LMFDB - Embedded newform 2303.4.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.48152 q^{2} -2.93802 q^{3} +22.0470 q^{4} +19.1722 q^{5} +16.1048 q^{6} -76.9989 q^{8} -18.3680 q^{9} +O(q^{10})$	\(q-5.48152 q^{2} -2.93802 q^{3} +22.0470 q^{4} +19.1722 q^{5} +16.1048 q^{6} -76.9989 q^{8} -18.3680 q^{9} -105.093 q^{10} +9.64200 q^{11} -64.7747 q^{12} +54.4817 q^{13} -56.3285 q^{15} +245.695 q^{16} +17.6901 q^{17} +100.685 q^{18} +112.706 q^{19} +422.691 q^{20} -52.8528 q^{22} +209.444 q^{23} +226.225 q^{24} +242.575 q^{25} -298.642 q^{26} +133.292 q^{27} +181.014 q^{29} +308.766 q^{30} +199.370 q^{31} -730.788 q^{32} -28.3284 q^{33} -96.9686 q^{34} -404.960 q^{36} -218.411 q^{37} -617.798 q^{38} -160.069 q^{39} -1476.24 q^{40} +118.255 q^{41} +295.325 q^{43} +212.577 q^{44} -352.156 q^{45} -1148.07 q^{46} +47.0000 q^{47} -721.857 q^{48} -1329.68 q^{50} -51.9740 q^{51} +1201.16 q^{52} +720.212 q^{53} -730.644 q^{54} +184.859 q^{55} -331.132 q^{57} -992.232 q^{58} -306.478 q^{59} -1241.88 q^{60} -12.8981 q^{61} -1092.85 q^{62} +2040.27 q^{64} +1044.54 q^{65} +155.283 q^{66} +513.735 q^{67} +390.014 q^{68} -615.353 q^{69} -53.3967 q^{71} +1414.32 q^{72} +495.566 q^{73} +1197.22 q^{74} -712.691 q^{75} +2484.82 q^{76} +877.418 q^{78} +356.564 q^{79} +4710.52 q^{80} +104.320 q^{81} -648.215 q^{82} -1264.26 q^{83} +339.159 q^{85} -1618.83 q^{86} -531.824 q^{87} -742.424 q^{88} -1239.01 q^{89} +1930.35 q^{90} +4617.63 q^{92} -585.753 q^{93} -257.631 q^{94} +2160.82 q^{95} +2147.07 q^{96} +1595.51 q^{97} -177.104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−5.48152	−1.93801	−0.969004	−	0.247044i	$-0.920541\pi$
$2$	−5.48152	−1.93801	−0.969004	+	0.247044i	$0.920541\pi$
$3$	−2.93802	−0.565423	−0.282712	−	0.959205i	$-0.591234\pi$
$3$	−2.93802	−0.565423	−0.282712	+	0.959205i	$0.591234\pi$
$4$	22.0470	2.75588
$5$	19.1722	1.71482	0.857409	−	0.514636i	$-0.172073\pi$
$5$	19.1722	1.71482	0.857409	+	0.514636i	$0.172073\pi$
$6$	16.1048	1.09579
$7$	0	0
$7$	0	0
$8$	−76.9989	−3.40290
$9$	−18.3680	−0.680297
$10$	−105.093	−3.32333
$11$	9.64200	0.264288	0.132144	−	0.991230i	$-0.457814\pi$
$11$	9.64200	0.264288	0.132144	+	0.991230i	$0.457814\pi$
$12$	−64.7747	−1.55824
$13$	54.4817	1.16235	0.581173	−	0.813780i	$-0.302594\pi$
$13$	54.4817	1.16235	0.581173	+	0.813780i	$0.302594\pi$
$14$	0	0
$15$	−56.3285	−0.969598
$16$	245.695	3.83898
$17$	17.6901	0.252381	0.126191	−	0.992006i	$-0.459725\pi$
$17$	17.6901	0.252381	0.126191	+	0.992006i	$0.459725\pi$
$18$	100.685	1.31842
$19$	112.706	1.36087	0.680433	−	0.732810i	$-0.261792\pi$
$19$	112.706	1.36087	0.680433	+	0.732810i	$0.261792\pi$
$20$	422.691	4.72583
$21$	0	0
$22$	−52.8528	−0.512193
$23$	209.444	1.89879	0.949396	−	0.314083i	$-0.101697\pi$
$23$	209.444	1.89879	0.949396	+	0.314083i	$0.101697\pi$
$24$	226.225	1.92408
$25$	242.575	1.94060
$26$	−298.642	−2.25264
$27$	133.292	0.950079
$28$	0	0
$29$	181.014	1.15909	0.579543	−	0.814942i	$-0.303231\pi$
$29$	181.014	1.15909	0.579543	+	0.814942i	$0.303231\pi$
$30$	308.766	1.87909
$31$	199.370	1.15509	0.577546	−	0.816358i	$-0.304010\pi$
$31$	199.370	1.15509	0.577546	+	0.816358i	$0.304010\pi$
$32$	−730.788	−4.03707
$33$	−28.3284	−0.149435
$34$	−96.9686	−0.489117
$35$	0	0
$36$	−404.960	−1.87481
$37$	−218.411	−0.970445	−0.485223	−	0.874391i	$-0.661261\pi$
$37$	−218.411	−0.970445	−0.485223	+	0.874391i	$0.661261\pi$
$38$	−617.798	−2.63737
$39$	−160.069	−0.657217
$40$	−1476.24	−5.83536
$41$	118.255	0.450446	0.225223	−	0.974307i	$-0.427689\pi$
$41$	118.255	0.450446	0.225223	+	0.974307i	$0.427689\pi$
$42$	0	0
$43$	295.325	1.04736	0.523682	−	0.851914i	$-0.324558\pi$
$43$	295.325	1.04736	0.523682	+	0.851914i	$0.324558\pi$
$44$	212.577	0.728347
$45$	−352.156	−1.16659
$46$	−1148.07	−3.67987
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−721.857	−2.17065
$49$	0	0
$50$	−1329.68	−3.76090
$51$	−51.9740	−0.142702
$52$	1201.16	3.20328
$53$	720.212	1.86658	0.933289	−	0.359125i	$-0.116925\pi$
$53$	720.212	1.86658	0.933289	+	0.359125i	$0.116925\pi$
$54$	−730.644	−1.84126
$55$	184.859	0.453207
$56$	0	0
$57$	−331.132	−0.769465
$58$	−992.232	−2.24632
$59$	−306.478	−0.676273	−0.338136	−	0.941097i	$-0.609797\pi$
$59$	−306.478	−0.676273	−0.338136	+	0.941097i	$0.609797\pi$
$60$	−1241.88	−2.67209
$61$	−12.8981	−0.0270726	−0.0135363	−	0.999908i	$-0.504309\pi$
$61$	−12.8981	−0.0270726	−0.0135363	+	0.999908i	$0.504309\pi$
$62$	−1092.85	−2.23858
$63$	0	0
$64$	2040.27	3.98490
$65$	1044.54	1.99321
$66$	155.283	0.289606
$67$	513.735	0.936758	0.468379	−	0.883528i	$-0.344838\pi$
$67$	513.735	0.936758	0.468379	+	0.883528i	$0.344838\pi$
$68$	390.014	0.695532
$69$	−615.353	−1.07362
$70$	0	0
$71$	−53.3967	−0.0892538	−0.0446269	−	0.999004i	$-0.514210\pi$
$71$	−53.3967	−0.0892538	−0.0446269	+	0.999004i	$0.514210\pi$
$72$	1414.32	2.31499
$73$	495.566	0.794542	0.397271	−	0.917701i	$-0.369957\pi$
$73$	495.566	0.794542	0.397271	+	0.917701i	$0.369957\pi$
$74$	1197.22	1.88073
$75$	−712.691	−1.09726
$76$	2484.82	3.75038
$77$	0	0
$78$	877.418	1.27369
$79$	356.564	0.507804	0.253902	−	0.967230i	$-0.418286\pi$
$79$	356.564	0.507804	0.253902	+	0.967230i	$0.418286\pi$
$80$	4710.52	6.58315
