LMFDB - Embedded newform 5054.2.a.f.1.2

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
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			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} -5.00000 q^{11} +0.618034 q^{12} -4.85410 q^{13} +1.00000 q^{14} +0.618034 q^{15} +1.00000 q^{16} +6.85410 q^{17} +2.61803 q^{18} +1.00000 q^{20} -0.618034 q^{21} +5.00000 q^{22} -3.76393 q^{23} -0.618034 q^{24} -4.00000 q^{25} +4.85410 q^{26} -3.47214 q^{27} -1.00000 q^{28} +8.23607 q^{29} -0.618034 q^{30} +6.70820 q^{31} -1.00000 q^{32} -3.09017 q^{33} -6.85410 q^{34} -1.00000 q^{35} -2.61803 q^{36} -5.94427 q^{37} -3.00000 q^{39} -1.00000 q^{40} +1.09017 q^{41} +0.618034 q^{42} -6.85410 q^{43} -5.00000 q^{44} -2.61803 q^{45} +3.76393 q^{46} +7.94427 q^{47} +0.618034 q^{48} +1.00000 q^{49} +4.00000 q^{50} +4.23607 q^{51} -4.85410 q^{52} +12.7082 q^{53} +3.47214 q^{54} -5.00000 q^{55} +1.00000 q^{56} -8.23607 q^{58} -11.0000 q^{59} +0.618034 q^{60} +7.47214 q^{61} -6.70820 q^{62} +2.61803 q^{63} +1.00000 q^{64} -4.85410 q^{65} +3.09017 q^{66} -7.85410 q^{67} +6.85410 q^{68} -2.32624 q^{69} +1.00000 q^{70} +10.0000 q^{71} +2.61803 q^{72} -14.5623 q^{73} +5.94427 q^{74} -2.47214 q^{75} +5.00000 q^{77} +3.00000 q^{78} +8.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -1.09017 q^{82} -15.4164 q^{83} -0.618034 q^{84} +6.85410 q^{85} +6.85410 q^{86} +5.09017 q^{87} +5.00000 q^{88} -4.85410 q^{89} +2.61803 q^{90} +4.85410 q^{91} -3.76393 q^{92} +4.14590 q^{93} -7.94427 q^{94} -0.618034 q^{96} +9.47214 q^{97} -1.00000 q^{98} +13.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} - 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} + 3 q^{18} + 2 q^{20} + q^{21} + 10 q^{22} - 12 q^{23} + q^{24} - 8 q^{25} + 3 q^{26} + 2 q^{27} - 2 q^{28} + 12 q^{29} + q^{30} - 2 q^{32} + 5 q^{33} - 7 q^{34} - 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 2 q^{40} - 9 q^{41} - q^{42} - 7 q^{43} - 10 q^{44} - 3 q^{45} + 12 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} + 8 q^{50} + 4 q^{51} - 3 q^{52} + 12 q^{53} - 2 q^{54} - 10 q^{55} + 2 q^{56} - 12 q^{58} - 22 q^{59} - q^{60} + 6 q^{61} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 5 q^{66} - 9 q^{67} + 7 q^{68} + 11 q^{69} + 2 q^{70} + 20 q^{71} + 3 q^{72} - 9 q^{73} - 6 q^{74} + 4 q^{75} + 10 q^{77} + 6 q^{78} + 11 q^{79} + 2 q^{80} - 2 q^{81} + 9 q^{82} - 4 q^{83} + q^{84} + 7 q^{85} + 7 q^{86} - q^{87} + 10 q^{88} - 3 q^{89} + 3 q^{90} + 3 q^{91} - 12 q^{92} + 15 q^{93} + 2 q^{94} + q^{96} + 10 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9 - 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 7 * q^17 + 3 * q^18 + 2 * q^20 + q^21 + 10 * q^22 - 12 * q^23 + q^24 - 8 * q^25 + 3 * q^26 + 2 * q^27 - 2 * q^28 + 12 * q^29 + q^30 - 2 * q^32 + 5 * q^33 - 7 * q^34 - 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 2 * q^40 - 9 * q^41 - q^42 - 7 * q^43 - 10 * q^44 - 3 * q^45 + 12 * q^46 - 2 * q^47 - q^48 + 2 * q^49 + 8 * q^50 + 4 * q^51 - 3 * q^52 + 12 * q^53 - 2 * q^54 - 10 * q^55 + 2 * q^56 - 12 * q^58 - 22 * q^59 - q^60 + 6 * q^61 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 5 * q^66 - 9 * q^67 + 7 * q^68 + 11 * q^69 + 2 * q^70 + 20 * q^71 + 3 * q^72 - 9 * q^73 - 6 * q^74 + 4 * q^75 + 10 * q^77 + 6 * q^78 + 11 * q^79 + 2 * q^80 - 2 * q^81 + 9 * q^82 - 4 * q^83 + q^84 + 7 * q^85 + 7 * q^86 - q^87 + 10 * q^88 - 3 * q^89 + 3 * q^90 + 3 * q^91 - 12 * q^92 + 15 * q^93 + 2 * q^94 + q^96 + 10 * q^97 - 2 * q^98 + 15 * 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
$3$	0.618034	0.356822	0.178411	−	0.983956i	$-0.442904\pi$
$3$	0.618034	0.356822	0.178411	+	0.983956i	$0.442904\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.618034	−0.252311
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.61803	−0.872678
$10$	−1.00000	−0.316228
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0.618034	0.178411
$13$	−4.85410	−1.34629	−0.673143	−	0.739512i	$-0.735056\pi$
$13$	−4.85410	−1.34629	−0.673143	+	0.739512i	$0.735056\pi$
$14$	1.00000	0.267261
$15$	0.618034	0.159576
$16$	1.00000	0.250000
$17$	6.85410	1.66236	0.831182	−	0.556001i	$-0.187665\pi$
$17$	6.85410	1.66236	0.831182	+	0.556001i	$0.187665\pi$
$18$	2.61803	0.617077
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	−0.618034	−0.134866
$22$	5.00000	1.06600
$23$	−3.76393	−0.784834	−0.392417	−	0.919787i	$-0.628361\pi$
$23$	−3.76393	−0.784834	−0.392417	+	0.919787i	$0.628361\pi$
$24$	−0.618034	−0.126156
$25$	−4.00000	−0.800000
$26$	4.85410	0.951968
$27$	−3.47214	−0.668213
$28$	−1.00000	−0.188982
$29$	8.23607	1.52940	0.764700	−	0.644387i	$-0.222887\pi$
$29$	8.23607	1.52940	0.764700	+	0.644387i	$0.222887\pi$
$30$	−0.618034	−0.112837
$31$	6.70820	1.20483	0.602414	−	0.798183i	$-0.294205\pi$
$31$	6.70820	1.20483	0.602414	+	0.798183i	$0.294205\pi$
$32$	−1.00000	−0.176777
$33$	−3.09017	−0.537930
$34$	−6.85410	−1.17547
$35$	−1.00000	−0.169031
$36$	−2.61803	−0.436339
$37$	−5.94427	−0.977232	−0.488616	−	0.872499i	$-0.662498\pi$
$37$	−5.94427	−0.977232	−0.488616	+	0.872499i	$0.662498\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	−1.00000	−0.158114
$41$	1.09017	0.170256	0.0851280	−	0.996370i	$-0.472870\pi$
$41$	1.09017	0.170256	0.0851280	+	0.996370i	$0.472870\pi$
$42$	0.618034	0.0953647
$43$	−6.85410	−1.04524	−0.522620	−	0.852566i	$-0.675045\pi$
$43$	−6.85410	−1.04524	−0.522620	+	0.852566i	$0.675045\pi$
$44$	−5.00000	−0.753778
$45$	−2.61803	−0.390273
$46$	3.76393	0.554962
$47$	7.94427	1.15879	0.579396	−	0.815046i	$-0.303289\pi$
$47$	7.94427	1.15879	0.579396	+	0.815046i	$0.303289\pi$
$48$	0.618034	0.0892055
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	4.23607	0.593168
$52$	−4.85410	−0.673143
$53$	12.7082	1.74561	0.872803	−	0.488073i	$-0.162300\pi$
$53$	12.7082	1.74561	0.872803	+	0.488073i	$0.162300\pi$
