LMFDB - Embedded newform 197.4.a.a.1.5

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			1.5
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)

$f(q)$	$=$	\(q-3.51341 q^{2} -5.88377 q^{3} +4.34403 q^{4} -3.63670 q^{5} +20.6721 q^{6} -4.62984 q^{7} +12.8449 q^{8} +7.61880 q^{9} +12.7772 q^{10} +11.9693 q^{11} -25.5593 q^{12} +47.3156 q^{13} +16.2665 q^{14} +21.3975 q^{15} -79.8816 q^{16} +102.213 q^{17} -26.7679 q^{18} +83.6282 q^{19} -15.7979 q^{20} +27.2409 q^{21} -42.0530 q^{22} -210.687 q^{23} -75.5766 q^{24} -111.774 q^{25} -166.239 q^{26} +114.035 q^{27} -20.1122 q^{28} -26.1307 q^{29} -75.1783 q^{30} +33.1328 q^{31} +177.897 q^{32} -70.4245 q^{33} -359.115 q^{34} +16.8374 q^{35} +33.0963 q^{36} -152.182 q^{37} -293.820 q^{38} -278.394 q^{39} -46.7132 q^{40} +87.5771 q^{41} -95.7085 q^{42} -374.361 q^{43} +51.9949 q^{44} -27.7073 q^{45} +740.229 q^{46} -389.406 q^{47} +470.006 q^{48} -321.565 q^{49} +392.709 q^{50} -601.397 q^{51} +205.540 q^{52} +543.187 q^{53} -400.650 q^{54} -43.5287 q^{55} -59.4699 q^{56} -492.050 q^{57} +91.8076 q^{58} +795.694 q^{59} +92.9515 q^{60} +27.1726 q^{61} -116.409 q^{62} -35.2738 q^{63} +14.0274 q^{64} -172.073 q^{65} +247.430 q^{66} -960.914 q^{67} +444.015 q^{68} +1239.63 q^{69} -59.1565 q^{70} +604.656 q^{71} +97.8628 q^{72} -355.684 q^{73} +534.678 q^{74} +657.655 q^{75} +363.283 q^{76} -55.4159 q^{77} +978.112 q^{78} -265.021 q^{79} +290.506 q^{80} -876.661 q^{81} -307.694 q^{82} -761.945 q^{83} +118.335 q^{84} -371.718 q^{85} +1315.28 q^{86} +153.747 q^{87} +153.744 q^{88} +1018.51 q^{89} +97.3470 q^{90} -219.064 q^{91} -915.230 q^{92} -194.946 q^{93} +1368.14 q^{94} -304.131 q^{95} -1046.71 q^{96} +240.467 q^{97} +1129.79 q^{98} +91.1915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.51341	−1.24218	−0.621088	−	0.783740i	$-0.713309\pi$
$2$	−3.51341	−1.24218	−0.621088	+	0.783740i	$0.713309\pi$
$3$	−5.88377	−1.13233	−0.566166	−	0.824291i	$-0.691574\pi$
$3$	−5.88377	−1.13233	−0.566166	+	0.824291i	$0.691574\pi$
$4$	4.34403	0.543003
$5$	−3.63670	−0.325277	−0.162638	−	0.986686i	$-0.552000\pi$
$5$	−3.63670	−0.325277	−0.162638	+	0.986686i	$0.552000\pi$
$6$	20.6721	1.40656
$7$	−4.62984	−0.249988	−0.124994	−	0.992158i	$-0.539891\pi$
$7$	−4.62984	−0.249988	−0.124994	+	0.992158i	$0.539891\pi$
$8$	12.8449	0.567671
$9$	7.61880	0.282178
$10$	12.7772	0.404051
$11$	11.9693	0.328079	0.164040	−	0.986454i	$-0.447547\pi$
$11$	11.9693	0.328079	0.164040	+	0.986454i	$0.447547\pi$
$12$	−25.5593	−0.614861
$13$	47.3156	1.00946	0.504730	−	0.863277i	$-0.331592\pi$
$13$	47.3156	1.00946	0.504730	+	0.863277i	$0.331592\pi$
$14$	16.2665	0.310529
$15$	21.3975	0.368322
$16$	−79.8816	−1.24815
$17$	102.213	1.45825	0.729125	−	0.684381i	$-0.239927\pi$
$17$	102.213	1.45825	0.729125	+	0.684381i	$0.239927\pi$
$18$	−26.7679	−0.350515
$19$	83.6282	1.00977	0.504885	−	0.863187i	$-0.331535\pi$
$19$	83.6282	1.00977	0.504885	+	0.863187i	$0.331535\pi$
$20$	−15.7979	−0.176626
$21$	27.2409	0.283070
$22$	−42.0530	−0.407533
$23$	−210.687	−1.91005	−0.955027	−	0.296517i	$-0.904175\pi$
$23$	−210.687	−1.91005	−0.955027	+	0.296517i	$0.904175\pi$
$24$	−75.5766	−0.642792
$25$	−111.774	−0.894195
$26$	−166.239	−1.25393
$27$	114.035	0.812814
$28$	−20.1122	−0.135744
$29$	−26.1307	−0.167322	−0.0836611	−	0.996494i	$-0.526661\pi$
$29$	−26.1307	−0.167322	−0.0836611	+	0.996494i	$0.526661\pi$
$30$	−75.1783	−0.457520
$31$	33.1328	0.191962	0.0959811	−	0.995383i	$-0.469401\pi$
$31$	33.1328	0.191962	0.0959811	+	0.995383i	$0.469401\pi$
$32$	177.897	0.982753
$33$	−70.4245	−0.371495
$34$	−359.115	−1.81140
$35$	16.8374	0.0813152
$36$	33.0963	0.153223
$37$	−152.182	−0.676178	−0.338089	−	0.941114i	$-0.609781\pi$
$37$	−152.182	−0.676178	−0.338089	+	0.941114i	$0.609781\pi$
$38$	−293.820	−1.25431
$39$	−278.394	−1.14304
$40$	−46.7132	−0.184650
$41$	87.5771	0.333591	0.166796	−	0.985991i	$-0.446658\pi$
$41$	87.5771	0.333591	0.166796	+	0.985991i	$0.446658\pi$
$42$	−95.7085	−0.351622
$43$	−374.361	−1.32766	−0.663832	−	0.747882i	$-0.731071\pi$
$43$	−374.361	−1.32766	−0.663832	+	0.747882i	$0.731071\pi$
$44$	51.9949	0.178148
$45$	−27.7073	−0.0917858
$46$	740.229	2.37263
$47$	−389.406	−1.20852	−0.604262	−	0.796785i	$-0.706532\pi$
$47$	−389.406	−1.20852	−0.604262	+	0.796785i	$0.706532\pi$
$48$	470.006	1.41332
$49$	−321.565	−0.937506
$50$	392.709	1.11075
$51$	−601.397	−1.65122
$52$	205.540	0.548140
$53$	543.187	1.40778	0.703891	−	0.710308i	$-0.251444\pi$
$53$	543.187	1.40778	0.703891	+	0.710308i	$0.251444\pi$
$54$	−400.650	−1.00966
$55$	−43.5287	−0.106717
$56$	−59.4699	−0.141911
$57$	−492.050	−1.14340
$58$	91.8076	0.207844
$59$	795.694	1.75577	0.877885	−	0.478871i	$-0.158954\pi$
$59$	795.694	1.75577	0.877885	+	0.478871i	$0.158954\pi$
$60$	92.9515	0.200000
$61$	27.1726	0.0570343	0.0285172	−	0.999593i	$-0.490921\pi$
$61$	27.1726	0.0570343	0.0285172	+	0.999593i	$0.490921\pi$
$62$	−116.409	−0.238451
$63$	−35.2738	−0.0705410
$64$	14.0274	0.0273973
$65$	−172.073	−0.328354
$66$	247.430	0.461463
$67$	−960.914	−1.75215	−0.876077	−	0.482171i	$-0.839848\pi$
$67$	−960.914	−1.75215	−0.876077	+	0.482171i	$0.839848\pi$
$68$	444.015	0.791835
$69$	1239.63	2.16282
$70$	−59.1565	−0.101008
$71$	604.656	1.01070	0.505348	−	0.862916i	$-0.331364\pi$
$71$	604.656	1.01070	0.505348	+	0.862916i	$0.331364\pi$
$72$	97.8628	0.160184
$73$	−355.684	−0.570269	−0.285135	−	0.958487i	$-0.592038\pi$
$73$	−355.684	−0.570269	−0.285135	+	0.958487i	$0.592038\pi$
$74$	534.678	0.839933
$75$	657.655	1.01253
