LMFDB - Embedded newform 5054.2.a.v.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$1$
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			1.2
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	$-0.716140\pi$
$3$	−2.17557	−1.25607	−0.628033	+	0.778187i	$0.716140\pi$
$4$	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	$-0.559701\pi$
$13$	−1.34458	−0.372918	−0.186459	+	0.982463i	$0.559701\pi$
$14$	−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	$-0.665507\pi$
$29$	−5.35114	−0.993682	−0.496841	+	0.867842i	$0.665507\pi$
$30$	7.65833	1.39821
$31$	3.32437	0.597075	0.298538	−	0.954398i	$-0.403501\pi$
$31$	3.32437	0.597075	0.298538	+	0.954398i	$0.403501\pi$
$32$	−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	$-0.803462\pi$
$37$	−9.91930	−1.63072	−0.815361	+	0.578952i	$0.803462\pi$
$38$	0	0
$39$	2.92522	0.468410
$40$	−3.52015	−0.556584
$41$	6.54795	1.02262	0.511309	−	0.859397i	$-0.329161\pi$
$41$	6.54795	1.02262	0.511309	+	0.859397i	$0.329161\pi$
$42$	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	$-0.445823\pi$
$53$	2.46621	0.338761	0.169380	+	0.985551i	$0.445823\pi$
$54$	−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	$-0.510385\pi$
$59$	−0.501096	−0.0652372	−0.0326186	+	0.999468i	$0.510385\pi$
$60$	−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	$-0.761552\pi$
$67$	−11.9882	−1.46459	−0.732297	+	0.680985i	$0.761552\pi$
$68$	−3.69572	−0.448172
$69$	−10.4519	−1.25826
$70$	−3.52015	−0.420738
$71$	13.3167	1.58040	0.790198	−	0.612851i	$-0.209978\pi$
$71$	13.3167	1.58040	0.790198	+	0.612851i	$0.209978\pi$
$72$	−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	$-0.944087\pi$
$79$	−17.5028	−1.96922	−0.984612	+	0.174754i	$0.944087\pi$
$80$	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	$-0.840214\pi$
$89$	−16.5402	−1.75326	−0.876631	+	0.481164i	$0.840214\pi$
$90$	−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	$-0.326719\pi$
$97$	10.2012	1.03577	0.517887	+	0.855449i	$0.326719\pi$
$98$	−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	$-0.673942\pi$
$103$	−10.5480	−1.03932	−0.519660	+	0.854373i	$0.673942\pi$
$104$	1.34458	0.131847
$105$	−7.65833	−0.747376
$106$	−2.46621	−0.239540
$107$	9.16850	0.886352	0.443176	−	0.896435i	$-0.353852\pi$
$107$	9.16850	0.886352	0.443176	+	0.896435i	$0.353852\pi$
$108$	2.75621	0.265217
$109$	5.46255	0.523218	0.261609	−	0.965174i	$-0.415747\pi$
$109$	5.46255	0.523218	0.261609	+	0.965174i	$0.415747\pi$
$110$	9.87129	0.941190
$111$	21.5801	2.04830
$112$	1.00000	0.0944911
$113$	2.00947	0.189035	0.0945175	−	0.995523i	$-0.469869\pi$
$113$	2.00947	0.189035	0.0945175	+	0.995523i	$0.469869\pi$
$114$	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	$-0.467359\pi$
$127$	2.30719	0.204730	0.102365	+	0.994747i	$0.467359\pi$
$128$	−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	$-0.483737\pi$
$151$	1.25512	0.102140	0.0510701	+	0.998695i	$0.483737\pi$
$152$	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	$-0.461115\pi$
$167$	3.14945	0.243711	0.121856	+	0.992548i	$0.461115\pi$
$168$	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	$-0.343396\pi$
$173$	12.4263	0.944755	0.472378	+	0.881396i	$0.343396\pi$
$174$	−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	$-0.370991\pi$
$179$	10.5505	0.788579	0.394289	+	0.918986i	$0.370991\pi$
$180$	6.10079	0.454726
$181$	22.4122	1.66588	0.832942	−	0.553361i	$-0.186655\pi$
$181$	22.4122	1.66588	0.832942	+	0.553361i	$0.186655\pi$
$182$	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	$-0.687436\pi$
$193$	−15.4318	−1.11081	−0.555404	+	0.831581i	$0.687436\pi$
$194$	−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	$-0.257982\pi$
$211$	20.0211	1.37831	0.689156	+	0.724613i	$0.257982\pi$
$212$	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	$-0.477445\pi$
$223$	2.11456	0.141602	0.0708008	+	0.997490i	$0.477445\pi$
$224$	−1.00000	−0.0668153
$225$	12.8101	0.854010
$226$	−2.00947	−0.133668
$227$	−4.53547	−0.301030	−0.150515	−	0.988608i	$-0.548093\pi$
$227$	−4.53547	−0.301030	−0.150515	+	0.988608i	$0.548093\pi$
