.1983	−0.0196308
$205$	294.782	0.100432
$206$	735.035	0.248604
$207$	4763.30	1.59938
$208$	3071.05	1.02375
$209$	0	0
$210$	−57.2931	−0.0188267
$211$	−356.297	−0.116249	−0.0581244	−	0.998309i	$-0.518512\pi$
$211$	−356.297	−0.116249	−0.0581244	+	0.998309i	$0.518512\pi$
$212$	723.941	0.234531
$213$	211.149	0.0679236
$214$	−1473.84	−0.470793
$215$	−319.790	−0.101439
$216$	704.190	0.221824
$217$	2000.37	0.625779
$218$	−3770.46	−1.17141
$219$	155.163	0.0478765
$220$	0	0
$221$	3789.75	1.15351
$222$	−278.184	−0.0841012
$223$	−292.544	−0.0878485	−0.0439242	−	0.999035i	$-0.513986\pi$
$223$	−292.544	−0.0878485	−0.0439242	+	0.999035i	$0.513986\pi$
$224$	−2406.28	−0.717753
$225$	3276.09	0.970692
$226$	372.105	0.109522
$227$	5604.04	1.63856	0.819280	−	0.573394i	$-0.194374\pi$
$227$	5604.04	1.63856	0.819280	+	0.573394i	$0.194374\pi$
$228$	57.0155	0.0165611
$229$	−5654.38	−1.63167	−0.815833	−	0.578287i	$-0.803721\pi$
$229$	−5654.38	−1.63167	−0.815833	+	0.578287i	$0.803721\pi$
$230$	−674.854	−0.193472
$231$	0	0
$232$	−2768.65	−0.783493
$233$	−2553.08	−0.717845	−0.358923	−	0.933367i	$-0.616856\pi$
$233$	−2553.08	−0.717845	−0.358923	+	0.933367i	$0.616856\pi$
$234$	−4506.52	−1.25898
$235$	−787.171	−0.218508
$236$	976.650	0.269383
$237$	−90.8814	−0.0249088
$238$	3853.05	1.04940
$239$	5297.27	1.43369	0.716845	−	0.697233i	$-0.245586\pi$
$239$	5297.27	1.43369	0.716845	+	0.697233i	$0.245586\pi$
$240$	−36.9207	−0.00993008
$241$	−4145.14	−1.10793	−0.553966	−	0.832539i	$-0.686886\pi$
$241$	−4145.14	−1.10793	−0.553966	+	0.832539i	$0.686886\pi$
$242$	0	0
$243$	−1155.43	−0.305025
$244$	−903.744	−0.237116
$245$	−698.818	−0.182228
$246$	−253.443	−0.0656867
$247$	−3777.64	−0.973139
$248$	1732.37	0.443571
$249$	−162.554	−0.0413714
$250$	−937.225	−0.237101
$251$	−1788.13	−0.449665	−0.224832	−	0.974397i	$-0.572183\pi$
$251$	−1788.13	−0.449665	−0.224832	+	0.974397i	$0.572183\pi$
$252$	1455.03	0.363723
$253$	0	0
$254$	−1714.40	−0.423507
$255$	−45.5609	−0.0111888
$256$	−2775.84	−0.677696
$257$	5167.01	1.25412	0.627061	−	0.778970i	$-0.284258\pi$
$257$	5167.01	1.25412	0.627061	+	0.778970i	$0.284258\pi$
$258$	274.943	0.0663458
$259$	−5950.99	−1.42771
$260$	−202.758	−0.0483636
$261$	3023.14	0.716963
$262$	4104.41	0.967829
$263$	57.6791	0.0135234	0.00676169	−	0.999977i	$-0.497848\pi$
$263$	57.6791	0.0135234	0.00676169	+	0.999977i	$0.497848\pi$
$264$	0	0
$265$	576.651	0.133673
$266$	−3840.74	−0.885304
$267$	614.505	0.140851
$268$	558.976	0.127406
$269$	−3028.06	−0.686335	−0.343167	−	0.939274i	$-0.611500\pi$
$269$	−3028.06	−0.686335	−0.343167	+	0.939274i	$0.611500\pi$
$270$	108.939	0.0245548
$271$	1487.84	0.333504	0.166752	−	0.985999i	$-0.446672\pi$
$271$	1487.84	0.333504	0.166752	+	0.985999i	$0.446672\pi$
$272$	2482.97	0.553501
$273$	1036.44	0.229774
$274$	3956.06	0.872241
$275$	0	0
$276$	−184.257	−0.0401847
$277$	−7460.46	−1.61825	−0.809126	−	0.587635i	$-0.800059\pi$
$277$	−7460.46	−1.61825	−0.809126	+	0.587635i	$0.800059\pi$
$278$	−2634.86	−0.568448
$279$	−1891.61	−0.405906
$280$	−1061.43	−0.226544
$281$	−900.155	−0.191099	−0.0955493	−	0.995425i	$-0.530461\pi$
$281$	−900.155	−0.191099	−0.0955493	+	0.995425i	$0.530461\pi$
$282$	676.781	0.142914
$283$	−6486.92	−1.36257	−0.681285	−	0.732018i	$-0.738578\pi$
$283$	−6486.92	−1.36257	−0.681285	+	0.732018i	$0.738578\pi$
$284$	759.732	0.158739
$285$	45.4153	0.00943920
$286$	0	0
$287$	−5421.72	−1.11510
$288$	2275.45	0.465564
$289$	−1848.95	−0.376339
$290$	−428.311	−0.0867286
$291$	−343.832	−0.0692639
$292$	558.289	0.111888
$293$	−6129.38	−1.22212	−0.611062	−	0.791583i	$-0.709257\pi$
$293$	−6129.38	−1.22212	−0.611062	+	0.791583i	$0.709257\pi$
$294$	600.818	0.119185
$295$	777.944	0.153538
$296$	−5153.71	−1.01200
$297$	0	0
$298$	−875.179	−0.170127
$299$	12208.2	2.36127
$300$	−126.728	−0.0243887
$301$	5881.67	1.12629
$302$	4631.41	0.882476
$303$	593.545	0.112535
$304$	−2475.04	−0.466951
$305$	−719.872	−0.135147
$306$	−3643.56	−0.680681
$307$	−5377.67	−0.999740	−0.499870	−	0.866101i	$-0.666619\pi$
$307$	−5377.67	−0.999740	−0.499870	+	0.866101i	$0.666619\pi$
$308$	0	0
$309$	159.857	0.0294303
$310$	267.999	0.0491010
$311$	−6066.41	−1.10609	−0.553046	−	0.833151i	$-0.686535\pi$
$311$	−6066.41	−1.10609	−0.553046	+	0.833151i	$0.686535\pi$
$312$	897.583	0.162871
