LMFDB - Embedded newform 197.4.a.b.1.12

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			1.12
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)

$f(q)$	$=$	\(q-0.598548 q^{2} +9.95206 q^{3} -7.64174 q^{4} -0.534457 q^{5} -5.95679 q^{6} -3.08049 q^{7} +9.36233 q^{8} +72.0436 q^{9} +0.319898 q^{10} -35.1356 q^{11} -76.0511 q^{12} +86.2233 q^{13} +1.84382 q^{14} -5.31895 q^{15} +55.5301 q^{16} +88.0473 q^{17} -43.1215 q^{18} +137.511 q^{19} +4.08418 q^{20} -30.6572 q^{21} +21.0303 q^{22} -55.1511 q^{23} +93.1745 q^{24} -124.714 q^{25} -51.6087 q^{26} +448.277 q^{27} +23.5403 q^{28} -49.5634 q^{29} +3.18365 q^{30} -244.216 q^{31} -108.136 q^{32} -349.671 q^{33} -52.7006 q^{34} +1.64639 q^{35} -550.538 q^{36} -131.348 q^{37} -82.3067 q^{38} +858.099 q^{39} -5.00376 q^{40} +141.107 q^{41} +18.3498 q^{42} +185.847 q^{43} +268.497 q^{44} -38.5042 q^{45} +33.0106 q^{46} +477.535 q^{47} +552.639 q^{48} -333.511 q^{49} +74.6475 q^{50} +876.253 q^{51} -658.896 q^{52} -513.592 q^{53} -268.315 q^{54} +18.7784 q^{55} -28.8405 q^{56} +1368.52 q^{57} +29.6661 q^{58} -468.048 q^{59} +40.6460 q^{60} +101.105 q^{61} +146.175 q^{62} -221.929 q^{63} -379.516 q^{64} -46.0826 q^{65} +209.295 q^{66} -18.8823 q^{67} -672.835 q^{68} -548.867 q^{69} -0.985441 q^{70} -34.0673 q^{71} +674.496 q^{72} -275.756 q^{73} +78.6181 q^{74} -1241.17 q^{75} -1050.82 q^{76} +108.235 q^{77} -513.614 q^{78} +345.569 q^{79} -29.6785 q^{80} +2516.10 q^{81} -84.4594 q^{82} +591.526 q^{83} +234.274 q^{84} -47.0575 q^{85} -111.238 q^{86} -493.258 q^{87} -328.951 q^{88} -643.531 q^{89} +23.0466 q^{90} -265.610 q^{91} +421.450 q^{92} -2430.45 q^{93} -285.827 q^{94} -73.4935 q^{95} -1076.18 q^{96} +1514.58 q^{97} +199.622 q^{98} -2531.29 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.598548	−0.211619	−0.105809	−	0.994386i	$-0.533743\pi$
$2$	−0.598548	−0.211619	−0.105809	+	0.994386i	$0.533743\pi$
$3$	9.95206	1.91528	0.957638	−	0.287975i	$-0.0929821\pi$
$3$	9.95206	1.91528	0.957638	+	0.287975i	$0.0929821\pi$
$4$	−7.64174	−0.955218
$5$	−0.534457	−0.0478033	−0.0239016	−	0.999714i	$-0.507609\pi$
$5$	−0.534457	−0.0478033	−0.0239016	+	0.999714i	$0.507609\pi$
$6$	−5.95679	−0.405308
$7$	−3.08049	−0.166331	−0.0831653	−	0.996536i	$-0.526503\pi$
$7$	−3.08049	−0.166331	−0.0831653	+	0.996536i	$0.526503\pi$
$8$	9.36233	0.413760
$9$	72.0436	2.66828
$10$	0.319898	0.0101161
$11$	−35.1356	−0.963070	−0.481535	−	0.876427i	$-0.659921\pi$
$11$	−35.1356	−0.963070	−0.481535	+	0.876427i	$0.659921\pi$
$12$	−76.0511	−1.82950
$13$	86.2233	1.83954	0.919770	−	0.392457i	$-0.128375\pi$
$13$	86.2233	1.83954	0.919770	+	0.392457i	$0.128375\pi$
$14$	1.84382	0.0351987
$15$	−5.31895	−0.0915564
$16$	55.5301	0.867658
$17$	88.0473	1.25615	0.628077	−	0.778151i	$-0.283842\pi$
$17$	88.0473	1.25615	0.628077	+	0.778151i	$0.283842\pi$
$18$	−43.1215	−0.564658
$19$	137.511	1.66037	0.830187	−	0.557485i	$-0.188233\pi$
$19$	137.511	1.66037	0.830187	+	0.557485i	$0.188233\pi$
$20$	4.08418	0.0456625
$21$	−30.6572	−0.318569
$22$	21.0303	0.203804
$23$	−55.1511	−0.499991	−0.249996	−	0.968247i	$-0.580429\pi$
$23$	−55.1511	−0.499991	−0.249996	+	0.968247i	$0.580429\pi$
$24$	93.1745	0.792465
$25$	−124.714	−0.997715
$26$	−51.6087	−0.389281
$27$	448.277	3.19522
$28$	23.5403	0.158882
$29$	−49.5634	−0.317369	−0.158684	−	0.987329i	$-0.550725\pi$
$29$	−49.5634	−0.317369	−0.158684	+	0.987329i	$0.550725\pi$
$30$	3.18365	0.0193750
$31$	−244.216	−1.41492	−0.707459	−	0.706755i	$-0.750158\pi$
$31$	−244.216	−1.41492	−0.707459	+	0.706755i	$0.750158\pi$
$32$	−108.136	−0.597373
$33$	−349.671	−1.84454
$34$	−52.7006	−0.265826
$35$	1.64639	0.00795115
$36$	−550.538	−2.54879
$37$	−131.348	−0.583608	−0.291804	−	0.956478i	$-0.594255\pi$
$37$	−131.348	−0.583608	−0.291804	+	0.956478i	$0.594255\pi$
$38$	−82.3067	−0.351366
$39$	858.099	3.52323
$40$	−5.00376	−0.0197791
$41$	141.107	0.537494	0.268747	−	0.963211i	$-0.413390\pi$
$41$	141.107	0.537494	0.268747	+	0.963211i	$0.413390\pi$
$42$	18.3498	0.0674151
$43$	185.847	0.659103	0.329552	−	0.944138i	$-0.393102\pi$
$43$	185.847	0.659103	0.329552	+	0.944138i	$0.393102\pi$
$44$	268.497	0.919941
$45$	−38.5042	−0.127553
$46$	33.0106	0.105807
$47$	477.535	1.48203	0.741017	−	0.671487i	$-0.234344\pi$
$47$	477.535	1.48203	0.741017	+	0.671487i	$0.234344\pi$
$48$	552.639	1.66180
$49$	−333.511	−0.972334
$50$	74.6475	0.211135
$51$	876.253	2.40588
$52$	−658.896	−1.75716
$53$	−513.592	−1.33108	−0.665540	−	0.746362i	$-0.731799\pi$
$53$	−513.592	−1.33108	−0.665540	+	0.746362i	$0.731799\pi$
$54$	−268.315	−0.676168
$55$	18.7784	0.0460379
$56$	−28.8405	−0.0688210
$57$	1368.52	3.18007
$58$	29.6661	0.0671611
$59$	−468.048	−1.03279	−0.516396	−	0.856350i	$-0.672727\pi$
$59$	−468.048	−1.03279	−0.516396	+	0.856350i	$0.672727\pi$
$60$	40.6460	0.0874563
$61$	101.105	0.212217	0.106108	−	0.994355i	$-0.466161\pi$
$61$	101.105	0.212217	0.106108	+	0.994355i	$0.466161\pi$
$62$	146.175	0.299423
$63$	−221.929	−0.443817
$64$	−379.516	−0.741243
$65$	−46.0826	−0.0879361
$66$	209.295	0.390340
$67$	−18.8823	−0.0344304	−0.0172152	−	0.999852i	$-0.505480\pi$
$67$	−18.8823	−0.0344304	−0.0172152	+	0.999852i	$0.505480\pi$
$68$	−672.835	−1.19990
$69$	−548.867	−0.957621
$70$	−0.985441	−0.00168261
$71$	−34.0673	−0.0569444	−0.0284722	−	0.999595i	$-0.509064\pi$
$71$	−34.0673	−0.0569444	−0.0284722	+	0.999595i	$0.509064\pi$
$72$	674.496	1.10403
$73$	−275.756	−0.442120	−0.221060	−	0.975260i	$-0.570952\pi$
$73$	−275.756	−0.442120	−0.221060	+	0.975260i	$0.570952\pi$
$74$	78.6181	0.123502
