LMFDB - Embedded newform 1859.4.a.o.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-0.532806 q^{2} +1.85539 q^{3} -7.71612 q^{4} -18.1107 q^{5} -0.988563 q^{6} -20.2803 q^{7} +8.37365 q^{8} -23.5575 q^{9} +O(q^{10})$	\(q-0.532806 q^{2} +1.85539 q^{3} -7.71612 q^{4} -18.1107 q^{5} -0.988563 q^{6} -20.2803 q^{7} +8.37365 q^{8} -23.5575 q^{9} +9.64951 q^{10} -11.0000 q^{11} -14.3164 q^{12} +10.8055 q^{14} -33.6025 q^{15} +57.2674 q^{16} -66.4926 q^{17} +12.5516 q^{18} +139.702 q^{19} +139.745 q^{20} -37.6279 q^{21} +5.86087 q^{22} -30.4210 q^{23} +15.5364 q^{24} +202.999 q^{25} -93.8039 q^{27} +156.485 q^{28} +195.977 q^{29} +17.9036 q^{30} -70.0869 q^{31} -97.5016 q^{32} -20.4093 q^{33} +35.4277 q^{34} +367.292 q^{35} +181.773 q^{36} +216.301 q^{37} -74.4342 q^{38} -151.653 q^{40} +450.129 q^{41} +20.0484 q^{42} -326.226 q^{43} +84.8773 q^{44} +426.644 q^{45} +16.2085 q^{46} +306.389 q^{47} +106.253 q^{48} +68.2916 q^{49} -108.159 q^{50} -123.370 q^{51} -582.391 q^{53} +49.9793 q^{54} +199.218 q^{55} -169.820 q^{56} +259.202 q^{57} -104.418 q^{58} -351.443 q^{59} +259.281 q^{60} -129.026 q^{61} +37.3428 q^{62} +477.754 q^{63} -406.190 q^{64} +10.8742 q^{66} +153.840 q^{67} +513.064 q^{68} -56.4428 q^{69} -195.695 q^{70} +1062.51 q^{71} -197.262 q^{72} +138.251 q^{73} -115.247 q^{74} +376.642 q^{75} -1077.96 q^{76} +223.084 q^{77} +1120.40 q^{79} -1037.15 q^{80} +462.010 q^{81} -239.832 q^{82} -377.947 q^{83} +290.341 q^{84} +1204.23 q^{85} +173.816 q^{86} +363.614 q^{87} -92.1101 q^{88} -1339.45 q^{89} -227.319 q^{90} +234.732 q^{92} -130.039 q^{93} -163.246 q^{94} -2530.11 q^{95} -180.903 q^{96} -1422.80 q^{97} -36.3862 q^{98} +259.133 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.532806	−0.188375	−0.0941877	−	0.995554i	$-0.530025\pi$
$2$	−0.532806	−0.188375	−0.0941877	+	0.995554i	$0.530025\pi$
$3$	1.85539	0.357070	0.178535	−	0.983934i	$-0.442864\pi$
$3$	1.85539	0.357070	0.178535	+	0.983934i	$0.442864\pi$
$4$	−7.71612	−0.964515
$5$	−18.1107	−1.61987	−0.809937	−	0.586517i	$-0.800499\pi$
$5$	−18.1107	−1.61987	−0.809937	+	0.586517i	$0.800499\pi$
$6$	−0.988563	−0.0672632
$7$	−20.2803	−1.09503	−0.547517	−	0.836794i	$-0.684427\pi$
$7$	−20.2803	−1.09503	−0.547517	+	0.836794i	$0.684427\pi$
$8$	8.37365	0.370066
$9$	−23.5575	−0.872501
$10$	9.64951	0.305144
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−14.3164	−0.344399
$13$	0	0
$13$	0	0
$14$	10.8055	0.206278
$15$	−33.6025	−0.578408
$16$	57.2674	0.894803
$17$	−66.4926	−0.948636	−0.474318	−	0.880354i	$-0.657305\pi$
$17$	−66.4926	−0.948636	−0.474318	+	0.880354i	$0.657305\pi$
$18$	12.5516	0.164358
$19$	139.702	1.68684	0.843418	−	0.537258i	$-0.180540\pi$
$19$	139.702	1.68684	0.843418	+	0.537258i	$0.180540\pi$
$20$	139.745	1.56239
$21$	−37.6279	−0.391004
$22$	5.86087	0.0567974
$23$	−30.4210	−0.275792	−0.137896	−	0.990447i	$-0.544034\pi$
$23$	−30.4210	−0.275792	−0.137896	+	0.990447i	$0.544034\pi$
$24$	15.5364	0.132140
$25$	202.999	1.62399
$26$	0	0
$27$	−93.8039	−0.668614
$28$	156.485	1.05618
$29$	195.977	1.25490	0.627448	−	0.778658i	$-0.284099\pi$
$29$	195.977	1.25490	0.627448	+	0.778658i	$0.284099\pi$
$30$	17.9036	0.108958
$31$	−70.0869	−0.406064	−0.203032	−	0.979172i	$-0.565080\pi$
$31$	−70.0869	−0.406064	−0.203032	+	0.979172i	$0.565080\pi$
$32$	−97.5016	−0.538625
$33$	−20.4093	−0.107661
$34$	35.4277	0.178700
$35$	367.292	1.77382
$36$	181.773	0.841540
$37$	216.301	0.961074	0.480537	−	0.876974i	$-0.340442\pi$
$37$	216.301	0.961074	0.480537	+	0.876974i	$0.340442\pi$
$38$	−74.4342	−0.317759
$39$	0	0
$40$	−151.653	−0.599461
$41$	450.129	1.71459	0.857297	−	0.514821i	$-0.172142\pi$
$41$	450.129	1.71459	0.857297	+	0.514821i	$0.172142\pi$
$42$	20.0484	0.0736556
$43$	−326.226	−1.15696	−0.578478	−	0.815698i	$-0.696353\pi$
$43$	−326.226	−1.15696	−0.578478	+	0.815698i	$0.696353\pi$
$44$	84.8773	0.290812
$45$	426.644	1.41334
$46$	16.2085	0.0519525
$47$	306.389	0.950883	0.475441	−	0.879747i	$-0.342288\pi$
$47$	306.389	0.950883	0.475441	+	0.879747i	$0.342288\pi$
$48$	106.253	0.319507
$49$	68.2916	0.199101
$50$	−108.159	−0.305920
$51$	−123.370	−0.338729
$52$	0	0
$53$	−582.391	−1.50939	−0.754693	−	0.656078i	$-0.772214\pi$
$53$	−582.391	−1.50939	−0.754693	+	0.656078i	$0.772214\pi$
$54$	49.9793	0.125950
$55$	199.218	0.488410
$56$	−169.820	−0.405236
$57$	259.202	0.602318
$58$	−104.418	−0.236392
$59$	−351.443	−0.775492	−0.387746	−	0.921766i	$-0.626746\pi$
$59$	−351.443	−0.775492	−0.387746	+	0.921766i	$0.626746\pi$
$60$	259.281	0.557883
$61$	−129.026	−0.270821	−0.135411	−	0.990790i	$-0.543235\pi$
$61$	−129.026	−0.270821	−0.135411	+	0.990790i	$0.543235\pi$
$62$	37.3428	0.0764925
$63$	477.754	0.955419
$64$	−406.190	−0.793339
$65$	0	0
$66$	10.8742	0.0202806
$67$	153.840	0.280515	0.140258	−	0.990115i	$-0.455207\pi$
$67$	153.840	0.280515	0.140258	+	0.990115i	$0.455207\pi$
$68$	513.064	0.914973
$69$	−56.4428	−0.0984771
$70$	−195.695	−0.334144
$71$	1062.51	1.77600	0.888002	−	0.459839i	$-0.152093\pi$
$71$	1062.51	1.77600	0.888002	+	0.459839i	$0.152093\pi$
$72$	−197.262	−0.322883
$73$	138.251	0.221658	0.110829	−	0.993840i	$-0.464649\pi$
$73$	138.251	0.221658	0.110829	+	0.993840i	$0.464649\pi$
$74$	−115.247	−0.181043
$75$	376.642	0.579878
$76$	−1077.96	−1.62698
$77$	223.084	0.330165
$78$	0	0
$79$	1120.40	1.59564	0.797818	−	0.602899i	$-0.205988\pi$
