LMFDB - Embedded newform 1859.4.a.n.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51874 q^{2} +1.77429 q^{3} -1.65593 q^{4} -18.5552 q^{5} -4.46898 q^{6} +4.77905 q^{7} +24.3208 q^{8} -23.8519 q^{9} +O(q^{10})$	\(q-2.51874 q^{2} +1.77429 q^{3} -1.65593 q^{4} -18.5552 q^{5} -4.46898 q^{6} +4.77905 q^{7} +24.3208 q^{8} -23.8519 q^{9} +46.7358 q^{10} +11.0000 q^{11} -2.93809 q^{12} -12.0372 q^{14} -32.9222 q^{15} -48.0105 q^{16} +71.8750 q^{17} +60.0768 q^{18} -28.5254 q^{19} +30.7261 q^{20} +8.47941 q^{21} -27.7062 q^{22} -217.599 q^{23} +43.1521 q^{24} +219.295 q^{25} -90.2259 q^{27} -7.91376 q^{28} -13.6433 q^{29} +82.9227 q^{30} -199.951 q^{31} -73.6404 q^{32} +19.5172 q^{33} -181.035 q^{34} -88.6762 q^{35} +39.4970 q^{36} +277.174 q^{37} +71.8482 q^{38} -451.277 q^{40} +287.370 q^{41} -21.3575 q^{42} +384.920 q^{43} -18.2152 q^{44} +442.577 q^{45} +548.075 q^{46} -39.6245 q^{47} -85.1844 q^{48} -320.161 q^{49} -552.349 q^{50} +127.527 q^{51} +193.052 q^{53} +227.256 q^{54} -204.107 q^{55} +116.230 q^{56} -50.6123 q^{57} +34.3639 q^{58} +351.253 q^{59} +54.5169 q^{60} -741.350 q^{61} +503.626 q^{62} -113.989 q^{63} +569.565 q^{64} -49.1587 q^{66} +584.940 q^{67} -119.020 q^{68} -386.083 q^{69} +223.353 q^{70} +959.400 q^{71} -580.098 q^{72} +935.806 q^{73} -698.130 q^{74} +389.093 q^{75} +47.2360 q^{76} +52.5696 q^{77} +624.047 q^{79} +890.844 q^{80} +483.915 q^{81} -723.811 q^{82} +941.454 q^{83} -14.0413 q^{84} -1333.65 q^{85} -969.516 q^{86} -24.2071 q^{87} +267.529 q^{88} +257.932 q^{89} -1114.74 q^{90} +360.328 q^{92} -354.771 q^{93} +99.8039 q^{94} +529.295 q^{95} -130.659 q^{96} -705.871 q^{97} +806.403 q^{98} -262.371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * 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 $

$2$	−2.51874	−0.890511	−0.445255	−	0.895404i	$-0.646887\pi$
$2$	−2.51874	−0.890511	−0.445255	+	0.895404i	$0.646887\pi$
$3$	1.77429	0.341462	0.170731	−	0.985318i	$-0.445387\pi$
$3$	1.77429	0.341462	0.170731	+	0.985318i	$0.445387\pi$
$4$	−1.65593	−0.206991
$5$	−18.5552	−1.65963	−0.829813	−	0.558041i	$-0.811553\pi$
$5$	−18.5552	−1.65963	−0.829813	+	0.558041i	$0.811553\pi$
$6$	−4.46898	−0.304075
$7$	4.77905	0.258045	0.129022	−	0.991642i	$-0.458816\pi$
$7$	4.77905	0.258045	0.129022	+	0.991642i	$0.458816\pi$
$8$	24.3208	1.07484
$9$	−23.8519	−0.883404
$10$	46.7358	1.47792
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−2.93809	−0.0706795
$13$	0	0
$13$	0	0
$14$	−12.0372	−0.229791
$15$	−32.9222	−0.566699
$16$	−48.0105	−0.750164
$17$	71.8750	1.02543	0.512713	−	0.858560i	$-0.328640\pi$
$17$	71.8750	1.02543	0.512713	+	0.858560i	$0.328640\pi$
$18$	60.0768	0.786680
$19$	−28.5254	−0.344430	−0.172215	−	0.985059i	$-0.555092\pi$
$19$	−28.5254	−0.344430	−0.172215	+	0.985059i	$0.555092\pi$
$20$	30.7261	0.343528
$21$	8.47941	0.0881124
$22$	−27.7062	−0.268499
$23$	−217.599	−1.97272	−0.986358	−	0.164617i	$-0.947361\pi$
$23$	−217.599	−1.97272	−0.986358	+	0.164617i	$0.947361\pi$
$24$	43.1521	0.367016
$25$	219.295	1.75436
$26$	0	0
$27$	−90.2259	−0.643110
$28$	−7.91376	−0.0534129
$29$	−13.6433	−0.0873617	−0.0436809	−	0.999046i	$-0.513908\pi$
$29$	−13.6433	−0.0873617	−0.0436809	+	0.999046i	$0.513908\pi$
$30$	82.9227	0.504652
$31$	−199.951	−1.15846	−0.579230	−	0.815164i	$-0.696647\pi$
$31$	−199.951	−1.15846	−0.579230	+	0.815164i	$0.696647\pi$
$32$	−73.6404	−0.406809
$33$	19.5172	0.102955
$34$	−181.035	−0.913153
$35$	−88.6762	−0.428258
$36$	39.4970	0.182857
$37$	277.174	1.23154	0.615772	−	0.787925i	$-0.288844\pi$
$37$	277.174	1.23154	0.615772	+	0.787925i	$0.288844\pi$
$38$	71.8482	0.306719
$39$	0	0
$40$	−451.277	−1.78383
$41$	287.370	1.09462	0.547312	−	0.836929i	$-0.315651\pi$
$41$	287.370	1.09462	0.547312	+	0.836929i	$0.315651\pi$
$42$	−21.3575	−0.0784650
$43$	384.920	1.36511	0.682556	−	0.730833i	$-0.260868\pi$
$43$	384.920	1.36511	0.682556	+	0.730833i	$0.260868\pi$
$44$	−18.2152	−0.0624101
$45$	442.577	1.46612
$46$	548.075	1.75672
$47$	−39.6245	−0.122975	−0.0614875	−	0.998108i	$-0.519584\pi$
$47$	−39.6245	−0.122975	−0.0614875	+	0.998108i	$0.519584\pi$
$48$	−85.1844	−0.256152
$49$	−320.161	−0.933413
$50$	−552.349	−1.56228
$51$	127.527	0.350144
$52$	0	0
$53$	193.052	0.500335	0.250167	−	0.968203i	$-0.419514\pi$
$53$	193.052	0.500335	0.250167	+	0.968203i	$0.419514\pi$
$54$	227.256	0.572697
$55$	−204.107	−0.500396
$56$	116.230	0.277356
$57$	−50.6123	−0.117610
$58$	34.3639	0.0777966
$59$	351.253	0.775072	0.387536	−	0.921855i	$-0.373326\pi$
$59$	351.253	0.775072	0.387536	+	0.921855i	$0.373326\pi$
$60$	54.5169	0.117302
$61$	−741.350	−1.55607	−0.778034	−	0.628222i	$-0.783783\pi$
$61$	−741.350	−1.55607	−0.778034	+	0.628222i	$0.783783\pi$
$62$	503.626	1.03162
$63$	−113.989	−0.227958
$64$	569.565	1.11243
$65$	0	0
$66$	−49.1587	−0.0916822
$67$	584.940	1.06659	0.533297	−	0.845928i	$-0.320953\pi$
$67$	584.940	1.06659	0.533297	+	0.845928i	$0.320953\pi$
$68$	−119.020	−0.212254
$69$	−386.083	−0.673607
$70$	223.353	0.381368
$71$	959.400	1.60366	0.801830	−	0.597552i	$-0.203860\pi$
$71$	959.400	1.60366	0.801830	+	0.597552i	$0.203860\pi$
$72$	−580.098	−0.949516
$73$	935.806	1.50038	0.750191	−	0.661222i	$-0.229962\pi$
$73$	935.806	1.50038	0.750191	+	0.661222i	$0.229962\pi$
$74$	−698.130	−1.09670
$75$	389.093	0.599047
$76$	47.2360	0.0712940
$77$	52.5696	0.0778034
$78$	0	0
$79$	624.047	0.888744	0.444372	−	0.895842i	$-0.353427\pi$
$79$	624.047	0.888744	0.444372	+	0.895842i	$0.353427\pi$
$80$	890.844	1.24499
$81$	483.915	0.663806
$82$	−723.811	−0.974774
$83$	941.454	1.24504	0.622518	−	0.782605i	$-0.286110\pi$
$83$	941.454	1.24504	0.622518	+	0.782605i	$0.286110\pi$
$84$	−14.0413	−0.0182385
$85$	−1333.65	−1.70183
