LMFDB - Embedded newform 4022.2.a.f.1.21

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			1.21
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.314271 q^{3} +1.00000 q^{4} +3.46435 q^{5} -0.314271 q^{6} -0.478329 q^{7} +1.00000 q^{8} -2.90123 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.314271 q^{3} +1.00000 q^{4} +3.46435 q^{5} -0.314271 q^{6} -0.478329 q^{7} +1.00000 q^{8} -2.90123 q^{9} +3.46435 q^{10} +2.30625 q^{11} -0.314271 q^{12} +1.35328 q^{13} -0.478329 q^{14} -1.08875 q^{15} +1.00000 q^{16} -0.642214 q^{17} -2.90123 q^{18} +1.56916 q^{19} +3.46435 q^{20} +0.150325 q^{21} +2.30625 q^{22} +2.29747 q^{23} -0.314271 q^{24} +7.00174 q^{25} +1.35328 q^{26} +1.85459 q^{27} -0.478329 q^{28} +0.990613 q^{29} -1.08875 q^{30} -2.42634 q^{31} +1.00000 q^{32} -0.724787 q^{33} -0.642214 q^{34} -1.65710 q^{35} -2.90123 q^{36} +1.54871 q^{37} +1.56916 q^{38} -0.425297 q^{39} +3.46435 q^{40} +0.666822 q^{41} +0.150325 q^{42} +6.84758 q^{43} +2.30625 q^{44} -10.0509 q^{45} +2.29747 q^{46} +8.00921 q^{47} -0.314271 q^{48} -6.77120 q^{49} +7.00174 q^{50} +0.201829 q^{51} +1.35328 q^{52} +3.07871 q^{53} +1.85459 q^{54} +7.98966 q^{55} -0.478329 q^{56} -0.493142 q^{57} +0.990613 q^{58} -11.6800 q^{59} -1.08875 q^{60} +12.3911 q^{61} -2.42634 q^{62} +1.38774 q^{63} +1.00000 q^{64} +4.68824 q^{65} -0.724787 q^{66} +1.96519 q^{67} -0.642214 q^{68} -0.722027 q^{69} -1.65710 q^{70} -5.97470 q^{71} -2.90123 q^{72} +2.10303 q^{73} +1.54871 q^{74} -2.20044 q^{75} +1.56916 q^{76} -1.10315 q^{77} -0.425297 q^{78} +16.2480 q^{79} +3.46435 q^{80} +8.12086 q^{81} +0.666822 q^{82} -9.39310 q^{83} +0.150325 q^{84} -2.22486 q^{85} +6.84758 q^{86} -0.311321 q^{87} +2.30625 q^{88} +6.44517 q^{89} -10.0509 q^{90} -0.647314 q^{91} +2.29747 q^{92} +0.762527 q^{93} +8.00921 q^{94} +5.43613 q^{95} -0.314271 q^{96} -14.9426 q^{97} -6.77120 q^{98} -6.69096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.314271	−0.181444	−0.0907222	−	0.995876i	$-0.528918\pi$
$3$	−0.314271	−0.181444	−0.0907222	+	0.995876i	$0.528918\pi$
$4$	1.00000	0.500000
$5$	3.46435	1.54931	0.774653	−	0.632387i	$-0.217925\pi$
$5$	3.46435	1.54931	0.774653	+	0.632387i	$0.217925\pi$
$6$	−0.314271	−0.128301
$7$	−0.478329	−0.180791	−0.0903957	−	0.995906i	$-0.528813\pi$
$7$	−0.478329	−0.180791	−0.0903957	+	0.995906i	$0.528813\pi$
$8$	1.00000	0.353553
$9$	−2.90123	−0.967078
$10$	3.46435	1.09552
$11$	2.30625	0.695360	0.347680	−	0.937613i	$-0.386970\pi$
$11$	2.30625	0.695360	0.347680	+	0.937613i	$0.386970\pi$
$12$	−0.314271	−0.0907222
$13$	1.35328	0.375333	0.187666	−	0.982233i	$-0.439908\pi$
$13$	1.35328	0.375333	0.187666	+	0.982233i	$0.439908\pi$
$14$	−0.478329	−0.127839
$15$	−1.08875	−0.281113
$16$	1.00000	0.250000
$17$	−0.642214	−0.155760	−0.0778799	−	0.996963i	$-0.524815\pi$
$17$	−0.642214	−0.155760	−0.0778799	+	0.996963i	$0.524815\pi$
$18$	−2.90123	−0.683827
$19$	1.56916	0.359991	0.179995	−	0.983667i	$-0.442392\pi$
$19$	1.56916	0.359991	0.179995	+	0.983667i	$0.442392\pi$
$20$	3.46435	0.774653
$21$	0.150325	0.0328036
$22$	2.30625	0.491694
$23$	2.29747	0.479055	0.239527	−	0.970890i	$-0.423008\pi$
$23$	2.29747	0.479055	0.239527	+	0.970890i	$0.423008\pi$
$24$	−0.314271	−0.0641503
$25$	7.00174	1.40035
$26$	1.35328	0.265400
$27$	1.85459	0.356915
$28$	−0.478329	−0.0903957
$29$	0.990613	0.183952	0.0919761	−	0.995761i	$-0.470682\pi$
$29$	0.990613	0.183952	0.0919761	+	0.995761i	$0.470682\pi$
$30$	−1.08875	−0.198777
$31$	−2.42634	−0.435783	−0.217891	−	0.975973i	$-0.569918\pi$
$31$	−2.42634	−0.435783	−0.217891	+	0.975973i	$0.569918\pi$
$32$	1.00000	0.176777
$33$	−0.724787	−0.126169
$34$	−0.642214	−0.110139
$35$	−1.65710	−0.280101
$36$	−2.90123	−0.483539
$37$	1.54871	0.254607	0.127304	−	0.991864i	$-0.459368\pi$
