LMFDB - Embedded newform 5054.2.a.z.1.5

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:	$6$
Coefficient field:	6.6.36538000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 13x^{4} - 4x^{3} + 41x^{2} + 16x - 16 $ x^6 - 13x^4 - 4x^3 + 41x^2 + 16x - 16
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			1.5
Root			$2.04245$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.04245 q^{3} +1.00000 q^{4} +2.05192 q^{5} -2.04245 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.17159 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.04245 q^{3} +1.00000 q^{4} +2.05192 q^{5} -2.04245 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.17159 q^{9} -2.05192 q^{10} -4.36252 q^{11} +2.04245 q^{12} -3.26816 q^{13} -1.00000 q^{14} +4.19094 q^{15} +1.00000 q^{16} -4.81674 q^{17} -1.17159 q^{18} +2.05192 q^{20} +2.04245 q^{21} +4.36252 q^{22} -0.277632 q^{23} -2.04245 q^{24} -0.789620 q^{25} +3.26816 q^{26} -3.73444 q^{27} +1.00000 q^{28} +6.08660 q^{29} -4.19094 q^{30} -8.21497 q^{31} -1.00000 q^{32} -8.91022 q^{33} +4.81674 q^{34} +2.05192 q^{35} +1.17159 q^{36} -0.511988 q^{37} -6.67503 q^{39} -2.05192 q^{40} -7.04416 q^{41} -2.04245 q^{42} +8.55346 q^{43} -4.36252 q^{44} +2.40400 q^{45} +0.277632 q^{46} +4.51008 q^{47} +2.04245 q^{48} +1.00000 q^{49} +0.789620 q^{50} -9.83792 q^{51} -3.26816 q^{52} -3.59185 q^{53} +3.73444 q^{54} -8.95156 q^{55} -1.00000 q^{56} -6.08660 q^{58} +5.00402 q^{59} +4.19094 q^{60} +12.2171 q^{61} +8.21497 q^{62} +1.17159 q^{63} +1.00000 q^{64} -6.70600 q^{65} +8.91022 q^{66} -11.9327 q^{67} -4.81674 q^{68} -0.567048 q^{69} -2.05192 q^{70} +0.0848922 q^{71} -1.17159 q^{72} -11.4985 q^{73} +0.511988 q^{74} -1.61276 q^{75} -4.36252 q^{77} +6.67503 q^{78} -9.44117 q^{79} +2.05192 q^{80} -11.1421 q^{81} +7.04416 q^{82} +6.18143 q^{83} +2.04245 q^{84} -9.88356 q^{85} -8.55346 q^{86} +12.4316 q^{87} +4.36252 q^{88} +2.29590 q^{89} -2.40400 q^{90} -3.26816 q^{91} -0.277632 q^{92} -16.7786 q^{93} -4.51008 q^{94} -2.04245 q^{96} +16.9140 q^{97} -1.00000 q^{98} -5.11107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 - 6 * q^8 + 8 * q^9	$ 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 15 q^{13} - 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 8 q^{18} - q^{20} - 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} + 12 q^{27} + 6 q^{28} - 7 q^{29} + 6 q^{30} - 4 q^{31} - 6 q^{32} - 28 q^{33} + 9 q^{34} - q^{35} + 8 q^{36} - 3 q^{37} - 8 q^{39} + q^{40} - 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} - 4 q^{46} + 12 q^{47} + 6 q^{49} - q^{50} - 44 q^{51} - 15 q^{52} + 5 q^{53} - 12 q^{54} - 8 q^{55} - 6 q^{56} + 7 q^{58} - 4 q^{59} - 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} + 20 q^{65} + 28 q^{66} - 14 q^{67} - 9 q^{68} + 24 q^{69} + q^{70} - 24 q^{71} - 8 q^{72} - 21 q^{73} + 3 q^{74} - 12 q^{75} + 4 q^{77} + 8 q^{78} - 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} + 10 q^{86} - 8 q^{87} - 4 q^{88} - 7 q^{89} - 19 q^{90} - 15 q^{91} + 4 q^{92} - 22 q^{93} - 12 q^{94} - 7 q^{97} - 6 q^{98} - 26 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 - 6 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 15 * q^13 - 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 8 * q^18 - q^20 - 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 + 12 * q^27 + 6 * q^28 - 7 * q^29 + 6 * q^30 - 4 * q^31 - 6 * q^32 - 28 * q^33 + 9 * q^34 - q^35 + 8 * q^36 - 3 * q^37 - 8 * q^39 + q^40 - 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 - 4 * q^46 + 12 * q^47 + 6 * q^49 - q^50 - 44 * q^51 - 15 * q^52 + 5 * q^53 - 12 * q^54 - 8 * q^55 - 6 * q^56 + 7 * q^58 - 4 * q^59 - 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 + 20 * q^65 + 28 * q^66 - 14 * q^67 - 9 * q^68 + 24 * q^69 + q^70 - 24 * q^71 - 8 * q^72 - 21 * q^73 + 3 * q^74 - 12 * q^75 + 4 * q^77 + 8 * q^78 - 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 + 10 * q^86 - 8 * q^87 - 4 * q^88 - 7 * q^89 - 19 * q^90 - 15 * q^91 + 4 * q^92 - 22 * q^93 - 12 * q^94 - 7 * q^97 - 6 * q^98 - 26 * 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
$3$	2.04245	1.17921	0.589603	−	0.807693i	$-0.299284\pi$
$3$	2.04245	1.17921	0.589603	+	0.807693i	$0.299284\pi$
$4$	1.00000	0.500000
$5$	2.05192	0.917647	0.458823	−	0.888527i	$-0.348271\pi$
$5$	2.05192	0.917647	0.458823	+	0.888527i	$0.348271\pi$
$6$	−2.04245	−0.833825
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.17159	0.390529
$10$	−2.05192	−0.648874
$11$	−4.36252	−1.31535	−0.657675	−	0.753302i	$-0.728460\pi$
$11$	−4.36252	−1.31535	−0.657675	+	0.753302i	$0.728460\pi$
$12$	2.04245	0.589603
$13$	−3.26816	−0.906424	−0.453212	−	0.891403i	$-0.649722\pi$
$13$	−3.26816	−0.906424	−0.453212	+	0.891403i	$0.649722\pi$
$14$	−1.00000	−0.267261
$15$	4.19094	1.08210
$16$	1.00000	0.250000
$17$	−4.81674	−1.16823	−0.584115	−	0.811671i	$-0.698558\pi$
$17$	−4.81674	−1.16823	−0.584115	+	0.811671i	$0.698558\pi$
$18$	−1.17159	−0.276145
$19$	0	0
$19$	0	0
$20$	2.05192	0.458823
$21$	2.04245	0.445698
$22$	4.36252	0.930093
$23$	−0.277632	−0.0578903	−0.0289451	−	0.999581i	$-0.509215\pi$
$23$	−0.277632	−0.0578903	−0.0289451	+	0.999581i	$0.509215\pi$
$24$	−2.04245	−0.416913
$25$	−0.789620	−0.157924
$26$	3.26816	0.640938
$27$	−3.73444	−0.718693
$28$	1.00000	0.188982
$29$	6.08660	1.13025	0.565127	−	0.825004i	$-0.308827\pi$
$29$	6.08660	1.13025	0.565127	+	0.825004i	$0.308827\pi$
$30$	−4.19094	−0.765157
$31$	−8.21497	−1.47545	−0.737726	−	0.675100i	$-0.764100\pi$
$31$	−8.21497	−1.47545	−0.737726	+	0.675100i	$0.764100\pi$
$32$	−1.00000	−0.176777
$33$	−8.91022	−1.55107
$34$	4.81674	0.826063
$35$	2.05192	0.346838
$36$	1.17159	0.195264
$37$	−0.511988	−0.0841703	−0.0420852	−	0.999114i	$-0.513400\pi$
$37$	−0.511988	−0.0841703	−0.0420852	+	0.999114i	$0.513400\pi$
$38$	0	0
$39$	−6.67503	−1.06886
$40$	−2.05192	−0.324437
$41$	−7.04416	−1.10011	−0.550056	−	0.835128i	$-0.685394\pi$
$41$	−7.04416	−1.10011	−0.550056	+	0.835128i	$0.685394\pi$
