LMFDB - Embedded newform 1859.4.a.q.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)

$f(q)$	$=$	$q-1.90937 q^{2} -0.199217 q^{3} -4.35431 q^{4} -18.1265 q^{5} +0.380379 q^{6} +33.8392 q^{7} +23.5889 q^{8} -26.9603 q^{9} +O(q^{10})$	\(q-1.90937 q^{2} -0.199217 q^{3} -4.35431 q^{4} -18.1265 q^{5} +0.380379 q^{6} +33.8392 q^{7} +23.5889 q^{8} -26.9603 q^{9} +34.6102 q^{10} +11.0000 q^{11} +0.867454 q^{12} -64.6116 q^{14} +3.61112 q^{15} -10.2055 q^{16} -10.0908 q^{17} +51.4772 q^{18} +8.33963 q^{19} +78.9285 q^{20} -6.74135 q^{21} -21.0031 q^{22} +20.4759 q^{23} -4.69932 q^{24} +203.571 q^{25} +10.7498 q^{27} -147.346 q^{28} +58.9818 q^{29} -6.89495 q^{30} +227.933 q^{31} -169.225 q^{32} -2.19139 q^{33} +19.2671 q^{34} -613.387 q^{35} +117.394 q^{36} +346.805 q^{37} -15.9234 q^{38} -427.585 q^{40} -273.173 q^{41} +12.8717 q^{42} -170.736 q^{43} -47.8974 q^{44} +488.697 q^{45} -39.0961 q^{46} -39.2213 q^{47} +2.03311 q^{48} +802.093 q^{49} -388.692 q^{50} +2.01027 q^{51} -506.883 q^{53} -20.5254 q^{54} -199.392 q^{55} +798.231 q^{56} -1.66140 q^{57} -112.618 q^{58} -65.6789 q^{59} -15.7239 q^{60} +572.018 q^{61} -435.209 q^{62} -912.316 q^{63} +404.758 q^{64} +4.18417 q^{66} -862.007 q^{67} +43.9386 q^{68} -4.07916 q^{69} +1171.18 q^{70} -325.372 q^{71} -635.965 q^{72} -467.819 q^{73} -662.178 q^{74} -40.5548 q^{75} -36.3133 q^{76} +372.231 q^{77} +752.948 q^{79} +184.990 q^{80} +725.787 q^{81} +521.589 q^{82} +113.590 q^{83} +29.3539 q^{84} +182.912 q^{85} +325.998 q^{86} -11.7502 q^{87} +259.478 q^{88} -1055.72 q^{89} -933.102 q^{90} -89.1586 q^{92} -45.4082 q^{93} +74.8880 q^{94} -151.168 q^{95} +33.7126 q^{96} +145.215 q^{97} -1531.49 q^{98} -296.563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.90937	−0.675064	−0.337532	−	0.941314i	$-0.609592\pi$
$2$	−1.90937	−0.675064	−0.337532	+	0.941314i	$0.609592\pi$
$3$	−0.199217	−0.0383394	−0.0191697	−	0.999816i	$-0.506102\pi$
$3$	−0.199217	−0.0383394	−0.0191697	+	0.999816i	$0.506102\pi$
$4$	−4.35431	−0.544289
$5$	−18.1265	−1.62129	−0.810643	−	0.585541i	$-0.800882\pi$
$5$	−18.1265	−1.62129	−0.810643	+	0.585541i	$0.800882\pi$
$6$	0.380379	0.0258815
$7$	33.8392	1.82715	0.913573	−	0.406675i	$-0.133312\pi$
$7$	33.8392	1.82715	0.913573	+	0.406675i	$0.133312\pi$
$8$	23.5889	1.04249
$9$	−26.9603	−0.998530
$10$	34.6102	1.09447
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	0.867454	0.0208677
$13$	0	0
$13$	0	0
$14$	−64.6116	−1.23344
$15$	3.61112	0.0621591
$16$	−10.2055	−0.159461
$17$	−10.0908	−0.143964	−0.0719819	−	0.997406i	$-0.522932\pi$
$17$	−10.0908	−0.143964	−0.0719819	+	0.997406i	$0.522932\pi$
$18$	51.4772	0.674072
$19$	8.33963	0.100697	0.0503485	−	0.998732i	$-0.483967\pi$
$19$	8.33963	0.100697	0.0503485	+	0.998732i	$0.483967\pi$
$20$	78.9285	0.882448
$21$	−6.74135	−0.0700516
$22$	−21.0031	−0.203539
$23$	20.4759	0.185632	0.0928158	−	0.995683i	$-0.470413\pi$
$23$	20.4759	0.185632	0.0928158	+	0.995683i	$0.470413\pi$
$24$	−4.69932	−0.0399685
$25$	203.571	1.62857
$26$	0	0
$27$	10.7498	0.0766224
$28$	−147.346	−0.994495
$29$	58.9818	0.377678	0.188839	−	0.982008i	$-0.439528\pi$
$29$	58.9818	0.377678	0.188839	+	0.982008i	$0.439528\pi$
$30$	−6.89495	−0.0419613
$31$	227.933	1.32058	0.660290	−	0.751010i	$-0.270433\pi$
$31$	227.933	1.32058	0.660290	+	0.751010i	$0.270433\pi$
$32$	−169.225	−0.934847
$33$	−2.19139	−0.0115598
$34$	19.2671	0.0971848
$35$	−613.387	−2.96233
$36$	117.394	0.543489
$37$	346.805	1.54093	0.770464	−	0.637483i	$-0.220025\pi$
$37$	346.805	1.54093	0.770464	+	0.637483i	$0.220025\pi$
$38$	−15.9234	−0.0679769
$39$	0	0
$40$	−427.585	−1.69018
$41$	−273.173	−1.04055	−0.520274	−	0.853999i	$-0.674170\pi$
$41$	−273.173	−1.04055	−0.520274	+	0.853999i	$0.674170\pi$
$42$	12.8717	0.0472893
$43$	−170.736	−0.605512	−0.302756	−	0.953068i	$-0.597907\pi$
$43$	−170.736	−0.605512	−0.302756	+	0.953068i	$0.597907\pi$
$44$	−47.8974	−0.164109
$45$	488.697	1.61890
$46$	−39.0961	−0.125313
$47$	−39.2213	−0.121724	−0.0608619	−	0.998146i	$-0.519385\pi$
$47$	−39.2213	−0.121724	−0.0608619	+	0.998146i	$0.519385\pi$
$48$	2.03311	0.00611363
$49$	802.093	2.33846
$50$	−388.692	−1.09939
$51$	2.01027	0.00551948
$52$	0	0
$53$	−506.883	−1.31369	−0.656847	−	0.754024i	$-0.728110\pi$
$53$	−506.883	−1.31369	−0.656847	+	0.754024i	$0.728110\pi$
$54$	−20.5254	−0.0517250
$55$	−199.392	−0.488836
$56$	798.231	1.90479
$57$	−1.66140	−0.00386066
$58$	−112.618	−0.254956
$59$	−65.6789	−0.144926	−0.0724632	−	0.997371i	$-0.523086\pi$
$59$	−65.6789	−0.144926	−0.0724632	+	0.997371i	$0.523086\pi$
$60$	−15.7239	−0.0338325
$61$	572.018	1.20064	0.600322	−	0.799758i	$-0.295039\pi$
$61$	572.018	1.20064	0.600322	+	0.799758i	$0.295039\pi$
$62$	−435.209	−0.891476
$63$	−912.316	−1.82446
$64$	404.758	0.790543
$65$	0	0
$66$	4.18417	0.00780357
$67$	−862.007	−1.57181	−0.785903	−	0.618350i	$-0.787801\pi$
$67$	−862.007	−1.57181	−0.785903	+	0.618350i	$0.787801\pi$
$68$	43.9386	0.0783579
$69$	−4.07916	−0.00711700
$70$	1171.18	1.99976
$71$	−325.372	−0.543866	−0.271933	−	0.962316i	$-0.587663\pi$
$71$	−325.372	−0.543866	−0.271933	+	0.962316i	$0.587663\pi$
$72$	−635.965	−1.04096
$73$	−467.819	−0.750056	−0.375028	−	0.927013i	$-0.622367\pi$
$73$	−467.819	−0.750056	−0.375028	+	0.927013i	$0.622367\pi$
$74$	−662.178	−1.04023
$75$	−40.5548	−0.0624382
$76$	−36.3133	−0.0548082
$77$	372.231	0.550905
$78$	0	0
