LMFDB - Embedded newform 5054.2.a.y.1.3

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:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.17557$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.17557 q^{3} +1.00000 q^{4} +3.52015 q^{5} +2.17557 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.73311 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.17557 q^{3} +1.00000 q^{4} +3.52015 q^{5} +2.17557 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.73311 q^{9} +3.52015 q^{10} -2.80423 q^{11} +2.17557 q^{12} +1.34458 q^{13} +1.00000 q^{14} +7.65833 q^{15} +1.00000 q^{16} -3.69572 q^{17} +1.73311 q^{18} +3.52015 q^{20} +2.17557 q^{21} -2.80423 q^{22} +4.80423 q^{23} +2.17557 q^{24} +7.39144 q^{25} +1.34458 q^{26} -2.75621 q^{27} +1.00000 q^{28} +5.35114 q^{29} +7.65833 q^{30} -3.32437 q^{31} +1.00000 q^{32} -6.10079 q^{33} -3.69572 q^{34} +3.52015 q^{35} +1.73311 q^{36} +9.91930 q^{37} +2.92522 q^{39} +3.52015 q^{40} -6.54795 q^{41} +2.17557 q^{42} +10.6583 q^{43} -2.80423 q^{44} +6.10079 q^{45} +4.80423 q^{46} -9.44537 q^{47} +2.17557 q^{48} +1.00000 q^{49} +7.39144 q^{50} -8.04029 q^{51} +1.34458 q^{52} -2.46621 q^{53} -2.75621 q^{54} -9.87129 q^{55} +1.00000 q^{56} +5.35114 q^{58} +0.501096 q^{59} +7.65833 q^{60} -9.22835 q^{61} -3.32437 q^{62} +1.73311 q^{63} +1.00000 q^{64} +4.73311 q^{65} -6.10079 q^{66} +11.9882 q^{67} -3.69572 q^{68} +10.4519 q^{69} +3.52015 q^{70} -13.3167 q^{71} +1.73311 q^{72} -1.92586 q^{73} +9.91930 q^{74} +16.0806 q^{75} -2.80423 q^{77} +2.92522 q^{78} +17.5028 q^{79} +3.52015 q^{80} -11.1957 q^{81} -6.54795 q^{82} +10.8576 q^{83} +2.17557 q^{84} -13.0095 q^{85} +10.6583 q^{86} +11.6418 q^{87} -2.80423 q^{88} +16.5402 q^{89} +6.10079 q^{90} +1.34458 q^{91} +4.80423 q^{92} -7.23241 q^{93} -9.44537 q^{94} +2.17557 q^{96} -10.2012 q^{97} +1.00000 q^{98} -4.86002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 2 q^{18} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 12 q^{29} + 2 q^{30} + 14 q^{31} + 4 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 24 q^{37} - 12 q^{39} + 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} + 4 q^{46} - 2 q^{47} + 4 q^{48} + 4 q^{49} - 4 q^{50} - 8 q^{51} - 2 q^{52} + 10 q^{54} - 18 q^{55} + 4 q^{56} + 12 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} + 14 q^{65} + 4 q^{66} + 22 q^{67} + 2 q^{68} + 4 q^{69} + 2 q^{70} + 4 q^{71} + 2 q^{72} + 10 q^{73} + 24 q^{74} + 16 q^{75} + 4 q^{77} - 12 q^{78} + 2 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{84} - 14 q^{85} + 14 q^{86} + 32 q^{87} + 4 q^{88} + 10 q^{89} - 4 q^{90} - 2 q^{91} + 4 q^{92} + 14 q^{93} - 2 q^{94} + 4 q^{96} - 22 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 2 * q^18 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 12 * q^29 + 2 * q^30 + 14 * q^31 + 4 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 24 * q^37 - 12 * q^39 + 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 + 4 * q^46 - 2 * q^47 + 4 * q^48 + 4 * q^49 - 4 * q^50 - 8 * q^51 - 2 * q^52 + 10 * q^54 - 18 * q^55 + 4 * q^56 + 12 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 + 14 * q^65 + 4 * q^66 + 22 * q^67 + 2 * q^68 + 4 * q^69 + 2 * q^70 + 4 * q^71 + 2 * q^72 + 10 * q^73 + 24 * q^74 + 16 * q^75 + 4 * q^77 - 12 * q^78 + 2 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^84 - 14 * q^85 + 14 * q^86 + 32 * q^87 + 4 * q^88 + 10 * q^89 - 4 * q^90 - 2 * q^91 + 4 * q^92 + 14 * q^93 - 2 * q^94 + 4 * q^96 - 22 * q^97 + 4 * q^98 + 2 * 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
$3$	2.17557	1.25607	0.628033	−	0.778187i	$-0.283860\pi$
$3$	2.17557	1.25607	0.628033	+	0.778187i	$0.283860\pi$
$4$	1.00000	0.500000
$5$	3.52015	1.57426	0.787129	−	0.616789i	$-0.211567\pi$
$5$	3.52015	1.57426	0.787129	+	0.616789i	$0.211567\pi$
$6$	2.17557	0.888173
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.73311	0.577702
$10$	3.52015	1.11317
$11$	−2.80423	−0.845506	−0.422753	−	0.906245i	$-0.638936\pi$
$11$	−2.80423	−0.845506	−0.422753	+	0.906245i	$0.638936\pi$
$12$	2.17557	0.628033
$13$	1.34458	0.372918	0.186459	−	0.982463i	$-0.440299\pi$
$13$	1.34458	0.372918	0.186459	+	0.982463i	$0.440299\pi$
$14$	1.00000	0.267261
$15$	7.65833	1.97737
$16$	1.00000	0.250000
$17$	−3.69572	−0.896343	−0.448172	−	0.893948i	$-0.647925\pi$
$17$	−3.69572	−0.896343	−0.448172	+	0.893948i	$0.647925\pi$
$18$	1.73311	0.408497
$19$	0	0
$19$	0	0
$20$	3.52015	0.787129
$21$	2.17557	0.474748
$22$	−2.80423	−0.597863
$23$	4.80423	1.00175	0.500875	−	0.865520i	$-0.333012\pi$
$23$	4.80423	1.00175	0.500875	+	0.865520i	$0.333012\pi$
$24$	2.17557	0.444086
$25$	7.39144	1.47829
$26$	1.34458	0.263693
$27$	−2.75621	−0.530434
$28$	1.00000	0.188982
$29$	5.35114	0.993682	0.496841	−	0.867842i	$-0.334493\pi$
$29$	5.35114	0.993682	0.496841	+	0.867842i	$0.334493\pi$
$30$	7.65833	1.39821
$31$	−3.32437	−0.597075	−0.298538	−	0.954398i	$-0.596499\pi$
$31$	−3.32437	−0.597075	−0.298538	+	0.954398i	$0.596499\pi$
$32$	1.00000	0.176777
$33$	−6.10079	−1.06201
$34$	−3.69572	−0.633810
$35$	3.52015	0.595013
$36$	1.73311	0.288851
$37$	9.91930	1.63072	0.815361	−	0.578952i	$-0.196538\pi$
$37$	9.91930	1.63072	0.815361	+	0.578952i	$0.196538\pi$
$38$	0	0
$39$	2.92522	0.468410
$40$	3.52015	0.556584
$41$	−6.54795	−1.02262	−0.511309	−	0.859397i	$-0.670839\pi$
$41$	−6.54795	−1.02262	−0.511309	+	0.859397i	$0.670839\pi$
$42$	2.17557	0.335698
$43$	10.6583	1.62538	0.812690	−	0.582696i	$-0.198002\pi$
$43$	10.6583	1.62538	0.812690	+	0.582696i	$0.198002\pi$
$44$	−2.80423	−0.422753
$45$	6.10079	0.909452
$46$	4.80423	0.708344
$47$	−9.44537	−1.37775	−0.688874	−	0.724881i	$-0.741895\pi$
$47$	−9.44537	−1.37775	−0.688874	+	0.724881i	$0.741895\pi$
$48$	2.17557	0.314017
$49$	1.00000	0.142857
$50$	7.39144	1.04531
$51$	−8.04029	−1.12587
$52$	1.34458	0.186459
$53$	−2.46621	−0.338761	−0.169380	−	0.985551i	$-0.554177\pi$