$313$	3241.18	0.585311	0.292655	−	0.956218i	$-0.405461\pi$
$313$	3241.18	0.585311	0.292655	+	0.956218i	$0.405461\pi$
$314$	−6160.23	−1.10714
$315$	1158.99	0.207307
$316$	−326.998	−0.0582123
$317$	6519.32	1.15508	0.577542	−	0.816361i	$-0.304012\pi$
$317$	6519.32	1.15508	0.577542	+	0.816361i	$0.304012\pi$
$318$	−495.783	−0.0874281
$319$	0	0
$320$	−873.540	−0.152601
$321$	−320.535	−0.0557336
$322$	12412.1	2.14814
$323$	−3054.25	−0.526140
$324$	−1360.97	−0.233362
$325$	8396.51	1.43309
$326$	−4590.68	−0.779921
$327$	−820.008	−0.138675
$328$	−4695.35	−0.790419
$329$	14477.9	2.42612
$330$	0	0
$331$	5879.55	0.976343	0.488171	−	0.872748i	$-0.337664\pi$
$331$	5879.55	0.976343	0.488171	+	0.872748i	$0.337664\pi$
$332$	−584.883	−0.0966857
$333$	5627.43	0.926070
$334$	−6523.13	−1.06865
$335$	445.249	0.0726166
$336$	679.056	0.110255
$337$	−1342.66	−0.217031	−0.108516	−	0.994095i	$-0.534610\pi$
$337$	−1342.66	−0.217031	−0.108516	+	0.994095i	$0.534610\pi$
$338$	−6136.43	−0.987509
$339$	80.9262	0.0129655
$340$	−163.932	−0.0261484
$341$	0	0
$342$	3631.91	0.574244
$343$	3163.56	0.498007
$344$	5093.68	0.798351
$345$	−146.769	−0.0229037
$346$	−5197.74	−0.807607
$347$	5650.03	0.874091	0.437046	−	0.899439i	$-0.356025\pi$
$347$	5650.03	0.874091	0.437046	+	0.899439i	$0.356025\pi$
$348$	−116.943	−0.0180138
$349$	1249.55	0.191653	0.0958266	−	0.995398i	$-0.469451\pi$
$349$	1249.55	0.191653	0.0958266	+	0.995398i	$0.469451\pi$
$350$	8536.76	1.30374
$351$	−1970.71	−0.299683
$352$	0	0
$353$	5984.25	0.902293	0.451147	−	0.892450i	$-0.351015\pi$
$353$	5984.25	0.902293	0.451147	+	0.892450i	$0.351015\pi$
$354$	−668.848	−0.100420
$355$	605.160	0.0904748
$356$	2211.04	0.329170
$357$	837.971	0.124230
$358$	−3428.17	−0.506102
$359$	2176.01	0.319904	0.159952	−	0.987125i	$-0.448866\pi$
$359$	2176.01	0.319904	0.159952	+	0.987125i	$0.448866\pi$
$360$	1003.72	0.146946
$361$	−3814.51	−0.556132
$362$	−9120.63	−1.32423
$363$	0	0
$364$	3729.19	0.536985
$365$	444.701	0.0637719
$366$	618.919	0.0883918
$367$	−8464.39	−1.20392	−0.601958	−	0.798528i	$-0.705613\pi$
$367$	−8464.39	−1.20392	−0.601958	+	0.798528i	$0.705613\pi$
$368$	7998.59	1.13303
$369$	5126.94	0.723301
$370$	−797.281	−0.112023
$371$	−10605.9	−1.48419
$372$	73.1723	0.0101984
$373$	4248.93	0.589816	0.294908	−	0.955526i	$-0.404711\pi$
$373$	4248.93	0.589816	0.294908	+	0.955526i	$0.404711\pi$
$374$	0	0
$375$	−203.830	−0.0280686
$376$	12538.2	1.71971
$377$	7748.20	1.05850
$378$	−2003.63	−0.272634
$379$	4852.93	0.657727	0.328863	−	0.944378i	$-0.393334\pi$
$379$	4852.93	0.657727	0.328863	+	0.944378i	$0.393334\pi$
$380$	163.408	0.0220596
$381$	−372.851	−0.0501357
$382$	8705.75	1.16603
$383$	−8181.81	−1.09157	−0.545785	−	0.837926i	$-0.683768\pi$
$383$	−8181.81	−1.09157	−0.545785	+	0.837926i	$0.683768\pi$
$384$	385.846	0.0512763
$385$	0	0
$386$	6420.61	0.846634
$387$	−5561.88	−0.730559
$388$	−1237.13	−0.161871
$389$	1254.82	0.163552	0.0817761	−	0.996651i	$-0.473941\pi$
$389$	1254.82	0.163552	0.0817761	+	0.996651i	$0.473941\pi$
$390$	138.857	0.0180289
$391$	9870.44	1.27665
$392$	11130.9	1.43417
$393$	892.636	0.114574
$394$	−1772.19	−0.226603
$395$	−260.469	−0.0331787
$396$	0	0
$397$	−11519.3	−1.45627	−0.728133	−	0.685436i	$-0.759612\pi$
$397$	−11519.3	−1.45627	−0.728133	+	0.685436i	$0.759612\pi$
$398$	−2550.72	−0.321247
$399$	−835.292	−0.104804
$400$	5501.24	0.687654
$401$	−1500.66	−0.186882	−0.0934409	−	0.995625i	$-0.529787\pi$
$401$	−1500.66	−0.186882	−0.0934409	+	0.995625i	$0.529787\pi$
$402$	−382.809	−0.0474944
$403$	−4848.13	−0.599262
$404$	2135.62	0.262998
$405$	−1084.07	−0.133007
$406$	7877.63	0.962956
$407$	0	0
$408$	725.704	0.0880581
$409$	−91.3936	−0.0110492	−0.00552460	−	0.999985i	$-0.501759\pi$
$409$	−91.3936	−0.0110492	−0.00552460	+	0.999985i	$0.501759\pi$
$410$	−726.373	−0.0874952
$411$	860.372	0.103258
$412$	575.178	0.0687791
$413$	−14308.2	−1.70475
$414$	−11737.3	−1.39337
$415$	−465.885	−0.0551070
$416$	5831.91	0.687339
$417$	−573.036	−0.0672942
$418$	0	0
$419$	−1880.83	−0.219295	−0.109648	−	0.993971i	$-0.534972\pi$
$419$	−1880.83	−0.219295	−0.109648	+	0.993971i	$0.534972\pi$
$420$	−44.8329	−0.00520862
$421$	−7279.83	−0.842748	−0.421374	−	0.906887i	$-0.638452\pi$
$421$	−7279.83	−0.842748	−0.421374	+	0.906887i	$0.638452\pi$
$422$	877.951	0.101275