$79$	752.948	1.07232	0.536160	−	0.844117i	$-0.319874\pi$
$79$	752.948	1.07232	0.536160	+	0.844117i	$0.319874\pi$
$80$	184.990	0.258532
$81$	725.787	0.995592
$82$	521.589	0.702437
$83$	113.590	0.150218	0.0751089	−	0.997175i	$-0.476070\pi$
$83$	113.590	0.150218	0.0751089	+	0.997175i	$0.476070\pi$
$84$	29.3539	0.0381283
$85$	182.912	0.233407
$86$	325.998	0.408759
$87$	−11.7502	−0.0144799
$88$	259.478	0.314324
$89$	−1055.72	−1.25738	−0.628688	−	0.777658i	$-0.716408\pi$
$89$	−1055.72	−1.25738	−0.628688	+	0.777658i	$0.716408\pi$
$90$	−933.102	−1.09286
$91$	0	0
$92$	−89.1586	−0.101037
$93$	−45.4082	−0.0506302
$94$	74.8880	0.0821713
$95$	−151.168	−0.163258
$96$	33.7126	0.0358415
$97$	145.215	0.152004	0.0760018	−	0.997108i	$-0.475785\pi$
$97$	145.215	0.152004	0.0760018	+	0.997108i	$0.475785\pi$
$98$	−1531.49	−1.57861
$99$	−296.563	−0.301068
$100$	−886.411	−0.886411
$101$	−717.670	−0.707038	−0.353519	−	0.935427i	$-0.615015\pi$
$101$	−717.670	−0.707038	−0.353519	+	0.935427i	$0.615015\pi$
$102$	−3.83834	−0.00372600
$103$	−1844.72	−1.76472	−0.882358	−	0.470579i	$-0.844045\pi$
$103$	−1844.72	−1.76472	−0.882358	+	0.470579i	$0.844045\pi$
$104$	0	0
$105$	122.197	0.113574
$106$	967.827	0.886827
$107$	−2174.19	−1.96437	−0.982183	−	0.187926i	$-0.939823\pi$
$107$	−2174.19	−1.96437	−0.982183	+	0.187926i	$0.939823\pi$
$108$	−46.8081	−0.0417047
$109$	−2117.61	−1.86083	−0.930415	−	0.366508i	$-0.880553\pi$
$109$	−2117.61	−1.86083	−0.930415	+	0.366508i	$0.880553\pi$
$110$	380.712	0.329996
$111$	−69.0895	−0.0590782
$112$	−345.346	−0.291358
$113$	796.934	0.663444	0.331722	−	0.943377i	$-0.392370\pi$
$113$	796.934	0.663444	0.331722	+	0.943377i	$0.392370\pi$
$114$	3.17222	0.00260619
$115$	−371.158	−0.300962
$116$	−256.825	−0.205566
$117$	0	0
$118$	125.405	0.0978346
$119$	−341.466	−0.263043
$120$	85.1824	0.0648004
$121$	121.000	0.0909091
$122$	−1092.19	−0.810512
$123$	54.4208	0.0398940
$124$	−992.492	−0.718777
$125$	−1424.22	−1.01909
$126$	1741.95	1.23163
$127$	−816.029	−0.570165	−0.285082	−	0.958503i	$-0.592021\pi$
$127$	−816.029	−0.570165	−0.285082	+	0.958503i	$0.592021\pi$
$128$	580.971	0.401180
$129$	34.0136	0.0232150
$130$	0	0
$131$	2775.76	1.85129	0.925646	−	0.378392i	$-0.123523\pi$
$131$	2775.76	1.85129	0.925646	+	0.378392i	$0.123523\pi$
$132$	9.54199	0.00629184
$133$	282.206	0.183988
$134$	1645.89	1.06107
$135$	−194.857	−0.124227
$136$	−238.032	−0.150081
$137$	936.952	0.584301	0.292151	−	0.956372i	$-0.405629\pi$
$137$	936.952	0.584301	0.292151	+	0.956372i	$0.405629\pi$
$138$	7.78862	0.00480443
$139$	897.658	0.547758	0.273879	−	0.961764i	$-0.411693\pi$
$139$	897.658	0.547758	0.273879	+	0.961764i	$0.411693\pi$
$140$	2670.88	1.61236
$141$	7.81356	0.00466681
$142$	621.254	0.367144
$143$	0	0
$144$	275.144	0.159227
$145$	−1069.14	−0.612323
$146$	893.240	0.506336
$147$	−159.791	−0.0896552
$148$	−1510.10	−0.838710
$149$	2873.64	1.57999	0.789993	−	0.613116i	$-0.210084\pi$
$149$	2873.64	1.57999	0.789993	+	0.613116i	$0.210084\pi$
$150$	77.4341	0.0421498
$151$	−1392.40	−0.750410	−0.375205	−	0.926942i	$-0.622428\pi$
$151$	−1392.40	−0.750410	−0.375205	+	0.926942i	$0.622428\pi$
$152$	196.723	0.104976
$153$	272.052	0.143752
$154$	−710.727	−0.371896
$155$	−4131.64	−2.14104
$156$	0	0
$157$	2962.70	1.50605	0.753023	−	0.657995i	$-0.228595\pi$
$157$	2962.70	1.50605	0.753023	+	0.657995i	$0.228595\pi$
$158$	−1437.65	−0.723884
$159$	100.980	0.0503662
$160$	3067.47	1.51565
$161$	692.890	0.339176
$162$	−1385.79	−0.672088
$163$	2307.66	1.10889	0.554446	−	0.832219i	$-0.312930\pi$
$163$	2307.66	1.10889	0.554446	+	0.832219i	$0.312930\pi$
$164$	1189.48	0.566359
$165$	39.7223	0.0187417
$166$	−216.884	−0.101407
$167$	−648.537	−0.300511	−0.150255	−	0.988647i	$-0.548010\pi$
$167$	−648.537	−0.300511	−0.150255	+	0.988647i	$0.548010\pi$
$168$	−159.021	−0.0730284
$169$	0	0
$170$	−349.246	−0.157564
$171$	−224.839	−0.100549
$172$	743.438	0.329573
$173$	−40.7589	−0.0179124	−0.00895620	−	0.999960i	$-0.502851\pi$
$173$	−40.7589	−0.0179124	−0.00895620	+	0.999960i	$0.502851\pi$
$174$	22.4355	0.00977487
$175$	6888.68	2.97563
$176$	−112.261	−0.0480793
$177$	13.0844	0.00555639
$178$	2015.77	0.848809
$179$	4020.20	1.67868	0.839340	−	0.543607i	$-0.182942\pi$
$179$	4020.20	1.67868	0.839340	+	0.543607i	$0.182942\pi$
$180$	−2127.94	−0.881150
$181$	3654.04	1.50057	0.750284	−	0.661115i	$-0.229917\pi$
$181$	3654.04	1.50057	0.750284	+	0.661115i	$0.229917\pi$
$182$	0	0
$183$	−113.956	−0.0460320
$184$	483.006	0.193520
$185$	−6286.36	−2.49828
$186$	86.7010	0.0341786
$187$	−110.999	−0.0434067
$188$	170.782	0.0662529
$189$	363.766	0.140000
$190$	288.636	0.110210
$191$	1922.96	0.728484	0.364242	−	0.931304i	$-0.381328\pi$
$191$	1922.96	0.728484	0.364242	+	0.931304i	$0.381328\pi$
$192$	−80.6347	−0.0303089
$193$	4280.06	1.59630	0.798149	−	0.602460i	$-0.205813\pi$
$193$	4280.06	1.59630	0.798149	+	0.602460i	$0.205813\pi$
$194$	−277.269	−0.102612
$195$	0	0
$196$	−3492.56	−1.27280
$197$	−3152.63	−1.14018	−0.570090	−	0.821582i	$-0.693092\pi$
$197$	−3152.63	−1.14018	−0.570090	+	0.821582i	$0.693092\pi$
$198$	566.249	0.203240
$199$	−2810.13	−1.00103	−0.500514	−	0.865728i	$-0.666856\pi$
$199$	−2810.13	−1.00103	−0.500514	+	0.865728i	$0.666856\pi$
$200$	4802.02	1.69777
$201$	171.727	0.0602620
$202$	1370.30	0.477296
$203$	1995.90	0.690072
$204$	−8.75333	−0.00300419
$205$	4951.68	1.68703
$206$	3522.25	1.19130
