LMFDB - Embedded newform 5054.2.a.x.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:	$4$
Coefficient field:	4.4.151572.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 8x + 4 $ x^4 - x^3 - 10x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.02917$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.02917 q^{3} +1.00000 q^{4} -3.36893 q^{5} -3.02917 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.17589 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.02917 q^{3} +1.00000 q^{4} -3.36893 q^{5} -3.02917 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.17589 q^{9} -3.36893 q^{10} +5.02917 q^{11} -3.02917 q^{12} +4.83613 q^{13} +1.00000 q^{14} +10.2051 q^{15} +1.00000 q^{16} -0.146715 q^{17} +6.17589 q^{18} -3.36893 q^{20} -3.02917 q^{21} +5.02917 q^{22} +4.56197 q^{23} -3.02917 q^{24} +6.34967 q^{25} +4.83613 q^{26} -9.62031 q^{27} +1.00000 q^{28} -7.52555 q^{29} +10.2051 q^{30} +1.46721 q^{31} +1.00000 q^{32} -15.2342 q^{33} -0.146715 q^{34} -3.36893 q^{35} +6.17589 q^{36} +4.73785 q^{37} -14.6495 q^{39} -3.36893 q^{40} +0.970827 q^{41} -3.02917 q^{42} +4.53279 q^{43} +5.02917 q^{44} -20.8061 q^{45} +4.56197 q^{46} -7.52555 q^{47} -3.02917 q^{48} +1.00000 q^{49} +6.34967 q^{50} +0.444424 q^{51} +4.83613 q^{52} +2.53279 q^{53} -9.62031 q^{54} -16.9429 q^{55} +1.00000 q^{56} -7.52555 q^{58} -2.54481 q^{59} +10.2051 q^{60} +13.0412 q^{61} +1.46721 q^{62} +6.17589 q^{63} +1.00000 q^{64} -16.2926 q^{65} -15.2342 q^{66} -0.882458 q^{67} -0.146715 q^{68} -13.8190 q^{69} -3.36893 q^{70} -1.29132 q^{71} +6.17589 q^{72} +9.85539 q^{73} +4.73785 q^{74} -19.2342 q^{75} +5.02917 q^{77} -14.6495 q^{78} -16.4101 q^{79} -3.36893 q^{80} +10.6139 q^{81} +0.970827 q^{82} -11.2243 q^{83} -3.02917 q^{84} +0.494271 q^{85} +4.53279 q^{86} +22.7962 q^{87} +5.02917 q^{88} -1.94165 q^{89} -20.8061 q^{90} +4.83613 q^{91} +4.56197 q^{92} -4.44442 q^{93} -7.52555 q^{94} -3.02917 q^{96} -11.0875 q^{97} +1.00000 q^{98} +31.0596 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} + q^{12} + 5 q^{13} + 4 q^{14} + 12 q^{15} + 4 q^{16} + 2 q^{17} + 9 q^{18} + q^{20} + q^{21} + 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} + q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + 6 q^{31} + 4 q^{32} - 19 q^{33} + 2 q^{34} + q^{35} + 9 q^{36} - 10 q^{37} - 6 q^{39} + q^{40} + 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} + 5 q^{46} - 4 q^{47} + q^{48} + 4 q^{49} + 15 q^{50} - 22 q^{51} + 5 q^{52} + 10 q^{53} + q^{54} - 10 q^{55} + 4 q^{56} - 4 q^{58} + 20 q^{59} + 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} + 3 q^{65} - 19 q^{66} + 7 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 10 q^{74} - 35 q^{75} + 7 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} + q^{84} + 10 q^{85} + 18 q^{86} + 36 q^{87} + 7 q^{88} - 34 q^{89} - 19 q^{90} + 5 q^{91} + 5 q^{92} + 6 q^{93} - 4 q^{94} + q^{96} - 5 q^{97} + 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 + q^12 + 5 * q^13 + 4 * q^14 + 12 * q^15 + 4 * q^16 + 2 * q^17 + 9 * q^18 + q^20 + q^21 + 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 + q^27 + 4 * q^28 - 4 * q^29 + 12 * q^30 + 6 * q^31 + 4 * q^32 - 19 * q^33 + 2 * q^34 + q^35 + 9 * q^36 - 10 * q^37 - 6 * q^39 + q^40 + 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 + 5 * q^46 - 4 * q^47 + q^48 + 4 * q^49 + 15 * q^50 - 22 * q^51 + 5 * q^52 + 10 * q^53 + q^54 - 10 * q^55 + 4 * q^56 - 4 * q^58 + 20 * q^59 + 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 + 3 * q^65 - 19 * q^66 + 7 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 10 * q^74 - 35 * q^75 + 7 * q^77 - 6 * q^78 - 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 + q^84 + 10 * q^85 + 18 * q^86 + 36 * q^87 + 7 * q^88 - 34 * q^89 - 19 * q^90 + 5 * q^91 + 5 * q^92 + 6 * q^93 - 4 * q^94 + q^96 - 5 * q^97 + 4 * q^98 + 14 * 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
$3$	−3.02917	−1.74889	−0.874447	−	0.485121i	$-0.838775\pi$
$3$	−3.02917	−1.74889	−0.874447	+	0.485121i	$0.838775\pi$
$4$	1.00000	0.500000
$5$	−3.36893	−1.50663	−0.753315	−	0.657660i	$-0.771546\pi$
$5$	−3.36893	−1.50663	−0.753315	+	0.657660i	$0.771546\pi$
$6$	−3.02917	−1.23665
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	6.17589	2.05863
$10$	−3.36893	−1.06535
$11$	5.02917	1.51635	0.758176	−	0.652050i	$-0.226091\pi$
$11$	5.02917	1.51635	0.758176	+	0.652050i	$0.226091\pi$
$12$	−3.02917	−0.874447
$13$	4.83613	1.34130	0.670651	−	0.741773i	$-0.266015\pi$
$13$	4.83613	1.34130	0.670651	+	0.741773i	$0.266015\pi$
$14$	1.00000	0.267261
$15$	10.2051	2.63494
$16$	1.00000	0.250000
$17$	−0.146715	−0.0355835	−0.0177918	−	0.999842i	$-0.505664\pi$
$17$	−0.146715	−0.0355835	−0.0177918	+	0.999842i	$0.505664\pi$
$18$	6.17589	1.45567
$19$	0	0
$19$	0	0
$20$	−3.36893	−0.753315
$21$	−3.02917	−0.661020
$22$	5.02917	1.07222
$23$	4.56197	0.951236	0.475618	−	0.879652i	$-0.342225\pi$
$23$	4.56197	0.951236	0.475618	+	0.879652i	$0.342225\pi$
$24$	−3.02917	−0.618327
$25$	6.34967	1.26993
$26$	4.83613	0.948444
$27$	−9.62031	−1.85143
$28$	1.00000	0.188982
$29$	−7.52555	−1.39746	−0.698730	−	0.715385i	$-0.746251\pi$
$29$	−7.52555	−1.39746	−0.698730	+	0.715385i	$0.746251\pi$
$30$	10.2051	1.86318
$31$	1.46721	0.263518	0.131759	−	0.991282i	$-0.457937\pi$
$31$	1.46721	0.263518	0.131759	+	0.991282i	$0.457937\pi$
$32$	1.00000	0.176777
$33$	−15.2342	−2.65194
$34$	−0.146715	−0.0251613
$35$	−3.36893	−0.569453
$36$	6.17589	1.02931
$37$	4.73785	0.778898	0.389449	−	0.921048i	$-0.372665\pi$
$37$	4.73785	0.778898	0.389449	+	0.921048i	$0.372665\pi$
$38$	0	0
$39$	−14.6495	−2.34579
$40$	−3.36893	−0.532674
$41$	0.970827	0.151618	0.0758089	−	0.997122i	$-0.475846\pi$
$41$	0.970827	0.151618	0.0758089	+	0.997122i	$0.475846\pi$
$42$	−3.02917	−0.467411
$43$	4.53279	0.691244	0.345622	−	0.938374i	$-0.387668\pi$
$43$	4.53279	0.691244	0.345622	+	0.938374i	$0.387668\pi$
$44$	5.02917	0.758176