$423$	−13690.7	−1.57368
$424$	−9185.01	−1.05204
$425$	6788.65	0.774819
$426$	−520.294	−0.0591745
$427$	13240.1	1.50055
$428$	−1153.31	−0.130251
$429$	0	0
$430$	787.994	0.0883732
$431$	−6870.61	−0.767855	−0.383928	−	0.923363i	$-0.625429\pi$
$431$	−6870.61	−0.767855	−0.383928	+	0.923363i	$0.625429\pi$
$432$	−1291.17	−0.143800
$433$	1121.32	0.124451	0.0622255	−	0.998062i	$-0.480180\pi$
$433$	1121.32	0.124451	0.0622255	+	0.998062i	$0.480180\pi$
$434$	−4929.11	−0.545173
$435$	−93.1500	−0.0102671
$436$	−2950.45	−0.324085
$437$	−9838.89	−1.07702
$438$	−382.338	−0.0417096
$439$	−7114.94	−0.773525	−0.386763	−	0.922179i	$-0.626407\pi$
$439$	−7114.94	−0.773525	−0.386763	+	0.922179i	$0.626407\pi$
$440$	0	0
$441$	−12154.1	−1.31239
$442$	−9338.33	−1.00493
$443$	−14057.4	−1.50764	−0.753822	−	0.657079i	$-0.771792\pi$
$443$	−14057.4	−1.50764	−0.753822	+	0.657079i	$0.771792\pi$
$444$	−217.684	−0.0232676
$445$	1761.19	0.187614
$446$	720.859	0.0765328
$447$	−190.336	−0.0201400
$448$	16066.4	1.69435
$449$	−15323.9	−1.61064	−0.805320	−	0.592840i	$-0.798007\pi$
$449$	−15323.9	−1.61064	−0.805320	+	0.592840i	$0.798007\pi$
$450$	−8072.61	−0.845659
$451$	0	0
$452$	291.179	0.0303006
$453$	1007.25	0.104470
$454$	−13808.9	−1.42750
$455$	2970.46	0.306060
$456$	−723.384	−0.0742885
$457$	7212.20	0.738233	0.369117	−	0.929383i	$-0.379660\pi$
$457$	7212.20	0.738233	0.369117	+	0.929383i	$0.379660\pi$
$458$	13933.0	1.42149
$459$	−1593.34	−0.162028
$460$	−528.085	−0.0535263
$461$	10159.6	1.02642	0.513212	−	0.858262i	$-0.328456\pi$
$461$	10159.6	1.02642	0.513212	+	0.858262i	$0.328456\pi$
$462$	0	0
$463$	−10292.0	−1.03306	−0.516532	−	0.856268i	$-0.672777\pi$
$463$	−10292.0	−1.03306	−0.516532	+	0.856268i	$0.672777\pi$
$464$	5076.48	0.507909
$465$	58.2850	0.00581269
$466$	6291.05	0.625380
$467$	18023.0	1.78588	0.892938	−	0.450180i	$-0.148640\pi$
$467$	18023.0	1.78588	0.892938	+	0.450180i	$0.148640\pi$
$468$	−3526.43	−0.348310
$469$	−8189.16	−0.806269
$470$	1939.67	0.190362
$471$	−1339.74	−0.131066
$472$	−12391.3	−1.20838
$473$	0	0
$474$	223.941	0.0217003
$475$	−6766.95	−0.653661
$476$	3015.08	0.290328
$477$	10029.3	0.962704
$478$	−13053.0	−1.24902
$479$	−17083.8	−1.62960	−0.814801	−	0.579741i	$-0.803154\pi$
$479$	−17083.8	−1.62960	−0.814801	+	0.579741i	$0.803154\pi$
$480$	−70.1121	−0.00666701
$481$	14422.9	1.36721
$482$	10214.0	0.965221
$483$	2699.42	0.254302
$484$	0	0
$485$	−985.432	−0.0922601
$486$	2847.10	0.265735
$487$	461.804	0.0429699	0.0214850	−	0.999769i	$-0.493161\pi$
$487$	461.804	0.0429699	0.0214850	+	0.999769i	$0.493161\pi$
$488$	11466.3	1.06363
$489$	−998.391	−0.0923288
$490$	1721.96	0.158755
$491$	12542.7	1.15284	0.576422	−	0.817152i	$-0.304448\pi$
$491$	12542.7	1.15284	0.576422	+	0.817152i	$0.304448\pi$
$492$	−198.323	−0.0181730
$493$	6264.49	0.572289
$494$	9308.48	0.847790
$495$	0	0
$496$	−3176.41	−0.287550
$497$	−11130.3	−1.00455
$498$	400.551	0.0360424
$499$	−18277.0	−1.63966	−0.819829	−	0.572608i	$-0.805932\pi$
$499$	−18277.0	−1.63966	−0.819829	+	0.572608i	$0.805932\pi$
$500$	−733.395	−0.0655968
$501$	−1418.67	−0.126510
$502$	4406.14	0.391744
$503$	2655.18	0.235365	0.117683	−	0.993051i	$-0.462453\pi$
$503$	2655.18	0.235365	0.117683	+	0.993051i	$0.462453\pi$
$504$	−18460.7	−1.63156
$505$	1701.11	0.149898
$506$	0	0
$507$	−1334.57	−0.116904
$508$	−1341.54	−0.117168
$509$	−4887.16	−0.425579	−0.212789	−	0.977098i	$-0.568255\pi$
$509$	−4887.16	−0.425579	−0.212789	+	0.977098i	$0.568255\pi$
$510$	112.267	0.00974756
$511$	−8179.08	−0.708065
$512$	12599.9	1.08759
$513$	1588.25	0.136692
$514$	−12732.0	−1.09258
$515$	458.155	0.0392014
$516$	215.148	0.0183554
$517$	0	0
$518$	14663.8	1.24381
$519$	−1130.42	−0.0956064
$520$	2572.50	0.216945
$521$	−21941.1	−1.84502	−0.922512	−	0.385969i	$-0.873867\pi$
$521$	−21941.1	−1.84502	−0.922512	+	0.385969i	$0.873867\pi$
$522$	−7449.31	−0.624612
$523$	6102.28	0.510199	0.255099	−	0.966915i	$-0.417892\pi$
$523$	6102.28	0.510199	0.255099	+	0.966915i	$0.417892\pi$
$524$	3211.77	0.267761
$525$	1856.59	0.154340
$526$	−142.127	−0.0117814
$527$	−3919.76	−0.323999
$528$	0	0
$529$	19629.4	1.61333
$530$	−1420.93	−0.116455
$531$	13530.2	1.10577
$532$	−3005.45	−0.244930
$533$	13140.2	1.06785
$534$	−1514.20	−0.122708
$535$	−918.660	−0.0742377