$207$	−552.038	−0.185359
$208$	0	0
$209$	91.7359	0.0303613
$210$	−233.320	−0.0766695
$211$	−1216.30	−0.396843	−0.198421	−	0.980117i	$-0.563581\pi$
$211$	−1216.30	−0.396843	−0.198421	+	0.980117i	$0.563581\pi$
$212$	2207.13	0.715029
$213$	64.8196	0.0208515
$214$	4151.34	1.32607
$215$	3094.85	0.981708
$216$	253.577	0.0798783
$217$	7713.08	2.41289
$218$	4043.30	1.25618
$219$	93.1976	0.0287567
$220$	868.214	0.266068
$221$	0	0
$222$	131.917	0.0398816
$223$	−16.4172	−0.00492995	−0.00246497	−	0.999997i	$-0.500785\pi$
$223$	−16.4172	−0.00492995	−0.00246497	+	0.999997i	$0.500785\pi$
$224$	−5726.46	−1.70810
$225$	−5488.33	−1.62617
$226$	−1521.64	−0.447867
$227$	4895.93	1.43152	0.715759	−	0.698348i	$-0.246081\pi$
$227$	4895.93	1.43152	0.715759	+	0.698348i	$0.246081\pi$
$228$	7.23424	0.00210131
$229$	−5681.41	−1.63947	−0.819735	−	0.572744i	$-0.805879\pi$
$229$	−5681.41	−1.63947	−0.819735	+	0.572744i	$0.805879\pi$
$230$	708.677	0.203168
$231$	−74.1549	−0.0211214
$232$	1391.32	0.393726
$233$	−1802.06	−0.506683	−0.253342	−	0.967377i	$-0.581530\pi$
$233$	−1802.06	−0.506683	−0.253342	+	0.967377i	$0.581530\pi$
$234$	0	0
$235$	710.946	0.197349
$236$	285.986	0.0788818
$237$	−150.000	−0.0411120
$238$	651.984	0.177571
$239$	3859.26	1.04450	0.522249	−	0.852793i	$-0.325093\pi$
$239$	3859.26	1.04450	0.522249	+	0.852793i	$0.325093\pi$
$240$	−36.8532	−0.00991195
$241$	−1311.23	−0.350472	−0.175236	−	0.984526i	$-0.556069\pi$
$241$	−1311.23	−0.350472	−0.175236	+	0.984526i	$0.556069\pi$
$242$	−231.034	−0.0613694
$243$	−434.834	−0.114793
$244$	−2490.74	−0.653498
$245$	−14539.2	−3.79132
$246$	−103.909	−0.0269310
$247$	0	0
$248$	5376.70	1.37670
$249$	−22.6290	−0.00575925
$250$	2719.36	0.687948
$251$	7547.43	1.89797	0.948983	−	0.315329i	$-0.102115\pi$
$251$	7547.43	1.89797	0.948983	+	0.315329i	$0.102115\pi$
$252$	3972.51	0.993033
$253$	225.235	0.0559700
$254$	1558.10	0.384898
$255$	−36.4392	−0.00894866
$256$	−4347.35	−1.06137
$257$	−2663.80	−0.646549	−0.323275	−	0.946305i	$-0.604784\pi$
$257$	−2663.80	−0.646549	−0.323275	+	0.946305i	$0.604784\pi$
$258$	−64.9445	−0.0156716
$259$	11735.6	2.81550
$260$	0	0
$261$	−1590.17	−0.377122
$262$	−5299.95	−1.24974
$263$	3461.19	0.811507	0.405754	−	0.913982i	$-0.367009\pi$
$263$	3461.19	0.811507	0.405754	+	0.913982i	$0.367009\pi$
$264$	−51.6925	−0.0120510
$265$	9188.03	2.12987
$266$	−538.836	−0.124204
$267$	210.318	0.0482070
$268$	3753.45	0.855516
$269$	3675.82	0.833155	0.416578	−	0.909100i	$-0.363229\pi$
$269$	3675.82	0.833155	0.416578	+	0.909100i	$0.363229\pi$
$270$	372.054	0.0838610
$271$	−2059.34	−0.461610	−0.230805	−	0.973000i	$-0.574136\pi$
$271$	−2059.34	−0.461610	−0.230805	+	0.973000i	$0.574136\pi$
$272$	102.982	0.0229566
$273$	0	0
$274$	−1788.99	−0.394441
$275$	2239.28	0.491031
$276$	17.7619	0.00387370
$277$	5878.10	1.27502	0.637510	−	0.770442i	$-0.279964\pi$
$277$	5878.10	1.27502	0.637510	+	0.770442i	$0.279964\pi$
$278$	−1713.96	−0.369772
$279$	−6145.15	−1.31864
$280$	−14469.2	−3.08821
$281$	3245.12	0.688924	0.344462	−	0.938800i	$-0.388061\pi$
$281$	3245.12	0.688924	0.344462	+	0.938800i	$0.388061\pi$
$282$	−14.9190	−0.00315040
$283$	−4022.28	−0.844875	−0.422438	−	0.906392i	$-0.638825\pi$
$283$	−4022.28	−0.844875	−0.422438	+	0.906392i	$0.638825\pi$
$284$	1416.77	0.296020
$285$	30.1154	0.00625923
$286$	0	0
$287$	−9243.97	−1.90123
$288$	4562.37	0.933473
$289$	−4811.18	−0.979274
$290$	2041.37	0.413357
$291$	−28.9293	−0.00582772
$292$	2037.03	0.408247
$293$	−5011.22	−0.999177	−0.499588	−	0.866263i	$-0.666515\pi$
$293$	−5011.22	−0.999177	−0.499588	+	0.866263i	$0.666515\pi$
$294$	305.099	0.0605230
$295$	1190.53	0.234967
$296$	8180.76	1.60641
$297$	118.248	0.0231025
$298$	−5486.84	−1.06659
$299$	0	0
$300$	176.588	0.0339844
$301$	−5777.58	−1.10636
$302$	2658.61	0.506575
$303$	142.972	0.0271074
$304$	−85.1101	−0.0160572
$305$	−10368.7	−1.94659
$306$	−519.448	−0.0970420
$307$	4865.68	0.904558	0.452279	−	0.891877i	$-0.350611\pi$
$307$	4865.68	0.904558	0.452279	+	0.891877i	$0.350611\pi$
$308$	−1620.81	−0.299852
$309$	367.500	0.0676581
$310$	7888.82	1.44534
$311$	−3850.72	−0.702103	−0.351051	−	0.936356i	$-0.614176\pi$
$311$	−3850.72	−0.702103	−0.351051	+	0.936356i	$0.614176\pi$
$312$	0	0
$313$	2183.17	0.394250	0.197125	−	0.980378i	$-0.436840\pi$
$313$	2183.17	0.394250	0.197125	+	0.980378i	$0.436840\pi$
$314$	−5656.89	−1.01668
$315$	16537.1	2.95797
$316$	−3278.57	−0.583651
$317$	−4002.12	−0.709089	−0.354545	−	0.935039i	$-0.615364\pi$
$317$	−4002.12	−0.709089	−0.354545	+	0.935039i	$0.615364\pi$
$318$	−192.808	−0.0340004
$319$	648.800	0.113874
$320$	−7336.85	−1.28170
$321$	433.137	0.0753126
$322$	−1322.98	−0.228966
$323$	−84.1538	−0.0144967
$324$	−3160.30	−0.541890
$325$	0	0
$326$	−4406.17	−0.748573
$327$	421.865	0.0713430
$328$	−6443.87	−1.08477
$329$	−1327.22	−0.222407
$330$	−75.8445	−0.0126518
$331$	6159.01	1.02275	0.511375	−	0.859358i	$-0.329136\pi$
$331$	6159.01	1.02275	0.511375	+	0.859358i	$0.329136\pi$
$332$	−494.604	−0.0817618
$333$	−9349.96	−1.53866
$334$	1238.30	0.202864
$335$	15625.2	2.54834
$336$	68.7989	0.0111705
$337$	6259.47	1.01180	0.505898	−	0.862593i	$-0.331161\pi$
$337$	6259.47	1.01180	0.505898	+	0.862593i	$0.331161\pi$
$338$	0	0
$339$	−158.763	−0.0254360
$340$	−796.454	−0.127041
$341$	2507.27	0.398170
$342$	429.300	0.0678769
$343$	15535.3	2.44557
$344$	−4027.48	−0.631242
$345$	73.9410	0.0115387
