LMFDB - Embedded newform 2303.4.a.h.1.16

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			1.16
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)

$f(q)$	$=$	$q-0.479509 q^{2} -5.23227 q^{3} -7.77007 q^{4} +17.2964 q^{5} +2.50892 q^{6} +7.56190 q^{8} +0.376695 q^{9} +O(q^{10})$	\(q-0.479509 q^{2} -5.23227 q^{3} -7.77007 q^{4} +17.2964 q^{5} +2.50892 q^{6} +7.56190 q^{8} +0.376695 q^{9} -8.29377 q^{10} -32.3351 q^{11} +40.6551 q^{12} +76.6038 q^{13} -90.4994 q^{15} +58.5346 q^{16} -37.2934 q^{17} -0.180629 q^{18} -131.177 q^{19} -134.394 q^{20} +15.5050 q^{22} +77.2038 q^{23} -39.5659 q^{24} +174.165 q^{25} -36.7323 q^{26} +139.300 q^{27} +87.1582 q^{29} +43.3953 q^{30} -196.457 q^{31} -88.5630 q^{32} +169.186 q^{33} +17.8825 q^{34} -2.92695 q^{36} +270.683 q^{37} +62.9005 q^{38} -400.812 q^{39} +130.793 q^{40} -387.969 q^{41} +398.703 q^{43} +251.246 q^{44} +6.51546 q^{45} -37.0199 q^{46} +47.0000 q^{47} -306.269 q^{48} -83.5135 q^{50} +195.129 q^{51} -595.217 q^{52} -452.095 q^{53} -66.7959 q^{54} -559.280 q^{55} +686.353 q^{57} -41.7932 q^{58} +148.972 q^{59} +703.187 q^{60} +846.832 q^{61} +94.2031 q^{62} -425.810 q^{64} +1324.97 q^{65} -81.1263 q^{66} -490.236 q^{67} +289.772 q^{68} -403.951 q^{69} +316.825 q^{71} +2.84853 q^{72} +1121.32 q^{73} -129.795 q^{74} -911.277 q^{75} +1019.25 q^{76} +192.193 q^{78} -916.264 q^{79} +1012.44 q^{80} -739.029 q^{81} +186.035 q^{82} -746.273 q^{83} -645.041 q^{85} -191.182 q^{86} -456.035 q^{87} -244.515 q^{88} +470.079 q^{89} -3.12423 q^{90} -599.879 q^{92} +1027.92 q^{93} -22.5369 q^{94} -2268.88 q^{95} +463.386 q^{96} -206.816 q^{97} -12.1805 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.479509	−0.169532	−0.0847661	−	0.996401i	$-0.527014\pi$
$2$	−0.479509	−0.169532	−0.0847661	+	0.996401i	$0.527014\pi$
$3$	−5.23227	−1.00695	−0.503476	−	0.864009i	$-0.667946\pi$
$3$	−5.23227	−1.00695	−0.503476	+	0.864009i	$0.667946\pi$
$4$	−7.77007	−0.971259
$5$	17.2964	1.54703	0.773517	−	0.633775i	$-0.218496\pi$
$5$	17.2964	1.54703	0.773517	+	0.633775i	$0.218496\pi$
$6$	2.50892	0.170711
$7$	0	0
$7$	0	0
$8$	7.56190	0.334192
$9$	0.376695	0.0139517
$10$	−8.29377	−0.262272
$11$	−32.3351	−0.886309	−0.443154	−	0.896445i	$-0.646141\pi$
$11$	−32.3351	−0.886309	−0.443154	+	0.896445i	$0.646141\pi$
$12$	40.6551	0.978011
$13$	76.6038	1.63431	0.817157	−	0.576415i	$-0.195549\pi$
$13$	76.6038	1.63431	0.817157	+	0.576415i	$0.195549\pi$
$14$	0	0
$15$	−90.4994	−1.55779
$16$	58.5346	0.914603
$17$	−37.2934	−0.532058	−0.266029	−	0.963965i	$-0.585712\pi$
$17$	−37.2934	−0.532058	−0.266029	+	0.963965i	$0.585712\pi$
$18$	−0.180629	−0.00236526
$19$	−131.177	−1.58389	−0.791947	−	0.610589i	$-0.790933\pi$
$19$	−131.177	−1.58389	−0.791947	+	0.610589i	$0.790933\pi$
$20$	−134.394	−1.50257
$21$	0	0
$22$	15.5050	0.150258
$23$	77.2038	0.699917	0.349959	−	0.936765i	$-0.386196\pi$
$23$	77.2038	0.699917	0.349959	+	0.936765i	$0.386196\pi$
$24$	−39.5659	−0.336515
$25$	174.165	1.39332
$26$	−36.7323	−0.277069
$27$	139.300	0.992903
$28$	0	0
$29$	87.1582	0.558099	0.279049	−	0.960277i	$-0.409981\pi$
$29$	87.1582	0.558099	0.279049	+	0.960277i	$0.409981\pi$
$30$	43.3953	0.264095
$31$	−196.457	−1.13822	−0.569109	−	0.822262i	$-0.692712\pi$
$31$	−196.457	−1.13822	−0.569109	+	0.822262i	$0.692712\pi$
$32$	−88.5630	−0.489246
$33$	169.186	0.892470
$34$	17.8825	0.0902009
$35$	0	0
$36$	−2.92695	−0.0135507
$37$	270.683	1.20270	0.601352	−	0.798984i	$-0.294629\pi$
$37$	270.683	1.20270	0.601352	+	0.798984i	$0.294629\pi$
$38$	62.9005	0.268521
$39$	−400.812	−1.64568
$40$	130.793	0.517006
$41$	−387.969	−1.47782	−0.738909	−	0.673805i	$-0.764659\pi$
$41$	−387.969	−1.47782	−0.738909	+	0.673805i	$0.764659\pi$
$42$	0	0
$43$	398.703	1.41399	0.706996	−	0.707217i	$-0.250050\pi$
$43$	398.703	1.41399	0.706996	+	0.707217i	$0.250050\pi$
$44$	251.246	0.860835
$45$	6.51546	0.0215837
$46$	−37.0199	−0.118658
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−306.269	−0.920961
$49$	0	0
$50$	−83.5135	−0.236212
$51$	195.129	0.535756
$52$	−595.217	−1.58734
$53$	−452.095	−1.17170	−0.585850	−	0.810420i	$-0.699239\pi$
$53$	−452.095	−1.17170	−0.585850	+	0.810420i	$0.699239\pi$
$54$	−66.7959	−0.168329
$55$	−559.280	−1.37115
$56$	0	0
$57$	686.353	1.59491
$58$	−41.7932	−0.0946157
$59$	148.972	0.328721	0.164360	−	0.986400i	$-0.447444\pi$
$59$	148.972	0.328721	0.164360	+	0.986400i	$0.447444\pi$
$60$	703.187	1.51302
$61$	846.832	1.77747	0.888735	−	0.458420i	$-0.151585\pi$
$61$	846.832	1.77747	0.888735	+	0.458420i	$0.151585\pi$
$62$	94.2031	0.192965
$63$	0	0
$64$	−425.810	−0.831660
$65$	1324.97	2.52834
$66$	−81.1263	−0.151302
$67$	−490.236	−0.893908	−0.446954	−	0.894557i	$-0.647491\pi$
$67$	−490.236	−0.893908	−0.446954	+	0.894557i	$0.647491\pi$
$68$	289.772	0.516766
$69$	−403.951	−0.704783
$70$	0	0
$71$	316.825	0.529580	0.264790	−	0.964306i	$-0.414697\pi$
$71$	316.825	0.529580	0.264790	+	0.964306i	$0.414697\pi$
$72$	2.84853	0.00466254
$73$	1121.32	1.79782	0.898911	−	0.438131i	$-0.144359\pi$
$73$	1121.32	1.79782	0.898911	+	0.438131i	$0.144359\pi$
$74$	−129.795	−0.203897
$75$	−911.277	−1.40300
$76$	1019.25	1.53837
$77$	0	0
$78$	192.193	0.278995
$79$	−916.264	−1.30491	−0.652454	−	0.757828i	$-0.726260\pi$