$54$	3.47214	0.472498
$55$	−5.00000	−0.674200
$56$	1.00000	0.133631
$57$	0	0
$58$	−8.23607	−1.08145
$59$	−11.0000	−1.43208	−0.716039	−	0.698060i	$-0.754047\pi$
$59$	−11.0000	−1.43208	−0.716039	+	0.698060i	$0.754047\pi$
$60$	0.618034	0.0797878
$61$	7.47214	0.956709	0.478354	−	0.878167i	$-0.341233\pi$
$61$	7.47214	0.956709	0.478354	+	0.878167i	$0.341233\pi$
$62$	−6.70820	−0.851943
$63$	2.61803	0.329841
$64$	1.00000	0.125000
$65$	−4.85410	−0.602077
$66$	3.09017	0.380374
$67$	−7.85410	−0.959531	−0.479766	−	0.877397i	$-0.659278\pi$
$67$	−7.85410	−0.959531	−0.479766	+	0.877397i	$0.659278\pi$
$68$	6.85410	0.831182
$69$	−2.32624	−0.280046
$70$	1.00000	0.119523
$71$	10.0000	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$71$	10.0000	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$72$	2.61803	0.308538
$73$	−14.5623	−1.70439	−0.852194	−	0.523225i	$-0.824729\pi$
$73$	−14.5623	−1.70439	−0.852194	+	0.523225i	$0.824729\pi$
$74$	5.94427	0.691008
$75$	−2.47214	−0.285458
$76$	0	0
$77$	5.00000	0.569803
$78$	3.00000	0.339683
$79$	8.85410	0.996164	0.498082	−	0.867130i	$-0.334038\pi$
$79$	8.85410	0.996164	0.498082	+	0.867130i	$0.334038\pi$
$80$	1.00000	0.111803
$81$	5.70820	0.634245
$82$	−1.09017	−0.120389
$83$	−15.4164	−1.69217	−0.846085	−	0.533048i	$-0.821047\pi$
$83$	−15.4164	−1.69217	−0.846085	+	0.533048i	$0.821047\pi$
$84$	−0.618034	−0.0674330
$85$	6.85410	0.743432
$86$	6.85410	0.739097
$87$	5.09017	0.545724
$88$	5.00000	0.533002
$89$	−4.85410	−0.514534	−0.257267	−	0.966340i	$-0.582822\pi$
$89$	−4.85410	−0.514534	−0.257267	+	0.966340i	$0.582822\pi$
$90$	2.61803	0.275965
$91$	4.85410	0.508848
$92$	−3.76393	−0.392417
$93$	4.14590	0.429910
$94$	−7.94427	−0.819389
$95$	0	0
$96$	−0.618034	−0.0630778
$97$	9.47214	0.961750	0.480875	−	0.876789i	$-0.340319\pi$
$97$	9.47214	0.961750	0.480875	+	0.876789i	$0.340319\pi$
$98$	−1.00000	−0.101015
$99$	13.0902	1.31561
$100$	−4.00000	−0.400000
$101$	4.14590	0.412532	0.206266	−	0.978496i	$-0.433869\pi$
$101$	4.14590	0.412532	0.206266	+	0.978496i	$0.433869\pi$
$102$	−4.23607	−0.419433
$103$	15.0902	1.48688	0.743439	−	0.668803i	$-0.233193\pi$
$103$	15.0902	1.48688	0.743439	+	0.668803i	$0.233193\pi$
$104$	4.85410	0.475984
$105$	−0.618034	−0.0603139
$106$	−12.7082	−1.23433
$107$	13.9443	1.34804	0.674022	−	0.738711i	$-0.264565\pi$
$107$	13.9443	1.34804	0.674022	+	0.738711i	$0.264565\pi$
$108$	−3.47214	−0.334106
$109$	13.5623	1.29903	0.649517	−	0.760347i	$-0.274971\pi$
$109$	13.5623	1.29903	0.649517	+	0.760347i	$0.274971\pi$
$110$	5.00000	0.476731
$111$	−3.67376	−0.348698
$112$	−1.00000	−0.0944911
$113$	−3.85410	−0.362563	−0.181282	−	0.983431i	$-0.558025\pi$
$113$	−3.85410	−0.362563	−0.181282	+	0.983431i	$0.558025\pi$
$114$	0	0
$115$	−3.76393	−0.350988
$116$	8.23607	0.764700
$117$	12.7082	1.17487
$118$	11.0000	1.01263
$119$	−6.85410	−0.628314
$120$	−0.618034	−0.0564185
$121$	14.0000	1.27273
$122$	−7.47214	−0.676495
$123$	0.673762	0.0607511
$124$	6.70820	0.602414
$125$	−9.00000	−0.804984
$126$	−2.61803	−0.233233
$127$	7.32624	0.650098	0.325049	−	0.945697i	$-0.394619\pi$
$127$	7.32624	0.650098	0.325049	+	0.945697i	$0.394619\pi$
$128$	−1.00000	−0.0883883
$129$	−4.23607	−0.372965
$130$	4.85410	0.425733
$131$	−4.38197	−0.382854	−0.191427	−	0.981507i	$-0.561312\pi$
$131$	−4.38197	−0.382854	−0.191427	+	0.981507i	$0.561312\pi$
$132$	−3.09017	−0.268965
$133$	0	0
$134$	7.85410	0.678491
$135$	−3.47214	−0.298834
$136$	−6.85410	−0.587734
$137$	21.1246	1.80480	0.902399	−	0.430902i	$-0.141805\pi$
$137$	21.1246	1.80480	0.902399	+	0.430902i	$0.141805\pi$
$138$	2.32624	0.198023
$139$	−0.236068	−0.0200230	−0.0100115	−	0.999950i	$-0.503187\pi$
$139$	−0.236068	−0.0200230	−0.0100115	+	0.999950i	$0.503187\pi$
$140$	−1.00000	−0.0845154
$141$	4.90983	0.413482
$142$	−10.0000	−0.839181
$143$	24.2705	2.02960
$144$	−2.61803	−0.218169
$145$	8.23607	0.683968
$146$	14.5623	1.20519
$147$	0.618034	0.0509746
$148$	−5.94427	−0.488616
$149$	1.38197	0.113215	0.0566075	−	0.998397i	$-0.481972\pi$
$149$	1.38197	0.113215	0.0566075	+	0.998397i	$0.481972\pi$
$150$	2.47214	0.201849
$151$	14.2361	1.15851	0.579257	−	0.815145i	$-0.303343\pi$
$151$	14.2361	1.15851	0.579257	+	0.815145i	$0.303343\pi$
$152$	0	0
$153$	−17.9443	−1.45071
$154$	−5.00000	−0.402911
$155$	6.70820	0.538816
$156$	−3.00000	−0.240192
$157$	22.3262	1.78183	0.890914	−	0.454172i	$-0.150065\pi$
$157$	22.3262	1.78183	0.890914	+	0.454172i	$0.150065\pi$
$158$	−8.85410	−0.704395
$159$	7.85410	0.622871
$160$	−1.00000	−0.0790569
$161$	3.76393	0.296639
$162$	−5.70820	−0.448479
$163$	0.472136	0.0369805	0.0184903	−	0.999829i	$-0.494114\pi$
$163$	0.472136	0.0369805	0.0184903	+	0.999829i	$0.494114\pi$
$164$	1.09017	0.0851280
$165$	−3.09017	−0.240569
$166$	15.4164	1.19655
$167$	−1.81966	−0.140810	−0.0704048	−	0.997519i	$-0.522429\pi$
$167$	−1.81966	−0.140810	−0.0704048	+	0.997519i	$0.522429\pi$
$168$	0.618034	0.0476824
$169$	10.5623	0.812485
$170$	−6.85410	−0.525686
$171$	0	0
$172$	−6.85410	−0.522620
$173$	−1.76393	−0.134109	−0.0670546	−	0.997749i	$-0.521360\pi$
$173$	−1.76393	−0.134109	−0.0670546	+	0.997749i	$0.521360\pi$
$174$	−5.09017	−0.385885
$175$	4.00000	0.302372
$176$	−5.00000	−0.376889
$177$	−6.79837	−0.510997
$178$	4.85410	0.363830
$179$	−9.03444	−0.675266	−0.337633	−	0.941278i	$-0.609626\pi$
$179$	−9.03444	−0.675266	−0.337633	+	0.941278i	$0.609626\pi$
$180$	−2.61803	−0.195137
$181$	15.7639	1.17172	0.585862	−	0.810411i	$-0.300756\pi$
$181$	15.7639	1.17172	0.585862	+	0.810411i	$0.300756\pi$
$182$	−4.85410	−0.359810
$183$	4.61803	0.341375
$184$	3.76393	0.277481
$185$	−5.94427	−0.437032
$186$	−4.14590	−0.303992
$187$	−34.2705	−2.50611
$188$	7.94427	0.579396
$189$	3.47214	0.252561
$190$	0	0
$191$	2.81966	0.204023	0.102012	−	0.994783i	$-0.467472\pi$
$191$	2.81966	0.204023	0.102012	+	0.994783i	$0.467472\pi$