$79$	1120.40	1.59564	0.797818	+	0.602899i	$0.205988\pi$
$80$	−1037.15	−1.44947
$81$	462.010	0.633759
$82$	−239.832	−0.322988
$83$	−377.947	−0.499820	−0.249910	−	0.968269i	$-0.580401\pi$
$83$	−377.947	−0.499820	−0.249910	+	0.968269i	$0.580401\pi$
$84$	290.341	0.377129
$85$	1204.23	1.53667
$86$	173.816	0.217942
$87$	363.614	0.448086
$88$	−92.1101	−0.111579
$89$	−1339.45	−1.59530	−0.797648	−	0.603123i	$-0.793923\pi$
$89$	−1339.45	−1.59530	−0.797648	+	0.603123i	$0.793923\pi$
$90$	−227.319	−0.266239
$91$	0	0
$92$	234.732	0.266006
$93$	−130.039	−0.144993
$94$	−163.246	−0.179123
$95$	−2530.11	−2.73246
$96$	−180.903	−0.192327
$97$	−1422.80	−1.48931	−0.744656	−	0.667448i	$-0.767387\pi$
$97$	−1422.80	−1.48931	−0.744656	+	0.667448i	$0.767387\pi$
$98$	−36.3862	−0.0375057
$99$	259.133	0.263069
$100$	−1566.36	−1.56636
$101$	−1354.30	−1.33423	−0.667117	−	0.744953i	$-0.732472\pi$
$101$	−1354.30	−1.33423	−0.667117	+	0.744953i	$0.732472\pi$
$102$	65.7321	0.0638083
$103$	−695.910	−0.665729	−0.332865	−	0.942975i	$-0.608015\pi$
$103$	−695.910	−0.665729	−0.332865	+	0.942975i	$0.608015\pi$
$104$	0	0
$105$	681.469	0.633377
$106$	310.301	0.284331
$107$	1471.74	1.32970	0.664851	−	0.746976i	$-0.268495\pi$
$107$	1471.74	1.32970	0.664851	+	0.746976i	$0.268495\pi$
$108$	723.802	0.644888
$109$	375.802	0.330232	0.165116	−	0.986274i	$-0.447200\pi$
$109$	375.802	0.330232	0.165116	+	0.986274i	$0.447200\pi$
$110$	−106.145	−0.0920045
$111$	401.323	0.343171
$112$	−1161.40	−0.979841
$113$	2218.94	1.84726	0.923631	−	0.383284i	$-0.125207\pi$
$113$	2218.94	1.84726	0.923631	+	0.383284i	$0.125207\pi$
$114$	−138.104	−0.113462
$115$	550.947	0.446748
$116$	−1512.18	−1.21037
$117$	0	0
$118$	187.251	0.146084
$119$	1348.49	1.03879
$120$	−281.375	−0.214049
$121$	121.000	0.0909091
$122$	68.7459	0.0510161
$123$	835.165	0.612230
$124$	540.799	0.391655
$125$	−1412.61	−1.01078
$126$	−254.551	−0.179978
$127$	83.5431	0.0583721	0.0291860	−	0.999574i	$-0.490708\pi$
$127$	83.5431	0.0583721	0.0291860	+	0.999574i	$0.490708\pi$
$128$	996.433	0.688071
$129$	−605.277	−0.413114
$130$	0	0
$131$	572.433	0.381784	0.190892	−	0.981611i	$-0.438862\pi$
$131$	572.433	0.381784	0.190892	+	0.981611i	$0.438862\pi$
$132$	157.480	0.103840
$133$	−2833.21	−1.84714
$134$	−81.9669	−0.0528422
$135$	1698.86	1.08307
$136$	−556.785	−0.351058
$137$	1304.87	0.813740	0.406870	−	0.913486i	$-0.366620\pi$
$137$	1304.87	0.813740	0.406870	+	0.913486i	$0.366620\pi$
$138$	30.0731	0.0185507
$139$	−1860.22	−1.13512	−0.567560	−	0.823332i	$-0.692112\pi$
$139$	−1860.22	−1.13512	−0.567560	+	0.823332i	$0.692112\pi$
$140$	−2834.06	−1.71087
$141$	568.472	0.339532
$142$	−566.110	−0.334556
$143$	0	0
$144$	−1349.08	−0.780717
$145$	−3549.29	−2.03277
$146$	−73.6608	−0.0417548
$147$	126.708	0.0710929
$148$	−1669.01	−0.926970
$149$	912.959	0.501963	0.250982	−	0.967992i	$-0.419247\pi$
$149$	912.959	0.501963	0.250982	+	0.967992i	$0.419247\pi$
$150$	−200.677	−0.109235
$151$	−628.608	−0.338777	−0.169389	−	0.985549i	$-0.554179\pi$
$151$	−628.608	−0.338777	−0.169389	+	0.985549i	$0.554179\pi$
$152$	1169.82	0.624241
$153$	1566.40	0.827686
$154$	−118.860	−0.0621951
$155$	1269.33	0.657772
$156$	0	0
$157$	−2361.86	−1.20062	−0.600308	−	0.799769i	$-0.704955\pi$
$157$	−2361.86	−1.20062	−0.600308	+	0.799769i	$0.704955\pi$
$158$	−596.958	−0.300579
$159$	−1080.56	−0.538957
$160$	1765.83	0.872505
$161$	616.948	0.302002
$162$	−246.162	−0.119385
$163$	3052.91	1.46701	0.733505	−	0.679684i	$-0.237883\pi$
$163$	3052.91	1.46701	0.733505	+	0.679684i	$0.237883\pi$
$164$	−3473.25	−1.65375
$165$	369.627	0.174397
$166$	201.373	0.0941539
$167$	−161.317	−0.0747490	−0.0373745	−	0.999301i	$-0.511899\pi$
$167$	−161.317	−0.0747490	−0.0373745	+	0.999301i	$0.511899\pi$
$168$	−315.083	−0.144697
$169$	0	0
$170$	−641.621	−0.289471
$171$	−3291.04	−1.47177
$172$	2517.20	1.11590
$173$	2093.60	0.920077	0.460039	−	0.887899i	$-0.347836\pi$
$173$	2093.60	0.920077	0.460039	+	0.887899i	$0.347836\pi$
$174$	−193.736	−0.0844084
$175$	−4116.88	−1.77832
$176$	−629.941	−0.269793
$177$	−652.064	−0.276905
$178$	713.668	0.300515
$179$	933.655	0.389859	0.194929	−	0.980817i	$-0.437552\pi$
$179$	933.655	0.389859	0.194929	+	0.980817i	$0.437552\pi$
$180$	−3292.04	−1.36319
$181$	−2163.06	−0.888282	−0.444141	−	0.895957i	$-0.646491\pi$
$181$	−2163.06	−0.888282	−0.444141	+	0.895957i	$0.646491\pi$
$182$	0	0
$183$	−239.394	−0.0967021
$184$	−254.735	−0.102061
$185$	−3917.38	−1.55682
$186$	69.2854	0.0273132
$187$	731.418	0.286025
$188$	−2364.14	−0.917140
$189$	1902.37	0.732155
$190$	1348.06	0.514729
$191$	−1970.14	−0.746360	−0.373180	−	0.927759i	$-0.621733\pi$
$191$	−1970.14	−0.746360	−0.373180	+	0.927759i	$0.621733\pi$
$192$	−753.640	−0.283278
$193$	−649.258	−0.242148	−0.121074	−	0.992643i	$-0.538634\pi$
$193$	−649.258	−0.242148	−0.121074	+	0.992643i	$0.538634\pi$
$194$	758.076	0.280550
$195$	0	0
$196$	−526.946	−0.192036
$197$	1638.82	0.592695	0.296348	−	0.955080i	$-0.404231\pi$
$197$	1638.82	0.592695	0.296348	+	0.955080i	$0.404231\pi$
$198$	−138.068	−0.0495558
$199$	−3319.18	−1.18237	−0.591183	−	0.806538i	$-0.701339\pi$
$199$	−3319.18	−1.18237	−0.591183	+	0.806538i	$0.701339\pi$
$200$	1699.84	0.600984
$201$	285.433	0.100164
$202$	721.578	0.251337
$203$	−3974.48	−1.37416
$204$	951.934	0.326709
$205$	−8152.17	−2.77743
$206$	370.786	0.125407
$207$	716.644	0.240629
$208$	0	0
$209$	−1536.72	−0.508600
