LMFDB - Embedded newform 4022.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.367906 q^{3} +1.00000 q^{4} +2.32640 q^{5} -0.367906 q^{6} +1.76735 q^{7} +1.00000 q^{8} -2.86465 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.367906 q^{3} +1.00000 q^{4} +2.32640 q^{5} -0.367906 q^{6} +1.76735 q^{7} +1.00000 q^{8} -2.86465 q^{9} +2.32640 q^{10} -4.04135 q^{11} -0.367906 q^{12} +6.40019 q^{13} +1.76735 q^{14} -0.855897 q^{15} +1.00000 q^{16} +7.48899 q^{17} -2.86465 q^{18} +4.29470 q^{19} +2.32640 q^{20} -0.650218 q^{21} -4.04135 q^{22} +2.11647 q^{23} -0.367906 q^{24} +0.412142 q^{25} +6.40019 q^{26} +2.15764 q^{27} +1.76735 q^{28} -2.61558 q^{29} -0.855897 q^{30} -4.42568 q^{31} +1.00000 q^{32} +1.48684 q^{33} +7.48899 q^{34} +4.11156 q^{35} -2.86465 q^{36} -1.37714 q^{37} +4.29470 q^{38} -2.35467 q^{39} +2.32640 q^{40} -8.98546 q^{41} -0.650218 q^{42} -1.17052 q^{43} -4.04135 q^{44} -6.66431 q^{45} +2.11647 q^{46} +5.71735 q^{47} -0.367906 q^{48} -3.87648 q^{49} +0.412142 q^{50} -2.75524 q^{51} +6.40019 q^{52} -8.17181 q^{53} +2.15764 q^{54} -9.40180 q^{55} +1.76735 q^{56} -1.58005 q^{57} -2.61558 q^{58} +9.38684 q^{59} -0.855897 q^{60} +8.55362 q^{61} -4.42568 q^{62} -5.06283 q^{63} +1.00000 q^{64} +14.8894 q^{65} +1.48684 q^{66} +12.0253 q^{67} +7.48899 q^{68} -0.778661 q^{69} +4.11156 q^{70} +6.77247 q^{71} -2.86465 q^{72} -7.93017 q^{73} -1.37714 q^{74} -0.151629 q^{75} +4.29470 q^{76} -7.14247 q^{77} -2.35467 q^{78} -4.66523 q^{79} +2.32640 q^{80} +7.80013 q^{81} -8.98546 q^{82} +17.8218 q^{83} -0.650218 q^{84} +17.4224 q^{85} -1.17052 q^{86} +0.962288 q^{87} -4.04135 q^{88} -5.40045 q^{89} -6.66431 q^{90} +11.3114 q^{91} +2.11647 q^{92} +1.62823 q^{93} +5.71735 q^{94} +9.99120 q^{95} -0.367906 q^{96} +8.58146 q^{97} -3.87648 q^{98} +11.5770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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
$3$	−0.367906	−0.212411	−0.106205	−	0.994344i	$-0.533870\pi$
$3$	−0.367906	−0.212411	−0.106205	+	0.994344i	$0.533870\pi$
$4$	1.00000	0.500000
$5$	2.32640	1.04040	0.520199	−	0.854045i	$-0.325858\pi$
$5$	2.32640	1.04040	0.520199	+	0.854045i	$0.325858\pi$
$6$	−0.367906	−0.150197
$7$	1.76735	0.667995	0.333997	−	0.942574i	$-0.391602\pi$
$7$	1.76735	0.667995	0.333997	+	0.942574i	$0.391602\pi$
$8$	1.00000	0.353553
$9$	−2.86465	−0.954882
$10$	2.32640	0.735673
$11$	−4.04135	−1.21851	−0.609256	−	0.792973i	$-0.708532\pi$
$11$	−4.04135	−1.21851	−0.609256	+	0.792973i	$0.708532\pi$
$12$	−0.367906	−0.106205
$13$	6.40019	1.77509	0.887546	−	0.460718i	$-0.152408\pi$
$13$	6.40019	1.77509	0.887546	+	0.460718i	$0.152408\pi$
$14$	1.76735	0.472344
$15$	−0.855897	−0.220992
$16$	1.00000	0.250000
$17$	7.48899	1.81635	0.908173	−	0.418595i	$-0.137477\pi$
$17$	7.48899	1.81635	0.908173	+	0.418595i	$0.137477\pi$
$18$	−2.86465	−0.675203
$19$	4.29470	0.985272	0.492636	−	0.870235i	$-0.336033\pi$
$19$	4.29470	0.985272	0.492636	+	0.870235i	$0.336033\pi$
$20$	2.32640	0.520199
$21$	−0.650218	−0.141889
$22$	−4.04135	−0.861618
$23$	2.11647	0.441314	0.220657	−	0.975351i	$-0.429180\pi$
$23$	2.11647	0.441314	0.220657	+	0.975351i	$0.429180\pi$
$24$	−0.367906	−0.0750985
$25$	0.412142	0.0824283
$26$	6.40019	1.25518
$27$	2.15764	0.415238
$28$	1.76735	0.333997
$29$	−2.61558	−0.485701	−0.242851	−	0.970064i	$-0.578082\pi$
$29$	−2.61558	−0.485701	−0.242851	+	0.970064i	$0.578082\pi$
$30$	−0.855897	−0.156265
$31$	−4.42568	−0.794876	−0.397438	−	0.917629i	$-0.630101\pi$
$31$	−4.42568	−0.794876	−0.397438	+	0.917629i	$0.630101\pi$
$32$	1.00000	0.176777
$33$	1.48684	0.258825
$34$	7.48899	1.28435
$35$	4.11156	0.694981
$36$	−2.86465	−0.477441
$37$	−1.37714	−0.226401	−0.113201	−	0.993572i	$-0.536110\pi$
$37$	−1.37714	−0.226401	−0.113201	+	0.993572i	$0.536110\pi$
$38$	4.29470	0.696693
$39$	−2.35467	−0.377048
$40$	2.32640	0.367836
$41$	−8.98546	−1.40329	−0.701646	−	0.712525i	$-0.747551\pi$
$41$	−8.98546	−1.40329	−0.701646	+	0.712525i	$0.747551\pi$
$42$	−0.650218	−0.100331
$43$	−1.17052	−0.178502	−0.0892510	−	0.996009i	$-0.528447\pi$
$43$	−1.17052	−0.178502	−0.0892510	+	0.996009i	$0.528447\pi$
$44$	−4.04135	−0.609256
$45$	−6.66431	−0.993457
$46$	2.11647	0.312056
$47$	5.71735	0.833961	0.416980	−	0.908915i	$-0.363088\pi$
$47$	5.71735	0.833961	0.416980	+	0.908915i	$0.363088\pi$
$48$	−0.367906	−0.0531026
$49$	−3.87648	−0.553783
$50$	0.412142	0.0582856
$51$	−2.75524	−0.385811
$52$	6.40019	0.887546
$53$	−8.17181	−1.12248	−0.561242	−	0.827652i	$-0.689676\pi$
$53$	−8.17181	−1.12248	−0.561242	+	0.827652i	$0.689676\pi$
$54$	2.15764	0.293617
$55$	−9.40180	−1.26774
$56$	1.76735	0.236172
$57$	−1.58005	−0.209282
$58$	−2.61558	−0.343443
$59$	9.38684	1.22206	0.611032	−	0.791606i	$-0.290755\pi$
$59$	9.38684	1.22206	0.611032	+	0.791606i	$0.290755\pi$
$60$	−0.855897	−0.110496
$61$	8.55362	1.09518	0.547589	−	0.836747i	$-0.315546\pi$
$61$	8.55362	1.09518	0.547589	+	0.836747i	$0.315546\pi$
$62$	−4.42568	−0.562062
$63$	−5.06283	−0.637856
$64$	1.00000	0.125000
$65$	14.8894	1.84680
$66$	1.48684	0.183017
$67$	12.0253	1.46912	0.734560	−	0.678544i	$-0.237389\pi$
$67$	12.0253	1.46912	0.734560	+	0.678544i	$0.237389\pi$
$68$	7.48899	0.908173
$69$	−0.778661	−0.0937398
$70$	4.11156	0.491426
$71$	6.77247	0.803744	0.401872	−	0.915696i	$-0.368360\pi$
$71$	6.77247	0.803744	0.401872	+	0.915696i	$0.368360\pi$
$72$	−2.86465	−0.337602
$73$	−7.93017	−0.928157	−0.464078	−	0.885794i	$-0.653614\pi$
$73$	−7.93017	−0.928157	−0.464078	+	0.885794i	$0.653614\pi$
$74$	−1.37714	−0.160090
$75$	−0.151629	−0.0175086
$76$	4.29470	0.492636