$42$	−2.04245	−0.315156
$43$	8.55346	1.30439	0.652195	−	0.758051i	$-0.273848\pi$
$43$	8.55346	1.30439	0.652195	+	0.758051i	$0.273848\pi$
$44$	−4.36252	−0.657675
$45$	2.40400	0.358367
$46$	0.277632	0.0409346
$47$	4.51008	0.657863	0.328931	−	0.944354i	$-0.393311\pi$
$47$	4.51008	0.657863	0.328931	+	0.944354i	$0.393311\pi$
$48$	2.04245	0.294802
$49$	1.00000	0.142857
$50$	0.789620	0.111669
$51$	−9.83792	−1.37758
$52$	−3.26816	−0.453212
$53$	−3.59185	−0.493379	−0.246690	−	0.969095i	$-0.579343\pi$
$53$	−3.59185	−0.493379	−0.246690	+	0.969095i	$0.579343\pi$
$54$	3.73444	0.508193
$55$	−8.95156	−1.20703
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−6.08660	−0.799210
$59$	5.00402	0.651468	0.325734	−	0.945461i	$-0.394389\pi$
$59$	5.00402	0.651468	0.325734	+	0.945461i	$0.394389\pi$
$60$	4.19094	0.541048
$61$	12.2171	1.56424	0.782118	−	0.623130i	$-0.214139\pi$
$61$	12.2171	1.56424	0.782118	+	0.623130i	$0.214139\pi$
$62$	8.21497	1.04330
$63$	1.17159	0.147606
$64$	1.00000	0.125000
$65$	−6.70600	−0.831777
$66$	8.91022	1.09677
$67$	−11.9327	−1.45781	−0.728903	−	0.684617i	$-0.759970\pi$
$67$	−11.9327	−1.45781	−0.728903	+	0.684617i	$0.759970\pi$
$68$	−4.81674	−0.584115
$69$	−0.567048	−0.0682646
$70$	−2.05192	−0.245251
$71$	0.0848922	0.0100748	0.00503742	−	0.999987i	$-0.498397\pi$
$71$	0.0848922	0.0100748	0.00503742	+	0.999987i	$0.498397\pi$
$72$	−1.17159	−0.138073
$73$	−11.4985	−1.34579	−0.672896	−	0.739737i	$-0.734950\pi$
$73$	−11.4985	−1.34579	−0.672896	+	0.739737i	$0.734950\pi$
$74$	0.511988	0.0595174
$75$	−1.61276	−0.186225
$76$	0	0
$77$	−4.36252	−0.497156
$78$	6.67503	0.755799
$79$	−9.44117	−1.06221	−0.531107	−	0.847305i	$-0.678224\pi$
$79$	−9.44117	−1.06221	−0.531107	+	0.847305i	$0.678224\pi$
$80$	2.05192	0.229412
$81$	−11.1421	−1.23802
$82$	7.04416	0.777897
$83$	6.18143	0.678500	0.339250	−	0.940696i	$-0.389827\pi$
$83$	6.18143	0.678500	0.339250	+	0.940696i	$0.389827\pi$
$84$	2.04245	0.222849
$85$	−9.88356	−1.07202
$86$	−8.55346	−0.922344
$87$	12.4316	1.33280
$88$	4.36252	0.465047
$89$	2.29590	0.243365	0.121683	−	0.992569i	$-0.461171\pi$
$89$	2.29590	0.243365	0.121683	+	0.992569i	$0.461171\pi$
$90$	−2.40400	−0.253404
$91$	−3.26816	−0.342596
$92$	−0.277632	−0.0289451
$93$	−16.7786	−1.73986
$94$	−4.51008	−0.465179
$95$	0	0
$96$	−2.04245	−0.208456
$97$	16.9140	1.71735	0.858677	−	0.512517i	$-0.171287\pi$
$97$	16.9140	1.71735	0.858677	+	0.512517i	$0.171287\pi$
$98$	−1.00000	−0.101015
$99$	−5.11107	−0.513682
$100$	−0.789620	−0.0789620
$101$	−5.51298	−0.548562	−0.274281	−	0.961650i	$-0.588440\pi$
$101$	−5.51298	−0.548562	−0.274281	+	0.961650i	$0.588440\pi$
$102$	9.83792	0.974099
$103$	−11.0716	−1.09092	−0.545459	−	0.838137i	$-0.683645\pi$
$103$	−11.0716	−1.09092	−0.545459	+	0.838137i	$0.683645\pi$
$104$	3.26816	0.320469
$105$	4.19094	0.408994
$106$	3.59185	0.348872
$107$	−0.255365	−0.0246870	−0.0123435	−	0.999924i	$-0.503929\pi$
$107$	−0.255365	−0.0246870	−0.0123435	+	0.999924i	$0.503929\pi$
$108$	−3.73444	−0.359346
$109$	−13.4745	−1.29062	−0.645311	−	0.763920i	$-0.723272\pi$
$109$	−13.4745	−1.29062	−0.645311	+	0.763920i	$0.723272\pi$
$110$	8.95156	0.853497
$111$	−1.04571	−0.0992542
$112$	1.00000	0.0944911
$113$	−11.6010	−1.09133	−0.545663	−	0.838005i	$-0.683722\pi$
$113$	−11.6010	−1.09133	−0.545663	+	0.838005i	$0.683722\pi$
$114$	0	0
$115$	−0.569679	−0.0531228
$116$	6.08660	0.565127
$117$	−3.82893	−0.353984
$118$	−5.00402	−0.460657
$119$	−4.81674	−0.441549
$120$	−4.19094	−0.382579
$121$	8.03162	0.730147
$122$	−12.2171	−1.10608
$123$	−14.3873	−1.29726
$124$	−8.21497	−0.737726
$125$	−11.8798	−1.06257
$126$	−1.17159	−0.104373
$127$	−19.8012	−1.75708	−0.878538	−	0.477672i	$-0.841481\pi$
$127$	−19.8012	−1.75708	−0.878538	+	0.477672i	$0.841481\pi$
$128$	−1.00000	−0.0883883
$129$	17.4700	1.53815
$130$	6.70600	0.588155
$131$	−13.2848	−1.16070	−0.580350	−	0.814367i	$-0.697084\pi$
$131$	−13.2848	−1.16070	−0.580350	+	0.814367i	$0.697084\pi$
$132$	−8.91022	−0.775535
$133$	0	0
$134$	11.9327	1.03082
$135$	−7.66277	−0.659506
$136$	4.81674	0.413032
$137$	17.4533	1.49114	0.745570	−	0.666427i	$-0.232177\pi$
$137$	17.4533	1.49114	0.745570	+	0.666427i	$0.232177\pi$
$138$	0.567048	0.0482704
$139$	0.679061	0.0575972	0.0287986	−	0.999585i	$-0.490832\pi$
$139$	0.679061	0.0575972	0.0287986	+	0.999585i	$0.490832\pi$
$140$	2.05192	0.173419
$141$	9.21160	0.775756
$142$	−0.0848922	−0.00712399
$143$	14.2574	1.19226
$144$	1.17159	0.0976322
$145$	12.4892	1.03717
$146$	11.4985	0.951619
$147$	2.04245	0.168458
$148$	−0.511988	−0.0420852
$149$	−19.4843	−1.59622	−0.798108	−	0.602514i	$-0.794166\pi$
$149$	−19.4843	−1.59622	−0.798108	+	0.602514i	$0.794166\pi$
$150$	1.61276	0.131681
$151$	−20.1790	−1.64214	−0.821071	−	0.570826i	$-0.806623\pi$
$151$	−20.1790	−1.64214	−0.821071	+	0.570826i	$0.806623\pi$
$152$	0	0
$153$	−5.64322	−0.456227
$154$	4.36252	0.351542
$155$	−16.8565	−1.35394
$156$	−6.67503	−0.534430
$157$	−16.1440	−1.28843	−0.644216	−	0.764844i	$-0.722816\pi$
$157$	−16.1440	−1.28843	−0.644216	+	0.764844i	$0.722816\pi$
$158$	9.44117	0.751099
$159$	−7.33617	−0.581796
$160$	−2.05192	−0.162219
$161$	−0.277632	−0.0218805
$162$	11.1421	0.875410
$163$	4.93527	0.386560	0.193280	−	0.981144i	$-0.438087\pi$
$163$	4.93527	0.386560	0.193280	+	0.981144i	$0.438087\pi$
$164$	−7.04416	−0.550056
$165$	−18.2831	−1.42333
$166$	−6.18143	−0.479772
$167$	4.95803	0.383664	0.191832	−	0.981428i	$-0.438557\pi$
$167$	4.95803	0.383664	0.191832	+	0.981428i	$0.438557\pi$
$168$	−2.04245	−0.157578
$169$	−2.31915	−0.178396
$170$	9.88356	0.758034
$171$	0	0
$172$	8.55346	0.652195
$173$	−7.90920	−0.601325	−0.300662	−	0.953731i	$-0.597208\pi$
$173$	−7.90920	−0.601325	−0.300662	+	0.953731i	$0.597208\pi$
$174$	−12.4316	−0.942434
$175$	−0.789620	−0.0596897
$176$	−4.36252	−0.328838
$177$	10.2204	0.768216
$178$	−2.29590	−0.172085
$179$	21.1631	1.58180	0.790901	−	0.611944i	$-0.209612\pi$
$179$	21.1631	1.58180	0.790901	+	0.611944i	$0.209612\pi$
