LMFDB - Embedded newform 5054.2.a.be.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.36538000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 $ x^6 - 13x^4 - 4x^3 + 41x^2 + 16x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.11392$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.11392 q^{3} +1.00000 q^{4} -0.959972 q^{5} -3.11392 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.69649 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.11392 q^{3} +1.00000 q^{4} -0.959972 q^{5} -3.11392 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.69649 q^{9} -0.959972 q^{10} -2.70721 q^{11} -3.11392 q^{12} +3.55327 q^{13} +1.00000 q^{14} +2.98927 q^{15} +1.00000 q^{16} -6.67457 q^{17} +6.69649 q^{18} -0.959972 q^{20} -3.11392 q^{21} -2.70721 q^{22} +3.52062 q^{23} -3.11392 q^{24} -4.07845 q^{25} +3.55327 q^{26} -11.5106 q^{27} +1.00000 q^{28} +7.12793 q^{29} +2.98927 q^{30} +2.50554 q^{31} +1.00000 q^{32} +8.43004 q^{33} -6.67457 q^{34} -0.959972 q^{35} +6.69649 q^{36} +7.59908 q^{37} -11.0646 q^{39} -0.959972 q^{40} -7.24185 q^{41} -3.11392 q^{42} -0.282061 q^{43} -2.70721 q^{44} -6.42844 q^{45} +3.52062 q^{46} +6.90889 q^{47} -3.11392 q^{48} +1.00000 q^{49} -4.07845 q^{50} +20.7841 q^{51} +3.55327 q^{52} -9.51902 q^{53} -11.5106 q^{54} +2.59885 q^{55} +1.00000 q^{56} +7.12793 q^{58} +10.2036 q^{59} +2.98927 q^{60} -13.3882 q^{61} +2.50554 q^{62} +6.69649 q^{63} +1.00000 q^{64} -3.41104 q^{65} +8.43004 q^{66} -4.15441 q^{67} -6.67457 q^{68} -10.9629 q^{69} -0.959972 q^{70} -2.22784 q^{71} +6.69649 q^{72} -8.57661 q^{73} +7.59908 q^{74} +12.7000 q^{75} -2.70721 q^{77} -11.0646 q^{78} +15.0035 q^{79} -0.959972 q^{80} +15.7535 q^{81} -7.24185 q^{82} -17.4698 q^{83} -3.11392 q^{84} +6.40740 q^{85} -0.282061 q^{86} -22.1958 q^{87} -2.70721 q^{88} -8.35574 q^{89} -6.42844 q^{90} +3.55327 q^{91} +3.52062 q^{92} -7.80203 q^{93} +6.90889 q^{94} -3.11392 q^{96} +13.2383 q^{97} +1.00000 q^{98} -18.1288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.11392	−1.79782	−0.898911	−	0.438132i	$-0.855640\pi$
$3$	−3.11392	−1.79782	−0.898911	+	0.438132i	$0.855640\pi$
$4$	1.00000	0.500000
$5$	−0.959972	−0.429312	−0.214656	−	0.976690i	$-0.568863\pi$
$5$	−0.959972	−0.429312	−0.214656	+	0.976690i	$0.568863\pi$
$6$	−3.11392	−1.27125
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	6.69649	2.23216
$10$	−0.959972	−0.303570
$11$	−2.70721	−0.816256	−0.408128	−	0.912925i	$-0.633818\pi$
$11$	−2.70721	−0.816256	−0.408128	+	0.912925i	$0.633818\pi$
$12$	−3.11392	−0.898911
$13$	3.55327	0.985499	0.492750	−	0.870171i	$-0.335992\pi$
$13$	3.55327	0.985499	0.492750	+	0.870171i	$0.335992\pi$
$14$	1.00000	0.267261
$15$	2.98927	0.771827
$16$	1.00000	0.250000
$17$	−6.67457	−1.61882	−0.809410	−	0.587243i	$-0.800213\pi$
$17$	−6.67457	−1.61882	−0.809410	+	0.587243i	$0.800213\pi$
$18$	6.69649	1.57838
$19$	0	0
$19$	0	0
$20$	−0.959972	−0.214656
$21$	−3.11392	−0.679513
$22$	−2.70721	−0.577180
$23$	3.52062	0.734101	0.367050	−	0.930201i	$-0.380368\pi$
$23$	3.52062	0.734101	0.367050	+	0.930201i	$0.380368\pi$
$24$	−3.11392	−0.635626
$25$	−4.07845	−0.815691
$26$	3.55327	0.696853
$27$	−11.5106	−2.21521
$28$	1.00000	0.188982
$29$	7.12793	1.32362	0.661812	−	0.749670i	$-0.269788\pi$
$29$	7.12793	1.32362	0.661812	+	0.749670i	$0.269788\pi$
$30$	2.98927	0.545764
$31$	2.50554	0.450007	0.225004	−	0.974358i	$-0.427761\pi$
$31$	2.50554	0.450007	0.225004	+	0.974358i	$0.427761\pi$
$32$	1.00000	0.176777
$33$	8.43004	1.46748
$34$	−6.67457	−1.14468
$35$	−0.959972	−0.162265
$36$	6.69649	1.11608
$37$	7.59908	1.24928	0.624640	−	0.780913i	$-0.285246\pi$
$37$	7.59908	1.24928	0.624640	+	0.780913i	$0.285246\pi$
$38$	0	0
$39$	−11.0646	−1.77175
$40$	−0.959972	−0.151785
$41$	−7.24185	−1.13099	−0.565493	−	0.824753i	$-0.691314\pi$
$41$	−7.24185	−1.13099	−0.565493	+	0.824753i	$0.691314\pi$
$42$	−3.11392	−0.480488
$43$	−0.282061	−0.0430138	−0.0215069	−	0.999769i	$-0.506846\pi$
$43$	−0.282061	−0.0430138	−0.0215069	+	0.999769i	$0.506846\pi$
$44$	−2.70721	−0.408128
$45$	−6.42844	−0.958295
$46$	3.52062	0.519088
$47$	6.90889	1.00777	0.503883	−	0.863772i	$-0.331904\pi$
$47$	6.90889	1.00777	0.503883	+	0.863772i	$0.331904\pi$
$48$	−3.11392	−0.449455
$49$	1.00000	0.142857
$50$	−4.07845	−0.576780
$51$	20.7841	2.91035
$52$	3.55327	0.492750
$53$	−9.51902	−1.30754	−0.653769	−	0.756694i	$-0.726813\pi$
$53$	−9.51902	−1.30754	−0.653769	+	0.756694i	$0.726813\pi$
$54$	−11.5106	−1.56639
$55$	2.59885	0.350429
$56$	1.00000	0.133631
$57$	0	0
$58$	7.12793	0.935943
$59$	10.2036	1.32839	0.664195	−	0.747559i	$-0.268774\pi$
$59$	10.2036	1.32839	0.664195	+	0.747559i	$0.268774\pi$
$60$	2.98927	0.385914
$61$	−13.3882	−1.71419	−0.857093	−	0.515162i	$-0.827732\pi$
$61$	−13.3882	−1.71419	−0.857093	+	0.515162i	$0.827732\pi$
$62$	2.50554	0.318203
$63$	6.69649	0.843678
$64$	1.00000	0.125000
$65$	−3.41104	−0.423087
$66$	8.43004	1.03767
$67$	−4.15441	−0.507542	−0.253771	−	0.967264i	$-0.581671\pi$
$67$	−4.15441	−0.507542	−0.253771	+	0.967264i	$0.581671\pi$
$68$	−6.67457	−0.809410
$69$	−10.9629	−1.31978
$70$	−0.959972	−0.114739
$71$	−2.22784	−0.264396	−0.132198	−	0.991223i	$-0.542203\pi$
$71$	−2.22784	−0.264396	−0.132198	+	0.991223i	$0.542203\pi$
$72$	6.69649	0.789189
$73$	−8.57661	−1.00382	−0.501908	−	0.864921i	$-0.667368\pi$
$73$	−8.57661	−1.00382	−0.501908	+	0.864921i	$0.667368\pi$
$74$	7.59908	0.883375
$75$	12.7000	1.46647
$76$	0	0
$77$	−2.70721	−0.308516
$78$	−11.0646	−1.25282
$79$	15.0035	1.68802	0.844012	−	0.536324i	$-0.180188\pi$
$79$	15.0035	1.68802	0.844012	+	0.536324i	$0.180188\pi$
$80$	−0.959972	−0.107328
$81$	15.7535	1.75039
$82$	−7.24185	−0.799729
