LMFDB - Embedded newform 1859.4.a.p.1.18

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:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.33473 q^{2} -7.99292 q^{3} -2.54902 q^{4} -16.6573 q^{5} +18.6613 q^{6} -33.9647 q^{7} +24.6291 q^{8} +36.8868 q^{9} +O(q^{10})$	\(q-2.33473 q^{2} -7.99292 q^{3} -2.54902 q^{4} -16.6573 q^{5} +18.6613 q^{6} -33.9647 q^{7} +24.6291 q^{8} +36.8868 q^{9} +38.8903 q^{10} -11.0000 q^{11} +20.3742 q^{12} +79.2986 q^{14} +133.140 q^{15} -37.1103 q^{16} +118.300 q^{17} -86.1209 q^{18} -89.6903 q^{19} +42.4598 q^{20} +271.478 q^{21} +25.6821 q^{22} +6.38970 q^{23} -196.859 q^{24} +152.465 q^{25} -79.0247 q^{27} +86.5769 q^{28} +166.913 q^{29} -310.847 q^{30} -192.375 q^{31} -110.391 q^{32} +87.9222 q^{33} -276.198 q^{34} +565.760 q^{35} -94.0254 q^{36} +130.163 q^{37} +209.403 q^{38} -410.255 q^{40} +66.4266 q^{41} -633.827 q^{42} -325.965 q^{43} +28.0393 q^{44} -614.434 q^{45} -14.9182 q^{46} -13.9559 q^{47} +296.620 q^{48} +810.603 q^{49} -355.965 q^{50} -945.561 q^{51} +77.4157 q^{53} +184.502 q^{54} +183.230 q^{55} -836.523 q^{56} +716.888 q^{57} -389.697 q^{58} -389.252 q^{59} -339.378 q^{60} -903.959 q^{61} +449.144 q^{62} -1252.85 q^{63} +554.615 q^{64} -205.275 q^{66} -351.300 q^{67} -301.549 q^{68} -51.0724 q^{69} -1320.90 q^{70} +133.656 q^{71} +908.491 q^{72} +880.373 q^{73} -303.895 q^{74} -1218.64 q^{75} +228.623 q^{76} +373.612 q^{77} -1302.98 q^{79} +618.156 q^{80} -364.306 q^{81} -155.088 q^{82} +707.164 q^{83} -692.003 q^{84} -1970.55 q^{85} +761.042 q^{86} -1334.12 q^{87} -270.921 q^{88} -194.512 q^{89} +1434.54 q^{90} -16.2875 q^{92} +1537.64 q^{93} +32.5832 q^{94} +1494.00 q^{95} +882.344 q^{96} -996.747 q^{97} -1892.54 q^{98} -405.755 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * 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 $

$2$	−2.33473	−0.825453	−0.412726	−	0.910855i	$-0.635423\pi$
$2$	−2.33473	−0.825453	−0.412726	+	0.910855i	$0.635423\pi$
$3$	−7.99292	−1.53824	−0.769119	−	0.639105i	$-0.779305\pi$
$3$	−7.99292	−1.53824	−0.769119	+	0.639105i	$0.779305\pi$
$4$	−2.54902	−0.318628
$5$	−16.6573	−1.48987	−0.744936	−	0.667136i	$-0.767520\pi$
$5$	−16.6573	−1.48987	−0.744936	+	0.667136i	$0.767520\pi$
$6$	18.6613	1.26974
$7$	−33.9647	−1.83392	−0.916962	−	0.398975i	$-0.869366\pi$
$7$	−33.9647	−1.83392	−0.916962	+	0.398975i	$0.869366\pi$
$8$	24.6291	1.08846
$9$	36.8868	1.36618
$10$	38.8903	1.22982
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	20.3742	0.490126
$13$	0	0
$13$	0	0
$14$	79.2986	1.51382
$15$	133.140	2.29178
$16$	−37.1103	−0.579848
$17$	118.300	1.68776	0.843879	−	0.536533i	$-0.180266\pi$
$17$	118.300	1.68776	0.843879	+	0.536533i	$0.180266\pi$
$18$	−86.1209	−1.12772
$19$	−89.6903	−1.08297	−0.541484	−	0.840711i	$-0.682137\pi$
$19$	−89.6903	−1.08297	−0.541484	+	0.840711i	$0.682137\pi$
$20$	42.4598	0.474715
$21$	271.478	2.82101
$22$	25.6821	0.248883
$23$	6.38970	0.0579280	0.0289640	−	0.999580i	$-0.490779\pi$
$23$	6.38970	0.0579280	0.0289640	+	0.999580i	$0.490779\pi$
$24$	−196.859	−1.67432
$25$	152.465	1.21972
$26$	0	0
$27$	−79.0247	−0.563271
$28$	86.5769	0.584339
$29$	166.913	1.06879	0.534396	−	0.845234i	$-0.320539\pi$
$29$	166.913	1.06879	0.534396	+	0.845234i	$0.320539\pi$
$30$	−310.847	−1.89176
$31$	−192.375	−1.11457	−0.557284	−	0.830322i	$-0.688156\pi$
$31$	−192.375	−1.11457	−0.557284	+	0.830322i	$0.688156\pi$
$32$	−110.391	−0.609828
$33$	87.9222	0.463796
$34$	−276.198	−1.39316
$35$	565.760	2.73231
$36$	−94.0254	−0.435303
$37$	130.163	0.578340	0.289170	−	0.957278i	$-0.406621\pi$
$37$	130.163	0.578340	0.289170	+	0.957278i	$0.406621\pi$
$38$	209.403	0.893938
$39$	0	0
$40$	−410.255	−1.62167
$41$	66.4266	0.253027	0.126513	−	0.991965i	$-0.459621\pi$
$41$	66.4266	0.253027	0.126513	+	0.991965i	$0.459621\pi$
$42$	−633.827	−2.32861
$43$	−325.965	−1.15603	−0.578014	−	0.816027i	$-0.696172\pi$
$43$	−325.965	−1.15603	−0.578014	+	0.816027i	$0.696172\pi$
$44$	28.0393	0.0960700
$45$	−614.434	−2.03543
$46$	−14.9182	−0.0478169
$47$	−13.9559	−0.0433122	−0.0216561	−	0.999765i	$-0.506894\pi$
$47$	−13.9559	−0.0433122	−0.0216561	+	0.999765i	$0.506894\pi$
$48$	296.620	0.891945
$49$	810.603	2.36327
$50$	−355.965	−1.00682
$51$	−945.561	−2.59618
$52$	0	0
$53$	77.4157	0.200639	0.100320	−	0.994955i	$-0.468014\pi$
$53$	77.4157	0.200639	0.100320	+	0.994955i	$0.468014\pi$
$54$	184.502	0.464953
$55$	183.230	0.449214
$56$	−836.523	−1.99616
$57$	716.888	1.66586
$58$	−389.697	−0.882237
$59$	−389.252	−0.858921	−0.429460	−	0.903086i	$-0.641296\pi$
$59$	−389.252	−0.858921	−0.429460	+	0.903086i	$0.641296\pi$
$60$	−339.378	−0.730225
$61$	−903.959	−1.89738	−0.948689	−	0.316210i	$-0.897589\pi$
$61$	−903.959	−1.89738	−0.948689	+	0.316210i	$0.897589\pi$
$62$	449.144	0.920022
$63$	−1252.85	−2.50547
$64$	554.615	1.08323
$65$	0	0
$66$	−205.275	−0.382842
$67$	−351.300	−0.640570	−0.320285	−	0.947321i	$-0.603779\pi$
$67$	−351.300	−0.640570	−0.320285	+	0.947321i	$0.603779\pi$
$68$	−301.549	−0.537767
$69$	−51.0724	−0.0891072
$70$	−1320.90	−2.25539
$71$	133.656	0.223408	0.111704	−	0.993742i	$-0.464369\pi$
$71$	133.656	0.223408	0.111704	+	0.993742i	$0.464369\pi$
$72$	908.491	1.48704
$73$	880.373	1.41150	0.705752	−	0.708459i	$-0.250609\pi$
$73$	880.373	1.41150	0.705752	+	0.708459i	$0.250609\pi$
$74$	−303.895	−0.477393
$75$	−1218.64	−1.87622
$76$	228.623	0.345064