$53$	−2.46621	−0.338761	−0.169380	+	0.985551i	$0.554177\pi$
$54$	−2.75621	−0.375073
$55$	−9.87129	−1.33104
$56$	1.00000	0.133631
$57$	0	0
$58$	5.35114	0.702639
$59$	0.501096	0.0652372	0.0326186	−	0.999468i	$-0.489615\pi$
$59$	0.501096	0.0652372	0.0326186	+	0.999468i	$0.489615\pi$
$60$	7.65833	0.988686
$61$	−9.22835	−1.18157	−0.590785	−	0.806829i	$-0.701182\pi$
$61$	−9.22835	−1.18157	−0.590785	+	0.806829i	$0.701182\pi$
$62$	−3.32437	−0.422196
$63$	1.73311	0.218351
$64$	1.00000	0.125000
$65$	4.73311	0.587070
$66$	−6.10079	−0.750956
$67$	11.9882	1.46459	0.732297	−	0.680985i	$-0.238448\pi$
$67$	11.9882	1.46459	0.732297	+	0.680985i	$0.238448\pi$
$68$	−3.69572	−0.448172
$69$	10.4519	1.25826
$70$	3.52015	0.420738
$71$	−13.3167	−1.58040	−0.790198	−	0.612851i	$-0.790022\pi$
$71$	−13.3167	−1.58040	−0.790198	+	0.612851i	$0.790022\pi$
$72$	1.73311	0.204249
$73$	−1.92586	−0.225405	−0.112703	−	0.993629i	$-0.535951\pi$
$73$	−1.92586	−0.225405	−0.112703	+	0.993629i	$0.535951\pi$
$74$	9.91930	1.15310
$75$	16.0806	1.85683
$76$	0	0
$77$	−2.80423	−0.319571
$78$	2.92522	0.331216
$79$	17.5028	1.96922	0.984612	−	0.174754i	$-0.0559130\pi$
$79$	17.5028	1.96922	0.984612	+	0.174754i	$0.0559130\pi$
$80$	3.52015	0.393564
$81$	−11.1957	−1.24396
$82$	−6.54795	−0.723101
$83$	10.8576	1.19178	0.595891	−	0.803065i	$-0.296799\pi$
$83$	10.8576	1.19178	0.595891	+	0.803065i	$0.296799\pi$
$84$	2.17557	0.237374
$85$	−13.0095	−1.41108
$86$	10.6583	1.14932
$87$	11.6418	1.24813
$88$	−2.80423	−0.298932
$89$	16.5402	1.75326	0.876631	−	0.481164i	$-0.159786\pi$
$89$	16.5402	1.75326	0.876631	+	0.481164i	$0.159786\pi$
$90$	6.10079	0.643080
$91$	1.34458	0.140950
$92$	4.80423	0.500875
$93$	−7.23241	−0.749966
$94$	−9.44537	−0.974215
$95$	0	0
$96$	2.17557	0.222043
$97$	−10.2012	−1.03577	−0.517887	−	0.855449i	$-0.673281\pi$
$97$	−10.2012	−1.03577	−0.517887	+	0.855449i	$0.673281\pi$
$98$	1.00000	0.101015
$99$	−4.86002	−0.488451
$100$	7.39144	0.739144
$101$	1.16025	0.115449	0.0577246	−	0.998333i	$-0.481615\pi$
$101$	1.16025	0.115449	0.0577246	+	0.998333i	$0.481615\pi$
$102$	−8.04029	−0.796108
$103$	10.5480	1.03932	0.519660	−	0.854373i	$-0.326058\pi$
$103$	10.5480	1.03932	0.519660	+	0.854373i	$0.326058\pi$
$104$	1.34458	0.131847
$105$	7.65833	0.747376
$106$	−2.46621	−0.239540
$107$	−9.16850	−0.886352	−0.443176	−	0.896435i	$-0.646148\pi$
$107$	−9.16850	−0.886352	−0.443176	+	0.896435i	$0.646148\pi$
$108$	−2.75621	−0.265217
$109$	−5.46255	−0.523218	−0.261609	−	0.965174i	$-0.584253\pi$
$109$	−5.46255	−0.523218	−0.261609	+	0.965174i	$0.584253\pi$
$110$	−9.87129	−0.941190
$111$	21.5801	2.04830
$112$	1.00000	0.0944911
$113$	−2.00947	−0.189035	−0.0945175	−	0.995523i	$-0.530131\pi$
$113$	−2.00947	−0.189035	−0.0945175	+	0.995523i	$0.530131\pi$
$114$	0	0
$115$	16.9116	1.57701
$116$	5.35114	0.496841
$117$	2.33030	0.215436
$118$	0.501096	0.0461296
$119$	−3.69572	−0.338786
$120$	7.65833	0.699107
$121$	−3.13632	−0.285120
$122$	−9.22835	−0.835496
$123$	−14.2455	−1.28448
$124$	−3.32437	−0.298538
$125$	8.41820	0.752947
$126$	1.73311	0.154397
$127$	−2.30719	−0.204730	−0.102365	−	0.994747i	$-0.532641\pi$
$127$	−2.30719	−0.204730	−0.102365	+	0.994747i	$0.532641\pi$
$128$	1.00000	0.0883883
$129$	23.1879	2.04158
$130$	4.73311	0.415121
$131$	−21.9508	−1.91785	−0.958927	−	0.283654i	$-0.908453\pi$
$131$	−21.9508	−1.91785	−0.958927	+	0.283654i	$0.908453\pi$
$132$	−6.10079	−0.531006
$133$	0	0
$134$	11.9882	1.03562
$135$	−9.70228	−0.835039
$136$	−3.69572	−0.316905
$137$	−22.7616	−1.94466	−0.972329	−	0.233618i	$-0.924944\pi$
$137$	−22.7616	−1.94466	−0.972329	+	0.233618i	$0.924944\pi$
$138$	10.4519	0.889728
$139$	−11.6162	−0.985271	−0.492635	−	0.870236i	$-0.663966\pi$
$139$	−11.6162	−0.985271	−0.492635	+	0.870236i	$0.663966\pi$
$140$	3.52015	0.297507
$141$	−20.5491	−1.73054
$142$	−13.3167	−1.11751
$143$	−3.77050	−0.315305
$144$	1.73311	0.144426
$145$	18.8368	1.56431
$146$	−1.92586	−0.159386
$147$	2.17557	0.179438
$148$	9.91930	0.815361
$149$	11.0770	0.907467	0.453733	−	0.891138i	$-0.350092\pi$
$149$	11.0770	0.907467	0.453733	+	0.891138i	$0.350092\pi$
$150$	16.0806	1.31297
$151$	−1.25512	−0.102140	−0.0510701	−	0.998695i	$-0.516263\pi$
$151$	−1.25512	−0.102140	−0.0510701	+	0.998695i	$0.516263\pi$
$152$	0	0
$153$	−6.40507	−0.517820
$154$	−2.80423	−0.225971
$155$	−11.7023	−0.939950
$156$	2.92522	0.234205
$157$	−0.350101	−0.0279411	−0.0139706	−	0.999902i	$-0.504447\pi$
$157$	−0.350101	−0.0279411	−0.0139706	+	0.999902i	$0.504447\pi$
$158$	17.5028	1.39245
$159$	−5.36542	−0.425506
$160$	3.52015	0.278292
$161$	4.80423	0.378626
$162$	−11.1957	−0.879614
$163$	16.4934	1.29186	0.645931	−	0.763396i	$-0.276470\pi$
$163$	16.4934	1.29186	0.645931	+	0.763396i	$0.276470\pi$
$164$	−6.54795	−0.511309
$165$	−21.4757	−1.67188
$166$	10.8576	0.842717
$167$	−3.14945	−0.243711	−0.121856	−	0.992548i	$-0.538885\pi$
$167$	−3.14945	−0.243711	−0.121856	+	0.992548i	$0.538885\pi$
$168$	2.17557	0.167849
$169$	−11.1921	−0.860932
$170$	−13.0095	−0.997781
$171$	0	0
$172$	10.6583	0.812690
$173$	−12.4263	−0.944755	−0.472378	−	0.881396i	$-0.656604\pi$
$173$	−12.4263	−0.944755	−0.472378	+	0.881396i	$0.656604\pi$
$174$	11.6418	0.882561
$175$	7.39144	0.558740
$176$	−2.80423	−0.211376
$177$	1.09017	0.0819422
$178$	16.5402	1.23974
$179$	−10.5505	−0.788579	−0.394289	−	0.918986i	$-0.629009\pi$
$179$	−10.5505	−0.788579	−0.394289	+	0.918986i	$0.629009\pi$
$180$	6.10079	0.454726
$181$	−22.4122	−1.66588	−0.832942	−	0.553361i	$-0.813345\pi$
$181$	−22.4122	−1.66588	−0.832942	+	0.553361i	$0.813345\pi$
$182$	1.34458	0.0996666
$183$	−20.0769	−1.48413
$184$	4.80423	0.354172
$185$	34.9174	2.56718
$186$	−7.23241	−0.530306
$187$	10.3636	0.757863
$188$	−9.44537	−0.688874
$189$	−2.75621	−0.200485
$190$	0	0
$191$	5.98468	0.433036	0.216518	−	0.976279i	$-0.430530\pi$