$180$	2.40400	0.179184
$181$	−6.33589	−0.470943	−0.235471	−	0.971881i	$-0.575663\pi$
$181$	−6.33589	−0.470943	−0.235471	+	0.971881i	$0.575663\pi$
$182$	3.26816	0.242252
$183$	24.9527	1.84456
$184$	0.277632	0.0204673
$185$	−1.05056	−0.0772386
$186$	16.7786	1.23027
$187$	21.0131	1.53663
$188$	4.51008	0.328931
$189$	−3.73444	−0.271640
$190$	0	0
$191$	16.7400	1.21126	0.605632	−	0.795745i	$-0.292920\pi$
$191$	16.7400	1.21126	0.605632	+	0.795745i	$0.292920\pi$
$192$	2.04245	0.147401
$193$	4.86964	0.350525	0.175262	−	0.984522i	$-0.443923\pi$
$193$	4.86964	0.350525	0.175262	+	0.984522i	$0.443923\pi$
$194$	−16.9140	−1.21435
$195$	−13.6966	−0.980837
$196$	1.00000	0.0714286
$197$	11.7609	0.837932	0.418966	−	0.908002i	$-0.362393\pi$
$197$	11.7609	0.837932	0.418966	+	0.908002i	$0.362393\pi$
$198$	5.11107	0.363228
$199$	21.3446	1.51308	0.756538	−	0.653950i	$-0.226889\pi$
$199$	21.3446	1.51308	0.756538	+	0.653950i	$0.226889\pi$
$200$	0.789620	0.0558346
$201$	−24.3718	−1.71906
$202$	5.51298	0.387892
$203$	6.08660	0.427196
$204$	−9.83792	−0.688792
$205$	−14.4541	−1.00952
$206$	11.0716	0.771396
$207$	−0.325270	−0.0226078
$208$	−3.26816	−0.226606
$209$	0	0
$210$	−4.19094	−0.289202
$211$	−8.75816	−0.602937	−0.301468	−	0.953476i	$-0.597477\pi$
$211$	−8.75816	−0.602937	−0.301468	+	0.953476i	$0.597477\pi$
$212$	−3.59185	−0.246690
$213$	0.173388	0.0118803
$214$	0.255365	0.0174564
$215$	17.5510	1.19697
$216$	3.73444	0.254096
$217$	−8.21497	−0.557668
$218$	13.4745	0.912608
$219$	−23.4850	−1.58697
$220$	−8.95156	−0.603514
$221$	15.7418	1.05891
$222$	1.04571	0.0701833
$223$	14.2519	0.954378	0.477189	−	0.878801i	$-0.341656\pi$
$223$	14.2519	0.954378	0.477189	+	0.878801i	$0.341656\pi$
$224$	−1.00000	−0.0668153
$225$	−0.925108	−0.0616738
$226$	11.6010	0.771684
$227$	4.01801	0.266685	0.133342	−	0.991070i	$-0.457429\pi$
$227$	4.01801	0.266685	0.133342	+	0.991070i	$0.457429\pi$
$228$	0	0
$229$	20.7056	1.36827	0.684133	−	0.729357i	$-0.260181\pi$
$229$	20.7056	1.36827	0.684133	+	0.729357i	$0.260181\pi$
$230$	0.569679	0.0375635
$231$	−8.91022	−0.586249
$232$	−6.08660	−0.399605
$233$	16.7011	1.09413	0.547064	−	0.837091i	$-0.315746\pi$
$233$	16.7011	1.09413	0.547064	+	0.837091i	$0.315746\pi$
$234$	3.82893	0.250305
$235$	9.25433	0.603686
$236$	5.00402	0.325734
$237$	−19.2831	−1.25257
$238$	4.81674	0.312223
$239$	13.5596	0.877095	0.438547	−	0.898708i	$-0.355493\pi$
$239$	13.5596	0.877095	0.438547	+	0.898708i	$0.355493\pi$
$240$	4.19094	0.270524
$241$	4.76021	0.306632	0.153316	−	0.988177i	$-0.451005\pi$
$241$	4.76021	0.306632	0.153316	+	0.988177i	$0.451005\pi$
$242$	−8.03162	−0.516292
$243$	−11.5539	−0.741184
$244$	12.2171	0.782118
$245$	2.05192	0.131092
$246$	14.3873	0.917302
$247$	0	0
$248$	8.21497	0.521651
$249$	12.6252	0.800092
$250$	11.8798	0.751347
$251$	−19.2884	−1.21747	−0.608735	−	0.793374i	$-0.708323\pi$
$251$	−19.2884	−1.21747	−0.608735	+	0.793374i	$0.708323\pi$
$252$	1.17159	0.0738030
$253$	1.21118	0.0761460
$254$	19.8012	1.24244
$255$	−20.1866	−1.26414
$256$	1.00000	0.0625000
$257$	−7.29981	−0.455349	−0.227675	−	0.973737i	$-0.573112\pi$
$257$	−7.29981	−0.455349	−0.227675	+	0.973737i	$0.573112\pi$
$258$	−17.4700	−1.08763
$259$	−0.511988	−0.0318134
$260$	−6.70600	−0.415888
$261$	7.13098	0.441397
$262$	13.2848	0.820739
$263$	−25.2700	−1.55821	−0.779106	−	0.626892i	$-0.784327\pi$
$263$	−25.2700	−1.55821	−0.779106	+	0.626892i	$0.784327\pi$
$264$	8.91022	0.548386
$265$	−7.37020	−0.452748
$266$	0	0
$267$	4.68926	0.286978
$268$	−11.9327	−0.728903
$269$	−11.6231	−0.708674	−0.354337	−	0.935118i	$-0.615293\pi$
$269$	−11.6231	−0.708674	−0.354337	+	0.935118i	$0.615293\pi$
$270$	7.66277	0.466341
$271$	−6.81546	−0.414010	−0.207005	−	0.978340i	$-0.566372\pi$
$271$	−6.81546	−0.414010	−0.207005	+	0.978340i	$0.566372\pi$
$272$	−4.81674	−0.292057
$273$	−6.67503	−0.403991
$274$	−17.4533	−1.05440
$275$	3.44474	0.207725
$276$	−0.567048	−0.0341323
$277$	7.44611	0.447393	0.223697	−	0.974659i	$-0.428188\pi$
$277$	7.44611	0.447393	0.223697	+	0.974659i	$0.428188\pi$
$278$	−0.679061	−0.0407274
$279$	−9.62454	−0.576206
$280$	−2.05192	−0.122626
$281$	25.1918	1.50281	0.751407	−	0.659839i	$-0.229375\pi$
$281$	25.1918	1.50281	0.751407	+	0.659839i	$0.229375\pi$
$282$	−9.21160	−0.548543
$283$	−21.8679	−1.29991	−0.649956	−	0.759972i	$-0.725213\pi$
$283$	−21.8679	−1.29991	−0.649956	+	0.759972i	$0.725213\pi$
$284$	0.0848922	0.00503742
$285$	0	0
$286$	−14.2574	−0.843059
$287$	−7.04416	−0.415803
$288$	−1.17159	−0.0690364
$289$	6.20094	0.364761
$290$	−12.4892	−0.733393
$291$	34.5459	2.02512
$292$	−11.4985	−0.672896
$293$	−21.4852	−1.25518	−0.627588	−	0.778545i	$-0.715958\pi$
$293$	−21.4852	−1.25518	−0.627588	+	0.778545i	$0.715958\pi$
$294$	−2.04245	−0.119118
$295$	10.2679	0.597818
$296$	0.511988	0.0297587
$297$	16.2916	0.945333
$298$	19.4843	1.12870
$299$	0.907345	0.0524731
$300$	−1.61276	−0.0931125
$301$	8.55346	0.493013
$302$	20.1790	1.16117
$303$	−11.2600	−0.646868
$304$	0	0
$305$	25.0685	1.43542
$306$	5.64322	0.322601
$307$	−22.8559	−1.30445	−0.652227	−	0.758024i	$-0.726165\pi$
$307$	−22.8559	−1.30445	−0.652227	+	0.758024i	$0.726165\pi$
$308$	−4.36252	−0.248578
$309$	−22.6132	−1.28642
$310$	16.8565	0.957383
$311$	12.3600	0.700873	0.350436	−	0.936587i	$-0.386033\pi$
$311$	12.3600	0.700873	0.350436	+	0.936587i	$0.386033\pi$
$312$	6.67503	0.377899
$313$	26.8988	1.52041	0.760205	−	0.649684i	$-0.225099\pi$
$313$	26.8988	1.52041	0.760205	+	0.649684i	$0.225099\pi$
$314$	16.1440	0.911058
$315$	2.40400	0.135450
$316$	−9.44117	−0.531107
$317$	3.26879	0.183593	0.0917967	−	0.995778i	$-0.470739\pi$
$317$	3.26879	0.183593	0.0917967	+	0.995778i	$0.470739\pi$
$318$	7.33617	0.411392
$319$	−26.5530	−1.48668
$320$	2.05192	0.114706
$321$	−0.521568	−0.0291111
$322$	0.277632	0.0154718
$323$	0	0
$324$	−11.1421	−0.619008
$325$	2.58060	0.143146
$326$	−4.93527	−0.273339
$327$	−27.5209	−1.52191
$328$	7.04416	0.388949
$329$	4.51008	0.248649