$81$	104.320	0.143101
$82$	−648.215	−0.872968
$83$	−1264.26	−1.67194	−0.835970	−	0.548774i	$-0.815095\pi$
$83$	−1264.26	−1.67194	−0.835970	+	0.548774i	$0.815095\pi$
$84$	0	0
$85$	339.159	0.432788
$86$	−1618.83	−2.02980
$87$	−531.824	−0.655374
$88$	−742.424	−0.899349
$89$	−1239.01	−1.47567	−0.737836	−	0.674980i	$-0.764152\pi$
$89$	−1239.01	−1.47567	−0.737836	+	0.674980i	$0.764152\pi$
$90$	1930.35	2.26085
$91$	0	0
$92$	4617.63	5.23283
$93$	−585.753	−0.653116
$94$	−257.631	−0.282688
$95$	2160.82	2.33364
$96$	2147.07	2.28265
$97$	1595.51	1.67010	0.835050	−	0.550174i	$-0.185439\pi$
$97$	1595.51	1.67010	0.835050	+	0.550174i	$0.185439\pi$
$98$	0	0
$99$	−177.104	−0.179795
$100$	5348.06	5.34806
$101$	438.755	0.432255	0.216128	−	0.976365i	$-0.430657\pi$
$101$	438.755	0.432255	0.216128	+	0.976365i	$0.430657\pi$
$102$	284.896	0.276558
$103$	−1279.61	−1.22411	−0.612055	−	0.790815i	$-0.709657\pi$
$103$	−1279.61	−1.22411	−0.612055	+	0.790815i	$0.709657\pi$
$104$	−4195.03	−3.95535
$105$	0	0
$106$	−3947.85	−3.61745
$107$	−491.307	−0.443892	−0.221946	−	0.975059i	$-0.571241\pi$
$107$	−491.307	−0.443892	−0.221946	+	0.975059i	$0.571241\pi$
$108$	2938.70	2.61830
$109$	36.6879	0.0322392	0.0161196	−	0.999870i	$-0.494869\pi$
$109$	36.6879	0.0322392	0.0161196	+	0.999870i	$0.494869\pi$
$110$	−1013.31	−0.878318
$111$	641.696	0.548712
$112$	0	0
$113$	−247.598	−0.206125	−0.103062	−	0.994675i	$-0.532864\pi$
$113$	−247.598	−0.206125	−0.103062	+	0.994675i	$0.532864\pi$
$114$	1815.11	1.49123
$115$	4015.52	3.25608
$116$	3990.82	3.19430
$117$	−1000.72	−0.790740
$118$	1679.97	1.31062
$119$	0	0
$120$	4337.24	3.29945
$121$	−1238.03	−0.930152
$122$	70.7010	0.0524669
$123$	−347.435	−0.254693
$124$	4395.51	3.18329
$125$	2254.18	1.61296
$126$	0	0
$127$	−1380.79	−0.964768	−0.482384	−	0.875960i	$-0.660229\pi$
$127$	−1380.79	−0.964768	−0.482384	+	0.875960i	$0.660229\pi$
$128$	−5337.46	−3.68570
$129$	−867.673	−0.592204
$130$	−5725.64	−3.86286
$131$	1334.33	0.889931	0.444966	−	0.895548i	$-0.353216\pi$
$131$	1334.33	0.889931	0.444966	+	0.895548i	$0.353216\pi$
$132$	−624.558	−0.411824
$133$	0	0
$134$	−2816.05	−1.81544
$135$	2555.51	1.62921
$136$	−1362.12	−0.858829
$137$	−800.780	−0.499381	−0.249691	−	0.968326i	$-0.580329\pi$
$137$	−800.780	−0.499381	−0.249691	+	0.968326i	$0.580329\pi$
$138$	3373.07	2.08069
$139$	−3069.50	−1.87303	−0.936515	−	0.350627i	$-0.885968\pi$
$139$	−3069.50	−1.87303	−0.936515	+	0.350627i	$0.885968\pi$
$140$	0	0
$141$	−138.087	−0.0824754
$142$	292.695	0.172975
$143$	525.313	0.307195
$144$	−4512.93	−2.61165
$145$	3470.45	1.98762
$146$	−2716.45	−1.53983
$147$	0	0
$148$	−4815.30	−2.67443
$149$	−277.057	−0.152331	−0.0761657	−	0.997095i	$-0.524268\pi$
$149$	−277.057	−0.152331	−0.0761657	+	0.997095i	$0.524268\pi$
$150$	3906.63	2.12650
$151$	1582.69	0.852962	0.426481	−	0.904497i	$-0.359753\pi$
$151$	1582.69	0.852962	0.426481	+	0.904497i	$0.359753\pi$
$152$	−8678.22	−4.63090
$153$	−324.932	−0.171694
$154$	0	0
$155$	3822.37	1.98077
$156$	−3529.03	−1.81121
$157$	441.650	0.224507	0.112253	−	0.993680i	$-0.464193\pi$
$157$	441.650	0.224507	0.112253	+	0.993680i	$0.464193\pi$
$158$	−1954.51	−0.984129
$159$	−2116.00	−1.05541
$160$	−14010.9	−6.92285
$161$	0	0
$162$	−571.833	−0.277330
$163$	−90.6987	−0.0435833	−0.0217916	−	0.999763i	$-0.506937\pi$
$163$	−90.6987	−0.0435833	−0.0217916	+	0.999763i	$0.506937\pi$
$164$	2607.16	1.24137
$165$	−543.120	−0.256253
$166$	6930.09	3.24024
$167$	−173.667	−0.0804718	−0.0402359	−	0.999190i	$-0.512811\pi$
$167$	−173.667	−0.0804718	−0.0402359	+	0.999190i	$0.512811\pi$
$168$	0	0
$169$	771.254	0.351049
$170$	−1859.11	−0.838747
$171$	−2070.18	−0.925793
$172$	6511.04	2.88641
$173$	2618.59	1.15080	0.575398	−	0.817874i	$-0.304847\pi$
$173$	2618.59	1.15080	0.575398	+	0.817874i	$0.304847\pi$
$174$	2915.20	1.27012
$175$	0	0
$176$	2368.99	1.01460
$177$	900.441	0.382380
$178$	6791.66	2.85987
$179$	1335.56	0.557677	0.278839	−	0.960338i	$-0.410051\pi$
$179$	1335.56	0.557677	0.278839	+	0.960338i	$0.410051\pi$
$180$	−7763.99	−3.21497
$181$	1293.77	0.531297	0.265649	−	0.964070i	$-0.414414\pi$
$181$	1293.77	0.531297	0.265649	+	0.964070i	$0.414414\pi$
$182$	0	0
$183$	37.8948	0.0153075
$184$	−16127.0	−6.46141
$185$	−4187.42	−1.66414
$186$	3210.81	1.26574
$187$	170.568	0.0667015
$188$	1036.21	0.401986
$189$	0	0
$190$	−11844.6	−4.52261
$191$	−1167.50	−0.442288	−0.221144	−	0.975241i	$-0.570979\pi$
$191$	−1167.50	−0.442288	−0.221144	+	0.975241i	$0.570979\pi$
$192$	−5994.36	−2.25316
$193$	3744.85	1.39669	0.698343	−	0.715764i	$-0.253921\pi$
$193$	3744.85	1.39669	0.698343	+	0.715764i	$0.253921\pi$
$194$	−8745.82	−3.23667
$195$	−3068.87	−1.12701
$196$	0	0
$197$	−4103.50	−1.48407	−0.742035	−	0.670361i	$-0.766139\pi$
$197$	−4103.50	−1.48407	−0.742035	+	0.670361i	$0.766139\pi$
$198$	970.801	0.348443
$199$	470.739	0.167687	0.0838437	−	0.996479i	$-0.473280\pi$
$199$	470.739	0.167687	0.0838437	+	0.996479i	$0.473280\pi$
$200$	−18678.0	−6.60368
$201$	−1509.37	−0.529664
$202$	−2405.04	−0.837715
$203$	0	0
$204$	−1145.87	−0.393270
$205$	2267.21	0.772433
$206$	7014.18	2.37234
$207$	−3847.08	−1.29174
$208$	13385.9	4.46222
$209$	1086.71	0.359661
$210$	0	0