$79$	−916.264	−1.30491	−0.652454	+	0.757828i	$0.726260\pi$
$80$	1012.44	1.41492
$81$	−739.029	−1.01376
$82$	186.035	0.250538
$83$	−746.273	−0.986917	−0.493459	−	0.869769i	$-0.664268\pi$
$83$	−746.273	−0.986917	−0.493459	+	0.869769i	$0.664268\pi$
$84$	0	0
$85$	−645.041	−0.823112
$86$	−191.182	−0.239717
$87$	−456.035	−0.561979
$88$	−244.515	−0.296197
$89$	470.079	0.559868	0.279934	−	0.960019i	$-0.409687\pi$
$89$	470.079	0.559868	0.279934	+	0.960019i	$0.409687\pi$
$90$	−3.12423	−0.00365914
$91$	0	0
$92$	−599.879	−0.679801
$93$	1027.92	1.14613
$94$	−22.5369	−0.0247288
$95$	−2268.88	−2.45034
$96$	463.386	0.492647
$97$	−206.816	−0.216485	−0.108242	−	0.994125i	$-0.534522\pi$
$97$	−206.816	−0.216485	−0.108242	+	0.994125i	$0.534522\pi$
$98$	0	0
$99$	−12.1805	−0.0123655
$100$	−1353.27	−1.35327
$101$	−511.634	−0.504055	−0.252027	−	0.967720i	$-0.581097\pi$
$101$	−511.634	−0.504055	−0.252027	+	0.967720i	$0.581097\pi$
$102$	−93.5663	−0.0908279
$103$	−459.863	−0.439919	−0.219959	−	0.975509i	$-0.570593\pi$
$103$	−459.863	−0.439919	−0.219959	+	0.975509i	$0.570593\pi$
$104$	579.270	0.546174
$105$	0	0
$106$	216.784	0.198641
$107$	−1837.38	−1.66006	−0.830031	−	0.557718i	$-0.811677\pi$
$107$	−1837.38	−1.66006	−0.830031	+	0.557718i	$0.811677\pi$
$108$	−1082.37	−0.964366
$109$	953.267	0.837673	0.418837	−	0.908062i	$-0.362438\pi$
$109$	953.267	0.837673	0.418837	+	0.908062i	$0.362438\pi$
$110$	268.180	0.232454
$111$	−1416.29	−1.21107
$112$	0	0
$113$	−1210.41	−1.00766	−0.503831	−	0.863802i	$-0.668076\pi$
$113$	−1210.41	−1.00766	−0.503831	+	0.863802i	$0.668076\pi$
$114$	−329.112	−0.270388
$115$	1335.34	1.08280
$116$	−677.225	−0.542058
$117$	28.8563	0.0228014
$118$	−71.4335	−0.0557287
$119$	0	0
$120$	−684.347	−0.520600
$121$	−285.442	−0.214457
$122$	−406.064	−0.301338
$123$	2029.96	1.48809
$124$	1526.49	1.10551
$125$	850.369	0.608474
$126$	0	0
$127$	2269.37	1.58562	0.792811	−	0.609468i	$-0.208617\pi$
$127$	2269.37	1.58562	0.792811	+	0.609468i	$0.208617\pi$
$128$	912.684	0.630239
$129$	−2086.12	−1.42382
$130$	−635.335	−0.428635
$131$	−1866.36	−1.24477	−0.622383	−	0.782713i	$-0.713835\pi$
$131$	−1866.36	−1.24477	−0.622383	+	0.782713i	$0.713835\pi$
$132$	−1314.59	−0.866819
$133$	0	0
$134$	235.073	0.151546
$135$	2409.39	1.53606
$136$	−282.009	−0.177809
$137$	−1947.34	−1.21440	−0.607199	−	0.794550i	$-0.707707\pi$
$137$	−1947.34	−1.21440	−0.607199	+	0.794550i	$0.707707\pi$
$138$	193.698	0.119483
$139$	1780.05	1.08620	0.543100	−	0.839668i	$-0.317251\pi$
$139$	1780.05	1.08620	0.543100	+	0.839668i	$0.317251\pi$
$140$	0	0
$141$	−245.917	−0.146879
$142$	−151.920	−0.0897808
$143$	−2476.99	−1.44851
$144$	22.0497	0.0127602
$145$	1507.52	0.863398
$146$	−537.685	−0.304789
$147$	0	0
$148$	−2103.23	−1.16814
$149$	3288.63	1.80816	0.904078	−	0.427367i	$-0.140559\pi$
$149$	3288.63	1.80816	0.904078	+	0.427367i	$0.140559\pi$
$150$	436.966	0.237854
$151$	−1319.95	−0.711362	−0.355681	−	0.934607i	$-0.615751\pi$
$151$	−1319.95	−0.711362	−0.355681	+	0.934607i	$0.615751\pi$
$152$	−991.945	−0.529325
$153$	−14.0483	−0.00742310
$154$	0	0
$155$	−3398.00	−1.76086
$156$	3114.34	1.59838
$157$	1240.85	0.630767	0.315383	−	0.948964i	$-0.397867\pi$
$157$	1240.85	0.630767	0.315383	+	0.948964i	$0.397867\pi$
$158$	439.357	0.221224
$159$	2365.49	1.17984
$160$	−1531.82	−0.756881
$161$	0	0
$162$	354.371	0.171864
$163$	−448.172	−0.215359	−0.107680	−	0.994186i	$-0.534342\pi$
$163$	−448.172	−0.215359	−0.107680	+	0.994186i	$0.534342\pi$
$164$	3014.55	1.43534
$165$	2926.31	1.38068
$166$	357.845	0.167314
$167$	−2998.43	−1.38937	−0.694686	−	0.719313i	$-0.744457\pi$
$167$	−2998.43	−1.38937	−0.694686	+	0.719313i	$0.744457\pi$
$168$	0	0
$169$	3671.15	1.67098
$170$	309.303	0.139544
$171$	−49.4137	−0.0220980
$172$	−3097.95	−1.37335
$173$	−3974.09	−1.74650	−0.873251	−	0.487271i	$-0.837992\pi$
$173$	−3974.09	−1.74650	−0.873251	+	0.487271i	$0.837992\pi$
$174$	218.673	0.0952734
$175$	0	0
$176$	−1892.72	−0.810620
$177$	−779.463	−0.331006
$178$	−225.407	−0.0949157
$179$	3301.40	1.37854	0.689268	−	0.724507i	$-0.257932\pi$
$179$	3301.40	1.37854	0.689268	+	0.724507i	$0.257932\pi$
$180$	−50.6256	−0.0209634
$181$	2512.23	1.03167	0.515836	−	0.856688i	$-0.327482\pi$
$181$	2512.23	1.03167	0.515836	+	0.856688i	$0.327482\pi$
$182$	0	0
$183$	−4430.86	−1.78983
$184$	583.807	0.233907
$185$	4681.84	1.86063
$186$	−492.897	−0.194306
$187$	1205.89	0.471567
$188$	−365.193	−0.141673
$189$	0	0
$190$	1087.95	0.415411
$191$	−423.757	−0.160534	−0.0802670	−	0.996773i	$-0.525577\pi$
$191$	−423.757	−0.160534	−0.0802670	+	0.996773i	$0.525577\pi$
$192$	2227.95	0.837441
$193$	1936.66	0.722299	0.361149	−	0.932508i	$-0.382384\pi$
$193$	1936.66	0.722299	0.361149	+	0.932508i	$0.382384\pi$
$194$	99.1703	0.0367011
$195$	−6932.60	−2.54592
$196$	0	0
$197$	−3165.90	−1.14498	−0.572489	−	0.819912i	$-0.694022\pi$
$197$	−3165.90	−1.14498	−0.572489	+	0.819912i	$0.694022\pi$
$198$	5.84065	0.00209635
$199$	369.971	0.131792	0.0658958	−	0.997827i	$-0.479009\pi$
$199$	369.971	0.131792	0.0658958	+	0.997827i	$0.479009\pi$
$200$	1317.01	0.465635
$201$	2565.05	0.900122
$202$	245.333	0.0854535
$203$	0	0
$204$	−1516.17	−0.520358
$205$	−6710.45	−2.28624
$206$	220.509	0.0745804
$207$	29.0823	0.00976502