$210$	−363.091	−0.119313
$211$	−1051.00	−0.342910	−0.171455	−	0.985192i	$-0.554847\pi$
$211$	−1051.00	−0.342910	−0.171455	+	0.985192i	$0.554847\pi$
$212$	4493.79	1.45583
$213$	1971.36	0.634158
$214$	−784.151	−0.250483
$215$	5908.20	1.87412
$216$	−785.481	−0.247432
$217$	1421.39	0.444654
$218$	−200.230	−0.0622077
$219$	256.509	0.0791472
$220$	−1537.19	−0.471079
$221$	0	0
$222$	−213.828	−0.0646449
$223$	−3506.27	−1.05290	−0.526451	−	0.850205i	$-0.676478\pi$
$223$	−3506.27	−1.05290	−0.526451	+	0.850205i	$0.676478\pi$
$224$	1977.36	0.589814
$225$	−4782.15	−1.41693
$226$	−1182.27	−0.347979
$227$	2532.46	0.740465	0.370232	−	0.928939i	$-0.379278\pi$
$227$	2532.46	0.740465	0.370232	+	0.928939i	$0.379278\pi$
$228$	−2000.03	−0.580945
$229$	1932.12	0.557546	0.278773	−	0.960357i	$-0.410072\pi$
$229$	1932.12	0.557546	0.278773	+	0.960357i	$0.410072\pi$
$230$	−293.548	−0.0841564
$231$	413.907	0.117892
$232$	1641.04	0.464395
$233$	1954.90	0.549655	0.274827	−	0.961494i	$-0.411379\pi$
$233$	1954.90	0.549655	0.274827	+	0.961494i	$0.411379\pi$
$234$	0	0
$235$	−5548.94	−1.54031
$236$	2711.78	0.747973
$237$	2078.78	0.569753
$238$	−718.484	−0.195682
$239$	−2227.90	−0.602973	−0.301487	−	0.953470i	$-0.597483\pi$
$239$	−2227.90	−0.602973	−0.301487	+	0.953470i	$0.597483\pi$
$240$	−1924.33	−0.517561
$241$	2685.93	0.717908	0.358954	−	0.933355i	$-0.383133\pi$
$241$	2685.93	0.717908	0.358954	+	0.933355i	$0.383133\pi$
$242$	−64.4696	−0.0171250
$243$	3389.92	0.894910
$244$	995.581	0.261211
$245$	−1236.81	−0.322518
$246$	−444.981	−0.115329
$247$	0	0
$248$	−586.883	−0.150271
$249$	−701.239	−0.178471
$250$	752.649	0.190407
$251$	−3634.46	−0.913964	−0.456982	−	0.889476i	$-0.651070\pi$
$251$	−3634.46	−0.913964	−0.456982	+	0.889476i	$0.651070\pi$
$252$	−3686.41	−0.921516
$253$	334.631	0.0831545
$254$	−44.5123	−0.0109959
$255$	2234.31	0.548699
$256$	2718.61	0.663724
$257$	−6634.63	−1.61034	−0.805169	−	0.593046i	$-0.797925\pi$
$257$	−6634.63	−1.61034	−0.805169	+	0.593046i	$0.797925\pi$
$258$	322.496	0.0778205
$259$	−4386.66	−1.05241
$260$	0	0
$261$	−4616.73	−1.09490
$262$	−304.996	−0.0719187
$263$	1714.66	0.402016	0.201008	−	0.979590i	$-0.435578\pi$
$263$	1714.66	0.402016	0.201008	+	0.979590i	$0.435578\pi$
$264$	−170.900	−0.0398416
$265$	10547.5	2.44502
$266$	1509.55	0.347957
$267$	−2485.20	−0.569633
$268$	−1187.05	−0.270561
$269$	131.138	0.0297235	0.0148618	−	0.999890i	$-0.495269\pi$
$269$	131.138	0.0297235	0.0148618	+	0.999890i	$0.495269\pi$
$270$	−905.162	−0.204024
$271$	7252.63	1.62570	0.812852	−	0.582470i	$-0.197914\pi$
$271$	7252.63	1.62570	0.812852	+	0.582470i	$0.197914\pi$
$272$	−3807.86	−0.848843
$273$	0	0
$274$	−695.242	−0.153289
$275$	−2232.99	−0.489651
$276$	435.520	0.0949826
$277$	2489.30	0.539956	0.269978	−	0.962867i	$-0.412984\pi$
$277$	2489.30	0.539956	0.269978	+	0.962867i	$0.412984\pi$
$278$	991.136	0.213829
$279$	1651.08	0.354291
$280$	3075.57	0.656430
$281$	1538.55	0.326627	0.163314	−	0.986574i	$-0.447782\pi$
$281$	1538.55	0.326627	0.163314	+	0.986574i	$0.447782\pi$
$282$	−302.885	−0.0639594
$283$	5557.67	1.16738	0.583691	−	0.811976i	$-0.301608\pi$
$283$	5557.67	1.16738	0.583691	+	0.811976i	$0.301608\pi$
$284$	−8198.43	−1.71298
$285$	−4694.34	−0.975679
$286$	0	0
$287$	−9128.77	−1.87754
$288$	2296.90	0.469951
$289$	−491.740	−0.100089
$290$	1891.08	0.382925
$291$	−2639.85	−0.531789
$292$	−1066.76	−0.213792
$293$	4317.41	0.860838	0.430419	−	0.902629i	$-0.358366\pi$
$293$	4317.41	0.860838	0.430419	+	0.902629i	$0.358366\pi$
$294$	−67.5106	−0.0133922
$295$	6364.90	1.25620
$296$	1811.23	0.355661
$297$	1031.84	0.201595
$298$	−486.430	−0.0945576
$299$	0	0
$300$	−2906.21	−0.559301
$301$	6615.98	1.26691
$302$	334.926	0.0638174
$303$	−2512.75	−0.476415
$304$	8000.38	1.50939
$305$	2336.76	0.438696
$306$	−834.588	−0.155916
$307$	7614.09	1.41550	0.707751	−	0.706462i	$-0.249710\pi$
$307$	7614.09	1.41550	0.707751	+	0.706462i	$0.249710\pi$
$308$	−1721.34	−0.318449
$309$	−1291.19	−0.237712
$310$	−676.305	−0.123908
$311$	2642.64	0.481834	0.240917	−	0.970546i	$-0.422552\pi$
$311$	2642.64	0.481834	0.240917	+	0.970546i	$0.422552\pi$
$312$	0	0
$313$	9486.65	1.71315	0.856577	−	0.516020i	$-0.172587\pi$
$313$	9486.65	1.71315	0.856577	+	0.516020i	$0.172587\pi$
$314$	1258.41	0.226167
$315$	−8652.48	−1.54766
$316$	−8645.16	−1.53901
$317$	9324.77	1.65215	0.826075	−	0.563561i	$-0.190569\pi$
$317$	9324.77	1.65215	0.826075	+	0.563561i	$0.190569\pi$
$318$	575.730	0.101526
$319$	−2155.75	−0.378366
$320$	7356.39	1.28511
$321$	2730.65	0.474797
$322$	−328.714	−0.0568898
$323$	−9289.16	−1.60019
$324$	−3564.93	−0.611270
$325$	0	0
$326$	−1626.61	−0.276349
$327$	697.260	0.117916
$328$	3769.22	0.634514
$329$	−6213.68	−1.04125
$330$	−196.940	−0.0328520
$331$	−6121.05	−1.01645	−0.508223	−	0.861226i	$-0.669697\pi$
$331$	−6121.05	−1.01645	−0.508223	+	0.861226i	$0.669697\pi$
$332$	2916.28	0.482084
$333$	−5095.53	−0.838538
$334$	85.9507	0.0140809
$335$	−2786.15	−0.454399
$336$	−2154.85	−0.349872
$337$	−80.5279	−0.0130167	−0.00650836	−	0.999979i	$-0.502072\pi$
$337$	−80.5279	−0.0130167	−0.00650836	+	0.999979i	$0.502072\pi$
$338$	0	0
$339$	4117.00	0.659601
$340$	−9291.97	−1.48214
$341$	770.956	0.122433
$342$	1753.49	0.277245
$343$	5571.18	0.877012
$344$	−2731.71	−0.428150
$345$	1022.22	0.159520
$346$	−1115.48	−0.173320
$347$	27.0819	0.00418971	0.00209486	−	0.999998i	$-0.499333\pi$