$330$	18.2831	1.00645
$331$	−2.19858	−0.120845	−0.0604223	−	0.998173i	$-0.519245\pi$
$331$	−2.19858	−0.120845	−0.0604223	+	0.998173i	$0.519245\pi$
$332$	6.18143	0.339250
$333$	−0.599838	−0.0328709
$334$	−4.95803	−0.271292
$335$	−24.4849	−1.33775
$336$	2.04245	0.111425
$337$	30.3973	1.65585	0.827923	−	0.560842i	$-0.189523\pi$
$337$	30.3973	1.65585	0.827923	+	0.560842i	$0.189523\pi$
$338$	2.31915	0.126145
$339$	−23.6943	−1.28690
$340$	−9.88356	−0.536011
$341$	35.8380	1.94074
$342$	0	0
$343$	1.00000	0.0539949
$344$	−8.55346	−0.461172
$345$	−1.16354	−0.0626428
$346$	7.90920	0.425201
$347$	32.0134	1.71857	0.859285	−	0.511498i	$-0.170909\pi$
$347$	32.0134	1.71857	0.859285	+	0.511498i	$0.170909\pi$
$348$	12.4316	0.666402
$349$	−6.37865	−0.341441	−0.170721	−	0.985319i	$-0.554610\pi$
$349$	−6.37865	−0.341441	−0.170721	+	0.985319i	$0.554610\pi$
$350$	0.789620	0.0422070
$351$	12.2047	0.651440
$352$	4.36252	0.232523
$353$	2.01486	0.107240	0.0536200	−	0.998561i	$-0.482924\pi$
$353$	2.01486	0.107240	0.0536200	+	0.998561i	$0.482924\pi$
$354$	−10.2204	−0.543210
$355$	0.174192	0.00924515
$356$	2.29590	0.121683
$357$	−9.83792	−0.520678
$358$	−21.1631	−1.11850
$359$	7.69404	0.406076	0.203038	−	0.979171i	$-0.434919\pi$
$359$	7.69404	0.406076	0.203038	+	0.979171i	$0.434919\pi$
$360$	−2.40400	−0.126702
$361$	0	0
$362$	6.33589	0.333007
$363$	16.4041	0.860994
$364$	−3.26816	−0.171298
$365$	−23.5939	−1.23496
$366$	−24.9527	−1.30430
$367$	23.1040	1.20602	0.603010	−	0.797733i	$-0.293968\pi$
$367$	23.1040	1.20602	0.603010	+	0.797733i	$0.293968\pi$
$368$	−0.277632	−0.0144726
$369$	−8.25284	−0.429626
$370$	1.05056	0.0546160
$371$	−3.59185	−0.186480
$372$	−16.7786	−0.869931
$373$	−28.9366	−1.49828	−0.749141	−	0.662410i	$-0.769534\pi$
$373$	−28.9366	−1.49828	−0.749141	+	0.662410i	$0.769534\pi$
$374$	−21.0131	−1.08656
$375$	−24.2639	−1.25298
$376$	−4.51008	−0.232590
$377$	−19.8920	−1.02449
$378$	3.73444	0.192079
$379$	−18.1710	−0.933382	−0.466691	−	0.884420i	$-0.654554\pi$
$379$	−18.1710	−0.933382	−0.466691	+	0.884420i	$0.654554\pi$
$380$	0	0
$381$	−40.4430	−2.07196
$382$	−16.7400	−0.856493
$383$	17.2859	0.883267	0.441633	−	0.897196i	$-0.354399\pi$
$383$	17.2859	0.883267	0.441633	+	0.897196i	$0.354399\pi$
$384$	−2.04245	−0.104228
$385$	−8.95156	−0.456213
$386$	−4.86964	−0.247858
$387$	10.0211	0.509402
$388$	16.9140	0.858677
$389$	−13.2603	−0.672324	−0.336162	−	0.941804i	$-0.609129\pi$
$389$	−13.2603	−0.672324	−0.336162	+	0.941804i	$0.609129\pi$
$390$	13.6966	0.693557
$391$	1.33728	0.0676291
$392$	−1.00000	−0.0505076
$393$	−27.1335	−1.36870
$394$	−11.7609	−0.592507
$395$	−19.3725	−0.974738
$396$	−5.11107	−0.256841
$397$	−0.0258087	−0.00129530	−0.000647650	−	1.00000i	$-0.500206\pi$
$397$	−0.0258087	−0.00129530	−0.000647650		1.00000i	$0.500206\pi$
$398$	−21.3446	−1.06991
$399$	0	0
$400$	−0.789620	−0.0394810
$401$	−37.0943	−1.85240	−0.926200	−	0.377033i	$-0.876944\pi$
$401$	−37.0943	−1.85240	−0.926200	+	0.377033i	$0.876944\pi$
$402$	24.3718	1.21556
$403$	26.8478	1.33738
$404$	−5.51298	−0.274281
$405$	−22.8628	−1.13606
$406$	−6.08660	−0.302073
$407$	2.23356	0.110713
$408$	9.83792	0.487050
$409$	32.0915	1.58682	0.793412	−	0.608684i	$-0.208302\pi$
$409$	32.0915	1.58682	0.793412	+	0.608684i	$0.208302\pi$
$410$	14.4541	0.713835
$411$	35.6475	1.75836
$412$	−11.0716	−0.545459
$413$	5.00402	0.246232
$414$	0.325270	0.0159861
$415$	12.6838	0.622624
$416$	3.26816	0.160235
$417$	1.38694	0.0679190
$418$	0	0
$419$	−8.47502	−0.414032	−0.207016	−	0.978338i	$-0.566375\pi$
$419$	−8.47502	−0.414032	−0.207016	+	0.978338i	$0.566375\pi$
$420$	4.19094	0.204497
$421$	17.4258	0.849280	0.424640	−	0.905362i	$-0.360401\pi$
$421$	17.4258	0.849280	0.424640	+	0.905362i	$0.360401\pi$
$422$	8.75816	0.426341
$423$	5.28395	0.256914
$424$	3.59185	0.174436
$425$	3.80339	0.184492
$426$	−0.173388	−0.00840066
$427$	12.2171	0.591226
$428$	−0.255365	−0.0123435
$429$	29.1200	1.40593
$430$	−17.5510	−0.846386
$431$	33.0212	1.59057	0.795286	−	0.606234i	$-0.207320\pi$
$431$	33.0212	1.59057	0.795286	+	0.606234i	$0.207320\pi$
$432$	−3.73444	−0.179673
$433$	5.15179	0.247579	0.123790	−	0.992308i	$-0.460495\pi$
$433$	5.15179	0.247579	0.123790	+	0.992308i	$0.460495\pi$
$434$	8.21497	0.394331
$435$	25.5086	1.22304
$436$	−13.4745	−0.645311
$437$	0	0
$438$	23.4850	1.12216
$439$	10.0297	0.478689	0.239345	−	0.970935i	$-0.423067\pi$
$439$	10.0297	0.478689	0.239345	+	0.970935i	$0.423067\pi$
$440$	8.95156	0.426749
$441$	1.17159	0.0557898
$442$	−15.7418	−0.748763
$443$	38.3277	1.82100	0.910502	−	0.413504i	$-0.135695\pi$
$443$	38.3277	1.82100	0.910502	+	0.413504i	$0.135695\pi$
$444$	−1.04571	−0.0496271
$445$	4.71101	0.223323
$446$	−14.2519	−0.674847
$447$	−39.7957	−1.88227
$448$	1.00000	0.0472456
$449$	33.5135	1.58160	0.790800	−	0.612075i	$-0.209665\pi$
$449$	33.5135	1.58160	0.790800	+	0.612075i	$0.209665\pi$
$450$	0.925108	0.0436100
$451$	30.7303	1.44703
$452$	−11.6010	−0.545663
$453$	−41.2145	−1.93642
$454$	−4.01801	−0.188575
$455$	−6.70600	−0.314382
$456$	0	0
$457$	0.889078	0.0415893	0.0207947	−	0.999784i	$-0.493380\pi$
$457$	0.889078	0.0415893	0.0207947	+	0.999784i	$0.493380\pi$
$458$	−20.7056	−0.967510
$459$	17.9878	0.839598
$460$	−0.569679	−0.0265614
$461$	5.45431	0.254032	0.127016	−	0.991901i	$-0.459460\pi$
$461$	5.45431	0.254032	0.127016	+	0.991901i	$0.459460\pi$
$462$	8.91022	0.414541
$463$	−33.4144	−1.55290	−0.776449	−	0.630180i	$-0.782981\pi$
$463$	−33.4144	−1.55290	−0.776449	+	0.630180i	$0.782981\pi$
$464$	6.08660	0.282563
$465$	−34.4284	−1.59658
$466$	−16.7011	−0.773665
$467$	7.78250	0.360131	0.180065	−	0.983655i	$-0.442369\pi$
$467$	7.78250	0.360131	0.180065	+	0.983655i	$0.442369\pi$
$468$	−3.82893	−0.176992
$469$	−11.9327	−0.550999
$470$	−9.25433	−0.426870
$471$	−32.9732	−1.51933
$472$	−5.00402	−0.230329
$473$	−37.3147	−1.71573
$474$	19.2831	0.885701
$475$	0	0
$476$	−4.81674	−0.220775
$477$	−4.20817	−0.192679
$478$	−13.5596	−0.620200