$208$	4483.97	1.49475
$209$	4241.61	1.40382
$210$	0	0
$211$	4458.41	1.45464	0.727322	−	0.686297i	$-0.240765\pi$
$211$	4458.41	1.45464	0.727322	+	0.686297i	$0.240765\pi$
$212$	3512.81	1.13802
$213$	−1657.71	−0.533261
$214$	881.042	0.281434
$215$	6896.12	2.18750
$216$	1053.38	0.331820
$217$	0	0
$218$	−457.100	−0.142013
$219$	−5867.07	−1.81032
$220$	4345.64	1.33174
$221$	−2856.82	−0.869549
$222$	679.124	0.205315
$223$	−166.393	−0.0499663	−0.0249832	−	0.999688i	$-0.507953\pi$
$223$	−166.393	−0.0499663	−0.0249832	+	0.999688i	$0.507953\pi$
$224$	0	0
$225$	65.6070	0.0194391
$226$	580.403	0.170831
$227$	6457.76	1.88818	0.944090	−	0.329689i	$-0.106944\pi$
$227$	6457.76	1.88818	0.944090	+	0.329689i	$0.106944\pi$
$228$	−5333.01	−1.54907
$229$	−2726.72	−0.786842	−0.393421	−	0.919358i	$-0.628709\pi$
$229$	−2726.72	−0.786842	−0.393421	+	0.919358i	$0.628709\pi$
$230$	−640.310	−0.183569
$231$	0	0
$232$	659.081	0.186512
$233$	−1430.78	−0.402290	−0.201145	−	0.979561i	$-0.564466\pi$
$233$	−1430.78	−0.402290	−0.201145	+	0.979561i	$0.564466\pi$
$234$	−13.8369	−0.00386557
$235$	812.930	0.225658
$236$	−1157.52	−0.319273
$237$	4794.14	1.31398
$238$	0	0
$239$	5824.13	1.57628	0.788142	−	0.615494i	$-0.211043\pi$
$239$	5824.13	1.57628	0.788142	+	0.615494i	$0.211043\pi$
$240$	−5297.34	−1.42476
$241$	−8.34103	−0.00222943	−0.00111472	−	0.999999i	$-0.500355\pi$
$241$	−8.34103	−0.00222943	−0.00111472	+	0.999999i	$0.500355\pi$
$242$	136.872	0.0363573
$243$	105.690	0.0279013
$244$	−6579.94	−1.72638
$245$	0	0
$246$	−973.384	−0.252279
$247$	−10048.6	−2.58858
$248$	−1485.59	−0.380383
$249$	3904.71	0.993778
$250$	−407.760	−0.103156
$251$	−441.989	−0.111148	−0.0555738	−	0.998455i	$-0.517699\pi$
$251$	−441.989	−0.111148	−0.0555738	+	0.998455i	$0.517699\pi$
$252$	0	0
$253$	−2496.39	−0.620343
$254$	−1088.18	−0.268814
$255$	3375.03	0.828834
$256$	2968.84	0.724814
$257$	3206.52	0.778278	0.389139	−	0.921179i	$-0.372773\pi$
$257$	3206.52	0.778278	0.389139	+	0.921179i	$0.372773\pi$
$258$	1000.32	0.241384
$259$	0	0
$260$	−10295.1	−2.45567
$261$	32.8321	0.00778642
$262$	894.935	0.211028
$263$	−3212.81	−0.753272	−0.376636	−	0.926361i	$-0.622919\pi$
$263$	−3212.81	−0.753272	−0.376636	+	0.926361i	$0.622919\pi$
$264$	1279.37	0.298256
$265$	−7819.61	−1.81266
$266$	0	0
$267$	−2459.58	−0.563760
$268$	3809.17	0.868216
$269$	5445.00	1.23415	0.617077	−	0.786902i	$-0.288317\pi$
$269$	5445.00	1.23415	0.617077	+	0.786902i	$0.288317\pi$
$270$	−1155.33	−0.260411
$271$	−1645.69	−0.368888	−0.184444	−	0.982843i	$-0.559048\pi$
$271$	−1645.69	−0.368888	−0.184444	+	0.982843i	$0.559048\pi$
$272$	−2182.95	−0.486621
$273$	0	0
$274$	933.768	0.205879
$275$	−5631.63	−1.23491
$276$	3138.73	0.684527
$277$	2718.19	0.589605	0.294802	−	0.955558i	$-0.404746\pi$
$277$	2718.19	0.589605	0.294802	+	0.955558i	$0.404746\pi$
$278$	−853.550	−0.184146
$279$	−74.0046	−0.0158801
$280$	0	0
$281$	−1270.16	−0.269650	−0.134825	−	0.990869i	$-0.543047\pi$
$281$	−1270.16	−0.269650	−0.134825	+	0.990869i	$0.543047\pi$
$282$	117.919	0.0249007
$283$	5289.84	1.11112	0.555562	−	0.831475i	$-0.312503\pi$
$283$	5289.84	1.11112	0.555562	+	0.831475i	$0.312503\pi$
$284$	−2461.75	−0.514359
$285$	11871.4	2.46737
$286$	1187.74	0.245568
$287$	0	0
$288$	−33.3613	−0.00682581
$289$	−3522.20	−0.716915
$290$	−722.870	−0.146374
$291$	1082.12	0.217989
$292$	−8712.77	−1.74615
$293$	5835.11	1.16345	0.581725	−	0.813385i	$-0.302378\pi$
$293$	5835.11	1.16345	0.581725	+	0.813385i	$0.302378\pi$
$294$	0	0
$295$	2576.68	0.508542
$296$	2046.88	0.401934
$297$	−4504.29	−0.880019
$298$	−1576.93	−0.306541
$299$	5914.10	1.14388
$300$	7080.69	1.36268
$301$	0	0
$302$	632.926	0.120599
$303$	2677.01	0.507559
$304$	−7678.37	−1.44863
$305$	14647.1	2.74981
$306$	6.73627	0.00125845
$307$	5458.32	1.01473	0.507366	−	0.861730i	$-0.330619\pi$
$307$	5458.32	1.01473	0.507366	+	0.861730i	$0.330619\pi$
$308$	0	0
$309$	2406.13	0.442977
$310$	1629.37	0.298523
$311$	3103.64	0.565888	0.282944	−	0.959136i	$-0.408689\pi$
$311$	3103.64	0.565888	0.282944	+	0.959136i	$0.408689\pi$
$312$	−3030.90	−0.549971
$313$	2608.46	0.471051	0.235525	−	0.971868i	$-0.424319\pi$
$313$	2608.46	0.471051	0.235525	+	0.971868i	$0.424319\pi$
$314$	−594.998	−0.106935
$315$	0	0
$316$	7119.43	1.26740
$317$	5588.24	0.990116	0.495058	−	0.868860i	$-0.335147\pi$
$317$	5588.24	0.990116	0.495058	+	0.868860i	$0.335147\pi$
$318$	−1134.27	−0.200022
$319$	−2818.27	−0.494648
$320$	−7364.96	−1.28661
$321$	9613.69	1.67160
$322$	0	0
$323$	4892.03	0.842724
$324$	5742.31	0.984620
$325$	13341.7	2.27712
$326$	214.903	0.0365103
$327$	−4987.75	−0.843497
$328$	−2933.78	−0.493875
$329$	0	0
$330$	−1403.19	−0.234070
$331$	11145.6	1.85080	0.925402	−	0.378988i	$-0.123728\pi$
$331$	11145.6	1.85080	0.925402	+	0.378988i	$0.123728\pi$
$332$	5798.60	0.958552
$333$	101.965	0.0167798
$334$	1437.77	0.235543
$335$	−8479.30	−1.38291
$336$	0	0
$337$	−3943.08	−0.637368	−0.318684	−	0.947861i	$-0.603241\pi$
$337$	−3943.08	−0.637368	−0.318684	+	0.947861i	$0.603241\pi$
$338$	−1760.35	−0.283285
$339$	6333.19	1.01467
$340$	5012.01	0.799455
$341$	6352.47	1.00881
$342$	23.6943	0.00374632
$343$	0	0
$344$	3014.95	0.472545
$345$	−6986.89	−1.09032
$346$	1905.61	0.296088
$347$	8533.71	1.32021	0.660106	−	0.751172i	$-0.270511\pi$