$77$	−7.14247	−0.813960
$78$	−2.35467	−0.266614
$79$	−4.66523	−0.524880	−0.262440	−	0.964948i	$-0.584527\pi$
$79$	−4.66523	−0.524880	−0.262440	+	0.964948i	$0.584527\pi$
$80$	2.32640	0.260100
$81$	7.80013	0.866681
$82$	−8.98546	−0.992278
$83$	17.8218	1.95620	0.978099	−	0.208142i	$-0.0667416\pi$
$83$	17.8218	1.95620	0.978099	+	0.208142i	$0.0667416\pi$
$84$	−0.650218	−0.0709446
$85$	17.4224	1.88972
$86$	−1.17052	−0.126220
$87$	0.962288	0.103168
$88$	−4.04135	−0.430809
$89$	−5.40045	−0.572446	−0.286223	−	0.958163i	$-0.592400\pi$
$89$	−5.40045	−0.572446	−0.286223	+	0.958163i	$0.592400\pi$
$90$	−6.66431	−0.702480
$91$	11.3114	1.18575
$92$	2.11647	0.220657
$93$	1.62823	0.168840
$94$	5.71735	0.589699
$95$	9.99120	1.02508
$96$	−0.367906	−0.0375492
$97$	8.58146	0.871315	0.435657	−	0.900113i	$-0.356516\pi$
$97$	8.58146	0.871315	0.435657	+	0.900113i	$0.356516\pi$
$98$	−3.87648	−0.391584
$99$	11.5770	1.16354
$100$	0.412142	0.0412142
$101$	−13.6639	−1.35960	−0.679802	−	0.733395i	$-0.737934\pi$
$101$	−13.6639	−1.35960	−0.679802	+	0.733395i	$0.737934\pi$
$102$	−2.75524	−0.272810
$103$	−0.937982	−0.0924221	−0.0462111	−	0.998932i	$-0.514715\pi$
$103$	−0.937982	−0.0924221	−0.0462111	+	0.998932i	$0.514715\pi$
$104$	6.40019	0.627590
$105$	−1.51267	−0.147621
$106$	−8.17181	−0.793716
$107$	3.50441	0.338784	0.169392	−	0.985549i	$-0.445820\pi$
$107$	3.50441	0.338784	0.169392	+	0.985549i	$0.445820\pi$
$108$	2.15764	0.207619
$109$	1.91373	0.183302	0.0916509	−	0.995791i	$-0.470786\pi$
$109$	1.91373	0.183302	0.0916509	+	0.995791i	$0.470786\pi$
$110$	−9.40180	−0.896426
$111$	0.506660	0.0480900
$112$	1.76735	0.166999
$113$	4.43216	0.416943	0.208471	−	0.978028i	$-0.433151\pi$
$113$	4.43216	0.416943	0.208471	+	0.978028i	$0.433151\pi$
$114$	−1.58005	−0.147985
$115$	4.92375	0.459142
$116$	−2.61558	−0.242851
$117$	−18.3343	−1.69500
$118$	9.38684	0.864129
$119$	13.2356	1.21331
$120$	−0.855897	−0.0781323
$121$	5.33250	0.484772
$122$	8.55362	0.774408
$123$	3.30580	0.298074
$124$	−4.42568	−0.397438
$125$	−10.6732	−0.954640
$126$	−5.06283	−0.451032
$127$	−19.9954	−1.77431	−0.887154	−	0.461474i	$-0.847321\pi$
$127$	−19.9954	−1.77431	−0.887154	+	0.461474i	$0.847321\pi$
$128$	1.00000	0.0883883
$129$	0.430640	0.0379157
$130$	14.8894	1.30589
$131$	4.66117	0.407249	0.203624	−	0.979049i	$-0.434728\pi$
$131$	4.66117	0.407249	0.203624	+	0.979049i	$0.434728\pi$
$132$	1.48684	0.129412
$133$	7.59023	0.658157
$134$	12.0253	1.03882
$135$	5.01953	0.432012
$136$	7.48899	0.642175
$137$	−20.0736	−1.71500	−0.857500	−	0.514483i	$-0.827984\pi$
$137$	−20.0736	−1.71500	−0.857500	+	0.514483i	$0.827984\pi$
$138$	−0.778661	−0.0662840
$139$	1.86061	0.157815	0.0789076	−	0.996882i	$-0.474857\pi$
$139$	1.86061	0.157815	0.0789076	+	0.996882i	$0.474857\pi$
$140$	4.11156	0.347490
$141$	−2.10345	−0.177142
$142$	6.77247	0.568333
$143$	−25.8654	−2.16297
$144$	−2.86465	−0.238720
$145$	−6.08489	−0.505323
$146$	−7.93017	−0.656306
$147$	1.42618	0.117629
$148$	−1.37714	−0.113201
$149$	15.8077	1.29501	0.647507	−	0.762059i	$-0.275812\pi$
$149$	15.8077	1.29501	0.647507	+	0.762059i	$0.275812\pi$
$150$	−0.151629	−0.0123805
$151$	19.8424	1.61475	0.807377	−	0.590036i	$-0.200886\pi$
$151$	19.8424	1.61475	0.807377	+	0.590036i	$0.200886\pi$
$152$	4.29470	0.348346
$153$	−21.4533	−1.73440
$154$	−7.14247	−0.575557
$155$	−10.2959	−0.826987
$156$	−2.35467	−0.188524
$157$	3.47786	0.277563	0.138782	−	0.990323i	$-0.455681\pi$
$157$	3.47786	0.277563	0.138782	+	0.990323i	$0.455681\pi$
$158$	−4.66523	−0.371146
$159$	3.00646	0.238427
$160$	2.32640	0.183918
$161$	3.74054	0.294796
$162$	7.80013	0.612836
$163$	14.4210	1.12954	0.564770	−	0.825249i	$-0.308965\pi$
$163$	14.4210	1.12954	0.564770	+	0.825249i	$0.308965\pi$
$164$	−8.98546	−0.701646
$165$	3.45898	0.269281
$166$	17.8218	1.38324
$167$	−3.60622	−0.279057	−0.139529	−	0.990218i	$-0.544559\pi$
$167$	−3.60622	−0.279057	−0.139529	+	0.990218i	$0.544559\pi$
$168$	−0.650218	−0.0501654
$169$	27.9624	2.15095
$170$	17.4224	1.33624
$171$	−12.3028	−0.940818
$172$	−1.17052	−0.0892510
$173$	−19.6416	−1.49332	−0.746661	−	0.665205i	$-0.768344\pi$
$173$	−19.6416	−1.49332	−0.746661	+	0.665205i	$0.768344\pi$
$174$	0.962288	0.0729508
$175$	0.728398	0.0550617
$176$	−4.04135	−0.304628
$177$	−3.45348	−0.259579
$178$	−5.40045	−0.404781
$179$	11.2969	0.844370	0.422185	−	0.906510i	$-0.361263\pi$
$179$	11.2969	0.844370	0.422185	+	0.906510i	$0.361263\pi$
$180$	−6.66431	−0.496729
$181$	−11.1813	−0.831102	−0.415551	−	0.909570i	$-0.636411\pi$
$181$	−11.1813	−0.831102	−0.415551	+	0.909570i	$0.636411\pi$
$182$	11.3114	0.838454
$183$	−3.14693	−0.232627
$184$	2.11647	0.156028
$185$	−3.20379	−0.235547
$186$	1.62823	0.119388
$187$	−30.2656	−2.21324
$188$	5.71735	0.416980
$189$	3.81330	0.277377
$190$	9.99120	0.724838
$191$	16.6157	1.20227	0.601136	−	0.799147i	$-0.294715\pi$
$191$	16.6157	1.20227	0.601136	+	0.799147i	$0.294715\pi$
$192$	−0.367906	−0.0265513
$193$	13.0858	0.941934	0.470967	−	0.882151i	$-0.343905\pi$
$193$	13.0858	0.941934	0.470967	+	0.882151i	$0.343905\pi$
$194$	8.58146	0.616113
$195$	−5.47790	−0.392281
$196$	−3.87648	−0.276891
$197$	5.21887	0.371829	0.185915	−	0.982566i	$-0.440475\pi$
$197$	5.21887	0.371829	0.185915	+	0.982566i	$0.440475\pi$
$198$	11.5770	0.822744
$199$	16.8422	1.19391	0.596955	−	0.802274i	$-0.296377\pi$
$199$	16.8422	1.19391	0.596955	+	0.802274i	$0.296377\pi$
$200$	0.412142	0.0291428
$201$	−4.42417	−0.312057
$202$	−13.6639	−0.961386
$203$	−4.62264	−0.324446
$204$	−2.75524	−0.192906
$205$	−20.9038	−1.45998
$206$	−0.937982	−0.0653523