$228$	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	$-0.534710\pi$
$241$	−3.37895	−0.217657	−0.108829	+	0.994061i	$0.534710\pi$
$242$	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	$-0.645190\pi$
$257$	−14.1227	−0.880948	−0.440474	+	0.897765i	$0.645190\pi$
$258$	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	$-0.269672\pi$
$269$	21.7180	1.32417	0.662085	+	0.749429i	$0.269672\pi$
$270$	−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	$-0.886252\pi$
$281$	−31.4082	−1.87365	−0.936827	+	0.349792i	$0.886252\pi$
$282$	−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	$-0.461717\pi$
$293$	4.10747	0.239961	0.119980	+	0.992776i	$0.461717\pi$
$294$	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	$-0.634177\pi$
$307$	−14.3380	−0.818314	−0.409157	+	0.912464i	$0.634177\pi$
$308$	−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	$-0.565083\pi$
$317$	−7.23015	−0.406085	−0.203043	+	0.979170i	$0.565083\pi$
$318$	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	$-0.669959\pi$
$331$	−18.5184	−1.01786	−0.508930	+	0.860808i	$0.669959\pi$
$332$	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	$-0.520035\pi$
$337$	−2.30938	−0.125800	−0.0629000	+	0.998020i	$0.520035\pi$
$338$	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	$-0.752177\pi$
$373$	−27.4991	−1.42385	−0.711925	+	0.702255i	$0.752177\pi$
$374$	−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	$-0.617731\pi$
$379$	−14.0748	−0.722976	−0.361488	+	0.932377i	$0.617731\pi$
$380$	0	0
$381$	−5.01945	−0.257154
$382$	−5.98468	−0.306203
$383$	29.2284	1.49350	0.746749	−	0.665105i	$-0.231613\pi$
$383$	29.2284	1.49350	0.746749	+	0.665105i	$0.231613\pi$
$384$	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	$-0.544276\pi$
$401$	−5.55284	−0.277295	−0.138648	+	0.990342i	$0.544276\pi$
$402$	−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	$-0.278823\pi$
$409$	25.8973	1.28054	0.640270	+	0.768150i	$0.278823\pi$
$410$	−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	$-0.877756\pi$
$421$	−38.0474	−1.85432	−0.927158	+	0.374670i	$0.877756\pi$
$422$	−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	$-0.533389\pi$
$431$	−4.34741	−0.209407	−0.104704	+	0.994503i	$0.533389\pi$
$432$	2.75621	0.132608
$433$	4.40984	0.211924	0.105962	−	0.994370i	$-0.466208\pi$
$433$	4.40984	0.211924	0.105962	+	0.994370i	$0.466208\pi$
$434$	−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	$-0.731688\pi$
$439$	−27.8784	−1.33056	−0.665281	+	0.746593i	$0.731688\pi$
$440$	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	$-0.370878\pi$
$449$	16.7235	0.789232	0.394616	+	0.918846i	$0.370878\pi$
$450$	−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	$-0.413525\pi$
$487$	11.8435	0.536680	0.268340	+	0.963324i	$0.413525\pi$
$488$	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	$-0.580903\pi$
$509$	−11.3454	−0.502874	−0.251437	+	0.967874i	$0.580903\pi$
$510$	−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	$-0.637445\pi$
$521$	−19.1051	−0.837007	−0.418504	+	0.908215i	$0.637445\pi$
$522$	9.27410	0.405916
$523$	−23.0875	−1.00955	−0.504774	−	0.863252i	$-0.668424\pi$
$523$	−23.0875	−1.00955	−0.504774	+	0.863252i	$0.668424\pi$
$524$	−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	$-0.588543\pi$
$547$	−12.8444	−0.549187	−0.274594	+	0.961560i	$0.588543\pi$
$548$	−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	$-0.746943\pi$
$563$	−33.2321	−1.40057	−0.700283	+	0.713865i	$0.746943\pi$
$564$	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	$-0.439719\pi$
$569$	8.98091	0.376499	0.188250	+	0.982121i	$0.439719\pi$
$570$	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	$-0.509174\pi$
$599$	−1.41049	−0.0576309	−0.0288154	+	0.999585i	$0.509174\pi$
$600$	16.0806	0.656487
$601$	−47.7648	−1.94837	−0.974184	−	0.225754i	$-0.927515\pi$
$601$	−47.7648	−1.94837	−0.974184	+	0.225754i	$0.927515\pi$
$602$	−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	$-0.629894\pi$
$607$	−19.5543	−0.793683	−0.396841	+	0.917887i	$0.629894\pi$