$75$	−1241.17	−1.91090
$76$	−1050.82	−1.58602
$77$	108.235	0.160188
$78$	−513.614	−0.745580
$79$	345.569	0.492146	0.246073	−	0.969251i	$-0.420860\pi$
$79$	345.569	0.492146	0.246073	+	0.969251i	$0.420860\pi$
$80$	−29.6785	−0.0414769
$81$	2516.10	3.45144
$82$	−84.4594	−0.113744
$83$	591.526	0.782270	0.391135	−	0.920333i	$-0.372083\pi$
$83$	591.526	0.782270	0.391135	+	0.920333i	$0.372083\pi$
$84$	234.274	0.304303
$85$	−47.0575	−0.0600483
$86$	−111.238	−0.139479
$87$	−493.258	−0.607848
$88$	−328.951	−0.398480
$89$	−643.531	−0.766451	−0.383225	−	0.923655i	$-0.625187\pi$
$89$	−643.531	−0.766451	−0.383225	+	0.923655i	$0.625187\pi$
$90$	23.0466	0.0269925
$91$	−265.610	−0.305972
$92$	421.450	0.477600
$93$	−2430.45	−2.70996
$94$	−285.827	−0.313626
$95$	−73.4935	−0.0793713
$96$	−1076.18	−1.14413
$97$	1514.58	1.58538	0.792691	−	0.609623i	$-0.208679\pi$
$97$	1514.58	1.58538	0.792691	+	0.609623i	$0.208679\pi$
$98$	199.622	0.205764
$99$	−2531.29	−2.56974
$100$	953.035	0.953035
$101$	−1754.23	−1.72824	−0.864122	−	0.503282i	$-0.832126\pi$
$101$	−1754.23	−1.72824	−0.864122	+	0.503282i	$0.832126\pi$
$102$	−524.479	−0.509129
$103$	−36.4364	−0.0348562	−0.0174281	−	0.999848i	$-0.505548\pi$
$103$	−36.4364	−0.0348562	−0.0174281	+	0.999848i	$0.505548\pi$
$104$	807.251	0.761129
$105$	16.3850	0.0152286
$106$	307.409	0.281681
$107$	−1826.82	−1.65052	−0.825258	−	0.564755i	$-0.808971\pi$
$107$	−1826.82	−1.65052	−0.825258	+	0.564755i	$0.808971\pi$
$108$	−3425.61	−3.05213
$109$	442.436	0.388786	0.194393	−	0.980924i	$-0.437726\pi$
$109$	442.436	0.388786	0.194393	+	0.980924i	$0.437726\pi$
$110$	−11.2398	−0.00974247
$111$	−1307.18	−1.11777
$112$	−171.060	−0.144318
$113$	−1955.40	−1.62786	−0.813931	−	0.580961i	$-0.802677\pi$
$113$	−1955.40	−1.62786	−0.813931	+	0.580961i	$0.802677\pi$
$114$	−819.122	−0.672963
$115$	29.4759	0.0239012
$116$	378.750	0.303156
$117$	6211.83	4.90841
$118$	280.149	0.218558
$119$	−271.229	−0.208937
$120$	−49.7978	−0.0378824
$121$	−96.4929	−0.0724966
$122$	−60.5165	−0.0449091
$123$	1404.31	1.02945
$124$	1866.23	1.35155
$125$	133.462	0.0954973
$126$	132.835	0.0939199
$127$	−2279.19	−1.59248	−0.796241	−	0.604979i	$-0.793181\pi$
$127$	−2279.19	−1.59248	−0.796241	+	0.604979i	$0.793181\pi$
$128$	1092.25	0.754234
$129$	1849.56	1.26236
$130$	27.5826	0.0186089
$131$	1104.61	0.736718	0.368359	−	0.929684i	$-0.379920\pi$
$131$	1104.61	0.736718	0.368359	+	0.929684i	$0.379920\pi$
$132$	2672.10	1.76194
$133$	−423.600	−0.276171
$134$	11.3020	0.00728612
$135$	−239.584	−0.152742
$136$	824.328	0.519747
$137$	65.6712	0.0409538	0.0204769	−	0.999790i	$-0.493482\pi$
$137$	65.6712	0.0409538	0.0204769	+	0.999790i	$0.493482\pi$
$138$	328.523	0.202650
$139$	2667.49	1.62772	0.813862	−	0.581058i	$-0.197361\pi$
$139$	2667.49	1.62772	0.813862	+	0.581058i	$0.197361\pi$
$140$	−12.5813	−0.00759508
$141$	4752.45	2.83850
$142$	20.3909	0.0120505
$143$	−3029.50	−1.77161
$144$	4000.59	2.31516
$145$	26.4895	0.0151713
$146$	165.053	0.0935608
$147$	−3319.12	−1.86229
$148$	1003.73	0.557472
$149$	−1084.08	−0.596047	−0.298023	−	0.954559i	$-0.596327\pi$
$149$	−1084.08	−0.596047	−0.298023	+	0.954559i	$0.596327\pi$
$150$	742.897	0.404382
$151$	1170.10	0.630603	0.315301	−	0.948992i	$-0.397894\pi$
$151$	1170.10	0.630603	0.315301	+	0.948992i	$0.397894\pi$
$152$	1287.42	0.686997
$153$	6343.25	3.35177
$154$	−64.7836	−0.0338988
$155$	130.523	0.0676377
$156$	−6557.37	−3.36545
$157$	−2484.51	−1.26297	−0.631483	−	0.775390i	$-0.717553\pi$
$157$	−2484.51	−1.26297	−0.631483	+	0.775390i	$0.717553\pi$
$158$	−206.840	−0.104147
$159$	−5111.30	−2.54939
$160$	57.7941	0.0285564
$161$	169.892	0.0831638
$162$	−1506.01	−0.730389
$163$	184.801	0.0888018	0.0444009	−	0.999014i	$-0.485862\pi$
$163$	184.801	0.0888018	0.0444009	+	0.999014i	$0.485862\pi$
$164$	−1078.30	−0.513423
$165$	186.884	0.0881752
$166$	−354.056	−0.165543
$167$	−1553.65	−0.719911	−0.359955	−	0.932970i	$-0.617208\pi$
$167$	−1553.65	−0.719911	−0.359955	+	0.932970i	$0.617208\pi$
$168$	−287.023	−0.131811
$169$	5237.45	2.38391
$170$	28.1662	0.0127073
$171$	9906.76	4.43034
$172$	−1420.20	−0.629587
$173$	−1523.45	−0.669513	−0.334757	−	0.942305i	$-0.608654\pi$
$173$	−1523.45	−0.669513	−0.334757	+	0.942305i	$0.608654\pi$
$174$	295.238	0.128632
$175$	384.181	0.165951
$176$	−1951.08	−0.835615
$177$	−4658.05	−1.97808
$178$	385.184	0.162195
$179$	2895.32	1.20898	0.604488	−	0.796614i	$-0.293378\pi$
$179$	2895.32	1.20898	0.604488	+	0.796614i	$0.293378\pi$
$180$	294.239	0.121840
$181$	2937.41	1.20628	0.603139	−	0.797636i	$-0.293917\pi$
$181$	2937.41	1.20628	0.603139	+	0.797636i	$0.293917\pi$
$182$	158.980	0.0647494
$183$	1006.21	0.406454
$184$	−516.343	−0.206877
$185$	70.1998	0.0278984
$186$	1454.74	0.573477
$187$	−3093.59	−1.20976
$188$	−3649.20	−1.41566
$189$	−1380.91	−0.531463
$190$	43.9894	0.0167965
$191$	3340.10	1.26534	0.632672	−	0.774420i	$-0.281958\pi$
$191$	3340.10	1.26534	0.632672	+	0.774420i	$0.281958\pi$
$192$	−3776.97	−1.41968
$193$	−1068.81	−0.398626	−0.199313	−	0.979936i	$-0.563871\pi$
$193$	−1068.81	−0.398626	−0.199313	+	0.979936i	$0.563871\pi$
$194$	−906.547	−0.335496
$195$	−458.617	−0.168422
$196$	2548.60	0.928791
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	1515.10	0.543805
$199$	−515.231	−0.183536	−0.0917682	−	0.995780i	$-0.529252\pi$
$199$	−515.231	−0.183536	−0.0917682	+	0.995780i	$0.529252\pi$
$200$	−1167.62	−0.412815
$201$	−187.918	−0.0659438
$202$	1049.99	0.365729
$203$	152.679	0.0527881
$204$	−6696.10	−2.29814
$205$	−75.4157	−0.0256940
$206$	21.8089	0.00737621