$347$	27.0819	0.00418971	0.00209486	+	0.999998i	$0.499333\pi$
$348$	−2805.68	−0.432185
$349$	−12746.6	−1.95505	−0.977525	−	0.210822i	$-0.932386\pi$
$349$	−12746.6	−1.95505	−0.977525	+	0.210822i	$0.932386\pi$
$350$	2193.50	0.334993
$351$	0	0
$352$	1072.52	0.162402
$353$	−2421.17	−0.365058	−0.182529	−	0.983200i	$-0.558428\pi$
$353$	−2421.17	−0.365058	−0.182529	+	0.983200i	$0.558428\pi$
$354$	347.424	0.0521621
$355$	−19242.8	−2.87690
$356$	10335.4	1.53869
$357$	2501.98	0.370920
$358$	−497.457	−0.0734398
$359$	−6526.98	−0.959556	−0.479778	−	0.877390i	$-0.659283\pi$
$359$	−6526.98	−0.959556	−0.479778	+	0.877390i	$0.659283\pi$
$360$	3572.57	0.523030
$361$	12657.7	1.84542
$362$	1152.49	0.167331
$363$	224.502	0.0324609
$364$	0	0
$365$	−2503.82	−0.359057
$366$	127.550	0.0182163
$367$	−1350.80	−0.192129	−0.0960646	−	0.995375i	$-0.530626\pi$
$367$	−1350.80	−0.192129	−0.0960646	+	0.995375i	$0.530626\pi$
$368$	−1742.13	−0.246780
$369$	−10603.9	−1.49599
$370$	2087.20	0.293266
$371$	11811.1	1.65283
$372$	1003.39	0.139848
$373$	4687.48	0.650694	0.325347	−	0.945595i	$-0.394519\pi$
$373$	4687.48	0.650694	0.325347	+	0.945595i	$0.394519\pi$
$374$	−389.704	−0.0538800
$375$	−2620.95	−0.360920
$376$	2565.60	0.351890
$377$	0	0
$378$	−1013.60	−0.137920
$379$	−8879.77	−1.20349	−0.601745	−	0.798688i	$-0.705528\pi$
$379$	−8879.77	−1.20349	−0.601745	+	0.798688i	$0.705528\pi$
$380$	19522.6	2.63550
$381$	155.005	0.0208429
$382$	1049.71	0.140596
$383$	6884.39	0.918474	0.459237	−	0.888314i	$-0.348123\pi$
$383$	6884.39	0.918474	0.459237	+	0.888314i	$0.348123\pi$
$384$	1848.77	0.245689
$385$	−4040.21	−0.534826
$386$	345.929	0.0456148
$387$	7685.09	1.00944
$388$	10978.5	1.43646
$389$	−7002.76	−0.912735	−0.456368	−	0.889791i	$-0.650850\pi$
$389$	−7002.76	−0.912735	−0.456368	+	0.889791i	$0.650850\pi$
$390$	0	0
$391$	2022.77	0.261626
$392$	571.850	0.0736805
$393$	1062.09	0.136324
$394$	−873.173	−0.111649
$395$	−20291.3	−2.58473
$396$	−1999.50	−0.253734
$397$	−6135.50	−0.775648	−0.387824	−	0.921734i	$-0.626773\pi$
$397$	−6135.50	−0.775648	−0.387824	+	0.921734i	$0.626773\pi$
$398$	1768.48	0.222729
$399$	−5256.70	−0.659559
$400$	11625.2	1.45315
$401$	−3072.45	−0.382620	−0.191310	−	0.981530i	$-0.561274\pi$
$401$	−3072.45	−0.382620	−0.191310	+	0.981530i	$0.561274\pi$
$402$	−152.080	−0.0188684
$403$	0	0
$404$	10449.9	1.28689
$405$	−8367.35	−1.02661
$406$	2117.63	0.258857
$407$	−2379.32	−0.289775
$408$	−1033.05	−0.125352
$409$	−1340.92	−0.162112	−0.0810562	−	0.996710i	$-0.525829\pi$
$409$	−1340.92	−0.162112	−0.0810562	+	0.996710i	$0.525829\pi$
$410$	4343.53	0.523199
$411$	2421.04	0.290562
$412$	5369.73	0.642105
$413$	7127.39	0.849191
$414$	−381.832	−0.0453286
$415$	6844.90	0.809646
$416$	0	0
$417$	−3451.43	−0.405317
$418$	818.777	0.0958078
$419$	−11501.5	−1.34102	−0.670509	−	0.741902i	$-0.733924\pi$
$419$	−11501.5	−1.34102	−0.670509	+	0.741902i	$0.733924\pi$
$420$	−5258.29	−0.610901
$421$	−4302.63	−0.498093	−0.249047	−	0.968491i	$-0.580117\pi$
$421$	−4302.63	−0.498093	−0.249047	+	0.968491i	$0.580117\pi$
$422$	559.980	0.0645957
$423$	−7217.78	−0.829646
$424$	−4876.73	−0.558573
$425$	−13497.9	−1.54058
$426$	−1050.36	−0.119460
$427$	2616.69	0.296559
$428$	−11356.1	−1.28252
$429$	0	0
$430$	−3147.93	−0.353038
$431$	3645.31	0.407397	0.203699	−	0.979034i	$-0.434704\pi$
$431$	3645.31	0.407397	0.203699	+	0.979034i	$0.434704\pi$
$432$	−5371.91	−0.598278
$433$	7572.29	0.840418	0.420209	−	0.907427i	$-0.361957\pi$
$433$	7572.29	0.840418	0.420209	+	0.907427i	$0.361957\pi$
$434$	−757.324	−0.0837620
$435$	−6585.31	−0.725842
$436$	−2899.73	−0.318514
$437$	−4249.88	−0.465216
$438$	−136.669	−0.0149094
$439$	−6220.80	−0.676316	−0.338158	−	0.941089i	$-0.609804\pi$
$439$	−6220.80	−0.676316	−0.338158	+	0.941089i	$0.609804\pi$
$440$	1668.18	0.180744
$441$	−1608.78	−0.173716
$442$	0	0
$443$	−7145.15	−0.766312	−0.383156	−	0.923684i	$-0.625163\pi$
$443$	−7145.15	−0.766312	−0.383156	+	0.923684i	$0.625163\pi$
$444$	−3096.66	−0.330993
$445$	24258.4	2.58418
$446$	1868.16	0.198341
$447$	1693.89	0.179236
$448$	8237.66	0.868734
$449$	1068.12	0.112267	0.0561335	−	0.998423i	$-0.482123\pi$
$449$	1068.12	0.112267	0.0561335	+	0.998423i	$0.482123\pi$
$450$	2547.96	0.266915
$451$	−4951.42	−0.516970
$452$	−17121.6	−1.78171
$453$	−1166.31	−0.120967
$454$	−1349.31	−0.139485
$455$	0	0
$456$	2170.47	0.222898
$457$	18959.1	1.94063	0.970317	−	0.241835i	$-0.0777492\pi$
$457$	18959.1	1.94063	0.970317	+	0.241835i	$0.0777492\pi$
$458$	−1029.45	−0.105028
$459$	6237.26	0.634271
$460$	−4251.17	−0.430895
$461$	17091.9	1.72679	0.863395	−	0.504529i	$-0.168334\pi$
$461$	17091.9	1.72679	0.863395	+	0.504529i	$0.168334\pi$
$462$	−220.532	−0.0222080
$463$	−11836.2	−1.18807	−0.594035	−	0.804439i	$-0.702466\pi$
$463$	−11836.2	−1.18807	−0.594035	+	0.804439i	$0.702466\pi$
$464$	11223.1	1.12289
$465$	2355.09	0.234871
$466$	−1041.58	−0.103541
$467$	−15266.9	−1.51278	−0.756391	−	0.654120i	$-0.773039\pi$
$467$	−15266.9	−1.51278	−0.756391	+	0.654120i	$0.773039\pi$
$468$	0	0
$469$	−3119.92	−0.307174
$470$	2956.51	0.290157
$471$	−4382.16	−0.428704
$472$	−2942.86	−0.286984
$473$	3588.49	0.348835
$474$	−1107.59	−0.107328
$475$	28359.4	2.73940
$476$	−10405.1	−1.00193
$477$	13719.7	1.31694
$478$	1187.04	0.113585
$479$	−12185.9	−1.16240	−0.581198	−	0.813762i	$-0.697416\pi$