$45$	−20.8061	−3.10159
$46$	4.56197	0.672625
$47$	−7.52555	−1.09771	−0.548857	−	0.835916i	$-0.684937\pi$
$47$	−7.52555	−1.09771	−0.548857	+	0.835916i	$0.684937\pi$
$48$	−3.02917	−0.437223
$49$	1.00000	0.142857
$50$	6.34967	0.897978
$51$	0.444424	0.0622318
$52$	4.83613	0.670651
$53$	2.53279	0.347906	0.173953	−	0.984754i	$-0.444346\pi$
$53$	2.53279	0.347906	0.173953	+	0.984754i	$0.444346\pi$
$54$	−9.62031	−1.30916
$55$	−16.9429	−2.28458
$56$	1.00000	0.133631
$57$	0	0
$58$	−7.52555	−0.988153
$59$	−2.54481	−0.331307	−0.165653	−	0.986184i	$-0.552973\pi$
$59$	−2.54481	−0.331307	−0.165653	+	0.986184i	$0.552973\pi$
$60$	10.2051	1.31747
$61$	13.0412	1.66975	0.834877	−	0.550437i	$-0.185539\pi$
$61$	13.0412	1.66975	0.834877	+	0.550437i	$0.185539\pi$
$62$	1.46721	0.186335
$63$	6.17589	0.778089
$64$	1.00000	0.125000
$65$	−16.2926	−2.02085
$66$	−15.2342	−1.87520
$67$	−0.882458	−0.107809	−0.0539047	−	0.998546i	$-0.517167\pi$
$67$	−0.882458	−0.107809	−0.0539047	+	0.998546i	$0.517167\pi$
$68$	−0.146715	−0.0177918
$69$	−13.8190	−1.66361
$70$	−3.36893	−0.402664
$71$	−1.29132	−0.153251	−0.0766257	−	0.997060i	$-0.524415\pi$
$71$	−1.29132	−0.153251	−0.0766257	+	0.997060i	$0.524415\pi$
$72$	6.17589	0.727835
$73$	9.85539	1.15349	0.576743	−	0.816925i	$-0.304323\pi$
$73$	9.85539	1.15349	0.576743	+	0.816925i	$0.304323\pi$
$74$	4.73785	0.550764
$75$	−19.2342	−2.22098
$76$	0	0
$77$	5.02917	0.573127
$78$	−14.6495	−1.65873
$79$	−16.4101	−1.84628	−0.923141	−	0.384461i	$-0.874387\pi$
$79$	−16.4101	−1.84628	−0.923141	+	0.384461i	$0.874387\pi$
$80$	−3.36893	−0.376657
$81$	10.6139	1.17932
$82$	0.970827	0.107210
$83$	−11.2243	−1.23203	−0.616015	−	0.787735i	$-0.711254\pi$
$83$	−11.2243	−1.23203	−0.616015	+	0.787735i	$0.711254\pi$
$84$	−3.02917	−0.330510
$85$	0.494271	0.0536112
$86$	4.53279	0.488784
$87$	22.7962	2.44401
$88$	5.02917	0.536112
$89$	−1.94165	−0.205815	−0.102907	−	0.994691i	$-0.532815\pi$
$89$	−1.94165	−0.205815	−0.102907	+	0.994691i	$0.532815\pi$
$90$	−20.8061	−2.19316
$91$	4.83613	0.506965
$92$	4.56197	0.475618
$93$	−4.44442	−0.460865
$94$	−7.52555	−0.776201
$95$	0	0
$96$	−3.02917	−0.309164
$97$	−11.0875	−1.12577	−0.562883	−	0.826536i	$-0.690308\pi$
$97$	−11.0875	−1.12577	−0.562883	+	0.826536i	$0.690308\pi$
$98$	1.00000	0.101015
$99$	31.0596	3.12161
$100$	6.34967	0.634967
$101$	−10.2051	−1.01544	−0.507721	−	0.861522i	$-0.669512\pi$
$101$	−10.2051	−1.01544	−0.507721	+	0.861522i	$0.669512\pi$
$102$	0.444424	0.0440045
$103$	−0.205060	−0.0202052	−0.0101026	−	0.999949i	$-0.503216\pi$
$103$	−0.205060	−0.0202052	−0.0101026	+	0.999949i	$0.503216\pi$
$104$	4.83613	0.474222
$105$	10.2051	0.995912
$106$	2.53279	0.246007
$107$	9.41736	0.910411	0.455205	−	0.890387i	$-0.349566\pi$
$107$	9.41736	0.910411	0.455205	+	0.890387i	$0.349566\pi$
$108$	−9.62031	−0.925715
$109$	19.6422	1.88139	0.940693	−	0.339259i	$-0.110176\pi$
$109$	19.6422	1.88139	0.940693	+	0.339259i	$0.110176\pi$
$110$	−16.9429	−1.61544
$111$	−14.3518	−1.36221
$112$	1.00000	0.0944911
$113$	−13.2051	−1.24223	−0.621114	−	0.783720i	$-0.713320\pi$
$113$	−13.2051	−1.24223	−0.621114	+	0.783720i	$0.713320\pi$
$114$	0	0
$115$	−15.3689	−1.43316
$116$	−7.52555	−0.698730
$117$	29.8674	2.76124
$118$	−2.54481	−0.234269
$119$	−0.146715	−0.0134493
$120$	10.2051	0.931590
$121$	14.2926	1.29933
$122$	13.0412	1.18069
$123$	−2.94080	−0.265163
$124$	1.46721	0.131759
$125$	−4.54692	−0.406689
$126$	6.17589	0.550192
$127$	−12.8554	−1.14073	−0.570366	−	0.821391i	$-0.693199\pi$
$127$	−12.8554	−1.14073	−0.570366	+	0.821391i	$0.693199\pi$
$128$	1.00000	0.0883883
$129$	−13.7306	−1.20891
$130$	−16.2926	−1.42895
$131$	20.1287	1.75865	0.879327	−	0.476219i	$-0.157993\pi$
$131$	20.1287	1.75865	0.879327	+	0.476219i	$0.157993\pi$
$132$	−15.2342	−1.32597
$133$	0	0
$134$	−0.882458	−0.0762328
$135$	32.4101	2.78942
$136$	−0.146715	−0.0125807
$137$	−4.67227	−0.399179	−0.199589	−	0.979880i	$-0.563961\pi$
$137$	−4.67227	−0.399179	−0.199589	+	0.979880i	$0.563961\pi$
$138$	−13.8190	−1.17635
$139$	10.1531	0.861175	0.430588	−	0.902549i	$-0.358306\pi$
$139$	10.1531	0.861175	0.430588	+	0.902549i	$0.358306\pi$
$140$	−3.36893	−0.284726
$141$	22.7962	1.91979
$142$	−1.29132	−0.108365
$143$	24.3218	2.03389
$144$	6.17589	0.514657
$145$	25.3530	2.10545
$146$	9.85539	0.815638
$147$	−3.02917	−0.249842
$148$	4.73785	0.389449
$149$	−0.737853	−0.0604473	−0.0302236	−	0.999543i	$-0.509622\pi$
$149$	−0.737853	−0.0604473	−0.0302236	+	0.999543i	$0.509622\pi$
$150$	−19.2342	−1.57047
$151$	14.2926	1.16311	0.581557	−	0.813506i	$-0.302444\pi$
$151$	14.2926	1.16311	0.581557	+	0.813506i	$0.302444\pi$
$152$	0	0
$153$	−0.906093	−0.0732532
$154$	5.02917	0.405262
$155$	−4.94291	−0.397024
$156$	−14.6495	−1.17290
$157$	7.90172	0.630626	0.315313	−	0.948988i	$-0.397891\pi$
$157$	7.90172	0.630626	0.315313	+	0.948988i	$0.397891\pi$
$158$	−16.4101	−1.30552
$159$	−7.67227	−0.608450
$160$	−3.36893	−0.266337
$161$	4.56197	0.359533
$162$	10.6139	0.833908
$163$	24.7598	1.93934	0.969668	−	0.244426i	$-0.0785994\pi$
$163$	24.7598	1.93934	0.969668	+	0.244426i	$0.0785994\pi$
$164$	0.970827	0.0758089
$165$	51.3230	3.99549
$166$	−11.2243	−0.871176
$167$	1.37884	0.106698	0.0533488	−	0.998576i	$-0.483010\pi$
$167$	1.37884	0.106698	0.0533488	+	0.998576i	$0.483010\pi$
$168$	−3.02917	−0.233706
$169$	10.3882	0.799091
$170$	0.494271	0.0379088
$171$	0	0
$172$	4.53279	0.345622
$173$	22.8446	1.73685	0.868423	−	0.495825i	$-0.165134\pi$
$173$	22.8446	1.73685	0.868423	+	0.495825i	$0.165134\pi$
$174$	22.7962	1.72818
$175$	6.34967	0.479990
$176$	5.02917	0.379088
$177$	7.70868	0.579420
$178$	−1.94165	−0.145533
$179$	9.38095	0.701165	0.350582	−	0.936532i	$-0.385984\pi$
$179$	9.38095	0.701165	0.350582	+	0.936532i	$0.385984\pi$
$180$	−20.8061	−1.55080
$181$	−19.0412	−1.41532	−0.707660	−	0.706553i	$-0.750249\pi$
$181$	−19.0412	−1.41532	−0.707660	+	0.706553i	$0.750249\pi$
$182$	4.83613	0.358478
$183$	−39.5040	−2.92022
$184$	4.56197	0.336313