$207$	−3973.28	−1.33412
$208$	4787.99	1.59609
$209$	−4831.51	−1.59906
$210$	−9.80718	−0.00322266
$211$	−4140.77	−1.35101	−0.675503	−	0.737357i	$-0.736073\pi$
$211$	−4140.77	−1.35101	−0.675503	+	0.737357i	$0.736073\pi$
$212$	3924.74	1.27147
$213$	−339.040	−0.109064
$214$	1093.44	0.349280
$215$	−99.3274	−0.0315073
$216$	4196.91	1.32205
$217$	752.303	0.235344
$218$	−264.819	−0.0822744
$219$	−2744.34	−0.846781
$220$	−143.500	−0.0439762
$221$	7591.73	2.31075
$222$	782.412	0.236541
$223$	3217.18	0.966090	0.483045	−	0.875596i	$-0.339531\pi$
$223$	3217.18	0.966090	0.483045	+	0.875596i	$0.339531\pi$
$224$	333.112	0.0993615
$225$	−8984.87	−2.66218
$226$	1170.40	0.344486
$227$	3949.08	1.15467	0.577334	−	0.816508i	$-0.304093\pi$
$227$	3949.08	1.15467	0.577334	+	0.816508i	$0.304093\pi$
$228$	−10457.8	−3.03766
$229$	−1792.04	−0.517123	−0.258561	−	0.965995i	$-0.583248\pi$
$229$	−1792.04	−0.517123	−0.258561	+	0.965995i	$0.583248\pi$
$230$	−17.6427	−0.00505794
$231$	1077.16	0.306804
$232$	−464.029	−0.131315
$233$	−912.067	−0.256444	−0.128222	−	0.991745i	$-0.540927\pi$
$233$	−912.067	−0.256444	−0.128222	+	0.991745i	$0.540927\pi$
$234$	−3718.08	−1.03871
$235$	−255.222	−0.0708461
$236$	3576.70	0.986541
$237$	3439.13	0.942596
$238$	162.343	0.0442149
$239$	3455.11	0.935116	0.467558	−	0.883962i	$-0.345134\pi$
$239$	3455.11	0.935116	0.467558	+	0.883962i	$0.345134\pi$
$240$	−295.362	−0.0794397
$241$	2165.17	0.578716	0.289358	−	0.957221i	$-0.406558\pi$
$241$	2165.17	0.578716	0.289358	+	0.957221i	$0.406558\pi$
$242$	57.7556	0.0153416
$243$	12936.9	3.41524
$244$	−772.622	−0.202713
$245$	178.247	0.0464808
$246$	−840.546	−0.217851
$247$	11856.6	3.05433
$248$	−2286.43	−0.585437
$249$	5886.90	1.49826
$250$	−79.8831	−0.0202090
$251$	−6754.75	−1.69863	−0.849315	−	0.527886i	$-0.822985\pi$
$251$	−6754.75	−1.69863	−0.849315	+	0.527886i	$0.822985\pi$
$252$	1695.93	0.423942
$253$	1937.76	0.481526
$254$	1364.20	0.336999
$255$	−468.319	−0.115009
$256$	2382.37	0.581633
$257$	−3565.47	−0.865401	−0.432701	−	0.901538i	$-0.642439\pi$
$257$	−3565.47	−0.865401	−0.432701	+	0.901538i	$0.642439\pi$
$258$	−1107.05	−0.267140
$259$	404.616	0.0970718
$260$	352.151	0.0839981
$261$	−3570.72	−0.846828
$262$	−661.160	−0.155903
$263$	−5952.80	−1.39569	−0.697843	−	0.716251i	$-0.745857\pi$
$263$	−5952.80	−1.39569	−0.697843	+	0.716251i	$0.745857\pi$
$264$	−3273.74	−0.763199
$265$	274.493	0.0636300
$266$	253.545	0.0584430
$267$	−6404.46	−1.46796
$268$	144.294	0.0328886
$269$	2023.05	0.458541	0.229271	−	0.973363i	$-0.426366\pi$
$269$	2023.05	0.458541	0.229271	+	0.973363i	$0.426366\pi$
$270$	143.403	0.0323230
$271$	167.280	0.0374964	0.0187482	−	0.999824i	$-0.494032\pi$
$271$	167.280	0.0374964	0.0187482	+	0.999824i	$0.494032\pi$
$272$	4889.28	1.08991
$273$	−2643.36	−0.586021
$274$	−39.3073	−0.00866658
$275$	4381.91	0.960869
$276$	4194.30	0.914736
$277$	−562.808	−0.122079	−0.0610395	−	0.998135i	$-0.519442\pi$
$277$	−562.808	−0.122079	−0.0610395	+	0.998135i	$0.519442\pi$
$278$	−1596.62	−0.344457
$279$	−17594.2	−3.77540
$280$	15.4140	0.00328987
$281$	−1165.11	−0.247346	−0.123673	−	0.992323i	$-0.539467\pi$
$281$	−1165.11	−0.247346	−0.123673	+	0.992323i	$0.539467\pi$
$282$	−2844.57	−0.600680
$283$	−152.604	−0.0320543	−0.0160272	−	0.999872i	$-0.505102\pi$
$283$	−152.604	−0.0320543	−0.0160272	+	0.999872i	$0.505102\pi$
$284$	260.334	0.0543943
$285$	−731.412	−0.152018
$286$	1813.30	0.374905
$287$	−434.679	−0.0894017
$288$	−7790.51	−1.59396
$289$	2839.34	0.577923
$290$	−15.8552	−0.00321052
$291$	15073.2	3.03644
$292$	2107.25	0.422321
$293$	−6876.82	−1.37115	−0.685577	−	0.728000i	$-0.740450\pi$
$293$	−6876.82	−1.37115	−0.685577	+	0.728000i	$0.740450\pi$
$294$	1986.65	0.394095
$295$	250.152	0.0493708
$296$	−1229.72	−0.241474
$297$	−15750.4	−3.07722
$298$	648.871	0.126135
$299$	−4755.31	−0.919754
$300$	9484.66	1.82532
$301$	−572.500	−0.109629
$302$	−700.358	−0.133447
$303$	−17458.2	−3.31007
$304$	7635.98	1.44064
$305$	−54.0365	−0.0101447
$306$	−3796.74	−0.709297
$307$	981.671	0.182498	0.0912491	−	0.995828i	$-0.470914\pi$
$307$	981.671	0.182498	0.0912491	+	0.995828i	$0.470914\pi$
$308$	−827.101	−0.153014
$309$	−362.617	−0.0667592
$310$	−78.1241	−0.0143134
$311$	−214.578	−0.0391240	−0.0195620	−	0.999809i	$-0.506227\pi$
$311$	−214.578	−0.0391240	−0.0195620	+	0.999809i	$0.506227\pi$
$312$	8033.81	1.45777
$313$	2224.97	0.401799	0.200899	−	0.979612i	$-0.435614\pi$
$313$	2224.97	0.401799	0.200899	+	0.979612i	$0.435614\pi$
$314$	1487.10	0.267267
$315$	118.612	0.0212159
$316$	−2640.75	−0.470107
$317$	−3814.30	−0.675812	−0.337906	−	0.941180i	$-0.609719\pi$
$317$	−3814.30	−0.675812	−0.337906	+	0.941180i	$0.609719\pi$
$318$	3059.36	0.539498
$319$	1741.44	0.305648
$320$	202.835	0.0354338
$321$	−18180.6	−3.16119
$322$	−101.689	−0.0175990
$323$	12107.5	2.08569
$324$	−19227.4	−3.29688
$325$	−10753.3	−1.83534
$326$	−110.612	−0.0187921
$327$	4403.15	0.744632
$328$	1321.09	0.222394
$329$	−1471.04	−0.246508
$330$	−111.859	−0.0186595
$331$	8442.98	1.40202	0.701009	−	0.713152i	$-0.252733\pi$
$331$	8442.98	1.40202	0.701009	+	0.713152i	$0.252733\pi$
$332$	−4520.29	−0.747238
$333$	−9462.78	−1.55723
$334$	929.934	0.152347
$335$	10.0918	0.00164589
$336$	−1702.40	−0.276409
$337$	2711.58	0.438306	0.219153	−	0.975690i	$-0.429671\pi$
$337$	2711.58	0.438306	0.219153	+	0.975690i	$0.429671\pi$
$338$	−3134.86	−0.504480
$339$	−19460.3	−3.11780
$340$	359.601	0.0573592
$341$	8580.65	1.36266
$342$	−5929.67	−0.937543
$343$	2083.98	0.328060
$344$	1739.96	0.272711
$345$	293.346	0.0457774