$211$	−1877.60	−0.612603	−0.306301	−	0.951935i	$-0.599092\pi$
$211$	−1877.60	−0.612603	−0.306301	+	0.951935i	$0.599092\pi$
$212$	15878.5	5.14406
$213$	156.881	0.0504661
$214$	2693.11	0.860267
$215$	5662.05	1.79604
$216$	−10263.4	−3.23303
$217$	0	0
$218$	−201.106	−0.0624798
$219$	−1455.98	−0.449253
$220$	4075.59	1.24898
$221$	963.787	0.293354
$222$	−3517.47	−1.06341
$223$	−1101.30	−0.330710	−0.165355	−	0.986234i	$-0.552877\pi$
$223$	−1101.30	−0.330710	−0.165355	+	0.986234i	$0.552877\pi$
$224$	0	0
$225$	−4455.62	−1.32018
$226$	1357.21	0.399471
$227$	941.633	0.275323	0.137662	−	0.990479i	$-0.456041\pi$
$227$	941.633	0.275323	0.137662	+	0.990479i	$0.456041\pi$
$228$	−7300.48	−2.12055
$229$	−6600.69	−1.90474	−0.952371	−	0.304943i	$-0.901363\pi$
$229$	−6600.69	−1.90474	−0.952371	+	0.304943i	$0.901363\pi$
$230$	−22011.1	−6.31031
$231$	0	0
$232$	−13937.9	−3.94426
$233$	−2067.86	−0.581416	−0.290708	−	0.956812i	$-0.593891\pi$
$233$	−2067.86	−0.581416	−0.290708	+	0.956812i	$0.593891\pi$
$234$	5485.46	1.53246
$235$	901.096	0.250132
$236$	−6756.94	−1.86372
$237$	−1047.59	−0.287124
$238$	0	0
$239$	−1480.75	−0.400759	−0.200380	−	0.979718i	$-0.564218\pi$
$239$	−1480.75	−0.400759	−0.200380	+	0.979718i	$0.564218\pi$
$240$	−13839.6	−3.72227
$241$	−4880.95	−1.30460	−0.652302	−	0.757959i	$-0.726197\pi$
$241$	−4880.95	−1.30460	−0.652302	+	0.757959i	$0.726197\pi$
$242$	6786.29	1.80264
$243$	−3905.39	−1.03099
$244$	−284.364	−0.0746087
$245$	0	0
$246$	1904.47	0.493596
$247$	6140.40	1.58180
$248$	−15351.3	−3.93067
$249$	3714.44	0.945354
$250$	−12356.3	−3.12593
$251$	−5715.46	−1.43728	−0.718639	−	0.695383i	$-0.755235\pi$
$251$	−5715.46	−1.43728	−0.718639	+	0.695383i	$0.755235\pi$
$252$	0	0
$253$	2019.46	0.501829
$254$	7568.84	1.86973
$255$	−996.458	−0.244708
$256$	12935.2	3.15802
$257$	−8111.08	−1.96870	−0.984349	−	0.176228i	$-0.943610\pi$
$257$	−8111.08	−1.96870	−0.984349	+	0.176228i	$0.943610\pi$
$258$	4756.16	1.14770
$259$	0	0
$260$	23028.9	5.49305
$261$	−3324.87	−0.788522
$262$	−7314.16	−1.72469
$263$	6540.02	1.53336	0.766682	−	0.642027i	$-0.221906\pi$
$263$	6540.02	1.53336	0.766682	+	0.642027i	$0.221906\pi$
$264$	2181.26	0.508512
$265$	13808.1	3.20084
$266$	0	0
$267$	3640.24	0.834379
$268$	11326.3	2.58159
$269$	−3722.88	−0.843821	−0.421910	−	0.906638i	$-0.638640\pi$
$269$	−3722.88	−0.843821	−0.421910	+	0.906638i	$0.638640\pi$
$270$	−14008.1	−3.15743
$271$	4581.24	1.02690	0.513451	−	0.858119i	$-0.328367\pi$
$271$	4581.24	1.02690	0.513451	+	0.858119i	$0.328367\pi$
$272$	4346.37	0.968887
$273$	0	0
$274$	4389.49	0.967805
$275$	2338.91	0.512878
$276$	−13566.7	−2.95877
$277$	−998.489	−0.216583	−0.108291	−	0.994119i	$-0.534538\pi$
$277$	−998.489	−0.216583	−0.108291	+	0.994119i	$0.534538\pi$
$278$	16825.5	3.62995
$279$	−3662.03	−0.785805
$280$	0	0
$281$	6455.29	1.37043	0.685214	−	0.728341i	$-0.259709\pi$
$281$	6455.29	1.37043	0.685214	+	0.728341i	$0.259709\pi$
$282$	756.927	0.159838
$283$	1171.95	0.246167	0.123084	−	0.992396i	$-0.460722\pi$
$283$	1171.95	0.246167	0.123084	+	0.992396i	$0.460722\pi$
$284$	−1177.24	−0.245972
$285$	−6348.55	−1.31949
$286$	−2879.51	−0.595346
$287$	0	0
$288$	13423.1	2.74641
$289$	−4600.06	−0.936304
$290$	−19023.3	−3.85203
$291$	−4687.65	−0.944313
$292$	10925.7	2.18966
$293$	1044.59	0.208278	0.104139	−	0.994563i	$-0.466791\pi$
$293$	1044.59	0.208278	0.104139	+	0.994563i	$0.466791\pi$
$294$	0	0
$295$	−5875.88	−1.15968
$296$	16817.4	3.30233
$297$	1285.21	0.251095
$298$	1518.69	0.295219
$299$	11410.9	2.20705
$300$	−15712.7	−3.02391
$301$	0	0
$302$	−8675.52	−1.65305
$303$	−1289.07	−0.244407
$304$	27691.2	5.22434
$305$	−247.285	−0.0464246
$306$	1781.12	0.332745
$307$	5979.13	1.11155	0.555777	−	0.831331i	$-0.312421\pi$
$307$	5979.13	1.11155	0.555777	+	0.831331i	$0.312421\pi$
$308$	0	0
$309$	3759.51	0.692140
$310$	−20952.4	−3.83875
$311$	−8026.71	−1.46351	−0.731757	−	0.681566i	$-0.761299\pi$
$311$	−8026.71	−1.46351	−0.731757	+	0.681566i	$0.761299\pi$
$312$	12325.1	2.23645
$313$	324.114	0.0585304	0.0292652	−	0.999572i	$-0.490683\pi$
$313$	324.114	0.0585304	0.0292652	+	0.999572i	$0.490683\pi$
$314$	−2420.91	−0.435096
$315$	0	0
$316$	7861.16	1.39945
$317$	−7413.28	−1.31347	−0.656737	−	0.754119i	$-0.728064\pi$
$317$	−7413.28	−1.31347	−0.656737	+	0.754119i	$0.728064\pi$
$318$	11598.9	2.04539
$319$	1745.34	0.306333
$320$	39116.6	6.83338
$321$	1443.47	0.250987
$322$	0	0
$323$	1993.78	0.343457
$324$	2299.95	0.394367
$325$	13215.9	2.25565
$326$	497.166	0.0844647
$327$	−107.790	−0.0182288
$328$	−9105.49	−1.53282
$329$	0	0
$330$	2977.12	0.496621
$331$	−1190.73	−0.197729	−0.0988646	−	0.995101i	$-0.531521\pi$
$331$	−1190.73	−0.197729	−0.0988646	+	0.995101i	$0.531521\pi$
$332$	−27873.3	−4.60766
$333$	4011.77	0.660191
$334$	951.961	0.155955
$335$	9849.46	1.60637
$336$	0	0
$337$	6139.47	0.992398	0.496199	−	0.868209i	$-0.334729\pi$
$337$	6139.47	0.992398	0.496199	+	0.868209i	$0.334729\pi$
$338$	−4227.64	−0.680335
$339$	727.449	0.116548
$340$	7477.45	1.19271
$341$	1922.32	0.305278
$342$	11347.7	1.79420
$343$	0	0
$344$	−22739.7	−3.56408
$345$	−11797.7	−1.84106
$346$	−14353.8	−2.23025
$347$	−6850.66	−1.05984	−0.529918	−	0.848049i	$-0.677777\pi$