$192$	0.618034	0.0446028
$193$	10.1803	0.732797	0.366398	−	0.930458i	$-0.380591\pi$
$193$	10.1803	0.732797	0.366398	+	0.930458i	$0.380591\pi$
$194$	−9.47214	−0.680060
$195$	−3.00000	−0.214834
$196$	1.00000	0.0714286
$197$	−7.56231	−0.538792	−0.269396	−	0.963029i	$-0.586824\pi$
$197$	−7.56231	−0.538792	−0.269396	+	0.963029i	$0.586824\pi$
$198$	−13.0902	−0.930278
$199$	−4.90983	−0.348049	−0.174024	−	0.984741i	$-0.555677\pi$
$199$	−4.90983	−0.348049	−0.174024	+	0.984741i	$0.555677\pi$
$200$	4.00000	0.282843
$201$	−4.85410	−0.342382
$202$	−4.14590	−0.291704
$203$	−8.23607	−0.578059
$204$	4.23607	0.296584
$205$	1.09017	0.0761408
$206$	−15.0902	−1.05138
$207$	9.85410	0.684907
$208$	−4.85410	−0.336571
$209$	0	0
$210$	0.618034	0.0426484
$211$	4.05573	0.279208	0.139604	−	0.990207i	$-0.455417\pi$
$211$	4.05573	0.279208	0.139604	+	0.990207i	$0.455417\pi$
$212$	12.7082	0.872803
$213$	6.18034	0.423470
$214$	−13.9443	−0.953211
$215$	−6.85410	−0.467446
$216$	3.47214	0.236249
$217$	−6.70820	−0.455383
$218$	−13.5623	−0.918555
$219$	−9.00000	−0.608164
$220$	−5.00000	−0.337100
$221$	−33.2705	−2.23802
$222$	3.67376	0.246567
$223$	−5.65248	−0.378518	−0.189259	−	0.981927i	$-0.560609\pi$
$223$	−5.65248	−0.378518	−0.189259	+	0.981927i	$0.560609\pi$
$224$	1.00000	0.0668153
$225$	10.4721	0.698142
$226$	3.85410	0.256371
$227$	14.2361	0.944881	0.472441	−	0.881363i	$-0.343373\pi$
$227$	14.2361	0.944881	0.472441	+	0.881363i	$0.343373\pi$
$228$	0	0
$229$	−10.0902	−0.666777	−0.333389	−	0.942790i	$-0.608192\pi$
$229$	−10.0902	−0.666777	−0.333389	+	0.942790i	$0.608192\pi$
$230$	3.76393	0.248186
$231$	3.09017	0.203318
$232$	−8.23607	−0.540724
$233$	−11.0344	−0.722890	−0.361445	−	0.932393i	$-0.617717\pi$
$233$	−11.0344	−0.722890	−0.361445	+	0.932393i	$0.617717\pi$
$234$	−12.7082	−0.830761
$235$	7.94427	0.518227
$236$	−11.0000	−0.716039
$237$	5.47214	0.355453
$238$	6.85410	0.444285
$239$	−11.1459	−0.720968	−0.360484	−	0.932765i	$-0.617388\pi$
$239$	−11.1459	−0.720968	−0.360484	+	0.932765i	$0.617388\pi$
$240$	0.618034	0.0398939
$241$	−7.90983	−0.509517	−0.254758	−	0.967005i	$-0.581996\pi$
$241$	−7.90983	−0.509517	−0.254758	+	0.967005i	$0.581996\pi$
$242$	−14.0000	−0.899954
$243$	13.9443	0.894525
$244$	7.47214	0.478354
$245$	1.00000	0.0638877
$246$	−0.673762	−0.0429575
$247$	0	0
$248$	−6.70820	−0.425971
$249$	−9.52786	−0.603804
$250$	9.00000	0.569210
$251$	6.47214	0.408518	0.204259	−	0.978917i	$-0.434522\pi$
$251$	6.47214	0.408518	0.204259	+	0.978917i	$0.434522\pi$
$252$	2.61803	0.164921
$253$	18.8197	1.18318
$254$	−7.32624	−0.459689
$255$	4.23607	0.265273
$256$	1.00000	0.0625000
$257$	−8.05573	−0.502503	−0.251251	−	0.967922i	$-0.580842\pi$
$257$	−8.05573	−0.502503	−0.251251	+	0.967922i	$0.580842\pi$
$258$	4.23607	0.263726
$259$	5.94427	0.369359
$260$	−4.85410	−0.301039
$261$	−21.5623	−1.33467
$262$	4.38197	0.270719
$263$	−25.1803	−1.55269	−0.776343	−	0.630311i	$-0.782928\pi$
$263$	−25.1803	−1.55269	−0.776343	+	0.630311i	$0.782928\pi$
$264$	3.09017	0.190187
$265$	12.7082	0.780659
$266$	0	0
$267$	−3.00000	−0.183597
$268$	−7.85410	−0.479766
$269$	−9.18034	−0.559735	−0.279868	−	0.960039i	$-0.590291\pi$
$269$	−9.18034	−0.559735	−0.279868	+	0.960039i	$0.590291\pi$
$270$	3.47214	0.211307
$271$	1.65248	0.100381	0.0501904	−	0.998740i	$-0.484017\pi$
$271$	1.65248	0.100381	0.0501904	+	0.998740i	$0.484017\pi$
$272$	6.85410	0.415591
$273$	3.00000	0.181568
$274$	−21.1246	−1.27618
$275$	20.0000	1.20605
$276$	−2.32624	−0.140023
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	0.236068	0.0141584
$279$	−17.5623	−1.05143
$280$	1.00000	0.0597614
$281$	12.2361	0.729943	0.364971	−	0.931019i	$-0.381079\pi$
$281$	12.2361	0.729943	0.364971	+	0.931019i	$0.381079\pi$
$282$	−4.90983	−0.292376
$283$	6.43769	0.382681	0.191341	−	0.981524i	$-0.438716\pi$
$283$	6.43769	0.382681	0.191341	+	0.981524i	$0.438716\pi$
$284$	10.0000	0.593391
$285$	0	0
$286$	−24.2705	−1.43515
$287$	−1.09017	−0.0643507
$288$	2.61803	0.154269
$289$	29.9787	1.76345
$290$	−8.23607	−0.483639
$291$	5.85410	0.343174
$292$	−14.5623	−0.852194
$293$	−16.2361	−0.948521	−0.474261	−	0.880385i	$-0.657285\pi$
$293$	−16.2361	−0.948521	−0.474261	+	0.880385i	$0.657285\pi$
$294$	−0.618034	−0.0360445
$295$	−11.0000	−0.640445
$296$	5.94427	0.345504
$297$	17.3607	1.00737
$298$	−1.38197	−0.0800551
$299$	18.2705	1.05661
$300$	−2.47214	−0.142729
$301$	6.85410	0.395064
$302$	−14.2361	−0.819194
$303$	2.56231	0.147201
$304$	0	0
$305$	7.47214	0.427853
$306$	17.9443	1.02581
$307$	−4.94427	−0.282185	−0.141092	−	0.989996i	$-0.545061\pi$
$307$	−4.94427	−0.282185	−0.141092	+	0.989996i	$0.545061\pi$
$308$	5.00000	0.284901
$309$	9.32624	0.530551
$310$	−6.70820	−0.381000
$311$	19.7639	1.12071	0.560355	−	0.828253i	$-0.310665\pi$
$311$	19.7639	1.12071	0.560355	+	0.828253i	$0.310665\pi$
$312$	3.00000	0.169842
$313$	18.9098	1.06885	0.534423	−	0.845217i	$-0.320529\pi$
$313$	18.9098	1.06885	0.534423	+	0.845217i	$0.320529\pi$
$314$	−22.3262	−1.25994
$315$	2.61803	0.147510
$316$	8.85410	0.498082
$317$	−8.41641	−0.472713	−0.236356	−	0.971666i	$-0.575953\pi$
$317$	−8.41641	−0.472713	−0.236356	+	0.971666i	$0.575953\pi$
$318$	−7.85410	−0.440436
$319$	−41.1803	−2.30566
$320$	1.00000	0.0559017
$321$	8.61803	0.481012
$322$	−3.76393	−0.209756
$323$	0	0
$324$	5.70820	0.317122
$325$	19.4164	1.07703
$326$	−0.472136	−0.0261492
$327$	8.38197	0.463524
$328$	−1.09017	−0.0601946
$329$	−7.94427	−0.437982
$330$	3.09017	0.170108
$331$	−12.4721	−0.685531	−0.342765	−	0.939421i	$-0.611364\pi$
$331$	−12.4721	−0.685531	−0.342765	+	0.939421i	$0.611364\pi$
$332$	−15.4164	−0.846085
$333$	15.5623	0.852809
$334$	1.81966	0.0995674
$335$	−7.85410	−0.429115
$336$	−0.618034	−0.0337165
$337$	33.4508	1.82218	0.911092	−	0.412203i	$-0.135241\pi$
$337$	33.4508	1.82218	0.911092	+	0.412203i	$0.135241\pi$
$338$	−10.5623	−0.574514
