LMFDB - Embedded newform 529.4.a.m.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, 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("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.17387 q^{2} +9.69393 q^{3} -6.62203 q^{4} -0.587346 q^{5} +11.3794 q^{6} -24.4606 q^{7} -17.1643 q^{8} +66.9723 q^{9} -0.689467 q^{10} -30.6659 q^{11} -64.1935 q^{12} -27.6225 q^{13} -28.7136 q^{14} -5.69369 q^{15} +32.8276 q^{16} +30.7916 q^{17} +78.6166 q^{18} -92.5849 q^{19} +3.88942 q^{20} -237.120 q^{21} -35.9977 q^{22} -166.390 q^{24} -124.655 q^{25} -32.4252 q^{26} +387.488 q^{27} +161.979 q^{28} -73.6185 q^{29} -6.68364 q^{30} -105.303 q^{31} +175.850 q^{32} -297.273 q^{33} +36.1452 q^{34} +14.3669 q^{35} -443.493 q^{36} -89.7975 q^{37} -108.682 q^{38} -267.771 q^{39} +10.0814 q^{40} -88.7884 q^{41} -278.347 q^{42} -365.622 q^{43} +203.070 q^{44} -39.3359 q^{45} +181.434 q^{47} +318.228 q^{48} +255.323 q^{49} -146.329 q^{50} +298.491 q^{51} +182.917 q^{52} -612.828 q^{53} +454.860 q^{54} +18.0115 q^{55} +419.851 q^{56} -897.511 q^{57} -86.4184 q^{58} +78.0294 q^{59} +37.7038 q^{60} -111.873 q^{61} -123.612 q^{62} -1638.18 q^{63} -56.1959 q^{64} +16.2240 q^{65} -348.959 q^{66} +408.709 q^{67} -203.903 q^{68} +16.8648 q^{70} +449.763 q^{71} -1149.53 q^{72} -93.4293 q^{73} -105.410 q^{74} -1208.40 q^{75} +613.100 q^{76} +750.107 q^{77} -314.328 q^{78} +277.946 q^{79} -19.2812 q^{80} +1948.03 q^{81} -104.226 q^{82} +1111.38 q^{83} +1570.21 q^{84} -18.0853 q^{85} -429.192 q^{86} -713.652 q^{87} +526.360 q^{88} +1272.90 q^{89} -46.1752 q^{90} +675.665 q^{91} -1020.80 q^{93} +212.979 q^{94} +54.3794 q^{95} +1704.68 q^{96} +1087.37 q^{97} +299.716 q^{98} -2053.76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * 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 $

$2$	1.17387	0.415025	0.207513	−	0.978232i	$-0.433463\pi$
$2$	1.17387	0.415025	0.207513	+	0.978232i	$0.433463\pi$
$3$	9.69393	1.86560	0.932799	−	0.360398i	$-0.117359\pi$
$3$	9.69393	1.86560	0.932799	+	0.360398i	$0.117359\pi$
$4$	−6.62203	−0.827754
$5$	−0.587346	−0.0525338	−0.0262669	−	0.999655i	$-0.508362\pi$
$5$	−0.587346	−0.0525338	−0.0262669	+	0.999655i	$0.508362\pi$
$6$	11.3794	0.774270
$7$	−24.4606	−1.32075	−0.660375	−	0.750936i	$-0.729603\pi$
$7$	−24.4606	−1.32075	−0.660375	+	0.750936i	$0.729603\pi$
$8$	−17.1643	−0.758564
$9$	66.9723	2.48045
$10$	−0.689467	−0.0218029
$11$	−30.6659	−0.840556	−0.420278	−	0.907396i	$-0.638067\pi$
$11$	−30.6659	−0.840556	−0.420278	+	0.907396i	$0.638067\pi$
$12$	−64.1935	−1.54426
$13$	−27.6225	−0.589317	−0.294658	−	0.955603i	$-0.595206\pi$
$13$	−27.6225	−0.589317	−0.294658	+	0.955603i	$0.595206\pi$
$14$	−28.7136	−0.548145
$15$	−5.69369	−0.0980070
$16$	32.8276	0.512931
$17$	30.7916	0.439297	0.219648	−	0.975579i	$-0.429509\pi$
$17$	30.7916	0.439297	0.219648	+	0.975579i	$0.429509\pi$
$18$	78.6166	1.02945
$19$	−92.5849	−1.11792	−0.558959	−	0.829196i	$-0.688799\pi$
$19$	−92.5849	−1.11792	−0.558959	+	0.829196i	$0.688799\pi$
$20$	3.88942	0.0434851
$21$	−237.120	−2.46399
$22$	−35.9977	−0.348852
$23$	0	0
$23$	0	0
$24$	−166.390	−1.41518
$25$	−124.655	−0.997240
$26$	−32.4252	−0.244581
$27$	387.488	2.76193
$28$	161.979	1.09326
$29$	−73.6185	−0.471400	−0.235700	−	0.971826i	$-0.575738\pi$
$29$	−73.6185	−0.471400	−0.235700	+	0.971826i	$0.575738\pi$
$30$	−6.68364	−0.0406754
$31$	−105.303	−0.610095	−0.305048	−	0.952337i	$-0.598672\pi$
$31$	−105.303	−0.610095	−0.305048	+	0.952337i	$0.598672\pi$
$32$	175.850	0.971443
$33$	−297.273	−1.56814
$34$	36.1452	0.182319
$35$	14.3669	0.0693841
$36$	−443.493	−2.05321
$37$	−89.7975	−0.398989	−0.199495	−	0.979899i	$-0.563930\pi$
$37$	−89.7975	−0.398989	−0.199495	+	0.979899i	$0.563930\pi$
$38$	−108.682	−0.463964
$39$	−267.771	−1.09943
$40$	10.0814	0.0398503
$41$	−88.7884	−0.338205	−0.169103	−	0.985598i	$-0.554087\pi$
$41$	−88.7884	−0.338205	−0.169103	+	0.985598i	$0.554087\pi$
$42$	−278.347	−1.02262
$43$	−365.622	−1.29667	−0.648334	−	0.761356i	$-0.724534\pi$
$43$	−365.622	−1.29667	−0.648334	+	0.761356i	$0.724534\pi$
$44$	203.070	0.695773
$45$	−39.3359	−0.130308
$46$	0	0
$47$	181.434	0.563082	0.281541	−	0.959549i	$-0.409154\pi$
$47$	181.434	0.563082	0.281541	+	0.959549i	$0.409154\pi$
$48$	318.228	0.956923
$49$	255.323	0.744382
$50$	−146.329	−0.413880
$51$	298.491	0.819551
$52$	182.917	0.487809
$53$	−612.828	−1.58827	−0.794136	−	0.607740i	$-0.792076\pi$
$53$	−612.828	−1.58827	−0.794136	+	0.607740i	$0.792076\pi$
$54$	454.860	1.14627
$55$	18.0115	0.0441576
$56$	419.851	1.00187
$57$	−897.511	−2.08558
$58$	−86.4184	−0.195643
$59$	78.0294	0.172179	0.0860895	−	0.996287i	$-0.472563\pi$
$59$	78.0294	0.172179	0.0860895	+	0.996287i	$0.472563\pi$
$60$	37.7038	0.0811257
$61$	−111.873	−0.234818	−0.117409	−	0.993084i	$-0.537459\pi$
$61$	−111.873	−0.234818	−0.117409	+	0.993084i	$0.537459\pi$
$62$	−123.612	−0.253205
$63$	−1638.18	−3.27606
$64$	−56.1959	−0.109758
$65$	16.2240	0.0309591
$66$	−348.959	−0.650817
$67$	408.709	0.745249	0.372625	−	0.927982i	$-0.378458\pi$
$67$	408.709	0.745249	0.372625	+	0.927982i	$0.378458\pi$
$68$	−203.903	−0.363630
$69$	0	0
$70$	16.8648	0.0287961
$71$	449.763	0.751790	0.375895	−	0.926662i	$-0.377335\pi$
$71$	449.763	0.751790	0.375895	+	0.926662i	$0.377335\pi$
$72$	−1149.53	−1.88158
$73$	−93.4293	−0.149796	−0.0748978	−	0.997191i	$-0.523863\pi$
$73$	−93.4293	−0.149796	−0.0748978	+	0.997191i	$0.523863\pi$
$74$	−105.410	−0.165591
$75$	−1208.40	−1.86045
$76$	613.100	0.925361