$608$	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	$-0.562511\pi$
$641$	−9.88036	−0.390251	−0.195125	+	0.980778i	$0.562511\pi$
$642$	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	$-0.656919\pi$
$659$	−24.2975	−0.946496	−0.473248	+	0.880929i	$0.656919\pi$
$660$	21.4757	0.835940
$661$	40.1393	1.56124	0.780619	−	0.625007i	$-0.214904\pi$
$661$	40.1393	1.56124	0.780619	+	0.625007i	$0.214904\pi$
$662$	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	$-0.592385\pi$
$673$	−14.8482	−0.572355	−0.286178	+	0.958177i	$0.592385\pi$
$674$	2.30938	0.0889540
$675$	20.3724	0.784133
$676$	−11.1921	−0.430466
$677$	−25.9381	−0.996883	−0.498442	−	0.866923i	$-0.666094\pi$
$677$	−25.9381	−0.996883	−0.498442	+	0.866923i	$0.666094\pi$
$678$	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	$-0.361481\pi$
$683$	22.0346	0.843129	0.421564	+	0.906798i	$0.361481\pi$
$684$	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	$-0.599465\pi$
$743$	−16.7593	−0.614837	−0.307419	+	0.951574i	$0.599465\pi$
$744$	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	$-0.559812\pi$
$751$	−10.2383	−0.373599	−0.186800	+	0.982398i	$0.559812\pi$
$752$	−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	$-0.578377\pi$
$773$	−13.5539	−0.487499	−0.243750	+	0.969838i	$0.578377\pi$
$774$	−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	$-0.478064\pi$
$787$	3.86358	0.137722	0.0688609	+	0.997626i	$0.478064\pi$
$788$	−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	$-0.586187\pi$
$797$	−15.1020	−0.534939	−0.267470	+	0.963566i	$0.586187\pi$
$798$	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	$-0.499105\pi$
$811$	0.160117	0.00562246	0.00281123	+	0.999996i	$0.499105\pi$
$812$	−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	$-0.257864\pi$
$827$	39.6523	1.37885	0.689423	+	0.724359i	$0.257864\pi$
$828$	8.32624	0.289357
$829$	37.8829	1.31573	0.657864	−	0.753137i	$-0.271460\pi$
$829$	37.8829	1.31573	0.657864	+	0.753137i	$0.271460\pi$
$830$	−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	$-0.377269\pi$
$839$	21.7871	0.752175	0.376087	+	0.926584i	$0.377269\pi$
$840$	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	$-0.581862\pi$
$857$	−14.8920	−0.508701	−0.254351	+	0.967112i	$0.581862\pi$
$858$	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	$-0.723509\pi$
$863$	−37.9478	−1.29176	−0.645879	+	0.763440i	$0.723509\pi$
$864$	−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	$-0.431736\pi$
$877$	12.6048	0.425634	0.212817	+	0.977092i	$0.431736\pi$
$878$	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	$-0.473402\pi$
$887$	4.97155	0.166928	0.0834642	+	0.996511i	$0.473402\pi$
$888$	−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	$-0.490327\pi$
$907$	1.83004	0.0607654	0.0303827	+	0.999538i	$0.490327\pi$
$908$	−4.53547	−0.150515
$909$	2.01084	0.0666952
$910$	4.73311	0.156901
$911$	−54.8341	−1.81673	−0.908367	−	0.418175i	$-0.862670\pi$
$911$	−54.8341	−1.81673	−0.908367	+	0.418175i	$0.862670\pi$
$912$	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	$-0.639294\pi$
$941$	−25.9990	−0.847543	−0.423771	+	0.905769i	$0.639294\pi$
$942$	−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	$-0.426750\pi$
$953$	14.0830	0.456193	0.228097	+	0.973638i	$0.426750\pi$
$954$	−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	$-0.343621\pi$
$971$	29.4006	0.943509	0.471755	+	0.881730i	$0.343621\pi$
$972$	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	$-0.593525\pi$
$977$	−18.1047	−0.579219	−0.289610	+	0.957145i	$0.593525\pi$
$978$	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	$-0.610499\pi$
$983$	−21.3333	−0.680426	−0.340213	+	0.940348i	$0.610499\pi$
$984$	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	$-0.589559\pi$
$991$	−17.4816	−0.555323	−0.277661	+	0.960679i	$0.589559\pi$
$992$	−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.v.1.2	✓	4
19.18	odd	2		5054.2.a.y.1.3	yes	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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