$339$	−2.38197	−0.129371
$340$	6.85410	0.371716
$341$	−33.5410	−1.81635
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	6.85410	0.369548
$345$	−2.32624	−0.125240
$346$	1.76393	0.0948296
$347$	−5.05573	−0.271406	−0.135703	−	0.990750i	$-0.543329\pi$
$347$	−5.05573	−0.271406	−0.135703	+	0.990750i	$0.543329\pi$
$348$	5.09017	0.272862
$349$	−6.70820	−0.359082	−0.179541	−	0.983750i	$-0.557461\pi$
$349$	−6.70820	−0.359082	−0.179541	+	0.983750i	$0.557461\pi$
$350$	−4.00000	−0.213809
$351$	16.8541	0.899605
$352$	5.00000	0.266501
$353$	13.0902	0.696719	0.348360	−	0.937361i	$-0.386739\pi$
$353$	13.0902	0.696719	0.348360	+	0.937361i	$0.386739\pi$
$354$	6.79837	0.361329
$355$	10.0000	0.530745
$356$	−4.85410	−0.257267
$357$	−4.23607	−0.224196
$358$	9.03444	0.477485
$359$	27.9443	1.47484	0.737421	−	0.675433i	$-0.236043\pi$
$359$	27.9443	1.47484	0.737421	+	0.675433i	$0.236043\pi$
$360$	2.61803	0.137983
$361$	0	0
$362$	−15.7639	−0.828534
$363$	8.65248	0.454137
$364$	4.85410	0.254424
$365$	−14.5623	−0.762226
$366$	−4.61803	−0.241389
$367$	9.67376	0.504966	0.252483	−	0.967601i	$-0.418753\pi$
$367$	9.67376	0.504966	0.252483	+	0.967601i	$0.418753\pi$
$368$	−3.76393	−0.196209
$369$	−2.85410	−0.148579
$370$	5.94427	0.309028
$371$	−12.7082	−0.659777
$372$	4.14590	0.214955
$373$	6.85410	0.354892	0.177446	−	0.984131i	$-0.443216\pi$
$373$	6.85410	0.354892	0.177446	+	0.984131i	$0.443216\pi$
$374$	34.2705	1.77209
$375$	−5.56231	−0.287236
$376$	−7.94427	−0.409695
$377$	−39.9787	−2.05901
$378$	−3.47214	−0.178587
$379$	−12.0344	−0.618168	−0.309084	−	0.951035i	$-0.600022\pi$
$379$	−12.0344	−0.618168	−0.309084	+	0.951035i	$0.600022\pi$
$380$	0	0
$381$	4.52786	0.231970
$382$	−2.81966	−0.144266
$383$	−5.94427	−0.303738	−0.151869	−	0.988401i	$-0.548529\pi$
$383$	−5.94427	−0.303738	−0.151869	+	0.988401i	$0.548529\pi$
$384$	−0.618034	−0.0315389
$385$	5.00000	0.254824
$386$	−10.1803	−0.518166
$387$	17.9443	0.912159
$388$	9.47214	0.480875
$389$	11.3820	0.577089	0.288544	−	0.957467i	$-0.406829\pi$
$389$	11.3820	0.577089	0.288544	+	0.957467i	$0.406829\pi$
$390$	3.00000	0.151911
$391$	−25.7984	−1.30468
$392$	−1.00000	−0.0505076
$393$	−2.70820	−0.136611
$394$	7.56231	0.380983
$395$	8.85410	0.445498
$396$	13.0902	0.657806
$397$	−32.2705	−1.61961	−0.809805	−	0.586699i	$-0.800427\pi$
$397$	−32.2705	−1.61961	−0.809805	+	0.586699i	$0.800427\pi$
$398$	4.90983	0.246108
$399$	0	0
$400$	−4.00000	−0.200000
$401$	6.58359	0.328769	0.164384	−	0.986396i	$-0.447436\pi$
$401$	6.58359	0.328769	0.164384	+	0.986396i	$0.447436\pi$
$402$	4.85410	0.242101
$403$	−32.5623	−1.62204
$404$	4.14590	0.206266
$405$	5.70820	0.283643
$406$	8.23607	0.408749
$407$	29.7214	1.47323
$408$	−4.23607	−0.209717
$409$	−17.2148	−0.851216	−0.425608	−	0.904908i	$-0.639940\pi$
$409$	−17.2148	−0.851216	−0.425608	+	0.904908i	$0.639940\pi$
$410$	−1.09017	−0.0538397
$411$	13.0557	0.643992
$412$	15.0902	0.743439
$413$	11.0000	0.541275
$414$	−9.85410	−0.484303
$415$	−15.4164	−0.756762
$416$	4.85410	0.237992
$417$	−0.145898	−0.00714466
$418$	0	0
$419$	−25.7426	−1.25761	−0.628805	−	0.777563i	$-0.716456\pi$
$419$	−25.7426	−1.25761	−0.628805	+	0.777563i	$0.716456\pi$
$420$	−0.618034	−0.0301570
$421$	8.05573	0.392612	0.196306	−	0.980543i	$-0.437105\pi$
$421$	8.05573	0.392612	0.196306	+	0.980543i	$0.437105\pi$
$422$	−4.05573	−0.197430
$423$	−20.7984	−1.01125
$424$	−12.7082	−0.617165
$425$	−27.4164	−1.32989
$426$	−6.18034	−0.299438
$427$	−7.47214	−0.361602
$428$	13.9443	0.674022
$429$	15.0000	0.724207
$430$	6.85410	0.330534
$431$	−2.94427	−0.141821	−0.0709103	−	0.997483i	$-0.522590\pi$
$431$	−2.94427	−0.141821	−0.0709103	+	0.997483i	$0.522590\pi$
$432$	−3.47214	−0.167053
$433$	27.6180	1.32724	0.663619	−	0.748071i	$-0.269020\pi$
$433$	27.6180	1.32724	0.663619	+	0.748071i	$0.269020\pi$
$434$	6.70820	0.322004
$435$	5.09017	0.244055
$436$	13.5623	0.649517
$437$	0	0
$438$	9.00000	0.430037
$439$	22.0557	1.05266	0.526331	−	0.850280i	$-0.323567\pi$
$439$	22.0557	1.05266	0.526331	+	0.850280i	$0.323567\pi$
$440$	5.00000	0.238366
$441$	−2.61803	−0.124668
$442$	33.2705	1.58252
$443$	17.2148	0.817899	0.408949	−	0.912557i	$-0.365895\pi$
$443$	17.2148	0.817899	0.408949	+	0.912557i	$0.365895\pi$
$444$	−3.67376	−0.174349
$445$	−4.85410	−0.230107
$446$	5.65248	0.267652
$447$	0.854102	0.0403976
$448$	−1.00000	−0.0472456
$449$	22.1803	1.04675	0.523377	−	0.852101i	$-0.324672\pi$
$449$	22.1803	1.04675	0.523377	+	0.852101i	$0.324672\pi$
$450$	−10.4721	−0.493661
$451$	−5.45085	−0.256670
$452$	−3.85410	−0.181282
$453$	8.79837	0.413384
$454$	−14.2361	−0.668132
$455$	4.85410	0.227564
$456$	0	0
$457$	29.8885	1.39813	0.699064	−	0.715060i	$-0.253600\pi$
$457$	29.8885	1.39813	0.699064	+	0.715060i	$0.253600\pi$
$458$	10.0902	0.471483
$459$	−23.7984	−1.11081
$460$	−3.76393	−0.175494
$461$	42.5410	1.98133	0.990666	−	0.136309i	$-0.0435239\pi$
$461$	42.5410	1.98133	0.990666	+	0.136309i	$0.0435239\pi$
$462$	−3.09017	−0.143768
$463$	−13.5623	−0.630294	−0.315147	−	0.949043i	$-0.602054\pi$
$463$	−13.5623	−0.630294	−0.315147	+	0.949043i	$0.602054\pi$
$464$	8.23607	0.382350
$465$	4.14590	0.192261
$466$	11.0344	0.511161
$467$	33.4721	1.54891	0.774453	−	0.632632i	$-0.218025\pi$
$467$	33.4721	1.54891	0.774453	+	0.632632i	$0.218025\pi$
$468$	12.7082	0.587437
$469$	7.85410	0.362669
$470$	−7.94427	−0.366442
$471$	13.7984	0.635796
$472$	11.0000	0.506316
$473$	34.2705	1.57576
$474$	−5.47214	−0.251344
$475$	0	0
$476$	−6.85410	−0.314157
$477$	−33.2705	−1.52335
$478$	11.1459	0.509802
$479$	−0.180340	−0.00823994	−0.00411997	−	0.999992i	$-0.501311\pi$
$479$	−0.180340	−0.00823994	−0.00411997	+	0.999992i	$0.501311\pi$
$480$	−0.618034	−0.0282093
$481$	28.8541	1.31563
$482$	7.90983	0.360283
$483$	2.32624	0.105847
$484$	14.0000	0.636364
$485$	9.47214	0.430108
$486$	−13.9443	−0.632525