$77$	373.612	0.552949
$78$	0	0
$79$	−1302.98	−1.85566	−0.927829	−	0.373005i	$-0.878327\pi$
$79$	−1302.98	−1.85566	−0.927829	+	0.373005i	$0.878327\pi$
$80$	618.156	0.863900
$81$	−364.306	−0.499734
$82$	−155.088	−0.208862
$83$	707.164	0.935197	0.467599	−	0.883941i	$-0.345119\pi$
$83$	707.164	0.935197	0.467599	+	0.883941i	$0.345119\pi$
$84$	−692.003	−0.898854
$85$	−1970.55	−2.51455
$86$	761.042	0.954247
$87$	−1334.12	−1.64406
$88$	−270.921	−0.328185
$89$	−194.512	−0.231666	−0.115833	−	0.993269i	$-0.536954\pi$
$89$	−194.512	−0.231666	−0.115833	+	0.993269i	$0.536954\pi$
$90$	1434.54	1.68015
$91$	0	0
$92$	−16.2875	−0.0184575
$93$	1537.64	1.71447
$94$	32.5832	0.0357522
$95$	1494.00	1.61348
$96$	882.344	0.938061
$97$	−996.747	−1.04334	−0.521672	−	0.853146i	$-0.674691\pi$
$97$	−996.747	−1.04334	−0.521672	+	0.853146i	$0.674691\pi$
$98$	−1892.54	−1.95077
$99$	−405.755	−0.411918
$100$	−388.637	−0.388637
$101$	1049.99	1.03443	0.517216	−	0.855855i	$-0.326968\pi$
$101$	1049.99	1.03443	0.517216	+	0.855855i	$0.326968\pi$
$102$	2207.63	2.14302
$103$	−1100.02	−1.05232	−0.526158	−	0.850387i	$-0.676368\pi$
$103$	−1100.02	−1.05232	−0.526158	+	0.850387i	$0.676368\pi$
$104$	0	0
$105$	−4522.08	−4.20295
$106$	−180.745	−0.165618
$107$	3.86811	0.00349481	0.00174740	−	0.999998i	$-0.499444\pi$
$107$	3.86811	0.00349481	0.00174740	+	0.999998i	$0.499444\pi$
$108$	201.436	0.179474
$109$	209.654	0.184232	0.0921158	−	0.995748i	$-0.470637\pi$
$109$	209.654	0.184232	0.0921158	+	0.995748i	$0.470637\pi$
$110$	−427.793	−0.370804
$111$	−1040.38	−0.889626
$112$	1260.44	1.06340
$113$	783.439	0.652210	0.326105	−	0.945334i	$-0.394264\pi$
$113$	783.439	0.652210	0.326105	+	0.945334i	$0.394264\pi$
$114$	−1673.74	−1.37509
$115$	−106.435	−0.0863054
$116$	−425.465	−0.340547
$117$	0	0
$118$	908.800	0.708998
$119$	−4018.02	−3.09522
$120$	3279.13	2.49452
$121$	121.000	0.0909091
$122$	2110.50	1.56620
$123$	−530.943	−0.389216
$124$	490.369	0.355132
$125$	−457.494	−0.327356
$126$	2925.07	2.06814
$127$	−1768.63	−1.23575	−0.617877	−	0.786274i	$-0.712007\pi$
$127$	−1768.63	−1.23575	−0.617877	+	0.786274i	$0.712007\pi$
$128$	−411.752	−0.284329
$129$	2605.42	1.77825
$130$	0	0
$131$	1844.74	1.23035	0.615173	−	0.788392i	$-0.289086\pi$
$131$	1844.74	1.23035	0.615173	+	0.788392i	$0.289086\pi$
$132$	−224.116	−0.147779
$133$	3046.31	1.98608
$134$	820.193	0.528760
$135$	1316.34	0.839202
$136$	2913.62	1.83707
$137$	−2669.72	−1.66489	−0.832445	−	0.554108i	$-0.813060\pi$
$137$	−2669.72	−1.66489	−0.832445	+	0.554108i	$0.813060\pi$
$138$	119.240	0.0735538
$139$	−916.463	−0.559233	−0.279617	−	0.960112i	$-0.590207\pi$
$139$	−916.463	−0.559233	−0.279617	+	0.960112i	$0.590207\pi$
$140$	−1442.14	−0.870591
$141$	111.548	0.0666245
$142$	−312.050	−0.184413
$143$	0	0
$144$	−1368.88	−0.792176
$145$	−2780.32	−1.59236
$146$	−2055.43	−1.16513
$147$	−6479.09	−3.63528
$148$	−331.787	−0.184275
$149$	1393.42	0.766132	0.383066	−	0.923721i	$-0.374868\pi$
$149$	1393.42	0.766132	0.383066	+	0.923721i	$0.374868\pi$
$150$	2845.20	1.54873
$151$	−719.501	−0.387763	−0.193881	−	0.981025i	$-0.562108\pi$
$151$	−719.501	−0.387763	−0.193881	+	0.981025i	$0.562108\pi$
$152$	−2209.00	−1.17877
$153$	4363.70	2.30578
$154$	−872.284	−0.456433
$155$	3204.45	1.66056
$156$	0	0
$157$	−1719.83	−0.874250	−0.437125	−	0.899401i	$-0.644003\pi$
$157$	−1719.83	−0.874250	−0.437125	+	0.899401i	$0.644003\pi$
$158$	3042.12	1.53176
$159$	−618.778	−0.308631
$160$	1838.81	0.908566
$161$	−217.025	−0.106236
$162$	850.557	0.412507
$163$	−3460.27	−1.66276	−0.831378	−	0.555707i	$-0.812447\pi$
$163$	−3460.27	−1.66276	−0.831378	+	0.555707i	$0.812447\pi$
$164$	−169.323	−0.0806214
$165$	−1464.54	−0.690998
$166$	−1651.04	−0.771961
$167$	−65.3362	−0.0302746	−0.0151373	−	0.999885i	$-0.504819\pi$
$167$	−65.3362	−0.0302746	−0.0151373	+	0.999885i	$0.504819\pi$
$168$	6686.26	3.07057
$169$	0	0
$170$	4600.71	2.07564
$171$	−3308.39	−1.47953
$172$	830.893	0.368343
$173$	117.015	0.0514249	0.0257124	−	0.999669i	$-0.491815\pi$
$173$	117.015	0.0514249	0.0257124	+	0.999669i	$0.491815\pi$
$174$	3114.82	1.35709
$175$	−5178.44	−2.23687
$176$	408.213	0.174831
$177$	3111.26	1.32123
$178$	454.134	0.191229
$179$	4693.07	1.95964	0.979822	−	0.199871i	$-0.0640523\pi$
$179$	4693.07	1.95964	0.979822	+	0.199871i	$0.0640523\pi$
$180$	1566.21	0.648546
$181$	2815.23	1.15610	0.578050	−	0.816001i	$-0.303814\pi$
$181$	2815.23	1.15610	0.578050	+	0.816001i	$0.303814\pi$
$182$	0	0
$183$	7225.27	2.91862
$184$	157.373	0.0630526
$185$	−2168.15	−0.861653
$186$	−3589.98	−1.41521
$187$	−1301.30	−0.508878
$188$	35.5739	0.0138005
$189$	2684.05	1.03300
$190$	−3488.08	−1.33185
$191$	−2541.77	−0.962910	−0.481455	−	0.876471i	$-0.659892\pi$
$191$	−2541.77	−0.962910	−0.481455	+	0.876471i	$0.659892\pi$
$192$	−4432.99	−1.66627
$193$	−3874.66	−1.44510	−0.722550	−	0.691319i	$-0.757030\pi$
$193$	−3874.66	−1.44510	−0.722550	+	0.691319i	$0.757030\pi$
$194$	2327.14	0.861230
$195$	0	0
$196$	−2066.25	−0.753006
$197$	530.630	0.191908	0.0959539	−	0.995386i	$-0.469410\pi$
$197$	530.630	0.191908	0.0959539	+	0.995386i	$0.469410\pi$
$198$	947.330	0.340019
$199$	−800.295	−0.285082	−0.142541	−	0.989789i	$-0.545527\pi$
$199$	−800.295	−0.285082	−0.142541	+	0.989789i	$0.545527\pi$
$200$	3755.09	1.32762
$201$	2807.92	0.985350
$202$	−2451.44	−0.853875
$203$	−5669.16	−1.96008
$204$	2410.26	0.827214