$83$	−17.4698	−1.91756	−0.958781	−	0.284145i	$-0.908290\pi$
$83$	−17.4698	−1.91756	−0.958781	+	0.284145i	$0.908290\pi$
$84$	−3.11392	−0.339756
$85$	6.40740	0.694980
$86$	−0.282061	−0.0304154
$87$	−22.1958	−2.37964
$88$	−2.70721	−0.288590
$89$	−8.35574	−0.885706	−0.442853	−	0.896594i	$-0.646034\pi$
$89$	−8.35574	−0.885706	−0.442853	+	0.896594i	$0.646034\pi$
$90$	−6.42844	−0.677617
$91$	3.55327	0.372484
$92$	3.52062	0.367050
$93$	−7.80203	−0.809033
$94$	6.90889	0.712598
$95$	0	0
$96$	−3.11392	−0.317813
$97$	13.2383	1.34414	0.672072	−	0.740486i	$-0.265405\pi$
$97$	13.2383	1.34414	0.672072	+	0.740486i	$0.265405\pi$
$98$	1.00000	0.101015
$99$	−18.1288	−1.82202
$100$	−4.07845	−0.407845
$101$	12.4091	1.23476	0.617378	−	0.786667i	$-0.288195\pi$
$101$	12.4091	1.23476	0.617378	+	0.786667i	$0.288195\pi$
$102$	20.7841	2.05793
$103$	−3.60252	−0.354967	−0.177483	−	0.984124i	$-0.556796\pi$
$103$	−3.60252	−0.354967	−0.177483	+	0.984124i	$0.556796\pi$
$104$	3.55327	0.348427
$105$	2.98927	0.291723
$106$	−9.51902	−0.924569
$107$	9.93200	0.960163	0.480082	−	0.877224i	$-0.340607\pi$
$107$	9.93200	0.960163	0.480082	+	0.877224i	$0.340607\pi$
$108$	−11.5106	−1.10760
$109$	−8.02328	−0.768491	−0.384245	−	0.923231i	$-0.625538\pi$
$109$	−8.02328	−0.768491	−0.384245	+	0.923231i	$0.625538\pi$
$110$	2.59885	0.247791
$111$	−23.6629	−2.24598
$112$	1.00000	0.0944911
$113$	−7.08000	−0.666030	−0.333015	−	0.942922i	$-0.608066\pi$
$113$	−7.08000	−0.666030	−0.333015	+	0.942922i	$0.608066\pi$
$114$	0	0
$115$	−3.37970	−0.315159
$116$	7.12793	0.661812
$117$	23.7944	2.19979
$118$	10.2036	0.939314
$119$	−6.67457	−0.611857
$120$	2.98927	0.272882
$121$	−3.67099	−0.333727
$122$	−13.3882	−1.21211
$123$	22.5505	2.03331
$124$	2.50554	0.225004
$125$	8.71506	0.779499
$126$	6.69649	0.596571
$127$	19.6653	1.74501	0.872505	−	0.488606i	$-0.162494\pi$
$127$	19.6653	1.74501	0.872505	+	0.488606i	$0.162494\pi$
$128$	1.00000	0.0883883
$129$	0.878313	0.0773312
$130$	−3.41104	−0.299168
$131$	7.89393	0.689696	0.344848	−	0.938659i	$-0.387931\pi$
$131$	7.89393	0.689696	0.344848	+	0.938659i	$0.387931\pi$
$132$	8.43004	0.733741
$133$	0	0
$134$	−4.15441	−0.358887
$135$	11.0498	0.951017
$136$	−6.67457	−0.572340
$137$	7.42167	0.634076	0.317038	−	0.948413i	$-0.397312\pi$
$137$	7.42167	0.634076	0.317038	+	0.948413i	$0.397312\pi$
$138$	−10.9629	−0.933227
$139$	16.4405	1.39447	0.697234	−	0.716844i	$-0.254414\pi$
$139$	16.4405	1.39447	0.697234	+	0.716844i	$0.254414\pi$
$140$	−0.959972	−0.0811324
$141$	−21.5137	−1.81178
$142$	−2.22784	−0.186956
$143$	−9.61945	−0.804419
$144$	6.69649	0.558041
$145$	−6.84261	−0.568248
$146$	−8.57661	−0.709805
$147$	−3.11392	−0.256832
$148$	7.59908	0.624640
$149$	5.05395	0.414036	0.207018	−	0.978337i	$-0.433624\pi$
$149$	5.05395	0.414036	0.207018	+	0.978337i	$0.433624\pi$
$150$	12.7000	1.03695
$151$	−7.51527	−0.611584	−0.305792	−	0.952098i	$-0.598921\pi$
$151$	−7.51527	−0.611584	−0.305792	+	0.952098i	$0.598921\pi$
$152$	0	0
$153$	−44.6962	−3.61347
$154$	−2.70721	−0.218153
$155$	−2.40524	−0.193194
$156$	−11.0646	−0.885876
$157$	2.10544	0.168032	0.0840162	−	0.996464i	$-0.473225\pi$
$157$	2.10544	0.168032	0.0840162	+	0.996464i	$0.473225\pi$
$158$	15.0035	1.19361
$159$	29.6415	2.35072
$160$	−0.959972	−0.0758924
$161$	3.52062	0.277464
$162$	15.7535	1.23771
$163$	7.58995	0.594491	0.297245	−	0.954801i	$-0.403932\pi$
$163$	7.58995	0.594491	0.297245	+	0.954801i	$0.403932\pi$
$164$	−7.24185	−0.565493
$165$	−8.09260	−0.630008
$166$	−17.4698	−1.35592
$167$	−8.82254	−0.682708	−0.341354	−	0.939935i	$-0.610886\pi$
$167$	−8.82254	−0.682708	−0.341354	+	0.939935i	$0.610886\pi$
$168$	−3.11392	−0.240244
$169$	−0.374292	−0.0287917
$170$	6.40740	0.491425
$171$	0	0
$172$	−0.282061	−0.0215069
$173$	3.13833	0.238603	0.119301	−	0.992858i	$-0.461935\pi$
$173$	3.13833	0.238603	0.119301	+	0.992858i	$0.461935\pi$
$174$	−22.1958	−1.68266
$175$	−4.07845	−0.308302
$176$	−2.70721	−0.204064
$177$	−31.7731	−2.38821
$178$	−8.35574	−0.626289
$179$	23.5378	1.75930	0.879648	−	0.475626i	$-0.157778\pi$
$179$	23.5378	1.75930	0.879648	+	0.475626i	$0.157778\pi$
$180$	−6.42844	−0.479148
$181$	11.0476	0.821158	0.410579	−	0.911825i	$-0.365327\pi$
$181$	11.0476	0.821158	0.410579	+	0.911825i	$0.365327\pi$
$182$	3.55327	0.263386
$183$	41.6898	3.08180
$184$	3.52062	0.259544
$185$	−7.29490	−0.536332
$186$	−7.80203	−0.572073
$187$	18.0695	1.32137
$188$	6.90889	0.503883
$189$	−11.5106	−0.837270
$190$	0	0
$191$	7.32300	0.529874	0.264937	−	0.964266i	$-0.414649\pi$
$191$	7.32300	0.529874	0.264937	+	0.964266i	$0.414649\pi$
$192$	−3.11392	−0.224728
$193$	21.2936	1.53275	0.766374	−	0.642395i	$-0.222059\pi$
$193$	21.2936	1.53275	0.766374	+	0.642395i	$0.222059\pi$
$194$	13.2383	0.950453
$195$	10.6217	0.760635
$196$	1.00000	0.0714286
$197$	26.9859	1.92266	0.961331	−	0.275394i	$-0.0888083\pi$
$197$	26.9859	1.92266	0.961331	+	0.275394i	$0.0888083\pi$
$198$	−18.1288	−1.28836
$199$	2.84678	0.201803	0.100901	−	0.994896i	$-0.467827\pi$
$199$	2.84678	0.201803	0.100901	+	0.994896i	$0.467827\pi$
$200$	−4.07845	−0.288390
$201$	12.9365	0.912471
$202$	12.4091	0.873104
$203$	7.12793	0.500283
$204$	20.7841	1.45518
$205$	6.95197	0.485547
$206$	−3.60252	−0.250999
$207$	23.5758	1.63863
$208$	3.55327	0.246375
$209$	0	0
$210$	2.98927	0.206280
$211$	14.4955	0.997910	0.498955	−	0.866628i	$-0.333717\pi$
$211$	14.4955	0.997910	0.498955	+	0.866628i	$0.333717\pi$
$212$	−9.51902	−0.653769
$213$	6.93730	0.475336
$214$	9.93200	0.678938
$215$	0.270770	0.0184664
$216$	−11.5106	−0.783195
$217$	2.50554	0.170087
$218$	−8.02328	−0.543405
$219$	26.7068	1.80468
$220$	2.59885	0.175214
$221$	−23.7165	−1.59535