$86$	−969.516	−1.21565
$87$	−24.2071	−0.0298307
$88$	267.529	0.324076
$89$	257.932	0.307200	0.153600	−	0.988133i	$-0.450913\pi$
$89$	257.932	0.307200	0.153600	+	0.988133i	$0.450913\pi$
$90$	−1114.74	−1.30560
$91$	0	0
$92$	360.328	0.408334
$93$	−354.771	−0.395570
$94$	99.8039	0.109510
$95$	529.295	0.571626
$96$	−130.659	−0.138910
$97$	−705.871	−0.738870	−0.369435	−	0.929257i	$-0.620449\pi$
$97$	−705.871	−0.738870	−0.369435	+	0.929257i	$0.620449\pi$
$98$	806.403	0.831214
$99$	−262.371	−0.266356
$100$	−363.137	−0.363137
$101$	90.6220	0.0892794	0.0446397	−	0.999003i	$-0.485786\pi$
$101$	90.6220	0.0892794	0.0446397	+	0.999003i	$0.485786\pi$
$102$	−321.208	−0.311807
$103$	−354.423	−0.339052	−0.169526	−	0.985526i	$-0.554224\pi$
$103$	−354.423	−0.339052	−0.169526	+	0.985526i	$0.554224\pi$
$104$	0	0
$105$	−157.337	−0.146234
$106$	−486.249	−0.445553
$107$	−848.540	−0.766649	−0.383325	−	0.923614i	$-0.625221\pi$
$107$	−848.540	−0.766649	−0.383325	+	0.923614i	$0.625221\pi$
$108$	149.408	0.133118
$109$	1110.33	0.975693	0.487847	−	0.872929i	$-0.337783\pi$
$109$	1110.33	0.975693	0.487847	+	0.872929i	$0.337783\pi$
$110$	514.094	0.445608
$111$	491.786	0.420525
$112$	−229.445	−0.193576
$113$	−334.015	−0.278066	−0.139033	−	0.990288i	$-0.544399\pi$
$113$	−334.015	−0.278066	−0.139033	+	0.990288i	$0.544399\pi$
$114$	127.479	0.104733
$115$	4037.58	3.27397
$116$	22.5923	0.0180831
$117$	0	0
$118$	−884.717	−0.690210
$119$	343.494	0.264606
$120$	−800.696	−0.609110
$121$	121.000	0.0909091
$122$	1867.27	1.38570
$123$	509.876	0.373772
$124$	331.105	0.239791
$125$	−1749.67	−1.25196
$126$	287.110	0.202999
$127$	−2042.29	−1.42696	−0.713481	−	0.700674i	$-0.752883\pi$
$127$	−2042.29	−1.42696	−0.713481	+	0.700674i	$0.752883\pi$
$128$	−845.466	−0.583823
$129$	682.959	0.466134
$130$	0	0
$131$	1794.77	1.19702	0.598511	−	0.801114i	$-0.295759\pi$
$131$	1794.77	1.19702	0.598511	+	0.801114i	$0.295759\pi$
$132$	−32.3190	−0.0213107
$133$	−136.324	−0.0888784
$134$	−1473.32	−0.949814
$135$	1674.16	1.06732
$136$	1748.06	1.10217
$137$	−223.019	−0.139079	−0.0695394	−	0.997579i	$-0.522153\pi$
$137$	−223.019	−0.139079	−0.0695394	+	0.997579i	$0.522153\pi$
$138$	972.443	0.599854
$139$	−1843.89	−1.12515	−0.562577	−	0.826745i	$-0.690190\pi$
$139$	−1843.89	−1.12515	−0.562577	+	0.826745i	$0.690190\pi$
$140$	146.841	0.0886455
$141$	−70.3052	−0.0419912
$142$	−2416.48	−1.42808
$143$	0	0
$144$	1145.14	0.662698
$145$	253.153	0.144988
$146$	−2357.06	−1.33611
$147$	−568.057	−0.318725
$148$	−458.980	−0.254918
$149$	−3484.40	−1.91579	−0.957895	−	0.287118i	$-0.907303\pi$
$149$	−3484.40	−1.91579	−0.957895	+	0.287118i	$0.907303\pi$
$150$	−980.025	−0.533458
$151$	−1431.63	−0.771553	−0.385776	−	0.922592i	$-0.626066\pi$
$151$	−1431.63	−0.771553	−0.385776	+	0.922592i	$0.626066\pi$
$152$	−693.761	−0.370207
$153$	−1714.36	−0.905866
$154$	−132.409	−0.0692847
$155$	3710.13	1.92261
$156$	0	0
$157$	645.980	0.328374	0.164187	−	0.986429i	$-0.447500\pi$
$157$	645.980	0.328374	0.164187	+	0.986429i	$0.447500\pi$
$158$	−1571.81	−0.791436
$159$	342.530	0.170845
$160$	1366.41	0.675152
$161$	−1039.92	−0.509048
$162$	−1218.86	−0.591126
$163$	−2468.03	−1.18596	−0.592979	−	0.805218i	$-0.702048\pi$
$163$	−2468.03	−1.18596	−0.592979	+	0.805218i	$0.702048\pi$
$164$	−475.863	−0.226577
$165$	−362.145	−0.170866
$166$	−2371.28	−1.10872
$167$	−617.938	−0.286332	−0.143166	−	0.989699i	$-0.545728\pi$
$167$	−617.938	−0.286332	−0.143166	+	0.989699i	$0.545728\pi$
$168$	206.226	0.0947065
$169$	0	0
$170$	3359.13	1.51549
$171$	680.385	0.304271
$172$	−637.400	−0.282566
$173$	−1648.51	−0.724475	−0.362238	−	0.932086i	$-0.617987\pi$
$173$	−1648.51	−0.724475	−0.362238	+	0.932086i	$0.617987\pi$
$174$	60.9714	0.0265646
$175$	1048.02	0.452704
$176$	−528.115	−0.226183
$177$	623.224	0.264657
$178$	−649.666	−0.273565
$179$	659.559	0.275407	0.137703	−	0.990474i	$-0.456028\pi$
$179$	659.559	0.275407	0.137703	+	0.990474i	$0.456028\pi$
$180$	−732.875	−0.303474
$181$	−4019.11	−1.65049	−0.825244	−	0.564776i	$-0.808962\pi$
$181$	−4019.11	−1.65049	−0.825244	+	0.564776i	$0.808962\pi$
$182$	0	0
$183$	−1315.37	−0.531338
$184$	−5292.18	−2.12035
$185$	−5143.01	−2.04390
$186$	893.577	0.352259
$187$	790.625	0.309178
$188$	65.6152	0.0254547
$189$	−431.194	−0.165951
$190$	−1333.16	−0.509039
$191$	535.504	0.202868	0.101434	−	0.994842i	$-0.467657\pi$
$191$	535.504	0.202868	0.101434	+	0.994842i	$0.467657\pi$
$192$	1010.57	0.379853
$193$	1308.43	0.487993	0.243997	−	0.969776i	$-0.421541\pi$
$193$	1308.43	0.487993	0.243997	+	0.969776i	$0.421541\pi$
$194$	1777.91	0.657971
$195$	0	0
$196$	530.163	0.193208
$197$	−4797.00	−1.73488	−0.867442	−	0.497539i	$-0.834237\pi$
$197$	−4797.00	−1.73488	−0.867442	+	0.497539i	$0.834237\pi$
$198$	660.845	0.237193
$199$	2179.31	0.776316	0.388158	−	0.921593i	$-0.373111\pi$
$199$	2179.31	0.776316	0.388158	+	0.921593i	$0.373111\pi$
$200$	5333.44	1.88565
$201$	1037.85	0.364201
$202$	−228.254	−0.0795043
$203$	−65.2019	−0.0225432
$204$	−211.175	−0.0724766
$205$	−5332.20	−1.81667
$206$	892.701	0.301929
$207$	5190.14	1.74270
$208$	0	0
$209$	−313.780	−0.103850
$210$	396.292	0.130223
$211$	2445.24	0.797808	0.398904	−	0.916993i	$-0.369391\pi$
$211$	2445.24	0.797808	0.398904	+	0.916993i	$0.369391\pi$
$212$	−319.680	−0.103565
$213$	1702.25	0.547589
$214$	2137.26	0.682709
$215$	−7142.27	−2.26558
$216$	−2194.37	−0.691240
$217$	−955.577	−0.298934
$218$	−2796.64	−0.868865
$219$	1660.39	0.512323
$220$	337.987	0.103578
$221$	0	0
$222$	−1238.68	−0.374482
$223$	2607.31	0.782953	0.391477	−	0.920188i	$-0.371964\pi$
$223$	2607.31	0.782953	0.391477	+	0.920188i	$0.371964\pi$
$224$	−351.931	−0.104975
$225$	−5230.61	−1.54981