$191$	5.98468	0.433036	0.216518	+	0.976279i	$0.430530\pi$
$192$	2.17557	0.157008
$193$	15.4318	1.11081	0.555404	−	0.831581i	$-0.312564\pi$
$193$	15.4318	1.11081	0.555404	+	0.831581i	$0.312564\pi$
$194$	−10.2012	−0.732402
$195$	10.2972	0.737398
$196$	1.00000	0.0714286
$197$	−4.97729	−0.354617	−0.177309	−	0.984155i	$-0.556739\pi$
$197$	−4.97729	−0.354617	−0.177309	+	0.984155i	$0.556739\pi$
$198$	−4.86002	−0.345387
$199$	0.473176	0.0335425	0.0167713	−	0.999859i	$-0.494661\pi$
$199$	0.473176	0.0335425	0.0167713	+	0.999859i	$0.494661\pi$
$200$	7.39144	0.522653
$201$	26.0812	1.83963
$202$	1.16025	0.0816349
$203$	5.35114	0.375576
$204$	−8.04029	−0.562933
$205$	−23.0498	−1.60987
$206$	10.5480	0.734911
$207$	8.32624	0.578714
$208$	1.34458	0.0932296
$209$	0	0
$210$	7.65833	0.528475
$211$	−20.0211	−1.37831	−0.689156	−	0.724613i	$-0.742018\pi$
$211$	−20.0211	−1.37831	−0.689156	+	0.724613i	$0.742018\pi$
$212$	−2.46621	−0.169380
$213$	−28.9713	−1.98508
$214$	−9.16850	−0.626745
$215$	37.5189	2.55877
$216$	−2.75621	−0.187537
$217$	−3.32437	−0.225673
$218$	−5.46255	−0.369971
$219$	−4.18985	−0.283124
$220$	−9.87129	−0.665522
$221$	−4.96917	−0.334263
$222$	21.5801	1.44836
$223$	−2.11456	−0.141602	−0.0708008	−	0.997490i	$-0.522555\pi$
$223$	−2.11456	−0.141602	−0.0708008	+	0.997490i	$0.522555\pi$
$224$	1.00000	0.0668153
$225$	12.8101	0.854010
$226$	−2.00947	−0.133668
$227$	4.53547	0.301030	0.150515	−	0.988608i	$-0.451907\pi$
$227$	4.53547	0.301030	0.150515	+	0.988608i	$0.451907\pi$
$228$	0	0
$229$	−22.8914	−1.51270	−0.756352	−	0.654164i	$-0.773020\pi$
$229$	−22.8914	−1.51270	−0.756352	+	0.654164i	$0.773020\pi$
$230$	16.9116	1.11512
$231$	−6.10079	−0.401403
$232$	5.35114	0.351320
$233$	−15.2646	−1.00002	−0.500008	−	0.866021i	$-0.666670\pi$
$233$	−15.2646	−1.00002	−0.500008	+	0.866021i	$0.666670\pi$
$234$	2.33030	0.152336
$235$	−33.2491	−2.16893
$236$	0.501096	0.0326186
$237$	38.0787	2.47348
$238$	−3.69572	−0.239558
$239$	−16.1839	−1.04685	−0.523424	−	0.852072i	$-0.675346\pi$
$239$	−16.1839	−1.04685	−0.523424	+	0.852072i	$0.675346\pi$
$240$	7.65833	0.494343
$241$	3.37895	0.217657	0.108829	−	0.994061i	$-0.465290\pi$
$241$	3.37895	0.217657	0.108829	+	0.994061i	$0.465290\pi$
$242$	−3.13632	−0.201610
$243$	−16.0883	−1.03207
$244$	−9.22835	−0.590785
$245$	3.52015	0.224894
$246$	−14.2455	−0.908262
$247$	0	0
$248$	−3.32437	−0.211098
$249$	23.6216	1.49696
$250$	8.41820	0.532414
$251$	−22.2609	−1.40510	−0.702549	−	0.711636i	$-0.747955\pi$
$251$	−22.2609	−1.40510	−0.702549	+	0.711636i	$0.747955\pi$
$252$	1.73311	0.109175
$253$	−13.4721	−0.846986
$254$	−2.30719	−0.144766
$255$	−28.3030	−1.77240
$256$	1.00000	0.0625000
$257$	14.1227	0.880948	0.440474	−	0.897765i	$-0.354810\pi$
$257$	14.1227	0.880948	0.440474	+	0.897765i	$0.354810\pi$
$258$	23.1879	1.44362
$259$	9.91930	0.616355
$260$	4.73311	0.293535
$261$	9.27410	0.574052
$262$	−21.9508	−1.35613
$263$	1.58732	0.0978785	0.0489392	−	0.998802i	$-0.484416\pi$
$263$	1.58732	0.0978785	0.0489392	+	0.998802i	$0.484416\pi$
$264$	−6.10079	−0.375478
$265$	−8.68144	−0.533296
$266$	0	0
$267$	35.9845	2.20221
$268$	11.9882	0.732297
$269$	−21.7180	−1.32417	−0.662085	−	0.749429i	$-0.730328\pi$
$269$	−21.7180	−1.32417	−0.662085	+	0.749429i	$0.730328\pi$
$270$	−9.70228	−0.590462
$271$	−16.0267	−0.973550	−0.486775	−	0.873527i	$-0.661827\pi$
$271$	−16.0267	−0.973550	−0.486775	+	0.873527i	$0.661827\pi$
$272$	−3.69572	−0.224086
$273$	2.92522	0.177042
$274$	−22.7616	−1.37508
$275$	−20.7273	−1.24990
$276$	10.4519	0.629132
$277$	−18.4186	−1.10667	−0.553333	−	0.832960i	$-0.686644\pi$
$277$	−18.4186	−1.10667	−0.553333	+	0.832960i	$0.686644\pi$
$278$	−11.6162	−0.696692
$279$	−5.76149	−0.344932
$280$	3.52015	0.210369
$281$	31.4082	1.87365	0.936827	−	0.349792i	$-0.113748\pi$
$281$	31.4082	1.87365	0.936827	+	0.349792i	$0.113748\pi$
$282$	−20.5491	−1.22368
$283$	24.7246	1.46972	0.734861	−	0.678217i	$-0.237247\pi$
$283$	24.7246	1.46972	0.734861	+	0.678217i	$0.237247\pi$
$284$	−13.3167	−0.790198
$285$	0	0
$286$	−3.77050	−0.222954
$287$	−6.54795	−0.386514
$288$	1.73311	0.102124
$289$	−3.34167	−0.196569
$290$	18.8368	1.10614
$291$	−22.1934	−1.30100
$292$	−1.92586	−0.112703
$293$	−4.10747	−0.239961	−0.119980	−	0.992776i	$-0.538283\pi$
$293$	−4.10747	−0.239961	−0.119980	+	0.992776i	$0.538283\pi$
$294$	2.17557	0.126882
$295$	1.76393	0.102700
$296$	9.91930	0.576548
$297$	7.72905	0.448485
$298$	11.0770	0.641676
$299$	6.45965	0.373571
$300$	16.0806	0.928413
$301$	10.6583	0.614336
$302$	−1.25512	−0.0722240
$303$	2.52420	0.145012
$304$	0	0
$305$	−32.4852	−1.86009
$306$	−6.40507	−0.366154
$307$	14.3380	0.818314	0.409157	−	0.912464i	$-0.365823\pi$
$307$	14.3380	0.818314	0.409157	+	0.912464i	$0.365823\pi$
$308$	−2.80423	−0.159786
$309$	22.9478	1.30546
$310$	−11.7023	−0.664645
$311$	−13.2034	−0.748695	−0.374347	−	0.927289i	$-0.622133\pi$
$311$	−13.2034	−0.748695	−0.374347	+	0.927289i	$0.622133\pi$
$312$	2.92522	0.165608
$313$	12.8412	0.725826	0.362913	−	0.931823i	$-0.381782\pi$
$313$	12.8412	0.725826	0.362913	+	0.931823i	$0.381782\pi$
$314$	−0.350101	−0.0197574
$315$	6.10079	0.343741
$316$	17.5028	0.984612
$317$	7.23015	0.406085	0.203043	−	0.979170i	$-0.434917\pi$
$317$	7.23015	0.406085	0.203043	+	0.979170i	$0.434917\pi$
$318$	−5.36542	−0.300878
$319$	−15.0058	−0.840164
$320$	3.52015	0.196782
$321$	−19.9467	−1.11332
$322$	4.80423	0.267729
$323$	0	0
$324$	−11.1957	−0.621981
$325$	9.93835	0.551280
$326$	16.4934	0.913484
$327$	−11.8842	−0.657196
$328$	−6.54795	−0.361550
$329$	−9.44537	−0.520740
$330$	−21.4757	−1.18220
$331$	18.5184	1.01786	0.508930	−	0.860808i	$-0.330041\pi$
$331$	18.5184	1.01786	0.508930	+	0.860808i	$0.330041\pi$
$332$	10.8576	0.595891
$333$	17.1912	0.942072
$334$	−3.14945	−0.172330
$335$	42.2003	2.30565
$336$	2.17557	0.118687
$337$	2.30938	0.125800	0.0629000	−	0.998020i	$-0.479965\pi$