$347$	8533.71	1.32021	0.660106	+	0.751172i	$0.270511\pi$
$348$	3543.43	0.545827
$349$	−2919.67	−0.447812	−0.223906	−	0.974611i	$-0.571881\pi$
$349$	−2919.67	−0.447812	−0.223906	+	0.974611i	$0.571881\pi$
$350$	0	0
$351$	10670.9	1.62272
$352$	2863.69	0.433623
$353$	6381.05	0.962121	0.481061	−	0.876687i	$-0.340252\pi$
$353$	6381.05	0.962121	0.481061	+	0.876687i	$0.340252\pi$
$354$	373.760	0.0561161
$355$	5479.92	0.819278
$356$	−3652.55	−0.543777
$357$	0	0
$358$	−1583.05	−0.233706
$359$	−274.959	−0.0404228	−0.0202114	−	0.999796i	$-0.506434\pi$
$359$	−274.959	−0.0404228	−0.0202114	+	0.999796i	$0.506434\pi$
$360$	49.2693	0.00721311
$361$	10348.3	1.50872
$362$	−1204.64	−0.174901
$363$	1493.51	0.215948
$364$	0	0
$365$	19394.8	2.78129
$366$	2124.64	0.303433
$367$	−1424.47	−0.202607	−0.101304	−	0.994856i	$-0.532301\pi$
$367$	−1424.47	−0.202607	−0.101304	+	0.994856i	$0.532301\pi$
$368$	4519.09	0.640146
$369$	−146.146	−0.0206180
$370$	−2244.99	−0.315436
$371$	0	0
$372$	−7987.00	−1.11319
$373$	4395.52	0.610165	0.305083	−	0.952326i	$-0.401316\pi$
$373$	4395.52	0.610165	0.305083	+	0.952326i	$0.401316\pi$
$374$	−578.233	−0.0799458
$375$	−4449.36	−0.612704
$376$	355.409	0.0487469
$377$	6676.65	0.912109
$378$	0	0
$379$	25.9169	0.00351257	0.00175628	−	0.999998i	$-0.499441\pi$
$379$	25.9169	0.00351257	0.00175628	+	0.999998i	$0.499441\pi$
$380$	17629.4	2.37991
$381$	−11874.0	−1.59664
$382$	203.196	0.0272157
$383$	176.894	0.0236001	0.0118001	−	0.999930i	$-0.496244\pi$
$383$	176.894	0.0236001	0.0118001	+	0.999930i	$0.496244\pi$
$384$	−4775.41	−0.634621
$385$	0	0
$386$	−928.645	−0.122453
$387$	150.190	0.0197276
$388$	1606.98	0.210263
$389$	5957.03	0.776436	0.388218	−	0.921568i	$-0.373091\pi$
$389$	5957.03	0.776436	0.388218	+	0.921568i	$0.373091\pi$
$390$	3324.25	0.431615
$391$	−2879.19	−0.372396
$392$	0	0
$393$	9765.29	1.25342
$394$	1518.08	0.194111
$395$	−15848.0	−2.01874
$396$	94.6432	0.0120101
$397$	4146.38	0.524184	0.262092	−	0.965043i	$-0.415588\pi$
$397$	4146.38	0.524184	0.262092	+	0.965043i	$0.415588\pi$
$398$	−177.405	−0.0223429
$399$	0	0
$400$	10194.6	1.27433
$401$	−852.308	−0.106140	−0.0530701	−	0.998591i	$-0.516901\pi$
$401$	−852.308	−0.106140	−0.0530701	+	0.998591i	$0.516901\pi$
$402$	−1229.96	−0.152600
$403$	−15049.4	−1.86021
$404$	3975.43	0.489567
$405$	−12782.5	−1.56832
$406$	0	0
$407$	−8752.57	−1.06597
$408$	1475.55	0.179045
$409$	14915.1	1.80318	0.901592	−	0.432588i	$-0.142399\pi$
$409$	14915.1	1.80318	0.901592	+	0.432588i	$0.142399\pi$
$410$	3217.73	0.387591
$411$	10189.0	1.22284
$412$	3573.17	0.427275
$413$	0	0
$414$	−13.9452	−0.00165548
$415$	−12907.8	−1.52680
$416$	−6784.27	−0.799582
$417$	−9313.70	−1.09375
$418$	−2033.89	−0.237993
$419$	−1376.48	−0.160490	−0.0802450	−	0.996775i	$-0.525570\pi$
$419$	−1376.48	−0.160490	−0.0802450	+	0.996775i	$0.525570\pi$
$420$	0	0
$421$	11667.9	1.35073	0.675367	−	0.737482i	$-0.263985\pi$
$421$	11667.9	1.35073	0.675367	+	0.737482i	$0.263985\pi$
$422$	−2137.85	−0.246609
$423$	17.7047	0.00203506
$424$	−3418.70	−0.391572
$425$	−6495.19	−0.741325
$426$	794.889	0.0904049
$427$	0	0
$428$	14276.6	1.61235
$429$	12960.3	1.45858
$430$	−3306.75	−0.370851
$431$	−15621.8	−1.74589	−0.872944	−	0.487821i	$-0.837792\pi$
$431$	−15621.8	−1.74589	−0.872944	+	0.487821i	$0.837792\pi$
$432$	8153.89	0.908112
$433$	10903.5	1.21014	0.605068	−	0.796174i	$-0.293146\pi$
$433$	10903.5	1.21014	0.605068	+	0.796174i	$0.293146\pi$
$434$	0	0
$435$	−7887.76	−0.869400
$436$	−7406.95	−0.813598
$437$	−10127.3	−1.10860
$438$	2813.32	0.306907
$439$	5646.47	0.613875	0.306938	−	0.951730i	$-0.400696\pi$
$439$	5646.47	0.613875	0.306938	+	0.951730i	$0.400696\pi$
$440$	−4229.22	−0.458227
$441$	0	0
$442$	1369.87	0.147417
$443$	4999.08	0.536148	0.268074	−	0.963398i	$-0.413613\pi$
$443$	4999.08	0.536148	0.268074	+	0.963398i	$0.413613\pi$
$444$	11004.7	1.17626
$445$	8130.66	0.866136
$446$	79.7869	0.00847089
$447$	−17207.0	−1.82073
$448$	0	0
$449$	8227.38	0.864752	0.432376	−	0.901693i	$-0.357675\pi$
$449$	8227.38	0.864752	0.432376	+	0.901693i	$0.357675\pi$
$450$	−31.4592	−0.00329555
$451$	12545.0	1.30980
$452$	9404.97	0.978700
$453$	6906.32	0.716307
$454$	−3096.56	−0.320107
$455$	0	0
$456$	5190.13	0.533004
$457$	2310.66	0.236517	0.118258	−	0.992983i	$-0.462269\pi$
$457$	2310.66	0.236517	0.118258	+	0.992983i	$0.462269\pi$
$458$	1307.49	0.133395
$459$	−5194.99	−0.528282
$460$	−10375.7	−1.05168
$461$	−10915.5	−1.10279	−0.551396	−	0.834244i	$-0.685905\pi$
$461$	−10915.5	−1.10279	−0.551396	+	0.834244i	$0.685905\pi$
$462$	0	0
$463$	−17622.9	−1.76891	−0.884456	−	0.466624i	$-0.845470\pi$
$463$	−17622.9	−1.76891	−0.884456	+	0.466624i	$0.845470\pi$
$464$	5101.77	0.510439
$465$	17779.3	1.77311
$466$	686.073	0.0682011
$467$	17329.9	1.71720	0.858600	−	0.512645i	$-0.171334\pi$
$467$	17329.9	1.71720	0.858600	+	0.512645i	$0.171334\pi$
$468$	−224.216	−0.0221461
$469$	0	0
$470$	−389.807	−0.0382563
$471$	−6492.45	−0.635152
$472$	1126.51	0.109856
$473$	−12892.1	−1.25323
$474$	−2298.84	−0.222762
$475$	−22846.3	−2.20687
$476$	0	0
$477$	−170.302	−0.0163472
$478$	−2792.72	−0.267231
$479$	−8323.09	−0.793928	−0.396964	−	0.917834i	$-0.629936\pi$
$479$	−8323.09	−0.793928	−0.396964	+	0.917834i	$0.629936\pi$
