LMFDB - Embedded newform 5054.2.a.ba.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.48952000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 13x^{4} + 44x^{2} + 36x + 4 $ x^6 - x^5 - 13x^4 + 44x^2 + 36*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.54615$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.16418 q^{3} +1.00000 q^{4} -2.51032 q^{5} +3.16418 q^{6} -1.00000 q^{7} -1.00000 q^{8} +7.01204 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.16418 q^{3} +1.00000 q^{4} -2.51032 q^{5} +3.16418 q^{6} -1.00000 q^{7} -1.00000 q^{8} +7.01204 q^{9} +2.51032 q^{10} -2.61272 q^{11} -3.16418 q^{12} +4.82572 q^{13} +1.00000 q^{14} +7.94311 q^{15} +1.00000 q^{16} -4.26658 q^{17} -7.01204 q^{18} -2.51032 q^{20} +3.16418 q^{21} +2.61272 q^{22} -7.62679 q^{23} +3.16418 q^{24} +1.30171 q^{25} -4.82572 q^{26} -12.6948 q^{27} -1.00000 q^{28} +3.60943 q^{29} -7.94311 q^{30} +7.24632 q^{31} -1.00000 q^{32} +8.26711 q^{33} +4.26658 q^{34} +2.51032 q^{35} +7.01204 q^{36} +3.23278 q^{37} -15.2694 q^{39} +2.51032 q^{40} +10.8831 q^{41} -3.16418 q^{42} -4.22746 q^{43} -2.61272 q^{44} -17.6025 q^{45} +7.62679 q^{46} +11.3593 q^{47} -3.16418 q^{48} +1.00000 q^{49} -1.30171 q^{50} +13.5002 q^{51} +4.82572 q^{52} -7.34872 q^{53} +12.6948 q^{54} +6.55876 q^{55} +1.00000 q^{56} -3.60943 q^{58} -13.2327 q^{59} +7.94311 q^{60} +2.33846 q^{61} -7.24632 q^{62} -7.01204 q^{63} +1.00000 q^{64} -12.1141 q^{65} -8.26711 q^{66} -8.50225 q^{67} -4.26658 q^{68} +24.1325 q^{69} -2.51032 q^{70} -4.76093 q^{71} -7.01204 q^{72} -1.27402 q^{73} -3.23278 q^{74} -4.11885 q^{75} +2.61272 q^{77} +15.2694 q^{78} -4.48417 q^{79} -2.51032 q^{80} +19.1326 q^{81} -10.8831 q^{82} -5.10293 q^{83} +3.16418 q^{84} +10.7105 q^{85} +4.22746 q^{86} -11.4209 q^{87} +2.61272 q^{88} -13.9034 q^{89} +17.6025 q^{90} -4.82572 q^{91} -7.62679 q^{92} -22.9287 q^{93} -11.3593 q^{94} +3.16418 q^{96} -16.4795 q^{97} -1.00000 q^{98} -18.3205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 23 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 5 q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 13 q^{25} - 23 q^{26} - 4 q^{27} - 6 q^{28} + 5 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 10 q^{33} + 3 q^{34} + 5 q^{35} + 12 q^{36} + q^{37} + 4 q^{39} + 5 q^{40} + 19 q^{41} + 2 q^{42} - 2 q^{43} - 4 q^{44} - 55 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 6 q^{49} - 13 q^{50} + 44 q^{51} + 23 q^{52} - 11 q^{53} + 4 q^{54} + 28 q^{55} + 6 q^{56} - 5 q^{58} - 4 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} - 12 q^{63} + 6 q^{64} - 24 q^{65} - 10 q^{66} - 14 q^{67} - 3 q^{68} + 10 q^{69} - 5 q^{70} - 8 q^{71} - 12 q^{72} + 5 q^{73} - q^{74} + 56 q^{75} + 4 q^{77} - 4 q^{78} + 30 q^{79} - 5 q^{80} + 30 q^{81} - 19 q^{82} - 12 q^{83} - 2 q^{84} - 16 q^{85} + 2 q^{86} - 14 q^{87} + 4 q^{88} + 11 q^{89} + 55 q^{90} - 23 q^{91} - 4 q^{92} + 10 q^{93} + 12 q^{94} - 2 q^{96} + 25 q^{97} - 6 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 23 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 5 * q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 13 * q^25 - 23 * q^26 - 4 * q^27 - 6 * q^28 + 5 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 10 * q^33 + 3 * q^34 + 5 * q^35 + 12 * q^36 + q^37 + 4 * q^39 + 5 * q^40 + 19 * q^41 + 2 * q^42 - 2 * q^43 - 4 * q^44 - 55 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 6 * q^49 - 13 * q^50 + 44 * q^51 + 23 * q^52 - 11 * q^53 + 4 * q^54 + 28 * q^55 + 6 * q^56 - 5 * q^58 - 4 * q^59 - 6 * q^60 - q^61 - 12 * q^62 - 12 * q^63 + 6 * q^64 - 24 * q^65 - 10 * q^66 - 14 * q^67 - 3 * q^68 + 10 * q^69 - 5 * q^70 - 8 * q^71 - 12 * q^72 + 5 * q^73 - q^74 + 56 * q^75 + 4 * q^77 - 4 * q^78 + 30 * q^79 - 5 * q^80 + 30 * q^81 - 19 * q^82 - 12 * q^83 - 2 * q^84 - 16 * q^85 + 2 * q^86 - 14 * q^87 + 4 * q^88 + 11 * q^89 + 55 * q^90 - 23 * q^91 - 4 * q^92 + 10 * q^93 + 12 * q^94 - 2 * q^96 + 25 * q^97 - 6 * q^98 - 50 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.16418	−1.82684	−0.913420	−	0.407018i	$-0.866569\pi$
$3$	−3.16418	−1.82684	−0.913420	+	0.407018i	$0.866569\pi$
$4$	1.00000	0.500000
$5$	−2.51032	−1.12265	−0.561325	−	0.827596i	$-0.689708\pi$
$5$	−2.51032	−1.12265	−0.561325	+	0.827596i	$0.689708\pi$
$6$	3.16418	1.29177
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	7.01204	2.33735
$10$	2.51032	0.793833
$11$	−2.61272	−0.787764	−0.393882	−	0.919161i	$-0.628868\pi$
$11$	−2.61272	−0.787764	−0.393882	+	0.919161i	$0.628868\pi$
$12$	−3.16418	−0.913420
$13$	4.82572	1.33841	0.669207	−	0.743076i	$-0.266634\pi$
$13$	4.82572	1.33841	0.669207	+	0.743076i	$0.266634\pi$
$14$	1.00000	0.267261
$15$	7.94311	2.05090
$16$	1.00000	0.250000
$17$	−4.26658	−1.03480	−0.517398	−	0.855745i	$-0.673099\pi$
$17$	−4.26658	−1.03480	−0.517398	+	0.855745i	$0.673099\pi$
$18$	−7.01204	−1.65275
$19$	0	0
$19$	0	0
$20$	−2.51032	−0.561325
$21$	3.16418	0.690481
$22$	2.61272	0.557033
$23$	−7.62679	−1.59029	−0.795147	−	0.606416i	$-0.792607\pi$
$23$	−7.62679	−1.59029	−0.795147	+	0.606416i	$0.792607\pi$
$24$	3.16418	0.645886
$25$	1.30171	0.260342
$26$	−4.82572	−0.946401
$27$	−12.6948	−2.44312
$28$	−1.00000	−0.188982
$29$	3.60943	0.670254	0.335127	−	0.942173i	$-0.391221\pi$
$29$	3.60943	0.670254	0.335127	+	0.942173i	$0.391221\pi$
$30$	−7.94311	−1.45021
$31$	7.24632	1.30148	0.650739	−	0.759302i	$-0.274459\pi$
$31$	7.24632	1.30148	0.650739	+	0.759302i	$0.274459\pi$
$32$	−1.00000	−0.176777
$33$	8.26711	1.43912
$34$	4.26658	0.731712
$35$	2.51032	0.424322
$36$	7.01204	1.16867
$37$	3.23278	0.531466	0.265733	−	0.964047i	$-0.414386\pi$
$37$	3.23278	0.531466	0.265733	+	0.964047i	$0.414386\pi$
$38$	0	0
$39$	−15.2694	−2.44507
$40$	2.51032	0.396917
$41$	10.8831	1.69966	0.849828	−	0.527060i	$-0.176706\pi$
$41$	10.8831	1.69966	0.849828	+	0.527060i	$0.176706\pi$
$42$	−3.16418	−0.488244
$43$	−4.22746	−0.644682	−0.322341	−	0.946624i	$-0.604470\pi$
