LMFDB - Embedded newform 1859.4.a.p.1.3

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			1.3
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)

$f(q)$	$=$	$q-5.50285 q^{2} +4.91472 q^{3} +22.2813 q^{4} -19.9510 q^{5} -27.0449 q^{6} -0.0210524 q^{7} -78.5880 q^{8} -2.84554 q^{9} +O(q^{10})$	\(q-5.50285 q^{2} +4.91472 q^{3} +22.2813 q^{4} -19.9510 q^{5} -27.0449 q^{6} -0.0210524 q^{7} -78.5880 q^{8} -2.84554 q^{9} +109.787 q^{10} -11.0000 q^{11} +109.506 q^{12} +0.115848 q^{14} -98.0537 q^{15} +254.207 q^{16} -82.6180 q^{17} +15.6586 q^{18} +28.9630 q^{19} -444.535 q^{20} -0.103467 q^{21} +60.5313 q^{22} -68.4191 q^{23} -386.238 q^{24} +273.043 q^{25} -146.682 q^{27} -0.469075 q^{28} +61.3270 q^{29} +539.574 q^{30} +274.440 q^{31} -770.158 q^{32} -54.0619 q^{33} +454.634 q^{34} +0.420017 q^{35} -63.4024 q^{36} -312.918 q^{37} -159.379 q^{38} +1567.91 q^{40} +366.564 q^{41} +0.569361 q^{42} -405.741 q^{43} -245.095 q^{44} +56.7714 q^{45} +376.500 q^{46} -594.007 q^{47} +1249.36 q^{48} -343.000 q^{49} -1502.51 q^{50} -406.044 q^{51} -187.715 q^{53} +807.171 q^{54} +219.461 q^{55} +1.65446 q^{56} +142.345 q^{57} -337.473 q^{58} -5.47713 q^{59} -2184.77 q^{60} -598.488 q^{61} -1510.20 q^{62} +0.0599054 q^{63} +2204.41 q^{64} +297.494 q^{66} -285.078 q^{67} -1840.84 q^{68} -336.261 q^{69} -2.31129 q^{70} -394.832 q^{71} +223.625 q^{72} -687.195 q^{73} +1721.94 q^{74} +1341.93 q^{75} +645.333 q^{76} +0.231576 q^{77} -181.218 q^{79} -5071.69 q^{80} -644.073 q^{81} -2017.15 q^{82} -635.266 q^{83} -2.30537 q^{84} +1648.31 q^{85} +2232.73 q^{86} +301.405 q^{87} +864.468 q^{88} -559.789 q^{89} -312.404 q^{90} -1524.47 q^{92} +1348.80 q^{93} +3268.73 q^{94} -577.841 q^{95} -3785.11 q^{96} +690.391 q^{97} +1887.47 q^{98} +31.3009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.50285	−1.94555	−0.972775	−	0.231751i	$-0.925555\pi$
$2$	−5.50285	−1.94555	−0.972775	+	0.231751i	$0.925555\pi$
$3$	4.91472	0.945838	0.472919	−	0.881106i	$-0.343200\pi$
$3$	4.91472	0.945838	0.472919	+	0.881106i	$0.343200\pi$
$4$	22.2813	2.78517
$5$	−19.9510	−1.78447	−0.892237	−	0.451568i	$-0.850865\pi$
$5$	−19.9510	−1.78447	−0.892237	+	0.451568i	$0.850865\pi$
$6$	−27.0449	−1.84018
$7$	−0.0210524	−0.00113672	−0.000568361	−	1.00000i	$-0.500181\pi$
$7$	−0.0210524	−0.00113672	−0.000568361		1.00000i	$0.500181\pi$
$8$	−78.5880	−3.47313
$9$	−2.84554	−0.105390
$10$	109.787	3.47178
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	109.506	2.63432
$13$	0	0
$13$	0	0
$14$	0.115848	0.00221155
$15$	−98.0537	−1.68782
$16$	254.207	3.97198
$17$	−82.6180	−1.17870	−0.589348	−	0.807880i	$-0.700615\pi$
$17$	−82.6180	−1.17870	−0.589348	+	0.807880i	$0.700615\pi$
$18$	15.6586	0.205042
$19$	28.9630	0.349714	0.174857	−	0.984594i	$-0.444054\pi$
$19$	28.9630	0.349714	0.174857	+	0.984594i	$0.444054\pi$
$20$	−444.535	−4.97005
$21$	−0.103467	−0.00107516
$22$	60.5313	0.586605
$23$	−68.4191	−0.620277	−0.310139	−	0.950691i	$-0.600375\pi$
$23$	−68.4191	−0.620277	−0.310139	+	0.950691i	$0.600375\pi$
$24$	−386.238	−3.28502
$25$	273.043	2.18435
$26$	0	0
$27$	−146.682	−1.04552
$28$	−0.469075	−0.00316596
$29$	61.3270	0.392694	0.196347	−	0.980534i	$-0.437092\pi$
$29$	61.3270	0.392694	0.196347	+	0.980534i	$0.437092\pi$
$30$	539.574	3.28374
$31$	274.440	1.59003	0.795015	−	0.606590i	$-0.207463\pi$
$31$	274.440	1.59003	0.795015	+	0.606590i	$0.207463\pi$
$32$	−770.158	−4.25456
$33$	−54.0619	−0.285181
$34$	454.634	2.29321
$35$	0.420017	0.00202845
$36$	−63.4024	−0.293529
$37$	−312.918	−1.39036	−0.695180	−	0.718836i	$-0.744675\pi$
$37$	−312.918	−1.39036	−0.695180	+	0.718836i	$0.744675\pi$
$38$	−159.379	−0.680385
$39$	0	0
$40$	1567.91	6.19771
$41$	366.564	1.39628	0.698142	−	0.715959i	$-0.254010\pi$
$41$	366.564	1.39628	0.698142	+	0.715959i	$0.254010\pi$
$42$	0.569361	0.00209177
$43$	−405.741	−1.43895	−0.719476	−	0.694518i	$-0.755618\pi$
$43$	−405.741	−1.43895	−0.719476	+	0.694518i	$0.755618\pi$
$44$	−245.095	−0.839759
$45$	56.7714	0.188066
$46$	376.500	1.20678
$47$	−594.007	−1.84351	−0.921753	−	0.387778i	$-0.873243\pi$
$47$	−594.007	−1.84351	−0.921753	+	0.387778i	$0.873243\pi$
$48$	1249.36	3.75685
$49$	−343.000	−0.999999
$50$	−1502.51	−4.24975
$51$	−406.044	−1.11485
$52$	0	0
$53$	−187.715	−0.486501	−0.243251	−	0.969963i	$-0.578214\pi$
$53$	−187.715	−0.486501	−0.243251	+	0.969963i	$0.578214\pi$
$54$	807.171	2.03411
$55$	219.461	0.538039
$56$	1.65446	0.00394798
$57$	142.345	0.330772
$58$	−337.473	−0.764006
$59$	−5.47713	−0.0120858	−0.00604290	−	0.999982i	$-0.501924\pi$
$59$	−5.47713	−0.0120858	−0.00604290	+	0.999982i	$0.501924\pi$
$60$	−2184.77	−4.70087
$61$	−598.488	−1.25620	−0.628102	−	0.778131i	$-0.716168\pi$
$61$	−598.488	−1.25620	−0.628102	+	0.778131i	$0.716168\pi$
$62$	−1510.20	−3.09348
$63$	0.0599054	0.000119799 0
$64$	2204.41	4.30548
$65$	0	0
$66$	297.494	0.554834
$67$	−285.078	−0.519818	−0.259909	−	0.965633i	$-0.583692\pi$
$67$	−285.078	−0.519818	−0.259909	+	0.965633i	$0.583692\pi$
$68$	−1840.84	−3.28286
$69$	−336.261	−0.586682
$70$	−2.31129	−0.00394645
$71$	−394.832	−0.659971	−0.329985	−	0.943986i	$-0.607044\pi$
$71$	−394.832	−0.659971	−0.329985	+	0.943986i	$0.607044\pi$
$72$	223.625	0.366034
$73$	−687.195	−1.10178	−0.550891	−	0.834577i	$-0.685712\pi$
$73$	−687.195	−1.10178	−0.550891	+	0.834577i	$0.685712\pi$
$74$	1721.94	2.70502
$75$	1341.93	2.06604
$76$	645.333	0.974010