$185$	−15.9615	−1.17351
$186$	−4.44442	−0.325881
$187$	−0.737853	−0.0539571
$188$	−7.52555	−0.548857
$189$	−9.62031	−0.699775
$190$	0	0
$191$	10.1459	0.734129	0.367064	−	0.930196i	$-0.380363\pi$
$191$	10.1459	0.734129	0.367064	+	0.930196i	$0.380363\pi$
$192$	−3.02917	−0.218612
$193$	−20.0875	−1.44593	−0.722966	−	0.690884i	$-0.757222\pi$
$193$	−20.0875	−1.44593	−0.722966	+	0.690884i	$0.757222\pi$
$194$	−11.0875	−0.796037
$195$	49.3530	3.53424
$196$	1.00000	0.0714286
$197$	5.50573	0.392267	0.196133	−	0.980577i	$-0.437161\pi$
$197$	5.50573	0.392267	0.196133	+	0.980577i	$0.437161\pi$
$198$	31.0596	2.20731
$199$	5.46721	0.387560	0.193780	−	0.981045i	$-0.437925\pi$
$199$	5.46721	0.387560	0.193780	+	0.981045i	$0.437925\pi$
$200$	6.34967	0.448989
$201$	2.67312	0.188547
$202$	−10.2051	−0.718026
$203$	−7.52555	−0.528190
$204$	0.444424	0.0311159
$205$	−3.27065	−0.228432
$206$	−0.205060	−0.0142872
$207$	28.1742	1.95824
$208$	4.83613	0.335326
$209$	0	0
$210$	10.2051	0.704216
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	2.53279	0.173953
$213$	3.91163	0.268021
$214$	9.41736	0.643757
$215$	−15.2706	−1.04145
$216$	−9.62031	−0.654579
$217$	1.46721	0.0996005
$218$	19.6422	1.33034
$219$	−29.8537	−2.01733
$220$	−16.9429	−1.14229
$221$	−0.709531	−0.0477282
$222$	−14.3518	−0.963228
$223$	4.93441	0.330433	0.165216	−	0.986257i	$-0.447168\pi$
$223$	4.93441	0.330433	0.165216	+	0.986257i	$0.447168\pi$
$224$	1.00000	0.0668153
$225$	39.2148	2.61432
$226$	−13.2051	−0.878388
$227$	2.00352	0.132978	0.0664892	−	0.997787i	$-0.478820\pi$
$227$	2.00352	0.132978	0.0664892	+	0.997787i	$0.478820\pi$
$228$	0	0
$229$	−2.72372	−0.179989	−0.0899943	−	0.995942i	$-0.528685\pi$
$229$	−2.72372	−0.179989	−0.0899943	+	0.995942i	$0.528685\pi$
$230$	−15.3689	−1.01340
$231$	−15.2342	−1.00234
$232$	−7.52555	−0.494077
$233$	−10.6723	−0.699163	−0.349582	−	0.936906i	$-0.613676\pi$
$233$	−10.6723	−0.699163	−0.349582	+	0.936906i	$0.613676\pi$
$234$	29.8674	1.95249
$235$	25.3530	1.65385
$236$	−2.54481	−0.165653
$237$	49.7091	3.22895
$238$	−0.146715	−0.00951009
$239$	19.2655	1.24618	0.623091	−	0.782149i	$-0.285877\pi$
$239$	19.2655	1.24618	0.623091	+	0.782149i	$0.285877\pi$
$240$	10.2051	0.658734
$241$	0.912482	0.0587781	0.0293891	−	0.999568i	$-0.490644\pi$
$241$	0.912482	0.0587781	0.0293891	+	0.999568i	$0.490644\pi$
$242$	14.2926	0.918762
$243$	−3.29047	−0.211084
$244$	13.0412	0.834877
$245$	−3.36893	−0.215233
$246$	−2.94080	−0.187499
$247$	0	0
$248$	1.46721	0.0931677
$249$	34.0004	2.15469
$250$	−4.54692	−0.287573
$251$	2.30123	0.145252	0.0726262	−	0.997359i	$-0.476862\pi$
$251$	2.30123	0.145252	0.0726262	+	0.997359i	$0.476862\pi$
$252$	6.17589	0.389044
$253$	22.9429	1.44241
$254$	−12.8554	−0.806619
$255$	−1.49723	−0.0937602
$256$	1.00000	0.0625000
$257$	12.2114	0.761729	0.380865	−	0.924631i	$-0.375626\pi$
$257$	12.2114	0.761729	0.380865	+	0.924631i	$0.375626\pi$
$258$	−13.7306	−0.854831
$259$	4.73785	0.294396
$260$	−16.2926	−1.01042
$261$	−46.4770	−2.87685
$262$	20.1287	1.24356
$263$	−0.356906	−0.0220077	−0.0110039	−	0.999939i	$-0.503503\pi$
$263$	−0.356906	−0.0220077	−0.0110039	+	0.999939i	$0.503503\pi$
$264$	−15.2342	−0.937602
$265$	−8.53279	−0.524165
$266$	0	0
$267$	5.88161	0.359949
$268$	−0.882458	−0.0539047
$269$	−0.591138	−0.0360423	−0.0180212	−	0.999838i	$-0.505737\pi$
$269$	−0.591138	−0.0360423	−0.0180212	+	0.999838i	$0.505737\pi$
$270$	32.4101	1.97242
$271$	25.1395	1.52711	0.763557	−	0.645740i	$-0.223451\pi$
$271$	25.1395	1.52711	0.763557	+	0.645740i	$0.223451\pi$
$272$	−0.146715	−0.00889588
$273$	−14.6495	−0.886627
$274$	−4.67227	−0.282262
$275$	31.9336	1.92567
$276$	−13.8190	−0.831805
$277$	−14.0824	−0.846129	−0.423064	−	0.906100i	$-0.639046\pi$
$277$	−14.0824	−0.846129	−0.423064	+	0.906100i	$0.639046\pi$
$278$	10.1531	0.608943
$279$	9.06131	0.542486
$280$	−3.36893	−0.201332
$281$	−11.1759	−0.666698	−0.333349	−	0.942804i	$-0.608179\pi$
$281$	−11.1759	−0.666698	−0.333349	+	0.942804i	$0.608179\pi$
$282$	22.7962	1.35749
$283$	−16.9507	−1.00762	−0.503808	−	0.863816i	$-0.668068\pi$
$283$	−16.9507	−1.00762	−0.503808	+	0.863816i	$0.668068\pi$
$284$	−1.29132	−0.0766257
$285$	0	0
$286$	24.3218	1.43818
$287$	0.970827	0.0573061
$288$	6.17589	0.363918
$289$	−16.9785	−0.998734
$290$	25.3530	1.48878
$291$	33.5860	1.96885
$292$	9.85539	0.576743
$293$	5.46158	0.319069	0.159534	−	0.987192i	$-0.449001\pi$
$293$	5.46158	0.319069	0.159534	+	0.987192i	$0.449001\pi$
$294$	−3.02917	−0.176665
$295$	8.57329	0.499156
$296$	4.73785	0.275382
$297$	−48.3822	−2.80742
$298$	−0.737853	−0.0427427
$299$	22.0623	1.27589
$300$	−19.2342	−1.11049
$301$	4.53279	0.261266
$302$	14.2926	0.822445
$303$	30.9129	1.77590
$304$	0	0
$305$	−43.9348	−2.51570
$306$	−0.906093	−0.0517979
$307$	−9.81124	−0.559957	−0.279979	−	0.960006i	$-0.590327\pi$
$307$	−9.81124	−0.559957	−0.279979	+	0.960006i	$0.590327\pi$
$308$	5.02917	0.286564
$309$	0.621162	0.0353367
$310$	−4.94291	−0.280739
$311$	−4.79620	−0.271967	−0.135984	−	0.990711i	$-0.543419\pi$
$311$	−4.79620	−0.271967	−0.135984	+	0.990711i	$0.543419\pi$
$312$	−14.6495	−0.829364
$313$	14.3582	0.811571	0.405786	−	0.913968i	$-0.366998\pi$
$313$	14.3582	0.811571	0.405786	+	0.913968i	$0.366998\pi$
$314$	7.90172	0.445920
$315$	−20.8061	−1.17229
$316$	−16.4101	−0.923141
$317$	−15.2208	−0.854885	−0.427443	−	0.904042i	$-0.640585\pi$
$317$	−15.2208	−0.854885	−0.427443	+	0.904042i	$0.640585\pi$
$318$	−7.67227	−0.430239
$319$	−37.8473	−2.11904
$320$	−3.36893	−0.188329
$321$	−28.5268	−1.59221
$322$	4.56197	0.254228
$323$	0	0
$324$	10.6139	0.589662
$325$	30.7078	1.70336
$326$	24.7598	1.37132
$327$	−59.4997	−3.29034
$328$	0.970827	0.0536050
$329$	−7.52555	−0.414897
$330$	51.3230	2.82524
$331$	−19.1260	−1.05126	−0.525631	−	0.850713i	$-0.676171\pi$
$331$	−19.1260	−1.05126	−0.525631	+	0.850713i	$0.676171\pi$
$332$	−11.2243	−0.616015
$333$	29.2604	1.60346
$334$	1.37884	0.0754467