$536$	−7092.02	−0.571508
$537$	−745.566	−0.0599135
$538$	7461.44	0.597929
$539$	0	0
$540$	85.2463	0.00679337
$541$	2099.35	0.166836	0.0834179	−	0.996515i	$-0.473416\pi$
$541$	2099.35	0.166836	0.0834179	+	0.996515i	$0.473416\pi$
$542$	−3666.18	−0.290546
$543$	−1983.58	−0.156765
$544$	4715.15	0.371619
$545$	−2350.16	−0.184716
$546$	−2553.89	−0.200177
$547$	9029.06	0.705767	0.352884	−	0.935667i	$-0.385201\pi$
$547$	9029.06	0.705767	0.352884	+	0.935667i	$0.385201\pi$
$548$	3095.68	0.241316
$549$	−12520.2	−0.973315
$550$	0	0
$551$	−6244.47	−0.482801
$552$	2337.76	0.180257
$553$	4790.62	0.368386
$554$	18383.3	1.40981
$555$	−173.394	−0.0132616
$556$	−2061.83	−0.157268
$557$	−7894.54	−0.600543	−0.300271	−	0.953854i	$-0.597077\pi$
$557$	−7894.54	−0.600543	−0.300271	+	0.953854i	$0.597077\pi$
$558$	4661.12	0.353621
$559$	−14254.9	−1.07857
$560$	1946.19	0.146860
$561$	0	0
$562$	2218.07	0.166484
$563$	22377.6	1.67514	0.837569	−	0.546332i	$-0.183976\pi$
$563$	22377.6	1.67514	0.837569	+	0.546332i	$0.183976\pi$
$564$	529.593	0.0395388
$565$	231.936	0.0172702
$566$	15984.4	1.18706
$567$	19938.5	1.47679
$568$	−9639.11	−0.712056
$569$	−16920.5	−1.24665	−0.623325	−	0.781963i	$-0.714219\pi$
$569$	−16920.5	−1.24665	−0.623325	+	0.781963i	$0.714219\pi$
$570$	−111.908	−0.00822335
$571$	16320.0	1.19609	0.598047	−	0.801461i	$-0.295944\pi$
$571$	16320.0	1.19609	0.598047	+	0.801461i	$0.295944\pi$
$572$	0	0
$573$	1893.35	0.138038
$574$	13359.7	0.971467
$575$	21868.8	1.58607
$576$	−15192.9	−1.09902
$577$	830.262	0.0599034	0.0299517	−	0.999551i	$-0.490465\pi$
$577$	830.262	0.0599034	0.0299517	+	0.999551i	$0.490465\pi$
$578$	4556.01	0.327863
$579$	1396.37	0.100226
$580$	−335.161	−0.0239945
$581$	8568.70	0.611858
$582$	847.238	0.0603422
$583$	0	0
$584$	−7083.29	−0.501899
$585$	−2808.96	−0.198523
$586$	15103.4	1.06470
$587$	21919.4	1.54124	0.770621	−	0.637294i	$-0.219946\pi$
$587$	21919.4	1.54124	0.770621	+	0.637294i	$0.219946\pi$
$588$	470.150	0.0329739
$589$	3907.23	0.273336
$590$	−1916.93	−0.133761
$591$	−385.419	−0.0268258
$592$	9449.63	0.656043
$593$	−8236.51	−0.570376	−0.285188	−	0.958472i	$-0.592056\pi$
$593$	−8236.51	−0.570376	−0.285188	+	0.958472i	$0.592056\pi$
$594$	0	0
$595$	2401.64	0.165475
$596$	−684.843	−0.0470676
$597$	−554.737	−0.0380299
$598$	−30082.2	−2.05711
$599$	−10922.0	−0.745009	−0.372505	−	0.928030i	$-0.621501\pi$
$599$	−10922.0	−0.745009	−0.372505	+	0.928030i	$0.621501\pi$
$600$	1607.86	0.109401
$601$	−1386.44	−0.0940997	−0.0470498	−	0.998893i	$-0.514982\pi$
$601$	−1386.44	−0.0940997	−0.0470498	+	0.998893i	$0.514982\pi$
$602$	−14493.0	−0.981216
$603$	7743.91	0.522979
$604$	3624.16	0.244147
$605$	0	0
$606$	−1462.55	−0.0980399
$607$	1417.78	0.0948035	0.0474017	−	0.998876i	$-0.484906\pi$
$607$	1417.78	0.0948035	0.0474017	+	0.998876i	$0.484906\pi$
$608$	−4700.08	−0.313509
$609$	1713.24	0.113997
$610$	1773.84	0.117739
$611$	−35088.9	−2.32331
$612$	−2851.15	−0.188318
$613$	−15424.9	−1.01632	−0.508162	−	0.861261i	$-0.669675\pi$
$613$	−15424.9	−1.01632	−0.508162	+	0.861261i	$0.669675\pi$
$614$	13251.1	0.870965
$615$	−157.973	−0.0103579
$616$	0	0
$617$	15169.5	0.989793	0.494897	−	0.868952i	$-0.335206\pi$
$617$	15169.5	0.989793	0.494897	+	0.868952i	$0.335206\pi$
$618$	−393.904	−0.0256394
$619$	−2081.56	−0.135162	−0.0675809	−	0.997714i	$-0.521528\pi$
$619$	−2081.56	−0.135162	−0.0675809	+	0.997714i	$0.521528\pi$
$620$	209.714	0.0135844
$621$	−5132.74	−0.331674
$622$	14948.3	0.963618
$623$	−32392.3	−2.08310
$624$	−1645.77	−0.105583
$625$	14745.9	0.943741
$626$	−7986.59	−0.509918
$627$	0	0
$628$	−4820.49	−0.306303
$629$	11661.1	0.739200
$630$	−2855.88	−0.180604
$631$	25249.7	1.59298	0.796492	−	0.604649i	$-0.206687\pi$
$631$	25249.7	1.59298	0.796492	+	0.604649i	$0.206687\pi$
$632$	4148.80	0.261124
$633$	190.939	0.0119892
$634$	−16064.3	−1.00630
$635$	−1068.60	−0.0667812
$636$	−387.959	−0.0241880
$637$	−31150.5	−1.93756
$638$	0	0
$639$	10525.1	0.651592
$640$	1105.84	0.0683005
$641$	−2626.57	−0.161846	−0.0809231	−	0.996720i	$-0.525787\pi$
$641$	−2626.57	−0.161846	−0.0809231	+	0.996720i	$0.525787\pi$
$642$	789.830	0.0485547
$643$	9229.61	0.566066	0.283033	−	0.959110i	$-0.408659\pi$
$643$	9229.61	0.566066	0.283033	+	0.959110i	$0.408659\pi$
$644$	9712.70	0.594308
$645$	171.375	0.0104618