$346$	77.8239	0.0120920
$347$	3095.33	0.478864	0.239432	−	0.970913i	$-0.423039\pi$
$347$	3095.33	0.478864	0.239432	+	0.970913i	$0.423039\pi$
$348$	51.1640	0.00788126
$349$	3934.14	0.603408	0.301704	−	0.953402i	$-0.402444\pi$
$349$	3934.14	0.603408	0.301704	+	0.953402i	$0.402444\pi$
$350$	−13153.0	−2.00874
$351$	0	0
$352$	−1861.48	−0.281867
$353$	−7978.21	−1.20294	−0.601469	−	0.798896i	$-0.705418\pi$
$353$	−7978.21	−1.20294	−0.601469	+	0.798896i	$0.705418\pi$
$354$	−24.9829	−0.00375092
$355$	5897.85	0.881762
$356$	4596.95	0.684375
$357$	68.0259	0.0100849
$358$	−7676.04	−1.13322
$359$	−9841.59	−1.44685	−0.723425	−	0.690403i	$-0.757433\pi$
$359$	−9841.59	−1.44685	−0.723425	+	0.690403i	$0.757433\pi$
$360$	11527.8	1.68770
$361$	−6789.45	−0.989860
$362$	−6976.92	−1.01298
$363$	−24.1053	−0.00348540
$364$	0	0
$365$	8479.94	1.21606
$366$	217.584	0.0310745
$367$	12310.8	1.75101	0.875503	−	0.483212i	$-0.160530\pi$
$367$	12310.8	1.75101	0.875503	+	0.483212i	$0.160530\pi$
$368$	−208.967	−0.0296010
$369$	7364.84	1.03902
$370$	12003.0	1.68650
$371$	−17152.5	−2.40031
$372$	197.721	0.0275575
$373$	2393.75	0.332289	0.166144	−	0.986101i	$-0.446868\pi$
$373$	2393.75	0.332289	0.166144	+	0.986101i	$0.446868\pi$
$374$	211.938	0.0293023
$375$	283.728	0.0390711
$376$	−925.189	−0.126896
$377$	0	0
$378$	−694.563	−0.0945091
$379$	1226.70	0.166257	0.0831287	−	0.996539i	$-0.473509\pi$
$379$	1226.70	0.166257	0.0831287	+	0.996539i	$0.473509\pi$
$380$	658.234	0.0888598
$381$	162.567	0.0218598
$382$	−3671.64	−0.491773
$383$	−1054.92	−0.140741	−0.0703703	−	0.997521i	$-0.522418\pi$
$383$	−1054.92	−0.140741	−0.0703703	+	0.997521i	$0.522418\pi$
$384$	−115.740	−0.0153810
$385$	−6747.26	−0.893175
$386$	−8172.21	−1.07760
$387$	4603.10	0.604622
$388$	−632.311	−0.0827338
$389$	−10634.6	−1.38611	−0.693056	−	0.720884i	$-0.743736\pi$
$389$	−10634.6	−1.38611	−0.693056	+	0.720884i	$0.743736\pi$
$390$	0	0
$391$	−206.619	−0.0267242
$392$	18920.5	2.43783
$393$	−552.979	−0.0709773
$394$	6019.53	0.769694
$395$	−13648.3	−1.73854
$396$	1291.33	0.163868
$397$	14374.0	1.81715	0.908576	−	0.417720i	$-0.137171\pi$
$397$	14374.0	1.81715	0.908576	+	0.417720i	$0.137171\pi$
$398$	5365.57	0.675758
$399$	−56.2204	−0.00705398
$400$	−2077.54	−0.259693
$401$	2121.46	0.264191	0.132096	−	0.991237i	$-0.457829\pi$
$401$	2121.46	0.264191	0.132096	+	0.991237i	$0.457829\pi$
$402$	−327.890	−0.0406807
$403$	0	0
$404$	3124.96	0.384833
$405$	−13156.0	−1.61414
$406$	−3810.91	−0.465843
$407$	3814.85	0.464607
$408$	47.4201	0.00575403
$409$	−8124.77	−0.982259	−0.491130	−	0.871087i	$-0.663416\pi$
$409$	−8124.77	−0.982259	−0.491130	+	0.871087i	$0.663416\pi$
$410$	−9454.59	−1.13885
$411$	−186.657	−0.0224017
$412$	8032.48	0.960515
$413$	−2222.52	−0.264802
$414$	1054.04	0.125129
$415$	−2058.98	−0.243546
$416$	0	0
$417$	−178.829	−0.0210007
$418$	−175.158	−0.0204958
$419$	−6059.14	−0.706464	−0.353232	−	0.935536i	$-0.614917\pi$
$419$	−6059.14	−0.706464	−0.353232	+	0.935536i	$0.614917\pi$
$420$	−532.085	−0.0618169
$421$	11454.9	1.32607	0.663035	−	0.748588i	$-0.269268\pi$
$421$	11454.9	1.32607	0.663035	+	0.748588i	$0.269268\pi$
$422$	2322.37	0.267894
$423$	1057.42	0.121545
$424$	−11956.8	−1.36952
$425$	−2054.20	−0.234455
$426$	−123.765	−0.0140761
$427$	19356.6	2.19375
$428$	9467.11	1.06918
$429$	0	0
$430$	−5909.22	−0.662716
$431$	−4758.35	−0.531790	−0.265895	−	0.964002i	$-0.585667\pi$
$431$	−4758.35	−0.531790	−0.265895	+	0.964002i	$0.585667\pi$
$432$	−109.707	−0.0122183
$433$	−1178.45	−0.130791	−0.0653956	−	0.997859i	$-0.520831\pi$
$433$	−1178.45	−0.130791	−0.0653956	+	0.997859i	$0.520831\pi$
$434$	−14727.1	−1.62886
$435$	212.990	0.0234761
$436$	9220.74	1.01283
$437$	170.762	0.0186925
$438$	−177.949	−0.0194126
$439$	6489.50	0.705528	0.352764	−	0.935712i	$-0.385242\pi$
$439$	6489.50	0.705528	0.352764	+	0.935712i	$0.385242\pi$
$440$	−4703.44	−0.509608
$441$	−21624.7	−2.33503
$442$	0	0
$443$	1317.48	0.141298	0.0706491	−	0.997501i	$-0.477493\pi$
$443$	1317.48	0.141298	0.0706491	+	0.997501i	$0.477493\pi$
$444$	300.837	0.0321556
$445$	19136.6	2.03857
$446$	31.3465	0.00332803
$447$	−572.479	−0.0605756
$448$	13696.7	1.44444
$449$	9610.16	1.01009	0.505046	−	0.863092i	$-0.331476\pi$
$449$	9610.16	1.01009	0.505046	+	0.863092i	$0.331476\pi$
$450$	10479.3	1.09777
$451$	−3004.91	−0.313737
$452$	−3470.10	−0.361105
$453$	277.390	0.0287702
$454$	−9348.14	−0.966365
$455$	0	0
$456$	−39.1906	−0.00402471
$457$	699.433	0.0715932	0.0357966	−	0.999359i	$-0.488603\pi$
$457$	699.433	0.0715932	0.0357966	+	0.999359i	$0.488603\pi$
$458$	10847.9	1.10675
$459$	−108.475	−0.0110309
$460$	1616.13	0.163810
$461$	−1621.15	−0.163784	−0.0818919	−	0.996641i	$-0.526096\pi$
$461$	−1621.15	−0.163784	−0.0818919	+	0.996641i	$0.526096\pi$
$462$	141.589	0.0142583
$463$	−6573.15	−0.659784	−0.329892	−	0.944019i	$-0.607012\pi$
$463$	−6573.15	−0.659784	−0.329892	+	0.944019i	$0.607012\pi$
$464$	−601.939	−0.0602248
$465$	823.093	0.0820861
$466$	3440.81	0.342043
$467$	14287.6	1.41574	0.707871	−	0.706342i	$-0.249656\pi$
$467$	14287.6	1.41574	0.707871	+	0.706342i	$0.249656\pi$
$468$	0	0
$469$	−29169.6	−2.87192
$470$	−1357.46	−0.133223
$471$	−590.221	−0.0577408
$472$	−1549.29	−0.151085
$473$	−1878.10	−0.182569
$474$	286.406	0.0277533
$475$	1697.70	0.163992
$476$	1486.85	0.143171
$477$	13665.7	1.31176
$478$	−7368.75	−0.705102