$335$	2.97294	0.162429
$336$	−3.02917	−0.165255
$337$	5.57132	0.303489	0.151744	−	0.988420i	$-0.451511\pi$
$337$	5.57132	0.303489	0.151744	+	0.988420i	$0.451511\pi$
$338$	10.3882	0.565043
$339$	40.0004	2.17252
$340$	0.494271	0.0268056
$341$	7.37884	0.399586
$342$	0	0
$343$	1.00000	0.0539949
$344$	4.53279	0.244392
$345$	46.5551	2.50644
$346$	22.8446	1.22814
$347$	−7.14158	−0.383380	−0.191690	−	0.981455i	$-0.561397\pi$
$347$	−7.14158	−0.383380	−0.191690	+	0.981455i	$0.561397\pi$
$348$	22.7962	1.22200
$349$	−9.13947	−0.489225	−0.244612	−	0.969621i	$-0.578661\pi$
$349$	−9.13947	−0.489225	−0.244612	+	0.969621i	$0.578661\pi$
$350$	6.34967	0.339404
$351$	−46.5251	−2.48333
$352$	5.02917	0.268056
$353$	−19.1459	−1.01903	−0.509516	−	0.860461i	$-0.670175\pi$
$353$	−19.1459	−1.01903	−0.509516	+	0.860461i	$0.670175\pi$
$354$	7.70868	0.409712
$355$	4.35036	0.230893
$356$	−1.94165	−0.102907
$357$	0.444424	0.0235214
$358$	9.38095	0.495798
$359$	26.2136	1.38350	0.691749	−	0.722138i	$-0.256840\pi$
$359$	26.2136	1.38350	0.691749	+	0.722138i	$0.256840\pi$
$360$	−20.8061	−1.09658
$361$	0	0
$362$	−19.0412	−1.00078
$363$	−43.2947	−2.27238
$364$	4.83613	0.253482
$365$	−33.2021	−1.73788
$366$	−39.5040	−2.06491
$367$	−13.6422	−0.712119	−0.356060	−	0.934463i	$-0.615880\pi$
$367$	−13.6422	−0.712119	−0.356060	+	0.934463i	$0.615880\pi$
$368$	4.56197	0.237809
$369$	5.99572	0.312125
$370$	−15.9615	−0.829798
$371$	2.53279	0.131496
$372$	−4.44442	−0.230433
$373$	−28.5328	−1.47737	−0.738686	−	0.674050i	$-0.764553\pi$
$373$	−28.5328	−1.47737	−0.738686	+	0.674050i	$0.764553\pi$
$374$	−0.737853	−0.0381535
$375$	13.7734	0.711256
$376$	−7.52555	−0.388101
$377$	−36.3946	−1.87442
$378$	−9.62031	−0.494815
$379$	2.00850	0.103170	0.0515848	−	0.998669i	$-0.483573\pi$
$379$	2.00850	0.103170	0.0515848	+	0.998669i	$0.483573\pi$
$380$	0	0
$381$	38.9412	1.99502
$382$	10.1459	0.519108
$383$	22.5028	1.14984	0.574919	−	0.818210i	$-0.305034\pi$
$383$	22.5028	1.14984	0.574919	+	0.818210i	$0.305034\pi$
$384$	−3.02917	−0.154582
$385$	−16.9429	−0.863491
$386$	−20.0875	−1.02243
$387$	27.9940	1.42302
$388$	−11.0875	−0.562883
$389$	13.7949	0.699431	0.349716	−	0.936856i	$-0.386278\pi$
$389$	13.7949	0.699431	0.349716	+	0.936856i	$0.386278\pi$
$390$	49.3530	2.49909
$391$	−0.669307	−0.0338483
$392$	1.00000	0.0505076
$393$	−60.9733	−3.07570
$394$	5.50573	0.277375
$395$	55.2845	2.78166
$396$	31.0596	1.56080
$397$	15.9700	0.801510	0.400755	−	0.916185i	$-0.368748\pi$
$397$	15.9700	0.801510	0.400755	+	0.916185i	$0.368748\pi$
$398$	5.46721	0.274046
$399$	0	0
$400$	6.34967	0.317483
$401$	−1.94291	−0.0970244	−0.0485122	−	0.998823i	$-0.515448\pi$
$401$	−1.94291	−0.0970244	−0.0485122	+	0.998823i	$0.515448\pi$
$402$	2.67312	0.133323
$403$	7.09561	0.353457
$404$	−10.2051	−0.507721
$405$	−35.7575	−1.77681
$406$	−7.52555	−0.373487
$407$	23.8275	1.18108
$408$	0.444424	0.0220023
$409$	−4.47234	−0.221143	−0.110571	−	0.993868i	$-0.535268\pi$
$409$	−4.47234	−0.221143	−0.110571	+	0.993868i	$0.535268\pi$
$410$	−3.27065	−0.161526
$411$	14.1531	0.698121
$412$	−0.205060	−0.0101026
$413$	−2.54481	−0.125222
$414$	28.1742	1.38469
$415$	37.8139	1.85621
$416$	4.83613	0.237111
$417$	−30.7555	−1.50610
$418$	0	0
$419$	−0.122673	−0.00599297	−0.00299648	−	0.999996i	$-0.500954\pi$
$419$	−0.122673	−0.00599297	−0.00299648	+	0.999996i	$0.500954\pi$
$420$	10.2051	0.497956
$421$	20.0085	0.975155	0.487577	−	0.873080i	$-0.337881\pi$
$421$	20.0085	0.975155	0.487577	+	0.873080i	$0.337881\pi$
$422$	4.00000	0.194717
$423$	−46.4770	−2.25979
$424$	2.53279	0.123003
$425$	−0.931588	−0.0451887
$426$	3.91163	0.189519
$427$	13.0412	0.631108
$428$	9.41736	0.455205
$429$	−73.6748	−3.55705
$430$	−15.2706	−0.736416
$431$	−0.737853	−0.0355411	−0.0177706	−	0.999842i	$-0.505657\pi$
$431$	−0.737853	−0.0355411	−0.0177706	+	0.999842i	$0.505657\pi$
$432$	−9.62031	−0.462857
$433$	31.0794	1.49358	0.746791	−	0.665059i	$-0.231594\pi$
$433$	31.0794	1.49358	0.746791	+	0.665059i	$0.231594\pi$
$434$	1.46721	0.0704282
$435$	−76.7987	−3.68222
$436$	19.6422	0.940693
$437$	0	0
$438$	−29.8537	−1.42646
$439$	3.33604	0.159220	0.0796101	−	0.996826i	$-0.474632\pi$
$439$	3.33604	0.159220	0.0796101	+	0.996826i	$0.474632\pi$
$440$	−16.9429	−0.807722
$441$	6.17589	0.294090
$442$	−0.709531	−0.0337490
$443$	35.0815	1.66677	0.833387	−	0.552690i	$-0.186399\pi$
$443$	35.0815	1.66677	0.833387	+	0.552690i	$0.186399\pi$
$444$	−14.3518	−0.681105
$445$	6.54129	0.310087
$446$	4.93441	0.233651
$447$	2.23508	0.105716
$448$	1.00000	0.0472456
$449$	4.86883	0.229774	0.114887	−	0.993379i	$-0.463349\pi$
$449$	4.86883	0.229774	0.114887	+	0.993379i	$0.463349\pi$
$450$	39.2148	1.84860
$451$	4.88246	0.229906
$452$	−13.2051	−0.621114
$453$	−43.2947	−2.03416
$454$	2.00352	0.0940300
$455$	−16.2926	−0.763808
$456$	0	0
$457$	−2.23212	−0.104414	−0.0522072	−	0.998636i	$-0.516626\pi$
$457$	−2.23212	−0.104414	−0.0522072	+	0.998636i	$0.516626\pi$
$458$	−2.72372	−0.127271
$459$	1.41144	0.0658804
$460$	−15.3689	−0.716580
$461$	−32.0425	−1.49237	−0.746183	−	0.665741i	$-0.768116\pi$
$461$	−32.0425	−1.49237	−0.746183	+	0.665741i	$0.768116\pi$
$462$	−15.2342	−0.708761
$463$	−1.99487	−0.0927094	−0.0463547	−	0.998925i	$-0.514760\pi$
$463$	−1.99487	−0.0927094	−0.0463547	+	0.998925i	$0.514760\pi$
$464$	−7.52555	−0.349365
$465$	14.9729	0.694353
$466$	−10.6723	−0.494383
$467$	−18.7014	−0.865399	−0.432700	−	0.901538i	$-0.642439\pi$
$467$	−18.7014	−0.865399	−0.432700	+	0.901538i	$0.642439\pi$
$468$	29.8674	1.38062
$469$	−0.882458	−0.0407481
$470$	25.3530	1.16945
$471$	−23.9357	−1.10290
$472$	−2.54481	−0.117135
$473$	22.7962	1.04817
$474$	49.7091	2.28321
$475$	0	0
$476$	−0.146715	−0.00672465
$477$	15.6422	0.716209
$478$	19.2655	0.881184
$479$	38.6537	1.76613	0.883066	−	0.469248i	$-0.155475\pi$
$479$	38.6537	1.76613	0.883066	+	0.469248i	$0.155475\pi$
$480$	10.2051	0.465795
$481$	22.9129	1.04474
$482$	0.912482	0.0415624