$479$	14.9950	0.685138	0.342569	−	0.939493i	$-0.388703\pi$
$479$	14.9950	0.685138	0.342569	+	0.939493i	$0.388703\pi$
$480$	−4.19094	−0.191289
$481$	1.67326	0.0762940
$482$	−4.76021	−0.216822
$483$	−0.567048	−0.0258016
$484$	8.03162	0.365073
$485$	34.7062	1.57593
$486$	11.5539	0.524096
$487$	32.2487	1.46133	0.730665	−	0.682737i	$-0.239210\pi$
$487$	32.2487	1.46133	0.730665	+	0.682737i	$0.239210\pi$
$488$	−12.2171	−0.553041
$489$	10.0800	0.455834
$490$	−2.05192	−0.0926963
$491$	−10.4214	−0.470311	−0.235155	−	0.971958i	$-0.575560\pi$
$491$	−10.4214	−0.470311	−0.235155	+	0.971958i	$0.575560\pi$
$492$	−14.3873	−0.648630
$493$	−29.3176	−1.32040
$494$	0	0
$495$	−10.4875	−0.471379
$496$	−8.21497	−0.368863
$497$	0.0848922	0.00380793
$498$	−12.6252	−0.565750
$499$	26.1994	1.17285	0.586423	−	0.810005i	$-0.300536\pi$
$499$	26.1994	1.17285	0.586423	+	0.810005i	$0.300536\pi$
$500$	−11.8798	−0.531283
$501$	10.1265	0.452419
$502$	19.2884	0.860881
$503$	39.6826	1.76936	0.884680	−	0.466199i	$-0.154377\pi$
$503$	39.6826	1.76936	0.884680	+	0.466199i	$0.154377\pi$
$504$	−1.17159	−0.0521866
$505$	−11.3122	−0.503386
$506$	−1.21118	−0.0538433
$507$	−4.73674	−0.210366
$508$	−19.8012	−0.878538
$509$	7.48133	0.331604	0.165802	−	0.986159i	$-0.446979\pi$
$509$	7.48133	0.331604	0.165802	+	0.986159i	$0.446979\pi$
$510$	20.1866	0.893879
$511$	−11.4985	−0.508662
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	7.29981	0.321981
$515$	−22.7181	−1.00108
$516$	17.4700	0.769073
$517$	−19.6753	−0.865320
$518$	0.511988	0.0224955
$519$	−16.1541	−0.709086
$520$	6.70600	0.294078
$521$	−26.5266	−1.16215	−0.581075	−	0.813850i	$-0.697368\pi$
$521$	−26.5266	−1.16215	−0.581075	+	0.813850i	$0.697368\pi$
$522$	−7.13098	−0.312115
$523$	−21.9149	−0.958271	−0.479136	−	0.877741i	$-0.659050\pi$
$523$	−21.9149	−0.958271	−0.479136	+	0.877741i	$0.659050\pi$
$524$	−13.2848	−0.580350
$525$	−1.61276	−0.0703865
$526$	25.2700	1.10182
$527$	39.5693	1.72367
$528$	−8.91022	−0.387768
$529$	−22.9229	−0.996649
$530$	7.37020	0.320141
$531$	5.86264	0.254417
$532$	0	0
$533$	23.0214	0.997168
$534$	−4.68926	−0.202924
$535$	−0.523988	−0.0226540
$536$	11.9327	0.515412
$537$	43.2244	1.86527
$538$	11.6231	0.501108
$539$	−4.36252	−0.187907
$540$	−7.66277	−0.329753
$541$	8.70781	0.374378	0.187189	−	0.982324i	$-0.440062\pi$
$541$	8.70781	0.374378	0.187189	+	0.982324i	$0.440062\pi$
$542$	6.81546	0.292749
$543$	−12.9407	−0.555339
$544$	4.81674	0.206516
$545$	−27.6486	−1.18434
$546$	6.67503	0.285665
$547$	−25.9804	−1.11084	−0.555421	−	0.831569i	$-0.687443\pi$
$547$	−25.9804	−1.11084	−0.555421	+	0.831569i	$0.687443\pi$
$548$	17.4533	0.745570
$549$	14.3134	0.610879
$550$	−3.44474	−0.146884
$551$	0	0
$552$	0.567048	0.0241352
$553$	−9.44117	−0.401479
$554$	−7.44611	−0.316355
$555$	−2.14571	−0.0910803
$556$	0.679061	0.0287986
$557$	−26.1999	−1.11012	−0.555062	−	0.831809i	$-0.687305\pi$
$557$	−26.1999	−1.11012	−0.555062	+	0.831809i	$0.687305\pi$
$558$	9.62454	0.407439
$559$	−27.9541	−1.18233
$560$	2.05192	0.0867095
$561$	42.9182	1.81201
$562$	−25.1918	−1.06265
$563$	10.6493	0.448813	0.224407	−	0.974496i	$-0.427956\pi$
$563$	10.6493	0.448813	0.224407	+	0.974496i	$0.427956\pi$
$564$	9.21160	0.387878
$565$	−23.8042	−1.00145
$566$	21.8679	0.919176
$567$	−11.1421	−0.467926
$568$	−0.0848922	−0.00356200
$569$	−0.469136	−0.0196672	−0.00983360	−	0.999952i	$-0.503130\pi$
$569$	−0.469136	−0.0196672	−0.00983360	+	0.999952i	$0.503130\pi$
$570$	0	0
$571$	−28.2038	−1.18029	−0.590146	−	0.807296i	$-0.700930\pi$
$571$	−28.2038	−1.18029	−0.590146	+	0.807296i	$0.700930\pi$
$572$	14.2574	0.596132
$573$	34.1905	1.42833
$574$	7.04416	0.294017
$575$	0.219224	0.00914226
$576$	1.17159	0.0488161
$577$	−31.6311	−1.31682	−0.658411	−	0.752659i	$-0.728771\pi$
$577$	−31.6311	−1.31682	−0.658411	+	0.752659i	$0.728771\pi$
$578$	−6.20094	−0.257925
$579$	9.94599	0.413341
$580$	12.4892	0.518587
$581$	6.18143	0.256449
$582$	−34.5459	−1.43197
$583$	15.6696	0.648966
$584$	11.4985	0.475809
$585$	−7.85666	−0.324833
$586$	21.4852	0.887544
$587$	2.36655	0.0976780	0.0488390	−	0.998807i	$-0.484448\pi$
$587$	2.36655	0.0976780	0.0488390	+	0.998807i	$0.484448\pi$
$588$	2.04245	0.0842291
$589$	0	0
$590$	−10.2679	−0.422721
$591$	24.0211	0.988095
$592$	−0.511988	−0.0210426
$593$	−17.2527	−0.708482	−0.354241	−	0.935154i	$-0.615261\pi$
$593$	−17.2527	−0.708482	−0.354241	+	0.935154i	$0.615261\pi$
$594$	−16.2916	−0.668451
$595$	−9.88356	−0.405186
$596$	−19.4843	−0.798108
$597$	43.5951	1.78423
$598$	−0.907345	−0.0371041
$599$	−18.6618	−0.762499	−0.381250	−	0.924472i	$-0.624506\pi$
$599$	−18.6618	−0.762499	−0.381250	+	0.924472i	$0.624506\pi$
$600$	1.61276	0.0658405
$601$	−40.0914	−1.63536	−0.817681	−	0.575671i	$-0.804741\pi$
$601$	−40.0914	−1.63536	−0.817681	+	0.575671i	$0.804741\pi$
$602$	−8.55346	−0.348613
$603$	−13.9801	−0.569315
$604$	−20.1790	−0.821071
$605$	16.4802	0.670017
$606$	11.2600	0.457405
$607$	41.9682	1.70344	0.851718	−	0.524001i	$-0.175561\pi$
$607$	41.9682	1.70344	0.851718	+	0.524001i	$0.175561\pi$
$608$	0	0
$609$	12.4316	0.503752
$610$	−25.0685	−1.01499
$611$	−14.7397	−0.596302
$612$	−5.64322	−0.228114
$613$	2.61461	0.105603	0.0528016	−	0.998605i	$-0.483185\pi$
$613$	2.61461	0.105603	0.0528016	+	0.998605i	$0.483185\pi$
$614$	22.8559	0.922388
$615$	−29.5216	−1.19043
$616$	4.36252	0.175771
$617$	−27.6152	−1.11174	−0.555872	−	0.831268i	$-0.687616\pi$
$617$	−27.6152	−1.11174	−0.555872	+	0.831268i	$0.687616\pi$
$618$	22.6132	0.909635
$619$	−15.3458	−0.616801	−0.308400	−	0.951257i	$-0.599794\pi$
$619$	−15.3458	−0.616801	−0.308400	+	0.951257i	$0.599794\pi$
$620$	−16.8565	−0.676972
$621$	1.03680	0.0416053
$622$	−12.3600	−0.495592
$623$	2.29590	0.0919834
$624$	−6.67503	−0.267215
$625$	−20.4284	−0.817136
$626$	−26.8988	−1.07509
$627$	0	0
$628$	−16.1440	−0.644216
$629$	2.46611	0.0983303
$630$	−2.40400	−0.0957777
$631$	−34.7131	−1.38190	−0.690952	−	0.722900i	$-0.742809\pi$
