LMFDB - Embedded newform 5054.2.a.p.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:	$1$
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			1.1
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	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	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	$-0.264944\pi$
$13$	4.85410	1.34629	0.673143	+	0.739512i	$0.264944\pi$
$14$	−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	$-0.777113\pi$
$29$	−8.23607	−1.52940	−0.764700	+	0.644387i	$0.777113\pi$
$30$	−0.618034	−0.112837
$31$	−6.70820	−1.20483	−0.602414	−	0.798183i	$-0.705795\pi$
$31$	−6.70820	−1.20483	−0.602414	+	0.798183i	$0.705795\pi$
$32$	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	$-0.337502\pi$
$37$	5.94427	0.977232	0.488616	+	0.872499i	$0.337502\pi$
$38$	0	0
$39$	−3.00000	−0.480384
$40$	1.00000	0.158114
$41$	−1.09017	−0.170256	−0.0851280	−	0.996370i	$-0.527130\pi$
$41$	−1.09017	−0.170256	−0.0851280	+	0.996370i	$0.527130\pi$
$42$	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	$-0.837700\pi$
$53$	−12.7082	−1.74561	−0.872803	+	0.488073i	$0.837700\pi$
$54$	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	$-0.245953\pi$
$59$	11.0000	1.43208	0.716039	+	0.698060i	$0.245953\pi$
$60$	−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	$-0.340722\pi$
$67$	7.85410	0.959531	0.479766	+	0.877397i	$0.340722\pi$
$68$	6.85410	0.831182
$69$	2.32624	0.280046
$70$	−1.00000	−0.119523
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−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	$-0.665962\pi$
$79$	−8.85410	−0.996164	−0.498082	+	0.867130i	$0.665962\pi$
$80$	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	$-0.417178\pi$
$89$	4.85410	0.514534	0.257267	+	0.966340i	$0.417178\pi$
$90$	−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	$-0.659681\pi$
$97$	−9.47214	−0.961750	−0.480875	+	0.876789i	$0.659681\pi$
$98$	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	$-0.766807\pi$
$103$	−15.0902	−1.48688	−0.743439	+	0.668803i	$0.766807\pi$
$104$	4.85410	0.475984
$105$	0.618034	0.0603139
$106$	−12.7082	−1.23433
$107$	−13.9443	−1.34804	−0.674022	−	0.738711i	$-0.735435\pi$
$107$	−13.9443	−1.34804	−0.674022	+	0.738711i	$0.735435\pi$
$108$	3.47214	0.334106
$109$	−13.5623	−1.29903	−0.649517	−	0.760347i	$-0.725029\pi$
$109$	−13.5623	−1.29903	−0.649517	+	0.760347i	$0.725029\pi$
$110$	−5.00000	−0.476731
$111$	−3.67376	−0.348698
$112$	−1.00000	−0.0944911
$113$	3.85410	0.362563	0.181282	−	0.983431i	$-0.441975\pi$
$113$	3.85410	0.362563	0.181282	+	0.983431i	$0.441975\pi$
$114$	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	$-0.605381\pi$
$127$	−7.32624	−0.650098	−0.325049	+	0.945697i	$0.605381\pi$
$128$	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	$-0.696657\pi$
$151$	−14.2361	−1.15851	−0.579257	+	0.815145i	$0.696657\pi$
$152$	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	$-0.477571\pi$
$167$	1.81966	0.140810	0.0704048	+	0.997519i	$0.477571\pi$
$168$	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	$-0.478640\pi$
$173$	1.76393	0.134109	0.0670546	+	0.997749i	$0.478640\pi$
$174$	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	$-0.390374\pi$
$179$	9.03444	0.675266	0.337633	+	0.941278i	$0.390374\pi$
$180$	−2.61803	−0.195137
$181$	−15.7639	−1.17172	−0.585862	−	0.810411i	$-0.699244\pi$
$181$	−15.7639	−1.17172	−0.585862	+	0.810411i	$0.699244\pi$
$182$	−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	$-0.619409\pi$
$193$	−10.1803	−0.732797	−0.366398	+	0.930458i	$0.619409\pi$
$194$	−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	$-0.544583\pi$
$211$	−4.05573	−0.279208	−0.139604	+	0.990207i	$0.544583\pi$
$212$	−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	$-0.439391\pi$
$223$	5.65248	0.378518	0.189259	+	0.981927i	$0.439391\pi$
$224$	−1.00000	−0.0668153
$225$	10.4721	0.698142
$226$	3.85410	0.256371
$227$	−14.2361	−0.944881	−0.472441	−	0.881363i	$-0.656627\pi$
$227$	−14.2361	−0.944881	−0.472441	+	0.881363i	$0.656627\pi$
