LMFDB - Embedded newform 1870.2.a.r.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,2,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1870.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3,0,3,-3,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$14.9320251780$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.940.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 7x - 4 $ x^3 - 7*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.89511$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.89511 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.89511 q^{6} -1.48654 q^{7} +1.00000 q^{8} +5.38164 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.89511 q^{12} +3.40857 q^{13} -1.48654 q^{14} -2.89511 q^{15} +1.00000 q^{16} -1.00000 q^{17} +5.38164 q^{18} +6.38164 q^{19} -1.00000 q^{20} -4.30368 q^{21} -1.00000 q^{22} +0.513465 q^{23} +2.89511 q^{24} +1.00000 q^{25} +3.40857 q^{26} +6.89511 q^{27} -1.48654 q^{28} +7.40857 q^{29} -2.89511 q^{30} -1.40857 q^{31} +1.00000 q^{32} -2.89511 q^{33} -1.00000 q^{34} +1.48654 q^{35} +5.38164 q^{36} +3.79021 q^{37} +6.38164 q^{38} +9.86818 q^{39} -1.00000 q^{40} -1.48654 q^{41} -4.30368 q^{42} -5.79021 q^{43} -1.00000 q^{44} -5.38164 q^{45} +0.513465 q^{46} +3.61836 q^{47} +2.89511 q^{48} -4.79021 q^{49} +1.00000 q^{50} -2.89511 q^{51} +3.40857 q^{52} -2.89511 q^{53} +6.89511 q^{54} +1.00000 q^{55} -1.48654 q^{56} +18.4755 q^{57} +7.40857 q^{58} +0.0779639 q^{59} -2.89511 q^{60} -5.19878 q^{61} -1.40857 q^{62} -8.00000 q^{63} +1.00000 q^{64} -3.40857 q^{65} -2.89511 q^{66} -12.2498 q^{67} -1.00000 q^{68} +1.48654 q^{69} +1.48654 q^{70} +8.38164 q^{71} +5.38164 q^{72} -15.4486 q^{73} +3.79021 q^{74} +2.89511 q^{75} +6.38164 q^{76} +1.48654 q^{77} +9.86818 q^{78} -1.23672 q^{79} -1.00000 q^{80} +3.81714 q^{81} -1.48654 q^{82} +9.48654 q^{83} -4.30368 q^{84} +1.00000 q^{85} -5.79021 q^{86} +21.4486 q^{87} -1.00000 q^{88} -2.38164 q^{89} -5.38164 q^{90} -5.06696 q^{91} +0.513465 q^{92} -4.07796 q^{93} +3.61836 q^{94} -6.38164 q^{95} +2.89511 q^{96} -10.5914 q^{97} -4.79021 q^{98} -5.38164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{13} - 2 q^{14} + 3 q^{16} - 3 q^{17} + 5 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} + 4 q^{23} + 3 q^{25}+ \cdots - 5 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^13 - 2 * q^14 + 3 * q^16 - 3 * q^17 + 5 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 + 4 * q^23 + 3 * q^25 + 4 * q^26 + 12 * q^27 - 2 * q^28 + 16 * q^29 + 2 * q^31 + 3 * q^32 - 3 * q^34 + 2 * q^35 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 16 * q^39 - 3 * q^40 - 2 * q^41 + 2 * q^42 - 3 * q^44 - 5 * q^45 + 4 * q^46 + 22 * q^47 + 3 * q^49 + 3 * q^50 + 4 * q^52 + 12 * q^54 + 3 * q^55 - 2 * q^56 + 12 * q^57 + 16 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 - 24 * q^63 + 3 * q^64 - 4 * q^65 - 12 * q^67 - 3 * q^68 + 2 * q^69 + 2 * q^70 + 14 * q^71 + 5 * q^72 + 2 * q^73 - 6 * q^74 + 8 * q^76 + 2 * q^77 + 16 * q^78 - 26 * q^79 - 3 * q^80 - q^81 - 2 * q^82 + 26 * q^83 + 2 * q^84 + 3 * q^85 + 16 * q^87 - 3 * q^88 + 4 * q^89 - 5 * q^90 + 22 * q^91 + 4 * q^92 - 16 * q^93 + 22 * q^94 - 8 * q^95 - 38 * q^97 + 3 * q^98 - 5 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.89511	1.67149	0.835745	−	0.549117i	$-0.185036\pi$
$3$	2.89511	1.67149	0.835745	+	0.549117i	$0.185036\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.89511	1.18192
$7$	−1.48654	−0.561858	−0.280929	−	0.959729i	$-0.590642\pi$
$7$	−1.48654	−0.561858	−0.280929	+	0.959729i	$0.590642\pi$
$8$	1.00000	0.353553
$9$	5.38164	1.79388
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.89511	0.835745
$13$	3.40857	0.945368	0.472684	−	0.881232i	$-0.343285\pi$
$13$	3.40857	0.945368	0.472684	+	0.881232i	$0.343285\pi$
$14$	−1.48654	−0.397293
$15$	−2.89511	−0.747513
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	5.38164	1.26847
$19$	6.38164	1.46405	0.732025	−	0.681278i	$-0.238576\pi$
$19$	6.38164	1.46405	0.732025	+	0.681278i	$0.238576\pi$
$20$	−1.00000	−0.223607
$21$	−4.30368	−0.939139
$22$	−1.00000	−0.213201
$23$	0.513465	0.107065	0.0535324	−	0.998566i	$-0.482952\pi$
$23$	0.513465	0.107065	0.0535324	+	0.998566i	$0.482952\pi$
$24$	2.89511	0.590961
$25$	1.00000	0.200000
$26$	3.40857	0.668476
$27$	6.89511	1.32696
$28$	−1.48654	−0.280929
$29$	7.40857	1.37574	0.687869	−	0.725835i	$-0.258547\pi$
$29$	7.40857	1.37574	0.687869	+	0.725835i	$0.258547\pi$
$30$	−2.89511	−0.528572
$31$	−1.40857	−0.252987	−0.126493	−	0.991967i	$-0.540372\pi$
$31$	−1.40857	−0.252987	−0.126493	+	0.991967i	$0.540372\pi$
$32$	1.00000	0.176777
$33$	−2.89511	−0.503973
$34$	−1.00000	−0.171499
$35$	1.48654	0.251270
$36$	5.38164	0.896940
$37$	3.79021	0.623107	0.311554	−	0.950229i	$-0.399151\pi$
$37$	3.79021	0.623107	0.311554	+	0.950229i	$0.399151\pi$
$38$	6.38164	1.03524
$39$	9.86818	1.58017
$40$	−1.00000	−0.158114
$41$	−1.48654	−0.232158	−0.116079	−	0.993240i	$-0.537033\pi$
$41$	−1.48654	−0.232158	−0.116079	+	0.993240i	$0.537033\pi$
$42$	−4.30368	−0.664072
$43$	−5.79021	−0.882999	−0.441500	−	0.897261i	$-0.645553\pi$
$43$	−5.79021	−0.882999	−0.441500	+	0.897261i	$0.645553\pi$
$44$	−1.00000	−0.150756
$45$	−5.38164	−0.802248
$46$	0.513465	0.0757063
$47$	3.61836	0.527792	0.263896	−	0.964551i	$-0.414992\pi$
$47$	3.61836	0.527792	0.263896	+	0.964551i	$0.414992\pi$
$48$	2.89511	0.417873
$49$	−4.79021	−0.684316
$50$	1.00000	0.141421
$51$	−2.89511	−0.405396
$52$	3.40857	0.472684
$53$	−2.89511	−0.397673	−0.198837	−	0.980033i	$-0.563716\pi$
$53$	−2.89511	−0.397673	−0.198837	+	0.980033i	$0.563716\pi$
$54$	6.89511	0.938305
$55$	1.00000	0.134840
$56$	−1.48654	−0.198647
$57$	18.4755	2.44714
$58$	7.40857	0.972793
$59$	0.0779639	0.0101500	0.00507502	−	0.999987i	$-0.498385\pi$
$59$	0.0779639	0.0101500	0.00507502	+	0.999987i	$0.498385\pi$