$205$	−1106.49	−0.376978
$206$	2568.26	0.868637
$207$	235.696	0.0791401
$208$	0	0
$209$	986.594	0.326527
$210$	10557.8	3.46934
$211$	900.647	0.293854	0.146927	−	0.989147i	$-0.453062\pi$
$211$	900.647	0.293854	0.146927	+	0.989147i	$0.453062\pi$
$212$	−197.335	−0.0639292
$213$	−1068.30	−0.343655
$214$	−9.03101	−0.00288480
$215$	5429.70	1.72234
$216$	−1946.31	−0.613100
$217$	6533.97	2.04403
$218$	−489.487	−0.152075
$219$	−7036.75	−2.17123
$220$	−467.058	−0.143132
$221$	0	0
$222$	2429.01	0.734344
$223$	3789.76	1.13803	0.569017	−	0.822326i	$-0.307324\pi$
$223$	3789.76	1.13803	0.569017	+	0.822326i	$0.307324\pi$
$224$	3749.39	1.11838
$225$	5623.95	1.66636
$226$	−1829.12	−0.538369
$227$	1182.73	0.345819	0.172909	−	0.984938i	$-0.444683\pi$
$227$	1182.73	0.345819	0.172909	+	0.984938i	$0.444683\pi$
$228$	−1827.36	−0.530790
$229$	−1451.80	−0.418941	−0.209471	−	0.977815i	$-0.567174\pi$
$229$	−1451.80	−0.418941	−0.209471	+	0.977815i	$0.567174\pi$
$230$	248.497	0.0712410
$231$	−2986.25	−0.850567
$232$	4110.93	1.16334
$233$	−4083.94	−1.14827	−0.574137	−	0.818759i	$-0.694662\pi$
$233$	−4083.94	−1.14827	−0.574137	+	0.818759i	$0.694662\pi$
$234$	0	0
$235$	232.467	0.0645297
$236$	992.213	0.273676
$237$	10414.6	2.85445
$238$	9381.00	2.55496
$239$	−1392.81	−0.376959	−0.188479	−	0.982077i	$-0.560356\pi$
$239$	−1392.81	−0.376959	−0.188479	+	0.982077i	$0.560356\pi$
$240$	−4940.88	−1.32888
$241$	−3061.76	−0.818361	−0.409181	−	0.912453i	$-0.634185\pi$
$241$	−3061.76	−0.818361	−0.409181	+	0.912453i	$0.634185\pi$
$242$	−282.503	−0.0750411
$243$	5045.54	1.33198
$244$	2304.21	0.604558
$245$	−13502.4	−3.52098
$246$	1239.61	0.321279
$247$	0	0
$248$	−4738.04	−1.21317
$249$	−5652.31	−1.43856
$250$	1068.13	0.270217
$251$	−4837.99	−1.21662	−0.608310	−	0.793700i	$-0.708152\pi$
$251$	−4837.99	−1.21662	−0.608310	+	0.793700i	$0.708152\pi$
$252$	3193.55	0.798312
$253$	−70.2867	−0.0174660
$254$	4129.29	1.02006
$255$	15750.5	3.86797
$256$	−3475.59	−0.848532
$257$	−8197.37	−1.98964	−0.994820	−	0.101648i	$-0.967588\pi$
$257$	−8197.37	−1.98964	−0.994820	+	0.101648i	$0.967588\pi$
$258$	−6082.95	−1.46786
$259$	−4420.94	−1.06063
$260$	0	0
$261$	6156.89	1.46016
$262$	−4306.97	−1.01559
$263$	−5988.14	−1.40397	−0.701986	−	0.712191i	$-0.747703\pi$
$263$	−5988.14	−1.40397	−0.701986	+	0.712191i	$0.747703\pi$
$264$	2165.45	0.504826
$265$	−1289.54	−0.298927
$266$	−7112.32	−1.63941
$267$	1554.72	0.356357
$268$	895.473	0.204104
$269$	4053.06	0.918661	0.459330	−	0.888266i	$-0.348089\pi$
$269$	4053.06	0.918661	0.459330	+	0.888266i	$0.348089\pi$
$270$	−3073.29	−0.692721
$271$	7520.77	1.68581	0.842905	−	0.538063i	$-0.180844\pi$
$271$	7520.77	1.68581	0.842905	+	0.538063i	$0.180844\pi$
$272$	−4390.14	−0.978644
$273$	0	0
$274$	6233.09	1.37429
$275$	−1677.12	−0.367760
$276$	130.185	0.0283920
$277$	2423.70	0.525726	0.262863	−	0.964833i	$-0.415333\pi$
$277$	2423.70	0.525726	0.262863	+	0.964833i	$0.415333\pi$
$278$	2139.70	0.461620
$279$	−7096.11	−1.52270
$280$	13934.2	2.97403
$281$	−4806.30	−1.02035	−0.510177	−	0.860069i	$-0.670420\pi$
$281$	−4806.30	−1.02035	−0.510177	+	0.860069i	$0.670420\pi$
$282$	−260.435	−0.0549954
$283$	−4192.88	−0.880710	−0.440355	−	0.897824i	$-0.645147\pi$
$283$	−4192.88	−0.880710	−0.440355	+	0.897824i	$0.645147\pi$
$284$	−340.691	−0.0711842
$285$	−11941.4	−2.48192
$286$	0	0
$287$	−2256.16	−0.464032
$288$	−4071.96	−0.833134
$289$	9081.82	1.84853
$290$	6491.30	1.31442
$291$	7966.92	1.60491
$292$	−2244.09	−0.449745
$293$	−1953.55	−0.389514	−0.194757	−	0.980852i	$-0.562392\pi$
$293$	−1953.55	−0.389514	−0.194757	+	0.980852i	$0.562392\pi$
$294$	15126.9	3.00075
$295$	6483.88	1.27968
$296$	3205.79	0.629503
$297$	869.272	0.169833
$298$	−3253.27	−0.632406
$299$	0	0
$300$	3106.35	0.597817
$301$	11071.3	2.12007
$302$	1679.84	0.320080
$303$	−8392.47	−1.59120
$304$	3328.43	0.627956
$305$	15057.5	2.82685
$306$	−10188.1	−1.90331
$307$	−1762.67	−0.327690	−0.163845	−	0.986486i	$-0.552390\pi$
$307$	−1762.67	−0.327690	−0.163845	+	0.986486i	$0.552390\pi$
$308$	−952.346	−0.176185
$309$	8792.41	1.61871
$310$	−7481.53	−1.37072
$311$	8219.25	1.49862	0.749310	−	0.662220i	$-0.230385\pi$
$311$	8219.25	1.49862	0.749310	+	0.662220i	$0.230385\pi$
$312$	0	0
$313$	−2330.26	−0.420811	−0.210406	−	0.977614i	$-0.567478\pi$
$313$	−2330.26	−0.420811	−0.210406	+	0.977614i	$0.567478\pi$
$314$	4015.34	0.721652
$315$	20869.1	3.73283
$316$	3321.33	0.591265
$317$	3158.88	0.559686	0.279843	−	0.960046i	$-0.409718\pi$
$317$	3158.88	0.559686	0.279843	+	0.960046i	$0.409718\pi$
$318$	1444.68	0.254760
$319$	−1836.04	−0.322253
$320$	−9238.38	−1.61388
$321$	−30.9175	−0.00537585
$322$	506.694	0.0876925
$323$	−10610.3	−1.82779
$324$	928.625	0.159229
$325$	0	0
$326$	8078.80	1.37253
$327$	−1675.75	−0.283392
$328$	1636.03	0.275411
$329$	474.008	0.0794313
$330$	3419.32	0.570386
$331$	−2925.88	−0.485864	−0.242932	−	0.970043i	$-0.578109\pi$
$331$	−2925.88	−0.485864	−0.242932	+	0.970043i	$0.578109\pi$
$332$	−1802.58	−0.297980
$333$	4801.28	0.790116
$334$	152.542	0.0249903
$335$	5851.71	0.954368
$336$	−10074.6	−1.63576
$337$	−9226.35	−1.49137	−0.745684	−	0.666299i	$-0.767877\pi$
$337$	−9226.35	−1.49137	−0.745684	+	0.666299i	$0.767877\pi$
$338$	0	0
$339$	−6261.97	−1.00325
$340$	5022.98	0.801205
$341$	2116.13	0.336055
$342$	7724.21	1.22128
$343$	−15882.0	−2.50014
$344$	−8028.25	−1.25830
