LMFDB - Embedded newform 197.4.a.a.1.14

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:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	\(q+1.28043 q^{2} +5.48907 q^{3} -6.36049 q^{4} +3.36905 q^{5} +7.02839 q^{6} -33.5513 q^{7} -18.3876 q^{8} +3.12992 q^{9} +4.31384 q^{10} -19.7791 q^{11} -34.9132 q^{12} -51.2996 q^{13} -42.9601 q^{14} +18.4930 q^{15} +27.3398 q^{16} -16.5725 q^{17} +4.00765 q^{18} +95.3714 q^{19} -21.4288 q^{20} -184.165 q^{21} -25.3258 q^{22} +104.997 q^{23} -100.931 q^{24} -113.650 q^{25} -65.6857 q^{26} -131.025 q^{27} +213.403 q^{28} +50.7371 q^{29} +23.6790 q^{30} +166.945 q^{31} +182.108 q^{32} -108.569 q^{33} -21.2200 q^{34} -113.036 q^{35} -19.9079 q^{36} -108.942 q^{37} +122.117 q^{38} -281.588 q^{39} -61.9489 q^{40} -164.171 q^{41} -235.811 q^{42} +58.6448 q^{43} +125.805 q^{44} +10.5449 q^{45} +134.441 q^{46} -562.799 q^{47} +150.070 q^{48} +782.688 q^{49} -145.521 q^{50} -90.9679 q^{51} +326.291 q^{52} -326.990 q^{53} -167.768 q^{54} -66.6367 q^{55} +616.929 q^{56} +523.501 q^{57} +64.9654 q^{58} -564.112 q^{59} -117.624 q^{60} +561.982 q^{61} +213.762 q^{62} -105.013 q^{63} +14.4584 q^{64} -172.831 q^{65} -139.015 q^{66} -656.686 q^{67} +105.410 q^{68} +576.336 q^{69} -144.735 q^{70} +128.411 q^{71} -57.5519 q^{72} -941.956 q^{73} -139.493 q^{74} -623.830 q^{75} -606.609 q^{76} +663.613 q^{77} -360.554 q^{78} +976.312 q^{79} +92.1092 q^{80} -803.712 q^{81} -210.209 q^{82} -999.531 q^{83} +1171.38 q^{84} -55.8337 q^{85} +75.0907 q^{86} +278.500 q^{87} +363.691 q^{88} +1309.14 q^{89} +13.5020 q^{90} +1721.17 q^{91} -667.832 q^{92} +916.373 q^{93} -720.626 q^{94} +321.311 q^{95} +999.604 q^{96} +330.844 q^{97} +1002.18 q^{98} -61.9070 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) $ 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * 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 $

$2$	1.28043	0.452701	0.226351	−	0.974046i	$-0.427320\pi$
$2$	1.28043	0.452701	0.226351	+	0.974046i	$0.427320\pi$
$3$	5.48907	1.05637	0.528186	−	0.849129i	$-0.322872\pi$
$3$	5.48907	1.05637	0.528186	+	0.849129i	$0.322872\pi$
$4$	−6.36049	−0.795062
$5$	3.36905	0.301337	0.150668	−	0.988584i	$-0.451857\pi$
$5$	3.36905	0.301337	0.150668	+	0.988584i	$0.451857\pi$
$6$	7.02839	0.478221
$7$	−33.5513	−1.81160	−0.905799	−	0.423707i	$-0.860728\pi$
$7$	−33.5513	−1.81160	−0.905799	+	0.423707i	$0.860728\pi$
$8$	−18.3876	−0.812627
$9$	3.12992	0.115923
$10$	4.31384	0.136416
$11$	−19.7791	−0.542147	−0.271074	−	0.962559i	$-0.587379\pi$
$11$	−19.7791	−0.542147	−0.271074	+	0.962559i	$0.587379\pi$
$12$	−34.9132	−0.839881
$13$	−51.2996	−1.09446	−0.547229	−	0.836983i	$-0.684317\pi$
$13$	−51.2996	−1.09446	−0.547229	+	0.836983i	$0.684317\pi$
$14$	−42.9601	−0.820113
$15$	18.4930	0.318324
$16$	27.3398	0.427185
$17$	−16.5725	−0.236437	−0.118219	−	0.992988i	$-0.537718\pi$
$17$	−16.5725	−0.236437	−0.118219	+	0.992988i	$0.537718\pi$
$18$	4.00765	0.0524785
$19$	95.3714	1.15156	0.575782	−	0.817604i	$-0.304698\pi$
$19$	95.3714	1.15156	0.575782	+	0.817604i	$0.304698\pi$
$20$	−21.4288	−0.239581
$21$	−184.165	−1.91372
$22$	−25.3258	−0.245431
$23$	104.997	0.951885	0.475943	−	0.879476i	$-0.342107\pi$
$23$	104.997	0.951885	0.475943	+	0.879476i	$0.342107\pi$
$24$	−100.931	−0.858436
$25$	−113.650	−0.909196
$26$	−65.6857	−0.495463
$27$	−131.025	−0.933915
$28$	213.403	1.44033
$29$	50.7371	0.324884	0.162442	−	0.986718i	$-0.448063\pi$
$29$	50.7371	0.324884	0.162442	+	0.986718i	$0.448063\pi$
$30$	23.6790	0.144106
$31$	166.945	0.967232	0.483616	−	0.875280i	$-0.339323\pi$
$31$	166.945	0.967232	0.483616	+	0.875280i	$0.339323\pi$
$32$	182.108	1.00601
$33$	−108.569	−0.572709
$34$	−21.2200	−0.107035
$35$	−113.036	−0.545901
$36$	−19.9079	−0.0921660
$37$	−108.942	−0.484054	−0.242027	−	0.970270i	$-0.577812\pi$
$37$	−108.942	−0.484054	−0.242027	+	0.970270i	$0.577812\pi$
$38$	122.117	0.521314
$39$	−281.588	−1.15616
$40$	−61.9489	−0.244874
$41$	−164.171	−0.625345	−0.312673	−	0.949861i	$-0.601224\pi$
$41$	−164.171	−0.625345	−0.312673	+	0.949861i	$0.601224\pi$
$42$	−235.811	−0.866345
$43$	58.6448	0.207982	0.103991	−	0.994578i	$-0.466839\pi$
$43$	58.6448	0.207982	0.103991	+	0.994578i	$0.466839\pi$
$44$	125.805	0.431040
$45$	10.5449	0.0349319
$46$	134.441	0.430920
$47$	−562.799	−1.74665	−0.873327	−	0.487135i	$-0.838042\pi$
$47$	−562.799	−1.74665	−0.873327	+	0.487135i	$0.838042\pi$
$48$	150.070	0.451266
$49$	782.688	2.28189
$50$	−145.521	−0.411594
$51$	−90.9679	−0.249766
$52$	326.291	0.870162
$53$	−326.990	−0.847462	−0.423731	−	0.905788i	$-0.639280\pi$
$53$	−326.990	−0.847462	−0.423731	+	0.905788i	$0.639280\pi$
$54$	−167.768	−0.422784
$55$	−66.6367	−0.163369
$56$	616.929	1.47215
$57$	523.501	1.21648
$58$	64.9654	0.147075
$59$	−564.112	−1.24476	−0.622382	−	0.782714i	$-0.713835\pi$
$59$	−564.112	−1.24476	−0.622382	+	0.782714i	$0.713835\pi$
$60$	−117.624	−0.253087
$61$	561.982	1.17958	0.589790	−	0.807557i	$-0.299211\pi$
$61$	561.982	1.17958	0.589790	+	0.807557i	$0.299211\pi$
$62$	213.762	0.437867
$63$	−105.013	−0.210006
$64$	14.4584	0.0282390
$65$	−172.831	−0.329801
$66$	−139.015	−0.259266
$67$	−656.686	−1.19742	−0.598708	−	0.800967i	$-0.704319\pi$
$67$	−656.686	−1.19742	−0.598708	+	0.800967i	$0.704319\pi$
$68$	105.410	0.187982
$69$	576.336	1.00555
$70$	−144.735	−0.247130
$71$	128.411	0.214643	0.107321	−	0.994224i	$-0.465773\pi$
$71$	128.411	0.214643	0.107321	+	0.994224i	$0.465773\pi$
$72$	−57.5519	−0.0942022
$73$	−941.956	−1.51024	−0.755121	−	0.655586i	$-0.772422\pi$