$60$	−2.89511	−0.373757
$61$	−5.19878	−0.665636	−0.332818	−	0.942991i	$-0.607999\pi$
$61$	−5.19878	−0.665636	−0.332818	+	0.942991i	$0.607999\pi$
$62$	−1.40857	−0.178889
$63$	−8.00000	−1.00791
$64$	1.00000	0.125000
$65$	−3.40857	−0.422781
$66$	−2.89511	−0.356363
$67$	−12.2498	−1.49655	−0.748277	−	0.663387i	$-0.769118\pi$
$67$	−12.2498	−1.49655	−0.748277	+	0.663387i	$0.769118\pi$
$68$	−1.00000	−0.121268
$69$	1.48654	0.178958
$70$	1.48654	0.177675
$71$	8.38164	0.994718	0.497359	−	0.867545i	$-0.334303\pi$
$71$	8.38164	0.994718	0.497359	+	0.867545i	$0.334303\pi$
$72$	5.38164	0.634233
$73$	−15.4486	−1.80812	−0.904061	−	0.427403i	$-0.859428\pi$
$73$	−15.4486	−1.80812	−0.904061	+	0.427403i	$0.859428\pi$
$74$	3.79021	0.440603
$75$	2.89511	0.334298
$76$	6.38164	0.732025
$77$	1.48654	0.169406
$78$	9.86818	1.11735
$79$	−1.23672	−0.139141	−0.0695707	−	0.997577i	$-0.522163\pi$
$79$	−1.23672	−0.139141	−0.0695707	+	0.997577i	$0.522163\pi$
$80$	−1.00000	−0.111803
$81$	3.81714	0.424127
$82$	−1.48654	−0.164160
$83$	9.48654	1.04128	0.520641	−	0.853776i	$-0.325693\pi$
$83$	9.48654	1.04128	0.520641	+	0.853776i	$0.325693\pi$
$84$	−4.30368	−0.469570
$85$	1.00000	0.108465
$86$	−5.79021	−0.624375
$87$	21.4486	2.29953
$88$	−1.00000	−0.106600
$89$	−2.38164	−0.252454	−0.126227	−	0.992001i	$-0.540287\pi$
$89$	−2.38164	−0.252454	−0.126227	+	0.992001i	$0.540287\pi$
$90$	−5.38164	−0.567275
$91$	−5.06696	−0.531162
$92$	0.513465	0.0535324
$93$	−4.07796	−0.422865
$94$	3.61836	0.373205
$95$	−6.38164	−0.654743
$96$	2.89511	0.295481
$97$	−10.5914	−1.07540	−0.537698	−	0.843137i	$-0.680706\pi$
$97$	−10.5914	−1.07540	−0.537698	+	0.843137i	$0.680706\pi$
$98$	−4.79021	−0.483885
$99$	−5.38164	−0.540875
$100$	1.00000	0.100000
$101$	9.33061	0.928430	0.464215	−	0.885723i	$-0.346336\pi$
$101$	9.33061	0.928430	0.464215	+	0.885723i	$0.346336\pi$
$102$	−2.89511	−0.286658
$103$	1.18286	0.116550	0.0582752	−	0.998301i	$-0.481440\pi$
$103$	1.18286	0.116550	0.0582752	+	0.998301i	$0.481440\pi$
$104$	3.40857	0.334238
$105$	4.30368	0.419996
$106$	−2.89511	−0.281198
$107$	−7.73635	−0.747902	−0.373951	−	0.927449i	$-0.621997\pi$
$107$	−7.73635	−0.747902	−0.373951	+	0.927449i	$0.621997\pi$
$108$	6.89511	0.663482
$109$	−8.43550	−0.807974	−0.403987	−	0.914765i	$-0.632376\pi$
$109$	−8.43550	−0.807974	−0.403987	+	0.914765i	$0.632376\pi$
$110$	1.00000	0.0953463
$111$	10.9731	1.04152
$112$	−1.48654	−0.140464
$113$	−9.14493	−0.860282	−0.430141	−	0.902762i	$-0.641536\pi$
$113$	−9.14493	−0.860282	−0.430141	+	0.902762i	$0.641536\pi$
$114$	18.4755	1.73039
$115$	−0.513465	−0.0478808
$116$	7.40857	0.687869
$117$	18.3437	1.69588
$118$	0.0779639	0.00717716
$119$	1.48654	0.136270
$120$	−2.89511	−0.264286
$121$	1.00000	0.0909091
$122$	−5.19878	−0.470676
$123$	−4.30368	−0.388050
$124$	−1.40857	−0.126493
$125$	−1.00000	−0.0894427
$126$	−8.00000	−0.712697
$127$	12.8412	1.13948	0.569738	−	0.821826i	$-0.307045\pi$
$127$	12.8412	1.13948	0.569738	+	0.821826i	$0.307045\pi$
$128$	1.00000	0.0883883
$129$	−16.7633	−1.47592
$130$	−3.40857	−0.298951
$131$	−18.8572	−1.64756	−0.823779	−	0.566910i	$-0.808139\pi$
$131$	−18.8572	−1.64756	−0.823779	+	0.566910i	$0.808139\pi$
$132$	−2.89511	−0.251987
$133$	−9.48654	−0.822587
$134$	−12.2498	−1.05822
$135$	−6.89511	−0.593436
$136$	−1.00000	−0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	1.48654	0.126542
$139$	1.48654	0.126086	0.0630431	−	0.998011i	$-0.479919\pi$
$139$	1.48654	0.126086	0.0630431	+	0.998011i	$0.479919\pi$
$140$	1.48654	0.125635
$141$	10.4755	0.882199
$142$	8.38164	0.703372
$143$	−3.40857	−0.285039
$144$	5.38164	0.448470
$145$	−7.40857	−0.615248
$146$	−15.4486	−1.27854
$147$	−13.8682	−1.14383
$148$	3.79021	0.311554
$149$	6.97307	0.571256	0.285628	−	0.958341i	$-0.407798\pi$
$149$	6.97307	0.571256	0.285628	+	0.958341i	$0.407798\pi$
$150$	2.89511	0.236384
$151$	0.155928	0.0126892	0.00634461	−	0.999980i	$-0.497980\pi$
$151$	0.155928	0.0126892	0.00634461	+	0.999980i	$0.497980\pi$
$152$	6.38164	0.517619
$153$	−5.38164	−0.435080
$154$	1.48654	0.119788
$155$	1.40857	0.113139
$156$	9.86818	0.790086
$157$	−19.4245	−1.55024	−0.775122	−	0.631812i	$-0.782312\pi$
$157$	−19.4245	−1.55024	−0.775122	+	0.631812i	$0.782312\pi$
$158$	−1.23672	−0.0983879
$159$	−8.38164	−0.664707
$160$	−1.00000	−0.0790569
$161$	−0.763283	−0.0601552
$162$	3.81714	0.299903
$163$	−18.5535	−1.45322	−0.726611	−	0.687049i	$-0.758906\pi$
$163$	−18.5535	−1.45322	−0.726611	+	0.687049i	$0.758906\pi$
$164$	−1.48654	−0.116079
$165$	2.89511	0.225384
$166$	9.48654	0.736298
$167$	19.3168	1.49478	0.747389	−	0.664387i	$-0.231307\pi$
$167$	19.3168	1.49478	0.747389	+	0.664387i	$0.231307\pi$
$168$	−4.30368	−0.332036
$169$	−1.38164	−0.106280
$170$	1.00000	0.0766965
$171$	34.3437	2.62633
$172$	−5.79021	−0.441500
$173$	2.45961	0.187000	0.0935002	−	0.995619i	$-0.470194\pi$
$173$	2.45961	0.187000	0.0935002	+	0.995619i	$0.470194\pi$
$174$	21.4486	1.62601
$175$	−1.48654	−0.112372
$176$	−1.00000	−0.0753778
$177$	0.225714	0.0169657
$178$	−2.38164	−0.178512
$179$	−4.15593	−0.310629	−0.155314	−	0.987865i	$-0.549639\pi$
$179$	−4.15593	−0.310629	−0.155314	+	0.987865i	$0.549639\pi$
$180$	−5.38164	−0.401124
$181$	3.02693	0.224990	0.112495	−	0.993652i	$-0.464116\pi$
$181$	3.02693	0.224990	0.112495	+	0.993652i	$0.464116\pi$
$182$	−5.06696	−0.375588
$183$	−15.0510	−1.11260
$184$	0.513465	0.0378531
$185$	−3.79021	−0.278662
$186$	−4.07796	−0.299011
$187$	1.00000	0.0731272
$188$	3.61836	0.263896
$189$	−10.2498	−0.745565
$190$	−6.38164	−0.462973
$191$	−4.45961	−0.322686	−0.161343	−	0.986898i	$-0.551582\pi$
$191$	−4.45961	−0.322686	−0.161343	+	0.986898i	$0.551582\pi$
$192$	2.89511	0.208936
$193$	10.3437	0.744557	0.372278	−	0.928121i	$-0.378577\pi$
$193$	10.3437	0.744557	0.372278	+	0.928121i	$0.378577\pi$