$345$	850.728	0.132758
$346$	−273.199	−0.0424488
$347$	7556.54	1.16904	0.584519	−	0.811380i	$-0.301283\pi$
$347$	7556.54	1.16904	0.584519	+	0.811380i	$0.301283\pi$
$348$	3400.71	0.523843
$349$	2793.29	0.428428	0.214214	−	0.976787i	$-0.431281\pi$
$349$	2793.29	0.428428	0.214214	+	0.976787i	$0.431281\pi$
$350$	12090.3	1.84643
$351$	0	0
$352$	1214.30	0.183870
$353$	−3988.45	−0.601371	−0.300685	−	0.953723i	$-0.597215\pi$
$353$	−3988.45	−0.601371	−0.300685	+	0.953723i	$0.597215\pi$
$354$	−7263.97	−1.09061
$355$	−2226.34	−0.332850
$356$	495.816	0.0738152
$357$	32115.7	4.76119
$358$	−10957.1	−1.61759
$359$	−4173.36	−0.613541	−0.306771	−	0.951783i	$-0.599248\pi$
$359$	−4173.36	−0.613541	−0.306771	+	0.951783i	$0.599248\pi$
$360$	−15133.0	−2.21550
$361$	1185.36	0.172818
$362$	−6572.80	−0.954306
$363$	−967.144	−0.139840
$364$	0	0
$365$	−14664.6	−2.10296
$366$	−16869.1	−2.40918
$367$	728.027	0.103550	0.0517748	−	0.998659i	$-0.483512\pi$
$367$	728.027	0.103550	0.0517748	+	0.998659i	$0.483512\pi$
$368$	−237.124	−0.0335895
$369$	2450.27	0.345680
$370$	5062.06	0.711254
$371$	−2629.40	−0.367957
$372$	−3919.48	−0.546278
$373$	8422.76	1.16921	0.584603	−	0.811320i	$-0.301250\pi$
$373$	8422.76	1.16921	0.584603	+	0.811320i	$0.301250\pi$
$374$	3038.18	0.420055
$375$	3656.71	0.503552
$376$	−343.721	−0.0471438
$377$	0	0
$378$	−6266.55	−0.852689
$379$	−10581.9	−1.43418	−0.717089	−	0.696982i	$-0.754526\pi$
$379$	−10581.9	−1.43418	−0.717089	+	0.696982i	$0.754526\pi$
$380$	−3808.24	−0.514101
$381$	14136.6	1.90089
$382$	5934.35	0.794837
$383$	−336.003	−0.0448276	−0.0224138	−	0.999749i	$-0.507135\pi$
$383$	−336.003	−0.0448276	−0.0224138	+	0.999749i	$0.507135\pi$
$384$	3291.11	0.437366
$385$	−6223.36	−0.823823
$386$	9046.30	1.19286
$387$	−12023.8	−1.57934
$388$	2540.73	0.332438
$389$	−1099.98	−0.143371	−0.0716855	−	0.997427i	$-0.522838\pi$
$389$	−1099.98	−0.143371	−0.0716855	+	0.997427i	$0.522838\pi$
$390$	0	0
$391$	755.900	0.0977685
$392$	19964.5	2.57234
$393$	−14744.8	−1.89257
$394$	−1238.88	−0.158411
$395$	21704.2	2.76470
$396$	1034.28	0.131249
$397$	−11829.8	−1.49551	−0.747757	−	0.663972i	$-0.768869\pi$
$397$	−11829.8	−1.49551	−0.747757	+	0.663972i	$0.768869\pi$
$398$	1868.47	0.235322
$399$	−24348.9	−3.05506
$400$	−5658.02	−0.707253
$401$	−4012.72	−0.499715	−0.249857	−	0.968283i	$-0.580384\pi$
$401$	−4012.72	−0.499715	−0.249857	+	0.968283i	$0.580384\pi$
$402$	−6555.74	−0.813359
$403$	0	0
$404$	−2676.44	−0.329599
$405$	6068.35	0.744540
$406$	13236.0	1.61796
$407$	−1431.79	−0.174376
$408$	−23288.4	−2.82585
$409$	−4302.17	−0.520119	−0.260059	−	0.965593i	$-0.583742\pi$
$409$	−4302.17	−0.520119	−0.260059	+	0.965593i	$0.583742\pi$
$410$	2583.35	0.311177
$411$	21338.9	2.56100
$412$	2803.99	0.335297
$413$	13220.8	1.57519
$414$	−550.287	−0.0653264
$415$	−11779.4	−1.39332
$416$	0	0
$417$	7325.22	0.860234
$418$	−2303.43	−0.269532
$419$	−3649.39	−0.425499	−0.212750	−	0.977107i	$-0.568242\pi$
$419$	−3649.39	−0.425499	−0.212750	+	0.977107i	$0.568242\pi$
$420$	11526.9	1.33918
$421$	−783.113	−0.0906570	−0.0453285	−	0.998972i	$-0.514433\pi$
$421$	−783.113	−0.0906570	−0.0453285	+	0.998972i	$0.514433\pi$
$422$	−2102.77	−0.242562
$423$	−514.788	−0.0591722
$424$	1906.68	0.218389
$425$	18036.6	2.05859
$426$	2494.19	0.283671
$427$	30702.7	3.47965
$428$	−9.85991	−0.00111354
$429$	0	0
$430$	−12676.9	−1.42171
$431$	6275.21	0.701314	0.350657	−	0.936504i	$-0.385958\pi$
$431$	6275.21	0.701314	0.350657	+	0.936504i	$0.385958\pi$
$432$	2932.63	0.326612
$433$	5452.06	0.605102	0.302551	−	0.953133i	$-0.402162\pi$
$433$	5452.06	0.605102	0.302551	+	0.953133i	$0.402162\pi$
$434$	−15255.1	−1.68725
$435$	22222.9	2.44944
$436$	−534.414	−0.0587014
$437$	−573.095	−0.0627342
$438$	16428.9	1.79225
$439$	1742.10	0.189398	0.0946992	−	0.995506i	$-0.469811\pi$
$439$	1742.10	0.189398	0.0946992	+	0.995506i	$0.469811\pi$
$440$	4512.80	0.488953
$441$	29900.6	3.22866
$442$	0	0
$443$	−7066.08	−0.757832	−0.378916	−	0.925431i	$-0.623703\pi$
$443$	−7066.08	−0.757832	−0.378916	+	0.925431i	$0.623703\pi$
$444$	2651.95	0.283460
$445$	3240.05	0.345153
$446$	−8848.09	−0.939392
$447$	−11137.5	−1.17849
$448$	−18837.3	−1.98656
$449$	−6932.46	−0.728648	−0.364324	−	0.931272i	$-0.618700\pi$
$449$	−6932.46	−0.728648	−0.364324	+	0.931272i	$0.618700\pi$
$450$	−13130.4	−1.37550
$451$	−730.693	−0.0762904
$452$	−1997.00	−0.207812
$453$	5750.92	0.596472
$454$	−2761.37	−0.285457
$455$	0	0
$456$	17656.3	1.81323
$457$	−12606.2	−1.29036	−0.645180	−	0.764031i	$-0.723217\pi$
$457$	−12606.2	−1.29036	−0.645180	+	0.764031i	$0.723217\pi$
$458$	3389.56	0.345816
$459$	−9348.60	−0.950665
$460$	271.306	0.0274993
$461$	2360.49	0.238479	0.119240	−	0.992866i	$-0.461954\pi$
$461$	2360.49	0.238479	0.119240	+	0.992866i	$0.461954\pi$
$462$	6972.10	0.702103
$463$	7498.70	0.752687	0.376343	−	0.926480i	$-0.377181\pi$
$463$	7498.70	0.752687	0.376343	+	0.926480i	$0.377181\pi$
$464$	−6194.19	−0.619737
$465$	−25612.9	−2.55434
$466$	9534.91	0.947846
$467$	14579.5	1.44467	0.722334	−	0.691545i	$-0.243069\pi$
$467$	14579.5	1.44467	0.722334	+	0.691545i	$0.243069\pi$
$468$	0	0
$469$	11931.8	1.17476
$470$	−542.748	−0.0532662
$471$	13746.5	1.34481
$472$	−9586.95	−0.934905
$473$	3585.62	0.348556
$474$	−24315.4	−2.35621
$475$	−13674.6	−1.32092
$476$	10242.0	0.986224
$477$	2855.62	0.274109
$478$	3251.83	0.311162