$37$	1.54871	0.254607	0.127304	+	0.991864i	$0.459368\pi$
$38$	1.56916	0.254552
$39$	−0.425297	−0.0681020
$40$	3.46435	0.547762
$41$	0.666822	0.104140	0.0520700	−	0.998643i	$-0.483418\pi$
$41$	0.666822	0.104140	0.0520700	+	0.998643i	$0.483418\pi$
$42$	0.150325	0.0231956
$43$	6.84758	1.04425	0.522123	−	0.852870i	$-0.325140\pi$
$43$	6.84758	1.04425	0.522123	+	0.852870i	$0.325140\pi$
$44$	2.30625	0.347680
$45$	−10.0509	−1.49830
$46$	2.29747	0.338743
$47$	8.00921	1.16826	0.584132	−	0.811659i	$-0.301435\pi$
$47$	8.00921	1.16826	0.584132	+	0.811659i	$0.301435\pi$
$48$	−0.314271	−0.0453611
$49$	−6.77120	−0.967314
$50$	7.00174	0.990195
$51$	0.201829	0.0282617
$52$	1.35328	0.187666
$53$	3.07871	0.422894	0.211447	−	0.977390i	$-0.432182\pi$
$53$	3.07871	0.422894	0.211447	+	0.977390i	$0.432182\pi$
$54$	1.85459	0.252377
$55$	7.98966	1.07733
$56$	−0.478329	−0.0639194
$57$	−0.493142	−0.0653183
$58$	0.990613	0.130074
$59$	−11.6800	−1.52061	−0.760306	−	0.649565i	$-0.774951\pi$
$59$	−11.6800	−1.52061	−0.760306	+	0.649565i	$0.774951\pi$
$60$	−1.08875	−0.140556
$61$	12.3911	1.58652	0.793260	−	0.608884i	$-0.208382\pi$
$61$	12.3911	1.58652	0.793260	+	0.608884i	$0.208382\pi$
$62$	−2.42634	−0.308145
$63$	1.38774	0.174839
$64$	1.00000	0.125000
$65$	4.68824	0.581505
$66$	−0.724787	−0.0892151
$67$	1.96519	0.240086	0.120043	−	0.992769i	$-0.461697\pi$
$67$	1.96519	0.240086	0.120043	+	0.992769i	$0.461697\pi$
$68$	−0.642214	−0.0778799
$69$	−0.722027	−0.0869218
$70$	−1.65710	−0.198061
$71$	−5.97470	−0.709066	−0.354533	−	0.935043i	$-0.615360\pi$
$71$	−5.97470	−0.709066	−0.354533	+	0.935043i	$0.615360\pi$
$72$	−2.90123	−0.341914
$73$	2.10303	0.246142	0.123071	−	0.992398i	$-0.460726\pi$
$73$	2.10303	0.246142	0.123071	+	0.992398i	$0.460726\pi$
$74$	1.54871	0.180034
$75$	−2.20044	−0.254085
$76$	1.56916	0.179995
$77$	−1.10315	−0.125715
$78$	−0.425297	−0.0481554
$79$	16.2480	1.82804	0.914021	−	0.405667i	$-0.132961\pi$
$79$	16.2480	1.82804	0.914021	+	0.405667i	$0.132961\pi$
$80$	3.46435	0.387326
$81$	8.12086	0.902318
$82$	0.666822	0.0736381
$83$	−9.39310	−1.03103	−0.515513	−	0.856882i	$-0.672399\pi$
$83$	−9.39310	−1.03103	−0.515513	+	0.856882i	$0.672399\pi$
$84$	0.150325	0.0164018
$85$	−2.22486	−0.241319
$86$	6.84758	0.738394
$87$	−0.311321	−0.0333771
$88$	2.30625	0.245847
$89$	6.44517	0.683187	0.341593	−	0.939848i	$-0.389033\pi$
$89$	6.44517	0.683187	0.341593	+	0.939848i	$0.389033\pi$
$90$	−10.0509	−1.05946
$91$	−0.647314	−0.0678570
$92$	2.29747	0.239527
$93$	0.762527	0.0790704
$94$	8.00921	0.826087
$95$	5.43613	0.557735
$96$	−0.314271	−0.0320751
$97$	−14.9426	−1.51719	−0.758595	−	0.651562i	$-0.774114\pi$
$97$	−14.9426	−1.51719	−0.758595	+	0.651562i	$0.774114\pi$
$98$	−6.77120	−0.683995
$99$	−6.69096	−0.672467
$100$	7.00174	0.700174
$101$	12.1183	1.20582	0.602910	−	0.797809i	$-0.294008\pi$
$101$	12.1183	1.20582	0.602910	+	0.797809i	$0.294008\pi$
$102$	0.201829	0.0199841
$103$	17.5896	1.73315	0.866577	−	0.499044i	$-0.166315\pi$
$103$	17.5896	1.73315	0.866577	+	0.499044i	$0.166315\pi$
$104$	1.35328	0.132700
$105$	0.520779	0.0508228
$106$	3.07871	0.299031
$107$	6.25808	0.604992	0.302496	−	0.953151i	$-0.402180\pi$
$107$	6.25808	0.604992	0.302496	+	0.953151i	$0.402180\pi$
$108$	1.85459	0.178458
$109$	−14.5391	−1.39259	−0.696294	−	0.717756i	$-0.745169\pi$
$109$	−14.5391	−1.39259	−0.696294	+	0.717756i	$0.745169\pi$
$110$	7.98966	0.761784
$111$	−0.486716	−0.0461970
$112$	−0.478329	−0.0451979
$113$	−3.69271	−0.347381	−0.173690	−	0.984800i	$-0.555569\pi$
$113$	−3.69271	−0.347381	−0.173690	+	0.984800i	$0.555569\pi$
$114$	−0.493142	−0.0461870
$115$	7.95923	0.742202
$116$	0.990613	0.0919761
$117$	−3.92619	−0.362976
$118$	−11.6800	−1.07523
$119$	0.307190	0.0281600
$120$	−1.08875	−0.0993884
$121$	−5.68122	−0.516475
$122$	12.3911	1.12184