$222$	−23.6629	−1.58815
$223$	17.6629	1.18280	0.591399	−	0.806379i	$-0.298576\pi$
$223$	17.6629	1.18280	0.591399	+	0.806379i	$0.298576\pi$
$224$	1.00000	0.0668153
$225$	−27.3113	−1.82075
$226$	−7.08000	−0.470954
$227$	0.588393	0.0390530	0.0195265	−	0.999809i	$-0.493784\pi$
$227$	0.588393	0.0390530	0.0195265	+	0.999809i	$0.493784\pi$
$228$	0	0
$229$	9.10188	0.601469	0.300735	−	0.953708i	$-0.402768\pi$
$229$	9.10188	0.601469	0.300735	+	0.953708i	$0.402768\pi$
$230$	−3.37970	−0.222851
$231$	8.43004	0.554656
$232$	7.12793	0.467972
$233$	−25.0109	−1.63852	−0.819261	−	0.573421i	$-0.805616\pi$
$233$	−25.0109	−1.63852	−0.819261	+	0.573421i	$0.805616\pi$
$234$	23.7944	1.55549
$235$	−6.63234	−0.432646
$236$	10.2036	0.664195
$237$	−46.7196	−3.03477
$238$	−6.67457	−0.432648
$239$	11.5301	0.745820	0.372910	−	0.927868i	$-0.378360\pi$
$239$	11.5301	0.745820	0.372910	+	0.927868i	$0.378360\pi$
$240$	2.98927	0.192957
$241$	3.81708	0.245880	0.122940	−	0.992414i	$-0.460768\pi$
$241$	3.81708	0.245880	0.122940	+	0.992414i	$0.460768\pi$
$242$	−3.67099	−0.235980
$243$	−14.5234	−0.931676
$244$	−13.3882	−0.857093
$245$	−0.959972	−0.0613304
$246$	22.5505	1.43777
$247$	0	0
$248$	2.50554	0.159102
$249$	54.3996	3.44744
$250$	8.71506	0.551189
$251$	22.0339	1.39077	0.695385	−	0.718637i	$-0.255234\pi$
$251$	22.0339	1.39077	0.695385	+	0.718637i	$0.255234\pi$
$252$	6.69649	0.421839
$253$	−9.53108	−0.599214
$254$	19.6653	1.23391
$255$	−19.9521	−1.24945
$256$	1.00000	0.0625000
$257$	−12.4193	−0.774697	−0.387349	−	0.921933i	$-0.626609\pi$
$257$	−12.4193	−0.774697	−0.387349	+	0.921933i	$0.626609\pi$
$258$	0.878313	0.0546814
$259$	7.59908	0.472184
$260$	−3.41104	−0.211544
$261$	47.7321	2.95454
$262$	7.89393	0.487689
$263$	−6.52472	−0.402332	−0.201166	−	0.979557i	$-0.564473\pi$
$263$	−6.52472	−0.402332	−0.201166	+	0.979557i	$0.564473\pi$
$264$	8.43004	0.518833
$265$	9.13799	0.561342
$266$	0	0
$267$	26.0191	1.59234
$268$	−4.15441	−0.253771
$269$	19.0246	1.15995	0.579974	−	0.814635i	$-0.303063\pi$
$269$	19.0246	1.15995	0.579974	+	0.814635i	$0.303063\pi$
$270$	11.0498	0.672470
$271$	−11.1907	−0.679789	−0.339895	−	0.940464i	$-0.610391\pi$
$271$	−11.1907	−0.679789	−0.339895	+	0.940464i	$0.610391\pi$
$272$	−6.67457	−0.404705
$273$	−11.0646	−0.669659
$274$	7.42167	0.448360
$275$	11.0412	0.665812
$276$	−10.9629	−0.659891
$277$	18.7528	1.12675	0.563374	−	0.826202i	$-0.309503\pi$
$277$	18.7528	1.12675	0.563374	+	0.826202i	$0.309503\pi$
$278$	16.4405	0.986037
$279$	16.7783	1.00449
$280$	−0.959972	−0.0573693
$281$	6.48900	0.387101	0.193551	−	0.981090i	$-0.438000\pi$
$281$	6.48900	0.387101	0.193551	+	0.981090i	$0.438000\pi$
$282$	−21.5137	−1.28112
$283$	23.6428	1.40542	0.702709	−	0.711478i	$-0.251974\pi$
$283$	23.6428	1.40542	0.702709	+	0.711478i	$0.251974\pi$
$284$	−2.22784	−0.132198
$285$	0	0
$286$	−9.61945	−0.568810
$287$	−7.24185	−0.427473
$288$	6.69649	0.394594
$289$	27.5499	1.62058
$290$	−6.84261	−0.401812
$291$	−41.2229	−2.41653
$292$	−8.57661	−0.501908
$293$	−23.2099	−1.35594	−0.677969	−	0.735090i	$-0.737140\pi$
$293$	−23.2099	−1.35594	−0.677969	+	0.735090i	$0.737140\pi$
$294$	−3.11392	−0.181607
$295$	−9.79514	−0.570295
$296$	7.59908	0.441687
$297$	31.1616	1.80818
$298$	5.05395	0.292767
$299$	12.5097	0.723455
$300$	12.7000	0.733233
$301$	−0.282061	−0.0162577
$302$	−7.51527	−0.432455
$303$	−38.6410	−2.21987
$304$	0	0
$305$	12.8523	0.735921
$306$	−44.6962	−2.55511
$307$	−25.0604	−1.43027	−0.715137	−	0.698984i	$-0.753636\pi$
$307$	−25.0604	−1.43027	−0.715137	+	0.698984i	$0.753636\pi$
$308$	−2.70721	−0.154258
$309$	11.2179	0.638166
$310$	−2.40524	−0.136609
$311$	−21.0148	−1.19164	−0.595820	−	0.803118i	$-0.703173\pi$
$311$	−21.0148	−1.19164	−0.595820	+	0.803118i	$0.703173\pi$
$312$	−11.0646	−0.626409
$313$	18.2477	1.03142	0.515711	−	0.856762i	$-0.327528\pi$
$313$	18.2477	1.03142	0.515711	+	0.856762i	$0.327528\pi$
$314$	2.10544	0.118817
$315$	−6.42844	−0.362202
$316$	15.0035	0.844012
$317$	−10.7596	−0.604321	−0.302160	−	0.953257i	$-0.597708\pi$
$317$	−10.7596	−0.604321	−0.302160	+	0.953257i	$0.597708\pi$
$318$	29.6415	1.66221
$319$	−19.2968	−1.08042
$320$	−0.959972	−0.0536641
$321$	−30.9275	−1.72620
$322$	3.52062	0.196197
$323$	0	0
$324$	15.7535	0.875194
$325$	−14.4918	−0.803862
$326$	7.58995	0.420368
$327$	24.9838	1.38161
$328$	−7.24185	−0.399864
$329$	6.90889	0.380900
$330$	−8.09260	−0.445483
$331$	36.1010	1.98429	0.992146	−	0.125087i	$-0.0399209\pi$
$331$	36.1010	1.98429	0.992146	+	0.125087i	$0.0399209\pi$
$332$	−17.4698	−0.958781
$333$	50.8871	2.78860
$334$	−8.82254	−0.482748
$335$	3.98812	0.217894
$336$	−3.11392	−0.169878
$337$	18.8352	1.02602	0.513009	−	0.858383i	$-0.328531\pi$
$337$	18.8352	1.02602	0.513009	+	0.858383i	$0.328531\pi$
$338$	−0.374292	−0.0203588
$339$	22.0465	1.19740
$340$	6.40740	0.347490
$341$	−6.78302	−0.367321
$342$	0	0
$343$	1.00000	0.0539949
$344$	−0.282061	−0.0152077
$345$	10.5241	0.566599
$346$	3.13833	0.168718
$347$	−12.6195	−0.677451	−0.338726	−	0.940885i	$-0.609996\pi$
$347$	−12.6195	−0.677451	−0.338726	+	0.940885i	$0.609996\pi$
$348$	−22.1958	−1.18982
$349$	0.227609	0.0121836	0.00609181	−	0.999981i	$-0.498061\pi$
$349$	0.227609	0.0121836	0.00609181	+	0.999981i	$0.498061\pi$
$350$	−4.07845	−0.218003
$351$	−40.9001	−2.18309
$352$	−2.70721	−0.144295
$353$	−11.9425	−0.635637	−0.317818	−	0.948152i	$-0.602950\pi$
$353$	−11.9425	−0.635637	−0.317818	+	0.948152i	$0.602950\pi$
$354$	−31.7731	−1.68872
$355$	2.13866	0.113508
$356$	−8.35574	−0.442853
$357$	20.7841	1.10001
$358$	23.5378	1.24401
$359$	−22.9370	−1.21057	−0.605285	−	0.796009i	$-0.706941\pi$
$359$	−22.9370	−1.21057	−0.605285	+	0.796009i	$0.706941\pi$