$77$	750.107	1.11016
$78$	−314.328	−0.456290
$79$	277.946	0.395840	0.197920	−	0.980218i	$-0.436581\pi$
$79$	277.946	0.395840	0.197920	+	0.980218i	$0.436581\pi$
$80$	−19.2812	−0.0269462
$81$	1948.03	2.67220
$82$	−104.226	−0.140364
$83$	1111.38	1.46976	0.734878	−	0.678199i	$-0.237239\pi$
$83$	1111.38	1.46976	0.734878	+	0.678199i	$0.237239\pi$
$84$	1570.21	2.03958
$85$	−18.0853	−0.0230779
$86$	−429.192	−0.538150
$87$	−713.652	−0.879443
$88$	526.360	0.637615
$89$	1272.90	1.51604	0.758018	−	0.652234i	$-0.226168\pi$
$89$	1272.90	1.51604	0.758018	+	0.652234i	$0.226168\pi$
$90$	−46.1752	−0.0540810
$91$	675.665	0.778340
$92$	0	0
$93$	−1020.80	−1.13819
$94$	212.979	0.233693
$95$	54.3794	0.0587285
$96$	1704.68	1.81232
$97$	1087.37	1.13821	0.569103	−	0.822266i	$-0.307290\pi$
$97$	1087.37	1.13821	0.569103	+	0.822266i	$0.307290\pi$
$98$	299.716	0.308937
$99$	−2053.76	−2.08496
$100$	825.470	0.825470
$101$	108.276	0.106672	0.0533359	−	0.998577i	$-0.483015\pi$
$101$	108.276	0.106672	0.0533359	+	0.998577i	$0.483015\pi$
$102$	350.389	0.340134
$103$	−11.9771	−0.0114577	−0.00572883	−	0.999984i	$-0.501824\pi$
$103$	−11.9771	−0.0114577	−0.00572883	+	0.999984i	$0.501824\pi$
$104$	474.123	0.447034
$105$	139.271	0.129443
$106$	−719.379	−0.659173
$107$	−1502.16	−1.35719	−0.678596	−	0.734511i	$-0.737411\pi$
$107$	−1502.16	−1.35719	−0.678596	+	0.734511i	$0.737411\pi$
$108$	−2565.96	−2.28620
$109$	−194.232	−0.170679	−0.0853395	−	0.996352i	$-0.527197\pi$
$109$	−194.232	−0.170679	−0.0853395	+	0.996352i	$0.527197\pi$
$110$	21.1431	0.0183265
$111$	−870.490	−0.744354
$112$	−802.984	−0.677454
$113$	1733.24	1.44292	0.721459	−	0.692457i	$-0.243472\pi$
$113$	1733.24	1.44292	0.721459	+	0.692457i	$0.243472\pi$
$114$	−1053.56	−0.865570
$115$	0	0
$116$	487.504	0.390204
$117$	−1849.94	−1.46177
$118$	91.5963	0.0714586
$119$	−753.181	−0.580202
$120$	97.7285	0.0743446
$121$	−390.604	−0.293466
$122$	−131.324	−0.0974554
$123$	−860.708	−0.630955
$124$	697.319	0.505009
$125$	146.634	0.104923
$126$	−1923.01	−1.35965
$127$	−2396.97	−1.67477	−0.837387	−	0.546611i	$-0.815918\pi$
$127$	−2396.97	−1.67477	−0.837387	+	0.546611i	$0.815918\pi$
$128$	−1472.77	−1.01700
$129$	−3544.31	−2.41906
$130$	19.0448	0.0128488
$131$	1316.52	0.878051	0.439026	−	0.898475i	$-0.355324\pi$
$131$	1316.52	0.878051	0.439026	+	0.898475i	$0.355324\pi$
$132$	1968.55	1.29803
$133$	2264.69	1.47649
$134$	479.770	0.309297
$135$	−227.590	−0.145095
$136$	−528.517	−0.333235
$137$	769.357	0.479785	0.239893	−	0.970799i	$-0.422888\pi$
$137$	769.357	0.479785	0.239893	+	0.970799i	$0.422888\pi$
$138$	0	0
$139$	−1772.15	−1.08138	−0.540691	−	0.841221i	$-0.681837\pi$
$139$	−1772.15	−1.08138	−0.540691	+	0.841221i	$0.681837\pi$
$140$	−95.1378	−0.0574330
$141$	1758.81	1.05048
$142$	527.963	0.312012
$143$	847.070	0.495353
$144$	2198.54	1.27230
$145$	43.2395	0.0247645
$146$	−109.674	−0.0621689
$147$	2475.08	1.38872
$148$	594.642	0.330265
$149$	1494.51	0.821712	0.410856	−	0.911700i	$-0.365230\pi$
$149$	1494.51	0.821712	0.410856	+	0.911700i	$0.365230\pi$
$150$	−1418.50	−0.772133
$151$	−528.951	−0.285069	−0.142535	−	0.989790i	$-0.545525\pi$
$151$	−528.951	−0.285069	−0.142535	+	0.989790i	$0.545525\pi$
$152$	1589.16	0.848012
$153$	2062.18	1.08966
$154$	880.527	0.460746
$155$	61.8492	0.0320506
$156$	1773.19	0.910056
$157$	−3442.60	−1.74999	−0.874997	−	0.484128i	$-0.839137\pi$
$157$	−3442.60	−1.74999	−0.874997	+	0.484128i	$0.839137\pi$
$158$	326.272	0.164284
$159$	−5940.71	−2.96308
$160$	−103.285	−0.0510336
$161$	0	0
$162$	2286.73	1.10903
$163$	377.403	0.181353	0.0906764	−	0.995880i	$-0.471097\pi$
$163$	377.403	0.181353	0.0906764	+	0.995880i	$0.471097\pi$
$164$	587.959	0.279951
$165$	174.602	0.0823803
$166$	1304.61	0.609986
$167$	−2896.03	−1.34192	−0.670962	−	0.741491i	$-0.734119\pi$
$167$	−2896.03	−1.34192	−0.670962	+	0.741491i	$0.734119\pi$
$168$	4070.00	1.86909
$169$	−1434.00	−0.652706
$170$	−21.2298	−0.00957793
$171$	−6200.62	−2.77294
$172$	2421.16	1.07332
$173$	1608.15	0.706736	0.353368	−	0.935484i	$-0.385036\pi$
$173$	1608.15	0.706736	0.353368	+	0.935484i	$0.385036\pi$
$174$	−837.734	−0.364991
$175$	3049.14	1.31711
$176$	−1006.69	−0.431147
$177$	756.412	0.321217
$178$	1494.22	0.629193
$179$	−1416.60	−0.591519	−0.295760	−	0.955262i	$-0.595573\pi$
$179$	−1416.60	−0.591519	−0.295760	+	0.955262i	$0.595573\pi$
$180$	260.484	0.107863
$181$	1568.05	0.643937	0.321968	−	0.946750i	$-0.395656\pi$
$181$	1568.05	0.643937	0.321968	+	0.946750i	$0.395656\pi$
$182$	793.142	0.323031
$183$	−1084.49	−0.438076
$184$	0	0
$185$	52.7422	0.0209604
$186$	−1198.28	−0.472378
$187$	−944.250	−0.369253
$188$	−1201.46	−0.466093
$189$	−9478.21	−3.64782
$190$	63.8342	0.0243738
$191$	384.504	0.145663	0.0728317	−	0.997344i	$-0.476796\pi$
$191$	384.504	0.145663	0.0728317	+	0.997344i	$0.476796\pi$
$192$	−544.759	−0.204764
$193$	−809.826	−0.302034	−0.151017	−	0.988531i	$-0.548255\pi$
$193$	−809.826	−0.302034	−0.151017	+	0.988531i	$0.548255\pi$
$194$	1276.43	0.472384
$195$	157.274	0.0577571
$196$	−1690.76	−0.616165
$197$	3503.08	1.26692	0.633462	−	0.773774i	$-0.281633\pi$
$197$	3503.08	1.26692	0.633462	+	0.773774i	$0.281633\pi$
$198$	−2410.85	−0.865311
$199$	−2373.06	−0.845337	−0.422669	−	0.906284i	$-0.638907\pi$
$199$	−2373.06	−0.845337	−0.422669	+	0.906284i	$0.638907\pi$
$200$	2139.62	0.756470
$201$	3961.99	1.39034
$202$	127.102	0.0442714
$203$	1800.76	0.622602
$204$	−1976.62	−0.678387
$205$	52.1495	0.0177672
$206$	−14.0596	−0.00475522
$207$	0	0