$337$	2.30938	0.125800	0.0629000	+	0.998020i	$0.479965\pi$
$338$	−11.1921	−0.608771
$339$	−4.37174	−0.237440
$340$	−13.0095	−0.705538
$341$	9.32229	0.504831
$342$	0	0
$343$	1.00000	0.0539949
$344$	10.6583	0.574659
$345$	36.7923	1.98083
$346$	−12.4263	−0.668043
$347$	28.7044	1.54093	0.770465	−	0.637482i	$-0.220024\pi$
$347$	28.7044	1.54093	0.770465	+	0.637482i	$0.220024\pi$
$348$	11.6418	0.624065
$349$	1.87129	0.100168	0.0500839	−	0.998745i	$-0.484051\pi$
$349$	1.87129	0.100168	0.0500839	+	0.998745i	$0.484051\pi$
$350$	7.39144	0.395089
$351$	−3.70594	−0.197809
$352$	−2.80423	−0.149466
$353$	−23.4056	−1.24575	−0.622877	−	0.782320i	$-0.714036\pi$
$353$	−23.4056	−1.24575	−0.622877	+	0.782320i	$0.714036\pi$
$354$	1.09017	0.0579419
$355$	−46.8766	−2.48795
$356$	16.5402	0.876631
$357$	−8.04029	−0.425537
$358$	−10.5505	−0.557609
$359$	8.35333	0.440872	0.220436	−	0.975401i	$-0.429252\pi$
$359$	8.35333	0.440872	0.220436	+	0.975401i	$0.429252\pi$
$360$	6.10079	0.321540
$361$	0	0
$362$	−22.4122	−1.17796
$363$	−6.82328	−0.358129
$364$	1.34458	0.0704750
$365$	−6.77932	−0.354846
$366$	−20.0769	−1.04944
$367$	9.73550	0.508189	0.254095	−	0.967179i	$-0.418223\pi$
$367$	9.73550	0.508189	0.254095	+	0.967179i	$0.418223\pi$
$368$	4.80423	0.250438
$369$	−11.3483	−0.590769
$370$	34.9174	1.81527
$371$	−2.46621	−0.128039
$372$	−7.23241	−0.374983
$373$	27.4991	1.42385	0.711925	−	0.702255i	$-0.247823\pi$
$373$	27.4991	1.42385	0.711925	+	0.702255i	$0.247823\pi$
$374$	10.3636	0.535890
$375$	18.3144	0.945751
$376$	−9.44537	−0.487108
$377$	7.19502	0.370562
$378$	−2.75621	−0.141764
$379$	14.0748	0.722976	0.361488	−	0.932377i	$-0.382269\pi$
$379$	14.0748	0.722976	0.361488	+	0.932377i	$0.382269\pi$
$380$	0	0
$381$	−5.01945	−0.257154
$382$	5.98468	0.306203
$383$	−29.2284	−1.49350	−0.746749	−	0.665105i	$-0.768387\pi$
$383$	−29.2284	−1.49350	−0.746749	+	0.665105i	$0.768387\pi$
$384$	2.17557	0.111022
$385$	−9.87129	−0.503087
$386$	15.4318	0.785460
$387$	18.4720	0.938986
$388$	−10.2012	−0.517887
$389$	−13.8753	−0.703508	−0.351754	−	0.936092i	$-0.614415\pi$
$389$	−13.8753	−0.703508	−0.351754	+	0.936092i	$0.614415\pi$
$390$	10.2972	0.521419
$391$	−17.7551	−0.897912
$392$	1.00000	0.0505076
$393$	−47.7556	−2.40895
$394$	−4.97729	−0.250752
$395$	61.6126	3.10007
$396$	−4.86002	−0.244225
$397$	−36.4442	−1.82908	−0.914541	−	0.404492i	$-0.867448\pi$
$397$	−36.4442	−1.82908	−0.914541	+	0.404492i	$0.867448\pi$
$398$	0.473176	0.0237182
$399$	0	0
$400$	7.39144	0.369572
$401$	5.55284	0.277295	0.138648	−	0.990342i	$-0.455724\pi$
$401$	5.55284	0.277295	0.138648	+	0.990342i	$0.455724\pi$
$402$	26.0812	1.30081
$403$	−4.46987	−0.222660
$404$	1.16025	0.0577246
$405$	−39.4104	−1.95832
$406$	5.35114	0.265573
$407$	−27.8160	−1.37879
$408$	−8.04029	−0.398054
$409$	−25.8973	−1.28054	−0.640270	−	0.768150i	$-0.721177\pi$
$409$	−25.8973	−1.28054	−0.640270	+	0.768150i	$0.721177\pi$
$410$	−23.0498	−1.13835
$411$	−49.5195	−2.44262
$412$	10.5480	0.519660
$413$	0.501096	0.0246573
$414$	8.32624	0.409212
$415$	38.2205	1.87617
$416$	1.34458	0.0659233
$417$	−25.2718	−1.23757
$418$	0	0
$419$	23.7413	1.15984	0.579919	−	0.814674i	$-0.303084\pi$
$419$	23.7413	1.15984	0.579919	+	0.814674i	$0.303084\pi$
$420$	7.65833	0.373688
$421$	38.0474	1.85432	0.927158	−	0.374670i	$-0.122244\pi$
$421$	38.0474	1.85432	0.927158	+	0.374670i	$0.122244\pi$
$422$	−20.0211	−0.974613
$423$	−16.3698	−0.795929
$424$	−2.46621	−0.119770
$425$	−27.3167	−1.32505
$426$	−28.9713	−1.40367
$427$	−9.22835	−0.446591
$428$	−9.16850	−0.443176
$429$	−8.20298	−0.396044
$430$	37.5189	1.80932
$431$	4.34741	0.209407	0.104704	−	0.994503i	$-0.466611\pi$
$431$	4.34741	0.209407	0.104704	+	0.994503i	$0.466611\pi$
$432$	−2.75621	−0.132608
$433$	−4.40984	−0.211924	−0.105962	−	0.994370i	$-0.533792\pi$
$433$	−4.40984	−0.211924	−0.105962	+	0.994370i	$0.533792\pi$
$434$	−3.32437	−0.159575
$435$	40.9808	1.96488
$436$	−5.46255	−0.261609
$437$	0	0
$438$	−4.18985	−0.200199
$439$	27.8784	1.33056	0.665281	−	0.746593i	$-0.268312\pi$
$439$	27.8784	1.33056	0.665281	+	0.746593i	$0.268312\pi$
$440$	−9.87129	−0.470595
$441$	1.73311	0.0825289
$442$	−4.96917	−0.236360
$443$	−12.3334	−0.585980	−0.292990	−	0.956116i	$-0.594650\pi$
$443$	−12.3334	−0.585980	−0.292990	+	0.956116i	$0.594650\pi$
$444$	21.5801	1.02415
$445$	58.2241	2.76009
$446$	−2.11456	−0.100127
$447$	24.0989	1.13984
$448$	1.00000	0.0472456
$449$	−16.7235	−0.789232	−0.394616	−	0.918846i	$-0.629122\pi$
$449$	−16.7235	−0.789232	−0.394616	+	0.918846i	$0.629122\pi$
$450$	12.8101	0.603876
$451$	18.3619	0.864630
$452$	−2.00947	−0.0945175
$453$	−2.73060	−0.128295
$454$	4.53547	0.212860
$455$	4.73311	0.221891
$456$	0	0
$457$	10.6854	0.499843	0.249922	−	0.968266i	$-0.419595\pi$
$457$	10.6854	0.499843	0.249922	+	0.968266i	$0.419595\pi$
$458$	−22.8914	−1.06964
$459$	10.1862	0.475451
$460$	16.9116	0.788507
$461$	−26.4779	−1.23320	−0.616600	−	0.787276i	$-0.711491\pi$
$461$	−26.4779	−1.23320	−0.616600	+	0.787276i	$0.711491\pi$
$462$	−6.10079	−0.283835
$463$	15.6061	0.725276	0.362638	−	0.931930i	$-0.381876\pi$
$463$	15.6061	0.725276	0.362638	+	0.931930i	$0.381876\pi$
$464$	5.35114	0.248420
$465$	−25.4591	−1.18064
$466$	−15.2646	−0.707118
$467$	−4.57730	−0.211812	−0.105906	−	0.994376i	$-0.533774\pi$
$467$	−4.57730	−0.211812	−0.105906	+	0.994376i	$0.533774\pi$
$468$	2.33030	0.107718
$469$	11.9882	0.553565
$470$	−33.2491	−1.53367
$471$	−0.761670	−0.0350959
$472$	0.501096	0.0230648
$473$	−29.8884	−1.37427
$474$	38.0787	1.74901
$475$	0	0
$476$	−3.69572	−0.169393
$477$	−4.27421	−0.195703
$478$	−16.1839	−0.740234
$479$	11.9098	0.544172	0.272086	−	0.962273i	$-0.412286\pi$
$479$	11.9098	0.544172	0.272086	+	0.962273i	$0.412286\pi$
$480$	7.65833	0.349553
$481$	13.3373	0.608127
$482$	3.37895	0.153907
$483$	10.4519	0.475579
$484$	−3.13632	−0.142560
$485$	−35.9097	−1.63057