$360$	−6.42844	−0.338809
$361$	0	0
$362$	11.0476	0.580646
$363$	11.4312	0.599981
$364$	3.55327	0.186242
$365$	8.23330	0.430951
$366$	41.6898	2.17916
$367$	14.2300	0.742802	0.371401	−	0.928473i	$-0.378878\pi$
$367$	14.2300	0.742802	0.371401	+	0.928473i	$0.378878\pi$
$368$	3.52062	0.183525
$369$	−48.4950	−2.52455
$370$	−7.29490	−0.379244
$371$	−9.51902	−0.494203
$372$	−7.80203	−0.404517
$373$	−5.07840	−0.262949	−0.131475	−	0.991320i	$-0.541971\pi$
$373$	−5.07840	−0.262949	−0.131475	+	0.991320i	$0.541971\pi$
$374$	18.0695	0.934351
$375$	−27.1380	−1.40140
$376$	6.90889	0.356299
$377$	25.3274	1.30443
$378$	−11.5106	−0.592039
$379$	−4.95870	−0.254711	−0.127356	−	0.991857i	$-0.540649\pi$
$379$	−4.95870	−0.254711	−0.127356	+	0.991857i	$0.540649\pi$
$380$	0	0
$381$	−61.2360	−3.13722
$382$	7.32300	0.374677
$383$	−3.11820	−0.159333	−0.0796663	−	0.996822i	$-0.525385\pi$
$383$	−3.11820	−0.159333	−0.0796663	+	0.996822i	$0.525385\pi$
$384$	−3.11392	−0.158906
$385$	2.59885	0.132450
$386$	21.2936	1.08382
$387$	−1.88881	−0.0960139
$388$	13.2383	0.672072
$389$	12.7019	0.644010	0.322005	−	0.946738i	$-0.395643\pi$
$389$	12.7019	0.644010	0.322005	+	0.946738i	$0.395643\pi$
$390$	10.6217	0.537850
$391$	−23.4986	−1.18838
$392$	1.00000	0.0505076
$393$	−24.5810	−1.23995
$394$	26.9859	1.35953
$395$	−14.4029	−0.724690
$396$	−18.1288	−0.911008
$397$	33.5926	1.68597	0.842983	−	0.537940i	$-0.180797\pi$
$397$	33.5926	1.68597	0.842983	+	0.537940i	$0.180797\pi$
$398$	2.84678	0.142696
$399$	0	0
$400$	−4.07845	−0.203923
$401$	−26.6682	−1.33174	−0.665872	−	0.746066i	$-0.731940\pi$
$401$	−26.6682	−1.33174	−0.665872	+	0.746066i	$0.731940\pi$
$402$	12.9365	0.645214
$403$	8.90284	0.443482
$404$	12.4091	0.617378
$405$	−15.1229	−0.751463
$406$	7.12793	0.353753
$407$	−20.5723	−1.01973
$408$	20.7841	1.02896
$409$	−4.35206	−0.215196	−0.107598	−	0.994195i	$-0.534316\pi$
$409$	−4.35206	−0.215196	−0.107598	+	0.994195i	$0.534316\pi$
$410$	6.95197	0.343333
$411$	−23.1105	−1.13996
$412$	−3.60252	−0.177483
$413$	10.2036	0.502085
$414$	23.5758	1.15869
$415$	16.7705	0.823234
$416$	3.55327	0.174213
$417$	−51.1945	−2.50700
$418$	0	0
$419$	9.26629	0.452688	0.226344	−	0.974047i	$-0.427323\pi$
$419$	9.26629	0.452688	0.226344	+	0.974047i	$0.427323\pi$
$420$	2.98927	0.145862
$421$	−17.3214	−0.844193	−0.422097	−	0.906551i	$-0.638706\pi$
$421$	−17.3214	−0.844193	−0.422097	+	0.906551i	$0.638706\pi$
$422$	14.4955	0.705629
$423$	46.2653	2.24950
$424$	−9.51902	−0.462285
$425$	27.2219	1.32046
$426$	6.93730	0.336113
$427$	−13.3882	−0.647901
$428$	9.93200	0.480082
$429$	29.9542	1.44620
$430$	0.270770	0.0130577
$431$	−21.3963	−1.03062	−0.515311	−	0.857003i	$-0.672324\pi$
$431$	−21.3963	−1.03062	−0.515311	+	0.857003i	$0.672324\pi$
$432$	−11.5106	−0.553802
$433$	19.2137	0.923353	0.461676	−	0.887048i	$-0.347248\pi$
$433$	19.2137	0.923353	0.461676	+	0.887048i	$0.347248\pi$
$434$	2.50554	0.120270
$435$	21.3073	1.02161
$436$	−8.02328	−0.384245
$437$	0	0
$438$	26.7068	1.27610
$439$	22.5139	1.07453	0.537265	−	0.843414i	$-0.319458\pi$
$439$	22.5139	1.07453	0.537265	+	0.843414i	$0.319458\pi$
$440$	2.59885	0.123895
$441$	6.69649	0.318880
$442$	−23.7165	−1.12808
$443$	0.978663	0.0464977	0.0232489	−	0.999730i	$-0.492599\pi$
$443$	0.978663	0.0464977	0.0232489	+	0.999730i	$0.492599\pi$
$444$	−23.6629	−1.12299
$445$	8.02127	0.380245
$446$	17.6629	0.836364
$447$	−15.7376	−0.744362
$448$	1.00000	0.0472456
$449$	32.9060	1.55293	0.776466	−	0.630159i	$-0.217010\pi$
$449$	32.9060	1.55293	0.776466	+	0.630159i	$0.217010\pi$
$450$	−27.3113	−1.28747
$451$	19.6052	0.923174
$452$	−7.08000	−0.333015
$453$	23.4019	1.09952
$454$	0.588393	0.0276147
$455$	−3.41104	−0.159912
$456$	0	0
$457$	18.9971	0.888649	0.444324	−	0.895866i	$-0.353444\pi$
$457$	18.9971	0.888649	0.444324	+	0.895866i	$0.353444\pi$
$458$	9.10188	0.425303
$459$	76.8280	3.58603
$460$	−3.37970	−0.157579
$461$	−37.7120	−1.75642	−0.878211	−	0.478274i	$-0.841263\pi$
$461$	−37.7120	−1.75642	−0.878211	+	0.478274i	$0.841263\pi$
$462$	8.43004	0.392201
$463$	−25.5830	−1.18894	−0.594470	−	0.804117i	$-0.702638\pi$
$463$	−25.5830	−1.18894	−0.594470	+	0.804117i	$0.702638\pi$
$464$	7.12793	0.330906
$465$	7.48973	0.347328
$466$	−25.0109	−1.15861
$467$	−4.52094	−0.209204	−0.104602	−	0.994514i	$-0.533357\pi$
$467$	−4.52094	−0.209204	−0.104602	+	0.994514i	$0.533357\pi$
$468$	23.7944	1.09990
$469$	−4.15441	−0.191833
$470$	−6.63234	−0.305927
$471$	−6.55617	−0.302092
$472$	10.2036	0.469657
$473$	0.763598	0.0351103
$474$	−46.7196	−2.14590
$475$	0	0
$476$	−6.67457	−0.305928
$477$	−63.7440	−2.91864
$478$	11.5301	0.527374
$479$	−7.34593	−0.335644	−0.167822	−	0.985817i	$-0.553673\pi$
$479$	−7.34593	−0.335644	−0.167822	+	0.985817i	$0.553673\pi$
$480$	2.98927	0.136441
$481$	27.0016	1.23116
$482$	3.81708	0.173863
$483$	−10.9629	−0.498831
$484$	−3.67099	−0.166863
$485$	−12.7084	−0.577058
$486$	−14.5234	−0.658794
$487$	−6.74975	−0.305860	−0.152930	−	0.988237i	$-0.548871\pi$
$487$	−6.74975	−0.305860	−0.152930	+	0.988237i	$0.548871\pi$
$488$	−13.3882	−0.606056
$489$	−23.6345	−1.06879
$490$	−0.959972	−0.0433671
$491$	−14.7330	−0.664890	−0.332445	−	0.943123i	$-0.607874\pi$
$491$	−14.7330	−0.664890	−0.332445	+	0.943123i	$0.607874\pi$
$492$	22.5505	1.01666
$493$	−47.5759	−2.14271
$494$	0	0
$495$	17.4032	0.782214
$496$	2.50554	0.112502
$497$	−2.22784	−0.0999321
$498$	54.3996	2.43771
$499$	11.6484	0.521454	0.260727	−	0.965413i	$-0.416038\pi$
$499$	11.6484	0.521454	0.260727	+	0.965413i	$0.416038\pi$
$500$	8.71506	0.389749
$501$	27.4727	1.22739
$502$	22.0339	0.983423
$503$	27.5583	1.22876	0.614382	−	0.789009i	$-0.289405\pi$