$346$	911.858	0.141681
$347$	−562.584	−0.0870348	−0.0435174	−	0.999053i	$-0.513856\pi$
$347$	−562.584	−0.0870348	−0.0435174	+	0.999053i	$0.513856\pi$
$348$	3769.35	0.580627
$349$	−3443.95	−0.528225	−0.264112	−	0.964492i	$-0.585079\pi$
$349$	−3443.95	−0.528225	−0.264112	+	0.964492i	$0.585079\pi$
$350$	−229.951	−0.0351182
$351$	38651.9	5.87773
$352$	3799.42	0.575312
$353$	4646.04	0.700521	0.350260	−	0.936652i	$-0.386093\pi$
$353$	4646.04	0.700521	0.350260	+	0.936652i	$0.386093\pi$
$354$	2788.06	0.418599
$355$	18.2075	0.00272213
$356$	4917.70	0.732127
$357$	−2699.29	−0.400172
$358$	−1732.99	−0.255842
$359$	2353.36	0.345977	0.172988	−	0.984924i	$-0.444658\pi$
$359$	2353.36	0.345977	0.172988	+	0.984924i	$0.444658\pi$
$360$	−360.489	−0.0527762
$361$	12050.2	1.75684
$362$	−1758.18	−0.255271
$363$	−960.304	−0.138851
$364$	2029.72	0.292270
$365$	147.379	0.0211348
$366$	−602.264	−0.0860132
$367$	231.534	0.0329319	0.0164659	−	0.999864i	$-0.494758\pi$
$367$	231.534	0.0329319	0.0164659	+	0.999864i	$0.494758\pi$
$368$	−3062.55	−0.433821
$369$	10165.9	1.43418
$370$	−42.0180	−0.00590381
$371$	1582.11	0.221400
$372$	18572.9	2.58860
$373$	2604.20	0.361502	0.180751	−	0.983529i	$-0.442147\pi$
$373$	2604.20	0.361502	0.180751	+	0.983529i	$0.442147\pi$
$374$	1851.66	0.256009
$375$	1328.22	0.182904
$376$	4470.84	0.613207
$377$	−4273.52	−0.583812
$378$	826.541	0.112467
$379$	−2575.36	−0.349043	−0.174521	−	0.984653i	$-0.555838\pi$
$379$	−2575.36	−0.349043	−0.174521	+	0.984653i	$0.555838\pi$
$380$	561.618	0.0758169
$381$	−22682.6	−3.05004
$382$	−1999.21	−0.267770
$383$	−12833.6	−1.71218	−0.856091	−	0.516824i	$-0.827114\pi$
$383$	−12833.6	−1.71218	−0.856091	+	0.516824i	$0.827114\pi$
$384$	10870.1	1.44457
$385$	−57.8467	−0.00765751
$386$	639.736	0.0843568
$387$	13389.1	1.75867
$388$	−11574.0	−1.51439
$389$	−8409.26	−1.09606	−0.548029	−	0.836459i	$-0.684622\pi$
$389$	−8409.26	−1.09606	−0.548029	+	0.836459i	$0.684622\pi$
$390$	274.504	0.0356412
$391$	−4855.91	−0.628066
$392$	−3122.44	−0.402313
$393$	10993.1	1.41102
$394$	117.914	0.0150772
$395$	−184.692	−0.0235262
$396$	19343.5	2.45466
$397$	−2614.58	−0.330535	−0.165267	−	0.986249i	$-0.552849\pi$
$397$	−2614.58	−0.330535	−0.165267	+	0.986249i	$0.552849\pi$
$398$	308.390	0.0388397
$399$	−4215.69	−0.528944
$400$	−6925.40	−0.865675
$401$	6318.83	0.786901	0.393450	−	0.919346i	$-0.371281\pi$
$401$	6318.83	0.786901	0.393450	+	0.919346i	$0.371281\pi$
$402$	112.478	0.0139549
$403$	−21057.1	−2.60280
$404$	13405.4	1.65085
$405$	−1344.75	−0.164990
$406$	−91.3859	−0.0111709
$407$	4614.99	0.562055
$408$	8203.77	0.995458
$409$	2384.33	0.288258	0.144129	−	0.989559i	$-0.453962\pi$
$409$	2384.33	0.288258	0.144129	+	0.989559i	$0.453962\pi$
$410$	45.1399	0.00543732
$411$	653.564	0.0784378
$412$	278.437	0.0332952
$413$	1441.82	0.171785
$414$	2378.20	0.282324
$415$	−316.145	−0.0373951
$416$	−9323.84	−1.09889
$417$	26547.0	3.11754
$418$	2891.89	0.338390
$419$	−3462.81	−0.403745	−0.201873	−	0.979412i	$-0.564703\pi$
$419$	−3462.81	−0.403745	−0.201873	+	0.979412i	$0.564703\pi$
$420$	−125.210	−0.0145467
$421$	−6339.21	−0.733858	−0.366929	−	0.930249i	$-0.619591\pi$
$421$	−6339.21	−0.733858	−0.366929	+	0.930249i	$0.619591\pi$
$422$	2478.45	0.285898
$423$	34403.3	3.95448
$424$	−4808.42	−0.550749
$425$	−10980.8	−1.25328
$426$	202.932	0.0230800
$427$	−311.454	−0.0352982
$428$	13960.1	1.57660
$429$	−30149.8	−3.39311
$430$	59.4522	0.00666753
$431$	−3161.87	−0.353369	−0.176684	−	0.984268i	$-0.556537\pi$
$431$	−3161.87	−0.353369	−0.176684	+	0.984268i	$0.556537\pi$
$432$	24892.9	2.77236
$433$	−3745.03	−0.415646	−0.207823	−	0.978166i	$-0.566638\pi$
$433$	−3745.03	−0.415646	−0.207823	+	0.978166i	$0.566638\pi$
$434$	−450.289	−0.0498032
$435$	263.625	0.0290571
$436$	−3380.98	−0.371375
$437$	−7583.86	−0.830172
$438$	1642.62	0.179195
$439$	−2990.15	−0.325085	−0.162542	−	0.986702i	$-0.551969\pi$
$439$	−2990.15	−0.325085	−0.162542	+	0.986702i	$0.551969\pi$
$440$	175.810	0.0190487
$441$	−24027.3	−2.59446
$442$	−4544.01	−0.488997
$443$	−2197.21	−0.235649	−0.117825	−	0.993034i	$-0.537592\pi$
$443$	−2197.21	−0.235649	−0.117825	+	0.993034i	$0.537592\pi$
$444$	9989.16	1.06771
$445$	343.939	0.0366389
$446$	−1925.63	−0.204443
$447$	−10788.8	−1.14159
$448$	1169.10	0.123291
$449$	8828.86	0.927973	0.463986	−	0.885842i	$-0.346419\pi$
$449$	8828.86	0.927973	0.463986	+	0.885842i	$0.346419\pi$
$450$	5377.87	0.563368
$451$	−4957.88	−0.517644
$452$	14942.6	1.55496
$453$	11644.9	1.20778
$454$	−2363.71	−0.244349
$455$	141.957	0.0146265
$456$	12812.5	1.31579
$457$	17804.2	1.82241	0.911207	−	0.411949i	$-0.135152\pi$
$457$	17804.2	1.82241	0.911207	+	0.411949i	$0.135152\pi$
$458$	1072.62	0.109433
$459$	39469.6	4.01369
$460$	−225.247	−0.0228309
$461$	1650.53	0.166753	0.0833763	−	0.996518i	$-0.473430\pi$
$461$	1650.53	0.166753	0.0833763	+	0.996518i	$0.473430\pi$
$462$	−644.730	−0.0649255
$463$	548.328	0.0550388	0.0275194	−	0.999621i	$-0.491239\pi$
$463$	548.328	0.0550388	0.0275194	+	0.999621i	$0.491239\pi$
$464$	−2752.26	−0.275367
$465$	1298.97	0.129545
$466$	545.916	0.0542684
$467$	13151.1	1.30313	0.651563	−	0.758595i	$-0.274114\pi$
$467$	13151.1	1.30313	0.651563	+	0.758595i	$0.274114\pi$
$468$	−47469.2	−4.68860
$469$	58.1667	0.00572684
$470$	152.762	0.0149923
$471$	−24726.0	−2.41893
$472$	−4382.02	−0.427328
$473$	−6529.85	−0.634763
$474$	−2058.48	−0.199471
$475$	−17149.6	−1.65658
$476$	2072.66	0.199580
$477$	−37001.0	−3.55170
$478$	−2068.05	−0.197888
$479$	2196.66	0.209536	0.104768	−	0.994497i	$-0.466590\pi$
