LMFDB - Embedded newform 197.4.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, 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("197.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.89943 q^{2} -3.98313 q^{3} -4.39218 q^{4} +11.9589 q^{5} +7.56566 q^{6} -5.63514 q^{7} +23.5380 q^{8} -11.1347 q^{9} -22.7151 q^{10} -22.5805 q^{11} +17.4946 q^{12} -87.2000 q^{13} +10.7035 q^{14} -47.6339 q^{15} -9.57134 q^{16} +79.3598 q^{17} +21.1495 q^{18} +30.3904 q^{19} -52.5257 q^{20} +22.4455 q^{21} +42.8900 q^{22} +150.510 q^{23} -93.7551 q^{24} +18.0156 q^{25} +165.630 q^{26} +151.895 q^{27} +24.7506 q^{28} +262.694 q^{29} +90.4771 q^{30} +64.1874 q^{31} -170.124 q^{32} +89.9411 q^{33} -150.738 q^{34} -67.3902 q^{35} +48.9054 q^{36} -262.024 q^{37} -57.7243 q^{38} +347.329 q^{39} +281.489 q^{40} +358.670 q^{41} -42.6336 q^{42} +403.293 q^{43} +99.1776 q^{44} -133.159 q^{45} -285.883 q^{46} -260.797 q^{47} +38.1239 q^{48} -311.245 q^{49} -34.2193 q^{50} -316.100 q^{51} +382.998 q^{52} +217.502 q^{53} -288.514 q^{54} -270.038 q^{55} -132.640 q^{56} -121.049 q^{57} -498.968 q^{58} +629.342 q^{59} +209.217 q^{60} +292.397 q^{61} -121.919 q^{62} +62.7455 q^{63} +399.709 q^{64} -1042.82 q^{65} -170.836 q^{66} -88.5113 q^{67} -348.562 q^{68} -599.502 q^{69} +128.003 q^{70} +327.077 q^{71} -262.088 q^{72} +550.522 q^{73} +497.696 q^{74} -71.7585 q^{75} -133.480 q^{76} +127.244 q^{77} -659.726 q^{78} +102.373 q^{79} -114.463 q^{80} -304.383 q^{81} -681.267 q^{82} +1172.18 q^{83} -98.5847 q^{84} +949.057 q^{85} -766.025 q^{86} -1046.34 q^{87} -531.500 q^{88} -1418.35 q^{89} +252.925 q^{90} +491.384 q^{91} -661.068 q^{92} -255.667 q^{93} +495.364 q^{94} +363.436 q^{95} +677.627 q^{96} +1273.08 q^{97} +591.187 q^{98} +251.426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) $ 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.89943	−0.671549	−0.335774	−	0.941942i	$-0.608998\pi$
$2$	−1.89943	−0.671549	−0.335774	+	0.941942i	$0.608998\pi$
$3$	−3.98313	−0.766554	−0.383277	−	0.923633i	$-0.625205\pi$
$3$	−3.98313	−0.766554	−0.383277	+	0.923633i	$0.625205\pi$
$4$	−4.39218	−0.549022
$5$	11.9589	1.06964	0.534819	−	0.844967i	$-0.320380\pi$
$5$	11.9589	1.06964	0.534819	+	0.844967i	$0.320380\pi$
$6$	7.56566	0.514778
$7$	−5.63514	−0.304269	−0.152135	−	0.988360i	$-0.548615\pi$
$7$	−5.63514	−0.304269	−0.152135	+	0.988360i	$0.548615\pi$
$8$	23.5380	1.04024
$9$	−11.1347	−0.412395
$10$	−22.7151	−0.718314
$11$	−22.5805	−0.618934	−0.309467	−	0.950910i	$-0.600151\pi$
$11$	−22.5805	−0.618934	−0.309467	+	0.950910i	$0.600151\pi$
$12$	17.4946	0.420855
$13$	−87.2000	−1.86038	−0.930189	−	0.367081i	$-0.880357\pi$
$13$	−87.2000	−1.86038	−0.930189	+	0.367081i	$0.880357\pi$
$14$	10.7035	0.204332
$15$	−47.6339	−0.819935
$16$	−9.57134	−0.149552
$17$	79.3598	1.13221	0.566105	−	0.824333i	$-0.308450\pi$
$17$	79.3598	1.13221	0.566105	+	0.824333i	$0.308450\pi$
$18$	21.1495	0.276943
$19$	30.3904	0.366949	0.183475	−	0.983024i	$-0.441265\pi$
$19$	30.3904	0.366949	0.183475	+	0.983024i	$0.441265\pi$
$20$	−52.5257	−0.587255
$21$	22.4455	0.233239
$22$	42.8900	0.415644
$23$	150.510	1.36450	0.682251	−	0.731118i	$-0.261001\pi$
$23$	150.510	1.36450	0.682251	+	0.731118i	$0.261001\pi$
$24$	−93.7551	−0.797403
$25$	18.0156	0.144125
$26$	165.630	1.24933
$27$	151.895	1.08268
$28$	24.7506	0.167051
$29$	262.694	1.68211	0.841053	−	0.540953i	$-0.181936\pi$
$29$	262.694	1.68211	0.841053	+	0.540953i	$0.181936\pi$
$30$	90.4771	0.550626
$31$	64.1874	0.371884	0.185942	−	0.982561i	$-0.440466\pi$
$31$	64.1874	0.371884	0.185942	+	0.982561i	$0.440466\pi$
$32$	−170.124	−0.939812
$33$	89.9411	0.474446
$34$	−150.738	−0.760335
$35$	−67.3902	−0.325458
$36$	48.9054	0.226414
$37$	−262.024	−1.16423	−0.582116	−	0.813106i	$-0.697775\pi$
$37$	−262.024	−1.16423	−0.582116	+	0.813106i	$0.697775\pi$
$38$	−57.7243	−0.246424
$39$	347.329	1.42608
$40$	281.489	1.11268
$41$	358.670	1.36622	0.683108	−	0.730317i	$-0.260628\pi$
$41$	358.670	1.36622	0.683108	+	0.730317i	$0.260628\pi$
$42$	−42.6336	−0.156631
$43$	403.293	1.43027	0.715135	−	0.698987i	$-0.246365\pi$
$43$	403.293	1.43027	0.715135	+	0.698987i	$0.246365\pi$
$44$	99.1776	0.339809
$45$	−133.159	−0.441113
$46$	−285.883	−0.916330
$47$	−260.797	−0.809385	−0.404693	−	0.914453i	$-0.632622\pi$
$47$	−260.797	−0.809385	−0.404693	+	0.914453i	$0.632622\pi$
$48$	38.1239	0.114640
$49$	−311.245	−0.907420
$50$	−34.2193	−0.0967868
$51$	−316.100	−0.867900
$52$	382.998	1.02139
$53$	217.502	0.563703	0.281851	−	0.959458i	$-0.409051\pi$
$53$	217.502	0.563703	0.281851	+	0.959458i	$0.409051\pi$
$54$	−288.514	−0.727070
$55$	−270.038	−0.662035
$56$	−132.640	−0.316514
$57$	−121.049	−0.281286
$58$	−498.968	−1.12962
$59$	629.342	1.38870	0.694350	−	0.719637i	$-0.255692\pi$
$59$	629.342	1.38870	0.694350	+	0.719637i	$0.255692\pi$
$60$	209.217	0.450163
$61$	292.397	0.613731	0.306866	−	0.951753i	$-0.400720\pi$
$61$	292.397	0.613731	0.306866	+	0.951753i	$0.400720\pi$
$62$	−121.919	−0.249738
$63$	62.7455	0.125479
$64$	399.709	0.780682
$65$	−1042.82	−1.98993
$66$	−170.836	−0.318614
$67$	−88.5113	−0.161394	−0.0806968	−	0.996739i	$-0.525715\pi$
$67$	−88.5113	−0.161394	−0.0806968	+	0.996739i	$0.525715\pi$
$68$	−348.562	−0.621609
$69$	−599.502	−1.04596
$70$	128.003	0.218561
$71$	327.077	0.546717	0.273358	−	0.961912i	$-0.411865\pi$
$71$	327.077	0.546717	0.273358	+	0.961912i	$0.411865\pi$
$72$	−262.088	−0.428992
$73$	550.522	0.882653	0.441327	−	0.897347i	$-0.354508\pi$
$73$	550.522	0.882653	0.441327	+	0.897347i	$0.354508\pi$