$503$	27.5583	1.22876	0.614382	+	0.789009i	$0.289405\pi$
$504$	6.69649	0.298285
$505$	−11.9124	−0.530096
$506$	−9.53108	−0.423708
$507$	1.16552	0.0517624
$508$	19.6653	0.872505
$509$	−9.56347	−0.423893	−0.211947	−	0.977281i	$-0.567980\pi$
$509$	−9.56347	−0.423893	−0.211947	+	0.977281i	$0.567980\pi$
$510$	−19.9521	−0.883495
$511$	−8.57661	−0.379407
$512$	1.00000	0.0441942
$513$	0	0
$514$	−12.4193	−0.547794
$515$	3.45831	0.152392
$516$	0.878313	0.0386656
$517$	−18.7038	−0.822594
$518$	7.59908	0.333884
$519$	−9.77251	−0.428965
$520$	−3.41104	−0.149584
$521$	−8.24050	−0.361023	−0.180511	−	0.983573i	$-0.557775\pi$
$521$	−8.24050	−0.361023	−0.180511	+	0.983573i	$0.557775\pi$
$522$	47.7321	2.08918
$523$	−5.11939	−0.223855	−0.111928	−	0.993716i	$-0.535702\pi$
$523$	−5.11939	−0.223855	−0.111928	+	0.993716i	$0.535702\pi$
$524$	7.89393	0.344848
$525$	12.7000	0.554272
$526$	−6.52472	−0.284491
$527$	−16.7234	−0.728481
$528$	8.43004	0.366871
$529$	−10.6052	−0.461096
$530$	9.13799	0.396929
$531$	68.3280	2.96518
$532$	0	0
$533$	−25.7322	−1.11459
$534$	26.0191	1.12596
$535$	−9.53445	−0.412210
$536$	−4.15441	−0.179443
$537$	−73.2947	−3.16290
$538$	19.0246	0.820207
$539$	−2.70721	−0.116608
$540$	11.0498	0.475508
$541$	−1.79356	−0.0771112	−0.0385556	−	0.999256i	$-0.512276\pi$
$541$	−1.79356	−0.0771112	−0.0385556	+	0.999256i	$0.512276\pi$
$542$	−11.1907	−0.480683
$543$	−34.4012	−1.47630
$544$	−6.67457	−0.286170
$545$	7.70212	0.329923
$546$	−11.0646	−0.473520
$547$	−35.6163	−1.52284	−0.761421	−	0.648257i	$-0.775498\pi$
$547$	−35.6163	−1.52284	−0.761421	+	0.648257i	$0.775498\pi$
$548$	7.42167	0.317038
$549$	−89.6540	−3.82634
$550$	11.0412	0.470800
$551$	0	0
$552$	−10.9629	−0.466613
$553$	15.0035	0.638013
$554$	18.7528	0.796732
$555$	22.7157	0.964229
$556$	16.4405	0.697234
$557$	−6.83610	−0.289655	−0.144827	−	0.989457i	$-0.546263\pi$
$557$	−6.83610	−0.289655	−0.144827	+	0.989457i	$0.546263\pi$
$558$	16.7783	0.710281
$559$	−1.00224	−0.0423901
$560$	−0.959972	−0.0405662
$561$	−56.2669	−2.37559
$562$	6.48900	0.273722
$563$	40.7543	1.71759	0.858795	−	0.512320i	$-0.171214\pi$
$563$	40.7543	1.71759	0.858795	+	0.512320i	$0.171214\pi$
$564$	−21.5137	−0.905891
$565$	6.79660	0.285935
$566$	23.6428	0.993780
$567$	15.7535	0.661584
$568$	−2.22784	−0.0934780
$569$	2.27766	0.0954843	0.0477422	−	0.998860i	$-0.484797\pi$
$569$	2.27766	0.0954843	0.0477422	+	0.998860i	$0.484797\pi$
$570$	0	0
$571$	34.3291	1.43663	0.718315	−	0.695718i	$-0.244914\pi$
$571$	34.3291	1.43663	0.718315	+	0.695718i	$0.244914\pi$
$572$	−9.61945	−0.402210
$573$	−22.8032	−0.952618
$574$	−7.24185	−0.302269
$575$	−14.3587	−0.598799
$576$	6.69649	0.279020
$577$	5.62687	0.234249	0.117125	−	0.993117i	$-0.462632\pi$
$577$	5.62687	0.234249	0.117125	+	0.993117i	$0.462632\pi$
$578$	27.5499	1.14592
$579$	−66.3066	−2.75561
$580$	−6.84261	−0.284124
$581$	−17.4698	−0.724771
$582$	−41.2229	−1.70874
$583$	25.7700	1.06729
$584$	−8.57661	−0.354902
$585$	−22.8420	−0.944399
$586$	−23.2099	−0.958793
$587$	12.0832	0.498725	0.249363	−	0.968410i	$-0.419779\pi$
$587$	12.0832	0.498725	0.249363	+	0.968410i	$0.419779\pi$
$588$	−3.11392	−0.128416
$589$	0	0
$590$	−9.79514	−0.403259
$591$	−84.0318	−3.45661
$592$	7.59908	0.312320
$593$	−12.7656	−0.524219	−0.262109	−	0.965038i	$-0.584418\pi$
$593$	−12.7656	−0.524219	−0.262109	+	0.965038i	$0.584418\pi$
$594$	31.1616	1.27857
$595$	6.40740	0.262678
$596$	5.05395	0.207018
$597$	−8.86464	−0.362805
$598$	12.5097	0.511560
$599$	15.9830	0.653047	0.326524	−	0.945189i	$-0.394123\pi$
$599$	15.9830	0.653047	0.326524	+	0.945189i	$0.394123\pi$
$600$	12.7000	0.518474
$601$	31.3548	1.27899	0.639494	−	0.768796i	$-0.279144\pi$
$601$	31.3548	1.27899	0.639494	+	0.768796i	$0.279144\pi$
$602$	−0.282061	−0.0114959
$603$	−27.8200	−1.13292
$604$	−7.51527	−0.305792
$605$	3.52405	0.143273
$606$	−38.6410	−1.56969
$607$	20.3460	0.825818	0.412909	−	0.910772i	$-0.364513\pi$
$607$	20.3460	0.825818	0.412909	+	0.910772i	$0.364513\pi$
$608$	0	0
$609$	−22.1958	−0.899419
$610$	12.8523	0.520375
$611$	24.5491	0.993152
$612$	−44.6962	−1.80674
$613$	−35.8659	−1.44861	−0.724306	−	0.689479i	$-0.757840\pi$
$613$	−35.8659	−1.44861	−0.724306	+	0.689479i	$0.757840\pi$
$614$	−25.0604	−1.01136
$615$	−21.6479	−0.872927
$616$	−2.70721	−0.109077
$617$	−42.3015	−1.70300	−0.851498	−	0.524358i	$-0.824305\pi$
$617$	−42.3015	−1.70300	−0.851498	+	0.524358i	$0.824305\pi$
$618$	11.2179	0.451252
$619$	−11.2595	−0.452557	−0.226279	−	0.974063i	$-0.572656\pi$
$619$	−11.2595	−0.452557	−0.226279	+	0.974063i	$0.572656\pi$
$620$	−2.40524	−0.0965969
$621$	−40.5244	−1.62619
$622$	−21.0148	−0.842617
$623$	−8.35574	−0.334766
$624$	−11.0646	−0.442938
$625$	12.0261	0.481042
$626$	18.2477	0.729326
$627$	0	0
$628$	2.10544	0.0840162
$629$	−50.7206	−2.02236
$630$	−6.42844	−0.256115
$631$	−10.4446	−0.415792	−0.207896	−	0.978151i	$-0.566661\pi$
$631$	−10.4446	−0.415792	−0.207896	+	0.978151i	$0.566661\pi$
$632$	15.0035	0.596807
$633$	−45.1377	−1.79406
$634$	−10.7596	−0.427319
$635$	−18.8781	−0.749154
$636$	29.6415	1.17536
$637$	3.55327	0.140786
$638$	−19.2968	−0.763969
$639$	−14.9187	−0.590174
$640$	−0.959972	−0.0379462
$641$	−10.5196	−0.415500	−0.207750	−	0.978182i	$-0.566614\pi$
$641$	−10.5196	−0.415500	−0.207750	+	0.978182i	$0.566614\pi$
$642$	−30.9275	−1.22061
$643$	−32.5808	−1.28486	−0.642430	−	0.766344i	$-0.722074\pi$
$643$	−32.5808	−1.28486	−0.642430	+	0.766344i	$0.722074\pi$
$644$	3.52062	0.138732
$645$	−0.843156	−0.0331992
$646$	0	0
$647$	−12.8195	−0.503985	−0.251993	−	0.967729i	$-0.581086\pi$
$647$	−12.8195	−0.503985	−0.251993	+	0.967729i	$0.581086\pi$
$648$	15.7535	0.618855
$649$	−27.6232	−1.08431