$479$	14633.8	1.39590	0.697949	−	0.716148i	$-0.254096\pi$
$479$	14633.8	1.39590	0.697949	+	0.716148i	$0.254096\pi$
$480$	−14697.5	−1.39759
$481$	0	0
$482$	7148.38	0.675518
$483$	1734.66	0.163416
$484$	−308.432	−0.0289662
$485$	16603.1	1.55445
$486$	−11780.0	−1.09949
$487$	15934.4	1.48267	0.741333	−	0.671138i	$-0.234194\pi$
$487$	15934.4	1.48267	0.741333	+	0.671138i	$0.234194\pi$
$488$	−22263.7	−2.06523
$489$	27657.7	2.55772
$490$	31524.6	2.90640
$491$	−14411.9	−1.32464	−0.662321	−	0.749220i	$-0.730429\pi$
$491$	−14411.9	−1.32464	−0.662321	+	0.749220i	$0.730429\pi$
$492$	1353.39	0.124015
$493$	19745.8	1.80386
$494$	0	0
$495$	6758.78	0.613706
$496$	7139.09	0.646280
$497$	−4539.57	−0.409714
$498$	13196.6	1.18746
$499$	16419.2	1.47300	0.736499	−	0.676439i	$-0.236478\pi$
$499$	16419.2	1.47300	0.736499	+	0.676439i	$0.236478\pi$
$500$	1166.16	0.104305
$501$	522.227	0.0465696
$502$	11295.4	1.00426
$503$	−9108.31	−0.807394	−0.403697	−	0.914893i	$-0.632275\pi$
$503$	−9108.31	−0.807394	−0.403697	+	0.914893i	$0.632275\pi$
$504$	−30856.7	−2.72711
$505$	−17489.9	−1.54117
$506$	164.101	0.0144173
$507$	0	0
$508$	4508.29	0.393746
$509$	16302.0	1.41960	0.709799	−	0.704405i	$-0.248786\pi$
$509$	16302.0	1.41960	0.709799	+	0.704405i	$0.248786\pi$
$510$	−36773.1	−3.19283
$511$	−29901.6	−2.58859
$512$	11408.6	0.984752
$513$	7087.75	0.610004
$514$	19138.7	1.64235
$515$	18323.4	1.56782
$516$	−6641.27	−0.566600
$517$	153.515	0.0130591
$518$	10321.7	0.875501
$519$	−935.293	−0.0791037
$520$	0	0
$521$	−14948.9	−1.25705	−0.628526	−	0.777788i	$-0.716342\pi$
$521$	−14948.9	−1.25705	−0.628526	+	0.777788i	$0.716342\pi$
$522$	−14374.7	−1.20529
$523$	−15602.0	−1.30445	−0.652226	−	0.758025i	$-0.726165\pi$
$523$	−15602.0	−1.30445	−0.652226	+	0.758025i	$0.726165\pi$
$524$	−4702.28	−0.392023
$525$	41390.8	3.44085
$526$	13980.7	1.15891
$527$	−22757.9	−1.88112
$528$	−3262.82	−0.268932
$529$	−12126.2	−0.996644
$530$	3010.72	0.246750
$531$	−14358.3	−1.17344
$532$	−7765.11	−0.632820
$533$	0	0
$534$	−3629.86	−0.294156
$535$	−64.4323	−0.00520682
$536$	−8652.23	−0.697238
$537$	−37511.3	−3.01440
$538$	−9462.82	−0.758311
$539$	−8916.64	−0.712554
$540$	−3355.37	−0.267393
$541$	−11558.1	−0.918522	−0.459261	−	0.888301i	$-0.651886\pi$
$541$	−11558.1	−0.918522	−0.459261	+	0.888301i	$0.651886\pi$
$542$	−17559.0	−1.39156
$543$	−22501.9	−1.77836
$544$	−13059.2	−1.02924
$545$	−3492.27	−0.274482
$546$	0	0
$547$	−2596.22	−0.202937	−0.101469	−	0.994839i	$-0.532354\pi$
$547$	−2596.22	−0.202937	−0.101469	+	0.994839i	$0.532354\pi$
$548$	6805.19	0.530481
$549$	−33344.2	−2.59216
$550$	3915.62	0.303568
$551$	−14970.5	−1.15747
$552$	−1257.87	−0.0969900
$553$	44255.5	3.40314
$554$	−5658.70	−0.433962
$555$	17329.9	1.32543
$556$	2336.09	0.178187
$557$	−21976.8	−1.67179	−0.835896	−	0.548888i	$-0.815051\pi$
$557$	−21976.8	−1.67179	−0.835896	+	0.548888i	$0.815051\pi$
$558$	16567.5	1.25692
$559$	0	0
$560$	−20995.5	−1.58433
$561$	10401.2	0.782776
$562$	11221.4	0.842255
$563$	−16081.3	−1.20381	−0.601905	−	0.798568i	$-0.705591\pi$
$563$	−16081.3	−1.20381	−0.601905	+	0.798568i	$0.705591\pi$
$564$	−284.339	−0.0212284
$565$	−13050.0	−0.971710
$566$	9789.26	0.726985
$567$	12373.6	0.916474
$568$	3291.82	0.243172
$569$	−19988.2	−1.47267	−0.736334	−	0.676618i	$-0.763445\pi$
$569$	−19988.2	−1.47267	−0.736334	+	0.676618i	$0.763445\pi$
$570$	27880.0	2.04871
$571$	−10911.2	−0.799680	−0.399840	−	0.916585i	$-0.630934\pi$
$571$	−10911.2	−0.799680	−0.399840	+	0.916585i	$0.630934\pi$
$572$	0	0
$573$	20316.1	1.48119
$574$	5267.54	0.383036
$575$	974.207	0.0706560
$576$	20458.0	1.47989
$577$	−759.217	−0.0547775	−0.0273887	−	0.999625i	$-0.508719\pi$
$577$	−759.217	−0.0547775	−0.0273887	+	0.999625i	$0.508719\pi$
$578$	−21203.6	−1.52587
$579$	30969.9	2.22291
$580$	7087.10	0.507372
$581$	−24018.6	−1.71508
$582$	−18600.6	−1.32478
$583$	−851.573	−0.0604949
$584$	21682.8	1.53637
$585$	0	0
$586$	4561.01	0.321525
$587$	1064.70	0.0748638	0.0374319	−	0.999299i	$-0.488082\pi$
$587$	1064.70	0.0748638	0.0374319	+	0.999299i	$0.488082\pi$
$588$	16515.4	1.15830
$589$	17254.2	1.20704
$590$	−15138.1	−1.05632
$591$	−4241.28	−0.295200
$592$	−4830.37	−0.335350
$593$	−28060.5	−1.94318	−0.971590	−	0.236671i	$-0.923944\pi$
$593$	−28060.5	−1.94318	−0.971590	+	0.236671i	$0.923944\pi$
$594$	−2029.52	−0.140189
$595$	66929.3	4.61148
$596$	−3551.87	−0.244111
$597$	6396.70	0.438525
$598$	0	0
$599$	11394.4	0.777234	0.388617	−	0.921399i	$-0.372953\pi$
$599$	11394.4	0.777234	0.388617	+	0.921399i	$0.372953\pi$
$600$	−30014.1	−2.04220
$601$	−9542.88	−0.647691	−0.323845	−	0.946110i	$-0.604976\pi$
$601$	−9542.88	−0.647691	−0.323845	+	0.946110i	$0.604976\pi$
$602$	−25848.6	−1.75002
$603$	−12958.4	−0.875133
$604$	1834.03	0.123552
$605$	−2015.53	−0.135443
$606$	19594.2	1.31346
$607$	−13703.0	−0.916291	−0.458145	−	0.888877i	$-0.651486\pi$
$607$	−13703.0	−0.916291	−0.458145	+	0.888877i	$0.651486\pi$
$608$	9900.97	0.660423
$609$	45313.2	3.01508
$610$	−35155.2	−2.33343
$611$	0	0
$612$	−11123.2	−0.734686
$613$	−24266.5	−1.59888	−0.799442	−	0.600743i	$-0.794872\pi$
$613$	−24266.5	−1.59888	−0.799442	+	0.600743i	$0.794872\pi$
$614$	4115.37	0.270493
$615$	8844.07	0.579882
$616$	9201.75	0.601865
$617$	−20960.2	−1.36763	−0.683815	−	0.729656i	$-0.739680\pi$
$617$	−20960.2	−1.36763	−0.683815	+	0.729656i	$0.739680\pi$
$618$	−20527.9	−1.33617