$479$	7774.11	0.741562	0.370781	−	0.928720i	$-0.379090\pi$
$479$	7774.11	0.741562	0.370781	+	0.928720i	$0.379090\pi$
$480$	−611.093	−0.0581092
$481$	0	0
$482$	2503.62	0.236591
$483$	−138.036	−0.0130038
$484$	−526.872	−0.0494808
$485$	−2632.24	−0.246441
$486$	830.259	0.0774925
$487$	4221.91	0.392840	0.196420	−	0.980520i	$-0.437068\pi$
$487$	4221.91	0.392840	0.196420	+	0.980520i	$0.437068\pi$
$488$	13493.3	1.25166
$489$	−459.725	−0.0425142
$490$	27760.6	2.55938
$491$	12502.5	1.14915	0.574574	−	0.818453i	$-0.305168\pi$
$491$	12502.5	1.14915	0.574574	+	0.818453i	$0.305168\pi$
$492$	−236.965	−0.0217138
$493$	−595.176	−0.0543719
$494$	0	0
$495$	5375.66	0.488117
$496$	−2326.17	−0.210581
$497$	−11010.3	−0.993723
$498$	43.2071	0.00388786
$499$	18331.9	1.64458	0.822291	−	0.569067i	$-0.192695\pi$
$499$	18331.9	1.64458	0.822291	+	0.569067i	$0.192695\pi$
$500$	6201.48	0.554677
$501$	129.200	0.0115214
$502$	−14410.8	−1.28125
$503$	−16706.1	−1.48089	−0.740447	−	0.672115i	$-0.765386\pi$
$503$	−16706.1	−1.48089	−0.740447	+	0.672115i	$0.765386\pi$
$504$	−21520.6	−1.90199
$505$	13008.9	1.14631
$506$	−430.057	−0.0377834
$507$	0	0
$508$	3553.25	0.310334
$509$	12932.1	1.12614	0.563072	−	0.826408i	$-0.309619\pi$
$509$	12932.1	1.12614	0.563072	+	0.826408i	$0.309619\pi$
$510$	69.5758	0.00604092
$511$	−15830.6	−1.37046
$512$	3652.93	0.315309
$513$	89.6495	0.00771564
$514$	5086.18	0.436462
$515$	33438.4	2.86111
$516$	−148.106	−0.0126356
$517$	−431.435	−0.0367011
$518$	−22407.6	−1.90064
$519$	8.11988	0.000686750 0
$520$	0	0
$521$	−4255.07	−0.357808	−0.178904	−	0.983867i	$-0.557255\pi$
$521$	−4255.07	−0.357808	−0.178904	+	0.983867i	$0.557255\pi$
$522$	3036.22	0.254582
$523$	−16522.2	−1.38139	−0.690695	−	0.723146i	$-0.742695\pi$
$523$	−16522.2	−1.38139	−0.690695	+	0.723146i	$0.742695\pi$
$524$	−12086.5	−1.00764
$525$	−1372.34	−0.114084
$526$	−6608.70	−0.547819
$527$	−2300.04	−0.190116
$528$	22.3642	0.00184333
$529$	−11747.7	−0.965541
$530$	−17543.3	−1.43780
$531$	1770.72	0.144713
$532$	−1228.81	−0.100143
$533$	0	0
$534$	−401.575	−0.0325428
$535$	39410.6	3.18480
$536$	−20333.8	−1.63860
$537$	−800.893	−0.0643595
$538$	−7018.50	−0.562433
$539$	8823.02	0.705073
$540$	848.467	0.0676152
$541$	−4776.14	−0.379560	−0.189780	−	0.981827i	$-0.560778\pi$
$541$	−4776.14	−0.379560	−0.189780	+	0.981827i	$0.560778\pi$
$542$	3932.05	0.311616
$543$	−727.948	−0.0575309
$544$	1707.62	0.134584
$545$	38384.9	3.01694
$546$	0	0
$547$	17166.7	1.34185	0.670927	−	0.741523i	$-0.265896\pi$
$547$	17166.7	1.34185	0.670927	+	0.741523i	$0.265896\pi$
$548$	−4079.78	−0.318029
$549$	−15421.8	−1.19888
$550$	−4275.61	−0.331478
$551$	491.886	0.0380310
$552$	−96.2230	−0.00741943
$553$	25479.2	1.95928
$554$	−11223.5	−0.860721
$555$	1252.35	0.0957827
$556$	−3908.68	−0.298139
$557$	−18657.8	−1.41931	−0.709654	−	0.704550i	$-0.751149\pi$
$557$	−18657.8	−1.41931	−0.709654	+	0.704550i	$0.751149\pi$
$558$	11733.4	0.890166
$559$	0	0
$560$	6259.93	0.472375
$561$	22.1129	0.00166419
$562$	−6196.13	−0.465068
$563$	5133.69	0.384297	0.192149	−	0.981366i	$-0.438454\pi$
$563$	5133.69	0.384297	0.192149	+	0.981366i	$0.438454\pi$
$564$	−34.0227	−0.00254009
$565$	−14445.6	−1.07563
$566$	7680.02	0.570345
$567$	24560.1	1.81909
$568$	−7675.17	−0.566977
$569$	17823.6	1.31319	0.656594	−	0.754244i	$-0.271997\pi$
$569$	17823.6	1.31319	0.656594	+	0.754244i	$0.271997\pi$
$570$	−57.5013	−0.00422538
$571$	8358.81	0.612619	0.306309	−	0.951932i	$-0.400906\pi$
$571$	8358.81	0.612619	0.306309	+	0.951932i	$0.400906\pi$
$572$	0	0
$573$	−383.086	−0.0279296
$574$	17650.1	1.28345
$575$	4168.30	0.302314
$576$	−10912.4	−0.789381
$577$	6306.96	0.455047	0.227524	−	0.973773i	$-0.426937\pi$
$577$	6306.96	0.455047	0.227524	+	0.973773i	$0.426937\pi$
$578$	9186.31	0.661073
$579$	−852.662	−0.0612011
$580$	4655.35	0.333281
$581$	3843.78	0.274470
$582$	55.2368	0.00393408
$583$	−5575.71	−0.396093
$584$	−11035.4	−0.781929
$585$	0	0
$586$	9568.28	0.674508
$587$	−7875.07	−0.553729	−0.276864	−	0.960909i	$-0.589295\pi$
$587$	−7875.07	−0.553729	−0.276864	+	0.960909i	$0.589295\pi$
$588$	695.778	0.0487983
$589$	1900.88	0.132978
$590$	−2273.16	−0.158618
$591$	628.058	0.0437138
$592$	−3539.32	−0.245718
$593$	−6797.18	−0.470703	−0.235352	−	0.971910i	$-0.575624\pi$
$593$	−6797.18	−0.470703	−0.235352	+	0.971910i	$0.575624\pi$
$594$	−225.779	−0.0155957
$595$	6189.59	0.426468
$596$	−12512.7	−0.859968
$597$	559.826	0.0383788
$598$	0	0
$599$	843.054	0.0575063	0.0287531	−	0.999587i	$-0.490846\pi$
$599$	843.054	0.0575063	0.0287531	+	0.999587i	$0.490846\pi$
$600$	−956.645	−0.0650915
$601$	27871.7	1.89170	0.945850	−	0.324605i	$-0.105231\pi$
$601$	27871.7	1.89170	0.945850	+	0.324605i	$0.105231\pi$
$602$	11031.5	0.746863
$603$	23240.0	1.56949
$604$	6062.94	0.408440
$605$	−2193.31	−0.147390
$606$	−272.987	−0.0182992
$607$	−14148.9	−0.946106	−0.473053	−	0.881034i	$-0.656848\pi$
$607$	−14148.9	−0.946106	−0.473053	+	0.881034i	$0.656848\pi$
$608$	−1411.28	−0.0941362
$609$	−397.617	−0.0264569
$610$	19797.7	1.31407
$611$	0	0
$612$	−1184.60	−0.0782427
$613$	−10452.5	−0.688699	−0.344349	−	0.938842i	$-0.611900\pi$
$613$	−10452.5	−0.688699	−0.344349	+	0.938842i	$0.611900\pi$
$614$	−9290.38	−0.610634
$615$	−986.460	−0.0646795
$616$	8780.54	0.574315
$617$	−13555.9	−0.884507	−0.442254	−	0.896890i	$-0.645821\pi$
$617$	−13555.9	−0.884507	−0.442254	+	0.896890i	$0.645821\pi$