$347$	−6850.66	−1.05984	−0.529918	+	0.848049i	$0.677777\pi$
$348$	−11725.1	−1.80613
$349$	−820.785	−0.125890	−0.0629450	−	0.998017i	$-0.520049\pi$
$349$	−820.785	−0.125890	−0.0629450	+	0.998017i	$0.520049\pi$
$350$	0	0
$351$	7261.99	1.10432
$352$	−7046.26	−1.06695
$353$	6101.56	0.919981	0.459991	−	0.887924i	$-0.347853\pi$
$353$	6101.56	0.919981	0.459991	+	0.887924i	$0.347853\pi$
$354$	−4935.78	−0.741056
$355$	−1023.73	−0.153054
$356$	−27316.5	−4.06677
$357$	0	0
$358$	−7320.88	−1.08078
$359$	−12167.7	−1.78882	−0.894411	−	0.447247i	$-0.852405\pi$
$359$	−12167.7	−1.78882	−0.894411	+	0.447247i	$0.852405\pi$
$360$	27115.6	3.96978
$361$	5843.58	0.851958
$362$	−7091.79	−1.02966
$363$	3637.37	0.525929
$364$	0	0
$365$	9501.11	1.36250
$366$	−207.721	−0.0296660
$367$	11337.4	1.61255	0.806276	−	0.591539i	$-0.201480\pi$
$367$	11337.4	1.61255	0.806276	+	0.591539i	$0.201480\pi$
$368$	51459.4	7.28942
$369$	−2172.10	−0.306437
$370$	22953.4	3.22511
$371$	0	0
$372$	−12914.1	−1.79991
$373$	−6552.40	−0.909572	−0.454786	−	0.890601i	$-0.650284\pi$
$373$	−6552.40	−0.909572	−0.454786	+	0.890601i	$0.650284\pi$
$374$	−934.972	−0.129268
$375$	−6622.83	−0.912004
$376$	−3618.95	−0.496365
$377$	9861.96	1.34726
$378$	0	0
$379$	−5869.88	−0.795555	−0.397778	−	0.917482i	$-0.630218\pi$
$379$	−5869.88	−0.795555	−0.397778	+	0.917482i	$0.630218\pi$
$380$	47639.7	6.43122
$381$	4056.80	0.545502
$382$	6399.65	0.857159
$383$	3361.00	0.448404	0.224202	−	0.974543i	$-0.428022\pi$
$383$	3361.00	0.448404	0.224202	+	0.974543i	$0.428022\pi$
$384$	15681.6	2.08398
$385$	0	0
$386$	−20527.5	−2.70679
$387$	−5424.54	−0.712519
$388$	35176.3	4.60259
$389$	−10233.5	−1.33383	−0.666917	−	0.745132i	$-0.732386\pi$
$389$	−10233.5	−1.33383	−0.666917	+	0.745132i	$0.732386\pi$
$390$	16822.1	2.18415
$391$	3705.10	0.479219
$392$	0	0
$393$	−3920.30	−0.503188
$394$	22493.4	2.87614
$395$	6836.12	0.870792
$396$	−3904.62	−0.495492
$397$	2719.75	0.343830	0.171915	−	0.985112i	$-0.445005\pi$
$397$	2719.75	0.343830	0.171915	+	0.985112i	$0.445005\pi$
$398$	−2580.36	−0.324980
$399$	0	0
$400$	59599.4	7.44993
$401$	8500.47	1.05859	0.529293	−	0.848439i	$-0.322457\pi$
$401$	8500.47	1.05859	0.529293	+	0.848439i	$0.322457\pi$
$402$	8273.62	1.02649
$403$	10862.0	1.34262
$404$	9673.25	1.19124
$405$	2000.05	0.245391
$406$	0	0
$407$	−2105.92	−0.256478
$408$	4001.94	0.485602
$409$	523.590	0.0633004	0.0316502	−	0.999499i	$-0.489924\pi$
$409$	523.590	0.0633004	0.0316502	+	0.999499i	$0.489924\pi$
$410$	−12427.7	−1.49698
$411$	2352.71	0.282362
$412$	−28211.5	−3.37350
$413$	0	0
$414$	21087.8	2.50341
$415$	−24238.8	−2.86707
$416$	−39814.6	−4.69248
$417$	9018.25	1.05905
$418$	−5956.81	−0.697027
$419$	−8991.39	−1.04835	−0.524174	−	0.851611i	$-0.675626\pi$
$419$	−8991.39	−1.04835	−0.524174	+	0.851611i	$0.675626\pi$
$420$	0	0
$421$	6247.69	0.723263	0.361632	−	0.932321i	$-0.382220\pi$
$421$	6247.69	0.723263	0.361632	+	0.932321i	$0.382220\pi$
$422$	10292.1	1.18723
$423$	−863.297	−0.0992315
$424$	−55455.5	−6.35179
$425$	4291.18	0.489771
$426$	−859.944	−0.0978038
$427$	0	0
$428$	−10831.9	−1.22331
$429$	−1543.38	−0.173695
$430$	−31036.6	−3.48074
$431$	6226.99	0.695924	0.347962	−	0.937509i	$-0.386874\pi$
$431$	6226.99	0.695924	0.347962	+	0.937509i	$0.386874\pi$
$432$	32749.2	3.64733
$433$	4105.91	0.455699	0.227849	−	0.973696i	$-0.426831\pi$
$433$	4105.91	0.455699	0.227849	+	0.973696i	$0.426831\pi$
$434$	0	0
$435$	−10196.3	−1.12385
$436$	808.860	0.0888471
$437$	23605.6	2.58400
$438$	7981.00	0.870655
$439$	−14646.6	−1.59236	−0.796180	−	0.605060i	$-0.793149\pi$
$439$	−14646.6	−1.59236	−0.796180	+	0.605060i	$0.793149\pi$
$440$	−14233.9	−1.54222
$441$	0	0
$442$	−5283.01	−0.568523
$443$	−14658.6	−1.57213	−0.786063	−	0.618147i	$-0.787884\pi$
$443$	−14658.6	−1.57213	−0.786063	+	0.618147i	$0.787884\pi$
$444$	14147.5	1.51218
$445$	−23754.6	−2.53051
$446$	6036.77	0.640918
$447$	813.999	0.0861316
$448$	0	0
$449$	8148.78	0.856491	0.428246	−	0.903662i	$-0.359132\pi$
$449$	8148.78	0.856491	0.428246	+	0.903662i	$0.359132\pi$
$450$	24423.6	2.55853
$451$	1140.21	0.119048
$452$	−5458.80	−0.568054
$453$	−4649.97	−0.482284
$454$	−5161.57	−0.533579
$455$	0	0
$456$	25496.8	2.61842
$457$	1313.48	0.134447	0.0672233	−	0.997738i	$-0.478586\pi$
$457$	1313.48	0.134447	0.0672233	+	0.997738i	$0.478586\pi$
$458$	36181.8	3.69140
$459$	2357.96	0.239782
$460$	88530.3	8.97336
$461$	−4482.85	−0.452901	−0.226450	−	0.974023i	$-0.572712\pi$
$461$	−4482.85	−0.452901	−0.226450	+	0.974023i	$0.572712\pi$
$462$	0	0
$463$	−1217.97	−0.122255	−0.0611275	−	0.998130i	$-0.519470\pi$
$463$	−1217.97	−0.122255	−0.0611275	+	0.998130i	$0.519470\pi$
$464$	44474.2	4.44971
$465$	−11230.2	−1.11997
$466$	11335.0	1.12679
$467$	−5986.81	−0.593226	−0.296613	−	0.954998i	$-0.595857\pi$
$467$	−5986.81	−0.593226	−0.296613	+	0.954998i	$0.595857\pi$
$468$	−22062.9	−2.17918
$469$	0	0
$470$	−4939.37	−0.484758
$471$	−1297.58	−0.126941
$472$	23598.5	2.30129
$473$	2847.53	0.276806
$474$	5742.39	0.556449
$475$	27339.6	2.64090
$476$	0	0
$477$	−13228.9	−1.26983
$478$	8116.73	0.776675
$479$	−13542.2	−1.29178	−0.645888	−	0.763432i	$-0.723513\pi$
$479$	−13542.2	−1.29178	−0.645888	+	0.763432i	$0.723513\pi$