$76$	363.283	0.548309
$77$	−55.4159	−0.0820159
$78$	978.112	1.41986
$79$	−265.021	−0.377432	−0.188716	−	0.982032i	$-0.560433\pi$
$79$	−265.021	−0.377432	−0.188716	+	0.982032i	$0.560433\pi$
$80$	290.506	0.405994
$81$	−876.661	−1.20255
$82$	−307.694	−0.414380
$83$	−761.945	−1.00764	−0.503821	−	0.863808i	$-0.668073\pi$
$83$	−761.945	−1.00764	−0.503821	+	0.863808i	$0.668073\pi$
$84$	118.335	0.153708
$85$	−371.718	−0.474335
$86$	1315.28	1.64919
$87$	153.747	0.189464
$88$	153.744	0.186241
$89$	1018.51	1.21305	0.606526	−	0.795063i	$-0.292562\pi$
$89$	1018.51	1.21305	0.606526	+	0.795063i	$0.292562\pi$
$90$	97.3470	0.114014
$91$	−219.064	−0.252353
$92$	−915.230	−1.03717
$93$	−194.946	−0.217365
$94$	1368.14	1.50120
$95$	−304.131	−0.328455
$96$	−1046.71	−1.11280
$97$	240.467	0.251708	0.125854	−	0.992049i	$-0.459833\pi$
$97$	240.467	0.251708	0.125854	+	0.992049i	$0.459833\pi$
$98$	1129.79	1.16455
$99$	91.1915	0.0925767
$100$	−485.551	−0.485551
$101$	−134.508	−0.132515	−0.0662577	−	0.997803i	$-0.521106\pi$
$101$	−134.508	−0.132515	−0.0662577	+	0.997803i	$0.521106\pi$
$102$	2112.95	2.05111
$103$	1479.83	1.41565	0.707823	−	0.706389i	$-0.249677\pi$
$103$	1479.83	1.41565	0.707823	+	0.706389i	$0.249677\pi$
$104$	607.765	0.573041
$105$	−99.0672	−0.0920759
$106$	−1908.44	−1.74871
$107$	−1032.55	−0.932899	−0.466449	−	0.884548i	$-0.654467\pi$
$107$	−1032.55	−0.932899	−0.466449	+	0.884548i	$0.654467\pi$
$108$	495.369	0.441361
$109$	−712.322	−0.625946	−0.312973	−	0.949762i	$-0.601325\pi$
$109$	−712.322	−0.625946	−0.312973	+	0.949762i	$0.601325\pi$
$110$	152.934	0.132561
$111$	895.405	0.765659
$112$	369.839	0.312023
$113$	−1764.43	−1.46888	−0.734442	−	0.678672i	$-0.762556\pi$
$113$	−1764.43	−1.46888	−0.734442	+	0.678672i	$0.762556\pi$
$114$	1728.77	1.42030
$115$	766.206	0.621296
$116$	−113.512	−0.0908565
$117$	360.488	0.284847
$118$	−2795.60	−2.18098
$119$	−473.229	−0.364545
$120$	274.850	0.209085
$121$	−1187.74	−0.892364
$122$	−95.4683	−0.0708467
$123$	−515.284	−0.377737
$124$	143.930	0.104236
$125$	861.078	0.616138
$126$	123.931	0.0876244
$127$	−2770.46	−1.93574	−0.967870	−	0.251452i	$-0.919092\pi$
$127$	−2770.46	−1.93574	−0.967870	+	0.251452i	$0.919092\pi$
$128$	−1472.46	−1.01679
$129$	2202.66	1.50336
$130$	604.562	0.407874
$131$	−1913.62	−1.27629	−0.638144	−	0.769917i	$-0.720297\pi$
$131$	−1913.62	−1.27629	−0.638144	+	0.769917i	$0.720297\pi$
$132$	−305.926	−0.201723
$133$	−387.185	−0.252430
$134$	3376.08	2.17649
$135$	−414.710	−0.264389
$136$	1312.92	0.827806
$137$	1182.75	0.737585	0.368793	−	0.929512i	$-0.379771\pi$
$137$	1182.75	0.737585	0.368793	+	0.929512i	$0.379771\pi$
$138$	−4355.34	−2.68660
$139$	−2026.77	−1.23675	−0.618376	−	0.785883i	$-0.712209\pi$
$139$	−2026.77	−1.23675	−0.618376	+	0.785883i	$0.712209\pi$
$140$	73.1420	0.0441545
$141$	2291.18	1.36845
$142$	−2124.40	−1.25546
$143$	566.333	0.331183
$144$	−608.602	−0.352200
$145$	95.0295	0.0544260
$146$	1249.66	0.708375
$147$	1892.01	1.06157
$148$	−661.083	−0.367167
$149$	1975.40	1.08612	0.543058	−	0.839695i	$-0.317266\pi$
$149$	1975.40	1.08612	0.543058	+	0.839695i	$0.317266\pi$
$150$	−2310.61	−1.25774
$151$	705.026	0.379962	0.189981	−	0.981788i	$-0.439157\pi$
$151$	705.026	0.379962	0.189981	+	0.981788i	$0.439157\pi$
$152$	1074.20	0.573217
$153$	778.739	0.411485
$154$	194.698	0.101878
$155$	−120.494	−0.0624408
$156$	−1209.35	−0.620677
$157$	−2465.45	−1.25328	−0.626638	−	0.779311i	$-0.715569\pi$
$157$	−2465.45	−1.25328	−0.626638	+	0.779311i	$0.715569\pi$
$158$	931.125	0.468838
$159$	−3195.99	−1.59408
$160$	−646.960	−0.319667
$161$	975.447	0.477491
$162$	3080.07	1.49378
$163$	−2593.81	−1.24640	−0.623198	−	0.782064i	$-0.714167\pi$
$163$	−2593.81	−1.24640	−0.623198	+	0.782064i	$0.714167\pi$
$164$	380.437	0.181141
$165$	256.113	0.120839
$166$	2677.02	1.25167
$167$	−2430.04	−1.12600	−0.563001	−	0.826456i	$-0.690353\pi$
$167$	−2430.04	−1.12600	−0.563001	+	0.826456i	$0.690353\pi$
$168$	349.908	0.160690
$169$	41.7639	0.0190095
$170$	1306.00	0.589208
$171$	637.146	0.284935
$172$	−1626.24	−0.720926
$173$	374.881	0.164749	0.0823747	−	0.996601i	$-0.473750\pi$
$173$	374.881	0.164749	0.0823747	+	0.996601i	$0.473750\pi$
$174$	−540.175	−0.235348
$175$	517.498	0.223538
$176$	−956.126	−0.409493
$177$	−4681.68	−1.98812
$178$	−3578.44	−1.50683
$179$	−124.416	−0.0519511	−0.0259756	−	0.999663i	$-0.508269\pi$
$179$	−124.416	−0.0519511	−0.0259756	+	0.999663i	$0.508269\pi$
$180$	−120.361	−0.0498400
$181$	−1985.43	−0.815337	−0.407669	−	0.913130i	$-0.633658\pi$
$181$	−1985.43	−0.815337	−0.407669	+	0.913130i	$0.633658\pi$
$182$	769.659	0.313467
$183$	−159.877	−0.0645818
$184$	−2706.26	−1.08428
$185$	553.442	0.219945
$186$	684.924	0.270006
$187$	1223.41	0.478422
$188$	−1691.59	−0.656233
$189$	−527.962	−0.203194
$190$	1068.54	0.407999
$191$	−3752.56	−1.42160	−0.710800	−	0.703395i	$-0.751667\pi$
$191$	−3752.56	−1.42160	−0.710800	+	0.703395i	$0.751667\pi$
$192$	−82.5341	−0.0310228
$193$	3875.49	1.44541	0.722704	−	0.691158i	$-0.242899\pi$
$193$	3875.49	1.44541	0.722704	+	0.691158i	$0.242899\pi$
$194$	−844.858	−0.312666
$195$	1012.44	0.371806
$196$	−1396.89	−0.509069
$197$	197.000	0.0712470
$197$	197.000	0.0712470
$198$	−320.393	−0.114997
$199$	2586.79	0.921471	0.460736	−	0.887537i	$-0.347586\pi$
$199$	2586.79	0.921471	0.460736	+	0.887537i	$0.347586\pi$
$200$	−1435.73	−0.507608
$201$	5653.80	1.98402
$202$	472.582	0.164608
$203$	120.981	0.0418285
$204$	−2612.49	−0.896620
$205$	−318.492	−0.108510
$206$	−5199.23	−1.75848
$207$	−1605.18	−0.538975