$208$	−906.781	−0.302279
$209$	2839.20	0.939672
$210$	163.486	0.0537220
$211$	−3176.30	−1.03633	−0.518165	−	0.855281i	$-0.673385\pi$
$211$	−3176.30	−1.03633	−0.518165	+	0.855281i	$0.673385\pi$
$212$	4058.17	1.31470
$213$	4359.97	1.40254
$214$	−1763.34	−0.563269
$215$	214.746	0.0681190
$216$	−6650.98	−2.09510
$217$	2575.77	0.805783
$218$	−228.002	−0.0708361
$219$	−905.697	−0.279458
$220$	−119.273	−0.0365516
$221$	−850.541	−0.258885
$222$	−1021.84	−0.308926
$223$	1100.91	0.330595	0.165297	−	0.986244i	$-0.447142\pi$
$223$	1100.91	0.330595	0.165297	+	0.986244i	$0.447142\pi$
$224$	−4301.40	−1.28303
$225$	−8348.43	−2.47361
$226$	2034.60	0.598847
$227$	−1829.06	−0.534796	−0.267398	−	0.963586i	$-0.586164\pi$
$227$	−1829.06	−0.534796	−0.267398	+	0.963586i	$0.586164\pi$
$228$	5943.35	1.72635
$229$	−4501.68	−1.29904	−0.649518	−	0.760346i	$-0.725029\pi$
$229$	−4501.68	−1.29904	−0.649518	+	0.760346i	$0.725029\pi$
$230$	0	0
$231$	7271.49	2.07112
$232$	1263.61	0.357587
$233$	1505.51	0.423302	0.211651	−	0.977345i	$-0.432116\pi$
$233$	1505.51	0.423302	0.211651	+	0.977345i	$0.432116\pi$
$234$	−2171.59	−0.606672
$235$	−106.564	−0.0295808
$236$	−516.713	−0.142522
$237$	2694.39	0.738479
$238$	−884.136	−0.240798
$239$	−3920.29	−1.06101	−0.530507	−	0.847680i	$-0.677999\pi$
$239$	−3920.29	−1.06101	−0.530507	+	0.847680i	$0.677999\pi$
$240$	−186.910	−0.0502708
$241$	1729.81	0.462352	0.231176	−	0.972912i	$-0.425743\pi$
$241$	1729.81	0.462352	0.231176	+	0.972912i	$0.425743\pi$
$242$	−458.517	−0.121796
$243$	8421.91	2.22332
$244$	740.828	0.194372
$245$	−149.963	−0.0391052
$246$	−1010.36	−0.261862
$247$	2557.43	0.658807
$248$	1807.45	0.462796
$249$	10773.6	2.74197
$250$	172.129	0.0435455
$251$	4882.48	1.22781	0.613903	−	0.789381i	$-0.289599\pi$
$251$	4882.48	1.22781	0.613903	+	0.789381i	$0.289599\pi$
$252$	10848.1	2.71177
$253$	0	0
$254$	−2813.72	−0.695073
$255$	−175.318	−0.0430542
$256$	−1279.27	−0.312321
$257$	−2123.46	−0.515399	−0.257699	−	0.966225i	$-0.582964\pi$
$257$	−2123.46	−0.515399	−0.257699	+	0.966225i	$0.582964\pi$
$258$	−4160.55	−1.00397
$259$	2196.50	0.526966
$260$	−107.436	−0.0256265
$261$	−4930.40	−1.16929
$262$	1545.42	0.364413
$263$	7204.31	1.68911	0.844556	−	0.535467i	$-0.179864\pi$
$263$	7204.31	1.68911	0.844556	+	0.535467i	$0.179864\pi$
$264$	5102.49	1.18953
$265$	359.942	0.0834380
$266$	2658.44	0.612781
$267$	12339.4	2.82831
$268$	−2706.48	−0.616883
$269$	4241.43	0.961355	0.480678	−	0.876897i	$-0.340391\pi$
$269$	4241.43	0.961355	0.480678	+	0.876897i	$0.340391\pi$
$270$	−267.160	−0.0602180
$271$	138.821	0.0311172	0.0155586	−	0.999879i	$-0.495047\pi$
$271$	138.821	0.0311172	0.0155586	+	0.999879i	$0.495047\pi$
$272$	1010.81	0.225329
$273$	6549.85	1.45207
$274$	903.124	0.199123
$275$	3822.66	0.838236
$276$	0	0
$277$	−4921.98	−1.06763	−0.533815	−	0.845601i	$-0.679242\pi$
$277$	−4921.98	−1.06763	−0.533815	+	0.845601i	$0.679242\pi$
$278$	−2080.27	−0.448801
$279$	−7052.37	−1.51331
$280$	−246.598	−0.0526323
$281$	283.484	0.0601824	0.0300912	−	0.999547i	$-0.490420\pi$
$281$	283.484	0.0601824	0.0300912	+	0.999547i	$0.490420\pi$
$282$	2064.61	0.435977
$283$	4333.16	0.910176	0.455088	−	0.890446i	$-0.349608\pi$
$283$	4333.16	0.910176	0.455088	+	0.890446i	$0.349608\pi$
$284$	−2978.35	−0.622297
$285$	527.150	0.109564
$286$	994.348	0.205584
$287$	2171.82	0.446685
$288$	11777.1	2.40962
$289$	−3964.88	−0.807018
$290$	50.7575	0.0102779
$291$	10540.9	2.12344
$292$	618.692	0.123994
$293$	−3837.64	−0.765179	−0.382590	−	0.923918i	$-0.624968\pi$
$293$	−3837.64	−0.765179	−0.382590	+	0.923918i	$0.624968\pi$
$294$	2905.42	0.576353
$295$	−45.8303	−0.00904523
$296$	1541.31	0.302659
$297$	−11882.7	−2.32156
$298$	1754.36	0.341031
$299$	0	0
$300$	8002.04	1.53999
$301$	8943.34	1.71258
$302$	−620.919	−0.118311
$303$	1049.62	0.199006
$304$	−3039.34	−0.573414
$305$	65.7083	0.0123359
$306$	2420.73	0.452235
$307$	8844.24	1.64419	0.822097	−	0.569348i	$-0.192804\pi$
$307$	8844.24	1.64419	0.822097	+	0.569348i	$0.192804\pi$
$308$	−4967.23	−0.918943
$309$	−116.105	−0.0213754
$310$	72.6028	0.0133018
$311$	−9833.47	−1.79294	−0.896471	−	0.443102i	$-0.853878\pi$
$311$	−9833.47	−1.79294	−0.896471	+	0.443102i	$0.853878\pi$
$312$	4596.11	0.833986
$313$	−3496.59	−0.631434	−0.315717	−	0.948853i	$-0.602245\pi$
$313$	−3496.59	−0.631434	−0.315717	+	0.948853i	$0.602245\pi$
$314$	−4041.16	−0.726292
$315$	962.181	0.172104
$316$	−1840.57	−0.327659
$317$	2612.24	0.462833	0.231417	−	0.972855i	$-0.425664\pi$
$317$	2612.24	0.462833	0.231417	+	0.972855i	$0.425664\pi$
$318$	−6973.61	−1.22975
$319$	2257.58	0.396238
$320$	33.0064	0.00576599
$321$	−14561.9	−2.53198
$322$	0	0
$323$	−2850.83	−0.491098
$324$	−12899.9	−2.21192
$325$	3443.29	0.587690
$326$	443.022	0.0752660
$327$	−1882.87	−0.318418
$328$	1523.99	0.256550
$329$	−4437.99	−0.743691
$330$	204.960	0.0341899
$331$	11428.7	1.89783	0.948913	−	0.315538i	$-0.102185\pi$
$331$	11428.7	1.89783	0.948913	+	0.315538i	$0.102185\pi$
$332$	−7359.59	−1.21660
$333$	−6013.94	−0.989675
$334$	−3399.56	−0.556933
$335$	−240.053	−0.0391508
$336$	−7784.07	−1.26386
$337$	−4033.06	−0.651913	−0.325957	−	0.945385i	$-0.605686\pi$
$337$	−4033.06	−0.651913	−0.325957	+	0.945385i	$0.605686\pi$
$338$	−1683.32	−0.270889
$339$	16801.9	2.69190
$340$	119.761	0.0191029
$341$	3229.20	0.512819
$342$	−7278.71	−1.15084
$343$	2144.63	0.337607
$344$	6275.65	0.983606
$345$	0	0
$346$	1887.75	0.293313
$347$	−3932.24	−0.608339	−0.304169	−	0.952618i	$-0.598379\pi$