$480$	41164.2	3.91434
$481$	−11899.4	−1.12799
$482$	26755.0	2.52834
$483$	0	0
$484$	−27294.9	−2.56338
$485$	30589.5	2.86392
$486$	21407.4	1.99807
$487$	−15145.7	−1.40928	−0.704639	−	0.709566i	$-0.748891\pi$
$487$	−15145.7	−1.40928	−0.704639	+	0.709566i	$0.748891\pi$
$488$	993.138	0.0921255
$489$	266.475	0.0246430
$490$	0	0
$491$	−12582.5	−1.15650	−0.578250	−	0.815860i	$-0.696264\pi$
$491$	−12582.5	−1.15650	−0.578250	+	0.815860i	$0.696264\pi$
$492$	−7659.91	−0.701901
$493$	3202.16	0.292532
$494$	−33658.7	−3.06554
$495$	−3395.49	−0.308315
$496$	48984.1	4.43438
$497$	0	0
$498$	−20360.8	−1.83210
$499$	−6018.49	−0.539929	−0.269964	−	0.962870i	$-0.587012\pi$
$499$	−6018.49	−0.539929	−0.269964	+	0.962870i	$0.587012\pi$
$500$	49697.9	4.44512
$501$	510.239	0.0455006
$502$	31329.4	2.78546
$503$	15950.7	1.41393	0.706966	−	0.707248i	$-0.250063\pi$
$503$	15950.7	1.41393	0.706966	+	0.707248i	$0.250063\pi$
$504$	0	0
$505$	8411.93	0.741239
$506$	−11069.7	−0.972548
$507$	−2265.96	−0.198491
$508$	−30442.4	−2.65878
$509$	−16734.7	−1.45727	−0.728635	−	0.684902i	$-0.759845\pi$
$509$	−16734.7	−1.45727	−0.728635	+	0.684902i	$0.759845\pi$
$510$	5462.10	0.474247
$511$	0	0
$512$	−28205.0	−2.43456
$513$	15022.8	1.29293
$514$	44461.0	3.81535
$515$	−24532.9	−2.09913
$516$	−19129.6	−1.63204
$517$	453.174	0.0385504
$518$	0	0
$519$	−7693.48	−0.650687
$520$	−80428.2	−6.78271
$521$	627.869	0.0527974	0.0263987	−	0.999651i	$-0.491596\pi$
$521$	627.869	0.0527974	0.0263987	+	0.999651i	$0.491596\pi$
$522$	18225.3	1.52816
$523$	−11665.8	−0.975357	−0.487678	−	0.873023i	$-0.662156\pi$
$523$	−11665.8	−0.975357	−0.487678	+	0.873023i	$0.662156\pi$
$524$	29418.0	2.45254
$525$	0	0
$526$	−35849.2	−2.97167
$527$	3526.87	0.291524
$528$	−6960.15	−0.573677
$529$	31700.0	2.60541
$530$	−75689.2	−6.20326
$531$	5629.40	0.460066
$532$	0	0
$533$	6442.72	0.523574
$534$	−19954.1	−1.61703
$535$	−9419.46	−0.761194
$536$	−39557.1	−3.18770
$537$	−3923.90	−0.315324
$538$	20407.0	1.63533
$539$	0	0
$540$	56341.4	4.48991
$541$	−5209.67	−0.414013	−0.207007	−	0.978340i	$-0.566372\pi$
$541$	−5209.67	−0.414013	−0.207007	+	0.978340i	$0.566372\pi$
$542$	−25112.1	−1.99014
$543$	−3801.11	−0.300408
$544$	−12927.7	−1.01888
$545$	703.390	0.0552843
$546$	0	0
$547$	−1083.71	−0.0847092	−0.0423546	−	0.999103i	$-0.513486\pi$
$547$	−1083.71	−0.0847092	−0.0423546	+	0.999103i	$0.513486\pi$
$548$	−17654.8	−1.37623
$549$	236.912	0.0184174
$550$	−12820.8	−0.993963
$551$	20401.3	1.57736
$552$	47381.5	3.65343
$553$	0	0
$554$	5473.23	0.419739
$555$	12302.7	0.940942
$556$	−67673.2	−5.16184
$557$	−8167.70	−0.621322	−0.310661	−	0.950521i	$-0.600550\pi$
$557$	−8167.70	−0.621322	−0.310661	+	0.950521i	$0.600550\pi$
$558$	20073.5	1.52290
$559$	16089.8	1.21740
$560$	0	0
$561$	−501.133	−0.0377145
$562$	−35384.8	−2.65590
$563$	10519.4	0.787461	0.393730	−	0.919226i	$-0.371184\pi$
$563$	10519.4	0.787461	0.393730	+	0.919226i	$0.371184\pi$
$564$	−3044.41	−0.227292
$565$	−4747.01	−0.353466
$566$	−6424.08	−0.477075
$567$	0	0
$568$	4111.49	0.303722
$569$	−13849.3	−1.02037	−0.510185	−	0.860065i	$-0.670423\pi$
$569$	−13849.3	−1.02037	−0.510185	+	0.860065i	$0.670423\pi$
$570$	34799.7	2.55719
$571$	−13980.4	−1.02462	−0.512312	−	0.858799i	$-0.671211\pi$
$571$	−13980.4	−1.02462	−0.512312	+	0.858799i	$0.671211\pi$
$572$	11581.6	0.846591
$573$	3430.13	0.250080
$574$	0	0
$575$	50806.0	3.68479
$576$	−37475.7	−2.71092
$577$	7559.04	0.545384	0.272692	−	0.962101i	$-0.412086\pi$
$577$	7559.04	0.545384	0.272692	+	0.962101i	$0.412086\pi$
$578$	25215.3	1.81456
$579$	−11002.5	−0.789718
$580$	76513.0	5.47764
$581$	0	0
$582$	25695.4	1.83009
$583$	6944.28	0.493315
$584$	−38158.0	−2.70375
$585$	−19186.1	−1.35598
$586$	−5725.92	−0.403644
$587$	−3545.49	−0.249298	−0.124649	−	0.992201i	$-0.539780\pi$
$587$	−3545.49	−0.249298	−0.124649	+	0.992201i	$0.539780\pi$
$588$	0	0
$589$	22470.1	1.57193
$590$	32208.7	2.24748
$591$	12056.2	0.839128
$592$	−53662.4	−3.72552
$593$	−4374.33	−0.302921	−0.151461	−	0.988463i	$-0.548398\pi$
$593$	−4374.33	−0.302921	−0.151461	+	0.988463i	$0.548398\pi$
$594$	−7044.87	−0.486624
$595$	0	0
$596$	−6108.27	−0.419806
$597$	−1383.04	−0.0948143
$598$	−62549.0	−4.27729
$599$	−11266.1	−0.768479	−0.384240	−	0.923233i	$-0.625536\pi$
$599$	−11266.1	−0.768479	−0.384240	+	0.923233i	$0.625536\pi$
$600$	54876.5	3.73387
$601$	23205.5	1.57500	0.787499	−	0.616316i	$-0.211376\pi$
$601$	23205.5	1.57500	0.787499	+	0.616316i	$0.211376\pi$
$602$	0	0
$603$	−9436.30	−0.637273
$604$	34893.5	2.35066
$605$	−23735.9	−1.59504
$606$	7066.08	0.473663
$607$	−7425.19	−0.496506	−0.248253	−	0.968695i	$-0.579856\pi$
$607$	−7425.19	−0.496506	−0.248253	+	0.968695i	$0.579856\pi$
$608$	−82364.0	−5.49392
$609$	0	0
$610$	1355.50	0.0899712
$611$	2560.64	0.169546
$612$	−7163.78	−0.473168
$613$	23169.6	1.52661	0.763304	−	0.646039i	$-0.223576\pi$
$613$	23169.6	1.52661	0.763304	+	0.646039i	$0.223576\pi$
$614$	−32774.7	−2.15420
$615$	−6661.12	−0.436751
$616$	0	0
$617$	−4372.50	−0.285300	−0.142650	−	0.989773i	$-0.545562\pi$
$617$	−4372.50	−0.285300	−0.142650	+	0.989773i	$0.545562\pi$
$618$	−20607.8	−1.34137
$619$	21639.3	1.40510	0.702549	−	0.711635i	$-0.252045\pi$