$207$	−6.06293	−0.421403
$208$	6.40019	0.443773
$209$	−17.3564	−1.20057
$210$	−1.51267	−0.104384
$211$	−4.10596	−0.282666	−0.141333	−	0.989962i	$-0.545139\pi$
$211$	−4.10596	−0.282666	−0.141333	+	0.989962i	$0.545139\pi$
$212$	−8.17181	−0.561242
$213$	−2.49163	−0.170724
$214$	3.50441	0.239556
$215$	−2.72309	−0.185713
$216$	2.15764	0.146809
$217$	−7.82172	−0.530973
$218$	1.91373	0.129614
$219$	2.91756	0.197150
$220$	−9.40180	−0.633869
$221$	47.9309	3.22418
$222$	0.506660	0.0340048
$223$	−2.96566	−0.198595	−0.0992975	−	0.995058i	$-0.531660\pi$
$223$	−2.96566	−0.198595	−0.0992975	+	0.995058i	$0.531660\pi$
$224$	1.76735	0.118086
$225$	−1.18064	−0.0787093
$226$	4.43216	0.294823
$227$	6.81507	0.452332	0.226166	−	0.974089i	$-0.427381\pi$
$227$	6.81507	0.452332	0.226166	+	0.974089i	$0.427381\pi$
$228$	−1.58005	−0.104641
$229$	−20.5488	−1.35790	−0.678950	−	0.734184i	$-0.737565\pi$
$229$	−20.5488	−1.35790	−0.678950	+	0.734184i	$0.737565\pi$
$230$	4.92375	0.324663
$231$	2.62776	0.172894
$232$	−2.61558	−0.171721
$233$	−21.4222	−1.40341	−0.701707	−	0.712466i	$-0.747578\pi$
$233$	−21.4222	−1.40341	−0.701707	+	0.712466i	$0.747578\pi$
$234$	−18.3343	−1.19855
$235$	13.3008	0.867651
$236$	9.38684	0.611032
$237$	1.71637	0.111490
$238$	13.2356	0.857940
$239$	−8.70103	−0.562823	−0.281412	−	0.959587i	$-0.590803\pi$
$239$	−8.70103	−0.562823	−0.281412	+	0.959587i	$0.590803\pi$
$240$	−0.855897	−0.0552479
$241$	−20.2985	−1.30754	−0.653772	−	0.756691i	$-0.726815\pi$
$241$	−20.2985	−1.30754	−0.653772	+	0.756691i	$0.726815\pi$
$242$	5.33250	0.342786
$243$	−9.34263	−0.599330
$244$	8.55362	0.547589
$245$	−9.01825	−0.576155
$246$	3.30580	0.210770
$247$	27.4869	1.74895
$248$	−4.42568	−0.281031
$249$	−6.55675	−0.415517
$250$	−10.6732	−0.675032
$251$	−24.9099	−1.57230	−0.786150	−	0.618035i	$-0.787929\pi$
$251$	−24.9099	−1.57230	−0.786150	+	0.618035i	$0.787929\pi$
$252$	−5.06283	−0.318928
$253$	−8.55339	−0.537747
$254$	−19.9954	−1.25463
$255$	−6.40980	−0.401397
$256$	1.00000	0.0625000
$257$	−10.4439	−0.651470	−0.325735	−	0.945461i	$-0.605612\pi$
$257$	−10.4439	−0.651470	−0.325735	+	0.945461i	$0.605612\pi$
$258$	0.430640	0.0268105
$259$	−2.43389	−0.151235
$260$	14.8894	0.923402
$261$	7.49271	0.463787
$262$	4.66117	0.287968
$263$	−0.0583532	−0.00359821	−0.00179911	−	0.999998i	$-0.500573\pi$
$263$	−0.0583532	−0.00359821	−0.00179911	+	0.999998i	$0.500573\pi$
$264$	1.48684	0.0915084
$265$	−19.0109	−1.16783
$266$	7.59023	0.465387
$267$	1.98686	0.121594
$268$	12.0253	0.734560
$269$	7.85246	0.478773	0.239387	−	0.970924i	$-0.423054\pi$
$269$	7.85246	0.478773	0.239387	+	0.970924i	$0.423054\pi$
$270$	5.01953	0.305479
$271$	10.1581	0.617062	0.308531	−	0.951214i	$-0.400163\pi$
$271$	10.1581	0.617062	0.308531	+	0.951214i	$0.400163\pi$
$272$	7.48899	0.454086
$273$	−4.16152	−0.251866
$274$	−20.0736	−1.21269
$275$	−1.66561	−0.100440
$276$	−0.778661	−0.0468699
$277$	20.6384	1.24004	0.620022	−	0.784584i	$-0.287124\pi$
$277$	20.6384	1.24004	0.620022	+	0.784584i	$0.287124\pi$
$278$	1.86061	0.111592
$279$	12.6780	0.759012
$280$	4.11156	0.245713
$281$	−20.7099	−1.23545	−0.617725	−	0.786394i	$-0.711945\pi$
$281$	−20.7099	−1.23545	−0.617725	+	0.786394i	$0.711945\pi$
$282$	−2.10345	−0.125258
$283$	−13.3739	−0.794997	−0.397499	−	0.917603i	$-0.630122\pi$
$283$	−13.3739	−0.794997	−0.397499	+	0.917603i	$0.630122\pi$
$284$	6.77247	0.401872
$285$	−3.67582	−0.217737
$286$	−25.8654	−1.52945
$287$	−15.8804	−0.937392
$288$	−2.86465	−0.168801
$289$	39.0849	2.29911
$290$	−6.08489	−0.357317
$291$	−3.15717	−0.185077
$292$	−7.93017	−0.464078
$293$	−32.7668	−1.91425	−0.957127	−	0.289668i	$-0.906455\pi$
$293$	−32.7668	−1.91425	−0.957127	+	0.289668i	$0.906455\pi$
$294$	1.42618	0.0831765
$295$	21.8376	1.27143
$296$	−1.37714	−0.0800449
$297$	−8.71977	−0.505972
$298$	15.8077	0.915713
$299$	13.5458	0.783373
$300$	−0.151629	−0.00875432
$301$	−2.06871	−0.119238
$302$	19.8424	1.14180
$303$	5.02701	0.288794
$304$	4.29470	0.246318
$305$	19.8991	1.13942
$306$	−21.4533	−1.22640
$307$	−2.22512	−0.126994	−0.0634972	−	0.997982i	$-0.520225\pi$
$307$	−2.22512	−0.126994	−0.0634972	+	0.997982i	$0.520225\pi$
$308$	−7.14247	−0.406980
$309$	0.345089	0.0196314
$310$	−10.2959	−0.584768
$311$	16.9451	0.960870	0.480435	−	0.877030i	$-0.340479\pi$
$311$	16.9451	0.960870	0.480435	+	0.877030i	$0.340479\pi$
$312$	−2.35467	−0.133307
$313$	24.5236	1.38616	0.693079	−	0.720862i	$-0.256254\pi$
$313$	24.5236	1.38616	0.693079	+	0.720862i	$0.256254\pi$
$314$	3.47786	0.196267
$315$	−11.7782	−0.663624
$316$	−4.66523	−0.262440
$317$	−13.6013	−0.763926	−0.381963	−	0.924178i	$-0.624752\pi$
$317$	−13.6013	−0.763926	−0.381963	+	0.924178i	$0.624752\pi$
$318$	3.00646	0.168594
$319$	10.5705	0.591833
$320$	2.32640	0.130050
$321$	−1.28929	−0.0719613
$322$	3.74054	0.208452
$323$	32.1630	1.78960
$324$	7.80013	0.433340
$325$	2.63778	0.146318
$326$	14.4210	0.798705
$327$	−0.704072	−0.0389352
$328$	−8.98546	−0.496139
$329$	10.1045	0.557082
$330$	3.45898	0.190410
$331$	−11.7103	−0.643658	−0.321829	−	0.946798i	$-0.604298\pi$
$331$	−11.7103	−0.643658	−0.321829	+	0.946798i	$0.604298\pi$
$332$	17.8218	0.978099
$333$	3.94503	0.216186
$334$	−3.60622	−0.197323
$335$	27.9756	1.52847
$336$	−0.650218	−0.0354723
$337$	17.3903	0.947313	0.473656	−	0.880710i	$-0.342934\pi$
$337$	17.3903	0.947313	0.473656	+	0.880710i	$0.342934\pi$
$338$	27.9624	1.52095
$339$	−1.63062	−0.0885631
$340$	17.4224	0.944861
$341$	17.8857	0.968566
$342$	−12.3028	−0.665259
$343$	−19.2225	−1.03792
$344$	−1.17052	−0.0631100
$345$	−1.81148	−0.0975267