$73$	−941.956	−1.51024	−0.755121	+	0.655586i	$0.772422\pi$
$74$	−139.493	−0.219132
$75$	−623.830	−0.960450
$76$	−606.609	−0.915564
$77$	663.613	0.982153
$78$	−360.554	−0.523393
$79$	976.312	1.39043	0.695213	−	0.718804i	$-0.255310\pi$
$79$	976.312	1.39043	0.695213	+	0.718804i	$0.255310\pi$
$80$	92.1092	0.128726
$81$	−803.712	−1.10248
$82$	−210.209	−0.283095
$83$	−999.531	−1.32184	−0.660921	−	0.750456i	$-0.729834\pi$
$83$	−999.531	−1.32184	−0.660921	+	0.750456i	$0.729834\pi$
$84$	1171.38	1.52153
$85$	−55.8337	−0.0712472
$86$	75.0907	0.0941539
$87$	278.500	0.343199
$88$	363.691	0.440563
$89$	1309.14	1.55919	0.779597	−	0.626281i	$-0.215424\pi$
$89$	1309.14	1.55919	0.779597	+	0.626281i	$0.215424\pi$
$90$	13.5020	0.0158137
$91$	1721.17	1.98272
$92$	−667.832	−0.756808
$93$	916.373	1.02176
$94$	−720.626	−0.790712
$95$	321.311	0.347008
$96$	999.604	1.06273
$97$	330.844	0.346311	0.173155	−	0.984895i	$-0.444604\pi$
$97$	330.844	0.346311	0.173155	+	0.984895i	$0.444604\pi$
$98$	1002.18	1.03301
$99$	−61.9070	−0.0628474
$100$	722.867	0.722867
$101$	−809.136	−0.797149	−0.398574	−	0.917136i	$-0.630495\pi$
$101$	−809.136	−0.797149	−0.398574	+	0.917136i	$0.630495\pi$
$102$	−116.478	−0.113069
$103$	447.693	0.428277	0.214138	−	0.976803i	$-0.431306\pi$
$103$	447.693	0.428277	0.214138	+	0.976803i	$0.431306\pi$
$104$	943.280	0.889386
$105$	−620.462	−0.576675
$106$	−418.688	−0.383647
$107$	−43.9196	−0.0396810	−0.0198405	−	0.999803i	$-0.506316\pi$
$107$	−43.9196	−0.0396810	−0.0198405	+	0.999803i	$0.506316\pi$
$108$	833.381	0.742520
$109$	1661.75	1.46025	0.730124	−	0.683315i	$-0.239462\pi$
$109$	1661.75	1.46025	0.730124	+	0.683315i	$0.239462\pi$
$110$	−85.3238	−0.0739573
$111$	−597.992	−0.511341
$112$	−917.285	−0.773887
$113$	1957.97	1.63000	0.815001	−	0.579459i	$-0.196736\pi$
$113$	1957.97	1.63000	0.815001	+	0.579459i	$0.196736\pi$
$114$	670.307	0.550702
$115$	353.740	0.286838
$116$	−322.713	−0.258303
$117$	−160.564	−0.126873
$118$	−722.307	−0.563506
$119$	556.030	0.428329
$120$	−340.042	−0.258679
$121$	−939.788	−0.706076
$122$	719.579	0.533997
$123$	−901.145	−0.660598
$124$	−1061.85	−0.769009
$125$	−804.022	−0.575311
$126$	−134.462	−0.0950700
$127$	−982.658	−0.686589	−0.343295	−	0.939228i	$-0.611543\pi$
$127$	−982.658	−0.686589	−0.343295	+	0.939228i	$0.611543\pi$
$128$	−1438.35	−0.993230
$129$	321.905	0.219707
$130$	−221.298	−0.149301
$131$	1646.70	1.09826	0.549132	−	0.835735i	$-0.314958\pi$
$131$	1646.70	1.09826	0.549132	+	0.835735i	$0.314958\pi$
$132$	690.551	0.455339
$133$	−3199.83	−2.08617
$134$	−840.842	−0.542072
$135$	−441.428	−0.281423
$136$	304.730	0.192135
$137$	−1840.40	−1.14771	−0.573853	−	0.818958i	$-0.694552\pi$
$137$	−1840.40	−1.14771	−0.573853	+	0.818958i	$0.694552\pi$
$138$	737.959	0.455212
$139$	−1497.04	−0.913508	−0.456754	−	0.889593i	$-0.650988\pi$
$139$	−1497.04	−0.913508	−0.456754	+	0.889593i	$0.650988\pi$
$140$	718.964	0.434025
$141$	−3089.25	−1.84512
$142$	164.422	0.0971690
$143$	1014.66	0.593358
$144$	85.5715	0.0495205
$145$	170.936	0.0978995
$146$	−1206.11	−0.683688
$147$	4296.23	2.41052
$148$	692.927	0.384853
$149$	716.544	0.393970	0.196985	−	0.980406i	$-0.436885\pi$
$149$	716.544	0.393970	0.196985	+	0.980406i	$0.436885\pi$
$150$	−798.773	−0.434797
$151$	−2209.74	−1.19090	−0.595449	−	0.803393i	$-0.703026\pi$
$151$	−2209.74	−1.19090	−0.595449	+	0.803393i	$0.703026\pi$
$152$	−1753.66	−0.935791
$153$	−51.8708	−0.0274085
$154$	849.712	0.444622
$155$	562.446	0.291463
$156$	1791.04	0.919215
$157$	−80.5150	−0.0409286	−0.0204643	−	0.999791i	$-0.506514\pi$
$157$	−80.5150	−0.0409286	−0.0204643	+	0.999791i	$0.506514\pi$
$158$	1250.10	0.629448
$159$	−1794.87	−0.895235
$160$	613.530	0.303149
$161$	−3522.78	−1.72443
$162$	−1029.10	−0.499096
$163$	−3081.89	−1.48093	−0.740467	−	0.672093i	$-0.765395\pi$
$163$	−3081.89	−1.48093	−0.740467	+	0.672093i	$0.765395\pi$
$164$	1044.21	0.497188
$165$	−365.774	−0.172578
$166$	−1279.83	−0.598399
$167$	889.369	0.412104	0.206052	−	0.978541i	$-0.433938\pi$
$167$	889.369	0.412104	0.206052	+	0.978541i	$0.433938\pi$
$168$	3386.37	1.55514
$169$	434.654	0.197840
$170$	−71.4913	−0.0322537
$171$	298.505	0.133493
$172$	−373.010	−0.165359
$173$	221.360	0.0972813	0.0486407	−	0.998816i	$-0.484511\pi$
$173$	221.360	0.0972813	0.0486407	+	0.998816i	$0.484511\pi$
$174$	356.600	0.155366
$175$	3813.09	1.64710
$176$	−540.756	−0.231597
$177$	−3096.45	−1.31493
$178$	1676.26	0.705849
$179$	−2983.82	−1.24593	−0.622965	−	0.782250i	$-0.714072\pi$
$179$	−2983.82	−1.24593	−0.622965	+	0.782250i	$0.714072\pi$
$180$	−67.0705	−0.0277730
$181$	−1301.11	−0.534315	−0.267157	−	0.963653i	$-0.586084\pi$
$181$	−1301.11	−0.534315	−0.267157	+	0.963653i	$0.586084\pi$
$182$	2203.84	0.897579
$183$	3084.76	1.24608
$184$	−1930.65	−0.773527
$185$	−367.032	−0.145863
$186$	1173.35	0.462551
$187$	327.790	0.128184
$188$	3579.68	1.38870
$189$	4396.04	1.69188
$190$	411.417	0.157091
$191$	−2858.59	−1.08293	−0.541467	−	0.840722i	$-0.682131\pi$
$191$	−2858.59	−1.08293	−0.541467	+	0.840722i	$0.682131\pi$
$192$	79.3630	0.0298309
$193$	−2742.39	−1.02281	−0.511403	−	0.859341i	$-0.670874\pi$
$193$	−2742.39	−1.02281	−0.511403	+	0.859341i	$0.670874\pi$
$194$	423.624	0.156775
$195$	−948.682	−0.348392
$196$	−4978.28	−1.81424
$197$	197.000	0.0712470
$197$	197.000	0.0712470
$198$	−79.2677	−0.0284511
$199$	681.145	0.242639	0.121319	−	0.992614i	$-0.461287\pi$
$199$	681.145	0.242639	0.121319	+	0.992614i	$0.461287\pi$
$200$	2089.75	0.738837
$201$	−3604.60	−1.26492
$202$	−1036.04	−0.360870