$43$	−4.22746	−0.644682	−0.322341	+	0.946624i	$0.604470\pi$
$44$	−2.61272	−0.393882
$45$	−17.6025	−2.62402
$46$	7.62679	1.12451
$47$	11.3593	1.65692	0.828459	−	0.560050i	$-0.189218\pi$
$47$	11.3593	1.65692	0.828459	+	0.560050i	$0.189218\pi$
$48$	−3.16418	−0.456710
$49$	1.00000	0.142857
$50$	−1.30171	−0.184090
$51$	13.5002	1.89041
$52$	4.82572	0.669207
$53$	−7.34872	−1.00942	−0.504712	−	0.863288i	$-0.668401\pi$
$53$	−7.34872	−1.00942	−0.504712	+	0.863288i	$0.668401\pi$
$54$	12.6948	1.72755
$55$	6.55876	0.884383
$56$	1.00000	0.133631
$57$	0	0
$58$	−3.60943	−0.473941
$59$	−13.2327	−1.72275	−0.861375	−	0.507970i	$-0.830396\pi$
$59$	−13.2327	−1.72275	−0.861375	+	0.507970i	$0.830396\pi$
$60$	7.94311	1.02545
$61$	2.33846	0.299410	0.149705	−	0.988731i	$-0.452168\pi$
$61$	2.33846	0.299410	0.149705	+	0.988731i	$0.452168\pi$
$62$	−7.24632	−0.920284
$63$	−7.01204	−0.883434
$64$	1.00000	0.125000
$65$	−12.1141	−1.50257
$66$	−8.26711	−1.01761
$67$	−8.50225	−1.03872	−0.519358	−	0.854557i	$-0.673829\pi$
$67$	−8.50225	−1.03872	−0.519358	+	0.854557i	$0.673829\pi$
$68$	−4.26658	−0.517398
$69$	24.1325	2.90522
$70$	−2.51032	−0.300041
$71$	−4.76093	−0.565019	−0.282509	−	0.959265i	$-0.591167\pi$
$71$	−4.76093	−0.565019	−0.282509	+	0.959265i	$0.591167\pi$
$72$	−7.01204	−0.826377
$73$	−1.27402	−0.149112	−0.0745562	−	0.997217i	$-0.523754\pi$
$73$	−1.27402	−0.149112	−0.0745562	+	0.997217i	$0.523754\pi$
$74$	−3.23278	−0.375803
$75$	−4.11885	−0.475604
$76$	0	0
$77$	2.61272	0.297747
$78$	15.2694	1.72892
$79$	−4.48417	−0.504509	−0.252255	−	0.967661i	$-0.581172\pi$
$79$	−4.48417	−0.504509	−0.252255	+	0.967661i	$0.581172\pi$
$80$	−2.51032	−0.280662
$81$	19.1326	2.12584
$82$	−10.8831	−1.20184
$83$	−5.10293	−0.560119	−0.280060	−	0.959983i	$-0.590354\pi$
$83$	−5.10293	−0.560119	−0.280060	+	0.959983i	$0.590354\pi$
$84$	3.16418	0.345240
$85$	10.7105	1.16171
$86$	4.22746	0.455859
$87$	−11.4209	−1.22445
$88$	2.61272	0.278517
$89$	−13.9034	−1.47375	−0.736877	−	0.676027i	$-0.763700\pi$
$89$	−13.9034	−1.47375	−0.736877	+	0.676027i	$0.763700\pi$
$90$	17.6025	1.85546
$91$	−4.82572	−0.505873
$92$	−7.62679	−0.795147
$93$	−22.9287	−2.37759
$94$	−11.3593	−1.17162
$95$	0	0
$96$	3.16418	0.322943
$97$	−16.4795	−1.67324	−0.836622	−	0.547781i	$-0.815473\pi$
$97$	−16.4795	−1.67324	−0.836622	+	0.547781i	$0.815473\pi$
$98$	−1.00000	−0.101015
$99$	−18.3205	−1.84128
$100$	1.30171	0.130171
$101$	−13.7706	−1.37023	−0.685114	−	0.728436i	$-0.740247\pi$
$101$	−13.7706	−1.37023	−0.685114	+	0.728436i	$0.740247\pi$
$102$	−13.5002	−1.33672
$103$	1.50789	0.148577	0.0742887	−	0.997237i	$-0.476331\pi$
$103$	1.50789	0.148577	0.0742887	+	0.997237i	$0.476331\pi$
$104$	−4.82572	−0.473200
$105$	−7.94311	−0.775168
$106$	7.34872	0.713770
$107$	−2.77137	−0.267919	−0.133959	−	0.990987i	$-0.542769\pi$
$107$	−2.77137	−0.267919	−0.133959	+	0.990987i	$0.542769\pi$
$108$	−12.6948	−1.22156
$109$	14.1042	1.35094	0.675468	−	0.737389i	$-0.263942\pi$
$109$	14.1042	1.35094	0.675468	+	0.737389i	$0.263942\pi$
$110$	−6.55876	−0.625353
$111$	−10.2291	−0.970904
$112$	−1.00000	−0.0944911
$113$	−9.83390	−0.925095	−0.462548	−	0.886594i	$-0.653065\pi$
$113$	−9.83390	−0.925095	−0.462548	+	0.886594i	$0.653065\pi$
$114$	0	0
$115$	19.1457	1.78534
$116$	3.60943	0.335127
$117$	33.8381	3.12833
$118$	13.2327	1.21817
$119$	4.26658	0.391116
$120$	−7.94311	−0.725103
$121$	−4.17371	−0.379428
$122$	−2.33846	−0.211715
$123$	−34.4361	−3.10500
$124$	7.24632	0.650739
$125$	9.28389	0.830376
$126$	7.01204	0.624682
$127$	−12.7218	−1.12888	−0.564440	−	0.825474i	$-0.690908\pi$
$127$	−12.7218	−1.12888	−0.564440	+	0.825474i	$0.690908\pi$
$128$	−1.00000	−0.0883883
$129$	13.3765	1.17773
$130$	12.1141	1.06248
$131$	−12.4181	−1.08498	−0.542489	−	0.840063i	$-0.682518\pi$
$131$	−12.4181	−1.08498	−0.542489	+	0.840063i	$0.682518\pi$
$132$	8.26711	0.719559
$133$	0	0
$134$	8.50225	0.734482
$135$	31.8681	2.74277
$136$	4.26658	0.365856
$137$	6.73772	0.575642	0.287821	−	0.957684i	$-0.407069\pi$
$137$	6.73772	0.575642	0.287821	+	0.957684i	$0.407069\pi$
$138$	−24.1325	−2.05430
$139$	−0.319255	−0.0270788	−0.0135394	−	0.999908i	$-0.504310\pi$
$139$	−0.319255	−0.0270788	−0.0135394	+	0.999908i	$0.504310\pi$
$140$	2.51032	0.212161
$141$	−35.9427	−3.02692
$142$	4.76093	0.399529
$143$	−12.6082	−1.05435
$144$	7.01204	0.584337
$145$	−9.06083	−0.752461
$146$	1.27402	0.105438
$147$	−3.16418	−0.260977
$148$	3.23278	0.265733
$149$	1.33005	0.108962	0.0544809	−	0.998515i	$-0.482650\pi$
$149$	1.33005	0.108962	0.0544809	+	0.998515i	$0.482650\pi$
$150$	4.11885	0.336303
$151$	3.22677	0.262591	0.131296	−	0.991343i	$-0.458086\pi$
$151$	3.22677	0.262591	0.131296	+	0.991343i	$0.458086\pi$
$152$	0	0
$153$	−29.9174	−2.41868
$154$	−2.61272	−0.210539
$155$	−18.1906	−1.46110
$156$	−15.2694	−1.22253
$157$	−16.9062	−1.34926	−0.674630	−	0.738156i	$-0.735697\pi$
$157$	−16.9062	−1.34926	−0.674630	+	0.738156i	$0.735697\pi$
$158$	4.48417	0.356742
$159$	23.2527	1.84406
$160$	2.51032	0.198458
$161$	7.62679	0.601075
$162$	−19.1326	−1.50320
$163$	−10.6944	−0.837653	−0.418826	−	0.908066i	$-0.637558\pi$
$163$	−10.6944	−0.837653	−0.418826	+	0.908066i	$0.637558\pi$
$164$	10.8831	0.849828
$165$	−20.7531	−1.61563
$166$	5.10293	0.396064
$167$	16.1334	1.24844	0.624222	−	0.781247i	$-0.285416\pi$
$167$	16.1334	1.24844	0.624222	+	0.781247i	$0.285416\pi$
$168$	−3.16418	−0.244122
$169$	10.2875	0.791349
$170$	−10.7105	−0.821456
$171$	0	0
$172$	−4.22746	−0.322341
$173$	7.34166	0.558176	0.279088	−	0.960266i	$-0.409968\pi$
$173$	7.34166	0.558176	0.279088	+	0.960266i	$0.409968\pi$
$174$	11.4209	0.865815
$175$	−1.30171	−0.0984001
$176$	−2.61272	−0.196941
$177$	41.8706	3.14719
$178$	13.9034	1.04210
$179$	−19.7327	−1.47489	−0.737447	−	0.675405i	$-0.763969\pi$
$179$	−19.7327	−1.47489	−0.737447	+	0.675405i	$0.763969\pi$
$180$	−17.6025	−1.31201
$181$	16.1374	1.19948	0.599742	−	0.800194i	$-0.295270\pi$