$487$	−11.1803	−0.506630	−0.253315	−	0.967384i	$-0.581521\pi$
$487$	−11.1803	−0.506630	−0.253315	+	0.967384i	$0.581521\pi$
$488$	−7.47214	−0.338248
$489$	0.291796	0.0131955
$490$	−1.00000	−0.0451754
$491$	−19.5967	−0.884389	−0.442194	−	0.896919i	$-0.645800\pi$
$491$	−19.5967	−0.884389	−0.442194	+	0.896919i	$0.645800\pi$
$492$	0.673762	0.0303755
$493$	56.4508	2.54242
$494$	0	0
$495$	13.0902	0.588359
$496$	6.70820	0.301207
$497$	−10.0000	−0.448561
$498$	9.52786	0.426954
$499$	16.4164	0.734899	0.367450	−	0.930043i	$-0.380231\pi$
$499$	16.4164	0.734899	0.367450	+	0.930043i	$0.380231\pi$
$500$	−9.00000	−0.402492
$501$	−1.12461	−0.0502439
$502$	−6.47214	−0.288866
$503$	31.7771	1.41687	0.708435	−	0.705776i	$-0.249401\pi$
$503$	31.7771	1.41687	0.708435	+	0.705776i	$0.249401\pi$
$504$	−2.61803	−0.116617
$505$	4.14590	0.184490
$506$	−18.8197	−0.836636
$507$	6.52786	0.289913
$508$	7.32624	0.325049
$509$	−1.41641	−0.0627812	−0.0313906	−	0.999507i	$-0.509994\pi$
$509$	−1.41641	−0.0627812	−0.0313906	+	0.999507i	$0.509994\pi$
$510$	−4.23607	−0.187576
$511$	14.5623	0.644198
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.05573	0.355323
$515$	15.0902	0.664952
$516$	−4.23607	−0.186482
$517$	−39.7214	−1.74694
$518$	−5.94427	−0.261176
$519$	−1.09017	−0.0478531
$520$	4.85410	0.212866
$521$	−25.6525	−1.12386	−0.561928	−	0.827186i	$-0.689940\pi$
$521$	−25.6525	−1.12386	−0.561928	+	0.827186i	$0.689940\pi$
$522$	21.5623	0.943756
$523$	35.1591	1.53740	0.768699	−	0.639611i	$-0.220904\pi$
$523$	35.1591	1.53740	0.768699	+	0.639611i	$0.220904\pi$
$524$	−4.38197	−0.191427
$525$	2.47214	0.107893
$526$	25.1803	1.09791
$527$	45.9787	2.00286
$528$	−3.09017	−0.134482
$529$	−8.83282	−0.384035
$530$	−12.7082	−0.552009
$531$	28.7984	1.24974
$532$	0	0
$533$	−5.29180	−0.229213
$534$	3.00000	0.129823
$535$	13.9443	0.602863
$536$	7.85410	0.339246
$537$	−5.58359	−0.240950
$538$	9.18034	0.395793
$539$	−5.00000	−0.215365
$540$	−3.47214	−0.149417
$541$	−30.3050	−1.30291	−0.651456	−	0.758687i	$-0.725841\pi$
$541$	−30.3050	−1.30291	−0.651456	+	0.758687i	$0.725841\pi$
$542$	−1.65248	−0.0709799
$543$	9.74265	0.418097
$544$	−6.85410	−0.293867
$545$	13.5623	0.580945
$546$	−3.00000	−0.128388
$547$	−9.18034	−0.392523	−0.196261	−	0.980552i	$-0.562880\pi$
$547$	−9.18034	−0.392523	−0.196261	+	0.980552i	$0.562880\pi$
$548$	21.1246	0.902399
$549$	−19.5623	−0.834899
$550$	−20.0000	−0.852803
$551$	0	0
$552$	2.32624	0.0990113
$553$	−8.85410	−0.376515
$554$	8.00000	0.339887
$555$	−3.67376	−0.155943
$556$	−0.236068	−0.0100115
$557$	−27.7639	−1.17640	−0.588198	−	0.808717i	$-0.700162\pi$
$557$	−27.7639	−1.17640	−0.588198	+	0.808717i	$0.700162\pi$
$558$	17.5623	0.743472
$559$	33.2705	1.40719
$560$	−1.00000	−0.0422577
$561$	−21.1803	−0.894235
$562$	−12.2361	−0.516147
$563$	−36.0689	−1.52012	−0.760061	−	0.649852i	$-0.774831\pi$
$563$	−36.0689	−1.52012	−0.760061	+	0.649852i	$0.774831\pi$
$564$	4.90983	0.206741
$565$	−3.85410	−0.162143
$566$	−6.43769	−0.270596
$567$	−5.70820	−0.239722
$568$	−10.0000	−0.419591
$569$	30.2705	1.26901	0.634503	−	0.772920i	$-0.281205\pi$
$569$	30.2705	1.26901	0.634503	+	0.772920i	$0.281205\pi$
$570$	0	0
$571$	31.0132	1.29786	0.648930	−	0.760848i	$-0.275217\pi$
$571$	31.0132	1.29786	0.648930	+	0.760848i	$0.275217\pi$
$572$	24.2705	1.01480
$573$	1.74265	0.0728001
$574$	1.09017	0.0455028
$575$	15.0557	0.627867
$576$	−2.61803	−0.109085
$577$	−3.29180	−0.137039	−0.0685196	−	0.997650i	$-0.521828\pi$
$577$	−3.29180	−0.137039	−0.0685196	+	0.997650i	$0.521828\pi$
$578$	−29.9787	−1.24695
$579$	6.29180	0.261478
$580$	8.23607	0.341984
$581$	15.4164	0.639580
$582$	−5.85410	−0.242660
$583$	−63.5410	−2.63160
$584$	14.5623	0.602593
$585$	12.7082	0.525420
$586$	16.2361	0.670706
$587$	−41.9443	−1.73123	−0.865613	−	0.500714i	$-0.833071\pi$
$587$	−41.9443	−1.73123	−0.865613	+	0.500714i	$0.833071\pi$
$588$	0.618034	0.0254873
$589$	0	0
$590$	11.0000	0.452863
$591$	−4.67376	−0.192253
$592$	−5.94427	−0.244308
$593$	5.43769	0.223299	0.111650	−	0.993748i	$-0.464387\pi$
$593$	5.43769	0.223299	0.111650	+	0.993748i	$0.464387\pi$
$594$	−17.3607	−0.712317
$595$	−6.85410	−0.280991
$596$	1.38197	0.0566075
$597$	−3.03444	−0.124191
$598$	−18.2705	−0.747137
$599$	−17.0000	−0.694601	−0.347301	−	0.937754i	$-0.612902\pi$
$599$	−17.0000	−0.694601	−0.347301	+	0.937754i	$0.612902\pi$
$600$	2.47214	0.100925
$601$	−14.1246	−0.576155	−0.288077	−	0.957607i	$-0.593016\pi$
$601$	−14.1246	−0.576155	−0.288077	+	0.957607i	$0.593016\pi$
$602$	−6.85410	−0.279352
$603$	20.5623	0.837362
$604$	14.2361	0.579257
$605$	14.0000	0.569181
$606$	−2.56231	−0.104087
$607$	−16.9443	−0.687747	−0.343873	−	0.939016i	$-0.611739\pi$
$607$	−16.9443	−0.687747	−0.343873	+	0.939016i	$0.611739\pi$
$608$	0	0
$609$	−5.09017	−0.206264
$610$	−7.47214	−0.302538
$611$	−38.5623	−1.56006
$612$	−17.9443	−0.725354
$613$	−10.6525	−0.430249	−0.215125	−	0.976587i	$-0.569016\pi$
$613$	−10.6525	−0.430249	−0.215125	+	0.976587i	$0.569016\pi$
$614$	4.94427	0.199535
$615$	0.673762	0.0271687
$616$	−5.00000	−0.201456
$617$	−24.3262	−0.979337	−0.489669	−	0.871909i	$-0.662882\pi$
$617$	−24.3262	−0.979337	−0.489669	+	0.871909i	$0.662882\pi$
$618$	−9.32624	−0.375156
$619$	−34.7984	−1.39866	−0.699332	−	0.714797i	$-0.746519\pi$
$619$	−34.7984	−1.39866	−0.699332	+	0.714797i	$0.746519\pi$
$620$	6.70820	0.269408
$621$	13.0689	0.524436
$622$	−19.7639	−0.792461
$623$	4.85410	0.194475
$624$	−3.00000	−0.120096
$625$	11.0000	0.440000
$626$	−18.9098	−0.755789
$627$	0	0
$628$	22.3262	0.890914
$629$	−40.7426	−1.62452
$630$	−2.61803	−0.104305
$631$	12.9443	0.515303	0.257652	−	0.966238i	$-0.417051\pi$
$631$	12.9443	0.515303	0.257652	+	0.966238i	$0.417051\pi$
$632$	−8.85410	−0.352197
$633$	2.50658	0.0996275
$634$	8.41641	0.334258
$635$	7.32624	0.290733
$636$	7.85410	0.311435
$637$	−4.85410	−0.192327
$638$	41.1803	1.63035