$228$	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	$-0.418004\pi$
$241$	7.90983	0.509517	0.254758	+	0.967005i	$0.418004\pi$
$242$	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	$-0.419158\pi$
$257$	8.05573	0.502503	0.251251	+	0.967922i	$0.419158\pi$
$258$	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	$-0.409709\pi$
$269$	9.18034	0.559735	0.279868	+	0.960039i	$0.409709\pi$
$270$	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	$-0.618921\pi$
$281$	−12.2361	−0.729943	−0.364971	+	0.931019i	$0.618921\pi$
$282$	−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	$-0.342715\pi$
$293$	16.2361	0.948521	0.474261	+	0.880385i	$0.342715\pi$
$294$	−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	$-0.454939\pi$
$307$	4.94427	0.282185	0.141092	+	0.989996i	$0.454939\pi$
$308$	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	$-0.424047\pi$
$317$	8.41641	0.472713	0.236356	+	0.971666i	$0.424047\pi$
$318$	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	$-0.388636\pi$
$331$	12.4721	0.685531	0.342765	+	0.939421i	$0.388636\pi$
$332$	−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	$-0.864759\pi$
$337$	−33.4508	−1.82218	−0.911092	+	0.412203i	$0.864759\pi$
$338$	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	$-0.556784\pi$
$373$	−6.85410	−0.354892	−0.177446	+	0.984131i	$0.556784\pi$
$374$	−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	$-0.399978\pi$
$379$	12.0344	0.618168	0.309084	+	0.951035i	$0.399978\pi$
$380$	0	0
$381$	4.52786	0.231970
$382$	2.81966	0.144266
$383$	5.94427	0.303738	0.151869	−	0.988401i	$-0.451471\pi$
$383$	5.94427	0.303738	0.151869	+	0.988401i	$0.451471\pi$
$384$	−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	$-0.552564\pi$
$401$	−6.58359	−0.328769	−0.164384	+	0.986396i	$0.552564\pi$
$402$	−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	$-0.360060\pi$
$409$	17.2148	0.851216	0.425608	+	0.904908i	$0.360060\pi$
$410$	−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	$-0.562895\pi$
$421$	−8.05573	−0.392612	−0.196306	+	0.980543i	$0.562895\pi$
$422$	−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	$-0.477410\pi$
$431$	2.94427	0.141821	0.0709103	+	0.997483i	$0.477410\pi$
$432$	3.47214	0.167053
$433$	−27.6180	−1.32724	−0.663619	−	0.748071i	$-0.730980\pi$
$433$	−27.6180	−1.32724	−0.663619	+	0.748071i	$0.730980\pi$
$434$	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	$-0.676433\pi$
$439$	−22.0557	−1.05266	−0.526331	+	0.850280i	$0.676433\pi$
$440$	−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	$-0.675328\pi$
$449$	−22.1803	−1.04675	−0.523377	+	0.852101i	$0.675328\pi$
$450$	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	$-0.418479\pi$
$487$	11.1803	0.506630	0.253315	+	0.967384i	$0.418479\pi$
$488$	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	$-0.490006\pi$
$509$	1.41641	0.0627812	0.0313906	+	0.999507i	$0.490006\pi$
$510$	−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	$-0.310060\pi$
$521$	25.6525	1.12386	0.561928	+	0.827186i	$0.310060\pi$
$522$	21.5623	0.943756
$523$	−35.1591	−1.53740	−0.768699	−	0.639611i	$-0.779096\pi$
$523$	−35.1591	−1.53740	−0.768699	+	0.639611i	$0.779096\pi$
$524$	−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	$-0.437120\pi$
$547$	9.18034	0.392523	0.196261	+	0.980552i	$0.437120\pi$
$548$	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	$-0.225169\pi$
$563$	36.0689	1.52012	0.760061	+	0.649852i	$0.225169\pi$
$564$	−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	$-0.718795\pi$
$569$	−30.2705	−1.26901	−0.634503	+	0.772920i	$0.718795\pi$
$570$	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	$-0.387098\pi$
$599$	17.0000	0.694601	0.347301	+	0.937754i	$0.387098\pi$
$600$	2.47214	0.100925
$601$	14.1246	0.576155	0.288077	−	0.957607i	$-0.406984\pi$
$601$	14.1246	0.576155	0.288077	+	0.957607i	$0.406984\pi$
$602$	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	$-0.388261\pi$
$607$	16.9443	0.687747	0.343873	+	0.939016i	$0.388261\pi$