$181$	16.1374	1.19948	0.599742	+	0.800194i	$0.295270\pi$
$182$	4.82572	0.357706
$183$	−7.39932	−0.546974
$184$	7.62679	0.562254
$185$	−8.11532	−0.596650
$186$	22.9287	1.68121
$187$	11.1474	0.815175
$188$	11.3593	0.828459
$189$	12.6948	0.923412
$190$	0	0
$191$	14.5883	1.05557	0.527785	−	0.849378i	$-0.323023\pi$
$191$	14.5883	1.05557	0.527785	+	0.849378i	$0.323023\pi$
$192$	−3.16418	−0.228355
$193$	16.7098	1.20280	0.601398	−	0.798949i	$-0.294610\pi$
$193$	16.7098	1.20280	0.601398	+	0.798949i	$0.294610\pi$
$194$	16.4795	1.18316
$195$	38.3312	2.74495
$196$	1.00000	0.0714286
$197$	8.22675	0.586131	0.293066	−	0.956092i	$-0.405325\pi$
$197$	8.22675	0.586131	0.293066	+	0.956092i	$0.405325\pi$
$198$	18.3205	1.30198
$199$	5.64589	0.400226	0.200113	−	0.979773i	$-0.435869\pi$
$199$	5.64589	0.400226	0.200113	+	0.979773i	$0.435869\pi$
$200$	−1.30171	−0.0920449
$201$	26.9027	1.89757
$202$	13.7706	0.968897
$203$	−3.60943	−0.253332
$204$	13.5002	0.945204
$205$	−27.3201	−1.90812
$206$	−1.50789	−0.105060
$207$	−53.4793	−3.71707
$208$	4.82572	0.334603
$209$	0	0
$210$	7.94311	0.548127
$211$	7.62726	0.525082	0.262541	−	0.964921i	$-0.415439\pi$
$211$	7.62726	0.525082	0.262541	+	0.964921i	$0.415439\pi$
$212$	−7.34872	−0.504712
$213$	15.0645	1.03220
$214$	2.77137	0.189447
$215$	10.6123	0.723752
$216$	12.6948	0.863773
$217$	−7.24632	−0.491912
$218$	−14.1042	−0.955256
$219$	4.03122	0.272405
$220$	6.55876	0.442191
$221$	−20.5893	−1.38499
$222$	10.2291	0.686533
$223$	28.3584	1.89902	0.949511	−	0.313734i	$-0.101580\pi$
$223$	28.3584	1.89902	0.949511	+	0.313734i	$0.101580\pi$
$224$	1.00000	0.0668153
$225$	9.12765	0.608510
$226$	9.83390	0.654141
$227$	14.4245	0.957386	0.478693	−	0.877982i	$-0.341111\pi$
$227$	14.4245	0.957386	0.478693	+	0.877982i	$0.341111\pi$
$228$	0	0
$229$	0.886492	0.0585810	0.0292905	−	0.999571i	$-0.490675\pi$
$229$	0.886492	0.0585810	0.0292905	+	0.999571i	$0.490675\pi$
$230$	−19.1457	−1.26243
$231$	−8.26711	−0.543936
$232$	−3.60943	−0.236971
$233$	−0.683492	−0.0447771	−0.0223885	−	0.999749i	$-0.507127\pi$
$233$	−0.683492	−0.0447771	−0.0223885	+	0.999749i	$0.507127\pi$
$234$	−33.8381	−2.21207
$235$	−28.5154	−1.86014
$236$	−13.2327	−0.861375
$237$	14.1887	0.921658
$238$	−4.26658	−0.276561
$239$	−17.1563	−1.10975	−0.554873	−	0.831935i	$-0.687233\pi$
$239$	−17.1563	−1.10975	−0.554873	+	0.831935i	$0.687233\pi$
$240$	7.94311	0.512725
$241$	17.6699	1.13822	0.569108	−	0.822263i	$-0.307288\pi$
$241$	17.6699	1.13822	0.569108	+	0.822263i	$0.307288\pi$
$242$	4.17371	0.268296
$243$	−22.4545	−1.44045
$244$	2.33846	0.149705
$245$	−2.51032	−0.160379
$246$	34.4361	2.19557
$247$	0	0
$248$	−7.24632	−0.460142
$249$	16.1466	1.02325
$250$	−9.28389	−0.587165
$251$	−5.85498	−0.369563	−0.184781	−	0.982780i	$-0.559158\pi$
$251$	−5.85498	−0.369563	−0.184781	+	0.982780i	$0.559158\pi$
$252$	−7.01204	−0.441717
$253$	19.9266	1.25278
$254$	12.7218	0.798238
$255$	−33.8899	−2.12227
$256$	1.00000	0.0625000
$257$	16.6251	1.03705	0.518523	−	0.855064i	$-0.326482\pi$
$257$	16.6251	1.03705	0.518523	+	0.855064i	$0.326482\pi$
$258$	−13.3765	−0.832782
$259$	−3.23278	−0.200875
$260$	−12.1141	−0.751284
$261$	25.3095	1.56662
$262$	12.4181	0.767195
$263$	−25.7076	−1.58520	−0.792600	−	0.609742i	$-0.791273\pi$
$263$	−25.7076	−1.58520	−0.792600	+	0.609742i	$0.791273\pi$
$264$	−8.26711	−0.508805
$265$	18.4476	1.13323
$266$	0	0
$267$	43.9928	2.69231
$268$	−8.50225	−0.519358
$269$	16.5490	1.00901	0.504506	−	0.863408i	$-0.331675\pi$
$269$	16.5490	1.00901	0.504506	+	0.863408i	$0.331675\pi$
$270$	−31.8681	−1.93943
$271$	−9.95109	−0.604486	−0.302243	−	0.953231i	$-0.597735\pi$
$271$	−9.95109	−0.604486	−0.302243	+	0.953231i	$0.597735\pi$
$272$	−4.26658	−0.258699
$273$	15.2694	0.924149
$274$	−6.73772	−0.407040
$275$	−3.40100	−0.205088
$276$	24.1325	1.45261
$277$	−21.2918	−1.27930	−0.639649	−	0.768667i	$-0.720920\pi$
$277$	−21.2918	−1.27930	−0.639649	+	0.768667i	$0.720920\pi$
$278$	0.319255	0.0191476
$279$	50.8115	3.04200
$280$	−2.51032	−0.150020
$281$	−23.4946	−1.40157	−0.700785	−	0.713373i	$-0.747167\pi$
$281$	−23.4946	−1.40157	−0.700785	+	0.713373i	$0.747167\pi$
$282$	35.9427	2.14036
$283$	−8.68308	−0.516155	−0.258078	−	0.966124i	$-0.583089\pi$
$283$	−8.68308	−0.516155	−0.258078	+	0.966124i	$0.583089\pi$
$284$	−4.76093	−0.282509
$285$	0	0
$286$	12.6082	0.745540
$287$	−10.8831	−0.642410
$288$	−7.01204	−0.413188
$289$	1.20367	0.0708044
$290$	9.06083	0.532070
$291$	52.1442	3.05675
$292$	−1.27402	−0.0745562
$293$	7.73691	0.451995	0.225998	−	0.974128i	$-0.427436\pi$
$293$	7.73691	0.451995	0.225998	+	0.974128i	$0.427436\pi$
$294$	3.16418	0.184539
$295$	33.2183	1.93404
$296$	−3.23278	−0.187902
$297$	33.1680	1.92460
$298$	−1.33005	−0.0770476
$299$	−36.8047	−2.12847
$300$	−4.11885	−0.237802
$301$	4.22746	0.243667
$302$	−3.22677	−0.185680
$303$	43.5727	2.50319
$304$	0	0
$305$	−5.87029	−0.336132
$306$	29.9174	1.71026
$307$	−10.2087	−0.582639	−0.291320	−	0.956626i	$-0.594094\pi$
$307$	−10.2087	−0.582639	−0.291320	+	0.956626i	$0.594094\pi$
$308$	2.61272	0.148873
$309$	−4.77125	−0.271427
$310$	18.1906	1.03316
$311$	1.99962	0.113388	0.0566940	−	0.998392i	$-0.481944\pi$
$311$	1.99962	0.113388	0.0566940	+	0.998392i	$0.481944\pi$
$312$	15.2694	0.864462
$313$	−17.6479	−0.997521	−0.498760	−	0.866740i	$-0.666211\pi$
$313$	−17.6479	−0.997521	−0.498760	+	0.866740i	$0.666211\pi$
$314$	16.9062	0.954071
$315$	17.6025	0.991787
$316$	−4.48417	−0.252255
$317$	−13.7019	−0.769576	−0.384788	−	0.923005i	$-0.625726\pi$
$317$	−13.7019	−0.769576	−0.384788	+	0.923005i	$0.625726\pi$
$318$	−23.2527	−1.30394
$319$	−9.43042	−0.528002
$320$	−2.51032	−0.140331
$321$	8.76912	0.489445
$322$	−7.62679	−0.425024
$323$	0	0
$324$	19.1326	1.06292
$325$	6.28169	0.348446
$326$	10.6944	0.592310
$327$	−44.6282	−2.46794
$328$	−10.8831	−0.600919
$329$	−11.3593	−0.626256
$330$	20.7531	1.14242
$331$	9.86386	0.542167	0.271083	−	0.962556i	$-0.412618\pi$