$203$	−1702.29	−0.588559
$204$	578.601	0.198579
$205$	−553.099	−0.188440
$206$	573.241	0.193881
$207$	328.632	0.110345
$208$	−1402.52	−0.467536
$209$	−1886.36	−0.624317
$210$	−794.460	−0.261062
$211$	−626.997	−0.204570	−0.102285	−	0.994755i	$-0.532615\pi$
$211$	−626.997	−0.204570	−0.102285	+	0.994755i	$0.532615\pi$
$212$	2079.82	0.673784
$213$	704.860	0.226743
$214$	−56.2361	−0.0179637
$215$	197.577	0.0626728
$216$	2409.23	0.758924
$217$	−5601.21	−1.75224
$218$	2127.76	0.661056
$219$	−5170.47	−1.59538
$220$	423.842	0.129888
$221$	850.166	0.258771
$222$	−765.688	−0.231485
$223$	661.306	0.198584	0.0992922	−	0.995058i	$-0.468342\pi$
$223$	661.306	0.198584	0.0992922	+	0.995058i	$0.468342\pi$
$224$	−6109.95	−1.82249
$225$	−355.714	−0.105397
$226$	2507.05	0.737904
$227$	2165.03	0.633031	0.316515	−	0.948587i	$-0.397487\pi$
$227$	2165.03	0.633031	0.316515	+	0.948587i	$0.397487\pi$
$228$	−3329.72	−0.967176
$229$	4339.90	1.25235	0.626176	−	0.779682i	$-0.284619\pi$
$229$	4339.90	1.25235	0.626176	+	0.779682i	$0.284619\pi$
$230$	452.940	0.129852
$231$	3642.62	1.03752
$232$	−932.935	−0.264009
$233$	6669.59	1.87528	0.937638	−	0.347613i	$-0.113008\pi$
$233$	6669.59	1.87528	0.937638	+	0.347613i	$0.113008\pi$
$234$	−205.591	−0.0574356
$235$	−1896.10	−0.526331
$236$	3588.03	0.989664
$237$	5359.05	1.46881
$238$	711.959	0.193905
$239$	4838.83	1.30961	0.654807	−	0.755796i	$-0.272750\pi$
$239$	4838.83	1.30961	0.654807	+	0.755796i	$0.272750\pi$
$240$	505.594	0.135983
$241$	810.076	0.216521	0.108260	−	0.994123i	$-0.465472\pi$
$241$	810.076	0.216521	0.108260	+	0.994123i	$0.465472\pi$
$242$	−1203.33	−0.319642
$243$	−873.967	−0.230720
$244$	−3574.48	−0.937839
$245$	2636.91	0.687617
$246$	−1153.86	−0.299053
$247$	−4892.52	−1.26034
$248$	−3069.72	−0.785999
$249$	−5486.50	−1.39636
$250$	−1029.50	−0.260444
$251$	−4272.91	−1.07452	−0.537258	−	0.843418i	$-0.680540\pi$
$251$	−4272.91	−1.07452	−0.537258	+	0.843418i	$0.680540\pi$
$252$	667.934	0.166968
$253$	−2076.74	−0.516062
$254$	−1258.23	−0.310820
$255$	−306.475	−0.0752636
$256$	−1957.38	−0.477875
$257$	−2504.82	−0.607964	−0.303982	−	0.952678i	$-0.598316\pi$
$257$	−2504.82	−0.607964	−0.303982	+	0.952678i	$0.598316\pi$
$258$	412.178	0.0994616
$259$	3655.15	0.876911
$260$	1099.29	0.262212
$261$	158.803	0.0376616
$262$	2108.48	0.497186
$263$	−4663.67	−1.09344	−0.546719	−	0.837316i	$-0.684123\pi$
$263$	−4663.67	−1.09344	−0.546719	+	0.837316i	$0.684123\pi$
$264$	1996.32	0.465399
$265$	−1101.64	−0.255371
$266$	−4097.17	−0.944412
$267$	7185.95	1.64709
$268$	4176.84	0.952020
$269$	7041.19	1.59594	0.797972	−	0.602694i	$-0.205906\pi$
$269$	7041.19	1.59594	0.797972	+	0.602694i	$0.205906\pi$
$270$	−565.219	−0.127400
$271$	3451.38	0.773641	0.386820	−	0.922155i	$-0.373573\pi$
$271$	3451.38	0.773641	0.386820	+	0.922155i	$0.373573\pi$
$272$	−453.090	−0.101002
$273$	9447.62	2.09449
$274$	−2356.50	−0.519568
$275$	2247.88	0.492918
$276$	−3665.78	−0.799471
$277$	4808.28	1.04297	0.521483	−	0.853262i	$-0.325379\pi$
$277$	4808.28	1.04297	0.521483	+	0.853262i	$0.325379\pi$
$278$	−1916.86	−0.413546
$279$	522.525	0.112125
$280$	2078.46	0.443614
$281$	−4856.85	−1.03109	−0.515543	−	0.856864i	$-0.672410\pi$
$281$	−4856.85	−1.03109	−0.515543	+	0.856864i	$0.672410\pi$
$282$	−3955.57	−0.835286
$283$	3611.19	0.758527	0.379263	−	0.925289i	$-0.376177\pi$
$283$	3611.19	0.758527	0.379263	+	0.925289i	$0.376177\pi$
$284$	−816.760	−0.170654
$285$	1763.70	0.366570
$286$	1299.20	0.268614
$287$	5508.13	1.13287
$288$	569.984	0.116620
$289$	−4638.35	−0.944097
$290$	218.872	0.0443192
$291$	1816.03	0.365833
$292$	5991.31	1.20074
$293$	1313.98	0.261991	0.130996	−	0.991383i	$-0.458183\pi$
$293$	1313.98	0.261991	0.130996	+	0.991383i	$0.458183\pi$
$294$	5501.03	1.09125
$295$	−1900.52	−0.375093
$296$	2003.19	0.393355
$297$	2591.55	0.506319
$298$	917.486	0.178351
$299$	−5386.30	−1.04180
$300$	3967.87	0.763617
$301$	−1967.61	−0.376781
$302$	−2829.42	−0.539121
$303$	−4441.41	−0.842086
$304$	2607.44	0.491930
$305$	1893.34	0.355451
$306$	−66.4170	−0.0124079
$307$	5192.49	0.965312	0.482656	−	0.875810i	$-0.339672\pi$
$307$	5192.49	0.965312	0.482656	+	0.875810i	$0.339672\pi$
$308$	−4220.91	−0.780872
$309$	2457.42	0.452420
$310$	720.174	0.131946
$311$	−3739.32	−0.681793	−0.340896	−	0.940101i	$-0.610730\pi$
$311$	−3739.32	−0.681793	−0.340896	+	0.940101i	$0.610730\pi$
$312$	5177.73	0.939523
$313$	−6589.50	−1.18997	−0.594985	−	0.803737i	$-0.702842\pi$
$313$	−6589.50	−1.18997	−0.594985	+	0.803737i	$0.702842\pi$
$314$	−103.094	−0.0185284
$315$	−353.794	−0.0632826
$316$	−6209.83	−1.10547
$317$	10880.6	1.92781	0.963907	−	0.266240i	$-0.0857815\pi$
$317$	10880.6	1.92781	0.963907	+	0.266240i	$0.0857815\pi$
$318$	−2298.21	−0.405274
$319$	−1003.53	−0.176135
$320$	48.7109	0.00850945
$321$	−241.078	−0.0419180
$322$	−4510.68	−0.780653
$323$	−1580.55	−0.272272
$324$	5112.00	0.876543
$325$	5830.18	0.995078
$326$	−3946.15	−0.670420
$327$	9121.48	1.54257
$328$	3018.71	0.508172
$329$	18882.6	3.16423
$330$	−468.348	−0.0781265
$331$	−3821.58	−0.634601	−0.317300	−	0.948325i	$-0.602776\pi$
$331$	−3821.58	−0.634601	−0.317300	+	0.948325i	$0.602776\pi$
$332$	6357.51	1.05095
$333$	−340.981	−0.0561130
$334$	1138.78	0.186560
$335$	−2212.41	−0.360826
$336$	−5035.05	−0.817513
$337$	−3698.97	−0.597909	−0.298955	−	0.954267i	$-0.596638\pi$
$337$	−3698.97	−0.597909	−0.298955	+	0.954267i	$0.596638\pi$
$338$	556.545	0.0895623
$339$	10747.4	1.72189
$340$	355.130	0.0566459
$341$	−3302.02	−0.524382
$342$	382.216	0.0604323
$343$	−14752.1	−2.32227