$347$	−3932.24	−0.608339	−0.304169	+	0.952618i	$0.598379\pi$
$348$	4725.83	0.727963
$349$	−3467.83	−0.531887	−0.265943	−	0.963989i	$-0.585683\pi$
$349$	−3467.83	−0.531887	−0.265943	+	0.963989i	$0.585683\pi$
$350$	3579.29	0.546632
$351$	−10703.4	−1.62765
$352$	−5392.60	−0.816552
$353$	−9825.60	−1.48148	−0.740742	−	0.671789i	$-0.765526\pi$
$353$	−9825.60	−1.48148	−0.740742	+	0.671789i	$0.765526\pi$
$354$	887.928	0.133313
$355$	−264.167	−0.0394944
$356$	−8429.19	−1.25490
$357$	−7301.28	−1.08242
$358$	−1662.91	−0.245495
$359$	−11970.2	−1.75979	−0.879893	−	0.475171i	$-0.842386\pi$
$359$	−11970.2	−1.75979	−0.879893	+	0.475171i	$0.842386\pi$
$360$	675.175	0.0988468
$361$	1712.96	0.249739
$362$	1840.69	0.267250
$363$	−3786.49	−0.547490
$364$	−4474.28	−0.644274
$365$	54.8753	0.00786933
$366$	−1273.05	−0.181813
$367$	−9653.91	−1.37311	−0.686553	−	0.727080i	$-0.740877\pi$
$367$	−9653.91	−1.37311	−0.686553	+	0.727080i	$0.740877\pi$
$368$	0	0
$369$	−5946.36	−0.838902
$370$	61.9124	0.00869911
$371$	14990.2	2.09771
$372$	6759.76	0.942143
$373$	−137.458	−0.0190812	−0.00954059	−	0.999954i	$-0.503037\pi$
$373$	−137.458	−0.0190812	−0.00954059	+	0.999954i	$0.503037\pi$
$374$	−1108.43	−0.153249
$375$	1421.46	0.195743
$376$	−3114.19	−0.427134
$377$	2033.53	0.277804
$378$	−11126.2	−1.51394
$379$	7890.04	1.06935	0.534676	−	0.845057i	$-0.320434\pi$
$379$	7890.04	1.06935	0.534676	+	0.845057i	$0.320434\pi$
$380$	−360.102	−0.0486127
$381$	−23236.0	−3.12445
$382$	451.357	0.0604540
$383$	−1807.71	−0.241174	−0.120587	−	0.992703i	$-0.538478\pi$
$383$	−1807.71	−0.241174	−0.120587	+	0.992703i	$0.538478\pi$
$384$	−14276.9	−1.89730
$385$	−440.572	−0.0583212
$386$	−950.629	−0.125352
$387$	−24486.5	−3.21633
$388$	−7200.62	−0.942155
$389$	−2162.74	−0.281891	−0.140945	−	0.990017i	$-0.545014\pi$
$389$	−2162.74	−0.281891	−0.140945	+	0.990017i	$0.545014\pi$
$390$	184.619	0.0239707
$391$	0	0
$392$	−4382.45	−0.564662
$393$	12762.2	1.63809
$394$	4112.15	0.525805
$395$	−163.251	−0.0207950
$396$	13600.1	1.72583
$397$	6355.14	0.803414	0.401707	−	0.915768i	$-0.368417\pi$
$397$	6355.14	0.803414	0.401707	+	0.915768i	$0.368417\pi$
$398$	−2785.67	−0.350836
$399$	21953.7	2.75454
$400$	−4092.12	−0.511515
$401$	−9645.56	−1.20119	−0.600594	−	0.799554i	$-0.705069\pi$
$401$	−9645.56	−1.20119	−0.600594	+	0.799554i	$0.705069\pi$
$402$	4650.86	0.577024
$403$	2908.73	0.359539
$404$	−717.006	−0.0882980
$405$	−1144.17	−0.140381
$406$	2113.85	0.258396
$407$	2753.72	0.335373
$408$	−5123.40	−0.621682
$409$	11477.1	1.38754	0.693772	−	0.720194i	$-0.255947\pi$
$409$	11477.1	1.38754	0.693772	+	0.720194i	$0.255947\pi$
$410$	61.2166	0.00737384
$411$	7458.09	0.895086
$412$	79.3128	0.00948413
$413$	−1908.65	−0.227406
$414$	0	0
$415$	−652.764	−0.0772119
$416$	−4857.42	−0.572488
$417$	−17179.1	−2.01742
$418$	3332.84	0.389987
$419$	3855.90	0.449577	0.224789	−	0.974408i	$-0.427831\pi$
$419$	3855.90	0.449577	0.224789	+	0.974408i	$0.427831\pi$
$420$	−922.259	−0.107147
$421$	4672.08	0.540862	0.270431	−	0.962739i	$-0.412834\pi$
$421$	4672.08	0.540862	0.270431	+	0.962739i	$0.412834\pi$
$422$	−3728.56	−0.430103
$423$	12151.0	1.39670
$424$	10518.8	1.20481
$425$	−3838.32	−0.438085
$426$	5118.03	0.582088
$427$	2736.49	0.310136
$428$	9947.38	1.12342
$429$	8211.43	0.924130
$430$	252.084	0.0282711
$431$	−4050.67	−0.452700	−0.226350	−	0.974046i	$-0.572679\pi$
$431$	−4050.67	−0.452700	−0.226350	+	0.974046i	$0.572679\pi$
$432$	12720.3	1.41668
$433$	5685.17	0.630974	0.315487	−	0.948930i	$-0.397832\pi$
$433$	5685.17	0.630974	0.315487	+	0.948930i	$0.397832\pi$
$434$	3023.62	0.334420
$435$	419.161	0.0462005
$436$	1286.21	0.141280
$437$	0	0
$438$	−1063.17	−0.115982
$439$	−13746.7	−1.49452	−0.747262	−	0.664530i	$-0.768632\pi$
$439$	−13746.7	−1.49452	−0.747262	+	0.664530i	$0.768632\pi$
$440$	−309.155	−0.0334964
$441$	17099.6	1.84641
$442$	−998.423	−0.107444
$443$	−15256.9	−1.63629	−0.818146	−	0.575011i	$-0.804998\pi$
$443$	−15256.9	−1.63629	−0.818146	+	0.575011i	$0.804998\pi$
$444$	5764.41	0.616142
$445$	−747.633	−0.0796431
$446$	1292.33	0.137205
$447$	14487.7	1.53298
$448$	1374.59	0.144962
$449$	15743.1	1.65471	0.827355	−	0.561680i	$-0.189845\pi$
$449$	15743.1	1.65471	0.827355	+	0.561680i	$0.189845\pi$
$450$	−9799.96	−1.02661
$451$	2722.77	0.284280
$452$	−11477.6	−1.19438
$453$	−5127.62	−0.531824
$454$	−2147.07	−0.221954
$455$	−396.849	−0.0408892
$456$	15405.2	1.58205
$457$	−10842.0	−1.10978	−0.554888	−	0.831925i	$-0.687239\pi$
$457$	−10842.0	−1.10978	−0.554888	+	0.831925i	$0.687239\pi$
$458$	−5284.38	−0.539133
$459$	11931.4	1.21331
$460$	0	0
$461$	7583.77	0.766185	0.383093	−	0.923710i	$-0.374859\pi$
$461$	7583.77	0.766185	0.383093	+	0.923710i	$0.374859\pi$
$462$	8535.77	0.859567
$463$	−19753.0	−1.98272	−0.991360	−	0.131172i	$-0.958126\pi$
$463$	−19753.0	−1.98272	−0.991360	+	0.131172i	$0.958126\pi$
$464$	−2416.72	−0.241796
$465$	599.562	0.0597936
$466$	1767.27	0.175681
$467$	−12056.0	−1.19462	−0.597308	−	0.802012i	$-0.703763\pi$
$467$	−12056.0	−1.19462	−0.597308	+	0.802012i	$0.703763\pi$
$468$	12250.4	1.20999
$469$	−9997.27	−0.984288
$470$	−125.093	−0.0122768
$471$	−33372.3	−3.26479
$472$	−1339.32	−0.130609
$473$	11212.1	1.08992
$474$	3162.86	0.306487
$475$	11541.2	1.11483
$476$	4987.59	0.480264
$477$	−41042.5	−3.93963
$478$	−4601.90	−0.440348
$479$	−18771.9	−1.79063	−0.895315	−	0.445434i	$-0.853049\pi$
$479$	−18771.9	−1.79063	−0.895315	+	0.445434i	$0.853049\pi$
$480$	−1001.24	−0.0952082
$481$	2480.43	0.235131