$226$	841.299	0.247621
$227$	−1466.56	−0.428806	−0.214403	−	0.976745i	$-0.568781\pi$
$227$	−1466.56	−0.428806	−0.214403	+	0.976745i	$0.568781\pi$
$228$	83.8103	0.0243442
$229$	4909.33	1.41667	0.708335	−	0.705876i	$-0.249446\pi$
$229$	4909.33	1.41667	0.708335	+	0.705876i	$0.249446\pi$
$230$	−10169.6	−2.91551
$231$	93.2735	0.0265669
$232$	−331.815	−0.0938997
$233$	2636.64	0.741339	0.370670	−	0.928765i	$-0.379128\pi$
$233$	2636.64	0.741339	0.370670	+	0.928765i	$0.379128\pi$
$234$	0	0
$235$	735.240	0.204093
$236$	−581.650	−0.160433
$237$	1107.24	0.303472
$238$	−865.174	−0.235634
$239$	2523.49	0.682974	0.341487	−	0.939886i	$-0.389069\pi$
$239$	2523.49	0.682974	0.341487	+	0.939886i	$0.389069\pi$
$240$	1580.61	0.425117
$241$	−3362.20	−0.898665	−0.449333	−	0.893364i	$-0.648338\pi$
$241$	−3362.20	−0.898665	−0.449333	+	0.893364i	$0.648338\pi$
$242$	−304.768	−0.0809555
$243$	3294.70	0.869775
$244$	1227.62	0.322092
$245$	5940.64	1.54912
$246$	−1284.25	−0.332848
$247$	0	0
$248$	−4862.97	−1.24516
$249$	1670.41	0.425132
$250$	4406.96	1.11488
$251$	233.864	0.0588103	0.0294052	−	0.999568i	$-0.490639\pi$
$251$	233.864	0.0588103	0.0294052	+	0.999568i	$0.490639\pi$
$252$	188.758	0.0471851
$253$	−2393.58	−0.594796
$254$	5144.01	1.27073
$255$	−2366.29	−0.581108
$256$	−2427.01	−0.592531
$257$	4510.70	1.09482	0.547412	−	0.836863i	$-0.315613\pi$
$257$	4510.70	1.09482	0.547412	+	0.836863i	$0.315613\pi$
$258$	−1720.20	−0.415097
$259$	1324.63	0.317793
$260$	0	0
$261$	325.418	0.0771757
$262$	−4520.57	−1.06596
$263$	−519.854	−0.121884	−0.0609421	−	0.998141i	$-0.519411\pi$
$263$	−519.854	−0.121884	−0.0609421	+	0.998141i	$0.519411\pi$
$264$	474.673	0.110660
$265$	−3582.12	−0.830369
$266$	343.366	0.0791472
$267$	457.646	0.104897
$268$	−968.619	−0.220775
$269$	−3961.34	−0.897870	−0.448935	−	0.893565i	$-0.648196\pi$
$269$	−3961.34	−0.897870	−0.448935	+	0.893565i	$0.648196\pi$
$270$	−4216.78	−0.950463
$271$	−7726.67	−1.73196	−0.865981	−	0.500077i	$-0.833305\pi$
$271$	−7726.67	−1.73196	−0.865981	+	0.500077i	$0.833305\pi$
$272$	−3450.75	−0.769238
$273$	0	0
$274$	561.728	0.123851
$275$	2412.25	0.528960
$276$	639.325	0.139431
$277$	−6212.28	−1.34751	−0.673754	−	0.738955i	$-0.735319\pi$
$277$	−6212.28	−1.34751	−0.673754	+	0.738955i	$0.735319\pi$
$278$	4644.28	1.00196
$279$	4769.21	1.02339
$280$	−2156.68	−0.460308
$281$	4239.22	0.899966	0.449983	−	0.893037i	$-0.351430\pi$
$281$	4239.22	0.899966	0.449983	+	0.893037i	$0.351430\pi$
$282$	177.081	0.0373936
$283$	1617.81	0.339820	0.169910	−	0.985460i	$-0.445652\pi$
$283$	1617.81	0.339820	0.169910	+	0.985460i	$0.445652\pi$
$284$	−1588.70	−0.331943
$285$	939.121	0.195188
$286$	0	0
$287$	1373.35	0.282462
$288$	1756.46	0.359377
$289$	253.015	0.0514991
$290$	−637.629	−0.129113
$291$	−1252.42	−0.252296
$292$	−1549.63	−0.310565
$293$	6135.39	1.22332	0.611661	−	0.791120i	$-0.290502\pi$
$293$	6135.39	1.22332	0.611661	+	0.791120i	$0.290502\pi$
$294$	1430.79	0.283828
$295$	−6517.57	−1.28633
$296$	6741.09	1.32371
$297$	−992.485	−0.193905
$298$	8776.30	1.70603
$299$	0	0
$300$	−644.309	−0.123997
$301$	1839.55	0.352260
$302$	3605.91	0.687076
$303$	160.789	0.0304855
$304$	1369.52	0.258379
$305$	13755.9	2.58249
$306$	4318.02	0.806683
$307$	467.667	0.0869419	0.0434709	−	0.999055i	$-0.486158\pi$
$307$	467.667	0.0869419	0.0434709	+	0.999055i	$0.486158\pi$
$308$	−87.0514	−0.0161046
$309$	−628.848	−0.115773
$310$	−9344.87	−1.71211
$311$	−5348.22	−0.975144	−0.487572	−	0.873083i	$-0.662117\pi$
$311$	−5348.22	−0.975144	−0.487572	+	0.873083i	$0.662117\pi$
$312$	0	0
$313$	−6225.27	−1.12419	−0.562097	−	0.827071i	$-0.690005\pi$
$313$	−6225.27	−1.12419	−0.562097	+	0.827071i	$0.690005\pi$
$314$	−1627.06	−0.292421
$315$	2115.10	0.378325
$316$	−1033.38	−0.183962
$317$	7083.56	1.25505	0.627527	−	0.778595i	$-0.284067\pi$
$317$	7083.56	1.25505	0.627527	+	0.778595i	$0.284067\pi$
$318$	−862.745	−0.152139
$319$	−150.076	−0.0263406
$320$	−10568.4	−1.84622
$321$	−1505.55	−0.261781
$322$	2619.28	0.453313
$323$	−2050.26	−0.353188
$324$	−801.328	−0.137402
$325$	0	0
$326$	6216.34	1.05611
$327$	1970.05	0.333162
$328$	6989.06	1.17654
$329$	−189.367	−0.0317330
$330$	912.150	0.152158
$331$	10209.1	1.69530	0.847652	−	0.530553i	$-0.178016\pi$
$331$	10209.1	1.69530	0.847652	+	0.530553i	$0.178016\pi$
$332$	−1558.98	−0.257711
$333$	−6611.12	−1.08795
$334$	1556.43	0.254982
$335$	−10853.7	−1.77015
$336$	−407.101	−0.0660987
$337$	9767.18	1.57879	0.789395	−	0.613886i	$-0.210395\pi$
$337$	9767.18	1.57879	0.789395	+	0.613886i	$0.210395\pi$
$338$	0	0
$339$	−592.639	−0.0949491
$340$	2208.44	0.352262
$341$	−2199.46	−0.349289
$342$	−1713.72	−0.270957
$343$	−3169.28	−0.498907
$344$	9361.58	1.46727
$345$	7163.84	1.11794
$346$	4152.19	0.645153
$347$	−10297.3	−1.59305	−0.796523	−	0.604609i	$-0.793330\pi$
$347$	−10297.3	−1.59305	−0.796523	+	0.604609i	$0.793330\pi$
$348$	40.0852	0.00617468
$349$	3655.45	0.560664	0.280332	−	0.959903i	$-0.409555\pi$
$349$	3655.45	0.560664	0.280332	+	0.959903i	$0.409555\pi$
$350$	−2639.70	−0.403137
$351$	0	0
$352$	−810.044	−0.122658
$353$	−2296.58	−0.346274	−0.173137	−	0.984898i	$-0.555390\pi$
$353$	−2296.58	−0.346274	−0.173137	+	0.984898i	$0.555390\pi$
$354$	−1569.74	−0.235680
$355$	−17801.9	−2.66148
$356$	−427.117	−0.0635876
$357$	609.458	0.0903527
$358$	−1661.26	−0.245252
$359$	−6902.21	−1.01472	−0.507360	−	0.861734i	$-0.669379\pi$
$359$	−6902.21	−1.01472	−0.507360	+	0.861734i	$0.669379\pi$
$360$	10763.8	1.57584
$361$	−6045.30	−0.881368
$362$	10123.1	1.46978
$363$	214.689	0.0310420
$364$	0	0
$365$	−17364.1	−2.49007
$366$	3313.08	0.473162
$367$	6596.77	0.938280	0.469140	−	0.883124i	$-0.344564\pi$
$367$	6596.77	0.938280	0.469140	+	0.883124i	$0.344564\pi$