$639$	−26.1803	−1.03568
$640$	−1.00000	−0.0395285
$641$	−18.9098	−0.746893	−0.373447	−	0.927652i	$-0.621824\pi$
$641$	−18.9098	−0.746893	−0.373447	+	0.927652i	$0.621824\pi$
$642$	−8.61803	−0.340127
$643$	22.6525	0.893326	0.446663	−	0.894702i	$-0.352612\pi$
$643$	22.6525	0.893326	0.446663	+	0.894702i	$0.352612\pi$
$644$	3.76393	0.148320
$645$	−4.23607	−0.166795
$646$	0	0
$647$	−41.1033	−1.61594	−0.807969	−	0.589225i	$-0.799433\pi$
$647$	−41.1033	−1.61594	−0.807969	+	0.589225i	$0.799433\pi$
$648$	−5.70820	−0.224239
$649$	55.0000	2.15894
$650$	−19.4164	−0.761574
$651$	−4.14590	−0.162491
$652$	0.472136	0.0184903
$653$	23.6869	0.926941	0.463470	−	0.886112i	$-0.346604\pi$
$653$	23.6869	0.926941	0.463470	+	0.886112i	$0.346604\pi$
$654$	−8.38197	−0.327761
$655$	−4.38197	−0.171218
$656$	1.09017	0.0425640
$657$	38.1246	1.48738
$658$	7.94427	0.309700
$659$	−33.5410	−1.30657	−0.653286	−	0.757111i	$-0.726610\pi$
$659$	−33.5410	−1.30657	−0.653286	+	0.757111i	$0.726610\pi$
$660$	−3.09017	−0.120285
$661$	11.8328	0.460243	0.230122	−	0.973162i	$-0.426088\pi$
$661$	11.8328	0.460243	0.230122	+	0.973162i	$0.426088\pi$
$662$	12.4721	0.484743
$663$	−20.5623	−0.798574
$664$	15.4164	0.598273
$665$	0	0
$666$	−15.5623	−0.603027
$667$	−31.0000	−1.20032
$668$	−1.81966	−0.0704048
$669$	−3.49342	−0.135064
$670$	7.85410	0.303430
$671$	−37.3607	−1.44229
$672$	0.618034	0.0238412
$673$	−20.9098	−0.806015	−0.403007	−	0.915197i	$-0.632035\pi$
$673$	−20.9098	−0.806015	−0.403007	+	0.915197i	$0.632035\pi$
$674$	−33.4508	−1.28848
$675$	13.8885	0.534570
$676$	10.5623	0.406243
$677$	−3.70820	−0.142518	−0.0712589	−	0.997458i	$-0.522702\pi$
$677$	−3.70820	−0.142518	−0.0712589	+	0.997458i	$0.522702\pi$
$678$	2.38197	0.0914789
$679$	−9.47214	−0.363507
$680$	−6.85410	−0.262843
$681$	8.79837	0.337154
$682$	33.5410	1.28435
$683$	20.2705	0.775630	0.387815	−	0.921737i	$-0.373230\pi$
$683$	20.2705	0.775630	0.387815	+	0.921737i	$0.373230\pi$
$684$	0	0
$685$	21.1246	0.807130
$686$	1.00000	0.0381802
$687$	−6.23607	−0.237921
$688$	−6.85410	−0.261310
$689$	−61.6869	−2.35008
$690$	2.32624	0.0885584
$691$	9.47214	0.360337	0.180169	−	0.983636i	$-0.442336\pi$
$691$	9.47214	0.360337	0.180169	+	0.983636i	$0.442336\pi$
$692$	−1.76393	−0.0670546
$693$	−13.0902	−0.497254
$694$	5.05573	0.191913
$695$	−0.236068	−0.00895457
$696$	−5.09017	−0.192942
$697$	7.47214	0.283027
$698$	6.70820	0.253909
$699$	−6.81966	−0.257943
$700$	4.00000	0.151186
$701$	1.72949	0.0653219	0.0326610	−	0.999466i	$-0.489602\pi$
$701$	1.72949	0.0653219	0.0326610	+	0.999466i	$0.489602\pi$
$702$	−16.8541	−0.636117
$703$	0	0
$704$	−5.00000	−0.188445
$705$	4.90983	0.184915
$706$	−13.0902	−0.492655
$707$	−4.14590	−0.155923
$708$	−6.79837	−0.255499
$709$	39.6525	1.48918	0.744590	−	0.667522i	$-0.232645\pi$
$709$	39.6525	1.48918	0.744590	+	0.667522i	$0.232645\pi$
$710$	−10.0000	−0.375293
$711$	−23.1803	−0.869331
$712$	4.85410	0.181915
$713$	−25.2492	−0.945591
$714$	4.23607	0.158531
$715$	24.2705	0.907666
$716$	−9.03444	−0.337633
$717$	−6.88854	−0.257257
$718$	−27.9443	−1.04287
$719$	39.8328	1.48551	0.742757	−	0.669561i	$-0.233518\pi$
$719$	39.8328	1.48551	0.742757	+	0.669561i	$0.233518\pi$
$720$	−2.61803	−0.0975684
$721$	−15.0902	−0.561987
$722$	0	0
$723$	−4.88854	−0.181807
$724$	15.7639	0.585862
$725$	−32.9443	−1.22352
$726$	−8.65248	−0.321123
$727$	7.87539	0.292082	0.146041	−	0.989279i	$-0.453347\pi$
$727$	7.87539	0.292082	0.146041	+	0.989279i	$0.453347\pi$
$728$	−4.85410	−0.179905
$729$	−8.50658	−0.315058
$730$	14.5623	0.538975
$731$	−46.9787	−1.73757
$732$	4.61803	0.170687
$733$	12.3475	0.456066	0.228033	−	0.973653i	$-0.426771\pi$
$733$	12.3475	0.456066	0.228033	+	0.973653i	$0.426771\pi$
$734$	−9.67376	−0.357065
$735$	0.618034	0.0227965
$736$	3.76393	0.138740
$737$	39.2705	1.44655
$738$	2.85410	0.105061
$739$	11.4164	0.419959	0.209980	−	0.977706i	$-0.432660\pi$
$739$	11.4164	0.419959	0.209980	+	0.977706i	$0.432660\pi$
$740$	−5.94427	−0.218516
$741$	0	0
$742$	12.7082	0.466533
$743$	50.5066	1.85291	0.926453	−	0.376410i	$-0.122841\pi$
$743$	50.5066	1.85291	0.926453	+	0.376410i	$0.122841\pi$
$744$	−4.14590	−0.151996
$745$	1.38197	0.0506313
$746$	−6.85410	−0.250947
$747$	40.3607	1.47672
$748$	−34.2705	−1.25305
$749$	−13.9443	−0.509513
$750$	5.56231	0.203107
$751$	−12.1803	−0.444467	−0.222233	−	0.974993i	$-0.571335\pi$
$751$	−12.1803	−0.444467	−0.222233	+	0.974993i	$0.571335\pi$
$752$	7.94427	0.289698
$753$	4.00000	0.145768
$754$	39.9787	1.45594
$755$	14.2361	0.518104
$756$	3.47214	0.126280
$757$	−5.88854	−0.214023	−0.107011	−	0.994258i	$-0.534128\pi$
$757$	−5.88854	−0.214023	−0.107011	+	0.994258i	$0.534128\pi$
$758$	12.0344	0.437111
$759$	11.6312	0.422185
$760$	0	0
$761$	13.8328	0.501439	0.250720	−	0.968060i	$-0.419333\pi$
$761$	13.8328	0.501439	0.250720	+	0.968060i	$0.419333\pi$
$762$	−4.52786	−0.164027
$763$	−13.5623	−0.490988
$764$	2.81966	0.102012
$765$	−17.9443	−0.648777
$766$	5.94427	0.214775
$767$	53.3951	1.92799
$768$	0.618034	0.0223014
$769$	39.4164	1.42139	0.710696	−	0.703499i	$-0.248380\pi$
$769$	39.4164	1.42139	0.710696	+	0.703499i	$0.248380\pi$
$770$	−5.00000	−0.180187
$771$	−4.97871	−0.179304
$772$	10.1803	0.366398
$773$	−0.437694	−0.0157428	−0.00787138	−	0.999969i	$-0.502506\pi$
$773$	−0.437694	−0.0157428	−0.00787138	+	0.999969i	$0.502506\pi$
$774$	−17.9443	−0.644994
$775$	−26.8328	−0.963863
$776$	−9.47214	−0.340030
$777$	3.67376	0.131795
$778$	−11.3820	−0.408063
$779$	0	0
$780$	−3.00000	−0.107417
$781$	−50.0000	−1.78914
$782$	25.7984	0.922548
$783$	−28.5967	−1.02196
$784$	1.00000	0.0357143
$785$	22.3262	0.796858
$786$	2.70820	0.0965984
$787$	18.6738	0.665648	0.332824	−	0.942989i	$-0.391999\pi$
$787$	18.6738	0.665648	0.332824	+	0.942989i	$0.391999\pi$
$788$	−7.56231	−0.269396
$789$	−15.5623	−0.554033
$790$	−8.85410	−0.315015