$486$	−16.0883	−0.729780
$487$	−11.8435	−0.536680	−0.268340	−	0.963324i	$-0.586475\pi$
$487$	−11.8435	−0.536680	−0.268340	+	0.963324i	$0.586475\pi$
$488$	−9.22835	−0.417748
$489$	35.8825	1.62266
$490$	3.52015	0.159024
$491$	5.95019	0.268528	0.134264	−	0.990946i	$-0.457133\pi$
$491$	5.95019	0.268528	0.134264	+	0.990946i	$0.457133\pi$
$492$	−14.2455	−0.642238
$493$	−19.7763	−0.890680
$494$	0	0
$495$	−17.1080	−0.768947
$496$	−3.32437	−0.149269
$497$	−13.3167	−0.597334
$498$	23.6216	1.05851
$499$	15.8576	0.709886	0.354943	−	0.934888i	$-0.384500\pi$
$499$	15.8576	0.709886	0.354943	+	0.934888i	$0.384500\pi$
$500$	8.41820	0.376473
$501$	−6.85184	−0.306118
$502$	−22.2609	−0.993554
$503$	10.6100	0.473076	0.236538	−	0.971622i	$-0.423987\pi$
$503$	10.6100	0.473076	0.236538	+	0.971622i	$0.423987\pi$
$504$	1.73311	0.0771987
$505$	4.08425	0.181747
$506$	−13.4721	−0.598909
$507$	−24.3492	−1.08139
$508$	−2.30719	−0.102365
$509$	11.3454	0.502874	0.251437	−	0.967874i	$-0.419097\pi$
$509$	11.3454	0.502874	0.251437	+	0.967874i	$0.419097\pi$
$510$	−28.3030	−1.25328
$511$	−1.92586	−0.0851952
$512$	1.00000	0.0441942
$513$	0	0
$514$	14.1227	0.622925
$515$	37.1304	1.63616
$516$	23.1879	1.02079
$517$	26.4869	1.16489
$518$	9.91930	0.435829
$519$	−27.0343	−1.18668
$520$	4.73311	0.207560
$521$	19.1051	0.837007	0.418504	−	0.908215i	$-0.362555\pi$
$521$	19.1051	0.837007	0.418504	+	0.908215i	$0.362555\pi$
$522$	9.27410	0.405916
$523$	23.0875	1.00955	0.504774	−	0.863252i	$-0.331576\pi$
$523$	23.0875	1.00955	0.504774	+	0.863252i	$0.331576\pi$
$524$	−21.9508	−0.958927
$525$	16.0806	0.701814
$526$	1.58732	0.0692105
$527$	12.2859	0.535184
$528$	−6.10079	−0.265503
$529$	0.0805881	0.00350383
$530$	−8.68144	−0.377097
$531$	0.868453	0.0376877
$532$	0	0
$533$	−8.80423	−0.381353
$534$	35.9845	1.55720
$535$	−32.2745	−1.39535
$536$	11.9882	0.517812
$537$	−22.9533	−0.990507
$538$	−21.7180	−0.936329
$539$	−2.80423	−0.120787
$540$	−9.70228	−0.417520
$541$	−15.6929	−0.674690	−0.337345	−	0.941381i	$-0.609529\pi$
$541$	−15.6929	−0.674690	−0.337345	+	0.941381i	$0.609529\pi$
$542$	−16.0267	−0.688404
$543$	−48.7593	−2.09246
$544$	−3.69572	−0.158453
$545$	−19.2290	−0.823680
$546$	2.92522	0.125188
$547$	12.8444	0.549187	0.274594	−	0.961560i	$-0.411457\pi$
$547$	12.8444	0.549187	0.274594	+	0.961560i	$0.411457\pi$
$548$	−22.7616	−0.972329
$549$	−15.9937	−0.682595
$550$	−20.7273	−0.883813
$551$	0	0
$552$	10.4519	0.444864
$553$	17.5028	0.744297
$554$	−18.4186	−0.782531
$555$	75.9652	3.22455
$556$	−11.6162	−0.492635
$557$	17.6165	0.746433	0.373217	−	0.927744i	$-0.378255\pi$
$557$	17.6165	0.746433	0.373217	+	0.927744i	$0.378255\pi$
$558$	−5.76149	−0.243904
$559$	14.3309	0.606134
$560$	3.52015	0.148753
$561$	22.5468	0.951927
$562$	31.4082	1.32487
$563$	33.2321	1.40057	0.700283	−	0.713865i	$-0.253057\pi$
$563$	33.2321	1.40057	0.700283	+	0.713865i	$0.253057\pi$
$564$	−20.5491	−0.865272
$565$	−7.07363	−0.297590
$566$	24.7246	1.03925
$567$	−11.1957	−0.470174
$568$	−13.3167	−0.558754
$569$	−8.98091	−0.376499	−0.188250	−	0.982121i	$-0.560281\pi$
$569$	−8.98091	−0.376499	−0.188250	+	0.982121i	$0.560281\pi$
$570$	0	0
$571$	−23.0380	−0.964110	−0.482055	−	0.876141i	$-0.660109\pi$
$571$	−23.0380	−0.964110	−0.482055	+	0.876141i	$0.660109\pi$
$572$	−3.77050	−0.157652
$573$	13.0201	0.543922
$574$	−6.54795	−0.273306
$575$	35.5101	1.48087
$576$	1.73311	0.0722128
$577$	21.3662	0.889487	0.444743	−	0.895658i	$-0.353295\pi$
$577$	21.3662	0.889487	0.444743	+	0.895658i	$0.353295\pi$
$578$	−3.34167	−0.138995
$579$	33.5731	1.39525
$580$	18.8368	0.782156
$581$	10.8576	0.450451
$582$	−22.1934	−0.919946
$583$	6.91582	0.286424
$584$	−1.92586	−0.0796928
$585$	8.20298	0.339152
$586$	−4.10747	−0.169678
$587$	6.45630	0.266480	0.133240	−	0.991084i	$-0.457462\pi$
$587$	6.45630	0.266480	0.133240	+	0.991084i	$0.457462\pi$
$588$	2.17557	0.0897190
$589$	0	0
$590$	1.76393	0.0726199
$591$	−10.8284	−0.445423
$592$	9.91930	0.407681
$593$	43.6349	1.79187	0.895935	−	0.444186i	$-0.146507\pi$
$593$	43.6349	1.79187	0.895935	+	0.444186i	$0.146507\pi$
$594$	7.72905	0.317127
$595$	−13.0095	−0.533336
$596$	11.0770	0.453733
$597$	1.02943	0.0421316
$598$	6.45965	0.264155
$599$	1.41049	0.0576309	0.0288154	−	0.999585i	$-0.490826\pi$
$599$	1.41049	0.0576309	0.0288154	+	0.999585i	$0.490826\pi$
$600$	16.0806	0.656487
$601$	47.7648	1.94837	0.974184	−	0.225754i	$-0.0724845\pi$
$601$	47.7648	1.94837	0.974184	+	0.225754i	$0.0724845\pi$
$602$	10.6583	0.434401
$603$	20.7769	0.846100
$604$	−1.25512	−0.0510701
$605$	−11.0403	−0.448852
$606$	2.52420	0.102539
$607$	19.5543	0.793683	0.396841	−	0.917887i	$-0.370106\pi$
$607$	19.5543	0.793683	0.396841	+	0.917887i	$0.370106\pi$
$608$	0	0
$609$	11.6418	0.471749
$610$	−32.4852	−1.31529
$611$	−12.7000	−0.513788
$612$	−6.40507	−0.258910
$613$	−38.2184	−1.54363	−0.771814	−	0.635848i	$-0.780650\pi$
$613$	−38.2184	−1.54363	−0.771814	+	0.635848i	$0.780650\pi$
$614$	14.3380	0.578635
$615$	−50.1464	−2.02210
$616$	−2.80423	−0.112985
$617$	39.4623	1.58869	0.794347	−	0.607465i	$-0.207813\pi$
$617$	39.4623	1.58869	0.794347	+	0.607465i	$0.207813\pi$
$618$	22.9478	0.923097
$619$	20.0816	0.807149	0.403574	−	0.914947i	$-0.367768\pi$
$619$	20.0816	0.807149	0.403574	+	0.914947i	$0.367768\pi$
$620$	−11.7023	−0.469975
$621$	−13.2415	−0.531362
$622$	−13.2034	−0.529407
$623$	16.5402	0.662671
$624$	2.92522	0.117103
$625$	−7.32386	−0.292955
$626$	12.8412	0.513237
$627$	0	0
$628$	−0.350101	−0.0139706
$629$	−36.6589	−1.46169
$630$	6.10079	0.243061
$631$	−33.1030	−1.31781	−0.658905	−	0.752226i	$-0.728980\pi$
$631$	−33.1030	−1.31781	−0.658905	+	0.752226i	$0.728980\pi$
$632$	17.5028	0.696226
$633$	−43.5574	−1.73125
$634$	7.23015	0.287146
$635$	−8.12164	−0.322297
$636$	−5.36542	−0.212753
$637$	1.34458	0.0532741
$638$	−15.0058	−0.594086
$639$	−23.0792	−0.912999
$640$	3.52015	0.139146