$482$	2030.57	0.191888
$483$	0	0
$484$	2586.59	0.242918
$485$	−638.664	−0.0597943
$486$	9886.21	0.922732
$487$	−7040.17	−0.655073	−0.327536	−	0.944839i	$-0.606218\pi$
$487$	−7040.17	−0.655073	−0.327536	+	0.944839i	$0.606218\pi$
$488$	1920.23	0.178124
$489$	3658.52	0.338331
$490$	−176.037	−0.0162297
$491$	4346.65	0.399514	0.199757	−	0.979845i	$-0.435985\pi$
$491$	4346.65	0.399514	0.199757	+	0.979845i	$0.435985\pi$
$492$	5699.64	0.522275
$493$	−2266.83	−0.207085
$494$	3002.09	0.273422
$495$	1206.27	0.109531
$496$	−3456.84	−0.312937
$497$	−11001.5	−0.992927
$498$	12646.8	1.13799
$499$	−16754.5	−1.50307	−0.751537	−	0.659691i	$-0.770687\pi$
$499$	−16754.5	−1.50307	−0.751537	+	0.659691i	$0.770687\pi$
$500$	−971.014	−0.0868502
$501$	−28073.9	−2.50349
$502$	5731.39	0.509571
$503$	3703.57	0.328298	0.164149	−	0.986436i	$-0.447512\pi$
$503$	3703.57	0.328298	0.164149	+	0.986436i	$0.447512\pi$
$504$	28118.4	2.48510
$505$	−63.5954	−0.00560387
$506$	0	0
$507$	−13901.0	−1.21769
$508$	15872.8	1.38630
$509$	6453.52	0.561979	0.280990	−	0.959711i	$-0.409337\pi$
$509$	6453.52	0.561979	0.280990	+	0.959711i	$0.409337\pi$
$510$	−205.800	−0.0178686
$511$	2285.34	0.197843
$512$	10280.4	0.887374
$513$	−35875.6	−3.08761
$514$	−2492.66	−0.213904
$515$	7.03471	0.000601915 0
$516$	23470.5	2.00239
$517$	−5563.83	−0.473301
$518$	2578.41	0.218704
$519$	15589.3	1.31848
$520$	−278.474	−0.0234844
$521$	−2429.94	−0.204333	−0.102167	−	0.994767i	$-0.532577\pi$
$521$	−2429.94	−0.204333	−0.102167	+	0.994767i	$0.532577\pi$
$522$	−5787.64	−0.485283
$523$	2969.98	0.248314	0.124157	−	0.992263i	$-0.460377\pi$
$523$	2969.98	0.248314	0.124157	+	0.992263i	$0.460377\pi$
$524$	−8718.02	−0.726810
$525$	29558.2	2.45719
$526$	8456.91	0.701024
$527$	−3242.44	−0.268013
$528$	−9758.75	−0.804347
$529$	0	0
$530$	422.525	0.0346289
$531$	5225.81	0.427082
$532$	−14996.8	−1.22217
$533$	2452.56	0.199310
$534$	14484.8	1.17382
$535$	882.290	0.0712985
$536$	−7015.21	−0.565319
$537$	−13732.5	−1.10354
$538$	4978.88	0.398987
$539$	−7829.71	−0.625695
$540$	1507.11	0.120103
$541$	8519.05	0.677011	0.338505	−	0.940964i	$-0.390079\pi$
$541$	8519.05	0.677011	0.338505	+	0.940964i	$0.390079\pi$
$542$	162.957	0.0129144
$543$	15200.6	1.20133
$544$	5414.69	0.426752
$545$	114.081	0.00896642
$546$	7688.66	0.602645
$547$	−3650.33	−0.285333	−0.142666	−	0.989771i	$-0.545568\pi$
$547$	−3650.33	−0.285333	−0.142666	+	0.989771i	$0.545568\pi$
$548$	−5094.71	−0.397144
$549$	−7492.40	−0.582455
$550$	4487.30	0.347889
$551$	6815.96	0.526987
$552$	0	0
$553$	−6798.74	−0.522807
$554$	−5777.76	−0.443093
$555$	511.279	0.0391038
$556$	11735.3	0.895118
$557$	−22573.5	−1.71718	−0.858590	−	0.512663i	$-0.828659\pi$
$557$	−22573.5	−1.71718	−0.858590	+	0.512663i	$0.828659\pi$
$558$	−8278.55	−0.628063
$559$	10099.4	0.764148
$560$	471.629	0.0355892
$561$	−9153.49	−0.688878
$562$	332.773	0.0249772
$563$	12613.2	0.944195	0.472098	−	0.881546i	$-0.343497\pi$
$563$	12613.2	0.944195	0.472098	+	0.881546i	$0.343497\pi$
$564$	−11646.9	−0.869542
$565$	−1018.01	−0.0758020
$566$	5086.56	0.377746
$567$	−47650.1	−3.52931
$568$	−7719.89	−0.570280
$569$	−9750.27	−0.718370	−0.359185	−	0.933266i	$-0.616945\pi$
$569$	−9750.27	−0.718370	−0.359185	+	0.933266i	$0.616945\pi$
$570$	618.804	0.0454717
$571$	−1830.62	−0.134167	−0.0670833	−	0.997747i	$-0.521369\pi$
$571$	−1830.62	−0.134167	−0.0670833	+	0.997747i	$0.521369\pi$
$572$	−5609.32	−0.410031
$573$	3727.35	0.271749
$574$	2549.43	0.185385
$575$	0	0
$576$	−3763.57	−0.272249
$577$	1268.49	0.0915216	0.0457608	−	0.998952i	$-0.485429\pi$
$577$	1268.49	0.0915216	0.0457608	+	0.998952i	$0.485429\pi$
$578$	−4654.25	−0.334933
$579$	−7850.40	−0.563474
$580$	−286.334	−0.0204989
$581$	−27185.1	−1.94118
$582$	12373.7	0.881279
$583$	18792.9	1.33503
$584$	1603.65	0.113629
$585$	1086.56	0.0767925
$586$	−4504.89	−0.317569
$587$	21071.6	1.48163	0.740815	−	0.671709i	$-0.234440\pi$
$587$	21071.6	1.48163	0.740815	+	0.671709i	$0.234440\pi$
$588$	−16390.1	−1.14952
$589$	9749.45	0.682036
$590$	−53.7987	−0.00375400
$591$	33958.6	2.36357
$592$	−2947.83	−0.204654
$593$	16139.6	1.11766	0.558832	−	0.829281i	$-0.311250\pi$
$593$	16139.6	1.11766	0.558832	+	0.829281i	$0.311250\pi$
$594$	−13948.7	−0.963504
$595$	442.378	0.0304802
$596$	−9896.70	−0.680175
$597$	−23004.3	−1.57706
$598$	0	0
$599$	16255.0	1.10878	0.554392	−	0.832256i	$-0.312951\pi$
$599$	16255.0	1.10878	0.554392	+	0.832256i	$0.312951\pi$
$600$	20741.3	1.41127
$601$	3605.45	0.244708	0.122354	−	0.992487i	$-0.460956\pi$
$601$	3605.45	0.244708	0.122354	+	0.992487i	$0.460956\pi$
$602$	10498.3	0.710762
$603$	27372.1	1.84856
$604$	3502.73	0.235967
$605$	229.420	0.0154169
$606$	1232.11	0.0825927
$607$	−16980.6	−1.13546	−0.567729	−	0.823216i	$-0.692178\pi$
$607$	−16980.6	−1.13546	−0.567729	+	0.823216i	$0.692178\pi$
$608$	−16281.1	−1.08599
$609$	17456.4	1.16153
$610$	77.1329	0.00511970
$611$	−5011.66	−0.331833
$612$	−13655.8	−0.901967
$613$	14497.7	0.955232	0.477616	−	0.878569i	$-0.341501\pi$
$613$	14497.7	0.955232	0.477616	+	0.878569i	$0.341501\pi$
$614$	10382.0	0.682382
$615$	505.534	0.0331465
$616$	−12875.1	−0.842131
$617$	−7868.94	−0.513439	−0.256719	−	0.966486i	$-0.582642\pi$
$617$	−7868.94	−0.513439	−0.256719	+	0.966486i	$0.582642\pi$
$618$	−136.292	−0.00887133
$619$	−18273.6	−1.18655	−0.593277	−	0.804998i	$-0.702166\pi$
$619$	−18273.6	−1.18655	−0.593277	+	0.804998i	$0.702166\pi$
$620$	−409.567	−0.0265300
$621$	0	0
$622$	−11543.2	−0.744116
$623$	−31136.0	−2.00230