$123$	−0.209563	−0.0188956
$124$	−2.42634	−0.217891
$125$	6.93473	0.620261
$126$	1.38774	0.123630
$127$	−21.0892	−1.87136	−0.935681	−	0.352847i	$-0.885214\pi$
$127$	−21.0892	−1.87136	−0.935681	+	0.352847i	$0.885214\pi$
$128$	1.00000	0.0883883
$129$	−2.15200	−0.189473
$130$	4.68824	0.411186
$131$	20.4892	1.79015	0.895075	−	0.445915i	$-0.147122\pi$
$131$	20.4892	1.79015	0.895075	+	0.445915i	$0.147122\pi$
$132$	−0.724787	−0.0630846
$133$	−0.750576	−0.0650832
$134$	1.96519	0.169767
$135$	6.42494	0.552971
$136$	−0.642214	−0.0550694
$137$	−6.77435	−0.578772	−0.289386	−	0.957213i	$-0.593451\pi$
$137$	−6.77435	−0.578772	−0.289386	+	0.957213i	$0.593451\pi$
$138$	−0.722027	−0.0614630
$139$	6.10316	0.517664	0.258832	−	0.965922i	$-0.416662\pi$
$139$	6.10316	0.517664	0.258832	+	0.965922i	$0.416662\pi$
$140$	−1.65710	−0.140051
$141$	−2.51706	−0.211975
$142$	−5.97470	−0.501386
$143$	3.12100	0.260991
$144$	−2.90123	−0.241769
$145$	3.43183	0.284998
$146$	2.10303	0.174048
$147$	2.12799	0.175514
$148$	1.54871	0.127304
$149$	11.4074	0.934527	0.467263	−	0.884118i	$-0.345240\pi$
$149$	11.4074	0.934527	0.467263	+	0.884118i	$0.345240\pi$
$150$	−2.20044	−0.179665
$151$	−4.81884	−0.392152	−0.196076	−	0.980589i	$-0.562820\pi$
$151$	−4.81884	−0.392152	−0.196076	+	0.980589i	$0.562820\pi$
$152$	1.56916	0.127276
$153$	1.86321	0.150632
$154$	−1.10315	−0.0888940
$155$	−8.40568	−0.675161
$156$	−0.425297	−0.0340510
$157$	−20.4494	−1.63204	−0.816021	−	0.578022i	$-0.803825\pi$
$157$	−20.4494	−1.63204	−0.816021	+	0.578022i	$0.803825\pi$
$158$	16.2480	1.29262
$159$	−0.967550	−0.0767317
$160$	3.46435	0.273881
$161$	−1.09895	−0.0866090
$162$	8.12086	0.638035
$163$	−10.5025	−0.822616	−0.411308	−	0.911496i	$-0.634928\pi$
$163$	−10.5025	−0.822616	−0.411308	+	0.911496i	$0.634928\pi$
$164$	0.666822	0.0520700
$165$	−2.51092	−0.195475
$166$	−9.39310	−0.729046
$167$	−12.0164	−0.929858	−0.464929	−	0.885348i	$-0.653920\pi$
$167$	−12.0164	−0.929858	−0.464929	+	0.885348i	$0.653920\pi$
$168$	0.150325	0.0115978
$169$	−11.1686	−0.859125
$170$	−2.22486	−0.170639
$171$	−4.55251	−0.348139
$172$	6.84758	0.522123
$173$	3.98349	0.302859	0.151430	−	0.988468i	$-0.451612\pi$
$173$	3.98349	0.302859	0.151430	+	0.988468i	$0.451612\pi$
$174$	−0.311321	−0.0236012
$175$	−3.34914	−0.253171
$176$	2.30625	0.173840
$177$	3.67070	0.275906
$178$	6.44517	0.483086
$179$	−2.15491	−0.161066	−0.0805329	−	0.996752i	$-0.525662\pi$
$179$	−2.15491	−0.161066	−0.0805329	+	0.996752i	$0.525662\pi$
$180$	−10.0509	−0.749150
$181$	−8.42497	−0.626223	−0.313111	−	0.949716i	$-0.601371\pi$
$181$	−8.42497	−0.626223	−0.313111	+	0.949716i	$0.601371\pi$
$182$	−0.647314	−0.0479821
$183$	−3.89417	−0.287865
$184$	2.29747	0.169371
$185$	5.36529	0.394464
$186$	0.762527	0.0559112
$187$	−1.48110	−0.108309
$188$	8.00921	0.584132
$189$	−0.887103	−0.0645272
$190$	5.43613	0.394378
$191$	−27.5604	−1.99420	−0.997102	−	0.0760783i	$-0.975760\pi$
$191$	−27.5604	−1.99420	−0.997102	+	0.0760783i	$0.975760\pi$
$192$	−0.314271	−0.0226806
$193$	10.7597	0.774500	0.387250	−	0.921975i	$-0.373425\pi$
$193$	10.7597	0.774500	0.387250	+	0.921975i	$0.373425\pi$
$194$	−14.9426	−1.07282
$195$	−1.47338	−0.105511
$196$	−6.77120	−0.483657
$197$	9.14463	0.651528	0.325764	−	0.945451i	$-0.394379\pi$
$197$	9.14463	0.651528	0.325764	+	0.945451i	$0.394379\pi$
$198$	−6.69096	−0.475506
$199$	8.65745	0.613710	0.306855	−	0.951756i	$-0.400723\pi$
$199$	8.65745	0.613710	0.306855	+	0.951756i	$0.400723\pi$
$200$	7.00174	0.495098
$201$	−0.617603	−0.0435623
$202$	12.1183	0.852643
$203$	−0.473839	−0.0332570
$204$	0.201829	0.0141309
$205$	2.31011	0.161345
$206$	17.5896	1.22552
$207$	−6.66549	−0.463283
$208$	1.35328	0.0938332
$209$	3.61888	0.250323
$210$	0.520779	0.0359371
$211$	16.7840	1.15546	0.577729	−	0.816228i	$-0.303939\pi$