$631$	−34.7131	−1.38190	−0.690952	+	0.722900i	$0.742809\pi$
$632$	9.44117	0.375550
$633$	−17.8881	−0.710987
$634$	−3.26879	−0.129820
$635$	−40.6306	−1.61238
$636$	−7.33617	−0.290898
$637$	−3.26816	−0.129489
$638$	26.5530	1.05124
$639$	0.0994585	0.00393452
$640$	−2.05192	−0.0811093
$641$	−42.8849	−1.69385	−0.846926	−	0.531711i	$-0.821549\pi$
$641$	−42.8849	−1.69385	−0.846926	+	0.531711i	$0.821549\pi$
$642$	0.521568	0.0205847
$643$	43.0009	1.69579	0.847896	−	0.530163i	$-0.177869\pi$
$643$	43.0009	1.69579	0.847896	+	0.530163i	$0.177869\pi$
$644$	−0.277632	−0.0109402
$645$	35.8470	1.41148
$646$	0	0
$647$	−35.0416	−1.37763	−0.688813	−	0.724939i	$-0.741868\pi$
$647$	−35.0416	−1.37763	−0.688813	+	0.724939i	$0.741868\pi$
$648$	11.1421	0.437705
$649$	−21.8302	−0.856909
$650$	−2.58060	−0.101220
$651$	−16.7786	−0.657606
$652$	4.93527	0.193280
$653$	−18.7761	−0.734766	−0.367383	−	0.930070i	$-0.619746\pi$
$653$	−18.7761	−0.734766	−0.367383	+	0.930070i	$0.619746\pi$
$654$	27.5209	1.07615
$655$	−27.2594	−1.06511
$656$	−7.04416	−0.275028
$657$	−13.4714	−0.525570
$658$	−4.51008	−0.175821
$659$	19.0162	0.740766	0.370383	−	0.928879i	$-0.379226\pi$
$659$	19.0162	0.740766	0.370383	+	0.928879i	$0.379226\pi$
$660$	−18.2831	−0.711667
$661$	14.3229	0.557097	0.278549	−	0.960422i	$-0.410147\pi$
$661$	14.3229	0.557097	0.278549	+	0.960422i	$0.410147\pi$
$662$	2.19858	0.0854501
$663$	32.1519	1.24868
$664$	−6.18143	−0.239886
$665$	0	0
$666$	0.599838	0.0232432
$667$	−1.68984	−0.0654307
$668$	4.95803	0.191832
$669$	29.1088	1.12541
$670$	24.4849	0.945933
$671$	−53.2973	−2.05752
$672$	−2.04245	−0.0787891
$673$	−12.3110	−0.474554	−0.237277	−	0.971442i	$-0.576255\pi$
$673$	−12.3110	−0.474554	−0.237277	+	0.971442i	$0.576255\pi$
$674$	−30.3973	−1.17086
$675$	2.94879	0.113499
$676$	−2.31915	−0.0891981
$677$	36.9084	1.41850	0.709252	−	0.704955i	$-0.249033\pi$
$677$	36.9084	1.41850	0.709252	+	0.704955i	$0.249033\pi$
$678$	23.6943	0.909975
$679$	16.9140	0.649099
$680$	9.88356	0.379017
$681$	8.20657	0.314476
$682$	−35.8380	−1.37231
$683$	−15.0652	−0.576452	−0.288226	−	0.957562i	$-0.593065\pi$
$683$	−15.0652	−0.576452	−0.288226	+	0.957562i	$0.593065\pi$
$684$	0	0
$685$	35.8129	1.36834
$686$	−1.00000	−0.0381802
$687$	42.2901	1.61347
$688$	8.55346	0.326098
$689$	11.7387	0.447210
$690$	1.16354	0.0442951
$691$	−8.49379	−0.323119	−0.161559	−	0.986863i	$-0.551652\pi$
$691$	−8.49379	−0.323119	−0.161559	+	0.986863i	$0.551652\pi$
$692$	−7.90920	−0.300662
$693$	−5.11107	−0.194154
$694$	−32.0134	−1.21521
$695$	1.39338	0.0528539
$696$	−12.4316	−0.471217
$697$	33.9298	1.28518
$698$	6.37865	0.241435
$699$	34.1112	1.29020
$700$	−0.789620	−0.0298448
$701$	45.0369	1.70102	0.850511	−	0.525958i	$-0.176293\pi$
$701$	45.0369	1.70102	0.850511	+	0.525958i	$0.176293\pi$
$702$	−12.2047	−0.460638
$703$	0	0
$704$	−4.36252	−0.164419
$705$	18.9015	0.711871
$706$	−2.01486	−0.0758302
$707$	−5.51298	−0.207337
$708$	10.2204	0.384108
$709$	17.1466	0.643954	0.321977	−	0.946747i	$-0.395653\pi$
$709$	17.1466	0.643954	0.321977	+	0.946747i	$0.395653\pi$
$710$	−0.174192	−0.00653731
$711$	−11.0611	−0.414825
$712$	−2.29590	−0.0860426
$713$	2.28074	0.0854143
$714$	9.83792	0.368175
$715$	29.2551	1.09408
$716$	21.1631	0.790901
$717$	27.6947	1.03428
$718$	−7.69404	−0.287139
$719$	3.85509	0.143771	0.0718853	−	0.997413i	$-0.477098\pi$
$719$	3.85509	0.143771	0.0718853	+	0.997413i	$0.477098\pi$
$720$	2.40400	0.0895919
$721$	−11.0716	−0.412328
$722$	0	0
$723$	9.72247	0.361583
$724$	−6.33589	−0.235471
$725$	−4.80610	−0.178494
$726$	−16.4041	−0.608815
$727$	−11.8726	−0.440332	−0.220166	−	0.975462i	$-0.570660\pi$
$727$	−11.8726	−0.440332	−0.220166	+	0.975462i	$0.570660\pi$
$728$	3.26816	0.121126
$729$	9.82818	0.364007
$730$	23.5939	0.873250
$731$	−41.1998	−1.52383
$732$	24.9527	0.922279
$733$	−41.5928	−1.53627	−0.768133	−	0.640290i	$-0.778814\pi$
$733$	−41.5928	−1.53627	−0.768133	+	0.640290i	$0.778814\pi$
$734$	−23.1040	−0.852786
$735$	4.19094	0.154585
$736$	0.277632	0.0102336
$737$	52.0565	1.91753
$738$	8.25284	0.303791
$739$	−5.01491	−0.184476	−0.0922382	−	0.995737i	$-0.529402\pi$
$739$	−5.01491	−0.184476	−0.0922382	+	0.995737i	$0.529402\pi$
$740$	−1.05056	−0.0386193
$741$	0	0
$742$	3.59185	0.131861
$743$	23.9859	0.879958	0.439979	−	0.898008i	$-0.354986\pi$
$743$	23.9859	0.879958	0.439979	+	0.898008i	$0.354986\pi$
$744$	16.7786	0.615134
$745$	−39.9803	−1.46476
$746$	28.9366	1.05945
$747$	7.24208	0.264974
$748$	21.0131	0.768316
$749$	−0.255365	−0.00933082
$750$	24.2639	0.885994
$751$	−12.7846	−0.466518	−0.233259	−	0.972415i	$-0.574939\pi$
$751$	−12.7846	−0.466518	−0.233259	+	0.972415i	$0.574939\pi$
$752$	4.51008	0.164466
$753$	−39.3954	−1.43565
$754$	19.8920	0.724423
$755$	−41.4057	−1.50691
$756$	−3.73444	−0.135820
$757$	21.6877	0.788254	0.394127	−	0.919056i	$-0.371047\pi$
$757$	21.6877	0.788254	0.394127	+	0.919056i	$0.371047\pi$
$758$	18.1710	0.660001
$759$	2.47376	0.0897919
$760$	0	0
$761$	18.0372	0.653847	0.326923	−	0.945051i	$-0.393988\pi$
$761$	18.0372	0.653847	0.326923	+	0.945051i	$0.393988\pi$
$762$	40.4430	1.46509
$763$	−13.4745	−0.487810
$764$	16.7400	0.605632
$765$	−11.5794	−0.418656
$766$	−17.2859	−0.624564
$767$	−16.3539	−0.590506
$768$	2.04245	0.0737004
$769$	−39.7615	−1.43383	−0.716917	−	0.697158i	$-0.754448\pi$
$769$	−39.7615	−1.43383	−0.716917	+	0.697158i	$0.754448\pi$
$770$	8.95156	0.322592
$771$	−14.9095	−0.536951
$772$	4.86964	0.175262
$773$	−27.2938	−0.981689	−0.490845	−	0.871247i	$-0.663312\pi$
$773$	−27.2938	−0.981689	−0.490845	+	0.871247i	$0.663312\pi$
$774$	−10.0211	−0.360202
$775$	6.48670	0.233009
$776$	−16.9140	−0.607177
$777$	−1.04571	−0.0375146
$778$	13.2603	0.475405
$779$	0	0
$780$	−13.6966	−0.490419
$781$	−0.370344	−0.0132520
$782$	−1.33728	−0.0478210
$783$	−22.7300	−0.812305
$784$	1.00000	0.0357143
$785$	−33.1262	−1.18232
$786$	27.1335	0.967820
$787$	25.2514	0.900114	0.450057	−	0.893000i	$-0.351404\pi$
$787$	25.2514	0.900114	0.450057	+	0.893000i	$0.351404\pi$