$74$	497.696	0.781838
$75$	−71.7585	−0.110479
$76$	−133.480	−0.201463
$77$	127.244	0.188323
$78$	−659.726	−0.957682
$79$	102.373	0.145796	0.0728979	−	0.997339i	$-0.476775\pi$
$79$	102.373	0.145796	0.0728979	+	0.997339i	$0.476775\pi$
$80$	−114.463	−0.159967
$81$	−304.383	−0.417535
$82$	−681.267	−0.917481
$83$	1172.18	1.55017	0.775083	−	0.631860i	$-0.217708\pi$
$83$	1172.18	1.55017	0.775083	+	0.631860i	$0.217708\pi$
$84$	−98.5847	−0.128053
$85$	949.057	1.21105
$86$	−766.025	−0.960495
$87$	−1046.34	−1.28942
$88$	−531.500	−0.643842
$89$	−1418.35	−1.68927	−0.844637	−	0.535340i	$-0.820183\pi$
$89$	−1418.35	−1.68927	−0.844637	+	0.535340i	$0.820183\pi$
$90$	252.925	0.296229
$91$	491.384	0.566056
$92$	−661.068	−0.749142
$93$	−255.667	−0.285069
$94$	495.364	0.543542
$95$	363.436	0.392503
$96$	677.627	0.720417
$97$	1273.08	1.33260	0.666299	−	0.745685i	$-0.267877\pi$
$97$	1273.08	1.33260	0.666299	+	0.745685i	$0.267877\pi$
$98$	591.187	0.609377
$99$	251.426	0.255245
$100$	−79.1277	−0.0791277
$101$	−1171.66	−1.15431	−0.577153	−	0.816636i	$-0.695836\pi$
$101$	−1171.66	−1.15431	−0.577153	+	0.816636i	$0.695836\pi$
$102$	600.410	0.582837
$103$	−1167.67	−1.11703	−0.558513	−	0.829496i	$-0.688628\pi$
$103$	−1167.67	−1.11703	−0.558513	+	0.829496i	$0.688628\pi$
$104$	−2052.52	−1.93525
$105$	268.424	0.249481
$106$	−413.130	−0.378554
$107$	258.507	0.233559	0.116780	−	0.993158i	$-0.462743\pi$
$107$	258.507	0.233559	0.116780	+	0.993158i	$0.462743\pi$
$108$	−667.152	−0.594414
$109$	−1013.80	−0.890871	−0.445435	−	0.895314i	$-0.646951\pi$
$109$	−1013.80	−0.890871	−0.445435	+	0.895314i	$0.646951\pi$
$110$	512.918	0.444589
$111$	1043.68	0.892446
$112$	53.9359	0.0455041
$113$	−529.107	−0.440480	−0.220240	−	0.975446i	$-0.570684\pi$
$113$	−529.107	−0.440480	−0.220240	+	0.975446i	$0.570684\pi$
$114$	229.924	0.188898
$115$	1799.94	1.45952
$116$	−1153.80	−0.923513
$117$	970.943	0.767211
$118$	−1195.39	−0.932580
$119$	−447.204	−0.344497
$120$	−1121.21	−0.852932
$121$	−821.121	−0.616921
$122$	−555.387	−0.412151
$123$	−1428.63	−1.04728
$124$	−281.922	−0.204172
$125$	−1279.42	−0.915476
$126$	−119.180	−0.0842653
$127$	734.433	0.513153	0.256576	−	0.966524i	$-0.417405\pi$
$127$	734.433	0.513153	0.256576	+	0.966524i	$0.417405\pi$
$128$	601.775	0.415546
$129$	−1606.37	−1.09638
$130$	1980.75	1.33634
$131$	2322.06	1.54870	0.774349	−	0.632758i	$-0.218077\pi$
$131$	2322.06	1.54870	0.774349	+	0.632758i	$0.218077\pi$
$132$	−395.037	−0.260482
$133$	−171.254	−0.111651
$134$	168.121	0.108384
$135$	1816.50	1.15807
$136$	1867.97	1.17778
$137$	1521.38	0.948760	0.474380	−	0.880320i	$-0.342672\pi$
$137$	1521.38	0.948760	0.474380	+	0.880320i	$0.342672\pi$
$138$	1138.71	0.702416
$139$	−2422.80	−1.47841	−0.739207	−	0.673478i	$-0.764799\pi$
$139$	−2422.80	−1.47841	−0.739207	+	0.673478i	$0.764799\pi$
$140$	295.990	0.178684
$141$	1038.79	0.620438
$142$	−621.259	−0.367147
$143$	1969.02	1.15145
$144$	106.574	0.0616746
$145$	3141.54	1.79924
$146$	−1045.68	−0.592745
$147$	1239.73	0.695587
$148$	1150.86	0.639189
$149$	−2695.25	−1.48190	−0.740951	−	0.671559i	$-0.765625\pi$
$149$	−2695.25	−1.48190	−0.740951	+	0.671559i	$0.765625\pi$
$150$	136.300	0.0741923
$151$	3198.20	1.72361	0.861807	−	0.507236i	$-0.169333\pi$
$151$	3198.20	1.72361	0.861807	+	0.507236i	$0.169333\pi$
$152$	715.330	0.381717
$153$	−883.645	−0.466918
$154$	−241.691	−0.126468
$155$	767.611	0.397781
$156$	−1525.53	−0.782950
$157$	2441.39	1.24105	0.620524	−	0.784188i	$-0.286920\pi$
$157$	2441.39	1.24105	0.620524	+	0.784188i	$0.286920\pi$
$158$	−194.450	−0.0979090
$159$	−866.340	−0.432109
$160$	−2034.50	−1.00526
$161$	−848.147	−0.415176
$162$	578.153	0.280395
$163$	3156.98	1.51702	0.758508	−	0.651664i	$-0.225929\pi$
$163$	3156.98	1.51702	0.758508	+	0.651664i	$0.225929\pi$
$164$	−1575.34	−0.750083
$165$	1075.60	0.507486
$166$	−2226.47	−1.04101
$167$	248.750	0.115263	0.0576313	−	0.998338i	$-0.481645\pi$
$167$	248.750	0.115263	0.0576313	+	0.998338i	$0.481645\pi$
$168$	528.323	0.242625
$169$	5406.83	2.46101
$170$	−1802.66	−0.813282
$171$	−338.387	−0.151328
$172$	−1771.33	−0.785250
$173$	−1162.07	−0.510696	−0.255348	−	0.966849i	$-0.582190\pi$
$173$	−1162.07	−0.510696	−0.255348	+	0.966849i	$0.582190\pi$
$174$	1987.46	0.865911
$175$	−101.520	−0.0438527
$176$	216.126	0.0925630
$177$	−2506.75	−1.06451
$178$	2694.06	1.13443
$179$	−1051.59	−0.439103	−0.219552	−	0.975601i	$-0.570459\pi$
$179$	−1051.59	−0.439103	−0.219552	+	0.975601i	$0.570459\pi$
$180$	584.856	0.242181
$181$	1264.73	0.519373	0.259686	−	0.965693i	$-0.416381\pi$
$181$	1264.73	0.519373	0.259686	+	0.965693i	$0.416381\pi$
$182$	−933.349	−0.380134
$183$	−1164.66	−0.470458
$184$	3542.72	1.41942
$185$	−3133.53	−1.24531
$186$	485.620	0.191438
$187$	−1791.98	−0.700764
$188$	1145.47	0.444371
$189$	−855.952	−0.329425
$190$	−690.320	−0.263585
$191$	2796.60	1.05945	0.529724	−	0.848170i	$-0.322295\pi$
$191$	2796.60	1.05945	0.529724	+	0.848170i	$0.322295\pi$
$192$	−1592.09	−0.598435
$193$	−3990.99	−1.48848	−0.744242	−	0.667910i	$-0.767189\pi$
$193$	−3990.99	−1.48848	−0.744242	+	0.667910i	$0.767189\pi$
$194$	−2418.13	−0.894905
$195$	4153.68	1.52539
$196$	1367.04	0.498194
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	−477.566	−0.171410
$199$	−5143.03	−1.83206	−0.916030	−	0.401111i	$-0.868624\pi$
$199$	−5143.03	−1.83206	−0.916030	+	0.401111i	$0.868624\pi$
$200$	424.052	0.149925
$201$	352.552	0.123717
$202$	2225.49	0.775173
$203$	−1480.32	−0.511813
$204$	1388.37	0.476497
$205$	4289.30	1.46136