$624$	−8790.27	−0.563930
$625$	15495.8	0.991728
$626$	−4104.53	−0.262061
$627$	27523.0	1.75305
$628$	22797.0	1.44857
$629$	−2765.00	−0.175275
$630$	1129.47	0.0714275
$631$	1634.71	0.103133	0.0515663	−	0.998670i	$-0.483579\pi$
$631$	1634.71	0.103133	0.0515663	+	0.998670i	$0.483579\pi$
$632$	−4770.76	−0.300270
$633$	−30790.8	−1.93337
$634$	3066.43	0.192087
$635$	1407.85	0.0879823
$636$	39339.6	2.45270
$637$	−7052.67	−0.438677
$638$	2650.10	0.164449
$639$	30121.7	1.86478
$640$	865.024	0.0534267
$641$	19755.3	1.21730	0.608649	−	0.793440i	$-0.291712\pi$
$641$	19755.3	1.21730	0.608649	+	0.793440i	$0.291712\pi$
$642$	−17093.7	−1.05083
$643$	24024.7	1.47347	0.736734	−	0.676183i	$-0.236367\pi$
$643$	24024.7	1.47347	0.736734	+	0.676183i	$0.236367\pi$
$644$	0	0
$645$	2081.74	0.127083
$646$	−3346.50	−0.203818
$647$	14166.4	0.860800	0.430400	−	0.902638i	$-0.358372\pi$
$647$	14166.4	0.860800	0.430400	+	0.902638i	$0.358372\pi$
$648$	−33436.7	−2.02703
$649$	−2392.84	−0.144726
$650$	4041.97	0.243906
$651$	24969.4	1.50327
$652$	−2499.18	−0.150116
$653$	11598.1	0.695052	0.347526	−	0.937670i	$-0.387022\pi$
$653$	11598.1	0.695052	0.347526	+	0.937670i	$0.387022\pi$
$654$	−2210.24	−0.132152
$655$	−773.252	−0.0461274
$656$	−2914.71	−0.173476
$657$	−6257.17	−0.371561
$658$	−5209.61	−0.308650
$659$	−30479.8	−1.80171	−0.900853	−	0.434125i	$-0.857058\pi$
$659$	−30479.8	−1.80171	−0.900853	+	0.434125i	$0.857058\pi$
$660$	−1156.22	−0.0681906
$661$	27809.9	1.63643	0.818216	−	0.574912i	$-0.194964\pi$
$661$	27809.9	1.63643	0.818216	+	0.574912i	$0.194964\pi$
$662$	13415.8	0.787646
$663$	−8245.08	−0.482975
$664$	−19076.1	−1.11490
$665$	−1330.15	−0.0775657
$666$	−7059.57	−0.410740
$667$	0	0
$668$	19177.6	1.11078
$669$	10672.2	0.616756
$670$	−281.791	−0.0162486
$671$	3430.69	0.197378
$672$	−41697.5	−2.39363
$673$	1539.86	0.0881978	0.0440989	−	0.999027i	$-0.485958\pi$
$673$	1539.86	0.0881978	0.0440989	+	0.999027i	$0.485958\pi$
$674$	−4734.28	−0.270560
$675$	−48302.4	−2.75431
$676$	9495.96	0.540280
$677$	−33929.3	−1.92616	−0.963078	−	0.269223i	$-0.913233\pi$
$677$	−33929.3	−1.92616	−0.963078	+	0.269223i	$0.913233\pi$
$678$	19723.2	1.11721
$679$	−26597.9	−1.50329
$680$	310.422	0.0175061
$681$	−17730.7	−0.997714
$682$	3790.66	0.212833
$683$	−10808.3	−0.605518	−0.302759	−	0.953067i	$-0.597908\pi$
$683$	−10808.3	−0.605518	−0.302759	+	0.953067i	$0.597908\pi$
$684$	41060.7	2.29531
$685$	−451.879	−0.0252050
$686$	2517.52	0.140116
$687$	−43639.0	−2.42348
$688$	−12002.5	−0.665102
$689$	16927.9	0.935995
$690$	0	0
$691$	28965.6	1.59465	0.797325	−	0.603551i	$-0.206248\pi$
$691$	28965.6	1.59465	0.797325	+	0.603551i	$0.206248\pi$
$692$	−10649.2	−0.585003
$693$	50236.4	2.75371
$694$	−4615.93	−0.252476
$695$	1040.87	0.0568091
$696$	12249.4	0.667114
$697$	−2733.93	−0.148573
$698$	−4070.77	−0.220746
$699$	14594.3	0.789712
$700$	−20191.5	−1.09024
$701$	−30041.4	−1.61861	−0.809307	−	0.587385i	$-0.800157\pi$
$701$	−30041.4	−1.61861	−0.809307	+	0.587385i	$0.800157\pi$
$702$	−12564.4	−0.675516
$703$	8313.89	0.446037
$704$	1723.30	0.0922574
$705$	−1033.03	−0.0551859
$706$	−11534.0	−0.614853
$707$	−2648.50	−0.140887
$708$	−5008.98	−0.265889
$709$	−14593.2	−0.773005	−0.386502	−	0.922288i	$-0.626317\pi$
$709$	−14593.2	−0.773005	−0.386502	+	0.922288i	$0.626317\pi$
$710$	−310.097	−0.0163912
$711$	18614.7	0.981864
$712$	−21848.5	−1.15001
$713$	0	0
$714$	−8570.75	−0.449233
$715$	−497.523	−0.0260228
$716$	9380.80	0.489633
$717$	−38003.0	−1.97943
$718$	−14051.5	−0.730356
$719$	−3122.74	−0.161973	−0.0809865	−	0.996715i	$-0.525807\pi$
$719$	−3122.74	−0.161973	−0.0809865	+	0.996715i	$0.525807\pi$
$720$	−1291.30	−0.0668389
$721$	292.968	0.0151327
$722$	2010.79	0.103648
$723$	16768.6	0.862562
$724$	−10383.7	−0.533021
$725$	9176.91	0.470099
$726$	−4444.84	−0.227222
$727$	−14918.8	−0.761083	−0.380542	−	0.924764i	$-0.624262\pi$
$727$	−14918.8	−0.761083	−0.380542	+	0.924764i	$0.624262\pi$
$728$	−11597.3	−0.590421
$729$	29044.5	1.47561
$730$	64.4164	0.00326597
$731$	−11258.1	−0.569623
$732$	7181.54	0.362619
$733$	26710.9	1.34596	0.672979	−	0.739661i	$-0.265014\pi$
$733$	26710.9	1.34596	0.672979	+	0.739661i	$0.265014\pi$
$734$	−11332.4	−0.569873
$735$	−1453.73	−0.0729547
$736$	0	0
$737$	−12533.4	−0.626423
$738$	−6980.24	−0.348166
$739$	−2964.37	−0.147559	−0.0737795	−	0.997275i	$-0.523506\pi$
$739$	−2964.37	−0.147559	−0.0737795	+	0.997275i	$0.523506\pi$
$740$	−349.260	−0.0173501
$741$	24791.5	1.22907
$742$	17596.5	0.870603
$743$	−26986.8	−1.33250	−0.666251	−	0.745727i	$-0.732102\pi$
$743$	−26986.8	−1.33250	−0.666251	+	0.745727i	$0.732102\pi$
$744$	17521.3	0.863391
$745$	−877.795	−0.0431677
$746$	−161.357	−0.00791917
$747$	74431.6	3.64566
$748$	6252.85	0.305651
$749$	36743.9	1.79251
$750$	1668.61	0.0812385
$751$	14830.2	0.720590	0.360295	−	0.932838i	$-0.382676\pi$
$751$	14830.2	0.720590	0.360295	+	0.932838i	$0.382676\pi$
$752$	5956.03	0.288822
$753$	47330.4	2.29059
$754$	2387.10	0.115296
$755$	310.677	0.0149758
$756$	62765.0	3.01950
$757$	9664.66	0.464026	0.232013	−	0.972713i	$-0.425469\pi$
$757$	9664.66	0.464026	0.232013	+	0.972713i	$0.425469\pi$
$758$	9261.87	0.443808
$759$	0	0
$760$	−933.386	−0.0445493
$761$	−36725.0	−1.74938	−0.874692	−	0.484679i	$-0.838937\pi$
$761$	−36725.0	−1.74938	−0.874692	+	0.484679i	$0.838937\pi$
$762$	−27276.0	−1.29673
$763$	4751.03	0.225424
$764$	−2546.20	−0.120574
$765$	−1211.21	−0.0572438
$766$	−2122.01	−0.100093
$767$	−2155.37	−0.101468
$768$	−12401.1	−0.582665