$650$	−14.4918	−0.568417
$651$	−7.80203	−0.305786
$652$	7.58995	0.297245
$653$	−7.65425	−0.299534	−0.149767	−	0.988721i	$-0.547852\pi$
$653$	−7.65425	−0.299534	−0.149767	+	0.988721i	$0.547852\pi$
$654$	24.9838	0.976945
$655$	−7.57795	−0.296095
$656$	−7.24185	−0.282747
$657$	−57.4331	−2.24068
$658$	6.90889	0.269337
$659$	40.6414	1.58317	0.791583	−	0.611062i	$-0.209257\pi$
$659$	40.6414	1.58317	0.791583	+	0.611062i	$0.209257\pi$
$660$	−8.09260	−0.315004
$661$	−16.5058	−0.642000	−0.321000	−	0.947079i	$-0.604019\pi$
$661$	−16.5058	−0.642000	−0.321000	+	0.947079i	$0.604019\pi$
$662$	36.1010	1.40311
$663$	73.8513	2.86815
$664$	−17.4698	−0.677961
$665$	0	0
$666$	50.8871	1.97184
$667$	25.0948	0.971673
$668$	−8.82254	−0.341354
$669$	−55.0009	−2.12646
$670$	3.98812	0.154075
$671$	36.2448	1.39921
$672$	−3.11392	−0.120122
$673$	23.2797	0.897366	0.448683	−	0.893691i	$-0.351893\pi$
$673$	23.2797	0.897366	0.448683	+	0.893691i	$0.351893\pi$
$674$	18.8352	0.725504
$675$	46.9453	1.80693
$676$	−0.374292	−0.0143959
$677$	−26.6199	−1.02309	−0.511544	−	0.859257i	$-0.670926\pi$
$677$	−26.6199	−1.02309	−0.511544	+	0.859257i	$0.670926\pi$
$678$	22.0465	0.846692
$679$	13.2383	0.508038
$680$	6.40740	0.245713
$681$	−1.83221	−0.0702104
$682$	−6.78302	−0.259735
$683$	7.15388	0.273736	0.136868	−	0.990589i	$-0.456296\pi$
$683$	7.15388	0.273736	0.136868	+	0.990589i	$0.456296\pi$
$684$	0	0
$685$	−7.12460	−0.272217
$686$	1.00000	0.0381802
$687$	−28.3425	−1.08133
$688$	−0.282061	−0.0107535
$689$	−33.8236	−1.28858
$690$	10.5241	0.400646
$691$	11.3824	0.433005	0.216503	−	0.976282i	$-0.430535\pi$
$691$	11.3824	0.433005	0.216503	+	0.976282i	$0.430535\pi$
$692$	3.13833	0.119301
$693$	−18.1288	−0.688657
$694$	−12.6195	−0.479030
$695$	−15.7824	−0.598662
$696$	−22.1958	−0.841330
$697$	48.3362	1.83087
$698$	0.227609	0.00861512
$699$	77.8820	2.94577
$700$	−4.07845	−0.154151
$701$	20.2961	0.766573	0.383286	−	0.923630i	$-0.374792\pi$
$701$	20.2961	0.766573	0.383286	+	0.923630i	$0.374792\pi$
$702$	−40.9001	−1.54367
$703$	0	0
$704$	−2.70721	−0.102032
$705$	20.6526	0.777821
$706$	−11.9425	−0.449463
$707$	12.4091	0.466694
$708$	−31.7731	−1.19411
$709$	26.3844	0.990887	0.495444	−	0.868640i	$-0.335006\pi$
$709$	26.3844	0.990887	0.495444	+	0.868640i	$0.335006\pi$
$710$	2.13866	0.0802625
$711$	100.471	3.76794
$712$	−8.35574	−0.313145
$713$	8.82105	0.330351
$714$	20.7841	0.777824
$715$	9.23441	0.345347
$716$	23.5378	0.879648
$717$	−35.9038	−1.34085
$718$	−22.9370	−0.856002
$719$	33.7903	1.26016	0.630082	−	0.776529i	$-0.283021\pi$
$719$	33.7903	1.26016	0.630082	+	0.776529i	$0.283021\pi$
$720$	−6.42844	−0.239574
$721$	−3.60252	−0.134165
$722$	0	0
$723$	−11.8861	−0.442048
$724$	11.0476	0.410579
$725$	−29.0709	−1.07967
$726$	11.4312	0.424251
$727$	−12.9012	−0.478479	−0.239239	−	0.970961i	$-0.576898\pi$
$727$	−12.9012	−0.478479	−0.239239	+	0.970961i	$0.576898\pi$
$728$	3.55327	0.131693
$729$	−2.03582	−0.0754007
$730$	8.23330	0.304728
$731$	1.88263	0.0696317
$732$	41.6898	1.54090
$733$	19.4232	0.717413	0.358706	−	0.933450i	$-0.383218\pi$
$733$	19.4232	0.717413	0.358706	+	0.933450i	$0.383218\pi$
$734$	14.2300	0.525240
$735$	2.98927	0.110261
$736$	3.52062	0.129772
$737$	11.2469	0.414284
$738$	−48.4950	−1.78512
$739$	1.37651	0.0506359	0.0253179	−	0.999679i	$-0.491940\pi$
$739$	1.37651	0.0506359	0.0253179	+	0.999679i	$0.491940\pi$
$740$	−7.29490	−0.268166
$741$	0	0
$742$	−9.51902	−0.349454
$743$	4.83509	0.177382	0.0886912	−	0.996059i	$-0.471732\pi$
$743$	4.83509	0.177382	0.0886912	+	0.996059i	$0.471732\pi$
$744$	−7.80203	−0.286036
$745$	−4.85165	−0.177751
$746$	−5.07840	−0.185933
$747$	−116.986	−4.28031
$748$	18.0695	0.660686
$749$	9.93200	0.362908
$750$	−27.1380	−0.990939
$751$	9.88523	0.360717	0.180359	−	0.983601i	$-0.442274\pi$
$751$	9.88523	0.360717	0.180359	+	0.983601i	$0.442274\pi$
$752$	6.90889	0.251941
$753$	−68.6119	−2.50036
$754$	25.3274	0.922371
$755$	7.21445	0.262561
$756$	−11.5106	−0.418635
$757$	20.3586	0.739947	0.369973	−	0.929042i	$-0.379367\pi$
$757$	20.3586	0.739947	0.369973	+	0.929042i	$0.379367\pi$
$758$	−4.95870	−0.180108
$759$	29.6790	1.07728
$760$	0	0
$761$	12.1626	0.440893	0.220446	−	0.975399i	$-0.429249\pi$
$761$	12.1626	0.440893	0.220446	+	0.975399i	$0.429249\pi$
$762$	−61.2360	−2.21835
$763$	−8.02328	−0.290462
$764$	7.32300	0.264937
$765$	42.9071	1.55131
$766$	−3.11820	−0.112665
$767$	36.2560	1.30913
$768$	−3.11392	−0.112364
$769$	43.6397	1.57369	0.786844	−	0.617151i	$-0.211713\pi$
$769$	43.6397	1.57369	0.786844	+	0.617151i	$0.211713\pi$
$770$	2.59885	0.0936560
$771$	38.6728	1.39277
$772$	21.2936	0.766374
$773$	24.2346	0.871660	0.435830	−	0.900029i	$-0.356455\pi$
$773$	24.2346	0.871660	0.435830	+	0.900029i	$0.356455\pi$
$774$	−1.88881	−0.0678921
$775$	−10.2187	−0.367067
$776$	13.2383	0.475226
$777$	−23.6629	−0.848902
$778$	12.7019	0.455384
$779$	0	0
$780$	10.6217	0.380318
$781$	6.03123	0.215814
$782$	−23.4986	−0.840310
$783$	−82.0465	−2.93210
$784$	1.00000	0.0357143
$785$	−2.02116	−0.0721384
$786$	−24.5810	−0.876777
$787$	−40.6719	−1.44980	−0.724898	−	0.688856i	$-0.758113\pi$
$787$	−40.6719	−1.44980	−0.724898	+	0.688856i	$0.758113\pi$
$788$	26.9859	0.961331
$789$	20.3175	0.723321
$790$	−14.4029	−0.512433
$791$	−7.08000	−0.251736
$792$	−18.1288	−0.644180
$793$	−47.5719	−1.68933
$794$	33.5926	1.19216
$795$	−28.4550	−1.00919
$796$	2.84678	0.100901
$797$	27.8150	0.985258	0.492629	−	0.870239i	$-0.336036\pi$
$797$	27.8150	0.985258	0.492629	+	0.870239i	$0.336036\pi$
$798$	0	0
$799$	−46.1139	−1.63139
$800$	−4.07845	−0.144195
$801$	−55.9541	−1.97704
$802$	−26.6682	−0.941686
$803$	23.2187	0.819370