$480$	8014.90	0.762143
$481$	20735.4	1.96560
$482$	3.99960	0.000377960 0
$483$	0	0
$484$	2217.91	0.208293
$485$	−3577.17	−0.334909
$486$	−50.6794	−0.00473017
$487$	−5059.26	−0.470753	−0.235377	−	0.971904i	$-0.575632\pi$
$487$	−5059.26	−0.470753	−0.235377	+	0.971904i	$0.575632\pi$
$488$	6403.66	0.594016
$489$	2344.96	0.216856
$490$	0	0
$491$	4251.41	0.390761	0.195380	−	0.980728i	$-0.437406\pi$
$491$	4251.41	0.390761	0.195380	+	0.980728i	$0.437406\pi$
$492$	−15772.9	−1.44532
$493$	−3250.43	−0.296941
$494$	4818.42	0.438848
$495$	−210.678	−0.0191299
$496$	−11499.5	−1.04102
$497$	0	0
$498$	−1872.34	−0.168477
$499$	−18629.8	−1.67131	−0.835656	−	0.549254i	$-0.814912\pi$
$499$	−18629.8	−1.67131	−0.835656	+	0.549254i	$0.814912\pi$
$500$	−6607.42	−0.590986
$501$	15688.6	1.39903
$502$	211.938	0.0188431
$503$	2747.70	0.243566	0.121783	−	0.992557i	$-0.461139\pi$
$503$	2747.70	0.243566	0.121783	+	0.992557i	$0.461139\pi$
$504$	0	0
$505$	−8849.42	−0.779790
$506$	1197.04	0.105168
$507$	−19208.5	−1.68260
$508$	−17633.2	−1.54005
$509$	−5689.72	−0.495467	−0.247733	−	0.968828i	$-0.579686\pi$
$509$	−5689.72	−0.495467	−0.247733	+	0.968828i	$0.579686\pi$
$510$	−1618.36	−0.140514
$511$	0	0
$512$	−8725.06	−0.753119
$513$	−18273.0	−1.57265
$514$	−1537.56	−0.131943
$515$	−7953.96	−0.680570
$516$	16209.3	1.38290
$517$	−1519.75	−0.129281
$518$	0	0
$519$	20793.5	1.75864
$520$	10019.3	0.844951
$521$	18673.5	1.57025	0.785126	−	0.619335i	$-0.212598\pi$
$521$	18673.5	1.57025	0.785126	+	0.619335i	$0.212598\pi$
$522$	−15.7433	−0.00132005
$523$	8511.97	0.711668	0.355834	−	0.934549i	$-0.384197\pi$
$523$	8511.97	0.711668	0.355834	+	0.934549i	$0.384197\pi$
$524$	14501.7	1.20899
$525$	0	0
$526$	1540.57	0.127704
$527$	7326.57	0.605598
$528$	9903.23	0.816255
$529$	−6206.58	−0.510116
$530$	3749.58	0.307304
$531$	56.1171	0.00458621
$532$	0	0
$533$	−29719.9	−2.41522
$534$	1179.39	0.0955755
$535$	−31780.1	−2.56817
$536$	−3707.11	−0.298737
$537$	−17273.8	−1.38812
$538$	−2610.93	−0.209229
$539$	0	0
$540$	−18721.2	−1.49191
$541$	9649.14	0.766818	0.383409	−	0.923579i	$-0.374750\pi$
$541$	9649.14	0.766818	0.383409	+	0.923579i	$0.374750\pi$
$542$	789.124	0.0625383
$543$	−13144.7	−1.03884
$544$	3302.82	0.260307
$545$	16488.1	1.29591
$546$	0	0
$547$	−10551.7	−0.824783	−0.412391	−	0.911007i	$-0.635306\pi$
$547$	−10551.7	−0.824783	−0.412391	+	0.911007i	$0.635306\pi$
$548$	15131.0	1.17949
$549$	318.998	0.0247987
$550$	2700.42	0.209357
$551$	−11433.1	−0.883970
$552$	−3054.64	−0.235533
$553$	0	0
$554$	−1303.40	−0.0999569
$555$	−24496.7	−1.87356
$556$	−13831.1	−1.05498
$557$	1698.61	0.129215	0.0646073	−	0.997911i	$-0.479421\pi$
$557$	1698.61	0.129215	0.0646073	+	0.997911i	$0.479421\pi$
$558$	35.4859	0.00269218
$559$	30542.2	2.31091
$560$	0	0
$561$	−6309.53	−0.474846
$562$	609.055	0.0457143
$563$	−3443.61	−0.257782	−0.128891	−	0.991659i	$-0.541142\pi$
$563$	−3443.61	−0.257782	−0.128891	+	0.991659i	$0.541142\pi$
$564$	1910.79	0.142658
$565$	−20935.7	−1.55889
$566$	−2536.53	−0.188371
$567$	0	0
$568$	2395.80	0.176981
$569$	9395.22	0.692211	0.346105	−	0.938196i	$-0.387504\pi$
$569$	9395.22	0.692211	0.346105	+	0.938196i	$0.387504\pi$
$570$	−5692.45	−0.418299
$571$	7824.48	0.573458	0.286729	−	0.958012i	$-0.407432\pi$
$571$	7824.48	0.573458	0.286729	+	0.958012i	$0.407432\pi$
$572$	19246.4	1.40687
$573$	2217.21	0.161650
$574$	0	0
$575$	13446.2	0.975206
$576$	−160.401	−0.0116030
$577$	5266.87	0.380004	0.190002	−	0.981784i	$-0.439150\pi$
$577$	5266.87	0.380004	0.190002	+	0.981784i	$0.439150\pi$
$578$	1688.93	0.121540
$579$	−10133.1	−0.727320
$580$	−11713.5	−0.838583
$581$	0	0
$582$	−518.886	−0.0369562
$583$	14618.5	1.03849
$584$	8479.33	0.600817
$585$	499.110	0.0352746
$586$	−2797.99	−0.197242
$587$	11682.3	0.821432	0.410716	−	0.911763i	$-0.365279\pi$
$587$	11682.3	0.821432	0.410716	+	0.911763i	$0.365279\pi$
$588$	0	0
$589$	25770.6	1.80282
$590$	−1235.54	−0.0862143
$591$	16564.8	1.15294
$592$	15844.3	1.10000
$593$	9378.73	0.649475	0.324737	−	0.945804i	$-0.394724\pi$
$593$	9378.73	0.649475	0.324737	+	0.945804i	$0.394724\pi$
$594$	2159.85	0.149191
$595$	0	0
$596$	−25552.9	−1.75619
$597$	−1935.79	−0.132708
$598$	−2835.87	−0.193925
$599$	4174.96	0.284782	0.142391	−	0.989811i	$-0.454521\pi$
$599$	4174.96	0.284782	0.142391	+	0.989811i	$0.454521\pi$
$600$	−6890.98	−0.468872
$601$	−8575.79	−0.582053	−0.291027	−	0.956715i	$-0.593997\pi$
$601$	−8575.79	−0.582053	−0.291027	+	0.956715i	$0.593997\pi$
$602$	0	0
$603$	−184.670	−0.0124715
$604$	10256.1	0.690917
$605$	−4937.11	−0.331772
$606$	−1283.65	−0.0860475
$607$	−15500.3	−1.03647	−0.518236	−	0.855238i	$-0.673411\pi$
$607$	−15500.3	−1.03647	−0.518236	+	0.855238i	$0.673411\pi$
$608$	11617.4	0.774915
$609$	0	0
$610$	−7023.43	−0.466181
$611$	3600.38	0.238389
$612$	109.156	0.00720975
$613$	−3000.37	−0.197690	−0.0988449	−	0.995103i	$-0.531515\pi$
$613$	−3000.37	−0.197690	−0.0988449	+	0.995103i	$0.531515\pi$
$614$	−2617.32	−0.172030
$615$	35110.9	2.30213
$616$	0	0
$617$	26682.2	1.74098	0.870489	−	0.492187i	$-0.163802\pi$
$617$	26682.2	1.74098	0.870489	+	0.492187i	$0.163802\pi$
$618$	−1153.76	−0.0750989
$619$	24156.8	1.56857	0.784283	−	0.620403i	$-0.213031\pi$