$194$	−10.5914	−0.760420
$195$	−9.86818	−0.706675
$196$	−4.79021	−0.342158
$197$	−21.3168	−1.51876	−0.759379	−	0.650649i	$-0.774497\pi$
$197$	−21.3168	−1.51876	−0.759379	+	0.650649i	$0.774497\pi$
$198$	−5.38164	−0.382457
$199$	1.40857	0.0998510	0.0499255	−	0.998753i	$-0.484102\pi$
$199$	1.40857	0.0998510	0.0499255	+	0.998753i	$0.484102\pi$
$200$	1.00000	0.0707107
$201$	−35.4645	−2.50148
$202$	9.33061	0.656499
$203$	−11.0131	−0.772968
$204$	−2.89511	−0.202698
$205$	1.48654	0.103824
$206$	1.18286	0.0824136
$207$	2.76328	0.192061
$208$	3.40857	0.236342
$209$	−6.38164	−0.441427
$210$	4.30368	0.296982
$211$	−18.3976	−1.26654	−0.633270	−	0.773931i	$-0.718288\pi$
$211$	−18.3976	−1.26654	−0.633270	+	0.773931i	$0.718288\pi$
$212$	−2.89511	−0.198837
$213$	24.2657	1.66266
$214$	−7.73635	−0.528846
$215$	5.79021	0.394889
$216$	6.89511	0.469153
$217$	2.09389	0.142143
$218$	−8.43550	−0.571324
$219$	−44.7254	−3.02226
$220$	1.00000	0.0674200
$221$	−3.40857	−0.229285
$222$	10.9731	0.736464
$223$	−0.537570	−0.0359983	−0.0179992	−	0.999838i	$-0.505730\pi$
$223$	−0.537570	−0.0359983	−0.0179992	+	0.999838i	$0.505730\pi$
$224$	−1.48654	−0.0993233
$225$	5.38164	0.358776
$226$	−9.14493	−0.608311
$227$	2.32778	0.154500	0.0772502	−	0.997012i	$-0.475386\pi$
$227$	2.32778	0.154500	0.0772502	+	0.997012i	$0.475386\pi$
$228$	18.4755	1.22357
$229$	5.58043	0.368765	0.184382	−	0.982855i	$-0.440971\pi$
$229$	5.58043	0.368765	0.184382	+	0.982855i	$0.440971\pi$
$230$	−0.513465	−0.0338569
$231$	4.30368	0.283161
$232$	7.40857	0.486397
$233$	24.8192	1.62596	0.812981	−	0.582290i	$-0.197843\pi$
$233$	24.8192	1.62596	0.812981	+	0.582290i	$0.197843\pi$
$234$	18.3437	1.19917
$235$	−3.61836	−0.236036
$236$	0.0779639	0.00507502
$237$	−3.58043	−0.232574
$238$	1.48654	0.0963578
$239$	6.09389	0.394181	0.197091	−	0.980385i	$-0.436851\pi$
$239$	6.09389	0.394181	0.197091	+	0.980385i	$0.436851\pi$
$240$	−2.89511	−0.186878
$241$	19.7364	1.27133	0.635665	−	0.771965i	$-0.280726\pi$
$241$	19.7364	1.27133	0.635665	+	0.771965i	$0.280726\pi$
$242$	1.00000	0.0642824
$243$	−9.63429	−0.618040
$244$	−5.19878	−0.332818
$245$	4.79021	0.306035
$246$	−4.30368	−0.274392
$247$	21.7523	1.38406
$248$	−1.40857	−0.0894444
$249$	27.4645	1.74049
$250$	−1.00000	−0.0632456
$251$	−17.5266	−1.10627	−0.553134	−	0.833093i	$-0.686568\pi$
$251$	−17.5266	−1.10627	−0.553134	+	0.833093i	$0.686568\pi$
$252$	−8.00000	−0.503953
$253$	−0.513465	−0.0322813
$254$	12.8412	0.805732
$255$	2.89511	0.181299
$256$	1.00000	0.0625000
$257$	18.6474	1.16319	0.581596	−	0.813478i	$-0.302428\pi$
$257$	18.6474	1.16319	0.581596	+	0.813478i	$0.302428\pi$
$258$	−16.7633	−1.04364
$259$	−5.63429	−0.350097
$260$	−3.40857	−0.211391
$261$	39.8703	2.46791
$262$	−18.8572	−1.16500
$263$	−11.7661	−0.725529	−0.362765	−	0.931881i	$-0.618167\pi$
$263$	−11.7661	−0.725529	−0.362765	+	0.931881i	$0.618167\pi$
$264$	−2.89511	−0.178181
$265$	2.89511	0.177845
$266$	−9.48654	−0.581657
$267$	−6.89511	−0.421974
$268$	−12.2498	−0.748277
$269$	−25.5025	−1.55491	−0.777456	−	0.628937i	$-0.783490\pi$
$269$	−25.5025	−1.55491	−0.777456	+	0.628937i	$0.783490\pi$
$270$	−6.89511	−0.419623
$271$	−1.22289	−0.0742852	−0.0371426	−	0.999310i	$-0.511826\pi$
$271$	−1.22289	−0.0742852	−0.0371426	+	0.999310i	$0.511826\pi$
$272$	−1.00000	−0.0606339
$273$	−14.6694	−0.887832
$274$	2.00000	0.120824
$275$	−1.00000	−0.0603023
$276$	1.48654	0.0894789
$277$	23.9862	1.44119	0.720595	−	0.693357i	$-0.243869\pi$
$277$	23.9862	1.44119	0.720595	+	0.693357i	$0.243869\pi$
$278$	1.48654	0.0891565
$279$	−7.58043	−0.453828
$280$	1.48654	0.0888375
$281$	15.8682	0.946616	0.473308	−	0.880897i	$-0.343060\pi$
$281$	15.8682	0.946616	0.473308	+	0.880897i	$0.343060\pi$
$282$	10.4755	0.623809
$283$	31.2788	1.85933	0.929667	−	0.368400i	$-0.120094\pi$
$283$	31.2788	1.85933	0.929667	+	0.368400i	$0.120094\pi$
$284$	8.38164	0.497359
$285$	−18.4755	−1.09440
$286$	−3.40857	−0.201553
$287$	2.20979	0.130440
$288$	5.38164	0.317116
$289$	1.00000	0.0588235
$290$	−7.40857	−0.435046
$291$	−30.6633	−1.79752
$292$	−15.4486	−0.904061
$293$	−5.19878	−0.303716	−0.151858	−	0.988402i	$-0.548526\pi$
$293$	−5.19878	−0.303716	−0.151858	+	0.988402i	$0.548526\pi$
$294$	−13.8682	−0.808809
$295$	−0.0779639	−0.00453924
$296$	3.79021	0.220302
$297$	−6.89511	−0.400095
$298$	6.97307	0.403939
$299$	1.75018	0.101216
$300$	2.89511	0.167149
$301$	8.60736	0.496120
$302$	0.155928	0.00897264
$303$	27.0131	1.55186
$304$	6.38164	0.366012
$305$	5.19878	0.297682
$306$	−5.38164	−0.307648
$307$	25.0670	1.43065	0.715324	−	0.698793i	$-0.246279\pi$
$307$	25.0670	1.43065	0.715324	+	0.698793i	$0.246279\pi$
$308$	1.48654	0.0847032
$309$	3.42450	0.194813
$310$	1.40857	0.0800015
$311$	−30.7413	−1.74318	−0.871589	−	0.490237i	$-0.836910\pi$
$311$	−30.7413	−1.74318	−0.871589	+	0.490237i	$0.836910\pi$
$312$	9.86818	0.558676
$313$	−32.6074	−1.84308	−0.921538	−	0.388287i	$-0.873067\pi$
$313$	−32.6074	−1.84308	−0.921538	+	0.388287i	$0.873067\pi$
$314$	−19.4245	−1.09619
$315$	8.00000	0.450749
$316$	−1.23672	−0.0695707
$317$	28.5935	1.60597	0.802986	−	0.595998i	$-0.203243\pi$
$317$	28.5935	1.60597	0.802986	+	0.595998i	$0.203243\pi$
$318$	−8.38164	−0.470019
$319$	−7.40857	−0.414800
$320$	−1.00000	−0.0559017
$321$	−22.3976	−1.25011
$322$	−0.763283	−0.0425361
$323$	−6.38164	−0.355084
$324$	3.81714	0.212063
$325$	3.40857	0.189074
$326$	−18.5535	−1.02758
$327$	−24.4217	−1.35052
$328$	−1.48654	−0.0820802
$329$	−5.37882	−0.296544
$330$	2.89511	0.159370
$331$	29.2927	1.61007	0.805036	−	0.593227i	$-0.202146\pi$
$331$	29.2927	1.61007	0.805036	+	0.593227i	$0.202146\pi$
$332$	9.48654	0.520641
$333$	20.3976	1.11778
$334$	19.3168	1.05697
$335$	12.2498	0.669279
$336$	−4.30368	−0.234785
$337$	9.39474	0.511764	0.255882	−	0.966708i	$-0.417634\pi$
$337$	9.39474	0.511764	0.255882	+	0.966708i	$0.417634\pi$