$368$	10447.0	1.47986
$369$	−6854.31	−0.966995
$370$	12953.9	1.82012
$371$	922.606	0.129109
$372$	587.475	0.0818794
$373$	−331.662	−0.0460397	−0.0230199	−	0.999735i	$-0.507328\pi$
$373$	−331.662	−0.0460397	−0.0230199	+	0.999735i	$0.507328\pi$
$374$	−1991.38	−0.275326
$375$	−3104.41	−0.427496
$376$	−963.699	−0.132178
$377$	0	0
$378$	1086.07	0.147781
$379$	−10980.1	−1.48815	−0.744075	−	0.668096i	$-0.767110\pi$
$379$	−10980.1	−1.48815	−0.744075	+	0.668096i	$0.767110\pi$
$380$	−876.473	−0.118321
$381$	−3623.62	−0.487253
$382$	−1348.80	−0.180656
$383$	−12796.1	−1.70718	−0.853589	−	0.520947i	$-0.825579\pi$
$383$	−12796.1	−1.70718	−0.853589	+	0.520947i	$0.825579\pi$
$384$	−1500.10	−0.199353
$385$	−975.439	−0.129125
$386$	−3295.60	−0.434563
$387$	−9181.08	−1.20595
$388$	1168.87	0.152939
$389$	7575.92	0.987441	0.493720	−	0.869621i	$-0.335637\pi$
$389$	7575.92	0.987441	0.493720	+	0.869621i	$0.335637\pi$
$390$	0	0
$391$	−15639.9	−2.02287
$392$	−7786.57	−1.00327
$393$	3184.44	0.408737
$394$	12082.4	1.54493
$395$	−11579.3	−1.47498
$396$	434.467	0.0551333
$397$	−2316.48	−0.292848	−0.146424	−	0.989222i	$-0.546776\pi$
$397$	−2316.48	−0.292848	−0.146424	+	0.989222i	$0.546776\pi$
$398$	−5489.11	−0.691318
$399$	−241.879	−0.0303486
$400$	−10528.5	−1.31606
$401$	7056.18	0.878725	0.439363	−	0.898310i	$-0.355204\pi$
$401$	7056.18	0.878725	0.439363	+	0.898310i	$0.355204\pi$
$402$	−2614.09	−0.324325
$403$	0	0
$404$	−150.063	−0.0184800
$405$	−8979.13	−1.10167
$406$	164.227	0.0200750
$407$	3048.91	0.371324
$408$	3101.56	0.376348
$409$	−11352.6	−1.37249	−0.686247	−	0.727368i	$-0.740743\pi$
$409$	−11352.6	−1.37249	−0.686247	+	0.727368i	$0.740743\pi$
$410$	13430.4	1.61776
$411$	−395.700	−0.0474901
$412$	586.899	0.0701807
$413$	1678.66	0.200003
$414$	−13072.6	−1.55190
$415$	−17468.9	−2.06630
$416$	0	0
$417$	−3271.58	−0.384197
$418$	790.330	0.0924792
$419$	82.1561	0.00957897	0.00478949	−	0.999989i	$-0.498475\pi$
$419$	82.1561	0.00957897	0.00478949	+	0.999989i	$0.498475\pi$
$420$	260.539	0.0302690
$421$	12000.0	1.38918	0.694588	−	0.719408i	$-0.255587\pi$
$421$	12000.0	1.38918	0.694588	+	0.719408i	$0.255587\pi$
$422$	−6158.94	−0.710456
$423$	945.119	0.108637
$424$	4695.18	0.537779
$425$	15761.8	1.79897
$426$	−4287.54	−0.487633
$427$	−3542.95	−0.401535
$428$	1405.12	0.158689
$429$	0	0
$430$	17989.6	2.01752
$431$	1692.34	0.189135	0.0945673	−	0.995518i	$-0.469853\pi$
$431$	1692.34	0.189135	0.0945673	+	0.995518i	$0.469853\pi$
$432$	4331.79	0.482438
$433$	−17769.9	−1.97220	−0.986102	−	0.166140i	$-0.946870\pi$
$433$	−17769.9	−1.97220	−0.986102	+	0.166140i	$0.946870\pi$
$434$	2406.85	0.266204
$435$	449.167	0.0495078
$436$	−1838.63	−0.201960
$437$	6207.09	0.679463
$438$	−4182.10	−0.456229
$439$	−5413.11	−0.588505	−0.294252	−	0.955728i	$-0.595071\pi$
$439$	−5413.11	−0.588505	−0.294252	+	0.955728i	$0.595071\pi$
$440$	−4964.05	−0.537845
$441$	7636.44	0.824581
$442$	0	0
$443$	11268.1	1.20850	0.604249	−	0.796795i	$-0.293473\pi$
$443$	11268.1	1.20850	0.604249	+	0.796795i	$0.293473\pi$
$444$	−814.362	−0.0870448
$445$	−4785.99	−0.509837
$446$	−6567.16	−0.697228
$447$	−6182.32	−0.654169
$448$	2721.98	0.287057
$449$	−5638.52	−0.592647	−0.296323	−	0.955088i	$-0.595761\pi$
$449$	−5638.52	−0.592647	−0.296323	+	0.955088i	$0.595761\pi$
$450$	13174.6	1.38012
$451$	3161.07	0.330042
$452$	553.105	0.0575572
$453$	−2540.12	−0.263456
$454$	3693.89	0.381856
$455$	0	0
$456$	−1230.93	−0.126412
$457$	−12771.3	−1.30725	−0.653627	−	0.756817i	$-0.726754\pi$
$457$	−12771.3	−1.30725	−0.653627	+	0.756817i	$0.726754\pi$
$458$	−12365.3	−1.26156
$459$	−6484.99	−0.659462
$460$	−6685.95	−0.677682
$461$	13324.9	1.34621	0.673107	−	0.739545i	$-0.264959\pi$
$461$	13324.9	1.34621	0.673107	+	0.739545i	$0.264959\pi$
$462$	−234.932	−0.0236581
$463$	−12728.6	−1.27764	−0.638822	−	0.769355i	$-0.720578\pi$
$463$	−12728.6	−1.27764	−0.638822	+	0.769355i	$0.720578\pi$
$464$	655.020	0.0655356
$465$	6582.84	0.656499
$466$	−6641.02	−0.660170
$467$	4533.72	0.449241	0.224620	−	0.974446i	$-0.427886\pi$
$467$	4533.72	0.449241	0.224620	+	0.974446i	$0.427886\pi$
$468$	0	0
$469$	2795.46	0.275229
$470$	−1851.88	−0.181747
$471$	1146.15	0.112127
$472$	8542.76	0.833077
$473$	4234.12	0.411597
$474$	−2788.85	−0.270245
$475$	−6255.49	−0.604256
$476$	−568.802	−0.0547710
$477$	−4604.66	−0.441998
$478$	−6356.02	−0.608196
$479$	702.920	0.0670506	0.0335253	−	0.999438i	$-0.489327\pi$
$479$	702.920	0.0670506	0.0335253	+	0.999438i	$0.489327\pi$
$480$	2424.41	0.230539
$481$	0	0
$482$	8468.52	0.800271
$483$	−1845.11	−0.173821
$484$	−200.367	−0.0188174
$485$	13097.6	1.22625
$486$	−8298.51	−0.774544
$487$	−10889.4	−1.01323	−0.506617	−	0.862171i	$-0.669104\pi$
$487$	−10889.4	−1.01323	−0.506617	+	0.862171i	$0.669104\pi$
$488$	−18030.2	−1.67252
$489$	−4379.00	−0.404959
$490$	−14963.0	−1.37951
$491$	8031.02	0.738156	0.369078	−	0.929398i	$-0.379673\pi$
$491$	8031.02	0.738156	0.369078	+	0.929398i	$0.379673\pi$
$492$	−844.318	−0.0773675
$493$	−980.610	−0.0895830
$494$	0	0
$495$	4868.34	0.442052
$496$	9599.75	0.869035
$497$	4585.02	0.413816
$498$	−4207.34	−0.378585
$499$	−12272.5	−1.10099	−0.550494	−	0.834839i	$-0.685561\pi$
$499$	−12272.5	−1.10099	−0.550494	+	0.834839i	$0.685561\pi$
$500$	2897.32	0.259144
$501$	−1096.40	−0.0977714
$502$	−589.045	−0.0523712
$503$	−12149.2	−1.07695	−0.538474	−	0.842642i	$-0.680999\pi$
$503$	−12149.2	−1.07695	−0.538474	+	0.842642i	$0.680999\pi$
$504$	−2772.32	−0.245017
$505$	−1681.51	−0.148171
$506$	6028.83	0.529672
$507$	0	0
$508$	3381.89	0.295368
$509$	−1779.07	−0.154923	−0.0774616	−	0.996995i	$-0.524682\pi$
$509$	−1779.07	−0.154923	−0.0774616	+	0.996995i	$0.524682\pi$