$211$	16.7840	1.15546	0.577729	+	0.816228i	$0.303939\pi$
$212$	3.07871	0.211447
$213$	1.87767	0.128656
$214$	6.25808	0.427794
$215$	23.7224	1.61786
$216$	1.85459	0.126189
$217$	1.16059	0.0787858
$218$	−14.5391	−0.984709
$219$	−0.660923	−0.0446610
$220$	7.98966	0.538663
$221$	−0.869096	−0.0584617
$222$	−0.486716	−0.0326662
$223$	3.93502	0.263508	0.131754	−	0.991282i	$-0.457939\pi$
$223$	3.93502	0.263508	0.131754	+	0.991282i	$0.457939\pi$
$224$	−0.478329	−0.0319597
$225$	−20.3137	−1.35425
$226$	−3.69271	−0.245635
$227$	−13.5216	−0.897459	−0.448729	−	0.893668i	$-0.648123\pi$
$227$	−13.5216	−0.897459	−0.448729	+	0.893668i	$0.648123\pi$
$228$	−0.493142	−0.0326591
$229$	23.2500	1.53641	0.768203	−	0.640207i	$-0.221151\pi$
$229$	23.2500	1.53641	0.768203	+	0.640207i	$0.221151\pi$
$230$	7.95923	0.524816
$231$	0.346687	0.0228103
$232$	0.990613	0.0650369
$233$	−24.6156	−1.61262	−0.806309	−	0.591494i	$-0.798538\pi$
$233$	−24.6156	−1.61262	−0.806309	+	0.591494i	$0.798538\pi$
$234$	−3.92619	−0.256663
$235$	27.7467	1.81000
$236$	−11.6800	−0.760306
$237$	−5.10627	−0.331688
$238$	0.307190	0.0199121
$239$	23.9147	1.54692	0.773458	−	0.633848i	$-0.218526\pi$
$239$	23.9147	1.54692	0.773458	+	0.633848i	$0.218526\pi$
$240$	−1.08875	−0.0702782
$241$	−19.5325	−1.25820	−0.629100	−	0.777325i	$-0.716576\pi$
$241$	−19.5325	−1.25820	−0.629100	+	0.777325i	$0.716576\pi$
$242$	−5.68122	−0.365203
$243$	−8.11591	−0.520636
$244$	12.3911	0.793260
$245$	−23.4578	−1.49867
$246$	−0.209563	−0.0133612
$247$	2.12352	0.135116
$248$	−2.42634	−0.154073
$249$	2.95198	0.187074
$250$	6.93473	0.438591
$251$	24.8127	1.56616	0.783082	−	0.621919i	$-0.213647\pi$
$251$	24.8127	1.56616	0.783082	+	0.621919i	$0.213647\pi$
$252$	1.38774	0.0874197
$253$	5.29853	0.333116
$254$	−21.0892	−1.32325
$255$	0.699207	0.0437861
$256$	1.00000	0.0625000
$257$	−9.39350	−0.585951	−0.292975	−	0.956120i	$-0.594645\pi$
$257$	−9.39350	−0.585951	−0.292975	+	0.956120i	$0.594645\pi$
$258$	−2.15200	−0.133977
$259$	−0.740795	−0.0460308
$260$	4.68824	0.290753
$261$	−2.87400	−0.177896
$262$	20.4892	1.26583
$263$	14.4741	0.892512	0.446256	−	0.894905i	$-0.352757\pi$
$263$	14.4741	0.892512	0.446256	+	0.894905i	$0.352757\pi$
$264$	−0.724787	−0.0446075
$265$	10.6657	0.655192
$266$	−0.750576	−0.0460208
$267$	−2.02553	−0.123960
$268$	1.96519	0.120043
$269$	11.8242	0.720937	0.360468	−	0.932771i	$-0.382617\pi$
$269$	11.8242	0.720937	0.360468	+	0.932771i	$0.382617\pi$
$270$	6.42494	0.391009
$271$	29.9811	1.82122	0.910610	−	0.413268i	$-0.135613\pi$
$271$	29.9811	1.82122	0.910610	+	0.413268i	$0.135613\pi$
$272$	−0.642214	−0.0389399
$273$	0.203432	0.0123123
$274$	−6.77435	−0.409253
$275$	16.1477	0.973746
$276$	−0.722027	−0.0434609
$277$	−18.3822	−1.10448	−0.552240	−	0.833685i	$-0.686227\pi$
$277$	−18.3822	−1.10448	−0.552240	+	0.833685i	$0.686227\pi$
$278$	6.10316	0.366043
$279$	7.03937	0.421436
$280$	−1.65710	−0.0990307
$281$	−0.195976	−0.0116909	−0.00584547	−	0.999983i	$-0.501861\pi$
$281$	−0.195976	−0.0116909	−0.00584547	+	0.999983i	$0.501861\pi$
$282$	−2.51706	−0.149889
$283$	15.9433	0.947733	0.473867	−	0.880597i	$-0.342858\pi$
$283$	15.9433	0.947733	0.473867	+	0.880597i	$0.342858\pi$
$284$	−5.97470	−0.354533
$285$	−1.70842	−0.101198
$286$	3.12100	0.184549
$287$	−0.318960	−0.0188276
$288$	−2.90123	−0.170957
$289$	−16.5876	−0.975739
$290$	3.43183	0.201524
$291$	4.69602	0.275286
$292$	2.10303	0.123071
$293$	−30.7103	−1.79411	−0.897056	−	0.441917i	$-0.854299\pi$
$293$	−30.7103	−1.79411	−0.897056	+	0.441917i	$0.854299\pi$
$294$	2.12799	0.124107
$295$	−40.4638	−2.35589
$296$	1.54871	0.0900172
$297$	4.27714	0.248185
$298$	11.4074	0.660810
$299$	3.10912	0.179805
$300$	−2.20044	−0.127043
$301$	−3.27540	−0.188791
$302$	−4.81884	−0.277293
$303$	−3.80844	−0.218789