$338$	−1.38164	−0.0751514
$339$	−26.4755	−1.43795
$340$	1.00000	0.0542326
$341$	1.40857	0.0762784
$342$	34.3437	1.85710
$343$	17.5266	0.946346
$344$	−5.79021	−0.312187
$345$	−1.48654	−0.0800324
$346$	2.45961	0.132229
$347$	15.0429	0.807543	0.403771	−	0.914860i	$-0.367699\pi$
$347$	15.0429	0.807543	0.403771	+	0.914860i	$0.367699\pi$
$348$	21.4486	1.14977
$349$	17.6343	0.943942	0.471971	−	0.881614i	$-0.343543\pi$
$349$	17.6343	0.943942	0.471971	+	0.881614i	$0.343543\pi$
$350$	−1.48654	−0.0794586
$351$	23.5025	1.25447
$352$	−1.00000	−0.0533002
$353$	4.36571	0.232364	0.116182	−	0.993228i	$-0.462934\pi$
$353$	4.36571	0.232364	0.116182	+	0.993228i	$0.462934\pi$
$354$	0.225714	0.0119966
$355$	−8.38164	−0.444851
$356$	−2.38164	−0.126227
$357$	4.30368	0.227775
$358$	−4.15593	−0.219648
$359$	18.2899	0.965301	0.482651	−	0.875813i	$-0.339674\pi$
$359$	18.2899	0.965301	0.482651	+	0.875813i	$0.339674\pi$
$360$	−5.38164	−0.283637
$361$	21.7254	1.14344
$362$	3.02693	0.159092
$363$	2.89511	0.151954
$364$	−5.06696	−0.265581
$365$	15.4486	0.808617
$366$	−15.0510	−0.786730
$367$	−7.06696	−0.368892	−0.184446	−	0.982843i	$-0.559049\pi$
$367$	−7.06696	−0.368892	−0.184446	+	0.982843i	$0.559049\pi$
$368$	0.513465	0.0267662
$369$	−8.00000	−0.416463
$370$	−3.79021	−0.197044
$371$	4.30368	0.223436
$372$	−4.07796	−0.211433
$373$	−18.3437	−0.949801	−0.474901	−	0.880039i	$-0.657516\pi$
$373$	−18.3437	−0.949801	−0.474901	+	0.880039i	$0.657516\pi$
$374$	1.00000	0.0517088
$375$	−2.89511	−0.149503
$376$	3.61836	0.186603
$377$	25.2526	1.30058
$378$	−10.2498	−0.527194
$379$	−12.9192	−0.663615	−0.331808	−	0.943347i	$-0.607658\pi$
$379$	−12.9192	−0.663615	−0.331808	+	0.943347i	$0.607658\pi$
$380$	−6.38164	−0.327371
$381$	37.1768	1.90462
$382$	−4.45961	−0.228173
$383$	10.9351	0.558759	0.279380	−	0.960181i	$-0.409871\pi$
$383$	10.9351	0.558759	0.279380	+	0.960181i	$0.409871\pi$
$384$	2.89511	0.147740
$385$	−1.48654	−0.0757609
$386$	10.3437	0.526481
$387$	−31.1609	−1.58400
$388$	−10.5914	−0.537698
$389$	10.0400	0.509050	0.254525	−	0.967066i	$-0.418081\pi$
$389$	10.0400	0.509050	0.254525	+	0.967066i	$0.418081\pi$
$390$	−9.86818	−0.499695
$391$	−0.513465	−0.0259670
$392$	−4.79021	−0.241942
$393$	−54.5935	−2.75388
$394$	−21.3168	−1.07392
$395$	1.23672	0.0622260
$396$	−5.38164	−0.270438
$397$	−35.2547	−1.76938	−0.884692	−	0.466175i	$-0.845632\pi$
$397$	−35.2547	−1.76938	−0.884692	+	0.466175i	$0.845632\pi$
$398$	1.40857	0.0706053
$399$	−27.4645	−1.37495
$400$	1.00000	0.0500000
$401$	19.2229	0.959945	0.479973	−	0.877283i	$-0.340647\pi$
$401$	19.2229	0.959945	0.479973	+	0.877283i	$0.340647\pi$
$402$	−35.4645	−1.76881
$403$	−4.80122	−0.239166
$404$	9.33061	0.464215
$405$	−3.81714	−0.189675
$406$	−11.0131	−0.546571
$407$	−3.79021	−0.187874
$408$	−2.89511	−0.143329
$409$	8.31960	0.411378	0.205689	−	0.978617i	$-0.434056\pi$
$409$	8.31960	0.411378	0.205689	+	0.978617i	$0.434056\pi$
$410$	1.48654	0.0734147
$411$	5.79021	0.285610
$412$	1.18286	0.0582752
$413$	−0.115896	−0.00570288
$414$	2.76328	0.135808
$415$	−9.48654	−0.465676
$416$	3.40857	0.167119
$417$	4.30368	0.210752
$418$	−6.38164	−0.312136
$419$	24.3437	1.18927	0.594634	−	0.803997i	$-0.297297\pi$
$419$	24.3437	1.18927	0.594634	+	0.803997i	$0.297297\pi$
$420$	4.30368	0.209998
$421$	1.12900	0.0550240	0.0275120	−	0.999621i	$-0.491242\pi$
$421$	1.12900	0.0550240	0.0275120	+	0.999621i	$0.491242\pi$
$422$	−18.3976	−0.895580
$423$	19.4727	0.946795
$424$	−2.89511	−0.140599
$425$	−1.00000	−0.0485071
$426$	24.2657	1.17568
$427$	7.72818	0.373993
$428$	−7.73635	−0.373951
$429$	−9.86818	−0.476440
$430$	5.79021	0.279229
$431$	−2.34371	−0.112893	−0.0564463	−	0.998406i	$-0.517977\pi$
$431$	−2.34371	−0.112893	−0.0564463	+	0.998406i	$0.517977\pi$
$432$	6.89511	0.331741
$433$	−21.0131	−1.00983	−0.504913	−	0.863170i	$-0.668475\pi$
$433$	−21.0131	−1.00983	−0.504913	+	0.863170i	$0.668475\pi$
$434$	2.09389	0.100510
$435$	−21.4486	−1.02838
$436$	−8.43550	−0.403987
$437$	3.27675	0.156748
$438$	−44.7254	−2.13706
$439$	−26.0801	−1.24473	−0.622367	−	0.782726i	$-0.713829\pi$
$439$	−26.0801	−1.24473	−0.622367	+	0.782726i	$0.713829\pi$
$440$	1.00000	0.0476731
$441$	−25.7792	−1.22758
$442$	−3.40857	−0.162129
$443$	−0.0938908	−0.00446089	−0.00223044	−	0.999998i	$-0.500710\pi$
$443$	−0.0938908	−0.00446089	−0.00223044	+	0.999998i	$0.500710\pi$
$444$	10.9731	0.520759
$445$	2.38164	0.112901
$446$	−0.537570	−0.0254547
$447$	20.1878	0.954849
$448$	−1.48654	−0.0702322
$449$	−27.5184	−1.29867	−0.649337	−	0.760501i	$-0.724953\pi$
$449$	−27.5184	−1.29867	−0.649337	+	0.760501i	$0.724953\pi$
$450$	5.38164	0.253693
$451$	1.48654	0.0699982
$452$	−9.14493	−0.430141
$453$	0.451428	0.0212099
$454$	2.32778	0.109248
$455$	5.06696	0.237543
$456$	18.4755	0.865196
$457$	−29.1690	−1.36447	−0.682235	−	0.731133i	$-0.738992\pi$
$457$	−29.1690	−1.36447	−0.682235	+	0.731133i	$0.738992\pi$
$458$	5.58043	0.260756
$459$	−6.89511	−0.321836
$460$	−0.513465	−0.0239404
$461$	19.1290	0.890926	0.445463	−	0.895300i	$-0.353039\pi$
$461$	19.1290	0.890926	0.445463	+	0.895300i	$0.353039\pi$
$462$	4.30368	0.200225
$463$	9.67222	0.449506	0.224753	−	0.974416i	$-0.427842\pi$
$463$	9.67222	0.449506	0.224753	+	0.974416i	$0.427842\pi$
$464$	7.40857	0.343934
$465$	4.07796	0.189111
$466$	24.8192	1.14973
$467$	−1.12082	−0.0518654	−0.0259327	−	0.999664i	$-0.508256\pi$
$467$	−1.12082	−0.0518654	−0.0259327	+	0.999664i	$0.508256\pi$
$468$	18.3437	0.847938
$469$	18.2098	0.840850
$470$	−3.61836	−0.166902
$471$	−56.2360	−2.59122
$472$	0.0779639	0.00358858
$473$	5.79021	0.266234
$474$	−3.58043	−0.164454
$475$	6.38164	0.292810
$476$	1.48654	0.0681352
$477$	−15.5804	−0.713379
$478$	6.09389	0.278728
$479$	−6.42167	−0.293414	−0.146707	−	0.989180i	$-0.546867\pi$