$346$	−19.6416	−1.05594
$347$	−2.94701	−0.158204	−0.0791019	−	0.996867i	$-0.525205\pi$
$347$	−2.94701	−0.158204	−0.0791019	+	0.996867i	$0.525205\pi$
$348$	0.962288	0.0515840
$349$	26.8217	1.43573	0.717866	−	0.696181i	$-0.245119\pi$
$349$	26.8217	1.43573	0.717866	+	0.696181i	$0.245119\pi$
$350$	0.728398	0.0389345
$351$	13.8093	0.737085
$352$	−4.04135	−0.215405
$353$	−29.9241	−1.59270	−0.796349	−	0.604837i	$-0.793238\pi$
$353$	−29.9241	−1.59270	−0.796349	+	0.604837i	$0.793238\pi$
$354$	−3.45348	−0.183550
$355$	15.7555	0.836214
$356$	−5.40045	−0.286223
$357$	−4.86947	−0.257720
$358$	11.2969	0.597060
$359$	−19.6860	−1.03899	−0.519493	−	0.854475i	$-0.673879\pi$
$359$	−19.6860	−1.03899	−0.519493	+	0.854475i	$0.673879\pi$
$360$	−6.66431	−0.351240
$361$	−0.555535	−0.0292387
$362$	−11.1813	−0.587678
$363$	−1.96186	−0.102971
$364$	11.3114	0.592876
$365$	−18.4488	−0.965653
$366$	−3.14693	−0.164492
$367$	−15.1459	−0.790609	−0.395305	−	0.918550i	$-0.629361\pi$
$367$	−15.1459	−0.790609	−0.395305	+	0.918550i	$0.629361\pi$
$368$	2.11647	0.110329
$369$	25.7401	1.33998
$370$	−3.20379	−0.166557
$371$	−14.4424	−0.749813
$372$	1.62823	0.0844200
$373$	19.5146	1.01043	0.505213	−	0.862995i	$-0.331414\pi$
$373$	19.5146	1.01043	0.505213	+	0.862995i	$0.331414\pi$
$374$	−30.2656	−1.56500
$375$	3.92673	0.202776
$376$	5.71735	0.294850
$377$	−16.7402	−0.862165
$378$	3.81330	0.196135
$379$	−34.5895	−1.77675	−0.888373	−	0.459123i	$-0.848164\pi$
$379$	−34.5895	−1.77675	−0.888373	+	0.459123i	$0.848164\pi$
$380$	9.99120	0.512538
$381$	7.35644	0.376882
$382$	16.6157	0.850134
$383$	3.81338	0.194854	0.0974272	−	0.995243i	$-0.468939\pi$
$383$	3.81338	0.194854	0.0974272	+	0.995243i	$0.468939\pi$
$384$	−0.367906	−0.0187746
$385$	−16.6162	−0.846843
$386$	13.0858	0.666048
$387$	3.35311	0.170448
$388$	8.58146	0.435657
$389$	4.92384	0.249649	0.124824	−	0.992179i	$-0.460163\pi$
$389$	4.92384	0.249649	0.124824	+	0.992179i	$0.460163\pi$
$390$	−5.47790	−0.277384
$391$	15.8502	0.801579
$392$	−3.87648	−0.195792
$393$	−1.71487	−0.0865039
$394$	5.21887	0.262923
$395$	−10.8532	−0.546084
$396$	11.5770	0.581768
$397$	27.6252	1.38647	0.693233	−	0.720713i	$-0.256185\pi$
$397$	27.6252	1.38647	0.693233	+	0.720713i	$0.256185\pi$
$398$	16.8422	0.844223
$399$	−2.79249	−0.139799
$400$	0.412142	0.0206071
$401$	−11.0056	−0.549594	−0.274797	−	0.961502i	$-0.588611\pi$
$401$	−11.0056	−0.549594	−0.274797	+	0.961502i	$0.588611\pi$
$402$	−4.42417	−0.220657
$403$	−28.3252	−1.41098
$404$	−13.6639	−0.679802
$405$	18.1462	0.901693
$406$	−4.62264	−0.229418
$407$	5.56552	0.275873
$408$	−2.75524	−0.136405
$409$	23.2530	1.14979	0.574893	−	0.818229i	$-0.305044\pi$
$409$	23.2530	1.14979	0.574893	+	0.818229i	$0.305044\pi$
$410$	−20.9038	−1.03236
$411$	7.38518	0.364284
$412$	−0.937982	−0.0462111
$413$	16.5898	0.816332
$414$	−6.06293	−0.297977
$415$	41.4607	2.03522
$416$	6.40019	0.313795
$417$	−0.684531	−0.0335216
$418$	−17.3564	−0.848929
$419$	1.25188	0.0611586	0.0305793	−	0.999532i	$-0.490265\pi$
$419$	1.25188	0.0611586	0.0305793	+	0.999532i	$0.490265\pi$
$420$	−1.51267	−0.0738106
$421$	−12.3100	−0.599954	−0.299977	−	0.953946i	$-0.596979\pi$
$421$	−12.3100	−0.599954	−0.299977	+	0.953946i	$0.596979\pi$
$422$	−4.10596	−0.199875
$423$	−16.3782	−0.796334
$424$	−8.17181	−0.396858
$425$	3.08652	0.149718
$426$	−2.49163	−0.120720
$427$	15.1172	0.731574
$428$	3.50441	0.169392
$429$	9.51603	0.459438
$430$	−2.72309	−0.131319
$431$	−27.5805	−1.32850	−0.664252	−	0.747508i	$-0.731250\pi$
$431$	−27.5805	−1.32850	−0.664252	+	0.747508i	$0.731250\pi$
$432$	2.15764	0.103809
$433$	−23.2077	−1.11529	−0.557646	−	0.830079i	$-0.688295\pi$
$433$	−23.2077	−1.11529	−0.557646	+	0.830079i	$0.688295\pi$
$434$	−7.82172	−0.375455
$435$	2.23867	0.107336
$436$	1.91373	0.0916509
$437$	9.08960	0.434815
$438$	2.91756	0.139406
$439$	23.6155	1.12711	0.563553	−	0.826080i	$-0.309434\pi$
$439$	23.6155	1.12711	0.563553	+	0.826080i	$0.309434\pi$
$440$	−9.40180	−0.448213
$441$	11.1047	0.528797
$442$	47.9309	2.27984
$443$	−18.3997	−0.874196	−0.437098	−	0.899414i	$-0.643994\pi$
$443$	−18.3997	−0.874196	−0.437098	+	0.899414i	$0.643994\pi$
$444$	0.506660	0.0240450
$445$	−12.5636	−0.595572
$446$	−2.96566	−0.140428
$447$	−5.81573	−0.275075
$448$	1.76735	0.0834994
$449$	−14.9756	−0.706744	−0.353372	−	0.935483i	$-0.614965\pi$
$449$	−14.9756	−0.706744	−0.353372	+	0.935483i	$0.614965\pi$
$450$	−1.18064	−0.0556559
$451$	36.3134	1.70993
$452$	4.43216	0.208471
$453$	−7.30015	−0.342991
$454$	6.81507	0.319847
$455$	26.3148	1.23366
$456$	−1.58005	−0.0739924
$457$	19.2451	0.900246	0.450123	−	0.892966i	$-0.351380\pi$
$457$	19.2451	0.900246	0.450123	+	0.892966i	$0.351380\pi$
$458$	−20.5488	−0.960180
$459$	16.1585	0.754215
$460$	4.92375	0.229571
$461$	17.9164	0.834451	0.417225	−	0.908803i	$-0.363003\pi$
$461$	17.9164	0.834451	0.417225	+	0.908803i	$0.363003\pi$
$462$	2.62776	0.122254
$463$	−33.4351	−1.55386	−0.776930	−	0.629587i	$-0.783224\pi$
$463$	−33.4351	−1.55386	−0.776930	+	0.629587i	$0.783224\pi$
$464$	−2.61558	−0.121425
$465$	3.78793	0.175661
$466$	−21.4222	−0.992363
$467$	−10.8339	−0.501331	−0.250665	−	0.968074i	$-0.580649\pi$
$467$	−10.8339	−0.501331	−0.250665	+	0.968074i	$0.580649\pi$
$468$	−18.3343	−0.847502
$469$	21.2528	0.981365
$470$	13.3008	0.613522
$471$	−1.27952	−0.0589574
$472$	9.38684	0.432065
$473$	4.73046	0.217507
$474$	1.71637	0.0788353
$475$	1.77003	0.0812143
$476$	13.2356	0.606655
$477$	23.4093	1.07184
$478$	−8.70103	−0.397976
$479$	−0.394156	−0.0180095	−0.00900473	−	0.999959i	$-0.502866\pi$