$510$	5960.07	0.517483
$511$	4472.27	0.387165
$512$	12876.7	1.11148
$513$	2573.73	0.221507
$514$	−11361.3	−0.974952
$515$	6576.39	0.562700
$516$	−1130.93	−0.0964854
$517$	−435.869	−0.0370783
$518$	−3336.40	−0.282998
$519$	−2924.94	−0.247381
$520$	0	0
$521$	475.344	0.0399716	0.0199858	−	0.999800i	$-0.493638\pi$
$521$	475.344	0.0399716	0.0199858	+	0.999800i	$0.493638\pi$
$522$	−819.644	−0.0687258
$523$	524.919	0.0438874	0.0219437	−	0.999759i	$-0.493015\pi$
$523$	524.919	0.0438874	0.0219437	+	0.999759i	$0.493015\pi$
$524$	−2972.01	−0.247773
$525$	1859.49	0.154581
$526$	1309.38	0.108539
$527$	−14371.5	−1.18792
$528$	−937.028	−0.0772328
$529$	35182.2	2.89161
$530$	9022.44	0.739452
$531$	−8378.05	−0.684702
$532$	225.743	0.0183970
$533$	0	0
$534$	−1152.69	−0.0934119
$535$	15744.8	1.27235
$536$	14226.2	1.14642
$537$	1170.25	0.0940408
$538$	9977.59	0.799562
$539$	−3521.77	−0.281435
$540$	−2772.29	−0.220926
$541$	−5796.06	−0.460614	−0.230307	−	0.973118i	$-0.573973\pi$
$541$	−5796.06	−0.460614	−0.230307	+	0.973118i	$0.573973\pi$
$542$	19461.5	1.54233
$543$	−7131.06	−0.563579
$544$	−5292.90	−0.417153
$545$	−20602.4	−1.61929
$546$	0	0
$547$	−13003.3	−1.01642	−0.508210	−	0.861233i	$-0.669693\pi$
$547$	−13003.3	−1.01642	−0.508210	+	0.861233i	$0.669693\pi$
$548$	369.303	0.0287881
$549$	17682.6	1.37464
$550$	−6075.83	−0.471044
$551$	389.180	0.0300900
$552$	−9389.84	−0.724018
$553$	2982.35	0.229335
$554$	15647.1	1.19997
$555$	−9125.19	−0.697914
$556$	3053.34	0.232897
$557$	−13793.7	−1.04930	−0.524648	−	0.851319i	$-0.675803\pi$
$557$	−13793.7	−1.04930	−0.524648	+	0.851319i	$0.675803\pi$
$558$	−12012.4	−0.911338
$559$	0	0
$560$	4257.39	0.321263
$561$	1402.80	0.105572
$562$	−10677.5	−0.801429
$563$	13478.6	1.00898	0.504489	−	0.863418i	$-0.331681\pi$
$563$	13478.6	1.00898	0.504489	+	0.863418i	$0.331681\pi$
$564$	116.420	0.00869181
$565$	6197.72	0.461487
$566$	−4074.86	−0.302613
$567$	2312.65	0.171292
$568$	23333.4	1.72368
$569$	5494.22	0.404798	0.202399	−	0.979303i	$-0.435126\pi$
$569$	5494.22	0.404798	0.202399	+	0.979303i	$0.435126\pi$
$570$	−2365.40	−0.173817
$571$	−4154.31	−0.304470	−0.152235	−	0.988344i	$-0.548647\pi$
$571$	−4154.31	−0.304470	−0.152235	+	0.988344i	$0.548647\pi$
$572$	0	0
$573$	950.139	0.0692716
$574$	−3459.13	−0.251535
$575$	−47718.3	−3.46086
$576$	−13585.2	−0.982727
$577$	−23460.7	−1.69269	−0.846345	−	0.532635i	$-0.821202\pi$
$577$	−23460.7	−1.69269	−0.846345	+	0.532635i	$0.821202\pi$
$578$	−637.280	−0.0458605
$579$	2321.53	0.166631
$580$	−419.204	−0.0300112
$581$	4499.26	0.321275
$582$	3154.52	0.224672
$583$	2123.57	0.150857
$584$	22759.6	1.61267
$585$	0	0
$586$	−15453.5	−1.08938
$587$	−10663.6	−0.749802	−0.374901	−	0.927065i	$-0.622323\pi$
$587$	−10663.6	−0.749802	−0.374901	+	0.927065i	$0.622323\pi$
$588$	940.661	0.0659732
$589$	5703.69	0.399009
$590$	16416.1	1.14549
$591$	−8511.26	−0.592396
$592$	−13307.2	−0.923859
$593$	171.306	0.0118629	0.00593146	−	0.999982i	$-0.498112\pi$
$593$	171.306	0.0118629	0.00593146	+	0.999982i	$0.498112\pi$
$594$	2499.82	0.172675
$595$	−6373.60	−0.439147
$596$	5769.91	0.396551
$597$	3866.71	0.265082
$598$	0	0
$599$	10394.2	0.709007	0.354503	−	0.935055i	$-0.384650\pi$
$599$	10394.2	0.709007	0.354503	+	0.935055i	$0.384650\pi$
$600$	9463.05	0.643879
$601$	−12416.5	−0.842731	−0.421365	−	0.906891i	$-0.638449\pi$
$601$	−12416.5	−0.842731	−0.421365	+	0.906891i	$0.638449\pi$
$602$	−4633.37	−0.313691
$603$	−13951.9	−0.942234
$604$	2370.68	0.159704
$605$	−2245.18	−0.150875
$606$	−404.987	−0.0271477
$607$	−1158.00	−0.0774329	−0.0387165	−	0.999250i	$-0.512327\pi$
$607$	−1158.00	−0.0774329	−0.0387165	+	0.999250i	$0.512327\pi$
$608$	2100.62	0.140118
$609$	−115.687	−0.00769765
$610$	−34647.6	−2.29974
$611$	0	0
$612$	2838.85	0.187506
$613$	−8557.32	−0.563829	−0.281914	−	0.959440i	$-0.590969\pi$
$613$	−8557.32	−0.563829	−0.281914	+	0.959440i	$0.590969\pi$
$614$	−1177.93	−0.0774227
$615$	−9460.85	−0.620323
$616$	1278.53	0.0836260
$617$	−1242.89	−0.0810972	−0.0405486	−	0.999178i	$-0.512911\pi$
$617$	−1242.89	−0.0810972	−0.0405486	+	0.999178i	$0.512911\pi$
$618$	1583.91	0.103097
$619$	−19579.2	−1.27133	−0.635665	−	0.771965i	$-0.719274\pi$
$619$	−19579.2	−1.27133	−0.635665	+	0.771965i	$0.719274\pi$
$620$	−6143.71	−0.397963
$621$	19633.0	1.26867
$622$	13470.8	0.868376
$623$	1232.67	0.0792712
$624$	0	0
$625$	5053.49	0.323423
$626$	15679.9	1.00111
$627$	−556.735	−0.0354607
$628$	−1069.70	−0.0679705
$629$	19921.9	1.26286
$630$	−5327.39	−0.336902
$631$	19340.9	1.22020	0.610102	−	0.792323i	$-0.291128\pi$
$631$	19340.9	1.22020	0.610102	+	0.792323i	$0.291128\pi$
$632$	15177.3	0.955256
$633$	4338.56	0.272421
$634$	−17841.7	−1.11764
$635$	37895.2	2.36823
$636$	−567.205	−0.0353634
$637$	0	0
$638$	378.003	0.0234565
$639$	−22883.5	−1.41668
$640$	15687.8	0.968928
$641$	19490.1	1.20096	0.600479	−	0.799641i	$-0.294977\pi$
$641$	19490.1	1.20096	0.600479	+	0.799641i	$0.294977\pi$
$642$	3792.11	0.233119
$643$	−15814.7	−0.969937	−0.484968	−	0.874532i	$-0.661169\pi$
$643$	−15814.7	−0.969937	−0.484968	+	0.874532i	$0.661169\pi$
$644$	1722.02	0.105368
$645$	−12672.4	−0.773608
$646$	5164.09	0.314518
$647$	15534.6	0.943936	0.471968	−	0.881616i	$-0.343544\pi$
$647$	15534.6	0.943936	0.471968	+	0.881616i	$0.343544\pi$
$648$	11769.2	0.713484
$649$	3863.78	0.233693
$650$	0	0
$651$	−1695.47	−0.102075
$652$	4086.88	0.245483
$653$	−27593.1	−1.65360	−0.826801	−	0.562495i	$-0.809841\pi$
$653$	−27593.1	−1.65360	−0.826801	+	0.562495i	$0.809841\pi$
$654$	−4962.05	−0.296684
$655$	−33302.3	−1.98661
$656$	−13796.8	−0.821148
$657$	−22320.8	−1.32544
$658$	476.968	0.0282586
$659$	−12069.3	−0.713435	−0.356718	−	0.934212i	$-0.616104\pi$