$479$	−6.42167	−0.293414	−0.146707	+	0.989180i	$0.546867\pi$
$480$	−2.89511	−0.132143
$481$	12.9192	0.589065
$482$	19.7364	0.898966
$483$	−2.20979	−0.100549
$484$	1.00000	0.0454545
$485$	10.5914	0.480932
$486$	−9.63429	−0.437020
$487$	−5.39264	−0.244364	−0.122182	−	0.992508i	$-0.538989\pi$
$487$	−5.39264	−0.244364	−0.122182	+	0.992508i	$0.538989\pi$
$488$	−5.19878	−0.235338
$489$	−53.7143	−2.42905
$490$	4.79021	0.216400
$491$	18.3816	0.829552	0.414776	−	0.909924i	$-0.363860\pi$
$491$	18.3816	0.829552	0.414776	+	0.909924i	$0.363860\pi$
$492$	−4.30368	−0.194025
$493$	−7.40857	−0.333665
$494$	21.7523	0.978681
$495$	5.38164	0.241887
$496$	−1.40857	−0.0632467
$497$	−12.4596	−0.558890
$498$	27.4645	1.23072
$499$	−30.8171	−1.37956	−0.689782	−	0.724017i	$-0.742294\pi$
$499$	−30.8171	−1.37956	−0.689782	+	0.724017i	$0.742294\pi$
$500$	−1.00000	−0.0447214
$501$	55.9241	2.49851
$502$	−17.5266	−0.782249
$503$	27.4727	1.22495	0.612474	−	0.790491i	$-0.290175\pi$
$503$	27.4727	1.22495	0.612474	+	0.790491i	$0.290175\pi$
$504$	−8.00000	−0.356348
$505$	−9.33061	−0.415207
$506$	−0.513465	−0.0228263
$507$	−4.00000	−0.177646
$508$	12.8412	0.569738
$509$	32.9054	1.45851	0.729253	−	0.684244i	$-0.239868\pi$
$509$	32.9054	1.45851	0.729253	+	0.684244i	$0.239868\pi$
$510$	2.89511	0.128197
$511$	22.9649	1.01591
$512$	1.00000	0.0441942
$513$	44.0021	1.94274
$514$	18.6474	0.822501
$515$	−1.18286	−0.0521229
$516$	−16.7633	−0.737962
$517$	−3.61836	−0.159135
$518$	−5.63429	−0.247556
$519$	7.12082	0.312569
$520$	−3.40857	−0.149476
$521$	−8.62936	−0.378059	−0.189030	−	0.981971i	$-0.560534\pi$
$521$	−8.62936	−0.378059	−0.189030	+	0.981971i	$0.560534\pi$
$522$	39.8703	1.74507
$523$	−11.1690	−0.488388	−0.244194	−	0.969726i	$-0.578523\pi$
$523$	−11.1690	−0.488388	−0.244194	+	0.969726i	$0.578523\pi$
$524$	−18.8572	−0.823779
$525$	−4.30368	−0.187828
$526$	−11.7661	−0.513027
$527$	1.40857	0.0613583
$528$	−2.89511	−0.125993
$529$	−22.7364	−0.988537
$530$	2.89511	0.125755
$531$	0.419574	0.0182080
$532$	−9.48654	−0.411293
$533$	−5.06696	−0.219474
$534$	−6.89511	−0.298380
$535$	7.73635	0.334472
$536$	−12.2498	−0.529112
$537$	−12.0319	−0.519213
$538$	−25.5025	−1.09949
$539$	4.79021	0.206329
$540$	−6.89511	−0.296718
$541$	13.8441	0.595203	0.297602	−	0.954690i	$-0.403813\pi$
$541$	13.8441	0.595203	0.297602	+	0.954690i	$0.403813\pi$
$542$	−1.22289	−0.0525276
$543$	8.76328	0.376068
$544$	−1.00000	−0.0428746
$545$	8.43550	0.361337
$546$	−14.6694	−0.627792
$547$	−29.7523	−1.27212	−0.636058	−	0.771641i	$-0.719436\pi$
$547$	−29.7523	−1.27212	−0.636058	+	0.771641i	$0.719436\pi$
$548$	2.00000	0.0854358
$549$	−27.9780	−1.19407
$550$	−1.00000	−0.0426401
$551$	47.2788	2.01415
$552$	1.48654	0.0632711
$553$	1.83842	0.0781777
$554$	23.9862	1.01907
$555$	−10.9731	−0.465781
$556$	1.48654	0.0630431
$557$	−37.5425	−1.59073	−0.795363	−	0.606133i	$-0.792720\pi$
$557$	−37.5425	−1.59073	−0.795363	+	0.606133i	$0.792720\pi$
$558$	−7.58043	−0.320905
$559$	−19.7364	−0.834759
$560$	1.48654	0.0628176
$561$	2.89511	0.122231
$562$	15.8682	0.669359
$563$	−5.22289	−0.220119	−0.110059	−	0.993925i	$-0.535104\pi$
$563$	−5.22289	−0.220119	−0.110059	+	0.993925i	$0.535104\pi$
$564$	10.4755	0.441099
$565$	9.14493	0.384730
$566$	31.2788	1.31475
$567$	−5.67432	−0.238299
$568$	8.38164	0.351686
$569$	−28.8951	−1.21135	−0.605673	−	0.795714i	$-0.707096\pi$
$569$	−28.8951	−1.21135	−0.605673	+	0.795714i	$0.707096\pi$
$570$	−18.4755	−0.773855
$571$	21.1829	0.886475	0.443237	−	0.896404i	$-0.353830\pi$
$571$	21.1829	0.886475	0.443237	+	0.896404i	$0.353830\pi$
$572$	−3.40857	−0.142520
$573$	−12.9110	−0.539366
$574$	2.20979	0.0922347
$575$	0.513465	0.0214130
$576$	5.38164	0.224235
$577$	25.4245	1.05844	0.529218	−	0.848486i	$-0.322485\pi$
$577$	25.4245	1.05844	0.529218	+	0.848486i	$0.322485\pi$
$578$	1.00000	0.0415945
$579$	29.9461	1.24452
$580$	−7.40857	−0.307624
$581$	−14.1021	−0.585052
$582$	−30.6633	−1.27104
$583$	2.89511	0.119903
$584$	−15.4486	−0.639268
$585$	−18.3437	−0.758419
$586$	−5.19878	−0.214760
$587$	14.4196	0.595160	0.297580	−	0.954697i	$-0.403821\pi$
$587$	14.4196	0.595160	0.297580	+	0.954697i	$0.403821\pi$
$588$	−13.8682	−0.571914
$589$	−8.98900	−0.370385
$590$	−0.0779639	−0.00320972
$591$	−61.7143	−2.53859
$592$	3.79021	0.155777
$593$	−13.3845	−0.549634	−0.274817	−	0.961497i	$-0.588617\pi$
$593$	−13.3845	−0.549634	−0.274817	+	0.961497i	$0.588617\pi$
$594$	−6.89511	−0.282910
$595$	−1.48654	−0.0609420
$596$	6.97307	0.285628
$597$	4.07796	0.166900
$598$	1.75018	0.0715702
$599$	13.2229	0.540273	0.270136	−	0.962822i	$-0.412931\pi$
$599$	13.2229	0.540273	0.270136	+	0.962822i	$0.412931\pi$
$600$	2.89511	0.118192
$601$	10.2498	0.418099	0.209049	−	0.977905i	$-0.432963\pi$
$601$	10.2498	0.418099	0.209049	+	0.977905i	$0.432963\pi$
$602$	8.60736	0.350810
$603$	−65.9241	−2.68464
$604$	0.155928	0.00634461
$605$	−1.00000	−0.0406558
$606$	27.0131	1.09733
$607$	−27.2091	−1.10438	−0.552191	−	0.833718i	$-0.686208\pi$
$607$	−27.2091	−1.10438	−0.552191	+	0.833718i	$0.686208\pi$
$608$	6.38164	0.258810
$609$	−31.8841	−1.29201
$610$	5.19878	0.210493
$611$	12.3334	0.498957
$612$	−5.38164	−0.217540
$613$	−42.4135	−1.71306	−0.856532	−	0.516093i	$-0.827386\pi$
$613$	−42.4135	−1.71306	−0.856532	+	0.516093i	$0.827386\pi$
$614$	25.0670	1.01162
$615$	4.30368	0.173541
$616$	1.48654	0.0598942
$617$	15.0110	0.604320	0.302160	−	0.953257i	$-0.402292\pi$
$617$	15.0110	0.604320	0.302160	+	0.953257i	$0.402292\pi$
$618$	3.42450	0.137754
$619$	−5.17468	−0.207988	−0.103994	−	0.994578i	$-0.533162\pi$
$619$	−5.17468	−0.207988	−0.103994	+	0.994578i	$0.533162\pi$
$620$	1.40857	0.0565696
$621$	3.54039	0.142071
$622$	−30.7413	−1.23261
$623$	3.54039	0.141843
$624$	9.86818	0.395043
$625$	1.00000	0.0400000
$626$	−32.6074	−1.30325
$627$	−18.4755	−0.737842
$628$	−19.4245	−0.775122