$344$	−1078.34	−0.169012
$345$	1941.70	0.303008
$346$	283.436	0.0440394
$347$	6761.30	1.04601	0.523005	−	0.852330i	$-0.324811\pi$
$347$	6761.30	1.04601	0.523005	+	0.852330i	$0.324811\pi$
$348$	−1771.39	−0.272864
$349$	−3540.23	−0.542992	−0.271496	−	0.962440i	$-0.587518\pi$
$349$	−3540.23	−0.542992	−0.271496	+	0.962440i	$0.587518\pi$
$350$	4882.40	0.745643
$351$	6721.52	1.02213
$352$	−3601.93	−0.545407
$353$	−2277.35	−0.343374	−0.171687	−	0.985152i	$-0.554922\pi$
$353$	−2277.35	−0.343374	−0.171687	+	0.985152i	$0.554922\pi$
$354$	−3964.80	−0.595273
$355$	432.624	0.0646798
$356$	−8326.76	−1.23966
$357$	3052.09	0.452475
$358$	−3820.58	−0.564034
$359$	−9517.84	−1.39925	−0.699627	−	0.714508i	$-0.746650\pi$
$359$	−9517.84	−1.39925	−0.699627	+	0.714508i	$0.746650\pi$
$360$	−193.895	−0.0283866
$361$	2236.71	0.326098
$362$	−1665.99	−0.241885
$363$	−5158.56	−0.745880
$364$	−10947.5	−1.57638
$365$	−3173.50	−0.455091
$366$	3949.82	0.564100
$367$	−12114.9	−1.72314	−0.861572	−	0.507635i	$-0.830520\pi$
$367$	−12114.9	−1.72314	−0.861572	+	0.507635i	$0.830520\pi$
$368$	2870.60	0.406631
$369$	−513.842	−0.0724919
$370$	−469.959	−0.0660325
$371$	10970.9	1.53526
$372$	−5828.58	−0.812360
$373$	−2552.10	−0.354270	−0.177135	−	0.984187i	$-0.556683\pi$
$373$	−2552.10	−0.354270	−0.177135	+	0.984187i	$0.556683\pi$
$374$	419.713	0.0580289
$375$	−4413.33	−0.607743
$376$	10348.5	1.41938
$377$	−2602.79	−0.355572
$378$	5628.83	0.765915
$379$	−10429.0	−1.41347	−0.706733	−	0.707480i	$-0.749832\pi$
$379$	−10429.0	−1.41347	−0.706733	+	0.707480i	$0.749832\pi$
$380$	−2043.70	−0.275893
$381$	−5393.88	−0.725294
$382$	−3660.23	−0.490246
$383$	−3159.73	−0.421552	−0.210776	−	0.977534i	$-0.567599\pi$
$383$	−3159.73	−0.421552	−0.210776	+	0.977534i	$0.567599\pi$
$384$	−7895.21	−1.04922
$385$	2235.75	0.295959
$386$	−3511.45	−0.463026
$387$	183.554	0.0241100
$388$	−2104.33	−0.275339
$389$	−8399.34	−1.09476	−0.547382	−	0.836883i	$-0.684376\pi$
$389$	−8399.34	−1.09476	−0.547382	+	0.836883i	$0.684376\pi$
$390$	−1214.72	−0.157718
$391$	−1740.07	−0.225061
$392$	−14391.8	−1.85432
$393$	9038.84	1.16018
$394$	252.245	0.0322536
$395$	3289.24	0.418987
$396$	393.759	0.0499675
$397$	11720.4	1.48169	0.740844	−	0.671677i	$-0.234426\pi$
$397$	11720.4	1.48169	0.740844	+	0.671677i	$0.234426\pi$
$398$	872.161	0.109843
$399$	−17564.1	−2.20377
$400$	−3107.16	−0.388395
$401$	11029.4	1.37352	0.686759	−	0.726885i	$-0.259033\pi$
$401$	11029.4	1.37352	0.686759	+	0.726885i	$0.259033\pi$
$402$	−4615.44	−0.572630
$403$	−8564.22	−1.05860
$404$	5146.50	0.633782
$405$	−2707.74	−0.332219
$406$	−2179.67	−0.266442
$407$	2154.78	0.262428
$408$	1672.69	0.202966
$409$	1713.84	0.207198	0.103599	−	0.994619i	$-0.466964\pi$
$409$	1713.84	0.207198	0.103599	+	0.994619i	$0.466964\pi$
$410$	−708.206	−0.0853068
$411$	−10102.1	−1.21241
$412$	−2847.55	−0.340506
$413$	18926.7	2.25501
$414$	420.791	0.0499535
$415$	−3367.47	−0.398319
$416$	−9342.07	−1.10104
$417$	−8217.38	−0.965005
$418$	−2415.36	−0.282629
$419$	5239.24	0.610868	0.305434	−	0.952213i	$-0.401198\pi$
$419$	5239.24	0.610868	0.305434	+	0.952213i	$0.401198\pi$
$420$	3946.44	0.458492
$421$	4658.66	0.539310	0.269655	−	0.962957i	$-0.413090\pi$
$421$	4658.66	0.539310	0.269655	+	0.962957i	$0.413090\pi$
$422$	−802.828	−0.0926091
$423$	−1761.52	−0.202477
$424$	6012.57	0.688670
$425$	1883.46	0.214968
$426$	902.525	0.102647
$427$	−18855.2	−2.13692
$428$	279.351	0.0315489
$429$	5569.54	0.626807
$430$	252.984	0.0283720
$431$	−2640.53	−0.295104	−0.147552	−	0.989054i	$-0.547139\pi$
$431$	−2640.53	−0.295104	−0.147552	+	0.989054i	$0.547139\pi$
$432$	−3582.19	−0.398954
$433$	13591.6	1.50848	0.754238	−	0.656601i	$-0.228007\pi$
$433$	13591.6	1.50848	0.754238	+	0.656601i	$0.228007\pi$
$434$	−7171.98	−0.793239
$435$	938.278	0.103418
$436$	−10569.6	−1.16099
$437$	10013.7	1.09616
$438$	−6620.43	−0.722230
$439$	1744.93	0.189706	0.0948528	−	0.995491i	$-0.469762\pi$
$439$	1744.93	0.189706	0.0948528	+	0.995491i	$0.469762\pi$
$440$	1225.29	0.132758
$441$	2449.75	0.264523
$442$	1088.58	0.117146
$443$	15140.5	1.62381	0.811905	−	0.583789i	$-0.198431\pi$
$443$	15140.5	1.62381	0.811905	+	0.583789i	$0.198431\pi$
$444$	3803.52	0.406548
$445$	4410.55	0.469843
$446$	846.757	0.0898994
$447$	3933.16	0.416179
$448$	−485.096	−0.0511577
$449$	2187.35	0.229905	0.114953	−	0.993371i	$-0.463328\pi$
$449$	2187.35	0.229905	0.114953	+	0.993371i	$0.463328\pi$
$450$	−455.468	−0.0477133
$451$	3247.15	0.339029
$452$	−12453.7	−1.29595
$453$	−12129.4	−1.25803
$454$	2772.17	0.286574
$455$	5798.70	0.597466
$456$	−9625.94	−0.988544
$457$	11522.0	1.17938	0.589689	−	0.807631i	$-0.299250\pi$
$457$	11522.0	1.17938	0.589689	+	0.807631i	$0.299250\pi$
$458$	5556.95	0.566941
$459$	2171.41	0.220812
$460$	−2249.96	−0.228054
$461$	−2489.47	−0.251510	−0.125755	−	0.992061i	$-0.540135\pi$
$461$	−2489.47	−0.251510	−0.125755	+	0.992061i	$0.540135\pi$
$462$	4664.13	0.469686
$463$	−641.369	−0.0643779	−0.0321889	−	0.999482i	$-0.510248\pi$
$463$	−641.369	−0.0643779	−0.0321889	+	0.999482i	$0.510248\pi$
$464$	1387.14	0.138785
$465$	3087.31	0.307893
$466$	8539.96	0.848940
$467$	−1370.99	−0.135849	−0.0679247	−	0.997690i	$-0.521638\pi$
$467$	−1370.99	−0.135849	−0.0679247	+	0.997690i	$0.521638\pi$
$468$	1021.27	0.100872
$469$	22032.6	2.16924
$470$	−2427.82	−0.238271
$471$	−441.953	−0.0432359
$472$	10372.7	1.01153
$473$	−1159.94	−0.112757
$474$	6861.90	0.664931
$475$	−10838.9	−1.04700
$476$	−3536.62	−0.340548
$477$	−1023.45	−0.0982404
$478$	6195.79	0.592864