$479$	2196.66	0.209536	0.104768	+	0.994497i	$0.466590\pi$
$480$	575.170	0.0546934
$481$	−11325.3	−1.07357
$482$	−1295.96	−0.122467
$483$	1690.78	0.159282
$484$	737.374	0.0692500
$485$	−809.477	−0.0757865
$486$	−7743.37	−0.722729
$487$	18031.8	1.67782	0.838912	−	0.544268i	$-0.183192\pi$
$487$	18031.8	1.67782	0.838912	+	0.544268i	$0.183192\pi$
$488$	946.583	0.0878070
$489$	1839.15	0.170080
$490$	−106.689	−0.00983619
$491$	−4008.04	−0.368392	−0.184196	−	0.982890i	$-0.558968\pi$
$491$	−4008.04	−0.368392	−0.184196	+	0.982890i	$0.558968\pi$
$492$	−10731.4	−0.983347
$493$	−4363.92	−0.398664
$494$	−7096.75	−0.646352
$495$	1352.87	0.122842
$496$	−13561.3	−1.22766
$497$	104.944	0.00947159
$498$	−3523.59	−0.317060
$499$	5973.29	0.535874	0.267937	−	0.963436i	$-0.413658\pi$
$499$	5973.29	0.535874	0.267937	+	0.963436i	$0.413658\pi$
$500$	−1019.88	−0.0912207
$501$	−15462.0	−1.37883
$502$	4043.04	0.359462
$503$	−6611.26	−0.586047	−0.293024	−	0.956105i	$-0.594661\pi$
$503$	−6611.26	−0.586047	−0.293024	+	0.956105i	$0.594661\pi$
$504$	−2077.78	−0.183634
$505$	937.562	0.0826158
$506$	−1159.84	−0.101900
$507$	52123.4	4.56584
$508$	17417.0	1.52117
$509$	−17754.1	−1.54605	−0.773023	−	0.634378i	$-0.781256\pi$
$509$	−17754.1	−1.54605	−0.773023	+	0.634378i	$0.781256\pi$
$510$	280.312	0.0243380
$511$	849.461	0.0735381
$512$	−10163.9	−0.877318
$513$	61642.8	5.30526
$514$	2134.11	0.183135
$515$	19.4737	0.00166624
$516$	−14133.9	−1.20583
$517$	−16778.4	−1.42730
$518$	−242.182	−0.0205422
$519$	−15161.5	−1.28230
$520$	−431.441	−0.0363845
$521$	4929.14	0.414491	0.207245	−	0.978289i	$-0.433550\pi$
$521$	4929.14	0.414491	0.207245	+	0.978289i	$0.433550\pi$
$522$	2137.25	0.179205
$523$	18950.7	1.58443	0.792215	−	0.610242i	$-0.208928\pi$
$523$	18950.7	1.58443	0.792215	+	0.610242i	$0.208928\pi$
$524$	−8441.12	−0.703726
$525$	3823.39	0.317841
$526$	3563.04	0.295353
$527$	−21502.5	−1.77735
$528$	−19417.3	−1.60043
$529$	−9125.36	−0.750009
$530$	−164.297	−0.0134653
$531$	−33719.9	−2.75578
$532$	3237.04	0.263804
$533$	12166.7	0.988742
$534$	3833.38	0.310649
$535$	976.356	0.0789001
$536$	−176.782	−0.0142460
$537$	28814.4	2.31552
$538$	−1210.89	−0.0970358
$539$	11718.1	0.936426
$540$	1830.84	0.145902
$541$	8341.79	0.662924	0.331462	−	0.943469i	$-0.392458\pi$
$541$	8341.79	0.662924	0.331462	+	0.943469i	$0.392458\pi$
$542$	−100.125	−0.00793493
$543$	29233.3	2.31035
$544$	−9521.09	−0.750393
$545$	−236.463	−0.0185852
$546$	1582.18	0.124013
$547$	11591.3	0.906049	0.453024	−	0.891498i	$-0.350345\pi$
$547$	11591.3	0.906049	0.453024	+	0.891498i	$0.350345\pi$
$548$	−501.842	−0.0391198
$549$	7284.00	0.566254
$550$	−2622.78	−0.203338
$551$	−6815.49	−0.526951
$552$	−5138.67	−0.396226
$553$	−1064.52	−0.0818590
$554$	336.868	0.0258342
$555$	698.633	0.0534330
$556$	−20384.3	−1.55483
$557$	4363.42	0.331928	0.165964	−	0.986132i	$-0.446926\pi$
$557$	4363.42	0.331928	0.165964	+	0.986132i	$0.446926\pi$
$558$	10531.0	0.798944
$559$	16024.4	1.21245
$560$	91.4241	0.00689888
$561$	−30787.6	−2.31703
$562$	697.371	0.0523431
$563$	−13184.8	−0.986985	−0.493492	−	0.869750i	$-0.664280\pi$
$563$	−13184.8	−0.986985	−0.493492	+	0.869750i	$0.664280\pi$
$564$	−36317.0	−2.71139
$565$	1045.08	0.0778171
$566$	91.3409	0.00678329
$567$	−7750.81	−0.574080
$568$	−318.950	−0.0235613
$569$	16407.0	1.20881	0.604407	−	0.796676i	$-0.293410\pi$
$569$	16407.0	1.20881	0.604407	+	0.796676i	$0.293410\pi$
$570$	437.785	0.0321698
$571$	8707.17	0.638150	0.319075	−	0.947729i	$-0.396628\pi$
$571$	8707.17	0.638150	0.319075	+	0.947729i	$0.396628\pi$
$572$	23150.7	1.69227
$573$	33240.8	2.42348
$574$	260.176	0.0189191
$575$	6878.13	0.498849
$576$	−27341.7	−1.97784
$577$	−10765.6	−0.776740	−0.388370	−	0.921504i	$-0.626962\pi$
$577$	−10765.6	−0.776740	−0.388370	+	0.921504i	$0.626962\pi$
$578$	−1699.48	−0.122299
$579$	−10636.9	−0.763479
$580$	−202.426	−0.0144918
$581$	−1822.19	−0.130115
$582$	−9022.02	−0.642568
$583$	18045.3	1.28192
$584$	−2581.71	−0.182932
$585$	−3319.96	−0.234638
$586$	4116.11	0.290162
$587$	−3571.44	−0.251123	−0.125561	−	0.992086i	$-0.540073\pi$
$587$	−3571.44	−0.251123	−0.125561	+	0.992086i	$0.540073\pi$
$588$	25363.8	1.77889
$589$	−33582.3	−2.34929
$590$	−149.728	−0.0104478
$591$	−1960.56	−0.136458
$592$	−7293.77	−0.506372
$593$	−19136.6	−1.32520	−0.662602	−	0.748971i	$-0.730548\pi$
$593$	−19136.6	−1.32520	−0.662602	+	0.748971i	$0.730548\pi$
$594$	9427.40	0.651197
$595$	144.960	0.00998787
$596$	8284.23	0.569354
$597$	−5127.61	−0.351523
$598$	2846.28	0.194637
$599$	−21227.1	−1.44794	−0.723971	−	0.689831i	$-0.757685\pi$
$599$	−21227.1	−1.44794	−0.723971	+	0.689831i	$0.757685\pi$
$600$	−11620.2	−0.790654
$601$	2571.93	0.174561	0.0872804	−	0.996184i	$-0.472182\pi$
$601$	2571.93	0.174561	0.0872804	+	0.996184i	$0.472182\pi$
$602$	342.669	0.0231996
$603$	−1360.35	−0.0918701
$604$	−8941.57	−0.602363
$605$	51.5713	0.00346557
$606$	10449.6	0.700471
$607$	18694.6	1.25007	0.625034	−	0.780598i	$-0.285085\pi$
$607$	18694.6	1.25007	0.625034	+	0.780598i	$0.285085\pi$
$608$	−14869.9	−0.991863
$609$	1519.47	0.101104
$610$	32.3434	0.00214680
$611$	41174.6	2.72626
$612$	−48473.4	−3.20167
$613$	−22253.5	−1.46625	−0.733125	−	0.680094i	$-0.761939\pi$
$613$	−22253.5	−1.46625	−0.733125	+	0.680094i	$0.761939\pi$
$614$	−587.577	−0.0386200
$615$	−750.542	−0.0492110
$616$	1013.33	0.0662795
$617$	−21486.5	−1.40197	−0.700985	−	0.713176i	$-0.747256\pi$
$617$	−21486.5	−1.40197	−0.700985	+	0.713176i	$0.747256\pi$
$618$	217.044	0.0141275