$629$	−3.79021	−0.151126
$630$	8.00000	0.318728
$631$	22.5535	0.897841	0.448920	−	0.893572i	$-0.351809\pi$
$631$	22.5535	0.897841	0.448920	+	0.893572i	$0.351809\pi$
$632$	−1.23672	−0.0491939
$633$	−53.2629	−2.11701
$634$	28.5935	1.13559
$635$	−12.8412	−0.509589
$636$	−8.38164	−0.332354
$637$	−16.3278	−0.646930
$638$	−7.40857	−0.293308
$639$	45.1070	1.78441
$640$	−1.00000	−0.0395285
$641$	11.9862	0.473425	0.236713	−	0.971580i	$-0.423930\pi$
$641$	11.9862	0.473425	0.236713	+	0.971580i	$0.423930\pi$
$642$	−22.3976	−0.883962
$643$	−15.1609	−0.597886	−0.298943	−	0.954271i	$-0.596634\pi$
$643$	−15.1609	−0.597886	−0.298943	+	0.954271i	$0.596634\pi$
$644$	−0.763283	−0.0300776
$645$	16.7633	0.660054
$646$	−6.38164	−0.251082
$647$	−23.5425	−0.925551	−0.462775	−	0.886476i	$-0.653146\pi$
$647$	−23.5425	−0.925551	−0.462775	+	0.886476i	$0.653146\pi$
$648$	3.81714	0.149952
$649$	−0.0779639	−0.00306035
$650$	3.40857	0.133695
$651$	6.06204	0.237590
$652$	−18.5535	−0.726611
$653$	−43.5985	−1.70614	−0.853070	−	0.521797i	$-0.825262\pi$
$653$	−43.5985	−1.70614	−0.853070	+	0.521797i	$0.825262\pi$
$654$	−24.4217	−0.954963
$655$	18.8572	0.736811
$656$	−1.48654	−0.0580394
$657$	−83.1388	−3.24356
$658$	−5.37882	−0.209688
$659$	47.4886	1.84989	0.924947	−	0.380095i	$-0.124109\pi$
$659$	47.4886	1.84989	0.924947	+	0.380095i	$0.124109\pi$
$660$	2.89511	0.112692
$661$	−12.4057	−0.482528	−0.241264	−	0.970460i	$-0.577562\pi$
$661$	−12.4057	−0.482528	−0.241264	+	0.970460i	$0.577562\pi$
$662$	29.2927	1.13849
$663$	−9.86818	−0.383248
$664$	9.48654	0.368149
$665$	9.48654	0.367872
$666$	20.3976	0.790390
$667$	3.80404	0.147293
$668$	19.3168	0.747389
$669$	−1.55632	−0.0601709
$670$	12.2498	0.473252
$671$	5.19878	0.200697
$672$	−4.30368	−0.166018
$673$	−36.9270	−1.42343	−0.711715	−	0.702468i	$-0.752081\pi$
$673$	−36.9270	−1.42343	−0.711715	+	0.702468i	$0.752081\pi$
$674$	9.39474	0.361872
$675$	6.89511	0.265393
$676$	−1.38164	−0.0531401
$677$	1.12082	0.0430766	0.0215383	−	0.999768i	$-0.493144\pi$
$677$	1.12082	0.0430766	0.0215383	+	0.999768i	$0.493144\pi$
$678$	−26.4755	−1.01679
$679$	15.7445	0.604220
$680$	1.00000	0.0383482
$681$	6.73918	0.258246
$682$	1.40857	0.0539370
$683$	15.3147	0.586000	0.293000	−	0.956112i	$-0.405346\pi$
$683$	15.3147	0.586000	0.293000	+	0.956112i	$0.405346\pi$
$684$	34.3437	1.31316
$685$	−2.00000	−0.0764161
$686$	17.5266	0.669167
$687$	16.1559	0.616387
$688$	−5.79021	−0.220750
$689$	−9.86818	−0.375948
$690$	−1.48654	−0.0565914
$691$	24.9110	0.947660	0.473830	−	0.880616i	$-0.342871\pi$
$691$	24.9110	0.947660	0.473830	+	0.880616i	$0.342871\pi$
$692$	2.45961	0.0935002
$693$	8.00000	0.303895
$694$	15.0429	0.571019
$695$	−1.48654	−0.0563875
$696$	21.4486	0.813007
$697$	1.48654	0.0563065
$698$	17.6343	0.667468
$699$	71.8543	2.71778
$700$	−1.48654	−0.0561858
$701$	−40.1201	−1.51532	−0.757658	−	0.652652i	$-0.773656\pi$
$701$	−40.1201	−1.51532	−0.757658	+	0.652652i	$0.773656\pi$
$702$	23.5025	0.887043
$703$	24.1878	0.912259
$704$	−1.00000	−0.0376889
$705$	−10.4755	−0.394531
$706$	4.36571	0.164306
$707$	−13.8703	−0.521645
$708$	0.225714	0.00848285
$709$	39.0290	1.46577	0.732883	−	0.680355i	$-0.238174\pi$
$709$	39.0290	1.46577	0.732883	+	0.680355i	$0.238174\pi$
$710$	−8.38164	−0.314557
$711$	−6.65557	−0.249603
$712$	−2.38164	−0.0892558
$713$	−0.723252	−0.0270860
$714$	4.30368	0.161061
$715$	3.40857	0.127473
$716$	−4.15593	−0.155314
$717$	17.6425	0.658870
$718$	18.2899	0.682571
$719$	10.9351	0.407812	0.203906	−	0.978990i	$-0.434636\pi$
$719$	10.9351	0.407812	0.203906	+	0.978990i	$0.434636\pi$
$720$	−5.38164	−0.200562
$721$	−1.75836	−0.0654847
$722$	21.7254	0.808534
$723$	57.1388	2.12502
$724$	3.02693	0.112495
$725$	7.40857	0.275147
$726$	2.89511	0.107447
$727$	−2.09179	−0.0775802	−0.0387901	−	0.999247i	$-0.512350\pi$
$727$	−2.09179	−0.0775802	−0.0387901	+	0.999247i	$0.512350\pi$
$728$	−5.06696	−0.187794
$729$	−39.3437	−1.45717
$730$	15.4486	0.571778
$731$	5.79021	0.214159
$732$	−15.0510	−0.556302
$733$	−19.2629	−0.711492	−0.355746	−	0.934583i	$-0.615773\pi$
$733$	−19.2629	−0.711492	−0.355746	+	0.934583i	$0.615773\pi$
$734$	−7.06696	−0.260846
$735$	13.8682	0.511535
$736$	0.513465	0.0189266
$737$	12.2498	0.451228
$738$	−8.00000	−0.294484
$739$	8.69915	0.320003	0.160002	−	0.987117i	$-0.448850\pi$
$739$	8.69915	0.320003	0.160002	+	0.987117i	$0.448850\pi$
$740$	−3.79021	−0.139331
$741$	62.9752	2.31345
$742$	4.30368	0.157993
$743$	−27.5404	−1.01036	−0.505180	−	0.863014i	$-0.668574\pi$
$743$	−27.5404	−1.01036	−0.505180	+	0.863014i	$0.668574\pi$
$744$	−4.07796	−0.149505
$745$	−6.97307	−0.255474
$746$	−18.3437	−0.671611
$747$	51.0531	1.86794
$748$	1.00000	0.0365636
$749$	11.5004	0.420214
$750$	−2.89511	−0.105714
$751$	34.1719	1.24695	0.623474	−	0.781844i	$-0.285721\pi$
$751$	34.1719	1.24695	0.623474	+	0.781844i	$0.285721\pi$
$752$	3.61836	0.131948
$753$	−50.7413	−1.84911
$754$	25.2526	0.919647
$755$	−0.155928	−0.00567480
$756$	−10.2498	−0.372782
$757$	−11.5783	−0.420821	−0.210411	−	0.977613i	$-0.567480\pi$
$757$	−11.5783	−0.420821	−0.210411	+	0.977613i	$0.567480\pi$
$758$	−12.9192	−0.469247
$759$	−1.48654	−0.0539578
$760$	−6.38164	−0.231486
$761$	−32.8171	−1.18962	−0.594810	−	0.803866i	$-0.702773\pi$
$761$	−32.8171	−1.18962	−0.594810	+	0.803866i	$0.702773\pi$
$762$	37.1768	1.34677
$763$	12.5397	0.453967
$764$	−4.45961	−0.161343
$765$	5.38164	0.194574
$766$	10.9351	0.395103
$767$	0.265746	0.00959552
$768$	2.89511	0.104468
$769$	42.4217	1.52976	0.764882	−	0.644170i	$-0.222797\pi$
$769$	42.4217	1.52976	0.764882	+	0.644170i	$0.222797\pi$
$770$	−1.48654	−0.0535710
$771$	53.9862	1.94426
$772$	10.3437	0.372278
$773$	−34.2899	−1.23332	−0.616660	−	0.787230i	$-0.711515\pi$
$773$	−34.2899	−1.23332	−0.616660	+	0.787230i	$0.711515\pi$
$774$	−31.1609	−1.12005
$775$	−1.40857	−0.0505974