$659$	−12069.3	−0.713435	−0.356718	+	0.934212i	$0.616104\pi$
$660$	599.685	0.0353678
$661$	−13806.0	−0.812392	−0.406196	−	0.913786i	$-0.633145\pi$
$661$	−13806.0	−0.812392	−0.406196	+	0.913786i	$0.633145\pi$
$662$	−25714.2	−1.50969
$663$	0	0
$664$	22896.9	1.33821
$665$	2529.53	0.147505
$666$	16651.7	0.968831
$667$	2968.76	0.172340
$668$	1023.26	0.0592681
$669$	4626.12	0.267349
$670$	27337.7	1.57634
$671$	−8154.86	−0.469172
$672$	−624.427	−0.0358449
$673$	15871.6	0.909072	0.454536	−	0.890728i	$-0.349805\pi$
$673$	15871.6	0.909072	0.454536	+	0.890728i	$0.349805\pi$
$674$	−24601.0	−1.40593
$675$	−19786.1	−1.12825
$676$	0	0
$677$	−24566.3	−1.39462	−0.697311	−	0.716769i	$-0.745620\pi$
$677$	−24566.3	−1.39462	−0.697311	+	0.716769i	$0.745620\pi$
$678$	1492.71	0.0845531
$679$	−3373.39	−0.190661
$680$	−32435.6	−1.82919
$681$	−2602.10	−0.146421
$682$	5539.88	0.311046
$683$	35009.3	1.96134	0.980670	−	0.195670i	$-0.0626881\pi$
$683$	35009.3	1.96134	0.980670	+	0.195670i	$0.0626881\pi$
$684$	−1126.67	−0.0629814
$685$	4138.16	0.230819
$686$	7982.60	0.444282
$687$	8710.56	0.483739
$688$	−18480.2	−1.02406
$689$	0	0
$690$	−18043.9	−0.995534
$691$	−1417.71	−0.0780494	−0.0390247	−	0.999238i	$-0.512425\pi$
$691$	−1417.71	−0.0780494	−0.0390247	+	0.999238i	$0.512425\pi$
$692$	2729.82	0.149960
$693$	−1253.88	−0.0687318
$694$	25936.2	1.41862
$695$	34213.7	1.86734
$696$	−588.736	−0.0320632
$697$	20654.7	1.12246
$698$	−9207.14	−0.499277
$699$	4678.16	0.253139
$700$	−1735.45	−0.0937055
$701$	36510.2	1.96715	0.983575	−	0.180500i	$-0.0577717\pi$
$701$	36510.2	1.96715	0.983575	+	0.180500i	$0.0577717\pi$
$702$	0	0
$703$	−7906.50	−0.424181
$704$	6265.22	0.335411
$705$	1304.53	0.0696898
$706$	5784.50	0.308361
$707$	433.087	0.0230381
$708$	−1032.01	−0.0547817
$709$	3185.77	0.168750	0.0843752	−	0.996434i	$-0.473111\pi$
$709$	3185.77	0.168750	0.0843752	+	0.996434i	$0.473111\pi$
$710$	44838.3	2.37007
$711$	−14884.7	−0.785120
$712$	6273.13	0.330190
$713$	43509.1	2.28531
$714$	−1535.07	−0.0804601
$715$	0	0
$716$	−1092.18	−0.0570067
$717$	4477.39	0.233210
$718$	17384.9	0.903619
$719$	18162.1	0.942046	0.471023	−	0.882121i	$-0.343885\pi$
$719$	18162.1	0.942046	0.471023	+	0.882121i	$0.343885\pi$
$720$	−21248.3	−1.09983
$721$	−1693.81	−0.0874905
$722$	15226.6	0.784867
$723$	−5965.51	−0.306860
$724$	6655.36	0.341636
$725$	−2991.90	−0.153264
$726$	−540.746	−0.0276432
$727$	10453.6	0.533290	0.266645	−	0.963795i	$-0.414085\pi$
$727$	10453.6	0.533290	0.266645	+	0.963795i	$0.414085\pi$
$728$	0	0
$729$	−7219.95	−0.366811
$730$	43735.6	2.21744
$731$	27666.2	1.39982
$732$	2178.16	0.109982
$733$	−3998.97	−0.201508	−0.100754	−	0.994911i	$-0.532125\pi$
$733$	−3998.97	−0.201508	−0.100754	+	0.994911i	$0.532125\pi$
$734$	−16615.6	−0.835548
$735$	10540.4	0.528964
$736$	16024.0	0.802519
$737$	6434.35	0.321590
$738$	17264.3	0.861120
$739$	25605.0	1.27455	0.637276	−	0.770636i	$-0.280061\pi$
$739$	25605.0	1.27455	0.637276	+	0.770636i	$0.280061\pi$
$740$	8516.46	0.423069
$741$	0	0
$742$	−2323.81	−0.114973
$743$	16222.7	0.801013	0.400507	−	0.916294i	$-0.368834\pi$
$743$	16222.7	0.801013	0.400507	+	0.916294i	$0.368834\pi$
$744$	−8628.31	−0.425174
$745$	64653.6	3.17950
$746$	835.372	0.0409989
$747$	−22455.5	−1.09987
$748$	−1309.22	−0.0639970
$749$	−4055.22	−0.197830
$750$	7819.22	0.380690
$751$	−12185.0	−0.592057	−0.296029	−	0.955179i	$-0.595662\pi$
$751$	−12185.0	−0.592057	−0.296029	+	0.955179i	$0.595662\pi$
$752$	1902.39	0.0922513
$753$	414.943	0.0200815
$754$	0	0
$755$	26564.2	1.28049
$756$	714.026	0.0343504
$757$	−26122.2	−1.25420	−0.627099	−	0.778940i	$-0.715758\pi$
$757$	−26122.2	−1.25420	−0.627099	+	0.778940i	$0.715758\pi$
$758$	27656.0	1.32521
$759$	−4246.91	−0.203100
$760$	12872.9	0.614406
$761$	25056.3	1.19355	0.596774	−	0.802409i	$-0.296449\pi$
$761$	25056.3	1.19355	0.596774	+	0.802409i	$0.296449\pi$
$762$	9126.96	0.433904
$763$	5306.34	0.251772
$764$	−886.756	−0.0419918
$765$	31810.2	1.50340
$766$	32230.1	1.52026
$767$	0	0
$768$	−4306.21	−0.202327
$769$	−2551.95	−0.119669	−0.0598345	−	0.998208i	$-0.519057\pi$
$769$	−2551.95	−0.119669	−0.0598345	+	0.998208i	$0.519057\pi$
$770$	2456.88	0.114987
$771$	8003.28	0.373840
$772$	−2166.66	−0.101010
$773$	−13650.3	−0.635146	−0.317573	−	0.948234i	$-0.602868\pi$
$773$	−13650.3	−0.635146	−0.317573	+	0.948234i	$0.602868\pi$
$774$	23124.8	1.07391
$775$	−43848.3	−2.03236
$776$	−17167.4	−0.794165
$777$	2350.27	0.108514
$778$	−19081.8	−0.879326
$779$	−8197.34	−0.377022
$780$	0	0
$781$	10553.4	0.483522
$782$	39392.9	1.80139
$783$	1230.98	0.0561832
$784$	15371.1	0.700213
$785$	−11986.3	−0.544979
$786$	−8020.79	−0.363985
$787$	27663.1	1.25296	0.626482	−	0.779436i	$-0.284494\pi$
$787$	27663.1	1.25296	0.626482	+	0.779436i	$0.284494\pi$
$788$	7943.48	0.359105
$789$	−922.370	−0.0416188
$790$	29165.3	1.31349
$791$	−1596.28	−0.0717535
$792$	−6381.07	−0.286290
$793$	0	0
$794$	5834.61	0.260784
$795$	−6355.71	−0.283539
$796$	−3608.77	−0.160690
$797$	−8110.59	−0.360466	−0.180233	−	0.983624i	$-0.557685\pi$
$797$	−8110.59	−0.360466	−0.180233	+	0.983624i	$0.557685\pi$
$798$	609.231	0.0270257
$799$	−2848.01	−0.126102
$800$	−16149.0	−0.713691
$801$	−6152.18	−0.271381
$802$	−17772.7	−0.782514
$803$	10293.9	0.452382
$804$	−1718.61	−0.0753864
$805$	19295.8	0.844831
$806$	0	0
$807$	−7028.55	−0.306588
$808$	2204.00	0.0959609
$809$	−10890.1	−0.473271	−0.236636	−	0.971598i	$-0.576045\pi$
$809$	−10890.1	−0.473271	−0.236636	+	0.971598i	$0.576045\pi$
$810$	22616.1	0.981049
$811$	−3721.83	−0.161148	−0.0805740	−	0.996749i	$-0.525675\pi$
$811$	−3721.83	−0.161148	−0.0805740	+	0.996749i	$0.525675\pi$
$812$	107.970	0.00466624
$813$	−13709.3	−0.591399