$331$	9.86386	0.542167	0.271083	+	0.962556i	$0.412618\pi$
$332$	−5.10293	−0.280060
$333$	22.6684	1.24222
$334$	−16.1334	−0.882783
$335$	21.3434	1.16611
$336$	3.16418	0.172620
$337$	−8.76205	−0.477299	−0.238650	−	0.971106i	$-0.576705\pi$
$337$	−8.76205	−0.477299	−0.238650	+	0.971106i	$0.576705\pi$
$338$	−10.2875	−0.559569
$339$	31.1162	1.69000
$340$	10.7105	0.580857
$341$	−18.9326	−1.02526
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	4.22746	0.227930
$345$	−60.5804	−3.26154
$346$	−7.34166	−0.394690
$347$	−1.44810	−0.0777383	−0.0388692	−	0.999244i	$-0.512376\pi$
$347$	−1.44810	−0.0777383	−0.0388692	+	0.999244i	$0.512376\pi$
$348$	−11.4209	−0.612224
$349$	0.953902	0.0510612	0.0255306	−	0.999674i	$-0.491872\pi$
$349$	0.953902	0.0510612	0.0255306	+	0.999674i	$0.491872\pi$
$350$	1.30171	0.0695794
$351$	−61.2616	−3.26990
$352$	2.61272	0.139258
$353$	14.3348	0.762967	0.381483	−	0.924376i	$-0.375413\pi$
$353$	14.3348	0.762967	0.381483	+	0.924376i	$0.375413\pi$
$354$	−41.8706	−2.22540
$355$	11.9515	0.634318
$356$	−13.9034	−0.736877
$357$	−13.5002	−0.714507
$358$	19.7327	1.04291
$359$	27.7145	1.46272	0.731358	−	0.681994i	$-0.238887\pi$
$359$	27.7145	1.46272	0.731358	+	0.681994i	$0.238887\pi$
$360$	17.6025	0.927732
$361$	0	0
$362$	−16.1374	−0.848163
$363$	13.2064	0.693155
$364$	−4.82572	−0.252936
$365$	3.19819	0.167401
$366$	7.39932	0.386769
$367$	16.2009	0.845679	0.422840	−	0.906205i	$-0.361033\pi$
$367$	16.2009	0.845679	0.422840	+	0.906205i	$0.361033\pi$
$368$	−7.62679	−0.397574
$369$	76.3128	3.97269
$370$	8.11532	0.421895
$371$	7.34872	0.381526
$372$	−22.9287	−1.18880
$373$	−16.2653	−0.842187	−0.421093	−	0.907017i	$-0.638354\pi$
$373$	−16.2653	−0.842187	−0.421093	+	0.907017i	$0.638354\pi$
$374$	−11.1474	−0.576416
$375$	−29.3759	−1.51697
$376$	−11.3593	−0.585809
$377$	17.4181	0.897077
$378$	−12.6948	−0.652951
$379$	−23.8634	−1.22578	−0.612891	−	0.790167i	$-0.709994\pi$
$379$	−23.8634	−1.22578	−0.612891	+	0.790167i	$0.709994\pi$
$380$	0	0
$381$	40.2542	2.06228
$382$	−14.5883	−0.746401
$383$	20.8386	1.06480	0.532401	−	0.846492i	$-0.321290\pi$
$383$	20.8386	1.06480	0.532401	+	0.846492i	$0.321290\pi$
$384$	3.16418	0.161471
$385$	−6.55876	−0.334265
$386$	−16.7098	−0.850506
$387$	−29.6431	−1.50685
$388$	−16.4795	−0.836622
$389$	7.14317	0.362173	0.181087	−	0.983467i	$-0.442039\pi$
$389$	7.14317	0.362173	0.181087	+	0.983467i	$0.442039\pi$
$390$	−38.3312	−1.94098
$391$	32.5403	1.64563
$392$	−1.00000	−0.0505076
$393$	39.2932	1.98208
$394$	−8.22675	−0.414457
$395$	11.2567	0.566387
$396$	−18.3205	−0.920638
$397$	−9.46179	−0.474874	−0.237437	−	0.971403i	$-0.576307\pi$
$397$	−9.46179	−0.474874	−0.237437	+	0.971403i	$0.576307\pi$
$398$	−5.64589	−0.283003
$399$	0	0
$400$	1.30171	0.0650856
$401$	26.3806	1.31738	0.658692	−	0.752413i	$-0.271110\pi$
$401$	26.3806	1.31738	0.658692	+	0.752413i	$0.271110\pi$
$402$	−26.9027	−1.34178
$403$	34.9687	1.74191
$404$	−13.7706	−0.685114
$405$	−48.0289	−2.38657
$406$	3.60943	0.179133
$407$	−8.44634	−0.418670
$408$	−13.5002	−0.668360
$409$	−19.1197	−0.945409	−0.472704	−	0.881221i	$-0.656722\pi$
$409$	−19.1197	−0.945409	−0.472704	+	0.881221i	$0.656722\pi$
$410$	27.3201	1.34924
$411$	−21.3194	−1.05161
$412$	1.50789	0.0742887
$413$	13.2327	0.651138
$414$	53.4793	2.62837
$415$	12.8100	0.628817
$416$	−4.82572	−0.236600
$417$	1.01018	0.0494687
$418$	0	0
$419$	28.8591	1.40986	0.704928	−	0.709278i	$-0.250979\pi$
$419$	28.8591	1.40986	0.704928	+	0.709278i	$0.250979\pi$
$420$	−7.94311	−0.387584
$421$	−10.2176	−0.497977	−0.248988	−	0.968506i	$-0.580098\pi$
$421$	−10.2176	−0.497977	−0.248988	+	0.968506i	$0.580098\pi$
$422$	−7.62726	−0.371289
$423$	79.6515	3.87279
$424$	7.34872	0.356885
$425$	−5.55385	−0.269401
$426$	−15.0645	−0.729875
$427$	−2.33846	−0.113166
$428$	−2.77137	−0.133959
$429$	39.8947	1.92614
$430$	−10.6123	−0.511770
$431$	4.64753	0.223863	0.111932	−	0.993716i	$-0.464296\pi$
$431$	4.64753	0.223863	0.111932	+	0.993716i	$0.464296\pi$
$432$	−12.6948	−0.610780
$433$	13.9797	0.671823	0.335912	−	0.941893i	$-0.390956\pi$
$433$	13.9797	0.671823	0.335912	+	0.941893i	$0.390956\pi$
$434$	7.24632	0.347834
$435$	28.6701	1.37463
$436$	14.1042	0.675468
$437$	0	0
$438$	−4.03122	−0.192619
$439$	28.4564	1.35815	0.679075	−	0.734069i	$-0.262381\pi$
$439$	28.4564	1.35815	0.679075	+	0.734069i	$0.262381\pi$
$440$	−6.55876	−0.312677
$441$	7.01204	0.333907
$442$	20.5893	0.979333
$443$	−18.2837	−0.868686	−0.434343	−	0.900748i	$-0.643019\pi$
$443$	−18.2837	−0.868686	−0.434343	+	0.900748i	$0.643019\pi$
$444$	−10.2291	−0.485452
$445$	34.9019	1.65451
$446$	−28.3584	−1.34281
$447$	−4.20851	−0.199056
$448$	−1.00000	−0.0472456
$449$	36.6290	1.72863	0.864315	−	0.502950i	$-0.167752\pi$
$449$	36.6290	1.72863	0.864315	+	0.502950i	$0.167752\pi$
$450$	−9.12765	−0.430282
$451$	−28.4345	−1.33893
$452$	−9.83390	−0.462548
$453$	−10.2101	−0.479712
$454$	−14.4245	−0.676974
$455$	12.1141	0.567918
$456$	0	0
$457$	−29.4723	−1.37866	−0.689328	−	0.724450i	$-0.742094\pi$
$457$	−29.4723	−1.37866	−0.689328	+	0.724450i	$0.742094\pi$
$458$	−0.886492	−0.0414231
$459$	54.1634	2.52813
$460$	19.1457	0.892672
$461$	−28.7851	−1.34066	−0.670328	−	0.742065i	$-0.733847\pi$
$461$	−28.7851	−1.34066	−0.670328	+	0.742065i	$0.733847\pi$
$462$	8.26711	0.384621
$463$	32.3700	1.50436	0.752181	−	0.658957i	$-0.229002\pi$
$463$	32.3700	1.50436	0.752181	+	0.658957i	$0.229002\pi$
$464$	3.60943	0.167564
$465$	57.5583	2.66920
$466$	0.683492	0.0316622
$467$	5.10108	0.236050	0.118025	−	0.993011i	$-0.462344\pi$
$467$	5.10108	0.236050	0.118025	+	0.993011i	$0.462344\pi$
$468$	33.8381	1.56417
$469$	8.50225	0.392597
$470$	28.5154	1.31532
$471$	53.4942	2.46488
$472$	13.2327	0.609084
$473$	11.0452	0.507857
$474$	−14.1887	−0.651710
$475$	0	0
$476$	4.26658	0.195558
$477$	−51.5295	−2.35937
$478$	17.1563	0.784709
$479$	23.9047	1.09223	0.546116	−	0.837709i	$-0.316106\pi$
$479$	23.9047	1.09223	0.546116	+	0.837709i	$0.316106\pi$