$788$	11.7609	0.418966
$789$	−51.6125	−1.83745
$790$	19.3725	0.689244
$791$	−11.6010	−0.412482
$792$	5.11107	0.181614
$793$	−39.9273	−1.41786
$794$	0.0258087	0.000915915 0
$795$	−15.0532	−0.533883
$796$	21.3446	0.756538
$797$	−10.2608	−0.363457	−0.181729	−	0.983349i	$-0.558169\pi$
$797$	−10.2608	−0.363457	−0.181729	+	0.983349i	$0.558169\pi$
$798$	0	0
$799$	−21.7239	−0.768535
$800$	0.789620	0.0279173
$801$	2.68985	0.0950411
$802$	37.0943	1.30984
$803$	50.1623	1.77019
$804$	−24.3718	−0.859528
$805$	−0.569679	−0.0200785
$806$	−26.8478	−0.945674
$807$	−23.7396	−0.835673
$808$	5.51298	0.193946
$809$	36.4640	1.28201	0.641004	−	0.767538i	$-0.278518\pi$
$809$	36.4640	1.28201	0.641004	+	0.767538i	$0.278518\pi$
$810$	22.8628	0.803317
$811$	20.8576	0.732411	0.366206	−	0.930534i	$-0.380657\pi$
$811$	20.8576	0.732411	0.366206	+	0.930534i	$0.380657\pi$
$812$	6.08660	0.213598
$813$	−13.9202	−0.488203
$814$	−2.23356	−0.0782862
$815$	10.1268	0.354726
$816$	−9.83792	−0.344396
$817$	0	0
$818$	−32.0915	−1.12205
$819$	−3.82893	−0.133794
$820$	−14.4541	−0.504758
$821$	25.4836	0.889385	0.444693	−	0.895683i	$-0.353313\pi$
$821$	25.4836	0.889385	0.444693	+	0.895683i	$0.353313\pi$
$822$	−35.6475	−1.24335
$823$	−7.60403	−0.265060	−0.132530	−	0.991179i	$-0.542310\pi$
$823$	−7.60403	−0.265060	−0.132530	+	0.991179i	$0.542310\pi$
$824$	11.0716	0.385698
$825$	7.03569	0.244951
$826$	−5.00402	−0.174112
$827$	−40.0484	−1.39262	−0.696309	−	0.717742i	$-0.745176\pi$
$827$	−40.0484	−1.39262	−0.696309	+	0.717742i	$0.745176\pi$
$828$	−0.325270	−0.0113039
$829$	−6.59681	−0.229117	−0.114558	−	0.993417i	$-0.536545\pi$
$829$	−6.59681	−0.229117	−0.114558	+	0.993417i	$0.536545\pi$
$830$	−12.6838	−0.440261
$831$	15.2083	0.527569
$832$	−3.26816	−0.113303
$833$	−4.81674	−0.166890
$834$	−1.38694	−0.0480260
$835$	10.1735	0.352068
$836$	0	0
$837$	30.6783	1.06040
$838$	8.47502	0.292765
$839$	31.8987	1.10126	0.550632	−	0.834748i	$-0.314387\pi$
$839$	31.8987	1.10126	0.550632	+	0.834748i	$0.314387\pi$
$840$	−4.19094	−0.144601
$841$	8.04675	0.277474
$842$	−17.4258	−0.600532
$843$	51.4528	1.77213
$844$	−8.75816	−0.301468
$845$	−4.75871	−0.163705
$846$	−5.28395	−0.181666
$847$	8.03162	0.275970
$848$	−3.59185	−0.123345
$849$	−44.6640	−1.53286
$850$	−3.80339	−0.130455
$851$	0.142144	0.00487264
$852$	0.173388	0.00594016
$853$	−46.5465	−1.59372	−0.796860	−	0.604164i	$-0.793507\pi$
$853$	−46.5465	−1.59372	−0.796860	+	0.604164i	$0.793507\pi$
$854$	−12.2171	−0.418060
$855$	0	0
$856$	0.255365	0.00872818
$857$	−1.84796	−0.0631250	−0.0315625	−	0.999502i	$-0.510048\pi$
$857$	−1.84796	−0.0631250	−0.0315625	+	0.999502i	$0.510048\pi$
$858$	−29.1200	−0.994140
$859$	−14.1195	−0.481750	−0.240875	−	0.970556i	$-0.577434\pi$
$859$	−14.1195	−0.481750	−0.240875	+	0.970556i	$0.577434\pi$
$860$	17.5510	0.598485
$861$	−14.3873	−0.490318
$862$	−33.0212	−1.12470
$863$	−10.8176	−0.368236	−0.184118	−	0.982904i	$-0.558943\pi$
$863$	−10.8176	−0.368236	−0.184118	+	0.982904i	$0.558943\pi$
$864$	3.73444	0.127048
$865$	−16.2290	−0.551804
$866$	−5.15179	−0.175065
$867$	12.6651	0.430129
$868$	−8.21497	−0.278834
$869$	41.1873	1.39718
$870$	−25.5086	−0.864822
$871$	38.9978	1.32139
$872$	13.4745	0.456304
$873$	19.8162	0.670676
$874$	0	0
$875$	−11.8798	−0.401612
$876$	−23.4850	−0.793484
$877$	19.6400	0.663195	0.331598	−	0.943421i	$-0.392412\pi$
$877$	19.6400	0.663195	0.331598	+	0.943421i	$0.392412\pi$
$878$	−10.0297	−0.338485
$879$	−43.8823	−1.48011
$880$	−8.95156	−0.301757
$881$	−22.9980	−0.774824	−0.387412	−	0.921907i	$-0.626631\pi$
$881$	−22.9980	−0.774824	−0.387412	+	0.921907i	$0.626631\pi$
$882$	−1.17159	−0.0394494
$883$	31.4417	1.05810	0.529048	−	0.848592i	$-0.322549\pi$
$883$	31.4417	1.05810	0.529048	+	0.848592i	$0.322549\pi$
$884$	15.7418	0.529456
$885$	20.9715	0.704951
$886$	−38.3277	−1.28764
$887$	20.4500	0.686643	0.343321	−	0.939218i	$-0.388448\pi$
$887$	20.4500	0.686643	0.343321	+	0.939218i	$0.388448\pi$
$888$	1.04571	0.0350917
$889$	−19.8012	−0.664112
$890$	−4.71101	−0.157914
$891$	48.6079	1.62843
$892$	14.2519	0.477189
$893$	0	0
$894$	39.7957	1.33097
$895$	43.4249	1.45154
$896$	−1.00000	−0.0334077
$897$	1.85320	0.0618766
$898$	−33.5135	−1.11836
$899$	−50.0013	−1.66764
$900$	−0.925108	−0.0308369
$901$	17.3010	0.576380
$902$	−30.7303	−1.02321
$903$	17.4700	0.581365
$904$	11.6010	0.385842
$905$	−13.0007	−0.432159
$906$	41.2145	1.36926
$907$	51.2755	1.70258	0.851288	−	0.524699i	$-0.175822\pi$
$907$	51.2755	1.70258	0.851288	+	0.524699i	$0.175822\pi$
$908$	4.01801	0.133342
$909$	−6.45893	−0.214229
$910$	6.70600	0.222302
$911$	28.2985	0.937570	0.468785	−	0.883312i	$-0.344692\pi$
$911$	28.2985	0.937570	0.468785	+	0.883312i	$0.344692\pi$
$912$	0	0
$913$	−26.9666	−0.892465
$914$	−0.889078	−0.0294081
$915$	51.2010	1.69265
$916$	20.7056	0.684133
$917$	−13.2848	−0.438703
$918$	−17.9878	−0.593686
$919$	−33.2973	−1.09838	−0.549188	−	0.835699i	$-0.685063\pi$
$919$	−33.2973	−1.09838	−0.549188	+	0.835699i	$0.685063\pi$
$920$	0.569679	0.0187818
$921$	−46.6819	−1.53822
$922$	−5.45431	−0.179628
$923$	−0.277441	−0.00913208
$924$	−8.91022	−0.293125
$925$	0.404276	0.0132925
$926$	33.4144	1.09806
$927$	−12.9713	−0.426035
$928$	−6.08660	−0.199803
$929$	31.8704	1.04563	0.522817	−	0.852445i	$-0.324881\pi$
$929$	31.8704	1.04563	0.522817	+	0.852445i	$0.324881\pi$
$930$	34.4284	1.12895
$931$	0	0
$932$	16.7011	0.547064
$933$	25.2447	0.826474
$934$	−7.78250	−0.254651
$935$	43.1173	1.41009
$936$	3.82893	0.125152
$937$	−32.9422	−1.07617	−0.538087	−	0.842889i	$-0.680853\pi$
$937$	−32.9422	−1.07617	−0.538087	+	0.842889i	$0.680853\pi$
$938$	11.9327	0.389615
$939$	54.9393	1.79288
$940$	9.25433	0.301843
$941$	39.7658	1.29633	0.648165	−	0.761500i	$-0.275537\pi$
$941$	39.7658	1.29633	0.648165	+	0.761500i	$0.275537\pi$
$942$	32.9732	1.07433
$943$	1.95568	0.0636858
$944$	5.00402	0.162867
$945$	−7.66277	−0.249270
$946$	37.3147	1.21321
$947$	−37.2476	−1.21038	−0.605192	−	0.796080i	$-0.706904\pi$