$208$	−3779.65	−1.25996
$209$	1000.97	0.331285
$210$	348.063	0.114375
$211$	1980.67	0.646231	0.323115	−	0.946360i	$-0.395270\pi$
$211$	1980.67	0.646231	0.323115	+	0.946360i	$0.395270\pi$
$212$	2359.62	0.764430
$213$	−3557.66	−1.14444
$214$	3627.76	1.15883
$215$	1361.44	0.431858
$216$	1464.77	0.461411
$217$	−153.400	−0.0479882
$218$	2502.68	0.777535
$219$	2092.76	0.645735
$220$	−189.090	−0.0579475
$221$	4836.26	1.47204
$222$	−3145.92	−0.951084
$223$	−1895.55	−0.569216	−0.284608	−	0.958644i	$-0.591863\pi$
$223$	−1895.55	−0.569216	−0.284608	+	0.958644i	$0.591863\pi$
$224$	−823.636	−0.245676
$225$	−851.586	−0.252322
$226$	6199.17	1.82461
$227$	−3582.02	−1.04734	−0.523672	−	0.851920i	$-0.675438\pi$
$227$	−3582.02	−1.04734	−0.523672	+	0.851920i	$0.675438\pi$
$228$	−2137.48	−0.620868
$229$	238.495	0.0688218	0.0344109	−	0.999408i	$-0.489045\pi$
$229$	238.495	0.0688218	0.0344109	+	0.999408i	$0.489045\pi$
$230$	−2691.99	−0.771760
$231$	326.054	0.0928693
$232$	−335.646	−0.0949838
$233$	7.62545	0.00214403	0.00107202	−	0.999999i	$-0.499659\pi$
$233$	7.62545	0.00214403	0.00107202	+	0.999999i	$0.499659\pi$
$234$	−1266.54	−0.353830
$235$	1416.15	0.393105
$236$	3456.51	0.953390
$237$	1559.32	0.427379
$238$	1662.65	0.452829
$239$	5651.03	1.52943	0.764716	−	0.644367i	$-0.222879\pi$
$239$	5651.03	1.52943	0.764716	+	0.644367i	$0.222879\pi$
$240$	−1709.27	−0.459721
$241$	4017.23	1.07375	0.536873	−	0.843663i	$-0.319606\pi$
$241$	4017.23	1.07375	0.536873	+	0.843663i	$0.319606\pi$
$242$	4173.00	1.10847
$243$	2079.14	0.548877
$244$	118.038	0.0309698
$245$	1169.44	0.304949
$246$	1810.40	0.469216
$247$	3956.92	1.01932
$248$	425.588	0.108971
$249$	4483.11	1.14099
$250$	−3025.32	−0.765352
$251$	−3710.14	−0.932996	−0.466498	−	0.884522i	$-0.654484\pi$
$251$	−3710.14	−0.932996	−0.466498	+	0.884522i	$0.654484\pi$
$252$	−153.230	−0.0383040
$253$	−2521.77	−0.626650
$254$	9733.77	2.40453
$255$	2187.10	0.537105
$256$	5061.14	1.23563
$257$	2881.37	0.699357	0.349679	−	0.936870i	$-0.386291\pi$
$257$	2881.37	0.699357	0.349679	+	0.936870i	$0.386291\pi$
$258$	−7738.83	−1.86744
$259$	704.579	0.169036
$260$	−747.489	−0.178297
$261$	−199.084	−0.0472146
$262$	6723.32	1.58537
$263$	3367.25	0.789482	0.394741	−	0.918792i	$-0.370834\pi$
$263$	3367.25	0.789482	0.394741	+	0.918792i	$0.370834\pi$
$264$	−904.598	−0.210887
$265$	−1975.41	−0.457919
$266$	1360.34	0.313563
$267$	−5992.68	−1.37358
$268$	−4174.24	−0.951426
$269$	456.004	0.103357	0.0516785	−	0.998664i	$-0.483543\pi$
$269$	456.004	0.103357	0.0516785	+	0.998664i	$0.483543\pi$
$270$	1457.05	0.328418
$271$	−6664.91	−1.49396	−0.746982	−	0.664844i	$-0.768498\pi$
$271$	−6664.91	−1.49396	−0.746982	+	0.664844i	$0.768498\pi$
$272$	−8164.93	−1.82012
$273$	1288.92	0.285747
$274$	−4155.48	−0.916211
$275$	−1337.86	−0.293367
$276$	5385.00	1.17442
$277$	1807.02	0.391961	0.195981	−	0.980608i	$-0.437211\pi$
$277$	1807.02	0.391961	0.195981	+	0.980608i	$0.437211\pi$
$278$	7120.87	1.53626
$279$	252.432	0.0541674
$280$	216.275	0.0461603
$281$	703.221	0.149291	0.0746453	−	0.997210i	$-0.476218\pi$
$281$	703.221	0.149291	0.0746453	+	0.997210i	$0.476218\pi$
$282$	−8049.83	−1.69986
$283$	−6732.12	−1.41407	−0.707037	−	0.707177i	$-0.749969\pi$
$283$	−6732.12	−1.41407	−0.707037	+	0.707177i	$0.749969\pi$
$284$	2626.64	0.548811
$285$	1789.44	0.371920
$286$	−1989.76	−0.411388
$287$	−405.468	−0.0833938
$288$	1355.36	0.277311
$289$	5534.46	1.12649
$290$	−333.877	−0.0676067
$291$	−1414.85	−0.285018
$292$	−1545.10	−0.309658
$293$	−1180.96	−0.235469	−0.117734	−	0.993045i	$-0.537563\pi$
$293$	−1180.96	−0.235469	−0.117734	+	0.993045i	$0.537563\pi$
$294$	−6647.41	−1.31866
$295$	−2893.70	−0.571111
$296$	−1954.77	−0.383847
$297$	1364.91	0.266668
$298$	−6940.40	−1.34915
$299$	−9968.77	−1.92812
$300$	2856.87	0.549805
$301$	1733.23	0.331900
$302$	−2477.04	−0.471980
$303$	791.415	0.150052
$304$	−6680.36	−1.26035
$305$	−98.8186	−0.0185519
$306$	−2736.03	−0.511138
$307$	5814.32	1.08091	0.540457	−	0.841372i	$-0.318251\pi$
$307$	5814.32	1.08091	0.540457	+	0.841372i	$0.318251\pi$
$308$	−240.728	−0.0445349
$309$	−8706.96	−1.60298
$310$	423.345	0.0775625
$311$	−2968.10	−0.541175	−0.270587	−	0.962695i	$-0.587218\pi$
$311$	−2968.10	−0.541175	−0.270587	+	0.962695i	$0.587218\pi$
$312$	−3575.95	−0.648873
$313$	3913.45	0.706714	0.353357	−	0.935489i	$-0.385040\pi$
$313$	3913.45	0.706714	0.353357	+	0.935489i	$0.385040\pi$
$314$	8662.12	1.55679
$315$	128.280	0.0229453
$316$	−1151.26	−0.204947
$317$	4522.87	0.801355	0.400677	−	0.916219i	$-0.368775\pi$
$317$	4522.87	0.801355	0.400677	+	0.916219i	$0.368775\pi$
$318$	11228.8	1.98013
$319$	−312.765	−0.0548949
$320$	−51.0135	−0.00891169
$321$	6075.28	1.05635
$322$	−3427.14	−0.593128
$323$	8547.88	1.47250
$324$	−3808.24	−0.652991
$325$	−5288.67	−0.902654
$326$	9113.10	1.54825
$327$	4191.14	0.708779
$328$	1124.92	0.189370
$329$	1802.89	0.302117
$330$	−899.830	−0.150103
$331$	−8845.28	−1.46882	−0.734411	−	0.678705i	$-0.762542\pi$
$331$	−8845.28	−1.46882	−0.734411	+	0.678705i	$0.762542\pi$
$332$	−3309.91	−0.547153
$333$	−1159.44	−0.190802
$334$	8537.73	1.39869
$335$	3494.56	0.569935
$336$	−2176.05	−0.353313
$337$	−1906.53	−0.308177	−0.154088	−	0.988057i	$-0.549244\pi$
$337$	−1906.53	−0.308177	−0.154088	+	0.988057i	$0.549244\pi$
$338$	−146.734	−0.0236132
$339$	10381.5	1.66326
$340$	−1614.75	−0.257565
$341$	396.576	0.0629788
$342$	−2238.55	−0.353939
$343$	3076.83	0.484353
$344$	−4808.64	−0.753676
$345$	−4508.18	−0.703514
$346$	−1317.11	−0.204648