$480$	−7.94311	−0.362552
$481$	15.6005	0.711321
$482$	−17.6699	−0.804841
$483$	−24.1325	−1.09807
$484$	−4.17371	−0.189714
$485$	41.3689	1.87847
$486$	22.4545	1.01856
$487$	−29.3065	−1.32801	−0.664003	−	0.747730i	$-0.731144\pi$
$487$	−29.3065	−1.32801	−0.664003	+	0.747730i	$0.731144\pi$
$488$	−2.33846	−0.105857
$489$	33.8391	1.53026
$490$	2.51032	0.113405
$491$	5.44211	0.245599	0.122799	−	0.992432i	$-0.460813\pi$
$491$	5.44211	0.245599	0.122799	+	0.992432i	$0.460813\pi$
$492$	−34.4361	−1.55250
$493$	−15.3999	−0.693577
$494$	0	0
$495$	45.9903	2.06711
$496$	7.24632	0.325369
$497$	4.76093	0.213557
$498$	−16.1466	−0.723546
$499$	−37.2672	−1.66831	−0.834155	−	0.551530i	$-0.814044\pi$
$499$	−37.2672	−1.66831	−0.834155	+	0.551530i	$0.814044\pi$
$500$	9.28389	0.415188
$501$	−51.0491	−2.28071
$502$	5.85498	0.261320
$503$	19.1779	0.855099	0.427549	−	0.903992i	$-0.359377\pi$
$503$	19.1779	0.855099	0.427549	+	0.903992i	$0.359377\pi$
$504$	7.01204	0.312341
$505$	34.5687	1.53829
$506$	−19.9266	−0.885847
$507$	−32.5516	−1.44567
$508$	−12.7218	−0.564440
$509$	−2.56925	−0.113880	−0.0569400	−	0.998378i	$-0.518134\pi$
$509$	−2.56925	−0.113880	−0.0569400	+	0.998378i	$0.518134\pi$
$510$	33.8899	1.50067
$511$	1.27402	0.0563592
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−16.6251	−0.733302
$515$	−3.78530	−0.166800
$516$	13.3765	0.588866
$517$	−29.6785	−1.30526
$518$	3.23278	0.142040
$519$	−23.2303	−1.01970
$520$	12.1141	0.531238
$521$	−33.0438	−1.44768	−0.723838	−	0.689970i	$-0.757624\pi$
$521$	−33.0438	−1.44768	−0.723838	+	0.689970i	$0.757624\pi$
$522$	−25.3095	−1.10777
$523$	−19.8963	−0.870006	−0.435003	−	0.900429i	$-0.643253\pi$
$523$	−19.8963	−0.870006	−0.435003	+	0.900429i	$0.643253\pi$
$524$	−12.4181	−0.542489
$525$	4.11885	0.179761
$526$	25.7076	1.12091
$527$	−30.9170	−1.34676
$528$	8.26711	0.359780
$529$	35.1679	1.52904
$530$	−18.4476	−0.801314
$531$	−92.7881	−4.02666
$532$	0	0
$533$	52.5188	2.27484
$534$	−43.9928	−1.90375
$535$	6.95703	0.300779
$536$	8.50225	0.367241
$537$	62.4379	2.69440
$538$	−16.5490	−0.713480
$539$	−2.61272	−0.112538
$540$	31.8681	1.37138
$541$	18.6579	0.802167	0.401084	−	0.916041i	$-0.368634\pi$
$541$	18.6579	0.802167	0.401084	+	0.916041i	$0.368634\pi$
$542$	9.95109	0.427436
$543$	−51.0616	−2.19126
$544$	4.26658	0.182928
$545$	−35.4060	−1.51663
$546$	−15.2694	−0.653472
$547$	2.16310	0.0924874	0.0462437	−	0.998930i	$-0.485275\pi$
$547$	2.16310	0.0924874	0.0462437	+	0.998930i	$0.485275\pi$
$548$	6.73772	0.287821
$549$	16.3974	0.699824
$550$	3.40100	0.145019
$551$	0	0
$552$	−24.1325	−1.02715
$553$	4.48417	0.190687
$554$	21.2918	0.904600
$555$	25.6783	1.08998
$556$	−0.319255	−0.0135394
$557$	12.6148	0.534505	0.267252	−	0.963627i	$-0.413884\pi$
$557$	12.6148	0.534505	0.267252	+	0.963627i	$0.413884\pi$
$558$	−50.8115	−2.15102
$559$	−20.4005	−0.862851
$560$	2.51032	0.106080
$561$	−35.2722	−1.48920
$562$	23.4946	0.991059
$563$	−22.8326	−0.962279	−0.481139	−	0.876644i	$-0.659777\pi$
$563$	−22.8326	−0.962279	−0.481139	+	0.876644i	$0.659777\pi$
$564$	−35.9427	−1.51346
$565$	24.6862	1.03856
$566$	8.68308	0.364977
$567$	−19.1326	−0.803492
$568$	4.76093	0.199764
$569$	21.5539	0.903585	0.451792	−	0.892123i	$-0.350785\pi$
$569$	21.5539	0.903585	0.451792	+	0.892123i	$0.350785\pi$
$570$	0	0
$571$	11.2685	0.471570	0.235785	−	0.971805i	$-0.424234\pi$
$571$	11.2685	0.471570	0.235785	+	0.971805i	$0.424234\pi$
$572$	−12.6082	−0.527177
$573$	−46.1599	−1.92836
$574$	10.8831	0.454252
$575$	−9.92788	−0.414021
$576$	7.01204	0.292168
$577$	12.3302	0.513314	0.256657	−	0.966503i	$-0.417379\pi$
$577$	12.3302	0.513314	0.256657	+	0.966503i	$0.417379\pi$
$578$	−1.20367	−0.0500663
$579$	−52.8728	−2.19732
$580$	−9.06083	−0.376230
$581$	5.10293	0.211705
$582$	−52.1442	−2.16145
$583$	19.2001	0.795187
$584$	1.27402	0.0527192
$585$	−84.9445	−3.51202
$586$	−7.73691	−0.319609
$587$	12.1757	0.502545	0.251273	−	0.967916i	$-0.419151\pi$
$587$	12.1757	0.502545	0.251273	+	0.967916i	$0.419151\pi$
$588$	−3.16418	−0.130489
$589$	0	0
$590$	−33.2183	−1.36758
$591$	−26.0309	−1.07077
$592$	3.23278	0.132867
$593$	38.1017	1.56465	0.782324	−	0.622871i	$-0.214034\pi$
$593$	38.1017	1.56465	0.782324	+	0.622871i	$0.214034\pi$
$594$	−33.1680	−1.36090
$595$	−10.7105	−0.439087
$596$	1.33005	0.0544809
$597$	−17.8646	−0.731150
$598$	36.8047	1.50506
$599$	1.39115	0.0568408	0.0284204	−	0.999596i	$-0.490952\pi$
$599$	1.39115	0.0568408	0.0284204	+	0.999596i	$0.490952\pi$
$600$	4.11885	0.168151
$601$	25.4572	1.03842	0.519211	−	0.854646i	$-0.326226\pi$
$601$	25.4572	1.03842	0.519211	+	0.854646i	$0.326226\pi$
$602$	−4.22746	−0.172299
$603$	−59.6181	−2.42784
$604$	3.22677	0.131296
$605$	10.4774	0.425965
$606$	−43.5727	−1.77002
$607$	20.1387	0.817407	0.408703	−	0.912667i	$-0.365981\pi$
$607$	20.1387	0.817407	0.408703	+	0.912667i	$0.365981\pi$
$608$	0	0
$609$	11.4209	0.462798
$610$	5.87029	0.237681
$611$	54.8165	2.21764
$612$	−29.9174	−1.20934
$613$	−13.1638	−0.531683	−0.265841	−	0.964017i	$-0.585650\pi$
$613$	−13.1638	−0.531683	−0.265841	+	0.964017i	$0.585650\pi$
$614$	10.2087	0.411988
$615$	86.4457	3.48583
$616$	−2.61272	−0.105269
$617$	−2.76914	−0.111481	−0.0557406	−	0.998445i	$-0.517752\pi$
$617$	−2.76914	−0.111481	−0.0557406	+	0.998445i	$0.517752\pi$
$618$	4.77125	0.191928
$619$	12.1729	0.489272	0.244636	−	0.969615i	$-0.421332\pi$
$619$	12.1729	0.489272	0.244636	+	0.969615i	$0.421332\pi$
$620$	−18.1906	−0.730552
$621$	96.8206	3.88528
$622$	−1.99962	−0.0801774
$623$	13.9034	0.557027
$624$	−15.2694	−0.611267
$625$	−29.8141	−1.19256
$626$	17.6479	0.705354
$627$	0	0
$628$	−16.9062	−0.674630
$629$	−13.7929	−0.549959
$630$	−17.6025	−0.701299
$631$	19.7011	0.784290	0.392145	−	0.919903i	$-0.371733\pi$
$631$	19.7011	0.784290	0.392145	+	0.919903i	$0.371733\pi$
$632$	4.48417	0.178371
$633$	−24.1340	−0.959241
$634$	13.7019	0.544173
$635$	31.9359	1.26734