$619$	2374.32	0.154171	0.0770857	−	0.997024i	$-0.475439\pi$
$619$	2374.32	0.154171	0.0770857	+	0.997024i	$0.475439\pi$
$620$	−997.421	−0.0646087
$621$	−24722.9	−1.59758
$622$	128.435	0.00827937
$623$	1982.39	0.127484
$624$	47650.4	3.05696
$625$	15518.0	0.993150
$626$	−1331.75	−0.0850281
$627$	−48083.5	−3.06263
$628$	18986.0	1.20641
$629$	−11564.8	−0.733101
$630$	−70.9947	−0.00448968
$631$	14272.2	0.900424	0.450212	−	0.892922i	$-0.351348\pi$
$631$	14272.2	0.900424	0.450212	+	0.892922i	$0.351348\pi$
$632$	3235.33	0.203631
$633$	−41209.2	−2.58755
$634$	2283.04	0.143014
$635$	1218.13	0.0761259
$636$	39059.2	2.43522
$637$	−28756.4	−1.78865
$638$	−1042.33	−0.0646808
$639$	−2454.33	−0.151944
$640$	−583.759	−0.0360548
$641$	26925.4	1.65911	0.829555	−	0.558425i	$-0.188594\pi$
$641$	26925.4	1.65911	0.829555	+	0.558425i	$0.188594\pi$
$642$	10882.0	0.668968
$643$	20130.9	1.23466	0.617330	−	0.786704i	$-0.288214\pi$
$643$	20130.9	1.23466	0.617330	+	0.786704i	$0.288214\pi$
$644$	−1298.27	−0.0794396
$645$	−988.512	−0.0603452
$646$	−7246.89	−0.441370
$647$	14275.6	0.867437	0.433719	−	0.901048i	$-0.357201\pi$
$647$	14275.6	0.867437	0.433719	+	0.901048i	$0.357201\pi$
$648$	23556.6	1.42807
$649$	16445.1	0.994650
$650$	6436.35	0.388391
$651$	7486.97	0.450749
$652$	−1412.20	−0.0848251
$653$	−1285.23	−0.0770216	−0.0385108	−	0.999258i	$-0.512261\pi$
$653$	−1285.23	−0.0770216	−0.0385108	+	0.999258i	$0.512261\pi$
$654$	−2635.50	−0.157578
$655$	−590.365	−0.0352175
$656$	7835.70	0.466361
$657$	−19866.4	−1.17970
$658$	880.487	0.0521656
$659$	−22123.4	−1.30775	−0.653873	−	0.756605i	$-0.726857\pi$
$659$	−22123.4	−1.30775	−0.653873	+	0.756605i	$0.726857\pi$
$660$	−1428.12	−0.0842265
$661$	−18671.9	−1.09872	−0.549359	−	0.835586i	$-0.685128\pi$
$661$	−18671.9	−1.09872	−0.549359	+	0.835586i	$0.685128\pi$
$662$	−5053.53	−0.296693
$663$	75553.4	4.42572
$664$	5538.06	0.323672
$665$	226.396	0.0132019
$666$	5663.93	0.329539
$667$	2733.47	0.158681
$668$	11872.6	0.687671
$669$	32017.5	1.85033
$670$	−6.04041	−0.000348300 0
$671$	−3552.40	−0.204380
$672$	3315.15	0.190305
$673$	−24212.2	−1.38680	−0.693398	−	0.720555i	$-0.743887\pi$
$673$	−24212.2	−1.38680	−0.693398	+	0.720555i	$0.743887\pi$
$674$	−1623.01	−0.0927537
$675$	−55906.5	−3.18792
$676$	−40023.2	−2.27715
$677$	8902.32	0.505383	0.252691	−	0.967547i	$-0.418684\pi$
$677$	8902.32	0.505383	0.252691	+	0.967547i	$0.418684\pi$
$678$	11647.9	0.659786
$679$	−4665.64	−0.263698
$680$	−440.568	−0.0248456
$681$	39301.5	2.21151
$682$	−5135.93	−0.288365
$683$	2932.45	0.164286	0.0821428	−	0.996621i	$-0.473824\pi$
$683$	2932.45	0.164286	0.0821428	+	0.996621i	$0.473824\pi$
$684$	−75704.9	−4.23194
$685$	−35.0984	−0.00195772
$686$	−1247.36	−0.0694235
$687$	−17834.5	−0.990433
$688$	10320.1	0.571876
$689$	−44283.6	−2.44858
$690$	−175.581	−0.00968735
$691$	−28385.2	−1.56270	−0.781350	−	0.624094i	$-0.785468\pi$
$691$	−28385.2	−1.56270	−0.781350	+	0.624094i	$0.785468\pi$
$692$	11641.8	0.639531
$693$	7797.61	0.427427
$694$	336.733	0.0184182
$695$	−1425.66	−0.0778105
$696$	−4618.04	−0.251504
$697$	12424.1	0.675175
$698$	2061.37	0.111782
$699$	−9076.95	−0.491161
$700$	−2935.81	−0.158519
$701$	−9151.54	−0.493080	−0.246540	−	0.969133i	$-0.579294\pi$
$701$	−9151.54	−0.493080	−0.246540	+	0.969133i	$0.579294\pi$
$702$	−23135.0	−1.24384
$703$	−18061.8	−0.969007
$704$	13334.5	0.713869
$705$	−2539.98	−0.135690
$706$	−2780.88	−0.148243
$707$	5403.89	0.287460
$708$	35595.6	1.88950
$709$	11857.8	0.628109	0.314055	−	0.949405i	$-0.398312\pi$
$709$	11857.8	0.628109	0.314055	+	0.949405i	$0.398312\pi$
$710$	−10.8981	−0.000576053 0
$711$	24896.0	1.31318
$712$	−6024.95	−0.317127
$713$	13468.8	0.707446
$714$	1615.65	0.0846838
$715$	1619.14	0.0846886
$716$	−22125.3	−1.15483
$717$	34385.5	1.79100
$718$	−1408.60	−0.0732151
$719$	−2846.20	−0.147629	−0.0738147	−	0.997272i	$-0.523517\pi$
$719$	−2846.20	−0.147629	−0.0738147	+	0.997272i	$0.523517\pi$
$720$	−2138.14	−0.110672
$721$	112.242	0.00579765
$722$	−7212.61	−0.371781
$723$	21547.9	1.10840
$724$	−22446.9	−1.15226
$725$	6181.26	0.316643
$726$	574.788	0.0293834
$727$	−29185.9	−1.48892	−0.744460	−	0.667667i	$-0.767293\pi$
$727$	−29185.9	−1.48892	−0.744460	+	0.667667i	$0.767293\pi$
$728$	−2486.72	−0.126599
$729$	60814.4	3.08969
$730$	−88.2136	−0.00447251
$731$	16363.4	0.827935
$732$	−7689.18	−0.388252
$733$	10162.5	0.512089	0.256044	−	0.966665i	$-0.417581\pi$
$733$	10162.5	0.512089	0.256044	+	0.966665i	$0.417581\pi$
$734$	−138.584	−0.00696900
$735$	1773.93	0.0890234
$736$	5963.82	0.298681
$737$	663.440	0.0331589
$738$	−6084.76	−0.303500
$739$	10937.9	0.544460	0.272230	−	0.962232i	$-0.412239\pi$
$739$	10937.9	0.544460	0.272230	+	0.962232i	$0.412239\pi$
$740$	−536.449	−0.0266490
$741$	117998.	5.84988
$742$	−946.970	−0.0468523
$743$	5742.52	0.283543	0.141772	−	0.989899i	$-0.454720\pi$
$743$	5742.52	0.283543	0.141772	+	0.989899i	$0.454720\pi$
$744$	−22754.7	−1.12127
$745$	579.392	0.0284930
$746$	−1558.74	−0.0765005
$747$	42615.6	2.08732
$748$	23640.4	1.15559
$749$	5627.49	0.274532
$750$	−795.002	−0.0387058
$751$	−18281.5	−0.888284	−0.444142	−	0.895957i	$-0.646491\pi$
$751$	−18281.5	−0.888284	−0.444142	+	0.895957i	$0.646491\pi$
$752$	26517.6	1.28590
$753$	−67223.7	−3.25335
$754$	2557.90	0.123546
$755$	−625.366	−0.0301449
$756$	10552.6	0.507662
$757$	9220.13	0.442684	0.221342	−	0.975196i	$-0.428956\pi$
$757$	9220.13	0.442684	0.221342	+	0.975196i	$0.428956\pi$
$758$	1541.47	0.0738640
$759$	19284.7	0.922256
$760$	−688.071	−0.0328407
$761$	−19148.7	−0.912144	−0.456072	−	0.889943i	$-0.650744\pi$