$479$	−0.394156	−0.0180095	−0.00900473	+	0.999959i	$0.502866\pi$
$480$	−0.855897	−0.0390662
$481$	−8.81398	−0.401883
$482$	−20.2985	−0.924573
$483$	−1.37617	−0.0626177
$484$	5.33250	0.242386
$485$	19.9639	0.906514
$486$	−9.34263	−0.423790
$487$	−33.6490	−1.52478	−0.762390	−	0.647118i	$-0.775974\pi$
$487$	−33.6490	−1.52478	−0.762390	+	0.647118i	$0.775974\pi$
$488$	8.55362	0.387204
$489$	−5.30557	−0.239926
$490$	−9.01825	−0.407403
$491$	−13.8084	−0.623163	−0.311581	−	0.950219i	$-0.600859\pi$
$491$	−13.8084	−0.623163	−0.311581	+	0.950219i	$0.600859\pi$
$492$	3.30580	0.149037
$493$	−19.5880	−0.882201
$494$	27.4869	1.23669
$495$	26.9328	1.21054
$496$	−4.42568	−0.198719
$497$	11.9693	0.536897
$498$	−6.55675	−0.293815
$499$	−33.7892	−1.51261	−0.756305	−	0.654219i	$-0.772997\pi$
$499$	−33.7892	−1.51261	−0.756305	+	0.654219i	$0.772997\pi$
$500$	−10.6732	−0.477320
$501$	1.32675	0.0592747
$502$	−24.9099	−1.11178
$503$	37.4476	1.66971	0.834853	−	0.550472i	$-0.185552\pi$
$503$	37.4476	1.66971	0.834853	+	0.550472i	$0.185552\pi$
$504$	−5.06283	−0.225516
$505$	−31.7876	−1.41453
$506$	−8.55339	−0.380244
$507$	−10.2875	−0.456885
$508$	−19.9954	−0.887154
$509$	−22.2523	−0.986318	−0.493159	−	0.869939i	$-0.664158\pi$
$509$	−22.2523	−0.986318	−0.493159	+	0.869939i	$0.664158\pi$
$510$	−6.40980	−0.283831
$511$	−14.0154	−0.620004
$512$	1.00000	0.0441942
$513$	9.26641	0.409122
$514$	−10.4439	−0.460659
$515$	−2.18212	−0.0961558
$516$	0.430640	0.0189579
$517$	−23.1058	−1.01619
$518$	−2.43389	−0.106939
$519$	7.22625	0.317197
$520$	14.8894	0.652944
$521$	40.4479	1.77206	0.886028	−	0.463632i	$-0.153454\pi$
$521$	40.4479	1.77206	0.886028	+	0.463632i	$0.153454\pi$
$522$	7.49271	0.327947
$523$	2.08425	0.0911381	0.0455690	−	0.998961i	$-0.485490\pi$
$523$	2.08425	0.0911381	0.0455690	+	0.998961i	$0.485490\pi$
$524$	4.66117	0.203624
$525$	−0.267982	−0.0116957
$526$	−0.0583532	−0.00254432
$527$	−33.1439	−1.44377
$528$	1.48684	0.0647062
$529$	−18.5206	−0.805242
$530$	−19.0109	−0.825781
$531$	−26.8900	−1.16693
$532$	7.59023	0.329078
$533$	−57.5086	−2.49097
$534$	1.98686	0.0859797
$535$	8.15266	0.352470
$536$	12.0253	0.519412
$537$	−4.15620	−0.179353
$538$	7.85246	0.338544
$539$	15.6662	0.674791
$540$	5.01953	0.216006
$541$	−14.0286	−0.603135	−0.301568	−	0.953445i	$-0.597510\pi$
$541$	−14.0286	−0.603135	−0.301568	+	0.953445i	$0.597510\pi$
$542$	10.1581	0.436329
$543$	4.11368	0.176535
$544$	7.48899	0.321088
$545$	4.45210	0.190707
$546$	−4.16152	−0.178096
$547$	−31.6184	−1.35190	−0.675952	−	0.736945i	$-0.736267\pi$
$547$	−31.6184	−1.35190	−0.675952	+	0.736945i	$0.736267\pi$
$548$	−20.0736	−0.857500
$549$	−24.5031	−1.04577
$550$	−1.66561	−0.0710217
$551$	−11.2331	−0.478548
$552$	−0.778661	−0.0331420
$553$	−8.24509	−0.350617
$554$	20.6384	0.876844
$555$	1.17869	0.0500327
$556$	1.86061	0.0789076
$557$	27.4755	1.16417	0.582087	−	0.813127i	$-0.302236\pi$
$557$	27.4755	1.16417	0.582087	+	0.813127i	$0.302236\pi$
$558$	12.6780	0.536703
$559$	−7.49152	−0.316858
$560$	4.11156	0.173745
$561$	11.1349	0.470116
$562$	−20.7099	−0.873595
$563$	−3.62066	−0.152593	−0.0762963	−	0.997085i	$-0.524309\pi$
$563$	−3.62066	−0.152593	−0.0762963	+	0.997085i	$0.524309\pi$
$564$	−2.10345	−0.0885710
$565$	10.3110	0.433786
$566$	−13.3739	−0.562148
$567$	13.7855	0.578938
$568$	6.77247	0.284166
$569$	24.6612	1.03385	0.516926	−	0.856030i	$-0.327076\pi$
$569$	24.6612	1.03385	0.516926	+	0.856030i	$0.327076\pi$
$570$	−3.67582	−0.153963
$571$	−1.30079	−0.0544362	−0.0272181	−	0.999630i	$-0.508665\pi$
$571$	−1.30079	−0.0544362	−0.0272181	+	0.999630i	$0.508665\pi$
$572$	−25.8654	−1.08149
$573$	−6.11302	−0.255375
$574$	−15.8804	−0.662836
$575$	0.872284	0.0363768
$576$	−2.86465	−0.119360
$577$	3.93057	0.163632	0.0818159	−	0.996647i	$-0.473928\pi$
$577$	3.93057	0.163632	0.0818159	+	0.996647i	$0.473928\pi$
$578$	39.0849	1.62572
$579$	−4.81433	−0.200077
$580$	−6.08489	−0.252661
$581$	31.4973	1.30673
$582$	−3.15717	−0.130869
$583$	33.0251	1.36776
$584$	−7.93017	−0.328153
$585$	−42.6529	−1.76348
$586$	−32.7668	−1.35358
$587$	−31.0130	−1.28004	−0.640022	−	0.768357i	$-0.721075\pi$
$587$	−31.0130	−1.28004	−0.640022	+	0.768357i	$0.721075\pi$
$588$	1.42618	0.0588147
$589$	−19.0070	−0.783169
$590$	21.8376	0.899038
$591$	−1.92005	−0.0789805
$592$	−1.37714	−0.0566003
$593$	−30.3154	−1.24491	−0.622453	−	0.782657i	$-0.713864\pi$
$593$	−30.3154	−1.24491	−0.622453	+	0.782657i	$0.713864\pi$
$594$	−8.71977	−0.357776
$595$	30.7914	1.26233
$596$	15.8077	0.647507
$597$	−6.19634	−0.253599
$598$	13.5458	0.553929
$599$	−35.5952	−1.45438	−0.727190	−	0.686437i	$-0.759174\pi$
$599$	−35.5952	−1.45438	−0.727190	+	0.686437i	$0.759174\pi$
$600$	−0.151629	−0.00619024
$601$	−29.8585	−1.21796	−0.608978	−	0.793187i	$-0.708420\pi$
$601$	−29.8585	−1.21796	−0.608978	+	0.793187i	$0.708420\pi$
$602$	−2.06871	−0.0843143
$603$	−34.4481	−1.40284
$604$	19.8424	0.807377
$605$	12.4055	0.504356
$606$	5.02701	0.204208
$607$	−9.71307	−0.394242	−0.197121	−	0.980379i	$-0.563159\pi$
$607$	−9.71307	−0.394242	−0.197121	+	0.980379i	$0.563159\pi$
$608$	4.29470	0.174173
$609$	1.70070	0.0689157
$610$	19.8991	0.805693
$611$	36.5921	1.48036
$612$	−21.4533	−0.867198
$613$	−4.04084	−0.163208	−0.0816039	−	0.996665i	$-0.526004\pi$
$613$	−4.04084	−0.163208	−0.0816039	+	0.996665i	$0.526004\pi$
$614$	−2.22512	−0.0897986
$615$	7.69062	0.310116
$616$	−7.14247	−0.287778
$617$	−1.46090	−0.0588135	−0.0294068	−	0.999568i	$-0.509362\pi$
$617$	−1.46090	−0.0588135	−0.0294068	+	0.999568i	$0.509362\pi$
$618$	0.345089	0.0138815