$619$	24156.8	1.56857	0.784283	+	0.620403i	$0.213031\pi$
$620$	26402.7	1.71025
$621$	10754.5	0.694950
$622$	−1488.22	−0.0959363
$623$	0	0
$624$	−23461.4	−1.50514
$625$	−7062.28	−0.451986
$626$	−1250.78	−0.0798582
$627$	−22193.3	−1.41358
$628$	−9641.47	−0.612638
$629$	−10094.7	−0.639908
$630$	0	0
$631$	−23616.8	−1.48997	−0.744983	−	0.667084i	$-0.767542\pi$
$631$	−23616.8	−1.48997	−0.744983	+	0.667084i	$0.767542\pi$
$632$	−6928.69	−0.436089
$633$	−23327.6	−1.46476
$634$	−2679.61	−0.167857
$635$	39251.9	2.45301
$636$	−18380.0	−1.14593
$637$	0	0
$638$	1351.39	0.0838587
$639$	119.346	0.00738853
$640$	15786.1	0.975002
$641$	6815.96	0.419991	0.209995	−	0.977702i	$-0.432655\pi$
$641$	6815.96	0.419991	0.209995	+	0.977702i	$0.432655\pi$
$642$	−4609.86	−0.283390
$643$	−772.226	−0.0473618	−0.0236809	−	0.999720i	$-0.507539\pi$
$643$	−772.226	−0.0473618	−0.0236809	+	0.999720i	$0.507539\pi$
$644$	0	0
$645$	−36082.4	−2.20270
$646$	−2345.77	−0.142869
$647$	13867.8	0.842655	0.421327	−	0.906909i	$-0.361564\pi$
$647$	13867.8	0.842655	0.421327	+	0.906909i	$0.361564\pi$
$648$	−5588.46	−0.338789
$649$	−4817.03	−0.291348
$650$	−6397.46	−0.386044
$651$	0	0
$652$	3482.33	0.209170
$653$	−5327.22	−0.319250	−0.159625	−	0.987178i	$-0.551029\pi$
$653$	−5327.22	−0.319250	−0.159625	+	0.987178i	$0.551029\pi$
$654$	2391.67	0.143000
$655$	−32281.2	−1.92570
$656$	−22709.6	−1.35162
$657$	422.397	0.0250826
$658$	0	0
$659$	13398.6	0.792013	0.396006	−	0.918248i	$-0.370396\pi$
$659$	13398.6	0.792013	0.396006	+	0.918248i	$0.370396\pi$
$660$	−22737.6	−1.34100
$661$	−10237.8	−0.602425	−0.301212	−	0.953557i	$-0.597391\pi$
$661$	−10237.8	−0.602425	−0.301212	+	0.953557i	$0.597391\pi$
$662$	−5344.40	−0.313771
$663$	14947.7	0.875594
$664$	−5643.24	−0.329820
$665$	0	0
$666$	−48.8933	−0.00284471
$667$	6728.94	0.390623
$668$	23298.0	1.34944
$669$	870.613	0.0503137
$670$	4065.90	0.234447
$671$	−27382.4	−1.57539
$672$	0	0
$673$	−7350.71	−0.421024	−0.210512	−	0.977591i	$-0.567513\pi$
$673$	−7350.71	−0.421024	−0.210512	+	0.977591i	$0.567513\pi$
$674$	1890.74	0.108054
$675$	24261.2	1.38343
$676$	−28525.1	−1.62296
$677$	−4034.48	−0.229037	−0.114518	−	0.993421i	$-0.536532\pi$
$677$	−4034.48	−0.229037	−0.114518	+	0.993421i	$0.536532\pi$
$678$	−3036.83	−0.172019
$679$	0	0
$680$	−4877.73	−0.275077
$681$	−33788.8	−1.90131
$682$	−3046.07	−0.171026
$683$	−3289.40	−0.184283	−0.0921417	−	0.995746i	$-0.529371\pi$
$683$	−3289.40	−0.184283	−0.0921417	+	0.995746i	$0.529371\pi$
$684$	383.948	0.0214629
$685$	−33681.9	−1.87872
$686$	0	0
$687$	14267.0	0.792312
$688$	23337.9	1.29324
$689$	−34632.2	−1.91492
$690$	3350.28	0.184845
$691$	9915.92	0.545903	0.272952	−	0.962028i	$-0.412000\pi$
$691$	9915.92	0.545903	0.272952	+	0.962028i	$0.412000\pi$
$692$	30879.0	1.69630
$693$	0	0
$694$	−4091.99	−0.223818
$695$	30788.4	1.68039
$696$	−3448.49	−0.187809
$697$	14468.7	0.786285
$698$	1400.01	0.0759186
$699$	7486.24	0.405087
$700$	0	0
$701$	−19314.6	−1.04066	−0.520330	−	0.853965i	$-0.674191\pi$
$701$	−19314.6	−1.04066	−0.520330	+	0.853965i	$0.674191\pi$
$702$	−5116.82	−0.275102
$703$	−35507.4	−1.90496
$704$	13768.6	0.737107
$705$	−4253.47	−0.227227
$706$	−3059.77	−0.163111
$707$	0	0
$708$	6056.48	0.321492
$709$	629.430	0.0333410	0.0166705	−	0.999861i	$-0.494693\pi$
$709$	629.430	0.0333410	0.0166705	+	0.999861i	$0.494693\pi$
$710$	−2627.67	−0.138894
$711$	−345.152	−0.0182057
$712$	3554.69	0.187103
$713$	−15167.2	−0.796659
$714$	0	0
$715$	−42843.0	−2.24089
$716$	−25652.1	−1.33891
$717$	−30473.4	−1.58724
$718$	131.846	0.00685297
$719$	−8388.82	−0.435118	−0.217559	−	0.976047i	$-0.569810\pi$
$719$	−8388.82	−0.435118	−0.217559	+	0.976047i	$0.569810\pi$
$720$	381.380	0.0197405
$721$	0	0
$722$	−4962.12	−0.255777
$723$	43.6425	0.00224493
$724$	−19520.2	−1.00202
$725$	15179.9	0.777608
$726$	−716.153	−0.0366101
$727$	3011.49	0.153631	0.0768156	−	0.997045i	$-0.475525\pi$
$727$	3011.49	0.153631	0.0768156	+	0.997045i	$0.475525\pi$
$728$	0	0
$729$	19400.8	0.985662
$730$	−9300.00	−0.471519
$731$	−14869.0	−0.752326
$732$	34428.1	1.73839
$733$	−9166.38	−0.461894	−0.230947	−	0.972966i	$-0.574182\pi$
$733$	−9166.38	−0.461894	−0.230947	+	0.972966i	$0.574182\pi$
$734$	683.049	0.0343485
$735$	0	0
$736$	−6837.40	−0.342432
$737$	15851.8	0.792278
$738$	70.0784	0.00349542
$739$	−12526.7	−0.623547	−0.311774	−	0.950156i	$-0.600923\pi$
$739$	−12526.7	−0.623547	−0.311774	+	0.950156i	$0.600923\pi$
$740$	−36378.2	−1.80715
$741$	52577.2	2.60658
$742$	0	0
$743$	−6178.90	−0.305090	−0.152545	−	0.988297i	$-0.548747\pi$
$743$	−6178.90	−0.305090	−0.152545	+	0.988297i	$0.548747\pi$
$744$	7773.02	0.383028
$745$	56881.4	2.79728
$746$	−2107.69	−0.103443
$747$	−281.118	−0.0137692
$748$	−9369.82	−0.458014
$749$	0	0
$750$	2133.51	0.103873
$751$	−13868.0	−0.673834	−0.336917	−	0.941534i	$-0.609384\pi$
$751$	−13868.0	−0.673834	−0.336917	+	0.941534i	$0.609384\pi$
$752$	2751.12	0.133409
$753$	2312.61	0.111920
$754$	−3201.52	−0.154632
$755$	−22830.3	−1.10050
$756$	0	0
$757$	−19417.2	−0.932271	−0.466135	−	0.884713i	$-0.654354\pi$
$757$	−19417.2	−0.932271	−0.466135	+	0.884713i	$0.654354\pi$
$758$	−12.4274	−0.000595493 0
$759$	13061.8	0.624655
$760$	−17157.0	−0.818884
$761$	39115.8	1.86327	0.931633	−	0.363402i	$-0.118385\pi$