$646$	7525.99	0.458369
$647$	316.901	0.0192561	0.00962803	−	0.999954i	$-0.496935\pi$
$647$	316.901	0.0192561	0.00962803	+	0.999954i	$0.496935\pi$
$648$	17267.3	1.04679
$649$	0	0
$650$	−20689.8	−1.24850
$651$	−1071.99	−0.0645389
$652$	−3592.29	−0.215774
$653$	−5022.66	−0.300998	−0.150499	−	0.988610i	$-0.548088\pi$
$653$	−5022.66	−0.300998	−0.150499	+	0.988610i	$0.548088\pi$
$654$	2020.58	0.120812
$655$	2558.32	0.152613
$656$	8609.21	0.512398
$657$	7734.38	0.459280
$658$	−35675.0	−2.11361
$659$	24927.5	1.47350	0.736752	−	0.676163i	$-0.236358\pi$
$659$	24927.5	1.47350	0.736752	+	0.676163i	$0.236358\pi$
$660$	0	0
$661$	−16440.5	−0.967418	−0.483709	−	0.875229i	$-0.660711\pi$
$661$	−16440.5	−0.967418	−0.483709	+	0.875229i	$0.660711\pi$
$662$	−14487.8	−0.850581
$663$	−2030.92	−0.118966
$664$	7420.72	0.433704
$665$	−2393.97	−0.139600
$666$	−13866.6	−0.806784
$667$	20180.3	1.17149
$668$	−5104.47	−0.295655
$669$	156.774	0.00906014
$670$	−1097.14	−0.0632630
$671$	0	0
$672$	1289.52	0.0740245
$673$	11777.4	0.674572	0.337286	−	0.941402i	$-0.390491\pi$
$673$	11777.4	0.674572	0.337286	+	0.941402i	$0.390491\pi$
$674$	3308.46	0.189076
$675$	−3530.17	−0.201298
$676$	−4801.87	−0.273206
$677$	2818.49	0.160005	0.0800025	−	0.996795i	$-0.474507\pi$
$677$	2818.49	0.160005	0.0800025	+	0.996795i	$0.474507\pi$
$678$	−199.410	−0.0112954
$679$	18124.4	1.02437
$680$	2079.89	0.117294
$681$	−3003.19	−0.168991
$682$	0	0
$683$	15803.2	0.885346	0.442673	−	0.896683i	$-0.354030\pi$
$683$	15803.2	0.885346	0.442673	+	0.896683i	$0.354030\pi$
$684$	2842.04	0.158871
$685$	2465.85	0.137540
$686$	−7795.34	−0.433860
$687$	3030.17	0.168280
$688$	−9339.56	−0.517540
$689$	25704.8	1.42130
$690$	361.653	0.0199535
$691$	3300.72	0.181716	0.0908578	−	0.995864i	$-0.471039\pi$
$691$	3300.72	0.181716	0.0908578	+	0.995864i	$0.471039\pi$
$692$	−4067.32	−0.223434
$693$	0	0
$694$	−13922.3	−0.761501
$695$	−1642.34	−0.0896365
$696$	1483.71	0.0808046
$697$	10624.0	0.577348
$698$	−3079.02	−0.166967
$699$	1368.19	0.0740340
$700$	6680.16	0.360695
$701$	29773.2	1.60416	0.802082	−	0.597214i	$-0.203726\pi$
$701$	29773.2	1.60416	0.802082	+	0.597214i	$0.203726\pi$
$702$	4856.04	0.261082
$703$	−11623.8	−0.623612
$704$	0	0
$705$	421.844	0.0225355
$706$	−14745.8	−0.786070
$707$	−31287.4	−1.66433
$708$	−523.385	−0.0277825
$709$	−24002.5	−1.27141	−0.635707	−	0.771931i	$-0.719291\pi$
$709$	−24002.5	−1.27141	−0.635707	+	0.771931i	$0.719291\pi$
$710$	−1491.18	−0.0788209
$711$	−4530.15	−0.238951
$712$	−28052.5	−1.47656
$713$	−12627.0	−0.663233
$714$	−2064.84	−0.108228
$715$	0	0
$716$	−2682.60	−0.140019
$717$	−2838.80	−0.147862
$718$	−5361.91	−0.278697
$719$	−20668.7	−1.07206	−0.536032	−	0.844198i	$-0.680077\pi$
$719$	−20668.7	−1.07206	−0.536032	+	0.844198i	$0.680077\pi$
$720$	−1840.38	−0.0952594
$721$	−8426.52	−0.435257
$722$	9399.34	0.484497
$723$	2221.37	0.114265
$724$	−7137.06	−0.366363
$725$	13879.5	0.710995
$726$	0	0
$727$	21928.9	1.11870	0.559351	−	0.828931i	$-0.311050\pi$
$727$	21928.9	1.11870	0.559351	+	0.828931i	$0.311050\pi$
$728$	−47314.1	−2.40876
$729$	−18438.0	−0.936745
$730$	−1095.79	−0.0555575
$731$	−11525.2	−0.583141
$732$	484.315	0.0244546
$733$	25124.0	1.26600	0.633000	−	0.774152i	$-0.281823\pi$
$733$	25124.0	1.26600	0.633000	+	0.774152i	$0.281823\pi$
$734$	20857.1	1.04884
$735$	374.495	0.0187938
$736$	15189.3	0.760712
$737$	0	0
$738$	−12633.3	−0.630133
$739$	−37038.1	−1.84367	−0.921833	−	0.387588i	$-0.873308\pi$
$739$	−37038.1	−1.84367	−0.921833	+	0.387588i	$0.873308\pi$
$740$	−623.887	−0.0309926
$741$	2024.43	0.100363
$742$	26134.1	1.29301
$743$	24798.0	1.22443	0.612213	−	0.790693i	$-0.290279\pi$
$743$	24798.0	1.22443	0.612213	+	0.790693i	$0.290279\pi$
$744$	−928.375	−0.0457471
$745$	−545.508	−0.0268267
$746$	−10469.8	−0.513843
$747$	−8102.82	−0.396876
$748$	0	0
$749$	16896.3	0.824268
$750$	502.257	0.0244531
$751$	13967.2	0.678654	0.339327	−	0.940668i	$-0.389801\pi$
$751$	13967.2	0.678654	0.339327	+	0.940668i	$0.389801\pi$
$752$	−22989.6	−1.11482
$753$	958.256	0.0463756
$754$	−19092.4	−0.922152
$755$	2886.80	0.139154
$756$	−1567.88	−0.0754274
$757$	−8515.45	−0.408850	−0.204425	−	0.978882i	$-0.565532\pi$
$757$	−8515.45	−0.408850	−0.204425	+	0.978882i	$0.565532\pi$
$758$	−11958.1	−0.573006
$759$	0	0