$619$	31.1153	1.25063	0.625315	−	0.780372i	$-0.284971\pi$
$619$	31.1153	1.25063	0.625315	+	0.780372i	$0.284971\pi$
$620$	−10.2959	−0.413494
$621$	4.56657	0.183250
$622$	16.9451	0.679438
$623$	−9.54447	−0.382391
$624$	−2.35467	−0.0942621
$625$	−26.8908	−1.07563
$626$	24.5236	0.980162
$627$	6.38552	0.255013
$628$	3.47786	0.138782
$629$	−10.3134	−0.411223
$630$	−11.7782	−0.469253
$631$	−12.2431	−0.487390	−0.243695	−	0.969852i	$-0.578360\pi$
$631$	−12.2431	−0.487390	−0.243695	+	0.969852i	$0.578360\pi$
$632$	−4.66523	−0.185573
$633$	1.51061	0.0600412
$634$	−13.6013	−0.540178
$635$	−46.5174	−1.84599
$636$	3.00646	0.119214
$637$	−24.8102	−0.983016
$638$	10.5705	0.418489
$639$	−19.4007	−0.767481
$640$	2.32640	0.0919591
$641$	−16.8744	−0.666500	−0.333250	−	0.942839i	$-0.608145\pi$
$641$	−16.8744	−0.666500	−0.333250	+	0.942839i	$0.608145\pi$
$642$	−1.28929	−0.0508843
$643$	23.0833	0.910316	0.455158	−	0.890411i	$-0.349583\pi$
$643$	23.0833	0.910316	0.455158	+	0.890411i	$0.349583\pi$
$644$	3.74054	0.147398
$645$	1.00184	0.0394474
$646$	32.1630	1.26543
$647$	−35.0716	−1.37881	−0.689403	−	0.724378i	$-0.742127\pi$
$647$	−35.0716	−1.37881	−0.689403	+	0.724378i	$0.742127\pi$
$648$	7.80013	0.306418
$649$	−37.9355	−1.48910
$650$	2.63778	0.103462
$651$	2.87766	0.112784
$652$	14.4210	0.564770
$653$	−25.5059	−0.998123	−0.499061	−	0.866567i	$-0.666322\pi$
$653$	−25.5059	−0.998123	−0.499061	+	0.866567i	$0.666322\pi$
$654$	−0.704072	−0.0275314
$655$	10.8438	0.423701
$656$	−8.98546	−0.350823
$657$	22.7171	0.886280
$658$	10.1045	0.393916
$659$	7.72934	0.301092	0.150546	−	0.988603i	$-0.451897\pi$
$659$	7.72934	0.301092	0.150546	+	0.988603i	$0.451897\pi$
$660$	3.45898	0.134640
$661$	−25.1136	−0.976806	−0.488403	−	0.872618i	$-0.662420\pi$
$661$	−25.1136	−0.976806	−0.488403	+	0.872618i	$0.662420\pi$
$662$	−11.7103	−0.455135
$663$	−17.6341	−0.684850
$664$	17.8218	0.691620
$665$	17.6579	0.684745
$666$	3.94503	0.152867
$667$	−5.53579	−0.214347
$668$	−3.60622	−0.139529
$669$	1.09108	0.0421837
$670$	27.9756	1.08079
$671$	−34.5681	−1.33449
$672$	−0.650218	−0.0250827
$673$	44.8931	1.73050	0.865252	−	0.501338i	$-0.167159\pi$
$673$	44.8931	1.73050	0.865252	+	0.501338i	$0.167159\pi$
$674$	17.3903	0.669851
$675$	0.889252	0.0342273
$676$	27.9624	1.07548
$677$	−4.28421	−0.164655	−0.0823277	−	0.996605i	$-0.526235\pi$
$677$	−4.28421	−0.164655	−0.0823277	+	0.996605i	$0.526235\pi$
$678$	−1.63062	−0.0626235
$679$	15.1664	0.582034
$680$	17.4224	0.668118
$681$	−2.50730	−0.0960801
$682$	17.8857	0.684880
$683$	50.6382	1.93762	0.968808	−	0.247813i	$-0.0797120\pi$
$683$	50.6382	1.93762	0.968808	+	0.247813i	$0.0797120\pi$
$684$	−12.3028	−0.470409
$685$	−46.6992	−1.78428
$686$	−19.2225	−0.733920
$687$	7.56001	0.288432
$688$	−1.17052	−0.0446255
$689$	−52.3011	−1.99251
$690$	−1.81148	−0.0689618
$691$	−1.08803	−0.0413905	−0.0206952	−	0.999786i	$-0.506588\pi$
$691$	−1.08803	−0.0413905	−0.0206952	+	0.999786i	$0.506588\pi$
$692$	−19.6416	−0.746661
$693$	20.4606	0.777236
$694$	−2.94701	−0.111867
$695$	4.32854	0.164191
$696$	0.962288	0.0364754
$697$	−67.2920	−2.54886
$698$	26.8217	1.01522
$699$	7.88134	0.298100
$700$	0.728398	0.0275308
$701$	36.6989	1.38610	0.693049	−	0.720891i	$-0.256267\pi$
$701$	36.6989	1.38610	0.693049	+	0.720891i	$0.256267\pi$
$702$	13.8093	0.521198
$703$	−5.91443	−0.223067
$704$	−4.04135	−0.152314
$705$	−4.89346	−0.184298
$706$	−29.9241	−1.12621
$707$	−24.1488	−0.908209
$708$	−3.45348	−0.129790
$709$	17.7373	0.666139	0.333069	−	0.942902i	$-0.391916\pi$
$709$	17.7373	0.666139	0.333069	+	0.942902i	$0.391916\pi$
$710$	15.7555	0.591292
$711$	13.3642	0.501198
$712$	−5.40045	−0.202390
$713$	−9.36681	−0.350790
$714$	−4.86947	−0.182235
$715$	−60.1733	−2.25035
$716$	11.2969	0.422185
$717$	3.20116	0.119550
$718$	−19.6860	−0.734674
$719$	−33.2840	−1.24128	−0.620641	−	0.784095i	$-0.713128\pi$
$719$	−33.2840	−1.24128	−0.620641	+	0.784095i	$0.713128\pi$
$720$	−6.66431	−0.248364
$721$	−1.65774	−0.0617375
$722$	−0.555535	−0.0206749
$723$	7.46795	0.277736
$724$	−11.1813	−0.415551
$725$	−1.07799	−0.0400355
$726$	−1.96186	−0.0728113
$727$	−2.52629	−0.0936948	−0.0468474	−	0.998902i	$-0.514917\pi$
$727$	−2.52629	−0.0936948	−0.0468474	+	0.998902i	$0.514917\pi$
$728$	11.3114	0.419227
$729$	−19.9632	−0.739377
$730$	−18.4488	−0.682819
$731$	−8.76598	−0.324221
$732$	−3.14693	−0.116314
$733$	−16.7813	−0.619830	−0.309915	−	0.950764i	$-0.600301\pi$
$733$	−16.7813	−0.619830	−0.309915	+	0.950764i	$0.600301\pi$
$734$	−15.1459	−0.559045
$735$	3.31787	0.122381
$736$	2.11647	0.0780140
$737$	−48.5983	−1.79014
$738$	25.7401	0.947508
$739$	−29.6906	−1.09219	−0.546093	−	0.837725i	$-0.683885\pi$
$739$	−29.6906	−1.09219	−0.546093	+	0.837725i	$0.683885\pi$
$740$	−3.20379	−0.117774
$741$	−10.1126	−0.371495
$742$	−14.4424	−0.530198
$743$	−26.5228	−0.973027	−0.486513	−	0.873673i	$-0.661732\pi$
$743$	−26.5228	−0.973027	−0.486513	+	0.873673i	$0.661732\pi$
$744$	1.62823	0.0596940
$745$	36.7750	1.34733
$746$	19.5146	0.714479
$747$	−51.0532	−1.86794
$748$	−30.2656	−1.10662
$749$	6.19351	0.226306
$750$	3.92673	0.143384
$751$	32.6869	1.19276	0.596381	−	0.802701i	$-0.296605\pi$
$751$	32.6869	1.19276	0.596381	+	0.802701i	$0.296605\pi$
$752$	5.71735	0.208490
$753$	9.16451	0.333973
$754$	−16.7402	−0.609642
$755$	46.1615	1.67999
$756$	3.81330	0.138688
$757$	−20.6796	−0.751614	−0.375807	−	0.926698i	$-0.622634\pi$
$757$	−20.6796	−0.751614	−0.375807	+	0.926698i	$0.622634\pi$
$758$	−34.5895	−1.25635
$759$	3.14684	0.114223
$760$	9.99120	0.362419
$761$	31.2968	1.13451	0.567254	−	0.823543i	$-0.308006\pi$