$636$	23.2527	0.922028
$637$	4.82572	0.191202
$638$	9.43042	0.373354
$639$	−33.3838	−1.32064
$640$	2.51032	0.0992292
$641$	−5.00932	−0.197856	−0.0989282	−	0.995095i	$-0.531541\pi$
$641$	−5.00932	−0.197856	−0.0989282	+	0.995095i	$0.531541\pi$
$642$	−8.76912	−0.346090
$643$	−40.1825	−1.58464	−0.792321	−	0.610104i	$-0.791128\pi$
$643$	−40.1825	−1.58464	−0.792321	+	0.610104i	$0.791128\pi$
$644$	7.62679	0.300537
$645$	−33.5792	−1.32218
$646$	0	0
$647$	−27.1866	−1.06882	−0.534408	−	0.845226i	$-0.679466\pi$
$647$	−27.1866	−1.06882	−0.534408	+	0.845226i	$0.679466\pi$
$648$	−19.1326	−0.751598
$649$	34.5733	1.35712
$650$	−6.28169	−0.246388
$651$	22.9287	0.898645
$652$	−10.6944	−0.418826
$653$	12.5304	0.490353	0.245176	−	0.969479i	$-0.421154\pi$
$653$	12.5304	0.490353	0.245176	+	0.969479i	$0.421154\pi$
$654$	44.6282	1.74510
$655$	31.1735	1.21805
$656$	10.8831	0.424914
$657$	−8.93346	−0.348527
$658$	11.3593	0.442830
$659$	−13.5356	−0.527272	−0.263636	−	0.964622i	$-0.584922\pi$
$659$	−13.5356	−0.527272	−0.263636	+	0.964622i	$0.584922\pi$
$660$	−20.7531	−0.807813
$661$	−2.51710	−0.0979038	−0.0489519	−	0.998801i	$-0.515588\pi$
$661$	−2.51710	−0.0979038	−0.0489519	+	0.998801i	$0.515588\pi$
$662$	−9.86386	−0.383370
$663$	65.1482	2.53015
$664$	5.10293	0.198032
$665$	0	0
$666$	−22.6684	−0.878382
$667$	−27.5284	−1.06590
$668$	16.1334	0.624222
$669$	−89.7312	−3.46921
$670$	−21.3434	−0.824567
$671$	−6.10974	−0.235864
$672$	−3.16418	−0.122061
$673$	29.4794	1.13635	0.568174	−	0.822908i	$-0.307650\pi$
$673$	29.4794	1.13635	0.568174	+	0.822908i	$0.307650\pi$
$674$	8.76205	0.337502
$675$	−16.5250	−0.636047
$676$	10.2875	0.395675
$677$	43.5055	1.67205	0.836026	−	0.548689i	$-0.184873\pi$
$677$	43.5055	1.67205	0.836026	+	0.548689i	$0.184873\pi$
$678$	−31.1162	−1.19501
$679$	16.4795	0.632427
$680$	−10.7105	−0.410728
$681$	−45.6416	−1.74899
$682$	18.9326	0.724966
$683$	−7.16379	−0.274115	−0.137057	−	0.990563i	$-0.543764\pi$
$683$	−7.16379	−0.274115	−0.137057	+	0.990563i	$0.543764\pi$
$684$	0	0
$685$	−16.9138	−0.646245
$686$	1.00000	0.0381802
$687$	−2.80502	−0.107018
$688$	−4.22746	−0.161171
$689$	−35.4628	−1.35103
$690$	60.5804	2.30626
$691$	26.5593	1.01036	0.505181	−	0.863013i	$-0.331426\pi$
$691$	26.5593	1.01036	0.505181	+	0.863013i	$0.331426\pi$
$692$	7.34166	0.279088
$693$	18.3205	0.695937
$694$	1.44810	0.0549693
$695$	0.801432	0.0304000
$696$	11.4209	0.432908
$697$	−46.4336	−1.75880
$698$	−0.953902	−0.0361057
$699$	2.16269	0.0818006
$700$	−1.30171	−0.0492001
$701$	40.2705	1.52100	0.760498	−	0.649340i	$-0.224955\pi$
$701$	40.2705	1.52100	0.760498	+	0.649340i	$0.224955\pi$
$702$	61.2616	2.31217
$703$	0	0
$704$	−2.61272	−0.0984705
$705$	90.2278	3.39818
$706$	−14.3348	−0.539499
$707$	13.7706	0.517897
$708$	41.8706	1.57359
$709$	3.54346	0.133077	0.0665387	−	0.997784i	$-0.478804\pi$
$709$	3.54346	0.133077	0.0665387	+	0.997784i	$0.478804\pi$
$710$	−11.9515	−0.448531
$711$	−31.4432	−1.17921
$712$	13.9034	0.521051
$713$	−55.2661	−2.06973
$714$	13.5002	0.505233
$715$	31.6507	1.18367
$716$	−19.7327	−0.737447
$717$	54.2855	2.02733
$718$	−27.7145	−1.03430
$719$	−7.64680	−0.285178	−0.142589	−	0.989782i	$-0.545543\pi$
$719$	−7.64680	−0.285178	−0.142589	+	0.989782i	$0.545543\pi$
$720$	−17.6025	−0.656005
$721$	−1.50789	−0.0561569
$722$	0	0
$723$	−55.9107	−2.07934
$724$	16.1374	0.599742
$725$	4.69844	0.174496
$726$	−13.2064	−0.490135
$727$	−35.6709	−1.32296	−0.661480	−	0.749963i	$-0.730071\pi$
$727$	−35.6709	−1.32296	−0.661480	+	0.749963i	$0.730071\pi$
$728$	4.82572	0.178853
$729$	13.6523	0.505640
$730$	−3.19819	−0.118370
$731$	18.0368	0.667115
$732$	−7.39932	−0.273487
$733$	12.1927	0.450347	0.225173	−	0.974319i	$-0.427705\pi$
$733$	12.1927	0.450347	0.225173	+	0.974319i	$0.427705\pi$
$734$	−16.2009	−0.597986
$735$	7.94311	0.292986
$736$	7.62679	0.281127
$737$	22.2140	0.818262
$738$	−76.3128	−2.80911
$739$	17.8349	0.656069	0.328034	−	0.944666i	$-0.393614\pi$
$739$	17.8349	0.656069	0.328034	+	0.944666i	$0.393614\pi$
$740$	−8.11532	−0.298325
$741$	0	0
$742$	−7.34872	−0.269780
$743$	−44.2875	−1.62475	−0.812376	−	0.583134i	$-0.801826\pi$
$743$	−44.2875	−1.62475	−0.812376	+	0.583134i	$0.801826\pi$
$744$	22.9287	0.840606
$745$	−3.33885	−0.122326
$746$	16.2653	0.595516
$747$	−35.7819	−1.30919
$748$	11.1474	0.407588
$749$	2.77137	0.101264
$750$	29.3759	1.07266
$751$	23.1436	0.844522	0.422261	−	0.906474i	$-0.361237\pi$
$751$	23.1436	0.844522	0.422261	+	0.906474i	$0.361237\pi$
$752$	11.3593	0.414229
$753$	18.5262	0.675132
$754$	−17.4181	−0.634329
$755$	−8.10024	−0.294798
$756$	12.6948	0.461706
$757$	13.9355	0.506494	0.253247	−	0.967402i	$-0.418501\pi$
$757$	13.9355	0.506494	0.253247	+	0.967402i	$0.418501\pi$
$758$	23.8634	0.866759
$759$	−63.0515	−2.28862
$760$	0	0
$761$	−28.7533	−1.04231	−0.521153	−	0.853463i	$-0.674498\pi$
$761$	−28.7533	−1.04231	−0.521153	+	0.853463i	$0.674498\pi$
$762$	−40.2542	−1.45825
$763$	−14.1042	−0.510606
$764$	14.5883	0.527785
$765$	75.1023	2.71533
$766$	−20.8386	−0.752929
$767$	−63.8572	−2.30575
$768$	−3.16418	−0.114178
$769$	−19.4159	−0.700155	−0.350078	−	0.936721i	$-0.613845\pi$
$769$	−19.4159	−0.700155	−0.350078	+	0.936721i	$0.613845\pi$
$770$	6.55876	0.236361
$771$	−52.6048	−1.89452
$772$	16.7098	0.601398
$773$	18.9513	0.681632	0.340816	−	0.940130i	$-0.389297\pi$
$773$	18.9513	0.681632	0.340816	+	0.940130i	$0.389297\pi$
$774$	29.6431	1.06550
$775$	9.43262	0.338830
$776$	16.4795	0.591581
$777$	10.2291	0.366967
$778$	−7.14317	−0.256095
$779$	0	0
$780$	38.3312	1.37248
$781$	12.4390	0.445101
$782$	−32.5403	−1.16364
$783$	−45.8211	−1.63751
$784$	1.00000	0.0357143
$785$	42.4399	1.51475
$786$	−39.2932	−1.40154
$787$	−25.2459	−0.899919	−0.449959	−	0.893049i	$-0.648562\pi$
$787$	−25.2459	−0.899919	−0.449959	+	0.893049i	$0.648562\pi$
$788$	8.22675	0.293066
$789$	81.3436	2.89591
$790$	−11.2567	−0.400496
$791$	9.83390	0.349653
$792$	18.3205	0.650990
$793$	11.2848	0.400734