$347$	−9716.49	−1.50319	−0.751597	−	0.659622i	$-0.770716\pi$
$347$	−9716.49	−1.50319	−0.751597	+	0.659622i	$0.770716\pi$
$348$	667.881	0.102880
$349$	−2145.53	−0.329077	−0.164538	−	0.986371i	$-0.552613\pi$
$349$	−2145.53	−0.329077	−0.164538	+	0.986371i	$0.552613\pi$
$350$	−1818.18	−0.277674
$351$	5395.61	0.820503
$352$	2129.30	0.322421
$353$	−10694.8	−1.61253	−0.806267	−	0.591552i	$-0.798516\pi$
$353$	−10694.8	−1.61253	−0.806267	+	0.591552i	$0.798516\pi$
$354$	16448.7	2.46959
$355$	−2198.95	−0.328756
$356$	4424.43	0.658692
$357$	2784.37	0.412786
$358$	437.122	0.0645325
$359$	245.687	0.0361193	0.0180597	−	0.999837i	$-0.494251\pi$
$359$	245.687	0.0361193	0.0180597	+	0.999837i	$0.494251\pi$
$360$	−355.898	−0.0521041
$361$	134.680	0.0196355
$362$	6975.63	1.01279
$363$	6988.37	1.01045
$364$	−951.618	−0.137028
$365$	1293.52	0.185495
$366$	561.714	0.0802220
$367$	−18.1550	−0.00258224	−0.00129112	−	0.999999i	$-0.500411\pi$
$367$	−18.1550	−0.00258224	−0.00129112	+	0.999999i	$0.500411\pi$
$368$	16830.0	2.38404
$369$	667.232	0.0941320
$370$	−1944.47	−0.273211
$371$	−2514.87	−0.351928
$372$	−846.850	−0.118030
$373$	−4819.38	−0.669003	−0.334502	−	0.942395i	$-0.608568\pi$
$373$	−4819.38	−0.669003	−0.334502	+	0.942395i	$0.608568\pi$
$374$	−4298.35	−0.594285
$375$	−5066.39	−0.697673
$376$	−5001.89	−0.686044
$377$	−1236.39	−0.168905
$378$	1854.95	0.252402
$379$	−5490.51	−0.744139	−0.372069	−	0.928205i	$-0.621352\pi$
$379$	−5490.51	−0.744139	−0.372069	+	0.928205i	$0.621352\pi$
$380$	−1321.15	−0.178352
$381$	16300.8	2.19190
$382$	13184.3	1.76588
$383$	−417.593	−0.0557127	−0.0278564	−	0.999612i	$-0.508868\pi$
$383$	−417.593	−0.0557127	−0.0278564	+	0.999612i	$0.508868\pi$
$384$	8663.64	1.15134
$385$	201.531	0.0266779
$386$	−13616.2	−1.79545
$387$	−2852.18	−0.374637
$388$	1044.60	0.136679
$389$	−9194.14	−1.19836	−0.599179	−	0.800615i	$-0.704506\pi$
$389$	−9194.14	−1.19836	−0.599179	+	0.800615i	$0.704506\pi$
$390$	−3557.10	−0.461849
$391$	−21534.9	−2.78534
$392$	−4130.47	−0.532195
$393$	11259.3	1.44518
$394$	−692.141	−0.0885014
$395$	963.802	0.122770
$396$	396.138	0.0502695
$397$	5772.66	0.729777	0.364888	−	0.931051i	$-0.381107\pi$
$397$	5772.66	0.729777	0.364888	+	0.931051i	$0.381107\pi$
$398$	−9088.45	−1.14463
$399$	2278.11	0.285835
$400$	8928.72	1.11609
$401$	−9572.53	−1.19209	−0.596047	−	0.802950i	$-0.703263\pi$
$401$	−9572.53	−1.19209	−0.596047	+	0.802950i	$0.703263\pi$
$402$	−19864.1	−2.46451
$403$	1567.70	0.193778
$404$	−584.307	−0.0719563
$405$	3188.16	0.391163
$406$	−425.055	−0.0519584
$407$	−1821.51	−0.221840
$408$	−7724.90	−0.937351
$409$	6083.06	0.735422	0.367711	−	0.929940i	$-0.380141\pi$
$409$	6083.06	0.735422	0.367711	+	0.929940i	$0.380141\pi$
$410$	1118.99	0.134788
$411$	−6959.03	−0.835192
$412$	6428.41	0.768701
$413$	−3683.93	−0.438921
$414$	5639.65	0.669502
$415$	2770.97	0.327763
$416$	8417.32	0.992050
$417$	11925.1	1.40041
$418$	−3516.81	−0.411514
$419$	13646.1	1.59106	0.795531	−	0.605913i	$-0.207192\pi$
$419$	13646.1	1.59106	0.795531	+	0.605913i	$0.207192\pi$
$420$	−430.351	−0.0499975
$421$	5423.37	0.627836	0.313918	−	0.949450i	$-0.398358\pi$
$421$	5423.37	0.627836	0.313918	+	0.949450i	$0.398358\pi$
$422$	−6958.89	−0.802733
$423$	−2966.80	−0.341019
$424$	6977.19	0.799156
$425$	−11424.8	−1.30396
$426$	12499.5	1.42160
$427$	−125.805	−0.0142579
$428$	−4485.42	−0.506567
$429$	−3332.18	−0.375010
$430$	−4783.30	−0.536444
$431$	1633.29	0.182535	0.0912675	−	0.995826i	$-0.470908\pi$
$431$	1633.29	0.182535	0.0912675	+	0.995826i	$0.470908\pi$
$432$	−9109.27	−1.01451
$433$	2114.38	0.234666	0.117333	−	0.993093i	$-0.462566\pi$
$433$	2114.38	0.234666	0.117333	+	0.993093i	$0.462566\pi$
$434$	538.955	0.0596099
$435$	−559.132	−0.0616283
$436$	−3094.35	−0.339891
$437$	−17619.4	−1.92872
$438$	−7352.73	−0.802117
$439$	3783.81	0.411370	0.205685	−	0.978618i	$-0.434058\pi$
$439$	3783.81	0.411370	0.205685	+	0.978618i	$0.434058\pi$
$440$	−559.123	−0.0605799
$441$	−2449.94	−0.264543
$442$	−16991.7	−1.82854
$443$	8583.75	0.920602	0.460301	−	0.887763i	$-0.347742\pi$
$443$	8583.75	0.920602	0.460301	+	0.887763i	$0.347742\pi$
$444$	3889.67	0.415755
$445$	−3704.02	−0.394578
$446$	6659.82	0.707067
$447$	−11622.8	−1.22985
$448$	−64.9446	−0.00684899
$449$	−157.096	−0.0165118	−0.00825592	−	0.999966i	$-0.502628\pi$
$449$	−157.096	−0.0165118	−0.00825592	+	0.999966i	$0.502628\pi$
$450$	2991.97	0.313428
$451$	1048.24	0.109445
$452$	−7664.74	−0.797609
$453$	−4148.21	−0.430243
$454$	12585.1	1.30099
$455$	796.669	0.0820845
$456$	−6320.34	−0.649072
$457$	−4026.15	−0.412113	−0.206056	−	0.978540i	$-0.566063\pi$
$457$	−4026.15	−0.412113	−0.206056	+	0.978540i	$0.566063\pi$
$458$	−837.930	−0.0854889
$459$	11655.8	1.18529
$460$	3328.42	0.337366
$461$	10761.9	1.08727	0.543634	−	0.839322i	$-0.317048\pi$
$461$	10761.9	1.08727	0.543634	+	0.839322i	$0.317048\pi$
$462$	−1145.56	−0.115360
$463$	−15863.2	−1.59228	−0.796138	−	0.605115i	$-0.793127\pi$
$463$	−15863.2	−1.59228	−0.796138	+	0.605115i	$0.793127\pi$
$464$	2087.36	0.208843
$465$	708.961	0.0707038
$466$	−26.7913	−0.00266327
$467$	−11916.9	−1.18084	−0.590418	−	0.807098i	$-0.701037\pi$
$467$	−11916.9	−1.18084	−0.590418	+	0.807098i	$0.701037\pi$
$468$	1565.97	0.154673
$469$	4448.88	0.438017
$470$	−4975.52	−0.488306
$471$	14506.1	1.41912
$472$	10220.6	0.996700
$473$	−4480.84	−0.435579
$474$	−5478.53	−0.530880
$475$	−9347.49	−0.902931
$476$	−2055.72	−0.197949
$477$	4138.43	0.397244
$478$	−19854.4	−1.89983
$479$	1105.98	0.105498	0.0527489	−	0.998608i	$-0.483202\pi$