$769$	18130.2	0.850185	0.425093	−	0.905150i	$-0.360242\pi$
$769$	18130.2	0.850185	0.425093	+	0.905150i	$0.360242\pi$
$770$	−517.174	−0.0242048
$771$	−20584.6	−0.961527
$772$	5362.70	0.250010
$773$	−11953.0	−0.556172	−0.278086	−	0.960556i	$-0.589700\pi$
$773$	−11953.0	−0.556172	−0.278086	+	0.960556i	$0.589700\pi$
$774$	−28743.9	−1.33486
$775$	13126.5	0.608411
$776$	−18664.0	−0.863402
$777$	21292.8	0.983106
$778$	−2538.78	−0.116992
$779$	8220.46	0.378085
$780$	−1041.48	−0.0478087
$781$	−13792.4	−0.631921
$782$	0	0
$783$	−28526.3	−1.30198
$784$	8381.64	0.381817
$785$	2022.00	0.0919339
$786$	14981.2	0.679849
$787$	−40503.7	−1.83456	−0.917281	−	0.398240i	$-0.869621\pi$
$787$	−40503.7	−1.83456	−0.917281	+	0.398240i	$0.869621\pi$
$788$	−23197.5	−1.04870
$789$	69838.0	3.15120
$790$	−191.635	−0.00863045
$791$	−42396.2	−1.90573
$792$	35251.5	1.58158
$793$	3090.22	0.138382
$794$	7460.10	0.333437
$795$	3489.25	0.155662
$796$	15714.5	0.699731
$797$	12298.0	0.546572	0.273286	−	0.961933i	$-0.411889\pi$
$797$	12298.0	0.546572	0.273286	+	0.961933i	$0.411889\pi$
$798$	25770.8	1.14320
$799$	5586.63	0.247360
$800$	−21920.6	−0.968762
$801$	85249.0	3.76046
$802$	−11322.6	−0.498523
$803$	2865.09	0.125911
$804$	−26236.4	−1.15086
$805$	0	0
$806$	3414.47	0.149218
$807$	41116.1	1.79350
$808$	−1858.48	−0.0809173
$809$	−16905.2	−0.734680	−0.367340	−	0.930087i	$-0.619731\pi$
$809$	−16905.2	−0.734680	−0.367340	+	0.930087i	$0.619731\pi$
$810$	−1343.10	−0.0582616
$811$	−16394.6	−0.709856	−0.354928	−	0.934894i	$-0.615495\pi$
$811$	−16394.6	−0.709856	−0.354928	+	0.934894i	$0.615495\pi$
$812$	−11924.7	−0.515362
$813$	1345.72	0.0580522
$814$	3232.50	0.139188
$815$	−221.666	−0.00952716
$816$	9798.74	0.420373
$817$	33851.0	1.44957
$818$	13472.6	0.575866
$819$	45250.8	1.93064
$820$	−345.336	−0.0147069
$821$	−12507.3	−0.531678	−0.265839	−	0.964017i	$-0.585649\pi$
$821$	−12507.3	−0.531678	−0.265839	+	0.964017i	$0.585649\pi$
$822$	8754.82	0.371483
$823$	−21644.9	−0.916762	−0.458381	−	0.888756i	$-0.651570\pi$
$823$	−21644.9	−0.916762	−0.458381	+	0.888756i	$0.651570\pi$
$824$	205.579	0.00869137
$825$	37056.6	1.56381
$826$	−2240.50	−0.0943791
$827$	27944.8	1.17501	0.587506	−	0.809220i	$-0.300110\pi$
$827$	27944.8	1.17501	0.587506	+	0.809220i	$0.300110\pi$
$828$	0	0
$829$	25947.0	1.08706	0.543532	−	0.839389i	$-0.317087\pi$
$829$	25947.0	1.08706	0.543532	+	0.839389i	$0.317087\pi$
$830$	−766.259	−0.0320449
$831$	−47713.4	−1.99177
$832$	1552.27	0.0646820
$833$	7861.79	0.327005
$834$	−20166.0	−0.837281
$835$	1700.97	0.0704964
$836$	−18801.3	−0.777817
$837$	−40803.6	−1.68504
$838$	4526.32	0.186586
$839$	−1120.66	−0.0461139	−0.0230569	−	0.999734i	$-0.507340\pi$
$839$	−1120.66	−0.0461139	−0.0230569	+	0.999734i	$0.507340\pi$
$840$	−2390.50	−0.0981906
$841$	−18969.3	−0.777782
$842$	5484.40	0.224472
$843$	2748.08	0.112276
$844$	21033.6	0.857826
$845$	842.251	0.0342891
$846$	14263.7	0.579665
$847$	9554.42	0.387596
$848$	−20117.7	−0.814674
$849$	42005.4	1.69802
$850$	−4505.68	−0.181816
$851$	0	0
$852$	−28871.9	−1.16096
$853$	−18601.6	−0.746667	−0.373333	−	0.927697i	$-0.621785\pi$
$853$	−18601.6	−0.746667	−0.373333	+	0.927697i	$0.621785\pi$
$854$	3212.28	0.128714
$855$	3641.91	0.145673
$856$	25783.6	1.02952
$857$	28344.3	1.12978	0.564892	−	0.825165i	$-0.308918\pi$
$857$	28344.3	1.12978	0.564892	+	0.825165i	$0.308918\pi$
$858$	9639.14	0.383537
$859$	−107.391	−0.00426559	−0.00213280	−	0.999998i	$-0.500679\pi$
$859$	−107.391	−0.00426559	−0.00213280	+	0.999998i	$0.500679\pi$
$860$	−1422.06	−0.0563858
$861$	21053.5	0.833334
$862$	−4754.95	−0.187882
$863$	35907.9	1.41636	0.708180	−	0.706032i	$-0.249517\pi$
$863$	35907.9	1.41636	0.708180	+	0.706032i	$0.249517\pi$
$864$	68139.8	2.68306
$865$	−944.539	−0.0371275
$866$	6673.64	0.261870
$867$	−38435.3	−1.50557
$868$	−17056.9	−0.666991
$869$	−8523.47	−0.332726
$870$	492.040	0.0191744
$871$	−11289.6	−0.439188
$872$	3333.86	0.129471
$873$	72823.8	2.82327
$874$	0	0
$875$	−3586.76	−0.138577
$876$	5997.56	0.231323
$877$	−8234.30	−0.317050	−0.158525	−	0.987355i	$-0.550674\pi$
$877$	−8234.30	−0.317050	−0.158525	+	0.987355i	$0.550674\pi$
$878$	−16136.9	−0.620265
$879$	−37201.8	−1.42752
$880$	591.273	0.0226498
$881$	−16025.9	−0.612854	−0.306427	−	0.951894i	$-0.599134\pi$
$881$	−16025.9	−0.612854	−0.306427	+	0.951894i	$0.599134\pi$
$882$	20072.6	0.766305
$883$	29326.1	1.11767	0.558834	−	0.829279i	$-0.311249\pi$
$883$	29326.1	1.11767	0.558834	+	0.829279i	$0.311249\pi$
$884$	5632.31	0.214293
$885$	−444.275	−0.0168748
$886$	−17909.6	−0.679102
$887$	39253.1	1.48590	0.742948	−	0.669349i	$-0.233427\pi$
$887$	39253.1	1.48590	0.742948	+	0.669349i	$0.233427\pi$
$888$	14941.4	0.564640
$889$	58631.3	2.21196
$890$	−877.623	−0.0330539
$891$	−59738.1	−2.24613
$892$	−7290.28	−0.273651
$893$	−16798.0	−0.629479
$894$	17006.6	0.636227
$895$	832.037	0.0310748
$896$	36024.8	1.34320
$897$	0	0
$898$	18480.4	0.686746
$899$	7752.23	0.287599
$900$	55283.6	2.04754
$901$	−18869.9	−0.697723
$902$	3196.18	0.117983
$903$	86696.1	3.19498
$904$	−29750.0	−1.09455
$905$	−920.990	−0.0338285
$906$	−6019.15	−0.220720
$907$	−18835.3	−0.689542	−0.344771	−	0.938687i	$-0.612043\pi$
$907$	−18835.3	−0.689542	−0.344771	+	0.938687i	$0.612043\pi$
$908$	12112.1	0.442680
$909$	7251.47	0.264594
$910$	−465.849	−0.0169700
$911$	−27434.4	−0.997742	−0.498871	−	0.866676i	$-0.666252\pi$
$911$	−27434.4	−0.997742	−0.498871	+	0.866676i	$0.666252\pi$
$912$	−29463.1	−1.06976
$913$	−34081.4	−1.23541