$77$	0.231576	0.000342735 0
$78$	0	0
$79$	−181.218	−0.258083	−0.129042	−	0.991639i	$-0.541190\pi$
$79$	−181.218	−0.258083	−0.129042	+	0.991639i	$0.541190\pi$
$80$	−5071.69	−7.08790
$81$	−644.073	−0.883503
$82$	−2017.15	−2.71654
$83$	−635.266	−0.840114	−0.420057	−	0.907498i	$-0.637990\pi$
$83$	−635.266	−0.840114	−0.420057	+	0.907498i	$0.637990\pi$
$84$	−2.30537	−0.00299449
$85$	1648.31	2.10335
$86$	2232.73	2.79955
$87$	301.405	0.371425
$88$	864.468	1.04719
$89$	−559.789	−0.666713	−0.333357	−	0.942801i	$-0.608181\pi$
$89$	−559.789	−0.666713	−0.333357	+	0.942801i	$0.608181\pi$
$90$	−312.404	−0.365892
$91$	0	0
$92$	−1524.47	−1.72757
$93$	1348.80	1.50391
$94$	3268.73	3.58663
$95$	−577.841	−0.624055
$96$	−3785.11	−4.02413
$97$	690.391	0.722666	0.361333	−	0.932437i	$-0.382322\pi$
$97$	690.391	0.722666	0.361333	+	0.932437i	$0.382322\pi$
$98$	1887.47	1.94555
$99$	31.3009	0.0317764
$100$	6083.76	6.08376
$101$	1354.61	1.33454	0.667271	−	0.744815i	$-0.267462\pi$
$101$	1354.61	1.33454	0.667271	+	0.744815i	$0.267462\pi$
$102$	2234.40	2.16901
$103$	−324.720	−0.310637	−0.155319	−	0.987864i	$-0.549640\pi$
$103$	−324.720	−0.310637	−0.155319	+	0.987864i	$0.549640\pi$
$104$	0	0
$105$	2.06426	0.00191859
$106$	1032.96	0.946513
$107$	−1235.21	−1.11601	−0.558003	−	0.829839i	$-0.688432\pi$
$107$	−1235.21	−1.11601	−0.558003	+	0.829839i	$0.688432\pi$
$108$	−3268.28	−2.91195
$109$	818.827	0.719536	0.359768	−	0.933042i	$-0.382856\pi$
$109$	818.827	0.719536	0.359768	+	0.933042i	$0.382856\pi$
$110$	−1207.66	−1.04678
$111$	−1537.90	−1.31506
$112$	−5.35166	−0.00451504
$113$	491.465	0.409143	0.204571	−	0.978852i	$-0.434420\pi$
$113$	491.465	0.409143	0.204571	+	0.978852i	$0.434420\pi$
$114$	−783.302	−0.643534
$115$	1365.03	1.10687
$116$	1366.45	1.09372
$117$	0	0
$118$	30.1398	0.0235135
$119$	1.73931	0.00133985
$120$	7705.84	5.86203
$121$	121.000	0.0909091
$122$	3293.39	2.44401
$123$	1801.56	1.32066
$124$	6114.89	4.42850
$125$	−2953.61	−2.11343
$126$	−0.329650	−0.000233076 0
$127$	126.079	0.0880923	0.0440461	−	0.999029i	$-0.485975\pi$
$127$	126.079	0.0880923	0.0440461	+	0.999029i	$0.485975\pi$
$128$	−5969.25	−4.12197
$129$	−1994.10	−1.36101
$130$	0	0
$131$	−1232.22	−0.821831	−0.410915	−	0.911674i	$-0.634791\pi$
$131$	−1232.22	−0.821831	−0.410915	+	0.911674i	$0.634791\pi$
$132$	−1204.57	−0.794276
$133$	−0.609739	−0.000397527 0
$134$	1568.74	1.01133
$135$	2926.46	1.86570
$136$	6492.78	4.09376
$137$	1511.34	0.942500	0.471250	−	0.882000i	$-0.343803\pi$
$137$	1511.34	0.942500	0.471250	+	0.882000i	$0.343803\pi$
$138$	1850.39	1.14142
$139$	1686.26	1.02897	0.514485	−	0.857499i	$-0.327983\pi$
$139$	1686.26	1.02897	0.514485	+	0.857499i	$0.327983\pi$
$140$	9.35853	0.00564957
$141$	−2919.38	−1.74366
$142$	2172.70	1.28401
$143$	0	0
$144$	−723.355	−0.418608
$145$	−1223.54	−0.700752
$146$	3781.53	2.14357
$147$	−1685.75	−0.945837
$148$	−6972.22	−3.87238
$149$	304.865	0.167621	0.0838105	−	0.996482i	$-0.473291\pi$
$149$	304.865	0.167621	0.0838105	+	0.996482i	$0.473291\pi$
$150$	−7384.44	−4.01958
$151$	1421.86	0.766285	0.383142	−	0.923689i	$-0.374842\pi$
$151$	1421.86	0.766285	0.383142	+	0.923689i	$0.374842\pi$
$152$	−2276.14	−1.21460
$153$	235.093	0.124223
$154$	−1.27433	−0.000666807 0
$155$	−5475.36	−2.83737
$156$	0	0
$157$	2401.68	1.22086	0.610429	−	0.792071i	$-0.290997\pi$
$157$	2401.68	1.22086	0.610429	+	0.792071i	$0.290997\pi$
$158$	997.214	0.502114
$159$	−922.564	−0.460152
$160$	15365.4	7.59216
$161$	1.44039	0.000705083 0
$162$	3544.24	1.71890
$163$	−2327.42	−1.11839	−0.559195	−	0.829036i	$-0.688890\pi$
$163$	−2327.42	−1.11839	−0.559195	+	0.829036i	$0.688890\pi$
$164$	8167.53	3.88888
$165$	1078.59	0.508898
$166$	3495.77	1.63448
$167$	−1455.95	−0.674640	−0.337320	−	0.941390i	$-0.609520\pi$
$167$	−1455.95	−0.674640	−0.337320	+	0.941390i	$0.609520\pi$
$168$	8.13123	0.00373415
$169$	0	0
$170$	−9070.42	−4.09217
$171$	−82.4152	−0.0368564
$172$	−9040.44	−4.00772
$173$	3236.05	1.42215	0.711075	−	0.703116i	$-0.248209\pi$
$173$	3236.05	1.42215	0.711075	+	0.703116i	$0.248209\pi$
$174$	−1658.58	−0.722626
$175$	−5.74821	−0.00248299
$176$	−2796.28	−1.19760
$177$	−26.9186	−0.0114312
$178$	3080.43	1.29712
$179$	1035.60	0.432428	0.216214	−	0.976346i	$-0.430629\pi$
$179$	1035.60	0.432428	0.216214	+	0.976346i	$0.430629\pi$
$180$	1264.94	0.523795
$181$	−849.939	−0.349036	−0.174518	−	0.984654i	$-0.555837\pi$
$181$	−849.939	−0.349036	−0.174518	+	0.984654i	$0.555837\pi$
$182$	0	0
$183$	−2941.40	−1.18817
$184$	5376.92	2.15430
$185$	6243.02	2.48106
$186$	−7422.22	−2.92593
$187$	908.798	0.355390
$188$	−13235.3	−5.13447
$189$	3.08802	0.00118847
$190$	3179.77	1.21413
$191$	−4523.99	−1.71384	−0.856922	−	0.515445i	$-0.827627\pi$
$191$	−4523.99	−1.71384	−0.856922	+	0.515445i	$0.827627\pi$
$192$	10834.0	4.07229
$193$	−1352.88	−0.504574	−0.252287	−	0.967653i	$-0.581183\pi$
$193$	−1352.88	−0.504574	−0.252287	+	0.967653i	$0.581183\pi$
$194$	−3799.12	−1.40598
$195$	0	0
$196$	−7642.49	−2.78516
$197$	481.342	0.174082	0.0870412	−	0.996205i	$-0.472259\pi$
$197$	481.342	0.174082	0.0870412	+	0.996205i	$0.472259\pi$
$198$	−172.244	−0.0618225
$199$	−2198.42	−0.783126	−0.391563	−	0.920151i	$-0.628065\pi$
$199$	−2198.42	−0.783126	−0.391563	+	0.920151i	$0.628065\pi$
$200$	−21457.9	−7.58652
$201$	−1401.08	−0.491663
$202$	−7454.21	−2.59642
$203$	−1.29108	−0.000446384 0
$204$	−9047.21	−3.10506
$205$	−7313.33	−2.49163