$483$	−13.8190	−0.628785
$484$	14.2926	0.649663
$485$	37.3530	1.69611
$486$	−3.29047	−0.149259
$487$	−20.7379	−0.939722	−0.469861	−	0.882740i	$-0.655696\pi$
$487$	−20.7379	−0.939722	−0.469861	+	0.882740i	$0.655696\pi$
$488$	13.0412	0.590347
$489$	−75.0017	−3.39169
$490$	−3.36893	−0.152193
$491$	−12.2934	−0.554795	−0.277397	−	0.960755i	$-0.589472\pi$
$491$	−12.2934	−0.554795	−0.277397	+	0.960755i	$0.589472\pi$
$492$	−2.94080	−0.132582
$493$	1.10411	0.0497265
$494$	0	0
$495$	−104.638	−4.70311
$496$	1.46721	0.0658795
$497$	−1.29132	−0.0579236
$498$	34.0004	1.52359
$499$	25.4976	1.14143	0.570716	−	0.821148i	$-0.306666\pi$
$499$	25.4976	1.14143	0.570716	+	0.821148i	$0.306666\pi$
$500$	−4.54692	−0.203345
$501$	−4.17674	−0.186603
$502$	2.30123	0.102709
$503$	−8.18524	−0.364962	−0.182481	−	0.983209i	$-0.558413\pi$
$503$	−8.18524	−0.364962	−0.182481	+	0.983209i	$0.558413\pi$
$504$	6.17589	0.275096
$505$	34.3801	1.52989
$506$	22.9429	1.01994
$507$	−31.4676	−1.39753
$508$	−12.8554	−0.570366
$509$	29.2119	1.29480	0.647398	−	0.762152i	$-0.275857\pi$
$509$	29.2119	1.29480	0.647398	+	0.762152i	$0.275857\pi$
$510$	−1.49723	−0.0662985
$511$	9.85539	0.435977
$512$	1.00000	0.0441942
$513$	0	0
$514$	12.2114	0.538624
$515$	0.690832	0.0304417
$516$	−13.7306	−0.604457
$517$	−37.8473	−1.66452
$518$	4.73785	0.208169
$519$	−69.2003	−3.03756
$520$	−16.2926	−0.714477
$521$	−7.75853	−0.339907	−0.169954	−	0.985452i	$-0.554362\pi$
$521$	−7.75853	−0.339907	−0.169954	+	0.985452i	$0.554362\pi$
$522$	−46.4770	−2.03424
$523$	−7.87733	−0.344451	−0.172226	−	0.985058i	$-0.555096\pi$
$523$	−7.87733	−0.344451	−0.172226	+	0.985058i	$0.555096\pi$
$524$	20.1287	0.879327
$525$	−19.2342	−0.839451
$526$	−0.356906	−0.0155618
$527$	−0.215261	−0.00937690
$528$	−15.2342	−0.662985
$529$	−2.18847	−0.0951509
$530$	−8.53279	−0.370641
$531$	−15.7165	−0.682037
$532$	0	0
$533$	4.69505	0.203365
$534$	5.88161	0.254522
$535$	−31.7264	−1.37165
$536$	−0.882458	−0.0381164
$537$	−28.4165	−1.22626
$538$	−0.591138	−0.0254858
$539$	5.02917	0.216622
$540$	32.4101	1.39471
$541$	−27.7547	−1.19327	−0.596633	−	0.802514i	$-0.703495\pi$
$541$	−27.7547	−1.19327	−0.596633	+	0.802514i	$0.703495\pi$
$542$	25.1395	1.07983
$543$	57.6791	2.47525
$544$	−0.146715	−0.00629033
$545$	−66.1733	−2.83455
$546$	−14.6495	−0.626940
$547$	22.4186	0.958551	0.479275	−	0.877665i	$-0.340899\pi$
$547$	22.4186	0.958551	0.479275	+	0.877665i	$0.340899\pi$
$548$	−4.67227	−0.199589
$549$	80.5409	3.43740
$550$	31.9336	1.36165
$551$	0	0
$552$	−13.8190	−0.588175
$553$	−16.4101	−0.697829
$554$	−14.0824	−0.598303
$555$	48.3501	2.05235
$556$	10.1531	0.430588
$557$	−27.1480	−1.15030	−0.575148	−	0.818049i	$-0.695056\pi$
$557$	−27.1480	−1.15030	−0.575148	+	0.818049i	$0.695056\pi$
$558$	9.06131	0.383596
$559$	21.9212	0.927168
$560$	−3.36893	−0.142363
$561$	2.23508	0.0943653
$562$	−11.1759	−0.471426
$563$	−22.2454	−0.937532	−0.468766	−	0.883322i	$-0.655301\pi$
$563$	−22.2454	−0.937532	−0.468766	+	0.883322i	$0.655301\pi$
$564$	22.7962	0.959893
$565$	44.4869	1.87158
$566$	−16.9507	−0.712492
$567$	10.6139	0.445743
$568$	−1.29132	−0.0541826
$569$	4.26426	0.178767	0.0893835	−	0.995997i	$-0.471510\pi$
$569$	4.26426	0.178767	0.0893835	+	0.995997i	$0.471510\pi$
$570$	0	0
$571$	18.1446	0.759328	0.379664	−	0.925124i	$-0.376040\pi$
$571$	18.1446	0.759328	0.379664	+	0.925124i	$0.376040\pi$
$572$	24.3218	1.01694
$573$	−30.7336	−1.28391
$574$	0.970827	0.0405215
$575$	28.9670	1.20801
$576$	6.17589	0.257329
$577$	−14.3196	−0.596134	−0.298067	−	0.954545i	$-0.596342\pi$
$577$	−14.3196	−0.596134	−0.298067	+	0.954545i	$0.596342\pi$
$578$	−16.9785	−0.706211
$579$	60.8486	2.52878
$580$	25.3530	1.05273
$581$	−11.2243	−0.465663
$582$	33.5860	1.39218
$583$	12.7379	0.527548
$584$	9.85539	0.407819
$585$	−100.621	−4.16017
$586$	5.46158	0.225616
$587$	−28.7277	−1.18572	−0.592859	−	0.805307i	$-0.702001\pi$
$587$	−28.7277	−1.18572	−0.592859	+	0.805307i	$0.702001\pi$
$588$	−3.02917	−0.124921
$589$	0	0
$590$	8.57329	0.352957
$591$	−16.6778	−0.686033
$592$	4.73785	0.194725
$593$	−36.2114	−1.48703	−0.743513	−	0.668721i	$-0.766842\pi$
$593$	−36.2114	−1.48703	−0.743513	+	0.668721i	$0.766842\pi$
$594$	−48.3822	−1.98515
$595$	0.494271	0.0202631
$596$	−0.737853	−0.0302236
$597$	−16.5611	−0.677801
$598$	22.0623	0.902194
$599$	−16.0490	−0.655744	−0.327872	−	0.944722i	$-0.606332\pi$
$599$	−16.0490	−0.655744	−0.327872	+	0.944722i	$0.606332\pi$
$600$	−19.2342	−0.785234
$601$	26.0004	1.06058	0.530289	−	0.847817i	$-0.322083\pi$
$601$	26.0004	1.06058	0.530289	+	0.847817i	$0.322083\pi$
$602$	4.53279	0.184743
$603$	−5.44996	−0.221940
$604$	14.2926	0.581557
$605$	−48.1506	−1.95760
$606$	30.9129	1.25575
$607$	−1.06559	−0.0432508	−0.0216254	−	0.999766i	$-0.506884\pi$
$607$	−1.06559	−0.0432508	−0.0216254	+	0.999766i	$0.506884\pi$
$608$	0	0
$609$	22.7962	0.923749
$610$	−43.9348	−1.77887
$611$	−36.3946	−1.47237
$612$	−0.906093	−0.0366266
$613$	−28.8390	−1.16480	−0.582398	−	0.812904i	$-0.697886\pi$
$613$	−28.8390	−1.16480	−0.582398	+	0.812904i	$0.697886\pi$
$614$	−9.81124	−0.395949
$615$	9.90735	0.399503
$616$	5.02917	0.202631
$617$	−21.6880	−0.873126	−0.436563	−	0.899674i	$-0.643804\pi$
$617$	−21.6880	−0.873126	−0.436563	+	0.899674i	$0.643804\pi$
$618$	0.621162	0.0249868
$619$	1.33890	0.0538150	0.0269075	−	0.999638i	$-0.491434\pi$
$619$	1.33890	0.0538150	0.0269075	+	0.999638i	$0.491434\pi$
$620$	−4.94291	−0.198512
$621$	−43.8875	−1.76115
$622$	−4.79620	−0.192310
$623$	−1.94165	−0.0777907
$624$	−14.6495	−0.586449
$625$	−16.4301	−0.657203
$626$	14.3582	0.573868
$627$	0	0
$628$	7.90172	0.315313
$629$	−0.695112	−0.0277159
$630$	−20.8061	−0.828935
$631$	−5.86883	−0.233634	−0.116817	−	0.993153i	$-0.537269\pi$
$631$	−5.86883	−0.233634	−0.116817	+	0.993153i	$0.537269\pi$
$632$	−16.4101	−0.652760
$633$	−12.1167	−0.481595
$634$	−15.2208	−0.604495
$635$	43.3089	1.71866
$636$	−7.67227	−0.304225
$637$	4.83613	0.191615