$804$	12.9365	0.456235
$805$	−3.37970	−0.119119
$806$	8.90284	0.313589
$807$	−59.2409	−2.08538
$808$	12.4091	0.436552
$809$	41.6235	1.46340	0.731702	−	0.681625i	$-0.238726\pi$
$809$	41.6235	1.46340	0.731702	+	0.681625i	$0.238726\pi$
$810$	−15.1229	−0.531365
$811$	26.2635	0.922236	0.461118	−	0.887339i	$-0.347449\pi$
$811$	26.2635	0.922236	0.461118	+	0.887339i	$0.347449\pi$
$812$	7.12793	0.250141
$813$	34.8471	1.22214
$814$	−20.5723	−0.721060
$815$	−7.28614	−0.255222
$816$	20.7841	0.727588
$817$	0	0
$818$	−4.35206	−0.152166
$819$	23.7944	0.831444
$820$	6.95197	0.242773
$821$	42.7713	1.49273	0.746365	−	0.665537i	$-0.231798\pi$
$821$	42.7713	1.49273	0.746365	+	0.665537i	$0.231798\pi$
$822$	−23.1105	−0.806070
$823$	−45.8586	−1.59853	−0.799265	−	0.600978i	$-0.794778\pi$
$823$	−45.8586	−1.59853	−0.799265	+	0.600978i	$0.794778\pi$
$824$	−3.60252	−0.125500
$825$	−34.3815	−1.19701
$826$	10.2036	0.355027
$827$	32.5669	1.13246	0.566232	−	0.824246i	$-0.308401\pi$
$827$	32.5669	1.13246	0.566232	+	0.824246i	$0.308401\pi$
$828$	23.5758	0.819316
$829$	27.5270	0.956052	0.478026	−	0.878346i	$-0.341353\pi$
$829$	27.5270	0.956052	0.478026	+	0.878346i	$0.341353\pi$
$830$	16.7705	0.582114
$831$	−58.3948	−2.02569
$832$	3.55327	0.123187
$833$	−6.67457	−0.231260
$834$	−51.1945	−1.77272
$835$	8.46939	0.293095
$836$	0	0
$837$	−28.8401	−0.996860
$838$	9.26629	0.320099
$839$	12.2800	0.423951	0.211976	−	0.977275i	$-0.432010\pi$
$839$	12.2800	0.423951	0.211976	+	0.977275i	$0.432010\pi$
$840$	2.98927	0.103140
$841$	21.8074	0.751979
$842$	−17.3214	−0.596935
$843$	−20.2062	−0.695939
$844$	14.4955	0.498955
$845$	0.359310	0.0123606
$846$	46.2653	1.59063
$847$	−3.67099	−0.126137
$848$	−9.51902	−0.326885
$849$	−73.6217	−2.52669
$850$	27.2219	0.933704
$851$	26.7535	0.917098
$852$	6.93730	0.237668
$853$	4.00634	0.137174	0.0685872	−	0.997645i	$-0.478151\pi$
$853$	4.00634	0.137174	0.0685872	+	0.997645i	$0.478151\pi$
$854$	−13.3882	−0.458135
$855$	0	0
$856$	9.93200	0.339469
$857$	33.0216	1.12800	0.563998	−	0.825776i	$-0.309262\pi$
$857$	33.0216	1.12800	0.563998	+	0.825776i	$0.309262\pi$
$858$	29.9542	1.02262
$859$	36.4962	1.24523	0.622616	−	0.782527i	$-0.286070\pi$
$859$	36.4962	1.24523	0.622616	+	0.782527i	$0.286070\pi$
$860$	0.270770	0.00923319
$861$	22.5505	0.768520
$862$	−21.3963	−0.728760
$863$	−1.98259	−0.0674882	−0.0337441	−	0.999431i	$-0.510743\pi$
$863$	−1.98259	−0.0674882	−0.0337441	+	0.999431i	$0.510743\pi$
$864$	−11.5106	−0.391597
$865$	−3.01271	−0.102435
$866$	19.2137	0.652909
$867$	−85.7881	−2.91352
$868$	2.50554	0.0850434
$869$	−40.6176	−1.37786
$870$	21.3073	0.722387
$871$	−14.7617	−0.500182
$872$	−8.02328	−0.271702
$873$	88.6500	3.00035
$874$	0	0
$875$	8.71506	0.294623
$876$	26.7068	0.902341
$877$	−51.5828	−1.74183	−0.870913	−	0.491437i	$-0.836472\pi$
$877$	−51.5828	−1.74183	−0.870913	+	0.491437i	$0.836472\pi$
$878$	22.5139	0.759807
$879$	72.2738	2.43773
$880$	2.59885	0.0876072
$881$	−22.2677	−0.750217	−0.375109	−	0.926981i	$-0.622395\pi$
$881$	−22.2677	−0.750217	−0.375109	+	0.926981i	$0.622395\pi$
$882$	6.69649	0.225482
$883$	−35.4865	−1.19421	−0.597107	−	0.802161i	$-0.703683\pi$
$883$	−35.4865	−1.19421	−0.597107	+	0.802161i	$0.703683\pi$
$884$	−23.7165	−0.797673
$885$	30.5013	1.02529
$886$	0.978663	0.0328788
$887$	0.426198	0.0143103	0.00715516	−	0.999974i	$-0.497722\pi$
$887$	0.426198	0.0143103	0.00715516	+	0.999974i	$0.497722\pi$
$888$	−23.6629	−0.794075
$889$	19.6653	0.659552
$890$	8.02127	0.268874
$891$	−42.6481	−1.42876
$892$	17.6629	0.591399
$893$	0	0
$894$	−15.7376	−0.526344
$895$	−22.5956	−0.755287
$896$	1.00000	0.0334077
$897$	−38.9542	−1.30064
$898$	32.9060	1.09809
$899$	17.8593	0.595640
$900$	−27.3113	−0.910377
$901$	63.5354	2.11667
$902$	19.6052	0.652783
$903$	0.878313	0.0292284
$904$	−7.08000	−0.235477
$905$	−10.6053	−0.352533
$906$	23.4019	0.777477
$907$	2.37171	0.0787515	0.0393757	−	0.999224i	$-0.487463\pi$
$907$	2.37171	0.0787515	0.0393757	+	0.999224i	$0.487463\pi$
$908$	0.588393	0.0195265
$909$	83.0976	2.75618
$910$	−3.41104	−0.113075
$911$	8.99634	0.298062	0.149031	−	0.988833i	$-0.452385\pi$
$911$	8.99634	0.298062	0.149031	+	0.988833i	$0.452385\pi$
$912$	0	0
$913$	47.2946	1.56522
$914$	18.9971	0.628369
$915$	−40.0210	−1.32305
$916$	9.10188	0.300735
$917$	7.89393	0.260680
$918$	76.8280	2.53570
$919$	−38.6656	−1.27546	−0.637730	−	0.770260i	$-0.720127\pi$
$919$	−38.6656	−1.27546	−0.637730	+	0.770260i	$0.720127\pi$
$920$	−3.37970	−0.111425
$921$	78.0361	2.57138
$922$	−37.7120	−1.24198
$923$	−7.91610	−0.260562
$924$	8.43004	0.277328
$925$	−30.9925	−1.01903
$926$	−25.5830	−0.840708
$927$	−24.1242	−0.792343
$928$	7.12793	0.233986
$929$	−34.6761	−1.13768	−0.568842	−	0.822447i	$-0.692609\pi$
$929$	−34.6761	−1.13768	−0.568842	+	0.822447i	$0.692609\pi$
$930$	7.48973	0.245598
$931$	0	0
$932$	−25.0109	−0.819261
$933$	65.4384	2.14236
$934$	−4.52094	−0.147930
$935$	−17.3462	−0.567281
$936$	23.7944	0.777745
$937$	−43.0749	−1.40720	−0.703598	−	0.710598i	$-0.748424\pi$
$937$	−43.0749	−1.40720	−0.703598	+	0.710598i	$0.748424\pi$
$938$	−4.15441	−0.135646
$939$	−56.8220	−1.85431
$940$	−6.63234	−0.216323
$941$	−14.5064	−0.472895	−0.236448	−	0.971644i	$-0.575983\pi$
$941$	−14.5064	−0.472895	−0.236448	+	0.971644i	$0.575983\pi$
$942$	−6.55617	−0.213612
$943$	−25.4958	−0.830258
$944$	10.2036	0.332098
$945$	11.0498	0.359451
$946$	0.763598	0.0248267
$947$	1.49014	0.0484230	0.0242115	−	0.999707i	$-0.492292\pi$
$947$	1.49014	0.0484230	0.0242115	+	0.999707i	$0.492292\pi$
$948$	−46.7196	−1.51738
$949$	−30.4750	−0.989259
$950$	0	0
$951$	33.5046	1.08646
$952$	−6.67457	−0.216324
$953$	−14.8975	−0.482579	−0.241289	−	0.970453i	$-0.577570\pi$