$479$	5216.84	0.497628	0.248814	−	0.968551i	$-0.419959\pi$
$479$	5216.84	0.497628	0.248814	+	0.968551i	$0.419959\pi$
$480$	3367.71	0.320238
$481$	5588.70	0.529777
$482$	1037.25	0.0980193
$483$	−19336.8	−1.82164
$484$	5977.51	0.561374
$485$	1114.63	0.104356
$486$	−1119.06	−0.104447
$487$	−16783.9	−1.56170	−0.780852	−	0.624716i	$-0.785215\pi$
$487$	−16783.9	−1.56170	−0.780852	+	0.624716i	$0.785215\pi$
$488$	−10333.5	−0.958558
$489$	−16916.7	−1.56442
$490$	3376.39	0.311285
$491$	−1804.24	−0.165833	−0.0829166	−	0.996556i	$-0.526424\pi$
$491$	−1804.24	−0.165833	−0.0829166	+	0.996556i	$0.526424\pi$
$492$	5731.73	0.525216
$493$	−840.842	−0.0768147
$494$	−6264.54	−0.570557
$495$	−208.568	−0.0189382
$496$	4564.24	0.413187
$497$	−4308.37	−0.388846
$498$	−7025.09	−0.632132
$499$	−8563.48	−0.768244	−0.384122	−	0.923282i	$-0.625496\pi$
$499$	−8563.48	−0.768244	−0.384122	+	0.923282i	$0.625496\pi$
$500$	5113.97	0.457408
$501$	4881.81	0.435336
$502$	−5471.17	−0.486435
$503$	7284.81	0.645753	0.322877	−	0.946441i	$-0.395350\pi$
$503$	7284.81	0.645753	0.322877	+	0.946441i	$0.395350\pi$
$504$	1930.94	0.170656
$505$	−2726.02	−0.240210
$506$	−2659.13	−0.233622
$507$	2385.85	0.208993
$508$	6250.19	0.545881
$509$	−10726.3	−0.934053	−0.467026	−	0.884243i	$-0.654675\pi$
$509$	−10726.3	−0.934053	−0.467026	+	0.884243i	$0.654675\pi$
$510$	−392.421	−0.0340719
$511$	31603.8	2.73595
$512$	9000.51	0.776895
$513$	−12496.0	−1.07546
$514$	−3207.26	−0.275226
$515$	1508.30	0.129056
$516$	−2047.48	−0.174681
$517$	11131.7	0.946943
$518$	4680.17	0.396979
$519$	1215.06	0.102765
$520$	3177.95	0.268005
$521$	−12272.2	−1.03197	−0.515986	−	0.856597i	$-0.672574\pi$
$521$	−12272.2	−1.03197	−0.515986	+	0.856597i	$0.672574\pi$
$522$	203.337	0.0170494
$523$	−7767.40	−0.649417	−0.324708	−	0.945814i	$-0.605266\pi$
$523$	−7767.40	−0.649417	−0.324708	+	0.945814i	$0.605266\pi$
$524$	−10473.8	−0.873188
$525$	20930.3	1.73995
$526$	−5971.51	−0.495001
$527$	−2766.70	−0.228690
$528$	−2968.25	−0.244653
$529$	−1142.65	−0.0939140
$530$	−1410.58	−0.115607
$531$	−1765.63	−0.144297
$532$	20352.5	1.65863
$533$	8421.90	0.684414
$534$	9201.13	0.745640
$535$	−147.967	−0.0119574
$536$	12074.9	0.973053
$537$	−16378.4	−1.31617
$538$	9015.77	0.722486
$539$	−15480.8	−1.23712
$540$	2807.70	0.223749
$541$	−6394.86	−0.508200	−0.254100	−	0.967178i	$-0.581779\pi$
$541$	−6394.86	−0.508200	−0.254100	+	0.967178i	$0.581779\pi$
$542$	4419.26	0.350228
$543$	−7141.90	−0.564435
$544$	−3017.99	−0.237859
$545$	5598.52	0.440026
$546$	12097.0	0.948178
$547$	−7621.67	−0.595757	−0.297878	−	0.954604i	$-0.596279\pi$
$547$	−7621.67	−0.595757	−0.297878	+	0.954604i	$0.596279\pi$
$548$	11705.8	0.912497
$549$	1758.96	0.136741
$550$	2878.26	0.223145
$551$	4838.87	0.374125
$552$	−10597.5	−0.817133
$553$	−32756.5	−2.51889
$554$	6156.68	0.472152
$555$	−2014.66	−0.154086
$556$	9521.94	0.726295
$557$	4885.78	0.371665	0.185832	−	0.982581i	$-0.440502\pi$
$557$	4885.78	0.371665	0.185832	+	0.982581i	$0.440502\pi$
$558$	669.058	0.0507589
$559$	−3008.46	−0.227628
$560$	−3090.38	−0.233201
$561$	1799.26	0.135410
$562$	−6218.87	−0.466774
$563$	−4019.32	−0.300878	−0.150439	−	0.988619i	$-0.548069\pi$
$563$	−4019.32	−0.300878	−0.150439	+	0.988619i	$0.548069\pi$
$564$	19649.1	1.46698
$565$	6596.49	0.491180
$566$	4623.89	0.343386
$567$	26965.5	1.99726
$568$	−2361.18	−0.174424
$569$	9079.78	0.668971	0.334485	−	0.942401i	$-0.391438\pi$
$569$	9079.78	0.668971	0.334485	+	0.942401i	$0.391438\pi$
$570$	2258.30	0.165947
$571$	−6527.11	−0.478373	−0.239186	−	0.970974i	$-0.576881\pi$
$571$	−6527.11	−0.478373	−0.239186	+	0.970974i	$0.576881\pi$
$572$	−6453.74	−0.471756
$573$	−15691.0	−1.14398
$574$	7052.79	0.512854
$575$	−11932.8	−0.865451
$576$	45.2536	0.00327355
$577$	−1432.41	−0.103348	−0.0516741	−	0.998664i	$-0.516456\pi$
$577$	−1432.41	−0.103348	−0.0516741	+	0.998664i	$0.516456\pi$
$578$	−5939.09	−0.427394
$579$	−15053.2	−1.08046
$580$	−1087.24	−0.0778362
$581$	33535.5	2.39465
$582$	2325.30	0.165613
$583$	6467.56	0.459449
$584$	17320.4	1.22726
$585$	−540.948	−0.0382315
$586$	1682.46	0.118604
$587$	−4257.56	−0.299367	−0.149683	−	0.988734i	$-0.547825\pi$
$587$	−4257.56	−0.299367	−0.149683	+	0.988734i	$0.547825\pi$
$588$	−27326.1	−1.91652
$589$	15921.8	1.11383
$590$	−2433.49	−0.169805
$591$	1081.35	0.0752634
$592$	−2978.46	−0.206780
$593$	−9322.26	−0.645564	−0.322782	−	0.946473i	$-0.604618\pi$
$593$	−9322.26	−0.645564	−0.322782	+	0.946473i	$0.604618\pi$
$594$	3318.30	0.229211
$595$	1873.29	0.129071
$596$	−4557.57	−0.313231
$597$	3738.86	0.256317
$598$	−6896.80	−0.471624
$599$	5717.27	0.389986	0.194993	−	0.980805i	$-0.437532\pi$
$599$	5717.27	0.389986	0.194993	+	0.980805i	$0.437532\pi$
$600$	11470.8	0.780487
$601$	28863.8	1.95903	0.979516	−	0.201365i	$-0.0645378\pi$
$601$	28863.8	1.95903	0.979516	+	0.201365i	$0.0645378\pi$
$602$	−2519.39	−0.170569
$603$	−2055.38	−0.138808
$604$	14055.0	0.946838
$605$	−3166.19	−0.212767
$606$	−5686.92	−0.381213
$607$	10014.8	0.669665	0.334833	−	0.942278i	$-0.391320\pi$
$607$	10014.8	0.669665	0.334833	+	0.942278i	$0.391320\pi$
$608$	17367.9	1.15849
$609$	−9344.01	−0.621738
$610$	2424.30	0.160913
$611$	28871.4	1.91164
$612$	329.924	0.0217915
$613$	−14673.4	−0.966807	−0.483404	−	0.875398i	$-0.660600\pi$
$613$	−14673.4	−0.966807	−0.483404	+	0.875398i	$0.660600\pi$
$614$	6648.63	0.436998
$615$	−3036.00	−0.199062
$616$	−12202.3	−0.798123
$617$	−28596.4	−1.86588	−0.932941	−	0.360029i	$-0.882767\pi$
$617$	−28596.4	−1.86588	−0.932941	+	0.360029i	$0.882767\pi$