$760$	−2073.24	−0.0989530
$761$	31658.0	1.50802	0.754009	−	0.656865i	$-0.228118\pi$
$761$	31658.0	1.50802	0.754009	+	0.656865i	$0.228118\pi$
$762$	918.742	0.0436778
$763$	43224.9	2.05091
$764$	6812.40	0.322597
$765$	−2271.07	−0.107334
$766$	20160.8	0.950966
$767$	34677.6	1.63251
$768$	1487.57	0.0698932
$769$	606.519	0.0284416	0.0142208	−	0.999899i	$-0.495473\pi$
$769$	606.519	0.0284416	0.0142208	+	0.999899i	$0.495473\pi$
$770$	0	0
$771$	−2768.99	−0.129342
$772$	5024.24	0.234231
$773$	−4699.76	−0.218679	−0.109339	−	0.994004i	$-0.534874\pi$
$773$	−4699.76	−0.218679	−0.109339	+	0.994004i	$0.534874\pi$
$774$	13705.0	0.636457
$775$	−8684.55	−0.402527
$776$	15696.2	0.726107
$777$	3189.12	0.147245
$778$	−3092.00	−0.142485
$779$	−10590.0	−0.487068
$780$	108.658	0.00498791
$781$	0	0
$782$	−24321.8	−1.11221
$783$	−3257.60	−0.148681
$784$	−20409.2	−0.929720
$785$	−3839.73	−0.174581
$786$	−2199.55	−0.0998158
$787$	−24078.1	−1.09059	−0.545293	−	0.838245i	$-0.683582\pi$
$787$	−24078.1	−1.09059	−0.545293	+	0.838245i	$0.683582\pi$
$788$	−1386.77	−0.0626923
$789$	−30.9101	−0.00139472
$790$	641.821	0.0289050
$791$	−4265.85	−0.191752
$792$	0	0
$793$	−32088.9	−1.43696
$794$	28384.8	1.26869
$795$	−309.026	−0.0137862
$796$	−1995.99	−0.0888767
$797$	−18977.7	−0.843443	−0.421722	−	0.906725i	$-0.638574\pi$
$797$	−18977.7	−0.843443	−0.421722	+	0.906725i	$0.638574\pi$
$798$	2058.25	0.0913046
$799$	−28369.7	−1.25613
$800$	10446.8	0.461688
$801$	30631.1	1.35118
$802$	3697.79	0.162810
$803$	0	0
$804$	−299.554	−0.0131399
$805$	7736.59	0.338732
$806$	11946.3	0.522072
$807$	1622.73	0.0707842
$808$	−27095.7	−1.17973
$809$	−9120.70	−0.396374	−0.198187	−	0.980164i	$-0.563505\pi$
$809$	−9120.70	−0.396374	−0.198187	+	0.980164i	$0.563505\pi$
$810$	2671.25	0.115874
$811$	−39874.2	−1.72648	−0.863239	−	0.504796i	$-0.831568\pi$
$811$	−39874.2	−1.72648	−0.863239	+	0.504796i	$0.831568\pi$
$812$	6164.38	0.266413
$813$	−797.329	−0.0343955
$814$	0	0
$815$	−2861.41	−0.122983
$816$	−1330.62	−0.0570847
$817$	11488.4	0.491956
$818$	225.203	0.00962597
$819$	51663.2	2.20422
$820$	−568.400	−0.0242066
$821$	−4913.94	−0.208889	−0.104444	−	0.994531i	$-0.533306\pi$
$821$	−4913.94	−0.208889	−0.104444	+	0.994531i	$0.533306\pi$
$822$	−2120.04	−0.0899575
$823$	2777.58	0.117643	0.0588215	−	0.998269i	$-0.481266\pi$
$823$	2777.58	0.117643	0.0588215	+	0.998269i	$0.481266\pi$
$824$	−7297.58	−0.308523
$825$	0	0
$826$	35256.8	1.48516
$827$	−20306.5	−0.853842	−0.426921	−	0.904289i	$-0.640402\pi$
$827$	−20306.5	−0.853842	−0.426921	+	0.904289i	$0.640402\pi$
$828$	−9184.62	−0.385492
$829$	−35572.7	−1.49034	−0.745170	−	0.666875i	$-0.767632\pi$
$829$	−35572.7	−1.49034	−0.745170	+	0.666875i	$0.767632\pi$
$830$	1147.99	0.0480088
$831$	3998.05	0.166896
$832$	−38938.9	−1.62255
$833$	−25185.4	−1.04757
$834$	1412.02	0.0586262
$835$	−4065.93	−0.168512
$836$	0	0
$837$	2038.32	0.0841751
$838$	4634.56	0.191048
$839$	7096.72	0.292021	0.146011	−	0.989283i	$-0.453357\pi$
$839$	7096.72	0.292021	0.146011	+	0.989283i	$0.453357\pi$
$840$	568.817	0.0233644
$841$	−11581.2	−0.474851
$842$	17938.2	0.734195
$843$	482.391	0.0197087
$844$	687.013	0.0280189
$845$	−3824.90	−0.155717
$846$	33735.3	1.37097
$847$	0	0
$848$	16841.3	0.681995
$849$	3476.33	0.140527
$850$	−16727.9	−0.675015
$851$	37564.6	1.51316
$852$	−407.139	−0.0163713
$853$	−24157.6	−0.969682	−0.484841	−	0.874602i	$-0.661123\pi$
$853$	−24157.6	−0.969682	−0.484841	+	0.874602i	$0.661123\pi$
$854$	−32624.9	−1.30726
$855$	2263.81	0.0905504
$856$	14632.6	0.584267
$857$	−28806.8	−1.14822	−0.574108	−	0.818779i	$-0.694651\pi$
$857$	−28806.8	−1.14822	−0.574108	+	0.818779i	$0.694651\pi$
$858$	0	0
$859$	11244.4	0.446628	0.223314	−	0.974747i	$-0.428312\pi$
$859$	11244.4	0.446628	0.223314	+	0.974747i	$0.428312\pi$
$860$	616.620	0.0244495
$861$	2905.49	0.115005
$862$	16929.9	0.668949
$863$	−1291.92	−0.0509589	−0.0254794	−	0.999675i	$-0.508111\pi$
$863$	−1291.92	−0.0509589	−0.0254794	+	0.999675i	$0.508111\pi$
$864$	−2451.93	−0.0965468
$865$	−3239.80	−0.127349
$866$	−2763.05	−0.108421
$867$	990.851	0.0388132
$868$	−3857.12	−0.150829
$869$	0	0
$870$	229.531	0.00894464
$871$	19847.4	0.772105
$872$	37433.9	1.45375
$873$	−17138.9	−0.664450
$874$	24244.0	0.938291
$875$	10744.4	0.415118
$876$	−299.186	−0.0115394