$479$	−12185.9	−1.16240	−0.581198	+	0.813762i	$0.697416\pi$
$480$	3276.29	0.311545
$481$	0	0
$482$	−1431.08	−0.135236
$483$	1144.68	0.107836
$484$	−933.650	−0.0876832
$485$	25767.9	2.41250
$486$	−1806.17	−0.168579
$487$	−15313.2	−1.42486	−0.712432	−	0.701741i	$-0.752406\pi$
$487$	−15313.2	−1.42486	−0.712432	+	0.701741i	$0.752406\pi$
$488$	−1080.42	−0.100222
$489$	5664.34	0.523825
$490$	658.981	0.0607545
$491$	−17450.6	−1.60394	−0.801969	−	0.597365i	$-0.796214\pi$
$491$	−17450.6	−1.60394	−0.801969	+	0.597365i	$0.796214\pi$
$492$	−6444.23	−0.590505
$493$	−13031.0	−1.19044
$494$	0	0
$495$	−4693.09	−0.426138
$496$	−4013.70	−0.363347
$497$	−21548.0	−1.94479
$498$	373.625	0.0336195
$499$	−6874.55	−0.616728	−0.308364	−	0.951268i	$-0.599781\pi$
$499$	−6874.55	−0.616728	−0.308364	+	0.951268i	$0.599781\pi$
$500$	10899.9	0.974916
$501$	−299.306	−0.0266906
$502$	1936.46	0.172168
$503$	−3229.46	−0.286271	−0.143136	−	0.989703i	$-0.545719\pi$
$503$	−3229.46	−0.286271	−0.143136	+	0.989703i	$0.545719\pi$
$504$	4000.55	0.353568
$505$	24527.3	2.16129
$506$	−178.294	−0.0156643
$507$	0	0
$508$	−644.629	−0.0563007
$509$	−663.235	−0.0577551	−0.0288776	−	0.999583i	$-0.509193\pi$
$509$	−663.235	−0.0577551	−0.0288776	+	0.999583i	$0.509193\pi$
$510$	−1190.46	−0.103361
$511$	−2803.77	−0.242723
$512$	−9419.96	−0.813100
$513$	−13104.6	−1.12784
$514$	3534.97	0.303348
$515$	12603.4	1.07840
$516$	4670.39	0.398454
$517$	−3370.28	−0.286702
$518$	2337.24	0.198248
$519$	3884.44	0.328532
$520$	0	0
$521$	6175.00	0.519255	0.259627	−	0.965709i	$-0.416400\pi$
$521$	6175.00	0.519255	0.259627	+	0.965709i	$0.416400\pi$
$522$	2459.82	0.206252
$523$	15879.9	1.32768	0.663842	−	0.747872i	$-0.268925\pi$
$523$	15879.9	1.32768	0.663842	+	0.747872i	$0.268925\pi$
$524$	−4416.96	−0.368236
$525$	−7638.42	−0.634986
$526$	−913.580	−0.0757300
$527$	4660.26	0.385207
$528$	−1168.79	−0.0963351
$529$	−11241.6	−0.923939
$530$	−5619.79	−0.460581
$531$	8279.14	0.676618
$532$	21861.4	1.78160
$533$	0	0
$534$	1324.13	0.107305
$535$	−26654.2	−2.15395
$536$	1288.20	0.103809
$537$	1732.29	0.139207
$538$	−69.8712	−0.00559919
$539$	−751.208	−0.0600312
$540$	−13108.6	−1.04464
$541$	−21809.1	−1.73317	−0.866586	−	0.499028i	$-0.833691\pi$
$541$	−21809.1	−1.73317	−0.866586	+	0.499028i	$0.833691\pi$
$542$	−3864.25	−0.306243
$543$	−4013.32	−0.317179
$544$	6483.13	0.510960
$545$	−6806.05	−0.534935
$546$	0	0
$547$	2454.85	0.191886	0.0959430	−	0.995387i	$-0.469413\pi$
$547$	2454.85	0.191886	0.0959430	+	0.995387i	$0.469413\pi$
$548$	−10068.5	−0.784864
$549$	3039.54	0.236292
$550$	1189.75	0.0922383
$551$	27378.4	2.11680
$552$	−472.632	−0.0364431
$553$	−22722.1	−1.74728
$554$	−1326.32	−0.101714
$555$	−7268.26	−0.555893
$556$	14353.7	1.09484
$557$	9861.58	0.750177	0.375089	−	0.926989i	$-0.377612\pi$
$557$	9861.58	0.750177	0.375089	+	0.926989i	$0.377612\pi$
$558$	−879.703	−0.0667398
$559$	0	0
$560$	21033.8	1.58722
$561$	1357.07	0.102131
$562$	−819.749	−0.0615285
$563$	15392.5	1.15225	0.576124	−	0.817362i	$-0.304565\pi$
$563$	15392.5	1.15225	0.576124	+	0.817362i	$0.304565\pi$
$564$	−4386.39	−0.327483
$565$	−40186.7	−2.99233
$566$	−2961.16	−0.219906
$567$	−9369.72	−0.693988
$568$	8897.06	0.657240
$569$	8296.79	0.611282	0.305641	−	0.952147i	$-0.401129\pi$
$569$	8296.79	0.611282	0.305641	+	0.952147i	$0.401129\pi$
$570$	2501.17	0.183794
$571$	6889.18	0.504909	0.252455	−	0.967609i	$-0.418762\pi$
$571$	6889.18	0.504909	0.252455	+	0.967609i	$0.418762\pi$
$572$	0	0
$573$	−3655.39	−0.266503
$574$	4863.87	0.353683
$575$	−6175.43	−0.447884
$576$	9568.83	0.692189
$577$	−14221.3	−1.02607	−0.513034	−	0.858368i	$-0.671479\pi$
$577$	−14221.3	−1.02607	−0.513034	+	0.858368i	$0.671479\pi$
$578$	262.002	0.0188544
$579$	−1204.63	−0.0864638
$580$	27386.7	1.96064
$581$	7664.89	0.547321
$582$	1406.53	0.100176
$583$	6406.30	0.455097
$584$	1157.66	0.0820280
$585$	0	0
$586$	−2300.34	−0.162161
$587$	13178.5	0.926635	0.463317	−	0.886192i	$-0.346659\pi$
$587$	13178.5	0.926635	0.463317	+	0.886192i	$0.346659\pi$
$588$	−977.690	−0.0685702
$589$	−9791.30	−0.684964
$590$	−3391.26	−0.236637
$591$	3040.65	0.211634
$592$	12387.0	0.859972
$593$	−7251.86	−0.502189	−0.251094	−	0.967963i	$-0.580790\pi$
$593$	−7251.86	−0.502189	−0.251094	+	0.967963i	$0.580790\pi$
$594$	−549.773	−0.0379755
$595$	−24422.2	−1.68271
$596$	−7044.50	−0.484151
$597$	−6158.38	−0.422187
$598$	0	0
$599$	−2803.96	−0.191263	−0.0956315	−	0.995417i	$-0.530487\pi$
$599$	−2803.96	−0.191263	−0.0956315	+	0.995417i	$0.530487\pi$
$600$	3153.86	0.214593
$601$	−24975.3	−1.69512	−0.847559	−	0.530701i	$-0.821929\pi$
$601$	−24975.3	−1.69512	−0.847559	+	0.530701i	$0.821929\pi$
$602$	−3525.04	−0.238654
$603$	−3624.09	−0.244750
$604$	4850.41	0.326756
$605$	−2191.40	−0.147261
$606$	1338.81	0.0897449
$607$	−23211.5	−1.55210	−0.776049	−	0.630672i	$-0.782779\pi$
$607$	−23211.5	−1.55210	−0.776049	+	0.630672i	$0.782779\pi$
$608$	−13621.2	−0.908573
$609$	−7374.20	−0.490669
$610$	−1245.04	−0.0826396
$611$	0	0
$612$	−12086.5	−0.798315
$613$	13858.3	0.913105	0.456553	−	0.889696i	$-0.349084\pi$
$613$	13858.3	0.913105	0.456553	+	0.889696i	$0.349084\pi$
$614$	−4056.84	−0.266646
$615$	−15125.5	−0.991735
$616$	1868.02	0.122183
$617$	−25877.8	−1.68849	−0.844246	−	0.535956i	$-0.819951\pi$
$617$	−25877.8	−1.68849	−0.844246	+	0.535956i	$0.819951\pi$
$618$	687.952	0.0447791
$619$	9159.05	0.594723	0.297361	−	0.954765i	$-0.403893\pi$