$953$	−14.8975	−0.482579	−0.241289	+	0.970453i	$0.577570\pi$
$954$	−63.7440	−2.06379
$955$	−7.02987	−0.227481
$956$	11.5301	0.372910
$957$	60.0888	1.94239
$958$	−7.34593	−0.237336
$959$	7.42167	0.239658
$960$	2.98927	0.0964784
$961$	−24.7223	−0.797493
$962$	27.0016	0.870565
$963$	66.5095	2.14324
$964$	3.81708	0.122940
$965$	−20.4413	−0.658028
$966$	−10.9629	−0.352727
$967$	39.8232	1.28063	0.640313	−	0.768114i	$-0.278805\pi$
$967$	39.8232	1.28063	0.640313	+	0.768114i	$0.278805\pi$
$968$	−3.67099	−0.117990
$969$	0	0
$970$	−12.7084	−0.408041
$971$	−29.2717	−0.939373	−0.469687	−	0.882833i	$-0.655633\pi$
$971$	−29.2717	−0.939373	−0.469687	+	0.882833i	$0.655633\pi$
$972$	−14.5234	−0.465838
$973$	16.4405	0.527059
$974$	−6.74975	−0.216276
$975$	45.1264	1.44520
$976$	−13.3882	−0.428546
$977$	−6.77567	−0.216773	−0.108386	−	0.994109i	$-0.534568\pi$
$977$	−6.77567	−0.216773	−0.108386	+	0.994109i	$0.534568\pi$
$978$	−23.6345	−0.755747
$979$	22.6208	0.722963
$980$	−0.959972	−0.0306652
$981$	−53.7278	−1.71540
$982$	−14.7330	−0.470148
$983$	−47.7387	−1.52263	−0.761313	−	0.648384i	$-0.775445\pi$
$983$	−47.7387	−1.52263	−0.761313	+	0.648384i	$0.775445\pi$
$984$	22.5505	0.718885
$985$	−25.9057	−0.825423
$986$	−47.5759	−1.51512
$987$	−21.5137	−0.684789
$988$	0	0
$989$	−0.993029	−0.0315765
$990$	17.4032	0.553109
$991$	6.87025	0.218241	0.109120	−	0.994029i	$-0.465197\pi$
$991$	6.87025	0.218241	0.109120	+	0.994029i	$0.465197\pi$
$992$	2.50554	0.0795508
$993$	−112.416	−3.56740
$994$	−2.22784	−0.0706627
$995$	−2.73283	−0.0866364
$996$	54.3996	1.72372
$997$	19.0339	0.602808	0.301404	−	0.953497i	$-0.402545\pi$
$997$	19.0339	0.602808	0.301404	+	0.953497i	$0.402545\pi$
$998$	11.6484	0.368724
$999$	−87.4696	−2.76742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.be.1.1	yes	6
19.18	odd	2		5054.2.a.z.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.z.1.6	✓	6	19.18	odd	2
5054.2.a.be.1.1	yes	6	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.11392 q^{3} +1.00000 q^{4} -0.959972 q^{5} -3.11392 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.69649 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.11392 q^{3} +1.00000 q^{4} -0.959972 q^{5} -3.11392 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.69649 q^{9} -0.959972 q^{10} -2.70721 q^{11} -3.11392 q^{12} +3.55327 q^{13} +1.00000 q^{14} +2.98927 q^{15} +1.00000 q^{16} -6.67457 q^{17} +6.69649 q^{18} -0.959972 q^{20} -3.11392 q^{21} -2.70721 q^{22} +3.52062 q^{23} -3.11392 q^{24} -4.07845 q^{25} +3.55327 q^{26} -11.5106 q^{27} +1.00000 q^{28} +7.12793 q^{29} +2.98927 q^{30} +2.50554 q^{31} +1.00000 q^{32} +8.43004 q^{33} -6.67457 q^{34} -0.959972 q^{35} +6.69649 q^{36} +7.59908 q^{37} -11.0646 q^{39} -0.959972 q^{40} -7.24185 q^{41} -3.11392 q^{42} -0.282061 q^{43} -2.70721 q^{44} -6.42844 q^{45} +3.52062 q^{46} +6.90889 q^{47} -3.11392 q^{48} +1.00000 q^{49} -4.07845 q^{50} +20.7841 q^{51} +3.55327 q^{52} -9.51902 q^{53} -11.5106 q^{54} +2.59885 q^{55} +1.00000 q^{56} +7.12793 q^{58} +10.2036 q^{59} +2.98927 q^{60} -13.3882 q^{61} +2.50554 q^{62} +6.69649 q^{63} +1.00000 q^{64} -3.41104 q^{65} +8.43004 q^{66} -4.15441 q^{67} -6.67457 q^{68} -10.9629 q^{69} -0.959972 q^{70} -2.22784 q^{71} +6.69649 q^{72} -8.57661 q^{73} +7.59908 q^{74} +12.7000 q^{75} -2.70721 q^{77} -11.0646 q^{78} +15.0035 q^{79} -0.959972 q^{80} +15.7535 q^{81} -7.24185 q^{82} -17.4698 q^{83} -3.11392 q^{84} +6.40740 q^{85} -0.282061 q^{86} -22.1958 q^{87} -2.70721 q^{88} -8.35574 q^{89} -6.42844 q^{90} +3.55327 q^{91} +3.52062 q^{92} -7.80203 q^{93} +6.90889 q^{94} -3.11392 q^{96} +13.2383 q^{97} +1.00000 q^{98} -18.1288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} - q^{10} + 4 q^{11} + 15 q^{13} + 6 q^{14} + 6 q^{15} + 6 q^{16} - 9 q^{17} + 8 q^{18} - q^{20} + 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} - 12 q^{27} + 6 q^{28} + 7 q^{29} + 6 q^{30} + 4 q^{31} + 6 q^{32} + 28 q^{33} - 9 q^{34} - q^{35} + 8 q^{36} + 3 q^{37} - 8 q^{39} - q^{40} + 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} + 4 q^{46} + 12 q^{47} + 6 q^{49} + q^{50} + 44 q^{51} + 15 q^{52} - 5 q^{53} - 12 q^{54} - 8 q^{55} + 6 q^{56} + 7 q^{58} + 4 q^{59} + 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} - 20 q^{65} + 28 q^{66} + 14 q^{67} - 9 q^{68} - 24 q^{69} - q^{70} + 24 q^{71} + 8 q^{72} - 21 q^{73} + 3 q^{74} + 12 q^{75} + 4 q^{77} - 8 q^{78} + 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} - 10 q^{86} - 8 q^{87} + 4 q^{88} + 7 q^{89} + 19 q^{90} + 15 q^{91} + 4 q^{92} - 22 q^{93} + 12 q^{94} + 7 q^{97} + 6 q^{98} - 26 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 - q^10 + 4 * q^11 + 15 * q^13 + 6 * q^14 + 6 * q^15 + 6 * q^16 - 9 * q^17 + 8 * q^18 - q^20 + 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 - 12 * q^27 + 6 * q^28 + 7 * q^29 + 6 * q^30 + 4 * q^31 + 6 * q^32 + 28 * q^33 - 9 * q^34 - q^35 + 8 * q^36 + 3 * q^37 - 8 * q^39 - q^40 + 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 + 4 * q^46 + 12 * q^47 + 6 * q^49 + q^50 + 44 * q^51 + 15 * q^52 - 5 * q^53 - 12 * q^54 - 8 * q^55 + 6 * q^56 + 7 * q^58 + 4 * q^59 + 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 - 20 * q^65 + 28 * q^66 + 14 * q^67 - 9 * q^68 - 24 * q^69 - q^70 + 24 * q^71 + 8 * q^72 - 21 * q^73 + 3 * q^74 + 12 * q^75 + 4 * q^77 - 8 * q^78 + 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 - 10 * q^86 - 8 * q^87 + 4 * q^88 + 7 * q^89 + 19 * q^90 + 15 * q^91 + 4 * q^92 - 22 * q^93 + 12 * q^94 + 7 * q^97 + 6 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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