$638$	−37.8473	−1.49839
$639$	−7.97505	−0.315488
$640$	−3.36893	−0.133169
$641$	46.9725	1.85530	0.927651	−	0.373448i	$-0.121825\pi$
$641$	46.9725	1.85530	0.927651	+	0.373448i	$0.121825\pi$
$642$	−28.5268	−1.12586
$643$	24.6615	0.972555	0.486277	−	0.873804i	$-0.338354\pi$
$643$	24.6615	0.972555	0.486277	+	0.873804i	$0.338354\pi$
$644$	4.56197	0.179767
$645$	46.2574	1.82138
$646$	0	0
$647$	−30.7662	−1.20954	−0.604772	−	0.796399i	$-0.706736\pi$
$647$	−30.7662	−1.20954	−0.604772	+	0.796399i	$0.706736\pi$
$648$	10.6139	0.416954
$649$	−12.7983	−0.502378
$650$	30.7078	1.20446
$651$	−4.44442	−0.174191
$652$	24.7598	0.969668
$653$	9.42164	0.368697	0.184349	−	0.982861i	$-0.440982\pi$
$653$	9.42164	0.368697	0.184349	+	0.982861i	$0.440982\pi$
$654$	−59.4997	−2.32662
$655$	−67.8121	−2.64964
$656$	0.970827	0.0379044
$657$	60.8658	2.37460
$658$	−7.52555	−0.293377
$659$	−2.18952	−0.0852915	−0.0426457	−	0.999090i	$-0.513579\pi$
$659$	−2.18952	−0.0852915	−0.0426457	+	0.999090i	$0.513579\pi$
$660$	51.3230	1.99775
$661$	25.9102	1.00779	0.503895	−	0.863765i	$-0.331900\pi$
$661$	25.9102	1.00779	0.503895	+	0.863765i	$0.331900\pi$
$662$	−19.1260	−0.743355
$663$	2.14929	0.0834716
$664$	−11.2243	−0.435588
$665$	0	0
$666$	29.2604	1.13382
$667$	−34.3313	−1.32931
$668$	1.37884	0.0533488
$669$	−14.9472	−0.577892
$670$	2.97294	0.114855
$671$	65.5864	2.53194
$672$	−3.02917	−0.116853
$673$	12.8169	0.494054	0.247027	−	0.969009i	$-0.420546\pi$
$673$	12.8169	0.494054	0.247027	+	0.969009i	$0.420546\pi$
$674$	5.57132	0.214599
$675$	−61.0858	−2.35119
$676$	10.3882	0.399546
$677$	24.5183	0.942315	0.471158	−	0.882049i	$-0.343836\pi$
$677$	24.5183	0.942315	0.471158	+	0.882049i	$0.343836\pi$
$678$	40.0004	1.53621
$679$	−11.0875	−0.425500
$680$	0.494271	0.0189544
$681$	−6.06901	−0.232565
$682$	7.37884	0.282550
$683$	42.3999	1.62239	0.811194	−	0.584777i	$-0.198818\pi$
$683$	42.3999	1.62239	0.811194	+	0.584777i	$0.198818\pi$
$684$	0	0
$685$	15.7405	0.601415
$686$	1.00000	0.0381802
$687$	8.25063	0.314781
$688$	4.53279	0.172811
$689$	12.2489	0.466647
$690$	46.5551	1.77232
$691$	47.8417	1.81998	0.909991	−	0.414627i	$-0.136088\pi$
$691$	47.8417	1.81998	0.909991	+	0.414627i	$0.136088\pi$
$692$	22.8446	0.868423
$693$	31.0596	1.17986
$694$	−7.14158	−0.271091
$695$	−34.2051	−1.29747
$696$	22.7962	0.864088
$697$	−0.142434	−0.00539509
$698$	−9.13947	−0.345934
$699$	32.3281	1.22276
$700$	6.34967	0.239995
$701$	−13.4570	−0.508264	−0.254132	−	0.967170i	$-0.581790\pi$
$701$	−13.4570	−0.508264	−0.254132	+	0.967170i	$0.581790\pi$
$702$	−46.5251	−1.75598
$703$	0	0
$704$	5.02917	0.189544
$705$	−76.7987	−2.89241
$706$	−19.1459	−0.720564
$707$	−10.2051	−0.383801
$708$	7.70868	0.289710
$709$	0.401621	0.0150832	0.00754160	−	0.999972i	$-0.497599\pi$
$709$	0.401621	0.0150832	0.00754160	+	0.999972i	$0.497599\pi$
$710$	4.35036	0.163266
$711$	−101.347	−3.80081
$712$	−1.94165	−0.0727666
$713$	6.69335	0.250668
$714$	0.444424	0.0166321
$715$	−81.9382	−3.06431
$716$	9.38095	0.350582
$717$	−58.3586	−2.17944
$718$	26.2136	0.978281
$719$	−25.5298	−0.952102	−0.476051	−	0.879418i	$-0.657932\pi$
$719$	−25.5298	−0.952102	−0.476051	+	0.879418i	$0.657932\pi$
$720$	−20.8061	−0.775398
$721$	−0.205060	−0.00763683
$722$	0	0
$723$	−2.76407	−0.102797
$724$	−19.0412	−0.707660
$725$	−47.7847	−1.77468
$726$	−43.2947	−1.60682
$727$	−13.9074	−0.515795	−0.257898	−	0.966172i	$-0.583030\pi$
$727$	−13.9074	−0.515795	−0.257898	+	0.966172i	$0.583030\pi$
$728$	4.83613	0.179239
$729$	−21.8744	−0.810162
$730$	−33.2021	−1.22886
$731$	−0.665027	−0.0245969
$732$	−39.5040	−1.46011
$733$	36.1591	1.33557	0.667784	−	0.744355i	$-0.267243\pi$
$733$	36.1591	1.33557	0.667784	+	0.744355i	$0.267243\pi$
$734$	−13.6422	−0.503544
$735$	10.2051	0.376419
$736$	4.56197	0.168156
$737$	−4.43803	−0.163477
$738$	5.99572	0.220706
$739$	44.2355	1.62723	0.813614	−	0.581405i	$-0.197497\pi$
$739$	44.2355	1.62723	0.813614	+	0.581405i	$0.197497\pi$
$740$	−15.9615	−0.586756
$741$	0	0
$742$	2.53279	0.0929818
$743$	28.4436	1.04349	0.521747	−	0.853100i	$-0.325281\pi$
$743$	28.4436	1.04349	0.521747	+	0.853100i	$0.325281\pi$
$744$	−4.44442	−0.162940
$745$	2.48577	0.0910716
$746$	−28.5328	−1.04466
$747$	−69.3201	−2.53629
$748$	−0.737853	−0.0269786
$749$	9.41736	0.344103
$750$	13.7734	0.502934
$751$	36.6393	1.33699	0.668493	−	0.743718i	$-0.266940\pi$
$751$	36.6393	1.33699	0.668493	+	0.743718i	$0.266940\pi$
$752$	−7.52555	−0.274429
$753$	−6.97083	−0.254031
$754$	−36.3946	−1.32541
$755$	−48.1506	−1.75238
$756$	−9.62031	−0.349887
$757$	−18.3886	−0.668345	−0.334172	−	0.942512i	$-0.608457\pi$
$757$	−18.3886	−0.668345	−0.334172	+	0.942512i	$0.608457\pi$
$758$	2.00850	0.0729520
$759$	−69.4980	−2.52262
$760$	0	0
$761$	50.0588	1.81463	0.907314	−	0.420453i	$-0.138129\pi$
$761$	50.0588	1.81463	0.907314	+	0.420453i	$0.138129\pi$
$762$	38.9412	1.41069
$763$	19.6422	0.711097
$764$	10.1459	0.367064
$765$	3.05256	0.110366
$766$	22.5028	0.813058
$767$	−12.3071	−0.444382
$768$	−3.02917	−0.109306
$769$	10.2874	0.370975	0.185487	−	0.982647i	$-0.440614\pi$
$769$	10.2874	0.370975	0.185487	+	0.982647i	$0.440614\pi$
$770$	−16.9429	−0.610580
$771$	−36.9906	−1.33218
$772$	−20.0875	−0.722966
$773$	24.8832	0.894985	0.447492	−	0.894288i	$-0.352317\pi$
$773$	24.8832	0.894985	0.447492	+	0.894288i	$0.352317\pi$
$774$	27.9940	1.00622
$775$	9.31627	0.334650
$776$	−11.0875	−0.398019
$777$	−14.3518	−0.514867
$778$	13.7949	0.494573
$779$	0	0
$780$	49.3530	1.76712
$781$	−6.49427	−0.232383
$782$	−0.669307	−0.0239344
$783$	72.3982	2.58730
$784$	1.00000	0.0357143
$785$	−26.6203	−0.950120
$786$	−60.9733	−2.17485
$787$	46.8751	1.67092	0.835458	−	0.549555i	$-0.185203\pi$
$787$	46.8751	1.67092	0.835458	+	0.549555i	$0.185203\pi$
$788$	5.50573	0.196133
$789$	1.08113	0.0384892
$790$	55.2845	1.96693
$791$	−13.2051	−0.469518
$792$	31.0596	1.10365
$793$	63.0690	2.23964
$794$	15.9700	0.566753
$795$	25.8473	0.916709
$796$	5.46721	0.193780