$479$	1105.98	0.105498	0.0527489	+	0.998608i	$0.483202\pi$
$480$	3806.57	0.361969
$481$	−7200.59	−0.682575
$482$	−14114.2	−1.33378
$483$	−5739.31	−0.540678
$484$	−5159.56	−0.484557
$485$	−874.507	−0.0818749
$486$	−7304.88	−0.681802
$487$	14741.6	1.37167	0.685837	−	0.727755i	$-0.259436\pi$
$487$	14741.6	1.37167	0.685837	+	0.727755i	$0.259436\pi$
$488$	349.030	0.0323767
$489$	15261.4	1.41134
$490$	−4108.70	−0.378800
$491$	−9379.41	−0.862091	−0.431046	−	0.902330i	$-0.641855\pi$
$491$	−9379.41	−0.862091	−0.431046	+	0.902330i	$0.641855\pi$
$492$	−2238.41	−0.205112
$493$	−2670.89	−0.243997
$494$	−13902.3	−1.26618
$495$	−331.637	−0.0301130
$496$	−2646.70	−0.239598
$497$	−2799.46	−0.252662
$498$	−15751.0	−1.41731
$499$	10270.7	0.921399	0.460699	−	0.887556i	$-0.347599\pi$
$499$	10270.7	0.921399	0.460699	+	0.887556i	$0.347599\pi$
$500$	3740.55	0.334565
$501$	14297.8	1.27501
$502$	13035.2	1.15895
$503$	6257.47	0.554685	0.277343	−	0.960771i	$-0.410546\pi$
$503$	6257.47	0.554685	0.277343	+	0.960771i	$0.410546\pi$
$504$	−453.089	−0.0400441
$505$	489.166	0.0431042
$506$	8860.01	0.778410
$507$	−245.729	−0.0215251
$508$	−12035.0	−1.05111
$509$	25.1849	0.00219313	0.00109656	−	0.999999i	$-0.499651\pi$
$509$	25.1849	0.00219313	0.00109656	+	0.999999i	$0.499651\pi$
$510$	−7684.18	−0.667179
$511$	1646.76	0.142560
$512$	−6002.15	−0.518086
$513$	9536.51	0.820755
$514$	−10123.4	−0.868725
$515$	−5381.69	−0.460477
$516$	9568.40	0.816328
$517$	−4660.91	−0.396492
$518$	−2475.47	−0.209973
$519$	−2205.71	−0.186551
$520$	−2210.26	−0.186397
$521$	−20463.8	−1.72080	−0.860400	−	0.509620i	$-0.829786\pi$
$521$	−20463.8	−1.72080	−0.860400	+	0.509620i	$0.829786\pi$
$522$	699.464	0.0586488
$523$	10921.2	0.913097	0.456548	−	0.889699i	$-0.349086\pi$
$523$	10921.2	0.913097	0.456548	+	0.889699i	$0.349086\pi$
$524$	−8312.81	−0.693028
$525$	−3044.84	−0.253119
$526$	−11830.5	−0.980676
$527$	3386.60	0.279929
$528$	5625.63	0.463682
$529$	32222.0	2.64831
$530$	6940.42	0.568816
$531$	6062.23	0.495439
$532$	−1681.94	−0.137071
$533$	4143.76	0.336747
$534$	21054.7	1.70623
$535$	3755.07	0.303450
$536$	−12342.9	−0.994646
$537$	732.033	0.0588260
$538$	−1602.13	−0.128388
$539$	−3848.90	−0.307576
$540$	−1801.51	−0.143564
$541$	−17288.3	−1.37390	−0.686951	−	0.726704i	$-0.741051\pi$
$541$	−17288.3	−1.37390	−0.686951	+	0.726704i	$0.741051\pi$
$542$	23416.5	1.85577
$543$	11681.8	0.923233
$544$	18183.4	1.43310
$545$	2590.50	0.203606
$546$	−4528.50	−0.354949
$547$	−11714.1	−0.915644	−0.457822	−	0.889044i	$-0.651370\pi$
$547$	−11714.1	−0.915644	−0.457822	+	0.889044i	$0.651370\pi$
$548$	5137.90	0.400511
$549$	207.022	0.0160938
$550$	4700.44	0.364414
$551$	−2185.26	−0.168957
$552$	15923.0	1.22777
$553$	1227.00	0.0943535
$554$	−6348.79	−0.486885
$555$	−3256.32	−0.249051
$556$	−8804.35	−0.671560
$557$	18721.2	1.42414	0.712068	−	0.702111i	$-0.247759\pi$
$557$	18721.2	1.42414	0.712068	+	0.702111i	$0.247759\pi$
$558$	−886.897	−0.0672855
$559$	−17713.1	−1.34022
$560$	−1345.00	−0.101494
$561$	−7198.29	−0.541733
$562$	−2470.70	−0.185445
$563$	−715.810	−0.0535840	−0.0267920	−	0.999641i	$-0.508529\pi$
$563$	−715.810	−0.0535840	−0.0267920	+	0.999641i	$0.508529\pi$
$564$	9952.93	0.743074
$565$	6416.72	0.477794
$566$	23652.7	1.75653
$567$	4058.80	0.300624
$568$	7766.75	0.573743
$569$	20488.7	1.50955	0.754773	−	0.655986i	$-0.227747\pi$
$569$	20488.7	1.50955	0.754773	+	0.655986i	$0.227747\pi$
$570$	−6287.03	−0.461990
$571$	−4689.14	−0.343668	−0.171834	−	0.985126i	$-0.554969\pi$
$571$	−4689.14	−0.343668	−0.171834	+	0.985126i	$0.554969\pi$
$572$	2460.17	0.179834
$573$	22079.2	1.60972
$574$	1424.57	0.103590
$575$	23549.4	1.70796
$576$	106.872	0.00773090
$577$	4798.38	0.346203	0.173102	−	0.984904i	$-0.444621\pi$
$577$	4798.38	0.346203	0.173102	+	0.984904i	$0.444621\pi$
$578$	−19444.8	−1.39930
$579$	−22802.5	−1.63668
$580$	412.811	0.0295535
$581$	3527.68	0.251898
$582$	4970.96	0.354042
$583$	6501.55	0.461864
$584$	−4568.73	−0.323725
$585$	−1310.99	−0.0926541
$586$	4149.19	0.292494
$587$	16210.2	1.13980	0.569902	−	0.821713i	$-0.306981\pi$
$587$	16210.2	1.13980	0.569902	+	0.821713i	$0.306981\pi$
$588$	8218.96	0.576435
$589$	2770.84	0.193838
$590$	10166.8	0.709421
$591$	−1159.10	−0.0806754
$592$	12156.6	0.843972
$593$	−3017.58	−0.208967	−0.104483	−	0.994527i	$-0.533319\pi$
$593$	−3017.58	−0.208967	−0.104483	+	0.994527i	$0.533319\pi$
$594$	−4795.49	−0.331248
$595$	1720.99	0.118578
$596$	8581.21	0.589765
$597$	−15220.1	−1.04341
$598$	35024.4	2.39507
$599$	23300.4	1.58936	0.794681	−	0.607027i	$-0.207638\pi$
$599$	23300.4	1.58936	0.794681	+	0.607027i	$0.207638\pi$
$600$	8447.53	0.574782
$601$	20904.9	1.41885	0.709423	−	0.704783i	$-0.248955\pi$
$601$	20904.9	1.41885	0.709423	+	0.704783i	$0.248955\pi$
$602$	−6089.55	−0.412278
$603$	−7321.01	−0.494419
$604$	3062.65	0.206320
$605$	4319.45	0.290265
$606$	−2780.56	−0.186391
$607$	−1814.07	−0.121303	−0.0606514	−	0.998159i	$-0.519318\pi$
$607$	−1814.07	−0.121303	−0.0606514	+	0.998159i	$0.519318\pi$
$608$	14877.2	0.992355
$609$	−711.824	−0.0473638
$610$	347.190	0.0230448
$611$	−18425.0	−1.21996
$612$	3382.86	0.223438
$613$	2776.88	0.182964	0.0914820	−	0.995807i	$-0.470840\pi$
$613$	2776.88	0.182964	0.0914820	+	0.995807i	$0.470840\pi$
$614$	−20428.1	−1.34269
$615$	1873.94	0.122869
$616$	−711.812	−0.0465580
$617$	−3610.10	−0.235555	−0.117777	−	0.993040i	$-0.537577\pi$
$617$	−3610.10	−0.235555	−0.117777	+	0.993040i	$0.537577\pi$
$618$	30591.1	1.99119
$619$	16764.1	1.08854	0.544270	−	0.838910i	$-0.316807\pi$