$794$	9.46179	0.335786
$795$	−58.3717	−2.07023
$796$	5.64589	0.200113
$797$	21.6363	0.766396	0.383198	−	0.923666i	$-0.374823\pi$
$797$	21.6363	0.766396	0.383198	+	0.923666i	$0.374823\pi$
$798$	0	0
$799$	−48.4651	−1.71457
$800$	−1.30171	−0.0460225
$801$	−97.4910	−3.44467
$802$	−26.3806	−0.931531
$803$	3.32865	0.117465
$804$	26.9027	0.948783
$805$	−19.1457	−0.674797
$806$	−34.9687	−1.23172
$807$	−52.3641	−1.84331
$808$	13.7706	0.484448
$809$	8.90217	0.312984	0.156492	−	0.987679i	$-0.449982\pi$
$809$	8.90217	0.312984	0.156492	+	0.987679i	$0.449982\pi$
$810$	48.0289	1.68756
$811$	−17.0926	−0.600202	−0.300101	−	0.953907i	$-0.597020\pi$
$811$	−17.0926	−0.600202	−0.300101	+	0.953907i	$0.597020\pi$
$812$	−3.60943	−0.126666
$813$	31.4870	1.10430
$814$	8.44634	0.296044
$815$	26.8465	0.940390
$816$	13.5002	0.472602
$817$	0	0
$818$	19.1197	0.668505
$819$	−33.8381	−1.18240
$820$	−27.3201	−0.954059
$821$	−25.5781	−0.892682	−0.446341	−	0.894863i	$-0.647273\pi$
$821$	−25.5781	−0.892682	−0.446341	+	0.894863i	$0.647273\pi$
$822$	21.3194	0.743598
$823$	50.5370	1.76161	0.880805	−	0.473479i	$-0.157002\pi$
$823$	50.5370	1.76161	0.880805	+	0.473479i	$0.157002\pi$
$824$	−1.50789	−0.0525300
$825$	10.7614	0.374664
$826$	−13.2327	−0.460424
$827$	−17.6121	−0.612432	−0.306216	−	0.951962i	$-0.599063\pi$
$827$	−17.6121	−0.612432	−0.306216	+	0.951962i	$0.599063\pi$
$828$	−53.4793	−1.85853
$829$	28.7775	0.999483	0.499742	−	0.866175i	$-0.333428\pi$
$829$	28.7775	0.999483	0.499742	+	0.866175i	$0.333428\pi$
$830$	−12.8100	−0.444641
$831$	67.3710	2.33707
$832$	4.82572	0.167302
$833$	−4.26658	−0.147828
$834$	−1.01018	−0.0349796
$835$	−40.5001	−1.40156
$836$	0	0
$837$	−91.9907	−3.17966
$838$	−28.8591	−0.996919
$839$	−0.596386	−0.0205895	−0.0102948	−	0.999947i	$-0.503277\pi$
$839$	−0.596386	−0.0205895	−0.0102948	+	0.999947i	$0.503277\pi$
$840$	7.94311	0.274063
$841$	−15.9720	−0.550759
$842$	10.2176	0.352123
$843$	74.3411	2.56044
$844$	7.62726	0.262541
$845$	−25.8250	−0.888408
$846$	−79.6515	−2.73848
$847$	4.17371	0.143410
$848$	−7.34872	−0.252356
$849$	27.4748	0.942934
$850$	5.55385	0.190496
$851$	−24.6557	−0.845188
$852$	15.0645	0.516100
$853$	−5.66868	−0.194092	−0.0970460	−	0.995280i	$-0.530939\pi$
$853$	−5.66868	−0.194092	−0.0970460	+	0.995280i	$0.530939\pi$
$854$	2.33846	0.0800206
$855$	0	0
$856$	2.77137	0.0947236
$857$	−10.8667	−0.371200	−0.185600	−	0.982625i	$-0.559423\pi$
$857$	−10.8667	−0.371200	−0.185600	+	0.982625i	$0.559423\pi$
$858$	−39.8947	−1.36198
$859$	4.29541	0.146557	0.0732787	−	0.997312i	$-0.476654\pi$
$859$	4.29541	0.146557	0.0732787	+	0.997312i	$0.476654\pi$
$860$	10.6123	0.361876
$861$	34.4361	1.17358
$862$	−4.64753	−0.158295
$863$	25.5992	0.871408	0.435704	−	0.900090i	$-0.356499\pi$
$863$	25.5992	0.871408	0.435704	+	0.900090i	$0.356499\pi$
$864$	12.6948	0.431886
$865$	−18.4299	−0.626636
$866$	−13.9797	−0.475051
$867$	−3.80864	−0.129348
$868$	−7.24632	−0.245956
$869$	11.7159	0.397434
$870$	−28.6701	−0.972007
$871$	−41.0294	−1.39023
$872$	−14.1042	−0.477628
$873$	−115.555	−3.91095
$874$	0	0
$875$	−9.28389	−0.313853
$876$	4.03122	0.136202
$877$	28.1708	0.951259	0.475630	−	0.879646i	$-0.342220\pi$
$877$	28.1708	0.951259	0.475630	+	0.879646i	$0.342220\pi$
$878$	−28.4564	−0.960357
$879$	−24.4810	−0.825723
$880$	6.55876	0.221096
$881$	−13.9995	−0.471656	−0.235828	−	0.971795i	$-0.575780\pi$
$881$	−13.9995	−0.471656	−0.235828	+	0.971795i	$0.575780\pi$
$882$	−7.01204	−0.236108
$883$	10.1917	0.342978	0.171489	−	0.985186i	$-0.445142\pi$
$883$	10.1917	0.342978	0.171489	+	0.985186i	$0.445142\pi$
$884$	−20.5893	−0.692493
$885$	−105.109	−3.53319
$886$	18.2837	0.614254
$887$	−15.7383	−0.528439	−0.264220	−	0.964463i	$-0.585114\pi$
$887$	−15.7383	−0.528439	−0.264220	+	0.964463i	$0.585114\pi$
$888$	10.2291	0.343266
$889$	12.7218	0.426676
$890$	−34.9019	−1.16992
$891$	−49.9880	−1.67466
$892$	28.3584	0.949511
$893$	0	0
$894$	4.20851	0.140754
$895$	49.5355	1.65579
$896$	1.00000	0.0334077
$897$	116.457	3.88838
$898$	−36.6290	−1.22233
$899$	26.1551	0.872321
$900$	9.12765	0.304255
$901$	31.3539	1.04455
$902$	28.4345	0.946765
$903$	−13.3765	−0.445141
$904$	9.83390	0.327071
$905$	−40.5100	−1.34660
$906$	10.2101	0.339208
$907$	4.10556	0.136323	0.0681614	−	0.997674i	$-0.478287\pi$
$907$	4.10556	0.136323	0.0681614	+	0.997674i	$0.478287\pi$
$908$	14.4245	0.478693
$909$	−96.5601	−3.20270
$910$	−12.1141	−0.401578
$911$	34.6692	1.14864	0.574321	−	0.818630i	$-0.305266\pi$
$911$	34.6692	1.14864	0.574321	+	0.818630i	$0.305266\pi$
$912$	0	0
$913$	13.3325	0.441241
$914$	29.4723	0.974857
$915$	18.5747	0.614060
$916$	0.886492	0.0292905
$917$	12.4181	0.410083
$918$	−54.1634	−1.78766
$919$	−43.8230	−1.44559	−0.722794	−	0.691063i	$-0.757143\pi$
$919$	−43.8230	−1.44559	−0.722794	+	0.691063i	$0.757143\pi$
$920$	−19.1457	−0.631214
$921$	32.3021	1.06439
$922$	28.7851	0.947988
$923$	−22.9749	−0.756229
$924$	−8.26711	−0.271968
$925$	4.20815	0.138363
$926$	−32.3700	−1.06374
$927$	10.5734	0.347277
$928$	−3.60943	−0.118485
$929$	49.2660	1.61637	0.808183	−	0.588932i	$-0.200451\pi$
$929$	49.2660	1.61637	0.808183	+	0.588932i	$0.200451\pi$
$930$	−57.5583	−1.88741
$931$	0	0
$932$	−0.683492	−0.0223885
$933$	−6.32715	−0.207142
$934$	−5.10108	−0.166912
$935$	−27.9834	−0.915156
$936$	−33.8381	−1.10603
$937$	−6.01950	−0.196648	−0.0983242	−	0.995154i	$-0.531348\pi$
$937$	−6.01950	−0.196648	−0.0983242	+	0.995154i	$0.531348\pi$
$938$	−8.50225	−0.277608
$939$	55.8413	1.82231
$940$	−28.5154	−0.930069
$941$	−3.25913	−0.106244	−0.0531222	−	0.998588i	$-0.516917\pi$
$941$	−3.25913	−0.106244	−0.0531222	+	0.998588i	$0.516917\pi$
$942$	−53.4942	−1.74294
$943$	−83.0032	−2.70295
$944$	−13.2327	−0.430687
$945$	−31.8681	−1.03667
$946$	−11.0452	−0.359109
$947$	−23.9751	−0.779085	−0.389543	−	0.921008i	$-0.627367\pi$
$947$	−23.9751	−0.779085	−0.389543	+	0.921008i	$0.627367\pi$
$948$	14.1887	0.460829
$949$	−6.14804	−0.199574