$619$	21639.3	1.40510	0.702549	+	0.711635i	$0.252045\pi$
$620$	84271.7	5.45877
$621$	27917.3	1.80400
$622$	43998.5	2.83630
$623$	0	0
$624$	−39328.0	−2.52304
$625$	12895.8	0.825330
$626$	−1776.64	−0.113432
$627$	−3192.78	−0.203361
$628$	9737.07	0.618712
$629$	−3863.71	−0.244922
$630$	0	0
$631$	13338.2	0.841498	0.420749	−	0.907177i	$-0.361767\pi$
$631$	13338.2	0.841498	0.420749	+	0.907177i	$0.361767\pi$
$632$	−27455.0	−1.72801
$633$	5516.43	0.346380
$634$	40636.0	2.54553
$635$	−26472.9	−1.65440
$636$	−46651.5	−2.90857
$637$	0	0
$638$	−9567.11	−0.593676
$639$	980.791	0.0607191
$640$	−102331.	−6.32030
$641$	−25561.8	−1.57508	−0.787542	−	0.616261i	$-0.788647\pi$
$641$	−25561.8	−1.57508	−0.787542	+	0.616261i	$0.788647\pi$
$642$	−7912.42	−0.486415
$643$	−3407.02	−0.208957	−0.104479	−	0.994527i	$-0.533317\pi$
$643$	−3407.02	−0.208957	−0.104479	+	0.994527i	$0.533317\pi$
$644$	0	0
$645$	−16635.2	−1.01552
$646$	−10928.9	−0.665623
$647$	−18113.0	−1.10061	−0.550305	−	0.834964i	$-0.685488\pi$
$647$	−18113.0	−1.10061	−0.550305	+	0.834964i	$0.685488\pi$
$648$	−8032.55	−0.486957
$649$	−2955.07	−0.178731
$650$	−72443.1	−4.37147
$651$	0	0
$652$	−1999.64	−0.120110
$653$	23650.5	1.41733	0.708665	−	0.705545i	$-0.249298\pi$
$653$	23650.5	1.41733	0.708665	+	0.705545i	$0.249298\pi$
$654$	590.853	0.0353275
$655$	25582.1	1.52607
$656$	29054.6	1.72925
$657$	−9102.56	−0.540525
$658$	0	0
$659$	−17119.7	−1.01197	−0.505986	−	0.862541i	$-0.668871\pi$
$659$	−17119.7	−1.01197	−0.505986	+	0.862541i	$0.668871\pi$
$660$	−11974.2	−0.706203
$661$	−7985.27	−0.469881	−0.234940	−	0.972010i	$-0.575489\pi$
$661$	−7985.27	−0.469881	−0.234940	+	0.972010i	$0.575489\pi$
$662$	6527.00	0.383201
$663$	−2831.63	−0.165869
$664$	97347.1	5.68946
$665$	0	0
$666$	−21990.6	−1.27946
$667$	37912.4	2.20086
$668$	−3828.85	−0.221770
$669$	3235.63	0.186991
$670$	−53990.0	−3.11316
$671$	−124.363	−0.00715498
$672$	0	0
$673$	−7705.83	−0.441364	−0.220682	−	0.975346i	$-0.570828\pi$
$673$	−7705.83	−0.441364	−0.220682	+	0.975346i	$0.570828\pi$
$674$	−33653.6	−1.92328
$675$	32333.4	1.84372
$676$	17003.8	0.967447
$677$	25873.1	1.46881	0.734404	−	0.678713i	$-0.237462\pi$
$677$	25873.1	1.46881	0.734404	+	0.678713i	$0.237462\pi$
$678$	−3987.52	−0.225870
$679$	0	0
$680$	−26114.9	−1.47274
$681$	−2766.54	−0.155674
$682$	−10537.2	−0.591631
$683$	−17498.6	−0.980331	−0.490165	−	0.871630i	$-0.663064\pi$
$683$	−17498.6	−0.980331	−0.490165	+	0.871630i	$0.663064\pi$
$684$	−45641.3	−2.55137
$685$	−15352.7	−0.856348
$686$	0	0
$687$	19393.0	1.07698
$688$	72559.9	4.02081
$689$	39238.3	2.16961
$690$	64669.3	3.56800
$691$	24689.5	1.35924	0.679619	−	0.733565i	$-0.262145\pi$
$691$	24689.5	1.35924	0.679619	+	0.733565i	$0.262145\pi$
$692$	57732.1	3.17145
$693$	0	0
$694$	37552.0	2.05397
$695$	−58849.1	−3.21191
$696$	40949.9	2.23017
$697$	2091.94	0.113684
$698$	4499.15	0.243976
$699$	6075.42	0.328746
$700$	0	0
$701$	−15717.0	−0.846822	−0.423411	−	0.905938i	$-0.639167\pi$
$701$	−15717.0	−0.846822	−0.423411	+	0.905938i	$0.639167\pi$
$702$	−39806.7	−2.14018
$703$	−24616.1	−1.32065
$704$	19672.3	1.05316
$705$	−2647.44	−0.141430
$706$	−33445.8	−1.78293
$707$	0	0
$708$	19852.0	1.05379
$709$	13879.1	0.735178	0.367589	−	0.929988i	$-0.380183\pi$
$709$	13879.1	0.735178	0.367589	+	0.929988i	$0.380183\pi$
$710$	5611.61	0.296620
$711$	−6549.36	−0.345458
$712$	95402.5	5.02157
$713$	41756.9	2.19328
$714$	0	0
$715$	10071.4	0.526783
$716$	29445.0	1.53689
$717$	4350.47	0.226599
$718$	66697.5	3.46675
$719$	−8867.55	−0.459950	−0.229975	−	0.973197i	$-0.573864\pi$
$719$	−8867.55	−0.459950	−0.229975	+	0.973197i	$0.573864\pi$
$720$	−86522.9	−4.47850
$721$	0	0
$722$	−32031.7	−1.65110
$723$	14340.4	0.737654
$724$	28523.7	1.46419
$725$	43909.5	2.24932
$726$	−19938.3	−1.01926
$727$	11246.2	0.573727	0.286864	−	0.957971i	$-0.407387\pi$
$727$	11246.2	0.573727	0.286864	+	0.957971i	$0.407387\pi$
$728$	0	0
$729$	8657.48	0.439845
$730$	−52080.5	−2.64053
$731$	5224.34	0.264335
$732$	835.468	0.0421855
$733$	10781.2	0.543263	0.271631	−	0.962401i	$-0.412437\pi$
$733$	10781.2	0.543263	0.271631	+	0.962401i	$0.412437\pi$
$734$	−62146.1	−3.12514
$735$	0	0
$736$	−153060.	−7.66556
$737$	4953.44	0.247574
$738$	11906.4	0.593878
$739$	5247.42	0.261203	0.130602	−	0.991435i	$-0.458309\pi$
$739$	5247.42	0.261203	0.130602	+	0.991435i	$0.458309\pi$
$740$	−92320.2	−4.58616
$741$	−18040.6	−0.894385
$742$	0	0
$743$	−34143.4	−1.68587	−0.842934	−	0.538018i	$-0.819173\pi$
$743$	−34143.4	−1.68587	−0.842934	+	0.538018i	$0.819173\pi$
$744$	45102.4	2.22249
$745$	−5311.80	−0.261220
$746$	35917.1	1.76276
$747$	23222.0	1.13742
$748$	3760.52	0.183821
$749$	0	0
$750$	36303.1	1.76747
$751$	14939.9	0.725920	0.362960	−	0.931805i	$-0.381766\pi$
$751$	14939.9	0.725920	0.362960	+	0.931805i	$0.381766\pi$
$752$	11547.7	0.559973
$753$	16792.2	0.812670
$754$	−54058.5	−2.61100
$755$	30343.7	1.46267
$756$	0	0
$757$	219.361	0.0105321	0.00526605	−	0.999986i	$-0.498324\pi$
$757$	219.361	0.0105321	0.00526605	+	0.999986i	$0.498324\pi$
$758$	32175.8	1.54179
$759$	−5933.24	−0.283745
$760$	−166381.	−7.94115
$761$	15250.1	0.726435	0.363217	−	0.931704i	$-0.381678\pi$
$761$	15250.1	0.726435	0.363217	+	0.931704i	$0.381678\pi$