$761$	31.2968	1.13451	0.567254	+	0.823543i	$0.308006\pi$
$762$	7.35644	0.266496
$763$	3.38222	0.122445
$764$	16.6157	0.601136
$765$	−49.9089	−1.80446
$766$	3.81338	0.137783
$767$	60.0776	2.16928
$768$	−0.367906	−0.0132757
$769$	−41.4407	−1.49439	−0.747194	−	0.664606i	$-0.768600\pi$
$769$	−41.4407	−1.49439	−0.747194	+	0.664606i	$0.768600\pi$
$770$	−16.6162	−0.598808
$771$	3.84236	0.138379
$772$	13.0858	0.470967
$773$	−14.2685	−0.513203	−0.256602	−	0.966517i	$-0.582603\pi$
$773$	−14.2685	−0.513203	−0.256602	+	0.966517i	$0.582603\pi$
$774$	3.35311	0.120525
$775$	−1.82401	−0.0655203
$776$	8.58146	0.308056
$777$	0.895444	0.0321239
$778$	4.92384	0.176528
$779$	−38.5899	−1.38263
$780$	−5.47790	−0.196140
$781$	−27.3699	−0.979372
$782$	15.8502	0.566802
$783$	−5.64348	−0.201681
$784$	−3.87648	−0.138446
$785$	8.09089	0.288776
$786$	−1.71487	−0.0611675
$787$	25.9833	0.926204	0.463102	−	0.886305i	$-0.346736\pi$
$787$	25.9833	0.926204	0.463102	+	0.886305i	$0.346736\pi$
$788$	5.21887	0.185915
$789$	0.0214685	0.000764298 0
$790$	−10.8532	−0.386140
$791$	7.83317	0.278516
$792$	11.5770	0.411372
$793$	54.7448	1.94404
$794$	27.6252	0.980380
$795$	6.99422	0.248059
$796$	16.8422	0.596955
$797$	26.3838	0.934561	0.467280	−	0.884109i	$-0.345234\pi$
$797$	26.3838	0.934561	0.467280	+	0.884109i	$0.345234\pi$
$798$	−2.79249	−0.0988531
$799$	42.8171	1.51476
$800$	0.412142	0.0145714
$801$	15.4704	0.546618
$802$	−11.0056	−0.388622
$803$	32.0486	1.13097
$804$	−4.42417	−0.156028
$805$	8.70199	0.306705
$806$	−28.3252	−0.997712
$807$	−2.88897	−0.101696
$808$	−13.6639	−0.480693
$809$	27.0679	0.951656	0.475828	−	0.879538i	$-0.342148\pi$
$809$	27.0679	0.951656	0.475828	+	0.879538i	$0.342148\pi$
$810$	18.1462	0.637593
$811$	−13.9703	−0.490564	−0.245282	−	0.969452i	$-0.578881\pi$
$811$	−13.9703	−0.490564	−0.245282	+	0.969452i	$0.578881\pi$
$812$	−4.62264	−0.162223
$813$	−3.73723	−0.131071
$814$	5.56552	0.195071
$815$	33.5490	1.17517
$816$	−2.75524	−0.0964528
$817$	−5.02702	−0.175873
$818$	23.2530	0.813021
$819$	−32.4030	−1.13225
$820$	−20.9038	−0.729991
$821$	32.7734	1.14380	0.571900	−	0.820323i	$-0.306206\pi$
$821$	32.7734	1.14380	0.571900	+	0.820323i	$0.306206\pi$
$822$	7.38518	0.257588
$823$	30.9964	1.08047	0.540233	−	0.841516i	$-0.318336\pi$
$823$	30.9964	1.08047	0.540233	+	0.841516i	$0.318336\pi$
$824$	−0.937982	−0.0326762
$825$	0.612787	0.0213345
$826$	16.5898	0.577234
$827$	23.6500	0.822393	0.411196	−	0.911547i	$-0.365111\pi$
$827$	23.6500	0.822393	0.411196	+	0.911547i	$0.365111\pi$
$828$	−6.06293	−0.210701
$829$	−20.8117	−0.722821	−0.361410	−	0.932407i	$-0.617705\pi$
$829$	−20.8117	−0.722821	−0.361410	+	0.932407i	$0.617705\pi$
$830$	41.4607	1.43912
$831$	−7.59301	−0.263399
$832$	6.40019	0.221887
$833$	−29.0309	−1.00586
$834$	−0.684531	−0.0237034
$835$	−8.38950	−0.290331
$836$	−17.3564	−0.600283
$837$	−9.54901	−0.330062
$838$	1.25188	0.0432456
$839$	12.4908	0.431231	0.215616	−	0.976478i	$-0.430824\pi$
$839$	12.4908	0.431231	0.215616	+	0.976478i	$0.430824\pi$
$840$	−1.51267	−0.0521920
$841$	−22.1587	−0.764094
$842$	−12.3100	−0.424232
$843$	7.61930	0.262422
$844$	−4.10596	−0.141333
$845$	65.0518	2.23785
$846$	−16.3782	−0.563093
$847$	9.42438	0.323826
$848$	−8.17181	−0.280621
$849$	4.92035	0.168866
$850$	3.08652	0.105867
$851$	−2.91468	−0.0999140
$852$	−2.49163	−0.0853619
$853$	3.88669	0.133078	0.0665389	−	0.997784i	$-0.478804\pi$
$853$	3.88669	0.133078	0.0665389	+	0.997784i	$0.478804\pi$
$854$	15.1172	0.517301
$855$	−28.6212	−0.978826
$856$	3.50441	0.119778
$857$	−29.1905	−0.997129	−0.498564	−	0.866853i	$-0.666139\pi$
$857$	−29.1905	−0.997129	−0.498564	+	0.866853i	$0.666139\pi$
$858$	9.51603	0.324872
$859$	−41.1807	−1.40507	−0.702533	−	0.711651i	$-0.747948\pi$
$859$	−41.1807	−1.40507	−0.702533	+	0.711651i	$0.747948\pi$
$860$	−2.72309	−0.0928566
$861$	5.84250	0.199112
$862$	−27.5805	−0.939395
$863$	−30.0183	−1.02183	−0.510917	−	0.859630i	$-0.670694\pi$
$863$	−30.0183	−1.02183	−0.510917	+	0.859630i	$0.670694\pi$
$864$	2.15764	0.0734043
$865$	−45.6942	−1.55365
$866$	−23.2077	−0.788631
$867$	−14.3796	−0.488356
$868$	−7.82172	−0.265486
$869$	18.8538	0.639572
$870$	2.23867	0.0758979
$871$	76.9640	2.60782
$872$	1.91373	0.0648070
$873$	−24.5828	−0.832003
$874$	9.08960	0.307460
$875$	−18.8633	−0.637695
$876$	2.91756	0.0985752
$877$	−2.05389	−0.0693551	−0.0346775	−	0.999399i	$-0.511040\pi$
$877$	−2.05389	−0.0693551	−0.0346775	+	0.999399i	$0.511040\pi$
$878$	23.6155	0.796985
$879$	12.0551	0.406608
$880$	−9.40180	−0.316935
$881$	−3.30958	−0.111503	−0.0557513	−	0.998445i	$-0.517755\pi$
$881$	−3.30958	−0.111503	−0.0557513	+	0.998445i	$0.517755\pi$
$882$	11.1047	0.373916
$883$	38.2955	1.28875	0.644373	−	0.764712i	$-0.277119\pi$
$883$	38.2955	1.28875	0.644373	+	0.764712i	$0.277119\pi$
$884$	47.9309	1.61209
$885$	−8.03417	−0.270066
$886$	−18.3997	−0.618150
$887$	1.58248	0.0531346	0.0265673	−	0.999647i	$-0.491542\pi$
$887$	1.58248	0.0531346	0.0265673	+	0.999647i	$0.491542\pi$
$888$	0.506660	0.0170024
$889$	−35.3389	−1.18523
$890$	−12.5636	−0.421133
$891$	−31.5230	−1.05606
$892$	−2.96566	−0.0992975
$893$	24.5543	0.821678
$894$	−5.81573	−0.194507
$895$	26.2811	0.878481
$896$	1.76735	0.0590430
$897$	−4.98358	−0.166397
$898$	−14.9756	−0.499743
$899$	11.5757	0.386072
$900$	−1.18064	−0.0393546
$901$	−61.1985	−2.03882
$902$	36.3134	1.20910
$903$	0.761091	0.0253275
$904$	4.43216	0.147412
$905$	−26.0123	−0.864677
$906$	−7.30015	−0.242531
$907$	40.1119	1.33189	0.665947	−	0.745999i	$-0.268028\pi$