$304$	1.56916	0.0899976
$305$	42.9272	2.45800
$306$	1.86321	0.106513
$307$	−23.1968	−1.32391	−0.661955	−	0.749544i	$-0.730273\pi$
$307$	−23.1968	−1.32391	−0.661955	+	0.749544i	$0.730273\pi$
$308$	−1.10315	−0.0628576
$309$	−5.52790	−0.314471
$310$	−8.40568	−0.477411
$311$	−24.8146	−1.40711	−0.703554	−	0.710642i	$-0.748405\pi$
$311$	−24.8146	−1.40711	−0.703554	+	0.710642i	$0.748405\pi$
$312$	−0.425297	−0.0240777
$313$	−26.0580	−1.47289	−0.736443	−	0.676500i	$-0.763496\pi$
$313$	−26.0580	−1.47289	−0.736443	+	0.676500i	$0.763496\pi$
$314$	−20.4494	−1.15403
$315$	4.80764	0.270880
$316$	16.2480	0.914021
$317$	28.4847	1.59986	0.799930	−	0.600093i	$-0.204870\pi$
$317$	28.4847	1.59986	0.799930	+	0.600093i	$0.204870\pi$
$318$	−0.967550	−0.0542575
$319$	2.28460	0.127913
$320$	3.46435	0.193663
$321$	−1.96673	−0.109772
$322$	−1.09895	−0.0612418
$323$	−1.00774	−0.0560720
$324$	8.12086	0.451159
$325$	9.47532	0.525596
$326$	−10.5025	−0.581677
$327$	4.56920	0.252677
$328$	0.666822	0.0368191
$329$	−3.83104	−0.211212
$330$	−2.51092	−0.138221
$331$	−0.587820	−0.0323095	−0.0161548	−	0.999870i	$-0.505142\pi$
$331$	−0.587820	−0.0323095	−0.0161548	+	0.999870i	$0.505142\pi$
$332$	−9.39310	−0.515513
$333$	−4.49318	−0.246225
$334$	−12.0164	−0.657509
$335$	6.80812	0.371967
$336$	0.150325	0.00820090
$337$	30.7637	1.67580	0.837902	−	0.545821i	$-0.183782\pi$
$337$	30.7637	1.67580	0.837902	+	0.545821i	$0.183782\pi$
$338$	−11.1686	−0.607493
$339$	1.16051	0.0630303
$340$	−2.22486	−0.120660
$341$	−5.59573	−0.303026
$342$	−4.55251	−0.246171
$343$	6.58717	0.355674
$344$	6.84758	0.369197
$345$	−2.50136	−0.134668
$346$	3.98349	0.214154
$347$	11.1277	0.597364	0.298682	−	0.954353i	$-0.403453\pi$
$347$	11.1277	0.597364	0.298682	+	0.954353i	$0.403453\pi$
$348$	−0.311321	−0.0166885
$349$	−16.7748	−0.897935	−0.448968	−	0.893548i	$-0.648208\pi$
$349$	−16.7748	−0.897935	−0.448968	+	0.893548i	$0.648208\pi$
$350$	−3.34914	−0.179019
$351$	2.50978	0.133962
$352$	2.30625	0.122923
$353$	0.786439	0.0418579	0.0209290	−	0.999781i	$-0.493338\pi$
$353$	0.786439	0.0418579	0.0209290	+	0.999781i	$0.493338\pi$
$354$	3.67070	0.195095
$355$	−20.6985	−1.09856
$356$	6.44517	0.341593
$357$	−0.0965408	−0.00510948
$358$	−2.15491	−0.113891
$359$	−6.16111	−0.325171	−0.162586	−	0.986694i	$-0.551983\pi$
$359$	−6.16111	−0.325171	−0.162586	+	0.986694i	$0.551983\pi$
$360$	−10.0509	−0.529729
$361$	−16.5377	−0.870407
$362$	−8.42497	−0.442806
$363$	1.78544	0.0937114
$364$	−0.647314	−0.0339285
$365$	7.28565	0.381349
$366$	−3.89417	−0.203551
$367$	−33.3152	−1.73904	−0.869520	−	0.493897i	$-0.835572\pi$
$367$	−33.3152	−1.73904	−0.869520	+	0.493897i	$0.835572\pi$
$368$	2.29747	0.119764
$369$	−1.93461	−0.100712
$370$	5.36529	0.278928
$371$	−1.47264	−0.0764556
$372$	0.762527	0.0395352
$373$	3.27399	0.169521	0.0847603	−	0.996401i	$-0.472988\pi$
$373$	3.27399	0.169521	0.0847603	+	0.996401i	$0.472988\pi$
$374$	−1.48110	−0.0765861
$375$	−2.17938	−0.112543
$376$	8.00921	0.413044
$377$	1.34058	0.0690433
$378$	−0.887103	−0.0456276
$379$	12.2391	0.628679	0.314340	−	0.949311i	$-0.398217\pi$
$379$	12.2391	0.628679	0.314340	+	0.949311i	$0.398217\pi$
$380$	5.43613	0.278868
$381$	6.62772	0.339548
$382$	−27.5604	−1.41011
$383$	−6.89651	−0.352395	−0.176198	−	0.984355i	$-0.556380\pi$
$383$	−6.89651	−0.352395	−0.176198	+	0.984355i	$0.556380\pi$
$384$	−0.314271	−0.0160376
$385$	−3.82169	−0.194771
$386$	10.7597	0.547655
$387$	−19.8664	−1.00987
$388$	−14.9426	−0.758595
$389$	2.21737	0.112425	0.0562124	−	0.998419i	$-0.482098\pi$
$389$	2.21737	0.112425	0.0562124	+	0.998419i	$0.482098\pi$
$390$	−1.47338	−0.0746075
$391$	−1.47546	−0.0746175
$392$	−6.77120	−0.341997
$393$	−6.43916	−0.324813
$394$	9.14463	0.460700
$395$	56.2888	2.83220
$396$	−6.69096	−0.336234