$618$	3146.56	0.204811
$619$	10815.1	0.702253	0.351127	−	0.936328i	$-0.385799\pi$
$619$	10815.1	0.702253	0.351127	+	0.936328i	$0.385799\pi$
$620$	−3577.43	−0.231731
$621$	−13757.2	−0.888980
$622$	−4787.95	−0.308648
$623$	−43923.2	−2.82463
$624$	−7698.55	−0.493892
$625$	11497.4	0.735834
$626$	−8437.41	−0.538701
$627$	−10354.4	−0.659511
$628$	512.115	0.0325408
$629$	1805.45	0.114448
$630$	−453.009	−0.0286481
$631$	−3162.40	−0.199514	−0.0997570	−	0.995012i	$-0.531807\pi$
$631$	−3162.40	−0.199514	−0.0997570	+	0.995012i	$0.531807\pi$
$632$	−17952.1	−1.12990
$633$	−3441.63	−0.216102
$634$	13931.9	0.872723
$635$	−3310.62	−0.206895
$636$	11416.3	0.711767
$637$	−40151.6	−2.49743
$638$	−1284.96	−0.0797365
$639$	401.918	0.0248820
$640$	−4845.87	−0.299297
$641$	8550.66	0.526881	0.263441	−	0.964676i	$-0.415143\pi$
$641$	8550.66	0.526881	0.263441	+	0.964676i	$0.415143\pi$
$642$	−308.684	−0.0189763
$643$	−4352.48	−0.266944	−0.133472	−	0.991053i	$-0.542613\pi$
$643$	−4352.48	−0.266944	−0.133472	+	0.991053i	$0.542613\pi$
$644$	22406.6	1.37103
$645$	1084.52	0.0662058
$646$	−2023.78	−0.123258
$647$	−158.350	−0.00962194	−0.00481097	−	0.999988i	$-0.501531\pi$
$647$	−158.350	−0.00962194	−0.00481097	+	0.999988i	$0.501531\pi$
$648$	14778.4	0.895909
$649$	11157.6	0.674845
$650$	7465.15	0.450473
$651$	−30745.5	−1.85101
$652$	19602.3	1.17743
$653$	−12526.7	−0.750698	−0.375349	−	0.926884i	$-0.622477\pi$
$653$	−12526.7	−0.750698	−0.375349	+	0.926884i	$0.622477\pi$
$654$	11679.4	0.698321
$655$	5547.80	0.330948
$656$	−4488.40	−0.267138
$657$	−2948.25	−0.175072
$658$	24177.9	1.43245
$659$	19989.6	1.18161	0.590806	−	0.806814i	$-0.298810\pi$
$659$	19989.6	1.18161	0.590806	+	0.806814i	$0.298810\pi$
$660$	2326.50	0.137210
$661$	25676.2	1.51088	0.755439	−	0.655219i	$-0.227424\pi$
$661$	25676.2	1.51088	0.755439	+	0.655219i	$0.227424\pi$
$662$	−4893.27	−0.287285
$663$	4666.62	0.273358
$664$	18379.0	1.07416
$665$	−10780.4	−0.628640
$666$	−436.603	−0.0254024
$667$	5327.24	0.309252
$668$	−5656.82	−0.327648
$669$	3629.96	0.209779
$670$	−2832.84	−0.163346
$671$	−11115.5	−0.639506
$672$	−33538.0	−1.92523
$673$	−17573.4	−1.00654	−0.503271	−	0.864128i	$-0.667870\pi$
$673$	−17573.4	−1.00654	−0.503271	+	0.864128i	$0.667870\pi$
$674$	−4736.28	−0.270674
$675$	14890.9	0.849112
$676$	−2764.61	−0.157295
$677$	−17973.3	−1.02034	−0.510169	−	0.860074i	$-0.670417\pi$
$677$	−17973.3	−1.02034	−0.510169	+	0.860074i	$0.670417\pi$
$678$	13761.4	0.779502
$679$	−11100.3	−0.627376
$680$	1026.65	0.0578974
$681$	11884.0	0.668716
$682$	−4228.01	−0.237388
$683$	−14933.1	−0.836600	−0.418300	−	0.908309i	$-0.637374\pi$
$683$	−14933.1	−0.836600	−0.418300	+	0.908309i	$0.637374\pi$
$684$	−1898.64	−0.106135
$685$	−6200.39	−0.345846
$686$	−18889.0	−1.05129
$687$	23822.0	1.32295
$688$	1603.34	0.0888469
$689$	16774.5	0.927512
$690$	2486.22	0.137172
$691$	−35013.2	−1.92759	−0.963794	−	0.266647i	$-0.914084\pi$
$691$	−35013.2	−1.92759	−0.963794	+	0.266647i	$0.914084\pi$
$692$	−1407.96	−0.0773446
$693$	2077.06	0.113854
$694$	8657.38	0.473530
$695$	−5043.61	−0.275274
$696$	−5120.95	−0.278892
$697$	2720.73	0.147855
$698$	−4533.03	−0.245813
$699$	36609.9	1.98099
$700$	−24253.1	−1.30954
$701$	20673.9	1.11390	0.556948	−	0.830548i	$-0.311972\pi$
$701$	20673.9	1.11390	0.556948	+	0.830548i	$0.311972\pi$
$702$	8606.45	0.462720
$703$	−10390.0	−0.557419
$704$	−285.973	−0.0153097
$705$	−10407.8	−0.556002
$706$	−2915.99	−0.155446
$707$	27147.5	1.44411
$708$	19695.0	1.04545
$709$	36773.5	1.94789	0.973947	−	0.226777i	$-0.0728188\pi$
$709$	36773.5	1.94789	0.973947	+	0.226777i	$0.0728188\pi$
$710$	553.946	0.0292806
$711$	3055.78	0.161183
$712$	−24072.0	−1.26704
$713$	17528.7	0.920694
$714$	3907.99	0.204836
$715$	3418.44	0.178801
$716$	18978.6	0.990591
$717$	26560.7	1.38344
$718$	−12186.9	−0.633444
$719$	−36037.3	−1.86921	−0.934606	−	0.355684i	$-0.884248\pi$
$719$	−36037.3	−1.86921	−0.934606	+	0.355684i	$0.884248\pi$
$720$	288.295	0.0149224
$721$	−15020.7	−0.775865
$722$	2863.95	0.147625
$723$	4446.56	0.228727
$724$	8275.72	0.424813
$725$	−5766.24	−0.295383
$726$	−6605.19	−0.337661
$727$	−35688.7	−1.82066	−0.910331	−	0.413880i	$-0.864173\pi$
$727$	−35688.7	−1.82066	−0.910331	+	0.413880i	$0.864173\pi$
$728$	−31648.2	−1.61121
$729$	16902.9	0.858758
$730$	−4063.45	−0.206020
$731$	−971.893	−0.0491748
$732$	−19620.6	−0.990707
$733$	1417.23	0.0714143	0.0357072	−	0.999362i	$-0.488632\pi$
$733$	1417.23	0.0714143	0.0357072	+	0.999362i	$0.488632\pi$
$734$	−15512.3	−0.780070
$735$	14474.2	0.726380
$736$	19120.8	0.957610
$737$	12988.6	0.649176
$738$	−657.939	−0.0328172
$739$	30798.0	1.53305	0.766525	−	0.642215i	$-0.221984\pi$
$739$	30798.0	1.53305	0.766525	+	0.642215i	$0.221984\pi$
$740$	2334.50	0.115970
$741$	−26855.4	−1.33139
$742$	14047.5	0.695014
$743$	36656.0	1.80993	0.904964	−	0.425488i	$-0.139898\pi$
$743$	36656.0	1.80993	0.904964	+	0.425488i	$0.139898\pi$
$744$	−16849.9	−0.830307
$745$	2414.07	0.118718
$746$	−3267.79	−0.160379
$747$	−3128.46	−0.153232
$748$	−2084.90	−0.101914
$749$	1473.56	0.0718861
$750$	−5650.98	−0.275126
$751$	18280.2	0.888222	0.444111	−	0.895972i	$-0.353520\pi$
$751$	18280.2	0.888222	0.444111	+	0.895972i	$0.353520\pi$
$752$	−15386.8	−0.746143
$753$	−23454.3	−1.13509
$754$	−3332.70	−0.160968
$755$	−7444.71	−0.358862
$756$	−27961.0	−1.34515
$757$	31820.1	1.52777	0.763886	−	0.645352i	$-0.223289\pi$
$757$	31820.1	1.52777	0.763886	+	0.645352i	$0.223289\pi$
$758$	−13353.7	−0.639878
$759$	−11399.4	−0.545154
$760$	−5908.15	−0.281988