$608$	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	$-0.378176\pi$
$641$	18.9098	0.746893	0.373447	+	0.927652i	$0.378176\pi$
$642$	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	$-0.273390\pi$
$659$	33.5410	1.30657	0.653286	+	0.757111i	$0.273390\pi$
$660$	3.09017	0.120285
$661$	−11.8328	−0.460243	−0.230122	−	0.973162i	$-0.573912\pi$
$661$	−11.8328	−0.460243	−0.230122	+	0.973162i	$0.573912\pi$
$662$	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	$-0.367965\pi$
$673$	20.9098	0.806015	0.403007	+	0.915197i	$0.367965\pi$
$674$	−33.4508	−1.28848
$675$	−13.8885	−0.534570
$676$	10.5623	0.406243
$677$	3.70820	0.142518	0.0712589	−	0.997458i	$-0.477298\pi$
$677$	3.70820	0.142518	0.0712589	+	0.997458i	$0.477298\pi$
$678$	−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	$-0.626770\pi$
$683$	−20.2705	−0.775630	−0.387815	+	0.921737i	$0.626770\pi$
$684$	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	$-0.877159\pi$
$743$	−50.5066	−1.85291	−0.926453	+	0.376410i	$0.877159\pi$
$744$	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	$-0.428665\pi$
$751$	12.1803	0.444467	0.222233	+	0.974993i	$0.428665\pi$
$752$	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	$-0.497494\pi$
$773$	0.437694	0.0157428	0.00787138	+	0.999969i	$0.497494\pi$
$774$	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	$-0.608001\pi$
$787$	−18.6738	−0.665648	−0.332824	+	0.942989i	$0.608001\pi$
$788$	−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	$-0.427216\pi$
$797$	12.7984	0.453342	0.226671	+	0.973971i	$0.427216\pi$
$798$	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	$-0.752117\pi$
$811$	−40.5410	−1.42359	−0.711794	+	0.702388i	$0.752117\pi$
$812$	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	$-0.425254\pi$
$827$	13.3820	0.465337	0.232668	+	0.972556i	$0.425254\pi$
$828$	9.85410	0.342454
$829$	6.88854	0.239249	0.119625	−	0.992819i	$-0.461831\pi$
$829$	6.88854	0.239249	0.119625	+	0.992819i	$0.461831\pi$
$830$	−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	$-0.248310\pi$
$839$	41.1803	1.42170	0.710852	+	0.703342i	$0.248310\pi$
$840$	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	$-0.401999\pi$
$857$	17.7426	0.606077	0.303039	+	0.952978i	$0.401999\pi$
$858$	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	$-0.539607\pi$
$863$	−7.29180	−0.248216	−0.124108	+	0.992269i	$0.539607\pi$
$864$	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	$-0.471337\pi$
$877$	5.32624	0.179854	0.0899271	+	0.995948i	$0.471337\pi$
$878$	−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	$-0.386267\pi$
$887$	20.8328	0.699497	0.349749	+	0.936844i	$0.386267\pi$
$888$	−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	$-0.410719\pi$
$907$	16.6738	0.553643	0.276822	+	0.960921i	$0.410719\pi$
$908$	−14.2361	−0.472441
$909$	−10.8541	−0.360008
$910$	−4.85410	−0.160912
$911$	46.1591	1.52932	0.764659	−	0.644435i	$-0.222907\pi$
$911$	46.1591	1.52932	0.764659	+	0.644435i	$0.222907\pi$
$912$	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	$-0.353705\pi$
$941$	27.2148	0.887177	0.443588	+	0.896231i	$0.353705\pi$
$942$	−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	$-0.666110\pi$
$953$	−30.7771	−0.996968	−0.498484	+	0.866899i	$0.666110\pi$
$954$	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	$-0.686226\pi$
$971$	−34.4164	−1.10448	−0.552238	+	0.833687i	$0.686226\pi$
$972$	−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	$-0.784913\pi$
$977$	−48.7771	−1.56052	−0.780259	+	0.625457i	$0.784913\pi$
$978$	−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	$-0.451623\pi$
$983$	9.49342	0.302793	0.151397	+	0.988473i	$0.451623\pi$
$984$	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	$-0.632272\pi$
$991$	−25.4164	−0.807379	−0.403689	+	0.914896i	$0.632272\pi$
$992$	−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.p.1.1	yes	2
19.18	odd	2		5054.2.a.f.1.2	✓	2

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

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

Related objects

Downloads

Learn more