$619$	9159.05	0.594723	0.297361	+	0.954765i	$0.403893\pi$
$620$	−9794.27	−0.634431
$621$	2853.61	0.184398
$622$	−1408.02	−0.0907658
$623$	27164.5	1.74691
$624$	0	0
$625$	208.630	0.0133523
$626$	−5054.55	−0.322716
$627$	−2851.22	−0.181606
$628$	18224.4	1.15801
$629$	−14382.4	−0.911709
$630$	4610.10	0.291541
$631$	−15826.3	−0.998471	−0.499236	−	0.866466i	$-0.666386\pi$
$631$	−15826.3	−0.998471	−0.499236	+	0.866466i	$0.666386\pi$
$632$	9381.86	0.590491
$633$	−1950.02	−0.122443
$634$	−4968.30	−0.311224
$635$	−1513.03	−0.0945554
$636$	8337.74	0.519831
$637$	0	0
$638$	1148.60	0.0712748
$639$	−25030.0	−1.54957
$640$	−18046.1	−1.11459
$641$	18916.4	1.16560	0.582802	−	0.812614i	$-0.301956\pi$
$641$	18916.4	1.16560	0.582802	+	0.812614i	$0.301956\pi$
$642$	−1454.91	−0.0894401
$643$	7185.74	0.440712	0.220356	−	0.975419i	$-0.429278\pi$
$643$	7185.74	0.440712	0.220356	+	0.975419i	$0.429278\pi$
$644$	−4760.44	−0.291285
$645$	10962.0	0.669192
$646$	4949.32	0.301437
$647$	−9696.04	−0.589166	−0.294583	−	0.955626i	$-0.595181\pi$
$647$	−9696.04	−0.589166	−0.294583	+	0.955626i	$0.595181\pi$
$648$	3868.71	0.234533
$649$	3865.88	0.233820
$650$	0	0
$651$	2637.22	0.158773
$652$	−23556.6	−1.41495
$653$	8550.44	0.512411	0.256206	−	0.966622i	$-0.417528\pi$
$653$	8550.44	0.512411	0.256206	+	0.966622i	$0.417528\pi$
$654$	−371.504	−0.0222125
$655$	−10367.2	−0.618442
$656$	25777.7	1.53423
$657$	−3256.84	−0.193396
$658$	3310.69	0.196146
$659$	4039.55	0.238784	0.119392	−	0.992847i	$-0.461905\pi$
$659$	4039.55	0.238784	0.119392	+	0.992847i	$0.461905\pi$
$660$	−2852.09	−0.168208
$661$	−5099.22	−0.300056	−0.150028	−	0.988682i	$-0.547936\pi$
$661$	−5099.22	−0.300056	−0.150028	+	0.988682i	$0.547936\pi$
$662$	3261.34	0.191473
$663$	0	0
$664$	−3164.80	−0.184967
$665$	51311.4	2.99214
$666$	2714.93	0.157960
$667$	−5961.82	−0.346091
$668$	1244.74	0.0720965
$669$	−6505.50	−0.375960
$670$	1484.48	0.0855977
$671$	1419.29	0.0816557
$672$	3668.78	0.210605
$673$	29495.6	1.68941	0.844705	−	0.535231i	$-0.179776\pi$
$673$	29495.6	1.68941	0.844705	+	0.535231i	$0.179776\pi$
$674$	42.9058	0.00245203
$675$	−19042.1	−1.08582
$676$	0	0
$677$	3505.83	0.199025	0.0995126	−	0.995036i	$-0.468272\pi$
$677$	3505.83	0.199025	0.0995126	+	0.995036i	$0.468272\pi$
$678$	−2193.57	−0.124253
$679$	28854.8	1.63085
$680$	10083.8	0.568670
$681$	4698.71	0.264398
$682$	−410.770	−0.0230634
$683$	−12888.1	−0.722036	−0.361018	−	0.932559i	$-0.617571\pi$
$683$	−12888.1	−0.722036	−0.361018	+	0.932559i	$0.617571\pi$
$684$	25394.0	1.41954
$685$	−23632.1	−1.31816
$686$	−2968.36	−0.165208
$687$	3584.83	0.199083
$688$	−18682.1	−1.03525
$689$	0	0
$690$	−544.646	−0.0300497
$691$	31766.2	1.74883	0.874417	−	0.485175i	$-0.161244\pi$
$691$	31766.2	1.74883	0.874417	+	0.485175i	$0.161244\pi$
$692$	−16154.4	−0.887428
$693$	−5255.30	−0.288070
$694$	−14.4294	−0.000789239 0
$695$	33689.9	1.83875
$696$	3044.77	0.165822
$697$	−29930.3	−1.62653
$698$	6791.49	0.368283
$699$	3627.09	0.196265
$700$	31766.3	1.71522
$701$	5416.68	0.291848	0.145924	−	0.989296i	$-0.453385\pi$
$701$	5416.68	0.291848	0.145924	+	0.989296i	$0.453385\pi$
$702$	0	0
$703$	30217.8	1.62117
$704$	4468.09	0.239201
$705$	−10295.4	−0.549998
$706$	1290.01	0.0687681
$707$	27465.6	1.46103
$708$	5031.41	0.267079
$709$	−8568.23	−0.453860	−0.226930	−	0.973911i	$-0.572869\pi$
$709$	−8568.23	−0.453860	−0.226930	+	0.973911i	$0.572869\pi$
$710$	10252.7	0.541938
$711$	−26393.9	−1.39219
$712$	−11216.1	−0.590366
$713$	2132.12	0.111989
$714$	−1333.07	−0.0698723
$715$	0	0
$716$	−7204.19	−0.376024
$717$	−4133.61	−0.215304
$718$	3477.62	0.180757
$719$	2851.15	0.147886	0.0739430	−	0.997262i	$-0.476442\pi$
$719$	2851.15	0.147886	0.0739430	+	0.997262i	$0.476442\pi$
$720$	24432.8	1.26466
$721$	14113.3	0.728996
$722$	−6744.11	−0.347631
$723$	4983.45	0.256343
$724$	16690.4	0.856761
$725$	39783.1	2.03794
$726$	−119.616	−0.00611484
$727$	27885.3	1.42257	0.711284	−	0.702904i	$-0.248114\pi$
$727$	27885.3	1.42257	0.711284	+	0.702904i	$0.248114\pi$
$728$	0	0
$729$	−6184.67	−0.314214
$730$	1334.05	0.0676376
$731$	21691.6	1.09753
$732$	1847.19	0.0932706
$733$	30251.4	1.52437	0.762185	−	0.647360i	$-0.224127\pi$
$733$	30251.4	1.52437	0.762185	+	0.647360i	$0.224127\pi$
$734$	719.717	0.0361924
$735$	−2294.77	−0.115162
$736$	2966.10	0.148549
$737$	−1692.24	−0.0845786
$738$	5649.84	0.281807
$739$	34343.6	1.70954	0.854771	−	0.519006i	$-0.173698\pi$
$739$	34343.6	1.70954	0.854771	+	0.519006i	$0.173698\pi$
$740$	30226.9	1.50157
$741$	0	0
$742$	−6293.01	−0.311353
$743$	−2659.30	−0.131306	−0.0656530	−	0.997843i	$-0.520913\pi$
$743$	−2659.30	−0.131306	−0.0656530	+	0.997843i	$0.520913\pi$
$744$	−1088.90	−0.0536571
$745$	−16534.4	−0.813117
$746$	−2497.52	−0.122575
$747$	8903.50	0.436094
$748$	−5643.71	−0.275875
$749$	−29847.3	−1.45607
$750$	1396.46	0.0679886
$751$	−6119.11	−0.297323	−0.148661	−	0.988888i	$-0.547496\pi$
$751$	−6119.11	−0.297323	−0.148661	+	0.988888i	$0.547496\pi$
$752$	17546.1	0.850853
$753$	−6743.33	−0.326349
$754$	0	0
$755$	11384.6	0.548776
$756$	−14678.9	−0.706174
$757$	−27230.5	−1.30741	−0.653705	−	0.756750i	$-0.726786\pi$
$757$	−27230.5	−1.30741	−0.653705	+	0.756750i	$0.726786\pi$
$758$	4731.20	0.226708
$759$	620.871	0.0296920
$760$	−21186.2	−1.01119
$761$	−38795.7	−1.84802	−0.924010	−	0.382369i	$-0.875108\pi$