$619$	−3102.31	−0.201442	−0.100721	−	0.994915i	$-0.532115\pi$
$619$	−3102.31	−0.201442	−0.100721	+	0.994915i	$0.532115\pi$
$620$	−8168.21	−0.529102
$621$	−504.944	−0.0326292
$622$	−19189.7	−1.23704
$623$	6606.56	0.424857
$624$	0	0
$625$	−11437.5	−0.732002
$626$	5440.52	0.347360
$627$	−7885.77	−0.502276
$628$	4383.89	0.278561
$629$	15398.2	0.976099
$630$	−48723.8	−3.08127
$631$	6711.28	0.423411	0.211705	−	0.977334i	$-0.432098\pi$
$631$	6711.28	0.423411	0.211705	+	0.977334i	$0.432098\pi$
$632$	−32091.4	−2.01982
$633$	−7198.80	−0.452017
$634$	−7375.15	−0.461995
$635$	29460.6	1.84112
$636$	1577.28	0.0983384
$637$	0	0
$638$	4286.67	0.266005
$639$	4930.13	0.305216
$640$	6858.68	0.423614
$641$	11620.5	0.716043	0.358022	−	0.933713i	$-0.383451\pi$
$641$	11620.5	0.716043	0.358022	+	0.933713i	$0.383451\pi$
$642$	72.1842	0.00443751
$643$	6215.83	0.381226	0.190613	−	0.981665i	$-0.438952\pi$
$643$	6215.83	0.381226	0.190613	+	0.981665i	$0.438952\pi$
$644$	553.201	0.0338496
$645$	−43399.1	−2.64936
$646$	24772.3	1.50875
$647$	19476.7	1.18348	0.591738	−	0.806130i	$-0.298442\pi$
$647$	19476.7	1.18348	0.591738	+	0.806130i	$0.298442\pi$
$648$	−8972.55	−0.543943
$649$	4281.77	0.258974
$650$	0	0
$651$	−52225.5	−3.14421
$652$	8820.31	0.529801
$653$	2150.39	0.128869	0.0644343	−	0.997922i	$-0.479476\pi$
$653$	2150.39	0.128869	0.0644343	+	0.997922i	$0.479476\pi$
$654$	3912.43	0.233927
$655$	−30728.3	−1.83306
$656$	−2465.11	−0.146717
$657$	32474.2	1.92837
$658$	−1106.68	−0.0655667
$659$	−665.476	−0.0393373	−0.0196686	−	0.999807i	$-0.506261\pi$
$659$	−665.476	−0.0393373	−0.0196686	+	0.999807i	$0.506261\pi$
$660$	3733.16	0.220171
$661$	−4090.73	−0.240712	−0.120356	−	0.992731i	$-0.538404\pi$
$661$	−4090.73	−0.240712	−0.120356	+	0.992731i	$0.538404\pi$
$662$	6831.16	0.401058
$663$	0	0
$664$	17416.9	1.01793
$665$	−50743.2	−2.95900
$666$	−11209.7	−0.652204
$667$	1066.52	0.0619131
$668$	166.543	0.00964635
$669$	−30291.3	−1.75057
$670$	−13662.2	−0.787785
$671$	9943.55	0.572081
$672$	−29968.6	−1.72033
$673$	−25365.5	−1.45285	−0.726425	−	0.687246i	$-0.758819\pi$
$673$	−25365.5	−1.45285	−0.726425	+	0.687246i	$0.758819\pi$
$674$	21541.1	1.23105
$675$	−12048.5	−0.687033
$676$	0	0
$677$	−14299.1	−0.811757	−0.405879	−	0.913927i	$-0.633034\pi$
$677$	−14299.1	−0.811757	−0.405879	+	0.913927i	$0.633034\pi$
$678$	14620.0	0.828139
$679$	33854.2	1.91341
$680$	−48533.0	−2.73699
$681$	−9453.51	−0.531952
$682$	−4940.59	−0.277397
$683$	−11034.7	−0.618198	−0.309099	−	0.951030i	$-0.600028\pi$
$683$	−11034.7	−0.618198	−0.309099	+	0.951030i	$0.600028\pi$
$684$	8433.17	0.471419
$685$	44470.4	2.48047
$686$	37080.3	2.06375
$687$	11604.1	0.644432
$688$	12096.7	0.670321
$689$	0	0
$690$	−1986.22	−0.109586
$691$	−864.722	−0.0476057	−0.0238029	−	0.999717i	$-0.507577\pi$
$691$	−864.722	−0.0476057	−0.0238029	+	0.999717i	$0.507577\pi$
$692$	−298.275	−0.0163854
$693$	13781.4	0.755427
$694$	−17642.5	−0.964986
$695$	15265.8	0.833186
$696$	−32858.3	−1.78950
$697$	7858.25	0.427048
$698$	−6521.59	−0.353647
$699$	32642.6	1.76632
$700$	13200.0	0.712731
$701$	−6806.47	−0.366729	−0.183364	−	0.983045i	$-0.558699\pi$
$701$	−6806.47	−0.366729	−0.183364	+	0.983045i	$0.558699\pi$
$702$	0	0
$703$	−11674.3	−0.626323
$704$	−6100.76	−0.326607
$705$	−1858.09	−0.0992620
$706$	9311.97	0.496403
$707$	−35662.6	−1.89707
$708$	−7930.69	−0.420979
$709$	−11850.2	−0.627706	−0.313853	−	0.949472i	$-0.601620\pi$
$709$	−11850.2	−0.627706	−0.313853	+	0.949472i	$0.601620\pi$
$710$	5197.90	0.274752
$711$	−48062.9	−2.53516
$712$	−4790.67	−0.252160
$713$	−1229.22	−0.0645647
$714$	−74981.6	−3.93013
$715$	0	0
$716$	−11962.7	−0.624398
$717$	11132.6	0.579853
$718$	9743.67	0.506449
$719$	−9796.79	−0.508148	−0.254074	−	0.967185i	$-0.581771\pi$
$719$	−9796.79	−0.508148	−0.254074	+	0.967185i	$0.581771\pi$
$720$	22801.8	1.18024
$721$	37362.0	1.92987
$722$	−2767.49	−0.142653
$723$	24472.4	1.25884
$724$	−7176.08	−0.368366
$725$	25448.4	1.30363
$726$	2258.02	0.115431
$727$	−8924.55	−0.455286	−0.227643	−	0.973745i	$-0.573102\pi$
$727$	−8924.55	−0.455286	−0.227643	+	0.973745i	$0.573102\pi$
$728$	0	0
$729$	−30492.3	−1.54917
$730$	34238.0	1.73590
$731$	−38561.6	−1.95110
$732$	−18417.4	−0.929954
$733$	−26304.6	−1.32549	−0.662743	−	0.748847i	$-0.730608\pi$
$733$	−26304.6	−1.32549	−0.662743	+	0.748847i	$0.730608\pi$
$734$	−1699.75	−0.0854753
$735$	107924.	5.41611
$736$	−705.363	−0.0353261
$737$	3864.31	0.193139
$738$	−5720.72	−0.285342
$739$	1004.49	0.0500012	0.0250006	−	0.999687i	$-0.492041\pi$
$739$	1004.49	0.0500012	0.0250006	+	0.999687i	$0.492041\pi$
$740$	5526.68	0.274547
$741$	0	0
$742$	6138.96	0.303731
$743$	−2938.23	−0.145078	−0.0725392	−	0.997366i	$-0.523110\pi$
$743$	−2938.23	−0.145078	−0.0725392	+	0.997366i	$0.523110\pi$
$744$	37870.8	1.86614
$745$	−23210.6	−1.14144
$746$	−19664.9	−0.965124
$747$	26085.0	1.27765
$748$	3317.04	0.162143
$749$	−131.379	−0.00640921
$750$	−8537.45	−0.415658
$751$	35111.1	1.70602	0.853012	−	0.521892i	$-0.174773\pi$
$751$	35111.1	1.70602	0.853012	+	0.521892i	$0.174773\pi$
$752$	517.906	0.0251145
$753$	38669.7	1.87145
$754$	0	0
$755$	11984.9	0.577717
$756$	−6841.72	−0.329141
$757$	−9727.34	−0.467036	−0.233518	−	0.972353i	$-0.575024\pi$
$757$	−9727.34	−0.467036	−0.233518	+	0.972353i	$0.575024\pi$
$758$	24705.8	1.18385
$759$	561.796	0.0268668
$760$	36795.9	1.75622
$761$	−13995.5	−0.666671	−0.333335	−	0.942808i	$-0.608174\pi$