$618$	−701.693	−0.0456735
$619$	9133.55	0.593067	0.296533	−	0.955022i	$-0.404169\pi$
$619$	9133.55	0.593067	0.296533	+	0.955022i	$0.404169\pi$
$620$	17990.4	1.16534
$621$	220.113	0.0142235
$622$	7352.44	0.473964
$623$	−35724.8	−2.29741
$624$	0	0
$625$	369.739	0.0236633
$626$	−4168.48	−0.266144
$627$	−18.2754	−0.00116403
$628$	−12900.5	−0.819724
$629$	−3499.55	−0.221838
$630$	−31575.5	−1.99682
$631$	398.019	0.0251108	0.0125554	−	0.999921i	$-0.496003\pi$
$631$	398.019	0.0251108	0.0125554	+	0.999921i	$0.496003\pi$
$632$	17761.2	1.11789
$633$	242.309	0.0152147
$634$	7641.52	0.478681
$635$	14791.8	0.924400
$636$	−439.698	−0.0274137
$637$	0	0
$638$	−1238.80	−0.0768723
$639$	8772.12	0.543067
$640$	−10531.0	−0.650428
$641$	10083.6	0.621339	0.310669	−	0.950518i	$-0.399447\pi$
$641$	10083.6	0.621339	0.310669	+	0.950518i	$0.399447\pi$
$642$	−827.018	−0.0508408
$643$	26556.4	1.62875	0.814373	−	0.580342i	$-0.197081\pi$
$643$	26556.4	1.62875	0.814373	+	0.580342i	$0.197081\pi$
$644$	−3017.06	−0.184610
$645$	−616.548	−0.0376381
$646$	160.681	0.00978621
$647$	14013.8	0.851529	0.425764	−	0.904834i	$-0.360005\pi$
$647$	14013.8	0.851529	0.425764	+	0.904834i	$0.360005\pi$
$648$	17120.5	1.03790
$649$	−722.467	−0.0436970
$650$	0	0
$651$	−1536.58	−0.0925088
$652$	−10048.2	−0.603558
$653$	−10085.9	−0.604429	−0.302215	−	0.953240i	$-0.597726\pi$
$653$	−10085.9	−0.604429	−0.302215	+	0.953240i	$0.597726\pi$
$654$	−805.495	−0.0481611
$655$	−50314.8	−3.00147
$656$	2787.87	0.165927
$657$	12612.6	0.748954
$658$	2534.15	0.150139
$659$	17733.6	1.04826	0.524129	−	0.851639i	$-0.324391\pi$
$659$	17733.6	1.04826	0.524129	+	0.851639i	$0.324391\pi$
$660$	−172.963	−0.0102009
$661$	982.186	0.0577952	0.0288976	−	0.999582i	$-0.490800\pi$
$661$	982.186	0.0577952	0.0288976	+	0.999582i	$0.490800\pi$
$662$	−11759.8	−0.690421
$663$	0	0
$664$	2679.46	0.156601
$665$	−5115.42	−0.298297
$666$	17852.5	1.03870
$667$	1207.71	0.0701089
$668$	2823.93	0.163565
$669$	3.27059	0.000189011 0
$670$	−29834.3	−1.72030
$671$	6292.19	0.362008
$672$	1140.81	0.0654876
$673$	6296.07	0.360618	0.180309	−	0.983610i	$-0.442290\pi$
$673$	6296.07	0.360618	0.180309	+	0.983610i	$0.442290\pi$
$674$	−11951.6	−0.683027
$675$	2188.35	0.124785
$676$	0	0
$677$	22621.0	1.28419	0.642093	−	0.766626i	$-0.278066\pi$
$677$	22621.0	1.28419	0.642093	+	0.766626i	$0.278066\pi$
$678$	303.137	0.0171710
$679$	4913.96	0.277733
$680$	4314.69	0.243325
$681$	−975.354	−0.0548835
$682$	−4787.29	−0.268790
$683$	3834.13	0.214801	0.107400	−	0.994216i	$-0.465747\pi$
$683$	3834.13	0.214801	0.107400	+	0.994216i	$0.465747\pi$
$684$	979.018	0.0547276
$685$	−16983.7	−0.947319
$686$	−29662.7	−1.65091
$687$	1131.84	0.0628562
$688$	1742.45	0.0965555
$689$	0	0
$690$	−141.181	−0.00778935
$691$	−1673.26	−0.0921182	−0.0460591	−	0.998939i	$-0.514666\pi$
$691$	−1673.26	−0.0921182	−0.0460591	+	0.998939i	$0.514666\pi$
$692$	177.477	0.00974952
$693$	−10035.5	−0.550095
$694$	−5910.12	−0.323264
$695$	−16271.4	−0.888072
$696$	−277.175	−0.0150952
$697$	2756.55	0.149801
$698$	−7511.72	−0.407339
$699$	359.002	0.0194259
$700$	−29995.4	−1.61960
$701$	23063.8	1.24267	0.621333	−	0.783547i	$-0.286591\pi$
$701$	23063.8	1.24267	0.621333	+	0.783547i	$0.286591\pi$
$702$	0	0
$703$	2892.22	0.155167
$704$	4452.34	0.238358
$705$	−141.633	−0.00756624
$706$	15233.4	0.812061
$707$	−24285.4	−1.29186
$708$	−56.9734	−0.00302428
$709$	−24496.6	−1.29759	−0.648794	−	0.760965i	$-0.724726\pi$
$709$	−24496.6	−1.29759	−0.648794	+	0.760965i	$0.724726\pi$
$710$	−11261.2	−0.595246
$711$	−20299.7	−1.07074
$712$	−24903.4	−1.31081
$713$	4667.14	0.245142
$714$	−129.886	−0.00680795
$715$	0	0
$716$	−17505.2	−0.913687
$717$	−768.831	−0.0400454
$718$	18791.2	0.976716
$719$	18322.2	0.950351	0.475176	−	0.879891i	$-0.342384\pi$
$719$	18322.2	0.950351	0.475176	+	0.879891i	$0.342384\pi$
$720$	−4987.40	−0.258152
$721$	−62423.9	−3.22439
$722$	12963.6	0.668219
$723$	261.220	0.0134369
$724$	−15910.8	−0.816743
$725$	12007.0	0.615073
$726$	46.0259	0.00235287
$727$	−13972.8	−0.712823	−0.356411	−	0.934329i	$-0.616000\pi$
$727$	−13972.8	−0.712823	−0.356411	+	0.934329i	$0.616000\pi$
$728$	0	0
$729$	−19509.6	−0.991191
$730$	−16191.3	−0.820915
$731$	1722.87	0.0871719
$732$	496.199	0.0250547
$733$	−10084.5	−0.508156	−0.254078	−	0.967184i	$-0.581772\pi$
$733$	−10084.5	−0.508156	−0.254078	+	0.967184i	$0.581772\pi$
$734$	−23505.9	−1.18204
$735$	2896.45	0.145357
$736$	−3465.05	−0.173537
$737$	−9482.08	−0.473917
$738$	−14062.2	−0.701404
$739$	21441.8	1.06732	0.533661	−	0.845699i	$-0.320816\pi$
$739$	21441.8	1.06732	0.533661	+	0.845699i	$0.320816\pi$
$740$	27372.8	1.35979
$741$	0	0
$742$	32750.5	1.62036
$743$	−23826.0	−1.17643	−0.588217	−	0.808703i	$-0.700170\pi$
$743$	−23826.0	−1.17643	−0.588217	+	0.808703i	$0.700170\pi$
$744$	−1071.13	−0.0527817
$745$	−52089.1	−2.56161
$746$	−4570.55	−0.224316
$747$	−3062.41	−0.149997
$748$	483.325	0.0236258
$749$	−73573.0	−3.58918
$750$	−541.742	−0.0263755
$751$	−6962.84	−0.338319	−0.169159	−	0.985589i	$-0.554105\pi$
$751$	−6962.84	−0.338319	−0.169159	+	0.985589i	$0.554105\pi$
$752$	400.273	0.0194102
$753$	−1503.58	−0.0727668
$754$	0	0
$755$	25239.4	1.21663
$756$	−1583.95	−0.0762006
$757$	−9945.61	−0.477516	−0.238758	−	0.971079i	$-0.576740\pi$
$757$	−9945.61	−0.477516	−0.238758	+	0.971079i	$0.576740\pi$
$758$	−2342.23	−0.112234
$759$	−44.8707	−0.00214586