$761$	39115.8	1.86327	0.931633	+	0.363402i	$0.118385\pi$
$762$	5693.67	0.270683
$763$	0	0
$764$	3292.62	0.155920
$765$	−242.984	−0.0114838
$766$	−84.8222	−0.00400098
$767$	11411.8	0.537233
$768$	−15533.8	−0.729852
$769$	18361.8	0.861045	0.430523	−	0.902580i	$-0.358329\pi$
$769$	18361.8	0.861045	0.430523	+	0.902580i	$0.358329\pi$
$770$	0	0
$771$	−16777.4	−0.783688
$772$	−15048.0	−0.701539
$773$	34555.1	1.60784	0.803920	−	0.594737i	$-0.202744\pi$
$773$	34555.1	1.60784	0.803920	+	0.594737i	$0.202744\pi$
$774$	−72.0173	−0.00334446
$775$	−34215.9	−1.58590
$776$	−1563.92	−0.0723473
$777$	0	0
$778$	−2856.45	−0.131631
$779$	50892.5	2.34071
$780$	53866.8	2.47274
$781$	−10244.6	−0.469371
$782$	1380.60	0.0631331
$783$	12141.2	0.554138
$784$	0	0
$785$	21462.2	0.975818
$786$	−4682.55	−0.212495
$787$	19987.5	0.905307	0.452653	−	0.891687i	$-0.350478\pi$
$787$	19987.5	0.905307	0.452653	+	0.891687i	$0.350478\pi$
$788$	24599.2	1.11207
$789$	16810.3	0.758509
$790$	7599.28	0.342241
$791$	0	0
$792$	−92.1075	−0.00413245
$793$	64870.6	2.90495
$794$	−1988.23	−0.0888660
$795$	40914.3	1.82526
$796$	−2874.70	−0.128004
$797$	26091.6	1.15962	0.579808	−	0.814753i	$-0.303128\pi$
$797$	26091.6	1.15962	0.579808	+	0.814753i	$0.303128\pi$
$798$	0	0
$799$	−1752.79	−0.0776086
$800$	−15424.5	−0.681675
$801$	177.077	0.00781110
$802$	408.690	0.0179942
$803$	−36258.1	−1.59343
$804$	−19930.6	−0.874252
$805$	0	0
$806$	7216.32	0.315365
$807$	−28489.7	−1.24273
$808$	−3868.92	−0.168451
$809$	−41941.3	−1.82271	−0.911357	−	0.411616i	$-0.864965\pi$
$809$	−41941.3	−1.82271	−0.911357	+	0.411616i	$0.864965\pi$
$810$	6129.34	0.265880
$811$	−1288.93	−0.0558084	−0.0279042	−	0.999611i	$-0.508883\pi$
$811$	−1288.93	−0.0558084	−0.0279042	+	0.999611i	$0.508883\pi$
$812$	0	0
$813$	8610.71	0.371452
$814$	4196.94	0.180716
$815$	−7751.76	−0.333168
$816$	11421.8	0.490004
$817$	−52300.6	−2.23962
$818$	−7151.91	−0.305698
$819$	0	0
$820$	52140.7	2.22053
$821$	14498.9	0.616341	0.308170	−	0.951331i	$-0.400283\pi$
$821$	14498.9	0.616341	0.308170	+	0.951331i	$0.400283\pi$
$822$	−4885.73	−0.207311
$823$	−36287.4	−1.53694	−0.768469	−	0.639886i	$-0.778981\pi$
$823$	−36287.4	−1.53694	−0.768469	+	0.639886i	$0.778981\pi$
$824$	−3477.44	−0.147017
$825$	29466.2	1.24349
$826$	0	0
$827$	−25704.4	−1.08081	−0.540404	−	0.841406i	$-0.681729\pi$
$827$	−25704.4	−1.08081	−0.540404	+	0.841406i	$0.681729\pi$
$828$	−225.971	−0.00948436
$829$	−37152.3	−1.55652	−0.778258	−	0.627944i	$-0.783896\pi$
$829$	−37152.3	−1.55652	−0.778258	+	0.627944i	$0.783896\pi$
$830$	6189.42	0.258841
$831$	−14222.3	−0.593703
$832$	−32618.7	−1.35919
$833$	0	0
$834$	4466.01	0.185426
$835$	−51861.9	−2.14941
$836$	−32957.6	−1.36347
$837$	−27366.6	−1.13014
$838$	660.034	0.0272082
$839$	28474.1	1.17167	0.585837	−	0.810429i	$-0.300766\pi$
$839$	28474.1	1.17167	0.585837	+	0.810429i	$0.300766\pi$
$840$	0	0
$841$	−16792.5	−0.688526
$842$	−5594.87	−0.228993
$843$	6645.84	0.271524
$844$	−34642.2	−1.41284
$845$	63497.6	2.58507
$846$	−8.48956	−0.000345008 0
$847$	0	0
$848$	−26463.2	−1.07164
$849$	−27677.9	−1.11885
$850$	3114.50	0.125678
$851$	20897.8	0.841794
$852$	12880.6	0.517935
$853$	32406.8	1.30081	0.650403	−	0.759589i	$-0.274600\pi$
$853$	32406.8	1.30081	0.650403	+	0.759589i	$0.274600\pi$
$854$	0	0
$855$	−854.677	−0.0341864
$856$	−13894.1	−0.554779
$857$	−24592.1	−0.980223	−0.490112	−	0.871660i	$-0.663044\pi$
$857$	−24592.1	−0.980223	−0.490112	+	0.871660i	$0.663044\pi$
$858$	−6214.59	−0.247276
$859$	16782.9	0.666619	0.333310	−	0.942817i	$-0.391835\pi$
$859$	16782.9	0.666619	0.333310	+	0.942817i	$0.391835\pi$
$860$	−53583.3	−2.12462
$861$	0	0
$862$	7490.82	0.295984
$863$	15068.1	0.594352	0.297176	−	0.954823i	$-0.403955\pi$
$863$	15068.1	0.594352	0.297176	+	0.954823i	$0.403955\pi$
$864$	−12336.9	−0.485774
$865$	−68737.4	−2.70190
$866$	−5228.33	−0.205157
$867$	18429.1	0.721898
$868$	0	0
$869$	29627.5	1.15655
$870$	3782.25	0.147391
$871$	−37553.9	−1.46093
$872$	7208.50	0.279944
$873$	−77.9067	−0.00302032
$874$	4856.15	0.187943
$875$	0	0
$876$	45587.6	1.75829
$877$	38761.7	1.49246	0.746231	−	0.665687i	$-0.231862\pi$
$877$	38761.7	1.49246	0.746231	+	0.665687i	$0.231862\pi$
$878$	−2707.53	−0.104072
$879$	−30530.9	−1.17154
$880$	−32737.2	−1.25406
$881$	18961.9	0.725133	0.362567	−	0.931958i	$-0.381900\pi$
$881$	18961.9	0.725133	0.362567	+	0.931958i	$0.381900\pi$
$882$	0	0
$883$	10610.9	0.404400	0.202200	−	0.979344i	$-0.435191\pi$
$883$	10610.9	0.404400	0.202200	+	0.979344i	$0.435191\pi$
$884$	22197.7	0.844558
$885$	−13481.9	−0.512078
$886$	−2397.11	−0.0908943
$887$	−16264.4	−0.615675	−0.307838	−	0.951439i	$-0.599605\pi$
$887$	−16264.4	−0.615675	−0.307838	+	0.951439i	$0.599605\pi$
$888$	−10709.8	−0.404728
$889$	0	0
$890$	−3898.73	−0.146838
$891$	23896.6	0.898502
$892$	1292.88	0.0485302
$893$	−6165.31	−0.231035
$894$	8250.93	0.308672
$895$	57102.2	2.13264
$896$	0	0
$897$	−30944.2	−1.15184
$898$	−3945.10	−0.146603
$899$	−17122.9	−0.635239
$900$	−509.771	−0.0188804
$901$	16860.2	0.623412
$902$	−6015.45	−0.222054
$903$	0	0
$904$	−9152.99	−0.336752
$905$	43452.5	1.59603
$906$	−3311.65	−0.121437
$907$	47280.8	1.73091	0.865455	−	0.500987i	$-0.167030\pi$
$907$	47280.8	1.73091	0.865455	+	0.500987i	$0.167030\pi$