$206$	1786.89	0.604360
$207$	194.689	0.0653712
$208$	0	0
$209$	−318.593	−0.105443
$210$	−11.3593	−0.00373271
$211$	775.284	0.252951	0.126476	−	0.991970i	$-0.459633\pi$
$211$	775.284	0.252951	0.126476	+	0.991970i	$0.459633\pi$
$212$	−4182.53	−1.35499
$213$	−1940.49	−0.624226
$214$	6797.19	2.17125
$215$	8094.94	2.56777
$216$	11527.5	3.63123
$217$	−5.77762	−0.00180742
$218$	−4505.88	−1.39989
$219$	−3377.37	−1.04211
$220$	4889.89	1.49853
$221$	0	0
$222$	8462.84	2.55851
$223$	−5886.71	−1.76773	−0.883864	−	0.467744i	$-0.845067\pi$
$223$	−5886.71	−1.76773	−0.883864	+	0.467744i	$0.845067\pi$
$224$	16.2137	0.00483626
$225$	−776.955	−0.230209
$226$	−2704.46	−0.796008
$227$	530.645	0.155155	0.0775774	−	0.996986i	$-0.475281\pi$
$227$	530.645	0.155155	0.0775774	+	0.996986i	$0.475281\pi$
$228$	3171.63	0.921256
$229$	−6126.53	−1.76791	−0.883957	−	0.467569i	$-0.845130\pi$
$229$	−6126.53	−1.76791	−0.883957	+	0.467569i	$0.845130\pi$
$230$	−7511.56	−2.15347
$231$	1.13813	0.000324171 0
$232$	−4819.56	−1.36388
$233$	5892.97	1.65691	0.828457	−	0.560052i	$-0.189219\pi$
$233$	5892.97	1.65691	0.828457	+	0.560052i	$0.189219\pi$
$234$	0	0
$235$	11851.0	3.28969
$236$	−122.038	−0.0336609
$237$	−890.634	−0.244105
$238$	−9.57114	−0.00260674
$239$	5877.10	1.59062	0.795309	−	0.606204i	$-0.207308\pi$
$239$	5877.10	1.59062	0.795309	+	0.606204i	$0.207308\pi$
$240$	−24925.9	−6.70401
$241$	3818.88	1.02073	0.510365	−	0.859958i	$-0.329510\pi$
$241$	3818.88	1.02073	0.510365	+	0.859958i	$0.329510\pi$
$242$	−665.845	−0.176868
$243$	794.986	0.209870
$244$	−13335.1	−3.49874
$245$	6843.19	1.78447
$246$	−9913.70	−2.56941
$247$	0	0
$248$	−21567.7	−5.52238
$249$	−3122.15	−0.794612
$250$	16253.3	4.11179
$251$	2115.13	0.531896	0.265948	−	0.963987i	$-0.414315\pi$
$251$	2115.13	0.531896	0.265948	+	0.963987i	$0.414315\pi$
$252$	1.33477	0.000333661 0
$253$	752.610	0.187021
$254$	−693.795	−0.171388
$255$	8101.00	1.98943
$256$	15212.6	3.71402
$257$	6290.62	1.52684	0.763420	−	0.645902i	$-0.223519\pi$
$257$	6290.62	1.52684	0.763420	+	0.645902i	$0.223519\pi$
$258$	10973.2	2.64792
$259$	6.58766	0.00158045
$260$	0	0
$261$	−174.508	−0.0413861
$262$	6780.73	1.59891
$263$	−2656.74	−0.622895	−0.311448	−	0.950263i	$-0.600814\pi$
$263$	−2656.74	−0.622895	−0.311448	+	0.950263i	$0.600814\pi$
$264$	4248.62	0.990470
$265$	3745.10	0.868149
$266$	3.35530	0.000773409 0
$267$	−2751.20	−0.630603
$268$	−6351.91	−1.44778
$269$	−302.328	−0.0685251	−0.0342626	−	0.999413i	$-0.510908\pi$
$269$	−302.328	−0.0685251	−0.0342626	+	0.999413i	$0.510908\pi$
$270$	−16103.9	−3.62982
$271$	−526.911	−0.118109	−0.0590545	−	0.998255i	$-0.518809\pi$
$271$	−526.911	−0.118109	−0.0590545	+	0.998255i	$0.518809\pi$
$272$	−21002.1	−4.68176
$273$	0	0
$274$	−8316.67	−1.83368
$275$	−3003.47	−0.658605
$276$	−7492.34	−1.63401
$277$	2203.35	0.477929	0.238964	−	0.971028i	$-0.423192\pi$
$277$	2203.35	0.477929	0.238964	+	0.971028i	$0.423192\pi$
$278$	−9279.24	−2.00191
$279$	−780.930	−0.167574
$280$	−33.0083	−0.00704507
$281$	80.1140	0.0170078	0.00850391	−	0.999964i	$-0.497293\pi$
$281$	80.1140	0.0170078	0.00850391	+	0.999964i	$0.497293\pi$
$282$	16064.9	3.39237
$283$	−71.1339	−0.0149416	−0.00747080	−	0.999972i	$-0.502378\pi$
$283$	−71.1339	−0.0149416	−0.00747080	+	0.999972i	$0.502378\pi$
$284$	−8797.38	−1.83813
$285$	−2839.92	−0.590255
$286$	0	0
$287$	−7.71705	−0.00158719
$288$	2191.51	0.448390
$289$	1912.74	0.389322
$290$	6732.93	1.36335
$291$	3393.08	0.683525
$292$	−15311.6	−3.06865
$293$	9412.04	1.87665	0.938323	−	0.345760i	$-0.112379\pi$
$293$	9412.04	1.87665	0.938323	+	0.345760i	$0.112379\pi$
$294$	9276.41	1.84017
$295$	109.274	0.0215668
$296$	24591.6	4.82890
$297$	1613.51	0.315236
$298$	−1677.63	−0.326115
$299$	0	0
$300$	29900.0	5.75426
$301$	8.54181	0.00163569
$302$	−7824.25	−1.49085
$303$	6657.53	1.26226
$304$	7362.59	1.38906
$305$	11940.4	2.24166
$306$	−1293.68	−0.241682
$307$	−3413.25	−0.634542	−0.317271	−	0.948335i	$-0.602766\pi$
$307$	−3413.25	−0.634542	−0.317271	+	0.948335i	$0.602766\pi$
$308$	5.15983	0.000954573 0
$309$	−1595.91	−0.293812
$310$	30130.1	5.52024
$311$	−3116.85	−0.568297	−0.284148	−	0.958780i	$-0.591711\pi$
$311$	−3116.85	−0.568297	−0.284148	+	0.958780i	$0.591711\pi$
$312$	0	0
$313$	−3775.05	−0.681720	−0.340860	−	0.940114i	$-0.610718\pi$
$313$	−3775.05	−0.681720	−0.340860	+	0.940114i	$0.610718\pi$
$314$	−13216.1	−2.37524
$315$	−1.19517	−0.000213779 0
$316$	−4037.77	−0.718805
$317$	−238.205	−0.0422048	−0.0211024	−	0.999777i	$-0.506718\pi$
$317$	−238.205	−0.0422048	−0.0211024	+	0.999777i	$0.506718\pi$
$318$	5076.73	0.895248
$319$	−674.597	−0.118402
$320$	−43980.2	−7.68302
$321$	−6070.73	−1.05556
$322$	−7.92623	−0.00137177
$323$	−2392.86	−0.412206
$324$	−14350.8	−2.46070
$325$	0	0
$326$	12807.4	2.17588
$327$	4024.30	0.680564
$328$	−28807.5	−4.84948
$329$	12.5053	0.00209555
$330$	−5935.32	−0.990086
$331$	8354.07	1.38725	0.693627	−	0.720334i	$-0.256012\pi$
$331$	8354.07	1.38725	0.693627	+	0.720334i	$0.256012\pi$
$332$	−14154.6	−2.33986
$333$	890.419	0.146530
$334$	8011.87	1.31255
$335$	5687.59	0.927601
$336$	−26.3019	−0.00427050
$337$	−763.092	−0.123348	−0.0616740	−	0.998096i	$-0.519644\pi$
$337$	−763.092	−0.123348	−0.0616740	+	0.998096i	$0.519644\pi$
$338$	0	0
$339$	2415.41	0.386983
$340$	36726.6	5.85818
$341$	−3018.84	−0.479412
$342$	453.518	0.0717060
$343$	14.4419	0.00227344
$344$	31886.3	4.99766