$877$	−26823.1	−1.03278	−0.516391	−	0.856353i	$-0.672725\pi$
$877$	−26823.1	−1.03278	−0.516391	+	0.856353i	$0.672725\pi$
$878$	17531.9	0.673889
$879$	3284.73	0.126042
$880$	0	0
$881$	−28515.7	−1.09049	−0.545243	−	0.838278i	$-0.683563\pi$
$881$	−28515.7	−1.09049	−0.545243	+	0.838278i	$0.683563\pi$
$882$	29948.8	1.14334
$883$	41686.4	1.58874	0.794371	−	0.607433i	$-0.207801\pi$
$883$	41686.4	1.58874	0.794371	+	0.607433i	$0.207801\pi$
$884$	−7307.41	−0.278026
$885$	−416.899	−0.0158349
$886$	34638.8	1.31345
$887$	−49179.3	−1.86164	−0.930822	−	0.365473i	$-0.880907\pi$
$887$	−49179.3	−1.86164	−0.930822	+	0.365473i	$0.880907\pi$
$888$	2761.86	0.104372
$889$	19654.0	0.741478
$890$	−4339.74	−0.163448
$891$	0	0
$892$	564.085	0.0211737
$893$	28279.0	1.05971
$894$	469.007	0.0175458
$895$	−2136.81	−0.0798053
$896$	−20339.0	−0.758346
$897$	−6542.35	−0.243526
$898$	37759.5	1.40318
$899$	−8014.01	−0.297310
$900$	−6316.96	−0.233962
$901$	20782.5	0.768442
$902$	0	0
$903$	−3151.98	−0.116159
$904$	−3694.33	−0.135920
$905$	−5684.98	−0.208812
$906$	−2481.97	−0.0910130
$907$	52977.8	1.93947	0.969734	−	0.244163i	$-0.0785133\pi$
$907$	52977.8	1.93947	0.969734	+	0.244163i	$0.0785133\pi$
$908$	−10805.7	−0.394934
$909$	29586.3	1.07955
$910$	−7319.52	−0.266637
$911$	−31469.8	−1.14450	−0.572251	−	0.820078i	$-0.693930\pi$
$911$	−31469.8	−1.14450	−0.572251	+	0.820078i	$0.693930\pi$
$912$	1326.37	0.0481584
$913$	0	0
$914$	−17771.6	−0.643143
$915$	385.778	0.0139382
$916$	10902.8	0.393273
$917$	−47053.4	−1.69448
$918$	3926.15	0.141157
$919$	42860.9	1.53847	0.769234	−	0.638967i	$-0.220638\pi$
$919$	42860.9	1.53847	0.769234	+	0.638967i	$0.220638\pi$
$920$	6700.09	0.240104
$921$	2881.89	0.103107
$922$	−25034.4	−0.894211
$923$	26975.6	0.961984
$924$	0	0
$925$	25836.1	0.918361
$926$	25360.5	0.899996
$927$	7968.37	0.282325
$928$	9640.20	0.341008
$929$	−20968.3	−0.740525	−0.370262	−	0.928927i	$-0.620732\pi$
$929$	−20968.3	−0.740525	−0.370262	+	0.928927i	$0.620732\pi$
$930$	−143.620	−0.00506397
$931$	25104.9	0.883760
$932$	4922.86	0.173019
$933$	3250.98	0.114075
$934$	−44410.4	−1.55584
$935$	0	0
$936$	44741.6	1.56242
$937$	−17126.8	−0.597127	−0.298563	−	0.954390i	$-0.596507\pi$
$937$	−17126.8	−0.597127	−0.298563	+	0.954390i	$0.596507\pi$
$938$	20178.9	0.702415
$939$	−1736.94	−0.0603652
$940$	1517.83	0.0526660
$941$	44021.2	1.52503	0.762513	−	0.646973i	$-0.223966\pi$
$941$	44021.2	1.52503	0.762513	+	0.646973i	$0.223966\pi$
$942$	3301.26	0.114183
$943$	34223.7	1.18184
$944$	22720.1	0.783344
$945$	−1248.88	−0.0429906
$946$	0	0
$947$	8692.03	0.298261	0.149130	−	0.988818i	$-0.452353\pi$
$947$	8692.03	0.298261	0.149130	+	0.988818i	$0.452353\pi$
$948$	175.238	0.00600365
$949$	19823.0	0.678062
$950$	16674.5	0.569464
$951$	−3493.69	−0.119128
$952$	−38253.9	−1.30233
$953$	−57906.0	−1.96827	−0.984133	−	0.177431i	$-0.943221\pi$
$953$	−57906.0	−1.96827	−0.984133	+	0.177431i	$0.943221\pi$
$954$	−24713.2	−0.838699
$955$	5426.38	0.183867
$956$	−10214.2	−0.345556
$957$	0	0
$958$	42096.2	1.41969
$959$	−45352.6	−1.52713
$960$	468.129	0.0157383
$961$	−24776.6	−0.831679
$962$	−35539.5	−1.19110
$963$	−15977.6	−0.534654
$964$	7992.67	0.267040
$965$	4002.03	0.133503
$966$	−6651.64	−0.221545
$967$	56564.3	1.88106	0.940530	−	0.339711i	$-0.110329\pi$
$967$	56564.3	1.88106	0.940530	+	0.339711i	$0.110329\pi$
$968$	0	0
$969$	1636.77	0.0542628
$970$	2428.20	0.0803762
$971$	−30894.7	−1.02107	−0.510534	−	0.859857i	$-0.670552\pi$
$971$	−30894.7	−1.02107	−0.510534	+	0.859857i	$0.670552\pi$
$972$	2227.91	0.0735187
$973$	30206.3	0.995242
$974$	−1137.93	−0.0374350
$975$	−4499.67	−0.147800
$976$	−21024.1	−0.689513
$977$	−29998.9	−0.982342	−0.491171	−	0.871063i	$-0.663431\pi$
$977$	−29998.9	−0.982342	−0.491171	+	0.871063i	$0.663431\pi$
$978$	2460.14	0.0804361
$979$	0	0
$980$	1347.46	0.0439216
$981$	−40874.8	−1.33031
$982$	−30906.6	−1.00435
$983$	−24485.9	−0.794485	−0.397242	−	0.917714i	$-0.630033\pi$
$983$	−24485.9	−0.794485	−0.397242	+	0.917714i	$0.630033\pi$
$984$	2516.23	0.0815188
$985$	−1104.62	−0.0357321
$986$	−15436.3	−0.498573
$987$	−7758.68	−0.250214
$988$	7284.05	0.234551
$989$	−37127.1	−1.19370
$990$	0	0
$991$	−52661.1	−1.68803	−0.844014	−	0.536321i	$-0.819814\pi$
$991$	−52661.1	−1.68803	−0.844014	+	0.536321i	$0.819814\pi$