$619$	16764.1	1.08854	0.544270	+	0.838910i	$0.316807\pi$
$620$	−523.430	−0.0339056
$621$	−24025.6	−1.55252
$622$	10428.1	0.672235
$623$	−4715.53	−0.303249
$624$	22238.6	1.42669
$625$	10840.3	0.693780
$626$	−13749.6	−0.877864
$627$	−5889.48	−0.375125
$628$	−10710.0	−0.680533
$629$	−15555.0	−0.986037
$630$	−450.701	−0.0285022
$631$	27442.2	1.73131	0.865654	−	0.500643i	$-0.166903\pi$
$631$	27442.2	1.73131	0.865654	+	0.500643i	$0.166903\pi$
$632$	−3404.17	−0.214257
$633$	−11653.8	−0.731748
$634$	−15890.7	−0.995424
$635$	10075.4	0.629651
$636$	−13883.5	−0.865589
$637$	−15215.0	−0.946375
$638$	1098.87	0.0681892
$639$	4606.75	0.285196
$640$	5354.91	0.330737
$641$	−29798.8	−1.83617	−0.918083	−	0.396389i	$-0.870263\pi$
$641$	−29798.8	−1.83617	−0.918083	+	0.396389i	$0.870263\pi$
$642$	−21344.9	−1.31218
$643$	17644.4	1.08216	0.541079	−	0.840972i	$-0.318016\pi$
$643$	17644.4	1.08216	0.541079	+	0.840972i	$0.318016\pi$
$644$	4237.37	0.259279
$645$	−8010.41	−0.489007
$646$	−30032.2	−1.82910
$647$	−17216.2	−1.04612	−0.523059	−	0.852297i	$-0.675209\pi$
$647$	−17216.2	−1.04612	−0.523059	+	0.852297i	$0.675209\pi$
$648$	−11260.6	−0.682654
$649$	9523.88	0.576032
$650$	18581.2	1.12126
$651$	902.569	0.0543386
$652$	−11267.6	−0.676798
$653$	−21029.6	−1.26026	−0.630131	−	0.776489i	$-0.716999\pi$
$653$	−21029.6	−1.26026	−0.630131	+	0.776489i	$0.716999\pi$
$654$	−14725.2	−0.880429
$655$	6959.27	0.415147
$656$	−6995.80	−0.416372
$657$	−2709.88	−0.160917
$658$	−6334.27	−0.375282
$659$	3220.71	0.190381	0.0951905	−	0.995459i	$-0.469654\pi$
$659$	3220.71	0.190381	0.0951905	+	0.995459i	$0.469654\pi$
$660$	1112.56	0.0656158
$661$	19631.1	1.15516	0.577580	−	0.816334i	$-0.303997\pi$
$661$	19631.1	1.15516	0.577580	+	0.816334i	$0.303997\pi$
$662$	31077.1	1.82454
$663$	−28455.4	−1.66684
$664$	−9787.12	−0.572009
$665$	1408.08	0.0821097
$666$	4073.60	0.237010
$667$	5505.39	0.319594
$668$	−10556.2	−0.611423
$669$	11153.0	0.644542
$670$	−12277.8	−0.707960
$671$	325.236	0.0187118
$672$	4846.09	0.278187
$673$	−14877.7	−0.852143	−0.426071	−	0.904690i	$-0.640103\pi$
$673$	−14877.7	−0.852143	−0.426071	+	0.904690i	$0.640103\pi$
$674$	6698.43	0.382810
$675$	−12746.1	−0.726814
$676$	181.424	0.0103222
$677$	−14479.6	−0.822002	−0.411001	−	0.911635i	$-0.634821\pi$
$677$	−14479.6	−0.822002	−0.411001	+	0.911635i	$0.634821\pi$
$678$	−36474.5	−2.06607
$679$	−1113.32	−0.0629241
$680$	−4774.68	−0.269266
$681$	21075.8	1.18594
$682$	−1393.33	−0.0782309
$683$	−3919.42	−0.219579	−0.109790	−	0.993955i	$-0.535018\pi$
$683$	−3919.42	−0.219579	−0.109790	+	0.993955i	$0.535018\pi$
$684$	2767.78	0.154720
$685$	−4301.31	−0.239919
$686$	−10810.1	−0.601652
$687$	−1403.25	−0.0779292
$688$	29904.6	1.65712
$689$	25701.2	1.42110
$690$	15839.1	0.873889
$691$	−19260.0	−1.06033	−0.530163	−	0.847896i	$-0.677869\pi$
$691$	−19260.0	−1.06033	−0.530163	+	0.847896i	$0.677869\pi$
$692$	1628.49	0.0894595
$693$	−422.202	−0.0231431
$694$	34138.0	1.86723
$695$	7370.77	0.402286
$696$	1974.87	0.107553
$697$	8951.50	0.486460
$698$	7538.13	0.408771
$699$	−44.8664	−0.00242776
$700$	2248.02	0.121382
$701$	6425.04	0.346178	0.173089	−	0.984906i	$-0.444625\pi$
$701$	6425.04	0.346178	0.173089	+	0.984906i	$0.444625\pi$
$702$	−18957.0	−1.01921
$703$	−12726.7	−0.682785
$704$	167.898	0.00898848
$705$	−8332.33	−0.445126
$706$	37575.0	2.00305
$707$	622.751	0.0331272
$708$	−20337.4	−1.07955
$709$	−12737.5	−0.674706	−0.337353	−	0.941378i	$-0.609532\pi$
$709$	−12737.5	−0.674706	−0.337353	+	0.941378i	$0.609532\pi$
$710$	7725.82	0.408373
$711$	−2019.14	−0.106503
$712$	13082.7	0.688615
$713$	−6980.65	−0.366658
$714$	−9782.63	−0.512753
$715$	−2059.59	−0.107726
$716$	−540.464	−0.0282096
$717$	−33249.4	−1.73183
$718$	−863.197	−0.0448666
$719$	−23885.0	−1.23889	−0.619444	−	0.785041i	$-0.712642\pi$
$719$	−23885.0	−1.23889	−0.619444	+	0.785041i	$0.712642\pi$
$720$	2213.31	0.114563
$721$	−6851.36	−0.353895
$722$	−473.185	−0.0243908
$723$	−23636.5	−1.21584
$724$	−8624.77	−0.442731
$725$	2920.74	0.149619
$726$	−24553.0	−1.25516
$727$	−8319.05	−0.424397	−0.212198	−	0.977227i	$-0.568062\pi$
$727$	−8319.05	−0.424397	−0.212198	+	0.977227i	$0.568062\pi$
$728$	−2813.85	−0.143253
$729$	11436.7	0.581042
$730$	−4544.65	−0.230418
$731$	−38264.5	−1.93607
$732$	−694.511	−0.0350681
$733$	−4689.86	−0.236322	−0.118161	−	0.992994i	$-0.537700\pi$
$733$	−4689.86	−0.236322	−0.118161	+	0.992994i	$0.537700\pi$
$734$	63.7858	0.00320760
$735$	−6880.69	−0.345304
$736$	−37480.6	−1.87711
$737$	−11501.5	−0.574846
$738$	−2344.26	−0.116929
$739$	−34851.5	−1.73482	−0.867410	−	0.497593i	$-0.834217\pi$
$739$	−34851.5	−1.73482	−0.867410	+	0.497593i	$0.834217\pi$
$740$	2404.17	0.119431
$741$	−23281.6	−1.15421
$742$	8835.75	0.437157
$743$	10196.6	0.503466	0.251733	−	0.967797i	$-0.418999\pi$
$743$	10196.6	0.503466	0.251733	+	0.967797i	$0.418999\pi$
$744$	−2504.06	−0.123392
$745$	−7183.96	−0.353289
$746$	16932.4	0.831020
$747$	−5805.10	−0.284334
$748$	5314.54	0.259785
$749$	4780.53	0.233213
$750$	17800.3	0.866633
$751$	−28155.8	−1.36807	−0.684035	−	0.729449i	$-0.739777\pi$
$751$	−28155.8	−1.36807	−0.684035	+	0.729449i	$0.739777\pi$
$752$	31106.4	1.50842
$753$	21829.6	1.05646
$754$	4343.93	0.209810
$755$	−2563.97	−0.123593
$756$	−2293.48	−0.110335
$757$	−25859.5	−1.24159	−0.620793	−	0.783975i	$-0.713189\pi$
$757$	−25859.5	−1.24159	−0.620793	+	0.783975i	$0.713189\pi$
$758$	19290.4	0.924352
$759$	14837.5	0.709576
$760$	−3906.54	−0.186454
$761$	16677.2	0.794412	0.397206	−	0.917729i	$-0.369980\pi$