$345$	6708.75	1.04692
$346$	−17807.5	−2.76687
$347$	5935.26	0.918217	0.459109	−	0.888380i	$-0.348169\pi$
$347$	5935.26	0.918217	0.459109	+	0.888380i	$0.348169\pi$
$348$	6715.70	1.03448
$349$	−1073.72	−0.164685	−0.0823424	−	0.996604i	$-0.526240\pi$
$349$	−1073.72	−0.164685	−0.0823424	+	0.996604i	$0.526240\pi$
$350$	31.6315	0.00483079
$351$	0	0
$352$	8471.74	1.28280
$353$	−6087.99	−0.917935	−0.458968	−	0.888453i	$-0.651781\pi$
$353$	−6087.99	−0.917935	−0.458968	+	0.888453i	$0.651781\pi$
$354$	148.129	0.0222400
$355$	7877.30	1.17770
$356$	−12472.8	−1.85691
$357$	8.54821	0.00126728
$358$	−5698.77	−0.841311
$359$	−2507.99	−0.368709	−0.184354	−	0.982860i	$-0.559019\pi$
$359$	−2507.99	−0.368709	−0.184354	+	0.982860i	$0.559019\pi$
$360$	−4461.55	−0.653178
$361$	−6020.15	−0.877700
$362$	4677.08	0.679066
$363$	594.681	0.0859853
$364$	0	0
$365$	13710.2	1.96610
$366$	16186.1	2.31164
$367$	11910.7	1.69410	0.847049	−	0.531515i	$-0.178377\pi$
$367$	11910.7	1.69410	0.847049	+	0.531515i	$0.178377\pi$
$368$	−17392.6	−2.46373
$369$	−1043.07	−0.147155
$370$	−34354.4	−4.82703
$371$	3.95184	0.000553017 0
$372$	30053.0	4.18864
$373$	12318.9	1.71005	0.855024	−	0.518589i	$-0.173542\pi$
$373$	12318.9	1.71005	0.855024	+	0.518589i	$0.173542\pi$
$374$	−5000.98	−0.691429
$375$	−14516.2	−1.99897
$376$	46681.8	6.40274
$377$	0	0
$378$	−16.9929	−0.00231222
$379$	−4917.34	−0.666456	−0.333228	−	0.942846i	$-0.608138\pi$
$379$	−4917.34	−0.666456	−0.333228	+	0.942846i	$0.608138\pi$
$380$	−12875.1	−1.73810
$381$	619.644	0.0833210
$382$	24894.8	3.33437
$383$	−3597.33	−0.479934	−0.239967	−	0.970781i	$-0.577137\pi$
$383$	−3597.33	−0.479934	−0.239967	+	0.970781i	$0.577137\pi$
$384$	−29337.2	−3.89872
$385$	−4.62018	−0.000611601 0
$386$	7444.71	0.981673
$387$	1154.55	0.151651
$388$	15382.8	2.01274
$389$	2156.80	0.281115	0.140558	−	0.990072i	$-0.455110\pi$
$389$	2156.80	0.281115	0.140558	+	0.990072i	$0.455110\pi$
$390$	0	0
$391$	5652.65	0.731118
$392$	26955.6	3.47313
$393$	−6056.03	−0.777319
$394$	−2648.75	−0.338686
$395$	3615.48	0.460543
$396$	697.426	0.0885025
$397$	−134.726	−0.0170320	−0.00851599	−	0.999964i	$-0.502711\pi$
$397$	−134.726	−0.0170320	−0.00851599	+	0.999964i	$0.502711\pi$
$398$	12097.6	1.52361
$399$	−2.99670	−0.000375996 0
$400$	69409.5	8.67618
$401$	−6923.43	−0.862194	−0.431097	−	0.902306i	$-0.641873\pi$
$401$	−6923.43	−0.862194	−0.431097	+	0.902306i	$0.641873\pi$
$402$	7709.91	0.956556
$403$	0	0
$404$	30182.5	3.71692
$405$	12849.9	1.57659
$406$	7.10461	0.000868463 0
$407$	3442.09	0.419209
$408$	31910.2	3.87204
$409$	5507.86	0.665883	0.332942	−	0.942947i	$-0.391959\pi$
$409$	5507.86	0.665883	0.332942	+	0.942947i	$0.391959\pi$
$410$	40244.1	4.84760
$411$	7427.81	0.891452
$412$	−7235.19	−0.865176
$413$	0.115307	1.37382e−5 0
$414$	−1071.35	−0.127183
$415$	12674.2	1.49916
$416$	0	0
$417$	8287.50	0.973239
$418$	1753.17	0.205144
$419$	−8486.24	−0.989451	−0.494726	−	0.869049i	$-0.664731\pi$
$419$	−8486.24	−0.989451	−0.494726	+	0.869049i	$0.664731\pi$
$420$	45.9945	0.00534358
$421$	2175.60	0.251859	0.125929	−	0.992039i	$-0.459809\pi$
$421$	2175.60	0.251859	0.125929	+	0.992039i	$0.459809\pi$
$422$	−4266.27	−0.492129
$423$	1690.27	0.194288
$424$	14752.1	1.68968
$425$	−22558.3	−2.57468
$426$	10678.2	1.21446
$427$	12.5996	0.00142796
$428$	−27522.2	−3.10826
$429$	0	0
$430$	−44545.2	−4.99573
$431$	602.045	0.0672842	0.0336421	−	0.999434i	$-0.489289\pi$
$431$	602.045	0.0672842	0.0336421	+	0.999434i	$0.489289\pi$
$432$	−37287.7	−4.15279
$433$	3796.23	0.421328	0.210664	−	0.977559i	$-0.432437\pi$
$433$	3796.23	0.421328	0.210664	+	0.977559i	$0.432437\pi$
$434$	31.7934	0.00351643
$435$	−6013.33	−0.662798
$436$	18244.6	2.00403
$437$	−1981.62	−0.216919
$438$	18585.2	2.02747
$439$	−11398.5	−1.23923	−0.619616	−	0.784905i	$-0.712712\pi$
$439$	−11398.5	−1.23923	−0.619616	+	0.784905i	$0.712712\pi$
$440$	−17247.0	−1.86868
$441$	976.018	0.105390
$442$	0	0
$443$	16036.8	1.71993	0.859967	−	0.510349i	$-0.170484\pi$
$443$	16036.8	1.71993	0.859967	+	0.510349i	$0.170484\pi$
$444$	−34266.5	−3.66265
$445$	11168.4	1.18973
$446$	32393.7	3.43920
$447$	1498.33	0.158542
$448$	−46.4081	−0.00489414
$449$	−5894.56	−0.619558	−0.309779	−	0.950809i	$-0.600255\pi$
$449$	−5894.56	−0.619558	−0.309779	+	0.950809i	$0.600255\pi$
$450$	4275.46	0.447883
$451$	−4032.20	−0.420996
$452$	10950.5	1.13953
$453$	6988.02	0.724781
$454$	−2920.06	−0.301862
$455$	0	0
$456$	−11186.6	−1.14882
$457$	−7278.25	−0.744994	−0.372497	−	0.928033i	$-0.621498\pi$
$457$	−7278.25	−0.744994	−0.372497	+	0.928033i	$0.621498\pi$
$458$	33713.3	3.43956
$459$	12118.6	1.23235
$460$	30414.7	3.08281
$461$	−4559.48	−0.460642	−0.230321	−	0.973115i	$-0.573978\pi$
$461$	−4559.48	−0.460642	−0.230321	+	0.973115i	$0.573978\pi$
$462$	−6.26297	−0.000630692 0
$463$	9360.87	0.939604	0.469802	−	0.882772i	$-0.344325\pi$
$463$	9360.87	0.939604	0.469802	+	0.882772i	$0.344325\pi$
$464$	15589.7	1.55977
$465$	−26909.9	−2.68369
$466$	−32428.1	−3.22361
$467$	3935.28	0.389942	0.194971	−	0.980809i	$-0.437539\pi$
$467$	3935.28	0.389942	0.194971	+	0.980809i	$0.437539\pi$
$468$	0	0
$469$	6.00156	0.000590888 0
$470$	−65214.5	−6.40025
$471$	11803.6	1.15473
$472$	430.437	0.0419755
$473$	4463.15	0.433860
$474$	4901.02	0.474919
$475$	7908.14	0.763895
$476$	38.7541	0.00373170
$477$	534.149	0.0512725
$478$	−32340.8	−3.09463
$479$	−2932.44	−0.279721	−0.139861	−	0.990171i	$-0.544665\pi$