$206$	2217.90	0.750137
$207$	−1675.88	−0.562714
$208$	834.621	0.278224
$209$	−686.230	−0.227117
$210$	−509.852	−0.167539
$211$	2864.89	0.934727	0.467364	−	0.884065i	$-0.345204\pi$
$211$	2864.89	0.934727	0.467364	+	0.884065i	$0.345204\pi$
$212$	−955.309	−0.309485
$213$	−1302.79	−0.419088
$214$	−491.016	−0.156846
$215$	4822.94	1.52987
$216$	3575.32	1.12625
$217$	−361.705	−0.113153
$218$	1925.65	0.598263
$219$	−2192.80	−0.676601
$220$	1186.06	0.363472
$221$	−6920.17	−2.10634
$222$	−1982.39	−0.599321
$223$	1494.92	0.448911	0.224455	−	0.974484i	$-0.427940\pi$
$223$	1494.92	0.448911	0.224455	+	0.974484i	$0.427940\pi$
$224$	958.674	0.285956
$225$	−200.598	−0.0594364
$226$	1005.00	0.295804
$227$	−83.7211	−0.0244791	−0.0122396	−	0.999925i	$-0.503896\pi$
$227$	−83.7211	−0.0244791	−0.0122396	+	0.999925i	$0.503896\pi$
$228$	531.669	0.154433
$229$	331.514	0.0956640	0.0478320	−	0.998855i	$-0.484769\pi$
$229$	331.514	0.0956640	0.0478320	+	0.998855i	$0.484769\pi$
$230$	−3418.85	−0.980141
$231$	−506.831	−0.144359
$232$	6183.30	1.74980
$233$	422.110	0.118684	0.0593420	−	0.998238i	$-0.481100\pi$
$233$	422.110	0.118684	0.0593420	+	0.998238i	$0.481100\pi$
$234$	−1844.23	−0.515220
$235$	−3118.85	−0.865749
$236$	−2764.18	−0.762428
$237$	−407.765	−0.111760
$238$	849.431	0.231346
$239$	−55.8633	−0.0151192	−0.00755962	−	0.999971i	$-0.502406\pi$
$239$	−55.8633	−0.0151192	−0.00755962	+	0.999971i	$0.502406\pi$
$240$	455.921	0.122623
$241$	−1480.06	−0.395599	−0.197799	−	0.980243i	$-0.563379\pi$
$241$	−1480.06	−0.395599	−0.197799	+	0.980243i	$0.563379\pi$
$242$	1559.66	0.414292
$243$	−2888.78	−0.762614
$244$	−1284.26	−0.336952
$245$	−3722.15	−0.970611
$246$	2713.58	0.703298
$247$	−2650.04	−0.682664
$248$	1510.84	0.386850
$249$	−4668.96	−1.18829
$250$	2430.16	0.614787
$251$	−4418.42	−1.11111	−0.555554	−	0.831480i	$-0.687494\pi$
$251$	−4418.42	−1.11111	−0.555554	+	0.831480i	$0.687494\pi$
$252$	−275.589	−0.0688908
$253$	−3398.60	−0.844537
$254$	−1395.00	−0.344607
$255$	−3780.22	−0.928339
$256$	−4340.70	−1.05974
$257$	3192.73	0.774931	0.387465	−	0.921884i	$-0.373351\pi$
$257$	3192.73	0.774931	0.387465	+	0.921884i	$0.373351\pi$
$258$	3051.18	0.736271
$259$	1476.55	0.354240
$260$	4580.24	1.09252
$261$	−2925.01	−0.693692
$262$	−4410.59	−1.04003
$263$	776.289	0.182008	0.0910038	−	0.995851i	$-0.470992\pi$
$263$	776.289	0.182008	0.0910038	+	0.995851i	$0.470992\pi$
$264$	2117.04	0.493540
$265$	2601.09	0.602958
$266$	325.285	0.0749793
$267$	5649.49	1.29492
$268$	388.757	0.0886087
$269$	6114.07	1.38581	0.692903	−	0.721031i	$-0.256332\pi$
$269$	6114.07	1.38581	0.692903	+	0.721031i	$0.256332\pi$
$270$	−3450.32	−0.777702
$271$	−6311.74	−1.41480	−0.707401	−	0.706813i	$-0.750132\pi$
$271$	−6311.74	−1.41480	−0.707401	+	0.706813i	$0.750132\pi$
$272$	−759.580	−0.169325
$273$	−1957.25	−0.433912
$274$	−2889.75	−0.637138
$275$	−406.801	−0.0892038
$276$	2633.12	0.574258
$277$	650.544	0.141110	0.0705549	−	0.997508i	$-0.477523\pi$
$277$	650.544	0.141110	0.0705549	+	0.997508i	$0.477523\pi$
$278$	4601.94	0.992827
$279$	−714.705	−0.153363
$280$	−1586.23	−0.338555
$281$	4454.83	0.945739	0.472870	−	0.881132i	$-0.343218\pi$
$281$	4454.83	0.945739	0.472870	+	0.881132i	$0.343218\pi$
$282$	−1973.10	−0.416654
$283$	4199.92	0.882189	0.441094	−	0.897461i	$-0.354590\pi$
$283$	4199.92	0.882189	0.441094	+	0.897461i	$0.354590\pi$
$284$	−1436.58	−0.300160
$285$	−1447.61	−0.300875
$286$	−3740.01	−0.773256
$287$	−2021.16	−0.415697
$288$	1894.28	0.387574
$289$	1384.98	0.281901
$290$	−5967.12	−1.20828
$291$	−5070.86	−1.02151
$292$	−2417.99	−0.484596
$293$	8512.06	1.69720	0.848600	−	0.529034i	$-0.177446\pi$
$293$	8512.06	1.69720	0.848600	+	0.529034i	$0.177446\pi$
$294$	−2354.78	−0.467120
$295$	7526.25	1.48541
$296$	−6167.54	−1.21108
$297$	−3429.87	−0.670106
$298$	5119.43	0.995170
$299$	−13124.5	−2.53849
$300$	315.176	0.0606557
$301$	−2272.61	−0.435187
$302$	−6074.75	−1.15749
$303$	4666.89	0.884838
$304$	−290.877	−0.0548781
$305$	3496.75	0.656470
$306$	1678.42	0.313558
$307$	513.625	0.0954857	0.0477429	−	0.998860i	$-0.484797\pi$
$307$	513.625	0.0954857	0.0477429	+	0.998860i	$0.484797\pi$
$308$	−558.880	−0.103393
$309$	4650.97	0.856260
$310$	−1458.02	−0.267129
$311$	212.630	0.0387689	0.0193844	−	0.999812i	$-0.493829\pi$
$311$	212.630	0.0387689	0.0193844	+	0.999812i	$0.493829\pi$
$312$	8175.44	1.48347
$313$	−3365.61	−0.607781	−0.303890	−	0.952707i	$-0.598286\pi$
$313$	−3365.61	−0.607781	−0.303890	+	0.952707i	$0.598286\pi$
$314$	−4637.25	−0.833424
$315$	750.367	0.134217
$316$	−449.641	−0.0800452
$317$	1231.34	0.218168	0.109084	−	0.994033i	$-0.465208\pi$
$317$	1231.34	0.218168	0.109084	+	0.994033i	$0.465208\pi$
$318$	1645.55	0.290182
$319$	−5931.76	−1.04111
$320$	4780.09	0.835047
$321$	−1029.67	−0.179036
$322$	1610.99	0.278811
$323$	2411.78	0.415464
$324$	1336.90	0.229236
$325$	−1570.96	−0.268127
$326$	−5996.45	−1.01875
$327$	4038.12	0.682900
$328$	8442.39	1.42120
$329$	1469.63	0.246271
$330$	−2043.02	−0.340801
$331$	2958.23	0.491235	0.245618	−	0.969367i	$-0.421009\pi$
$331$	2958.23	0.491235	0.245618	+	0.969367i	$0.421009\pi$
$332$	−5148.43	−0.851075
$333$	2917.56	0.480123
$334$	−472.483	−0.0774045
$335$	−1058.50	−0.172633
$336$	−214.834	−0.0348814
$337$	5192.84	0.839382	0.419691	−	0.907667i	$-0.362138\pi$
$337$	5192.84	0.839382	0.419691	+	0.907667i	$0.362138\pi$
$338$	−10269.9	−1.65269
$339$	2107.50	0.337651
$340$	−4168.43	−0.664896
$341$	−1449.38	−0.230171
$342$	642.741	0.101624
$343$	3686.77	0.580369
$344$	9492.72	1.48783