$760$	−3565.90	−0.170196
$761$	−22787.2	−1.08546	−0.542730	−	0.839907i	$-0.682609\pi$
$761$	−22787.2	−1.08546	−0.542730	+	0.839907i	$0.682609\pi$
$762$	−310.401	−0.0147567
$763$	−71658.3	−3.40001
$764$	−8373.16	−0.396505
$765$	−4931.36	−0.233063
$766$	2014.22	0.0950089
$767$	0	0
$768$	866.067	0.0406921
$769$	29567.3	1.38651	0.693254	−	0.720693i	$-0.256176\pi$
$769$	29567.3	1.38651	0.693254	+	0.720693i	$0.256176\pi$
$770$	12883.0	0.602950
$771$	530.675	0.0247883
$772$	−18636.7	−0.868847
$773$	27849.8	1.29584	0.647922	−	0.761706i	$-0.275638\pi$
$773$	27849.8	1.29584	0.647922	+	0.761706i	$0.275638\pi$
$774$	−8789.02	−0.408158
$775$	46400.6	2.15065
$776$	3425.47	0.158463
$777$	−2337.93	−0.107945
$778$	20305.4	0.935714
$779$	−2278.16	−0.104780
$780$	0	0
$781$	−3579.09	−0.163982
$782$	394.512	0.0180406
$783$	634.044	0.0289386
$784$	−8185.76	−0.372893
$785$	−53703.4	−2.44173
$786$	1055.84	0.0479142
$787$	−20731.4	−0.939003	−0.469501	−	0.882932i	$-0.655566\pi$
$787$	−20731.4	−0.939003	−0.469501	+	0.882932i	$0.655566\pi$
$788$	13727.5	0.620587
$789$	−689.530	−0.0311127
$790$	26059.7	1.17362
$791$	26967.6	1.21221
$792$	−6995.62	−0.313862
$793$	0	0
$794$	−27445.2	−1.22669
$795$	−1830.41	−0.0816580
$796$	12236.2	0.544849
$797$	16302.0	0.724527	0.362264	−	0.932076i	$-0.382004\pi$
$797$	16302.0	0.724527	0.362264	+	0.932076i	$0.382004\pi$
$798$	107.345	0.00476189
$799$	395.776	0.0175238
$800$	−34449.4	−1.52246
$801$	28462.6	1.25553
$802$	−4050.65	−0.178346
$803$	−5146.01	−0.226150
$804$	−747.751	−0.0327999
$805$	−12559.7	−0.549901
$806$	0	0
$807$	−732.287	−0.0319426
$808$	−16929.1	−0.737083
$809$	−18343.4	−0.797179	−0.398590	−	0.917129i	$-0.630500\pi$
$809$	−18343.4	−0.797179	−0.398590	+	0.917129i	$0.630500\pi$
$810$	25119.6	1.08965
$811$	21296.4	0.922096	0.461048	−	0.887375i	$-0.347474\pi$
$811$	21296.4	0.922096	0.461048	+	0.887375i	$0.347474\pi$
$812$	−8690.76	−0.375598
$813$	410.257	0.0176978
$814$	−7283.96	−0.313640
$815$	−41829.8	−1.79783
$816$	−20.5158	−0.000880142 0
$817$	−1423.88	−0.0609732
$818$	15513.2	0.663088
$819$	0	0
$820$	−21561.2	−0.918230
$821$	−42957.7	−1.82611	−0.913054	−	0.407838i	$-0.866283\pi$
$821$	−42957.7	−1.82611	−0.913054	+	0.407838i	$0.866283\pi$
$822$	356.397	0.0151226
$823$	−10683.5	−0.452495	−0.226248	−	0.974070i	$-0.572646\pi$
$823$	−10683.5	−0.452495	−0.226248	+	0.974070i	$0.572646\pi$
$824$	−43515.0	−1.83970
$825$	−446.103	−0.0188258
$826$	4243.61	0.178758
$827$	24791.9	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$827$	24791.9	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$828$	2403.74	0.100889
$829$	−9749.70	−0.408469	−0.204235	−	0.978922i	$-0.565471\pi$
$829$	−9749.70	−0.408469	−0.204235	+	0.978922i	$0.565471\pi$
$830$	3931.36	0.164409
$831$	−1171.02	−0.0488835
$832$	0	0
$833$	−8093.78	−0.336654
$834$	341.450	0.0141768
$835$	11755.7	0.487214
$836$	−399.447	−0.0165253
$837$	2450.24	0.101186
$838$	11569.1	0.476908
$839$	27080.3	1.11432	0.557160	−	0.830405i	$-0.311891\pi$
$839$	27080.3	1.11432	0.557160	+	0.830405i	$0.311891\pi$
$840$	2882.50	0.118400
$841$	−20910.1	−0.857360
$842$	−21871.6	−0.895182
$843$	−646.484	−0.0264129
$844$	5296.17	0.215997
$845$	0	0
$846$	−2019.00	−0.0820505
$847$	4094.55	0.166104
$848$	5173.00	0.209483
$849$	801.307	0.0323920
$850$	3922.22	0.158272
$851$	7101.15	0.286045
$852$	−282.245	−0.0113492
$853$	10935.9	0.438966	0.219483	−	0.975616i	$-0.429563\pi$
$853$	10935.9	0.438966	0.219483	+	0.975616i	$0.429563\pi$
$854$	−36958.9	−1.48092
$855$	4075.55	0.163018
$856$	−51286.9	−2.04784
$857$	37574.7	1.49770	0.748849	−	0.662741i	$-0.230607\pi$
$857$	37574.7	1.49770	0.748849	+	0.662741i	$0.230607\pi$
$858$	0	0
$859$	−16817.4	−0.667990	−0.333995	−	0.942575i	$-0.608397\pi$
$859$	−16817.4	−0.667990	−0.333995	+	0.942575i	$0.608397\pi$
$860$	−13475.9	−0.534333
$861$	1841.56	0.0728921
$862$	9085.44	0.358992
$863$	241.898	0.00954147	0.00477073	−	0.999989i	$-0.498481\pi$
$863$	241.898	0.00954147	0.00477073	+	0.999989i	$0.498481\pi$
$864$	−1819.14	−0.0716302
$865$	738.818	0.0290411
$866$	2250.09	0.0882924
$867$	958.469	0.0375448
$868$	−33585.1	−1.31331
$869$	8282.42	0.323316
$870$	−406.677	−0.0158479
$871$	0	0
$872$	−49952.2	−1.93990
$873$	−3915.04	−0.151780
$874$	−326.047	−0.0126187
$875$	−48194.4	−1.86202
$876$	−405.811	−0.0156519
$877$	13037.7	0.501996	0.250998	−	0.967988i	$-0.419241\pi$
$877$	13037.7	0.501996	0.250998	+	0.967988i	$0.419241\pi$
$878$	−12390.8	−0.476276
$879$	998.322	0.0383078
$880$	2034.89	0.0779503
$881$	−41123.2	−1.57262	−0.786308	−	0.617835i	$-0.788010\pi$
$881$	−41123.2	−1.57262	−0.786308	+	0.617835i	$0.788010\pi$
$882$	41289.5	1.57629
$883$	−25072.5	−0.955556	−0.477778	−	0.878481i	$-0.658558\pi$
$883$	−25072.5	−0.955556	−0.477778	+	0.878481i	$0.658558\pi$
$884$	0	0
$885$	−237.174	−0.00900849
$886$	−2515.55	−0.0953854
$887$	−45227.0	−1.71203	−0.856017	−	0.516947i	$-0.827068\pi$
$887$	−45227.0	−1.71203	−0.856017	+	0.516947i	$0.827068\pi$
$888$	−1629.75	−0.0615887
$889$	−27613.8	−1.04177
$890$	−36538.8	−1.37616
$891$	7983.66	0.300182
$892$	71.4856	0.00268331
$893$	−327.091	−0.0122572
$894$	1093.07	0.0408924
$895$	−72872.2	−2.72162
$896$	19659.6	0.733015
$897$	0	0
$898$	−18349.3	−0.681877
$899$	13443.9	0.498754
$900$	23897.9	0.885108
$901$	5114.87	0.189124
$902$	5737.47	0.211793
$903$	1150.99	0.0424171
$904$	18798.8	0.691637