$762$	−22237.4	−1.05719
$763$	0	0
$764$	−25739.8	−1.21889
$765$	−6229.68	−0.294424
$766$	−18423.4	−0.869012
$767$	−16697.5	−0.786063
$768$	−38004.0	−1.78562
$769$	−21640.5	−1.01479	−0.507396	−	0.861713i	$-0.669392\pi$
$769$	−21640.5	−1.01479	−0.507396	+	0.861713i	$0.669392\pi$
$770$	0	0
$771$	23830.6	1.11315
$772$	82562.8	3.84909
$773$	−19947.3	−0.928144	−0.464072	−	0.885797i	$-0.653612\pi$
$773$	−19947.3	−0.928144	−0.464072	+	0.885797i	$0.653612\pi$
$774$	29734.7	1.38087
$775$	48362.1	2.24157
$776$	−122853.	−5.68319
$777$	0	0
$778$	56095.3	2.58498
$779$	13328.0	0.612997
$780$	−67659.5	−3.10590
$781$	−514.851	−0.0235887
$782$	−20309.5	−0.928731
$783$	24127.8	1.10122
$784$	0	0
$785$	8467.43	0.384988
$786$	21489.2	0.975182
$787$	40888.7	1.85200	0.926000	−	0.377523i	$-0.123224\pi$
$787$	40888.7	1.85200	0.926000	+	0.377523i	$0.123224\pi$
$788$	−90469.8	−4.08992
$789$	−19214.7	−0.867000
$790$	−37472.3	−1.68760
$791$	0	0
$792$	13636.9	0.611824
$793$	−702.708	−0.0314677
$794$	−14908.4	−0.666346
$795$	−40568.5	−1.80983
$796$	10378.4	0.462126
$797$	36866.7	1.63850	0.819250	−	0.573437i	$-0.194390\pi$
$797$	36866.7	1.63850	0.819250	+	0.573437i	$0.194390\pi$
$798$	0	0
$799$	831.435	0.0368136
$800$	−177271.	−7.83435
$801$	22758.2	1.00390
$802$	−46595.4	−2.05155
$803$	4778.25	0.209988
$804$	−33277.0	−1.45969
$805$	0	0
$806$	−59540.2	−2.60200
$807$	10937.9	0.477116
$808$	−33783.7	−1.47092
$809$	−30431.2	−1.32250	−0.661251	−	0.750165i	$-0.729974\pi$
$809$	−30431.2	−1.32250	−0.661251	+	0.750165i	$0.729974\pi$
$810$	−10963.3	−0.475570
$811$	−910.778	−0.0394349	−0.0197175	−	0.999806i	$-0.506277\pi$
$811$	−910.778	−0.0394349	−0.0197175	+	0.999806i	$0.506277\pi$
$812$	0	0
$813$	−13459.8	−0.580634
$814$	11543.6	0.497056
$815$	−1738.90	−0.0747374
$816$	−12769.7	−0.547831
$817$	33284.9	1.42532
$818$	−2870.07	−0.122677
$819$	0	0
$820$	49985.2	2.12873
$821$	42791.0	1.81902	0.909510	−	0.415682i	$-0.136457\pi$
$821$	42791.0	1.81902	0.909510	+	0.415682i	$0.136457\pi$
$822$	−12896.4	−0.547219
$823$	998.654	0.0422976	0.0211488	−	0.999776i	$-0.493268\pi$
$823$	998.654	0.0422976	0.0211488	+	0.999776i	$0.493268\pi$
$824$	98528.3	4.16553
$825$	−6871.77	−0.289993
$826$	0	0
$827$	1587.89	0.0667671	0.0333836	−	0.999443i	$-0.489372\pi$
$827$	1587.89	0.0667671	0.0333836	+	0.999443i	$0.489372\pi$
$828$	−84816.6	−3.55988
$829$	35928.0	1.50522	0.752612	−	0.658464i	$-0.228794\pi$
$829$	35928.0	1.50522	0.752612	+	0.658464i	$0.228794\pi$
$830$	132865.	5.55641
$831$	2933.58	0.122461
$832$	111157.	4.63184
$833$	0	0
$834$	−49433.7	−2.05246
$835$	−3329.59	−0.137994
$836$	23958.7	0.991183
$837$	26574.5	1.09743
$838$	49286.4	2.03171
$839$	−24861.1	−1.02300	−0.511501	−	0.859283i	$-0.670910\pi$
$839$	−24861.1	−1.02300	−0.511501	+	0.859283i	$0.670910\pi$
$840$	0	0
$841$	8377.13	0.343480
$842$	−34246.8	−1.40169
$843$	−18965.8	−0.774872
$844$	−41395.4	−1.68826
$845$	14786.7	0.601984
$846$	4732.17	0.192311
$847$	0	0
$848$	176952.	7.16576
$849$	−3443.23	−0.139189
$850$	−23522.2	−0.949181
$851$	−45744.9	−1.84267
$852$	3458.75	0.139078
$853$	−22170.3	−0.889914	−0.444957	−	0.895552i	$-0.646781\pi$
$853$	−22170.3	−0.889914	−0.444957	+	0.895552i	$0.646781\pi$
$854$	0	0
$855$	−39690.0	−1.58757
$856$	37830.1	1.51052
$857$	5816.95	0.231859	0.115930	−	0.993257i	$-0.463015\pi$
$857$	5816.95	0.231859	0.115930	+	0.993257i	$0.463015\pi$
$858$	8460.07	0.336622
$859$	30490.0	1.21106	0.605532	−	0.795821i	$-0.292960\pi$
$859$	30490.0	1.21106	0.605532	+	0.795821i	$0.292960\pi$
$860$	124831.	4.94967
$861$	0	0
$862$	−34133.3	−1.34871
$863$	−34946.8	−1.37845	−0.689225	−	0.724548i	$-0.742049\pi$
$863$	−34946.8	−1.37845	−0.689225	+	0.724548i	$0.742049\pi$
$864$	−97408.5	−3.83554
$865$	50204.3	1.97341
$866$	−22506.6	−0.883148
$867$	13515.1	0.529408
$868$	0	0
$869$	3437.99	0.134207
$870$	55891.0	2.17802
$871$	27989.2	1.08884
$872$	−2824.93	−0.109707
$873$	−29306.4	−1.13616
$874$	−129394.	−5.00782
$875$	0	0
$876$	−32100.1	−1.23808
$877$	44087.0	1.69751	0.848753	−	0.528790i	$-0.177354\pi$
$877$	44087.0	1.69751	0.848753	+	0.528790i	$0.177354\pi$
$878$	80285.8	3.08601
$879$	−3069.02	−0.117765
$880$	45418.9	1.73985
$881$	9687.48	0.370465	0.185232	−	0.982695i	$-0.440696\pi$
$881$	9687.48	0.370465	0.185232	+	0.982695i	$0.440696\pi$
$882$	0	0
$883$	5405.06	0.205996	0.102998	−	0.994682i	$-0.467156\pi$
$883$	5405.06	0.205996	0.102998	+	0.994682i	$0.467156\pi$
$884$	21248.6	0.808449
$885$	17263.5	0.655712
$886$	80351.4	3.04679
$887$	−6848.47	−0.259244	−0.129622	−	0.991564i	$-0.541376\pi$
$887$	−6848.47	−0.259244	−0.129622	+	0.991564i	$0.541376\pi$
$888$	−49409.9	−1.86722
$889$	0	0
$890$	130211.	4.90415
$891$	1005.86	0.0378198
$892$	−24280.3	−0.911395
$893$	5297.17	0.198503
$894$	−4461.95	−0.166924
$895$	25605.6	0.956315
$896$	0	0
$897$	−33525.5	−1.24792
$898$	−44667.7	−1.65989
$899$	36088.7	1.33885
$900$	−98233.2	−3.63827
$901$	12740.6	0.471090
$902$	−6250.09	−0.230715
$903$	0	0
$904$	19064.8	0.701422
$905$	24804.4	0.911078
$906$	25488.9	0.934671
$907$	3151.21	0.115363	0.0576814	−	0.998335i	$-0.481629\pi$
$907$	3151.21	0.115363	0.0576814	+	0.998335i	$0.481629\pi$
$908$	20760.2	0.758757