$761$	16677.2	0.794412	0.397206	+	0.917729i	$0.369980\pi$
$762$	−57271.3	−2.72273
$763$	3297.94	0.156479
$764$	−16301.2	−0.771933
$765$	−2832.04	−0.133847
$766$	1467.17	0.0692051
$767$	37648.7	1.77238
$768$	−29778.6	−1.39914
$769$	27179.3	1.27453	0.637263	−	0.770646i	$-0.280066\pi$
$769$	27179.3	1.27453	0.637263	+	0.770646i	$0.280066\pi$
$770$	−708.061	−0.0331386
$771$	−16953.3	−0.791905
$772$	16835.2	0.784861
$773$	22292.2	1.03725	0.518624	−	0.855002i	$-0.326444\pi$
$773$	22292.2	1.03725	0.518624	+	0.855002i	$0.326444\pi$
$774$	10020.9	0.465366
$775$	−3703.40	−0.171652
$776$	3088.78	0.142888
$777$	−4145.58	−0.191405
$778$	32302.8	1.48857
$779$	7323.92	0.336851
$780$	4398.05	0.201892
$781$	7237.29	0.331589
$782$	75660.9	3.45988
$783$	−2979.80	−0.136002
$784$	25687.1	1.17015
$785$	8966.11	0.407661
$786$	−39558.5	−1.79517
$787$	−32054.0	−1.45184	−0.725922	−	0.687777i	$-0.758587\pi$
$787$	−32054.0	−1.45184	−0.725922	+	0.687777i	$0.758587\pi$
$788$	855.773	0.0386874
$789$	−19812.2	−0.893956
$790$	−3386.23	−0.152502
$791$	8169.04	0.367203
$792$	1171.35	0.0525531
$793$	1285.69	0.0575738
$794$	−20281.7	−0.906512
$795$	11622.9	0.518516
$796$	11237.1	0.500362
$797$	−33811.7	−1.50273	−0.751363	−	0.659889i	$-0.770603\pi$
$797$	−33811.7	−1.50273	−0.751363	+	0.659889i	$0.770603\pi$
$798$	−8003.93	−0.355058
$799$	−39802.3	−1.76233
$800$	−19884.4	−0.878773
$801$	7759.81	0.342296
$802$	33632.2	1.48079
$803$	−4257.28	−0.187094
$804$	24560.3	1.07733
$805$	−3547.41	−0.155317
$806$	−5507.96	−0.240707
$807$	−2683.02	−0.117035
$808$	−1727.75	−0.0752251
$809$	8201.55	0.356429	0.178215	−	0.983992i	$-0.442968\pi$
$809$	8201.55	0.356429	0.178215	+	0.983992i	$0.442968\pi$
$810$	−11201.3	−0.485893
$811$	−19971.3	−0.864719	−0.432360	−	0.901701i	$-0.642319\pi$
$811$	−19971.3	−0.864719	−0.432360	+	0.901701i	$0.642319\pi$
$812$	525.544	0.0227130
$813$	39214.8	1.69166
$814$	6399.71	0.275565
$815$	9432.91	0.405424
$816$	48040.6	2.06098
$817$	−31307.2	−1.34064
$818$	−21372.3	−0.913525
$819$	−1669.00	−0.0712083
$820$	−1383.54	−0.0589210
$821$	−36634.6	−1.55731	−0.778657	−	0.627450i	$-0.784099\pi$
$821$	−36634.6	−1.55731	−0.778657	+	0.627450i	$0.784099\pi$
$822$	24449.9	1.03746
$823$	13329.2	0.564551	0.282276	−	0.959333i	$-0.408911\pi$
$823$	13329.2	0.564551	0.282276	+	0.959333i	$0.408911\pi$
$824$	19008.3	0.803621
$825$	7871.66	0.332189
$826$	12943.2	0.545218
$827$	−9004.64	−0.378624	−0.189312	−	0.981917i	$-0.560626\pi$
$827$	−9004.64	−0.378624	−0.189312	+	0.981917i	$0.560626\pi$
$828$	−6972.95	−0.292665
$829$	17302.1	0.724882	0.362441	−	0.932007i	$-0.381944\pi$
$829$	17302.1	0.724882	0.362441	+	0.932007i	$0.381944\pi$
$830$	−9735.54	−0.407139
$831$	−10632.1	−0.443830
$832$	663.715	0.0276564
$833$	−32868.0	−1.36712
$834$	−41897.6	−1.73956
$835$	8837.35	0.366262
$836$	4348.24	0.179889
$837$	3778.29	0.156029
$838$	−47944.3	−1.97638
$839$	32032.1	1.31808	0.659040	−	0.752108i	$-0.270963\pi$
$839$	32032.1	1.31808	0.659040	+	0.752108i	$0.270963\pi$
$840$	−1272.51	−0.0522688
$841$	−23706.2	−0.972003
$842$	−19054.5	−0.779883
$843$	−4137.59	−0.169047
$844$	8604.07	0.350905
$845$	−151.883	−0.00618335
$846$	10423.6	0.423606
$847$	5499.03	0.223080
$848$	−43390.6	−1.75712
$849$	39610.3	1.60120
$850$	40139.9	1.61975
$851$	32062.8	1.29154
$852$	−15454.6	−0.621437
$853$	7865.31	0.315713	0.157856	−	0.987462i	$-0.449542\pi$
$853$	7865.31	0.315713	0.157856	+	0.987462i	$0.449542\pi$
$854$	442.003	0.0177108
$855$	−2317.11	−0.0926826
$856$	−13263.0	−0.529579
$857$	36568.0	1.45757	0.728787	−	0.684741i	$-0.240085\pi$
$857$	36568.0	1.45757	0.728787	+	0.684741i	$0.240085\pi$
$858$	11707.3	0.465828
$859$	30481.8	1.21074	0.605370	−	0.795944i	$-0.293025\pi$
$859$	30481.8	1.21074	0.605370	+	0.795944i	$0.293025\pi$
$860$	5914.14	0.234500
$861$	2385.68	0.0944296
$862$	−5738.40	−0.226741
$863$	21264.0	0.838742	0.419371	−	0.907815i	$-0.362251\pi$
$863$	21264.0	0.838742	0.419371	+	0.907815i	$0.362251\pi$
$864$	20286.5	0.798795
$865$	−1363.33	−0.0535892
$866$	−7428.66	−0.291497
$867$	−32563.5	−1.27556
$868$	−666.372	−0.0260578
$869$	−3172.11	−0.123828
$870$	1964.46	0.0765533
$871$	−45466.2	−1.76873
$872$	−9149.72	−0.355331
$873$	1832.07	0.0710265
$874$	61904.0	2.39581
$875$	−3986.66	−0.154027
$876$	9091.02	0.350636
$877$	18451.3	0.710442	0.355221	−	0.934782i	$-0.384406\pi$
$877$	18451.3	0.710442	0.355221	+	0.934782i	$0.384406\pi$
$878$	−13294.1	−0.510995
$879$	6948.50	0.266629
$880$	3477.15	0.133198
$881$	3831.34	0.146517	0.0732583	−	0.997313i	$-0.476660\pi$
$881$	3831.34	0.146517	0.0732583	+	0.997313i	$0.476660\pi$
$882$	8607.62	0.328610
$883$	42640.9	1.62512	0.812560	−	0.582878i	$-0.198073\pi$
$883$	42640.9	1.62512	0.812560	+	0.582878i	$0.198073\pi$
$884$	21008.8	0.799325
$885$	17025.9	0.646688
$886$	−30158.2	−1.14355
$887$	−32452.3	−1.22846	−0.614228	−	0.789129i	$-0.710532\pi$
$887$	−32452.3	−1.22846	−0.614228	+	0.789129i	$0.710532\pi$
$888$	11501.4	0.434642
$889$	12826.8	0.483911
$890$	13013.7	0.490136
$891$	−10493.0	−0.394533
$892$	−8234.30	−0.309086
$893$	−32565.3	−1.22033
$894$	40835.7	1.52769
$895$	452.462	0.0168985
$896$	6817.27	0.254184
$897$	58654.0	2.18328
$898$	551.942	0.0205106
$899$	−865.782	−0.0321195
$900$	−3699.31	−0.137012
$901$	55520.6	2.05290
$902$	−3682.88	−0.135949
$903$	−10198.0	−0.375821
$904$	−22664.0	−0.833842
$905$	7220.43	0.265210
$906$	14574.4	0.534438
$907$	−5785.55	−0.211804	−0.105902	−	0.994377i	$-0.533773\pi$
$907$	−5785.55	−0.211804	−0.105902	+	0.994377i	$0.533773\pi$