$761$	−2627.12	−0.125142	−0.0625710	−	0.998041i	$-0.519930\pi$
$761$	−2627.12	−0.125142	−0.0625710	+	0.998041i	$0.519930\pi$
$762$	−6906.50	−0.328341
$763$	−55753.9	−2.64538
$764$	18182.1	0.861000
$765$	−174.755	−0.00825920
$766$	−4045.82	−0.190837
$767$	28938.7	1.36234
$768$	−10744.2	−0.504814
$769$	−35175.3	−1.64948	−0.824741	−	0.565510i	$-0.808679\pi$
$769$	−35175.3	−1.64948	−0.824741	+	0.565510i	$0.808679\pi$
$770$	2862.72	0.133981
$771$	−13749.2	−0.642236
$772$	17443.0	0.813194
$773$	−6097.64	−0.283721	−0.141861	−	0.989887i	$-0.545309\pi$
$773$	−6097.64	−0.283721	−0.141861	+	0.989887i	$0.545309\pi$
$774$	235.028	0.0109146
$775$	−18973.2	−0.879404
$776$	−6083.45	−0.281421
$777$	20063.4	0.926345
$778$	−10754.8	−0.495601
$779$	−15657.2	−0.720125
$780$	6034.09	0.276993
$781$	−2539.86	−0.116368
$782$	−2228.04	−0.101885
$783$	−6647.80	−0.303414
$784$	21398.5	0.974787
$785$	−271.259	−0.0123333
$786$	11573.6	0.525213
$787$	25126.9	1.13809	0.569046	−	0.822306i	$-0.307313\pi$
$787$	25126.9	1.13809	0.569046	+	0.822306i	$0.307313\pi$
$788$	−1253.02	−0.0566458
$789$	−25599.2	−1.15508
$790$	4211.65	0.189676
$791$	−65692.4	−2.95291
$792$	1138.32	0.0510714
$793$	−28829.5	−1.29100
$794$	15007.2	0.670762
$795$	−6047.00	−0.269767
$796$	−4332.42	−0.192913
$797$	−36271.5	−1.61205	−0.806023	−	0.591884i	$-0.798384\pi$
$797$	−36271.5	−1.61205	−0.806023	+	0.591884i	$0.798384\pi$
$798$	−22489.7	−0.997651
$799$	9327.01	0.412974
$800$	−20696.5	−0.914664
$801$	4097.50	0.180747
$802$	14122.4	0.621793
$803$	18631.0	0.818773
$804$	22927.0	1.00569
$805$	−11868.4	−0.519636
$806$	−10965.9	−0.479228
$807$	38649.6	1.68591
$808$	14878.1	0.647784
$809$	34699.5	1.50800	0.753998	−	0.656877i	$-0.228123\pi$
$809$	34699.5	1.50800	0.753998	+	0.656877i	$0.228123\pi$
$810$	−3467.08	−0.150396
$811$	−33189.1	−1.43703	−0.718513	−	0.695514i	$-0.755177\pi$
$811$	−33189.1	−1.43703	−0.718513	+	0.695514i	$0.755177\pi$
$812$	10827.4	0.467941
$813$	18944.9	0.817253
$814$	2759.05	0.118802
$815$	−10383.0	−0.446260
$816$	−2487.05	−0.106696
$817$	5593.04	0.239505
$818$	2194.46	0.0937988
$819$	5387.12	0.229843
$820$	3517.98	0.149821
$821$	−26460.5	−1.12482	−0.562411	−	0.826858i	$-0.690126\pi$
$821$	−26460.5	−1.12482	−0.562411	+	0.826858i	$0.690126\pi$
$822$	−12935.0	−0.548857
$823$	5315.08	0.225118	0.112559	−	0.993645i	$-0.464095\pi$
$823$	5315.08	0.225118	0.112559	+	0.993645i	$0.464095\pi$
$824$	−8232.02	−0.348029
$825$	12338.8	0.520705
$826$	24234.3	1.02085
$827$	−45568.7	−1.91606	−0.958028	−	0.286676i	$-0.907450\pi$
$827$	−45568.7	−1.91606	−0.958028	+	0.286676i	$0.907450\pi$
$828$	−2090.26	−0.0877315
$829$	−41447.0	−1.73645	−0.868223	−	0.496174i	$-0.834738\pi$
$829$	−41447.0	−1.73645	−0.868223	+	0.496174i	$0.834738\pi$
$830$	−4311.82	−0.180320
$831$	26393.0	1.10176
$832$	−741.709	−0.0309064
$833$	−12971.1	−0.539523
$834$	−10521.8	−0.436859
$835$	2996.33	0.124182
$836$	11998.2	0.496370
$837$	−21873.9	−0.903312
$838$	6708.50	0.276541
$839$	9431.62	0.388100	0.194050	−	0.980992i	$-0.437838\pi$
$839$	9431.62	0.388100	0.194050	+	0.980992i	$0.437838\pi$
$840$	11408.8	0.468622
$841$	−21814.7	−0.894450
$842$	5965.10	0.244146
$843$	−26659.6	−1.08921
$844$	3988.01	0.162646
$845$	1464.37	0.0596164
$846$	−2255.50	−0.0916618
$847$	31531.1	1.27913
$848$	−8939.83	−0.362023
$849$	19822.1	0.801287
$850$	2411.65	0.0973162
$851$	−11438.6	−0.460764
$852$	−4483.25	−0.180274
$853$	25623.7	1.02853	0.514266	−	0.857631i	$-0.328064\pi$
$853$	25623.7	1.02853	0.514266	+	0.857631i	$0.328064\pi$
$854$	−24142.8	−0.967388
$855$	1005.68	0.0402263
$856$	807.579	0.0322459
$857$	40420.2	1.61112	0.805559	−	0.592516i	$-0.201865\pi$
$857$	40420.2	1.61112	0.805559	+	0.592516i	$0.201865\pi$
$858$	7131.42	0.283756
$859$	25030.5	0.994215	0.497107	−	0.867689i	$-0.334395\pi$
$859$	25030.5	0.994215	0.497107	+	0.867689i	$0.334395\pi$
$860$	−1256.69	−0.0498287
$861$	30234.6	1.19674
$862$	−3381.02	−0.133594
$863$	8531.44	0.336516	0.168258	−	0.985743i	$-0.446186\pi$
$863$	8531.44	0.336516	0.168258	+	0.985743i	$0.446186\pi$
$864$	−23860.6	−0.939531
$865$	745.772	0.0293144
$866$	17403.1	0.682889
$867$	−25460.2	−0.997319
$868$	35626.5	1.39314
$869$	−19310.6	−0.753816
$870$	1201.40	0.0468176
$871$	33687.7	1.31052
$872$	−30555.7	−1.18664
$873$	1035.52	0.0401454
$874$	12821.9	0.496231
$875$	26976.0	1.04223
$876$	32886.7	1.26842
$877$	−31290.3	−1.20479	−0.602394	−	0.798199i	$-0.705787\pi$
$877$	−31290.3	−1.20479	−0.602394	+	0.798199i	$0.705787\pi$
$878$	2234.26	0.0858799
$879$	7212.52	0.276760
$880$	−1821.83	−0.0697887
$881$	−39738.7	−1.51967	−0.759835	−	0.650116i	$-0.774720\pi$
$881$	−39738.7	−1.51967	−0.759835	+	0.650116i	$0.774720\pi$
$882$	3136.74	0.119750
$883$	−7536.77	−0.287239	−0.143620	−	0.989633i	$-0.545874\pi$
$883$	−7536.77	−0.287239	−0.143620	+	0.989633i	$0.545874\pi$
$884$	−5407.47	−0.205739
$885$	−10432.1	−0.396238
$886$	19386.4	0.735101
$887$	42554.5	1.61087	0.805435	−	0.592684i	$-0.201932\pi$
$887$	42554.5	1.61087	0.805435	+	0.592684i	$0.201932\pi$
$888$	10995.7	0.415530
$889$	32969.4	1.24382
$890$	5647.41	0.212698
$891$	15896.7	0.597709
$892$	−4206.23	−0.157887
$893$	−53675.0	−2.01138
$894$	5036.15	0.188405
$895$	−10052.6	−0.375445
$896$	48258.5	1.79933
$897$	−29565.8	−1.10053
$898$	2800.75	0.104078
$899$	8470.30	0.314238
$900$	2262.52	0.0837970
$901$	5419.05	0.200371
$902$	4157.75	0.153479
$903$	−10800.3	−0.398021
$904$	−36002.4	−1.32458
$905$	−4383.51	−0.161009
$906$	−15530.9	−0.569513
$907$	24765.4	0.906641	0.453320	−	0.891348i	$-0.350239\pi$