$814$	−7679.43	−0.330668
$815$	45794.8	1.96825
$816$	−6122.63	−0.262665
$817$	−10980.0	−0.470186
$818$	28594.3	1.22222
$819$	0	0
$820$	8829.73	0.376034
$821$	10247.0	0.435593	0.217796	−	0.975994i	$-0.430113\pi$
$821$	10247.0	0.435593	0.217796	+	0.975994i	$0.430113\pi$
$822$	996.667	0.0422904
$823$	−13763.5	−0.582946	−0.291473	−	0.956579i	$-0.594145\pi$
$823$	−13763.5	−0.582946	−0.291473	+	0.956579i	$0.594145\pi$
$824$	−8619.86	−0.364426
$825$	4280.02	0.180620
$826$	−4228.11	−0.178105
$827$	−16953.7	−0.712864	−0.356432	−	0.934321i	$-0.616007\pi$
$827$	−16953.7	−0.712864	−0.356432	+	0.934321i	$0.616007\pi$
$828$	−8594.50	−0.360724
$829$	39597.6	1.65896	0.829482	−	0.558534i	$-0.188636\pi$
$829$	39597.6	1.65896	0.829482	+	0.558534i	$0.188636\pi$
$830$	43999.6	1.84006
$831$	−11022.4	−0.460123
$832$	0	0
$833$	−23011.5	−0.957146
$834$	8240.28	0.342131
$835$	11466.0	0.475204
$836$	519.596	0.0214959
$837$	18040.8	0.745018
$838$	−206.930	−0.00853018
$839$	−1739.10	−0.0715620	−0.0357810	−	0.999360i	$-0.511392\pi$
$839$	−1739.10	−0.0715620	−0.0357810	+	0.999360i	$0.511392\pi$
$840$	−3826.57	−0.157178
$841$	−24202.9	−0.992368
$842$	−30224.9	−1.23708
$843$	7521.59	0.307304
$844$	−4049.14	−0.165139
$845$	0	0
$846$	−2380.51	−0.0967420
$847$	578.265	0.0234586
$848$	−9268.52	−0.375333
$849$	2870.46	0.116035
$850$	−39700.0	−1.60200
$851$	−60312.6	−2.42948
$852$	−2818.81	−0.113346
$853$	7698.90	0.309033	0.154517	−	0.987990i	$-0.450618\pi$
$853$	7698.90	0.309033	0.154517	+	0.987990i	$0.450618\pi$
$854$	8923.79	0.357571
$855$	−12624.7	−0.504977
$856$	−20637.2	−0.824024
$857$	−39142.3	−1.56018	−0.780090	−	0.625667i	$-0.784827\pi$
$857$	−39142.3	−1.56018	−0.780090	+	0.625667i	$0.784827\pi$
$858$	0	0
$859$	−2007.52	−0.0797387	−0.0398693	−	0.999205i	$-0.512694\pi$
$859$	−2007.52	−0.0797387	−0.0398693	+	0.999205i	$0.512694\pi$
$860$	11827.1	0.468954
$861$	2436.73	0.0964499
$862$	−4262.57	−0.168426
$863$	10800.6	0.426022	0.213011	−	0.977050i	$-0.431673\pi$
$863$	10800.6	0.426022	0.213011	+	0.977050i	$0.431673\pi$
$864$	6644.27	0.261623
$865$	30588.5	1.20236
$866$	44757.7	1.75627
$867$	448.921	0.0175850
$868$	1582.37	0.0618767
$869$	6864.51	0.267966
$870$	−1131.34	−0.0440872
$871$	0	0
$872$	27004.2	1.04871
$873$	16836.4	0.652720
$874$	−15634.1	−0.605069
$875$	−8361.75	−0.323061
$876$	−2749.48	−0.106046
$877$	−7063.44	−0.271968	−0.135984	−	0.990711i	$-0.543419\pi$
$877$	−7063.44	−0.271968	−0.135984	+	0.990711i	$0.543419\pi$
$878$	13634.2	0.524070
$879$	10885.9	0.417718
$880$	9799.28	0.375379
$881$	−5205.07	−0.199050	−0.0995251	−	0.995035i	$-0.531732\pi$
$881$	−5205.07	−0.199050	−0.0995251	+	0.995035i	$0.531732\pi$
$882$	−19234.2	−0.734298
$883$	51513.7	1.96328	0.981638	−	0.190754i	$-0.0610934\pi$
$883$	51513.7	1.96328	0.981638	+	0.190754i	$0.0610934\pi$
$884$	0	0
$885$	−11564.0	−0.439233
$886$	−28381.5	−1.07618
$887$	−20821.8	−0.788194	−0.394097	−	0.919069i	$-0.628943\pi$
$887$	−20821.8	−0.788194	−0.394097	+	0.919069i	$0.628943\pi$
$888$	11960.6	0.451996
$889$	−9760.23	−0.368220
$890$	12054.7	0.454015
$891$	5323.06	0.200145
$892$	−4317.52	−0.162064
$893$	1130.30	0.0423563
$894$	15571.7	0.582545
$895$	−12238.2	−0.457072
$896$	−4040.53	−0.150652
$897$	0	0
$898$	14202.0	0.527758
$899$	2727.99	0.101205
$900$	8661.51	0.320797
$901$	13875.6	0.513056
$902$	−7961.92	−0.293906
$903$	3263.90	0.120283
$904$	−8123.52	−0.298876
$905$	74575.4	2.73919
$906$	6397.92	0.234610
$907$	−16553.7	−0.606016	−0.303008	−	0.952988i	$-0.597991\pi$
$907$	−16553.7	−0.606016	−0.303008	+	0.952988i	$0.597991\pi$
$908$	2428.52	0.0887590
$909$	−2161.51	−0.0788698
$910$	0	0
$911$	2783.49	0.101231	0.0506154	−	0.998718i	$-0.483882\pi$
$911$	2783.49	0.101231	0.0506154	+	0.998718i	$0.483882\pi$
$912$	2429.92	0.0882266
$913$	10356.0	0.375392
$914$	32167.6	1.16412
$915$	24406.9	0.881823
$916$	−8129.49	−0.293238
$917$	8577.31	0.308885
$918$	16334.0	0.587258
$919$	6559.96	0.235466	0.117733	−	0.993045i	$-0.462437\pi$
$919$	6559.96	0.235466	0.117733	+	0.993045i	$0.462437\pi$
$920$	98197.3	3.51899
$921$	829.775	0.0296873
$922$	−33562.1	−1.19882
$923$	0	0
$924$	−154.454	−0.00549910
$925$	60782.9	2.16057
$926$	32060.1	1.13776
$927$	8453.66	0.299520
$928$	1004.69	0.0355396
$929$	−39337.6	−1.38926	−0.694631	−	0.719366i	$-0.744432\pi$
$929$	−39337.6	−1.38926	−0.694631	+	0.719366i	$0.744432\pi$
$930$	−16580.5	−0.584619
$931$	9132.71	0.321496
$932$	−4366.08	−0.153450
$933$	−9489.28	−0.332974
$934$	−11419.3	−0.400054
$935$	−14670.2	−0.513120
$936$	0	0
$937$	24308.9	0.847530	0.423765	−	0.905772i	$-0.360708\pi$
$937$	24308.9	0.847530	0.423765	+	0.905772i	$0.360708\pi$
$938$	−7041.05	−0.245094
$939$	−11045.4	−0.383870
$940$	−1217.50	−0.0422453
$941$	7465.43	0.258625	0.129312	−	0.991604i	$-0.458723\pi$
$941$	7465.43	0.258625	0.129312	+	0.991604i	$0.458723\pi$
$942$	−2886.87	−0.0998505
$943$	−62531.2	−2.15938
$944$	−16863.8	−0.581431
$945$	8000.89	0.275417
$946$	−10664.7	−0.366531
$947$	−19241.8	−0.660270	−0.330135	−	0.943934i	$-0.607094\pi$
$947$	−19241.8	−0.660270	−0.330135	+	0.943934i	$0.607094\pi$
$948$	−1833.51	−0.0628159
$949$	0	0
$950$	15756.0	0.538096
$951$	12568.3	0.428553
$952$	8354.06	0.284408
$953$	−47957.2	−1.63010	−0.815050	−	0.579391i	$-0.803291\pi$
$953$	−47957.2	−1.63010	−0.815050	+	0.579391i	$0.803291\pi$
$954$	11598.0	0.393604
$955$	−9936.39	−0.336685
$956$	−4178.71	−0.141369
$957$	−266.278	−0.00899429
$958$	−1770.48	−0.0597093
$959$	−1065.82	−0.0358885
$960$	−18751.4	−0.630414
$961$	10189.4	0.342031
$962$	0	0
$963$	20239.3	0.677261
$964$	5567.56	0.186016
$965$	−24278.1	−0.809887
$966$	4647.36	0.154789
$967$	−39784.3	−1.32304	−0.661518	−	0.749929i	$-0.730087\pi$