$908$	−15560.4	−0.568712
$909$	−1024.79	−0.0373929
$910$	−2799.02	−0.101963
$911$	−37621.9	−1.36824	−0.684122	−	0.729368i	$-0.739814\pi$
$911$	−37621.9	−1.36824	−0.684122	+	0.729368i	$0.739814\pi$
$912$	39305.7	1.42713
$913$	−9119.93	−0.330587
$914$	14145.5	0.511917
$915$	581.427	0.0210070
$916$	1036.03	0.0373705
$917$	8859.75	0.319056
$918$	−40951.6	−1.47233
$919$	−19246.2	−0.690832	−0.345416	−	0.938450i	$-0.612262\pi$
$919$	−19246.2	−0.690832	−0.345416	+	0.938450i	$0.612262\pi$
$920$	9841.86	0.352692
$921$	−34210.1	−1.22395
$922$	−37810.8	−1.35058
$923$	28609.6	1.02026
$924$	1416.39	0.0504283
$925$	17010.1	0.604635
$926$	55733.8	1.97789
$927$	11274.5	0.399464
$928$	−4648.57	−0.164436
$929$	41377.0	1.46129	0.730643	−	0.682760i	$-0.239220\pi$
$929$	41377.0	1.46129	0.730643	+	0.682760i	$0.239220\pi$
$930$	−2490.87	−0.0878266
$931$	−26891.9	−0.946666
$932$	33.1252	0.00116422
$933$	17463.6	0.612790
$934$	41869.1	1.46681
$935$	−4449.19	−0.155619
$936$	4630.44	0.161699
$937$	4818.31	0.167991	0.0839953	−	0.996466i	$-0.473232\pi$
$937$	4818.31	0.167991	0.0839953	+	0.996466i	$0.473232\pi$
$938$	−15630.7	−0.544095
$939$	−23025.9	−0.800235
$940$	6151.81	0.213457
$941$	−31759.2	−1.10023	−0.550117	−	0.835087i	$-0.685417\pi$
$941$	−31759.2	−1.10023	−0.550117	+	0.835087i	$0.685417\pi$
$942$	−50966.0	−1.76280
$943$	−18451.4	−0.637178
$944$	−63561.3	−2.19147
$945$	1920.04	0.0660942
$946$	15743.0	0.541067
$947$	−9928.44	−0.340687	−0.170344	−	0.985385i	$-0.554488\pi$
$947$	−9928.44	−0.340687	−0.170344	+	0.985385i	$0.554488\pi$
$948$	6773.74	0.232068
$949$	−16829.4	−0.575664
$950$	32841.5	1.12160
$951$	−26611.5	−0.907400
$952$	−6078.59	−0.206941
$953$	8177.27	0.277952	0.138976	−	0.990296i	$-0.455619\pi$
$953$	8177.27	0.277952	0.138976	+	0.990296i	$0.455619\pi$
$954$	−14540.0	−0.493448
$955$	13646.9	0.462413
$956$	24548.2	0.830487
$957$	1840.24	0.0621594
$958$	−3885.75	−0.131047
$959$	−5475.94	−0.184387
$960$	300.152	0.0100910
$961$	−28693.2	−0.963151
$962$	25298.6	0.847879
$963$	−7866.77	−0.263243
$964$	17451.0	0.583047
$965$	−14094.0	−0.470157
$966$	20164.5	0.671618
$967$	−11001.0	−0.365842	−0.182921	−	0.983128i	$-0.558555\pi$
$967$	−11001.0	−0.365842	−0.182921	+	0.983128i	$0.558555\pi$
$968$	−15256.4	−0.506569
$969$	−50293.8	−1.66736
$970$	3072.50	0.101703
$971$	21841.1	0.721848	0.360924	−	0.932595i	$-0.382461\pi$
$971$	21841.1	0.721848	0.360924	+	0.932595i	$0.382461\pi$
$972$	9031.85	0.298042
$973$	9383.63	0.309173
$974$	−51793.2	−1.70386
$975$	31117.3	1.02210
$976$	−2170.59	−0.0711874
$977$	11260.0	0.368720	0.184360	−	0.982859i	$-0.440979\pi$
$977$	11260.0	0.368720	0.184360	+	0.982859i	$0.440979\pi$
$978$	−53619.4	−1.75313
$979$	12190.8	0.397978
$980$	5080.06	0.165588
$981$	−5427.04	−0.176628
$982$	32953.7	1.07087
$983$	−1782.46	−0.0578347	−0.0289174	−	0.999582i	$-0.509206\pi$
$983$	−1782.46	−0.0578347	−0.0289174	+	0.999582i	$0.509206\pi$
$984$	−6618.78	−0.214430
$985$	−716.431	−0.0231750
$986$	9383.91	0.303088
$987$	−10607.8	−0.342097
$988$	17189.0	0.553496
$989$	78873.0	2.53591
$990$	1165.17	0.0374057
$991$	44215.1	1.41729	0.708647	−	0.705564i	$-0.249306\pi$
$991$	44215.1	1.41729	0.708647	+	0.705564i	$0.249306\pi$
$992$	5894.24	0.188651
$993$	52043.6	1.66320
$994$	9835.64	0.313851
$995$	−9407.39	−0.299733
$996$	19474.8	0.619560
$997$	633.381	0.0201197	0.0100599	−	0.999949i	$-0.496798\pi$
$997$	633.381	0.0201197	0.0100599	+	0.999949i	$0.496798\pi$
$998$	−36085.0	−1.14454
$999$	−17354.0	−0.549607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.a.1.5	✓	22
3.2	odd	2		1773.4.a.c.1.18		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.a.1.5	✓	22	1.1	even	1	trivial
1773.4.a.c.1.18		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)

\(f(q)\)	\(=\)	\(q-3.51341 q^{2} -5.88377 q^{3} +4.34403 q^{4} -3.63670 q^{5} +20.6721 q^{6} -4.62984 q^{7} +12.8449 q^{8} +7.61880 q^{9} +12.7772 q^{10} +11.9693 q^{11} -25.5593 q^{12} +47.3156 q^{13} +16.2665 q^{14} +21.3975 q^{15} -79.8816 q^{16} +102.213 q^{17} -26.7679 q^{18} +83.6282 q^{19} -15.7979 q^{20} +27.2409 q^{21} -42.0530 q^{22} -210.687 q^{23} -75.5766 q^{24} -111.774 q^{25} -166.239 q^{26} +114.035 q^{27} -20.1122 q^{28} -26.1307 q^{29} -75.1783 q^{30} +33.1328 q^{31} +177.897 q^{32} -70.4245 q^{33} -359.115 q^{34} +16.8374 q^{35} +33.0963 q^{36} -152.182 q^{37} -293.820 q^{38} -278.394 q^{39} -46.7132 q^{40} +87.5771 q^{41} -95.7085 q^{42} -374.361 q^{43} +51.9949 q^{44} -27.7073 q^{45} +740.229 q^{46} -389.406 q^{47} +470.006 q^{48} -321.565 q^{49} +392.709 q^{50} -601.397 q^{51} +205.540 q^{52} +543.187 q^{53} -400.650 q^{54} -43.5287 q^{55} -59.4699 q^{56} -492.050 q^{57} +91.8076 q^{58} +795.694 q^{59} +92.9515 q^{60} +27.1726 q^{61} -116.409 q^{62} -35.2738 q^{63} +14.0274 q^{64} -172.073 q^{65} +247.430 q^{66} -960.914 q^{67} +444.015 q^{68} +1239.63 q^{69} -59.1565 q^{70} +604.656 q^{71} +97.8628 q^{72} -355.684 q^{73} +534.678 q^{74} +657.655 q^{75} +363.283 q^{76} -55.4159 q^{77} +978.112 q^{78} -265.021 q^{79} +290.506 q^{80} -876.661 q^{81} -307.694 q^{82} -761.945 q^{83} +118.335 q^{84} -371.718 q^{85} +1315.28 q^{86} +153.747 q^{87} +153.744 q^{88} +1018.51 q^{89} +97.3470 q^{90} -219.064 q^{91} -915.230 q^{92} -194.946 q^{93} +1368.14 q^{94} -304.131 q^{95} -1046.71 q^{96} +240.467 q^{97} +1129.79 q^{98} +91.1915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) \) 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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