$761$	−19148.7	−0.912144	−0.456072	+	0.889943i	$0.650744\pi$
$762$	13576.6	0.645446
$763$	−1362.92	−0.0646670
$764$	−25524.1	−1.20868
$765$	−3390.19	−0.160226
$766$	7681.52	0.362330
$767$	−40356.7	−1.89986
$768$	23709.5	1.11399
$769$	20136.0	0.944244	0.472122	−	0.881533i	$-0.343488\pi$
$769$	20136.0	0.944244	0.472122	+	0.881533i	$0.343488\pi$
$770$	34.6240	0.00162047
$771$	−35483.8	−1.65748
$772$	8167.60	0.380775
$773$	15783.5	0.734402	0.367201	−	0.930142i	$-0.380316\pi$
$773$	15783.5	0.734402	0.367201	+	0.930142i	$0.380316\pi$
$774$	−8014.02	−0.372168
$775$	30457.2	1.41168
$776$	14180.0	0.655969
$777$	4026.76	0.185919
$778$	5033.35	0.231946
$779$	19403.7	0.892441
$780$	3504.63	0.160879
$781$	1196.98	0.0548414
$782$	2906.49	0.132910
$783$	−22218.1	−1.01406
$784$	−18519.9	−0.843654
$785$	1327.86	0.0603739
$786$	−6579.91	−0.298598
$787$	−11867.8	−0.537535	−0.268767	−	0.963205i	$-0.586616\pi$
$787$	−11867.8	−0.537535	−0.268767	+	0.963205i	$0.586616\pi$
$788$	1505.42	0.0680564
$789$	−59242.7	−2.67312
$790$	110.547	0.00497858
$791$	6023.58	0.270763
$792$	−23698.8	−1.06326
$793$	8717.64	0.390382
$794$	1564.95	0.0699473
$795$	2731.77	0.121869
$796$	3937.26	0.175317
$797$	28888.8	1.28393	0.641965	−	0.766734i	$-0.278119\pi$
$797$	28888.8	1.28393	0.641965	+	0.766734i	$0.278119\pi$
$798$	2523.29	0.111934
$799$	42045.7	1.86166
$800$	13486.1	0.596008
$801$	−46362.3	−2.04511
$802$	−3782.12	−0.166523
$803$	9688.82	0.425792
$804$	1436.02	0.0629907
$805$	−90.8000	−0.00397550
$806$	12603.7	0.550800
$807$	20133.5	0.878233
$808$	−16423.7	−0.715079
$809$	35055.2	1.52345	0.761727	−	0.647898i	$-0.224352\pi$
$809$	35055.2	1.52345	0.761727	+	0.647898i	$0.224352\pi$
$810$	804.896	0.0349150
$811$	34699.2	1.50241	0.751205	−	0.660069i	$-0.229473\pi$
$811$	34699.2	1.50241	0.751205	+	0.660069i	$0.229473\pi$
$812$	−1166.74	−0.0504241
$813$	1664.78	0.0718159
$814$	−2762.29	−0.118941
$815$	−98.7679	−0.00424502
$816$	48658.4	2.08748
$817$	25556.0	1.09436
$818$	−1427.13	−0.0610007
$819$	−19135.5	−0.816419
$820$	576.307	0.0245433
$821$	−34944.7	−1.48548	−0.742739	−	0.669581i	$-0.766474\pi$
$821$	−34944.7	−1.48548	−0.742739	+	0.669581i	$0.766474\pi$
$822$	−391.189	−0.0165989
$823$	−3741.75	−0.158480	−0.0792401	−	0.996856i	$-0.525249\pi$
$823$	−3741.75	−0.158480	−0.0792401	+	0.996856i	$0.525249\pi$
$824$	−341.130	−0.0144221
$825$	43609.0	1.84033
$826$	−862.996	−0.0363529
$827$	38429.9	1.61589	0.807944	−	0.589259i	$-0.200580\pi$
$827$	38429.9	1.61589	0.807944	+	0.589259i	$0.200580\pi$
$828$	30362.8	1.27437
$829$	−22835.1	−0.956688	−0.478344	−	0.878172i	$-0.658763\pi$
$829$	−22835.1	−0.956688	−0.478344	+	0.878172i	$0.658763\pi$
$830$	189.228	0.00791349
$831$	−5601.10	−0.233815
$832$	−32723.1	−1.36355
$833$	−29364.7	−1.22140
$834$	−15889.7	−0.659729
$835$	830.359	0.0344141
$836$	36921.2	1.52745
$837$	−109476.	−4.52097
$838$	2072.66	0.0854400
$839$	2527.92	0.104021	0.0520104	−	0.998647i	$-0.483437\pi$
$839$	2527.92	0.104021	0.0520104	+	0.998647i	$0.483437\pi$
$840$	153.401	0.00630101
$841$	−21932.5	−0.899277
$842$	3794.32	0.155298
$843$	−11595.2	−0.473737
$844$	31642.7	1.29050
$845$	−2799.19	−0.113959
$846$	−20592.0	−0.836842
$847$	297.245	0.0120584
$848$	−28519.8	−1.15492
$849$	−1518.73	−0.0613929
$850$	6572.52	0.265218
$851$	7243.98	0.291799
$852$	2590.86	0.104180
$853$	−39237.0	−1.57497	−0.787485	−	0.616334i	$-0.788617\pi$
$853$	−39237.0	−1.57497	−0.787485	+	0.616334i	$0.788617\pi$
$854$	186.420	0.00746975
$855$	−5294.74	−0.211785
$856$	−17103.3	−0.682919
$857$	21820.2	0.869735	0.434868	−	0.900494i	$-0.356795\pi$
$857$	21820.2	0.869735	0.434868	+	0.900494i	$0.356795\pi$
$858$	18046.1	0.718046
$859$	−13053.3	−0.518476	−0.259238	−	0.965813i	$-0.583471\pi$
$859$	−13053.3	−0.518476	−0.259238	+	0.965813i	$0.583471\pi$
$860$	759.034	0.0300963
$861$	−4325.95	−0.171229
$862$	1892.53	0.0747794
$863$	35049.0	1.38248	0.691241	−	0.722625i	$-0.257064\pi$
$863$	35049.0	1.38248	0.691241	+	0.722625i	$0.257064\pi$
$864$	−48474.9	−1.90874
$865$	814.218	0.0320049
$866$	2241.58	0.0879585
$867$	28257.2	1.10688
$868$	−5748.91	−0.224805
$869$	−12141.8	−0.473971
$870$	−157.792	−0.00614903
$871$	−1628.09	−0.0633362
$872$	4142.23	0.160864
$873$	109116.	4.23025
$874$	4539.30	0.175680
$875$	−411.127	−0.0158841
$876$	20971.5	0.808860
$877$	25601.9	0.985763	0.492882	−	0.870096i	$-0.335944\pi$
$877$	25601.9	0.985763	0.492882	+	0.870096i	$0.335944\pi$
$878$	1789.75	0.0687940
$879$	−68438.6	−2.62614
$880$	1042.77	0.0399451
$881$	26675.2	1.02010	0.510052	−	0.860144i	$-0.329626\pi$
$881$	26675.2	1.02010	0.510052	+	0.860144i	$0.329626\pi$
$882$	14381.5	0.549036
$883$	−26427.6	−1.00720	−0.503601	−	0.863936i	$-0.667992\pi$
$883$	−26427.6	−1.00720	−0.503601	+	0.863936i	$0.667992\pi$
$884$	−58014.0	−2.20727
$885$	2489.53	0.0945587
$886$	1315.14	0.0498678
$887$	−30546.5	−1.15631	−0.578157	−	0.815925i	$-0.696228\pi$
$887$	−30546.5	−1.15631	−0.578157	+	0.815925i	$0.696228\pi$
$888$	−12238.3	−0.462489
$889$	7021.01	0.264879
$890$	−205.864	−0.00775347
$891$	−88404.6	−3.32398
$892$	−24584.8	−0.922826
$893$	65666.1	2.46073
$894$	6457.61	0.241582
$895$	−1547.43	−0.0577930
$896$	−3364.65	−0.125452
$897$	−47325.1	−1.76158
$898$	−5284.50	−0.196376
$899$	12104.2	0.449050
$900$	68660.0	2.54296
$901$	−45220.4	−1.67204
$902$	2967.53	0.109543
$903$	−5697.56	−0.209970
$904$	−18307.1	−0.673545
$905$	−1569.92	−0.0576640
$906$	−6970.01	−0.255588
$907$	22864.0	0.837029	0.418514	−	0.908210i	$-0.362551\pi$
$907$	22864.0	0.837029	0.418514	+	0.908210i	$0.362551\pi$