$905$	−66235.1	−2.43285
$906$	−529.640	−0.0194218
$907$	−30940.2	−1.13269	−0.566347	−	0.824167i	$-0.691644\pi$
$907$	−30940.2	−1.13269	−0.566347	+	0.824167i	$0.691644\pi$
$908$	−21318.4	−0.779159
$909$	19348.6	0.705999
$910$	0	0
$911$	21497.1	0.781811	0.390905	−	0.920431i	$-0.372162\pi$
$911$	21497.1	0.781811	0.390905	+	0.920431i	$0.372162\pi$
$912$	16.9554	0.000615624 0
$913$	1249.48	0.0452923
$914$	−1335.48	−0.0483300
$915$	2065.62	0.0746310
$916$	24738.6	0.892345
$917$	93929.5	3.38258
$918$	207.118	0.00744653
$919$	29633.2	1.06367	0.531833	−	0.846849i	$-0.321503\pi$
$919$	29633.2	1.06367	0.531833	+	0.846849i	$0.321503\pi$
$920$	−8755.21	−0.313751
$921$	−969.328	−0.0346802
$922$	3095.37	0.110565
$923$	0	0
$924$	322.893	0.0114961
$925$	70599.3	2.50950
$926$	12550.6	0.445396
$927$	49734.2	1.76212
$928$	−9981.22	−0.353071
$929$	−29615.7	−1.04592	−0.522959	−	0.852358i	$-0.675172\pi$
$929$	−29615.7	−1.04592	−0.522959	+	0.852358i	$0.675172\pi$
$930$	−1571.59	−0.0554133
$931$	6689.15	0.235476
$932$	7846.75	0.275782
$933$	767.129	0.0269182
$934$	−27280.3	−0.955716
$935$	2012.03	0.0703747
$936$	0	0
$937$	53059.8	1.84993	0.924967	−	0.380048i	$-0.124093\pi$
$937$	53059.8	1.84993	0.924967	+	0.380048i	$0.124093\pi$
$938$	55695.6	1.93873
$939$	−434.926	−0.0151153
$940$	−3095.68	−0.107415
$941$	−13233.4	−0.458445	−0.229222	−	0.973374i	$-0.573618\pi$
$941$	−13233.4	−0.458445	−0.229222	+	0.973374i	$0.573618\pi$
$942$	1126.95	0.0389788
$943$	−5593.48	−0.193159
$944$	670.286	0.0231101
$945$	−6593.81	−0.226980
$946$	3585.98	0.123246
$947$	25078.2	0.860541	0.430270	−	0.902700i	$-0.358418\pi$
$947$	25078.2	0.860541	0.430270	+	0.902700i	$0.358418\pi$
$948$	653.147	0.0223768
$949$	0	0
$950$	−3241.55	−0.110705
$951$	797.291	0.0271860
$952$	−8054.81	−0.274221
$953$	28833.1	0.980057	0.490028	−	0.871706i	$-0.336986\pi$
$953$	28833.1	0.980057	0.490028	+	0.871706i	$0.336986\pi$
$954$	−26092.9	−0.885523
$955$	−34856.5	−1.18108
$956$	−16804.4	−0.568508
$957$	−129.252	−0.00436586
$958$	−14843.6	−0.500601
$959$	31705.7	1.06760
$960$	1461.63	0.0491394
$961$	22162.5	0.743934
$962$	0	0
$963$	58616.9	1.96148
$964$	5709.50	0.190758
$965$	−77582.6	−2.58805
$966$	263.561	0.00877839
$967$	55407.5	1.84259	0.921295	−	0.388865i	$-0.127133\pi$
$967$	55407.5	1.84259	0.921295	+	0.388865i	$0.127133\pi$
$968$	2854.26	0.0947721
$969$	16.7649	0.000555795 0
$970$	5025.92	0.166364
$971$	−17869.8	−0.590595	−0.295298	−	0.955405i	$-0.595419\pi$
$971$	−17869.8	−0.590595	−0.295298	+	0.955405i	$0.595419\pi$
$972$	1893.40	0.0624804
$973$	30376.0	1.00083
$974$	−8061.19	−0.265192
$975$	0	0
$976$	−5837.73	−0.191456
$977$	25610.6	0.838646	0.419323	−	0.907837i	$-0.362268\pi$
$977$	25610.6	0.838646	0.419323	+	0.907837i	$0.362268\pi$
$978$	877.784	0.0286998
$979$	−11613.0	−0.379113
$980$	63308.0	2.06357
$981$	57091.5	1.85809
$982$	−23871.9	−0.775748
$983$	35744.2	1.15978	0.579890	−	0.814695i	$-0.303095\pi$
$983$	35744.2	1.15978	0.579890	+	0.814695i	$0.303095\pi$
$984$	1283.73	0.0415892
$985$	57146.2	1.84856
$986$	1136.41	0.0367045
$987$	264.405	0.00852695
$988$	0	0
$989$	−3495.98	−0.112402
$990$	−10264.1	−0.329510
$991$	37245.9	1.19390	0.596949	−	0.802279i	$-0.296379\pi$
$991$	37245.9	1.19390	0.596949	+	0.802279i	$0.296379\pi$
$992$	−38572.1	−1.23454
$993$	−1226.98	−0.0392116
$994$	21022.8	0.670826
$995$	50937.8	1.62295
$996$	98.5336	0.00313470
$997$	31744.3	1.00838	0.504189	−	0.863593i	$-0.331792\pi$
$997$	31744.3	1.00838	0.504189	+	0.863593i	$0.331792\pi$
$998$	−35002.3	−1.11020
$999$	3728.09	0.118070

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.90937 q^{2} -0.199217 q^{3} -4.35431 q^{4} -18.1265 q^{5} +0.380379 q^{6} +33.8392 q^{7} +23.5889 q^{8} -26.9603 q^{9} +O(q^{10})\)	\(q-1.90937 q^{2} -0.199217 q^{3} -4.35431 q^{4} -18.1265 q^{5} +0.380379 q^{6} +33.8392 q^{7} +23.5889 q^{8} -26.9603 q^{9} +34.6102 q^{10} +11.0000 q^{11} +0.867454 q^{12} -64.6116 q^{14} +3.61112 q^{15} -10.2055 q^{16} -10.0908 q^{17} +51.4772 q^{18} +8.33963 q^{19} +78.9285 q^{20} -6.74135 q^{21} -21.0031 q^{22} +20.4759 q^{23} -4.69932 q^{24} +203.571 q^{25} +10.7498 q^{27} -147.346 q^{28} +58.9818 q^{29} -6.89495 q^{30} +227.933 q^{31} -169.225 q^{32} -2.19139 q^{33} +19.2671 q^{34} -613.387 q^{35} +117.394 q^{36} +346.805 q^{37} -15.9234 q^{38} -427.585 q^{40} -273.173 q^{41} +12.8717 q^{42} -170.736 q^{43} -47.8974 q^{44} +488.697 q^{45} -39.0961 q^{46} -39.2213 q^{47} +2.03311 q^{48} +802.093 q^{49} -388.692 q^{50} +2.01027 q^{51} -506.883 q^{53} -20.5254 q^{54} -199.392 q^{55} +798.231 q^{56} -1.66140 q^{57} -112.618 q^{58} -65.6789 q^{59} -15.7239 q^{60} +572.018 q^{61} -435.209 q^{62} -912.316 q^{63} +404.758 q^{64} +4.18417 q^{66} -862.007 q^{67} +43.9386 q^{68} -4.07916 q^{69} +1171.18 q^{70} -325.372 q^{71} -635.965 q^{72} -467.819 q^{73} -662.178 q^{74} -40.5548 q^{75} -36.3133 q^{76} +372.231 q^{77} +752.948 q^{79} +184.990 q^{80} +725.787 q^{81} +521.589 q^{82} +113.590 q^{83} +29.3539 q^{84} +182.912 q^{85} +325.998 q^{86} -11.7502 q^{87} +259.478 q^{88} -1055.72 q^{89} -933.102 q^{90} -89.1586 q^{92} -45.4082 q^{93} +74.8880 q^{94} -151.168 q^{95} +33.7126 q^{96} +145.215 q^{97} -1531.49 q^{98} -296.563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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

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