$908$	−50177.3	−1.83391
$909$	−192.730	−0.00703241
$910$	0	0
$911$	16496.0	0.599929	0.299965	−	0.953950i	$-0.403025\pi$
$911$	16496.0	0.599929	0.299965	+	0.953950i	$0.403025\pi$
$912$	40175.4	1.45870
$913$	24130.8	0.874713
$914$	−1107.98	−0.0400972
$915$	−76637.8	−2.76892
$916$	21186.8	0.764227
$917$	0	0
$918$	2491.05	0.0895607
$919$	−36931.9	−1.32565	−0.662824	−	0.748775i	$-0.730642\pi$
$919$	−36931.9	−1.32565	−0.662824	+	0.748775i	$0.730642\pi$
$920$	10097.7	0.361862
$921$	−28559.4	−1.02179
$922$	5234.10	0.186959
$923$	24270.0	0.865500
$924$	0	0
$925$	47143.5	1.67575
$926$	8450.35	0.299887
$927$	−173.228	−0.00613761
$928$	−7718.99	−0.273048
$929$	−41068.1	−1.45038	−0.725188	−	0.688551i	$-0.758247\pi$
$929$	−41068.1	−1.45038	−0.725188	+	0.688551i	$0.758247\pi$
$930$	−8525.33	−0.300598
$931$	0	0
$932$	11117.3	0.390728
$933$	−16239.1	−0.569822
$934$	−8309.86	−0.291121
$935$	20857.5	0.729531
$936$	218.208	0.00762005
$937$	−1261.78	−0.0439922	−0.0219961	−	0.999758i	$-0.507002\pi$
$937$	−1261.78	−0.0439922	−0.0219961	+	0.999758i	$0.507002\pi$
$938$	0	0
$939$	−13648.2	−0.474325
$940$	−6316.52	−0.219173
$941$	−22794.4	−0.789666	−0.394833	−	0.918753i	$-0.629198\pi$
$941$	−22794.4	−0.789666	−0.394833	+	0.918753i	$0.629198\pi$
$942$	3113.19	0.107679
$943$	−29952.6	−1.03435
$944$	8720.02	0.300649
$945$	0	0
$946$	6181.88	0.212463
$947$	−29500.5	−1.01229	−0.506144	−	0.862449i	$-0.668930\pi$
$947$	−29500.5	−1.01229	−0.506144	+	0.862449i	$0.668930\pi$
$948$	−37250.8	−1.27621
$949$	85897.7	2.93821
$950$	10955.0	0.374135
$951$	−29239.2	−0.996999
$952$	0	0
$953$	−30732.7	−1.04463	−0.522313	−	0.852754i	$-0.674931\pi$
$953$	−30732.7	−1.04463	−0.522313	+	0.852754i	$0.674931\pi$
$954$	81.6615	0.00277137
$955$	−7329.46	−0.248352
$956$	−45253.9	−1.53098
$957$	14745.9	0.498086
$958$	3991.00	0.134596
$959$	0	0
$960$	38535.5	1.29555
$961$	8804.50	0.295542
$962$	−9942.81	−0.333232
$963$	−692.134	−0.0231606
$964$	64.8104	0.00216535
$965$	33497.2	1.11742
$966$	0	0
$967$	19705.2	0.655300	0.327650	−	0.944799i	$-0.393743\pi$
$967$	19705.2	0.655300	0.327650	+	0.944799i	$0.393743\pi$
$968$	−2158.48	−0.0716697
$969$	−25596.4	−0.848582
$970$	1715.29	0.0567779
$971$	5477.77	0.181040	0.0905201	−	0.995895i	$-0.471147\pi$
$971$	5477.77	0.181040	0.0905201	+	0.995895i	$0.471147\pi$
$972$	−821.220	−0.0270994
$973$	0	0
$974$	2425.96	0.0798078
$975$	−69807.3	−2.29295
$976$	49568.9	1.62568
$977$	−17359.8	−0.568463	−0.284232	−	0.958756i	$-0.591738\pi$
$977$	−17359.8	−0.568463	−0.284232	+	0.958756i	$0.591738\pi$
$978$	−1124.43	−0.0367641
$979$	−15200.0	−0.496216
$980$	0	0
$981$	359.091	0.0116870
$982$	−2038.59	−0.0662465
$983$	−24750.4	−0.803067	−0.401533	−	0.915844i	$-0.631523\pi$
$983$	−24750.4	−0.803067	−0.401533	+	0.915844i	$0.631523\pi$
$984$	15350.3	0.497308
$985$	−54758.5	−1.77132
$986$	1558.61	0.0503410
$987$	0	0
$988$	78078.6	2.51418
$989$	30781.4	0.989678
$990$	101.022	0.00324312
$991$	29698.5	0.951972	0.475986	−	0.879453i	$-0.342091\pi$
$991$	29698.5	0.951972	0.475986	+	0.879453i	$0.342091\pi$
$992$	17398.9	0.556869
$993$	−58316.7	−1.86367
$994$	0	0
$995$	6399.16	0.203886
$996$	−30339.8	−0.965216
$997$	62252.9	1.97750	0.988751	−	0.149569i	$-0.0477886\pi$
$997$	62252.9	1.97750	0.988751	+	0.149569i	$0.0477886\pi$
$998$	8933.16	0.283341
$999$	37706.3	1.19417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.16	yes	35
7.6	odd	2		2303.4.a.g.1.16	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.16	✓	35	7.6	odd	2
2303.4.a.h.1.16	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)

\(f(q)\)	\(=\)	\(q-0.479509 q^{2} -5.23227 q^{3} -7.77007 q^{4} +17.2964 q^{5} +2.50892 q^{6} +7.56190 q^{8} +0.376695 q^{9} +O(q^{10})\)	\(q-0.479509 q^{2} -5.23227 q^{3} -7.77007 q^{4} +17.2964 q^{5} +2.50892 q^{6} +7.56190 q^{8} +0.376695 q^{9} -8.29377 q^{10} -32.3351 q^{11} +40.6551 q^{12} +76.6038 q^{13} -90.4994 q^{15} +58.5346 q^{16} -37.2934 q^{17} -0.180629 q^{18} -131.177 q^{19} -134.394 q^{20} +15.5050 q^{22} +77.2038 q^{23} -39.5659 q^{24} +174.165 q^{25} -36.7323 q^{26} +139.300 q^{27} +87.1582 q^{29} +43.3953 q^{30} -196.457 q^{31} -88.5630 q^{32} +169.186 q^{33} +17.8825 q^{34} -2.92695 q^{36} +270.683 q^{37} +62.9005 q^{38} -400.812 q^{39} +130.793 q^{40} -387.969 q^{41} +398.703 q^{43} +251.246 q^{44} +6.51546 q^{45} -37.0199 q^{46} +47.0000 q^{47} -306.269 q^{48} -83.5135 q^{50} +195.129 q^{51} -595.217 q^{52} -452.095 q^{53} -66.7959 q^{54} -559.280 q^{55} +686.353 q^{57} -41.7932 q^{58} +148.972 q^{59} +703.187 q^{60} +846.832 q^{61} +94.2031 q^{62} -425.810 q^{64} +1324.97 q^{65} -81.1263 q^{66} -490.236 q^{67} +289.772 q^{68} -403.951 q^{69} +316.825 q^{71} +2.84853 q^{72} +1121.32 q^{73} -129.795 q^{74} -911.277 q^{75} +1019.25 q^{76} +192.193 q^{78} -916.264 q^{79} +1012.44 q^{80} -739.029 q^{81} +186.035 q^{82} -746.273 q^{83} -645.041 q^{85} -191.182 q^{86} -456.035 q^{87} -244.515 q^{88} +470.079 q^{89} -3.12423 q^{90} -599.879 q^{92} +1027.92 q^{93} -22.5369 q^{94} -2268.88 q^{95} +463.386 q^{96} -206.816 q^{97} -12.1805 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 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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