$479$	−2932.44	−0.279721	−0.139861	+	0.990171i	$0.544665\pi$
$480$	75516.8	7.18095
$481$	0	0
$482$	−21014.7	−1.98588
$483$	7.07909	0.000666894 0
$484$	2696.04	0.253197
$485$	−13774.0	−1.28958
$486$	−4374.69	−0.408312
$487$	−262.144	−0.0243920	−0.0121960	−	0.999926i	$-0.503882\pi$
$487$	−262.144	−0.0243920	−0.0121960	+	0.999926i	$0.503882\pi$
$488$	47033.9	4.36296
$489$	−11438.6	−1.05782
$490$	−37657.0	−3.47178
$491$	1598.74	0.146946	0.0734728	−	0.997297i	$-0.476592\pi$
$491$	1598.74	0.146946	0.0734728	+	0.997297i	$0.476592\pi$
$492$	40141.1	3.67826
$493$	−5066.71	−0.462867
$494$	0	0
$495$	−624.485	−0.0567041
$496$	69764.6	6.31557
$497$	8.31215	0.000750203 0
$498$	17180.7	1.54596
$499$	11032.8	0.989775	0.494888	−	0.868957i	$-0.335209\pi$
$499$	11032.8	0.989775	0.494888	+	0.868957i	$0.335209\pi$
$500$	−65810.4	−5.88626
$501$	−7155.59	−0.638100
$502$	−11639.3	−1.03483
$503$	16037.7	1.42165	0.710823	−	0.703371i	$-0.248323\pi$
$503$	16037.7	1.42165	0.710823	+	0.703371i	$0.248323\pi$
$504$	−4.70784	−0.000416079 0
$505$	−27025.9	−2.38146
$506$	−4141.50	−0.363858
$507$	0	0
$508$	2809.21	0.245352
$509$	9419.64	0.820272	0.410136	−	0.912024i	$-0.365481\pi$
$509$	9419.64	0.820272	0.410136	+	0.912024i	$0.365481\pi$
$510$	−44578.6	−3.87053
$511$	14.4671	0.00125242
$512$	−35958.7	−3.10384
$513$	−4248.36	−0.365633
$514$	−34616.3	−2.97054
$515$	6478.50	0.554324
$516$	−44431.2	−3.79065
$517$	6534.07	0.555838
$518$	−36.2509	−0.00307485
$519$	15904.3	1.34512
$520$	0	0
$521$	−5043.93	−0.424143	−0.212072	−	0.977254i	$-0.568021\pi$
$521$	−5043.93	−0.424143	−0.212072	+	0.977254i	$0.568021\pi$
$522$	960.292	0.0805188
$523$	−14254.0	−1.19175	−0.595874	−	0.803078i	$-0.703194\pi$
$523$	−14254.0	−1.19175	−0.595874	+	0.803078i	$0.703194\pi$
$524$	−27455.6	−2.28893
$525$	−28.2508	−0.00234851
$526$	14619.6	1.21187
$527$	−22673.7	−1.87416
$528$	−13742.9	−1.13273
$529$	−7485.82	−0.615256
$530$	−20608.7	−1.68903
$531$	15.5854	0.00127373
$532$	−13.5858	−0.00110718
$533$	0	0
$534$	15139.5	1.22687
$535$	24643.8	1.99148
$536$	22403.7	1.80539
$537$	5089.70	0.409007
$538$	1663.66	0.133319
$539$	3773.00	0.301511
$540$	65205.5	5.19629
$541$	14220.1	1.13007	0.565036	−	0.825066i	$-0.308862\pi$
$541$	14220.1	1.13007	0.565036	+	0.825066i	$0.308862\pi$
$542$	2899.51	0.229787
$543$	−4177.21	−0.330131
$544$	63629.0	5.01483
$545$	−16336.4	−1.28399
$546$	0	0
$547$	−17391.2	−1.35941	−0.679703	−	0.733487i	$-0.737891\pi$
$547$	−17391.2	−1.35941	−0.679703	+	0.733487i	$0.737891\pi$
$548$	33674.7	2.62502
$549$	1703.02	0.132392
$550$	16527.7	1.28135
$551$	1776.21	0.137330
$552$	26426.1	2.03762
$553$	3.81507	0.000293369 0
$554$	−12124.7	−0.929834
$555$	30682.7	2.34668
$556$	37572.1	2.86585
$557$	−9921.78	−0.754756	−0.377378	−	0.926059i	$-0.623174\pi$
$557$	−9921.78	−0.754756	−0.377378	+	0.926059i	$0.623174\pi$
$558$	4297.34	0.326023
$559$	0	0
$560$	106.771	0.00805697
$561$	4466.49	0.336141
$562$	−440.855	−0.0330896
$563$	9352.12	0.700080	0.350040	−	0.936735i	$-0.386168\pi$
$563$	9352.12	0.700080	0.350040	+	0.936735i	$0.386168\pi$
$564$	−65047.6	−4.85638
$565$	−9805.22	−0.730104
$566$	391.439	0.0290696
$567$	13.5593	0.00100430
$568$	31029.0	2.29216
$569$	−3142.55	−0.231534	−0.115767	−	0.993276i	$-0.536933\pi$
$569$	−3142.55	−0.231534	−0.115767	+	0.993276i	$0.536933\pi$
$570$	15627.7	1.14837
$571$	316.176	0.0231726	0.0115863	−	0.999933i	$-0.496312\pi$
$571$	316.176	0.0231726	0.0115863	+	0.999933i	$0.496312\pi$
$572$	0	0
$573$	−22234.1	−1.62102
$574$	42.4657	0.00308795
$575$	−18681.4	−1.35490
$576$	−6272.73	−0.453756
$577$	17713.9	1.27806	0.639028	−	0.769184i	$-0.279337\pi$
$577$	17713.9	1.27806	0.639028	+	0.769184i	$0.279337\pi$
$578$	−10525.5	−0.757446
$579$	−6649.04	−0.477245
$580$	−27262.0	−1.95171
$581$	13.3739	0.000954976 0
$582$	−18671.6	−1.32983
$583$	2064.86	0.146686
$584$	54005.3	3.82664
$585$	0	0
$586$	−51793.0	−3.65111
$587$	−2637.10	−0.185426	−0.0927128	−	0.995693i	$-0.529554\pi$
$587$	−2637.10	−0.185426	−0.0927128	+	0.995693i	$0.529554\pi$
$588$	−37560.7	−2.63431
$589$	7948.60	0.556055
$590$	−601.320	−0.0419592
$591$	2365.66	0.164654
$592$	−79545.8	−5.52249
$593$	20026.2	1.38681	0.693405	−	0.720548i	$-0.256110\pi$
$593$	20026.2	1.38681	0.693405	+	0.720548i	$0.256110\pi$
$594$	−8878.88	−0.613308
$595$	−34.7009	−0.00239092
$596$	6792.80	0.466853
$597$	−10804.6	−0.740710
$598$	0	0
$599$	−11166.5	−0.761685	−0.380843	−	0.924640i	$-0.624366\pi$
$599$	−11166.5	−0.761685	−0.380843	+	0.924640i	$0.624366\pi$
$600$	−105460.	−7.17562
$601$	23305.3	1.58177	0.790884	−	0.611967i	$-0.209621\pi$
$601$	23305.3	1.58177	0.790884	+	0.611967i	$0.209621\pi$
$602$	−47.0043	−0.00318231
$603$	811.199	0.0547837
$604$	31680.8	2.13423
$605$	−2414.07	−0.162225
$606$	−36635.4	−2.45579
$607$	−11882.7	−0.794569	−0.397285	−	0.917695i	$-0.630047\pi$
$607$	−11882.7	−0.794569	−0.397285	+	0.917695i	$0.630047\pi$
$608$	−22306.1	−1.48788
$609$	−6.34529	−0.000422207 0
$610$	−65706.4	−4.36127
$611$	0	0
$612$	5238.18	0.345982
$613$	24421.2	1.60908	0.804539	−	0.593900i	$-0.202412\pi$
$613$	24421.2	1.60908	0.804539	+	0.593900i	$0.202412\pi$
$614$	18782.6	1.23453
$615$	−35942.9	−2.35668
$616$	−18.1991	−0.00119036
$617$	−7231.98	−0.471878	−0.235939	−	0.971768i	$-0.575817\pi$
$617$	−7231.98	−0.471878	−0.235939	+	0.971768i	$0.575817\pi$
$618$	8782.04	0.571627
$619$	−1657.44	−0.107622	−0.0538111	−	0.998551i	$-0.517137\pi$