$914$	−12727.1	−0.460585
$915$	636.972	0.0230138
$916$	29810.3	1.07528
$917$	−32202.9	−1.15969
$918$	14005.9	0.503553
$919$	−35828.5	−1.28604	−0.643022	−	0.765848i	$-0.722319\pi$
$919$	−35828.5	−1.28604	−0.643022	+	0.765848i	$0.722319\pi$
$920$	0	0
$921$	85735.4	3.06740
$922$	8902.35	0.317986
$923$	−12423.6	−0.443042
$924$	−48152.0	−1.71438
$925$	11193.7	0.397888
$926$	−23187.4	−0.822878
$927$	−802.134	−0.0284202
$928$	−12945.8	−0.457939
$929$	−17665.4	−0.623880	−0.311940	−	0.950102i	$-0.600979\pi$
$929$	−17665.4	−0.623880	−0.311940	+	0.950102i	$0.600979\pi$
$930$	703.807	0.0248158
$931$	−23639.1	−0.832158
$932$	−9969.56	−0.350390
$933$	−95325.0	−3.34491
$934$	−14152.2	−0.495796
$935$	554.602	0.0193983
$936$	31753.1	1.10885
$937$	21572.6	0.752132	0.376066	−	0.926593i	$-0.377277\pi$
$937$	21572.6	0.752132	0.376066	+	0.926593i	$0.377277\pi$
$938$	−11735.5	−0.408504
$939$	−33895.7	−1.17800
$940$	705.673	0.0244857
$941$	37167.1	1.28758	0.643791	−	0.765202i	$-0.277361\pi$
$941$	37167.1	1.28758	0.643791	+	0.765202i	$0.277361\pi$
$942$	−39174.7	−1.35497
$943$	0	0
$944$	2561.52	0.0883160
$945$	5566.99	0.191634
$946$	13161.5	0.452345
$947$	−10055.1	−0.345035	−0.172517	−	0.985006i	$-0.555190\pi$
$947$	−10055.1	−0.345035	−0.172517	+	0.985006i	$0.555190\pi$
$948$	−17842.3	−0.611279
$949$	2580.76	0.0882770
$950$	13547.8	0.462683
$951$	25322.9	0.863460
$952$	12927.9	0.440120
$953$	−1049.91	−0.0356873	−0.0178436	−	0.999841i	$-0.505680\pi$
$953$	−1049.91	−0.0356873	−0.0178436	+	0.999841i	$0.505680\pi$
$954$	−48178.5	−1.63505
$955$	−225.837	−0.00765226
$956$	25960.3	0.878259
$957$	21884.8	0.739221
$958$	−22035.8	−0.743156
$959$	−18819.0	−0.633677
$960$	319.962	0.0107570
$961$	−18702.3	−0.627784
$962$	2911.70	0.0975853
$963$	−100603.	−3.36645
$964$	−11454.9	−0.382714
$965$	475.648	0.0158670
$966$	0	0
$967$	−24917.6	−0.828640	−0.414320	−	0.910131i	$-0.635980\pi$
$967$	−24917.6	−0.828640	−0.414320	+	0.910131i	$0.635980\pi$
$968$	6704.46	0.222613
$969$	−27635.8	−0.916191
$970$	−749.708	−0.0248162
$971$	−21004.4	−0.694195	−0.347098	−	0.937829i	$-0.612833\pi$
$971$	−21004.4	−0.694195	−0.347098	+	0.937829i	$0.612833\pi$
$972$	−55770.1	−1.84036
$973$	43348.0	1.42824
$974$	−8264.23	−0.271872
$975$	33379.0	1.09639
$976$	−3672.53	−0.120445
$977$	−18007.4	−0.589669	−0.294835	−	0.955548i	$-0.595265\pi$
$977$	−18007.4	−0.589669	−0.294835	+	0.955548i	$0.595265\pi$
$978$	4294.62	0.140416
$979$	−39034.6	−1.27431
$980$	993.060	0.0323695
$981$	−13008.1	−0.423361
$982$	5102.39	0.165808
$983$	−17906.3	−0.581000	−0.290500	−	0.956875i	$-0.593822\pi$
$983$	−17906.3	−0.581000	−0.290500	+	0.956875i	$0.593822\pi$
$984$	14773.5	0.478620
$985$	−2057.52	−0.0665563
$986$	−2660.96	−0.0859454
$987$	−43021.5	−1.38743
$988$	−16935.4	−0.545330
$989$	0	0
$990$	1416.00	0.0454581
$991$	13666.0	0.438056	0.219028	−	0.975719i	$-0.429711\pi$
$991$	13666.0	0.438056	0.219028	+	0.975719i	$0.429711\pi$
$992$	−18517.5	−0.592673
$993$	110789.	3.54058
$994$	−12914.3	−0.412089
$995$	1393.81	0.0444088
$996$	−71343.4	−2.26968
$997$	38464.7	1.22185	0.610927	−	0.791687i	$-0.290797\pi$
$997$	38464.7	1.22185	0.610927	+	0.791687i	$0.290797\pi$
$998$	−19667.6	−0.623813
$999$	−34795.5	−1.10198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.16		25
23.15	odd	22		23.4.c.a.18.3	yes	50
23.20	odd	22		23.4.c.a.9.3	✓	50
23.22	odd	2		529.4.a.n.1.16		25
69.20	even	22		207.4.i.a.55.3		50
69.38	even	22		207.4.i.a.64.3		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.3	✓	50	23.20	odd	22
23.4.c.a.18.3	yes	50	23.15	odd	22
207.4.i.a.55.3		50	69.20	even	22
207.4.i.a.64.3		50	69.38	even	22
529.4.a.m.1.16		25	1.1	even	1	trivial
529.4.a.n.1.16		25	23.22	odd	2

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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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+1.17387 q^{2} +9.69393 q^{3} -6.62203 q^{4} -0.587346 q^{5} +11.3794 q^{6} -24.4606 q^{7} -17.1643 q^{8} +66.9723 q^{9} -0.689467 q^{10} -30.6659 q^{11} -64.1935 q^{12} -27.6225 q^{13} -28.7136 q^{14} -5.69369 q^{15} +32.8276 q^{16} +30.7916 q^{17} +78.6166 q^{18} -92.5849 q^{19} +3.88942 q^{20} -237.120 q^{21} -35.9977 q^{22} -166.390 q^{24} -124.655 q^{25} -32.4252 q^{26} +387.488 q^{27} +161.979 q^{28} -73.6185 q^{29} -6.68364 q^{30} -105.303 q^{31} +175.850 q^{32} -297.273 q^{33} +36.1452 q^{34} +14.3669 q^{35} -443.493 q^{36} -89.7975 q^{37} -108.682 q^{38} -267.771 q^{39} +10.0814 q^{40} -88.7884 q^{41} -278.347 q^{42} -365.622 q^{43} +203.070 q^{44} -39.3359 q^{45} +181.434 q^{47} +318.228 q^{48} +255.323 q^{49} -146.329 q^{50} +298.491 q^{51} +182.917 q^{52} -612.828 q^{53} +454.860 q^{54} +18.0115 q^{55} +419.851 q^{56} -897.511 q^{57} -86.4184 q^{58} +78.0294 q^{59} +37.7038 q^{60} -111.873 q^{61} -123.612 q^{62} -1638.18 q^{63} -56.1959 q^{64} +16.2240 q^{65} -348.959 q^{66} +408.709 q^{67} -203.903 q^{68} +16.8648 q^{70} +449.763 q^{71} -1149.53 q^{72} -93.4293 q^{73} -105.410 q^{74} -1208.40 q^{75} +613.100 q^{76} +750.107 q^{77} -314.328 q^{78} +277.946 q^{79} -19.2812 q^{80} +1948.03 q^{81} -104.226 q^{82} +1111.38 q^{83} +1570.21 q^{84} -18.0853 q^{85} -429.192 q^{86} -713.652 q^{87} +526.360 q^{88} +1272.90 q^{89} -46.1752 q^{90} +675.665 q^{91} -1020.80 q^{93} +212.979 q^{94} +54.3794 q^{95} +1704.68 q^{96} +1087.37 q^{97} +299.716 q^{98} -2053.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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