$641$	9.88036	0.390251	0.195125	−	0.980778i	$-0.437489\pi$
$641$	9.88036	0.390251	0.195125	+	0.980778i	$0.437489\pi$
$642$	−19.9467	−0.787234
$643$	−26.7710	−1.05575	−0.527873	−	0.849323i	$-0.677010\pi$
$643$	−26.7710	−1.05575	−0.527873	+	0.849323i	$0.677010\pi$
$644$	4.80423	0.189313
$645$	81.6250	3.21398
$646$	0	0
$647$	14.3101	0.562588	0.281294	−	0.959622i	$-0.409236\pi$
$647$	14.3101	0.562588	0.281294	+	0.959622i	$0.409236\pi$
$648$	−11.1957	−0.439807
$649$	−1.40519	−0.0551584
$650$	9.93835	0.389814
$651$	−7.23241	−0.283460
$652$	16.4934	0.645931
$653$	30.2338	1.18314	0.591571	−	0.806253i	$-0.298508\pi$
$653$	30.2338	1.18314	0.591571	+	0.806253i	$0.298508\pi$
$654$	−11.8842	−0.464708
$655$	−77.2702	−3.01920
$656$	−6.54795	−0.255655
$657$	−3.33773	−0.130217
$658$	−9.44537	−0.368219
$659$	24.2975	0.946496	0.473248	−	0.880929i	$-0.343081\pi$
$659$	24.2975	0.946496	0.473248	+	0.880929i	$0.343081\pi$
$660$	−21.4757	−0.835940
$661$	−40.1393	−1.56124	−0.780619	−	0.625007i	$-0.785096\pi$
$661$	−40.1393	−1.56124	−0.780619	+	0.625007i	$0.785096\pi$
$662$	18.5184	0.719736
$663$	−10.8108	−0.419856
$664$	10.8576	0.421359
$665$	0	0
$666$	17.1912	0.666146
$667$	25.7081	0.995421
$668$	−3.14945	−0.121856
$669$	−4.60038	−0.177861
$670$	42.2003	1.63034
$671$	25.8784	0.999024
$672$	2.17557	0.0839245
$673$	14.8482	0.572355	0.286178	−	0.958177i	$-0.407615\pi$
$673$	14.8482	0.572355	0.286178	+	0.958177i	$0.407615\pi$
$674$	2.30938	0.0889540
$675$	−20.3724	−0.784133
$676$	−11.1921	−0.430466
$677$	25.9381	0.996883	0.498442	−	0.866923i	$-0.333906\pi$
$677$	25.9381	0.996883	0.498442	+	0.866923i	$0.333906\pi$
$678$	−4.37174	−0.167896
$679$	−10.2012	−0.391486
$680$	−13.0095	−0.498890
$681$	9.86723	0.378113
$682$	9.32229	0.356969
$683$	−22.0346	−0.843129	−0.421564	−	0.906798i	$-0.638519\pi$
$683$	−22.0346	−0.843129	−0.421564	+	0.906798i	$0.638519\pi$
$684$	0	0
$685$	−80.1243	−3.06139
$686$	1.00000	0.0381802
$687$	−49.8018	−1.90006
$688$	10.6583	0.406345
$689$	−3.31601	−0.126330
$690$	36.7923	1.40066
$691$	−18.1301	−0.689703	−0.344851	−	0.938657i	$-0.612071\pi$
$691$	−18.1301	−0.689703	−0.344851	+	0.938657i	$0.612071\pi$
$692$	−12.4263	−0.472378
$693$	−4.86002	−0.184617
$694$	28.7044	1.08960
$695$	−40.8906	−1.55107
$696$	11.6418	0.441281
$697$	24.1994	0.916617
$698$	1.87129	0.0708293
$699$	−33.2092	−1.25609
$700$	7.39144	0.279370
$701$	35.8742	1.35495	0.677475	−	0.735546i	$-0.263074\pi$
$701$	35.8742	1.35495	0.677475	+	0.735546i	$0.263074\pi$
$702$	−3.70594	−0.139872
$703$	0	0
$704$	−2.80423	−0.105688
$705$	−72.3357	−2.72432
$706$	−23.4056	−0.880882
$707$	1.16025	0.0436357
$708$	1.09017	0.0409711
$709$	1.44343	0.0542093	0.0271046	−	0.999633i	$-0.491371\pi$
$709$	1.44343	0.0542093	0.0271046	+	0.999633i	$0.491371\pi$
$710$	−46.8766	−1.75925
$711$	30.3343	1.13763
$712$	16.5402	0.619872
$713$	−15.9710	−0.598120
$714$	−8.04029	−0.300900
$715$	−13.2727	−0.496371
$716$	−10.5505	−0.394289
$717$	−35.2092	−1.31491
$718$	8.35333	0.311744
$719$	22.9686	0.856585	0.428293	−	0.903640i	$-0.359115\pi$
$719$	22.9686	0.856585	0.428293	+	0.903640i	$0.359115\pi$
$720$	6.10079	0.227363
$721$	10.5480	0.392826
$722$	0	0
$723$	7.35114	0.273392
$724$	−22.4122	−0.832942
$725$	39.5526	1.46895
$726$	−6.82328	−0.253236
$727$	−23.4373	−0.869240	−0.434620	−	0.900614i	$-0.643117\pi$
$727$	−23.4373	−0.869240	−0.434620	+	0.900614i	$0.643117\pi$
$728$	1.34458	0.0498333
$729$	−1.41426	−0.0523800
$730$	−6.77932	−0.250914
$731$	−39.3902	−1.45690
$732$	−20.0769	−0.742065
$733$	39.9842	1.47685	0.738424	−	0.674336i	$-0.235570\pi$
$733$	39.9842	1.47685	0.738424	+	0.674336i	$0.235570\pi$
$734$	9.73550	0.359344
$735$	7.65833	0.282482
$736$	4.80423	0.177086
$737$	−33.6177	−1.23832
$738$	−11.3483	−0.417737
$739$	2.93035	0.107795	0.0538973	−	0.998546i	$-0.482836\pi$
$739$	2.93035	0.107795	0.0538973	+	0.998546i	$0.482836\pi$
$740$	34.9174	1.28359
$741$	0	0
$742$	−2.46621	−0.0905376
$743$	16.7593	0.614837	0.307419	−	0.951574i	$-0.400535\pi$
$743$	16.7593	0.614837	0.307419	+	0.951574i	$0.400535\pi$
$744$	−7.23241	−0.265153
$745$	38.9928	1.42859
$746$	27.4991	1.00681
$747$	18.8175	0.688495
$748$	10.3636	0.378932
$749$	−9.16850	−0.335010
$750$	18.3144	0.668747
$751$	10.2383	0.373599	0.186800	−	0.982398i	$-0.440188\pi$
$751$	10.2383	0.373599	0.186800	+	0.982398i	$0.440188\pi$
$752$	−9.44537	−0.344437
$753$	−48.4302	−1.76490
$754$	7.19502	0.262027
$755$	−4.41820	−0.160795
$756$	−2.75621	−0.100243
$757$	−51.8313	−1.88384	−0.941920	−	0.335838i	$-0.890981\pi$
$757$	−51.8313	−1.88384	−0.941920	+	0.335838i	$0.890981\pi$
$758$	14.0748	0.511222
$759$	−29.3096	−1.06387
$760$	0	0
$761$	1.45246	0.0526517	0.0263259	−	0.999653i	$-0.491619\pi$
$761$	1.45246	0.0526517	0.0263259	+	0.999653i	$0.491619\pi$
$762$	−5.01945	−0.181835
$763$	−5.46255	−0.197758
$764$	5.98468	0.216518
$765$	−22.5468	−0.815181
$766$	−29.2284	−1.05606
$767$	0.673762	0.0243281
$768$	2.17557	0.0785041
$769$	−0.848905	−0.0306123	−0.0153061	−	0.999883i	$-0.504872\pi$
$769$	−0.848905	−0.0306123	−0.0153061	+	0.999883i	$0.504872\pi$
$770$	−9.87129	−0.355737
$771$	30.7249	1.10653
$772$	15.4318	0.555404
$773$	13.5539	0.487499	0.243750	−	0.969838i	$-0.421623\pi$
$773$	13.5539	0.487499	0.243750	+	0.969838i	$0.421623\pi$
$774$	18.4720	0.663963
$775$	−24.5719	−0.882648
$776$	−10.2012	−0.366201
$777$	21.5801	0.774183
$778$	−13.8753	−0.497455
$779$	0	0
$780$	10.2972	0.368699
$781$	37.3429	1.33623
$782$	−17.7551	−0.634920
$783$	−14.7489	−0.527083
$784$	1.00000	0.0357143
$785$	−1.23241	−0.0439865
$786$	−47.7556	−1.70339
$787$	−3.86358	−0.137722	−0.0688609	−	0.997626i	$-0.521936\pi$
$787$	−3.86358	−0.137722	−0.0688609	+	0.997626i	$0.521936\pi$
$788$	−4.97729	−0.177309
$789$	3.45333	0.122942
$790$	61.6126	2.19208
$791$	−2.00947	−0.0714485
$792$	−4.86002	−0.172693
$793$	−12.4082	−0.440629