$619$	−1657.44	−0.107622	−0.0538111	+	0.998551i	$0.517137\pi$
$620$	−121998.	−7.90253
$621$	10035.9	0.648512
$622$	17151.5	1.10565
$623$	11.7849	0.000757868 0
$624$	0	0
$625$	24797.2	1.58702
$626$	20773.5	1.32632
$627$	−1565.79	−0.0997316
$628$	53512.5	3.40029
$629$	25852.6	1.63881
$630$	6.57686	0.000415918 0
$631$	18255.5	1.15173	0.575864	−	0.817545i	$-0.304666\pi$
$631$	18255.5	1.15173	0.575864	+	0.817545i	$0.304666\pi$
$632$	14241.5	0.896357
$633$	3810.30	0.239251
$634$	1310.81	0.0821116
$635$	−2515.41	−0.157198
$636$	−20556.0	−1.28160
$637$	0	0
$638$	3712.20	0.230357
$639$	1123.51	0.0695545
$640$	119093.	7.35555
$641$	2418.51	0.149025	0.0745127	−	0.997220i	$-0.476260\pi$
$641$	2418.51	0.149025	0.0745127	+	0.997220i	$0.476260\pi$
$642$	33406.3	2.05365
$643$	−988.340	−0.0606164	−0.0303082	−	0.999541i	$-0.509649\pi$
$643$	−988.340	−0.0606164	−0.0303082	+	0.999541i	$0.509649\pi$
$644$	32.0937	0.00196377
$645$	39784.4	2.42869
$646$	13167.6	0.801967
$647$	−22175.5	−1.34746	−0.673731	−	0.738976i	$-0.735309\pi$
$647$	−22175.5	−1.34746	−0.673731	+	0.738976i	$0.735309\pi$
$648$	50616.4	3.06852
$649$	60.2484	0.00364400
$650$	0	0
$651$	−28.3954	−0.00170953
$652$	−51858.0	−3.11490
$653$	16877.1	1.01141	0.505705	−	0.862706i	$-0.331232\pi$
$653$	16877.1	1.01141	0.505705	+	0.862706i	$0.331232\pi$
$654$	−22145.1	−1.32407
$655$	24584.1	1.46653
$656$	93183.1	5.54602
$657$	1955.44	0.116117
$658$	−68.8145	−0.00407701
$659$	15924.6	0.941326	0.470663	−	0.882313i	$-0.344015\pi$
$659$	15924.6	0.941326	0.470663	+	0.882313i	$0.344015\pi$
$660$	24032.4	1.41736
$661$	7903.54	0.465071	0.232536	−	0.972588i	$-0.425298\pi$
$661$	7903.54	0.465071	0.232536	+	0.972588i	$0.425298\pi$
$662$	−45971.2	−2.69897
$663$	0	0
$664$	49924.2	2.91783
$665$	12.1649	0.000709377 0
$666$	−4899.84	−0.285082
$667$	−4195.94	−0.243579
$668$	−32440.5	−1.87898
$669$	−28931.5	−1.67198
$670$	−31297.9	−1.80469
$671$	6583.36	0.378760
$672$	79.6856	0.00457432
$673$	−24453.0	−1.40058	−0.700292	−	0.713856i	$-0.746947\pi$
$673$	−24453.0	−1.40058	−0.700292	+	0.713856i	$0.746947\pi$
$674$	4199.18	0.239980
$675$	−40050.6	−2.28378
$676$	0	0
$677$	33030.6	1.87514	0.937570	−	0.347796i	$-0.113070\pi$
$677$	33030.6	1.87514	0.937570	+	0.347796i	$0.113070\pi$
$678$	−13291.6	−0.752894
$679$	−14.5344	−0.000821470 0
$680$	−129538.	−7.30521
$681$	2607.97	0.146751
$682$	16612.2	0.932720
$683$	10308.4	0.577514	0.288757	−	0.957402i	$-0.406758\pi$
$683$	10308.4	0.577514	0.288757	+	0.957402i	$0.406758\pi$
$684$	−1836.32	−0.102651
$685$	−30152.8	−1.68187
$686$	−79.4717	−0.00442310
$687$	−30110.2	−1.67216
$688$	−103142.	−5.71549
$689$	0	0
$690$	−36917.2	−2.03683
$691$	−17197.4	−0.946771	−0.473385	−	0.880855i	$-0.656968\pi$
$691$	−17197.4	−0.946771	−0.473385	+	0.880855i	$0.656968\pi$
$692$	72103.4	3.96093
$693$	−0.658959	−3.61209e−5 0
$694$	−32660.8	−1.78644
$695$	−33642.6	−1.83617
$696$	−23686.8	−1.29001
$697$	−30284.8	−1.64579
$698$	5908.53	0.320403
$699$	28962.3	1.56717
$700$	−128.078	−0.00691555
$701$	−25956.7	−1.39853	−0.699267	−	0.714860i	$-0.746490\pi$
$701$	−25956.7	−1.39853	−0.699267	+	0.714860i	$0.746490\pi$
$702$	0	0
$703$	−9063.02	−0.486228
$704$	−24248.5	−1.29815
$705$	58244.5	3.11151
$706$	33501.3	1.78589
$707$	−28.5178	−0.00151700
$708$	−599.781	−0.0318378
$709$	2704.73	0.143270	0.0716349	−	0.997431i	$-0.477178\pi$
$709$	2704.73	0.143270	0.0716349	+	0.997431i	$0.477178\pi$
$710$	−43347.6	−2.29128
$711$	515.662	0.0271995
$712$	43992.6	2.31558
$713$	−18777.0	−0.986259
$714$	−47.0395	−0.00246556
$715$	0	0
$716$	23074.6	1.20438
$717$	28884.3	1.50447
$718$	13801.1	0.717341
$719$	23346.3	1.21094	0.605472	−	0.795867i	$-0.292984\pi$
$719$	23346.3	1.21094	0.605472	+	0.795867i	$0.292984\pi$
$720$	14431.7	0.746996
$721$	6.83613	0.000353108 0
$722$	33127.9	1.70761
$723$	18768.7	0.965445
$724$	−18937.8	−0.972122
$725$	16744.9	0.857780
$726$	−3272.44	−0.167289
$727$	−23413.7	−1.19445	−0.597224	−	0.802074i	$-0.703730\pi$
$727$	−23413.7	−1.19445	−0.597224	+	0.802074i	$0.703730\pi$
$728$	0	0
$729$	21297.1	1.08201
$730$	−75445.4	−3.82515
$731$	33521.5	1.69608
$732$	−65538.3	−3.30924
$733$	22962.9	1.15710	0.578551	−	0.815646i	$-0.303618\pi$
$733$	22962.9	1.15710	0.578551	+	0.815646i	$0.303618\pi$
$734$	−65542.8	−3.29595
$735$	33632.4	1.68782
$736$	52693.6	2.63901
$737$	3135.85	0.156731
$738$	5739.86	0.286297
$739$	28123.7	1.39993	0.699965	−	0.714177i	$-0.253199\pi$
$739$	28123.7	1.39993	0.699965	+	0.714177i	$0.253199\pi$
$740$	139103.	6.91017
$741$	0	0
$742$	−21.7464	−0.00107592
$743$	34313.9	1.69429	0.847143	−	0.531366i	$-0.178321\pi$
$743$	34313.9	1.69429	0.847143	+	0.531366i	$0.178321\pi$
$744$	−105999.	−5.22328
$745$	−6082.37	−0.299115
$746$	−67789.0	−3.32698
$747$	1807.67	0.0885399
$748$	20249.2	0.989820
$749$	26.0042	0.00126859
$750$	79880.3	3.88909
$751$	25382.3	1.23331	0.616654	−	0.787234i	$-0.288488\pi$
$751$	25382.3	1.23331	0.616654	+	0.787234i	$0.288488\pi$
$752$	−151001.	−7.32238
$753$	10395.3	0.503088
$754$	0	0
$755$	−28367.5	−1.36741
$756$	68.8051	0.00331008
$757$	−481.805	−0.0231328	−0.0115664	−	0.999933i	$-0.503682\pi$
$757$	−481.805	−0.0231328	−0.0115664	+	0.999933i	$0.503682\pi$
$758$	27059.4	1.29662
$759$	3698.87	0.176891
$760$	45411.3	2.16742
$761$	−4108.73	−0.195718	−0.0978591	−	0.995200i	$-0.531199\pi$
$761$	−4108.73	−0.195718	−0.0978591	+	0.995200i	$0.531199\pi$