$345$	−7169.39	−1.11880
$346$	2207.27	0.342958
$347$	982.694	0.152028	0.0760141	−	0.997107i	$-0.475781\pi$
$347$	982.694	0.152028	0.0760141	+	0.997107i	$0.475781\pi$
$348$	4595.73	0.707923
$349$	−6493.70	−0.995988	−0.497994	−	0.867180i	$-0.665930\pi$
$349$	−6493.70	−0.995988	−0.497994	+	0.867180i	$0.665930\pi$
$350$	192.831	0.0294492
$351$	−13245.3	−2.01419
$352$	3841.49	0.581682
$353$	−8829.24	−1.33125	−0.665627	−	0.746284i	$-0.731836\pi$
$353$	−8829.24	−1.33125	−0.665627	+	0.746284i	$0.731836\pi$
$354$	4761.39	0.714873
$355$	3911.49	0.584789
$356$	6229.67	0.927449
$357$	1781.27	0.264075
$358$	1997.42	0.294879
$359$	12148.8	1.78604	0.893020	−	0.450016i	$-0.148582\pi$
$359$	12148.8	1.78604	0.893020	+	0.450016i	$0.148582\pi$
$360$	−3134.29	−0.458866
$361$	−5935.42	−0.865348
$362$	−2402.26	−0.348784
$363$	3270.63	0.472903
$364$	−2158.25	−0.310777
$365$	6583.64	0.944119
$366$	2212.18	0.315936
$367$	11297.2	1.60684	0.803421	−	0.595412i	$-0.203011\pi$
$367$	11297.2	1.60684	0.803421	+	0.595412i	$0.203011\pi$
$368$	−1440.59	−0.204064
$369$	−3993.67	−0.563421
$370$	5951.91	0.836283
$371$	−1225.66	−0.171517
$372$	1122.93	0.156509
$373$	1916.96	0.266104	0.133052	−	0.991109i	$-0.457522\pi$
$373$	1916.96	0.266104	0.133052	+	0.991109i	$0.457522\pi$
$374$	3403.74	0.470597
$375$	5096.09	0.701762
$376$	−6138.64	−0.841958
$377$	−22906.9	−3.12935
$378$	1625.82	0.221225
$379$	−11418.2	−1.54752	−0.773762	−	0.633476i	$-0.781627\pi$
$379$	−11418.2	−1.54752	−0.773762	+	0.633476i	$0.781627\pi$
$380$	−1596.28	−0.215493
$381$	−2925.34	−0.393359
$382$	−5311.93	−0.711471
$383$	14609.5	1.94912	0.974560	−	0.224128i	$-0.0719533\pi$
$383$	14609.5	1.94912	0.974560	+	0.224128i	$0.0719533\pi$
$384$	−2396.95	−0.318539
$385$	1521.70	0.201437
$386$	7580.59	0.999590
$387$	−4490.53	−0.589836
$388$	−5591.61	−0.731626
$389$	4002.38	0.521668	0.260834	−	0.965384i	$-0.416002\pi$
$389$	4002.38	0.521668	0.260834	+	0.965384i	$0.416002\pi$
$390$	−7889.60	−1.02437
$391$	11944.5	1.54490
$392$	−7326.10	−0.943938
$393$	−9249.08	−1.18716
$394$	374.187	0.0478459
$395$	1224.27	0.155949
$396$	−1104.31	−0.140135
$397$	2527.43	0.319516	0.159758	−	0.987156i	$-0.448929\pi$
$397$	2527.43	0.319516	0.159758	+	0.987156i	$0.448929\pi$
$398$	9768.81	1.23032
$399$	682.128	0.0855868
$400$	−172.433	−0.0215542
$401$	12391.8	1.54318	0.771591	−	0.636119i	$-0.219461\pi$
$401$	12391.8	1.54318	0.771591	+	0.636119i	$0.219461\pi$
$402$	−669.647	−0.0830819
$403$	−5597.14	−0.691844
$404$	5146.16	0.633740
$405$	−3640.09	−0.446611
$406$	2811.76	0.343707
$407$	5916.64	0.720582
$408$	−7440.38	−0.902828
$409$	−2130.38	−0.257556	−0.128778	−	0.991673i	$-0.541105\pi$
$409$	−2130.38	−0.257556	−0.128778	+	0.991673i	$0.541105\pi$
$410$	−8147.22	−0.981372
$411$	−6059.85	−0.727275
$412$	5128.60	0.613272
$413$	−3546.43	−0.422539
$414$	3183.22	0.377890
$415$	14018.0	1.65812
$416$	14834.8	1.74841
$417$	9650.34	1.13328
$418$	1303.44	0.152520
$419$	−6513.82	−0.759477	−0.379738	−	0.925094i	$-0.623986\pi$
$419$	−6513.82	−0.759477	−0.379738	+	0.925094i	$0.623986\pi$
$420$	−1178.97	−0.136971
$421$	925.667	0.107160	0.0535799	−	0.998564i	$-0.482937\pi$
$421$	925.667	0.107160	0.0535799	+	0.998564i	$0.482937\pi$
$422$	−5441.66	−0.627715
$423$	2903.89	0.333787
$424$	5119.58	0.586388
$425$	1429.71	0.163180
$426$	2474.56	0.281438
$427$	−1647.70	−0.186740
$428$	−1135.41	−0.128229
$429$	−7842.86	−0.882650
$430$	−9160.83	−1.02738
$431$	−3912.97	−0.437311	−0.218655	−	0.975802i	$-0.570167\pi$
$431$	−3912.97	−0.437311	−0.218655	+	0.975802i	$0.570167\pi$
$432$	−1453.84	−0.161917
$433$	5733.21	0.636306	0.318153	−	0.948039i	$-0.396937\pi$
$433$	5733.21	0.636306	0.318153	+	0.948039i	$0.396937\pi$
$434$	687.032	0.0759876
$435$	−12513.1	−1.37922
$436$	4452.81	0.489108
$437$	4574.07	0.500703
$438$	4165.06	0.454371
$439$	−16261.7	−1.76794	−0.883971	−	0.467541i	$-0.845140\pi$
$439$	−16261.7	−1.76794	−0.883971	+	0.467541i	$0.845140\pi$
$440$	−6356.17	−0.688678
$441$	3465.61	0.374216
$442$	13144.4	1.41451
$443$	14894.0	1.59737	0.798685	−	0.601749i	$-0.205529\pi$
$443$	14894.0	1.59737	0.798685	+	0.601749i	$0.205529\pi$
$444$	−4584.02	−0.489973
$445$	−16962.0	−1.80691
$446$	−2839.49	−0.301465
$447$	10735.5	1.13596
$448$	−2252.42	−0.237537
$449$	−2544.23	−0.267415	−0.133708	−	0.991021i	$-0.542688\pi$
$449$	−2544.23	−0.267415	−0.133708	+	0.991021i	$0.542688\pi$
$450$	381.021	0.0399144
$451$	−8098.95	−0.845598
$452$	2323.93	0.241833
$453$	−12738.8	−1.32124
$454$	159.022	0.0164389
$455$	5876.42	0.605475
$456$	−2849.25	−0.292606
$457$	1110.28	0.113647	0.0568234	−	0.998384i	$-0.481903\pi$
$457$	1110.28	0.113647	0.0568234	+	0.998384i	$0.481903\pi$
$458$	−629.687	−0.0642431
$459$	12054.4	1.22582
$460$	−7905.65	−0.801311
$461$	16810.5	1.69836	0.849180	−	0.528103i	$-0.177096\pi$
$461$	16810.5	1.69836	0.849180	+	0.528103i	$0.177096\pi$
$462$	962.688	0.0969444
$463$	−3014.56	−0.302588	−0.151294	−	0.988489i	$-0.548344\pi$
$463$	−3014.56	−0.302588	−0.151294	+	0.988489i	$0.548344\pi$
$464$	−2514.33	−0.251563
$465$	−3057.50	−0.304920
$466$	−801.768	−0.0797021
$467$	3620.59	0.358760	0.179380	−	0.983780i	$-0.442591\pi$
$467$	3620.59	0.358760	0.179380	+	0.983780i	$0.442591\pi$
$468$	−4264.55	−0.421216
$469$	498.774	0.0491071
$470$	5924.02	0.581393
$471$	−9724.39	−0.951330
$472$	14813.5	1.44459
$473$	−9106.55	−0.885242
$474$	774.520	0.0750525
$475$	547.501	0.0528865
$476$	1964.20	0.189136
$477$	−2421.82	−0.232468
$478$	106.108	0.0101533
$479$	1417.53	0.135216	0.0676079	−	0.997712i	$-0.478463\pi$