$797$	−19.9456	−0.706509	−0.353254	−	0.935527i	$-0.614925\pi$
$797$	−19.9456	−0.706509	−0.353254	+	0.935527i	$0.614925\pi$
$798$	0	0
$799$	1.10411	0.0390605
$800$	6.34967	0.224495
$801$	−11.9914	−0.423697
$802$	−1.94291	−0.0686066
$803$	49.5645	1.74909
$804$	2.67312	0.0942736
$805$	−15.3689	−0.541683
$806$	7.09561	0.249932
$807$	1.79066	0.0630342
$808$	−10.2051	−0.359013
$809$	32.1635	1.13081	0.565404	−	0.824814i	$-0.308720\pi$
$809$	32.1635	1.13081	0.565404	+	0.824814i	$0.308720\pi$
$810$	−35.7575	−1.25639
$811$	26.3801	0.926330	0.463165	−	0.886272i	$-0.346714\pi$
$811$	26.3801	0.926330	0.463165	+	0.886272i	$0.346714\pi$
$812$	−7.52555	−0.264095
$813$	−76.1518	−2.67076
$814$	23.8275	0.835153
$815$	−83.4139	−2.92186
$816$	0.444424	0.0155579
$817$	0	0
$818$	−4.47234	−0.156372
$819$	29.8674	1.04365
$820$	−3.27065	−0.114216
$821$	−23.9272	−0.835064	−0.417532	−	0.908662i	$-0.637105\pi$
$821$	−23.9272	−0.835064	−0.417532	+	0.908662i	$0.637105\pi$
$822$	14.1531	0.493646
$823$	44.5747	1.55378	0.776888	−	0.629639i	$-0.216797\pi$
$823$	44.5747	1.55378	0.776888	+	0.629639i	$0.216797\pi$
$824$	−0.205060	−0.00714360
$825$	−96.7323	−3.36779
$826$	−2.54481	−0.0885454
$827$	−38.2553	−1.33027	−0.665134	−	0.746724i	$-0.731626\pi$
$827$	−38.2553	−1.33027	−0.665134	+	0.746724i	$0.731626\pi$
$828$	28.1742	0.979121
$829$	22.3203	0.775217	0.387609	−	0.921824i	$-0.373301\pi$
$829$	22.3203	0.775217	0.387609	+	0.921824i	$0.373301\pi$
$830$	37.8139	1.31254
$831$	42.6580	1.47979
$832$	4.83613	0.167663
$833$	−0.146715	−0.00508336
$834$	−30.7555	−1.06498
$835$	−4.64520	−0.160754
$836$	0	0
$837$	−14.1150	−0.487885
$838$	−0.122673	−0.00423767
$839$	5.55558	0.191800	0.0958999	−	0.995391i	$-0.469427\pi$
$839$	5.55558	0.191800	0.0958999	+	0.995391i	$0.469427\pi$
$840$	10.2051	0.352108
$841$	27.6339	0.952895
$842$	20.0085	0.689538
$843$	33.8537	1.16598
$844$	4.00000	0.137686
$845$	−34.9970	−1.20393
$846$	−46.4770	−1.59791
$847$	14.2926	0.491099
$848$	2.53279	0.0869765
$849$	51.3466	1.76221
$850$	−0.931588	−0.0319532
$851$	21.6139	0.740916
$852$	3.91163	0.134010
$853$	49.2604	1.68664	0.843322	−	0.537409i	$-0.180597\pi$
$853$	49.2604	1.68664	0.843322	+	0.537409i	$0.180597\pi$
$854$	13.0412	0.446260
$855$	0	0
$856$	9.41736	0.321879
$857$	8.49638	0.290231	0.145115	−	0.989415i	$-0.453645\pi$
$857$	8.49638	0.290231	0.145115	+	0.989415i	$0.453645\pi$
$858$	−73.6748	−2.51522
$859$	17.8254	0.608194	0.304097	−	0.952641i	$-0.401645\pi$
$859$	17.8254	0.608194	0.304097	+	0.952641i	$0.401645\pi$
$860$	−15.2706	−0.520725
$861$	−2.94080	−0.100222
$862$	−0.737853	−0.0251314
$863$	11.3403	0.386029	0.193014	−	0.981196i	$-0.438174\pi$
$863$	11.3403	0.386029	0.193014	+	0.981196i	$0.438174\pi$
$864$	−9.62031	−0.327290
$865$	−76.9619	−2.61678
$866$	31.0794	1.05612
$867$	51.4307	1.74668
$868$	1.46721	0.0498003
$869$	−82.5293	−2.79962
$870$	−76.7987	−2.60372
$871$	−4.26769	−0.144605
$872$	19.6422	0.665170
$873$	−68.4753	−2.31754
$874$	0	0
$875$	−4.54692	−0.153714
$876$	−29.8537	−1.00866
$877$	−13.7349	−0.463794	−0.231897	−	0.972740i	$-0.574493\pi$
$877$	−13.7349	−0.463794	−0.231897	+	0.972740i	$0.574493\pi$
$878$	3.33604	0.112586
$879$	−16.5441	−0.558017
$880$	−16.9429	−0.571145
$881$	8.29554	0.279484	0.139742	−	0.990188i	$-0.455373\pi$
$881$	8.29554	0.279484	0.139742	+	0.990188i	$0.455373\pi$
$882$	6.17589	0.207953
$883$	31.0034	1.04335	0.521673	−	0.853145i	$-0.325308\pi$
$883$	31.0034	1.04335	0.521673	+	0.853145i	$0.325308\pi$
$884$	−0.709531	−0.0238641
$885$	−25.9700	−0.872971
$886$	35.0815	1.17859
$887$	58.3543	1.95935	0.979673	−	0.200603i	$-0.0642901\pi$
$887$	58.3543	1.95935	0.979673	+	0.200603i	$0.0642901\pi$
$888$	−14.3518	−0.481614
$889$	−12.8554	−0.431156
$890$	6.54129	0.219265
$891$	53.3792	1.78827
$892$	4.93441	0.165216
$893$	0	0
$894$	2.23508	0.0747524
$895$	−31.6037	−1.05640
$896$	1.00000	0.0334077
$897$	−66.8304	−2.23140
$898$	4.86883	0.162475
$899$	−11.0415	−0.368256
$900$	39.2148	1.30716
$901$	−0.371598	−0.0123797
$902$	4.88246	0.162568
$903$	−13.7306	−0.456926
$904$	−13.2051	−0.439194
$905$	64.1484	2.13236
$906$	−43.2947	−1.43837
$907$	16.9751	0.563649	0.281825	−	0.959466i	$-0.409060\pi$
$907$	16.9751	0.563649	0.281825	+	0.959466i	$0.409060\pi$
$908$	2.00352	0.0664892
$909$	−63.0253	−2.09042
$910$	−16.2926	−0.540094
$911$	−16.8339	−0.557731	−0.278865	−	0.960330i	$-0.589958\pi$
$911$	−16.8339	−0.557731	−0.278865	+	0.960330i	$0.589958\pi$
$912$	0	0
$913$	−56.4490	−1.86819
$914$	−2.23212	−0.0738321
$915$	133.086	4.39969
$916$	−2.72372	−0.0899943
$917$	20.1287	0.664709
$918$	1.41144	0.0465845
$919$	50.2084	1.65622	0.828112	−	0.560563i	$-0.189415\pi$
$919$	50.2084	1.65622	0.828112	+	0.560563i	$0.189415\pi$
$920$	−15.3689	−0.506698
$921$	29.7199	0.979305
$922$	−32.0425	−1.05526
$923$	−6.24500	−0.205557
$924$	−15.2342	−0.501169
$925$	30.0838	0.989149
$926$	−1.99487	−0.0655555
$927$	−1.26643	−0.0415949
$928$	−7.52555	−0.247038
$929$	−41.5988	−1.36481	−0.682406	−	0.730973i	$-0.739066\pi$
$929$	−41.5988	−1.36481	−0.682406	+	0.730973i	$0.739066\pi$
$930$	14.9729	0.490982
$931$	0	0
$932$	−10.6723	−0.349582
$933$	14.5285	0.475642
$934$	−18.7014	−0.611930
$935$	2.48577	0.0812934
$936$	29.8674	0.976247
$937$	−24.6474	−0.805195	−0.402597	−	0.915377i	$-0.631892\pi$
$937$	−24.6474	−0.805195	−0.402597	+	0.915377i	$0.631892\pi$
$938$	−0.882458	−0.0288133
$939$	−43.4934	−1.41935
$940$	25.3530	0.826925
$941$	−21.8632	−0.712720	−0.356360	−	0.934349i	$-0.615982\pi$
$941$	−21.8632	−0.712720	−0.356360	+	0.934349i	$0.615982\pi$
$942$	−23.9357	−0.779866
$943$	4.42888	0.144224
$944$	−2.54481	−0.0828266
$945$	32.4101	1.05430
$946$	22.7962	0.741168
$947$	−43.4810	−1.41294	−0.706472	−	0.707741i	$-0.749714\pi$
$947$	−43.4810	−1.41294	−0.706472	+	0.707741i	$0.749714\pi$
$948$	49.7091	1.61448
$949$	47.6620	1.54717
$950$	0	0
$951$	46.1064	1.49510
$952$	−0.146715	−0.00475505