$791$	3.85410	0.137036
$792$	−13.0902	−0.465139
$793$	−36.2705	−1.28800
$794$	32.2705	1.14524
$795$	7.85410	0.278556
$796$	−4.90983	−0.174024
$797$	−12.7984	−0.453342	−0.226671	−	0.973971i	$-0.572784\pi$
$797$	−12.7984	−0.453342	−0.226671	+	0.973971i	$0.572784\pi$
$798$	0	0
$799$	54.4508	1.92633
$800$	4.00000	0.141421
$801$	12.7082	0.449022
$802$	−6.58359	−0.232475
$803$	72.8115	2.56946
$804$	−4.85410	−0.171191
$805$	3.76393	0.132661
$806$	32.5623	1.14696
$807$	−5.67376	−0.199726
$808$	−4.14590	−0.145852
$809$	−26.1459	−0.919241	−0.459620	−	0.888115i	$-0.652015\pi$
$809$	−26.1459	−0.919241	−0.459620	+	0.888115i	$0.652015\pi$
$810$	−5.70820	−0.200566
$811$	40.5410	1.42359	0.711794	−	0.702388i	$-0.247883\pi$
$811$	40.5410	1.42359	0.711794	+	0.702388i	$0.247883\pi$
$812$	−8.23607	−0.289029
$813$	1.02129	0.0358181
$814$	−29.7214	−1.04173
$815$	0.472136	0.0165382
$816$	4.23607	0.148292
$817$	0	0
$818$	17.2148	0.601901
$819$	−12.7082	−0.444061
$820$	1.09017	0.0380704
$821$	9.76393	0.340764	0.170382	−	0.985378i	$-0.445500\pi$
$821$	9.76393	0.340764	0.170382	+	0.985378i	$0.445500\pi$
$822$	−13.0557	−0.455371
$823$	−33.7639	−1.17694	−0.588468	−	0.808520i	$-0.700269\pi$
$823$	−33.7639	−1.17694	−0.588468	+	0.808520i	$0.700269\pi$
$824$	−15.0902	−0.525691
$825$	12.3607	0.430344
$826$	−11.0000	−0.382739
$827$	−13.3820	−0.465337	−0.232668	−	0.972556i	$-0.574746\pi$
$827$	−13.3820	−0.465337	−0.232668	+	0.972556i	$0.574746\pi$
$828$	9.85410	0.342454
$829$	−6.88854	−0.239249	−0.119625	−	0.992819i	$-0.538169\pi$
$829$	−6.88854	−0.239249	−0.119625	+	0.992819i	$0.538169\pi$
$830$	15.4164	0.535111
$831$	−4.94427	−0.171515
$832$	−4.85410	−0.168286
$833$	6.85410	0.237481
$834$	0.145898	0.00505204
$835$	−1.81966	−0.0629719
$836$	0	0
$837$	−23.2918	−0.805082
$838$	25.7426	0.889265
$839$	−41.1803	−1.42170	−0.710852	−	0.703342i	$-0.751690\pi$
$839$	−41.1803	−1.42170	−0.710852	+	0.703342i	$0.751690\pi$
$840$	0.618034	0.0213242
$841$	38.8328	1.33906
$842$	−8.05573	−0.277619
$843$	7.56231	0.260460
$844$	4.05573	0.139604
$845$	10.5623	0.363354
$846$	20.7984	0.715063
$847$	−14.0000	−0.481046
$848$	12.7082	0.436402
$849$	3.97871	0.136549
$850$	27.4164	0.940375
$851$	22.3738	0.766965
$852$	6.18034	0.211735
$853$	38.9574	1.33388	0.666938	−	0.745113i	$-0.267604\pi$
$853$	38.9574	1.33388	0.666938	+	0.745113i	$0.267604\pi$
$854$	7.47214	0.255691
$855$	0	0
$856$	−13.9443	−0.476605
$857$	−17.7426	−0.606077	−0.303039	−	0.952978i	$-0.598001\pi$
$857$	−17.7426	−0.606077	−0.303039	+	0.952978i	$0.598001\pi$
$858$	−15.0000	−0.512092
$859$	−5.06888	−0.172948	−0.0864740	−	0.996254i	$-0.527560\pi$
$859$	−5.06888	−0.172948	−0.0864740	+	0.996254i	$0.527560\pi$
$860$	−6.85410	−0.233723
$861$	−0.673762	−0.0229618
$862$	2.94427	0.100282
$863$	7.29180	0.248216	0.124108	−	0.992269i	$-0.460393\pi$
$863$	7.29180	0.248216	0.124108	+	0.992269i	$0.460393\pi$
$864$	3.47214	0.118124
$865$	−1.76393	−0.0599755
$866$	−27.6180	−0.938499
$867$	18.5279	0.629239
$868$	−6.70820	−0.227691
$869$	−44.2705	−1.50177
$870$	−5.09017	−0.172573
$871$	38.1246	1.29180
$872$	−13.5623	−0.459278
$873$	−24.7984	−0.839298
$874$	0	0
$875$	9.00000	0.304256
$876$	−9.00000	−0.304082
$877$	−5.32624	−0.179854	−0.0899271	−	0.995948i	$-0.528663\pi$
$877$	−5.32624	−0.179854	−0.0899271	+	0.995948i	$0.528663\pi$
$878$	−22.0557	−0.744345
$879$	−10.0344	−0.338453
$880$	−5.00000	−0.168550
$881$	14.1459	0.476587	0.238294	−	0.971193i	$-0.423412\pi$
$881$	14.1459	0.476587	0.238294	+	0.971193i	$0.423412\pi$
$882$	2.61803	0.0881538
$883$	−11.0213	−0.370896	−0.185448	−	0.982654i	$-0.559374\pi$
$883$	−11.0213	−0.370896	−0.185448	+	0.982654i	$0.559374\pi$
$884$	−33.2705	−1.11901
$885$	−6.79837	−0.228525
$886$	−17.2148	−0.578342
$887$	−20.8328	−0.699497	−0.349749	−	0.936844i	$-0.613733\pi$
$887$	−20.8328	−0.699497	−0.349749	+	0.936844i	$0.613733\pi$
$888$	3.67376	0.123283
$889$	−7.32624	−0.245714
$890$	4.85410	0.162710
$891$	−28.5410	−0.956160
$892$	−5.65248	−0.189259
$893$	0	0
$894$	−0.854102	−0.0285654
$895$	−9.03444	−0.301988
$896$	1.00000	0.0334077
$897$	11.2918	0.377022
$898$	−22.1803	−0.740168
$899$	55.2492	1.84266
$900$	10.4721	0.349071
$901$	87.1033	2.90183
$902$	5.45085	0.181493
$903$	4.23607	0.140968
$904$	3.85410	0.128186
$905$	15.7639	0.524011
$906$	−8.79837	−0.292306
$907$	−16.6738	−0.553643	−0.276822	−	0.960921i	$-0.589281\pi$
$907$	−16.6738	−0.553643	−0.276822	+	0.960921i	$0.589281\pi$
$908$	14.2361	0.472441
$909$	−10.8541	−0.360008
$910$	−4.85410	−0.160912
$911$	−46.1591	−1.52932	−0.764659	−	0.644435i	$-0.777093\pi$
$911$	−46.1591	−1.52932	−0.764659	+	0.644435i	$0.777093\pi$
$912$	0	0
$913$	77.0820	2.55104
$914$	−29.8885	−0.988625
$915$	4.61803	0.152667
$916$	−10.0902	−0.333389
$917$	4.38197	0.144705
$918$	23.7984	0.785463
$919$	10.0344	0.331006	0.165503	−	0.986209i	$-0.447075\pi$
$919$	10.0344	0.331006	0.165503	+	0.986209i	$0.447075\pi$
$920$	3.76393	0.124093
$921$	−3.05573	−0.100690
$922$	−42.5410	−1.40101
$923$	−48.5410	−1.59775
$924$	3.09017	0.101659
$925$	23.7771	0.781786
$926$	13.5623	0.445685
$927$	−39.5066	−1.29757
$928$	−8.23607	−0.270362
$929$	−26.8885	−0.882185	−0.441092	−	0.897462i	$-0.645409\pi$
$929$	−26.8885	−0.882185	−0.441092	+	0.897462i	$0.645409\pi$
$930$	−4.14590	−0.135949
$931$	0	0
$932$	−11.0344	−0.361445
$933$	12.2148	0.399894
$934$	−33.4721	−1.09524
$935$	−34.2705	−1.12077
$936$	−12.7082	−0.415381
$937$	40.3951	1.31965	0.659826	−	0.751419i	$-0.270630\pi$
$937$	40.3951	1.31965	0.659826	+	0.751419i	$0.270630\pi$
$938$	−7.85410	−0.256446
$939$	11.6869	0.381388
$940$	7.94427	0.259114
$941$	−27.2148	−0.887177	−0.443588	−	0.896231i	$-0.646295\pi$
$941$	−27.2148	−0.887177	−0.443588	+	0.896231i	$0.646295\pi$
$942$	−13.7984	−0.449575
$943$	−4.10333	−0.133623
$944$	−11.0000	−0.358020
$945$	3.47214	0.112949
$946$	−34.2705	−1.11423