$479$	1417.53	0.135216	0.0676079	+	0.997712i	$0.478463\pi$
$480$	8103.68	0.770585
$481$	22848.5	2.16591
$482$	2811.27	0.265664
$483$	3378.28	0.318255
$484$	3606.51	0.338703
$485$	15224.7	1.42540
$486$	5487.02	0.512132
$487$	14796.2	1.37675	0.688377	−	0.725353i	$-0.258323\pi$
$487$	14796.2	1.37675	0.688377	+	0.725353i	$0.258323\pi$
$488$	6882.45	0.638430
$489$	−12574.6	−1.16287
$490$	7069.96	0.651813
$491$	10827.7	0.995207	0.497603	−	0.867405i	$-0.334214\pi$
$491$	10827.7	0.995207	0.497603	+	0.867405i	$0.334214\pi$
$492$	6274.80	0.574979
$493$	20847.3	1.90450
$494$	5033.56	0.458442
$495$	3006.79	0.273020
$496$	−614.359	−0.0556160
$497$	−1843.13	−0.166349
$498$	8868.34	0.797991
$499$	−7937.33	−0.712072	−0.356036	−	0.934472i	$-0.615872\pi$
$499$	−7937.33	−0.712072	−0.356036	+	0.934472i	$0.615872\pi$
$500$	5619.43	0.502617
$501$	−990.805	−0.0883551
$502$	8392.46	0.746163
$503$	−6418.43	−0.568954	−0.284477	−	0.958683i	$-0.591820\pi$
$503$	−6418.43	−0.568954	−0.284477	+	0.958683i	$0.591820\pi$
$504$	1476.90	0.130529
$505$	−14011.8	−1.23469
$506$	6455.39	0.567148
$507$	−21536.1	−1.88649
$508$	−3225.76	−0.281732
$509$	−4309.22	−0.375251	−0.187625	−	0.982241i	$-0.560079\pi$
$509$	−4309.22	−0.375251	−0.187625	+	0.982241i	$0.560079\pi$
$510$	7180.25	0.623425
$511$	−3102.27	−0.268564
$512$	3430.64	0.296122
$513$	4616.16	0.397288
$514$	−6064.36	−0.520404
$515$	−13964.0	−1.19481
$516$	7055.45	0.601936
$517$	5888.92	0.500956
$518$	−2804.59	−0.237889
$519$	4628.67	0.391476
$520$	−24545.9	−2.07001
$521$	−10877.5	−0.914683	−0.457342	−	0.889291i	$-0.651198\pi$
$521$	−10877.5	−0.914683	−0.457342	+	0.889291i	$0.651198\pi$
$522$	5555.84	0.465848
$523$	−968.868	−0.0810051	−0.0405025	−	0.999179i	$-0.512896\pi$
$523$	−968.868	−0.0810051	−0.0405025	+	0.999179i	$0.512896\pi$
$524$	−10198.9	−0.850270
$525$	404.369	0.0336155
$526$	−1474.50	−0.122227
$527$	5093.90	0.421051
$528$	−860.857	−0.0709545
$529$	10486.3	0.861868
$530$	−4940.58	−0.404916
$531$	−7007.52	−0.572694
$532$	752.179	0.0612991
$533$	−31276.0	−2.54168
$534$	−10730.8	−0.869601
$535$	3091.47	0.249824
$536$	−2083.38	−0.167889
$537$	4188.62	0.336596
$538$	−11613.2	−0.930636
$539$	7028.07	0.561633
$540$	−7978.41	−0.635807
$541$	−999.683	−0.0794450	−0.0397225	−	0.999211i	$-0.512647\pi$
$541$	−999.683	−0.0794450	−0.0397225	+	0.999211i	$0.512647\pi$
$542$	11988.7	0.950108
$543$	−5037.58	−0.398127
$544$	−13501.0	−1.06407
$545$	−12124.0	−0.952909
$546$	3717.65	0.291393
$547$	6054.68	0.473272	0.236636	−	0.971598i	$-0.423955\pi$
$547$	6054.68	0.473272	0.236636	+	0.971598i	$0.423955\pi$
$548$	−6682.16	−0.520890
$549$	−3255.74	−0.253100
$550$	772.689	0.0599047
$551$	7983.38	0.617247
$552$	−14111.1	−1.08806
$553$	−576.887	−0.0443612
$554$	−1235.66	−0.0947621
$555$	12481.2	0.954594
$556$	10641.4	0.811682
$557$	−14608.1	−1.11124	−0.555622	−	0.831435i	$-0.687520\pi$
$557$	−14608.1	−1.11124	−0.555622	+	0.831435i	$0.687520\pi$
$558$	1357.53	0.102991
$559$	−35167.1	−2.66084
$560$	645.015	0.0486729
$561$	7137.70	0.537173
$562$	−8461.62	−0.635110
$563$	−22986.3	−1.72071	−0.860354	−	0.509697i	$-0.829758\pi$
$563$	−22986.3	−1.72071	−0.860354	+	0.509697i	$0.829758\pi$
$564$	−4562.54	−0.340634
$565$	−6327.55	−0.471154
$566$	−7977.44	−0.592433
$567$	1715.24	0.127043
$568$	7698.75	0.568719
$569$	−14110.5	−1.03962	−0.519810	−	0.854282i	$-0.673997\pi$
$569$	−14110.5	−1.03962	−0.519810	+	0.854282i	$0.673997\pi$
$570$	2749.64	0.202052
$571$	−4022.58	−0.294816	−0.147408	−	0.989076i	$-0.547093\pi$
$571$	−4022.58	−0.294816	−0.147408	+	0.989076i	$0.547093\pi$
$572$	−8648.28	−0.632173
$573$	−11139.2	−0.812124
$574$	3839.04	0.279161
$575$	2711.53	0.196659
$576$	−4450.63	−0.321949
$577$	−6002.63	−0.433090	−0.216545	−	0.976273i	$-0.569479\pi$
$577$	−6002.63	−0.433090	−0.216545	+	0.976273i	$0.569479\pi$
$578$	−2630.66	−0.189310
$579$	15896.6	1.14100
$580$	−13798.2	−0.987825
$581$	−6605.42	−0.471668
$582$	9631.72	0.685993
$583$	−4911.31	−0.348895
$584$	12958.2	0.918175
$585$	11611.4	0.820638
$586$	−16168.0	−1.13975
$587$	−4828.12	−0.339485	−0.169743	−	0.985488i	$-0.554294\pi$
$587$	−4828.12	−0.339485	−0.169743	+	0.985488i	$0.554294\pi$
$588$	−5445.12	−0.381893
$589$	1950.68	0.136462
$590$	−14295.6	−0.997523
$591$	784.677	0.0546147
$592$	2507.93	0.174113
$593$	14991.1	1.03813	0.519066	−	0.854734i	$-0.326280\pi$
$593$	14991.1	1.03813	0.519066	+	0.854734i	$0.326280\pi$
$594$	6514.79	0.450009
$595$	−5348.07	−0.368487
$596$	11838.0	0.813598
$597$	20485.4	1.40437
$598$	24929.0	1.70472
$599$	4045.80	0.275971	0.137986	−	0.990434i	$-0.455937\pi$
$599$	4045.80	0.275971	0.137986	+	0.990434i	$0.455937\pi$
$600$	−1689.05	−0.114926
$601$	7546.73	0.512209	0.256104	−	0.966649i	$-0.417561\pi$
$601$	7546.73	0.512209	0.256104	+	0.966649i	$0.417561\pi$
$602$	4316.66	0.292249
$603$	985.544	0.0665580
$604$	−14047.1	−0.946303
$605$	−9819.72	−0.659881
$606$	−8864.42	−0.594212
$607$	−11732.2	−0.784506	−0.392253	−	0.919857i	$-0.628304\pi$
$607$	−11732.2	−0.784506	−0.392253	+	0.919857i	$0.628304\pi$
$608$	−5170.14	−0.344863
$609$	5896.30	0.392332
$610$	−6641.82	−0.440852
$611$	22741.5	1.50576
$612$	3881.13	0.256348
$613$	−4436.45	−0.292311	−0.146155	−	0.989262i	$-0.546690\pi$
$613$	−4436.45	−0.292311	−0.146155	+	0.989262i	$0.546690\pi$
$614$	−975.593	−0.0641233
$615$	−17084.9	−1.12021
$616$	2995.08	0.195901
$617$	−26471.6	−1.72724	−0.863620	−	0.504143i	$-0.831808\pi$
$617$	−26471.6	−1.72724	−0.863620	+	0.504143i	$0.831808\pi$
$618$	−8834.17	−0.575020
$619$	926.080	0.0601330	0.0300665	−	0.999548i	$-0.490428\pi$