$794$	−36.4442	−1.29336
$795$	−18.8871	−0.669856
$796$	0.473176	0.0167713
$797$	15.1020	0.534939	0.267470	−	0.963566i	$-0.413813\pi$
$797$	15.1020	0.534939	0.267470	+	0.963566i	$0.413813\pi$
$798$	0	0
$799$	34.9074	1.23494
$800$	7.39144	0.261327
$801$	28.6660	1.01286
$802$	5.55284	0.196077
$803$	5.40056	0.190582
$804$	26.0812	0.919814
$805$	16.9116	0.596055
$806$	−4.46987	−0.157445
$807$	−47.2490	−1.66325
$808$	1.16025	0.0408174
$809$	9.73661	0.342321	0.171161	−	0.985243i	$-0.445248\pi$
$809$	9.73661	0.342321	0.171161	+	0.985243i	$0.445248\pi$
$810$	−39.4104	−1.38474
$811$	−0.160117	−0.00562246	−0.00281123	−	0.999996i	$-0.500895\pi$
$811$	−0.160117	−0.00562246	−0.00281123	+	0.999996i	$0.500895\pi$
$812$	5.35114	0.187788
$813$	−34.8671	−1.22284
$814$	−27.8160	−0.974949
$815$	58.0591	2.03372
$816$	−8.04029	−0.281467
$817$	0	0
$818$	−25.8973	−0.905478
$819$	2.33030	0.0814271
$820$	−23.0498	−0.804933
$821$	−36.7541	−1.28273	−0.641363	−	0.767238i	$-0.721631\pi$
$821$	−36.7541	−1.28273	−0.641363	+	0.767238i	$0.721631\pi$
$822$	−49.5195	−1.72719
$823$	5.24097	0.182689	0.0913444	−	0.995819i	$-0.470884\pi$
$823$	5.24097	0.182689	0.0913444	+	0.995819i	$0.470884\pi$
$824$	10.5480	0.367455
$825$	−45.0936	−1.56996
$826$	0.501096	0.0174354
$827$	−39.6523	−1.37885	−0.689423	−	0.724359i	$-0.742136\pi$
$827$	−39.6523	−1.37885	−0.689423	+	0.724359i	$0.742136\pi$
$828$	8.32624	0.289357
$829$	−37.8829	−1.31573	−0.657864	−	0.753137i	$-0.728540\pi$
$829$	−37.8829	−1.31573	−0.657864	+	0.753137i	$0.728540\pi$
$830$	38.2205	1.32665
$831$	−40.0710	−1.39005
$832$	1.34458	0.0466148
$833$	−3.69572	−0.128049
$834$	−25.2718	−0.875091
$835$	−11.0865	−0.383664
$836$	0	0
$837$	9.16269	0.316709
$838$	23.7413	0.820130
$839$	−21.7871	−0.752175	−0.376087	−	0.926584i	$-0.622731\pi$
$839$	−21.7871	−0.752175	−0.376087	+	0.926584i	$0.622731\pi$
$840$	7.65833	0.264237
$841$	−0.365290	−0.0125962
$842$	38.0474	1.31120
$843$	68.3307	2.35343
$844$	−20.0211	−0.689156
$845$	−39.3979	−1.35533
$846$	−16.3698	−0.562806
$847$	−3.13632	−0.107765
$848$	−2.46621	−0.0846901
$849$	53.7900	1.84607
$850$	−27.3167	−0.936954
$851$	47.6546	1.63358
$852$	−28.9713	−0.992541
$853$	45.5176	1.55849	0.779247	−	0.626717i	$-0.215602\pi$
$853$	45.5176	1.55849	0.779247	+	0.626717i	$0.215602\pi$
$854$	−9.22835	−0.315788
$855$	0	0
$856$	−9.16850	−0.313373
$857$	14.8920	0.508701	0.254351	−	0.967112i	$-0.418138\pi$
$857$	14.8920	0.508701	0.254351	+	0.967112i	$0.418138\pi$
$858$	−8.20298	−0.280045
$859$	−5.73987	−0.195842	−0.0979210	−	0.995194i	$-0.531219\pi$
$859$	−5.73987	−0.195842	−0.0979210	+	0.995194i	$0.531219\pi$
$860$	37.5189	1.27938
$861$	−14.2455	−0.485487
$862$	4.34741	0.148073
$863$	37.9478	1.29176	0.645879	−	0.763440i	$-0.276491\pi$
$863$	37.9478	1.29176	0.645879	+	0.763440i	$0.276491\pi$
$864$	−2.75621	−0.0937683
$865$	−43.7425	−1.48729
$866$	−4.40984	−0.149853
$867$	−7.27004	−0.246904
$868$	−3.32437	−0.112837
$869$	−49.0819	−1.66499
$870$	40.9808	1.38938
$871$	16.1191	0.546174
$872$	−5.46255	−0.184985
$873$	−17.6797	−0.598369
$874$	0	0
$875$	8.41820	0.284587
$876$	−4.18985	−0.141562
$877$	−12.6048	−0.425634	−0.212817	−	0.977092i	$-0.568264\pi$
$877$	−12.6048	−0.425634	−0.212817	+	0.977092i	$0.568264\pi$
$878$	27.8784	0.940850
$879$	−8.93609	−0.301407
$880$	−9.87129	−0.332761
$881$	47.5368	1.60156	0.800778	−	0.598962i	$-0.204420\pi$
$881$	47.5368	1.60156	0.800778	+	0.598962i	$0.204420\pi$
$882$	1.73311	0.0583567
$883$	29.6583	0.998082	0.499041	−	0.866578i	$-0.333686\pi$
$883$	29.6583	0.998082	0.499041	+	0.866578i	$0.333686\pi$
$884$	−4.96917	−0.167131
$885$	3.83756	0.128998
$886$	−12.3334	−0.414350
$887$	−4.97155	−0.166928	−0.0834642	−	0.996511i	$-0.526598\pi$
$887$	−4.97155	−0.166928	−0.0834642	+	0.996511i	$0.526598\pi$
$888$	21.5801	0.724182
$889$	−2.30719	−0.0773806
$890$	58.2241	1.95168
$891$	31.3952	1.05178
$892$	−2.11456	−0.0708008
$893$	0	0
$894$	24.0989	0.805987
$895$	−37.1392	−1.24143
$896$	1.00000	0.0334077
$897$	14.0534	0.469230
$898$	−16.7235	−0.558071
$899$	−17.7892	−0.593303
$900$	12.8101	0.427005
$901$	9.11443	0.303646
$902$	18.3619	0.611386
$903$	23.1879	0.771646
$904$	−2.00947	−0.0668339
$905$	−78.8941	−2.62253
$906$	−2.73060	−0.0907181
$907$	−1.83004	−0.0607654	−0.0303827	−	0.999538i	$-0.509673\pi$
$907$	−1.83004	−0.0607654	−0.0303827	+	0.999538i	$0.509673\pi$
$908$	4.53547	0.150515
$909$	2.01084	0.0666952
$910$	4.73311	0.156901
$911$	54.8341	1.81673	0.908367	−	0.418175i	$-0.137330\pi$
$911$	54.8341	1.81673	0.908367	+	0.418175i	$0.137330\pi$
$912$	0	0
$913$	−30.4473	−1.00766
$914$	10.6854	0.353442
$915$	−70.6737	−2.33640
$916$	−22.8914	−0.756352
$917$	−21.9508	−0.724880
$918$	10.1862	0.336194
$919$	−10.5422	−0.347756	−0.173878	−	0.984767i	$-0.555630\pi$
$919$	−10.5422	−0.347756	−0.173878	+	0.984767i	$0.555630\pi$
$920$	16.9116	0.557558
$921$	31.1934	1.02786
$922$	−26.4779	−0.872005
$923$	−17.9053	−0.589359
$924$	−6.10079	−0.200701
$925$	73.3179	2.41068
$926$	15.6061	0.512848
$927$	18.2807	0.600418
$928$	5.35114	0.175660
$929$	−49.4703	−1.62307	−0.811535	−	0.584304i	$-0.801367\pi$
$929$	−49.4703	−1.62307	−0.811535	+	0.584304i	$0.801367\pi$
$930$	−25.4591	−0.834838
$931$	0	0
$932$	−15.2646	−0.500008
$933$	−28.7249	−0.940410
$934$	−4.57730	−0.149774
$935$	36.4815	1.19307
$936$	2.33030	0.0761681
$937$	−9.69970	−0.316876	−0.158438	−	0.987369i	$-0.550646\pi$
$937$	−9.69970	−0.316876	−0.158438	+	0.987369i	$0.550646\pi$
$938$	11.9882	0.391429
$939$	27.9369	0.911686
$940$	−33.2491	−1.08447
$941$	25.9990	0.847543	0.423771	−	0.905769i	$-0.360706\pi$
$941$	25.9990	0.847543	0.423771	+	0.905769i	$0.360706\pi$
$942$	−0.761670	−0.0248166
$943$	−31.4579	−1.02441
$944$	0.501096	0.0163093
$945$	−9.70228	−0.315615
$946$	−29.8884	−0.971754
$947$	47.0532	1.52902	0.764512	−	0.644610i	$-0.222980\pi$
$947$	47.0532	1.52902	0.764512	+	0.644610i	$0.222980\pi$