$397$	24.3756	1.22337	0.611687	−	0.791100i	$-0.290491\pi$
$397$	24.3756	1.22337	0.611687	+	0.791100i	$0.290491\pi$
$398$	8.65745	0.433959
$399$	0.235884	0.0118090
$400$	7.00174	0.350087
$401$	−10.6732	−0.532993	−0.266496	−	0.963836i	$-0.585866\pi$
$401$	−10.6732	−0.532993	−0.266496	+	0.963836i	$0.585866\pi$
$402$	−0.617603	−0.0308032
$403$	−3.28352	−0.163564
$404$	12.1183	0.602910
$405$	28.1335	1.39797
$406$	−0.473839	−0.0235162
$407$	3.57172	0.177044
$408$	0.201829	0.00999203
$409$	−29.8281	−1.47490	−0.737451	−	0.675400i	$-0.763971\pi$
$409$	−29.8281	−1.47490	−0.737451	+	0.675400i	$0.763971\pi$
$410$	2.31011	0.114088
$411$	2.12898	0.105015
$412$	17.5896	0.866577
$413$	5.58690	0.274914
$414$	−6.66549	−0.327591
$415$	−32.5410	−1.59738
$416$	1.35328	0.0663501
$417$	−1.91805	−0.0939272
$418$	3.61888	0.177005
$419$	3.31617	0.162005	0.0810027	−	0.996714i	$-0.474188\pi$
$419$	3.31617	0.162005	0.0810027	+	0.996714i	$0.474188\pi$
$420$	0.520779	0.0254114
$421$	21.4408	1.04496	0.522481	−	0.852651i	$-0.325006\pi$
$421$	21.4408	1.04496	0.522481	+	0.852651i	$0.325006\pi$
$422$	16.7840	0.817033
$423$	−23.2366	−1.12980
$424$	3.07871	0.149515
$425$	−4.49661	−0.218118
$426$	1.87767	0.0909736
$427$	−5.92703	−0.286829
$428$	6.25808	0.302496
$429$	−0.980841	−0.0473554
$430$	23.7224	1.14400
$431$	−28.2814	−1.36227	−0.681135	−	0.732158i	$-0.738513\pi$
$431$	−28.2814	−1.36227	−0.681135	+	0.732158i	$0.738513\pi$
$432$	1.85459	0.0892288
$433$	3.18962	0.153284	0.0766418	−	0.997059i	$-0.475580\pi$
$433$	3.18962	0.153284	0.0766418	+	0.997059i	$0.475580\pi$
$434$	1.16059	0.0557100
$435$	−1.07852	−0.0517113
$436$	−14.5391	−0.696294
$437$	3.60510	0.172455
$438$	−0.660923	−0.0315801
$439$	−36.0339	−1.71980	−0.859902	−	0.510460i	$-0.829475\pi$
$439$	−36.0339	−1.71980	−0.859902	+	0.510460i	$0.829475\pi$
$440$	7.98966	0.380892
$441$	19.6448	0.935468
$442$	−0.869096	−0.0413387
$443$	5.59748	0.265944	0.132972	−	0.991120i	$-0.457548\pi$
$443$	5.59748	0.265944	0.132972	+	0.991120i	$0.457548\pi$
$444$	−0.486716	−0.0230985
$445$	22.3283	1.05847
$446$	3.93502	0.186329
$447$	−3.58500	−0.169565
$448$	−0.478329	−0.0225989
$449$	−19.0659	−0.899775	−0.449887	−	0.893085i	$-0.648536\pi$
$449$	−19.0659	−0.899775	−0.449887	+	0.893085i	$0.648536\pi$
$450$	−20.3137	−0.957596
$451$	1.53786	0.0724148
$452$	−3.69271	−0.173690
$453$	1.51442	0.0711538
$454$	−13.5216	−0.634599
$455$	−2.24252	−0.105131
$456$	−0.493142	−0.0230935
$457$	−7.91818	−0.370397	−0.185198	−	0.982701i	$-0.559293\pi$
$457$	−7.91818	−0.370397	−0.185198	+	0.982701i	$0.559293\pi$
$458$	23.2500	1.08640
$459$	−1.19104	−0.0555930
$460$	7.95923	0.371101
$461$	−22.7830	−1.06111	−0.530555	−	0.847650i	$-0.678017\pi$
$461$	−22.7830	−1.06111	−0.530555	+	0.847650i	$0.678017\pi$
$462$	0.346687	0.0161293
$463$	39.3578	1.82911	0.914556	−	0.404459i	$-0.132540\pi$
$463$	39.3578	1.82911	0.914556	+	0.404459i	$0.132540\pi$
$464$	0.990613	0.0459880
$465$	2.64166	0.122504
$466$	−24.6156	−1.14029
$467$	32.5055	1.50418	0.752088	−	0.659062i	$-0.229047\pi$
$467$	32.5055	1.50418	0.752088	+	0.659062i	$0.229047\pi$
$468$	−3.92619	−0.181488
$469$	−0.940009	−0.0434056
$470$	27.7467	1.27986
$471$	6.42666	0.296125
$472$	−11.6800	−0.537617
$473$	15.7922	0.726127
$474$	−5.10627	−0.234539
$475$	10.9869	0.504112
$476$	0.307190	0.0140800
$477$	−8.93206	−0.408971
$478$	23.9147	1.09383
$479$	4.55971	0.208339	0.104169	−	0.994560i	$-0.466782\pi$
$479$	4.55971	0.208339	0.104169	+	0.994560i	$0.466782\pi$
$480$	−1.08875	−0.0496942
$481$	2.09585	0.0955624
$482$	−19.5325	−0.889682
$483$	0.345367	0.0157147
$484$	−5.68122	−0.258237
$485$	−51.7664	−2.35059
$486$	−8.11591	−0.368145
$487$	31.6498	1.43419	0.717096	−	0.696975i	$-0.245471\pi$
$487$	31.6498	1.43419	0.717096	+	0.696975i	$0.245471\pi$
$488$	12.3911	0.560919