$761$	−13995.5	−0.666671	−0.333335	+	0.942808i	$0.608174\pi$
$762$	−33005.1	−1.56909
$763$	−7120.86	−0.337867
$764$	6479.03	0.306810
$765$	−72687.4	−3.43532
$766$	784.478	0.0370031
$767$	0	0
$768$	27780.1	1.30524
$769$	32698.3	1.53333	0.766665	−	0.642047i	$-0.221915\pi$
$769$	32698.3	1.53333	0.766665	+	0.642047i	$0.221915\pi$
$770$	14529.9	0.680027
$771$	65520.9	3.06054
$772$	9876.61	0.460449
$773$	36743.4	1.70966	0.854831	−	0.518906i	$-0.173661\pi$
$773$	36743.4	1.70966	0.854831	+	0.518906i	$0.173661\pi$
$774$	28072.4	1.30367
$775$	−29330.5	−1.35946
$776$	−24549.0	−1.13564
$777$	35336.2	1.63151
$778$	2568.16	0.118346
$779$	−5957.83	−0.274020
$780$	0	0
$781$	−1470.21	−0.0673601
$782$	−1764.82	−0.0807033
$783$	−13190.3	−0.602020
$784$	−30081.7	−1.37034
$785$	28647.7	1.30252
$786$	34425.3	1.56222
$787$	−9130.90	−0.413572	−0.206786	−	0.978386i	$-0.566300\pi$
$787$	−9130.90	−0.413572	−0.206786	+	0.978386i	$0.566300\pi$
$788$	−1352.59	−0.0611472
$789$	47862.7	2.15964
$790$	−50673.4	−2.28212
$791$	−26609.3	−1.19610
$792$	−9993.40	−0.448359
$793$	0	0
$794$	27619.4	1.23448
$795$	10307.2	0.459821
$796$	2039.97	0.0908352
$797$	5541.55	0.246288	0.123144	−	0.992389i	$-0.460702\pi$
$797$	5541.55	0.246288	0.123144	+	0.992389i	$0.460702\pi$
$798$	56848.2	2.52181
$799$	−1650.98	−0.0731005
$800$	−16830.7	−0.743820
$801$	−7174.94	−0.316497
$802$	9368.62	0.412491
$803$	−9684.10	−0.425585
$804$	−7157.45	−0.313960
$805$	3615.04	0.158278
$806$	0	0
$807$	−32395.8	−1.41312
$808$	25860.3	1.12594
$809$	−22225.5	−0.965892	−0.482946	−	0.875650i	$-0.660433\pi$
$809$	−22225.5	−0.965892	−0.482946	+	0.875650i	$0.660433\pi$
$810$	−14168.0	−0.614582
$811$	32142.3	1.39170	0.695850	−	0.718187i	$-0.255028\pi$
$811$	32142.3	1.39170	0.695850	+	0.718187i	$0.255028\pi$
$812$	14450.8	0.624537
$813$	−60113.0	−2.59318
$814$	3342.84	0.143939
$815$	57638.7	2.47729
$816$	35090.0	1.50539
$817$	29235.9	1.25194
$818$	10044.4	0.429333
$819$	0	0
$820$	2820.46	0.120116
$821$	17467.5	0.742535	0.371268	−	0.928526i	$-0.378923\pi$
$821$	17467.5	0.742535	0.371268	+	0.928526i	$0.378923\pi$
$822$	−49820.6	−2.11398
$823$	11310.6	0.479056	0.239528	−	0.970889i	$-0.423007\pi$
$823$	11310.6	0.479056	0.239528	+	0.970889i	$0.423007\pi$
$824$	−27092.6	−1.14541
$825$	13405.1	0.565702
$826$	−30867.1	−1.30025
$827$	−16756.0	−0.704550	−0.352275	−	0.935897i	$-0.614592\pi$
$827$	−16756.0	−0.704550	−0.352275	+	0.935897i	$0.614592\pi$
$828$	−600.795	−0.0252162
$829$	12118.1	0.507694	0.253847	−	0.967244i	$-0.418304\pi$
$829$	12118.1	0.507694	0.253847	+	0.967244i	$0.418304\pi$
$830$	27501.8	1.15012
$831$	−19372.5	−0.808692
$832$	0	0
$833$	95894.1	3.98864
$834$	−17102.4	−0.710082
$835$	1088.32	0.0451053
$836$	−2514.85	−0.104041
$837$	15202.4	0.627803
$838$	8520.35	0.351230
$839$	−940.224	−0.0386891	−0.0193445	−	0.999813i	$-0.506158\pi$
$839$	−940.224	−0.0386891	−0.0193445	+	0.999813i	$0.506158\pi$
$840$	−111375.	−4.57476
$841$	3470.97	0.142317
$842$	1828.36	0.0748331
$843$	38416.4	1.56955
$844$	−2295.77	−0.0936300
$845$	0	0
$846$	1201.89	0.0488439
$847$	−4109.73	−0.166720
$848$	−2872.92	−0.116340
$849$	33513.4	1.35474
$850$	−42110.6	−1.69927
$851$	831.700	0.0335021
$852$	2723.12	0.109498
$853$	−4658.69	−0.186999	−0.0934997	−	0.995619i	$-0.529805\pi$
$853$	−4658.69	−0.186999	−0.0934997	+	0.995619i	$0.529805\pi$
$854$	−71682.6	−2.87228
$855$	55108.8	2.20431
$856$	95.2683	0.00380398
$857$	14666.2	0.584583	0.292292	−	0.956329i	$-0.405582\pi$
$857$	14666.2	0.584583	0.292292	+	0.956329i	$0.405582\pi$
$858$	0	0
$859$	−22796.4	−0.905475	−0.452737	−	0.891644i	$-0.649553\pi$
$859$	−22796.4	−0.905475	−0.452737	+	0.891644i	$0.649553\pi$
$860$	−13840.4	−0.548784
$861$	18033.3	0.713792
$862$	−14650.9	−0.578902
$863$	579.744	0.0228676	0.0114338	−	0.999935i	$-0.496360\pi$
$863$	579.744	0.0228676	0.0114338	+	0.999935i	$0.496360\pi$
$864$	8723.59	0.343498
$865$	−1949.15	−0.0766165
$866$	−12729.1	−0.499483
$867$	−72590.3	−2.84348
$868$	−16655.2	−0.651286
$869$	14332.8	0.559502
$870$	−51884.5	−2.02189
$871$	0	0
$872$	5163.61	0.200530
$873$	−36766.8	−1.42539
$874$	1338.02	0.0517841
$875$	15538.7	0.600346
$876$	17936.8	0.691815
$877$	−12584.6	−0.484553	−0.242276	−	0.970207i	$-0.577894\pi$
$877$	−12584.6	−0.484553	−0.242276	+	0.970207i	$0.577894\pi$
$878$	−4067.34	−0.156339
$879$	15614.6	0.599165
$880$	−6799.72	−0.260476
$881$	−3542.99	−0.135490	−0.0677448	−	0.997703i	$-0.521580\pi$
$881$	−3542.99	−0.135490	−0.0677448	+	0.997703i	$0.521580\pi$
$882$	−69809.9	−2.66510
$883$	−24693.4	−0.941109	−0.470555	−	0.882371i	$-0.655946\pi$
$883$	−24693.4	−0.941109	−0.470555	+	0.882371i	$0.655946\pi$
$884$	0	0
$885$	−51825.2	−1.96846
$886$	16497.4	0.625554
$887$	17233.5	0.652362	0.326181	−	0.945307i	$-0.394238\pi$
$887$	17233.5	0.652362	0.326181	+	0.945307i	$0.394238\pi$
$888$	−25623.7	−0.968326
$889$	60071.2	2.26628
$890$	−7564.64	−0.284907
$891$	4007.37	0.150675
$892$	−9660.20	−0.362609
$893$	1251.71	0.0469057
$894$	26003.1	0.972791
$895$	−78173.8	−2.91962
$896$	13985.1	0.521438
$897$	0	0
$898$	16185.4	0.601464
$899$	−32109.9	−1.19124
$900$	−14335.6	−0.530948
$901$	9158.26	0.338630
$902$	1705.97	0.0629741
$903$	−88492.3	−3.26117
$904$	19295.4	0.709908
$905$	−46894.0	−1.72244
$906$	−13426.9	−0.492359
$907$	11534.6	0.422273	0.211136	−	0.977457i	$-0.432284\pi$