$950$	0	0
$951$	43.3553	1.40589
$952$	−4.26658	−0.138281
$953$	7.02484	0.227557	0.113778	−	0.993506i	$-0.463705\pi$
$953$	7.02484	0.227557	0.113778	+	0.993506i	$0.463705\pi$
$954$	51.5295	1.66833
$955$	−36.6212	−1.18504
$956$	−17.1563	−0.554873
$957$	29.8396	0.964576
$958$	−23.9047	−0.772325
$959$	−6.73772	−0.217572
$960$	7.94311	0.256363
$961$	21.5092	0.693844
$962$	−15.6005	−0.502980
$963$	−19.4330	−0.626219
$964$	17.6699	0.569108
$965$	−41.9469	−1.35032
$966$	24.1325	0.776451
$967$	7.21004	0.231859	0.115930	−	0.993257i	$-0.463015\pi$
$967$	7.21004	0.231859	0.115930	+	0.993257i	$0.463015\pi$
$968$	4.17371	0.134148
$969$	0	0
$970$	−41.3689	−1.32828
$971$	−22.9179	−0.735469	−0.367735	−	0.929931i	$-0.619866\pi$
$971$	−22.9179	−0.735469	−0.367735	+	0.929931i	$0.619866\pi$
$972$	−22.4545	−0.720227
$973$	0.319255	0.0102348
$974$	29.3065	0.939042
$975$	−19.8764	−0.636554
$976$	2.33846	0.0748524
$977$	29.3091	0.937680	0.468840	−	0.883283i	$-0.344672\pi$
$977$	29.3091	0.937680	0.468840	+	0.883283i	$0.344672\pi$
$978$	−33.8391	−1.08206
$979$	36.3256	1.16097
$980$	−2.51032	−0.0801893
$981$	98.8991	3.15760
$982$	−5.44211	−0.173665
$983$	29.9806	0.956233	0.478117	−	0.878296i	$-0.341320\pi$
$983$	29.9806	0.956233	0.478117	+	0.878296i	$0.341320\pi$
$984$	34.4361	1.09778
$985$	−20.6518	−0.658020
$986$	15.3999	0.490433
$987$	35.9427	1.14407
$988$	0	0
$989$	32.2420	1.02524
$990$	−45.9903	−1.46167
$991$	8.74902	0.277922	0.138961	−	0.990298i	$-0.455624\pi$
$991$	8.74902	0.277922	0.138961	+	0.990298i	$0.455624\pi$
$992$	−7.24632	−0.230071
$993$	−31.2110	−0.990452
$994$	−4.76093	−0.151008
$995$	−14.1730	−0.449314
$996$	16.1466	0.511624
$997$	27.6680	0.876256	0.438128	−	0.898913i	$-0.355642\pi$
$997$	27.6680	0.876256	0.438128	+	0.898913i	$0.355642\pi$
$998$	37.2672	1.17967
$999$	−41.0396	−1.29843

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.ba.1.1	✓	6	1.1	even	1	trivial
5054.2.a.bd.1.6	yes	6	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.16418 q^{3} +1.00000 q^{4} -2.51032 q^{5} +3.16418 q^{6} -1.00000 q^{7} -1.00000 q^{8} +7.01204 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.16418 q^{3} +1.00000 q^{4} -2.51032 q^{5} +3.16418 q^{6} -1.00000 q^{7} -1.00000 q^{8} +7.01204 q^{9} +2.51032 q^{10} -2.61272 q^{11} -3.16418 q^{12} +4.82572 q^{13} +1.00000 q^{14} +7.94311 q^{15} +1.00000 q^{16} -4.26658 q^{17} -7.01204 q^{18} -2.51032 q^{20} +3.16418 q^{21} +2.61272 q^{22} -7.62679 q^{23} +3.16418 q^{24} +1.30171 q^{25} -4.82572 q^{26} -12.6948 q^{27} -1.00000 q^{28} +3.60943 q^{29} -7.94311 q^{30} +7.24632 q^{31} -1.00000 q^{32} +8.26711 q^{33} +4.26658 q^{34} +2.51032 q^{35} +7.01204 q^{36} +3.23278 q^{37} -15.2694 q^{39} +2.51032 q^{40} +10.8831 q^{41} -3.16418 q^{42} -4.22746 q^{43} -2.61272 q^{44} -17.6025 q^{45} +7.62679 q^{46} +11.3593 q^{47} -3.16418 q^{48} +1.00000 q^{49} -1.30171 q^{50} +13.5002 q^{51} +4.82572 q^{52} -7.34872 q^{53} +12.6948 q^{54} +6.55876 q^{55} +1.00000 q^{56} -3.60943 q^{58} -13.2327 q^{59} +7.94311 q^{60} +2.33846 q^{61} -7.24632 q^{62} -7.01204 q^{63} +1.00000 q^{64} -12.1141 q^{65} -8.26711 q^{66} -8.50225 q^{67} -4.26658 q^{68} +24.1325 q^{69} -2.51032 q^{70} -4.76093 q^{71} -7.01204 q^{72} -1.27402 q^{73} -3.23278 q^{74} -4.11885 q^{75} +2.61272 q^{77} +15.2694 q^{78} -4.48417 q^{79} -2.51032 q^{80} +19.1326 q^{81} -10.8831 q^{82} -5.10293 q^{83} +3.16418 q^{84} +10.7105 q^{85} +4.22746 q^{86} -11.4209 q^{87} +2.61272 q^{88} -13.9034 q^{89} +17.6025 q^{90} -4.82572 q^{91} -7.62679 q^{92} -22.9287 q^{93} -11.3593 q^{94} +3.16418 q^{96} -16.4795 q^{97} -1.00000 q^{98} -18.3205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} - 6 q^{7} - 6 q^{8} + 12 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 23 q^{13} + 6 q^{14} - 6 q^{15} + 6 q^{16} - 3 q^{17} - 12 q^{18} - 5 q^{20} - 2 q^{21} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 13 q^{25} - 23 q^{26} - 4 q^{27} - 6 q^{28} + 5 q^{29} + 6 q^{30} + 12 q^{31} - 6 q^{32} + 10 q^{33} + 3 q^{34} + 5 q^{35} + 12 q^{36} + q^{37} + 4 q^{39} + 5 q^{40} + 19 q^{41} + 2 q^{42} - 2 q^{43} - 4 q^{44} - 55 q^{45} + 4 q^{46} - 12 q^{47} + 2 q^{48} + 6 q^{49} - 13 q^{50} + 44 q^{51} + 23 q^{52} - 11 q^{53} + 4 q^{54} + 28 q^{55} + 6 q^{56} - 5 q^{58} - 4 q^{59} - 6 q^{60} - q^{61} - 12 q^{62} - 12 q^{63} + 6 q^{64} - 24 q^{65} - 10 q^{66} - 14 q^{67} - 3 q^{68} + 10 q^{69} - 5 q^{70} - 8 q^{71} - 12 q^{72} + 5 q^{73} - q^{74} + 56 q^{75} + 4 q^{77} - 4 q^{78} + 30 q^{79} - 5 q^{80} + 30 q^{81} - 19 q^{82} - 12 q^{83} - 2 q^{84} - 16 q^{85} + 2 q^{86} - 14 q^{87} + 4 q^{88} + 11 q^{89} + 55 q^{90} - 23 q^{91} - 4 q^{92} + 10 q^{93} + 12 q^{94} - 2 q^{96} + 25 q^{97} - 6 q^{98} - 50 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 - 6 * q^7 - 6 * q^8 + 12 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 23 * q^13 + 6 * q^14 - 6 * q^15 + 6 * q^16 - 3 * q^17 - 12 * q^18 - 5 * q^20 - 2 * q^21 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 13 * q^25 - 23 * q^26 - 4 * q^27 - 6 * q^28 + 5 * q^29 + 6 * q^30 + 12 * q^31 - 6 * q^32 + 10 * q^33 + 3 * q^34 + 5 * q^35 + 12 * q^36 + q^37 + 4 * q^39 + 5 * q^40 + 19 * q^41 + 2 * q^42 - 2 * q^43 - 4 * q^44 - 55 * q^45 + 4 * q^46 - 12 * q^47 + 2 * q^48 + 6 * q^49 - 13 * q^50 + 44 * q^51 + 23 * q^52 - 11 * q^53 + 4 * q^54 + 28 * q^55 + 6 * q^56 - 5 * q^58 - 4 * q^59 - 6 * q^60 - q^61 - 12 * q^62 - 12 * q^63 + 6 * q^64 - 24 * q^65 - 10 * q^66 - 14 * q^67 - 3 * q^68 + 10 * q^69 - 5 * q^70 - 8 * q^71 - 12 * q^72 + 5 * q^73 - q^74 + 56 * q^75 + 4 * q^77 - 4 * q^78 + 30 * q^79 - 5 * q^80 + 30 * q^81 - 19 * q^82 - 12 * q^83 - 2 * q^84 - 16 * q^85 + 2 * q^86 - 14 * q^87 + 4 * q^88 + 11 * q^89 + 55 * q^90 - 23 * q^91 - 4 * q^92 + 10 * q^93 + 12 * q^94 - 2 * q^96 + 25 * q^97 - 6 * q^98 - 50 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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