$907$	24765.4	0.906641	0.453320	+	0.891348i	$0.350239\pi$
$908$	−13770.6	−0.503298
$909$	−2532.53	−0.0924079
$910$	7424.84	0.270474
$911$	28536.6	1.03783	0.518913	−	0.854827i	$-0.326337\pi$
$911$	28536.6	1.03783	0.518913	+	0.854827i	$0.326337\pi$
$912$	14312.4	0.519661
$913$	19769.8	0.716632
$914$	14753.1	0.533906
$915$	10392.7	0.375489
$916$	−27603.9	−0.995697
$917$	−55248.8	−1.98961
$918$	2780.34	0.0999619
$919$	−15399.2	−0.552746	−0.276373	−	0.961050i	$-0.589133\pi$
$919$	−15399.2	−0.552746	−0.276373	+	0.961050i	$0.589133\pi$
$920$	−6504.44	−0.233092
$921$	28501.9	1.01973
$922$	−3187.59	−0.113859
$923$	−6587.46	−0.234918
$924$	−23168.9	−0.824892
$925$	12381.2	0.440100
$926$	−821.230	−0.0291439
$927$	1401.24	0.0496472
$928$	9239.62	0.326838
$929$	22644.6	0.799727	0.399864	−	0.916575i	$-0.369057\pi$
$929$	22644.6	0.799727	0.399864	+	0.916575i	$0.369057\pi$
$930$	3953.09	0.139384
$931$	74646.0	2.62774
$932$	−42421.9	−1.49096
$933$	−20525.4	−0.720227
$934$	−1755.45	−0.0614992
$935$	1104.34	0.0386265
$936$	2952.39	0.103100
$937$	20900.5	0.728699	0.364349	−	0.931262i	$-0.381291\pi$
$937$	20900.5	0.728699	0.364349	+	0.931262i	$0.381291\pi$
$938$	28211.3	0.982017
$939$	−36170.2	−1.25705
$940$	12060.1	0.418466
$941$	−25147.2	−0.871175	−0.435587	−	0.900146i	$-0.643459\pi$
$941$	−25147.2	−0.871175	−0.435587	+	0.900146i	$0.643459\pi$
$942$	−565.891	−0.0195729
$943$	−17237.4	−0.595257
$944$	−15422.7	−0.531744
$945$	14810.5	0.509825
$946$	−1485.22	−0.0510453
$947$	−8533.36	−0.292816	−0.146408	−	0.989224i	$-0.546771\pi$
$947$	−8533.36	−0.292816	−0.146408	+	0.989224i	$0.546771\pi$
$948$	−34086.2	−1.16779
$949$	48322.0	1.65290
$950$	−13878.5	−0.473977
$951$	59724.6	2.03649
$952$	−10224.1	−0.348072
$953$	9510.59	0.323272	0.161636	−	0.986850i	$-0.448323\pi$
$953$	9510.59	0.323272	0.161636	+	0.986850i	$0.448323\pi$
$954$	−1310.46	−0.0444735
$955$	−9630.74	−0.326328
$956$	−30777.3	−1.04122
$957$	−5508.47	−0.186064
$958$	6679.81	0.225277
$959$	61747.6	2.07918
$960$	267.378	0.00898915
$961$	−1920.38	−0.0644619
$962$	7155.95	0.239831
$963$	−137.465	−0.00459995
$964$	−5152.48	−0.172148
$965$	−9239.25	−0.308209
$966$	−24759.5	−0.824661
$967$	18948.6	0.630141	0.315071	−	0.949068i	$-0.397972\pi$
$967$	18948.6	0.630141	0.315071	+	0.949068i	$0.397972\pi$
$968$	17280.5	0.573777
$969$	−8675.74	−0.287621
$970$	1427.21	0.0472422
$971$	−54648.7	−1.80614	−0.903069	−	0.429495i	$-0.858691\pi$
$971$	−54648.7	−1.80614	−0.903069	+	0.429495i	$0.858691\pi$
$972$	5558.86	0.183437
$973$	50227.7	1.65491
$974$	−21490.6	−0.706986
$975$	32002.3	1.05117
$976$	15364.5	0.503898
$977$	25948.5	0.849710	0.424855	−	0.905261i	$-0.360325\pi$
$977$	25948.5	0.849710	0.424855	+	0.905261i	$0.360325\pi$
$978$	−21660.7	−0.708214
$979$	−25893.5	−0.845313
$980$	−16772.1	−0.546698
$981$	5201.16	0.169276
$982$	−2310.21	−0.0750729
$983$	−19921.4	−0.646382	−0.323191	−	0.946334i	$-0.604756\pi$
$983$	−19921.4	−0.646382	−0.323191	+	0.946334i	$0.604756\pi$
$984$	16569.9	0.536819
$985$	663.703	0.0214694
$986$	−1076.64	−0.0347741
$987$	103648.	3.34261
$988$	31118.8	1.00205
$989$	6157.52	0.197975
$990$	−267.057	−0.00857336
$991$	−30682.1	−0.983502	−0.491751	−	0.870736i	$-0.663643\pi$
$991$	−30682.1	−0.983502	−0.491751	+	0.870736i	$0.663643\pi$
$992$	30402.0	0.973049
$993$	−20976.9	−0.670375
$994$	−5516.57	−0.176031
$995$	2294.81	0.0731160
$996$	34896.8	1.11019
$997$	40566.9	1.28863	0.644316	−	0.764759i	$-0.277142\pi$
$997$	40566.9	1.28863	0.644316	+	0.764759i	$0.277142\pi$
$998$	−10965.0	−0.347785
$999$	14274.1	0.452065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.a.1.14	✓	22
3.2	odd	2		1773.4.a.c.1.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.a.1.14	✓	22	1.1	even	1	trivial
1773.4.a.c.1.9		22	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)

\(f(q)\)	\(=\)	\(q+1.28043 q^{2} +5.48907 q^{3} -6.36049 q^{4} +3.36905 q^{5} +7.02839 q^{6} -33.5513 q^{7} -18.3876 q^{8} +3.12992 q^{9} +4.31384 q^{10} -19.7791 q^{11} -34.9132 q^{12} -51.2996 q^{13} -42.9601 q^{14} +18.4930 q^{15} +27.3398 q^{16} -16.5725 q^{17} +4.00765 q^{18} +95.3714 q^{19} -21.4288 q^{20} -184.165 q^{21} -25.3258 q^{22} +104.997 q^{23} -100.931 q^{24} -113.650 q^{25} -65.6857 q^{26} -131.025 q^{27} +213.403 q^{28} +50.7371 q^{29} +23.6790 q^{30} +166.945 q^{31} +182.108 q^{32} -108.569 q^{33} -21.2200 q^{34} -113.036 q^{35} -19.9079 q^{36} -108.942 q^{37} +122.117 q^{38} -281.588 q^{39} -61.9489 q^{40} -164.171 q^{41} -235.811 q^{42} +58.6448 q^{43} +125.805 q^{44} +10.5449 q^{45} +134.441 q^{46} -562.799 q^{47} +150.070 q^{48} +782.688 q^{49} -145.521 q^{50} -90.9679 q^{51} +326.291 q^{52} -326.990 q^{53} -167.768 q^{54} -66.6367 q^{55} +616.929 q^{56} +523.501 q^{57} +64.9654 q^{58} -564.112 q^{59} -117.624 q^{60} +561.982 q^{61} +213.762 q^{62} -105.013 q^{63} +14.4584 q^{64} -172.831 q^{65} -139.015 q^{66} -656.686 q^{67} +105.410 q^{68} +576.336 q^{69} -144.735 q^{70} +128.411 q^{71} -57.5519 q^{72} -941.956 q^{73} -139.493 q^{74} -623.830 q^{75} -606.609 q^{76} +663.613 q^{77} -360.554 q^{78} +976.312 q^{79} +92.1092 q^{80} -803.712 q^{81} -210.209 q^{82} -999.531 q^{83} +1171.38 q^{84} -55.8337 q^{85} +75.0907 q^{86} +278.500 q^{87} +363.691 q^{88} +1309.14 q^{89} +13.5020 q^{90} +1721.17 q^{91} -667.832 q^{92} +916.373 q^{93} -720.626 q^{94} +321.311 q^{95} +999.604 q^{96} +330.844 q^{97} +1002.18 q^{98} -61.9070 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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