$907$	11534.6	0.422273	0.211136	+	0.977457i	$0.432284\pi$
$908$	−3014.82	−0.110188
$909$	38730.7	1.41322
$910$	0	0
$911$	−2770.16	−0.100746	−0.0503730	−	0.998730i	$-0.516041\pi$
$911$	−2770.16	−0.100746	−0.0503730	+	0.998730i	$0.516041\pi$
$912$	−26603.9	−0.965947
$913$	−7778.81	−0.281973
$914$	29432.2	1.06513
$915$	−120353.	−4.34837
$916$	3700.67	0.133486
$917$	−62656.0	−2.25636
$918$	21826.5	0.784729
$919$	−25610.8	−0.919286	−0.459643	−	0.888104i	$-0.652023\pi$
$919$	−25610.8	−0.919286	−0.459643	+	0.888104i	$0.652023\pi$
$920$	−2621.41	−0.0939404
$921$	14088.9	0.504066
$922$	−5511.11	−0.196853
$923$	0	0
$924$	7612.03	0.271015
$925$	19845.2	0.705414
$926$	−17507.4	−0.621307
$927$	−40576.4	−1.43765
$928$	−18425.6	−0.651779
$929$	−9529.34	−0.336542	−0.168271	−	0.985741i	$-0.553818\pi$
$929$	−9529.34	−0.336542	−0.168271	+	0.985741i	$0.553818\pi$
$930$	59799.3	2.10849
$931$	−72703.3	−2.55935
$932$	10410.1	0.365872
$933$	−65695.8	−2.30524
$934$	−34039.3	−1.19250
$935$	21676.1	0.758164
$936$	0	0
$937$	18771.0	0.654452	0.327226	−	0.944946i	$-0.393886\pi$
$937$	18771.0	0.654452	0.327226	+	0.944946i	$0.393886\pi$
$938$	−27857.6	−0.969705
$939$	18625.6	0.647308
$940$	−592.564	−0.0205610
$941$	−39655.2	−1.37378	−0.686888	−	0.726763i	$-0.741024\pi$
$941$	−39655.2	−1.37378	−0.686888	+	0.726763i	$0.741024\pi$
$942$	−32094.3	−1.11007
$943$	424.446	0.0146573
$944$	14445.3	0.498044
$945$	−44709.0	−1.53903
$946$	−8371.46	−0.287716
$947$	−14491.1	−0.497252	−0.248626	−	0.968600i	$-0.579979\pi$
$947$	−14491.1	−0.497252	−0.248626	+	0.968600i	$0.579979\pi$
$948$	−26547.2	−0.909507
$949$	0	0
$950$	31926.6	1.09035
$951$	−25248.7	−0.860931
$952$	−98960.4	−3.36904
$953$	49118.5	1.66958	0.834788	−	0.550572i	$-0.185590\pi$
$953$	49118.5	1.66958	0.834788	+	0.550572i	$0.185590\pi$
$954$	−6667.11	−0.226264
$955$	42338.9	1.43461
$956$	3550.30	0.120110
$957$	14675.4	0.495702
$958$	−34166.0	−1.15225
$959$	90676.5	3.05328
$960$	73841.6	2.48253
$961$	7217.18	0.242260
$962$	0	0
$963$	142.682	0.00477454
$964$	7804.49	0.260753
$965$	64541.4	2.15302
$966$	−4049.97	−0.134892
$967$	19980.1	0.664445	0.332222	−	0.943201i	$-0.392202\pi$
$967$	19980.1	0.664445	0.332222	+	0.943201i	$0.392202\pi$
$968$	2980.13	0.0989514
$969$	84807.6	2.81157
$970$	−38763.8	−1.28312
$971$	43625.8	1.44183	0.720916	−	0.693022i	$-0.243721\pi$
$971$	43625.8	1.44183	0.720916	+	0.693022i	$0.243721\pi$
$972$	−12861.2	−0.424406
$973$	31127.4	1.02559
$974$	−37202.6	−1.22387
$975$	0	0
$976$	33546.2	1.10019
$977$	−22922.5	−0.750619	−0.375309	−	0.926900i	$-0.622464\pi$
$977$	−22922.5	−0.750619	−0.375309	+	0.926900i	$0.622464\pi$
$978$	−64573.3	−2.11127
$979$	2139.64	0.0698499
$980$	34418.1	1.12188
$981$	7733.49	0.251693
$982$	33647.9	1.09343
$983$	−54348.7	−1.76343	−0.881717	−	0.471779i	$-0.843612\pi$
$983$	−54348.7	−1.76343	−0.881717	+	0.471779i	$0.843612\pi$
$984$	−13076.7	−0.423648
$985$	−8838.85	−0.285918
$986$	−46101.1	−1.48900
$987$	−3788.71	−0.122184
$988$	0	0
$989$	−2082.82	−0.0669665
$990$	−15779.9	−0.506585
$991$	−34811.4	−1.11586	−0.557931	−	0.829887i	$-0.688405\pi$
$991$	−34811.4	−1.11586	−0.557931	+	0.829887i	$0.688405\pi$
$992$	21236.4	0.679694
$993$	23386.4	0.747376
$994$	10598.7	0.338199
$995$	13330.7	0.424736
$996$	14407.9	0.458364
$997$	3710.76	0.117875	0.0589374	−	0.998262i	$-0.481229\pi$
$997$	3710.76	0.117875	0.0589374	+	0.998262i	$0.481229\pi$
$998$	−38334.5	−1.21589
$999$	−10286.1	−0.325762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.p.1.18	✓	51
13.12	even	2		1859.4.a.q.1.34	yes	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.18	✓	51	1.1	even	1	trivial
1859.4.a.q.1.34	yes	51	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)

\(f(q)\)	\(=\)	\(q-2.33473 q^{2} -7.99292 q^{3} -2.54902 q^{4} -16.6573 q^{5} +18.6613 q^{6} -33.9647 q^{7} +24.6291 q^{8} +36.8868 q^{9} +O(q^{10})\)	\(q-2.33473 q^{2} -7.99292 q^{3} -2.54902 q^{4} -16.6573 q^{5} +18.6613 q^{6} -33.9647 q^{7} +24.6291 q^{8} +36.8868 q^{9} +38.8903 q^{10} -11.0000 q^{11} +20.3742 q^{12} +79.2986 q^{14} +133.140 q^{15} -37.1103 q^{16} +118.300 q^{17} -86.1209 q^{18} -89.6903 q^{19} +42.4598 q^{20} +271.478 q^{21} +25.6821 q^{22} +6.38970 q^{23} -196.859 q^{24} +152.465 q^{25} -79.0247 q^{27} +86.5769 q^{28} +166.913 q^{29} -310.847 q^{30} -192.375 q^{31} -110.391 q^{32} +87.9222 q^{33} -276.198 q^{34} +565.760 q^{35} -94.0254 q^{36} +130.163 q^{37} +209.403 q^{38} -410.255 q^{40} +66.4266 q^{41} -633.827 q^{42} -325.965 q^{43} +28.0393 q^{44} -614.434 q^{45} -14.9182 q^{46} -13.9559 q^{47} +296.620 q^{48} +810.603 q^{49} -355.965 q^{50} -945.561 q^{51} +77.4157 q^{53} +184.502 q^{54} +183.230 q^{55} -836.523 q^{56} +716.888 q^{57} -389.697 q^{58} -389.252 q^{59} -339.378 q^{60} -903.959 q^{61} +449.144 q^{62} -1252.85 q^{63} +554.615 q^{64} -205.275 q^{66} -351.300 q^{67} -301.549 q^{68} -51.0724 q^{69} -1320.90 q^{70} +133.656 q^{71} +908.491 q^{72} +880.373 q^{73} -303.895 q^{74} -1218.64 q^{75} +228.623 q^{76} +373.612 q^{77} -1302.98 q^{79} +618.156 q^{80} -364.306 q^{81} -155.088 q^{82} +707.164 q^{83} -692.003 q^{84} -1970.55 q^{85} +761.042 q^{86} -1334.12 q^{87} -270.921 q^{88} -194.512 q^{89} +1434.54 q^{90} -16.2875 q^{92} +1537.64 q^{93} +32.5832 q^{94} +1494.00 q^{95} +882.344 q^{96} -996.747 q^{97} -1892.54 q^{98} -405.755 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more