$619$	926.080	0.0601330	0.0300665	+	0.999548i	$0.490428\pi$
$620$	−3371.49	−0.218390
$621$	22861.8	1.47732
$622$	−403.874	−0.0260352
$623$	7992.63	0.513994
$624$	−3324.40	−0.213273
$625$	−17552.4	−1.12335
$626$	6392.73	0.408155
$627$	2733.35	0.174098
$628$	−10723.0	−0.681363
$629$	−20794.2	−1.31815
$630$	−1425.27	−0.0901334
$631$	−2490.09	−0.157098	−0.0785491	−	0.996910i	$-0.525029\pi$
$631$	−2490.09	−0.157098	−0.0785491	+	0.996910i	$0.525029\pi$
$632$	2409.66	0.151663
$633$	−11411.2	−0.716519
$634$	−2338.85	−0.146510
$635$	8783.02	0.548888
$636$	3805.12	0.237237
$637$	27140.6	1.68814
$638$	11266.9	0.699158
$639$	−3641.89	−0.225463
$640$	7196.58	0.444484
$641$	−10314.1	−0.635545	−0.317772	−	0.948167i	$-0.602935\pi$
$641$	−10314.1	−0.635545	−0.317772	+	0.948167i	$0.602935\pi$
$642$	1955.78	0.120231
$643$	24072.7	1.47642	0.738208	−	0.674573i	$-0.235672\pi$
$643$	24072.7	1.47642	0.738208	+	0.674573i	$0.235672\pi$
$644$	3725.21	0.227941
$645$	−19210.4	−1.17273
$646$	−4580.99	−0.279004
$647$	−6762.91	−0.410939	−0.205469	−	0.978664i	$-0.565872\pi$
$647$	−6762.91	−0.410939	−0.205469	+	0.978664i	$0.565872\pi$
$648$	−7164.58	−0.434338
$649$	−14210.9	−0.859514
$650$	2983.92	0.180060
$651$	1440.72	0.0867377
$652$	−13866.0	−0.832875
$653$	8106.52	0.485808	0.242904	−	0.970050i	$-0.421900\pi$
$653$	8106.52	0.485808	0.242904	+	0.970050i	$0.421900\pi$
$654$	−7670.11	−0.458601
$655$	27769.3	1.65655
$656$	−3432.95	−0.204321
$657$	−6129.88	−0.364002
$658$	−2791.45	−0.165383
$659$	20944.1	1.23803	0.619017	−	0.785377i	$-0.287531\pi$
$659$	20944.1	1.23803	0.619017	+	0.785377i	$0.287531\pi$
$660$	−4724.22	−0.278621
$661$	−2553.97	−0.150284	−0.0751422	−	0.997173i	$-0.523941\pi$
$661$	−2553.97	−0.150284	−0.0751422	+	0.997173i	$0.523941\pi$
$662$	−5618.93	−0.329888
$663$	27563.9	1.61462
$664$	27590.9	1.61255
$665$	−2048.02	−0.119427
$666$	−5541.68	−0.322426
$667$	39538.2	2.29524
$668$	−1092.56	−0.0632818
$669$	−5954.45	−0.344114
$670$	2010.54	0.115931
$671$	−6602.47	−0.379859
$672$	−3818.53	−0.219201
$673$	2232.10	0.127847	0.0639237	−	0.997955i	$-0.479639\pi$
$673$	2232.10	0.127847	0.0639237	+	0.997955i	$0.479639\pi$
$674$	−9863.41	−0.563686
$675$	2736.49	0.156041
$676$	−23747.8	−1.35115
$677$	25956.1	1.47352	0.736761	−	0.676154i	$-0.236354\pi$
$677$	25956.1	1.47352	0.736761	+	0.676154i	$0.236354\pi$
$678$	−4003.05	−0.226749
$679$	−7174.01	−0.405469
$680$	22338.9	1.25979
$681$	333.472	0.0187646
$682$	2753.00	0.154571
$683$	12166.4	0.681600	0.340800	−	0.940136i	$-0.389302\pi$
$683$	12166.4	0.681600	0.340800	+	0.940136i	$0.389302\pi$
$684$	1486.26	0.0830825
$685$	18194.0	1.01483
$686$	−7002.74	−0.389746
$687$	−1320.46	−0.0733316
$688$	−3860.05	−0.213900
$689$	−18966.2	−1.04870
$690$	13617.7	0.751331
$691$	29590.1	1.62903	0.814516	−	0.580141i	$-0.197003\pi$
$691$	29590.1	1.62903	0.814516	+	0.580141i	$0.197003\pi$
$692$	5104.02	0.280384
$693$	−1416.82	−0.0776633
$694$	−1866.55	−0.102094
$695$	−28974.1	−1.58137
$696$	−24628.9	−1.34132
$697$	28464.0	1.54684
$698$	12334.3	0.668855
$699$	−1681.32	−0.0909777
$700$	445.896	0.0240761
$701$	9280.59	0.500033	0.250016	−	0.968242i	$-0.419564\pi$
$701$	9280.59	0.500033	0.250016	+	0.968242i	$0.419564\pi$
$702$	25158.4	1.35263
$703$	−7963.03	−0.427214
$704$	−9025.63	−0.483191
$705$	12422.8	0.663643
$706$	16770.5	0.894002
$707$	6602.49	0.351220
$708$	11010.1	0.584442
$709$	−24897.9	−1.31885	−0.659423	−	0.751772i	$-0.729199\pi$
$709$	−24897.9	−1.31885	−0.659423	+	0.751772i	$0.729199\pi$
$710$	−7429.58	−0.392714
$711$	−1139.89	−0.0601255
$712$	−33385.3	−1.75726
$713$	9660.86	0.507436
$714$	−3383.39	−0.177339
$715$	23547.3	1.23164
$716$	4618.77	0.241078
$717$	222.511	0.0115897
$718$	−23075.7	−1.19941
$719$	−23293.9	−1.20823	−0.604115	−	0.796897i	$-0.706473\pi$
$719$	−23293.9	−1.20823	−0.604115	+	0.796897i	$0.706473\pi$
$720$	1274.51	0.0659695
$721$	6579.97	0.339876
$722$	11273.9	0.581124
$723$	5895.29	0.303248
$724$	−5554.91	−0.285147
$725$	4732.59	0.242433
$726$	−6212.33	−0.317577
$727$	−21488.2	−1.09622	−0.548110	−	0.836406i	$-0.684652\pi$
$727$	−21488.2	−1.09622	−0.548110	+	0.836406i	$0.684652\pi$
$728$	11566.2	0.588836
$729$	19724.7	1.00212
$730$	−12505.1	−0.634022
$731$	32005.2	1.61937
$732$	5115.38	0.258292
$733$	6967.93	0.351114	0.175557	−	0.984469i	$-0.443827\pi$
$733$	6967.93	0.351114	0.175557	+	0.984469i	$0.443827\pi$
$734$	−21458.3	−1.07907
$735$	14825.8	0.744026
$736$	−25605.4	−1.28238
$737$	1998.63	0.0998920
$738$	7585.69	0.378365
$739$	8586.91	0.427435	0.213718	−	0.976895i	$-0.431443\pi$
$739$	8586.91	0.427435	0.213718	+	0.976895i	$0.431443\pi$
$740$	13763.0	0.683700
$741$	10555.5	0.523299
$742$	2328.05	0.115182
$743$	13153.5	0.649468	0.324734	−	0.945805i	$-0.394725\pi$
$743$	13153.5	0.649468	0.324734	+	0.945805i	$0.394725\pi$
$744$	−6017.89	−0.296541
$745$	−32232.3	−1.58510
$746$	−3641.13	−0.178701
$747$	−13051.9	−0.639281
$748$	7870.71	0.384735
$749$	−1456.73	−0.0710649
$750$	−9679.64	−0.471267
$751$	−22130.8	−1.07532	−0.537658	−	0.843163i	$-0.680691\pi$
$751$	−22130.8	−1.07532	−0.537658	+	0.843163i	$0.680691\pi$
$752$	2496.18	0.121045
$753$	17599.1	0.851724
$754$	43510.0	2.10151
$755$	38247.0	1.84364
$756$	3759.50	0.180862
$757$	−11600.7	−0.556983	−0.278491	−	0.960439i	$-0.589834\pi$
$757$	−11600.7	−0.556983	−0.278491	+	0.960439i	$0.589834\pi$
$758$	21688.0	1.03924
$759$	13537.1	0.647383
$760$	8554.57	0.408299
$761$	−13370.6	−0.636903	−0.318452	−	0.947939i	$-0.603163\pi$