$489$	3.30062	0.149259
$490$	−23.4578	−1.05972
$491$	28.6966	1.29506	0.647530	−	0.762040i	$-0.275802\pi$
$491$	28.6966	1.29506	0.647530	+	0.762040i	$0.275802\pi$
$492$	−0.209563	−0.00944781
$493$	−0.636185	−0.0286523
$494$	2.12352	0.0955416
$495$	−23.1799	−1.04186
$496$	−2.42634	−0.108946
$497$	2.85787	0.128193
$498$	2.95198	0.132281
$499$	−14.0587	−0.629355	−0.314677	−	0.949199i	$-0.601896\pi$
$499$	−14.0587	−0.629355	−0.314677	+	0.949199i	$0.601896\pi$
$500$	6.93473	0.310130
$501$	3.77641	0.168717
$502$	24.8127	1.10744
$503$	16.8383	0.750780	0.375390	−	0.926867i	$-0.377509\pi$
$503$	16.8383	0.750780	0.375390	+	0.926867i	$0.377509\pi$
$504$	1.38774	0.0618151
$505$	41.9822	1.86818
$506$	5.29853	0.235548
$507$	3.50998	0.155883
$508$	−21.0892	−0.935681
$509$	1.89909	0.0841756	0.0420878	−	0.999114i	$-0.486599\pi$
$509$	1.89909	0.0841756	0.0420878	+	0.999114i	$0.486599\pi$
$510$	0.699207	0.0309614
$511$	−1.00594	−0.0445003
$512$	1.00000	0.0441942
$513$	2.91015	0.128486
$514$	−9.39350	−0.414330
$515$	60.9365	2.68518
$516$	−2.15200	−0.0947363
$517$	18.4712	0.812364
$518$	−0.740795	−0.0325487
$519$	−1.25190	−0.0549521
$520$	4.68824	0.205593
$521$	−42.4958	−1.86177	−0.930887	−	0.365307i	$-0.880964\pi$
$521$	−42.4958	−1.86177	−0.930887	+	0.365307i	$0.880964\pi$
$522$	−2.87400	−0.125791
$523$	11.3011	0.494165	0.247082	−	0.968994i	$-0.420528\pi$
$523$	11.3011	0.494165	0.247082	+	0.968994i	$0.420528\pi$
$524$	20.4892	0.895075
$525$	1.05254	0.0459364
$526$	14.4741	0.631101
$527$	1.55823	0.0678774
$528$	−0.724787	−0.0315423
$529$	−17.7216	−0.770506
$530$	10.6657	0.463290
$531$	33.8865	1.47055
$532$	−0.750576	−0.0325416
$533$	0.902397	0.0390872
$534$	−2.02553	−0.0876533
$535$	21.6802	0.937317
$536$	1.96519	0.0848834
$537$	0.677227	0.0292245
$538$	11.8242	0.509779
$539$	−15.6161	−0.672632
$540$	6.42494	0.276485
$541$	−28.2214	−1.21333	−0.606666	−	0.794957i	$-0.707494\pi$
$541$	−28.2214	−1.21333	−0.606666	+	0.794957i	$0.707494\pi$
$542$	29.9811	1.28780
$543$	2.64772	0.113625
$544$	−0.642214	−0.0275347
$545$	−50.3684	−2.15755
$546$	0.203432	0.00870609
$547$	−17.4716	−0.747034	−0.373517	−	0.927623i	$-0.621848\pi$
$547$	−17.4716	−0.747034	−0.373517	+	0.927623i	$0.621848\pi$
$548$	−6.77435	−0.289386
$549$	−35.9495	−1.53429
$550$	16.1477	0.688542
$551$	1.55443	0.0662210
$552$	−0.722027	−0.0307315
$553$	−7.77189	−0.330494
$554$	−18.3822	−0.780985
$555$	−1.68616	−0.0715733
$556$	6.10316	0.258832
$557$	6.44772	0.273199	0.136599	−	0.990626i	$-0.456383\pi$
$557$	6.44772	0.273199	0.136599	+	0.990626i	$0.456383\pi$
$558$	7.03937	0.298000
$559$	9.26671	0.391940
$560$	−1.65710	−0.0700253
$561$	0.465468	0.0196521
$562$	−0.195976	−0.00826675
$563$	11.7626	0.495734	0.247867	−	0.968794i	$-0.420270\pi$
$563$	11.7626	0.495734	0.247867	+	0.968794i	$0.420270\pi$
$564$	−2.51706	−0.105987
$565$	−12.7928	−0.538199
$566$	15.9433	0.670149
$567$	−3.88444	−0.163131
$568$	−5.97470	−0.250693
$569$	−2.36349	−0.0990825	−0.0495413	−	0.998772i	$-0.515776\pi$
$569$	−2.36349	−0.0990825	−0.0495413	+	0.998772i	$0.515776\pi$
$570$	−1.70842	−0.0715578
$571$	8.14332	0.340787	0.170394	−	0.985376i	$-0.445496\pi$
$571$	8.14332	0.340787	0.170394	+	0.985376i	$0.445496\pi$
$572$	3.12100	0.130496
$573$	8.66145	0.361837
$574$	−0.318960	−0.0133131
$575$	16.0863	0.670843
$576$	−2.90123	−0.120885
$577$	−37.0660	−1.54308	−0.771538	−	0.636183i	$-0.780512\pi$
$577$	−37.0660	−1.54308	−0.771538	+	0.636183i	$0.780512\pi$
$578$	−16.5876	−0.689952
$579$	−3.38146	−0.140529
$580$	3.43183	0.142499
$581$	4.49299	0.186401
$582$	4.69602	0.194656
$583$	7.10027	0.294063
$584$	2.10303	0.0870242
$585$	−13.6017	−0.562361
$586$	−30.7103	−1.26863
$587$	12.3575	0.510048	0.255024	−	0.966935i	$-0.417917\pi$
$587$	12.3575	0.510048	0.255024	+	0.966935i	$0.417917\pi$