$761$	−38795.7	−1.84802	−0.924010	+	0.382369i	$0.875108\pi$
$762$	−82.5877	−0.00392629
$763$	−7621.39	−0.361616
$764$	15201.9	0.719875
$765$	−28368.7	−1.34075
$766$	−3668.04	−0.173018
$767$	0	0
$768$	5044.08	0.236996
$769$	11740.6	0.550554	0.275277	−	0.961365i	$-0.411230\pi$
$769$	11740.6	0.550554	0.275277	+	0.961365i	$0.411230\pi$
$770$	2152.65	0.100748
$771$	−12309.8	−0.575003
$772$	5009.75	0.233556
$773$	20366.5	0.947650	0.473825	−	0.880619i	$-0.342873\pi$
$773$	20366.5	0.947650	0.473825	+	0.880619i	$0.342873\pi$
$774$	−4094.66	−0.190155
$775$	−14227.6	−0.659444
$776$	−11914.0	−0.551145
$777$	−8138.97	−0.375784
$778$	3731.11	0.171937
$779$	62884.1	2.89224
$780$	0	0
$781$	−11687.6	−0.535486
$782$	−1077.75	−0.0492840
$783$	−18383.4	−0.839041
$784$	3910.88	0.178156
$785$	42775.0	1.94485
$786$	−565.886	−0.0256800
$787$	−22547.7	−1.02127	−0.510634	−	0.859798i	$-0.670589\pi$
$787$	−22547.7	−1.02127	−0.510634	+	0.859798i	$0.670589\pi$
$788$	−12645.3	−0.571663
$789$	3181.36	0.143548
$790$	10811.3	0.486899
$791$	−45000.9	−2.02282
$792$	2169.89	0.0973530
$793$	0	0
$794$	3269.04	0.146113
$795$	19569.8	0.873041
$796$	25611.2	1.14041
$797$	−14166.6	−0.629619	−0.314810	−	0.949155i	$-0.601941\pi$
$797$	−14166.6	−0.629619	−0.314810	+	0.949155i	$0.601941\pi$
$798$	2800.80	0.124245
$799$	−20372.6	−0.902042
$800$	−19792.7	−0.874722
$801$	31554.1	1.39190
$802$	1637.02	0.0720762
$803$	−1520.76	−0.0668323
$804$	−2202.43	−0.0966093
$805$	−11173.4	−0.489205
$806$	0	0
$807$	243.312	0.0106134
$808$	−11340.4	−0.493755
$809$	37171.0	1.61540	0.807702	−	0.589591i	$-0.200711\pi$
$809$	37171.0	1.61540	0.807702	+	0.589591i	$0.200711\pi$
$810$	4458.18	0.193388
$811$	−38019.5	−1.64617	−0.823086	−	0.567916i	$-0.807750\pi$
$811$	−38019.5	−1.64617	−0.823086	+	0.567916i	$0.807750\pi$
$812$	30667.5	1.32539
$813$	13456.5	0.580490
$814$	1267.71	0.0545864
$815$	−55290.5	−2.37637
$816$	−7065.06	−0.303096
$817$	−45574.6	−1.95159
$818$	714.448	0.0305380
$819$	0	0
$820$	62903.1	2.67887
$821$	11848.2	0.503661	0.251831	−	0.967771i	$-0.418967\pi$
$821$	11848.2	0.503661	0.251831	+	0.967771i	$0.418967\pi$
$822$	−1289.94	−0.0547348
$823$	−21410.6	−0.906835	−0.453418	−	0.891298i	$-0.649795\pi$
$823$	−21410.6	−0.906835	−0.453418	+	0.891298i	$0.649795\pi$
$824$	−5827.31	−0.246364
$825$	−4143.06	−0.174840
$826$	−3797.52	−0.159967
$827$	18374.6	0.772610	0.386305	−	0.922371i	$-0.373751\pi$
$827$	18374.6	0.772610	0.386305	+	0.922371i	$0.373751\pi$
$828$	−5529.71	−0.232090
$829$	−6589.77	−0.276082	−0.138041	−	0.990426i	$-0.544081\pi$
$829$	−6589.77	−0.276082	−0.138041	+	0.990426i	$0.544081\pi$
$830$	−3647.01	−0.152517
$831$	4618.63	0.192802
$832$	0	0
$833$	−4540.88	−0.188874
$834$	1838.94	0.0763518
$835$	2921.57	0.121084
$836$	11857.5	0.490552
$837$	6574.43	0.271500
$838$	6128.09	0.252615
$839$	19114.9	0.786556	0.393278	−	0.919420i	$-0.371341\pi$
$839$	19114.9	0.786556	0.393278	+	0.919420i	$0.371341\pi$
$840$	5706.38	0.234391
$841$	14018.0	0.574765
$842$	2292.47	0.0938286
$843$	2854.61	0.116629
$844$	8109.65	0.330741
$845$	0	0
$846$	3845.68	0.156285
$847$	−2453.92	−0.0995486
$848$	−33352.0	−1.35060
$849$	10311.6	0.416837
$850$	7191.77	0.290207
$851$	−6580.11	−0.265057
$852$	−15211.3	−0.611655
$853$	−1750.62	−0.0702697	−0.0351348	−	0.999383i	$-0.511186\pi$
$853$	−1750.62	−0.0702697	−0.0351348	+	0.999383i	$0.511186\pi$
$854$	−1394.19	−0.0558644
$855$	59603.1	2.38407
$856$	12323.8	0.492078
$857$	20026.2	0.798230	0.399115	−	0.916901i	$-0.369317\pi$
$857$	20026.2	0.798230	0.399115	+	0.916901i	$0.369317\pi$
$858$	0	0
$859$	−19886.2	−0.789881	−0.394940	−	0.918707i	$-0.629235\pi$
$859$	−19886.2	−0.789881	−0.394940	+	0.918707i	$0.629235\pi$
$860$	−45588.4	−1.80762
$861$	−16937.4	−0.670413
$862$	−1942.24	−0.0767437
$863$	−40287.0	−1.58909	−0.794546	−	0.607204i	$-0.792291\pi$
$863$	−40287.0	−1.58909	−0.794546	+	0.607204i	$0.792291\pi$
$864$	9146.03	0.360132
$865$	−37916.6	−1.49041
$866$	−4034.56	−0.158314
$867$	−912.369	−0.0357389
$868$	−10967.6	−0.428876
$869$	−12324.4	−0.481102
$870$	3508.69	0.136731
$871$	0	0
$872$	3146.84	0.122208
$873$	33517.6	1.29943
$874$	2264.36	0.0876353
$875$	28648.3	1.10684
$876$	−1979.25	−0.0763387
$877$	8909.33	0.343041	0.171520	−	0.985181i	$-0.445132\pi$
$877$	8909.33	0.343041	0.171520	+	0.985181i	$0.445132\pi$
$878$	3314.48	0.127401
$879$	8010.47	0.307379
$880$	11408.7	0.437031
$881$	27174.7	1.03921	0.519603	−	0.854408i	$-0.326080\pi$
$881$	27174.7	1.03921	0.519603	+	0.854408i	$0.326080\pi$
$882$	857.169	0.0327238
$883$	43149.7	1.64451	0.822256	−	0.569117i	$-0.192715\pi$
$883$	43149.7	1.64451	0.822256	+	0.569117i	$0.192715\pi$
$884$	0	0
$885$	11809.4	0.448551
$886$	3806.98	0.144354
$887$	−26975.3	−1.02113	−0.510565	−	0.859839i	$-0.670564\pi$
$887$	−26975.3	−1.02113	−0.510565	+	0.859839i	$0.670564\pi$
$888$	3360.54	0.126996
$889$	−1694.28	−0.0639194
$890$	−12925.0	−0.486796
$891$	−5082.12	−0.191086
$892$	27054.8	1.01554
$893$	42803.3	1.60398
$894$	−902.518	−0.0337637
$895$	−16909.2	−0.631521
$896$	−20208.0	−0.753462
$897$	0	0
$898$	−569.103	−0.0211484
$899$	−13735.4	−0.509568
$900$	36899.6	1.36665
$901$	38724.6	1.43186
$902$	2638.15	0.0973845
$903$	12275.2	0.452374
$904$	18580.6	0.683609
$905$	39174.6	1.43890
$906$	621.419	0.0227873
$907$	27107.5	0.992383	0.496191	−	0.868213i	$-0.334731\pi$
$907$	27107.5	0.992383	0.496191	+	0.868213i	$0.334731\pi$