$761$	−13370.6	−0.636903	−0.318452	+	0.947939i	$0.603163\pi$
$762$	5556.47	0.264160
$763$	5712.94	0.271064
$764$	−12283.1	−0.581661
$765$	−10567.4	−0.499433
$766$	−27749.8	−1.30893
$767$	−54878.6	−2.58351
$768$	17289.6	0.812349
$769$	−8023.82	−0.376263	−0.188132	−	0.982144i	$-0.560243\pi$
$769$	−8023.82	−0.376263	−0.188132	+	0.982144i	$0.560243\pi$
$770$	−2890.37	−0.135275
$771$	−12717.1	−0.594026
$772$	17529.1	0.817211
$773$	32465.7	1.51062	0.755310	−	0.655367i	$-0.227486\pi$
$773$	32465.7	1.51062	0.755310	+	0.655367i	$0.227486\pi$
$774$	8529.43	0.396104
$775$	1156.37	0.0535976
$776$	29965.9	1.38623
$777$	−5881.27	−0.271544
$778$	−7602.23	−0.350325
$779$	10900.1	0.501332
$780$	−18243.7	−0.837473
$781$	−7385.56	−0.338382
$782$	−22687.6	−1.03748
$783$	39902.0	1.82118
$784$	2979.03	0.135707
$785$	29196.4	1.32747
$786$	17567.9	0.797236
$787$	34046.3	1.54208	0.771042	−	0.636784i	$-0.219736\pi$
$787$	34046.3	1.54208	0.771042	+	0.636784i	$0.219736\pi$
$788$	865.259	0.0391162
$789$	−3092.06	−0.139519
$790$	−2325.41	−0.104727
$791$	2981.60	0.134024
$792$	5918.08	0.265518
$793$	−25497.0	−1.14177
$794$	−4800.66	−0.214571
$795$	−10360.5	−0.462200
$796$	22589.1	1.00584
$797$	22024.5	0.978857	0.489428	−	0.872043i	$-0.337205\pi$
$797$	22024.5	0.978857	0.489428	+	0.872043i	$0.337205\pi$
$798$	−1295.65	−0.0574757
$799$	−20696.8	−0.916395
$800$	−3064.89	−0.135450
$801$	15792.9	0.696648
$802$	−23537.3	−1.03632
$803$	−12431.1	−0.546304
$804$	−1548.47	−0.0679234
$805$	−10142.9	−0.444088
$806$	10631.3	0.464607
$807$	−24353.2	−1.06229
$808$	−27578.7	−1.20076
$809$	−15185.0	−0.659923	−0.329961	−	0.943994i	$-0.607036\pi$
$809$	−15185.0	−0.659923	−0.329961	+	0.943994i	$0.607036\pi$
$810$	6914.09	0.299921
$811$	−11110.2	−0.481050	−0.240525	−	0.970643i	$-0.577320\pi$
$811$	−11110.2	−0.481050	−0.240525	+	0.970643i	$0.577320\pi$
$812$	6501.82	0.280997
$813$	25140.5	1.08452
$814$	−11238.2	−0.483906
$815$	37754.0	1.62266
$816$	3025.51	0.129796
$817$	12256.2	0.524836
$818$	4046.50	0.172961
$819$	−5471.40	−0.233439
$820$	−18839.4	−0.802317
$821$	−27791.5	−1.18140	−0.590701	−	0.806890i	$-0.701149\pi$
$821$	−27791.5	−1.18140	−0.590701	+	0.806890i	$0.701149\pi$
$822$	11510.2	0.488401
$823$	−3444.59	−0.145894	−0.0729470	−	0.997336i	$-0.523240\pi$
$823$	−3444.59	−0.145894	−0.0729470	+	0.997336i	$0.523240\pi$
$824$	−27484.6	−1.16198
$825$	1620.34	0.0683795
$826$	6736.19	0.283755
$827$	−9205.70	−0.387078	−0.193539	−	0.981093i	$-0.561997\pi$
$827$	−9205.70	−0.387078	−0.193539	+	0.981093i	$0.561997\pi$
$828$	7360.77	0.308943
$829$	4298.54	0.180090	0.0900448	−	0.995938i	$-0.471299\pi$
$829$	4298.54	0.180090	0.0900448	+	0.995938i	$0.471299\pi$
$830$	−26626.2	−1.11351
$831$	−2591.20	−0.108168
$832$	−34854.6	−1.45236
$833$	−24700.4	−1.02739
$834$	−18330.1	−0.761055
$835$	2974.78	0.123289
$836$	3014.05	0.124693
$837$	9749.76	0.402630
$838$	12372.5	0.510026
$839$	23093.6	0.950274	0.475137	−	0.879912i	$-0.342398\pi$
$839$	23093.6	0.950274	0.475137	+	0.879912i	$0.342398\pi$
$840$	6318.17	0.259521
$841$	44619.2	1.82948
$842$	−1758.24	−0.0719630
$843$	−17744.2	−0.724960
$844$	−12583.1	−0.513186
$845$	64659.8	2.63239
$846$	−5515.72	−0.224154
$847$	4627.14	0.187710
$848$	−2081.79	−0.0843030
$849$	−16728.8	−0.676245
$850$	−2715.64	−0.109583
$851$	−39437.4	−1.58860
$852$	5722.09	0.230089
$853$	8850.47	0.355257	0.177629	−	0.984098i	$-0.443157\pi$
$853$	8850.47	0.355257	0.177629	+	0.984098i	$0.443157\pi$
$854$	3129.68	0.125405
$855$	−4046.74	−0.161866
$856$	6084.76	0.242959
$857$	−34059.8	−1.35760	−0.678798	−	0.734325i	$-0.737499\pi$
$857$	−34059.8	−1.35760	−0.678798	+	0.734325i	$0.737499\pi$
$858$	14896.9	0.592742
$859$	22811.9	0.906090	0.453045	−	0.891488i	$-0.350338\pi$
$859$	22811.9	0.906090	0.453045	+	0.891488i	$0.350338\pi$
$860$	−21183.2	−0.839933
$861$	8050.53	0.318654
$862$	7432.39	0.293675
$863$	−20426.7	−0.805717	−0.402859	−	0.915262i	$-0.631983\pi$
$863$	−20426.7	−0.805717	−0.402859	+	0.915262i	$0.631983\pi$
$864$	−25841.1	−1.01751
$865$	−13897.1	−0.546260
$866$	−10889.8	−0.427310
$867$	−5516.55	−0.216092
$868$	1588.67	0.0621234
$869$	−2311.63	−0.0902380
$870$	23767.8	0.926212
$871$	7718.18	0.300253
$872$	−23863.0	−0.926723
$873$	−14175.4	−0.549557
$874$	−8688.11	−0.336247
$875$	7209.70	0.278551
$876$	9631.17	0.371469
$877$	−45651.0	−1.75773	−0.878863	−	0.477074i	$-0.841697\pi$
$877$	−45651.0	−1.75773	−0.878863	+	0.477074i	$0.841697\pi$
$878$	30887.8	1.18726
$879$	−33904.7	−1.30100
$880$	2584.63	0.0990089
$881$	24498.2	0.936849	0.468424	−	0.883504i	$-0.344822\pi$
$881$	24498.2	0.936849	0.468424	+	0.883504i	$0.344822\pi$
$882$	−6582.68	−0.251304
$883$	−16631.7	−0.633863	−0.316931	−	0.948448i	$-0.602652\pi$
$883$	−16631.7	−0.633863	−0.316931	+	0.948448i	$0.602652\pi$
$884$	30394.6	1.15643
$885$	−29978.0	−1.13864
$886$	−28290.0	−1.07271
$887$	−6606.84	−0.250097	−0.125048	−	0.992151i	$-0.539909\pi$
$887$	−6606.84	−0.250097	−0.125048	+	0.992151i	$0.539909\pi$
$888$	24566.1	0.928361
$889$	−4138.64	−0.156137
$890$	32218.0	1.21343
$891$	6873.12	0.258427
$892$	−6565.94	−0.246462
$893$	−7925.72	−0.297003
$894$	−20391.4	−0.762851
$895$	−12575.9	−0.469682
$896$	−3391.09	−0.126438
$897$	52276.6	1.94589
$898$	4832.57	0.179582
$899$	16861.6	0.625548
$900$	881.061	0.0326319
$901$	17260.9	0.638230
$902$	15383.4	0.567860
$903$	9052.11	0.333594
$904$	−12454.1	−0.458206
$905$	15124.8	0.555541
$906$	24196.5	0.887279
$907$	−17187.9	−0.629235	−0.314618	−	0.949218i	$-0.601876\pi$
$907$	−17187.9	−0.629235	−0.314618	+	0.949218i	$0.601876\pi$