$953$	−55.7155	−1.80480	−0.902401	−	0.430898i	$-0.858197\pi$
$953$	−55.7155	−1.80480	−0.902401	+	0.430898i	$0.858197\pi$
$954$	15.6422	0.506436
$955$	−34.1807	−1.10606
$956$	19.2655	0.623091
$957$	114.646	3.70598
$958$	38.6537	1.24884
$959$	−4.67227	−0.150875
$960$	10.2051	0.329367
$961$	−28.8473	−0.930558
$962$	22.9129	0.738741
$963$	58.1606	1.87420
$964$	0.912482	0.0293891
$965$	67.6734	2.17848
$966$	−13.8190	−0.444618
$967$	21.4621	0.690174	0.345087	−	0.938571i	$-0.387849\pi$
$967$	21.4621	0.690174	0.345087	+	0.938571i	$0.387849\pi$
$968$	14.2926	0.459381
$969$	0	0
$970$	37.3530	1.19933
$971$	−29.5274	−0.947578	−0.473789	−	0.880638i	$-0.657114\pi$
$971$	−29.5274	−0.947578	−0.473789	+	0.880638i	$0.657114\pi$
$972$	−3.29047	−0.105542
$973$	10.1531	0.325494
$974$	−20.7379	−0.664484
$975$	−93.0193	−2.97900
$976$	13.0412	0.417438
$977$	21.2988	0.681408	0.340704	−	0.940171i	$-0.389335\pi$
$977$	21.2988	0.681408	0.340704	+	0.940171i	$0.389335\pi$
$978$	−75.0017	−2.39829
$979$	−9.76492	−0.312088
$980$	−3.36893	−0.107616
$981$	121.308	3.87308
$982$	−12.2934	−0.392299
$983$	−4.05835	−0.129441	−0.0647206	−	0.997903i	$-0.520616\pi$
$983$	−4.05835	−0.129441	−0.0647206	+	0.997903i	$0.520616\pi$
$984$	−2.94080	−0.0937494
$985$	−18.5484	−0.591001
$986$	1.10411	0.0351620
$987$	22.7962	0.725611
$988$	0	0
$989$	20.6784	0.657536
$990$	−104.638	−3.32560
$991$	33.8422	1.07503	0.537516	−	0.843254i	$-0.319363\pi$
$991$	33.8422	1.07503	0.537516	+	0.843254i	$0.319363\pi$
$992$	1.46721	0.0465839
$993$	57.9361	1.83855
$994$	−1.29132	−0.0409582
$995$	−18.4186	−0.583909
$996$	34.0004	1.07734
$997$	51.3612	1.62663	0.813313	−	0.581826i	$-0.197661\pi$
$997$	51.3612	1.62663	0.813313	+	0.581826i	$0.197661\pi$
$998$	25.4976	0.807114
$999$	−45.5796	−1.44208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.x.1.1		4
19.8	odd	6		266.2.f.d.197.1	✓	8
19.12	odd	6		266.2.f.d.239.1	yes	8
19.18	odd	2		5054.2.a.w.1.4		4
57.8	even	6		2394.2.o.v.1261.1		8
57.50	even	6		2394.2.o.v.505.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.d.197.1	✓	8	19.8	odd	6
266.2.f.d.239.1	yes	8	19.12	odd	6
2394.2.o.v.505.1		8	57.50	even	6
2394.2.o.v.1261.1		8	57.8	even	6
5054.2.a.w.1.4		4	19.18	odd	2
5054.2.a.x.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.02917 q^{3} +1.00000 q^{4} -3.36893 q^{5} -3.02917 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.17589 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.02917 q^{3} +1.00000 q^{4} -3.36893 q^{5} -3.02917 q^{6} +1.00000 q^{7} +1.00000 q^{8} +6.17589 q^{9} -3.36893 q^{10} +5.02917 q^{11} -3.02917 q^{12} +4.83613 q^{13} +1.00000 q^{14} +10.2051 q^{15} +1.00000 q^{16} -0.146715 q^{17} +6.17589 q^{18} -3.36893 q^{20} -3.02917 q^{21} +5.02917 q^{22} +4.56197 q^{23} -3.02917 q^{24} +6.34967 q^{25} +4.83613 q^{26} -9.62031 q^{27} +1.00000 q^{28} -7.52555 q^{29} +10.2051 q^{30} +1.46721 q^{31} +1.00000 q^{32} -15.2342 q^{33} -0.146715 q^{34} -3.36893 q^{35} +6.17589 q^{36} +4.73785 q^{37} -14.6495 q^{39} -3.36893 q^{40} +0.970827 q^{41} -3.02917 q^{42} +4.53279 q^{43} +5.02917 q^{44} -20.8061 q^{45} +4.56197 q^{46} -7.52555 q^{47} -3.02917 q^{48} +1.00000 q^{49} +6.34967 q^{50} +0.444424 q^{51} +4.83613 q^{52} +2.53279 q^{53} -9.62031 q^{54} -16.9429 q^{55} +1.00000 q^{56} -7.52555 q^{58} -2.54481 q^{59} +10.2051 q^{60} +13.0412 q^{61} +1.46721 q^{62} +6.17589 q^{63} +1.00000 q^{64} -16.2926 q^{65} -15.2342 q^{66} -0.882458 q^{67} -0.146715 q^{68} -13.8190 q^{69} -3.36893 q^{70} -1.29132 q^{71} +6.17589 q^{72} +9.85539 q^{73} +4.73785 q^{74} -19.2342 q^{75} +5.02917 q^{77} -14.6495 q^{78} -16.4101 q^{79} -3.36893 q^{80} +10.6139 q^{81} +0.970827 q^{82} -11.2243 q^{83} -3.02917 q^{84} +0.494271 q^{85} +4.53279 q^{86} +22.7962 q^{87} +5.02917 q^{88} -1.94165 q^{89} -20.8061 q^{90} +4.83613 q^{91} +4.56197 q^{92} -4.44442 q^{93} -7.52555 q^{94} -3.02917 q^{96} -11.0875 q^{97} +1.00000 q^{98} +31.0596 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} + q^{12} + 5 q^{13} + 4 q^{14} + 12 q^{15} + 4 q^{16} + 2 q^{17} + 9 q^{18} + q^{20} + q^{21} + 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} + q^{27} + 4 q^{28} - 4 q^{29} + 12 q^{30} + 6 q^{31} + 4 q^{32} - 19 q^{33} + 2 q^{34} + q^{35} + 9 q^{36} - 10 q^{37} - 6 q^{39} + q^{40} + 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} + 5 q^{46} - 4 q^{47} + q^{48} + 4 q^{49} + 15 q^{50} - 22 q^{51} + 5 q^{52} + 10 q^{53} + q^{54} - 10 q^{55} + 4 q^{56} - 4 q^{58} + 20 q^{59} + 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} + 3 q^{65} - 19 q^{66} + 7 q^{67} + 2 q^{68} - 24 q^{69} + q^{70} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 10 q^{74} - 35 q^{75} + 7 q^{77} - 6 q^{78} - 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} + q^{84} + 10 q^{85} + 18 q^{86} + 36 q^{87} + 7 q^{88} - 34 q^{89} - 19 q^{90} + 5 q^{91} + 5 q^{92} + 6 q^{93} - 4 q^{94} + q^{96} - 5 q^{97} + 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 + q^12 + 5 * q^13 + 4 * q^14 + 12 * q^15 + 4 * q^16 + 2 * q^17 + 9 * q^18 + q^20 + q^21 + 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 + q^27 + 4 * q^28 - 4 * q^29 + 12 * q^30 + 6 * q^31 + 4 * q^32 - 19 * q^33 + 2 * q^34 + q^35 + 9 * q^36 - 10 * q^37 - 6 * q^39 + q^40 + 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 + 5 * q^46 - 4 * q^47 + q^48 + 4 * q^49 + 15 * q^50 - 22 * q^51 + 5 * q^52 + 10 * q^53 + q^54 - 10 * q^55 + 4 * q^56 - 4 * q^58 + 20 * q^59 + 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 + 3 * q^65 - 19 * q^66 + 7 * q^67 + 2 * q^68 - 24 * q^69 + q^70 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 10 * q^74 - 35 * q^75 + 7 * q^77 - 6 * q^78 - 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 + q^84 + 10 * q^85 + 18 * q^86 + 36 * q^87 + 7 * q^88 - 34 * q^89 - 19 * q^90 + 5 * q^91 + 5 * q^92 + 6 * q^93 - 4 * q^94 + q^96 - 5 * q^97 + 4 * q^98 + 14 * q^99

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