$762$	−3409.81	−0.162105
$763$	−17.2383	−0.000817912 0
$764$	−100800.	−4.77334
$765$	−4690.34	−0.221673
$766$	19795.5	0.933736
$767$	0	0
$768$	74765.8	3.51286
$769$	−17654.4	−0.827870	−0.413935	−	0.910306i	$-0.635846\pi$
$769$	−17654.4	−0.827870	−0.413935	+	0.910306i	$0.635846\pi$
$770$	25.4242	0.00118990
$771$	30916.6	1.44414
$772$	−30144.0	−1.40532
$773$	−3895.81	−0.181271	−0.0906356	−	0.995884i	$-0.528890\pi$
$773$	−3895.81	−0.181271	−0.0906356	+	0.995884i	$0.528890\pi$
$774$	−6353.32	−0.295046
$775$	74934.0	3.47317
$776$	−54256.4	−2.50991
$777$	32.3765	0.00149485
$778$	−11868.5	−0.546924
$779$	10616.8	0.488300
$780$	0	0
$781$	4343.15	0.198989
$782$	−31105.7	−1.42243
$783$	−8995.59	−0.410570
$784$	−87192.9	−3.97198
$785$	−47915.9	−2.17859
$786$	33325.4	1.51231
$787$	12042.7	0.545457	0.272728	−	0.962091i	$-0.412074\pi$
$787$	12042.7	0.545457	0.272728	+	0.962091i	$0.412074\pi$
$788$	10724.9	0.484848
$789$	−13057.1	−0.589158
$790$	−19895.4	−0.896010
$791$	−10.3465	−0.000465082 0
$792$	−2459.88	−0.110363
$793$	0	0
$794$	741.376	0.0331366
$795$	18406.1	0.821128
$796$	−48983.8	−2.18113
$797$	−23030.4	−1.02356	−0.511780	−	0.859117i	$-0.671014\pi$
$797$	−23030.4	−1.02356	−0.511780	+	0.859117i	$0.671014\pi$
$798$	16.4904	0.000731520 0
$799$	49075.7	2.17293
$800$	−210286.	−9.29344
$801$	1592.90	0.0702651
$802$	38098.6	1.67744
$803$	7559.15	0.332200
$804$	−31217.8	−1.36936
$805$	−28.7372	−0.00125820
$806$	0	0
$807$	−1485.86	−0.0648137
$808$	−106456.	−4.63504
$809$	−31390.3	−1.36418	−0.682092	−	0.731266i	$-0.738930\pi$
$809$	−31390.3	−1.36418	−0.682092	+	0.731266i	$0.738930\pi$
$810$	−70711.2	−3.06733
$811$	−5068.92	−0.219475	−0.109737	−	0.993961i	$-0.535001\pi$
$811$	−5068.92	−0.219475	−0.109737	+	0.993961i	$0.535001\pi$
$812$	−28.7670	−0.00124325
$813$	−2589.62	−0.111712
$814$	−18941.3	−0.815593
$815$	46434.4	1.99574
$816$	−103219.	−4.42818
$817$	−11751.5	−0.503221
$818$	−30308.9	−1.29551
$819$	0	0
$820$	−162951.	−6.93961
$821$	38377.4	1.63140	0.815701	−	0.578474i	$-0.196352\pi$
$821$	38377.4	1.63140	0.815701	+	0.578474i	$0.196352\pi$
$822$	−40874.1	−1.73437
$823$	−15895.4	−0.673241	−0.336620	−	0.941640i	$-0.609284\pi$
$823$	−15895.4	−0.673241	−0.336620	+	0.941640i	$0.609284\pi$
$824$	25519.1	1.07888
$825$	−14761.2	−0.622934
$826$	−0.634515	−2.67283e−5 0
$827$	−18167.2	−0.763887	−0.381944	−	0.924186i	$-0.624745\pi$
$827$	−18167.2	−0.763887	−0.381944	+	0.924186i	$0.624745\pi$
$828$	4337.93	0.182070
$829$	−25570.2	−1.07128	−0.535640	−	0.844447i	$-0.679930\pi$
$829$	−25570.2	−1.07128	−0.535640	+	0.844447i	$0.679930\pi$
$830$	−69744.2	−2.91669
$831$	10828.8	0.452043
$832$	0	0
$833$	28337.9	1.17869
$834$	−45604.8	−1.89349
$835$	29047.7	1.20388
$836$	−7098.67	−0.293675
$837$	−40255.6	−1.66241
$838$	46698.5	1.92503
$839$	−16444.9	−0.676687	−0.338343	−	0.941023i	$-0.609867\pi$
$839$	−16444.9	−0.676687	−0.338343	+	0.941023i	$0.609867\pi$
$840$	−162.226	−0.00666350
$841$	−20628.0	−0.845791
$842$	−11972.0	−0.490003
$843$	393.738	0.0160866
$844$	17274.3	0.704511
$845$	0	0
$846$	−9301.29	−0.377996
$847$	−2.54734	−0.000103338 0
$848$	−47718.3	−1.93238
$849$	−349.603	−0.0141323
$850$	124135.	5.00916
$851$	21409.5	0.862409
$852$	−43236.6	−1.73857
$853$	−34970.7	−1.40372	−0.701860	−	0.712315i	$-0.747647\pi$
$853$	−34970.7	−1.40372	−0.701860	+	0.712315i	$0.747647\pi$
$854$	−69.3336	−0.00277816
$855$	1644.27	0.0657693
$856$	97073.0	3.87603
$857$	−13266.1	−0.528777	−0.264389	−	0.964416i	$-0.585170\pi$
$857$	−13266.1	−0.528777	−0.264389	+	0.964416i	$0.585170\pi$
$858$	0	0
$859$	−21088.9	−0.837655	−0.418828	−	0.908066i	$-0.637559\pi$
$859$	−21088.9	−0.837655	−0.418828	+	0.908066i	$0.637559\pi$
$860$	180366.	7.15167
$861$	−37.9271	−0.00150122
$862$	−3312.96	−0.130905
$863$	13677.1	0.539483	0.269742	−	0.962933i	$-0.413062\pi$
$863$	13677.1	0.539483	0.269742	+	0.962933i	$0.413062\pi$
$864$	112969.	4.44823
$865$	−64562.4	−2.53779
$866$	−20890.1	−0.819715
$867$	9400.58	0.368236
$868$	−128.733	−0.00503397
$869$	1993.40	0.0778151
$870$	33090.4	1.28951
$871$	0	0
$872$	−64349.9	−2.49904
$873$	−1964.53	−0.0761620
$874$	10904.6	0.422028
$875$	62.1806	0.00240239
$876$	−75252.3	−2.90244
$877$	5995.46	0.230847	0.115423	−	0.993316i	$-0.463178\pi$
$877$	5995.46	0.230847	0.115423	+	0.993316i	$0.463178\pi$
$878$	62724.5	2.41099
$879$	46257.5	1.77500
$880$	55788.6	2.13708
$881$	−16033.2	−0.613137	−0.306569	−	0.951849i	$-0.599181\pi$
$881$	−16033.2	−0.613137	−0.306569	+	0.951849i	$0.599181\pi$
$882$	−5370.88	−0.205042
$883$	7865.05	0.299751	0.149875	−	0.988705i	$-0.452113\pi$
$883$	7865.05	0.299751	0.149875	+	0.988705i	$0.452113\pi$
$884$	0	0
$885$	537.053	0.0203987
$886$	−88248.0	−3.34622
$887$	−28944.0	−1.09565	−0.547827	−	0.836592i	$-0.684545\pi$
$887$	−28944.0	−1.09565	−0.547827	+	0.836592i	$0.684545\pi$
$888$	120861.	4.56736
$889$	−2.65427	−0.000100136 0
$890$	−61457.7	−2.31468
$891$	7084.81	0.266386
$892$	−131164.	−4.92341
$893$	−17204.2	−0.644699
$894$	−8245.07	−0.308452
$895$	−20661.4	−0.771657
$896$	125.667	0.00468554
$897$	0	0
$898$	32436.9	1.20538
$899$	16830.6	0.624395
$900$	−17311.6	−0.641170
$901$	15508.6	0.573437
$902$	22188.6	0.819068
$903$	41.9806	0.00154710
$904$	−38623.2	−1.42101
$905$	16957.1	0.622845
$906$	−38454.0	−1.41010
$907$	13460.3	0.492769	0.246385	−	0.969172i	$-0.420757\pi$
$907$	13460.3	0.492769	0.246385	+	0.969172i	$0.420757\pi$