$907$	40.1119	1.33189	0.665947	+	0.745999i	$0.268028\pi$
$908$	6.81507	0.226166
$909$	39.1421	1.29826
$910$	26.3148	0.872326
$911$	18.9924	0.629248	0.314624	−	0.949216i	$-0.398122\pi$
$911$	18.9924	0.629248	0.314624	+	0.949216i	$0.398122\pi$
$912$	−1.58005	−0.0523206
$913$	−72.0241	−2.38365
$914$	19.2451	0.636570
$915$	−7.32101	−0.242025
$916$	−20.5488	−0.678950
$917$	8.23792	0.272040
$918$	16.1585	0.533311
$919$	−40.1371	−1.32400	−0.662001	−	0.749503i	$-0.730292\pi$
$919$	−40.1371	−1.32400	−0.662001	+	0.749503i	$0.730292\pi$
$920$	4.92375	0.162331
$921$	0.818636	0.0269750
$922$	17.9164	0.590046
$923$	43.3451	1.42672
$924$	2.62776	0.0864469
$925$	−0.567578	−0.0186619
$926$	−33.4351	−1.09874
$927$	2.68699	0.0882522
$928$	−2.61558	−0.0858606
$929$	17.0141	0.558216	0.279108	−	0.960260i	$-0.409961\pi$
$929$	17.0141	0.558216	0.279108	+	0.960260i	$0.409961\pi$
$930$	3.78793	0.124211
$931$	−16.6483	−0.545627
$932$	−21.4222	−0.701707
$933$	−6.23422	−0.204099
$934$	−10.8339	−0.354495
$935$	−70.4099	−2.30265
$936$	−18.3343	−0.599274
$937$	26.2003	0.855927	0.427964	−	0.903796i	$-0.359231\pi$
$937$	26.2003	0.855927	0.427964	+	0.903796i	$0.359231\pi$
$938$	21.2528	0.693930
$939$	−9.02239	−0.294435
$940$	13.3008	0.433826
$941$	39.0670	1.27355	0.636774	−	0.771051i	$-0.280269\pi$
$941$	39.0670	1.27355	0.636774	+	0.771051i	$0.280269\pi$
$942$	−1.27952	−0.0416892
$943$	−19.0174	−0.619293
$944$	9.38684	0.305516
$945$	8.87126	0.288582
$946$	4.73046	0.153801
$947$	−9.25911	−0.300880	−0.150440	−	0.988619i	$-0.548069\pi$
$947$	−9.25911	−0.300880	−0.150440	+	0.988619i	$0.548069\pi$
$948$	1.71637	0.0557450
$949$	−50.7546	−1.64756
$950$	1.77003	0.0574272
$951$	5.00401	0.162266
$952$	13.2356	0.428970
$953$	17.5482	0.568442	0.284221	−	0.958759i	$-0.408265\pi$
$953$	17.5482	0.568442	0.284221	+	0.958759i	$0.408265\pi$
$954$	23.4093	0.757905
$955$	38.6548	1.25084
$956$	−8.70103	−0.281412
$957$	−3.88894	−0.125712
$958$	−0.394156	−0.0127346
$959$	−35.4770	−1.14561
$960$	−0.855897	−0.0276239
$961$	−11.4134	−0.368173
$962$	−8.81398	−0.284174
$963$	−10.0389	−0.323499
$964$	−20.2985	−0.653772
$965$	30.4427	0.979987
$966$	−1.37617	−0.0442774
$967$	−35.0657	−1.12764	−0.563819	−	0.825899i	$-0.690668\pi$
$967$	−35.0657	−1.12764	−0.563819	+	0.825899i	$0.690668\pi$
$968$	5.33250	0.171393
$969$	−11.8329	−0.380129
$970$	19.9639	0.641003
$971$	−60.8052	−1.95133	−0.975666	−	0.219264i	$-0.929635\pi$
$971$	−60.8052	−1.95133	−0.975666	+	0.219264i	$0.929635\pi$
$972$	−9.34263	−0.299665
$973$	3.28835	0.105420
$974$	−33.6490	−1.07818
$975$	−0.970456	−0.0310795
$976$	8.55362	0.273795
$977$	−42.9689	−1.37470	−0.687348	−	0.726328i	$-0.741225\pi$
$977$	−42.9689	−1.37470	−0.687348	+	0.726328i	$0.741225\pi$
$978$	−5.30557	−0.169653
$979$	21.8251	0.697533
$980$	−9.01825	−0.288077
$981$	−5.48215	−0.175032
$982$	−13.8084	−0.440643
$983$	30.7999	0.982364	0.491182	−	0.871057i	$-0.336565\pi$
$983$	30.7999	0.982364	0.491182	+	0.871057i	$0.336565\pi$
$984$	3.30580	0.105385
$985$	12.1412	0.386851
$986$	−19.5880	−0.623810
$987$	−3.71752	−0.118330
$988$	27.4869	0.874475
$989$	−2.47736	−0.0787755
$990$	26.9328	0.855981
$991$	−5.31470	−0.168827	−0.0844134	−	0.996431i	$-0.526902\pi$
$991$	−5.31470	−0.168827	−0.0844134	+	0.996431i	$0.526902\pi$
$992$	−4.42568	−0.140515
$993$	4.30830	0.136720
$994$	11.9693	0.379643
$995$	39.1817	1.24214
$996$	−6.55675	−0.207758
$997$	−15.4028	−0.487812	−0.243906	−	0.969799i	$-0.578429\pi$
$997$	−15.4028	−0.487812	−0.243906	+	0.969799i	$0.578429\pi$
$998$	−33.7892	−1.06958
$999$	−2.97138	−0.0940103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.20	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.20	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.367906 q^{3} +1.00000 q^{4} +2.32640 q^{5} -0.367906 q^{6} +1.76735 q^{7} +1.00000 q^{8} -2.86465 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.367906 q^{3} +1.00000 q^{4} +2.32640 q^{5} -0.367906 q^{6} +1.76735 q^{7} +1.00000 q^{8} -2.86465 q^{9} +2.32640 q^{10} -4.04135 q^{11} -0.367906 q^{12} +6.40019 q^{13} +1.76735 q^{14} -0.855897 q^{15} +1.00000 q^{16} +7.48899 q^{17} -2.86465 q^{18} +4.29470 q^{19} +2.32640 q^{20} -0.650218 q^{21} -4.04135 q^{22} +2.11647 q^{23} -0.367906 q^{24} +0.412142 q^{25} +6.40019 q^{26} +2.15764 q^{27} +1.76735 q^{28} -2.61558 q^{29} -0.855897 q^{30} -4.42568 q^{31} +1.00000 q^{32} +1.48684 q^{33} +7.48899 q^{34} +4.11156 q^{35} -2.86465 q^{36} -1.37714 q^{37} +4.29470 q^{38} -2.35467 q^{39} +2.32640 q^{40} -8.98546 q^{41} -0.650218 q^{42} -1.17052 q^{43} -4.04135 q^{44} -6.66431 q^{45} +2.11647 q^{46} +5.71735 q^{47} -0.367906 q^{48} -3.87648 q^{49} +0.412142 q^{50} -2.75524 q^{51} +6.40019 q^{52} -8.17181 q^{53} +2.15764 q^{54} -9.40180 q^{55} +1.76735 q^{56} -1.58005 q^{57} -2.61558 q^{58} +9.38684 q^{59} -0.855897 q^{60} +8.55362 q^{61} -4.42568 q^{62} -5.06283 q^{63} +1.00000 q^{64} +14.8894 q^{65} +1.48684 q^{66} +12.0253 q^{67} +7.48899 q^{68} -0.778661 q^{69} +4.11156 q^{70} +6.77247 q^{71} -2.86465 q^{72} -7.93017 q^{73} -1.37714 q^{74} -0.151629 q^{75} +4.29470 q^{76} -7.14247 q^{77} -2.35467 q^{78} -4.66523 q^{79} +2.32640 q^{80} +7.80013 q^{81} -8.98546 q^{82} +17.8218 q^{83} -0.650218 q^{84} +17.4224 q^{85} -1.17052 q^{86} +0.962288 q^{87} -4.04135 q^{88} -5.40045 q^{89} -6.66431 q^{90} +11.3114 q^{91} +2.11647 q^{92} +1.62823 q^{93} +5.71735 q^{94} +9.99120 q^{95} -0.367906 q^{96} +8.58146 q^{97} -3.87648 q^{98} +11.5770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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