$992$	−6031.98	−0.193060
$993$	−3150.84	−0.100694
$994$	27426.1	0.875156
$995$	−1589.89	−0.0506562
$996$	313.438	0.00997155
$997$	54748.6	1.73912	0.869561	−	0.493826i	$-0.164402\pi$
$997$	54748.6	1.73912	0.869561	+	0.493826i	$0.164402\pi$
$998$	45036.3	1.42846
$999$	−6063.88	−0.192045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.4.a.e.1.1	yes	2
3.2	odd	2		1089.4.a.k.1.2		2
4.3	odd	2		1936.4.a.y.1.1		2
11.2	odd	10		121.4.c.g.81.1		8
11.3	even	5		121.4.c.d.9.1		8
11.4	even	5		121.4.c.d.27.1		8
11.5	even	5		121.4.c.d.3.2		8
11.6	odd	10		121.4.c.g.3.1		8
11.7	odd	10		121.4.c.g.27.2		8
11.8	odd	10		121.4.c.g.9.2		8
11.9	even	5		121.4.c.d.81.2		8
11.10	odd	2		121.4.a.b.1.2	✓	2
33.32	even	2		1089.4.a.x.1.1		2
44.43	even	2		1936.4.a.z.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.4.a.b.1.2	✓	2	11.10	odd	2
121.4.a.e.1.1	yes	2	1.1	even	1	trivial
121.4.c.d.3.2		8	11.5	even	5
121.4.c.d.9.1		8	11.3	even	5
121.4.c.d.27.1		8	11.4	even	5
121.4.c.d.81.2		8	11.9	even	5
121.4.c.g.3.1		8	11.6	odd	10
121.4.c.g.9.2		8	11.8	odd	10
121.4.c.g.27.2		8	11.7	odd	10
121.4.c.g.81.1		8	11.2	odd	10
1089.4.a.k.1.2		2	3.2	odd	2
1089.4.a.x.1.1		2	33.32	even	2
1936.4.a.y.1.1		2	4.3	odd	2
1936.4.a.z.1.1		2	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)

\(f(q)\)	\(=\)	\(q-2.46410 q^{2} -0.535898 q^{3} -1.92820 q^{4} -1.53590 q^{5} +1.32051 q^{6} +28.2487 q^{7} +24.4641 q^{8} -26.7128 q^{9} +3.78461 q^{10} +1.03332 q^{12} -68.4641 q^{13} -69.6077 q^{14} +0.823085 q^{15} -44.8564 q^{16} -55.3538 q^{17} +65.8231 q^{18} +55.1769 q^{19} +2.96152 q^{20} -15.1384 q^{21} -178.315 q^{23} -13.1103 q^{24} -122.641 q^{25} +168.703 q^{26} +28.7846 q^{27} -54.4693 q^{28} -113.172 q^{29} -2.02817 q^{30} +70.8128 q^{31} -85.1821 q^{32} +136.397 q^{34} -43.3872 q^{35} +51.5077 q^{36} -210.664 q^{37} -135.962 q^{38} +36.6898 q^{39} -37.5744 q^{40} -191.928 q^{41} +37.3027 q^{42} +208.210 q^{43} +41.0282 q^{45} +439.387 q^{46} +512.515 q^{47} +24.0385 q^{48} +454.990 q^{49} +302.200 q^{50} +29.6640 q^{51} +132.013 q^{52} -375.449 q^{53} -70.9282 q^{54} +691.079 q^{56} -29.5692 q^{57} +278.867 q^{58} -506.508 q^{59} -1.58708 q^{60} +468.697 q^{61} -174.490 q^{62} -754.603 q^{63} +568.749 q^{64} +105.154 q^{65} -289.895 q^{67} +106.733 q^{68} +95.5589 q^{69} +106.910 q^{70} -394.010 q^{71} -653.505 q^{72} -289.538 q^{73} +519.098 q^{74} +65.7231 q^{75} -106.392 q^{76} -90.4074 q^{78} +169.587 q^{79} +68.8949 q^{80} +705.820 q^{81} +472.931 q^{82} +303.331 q^{83} +29.1900 q^{84} +85.0179 q^{85} -513.051 q^{86} +60.6486 q^{87} -1146.68 q^{89} -101.098 q^{90} -1934.02 q^{91} +343.828 q^{92} -37.9485 q^{93} -1262.89 q^{94} -84.7461 q^{95} +45.6489 q^{96} +641.600 q^{97} -1121.14 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 8 q^{3} + 10 q^{4} - 10 q^{5} - 32 q^{6} + 8 q^{7} + 42 q^{8} + 2 q^{9} - 34 q^{10} - 88 q^{12} - 130 q^{13} - 160 q^{14} + 64 q^{15} - 62 q^{16} + 14 q^{17} + 194 q^{18} + 48 q^{19} - 98 q^{20}+ \cdots - 822 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 8 * q^3 + 10 * q^4 - 10 * q^5 - 32 * q^6 + 8 * q^7 + 42 * q^8 + 2 * q^9 - 34 * q^10 - 88 * q^12 - 130 * q^13 - 160 * q^14 + 64 * q^15 - 62 * q^16 + 14 * q^17 + 194 * q^18 + 48 * q^19 - 98 * q^20 + 136 * q^21 - 128 * q^23 - 144 * q^24 - 176 * q^25 - 106 * q^26 + 16 * q^27 - 296 * q^28 + 30 * q^29 + 280 * q^30 - 184 * q^31 - 302 * q^32 + 446 * q^34 + 128 * q^35 + 394 * q^36 + 126 * q^37 - 168 * q^38 + 496 * q^39 - 186 * q^40 - 370 * q^41 + 712 * q^42 + 264 * q^43 - 202 * q^45 + 664 * q^46 + 256 * q^47 + 152 * q^48 + 522 * q^49 + 64 * q^50 - 488 * q^51 - 602 * q^52 - 162 * q^53 - 128 * q^54 + 336 * q^56 + 24 * q^57 + 918 * q^58 - 1304 * q^59 + 752 * q^60 + 300 * q^61 - 1312 * q^62 - 1336 * q^63 - 262 * q^64 + 626 * q^65 - 656 * q^67 + 934 * q^68 - 280 * q^69 + 872 * q^70 - 1176 * q^71 - 150 * q^72 + 668 * q^73 + 2022 * q^74 + 464 * q^75 - 192 * q^76 + 1960 * q^78 - 416 * q^79 + 214 * q^80 + 26 * q^81 - 322 * q^82 + 960 * q^83 + 1832 * q^84 - 502 * q^85 - 264 * q^86 - 1008 * q^87 - 1074 * q^89 - 1186 * q^90 - 688 * q^91 + 944 * q^92 + 1864 * q^93 - 2408 * q^94 - 24 * q^95 + 1664 * q^96 - 338 * q^97 - 822 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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