$948$	38.0787	1.23674
$949$	−2.58947	−0.0840578
$950$	0	0
$951$	15.7297	0.510070
$952$	−3.69572	−0.119779
$953$	−14.0830	−0.456193	−0.228097	−	0.973638i	$-0.573250\pi$
$953$	−14.0830	−0.456193	−0.228097	+	0.973638i	$0.573250\pi$
$954$	−4.27421	−0.138383
$955$	21.0669	0.681710
$956$	−16.1839	−0.523424
$957$	−32.6462	−1.05530
$958$	11.9098	0.384788
$959$	−22.7616	−0.735011
$960$	7.65833	0.247171
$961$	−19.9485	−0.643501
$962$	13.3373	0.430010
$963$	−15.8900	−0.512048
$964$	3.37895	0.108829
$965$	54.3224	1.74870
$966$	10.4519	0.336285
$967$	−21.5394	−0.692661	−0.346330	−	0.938113i	$-0.612572\pi$
$967$	−21.5394	−0.692661	−0.346330	+	0.938113i	$0.612572\pi$
$968$	−3.13632	−0.100805
$969$	0	0
$970$	−35.9097	−1.15299
$971$	−29.4006	−0.943509	−0.471755	−	0.881730i	$-0.656379\pi$
$971$	−29.4006	−0.943509	−0.471755	+	0.881730i	$0.656379\pi$
$972$	−16.0883	−0.516033
$973$	−11.6162	−0.372397
$974$	−11.8435	−0.379490
$975$	21.6216	0.692445
$976$	−9.22835	−0.295392
$977$	18.1047	0.579219	0.289610	−	0.957145i	$-0.406475\pi$
$977$	18.1047	0.579219	0.289610	+	0.957145i	$0.406475\pi$
$978$	35.8825	1.14740
$979$	−46.3826	−1.48239
$980$	3.52015	0.112447
$981$	−9.46719	−0.302264
$982$	5.95019	0.189878
$983$	21.3333	0.680426	0.340213	−	0.940348i	$-0.389501\pi$
$983$	21.3333	0.680426	0.340213	+	0.940348i	$0.389501\pi$
$984$	−14.2455	−0.454131
$985$	−17.5208	−0.558259
$986$	−19.7763	−0.629806
$987$	−20.5491	−0.654084
$988$	0	0
$989$	51.2050	1.62822
$990$	−17.1080	−0.543728
$991$	17.4816	0.555323	0.277661	−	0.960679i	$-0.410441\pi$
$991$	17.4816	0.555323	0.277661	+	0.960679i	$0.410441\pi$
$992$	−3.32437	−0.105549
$993$	40.2880	1.27850
$994$	−13.3167	−0.422379
$995$	1.66565	0.0528046
$996$	23.6216	0.748478
$997$	24.4311	0.773740	0.386870	−	0.922134i	$-0.373556\pi$
$997$	24.4311	0.773740	0.386870	+	0.922134i	$0.373556\pi$
$998$	15.8576	0.501965
$999$	−27.3397	−0.864990

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.y.1.3	yes	4
19.18	odd	2		5054.2.a.v.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.v.1.2	✓	4	19.18	odd	2
5054.2.a.y.1.3	yes	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.17557 q^{3} +1.00000 q^{4} +3.52015 q^{5} +2.17557 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.73311 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.17557 q^{3} +1.00000 q^{4} +3.52015 q^{5} +2.17557 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.73311 q^{9} +3.52015 q^{10} -2.80423 q^{11} +2.17557 q^{12} +1.34458 q^{13} +1.00000 q^{14} +7.65833 q^{15} +1.00000 q^{16} -3.69572 q^{17} +1.73311 q^{18} +3.52015 q^{20} +2.17557 q^{21} -2.80423 q^{22} +4.80423 q^{23} +2.17557 q^{24} +7.39144 q^{25} +1.34458 q^{26} -2.75621 q^{27} +1.00000 q^{28} +5.35114 q^{29} +7.65833 q^{30} -3.32437 q^{31} +1.00000 q^{32} -6.10079 q^{33} -3.69572 q^{34} +3.52015 q^{35} +1.73311 q^{36} +9.91930 q^{37} +2.92522 q^{39} +3.52015 q^{40} -6.54795 q^{41} +2.17557 q^{42} +10.6583 q^{43} -2.80423 q^{44} +6.10079 q^{45} +4.80423 q^{46} -9.44537 q^{47} +2.17557 q^{48} +1.00000 q^{49} +7.39144 q^{50} -8.04029 q^{51} +1.34458 q^{52} -2.46621 q^{53} -2.75621 q^{54} -9.87129 q^{55} +1.00000 q^{56} +5.35114 q^{58} +0.501096 q^{59} +7.65833 q^{60} -9.22835 q^{61} -3.32437 q^{62} +1.73311 q^{63} +1.00000 q^{64} +4.73311 q^{65} -6.10079 q^{66} +11.9882 q^{67} -3.69572 q^{68} +10.4519 q^{69} +3.52015 q^{70} -13.3167 q^{71} +1.73311 q^{72} -1.92586 q^{73} +9.91930 q^{74} +16.0806 q^{75} -2.80423 q^{77} +2.92522 q^{78} +17.5028 q^{79} +3.52015 q^{80} -11.1957 q^{81} -6.54795 q^{82} +10.8576 q^{83} +2.17557 q^{84} -13.0095 q^{85} +10.6583 q^{86} +11.6418 q^{87} -2.80423 q^{88} +16.5402 q^{89} +6.10079 q^{90} +1.34458 q^{91} +4.80423 q^{92} -7.23241 q^{93} -9.44537 q^{94} +2.17557 q^{96} -10.2012 q^{97} +1.00000 q^{98} -4.86002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 4 q^{11} + 4 q^{12} - 2 q^{13} + 4 q^{14} + 2 q^{15} + 4 q^{16} + 2 q^{17} + 2 q^{18} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} + 4 q^{24} - 4 q^{25} - 2 q^{26} + 10 q^{27} + 4 q^{28} + 12 q^{29} + 2 q^{30} + 14 q^{31} + 4 q^{32} + 4 q^{33} + 2 q^{34} + 2 q^{35} + 2 q^{36} + 24 q^{37} - 12 q^{39} + 2 q^{40} + 4 q^{42} + 14 q^{43} + 4 q^{44} - 4 q^{45} + 4 q^{46} - 2 q^{47} + 4 q^{48} + 4 q^{49} - 4 q^{50} - 8 q^{51} - 2 q^{52} + 10 q^{54} - 18 q^{55} + 4 q^{56} + 12 q^{58} + 2 q^{59} + 2 q^{60} + 2 q^{61} + 14 q^{62} + 2 q^{63} + 4 q^{64} + 14 q^{65} + 4 q^{66} + 22 q^{67} + 2 q^{68} + 4 q^{69} + 2 q^{70} + 4 q^{71} + 2 q^{72} + 10 q^{73} + 24 q^{74} + 16 q^{75} + 4 q^{77} - 12 q^{78} + 2 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{84} - 14 q^{85} + 14 q^{86} + 32 q^{87} + 4 q^{88} + 10 q^{89} - 4 q^{90} - 2 q^{91} + 4 q^{92} + 14 q^{93} - 2 q^{94} + 4 q^{96} - 22 q^{97} + 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 4 * q^11 + 4 * q^12 - 2 * q^13 + 4 * q^14 + 2 * q^15 + 4 * q^16 + 2 * q^17 + 2 * q^18 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 + 10 * q^27 + 4 * q^28 + 12 * q^29 + 2 * q^30 + 14 * q^31 + 4 * q^32 + 4 * q^33 + 2 * q^34 + 2 * q^35 + 2 * q^36 + 24 * q^37 - 12 * q^39 + 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 + 4 * q^46 - 2 * q^47 + 4 * q^48 + 4 * q^49 - 4 * q^50 - 8 * q^51 - 2 * q^52 + 10 * q^54 - 18 * q^55 + 4 * q^56 + 12 * q^58 + 2 * q^59 + 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 + 14 * q^65 + 4 * q^66 + 22 * q^67 + 2 * q^68 + 4 * q^69 + 2 * q^70 + 4 * q^71 + 2 * q^72 + 10 * q^73 + 24 * q^74 + 16 * q^75 + 4 * q^77 - 12 * q^78 + 2 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^84 - 14 * q^85 + 14 * q^86 + 32 * q^87 + 4 * q^88 + 10 * q^89 - 4 * q^90 - 2 * q^91 + 4 * q^92 + 14 * q^93 - 2 * q^94 + 4 * q^96 - 22 * q^97 + 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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