$967$	−39784.3	−1.32304	−0.661518	+	0.749929i	$0.730087\pi$
$968$	2942.82	0.0977126
$969$	−3637.76	−0.120600
$970$	−32989.4	−1.09199
$971$	−10413.2	−0.344157	−0.172079	−	0.985083i	$-0.555048\pi$
$971$	−10413.2	−0.344157	−0.172079	+	0.985083i	$0.555048\pi$
$972$	−5455.79	−0.180036
$973$	−8812.03	−0.290340
$974$	27427.6	0.902296
$975$	0	0
$976$	35592.6	1.16731
$977$	−33806.3	−1.10702	−0.553510	−	0.832843i	$-0.686712\pi$
$977$	−33806.3	−1.10702	−0.553510	+	0.832843i	$0.686712\pi$
$978$	11029.6	0.360621
$979$	2837.26	0.0926242
$980$	−9837.27	−0.320653
$981$	−26483.5	−0.861931
$982$	−20228.1	−0.657336
$983$	5865.21	0.190306	0.0951532	−	0.995463i	$-0.469666\pi$
$983$	5865.21	0.190306	0.0951532	+	0.995463i	$0.469666\pi$
$984$	12400.6	0.401745
$985$	89009.3	2.87926
$986$	2469.90	0.0797746
$987$	−335.992	−0.0108356
$988$	0	0
$989$	−83758.1	−2.69298
$990$	−12262.1	−0.393652
$991$	43430.0	1.39213	0.696065	−	0.717979i	$-0.254933\pi$
$991$	43430.0	1.39213	0.696065	+	0.717979i	$0.254933\pi$
$992$	14724.5	0.471273
$993$	18114.0	0.578881
$994$	−11548.5	−0.368507
$995$	−40437.4	−1.28839
$996$	−2766.08	−0.0879985
$997$	−4855.10	−0.154225	−0.0771127	−	0.997022i	$-0.524570\pi$
$997$	−4855.10	−0.154225	−0.0771127	+	0.997022i	$0.524570\pi$
$998$	30911.3	0.980442
$999$	−25008.3	−0.792018

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.n.1.11	✓	39
13.12	even	2		1859.4.a.o.1.29	yes	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.11	✓	39	1.1	even	1	trivial
1859.4.a.o.1.29	yes	39	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51874 q^{2} +1.77429 q^{3} -1.65593 q^{4} -18.5552 q^{5} -4.46898 q^{6} +4.77905 q^{7} +24.3208 q^{8} -23.8519 q^{9} +O(q^{10})\)	\(q-2.51874 q^{2} +1.77429 q^{3} -1.65593 q^{4} -18.5552 q^{5} -4.46898 q^{6} +4.77905 q^{7} +24.3208 q^{8} -23.8519 q^{9} +46.7358 q^{10} +11.0000 q^{11} -2.93809 q^{12} -12.0372 q^{14} -32.9222 q^{15} -48.0105 q^{16} +71.8750 q^{17} +60.0768 q^{18} -28.5254 q^{19} +30.7261 q^{20} +8.47941 q^{21} -27.7062 q^{22} -217.599 q^{23} +43.1521 q^{24} +219.295 q^{25} -90.2259 q^{27} -7.91376 q^{28} -13.6433 q^{29} +82.9227 q^{30} -199.951 q^{31} -73.6404 q^{32} +19.5172 q^{33} -181.035 q^{34} -88.6762 q^{35} +39.4970 q^{36} +277.174 q^{37} +71.8482 q^{38} -451.277 q^{40} +287.370 q^{41} -21.3575 q^{42} +384.920 q^{43} -18.2152 q^{44} +442.577 q^{45} +548.075 q^{46} -39.6245 q^{47} -85.1844 q^{48} -320.161 q^{49} -552.349 q^{50} +127.527 q^{51} +193.052 q^{53} +227.256 q^{54} -204.107 q^{55} +116.230 q^{56} -50.6123 q^{57} +34.3639 q^{58} +351.253 q^{59} +54.5169 q^{60} -741.350 q^{61} +503.626 q^{62} -113.989 q^{63} +569.565 q^{64} -49.1587 q^{66} +584.940 q^{67} -119.020 q^{68} -386.083 q^{69} +223.353 q^{70} +959.400 q^{71} -580.098 q^{72} +935.806 q^{73} -698.130 q^{74} +389.093 q^{75} +47.2360 q^{76} +52.5696 q^{77} +624.047 q^{79} +890.844 q^{80} +483.915 q^{81} -723.811 q^{82} +941.454 q^{83} -14.0413 q^{84} -1333.65 q^{85} -969.516 q^{86} -24.2071 q^{87} +267.529 q^{88} +257.932 q^{89} -1114.74 q^{90} +360.328 q^{92} -354.771 q^{93} +99.8039 q^{94} +529.295 q^{95} -130.659 q^{96} -705.871 q^{97} +806.403 q^{98} -262.371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} - 23 q^{5} - 77 q^{6} + 4 q^{7} + 21 q^{8} + 260 q^{9} - 158 q^{10} + 429 q^{11} - 351 q^{12} - 176 q^{14} - 30 q^{15} + 230 q^{16} - 244 q^{17} - 21 q^{18} + 70 q^{19} - 366 q^{20} + 142 q^{21} - 47 q^{23} - 846 q^{24} + 322 q^{25} - 416 q^{27} - 1131 q^{28} - 838 q^{29} - 293 q^{30} - 507 q^{31} + 1433 q^{32} - 253 q^{33} - 166 q^{34} - 498 q^{35} + 815 q^{36} - 89 q^{37} + 81 q^{38} - 2917 q^{40} - 618 q^{41} - 318 q^{42} - 1064 q^{43} + 1254 q^{44} - 238 q^{45} + 1331 q^{46} - 1499 q^{47} - 1460 q^{48} - 413 q^{49} + 2459 q^{50} - 2350 q^{51} - 2745 q^{53} + 845 q^{54} - 253 q^{55} - 2904 q^{56} - 1450 q^{57} + 2509 q^{58} - 2285 q^{59} + 3566 q^{60} - 6218 q^{61} - 911 q^{62} + 1930 q^{63} + 67 q^{64} - 847 q^{66} - 546 q^{67} - 170 q^{68} - 5254 q^{69} + 2195 q^{70} + 263 q^{71} + 2393 q^{72} + 1148 q^{73} + 775 q^{74} - 5385 q^{75} + 7247 q^{76} + 44 q^{77} - 3666 q^{79} - 5594 q^{80} - 1901 q^{81} - 4414 q^{82} - 2722 q^{83} + 9971 q^{84} - 1858 q^{85} - 2478 q^{86} - 2284 q^{87} + 231 q^{88} - 13 q^{89} - 6771 q^{90} - 2232 q^{92} + 1082 q^{93} - 7330 q^{94} - 2352 q^{95} - 5770 q^{96} + 1197 q^{97} - 6813 q^{98} + 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 - 23 * q^5 - 77 * q^6 + 4 * q^7 + 21 * q^8 + 260 * q^9 - 158 * q^10 + 429 * q^11 - 351 * q^12 - 176 * q^14 - 30 * q^15 + 230 * q^16 - 244 * q^17 - 21 * q^18 + 70 * q^19 - 366 * q^20 + 142 * q^21 - 47 * q^23 - 846 * q^24 + 322 * q^25 - 416 * q^27 - 1131 * q^28 - 838 * q^29 - 293 * q^30 - 507 * q^31 + 1433 * q^32 - 253 * q^33 - 166 * q^34 - 498 * q^35 + 815 * q^36 - 89 * q^37 + 81 * q^38 - 2917 * q^40 - 618 * q^41 - 318 * q^42 - 1064 * q^43 + 1254 * q^44 - 238 * q^45 + 1331 * q^46 - 1499 * q^47 - 1460 * q^48 - 413 * q^49 + 2459 * q^50 - 2350 * q^51 - 2745 * q^53 + 845 * q^54 - 253 * q^55 - 2904 * q^56 - 1450 * q^57 + 2509 * q^58 - 2285 * q^59 + 3566 * q^60 - 6218 * q^61 - 911 * q^62 + 1930 * q^63 + 67 * q^64 - 847 * q^66 - 546 * q^67 - 170 * q^68 - 5254 * q^69 + 2195 * q^70 + 263 * q^71 + 2393 * q^72 + 1148 * q^73 + 775 * q^74 - 5385 * q^75 + 7247 * q^76 + 44 * q^77 - 3666 * q^79 - 5594 * q^80 - 1901 * q^81 - 4414 * q^82 - 2722 * q^83 + 9971 * q^84 - 1858 * q^85 - 2478 * q^86 - 2284 * q^87 + 231 * q^88 - 13 * q^89 - 6771 * q^90 - 2232 * q^92 + 1082 * q^93 - 7330 * q^94 - 2352 * q^95 - 5770 * q^96 + 1197 * q^97 - 6813 * q^98 + 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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