$908$	−19540.8	−0.714189
$909$	31903.9	1.16412
$910$	0	0
$911$	−6281.05	−0.228431	−0.114215	−	0.993456i	$-0.536435\pi$
$911$	−6281.05	−0.228431	−0.114215	+	0.993456i	$0.536435\pi$
$912$	14843.8	0.538956
$913$	4157.42	0.150702
$914$	−10101.5	−0.365568
$915$	4335.60	0.156645
$916$	−14908.5	−0.537761
$917$	−11609.1	−0.418067
$918$	−3323.25	−0.119481
$919$	35324.6	1.26796	0.633978	−	0.773351i	$-0.281421\pi$
$919$	35324.6	1.26796	0.633978	+	0.773351i	$0.281421\pi$
$920$	4613.44	0.165327
$921$	14127.1	0.505433
$922$	−9106.68	−0.325285
$923$	0	0
$924$	−3193.75	−0.113709
$925$	43908.9	1.56077
$926$	6306.42	0.223803
$927$	16393.9	0.580849
$928$	−19108.1	−0.675919
$929$	18854.6	0.665876	0.332938	−	0.942949i	$-0.391960\pi$
$929$	18854.6	0.665876	0.332938	+	0.942949i	$0.391960\pi$
$930$	−1254.81	−0.0442439
$931$	9540.49	0.335851
$932$	−15084.2	−0.530150
$933$	4903.13	0.172049
$934$	8134.32	0.284971
$935$	−13246.5	−0.463324
$936$	0	0
$937$	46461.2	1.61987	0.809936	−	0.586518i	$-0.199502\pi$
$937$	46461.2	1.61987	0.809936	+	0.586518i	$0.199502\pi$
$938$	1662.31	0.0578641
$939$	17601.4	0.611715
$940$	42816.2	1.48565
$941$	−31917.7	−1.10573	−0.552863	−	0.833272i	$-0.686465\pi$
$941$	−31917.7	−1.10573	−0.552863	+	0.833272i	$0.686465\pi$
$942$	2334.84	0.0807573
$943$	−13693.4	−0.472872
$944$	−20126.3	−0.693913
$945$	−34453.4	−1.18600
$946$	−1911.97	−0.0657120
$947$	25207.9	0.864990	0.432495	−	0.901636i	$-0.357633\pi$
$947$	25207.9	0.864990	0.432495	+	0.901636i	$0.357633\pi$
$948$	−16040.1	−0.549535
$949$	0	0
$950$	−15110.1	−0.516037
$951$	17301.1	0.589933
$952$	11291.8	0.384421
$953$	−22064.1	−0.749975	−0.374987	−	0.927030i	$-0.622353\pi$
$953$	−22064.1	−0.749975	−0.374987	+	0.927030i	$0.622353\pi$
$954$	−7309.93	−0.248080
$955$	35680.8	1.20901
$956$	17190.7	0.581576
$957$	−3999.75	−0.135103
$958$	6492.73	0.218967
$959$	−26463.1	−0.891073
$960$	13649.0	0.458874
$961$	−24878.8	−0.835112
$962$	0	0
$963$	−34670.5	−1.16017
$964$	−20724.9	−0.692433
$965$	11758.5	0.392249
$966$	−609.892	−0.0203136
$967$	−53211.1	−1.76955	−0.884774	−	0.466021i	$-0.845687\pi$
$967$	−53211.1	−1.76955	−0.884774	+	0.466021i	$0.845687\pi$
$968$	1013.21	0.0336424
$969$	−17235.0	−0.571381
$970$	−13729.3	−0.454455
$971$	50826.8	1.67982	0.839912	−	0.542723i	$-0.182607\pi$
$971$	50826.8	1.67982	0.839912	+	0.542723i	$0.182607\pi$
$972$	−26157.0	−0.863154
$973$	37725.8	1.24300
$974$	8158.99	0.268409
$975$	0	0
$976$	−7388.99	−0.242332
$977$	37320.6	1.22210	0.611050	−	0.791592i	$-0.290747\pi$
$977$	37320.6	1.22210	0.611050	+	0.791592i	$0.290747\pi$
$978$	−3018.00	−0.0986758
$979$	14734.0	0.481000
$980$	9543.38	0.311074
$981$	−8852.97	−0.288128
$982$	9297.78	0.302143
$983$	3427.86	0.111223	0.0556113	−	0.998452i	$-0.482289\pi$
$983$	3427.86	0.111223	0.0556113	+	0.998452i	$0.482289\pi$
$984$	6993.38	0.226566
$985$	−29680.2	−0.960091
$986$	6943.00	0.224250
$987$	−11528.8	−0.371799
$988$	0	0
$989$	9924.14	0.319079
$990$	2500.51	0.0802740
$991$	9320.29	0.298757	0.149379	−	0.988780i	$-0.452273\pi$
$991$	9320.29	0.298757	0.149379	+	0.988780i	$0.452273\pi$
$992$	6833.59	0.218716
$993$	−11356.9	−0.362942
$994$	11480.9	0.366350
$995$	60112.8	1.91528
$996$	5410.84	0.172138
$997$	−8615.13	−0.273665	−0.136833	−	0.990594i	$-0.543692\pi$
$997$	−8615.13	−0.273665	−0.136833	+	0.990594i	$0.543692\pi$
$998$	3662.81	0.116176
$999$	−20289.9	−0.642587

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.19	yes	39
13.12	even	2		1859.4.a.n.1.21	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.21	✓	39	13.12	even	2
1859.4.a.o.1.19	yes	39	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)

\(f(q)\)	\(=\)	\(q-0.532806 q^{2} +1.85539 q^{3} -7.71612 q^{4} -18.1107 q^{5} -0.988563 q^{6} -20.2803 q^{7} +8.37365 q^{8} -23.5575 q^{9} +O(q^{10})\)	\(q-0.532806 q^{2} +1.85539 q^{3} -7.71612 q^{4} -18.1107 q^{5} -0.988563 q^{6} -20.2803 q^{7} +8.37365 q^{8} -23.5575 q^{9} +9.64951 q^{10} -11.0000 q^{11} -14.3164 q^{12} +10.8055 q^{14} -33.6025 q^{15} +57.2674 q^{16} -66.4926 q^{17} +12.5516 q^{18} +139.702 q^{19} +139.745 q^{20} -37.6279 q^{21} +5.86087 q^{22} -30.4210 q^{23} +15.5364 q^{24} +202.999 q^{25} -93.8039 q^{27} +156.485 q^{28} +195.977 q^{29} +17.9036 q^{30} -70.0869 q^{31} -97.5016 q^{32} -20.4093 q^{33} +35.4277 q^{34} +367.292 q^{35} +181.773 q^{36} +216.301 q^{37} -74.4342 q^{38} -151.653 q^{40} +450.129 q^{41} +20.0484 q^{42} -326.226 q^{43} +84.8773 q^{44} +426.644 q^{45} +16.2085 q^{46} +306.389 q^{47} +106.253 q^{48} +68.2916 q^{49} -108.159 q^{50} -123.370 q^{51} -582.391 q^{53} +49.9793 q^{54} +199.218 q^{55} -169.820 q^{56} +259.202 q^{57} -104.418 q^{58} -351.443 q^{59} +259.281 q^{60} -129.026 q^{61} +37.3428 q^{62} +477.754 q^{63} -406.190 q^{64} +10.8742 q^{66} +153.840 q^{67} +513.064 q^{68} -56.4428 q^{69} -195.695 q^{70} +1062.51 q^{71} -197.262 q^{72} +138.251 q^{73} -115.247 q^{74} +376.642 q^{75} -1077.96 q^{76} +223.084 q^{77} +1120.40 q^{79} -1037.15 q^{80} +462.010 q^{81} -239.832 q^{82} -377.947 q^{83} +290.341 q^{84} +1204.23 q^{85} +173.816 q^{86} +363.614 q^{87} -92.1101 q^{88} -1339.45 q^{89} -227.319 q^{90} +234.732 q^{92} -130.039 q^{93} -163.246 q^{94} -2530.11 q^{95} -180.903 q^{96} -1422.80 q^{97} -36.3862 q^{98} +259.133 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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