$776$	−10.5914	−0.380210
$777$	−16.3119	−0.585185
$778$	10.0400	0.359953
$779$	−9.48654	−0.339890
$780$	−9.86818	−0.353337
$781$	−8.38164	−0.299919
$782$	−0.513465	−0.0183615
$783$	51.0829	1.82555
$784$	−4.79021	−0.171079
$785$	19.4245	0.693290
$786$	−54.5935	−1.94729
$787$	−17.3327	−0.617844	−0.308922	−	0.951087i	$-0.599968\pi$
$787$	−17.3327	−0.617844	−0.308922	+	0.951087i	$0.599968\pi$
$788$	−21.3168	−0.759379
$789$	−34.0641	−1.21272
$790$	1.23672	0.0440004
$791$	13.5943	0.483356
$792$	−5.38164	−0.191228
$793$	−17.7204	−0.629271
$794$	−35.2547	−1.25114
$795$	8.38164	0.297266
$796$	1.40857	0.0499255
$797$	24.7633	0.877161	0.438580	−	0.898692i	$-0.355481\pi$
$797$	24.7633	0.877161	0.438580	+	0.898692i	$0.355481\pi$
$798$	−27.4645	−0.972234
$799$	−3.61836	−0.128008
$800$	1.00000	0.0353553
$801$	−12.8171	−0.452871
$802$	19.2229	0.678784
$803$	15.4486	0.545169
$804$	−35.4645	−1.25074
$805$	0.763283	0.0269022
$806$	−4.80122	−0.169116
$807$	−73.8323	−2.59902
$808$	9.33061	0.328250
$809$	8.57550	0.301499	0.150749	−	0.988572i	$-0.451831\pi$
$809$	8.57550	0.301499	0.150749	+	0.988572i	$0.451831\pi$
$810$	−3.81714	−0.134121
$811$	33.8703	1.18935	0.594673	−	0.803968i	$-0.297281\pi$
$811$	33.8703	1.18935	0.594673	+	0.803968i	$0.297281\pi$
$812$	−11.0131	−0.386484
$813$	−3.54039	−0.124167
$814$	−3.79021	−0.132847
$815$	18.5535	0.649901
$816$	−2.89511	−0.101349
$817$	−36.9511	−1.29275
$818$	8.31960	0.290888
$819$	−27.2686	−0.952841
$820$	1.48654	0.0519121
$821$	−20.8869	−0.728959	−0.364479	−	0.931211i	$-0.618753\pi$
$821$	−20.8869	−0.728959	−0.364479	+	0.931211i	$0.618753\pi$
$822$	5.79021	0.201957
$823$	37.9323	1.32224	0.661119	−	0.750281i	$-0.270082\pi$
$823$	37.9323	1.32224	0.661119	+	0.750281i	$0.270082\pi$
$824$	1.18286	0.0412068
$825$	−2.89511	−0.100795
$826$	−0.115896	−0.00403254
$827$	44.8433	1.55936	0.779678	−	0.626181i	$-0.215383\pi$
$827$	44.8433	1.55936	0.779678	+	0.626181i	$0.215383\pi$
$828$	2.76328	0.0960307
$829$	−21.7282	−0.754651	−0.377325	−	0.926081i	$-0.623156\pi$
$829$	−21.7282	−0.754651	−0.377325	+	0.926081i	$0.623156\pi$
$830$	−9.48654	−0.329282
$831$	69.4425	2.40893
$832$	3.40857	0.118171
$833$	4.79021	0.165971
$834$	4.30368	0.149024
$835$	−19.3168	−0.668485
$836$	−6.38164	−0.220714
$837$	−9.71225	−0.335704
$838$	24.3437	0.840939
$839$	0.801216	0.0276610	0.0138305	−	0.999904i	$-0.495597\pi$
$839$	0.801216	0.0276610	0.0138305	+	0.999904i	$0.495597\pi$
$840$	4.30368	0.148491
$841$	25.8869	0.892653
$842$	1.12900	0.0389079
$843$	45.9401	1.58226
$844$	−18.3976	−0.633270
$845$	1.38164	0.0475299
$846$	19.4727	0.669485
$847$	−1.48654	−0.0510780
$848$	−2.89511	−0.0994184
$849$	90.5556	3.10786
$850$	−1.00000	−0.0342997
$851$	1.94614	0.0667129
$852$	24.2657	0.831331
$853$	−48.6336	−1.66518	−0.832591	−	0.553889i	$-0.813143\pi$
$853$	−48.6336	−1.66518	−0.832591	+	0.553889i	$0.813143\pi$
$854$	7.72818	0.264453
$855$	−34.3437	−1.17453
$856$	−7.73635	−0.264423
$857$	53.6584	1.83294	0.916468	−	0.400108i	$-0.131028\pi$
$857$	53.6584	1.83294	0.916468	+	0.400108i	$0.131028\pi$
$858$	−9.86818	−0.336894
$859$	40.8731	1.39457	0.697286	−	0.716793i	$-0.254391\pi$
$859$	40.8731	1.39457	0.697286	+	0.716793i	$0.254391\pi$
$860$	5.79021	0.197445
$861$	6.39757	0.218029
$862$	−2.34371	−0.0798271
$863$	−11.7364	−0.399510	−0.199755	−	0.979846i	$-0.564015\pi$
$863$	−11.7364	−0.399510	−0.199755	+	0.979846i	$0.564015\pi$
$864$	6.89511	0.234576
$865$	−2.45961	−0.0836291
$866$	−21.0131	−0.714054
$867$	2.89511	0.0983230
$868$	2.09389	0.0710713
$869$	1.23672	0.0419527
$870$	−21.4486	−0.727176
$871$	−41.7544	−1.41479
$872$	−8.43550	−0.285662
$873$	−56.9993	−1.92913
$874$	3.27675	0.110838
$875$	1.48654	0.0502541
$876$	−44.7254	−1.51113
$877$	4.98125	0.168205	0.0841024	−	0.996457i	$-0.473198\pi$
$877$	4.98125	0.168205	0.0841024	+	0.996457i	$0.473198\pi$
$878$	−26.0801	−0.880160
$879$	−15.0510	−0.507659
$880$	1.00000	0.0337100
$881$	7.67432	0.258554	0.129277	−	0.991609i	$-0.458734\pi$
$881$	7.67432	0.258554	0.129277	+	0.991609i	$0.458734\pi$
$882$	−25.7792	−0.868031
$883$	−7.10699	−0.239169	−0.119585	−	0.992824i	$-0.538156\pi$
$883$	−7.10699	−0.239169	−0.119585	+	0.992824i	$0.538156\pi$
$884$	−3.40857	−0.114643
$885$	−0.225714	−0.00758729
$886$	−0.0938908	−0.00315432
$887$	36.2278	1.21641	0.608205	−	0.793780i	$-0.291890\pi$
$887$	36.2278	1.21641	0.608205	+	0.793780i	$0.291890\pi$
$888$	10.9731	0.368232
$889$	−19.0890	−0.640223
$890$	2.38164	0.0798328
$891$	−3.81714	−0.127879
$892$	−0.537570	−0.0179992
$893$	23.0911	0.772713
$894$	20.1878	0.675180
$895$	4.15593	0.138917
$896$	−1.48654	−0.0496617
$897$	5.06696	0.169181
$898$	−27.5184	−0.918301
$899$	−10.4355	−0.348043
$900$	5.38164	0.179388
$901$	2.89511	0.0964500
$902$	1.48654	0.0494962
$903$	24.9192	0.829259
$904$	−9.14493	−0.304156
$905$	−3.02693	−0.100619
$906$	0.451428	0.0149977
$907$	8.10982	0.269282	0.134641	−	0.990894i	$-0.457012\pi$
$907$	8.10982	0.269282	0.134641	+	0.990894i	$0.457012\pi$
$908$	2.32778	0.0772502
$909$	50.2140	1.66549
$910$	5.06696	0.167968
$911$	3.73635	0.123791	0.0618955	−	0.998083i	$-0.480285\pi$
$911$	3.73635	0.123791	0.0618955	+	0.998083i	$0.480285\pi$
$912$	18.4755	0.611786
$913$	−9.48654	−0.313958
$914$	−29.1690	−0.964826
$915$	15.0510	0.497572
$916$	5.58043	0.184382
$917$	28.0319	0.925693
$918$	−6.89511	−0.227572
$919$	47.2009	1.55701	0.778507	−	0.627636i	$-0.215977\pi$
$919$	47.2009	1.55701	0.778507	+	0.627636i	$0.215977\pi$
$920$	−0.513465	−0.0169284
$921$	72.5715	2.39131
$922$	19.1290	0.629980
$923$	28.5694	0.940374
$924$	4.30368	0.141581
$925$	3.79021	0.124621
$926$	9.67222	0.317849
$927$	6.36571	0.209078
$928$	7.40857	0.243198
$929$	39.7820	1.30521	0.652603	−	0.757700i	$-0.273677\pi$
$929$	39.7820	1.30521	0.652603	+	0.757700i	$0.273677\pi$
$930$	4.07796	0.133722