$909$	−8059.07	−0.294062
$910$	0	0
$911$	2133.29	0.0775839	0.0387919	−	0.999247i	$-0.487649\pi$
$911$	2133.29	0.0775839	0.0387919	+	0.999247i	$0.487649\pi$
$912$	−81357.4	−2.95396
$913$	−12190.0	−0.441875
$914$	−7199.87	−0.260559
$915$	726.529	0.0262495
$916$	−145525.	−5.24923
$917$	0	0
$918$	−12925.2	−0.464700
$919$	−41212.0	−1.47928	−0.739640	−	0.673003i	$-0.765004\pi$
$919$	−41212.0	−1.47928	−0.739640	+	0.673003i	$0.765004\pi$
$920$	−309191.	−11.0801
$921$	−17566.8	−0.628498
$922$	24572.8	0.877726
$923$	−2909.14	−0.103744
$924$	0	0
$925$	−52981.0	−1.88325
$926$	6676.34	0.236931
$927$	23503.8	0.832758
$928$	−132283.	−4.67931
$929$	−49258.4	−1.73963	−0.869815	−	0.493377i	$-0.835762\pi$
$929$	−49258.4	−1.73963	−0.869815	+	0.493377i	$0.835762\pi$
$930$	61558.5	2.17052
$931$	0	0
$932$	−45590.1	−1.60231
$933$	23582.7	0.827504
$934$	32816.8	1.14968
$935$	3270.17	0.114381
$936$	77054.4	2.69081
$937$	−1667.24	−0.0581285	−0.0290642	−	0.999578i	$-0.509253\pi$
$937$	−1667.24	−0.0581285	−0.0290642	+	0.999578i	$0.509253\pi$
$938$	0	0
$939$	−952.255	−0.0330944
$940$	19866.5	0.689333
$941$	−11460.7	−0.397034	−0.198517	−	0.980097i	$-0.563612\pi$
$941$	−11460.7	−0.397034	−0.198517	+	0.980097i	$0.563612\pi$
$942$	7112.70	0.246013
$943$	24767.8	0.855303
$944$	−75300.2	−2.59620
$945$	0	0
$946$	−15608.8	−0.536453
$947$	25910.5	0.889100	0.444550	−	0.895754i	$-0.353364\pi$
$947$	25910.5	0.889100	0.444550	+	0.895754i	$0.353364\pi$
$948$	−23096.3	−0.791279
$949$	26999.3	0.923533
$950$	−149862.	−5.11808
$951$	21780.4	0.742669
$952$	0	0
$953$	−9117.50	−0.309911	−0.154955	−	0.987921i	$-0.549523\pi$
$953$	−9117.50	−0.309911	−0.154955	+	0.987921i	$0.549523\pi$
$954$	72514.2	2.46094
$955$	−22383.5	−0.758444
$956$	−32646.0	−1.10444
$957$	−5127.85	−0.173208
$958$	74232.0	2.50347
$959$	0	0
$960$	−114925.	−3.86375
$961$	9957.28	0.334238
$962$	65226.6	2.18606
$963$	9024.34	0.301978
$964$	−107610.	−3.59533
$965$	71797.2	2.39506
$966$	0	0
$967$	−23263.0	−0.773616	−0.386808	−	0.922160i	$-0.626422\pi$
$967$	−23263.0	−0.773616	−0.386808	+	0.922160i	$0.626422\pi$
$968$	95327.1	3.16522
$969$	−5857.76	−0.194199
$970$	−167677.	−5.55029
$971$	−10658.4	−0.352261	−0.176130	−	0.984367i	$-0.556358\pi$
$971$	−10658.4	−0.352261	−0.176130	+	0.984367i	$0.556358\pi$
$972$	−86102.2	−2.84128
$973$	0	0
$974$	83021.5	2.73119
$975$	−38828.6	−1.27540
$976$	−3168.99	−0.103931
$977$	20162.8	0.660250	0.330125	−	0.943937i	$-0.392909\pi$
$977$	20162.8	0.660250	0.330125	+	0.943937i	$0.392909\pi$
$978$	−1460.69	−0.0477583
$979$	−11946.5	−0.390003
$980$	0	0
$981$	−673.885	−0.0219322
$982$	68971.3	2.24131
$983$	−15600.2	−0.506173	−0.253086	−	0.967444i	$-0.581446\pi$
$983$	−15600.2	−0.506173	−0.253086	+	0.967444i	$0.581446\pi$
$984$	26752.2	0.866695
$985$	−78673.2	−2.54491
$986$	−17552.7	−0.566929
$987$	0	0
$988$	135377.	4.35924
$989$	61854.3	1.98873
$990$	18612.4	0.597517
$991$	5150.15	0.165086	0.0825429	−	0.996588i	$-0.473696\pi$
$991$	5150.15	0.165086	0.0825429	+	0.996588i	$0.473696\pi$
$992$	−145697.	−4.66319
$993$	3498.39	0.111801
$994$	0	0
$995$	9025.12	0.287553
$996$	81892.3	2.60528
$997$	−55448.3	−1.76135	−0.880675	−	0.473722i	$-0.842910\pi$
$997$	−55448.3	−1.76135	−0.880675	+	0.473722i	$0.842910\pi$
$998$	32990.4	1.04639
$999$	−29112.5	−0.921999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.1	yes	35
7.6	odd	2		2303.4.a.g.1.1	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.1	✓	35	7.6	odd	2
2303.4.a.h.1.1	yes	35	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-5.48152 q^{2} -2.93802 q^{3} +22.0470 q^{4} +19.1722 q^{5} +16.1048 q^{6} -76.9989 q^{8} -18.3680 q^{9} +O(q^{10})\)	\(q-5.48152 q^{2} -2.93802 q^{3} +22.0470 q^{4} +19.1722 q^{5} +16.1048 q^{6} -76.9989 q^{8} -18.3680 q^{9} -105.093 q^{10} +9.64200 q^{11} -64.7747 q^{12} +54.4817 q^{13} -56.3285 q^{15} +245.695 q^{16} +17.6901 q^{17} +100.685 q^{18} +112.706 q^{19} +422.691 q^{20} -52.8528 q^{22} +209.444 q^{23} +226.225 q^{24} +242.575 q^{25} -298.642 q^{26} +133.292 q^{27} +181.014 q^{29} +308.766 q^{30} +199.370 q^{31} -730.788 q^{32} -28.3284 q^{33} -96.9686 q^{34} -404.960 q^{36} -218.411 q^{37} -617.798 q^{38} -160.069 q^{39} -1476.24 q^{40} +118.255 q^{41} +295.325 q^{43} +212.577 q^{44} -352.156 q^{45} -1148.07 q^{46} +47.0000 q^{47} -721.857 q^{48} -1329.68 q^{50} -51.9740 q^{51} +1201.16 q^{52} +720.212 q^{53} -730.644 q^{54} +184.859 q^{55} -331.132 q^{57} -992.232 q^{58} -306.478 q^{59} -1241.88 q^{60} -12.8981 q^{61} -1092.85 q^{62} +2040.27 q^{64} +1044.54 q^{65} +155.283 q^{66} +513.735 q^{67} +390.014 q^{68} -615.353 q^{69} -53.3967 q^{71} +1414.32 q^{72} +495.566 q^{73} +1197.22 q^{74} -712.691 q^{75} +2484.82 q^{76} +877.418 q^{78} +356.564 q^{79} +4710.52 q^{80} +104.320 q^{81} -648.215 q^{82} -1264.26 q^{83} +339.159 q^{85} -1618.83 q^{86} -531.824 q^{87} -742.424 q^{88} -1239.01 q^{89} +1930.35 q^{90} +4617.63 q^{92} -585.753 q^{93} -257.631 q^{94} +2160.82 q^{95} +2147.07 q^{96} +1595.51 q^{97} -177.104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

Modular forms

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Database

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