$908$	367.718	0.0134396
$909$	13046.1	0.476030
$910$	−11161.8	−0.406606
$911$	23791.8	0.865266	0.432633	−	0.901570i	$-0.357585\pi$
$911$	23791.8	0.865266	0.432633	+	0.901570i	$0.357585\pi$
$912$	1158.60	0.0420670
$913$	−26468.5	−0.959450
$914$	−2108.89	−0.0763193
$915$	−13928.0	−0.503220
$916$	−1456.07	−0.0525217
$917$	−13085.2	−0.471221
$918$	−22896.4	−0.823197
$919$	−11632.8	−0.417553	−0.208776	−	0.977963i	$-0.566948\pi$
$919$	−11632.8	−0.417553	−0.208776	+	0.977963i	$0.566948\pi$
$920$	42367.0	1.51826
$921$	−2045.83	−0.0731949
$922$	−31930.4	−1.14053
$923$	−28521.1	−1.01710
$924$	2226.09	0.0792565
$925$	−4720.53	−0.167795
$926$	5725.93	0.203203
$927$	13001.6	0.460656
$928$	−44690.6	−1.58086
$929$	50851.7	1.79590	0.897949	−	0.440099i	$-0.145057\pi$
$929$	50851.7	1.79590	0.897949	+	0.440099i	$0.145057\pi$
$930$	5807.49	0.204769
$931$	−9458.87	−0.332977
$932$	−1853.98	−0.0651602
$933$	−846.932	−0.0297184
$934$	−6877.05	−0.240925
$935$	−21430.2	−0.749563
$936$	22854.1	0.798087
$937$	27333.5	0.952984	0.476492	−	0.879179i	$-0.341908\pi$
$937$	27333.5	0.952984	0.476492	+	0.879179i	$0.341908\pi$
$938$	−947.384	−0.0329778
$939$	13405.7	0.465897
$940$	13698.5	0.475316
$941$	−47354.0	−1.64048	−0.820242	−	0.572017i	$-0.806161\pi$
$941$	−47354.0	−1.64048	−0.820242	+	0.572017i	$0.806161\pi$
$942$	18470.8	0.638864
$943$	53983.5	1.86421
$944$	−6023.65	−0.207683
$945$	−10236.3	−0.352366
$946$	17297.2	0.594483
$947$	−14880.9	−0.510627	−0.255314	−	0.966858i	$-0.582179\pi$
$947$	−14880.9	−0.510627	−0.255314	+	0.966858i	$0.582179\pi$
$948$	1790.98	0.0613589
$949$	−48005.5	−1.64207
$950$	−1039.94	−0.0355159
$951$	−4904.61	−0.167237
$952$	−10526.3	−0.358361
$953$	−15041.0	−0.511254	−0.255627	−	0.966775i	$-0.582282\pi$
$953$	−15041.0	−0.511254	−0.255627	+	0.966775i	$0.582282\pi$
$954$	4600.06	0.156114
$955$	33444.2	1.13323
$956$	245.362	0.00830080
$957$	23627.0	0.798069
$958$	−2692.49	−0.0908041
$959$	−8573.18	−0.288678
$960$	−19039.7	−0.640108
$961$	−25671.0	−0.861703
$962$	−43399.1	−1.45451
$963$	−2878.39	−0.0963187
$964$	6500.70	0.217193
$965$	−47727.9	−1.59214
$966$	−6416.80	−0.213724
$967$	−15266.6	−0.507696	−0.253848	−	0.967244i	$-0.581696\pi$
$967$	−15266.6	−0.507696	−0.253848	+	0.967244i	$0.581696\pi$
$968$	−19327.6	−0.641748
$969$	−9606.42	−0.318475
$970$	−28918.2	−0.957224
$971$	−23665.9	−0.782159	−0.391079	−	0.920357i	$-0.627898\pi$
$971$	−23665.9	−0.782159	−0.391079	+	0.920357i	$0.627898\pi$
$972$	12688.0	0.418692
$973$	13652.8	0.449836
$974$	−28104.3	−0.924558
$975$	6257.34	0.205534
$976$	−2798.63	−0.0917849
$977$	28236.8	0.924641	0.462321	−	0.886713i	$-0.347017\pi$
$977$	28236.8	0.924641	0.462321	+	0.886713i	$0.347017\pi$
$978$	23884.6	0.780926
$979$	32027.2	1.04555
$980$	16348.4	0.532887
$981$	11288.4	0.367391
$982$	−20566.4	−0.668330
$983$	−11989.7	−0.389027	−0.194513	−	0.980900i	$-0.562313\pi$
$983$	−11989.7	−0.389027	−0.194513	+	0.980900i	$0.562313\pi$
$984$	−33627.1	−1.08942
$985$	−2355.91	−0.0762085
$986$	−39598.0	−1.27896
$987$	−5853.72	−0.188780
$988$	11639.5	0.374798
$989$	60699.7	1.95161
$990$	−5711.17	−0.183346
$991$	−16649.6	−0.533695	−0.266847	−	0.963739i	$-0.585982\pi$
$991$	−16649.6	−0.533695	−0.266847	+	0.963739i	$0.585982\pi$
$992$	−10919.8	−0.349501
$993$	−11783.0	−0.376558
$994$	3500.88	0.111712
$995$	−61505.1	−1.95964
$996$	20506.9	0.652395
$997$	12766.7	0.405544	0.202772	−	0.979226i	$-0.435005\pi$
$997$	12766.7	0.405544	0.202772	+	0.979226i	$0.435005\pi$
$998$	15076.4	0.478191
$999$	−39800.3	−1.26049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.b.1.9	✓	27
3.2	odd	2		1773.4.a.d.1.19		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.b.1.9	✓	27	1.1	even	1	trivial
1773.4.a.d.1.19		27	3.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-1.89943 q^{2} -3.98313 q^{3} -4.39218 q^{4} +11.9589 q^{5} +7.56566 q^{6} -5.63514 q^{7} +23.5380 q^{8} -11.1347 q^{9} -22.7151 q^{10} -22.5805 q^{11} +17.4946 q^{12} -87.2000 q^{13} +10.7035 q^{14} -47.6339 q^{15} -9.57134 q^{16} +79.3598 q^{17} +21.1495 q^{18} +30.3904 q^{19} -52.5257 q^{20} +22.4455 q^{21} +42.8900 q^{22} +150.510 q^{23} -93.7551 q^{24} +18.0156 q^{25} +165.630 q^{26} +151.895 q^{27} +24.7506 q^{28} +262.694 q^{29} +90.4771 q^{30} +64.1874 q^{31} -170.124 q^{32} +89.9411 q^{33} -150.738 q^{34} -67.3902 q^{35} +48.9054 q^{36} -262.024 q^{37} -57.7243 q^{38} +347.329 q^{39} +281.489 q^{40} +358.670 q^{41} -42.6336 q^{42} +403.293 q^{43} +99.1776 q^{44} -133.159 q^{45} -285.883 q^{46} -260.797 q^{47} +38.1239 q^{48} -311.245 q^{49} -34.2193 q^{50} -316.100 q^{51} +382.998 q^{52} +217.502 q^{53} -288.514 q^{54} -270.038 q^{55} -132.640 q^{56} -121.049 q^{57} -498.968 q^{58} +629.342 q^{59} +209.217 q^{60} +292.397 q^{61} -121.919 q^{62} +62.7455 q^{63} +399.709 q^{64} -1042.82 q^{65} -170.836 q^{66} -88.5113 q^{67} -348.562 q^{68} -599.502 q^{69} +128.003 q^{70} +327.077 q^{71} -262.088 q^{72} +550.522 q^{73} +497.696 q^{74} -71.7585 q^{75} -133.480 q^{76} +127.244 q^{77} -659.726 q^{78} +102.373 q^{79} -114.463 q^{80} -304.383 q^{81} -681.267 q^{82} +1172.18 q^{83} -98.5847 q^{84} +949.057 q^{85} -766.025 q^{86} -1046.34 q^{87} -531.500 q^{88} -1418.35 q^{89} +252.925 q^{90} +491.384 q^{91} -661.068 q^{92} -255.667 q^{93} +495.364 q^{94} +363.436 q^{95} +677.627 q^{96} +1273.08 q^{97} +591.187 q^{98} +251.426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) \) 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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