$908$	11823.5	0.432132
$909$	−3854.59	−0.140648
$910$	0	0
$911$	−22224.3	−0.808258	−0.404129	−	0.914702i	$-0.632425\pi$
$911$	−22224.3	−0.808258	−0.404129	+	0.914702i	$0.632425\pi$
$912$	36185.0	1.31382
$913$	6987.92	0.253304
$914$	40051.1	1.44942
$915$	58683.9	2.12025
$916$	−136507.	−4.92393
$917$	25.9412	0.000934193 0
$918$	−66686.9	−2.39760
$919$	12565.6	0.451035	0.225517	−	0.974239i	$-0.427593\pi$
$919$	12565.6	0.451035	0.225517	+	0.974239i	$0.427593\pi$
$920$	−107275.	−3.84430
$921$	−16775.2	−0.600174
$922$	25090.1	0.896202
$923$	0	0
$924$	25.3591	0.000902871 0
$925$	−85440.0	−3.03703
$926$	−51511.4	−1.82805
$927$	924.003	0.0327381
$928$	−47231.5	−1.67074
$929$	10359.7	0.365868	0.182934	−	0.983125i	$-0.441441\pi$
$929$	10359.7	0.365868	0.182934	+	0.983125i	$0.441441\pi$
$930$	148081.	5.22125
$931$	−9934.28	−0.349713
$932$	131303.	4.61478
$933$	−15318.4	−0.537517
$934$	−21655.2	−0.758651
$935$	−18131.5	−0.634184
$936$	0	0
$937$	45186.8	1.57544	0.787720	−	0.616034i	$-0.211261\pi$
$937$	45186.8	1.57544	0.787720	+	0.616034i	$0.211261\pi$
$938$	−33.0257	−0.00114960
$939$	−18553.3	−0.644797
$940$	264057.	9.16233
$941$	−33945.3	−1.17597	−0.587984	−	0.808873i	$-0.700078\pi$
$941$	−33945.3	−1.17597	−0.587984	+	0.808873i	$0.700078\pi$
$942$	−64953.2	−2.24659
$943$	−25080.0	−0.866084
$944$	−1392.32	−0.0480046
$945$	−61.6091	−0.00212079
$946$	−24560.0	−0.844097
$947$	−42756.6	−1.46716	−0.733582	−	0.679601i	$-0.762153\pi$
$947$	−42756.6	−1.46716	−0.733582	+	0.679601i	$0.762153\pi$
$948$	−19844.5	−0.679873
$949$	0	0
$950$	−43517.3	−1.48620
$951$	−1170.71	−0.0399189
$952$	−136.689	−0.00465347
$953$	−26775.3	−0.910113	−0.455056	−	0.890463i	$-0.650381\pi$
$953$	−26775.3	−0.910113	−0.455056	+	0.890463i	$0.650381\pi$
$954$	−2939.34	−0.0997533
$955$	90258.2	3.05831
$956$	130950.	4.43014
$957$	−3315.45	−0.111989
$958$	16136.8	0.544212
$959$	−31.8173	−0.00107136
$960$	−216150.	−7.26690
$961$	45526.4	1.52819
$962$	0	0
$963$	3514.85	0.117616
$964$	85089.8	2.84290
$965$	26991.4	0.900398
$966$	−38.9552	−0.00129748
$967$	−1343.44	−0.0446764	−0.0223382	−	0.999750i	$-0.507111\pi$
$967$	−1343.44	−0.0446764	−0.0223382	+	0.999750i	$0.507111\pi$
$968$	−9509.14	−0.315739
$969$	−11760.2	−0.389880
$970$	75796.2	2.50894
$971$	−22061.2	−0.729122	−0.364561	−	0.931179i	$-0.618781\pi$
$971$	−22061.2	−0.729122	−0.364561	+	0.931179i	$0.618781\pi$
$972$	17713.3	0.584522
$973$	−35.4998	−0.00116965
$974$	1442.54	0.0474558
$975$	0	0
$976$	−152140.	−4.98962
$977$	−55622.0	−1.82140	−0.910700	−	0.413069i	$-0.864457\pi$
$977$	−55622.0	−1.82140	−0.910700	+	0.413069i	$0.864457\pi$
$978$	62944.9	2.05803
$979$	6157.67	0.201022
$980$	152475.	4.97005
$981$	−2330.00	−0.0758321
$982$	−8797.64	−0.285890
$983$	38020.5	1.23364	0.616819	−	0.787105i	$-0.288421\pi$
$983$	38020.5	1.23364	0.616819	+	0.787105i	$0.288421\pi$
$984$	−141581.	−4.58682
$985$	−9603.27	−0.310645
$986$	27881.3	0.900530
$987$	61.4598	0.00198205
$988$	0	0
$989$	27760.4	0.892549
$990$	3436.45	0.110321
$991$	24002.8	0.769399	0.384699	−	0.923042i	$-0.374305\pi$
$991$	24002.8	0.769399	0.384699	+	0.923042i	$0.374305\pi$
$992$	−211362.	−6.76488
$993$	41057.9	1.31212
$994$	−45.7405	−0.00145956
$995$	43860.8	1.39747
$996$	−69565.7	−2.21313
$997$	55296.7	1.75653	0.878267	−	0.478171i	$-0.158700\pi$
$997$	55296.7	1.75653	0.878267	+	0.478171i	$0.158700\pi$
$998$	−60712.0	−1.92566
$999$	45899.5	1.45365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.p.1.3	✓	51
13.12	even	2		1859.4.a.q.1.49	yes	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.3	✓	51	1.1	even	1	trivial
1859.4.a.q.1.49	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)

\(f(q)\)	\(=\)	\(q-5.50285 q^{2} +4.91472 q^{3} +22.2813 q^{4} -19.9510 q^{5} -27.0449 q^{6} -0.0210524 q^{7} -78.5880 q^{8} -2.84554 q^{9} +O(q^{10})\)	\(q-5.50285 q^{2} +4.91472 q^{3} +22.2813 q^{4} -19.9510 q^{5} -27.0449 q^{6} -0.0210524 q^{7} -78.5880 q^{8} -2.84554 q^{9} +109.787 q^{10} -11.0000 q^{11} +109.506 q^{12} +0.115848 q^{14} -98.0537 q^{15} +254.207 q^{16} -82.6180 q^{17} +15.6586 q^{18} +28.9630 q^{19} -444.535 q^{20} -0.103467 q^{21} +60.5313 q^{22} -68.4191 q^{23} -386.238 q^{24} +273.043 q^{25} -146.682 q^{27} -0.469075 q^{28} +61.3270 q^{29} +539.574 q^{30} +274.440 q^{31} -770.158 q^{32} -54.0619 q^{33} +454.634 q^{34} +0.420017 q^{35} -63.4024 q^{36} -312.918 q^{37} -159.379 q^{38} +1567.91 q^{40} +366.564 q^{41} +0.569361 q^{42} -405.741 q^{43} -245.095 q^{44} +56.7714 q^{45} +376.500 q^{46} -594.007 q^{47} +1249.36 q^{48} -343.000 q^{49} -1502.51 q^{50} -406.044 q^{51} -187.715 q^{53} +807.171 q^{54} +219.461 q^{55} +1.65446 q^{56} +142.345 q^{57} -337.473 q^{58} -5.47713 q^{59} -2184.77 q^{60} -598.488 q^{61} -1510.20 q^{62} +0.0599054 q^{63} +2204.41 q^{64} +297.494 q^{66} -285.078 q^{67} -1840.84 q^{68} -336.261 q^{69} -2.31129 q^{70} -394.832 q^{71} +223.625 q^{72} -687.195 q^{73} +1721.94 q^{74} +1341.93 q^{75} +645.333 q^{76} +0.231576 q^{77} -181.218 q^{79} -5071.69 q^{80} -644.073 q^{81} -2017.15 q^{82} -635.266 q^{83} -2.30537 q^{84} +1648.31 q^{85} +2232.73 q^{86} +301.405 q^{87} +864.468 q^{88} -559.789 q^{89} -312.404 q^{90} -1524.47 q^{92} +1348.80 q^{93} +3268.73 q^{94} -577.841 q^{95} -3785.11 q^{96} +690.391 q^{97} +1887.47 q^{98} +31.3009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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