$931$	−30.5694	−1.00187
$932$	24.8192	0.812981
$933$	−88.9993	−2.91371
$934$	−1.12082	−0.0366744
$935$	−1.00000	−0.0327035
$936$	18.3437	0.599583
$937$	51.1388	1.67063	0.835317	−	0.549769i	$-0.185284\pi$
$937$	51.1388	1.67063	0.835317	+	0.549769i	$0.185284\pi$
$938$	18.2098	0.594571
$939$	−94.4018	−3.08069
$940$	−3.61836	−0.118018
$941$	54.3058	1.77032	0.885159	−	0.465289i	$-0.154050\pi$
$941$	54.3058	1.77032	0.885159	+	0.465289i	$0.154050\pi$
$942$	−56.2360	−1.83227
$943$	−0.763283	−0.0248559
$944$	0.0779639	0.00253751
$945$	10.2498	0.333427
$946$	5.79021	0.188256
$947$	−30.1637	−0.980188	−0.490094	−	0.871670i	$-0.663038\pi$
$947$	−30.1637	−0.980188	−0.490094	+	0.871670i	$0.663038\pi$
$948$	−3.58043	−0.116287
$949$	−52.6577	−1.70934
$950$	6.38164	0.207048
$951$	82.7813	2.68437
$952$	1.48654	0.0481789
$953$	−39.8621	−1.29126	−0.645630	−	0.763650i	$-0.723405\pi$
$953$	−39.8621	−1.29126	−0.645630	+	0.763650i	$0.723405\pi$
$954$	−15.5804	−0.504435
$955$	4.45961	0.144309
$956$	6.09389	0.197091
$957$	−21.4486	−0.693335
$958$	−6.42167	−0.207475
$959$	−2.97307	−0.0960055
$960$	−2.89511	−0.0934392
$961$	−29.0159	−0.935998
$962$	12.9192	0.416532
$963$	−41.6343	−1.34165
$964$	19.7364	0.635665
$965$	−10.3437	−0.332976
$966$	−2.20979	−0.0710987
$967$	29.1070	0.936018	0.468009	−	0.883724i	$-0.344972\pi$
$967$	29.1070	0.936018	0.468009	+	0.883724i	$0.344972\pi$
$968$	1.00000	0.0321412
$969$	−18.4755	−0.593520
$970$	10.5914	0.340070
$971$	−3.31468	−0.106373	−0.0531866	−	0.998585i	$-0.516938\pi$
$971$	−3.31468	−0.106373	−0.0531866	+	0.998585i	$0.516938\pi$
$972$	−9.63429	−0.309020
$973$	−2.20979	−0.0708425
$974$	−5.39264	−0.172791
$975$	9.86818	0.316035
$976$	−5.19878	−0.166409
$977$	27.4107	0.876945	0.438473	−	0.898745i	$-0.355520\pi$
$977$	27.4107	0.876945	0.438473	+	0.898745i	$0.355520\pi$
$978$	−53.7143	−1.71760
$979$	2.38164	0.0761176
$980$	4.79021	0.153018
$981$	−45.3968	−1.44941
$982$	18.3816	0.586582
$983$	−35.5666	−1.13440	−0.567199	−	0.823581i	$-0.691973\pi$
$983$	−35.5666	−1.13440	−0.567199	+	0.823581i	$0.691973\pi$
$984$	−4.30368	−0.137196
$985$	21.3168	0.679209
$986$	−7.40857	−0.235937
$987$	−15.5722	−0.495670
$988$	21.7523	0.692032
$989$	−2.97307	−0.0945381
$990$	5.38164	0.171040
$991$	18.5156	0.588166	0.294083	−	0.955780i	$-0.404986\pi$
$991$	18.5156	0.588166	0.294083	+	0.955780i	$0.404986\pi$
$992$	−1.40857	−0.0447222
$993$	84.8054	2.69122
$994$	−12.4596	−0.395195
$995$	−1.40857	−0.0446547
$996$	27.4645	0.870247
$997$	−8.97307	−0.284180	−0.142090	−	0.989854i	$-0.545382\pi$
$997$	−8.97307	−0.284180	−0.142090	+	0.989854i	$0.545382\pi$
$998$	−30.8171	−0.975500
$999$	26.1339	0.826841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.2.a.r.1.3	✓	3
5.4	even	2		9350.2.a.by.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.2.a.r.1.3	✓	3	1.1	even	1	trivial
9350.2.a.by.1.1		3	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.89511 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.89511 q^{6} -1.48654 q^{7} +1.00000 q^{8} +5.38164 q^{9} -1.00000 q^{10} -1.00000 q^{11} +2.89511 q^{12} +3.40857 q^{13} -1.48654 q^{14} -2.89511 q^{15} +1.00000 q^{16} -1.00000 q^{17} +5.38164 q^{18} +6.38164 q^{19} -1.00000 q^{20} -4.30368 q^{21} -1.00000 q^{22} +0.513465 q^{23} +2.89511 q^{24} +1.00000 q^{25} +3.40857 q^{26} +6.89511 q^{27} -1.48654 q^{28} +7.40857 q^{29} -2.89511 q^{30} -1.40857 q^{31} +1.00000 q^{32} -2.89511 q^{33} -1.00000 q^{34} +1.48654 q^{35} +5.38164 q^{36} +3.79021 q^{37} +6.38164 q^{38} +9.86818 q^{39} -1.00000 q^{40} -1.48654 q^{41} -4.30368 q^{42} -5.79021 q^{43} -1.00000 q^{44} -5.38164 q^{45} +0.513465 q^{46} +3.61836 q^{47} +2.89511 q^{48} -4.79021 q^{49} +1.00000 q^{50} -2.89511 q^{51} +3.40857 q^{52} -2.89511 q^{53} +6.89511 q^{54} +1.00000 q^{55} -1.48654 q^{56} +18.4755 q^{57} +7.40857 q^{58} +0.0779639 q^{59} -2.89511 q^{60} -5.19878 q^{61} -1.40857 q^{62} -8.00000 q^{63} +1.00000 q^{64} -3.40857 q^{65} -2.89511 q^{66} -12.2498 q^{67} -1.00000 q^{68} +1.48654 q^{69} +1.48654 q^{70} +8.38164 q^{71} +5.38164 q^{72} -15.4486 q^{73} +3.79021 q^{74} +2.89511 q^{75} +6.38164 q^{76} +1.48654 q^{77} +9.86818 q^{78} -1.23672 q^{79} -1.00000 q^{80} +3.81714 q^{81} -1.48654 q^{82} +9.48654 q^{83} -4.30368 q^{84} +1.00000 q^{85} -5.79021 q^{86} +21.4486 q^{87} -1.00000 q^{88} -2.38164 q^{89} -5.38164 q^{90} -5.06696 q^{91} +0.513465 q^{92} -4.07796 q^{93} +3.61836 q^{94} -6.38164 q^{95} +2.89511 q^{96} -10.5914 q^{97} -4.79021 q^{98} -5.38164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 2 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} - 3 q^{11} + 4 q^{13} - 2 q^{14} + 3 q^{16} - 3 q^{17} + 5 q^{18} + 8 q^{19} - 3 q^{20} + 2 q^{21} - 3 q^{22} + 4 q^{23} + 3 q^{25}+ \cdots - 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 2 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 - 3 * q^11 + 4 * q^13 - 2 * q^14 + 3 * q^16 - 3 * q^17 + 5 * q^18 + 8 * q^19 - 3 * q^20 + 2 * q^21 - 3 * q^22 + 4 * q^23 + 3 * q^25 + 4 * q^26 + 12 * q^27 - 2 * q^28 + 16 * q^29 + 2 * q^31 + 3 * q^32 - 3 * q^34 + 2 * q^35 + 5 * q^36 - 6 * q^37 + 8 * q^38 + 16 * q^39 - 3 * q^40 - 2 * q^41 + 2 * q^42 - 3 * q^44 - 5 * q^45 + 4 * q^46 + 22 * q^47 + 3 * q^49 + 3 * q^50 + 4 * q^52 + 12 * q^54 + 3 * q^55 - 2 * q^56 + 12 * q^57 + 16 * q^58 + 4 * q^59 + 8 * q^61 + 2 * q^62 - 24 * q^63 + 3 * q^64 - 4 * q^65 - 12 * q^67 - 3 * q^68 + 2 * q^69 + 2 * q^70 + 14 * q^71 + 5 * q^72 + 2 * q^73 - 6 * q^74 + 8 * q^76 + 2 * q^77 + 16 * q^78 - 26 * q^79 - 3 * q^80 - q^81 - 2 * q^82 + 26 * q^83 + 2 * q^84 + 3 * q^85 + 16 * q^87 - 3 * q^88 + 4 * q^89 - 5 * q^90 + 22 * q^91 + 4 * q^92 - 16 * q^93 + 22 * q^94 - 8 * q^95 - 38 * q^97 + 3 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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