$947$	−37.2476	−1.21038	−0.605192	+	0.796080i	$0.706904\pi$
$948$	−19.2831	−0.626285
$949$	37.5788	1.21986
$950$	0	0
$951$	6.67632	0.216495
$952$	4.81674	0.156111
$953$	−36.4097	−1.17942	−0.589712	−	0.807613i	$-0.700759\pi$
$953$	−36.4097	−1.17942	−0.589712	+	0.807613i	$0.700759\pi$
$954$	4.20817	0.136244
$955$	34.3491	1.11151
$956$	13.5596	0.438547
$957$	−54.2330	−1.75310
$958$	−14.9950	−0.484466
$959$	17.4533	0.563598
$960$	4.19094	0.135262
$961$	36.4857	1.17696
$962$	−1.67326	−0.0539480
$963$	−0.299182	−0.00964099
$964$	4.76021	0.153316
$965$	9.99213	0.321658
$966$	0.567048	0.0182445
$967$	−51.7512	−1.66421	−0.832103	−	0.554622i	$-0.812863\pi$
$967$	−51.7512	−1.66421	−0.832103	+	0.554622i	$0.812863\pi$
$968$	−8.03162	−0.258146
$969$	0	0
$970$	−34.7062	−1.11435
$971$	−35.2225	−1.13034	−0.565171	−	0.824974i	$-0.691190\pi$
$971$	−35.2225	−1.13034	−0.565171	+	0.824974i	$0.691190\pi$
$972$	−11.5539	−0.370592
$973$	0.679061	0.0217697
$974$	−32.2487	−1.03332
$975$	5.27074	0.168799
$976$	12.2171	0.391059
$977$	21.0128	0.672258	0.336129	−	0.941816i	$-0.390882\pi$
$977$	21.0128	0.672258	0.336129	+	0.941816i	$0.390882\pi$
$978$	−10.0800	−0.322324
$979$	−10.0159	−0.320111
$980$	2.05192	0.0655462
$981$	−15.7865	−0.504025
$982$	10.4214	0.332560
$983$	13.1608	0.419764	0.209882	−	0.977727i	$-0.432692\pi$
$983$	13.1608	0.419764	0.209882	+	0.977727i	$0.432692\pi$
$984$	14.3873	0.458651
$985$	24.1325	0.768926
$986$	29.3176	0.933661
$987$	9.21160	0.293208
$988$	0	0
$989$	−2.37471	−0.0755115
$990$	10.4875	0.333315
$991$	−27.3742	−0.869569	−0.434785	−	0.900535i	$-0.643175\pi$
$991$	−27.3742	−0.869569	−0.434785	+	0.900535i	$0.643175\pi$
$992$	8.21497	0.260825
$993$	−4.49047	−0.142501
$994$	−0.0848922	−0.00269262
$995$	43.7974	1.38847
$996$	12.6252	0.400046
$997$	−35.3955	−1.12099	−0.560494	−	0.828158i	$-0.689389\pi$
$997$	−35.3955	−1.12099	−0.560494	+	0.828158i	$0.689389\pi$
$998$	−26.1994	−0.829328
$999$	1.91199	0.0604926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.z.1.5	✓	6
19.18	odd	2		5054.2.a.be.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.z.1.5	✓	6	1.1	even	1	trivial
5054.2.a.be.1.2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.04245 q^{3} +1.00000 q^{4} +2.05192 q^{5} -2.04245 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.17159 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.04245 q^{3} +1.00000 q^{4} +2.05192 q^{5} -2.04245 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.17159 q^{9} -2.05192 q^{10} -4.36252 q^{11} +2.04245 q^{12} -3.26816 q^{13} -1.00000 q^{14} +4.19094 q^{15} +1.00000 q^{16} -4.81674 q^{17} -1.17159 q^{18} +2.05192 q^{20} +2.04245 q^{21} +4.36252 q^{22} -0.277632 q^{23} -2.04245 q^{24} -0.789620 q^{25} +3.26816 q^{26} -3.73444 q^{27} +1.00000 q^{28} +6.08660 q^{29} -4.19094 q^{30} -8.21497 q^{31} -1.00000 q^{32} -8.91022 q^{33} +4.81674 q^{34} +2.05192 q^{35} +1.17159 q^{36} -0.511988 q^{37} -6.67503 q^{39} -2.05192 q^{40} -7.04416 q^{41} -2.04245 q^{42} +8.55346 q^{43} -4.36252 q^{44} +2.40400 q^{45} +0.277632 q^{46} +4.51008 q^{47} +2.04245 q^{48} +1.00000 q^{49} +0.789620 q^{50} -9.83792 q^{51} -3.26816 q^{52} -3.59185 q^{53} +3.73444 q^{54} -8.95156 q^{55} -1.00000 q^{56} -6.08660 q^{58} +5.00402 q^{59} +4.19094 q^{60} +12.2171 q^{61} +8.21497 q^{62} +1.17159 q^{63} +1.00000 q^{64} -6.70600 q^{65} +8.91022 q^{66} -11.9327 q^{67} -4.81674 q^{68} -0.567048 q^{69} -2.05192 q^{70} +0.0848922 q^{71} -1.17159 q^{72} -11.4985 q^{73} +0.511988 q^{74} -1.61276 q^{75} -4.36252 q^{77} +6.67503 q^{78} -9.44117 q^{79} +2.05192 q^{80} -11.1421 q^{81} +7.04416 q^{82} +6.18143 q^{83} +2.04245 q^{84} -9.88356 q^{85} -8.55346 q^{86} +12.4316 q^{87} +4.36252 q^{88} +2.29590 q^{89} -2.40400 q^{90} -3.26816 q^{91} -0.277632 q^{92} -16.7786 q^{93} -4.51008 q^{94} -2.04245 q^{96} +16.9140 q^{97} -1.00000 q^{98} -5.11107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} + 6 q^{4} - q^{5} + 6 q^{7} - 6 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 15 q^{13} - 6 q^{14} - 6 q^{15} + 6 q^{16} - 9 q^{17} - 8 q^{18} - q^{20} - 4 q^{22} + 4 q^{23} + q^{25} + 15 q^{26} + 12 q^{27} + 6 q^{28} - 7 q^{29} + 6 q^{30} - 4 q^{31} - 6 q^{32} - 28 q^{33} + 9 q^{34} - q^{35} + 8 q^{36} - 3 q^{37} - 8 q^{39} + q^{40} - 11 q^{41} - 10 q^{43} + 4 q^{44} + 19 q^{45} - 4 q^{46} + 12 q^{47} + 6 q^{49} - q^{50} - 44 q^{51} - 15 q^{52} + 5 q^{53} - 12 q^{54} - 8 q^{55} - 6 q^{56} + 7 q^{58} - 4 q^{59} - 6 q^{60} - 21 q^{61} + 4 q^{62} + 8 q^{63} + 6 q^{64} + 20 q^{65} + 28 q^{66} - 14 q^{67} - 9 q^{68} + 24 q^{69} + q^{70} - 24 q^{71} - 8 q^{72} - 21 q^{73} + 3 q^{74} - 12 q^{75} + 4 q^{77} + 8 q^{78} - 58 q^{79} - q^{80} - 6 q^{81} + 11 q^{82} + 20 q^{83} - 4 q^{85} + 10 q^{86} - 8 q^{87} - 4 q^{88} - 7 q^{89} - 19 q^{90} - 15 q^{91} + 4 q^{92} - 22 q^{93} - 12 q^{94} - 7 q^{97} - 6 q^{98} - 26 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^4 - q^5 + 6 * q^7 - 6 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 15 * q^13 - 6 * q^14 - 6 * q^15 + 6 * q^16 - 9 * q^17 - 8 * q^18 - q^20 - 4 * q^22 + 4 * q^23 + q^25 + 15 * q^26 + 12 * q^27 + 6 * q^28 - 7 * q^29 + 6 * q^30 - 4 * q^31 - 6 * q^32 - 28 * q^33 + 9 * q^34 - q^35 + 8 * q^36 - 3 * q^37 - 8 * q^39 + q^40 - 11 * q^41 - 10 * q^43 + 4 * q^44 + 19 * q^45 - 4 * q^46 + 12 * q^47 + 6 * q^49 - q^50 - 44 * q^51 - 15 * q^52 + 5 * q^53 - 12 * q^54 - 8 * q^55 - 6 * q^56 + 7 * q^58 - 4 * q^59 - 6 * q^60 - 21 * q^61 + 4 * q^62 + 8 * q^63 + 6 * q^64 + 20 * q^65 + 28 * q^66 - 14 * q^67 - 9 * q^68 + 24 * q^69 + q^70 - 24 * q^71 - 8 * q^72 - 21 * q^73 + 3 * q^74 - 12 * q^75 + 4 * q^77 + 8 * q^78 - 58 * q^79 - q^80 - 6 * q^81 + 11 * q^82 + 20 * q^83 - 4 * q^85 + 10 * q^86 - 8 * q^87 - 4 * q^88 - 7 * q^89 - 19 * q^90 - 15 * q^91 + 4 * q^92 - 22 * q^93 - 12 * q^94 - 7 * q^97 - 6 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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