$947$	49.8885	1.62116	0.810580	−	0.585628i	$-0.199152\pi$
$947$	49.8885	1.62116	0.810580	+	0.585628i	$0.199152\pi$
$948$	5.47214	0.177727
$949$	70.6869	2.29459
$950$	0	0
$951$	−5.20163	−0.168674
$952$	6.85410	0.222143
$953$	30.7771	0.996968	0.498484	−	0.866899i	$-0.333890\pi$
$953$	30.7771	0.996968	0.498484	+	0.866899i	$0.333890\pi$
$954$	33.2705	1.07717
$955$	2.81966	0.0912421
$956$	−11.1459	−0.360484
$957$	−25.4508	−0.822709
$958$	0.180340	0.00582652
$959$	−21.1246	−0.682149
$960$	0.618034	0.0199470
$961$	14.0000	0.451613
$962$	−28.8541	−0.930294
$963$	−36.5066	−1.17641
$964$	−7.90983	−0.254758
$965$	10.1803	0.327717
$966$	−2.32624	−0.0748455
$967$	−55.2705	−1.77738	−0.888690	−	0.458509i	$-0.848384\pi$
$967$	−55.2705	−1.77738	−0.888690	+	0.458509i	$0.848384\pi$
$968$	−14.0000	−0.449977
$969$	0	0
$970$	−9.47214	−0.304132
$971$	34.4164	1.10448	0.552238	−	0.833687i	$-0.313774\pi$
$971$	34.4164	1.10448	0.552238	+	0.833687i	$0.313774\pi$
$972$	13.9443	0.447263
$973$	0.236068	0.00756799
$974$	11.1803	0.358241
$975$	12.0000	0.384308
$976$	7.47214	0.239177
$977$	48.7771	1.56052	0.780259	−	0.625457i	$-0.215087\pi$
$977$	48.7771	1.56052	0.780259	+	0.625457i	$0.215087\pi$
$978$	−0.291796	−0.00933061
$979$	24.2705	0.775689
$980$	1.00000	0.0319438
$981$	−35.5066	−1.13364
$982$	19.5967	0.625357
$983$	−9.49342	−0.302793	−0.151397	−	0.988473i	$-0.548377\pi$
$983$	−9.49342	−0.302793	−0.151397	+	0.988473i	$0.548377\pi$
$984$	−0.673762	−0.0214788
$985$	−7.56231	−0.240955
$986$	−56.4508	−1.79776
$987$	−4.90983	−0.156282
$988$	0	0
$989$	25.7984	0.820341
$990$	−13.0902	−0.416033
$991$	25.4164	0.807379	0.403689	−	0.914896i	$-0.367728\pi$
$991$	25.4164	0.807379	0.403689	+	0.914896i	$0.367728\pi$
$992$	−6.70820	−0.212986
$993$	−7.70820	−0.244612
$994$	10.0000	0.317181
$995$	−4.90983	−0.155652
$996$	−9.52786	−0.301902
$997$	31.0344	0.982871	0.491435	−	0.870914i	$-0.336472\pi$
$997$	31.0344	0.982871	0.491435	+	0.870914i	$0.336472\pi$
$998$	−16.4164	−0.519652
$999$	20.6393	0.652999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.f.1.2	✓	2
19.18	odd	2		5054.2.a.p.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.f.1.2	✓	2	1.1	even	1	trivial
5054.2.a.p.1.1	yes	2	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.618034 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.618034 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.61803 q^{9} -1.00000 q^{10} -5.00000 q^{11} +0.618034 q^{12} -4.85410 q^{13} +1.00000 q^{14} +0.618034 q^{15} +1.00000 q^{16} +6.85410 q^{17} +2.61803 q^{18} +1.00000 q^{20} -0.618034 q^{21} +5.00000 q^{22} -3.76393 q^{23} -0.618034 q^{24} -4.00000 q^{25} +4.85410 q^{26} -3.47214 q^{27} -1.00000 q^{28} +8.23607 q^{29} -0.618034 q^{30} +6.70820 q^{31} -1.00000 q^{32} -3.09017 q^{33} -6.85410 q^{34} -1.00000 q^{35} -2.61803 q^{36} -5.94427 q^{37} -3.00000 q^{39} -1.00000 q^{40} +1.09017 q^{41} +0.618034 q^{42} -6.85410 q^{43} -5.00000 q^{44} -2.61803 q^{45} +3.76393 q^{46} +7.94427 q^{47} +0.618034 q^{48} +1.00000 q^{49} +4.00000 q^{50} +4.23607 q^{51} -4.85410 q^{52} +12.7082 q^{53} +3.47214 q^{54} -5.00000 q^{55} +1.00000 q^{56} -8.23607 q^{58} -11.0000 q^{59} +0.618034 q^{60} +7.47214 q^{61} -6.70820 q^{62} +2.61803 q^{63} +1.00000 q^{64} -4.85410 q^{65} +3.09017 q^{66} -7.85410 q^{67} +6.85410 q^{68} -2.32624 q^{69} +1.00000 q^{70} +10.0000 q^{71} +2.61803 q^{72} -14.5623 q^{73} +5.94427 q^{74} -2.47214 q^{75} +5.00000 q^{77} +3.00000 q^{78} +8.85410 q^{79} +1.00000 q^{80} +5.70820 q^{81} -1.09017 q^{82} -15.4164 q^{83} -0.618034 q^{84} +6.85410 q^{85} +6.85410 q^{86} +5.09017 q^{87} +5.00000 q^{88} -4.85410 q^{89} +2.61803 q^{90} +4.85410 q^{91} -3.76393 q^{92} +4.14590 q^{93} -7.94427 q^{94} -0.618034 q^{96} +9.47214 q^{97} -1.00000 q^{98} +13.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} - 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} + 3 q^{18} + 2 q^{20} + q^{21} + 10 q^{22} - 12 q^{23} + q^{24} - 8 q^{25} + 3 q^{26} + 2 q^{27} - 2 q^{28} + 12 q^{29} + q^{30} - 2 q^{32} + 5 q^{33} - 7 q^{34} - 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 2 q^{40} - 9 q^{41} - q^{42} - 7 q^{43} - 10 q^{44} - 3 q^{45} + 12 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} + 8 q^{50} + 4 q^{51} - 3 q^{52} + 12 q^{53} - 2 q^{54} - 10 q^{55} + 2 q^{56} - 12 q^{58} - 22 q^{59} - q^{60} + 6 q^{61} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 5 q^{66} - 9 q^{67} + 7 q^{68} + 11 q^{69} + 2 q^{70} + 20 q^{71} + 3 q^{72} - 9 q^{73} - 6 q^{74} + 4 q^{75} + 10 q^{77} + 6 q^{78} + 11 q^{79} + 2 q^{80} - 2 q^{81} + 9 q^{82} - 4 q^{83} + q^{84} + 7 q^{85} + 7 q^{86} - q^{87} + 10 q^{88} - 3 q^{89} + 3 q^{90} + 3 q^{91} - 12 q^{92} + 15 q^{93} + 2 q^{94} + q^{96} + 10 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 2 * q^7 - 2 * q^8 - 3 * q^9 - 2 * q^10 - 10 * q^11 - q^12 - 3 * q^13 + 2 * q^14 - q^15 + 2 * q^16 + 7 * q^17 + 3 * q^18 + 2 * q^20 + q^21 + 10 * q^22 - 12 * q^23 + q^24 - 8 * q^25 + 3 * q^26 + 2 * q^27 - 2 * q^28 + 12 * q^29 + q^30 - 2 * q^32 + 5 * q^33 - 7 * q^34 - 2 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 2 * q^40 - 9 * q^41 - q^42 - 7 * q^43 - 10 * q^44 - 3 * q^45 + 12 * q^46 - 2 * q^47 - q^48 + 2 * q^49 + 8 * q^50 + 4 * q^51 - 3 * q^52 + 12 * q^53 - 2 * q^54 - 10 * q^55 + 2 * q^56 - 12 * q^58 - 22 * q^59 - q^60 + 6 * q^61 + 3 * q^63 + 2 * q^64 - 3 * q^65 - 5 * q^66 - 9 * q^67 + 7 * q^68 + 11 * q^69 + 2 * q^70 + 20 * q^71 + 3 * q^72 - 9 * q^73 - 6 * q^74 + 4 * q^75 + 10 * q^77 + 6 * q^78 + 11 * q^79 + 2 * q^80 - 2 * q^81 + 9 * q^82 - 4 * q^83 + q^84 + 7 * q^85 + 7 * q^86 - q^87 + 10 * q^88 - 3 * q^89 + 3 * q^90 + 3 * q^91 - 12 * q^92 + 15 * q^93 + 2 * q^94 + q^96 + 10 * q^97 - 2 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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