$908$	−30177.9	−1.10296
$909$	−126381.	−4.61144
$910$	−84.9680	−0.00309523
$911$	28263.9	1.02791	0.513954	−	0.857818i	$-0.328180\pi$
$911$	28263.9	1.02791	0.513954	+	0.857818i	$0.328180\pi$
$912$	75993.8	2.75922
$913$	−20783.6	−0.753380
$914$	−10656.6	−0.385657
$915$	−537.775	−0.0194298
$916$	13694.3	0.493965
$917$	−3402.73	−0.122539
$918$	−23624.4	−0.849371
$919$	13110.3	0.470587	0.235294	−	0.971924i	$-0.424395\pi$
$919$	13110.3	0.470587	0.235294	+	0.971924i	$0.424395\pi$
$920$	275.963	0.00988937
$921$	9769.65	0.349534
$922$	−987.923	−0.0352880
$923$	−2937.40	−0.104751
$924$	−8231.36	−0.293065
$925$	16381.0	0.582274
$926$	−328.200	−0.0116472
$927$	−2625.01	−0.0930060
$928$	5359.59	0.189587
$929$	9009.14	0.318170	0.159085	−	0.987265i	$-0.449146\pi$
$929$	9009.14	0.318170	0.159085	+	0.987265i	$0.449146\pi$
$930$	−777.496	−0.0274141
$931$	−45861.3	−1.61444
$932$	6969.78	0.244960
$933$	−2135.49	−0.0749333
$934$	−7871.55	−0.275766
$935$	1653.39	0.0578307
$936$	58157.2	2.03091
$937$	−30597.9	−1.06680	−0.533400	−	0.845863i	$-0.679086\pi$
$937$	−30597.9	−1.06680	−0.533400	+	0.845863i	$0.679086\pi$
$938$	−34.8155	−0.00121191
$939$	22143.1	0.769555
$940$	1950.34	0.0676734
$941$	39597.4	1.37177	0.685887	−	0.727708i	$-0.259414\pi$
$941$	39597.4	1.37177	0.685887	+	0.727708i	$0.259414\pi$
$942$	14799.7	0.511890
$943$	−7782.21	−0.268742
$944$	−25990.8	−0.896110
$945$	738.037	0.0254056
$946$	3908.43	0.134328
$947$	−34858.0	−1.19613	−0.598063	−	0.801449i	$-0.704063\pi$
$947$	−34858.0	−1.19613	−0.598063	+	0.801449i	$0.704063\pi$
$948$	−26280.9	−0.900384
$949$	−23776.5	−0.813297
$950$	10264.8	0.350563
$951$	−37960.2	−1.29437
$952$	−2539.33	−0.0864498
$953$	1142.84	0.0388459	0.0194230	−	0.999811i	$-0.493817\pi$
$953$	1142.84	0.0388459	0.0194230	+	0.999811i	$0.493817\pi$
$954$	22146.9	0.751605
$955$	−1785.14	−0.0604876
$956$	−26403.1	−0.893239
$957$	17330.9	0.585400
$958$	−1314.81	−0.0443418
$959$	−202.299	−0.00681187
$960$	2018.63	0.0678656
$961$	29850.3	1.00199
$962$	6778.71	0.227187
$963$	−131611.	−4.40404
$964$	−16545.6	−0.552800
$965$	571.235	0.0190556
$966$	−1012.01	−0.0337070
$967$	48698.7	1.61949	0.809744	−	0.586784i	$-0.199606\pi$
$967$	48698.7	1.61949	0.809744	+	0.586784i	$0.199606\pi$
$968$	−903.399	−0.0299962
$969$	120494.	3.99466
$970$	484.510	0.0160378
$971$	25949.0	0.857614	0.428807	−	0.903396i	$-0.358934\pi$
$971$	25949.0	0.857614	0.428807	+	0.903396i	$0.358934\pi$
$972$	−98860.6	−3.26230
$973$	−8217.17	−0.270740
$974$	−10792.9	−0.355059
$975$	−107017.	−3.51518
$976$	5614.40	0.184132
$977$	26914.5	0.881344	0.440672	−	0.897668i	$-0.354740\pi$
$977$	26914.5	0.881344	0.440672	+	0.897668i	$0.354740\pi$
$978$	−1100.82	−0.0359921
$979$	22610.8	0.738146
$980$	−1362.12	−0.0443992
$981$	31874.7	1.03739
$982$	2399.01	0.0779586
$983$	46122.3	1.49651	0.748256	−	0.663410i	$-0.230891\pi$
$983$	46122.3	1.49651	0.748256	+	0.663410i	$0.230891\pi$
$984$	13147.6	0.425945
$985$	105.288	0.00340584
$986$	2612.02	0.0843647
$987$	−14639.9	−0.472130
$988$	−90605.2	−2.91755
$989$	−10249.7	−0.329546
$990$	−809.755	−0.0259957
$991$	−49216.6	−1.57761	−0.788807	−	0.614640i	$-0.789301\pi$
$991$	−49216.6	−1.57761	−0.788807	+	0.614640i	$0.789301\pi$
$992$	26408.5	0.845233
$993$	84025.1	2.68525
$994$	−62.8140	−0.00200437
$995$	275.369	0.00877364
$996$	−44986.2	−1.43117
$997$	25414.3	0.807302	0.403651	−	0.914913i	$-0.367741\pi$
$997$	25414.3	0.807302	0.403651	+	0.914913i	$0.367741\pi$
$998$	−3575.30	−0.113401
$999$	−58880.2	−1.86475

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.b.1.12	✓	27
3.2	odd	2		1773.4.a.d.1.16		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.b.1.12	✓	27	1.1	even	1	trivial
1773.4.a.d.1.16		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)

\(f(q)\)	\(=\)	\(q-0.598548 q^{2} +9.95206 q^{3} -7.64174 q^{4} -0.534457 q^{5} -5.95679 q^{6} -3.08049 q^{7} +9.36233 q^{8} +72.0436 q^{9} +0.319898 q^{10} -35.1356 q^{11} -76.0511 q^{12} +86.2233 q^{13} +1.84382 q^{14} -5.31895 q^{15} +55.5301 q^{16} +88.0473 q^{17} -43.1215 q^{18} +137.511 q^{19} +4.08418 q^{20} -30.6572 q^{21} +21.0303 q^{22} -55.1511 q^{23} +93.1745 q^{24} -124.714 q^{25} -51.6087 q^{26} +448.277 q^{27} +23.5403 q^{28} -49.5634 q^{29} +3.18365 q^{30} -244.216 q^{31} -108.136 q^{32} -349.671 q^{33} -52.7006 q^{34} +1.64639 q^{35} -550.538 q^{36} -131.348 q^{37} -82.3067 q^{38} +858.099 q^{39} -5.00376 q^{40} +141.107 q^{41} +18.3498 q^{42} +185.847 q^{43} +268.497 q^{44} -38.5042 q^{45} +33.0106 q^{46} +477.535 q^{47} +552.639 q^{48} -333.511 q^{49} +74.6475 q^{50} +876.253 q^{51} -658.896 q^{52} -513.592 q^{53} -268.315 q^{54} +18.7784 q^{55} -28.8405 q^{56} +1368.52 q^{57} +29.6661 q^{58} -468.048 q^{59} +40.6460 q^{60} +101.105 q^{61} +146.175 q^{62} -221.929 q^{63} -379.516 q^{64} -46.0826 q^{65} +209.295 q^{66} -18.8823 q^{67} -672.835 q^{68} -548.867 q^{69} -0.985441 q^{70} -34.0673 q^{71} +674.496 q^{72} -275.756 q^{73} +78.6181 q^{74} -1241.17 q^{75} -1050.82 q^{76} +108.235 q^{77} -513.614 q^{78} +345.569 q^{79} -29.6785 q^{80} +2516.10 q^{81} -84.4594 q^{82} +591.526 q^{83} +234.274 q^{84} -47.0575 q^{85} -111.238 q^{86} -493.258 q^{87} -328.951 q^{88} -643.531 q^{89} +23.0466 q^{90} -265.610 q^{91} +421.450 q^{92} -2430.45 q^{93} -285.827 q^{94} -73.4935 q^{95} -1076.18 q^{96} +1514.58 q^{97} +199.622 q^{98} -2531.29 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) \) 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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