$588$	2.12799	0.0877569
$589$	−3.80732	−0.156878
$590$	−40.4638	−1.66587
$591$	−2.87389	−0.118216
$592$	1.54871	0.0636518
$593$	6.68299	0.274437	0.137219	−	0.990541i	$-0.456184\pi$
$593$	6.68299	0.274437	0.137219	+	0.990541i	$0.456184\pi$
$594$	4.27714	0.175493
$595$	1.06421	0.0436285
$596$	11.4074	0.467263
$597$	−2.72078	−0.111354
$598$	3.10912	0.127141
$599$	−11.2852	−0.461099	−0.230550	−	0.973061i	$-0.574052\pi$
$599$	−11.2852	−0.461099	−0.230550	+	0.973061i	$0.574052\pi$
$600$	−2.20044	−0.0898327
$601$	−24.7914	−1.01126	−0.505631	−	0.862750i	$-0.668740\pi$
$601$	−24.7914	−1.01126	−0.505631	+	0.862750i	$0.668740\pi$
$602$	−3.27540	−0.133495
$603$	−5.70148	−0.232182
$604$	−4.81884	−0.196076
$605$	−19.6817	−0.800177
$606$	−3.80844	−0.154707
$607$	−47.9073	−1.94450	−0.972248	−	0.233951i	$-0.924835\pi$
$607$	−47.9073	−1.94450	−0.972248	+	0.233951i	$0.924835\pi$
$608$	1.56916	0.0636379
$609$	0.148914	0.00603429
$610$	42.9272	1.73807
$611$	10.8387	0.438488
$612$	1.86321	0.0753159
$613$	32.8683	1.32754	0.663769	−	0.747938i	$-0.268956\pi$
$613$	32.8683	1.32754	0.663769	+	0.747938i	$0.268956\pi$
$614$	−23.1968	−0.936145
$615$	−0.725999	−0.0292751
$616$	−1.10315	−0.0444470
$617$	22.8301	0.919107	0.459553	−	0.888150i	$-0.348009\pi$
$617$	22.8301	0.919107	0.459553	+	0.888150i	$0.348009\pi$
$618$	−5.52790	−0.222365
$619$	−9.25439	−0.371965	−0.185983	−	0.982553i	$-0.559547\pi$
$619$	−9.25439	−0.371965	−0.185983	+	0.982553i	$0.559547\pi$
$620$	−8.40568	−0.337580
$621$	4.26085	0.170982
$622$	−24.8146	−0.994976
$623$	−3.08291	−0.123514
$624$	−0.425297	−0.0170255
$625$	−10.9843	−0.439374
$626$	−26.0580	−1.04149
$627$	−1.13731	−0.0454197
$628$	−20.4494	−0.816021
$629$	−0.994606	−0.0396575
$630$	4.80764	0.191541
$631$	7.75577	0.308753	0.154376	−	0.988012i	$-0.450663\pi$
$631$	7.75577	0.308753	0.154376	+	0.988012i	$0.450663\pi$
$632$	16.2480	0.646310
$633$	−5.27473	−0.209652
$634$	28.4847	1.13127
$635$	−73.0603	−2.89931
$636$	−0.967550	−0.0383659
$637$	−9.16334	−0.363065
$638$	2.28460	0.0904481
$639$	17.3340	0.685723
$640$	3.46435	0.136941
$641$	0.206932	0.00817331	0.00408666	−	0.999992i	$-0.498699\pi$
$641$	0.206932	0.00817331	0.00408666	+	0.999992i	$0.498699\pi$
$642$	−1.96673	−0.0776208
$643$	−9.91078	−0.390843	−0.195421	−	0.980719i	$-0.562607\pi$
$643$	−9.91078	−0.390843	−0.195421	+	0.980719i	$0.562607\pi$
$644$	−1.09895	−0.0433045
$645$	−7.45527	−0.293551
$646$	−1.00774	−0.0396489
$647$	−28.0931	−1.10445	−0.552227	−	0.833694i	$-0.686222\pi$
$647$	−28.0931	−1.10445	−0.552227	+	0.833694i	$0.686222\pi$
$648$	8.12086	0.319017
$649$	−26.9371	−1.05737
$650$	9.47532	0.371653
$651$	−0.364739	−0.0142952
$652$	−10.5025	−0.411308
$653$	−17.6814	−0.691928	−0.345964	−	0.938248i	$-0.612448\pi$
$653$	−17.6814	−0.691928	−0.345964	+	0.938248i	$0.612448\pi$
$654$	4.56920	0.178670
$655$	70.9818	2.77349
$656$	0.666822	0.0260350
$657$	−6.10139	−0.238038
$658$	−3.83104	−0.149349
$659$	−14.1776	−0.552281	−0.276140	−	0.961117i	$-0.589055\pi$
$659$	−14.1776	−0.552281	−0.276140	+	0.961117i	$0.589055\pi$
$660$	−2.51092	−0.0977373
$661$	−7.47215	−0.290633	−0.145316	−	0.989385i	$-0.546420\pi$
$661$	−7.47215	−0.290633	−0.145316	+	0.989385i	$0.546420\pi$
$662$	−0.587820	−0.0228463
$663$	0.273132	0.0106076
$664$	−9.39310	−0.364523
$665$	−2.60026	−0.100834
$666$	−4.49318	−0.174107
$667$	2.27590	0.0881232
$668$	−12.0164	−0.464929
$669$	−1.23666	−0.0478121
$670$	6.80812	0.263021
$671$	28.5770	1.10320
$672$	0.150325	0.00579891
$673$	−45.7368	−1.76303	−0.881513	−	0.472160i	$-0.843474\pi$
$673$	−45.7368	−1.76303	−0.881513	+	0.472160i	$0.843474\pi$
$674$	30.7637	1.18497
$675$	12.9853	0.499806
$676$	−11.1686	−0.429563
$677$	15.4444	0.593578	0.296789	−	0.954943i	$-0.404084\pi$
$677$	15.4444	0.593578	0.296789	+	0.954943i	$0.404084\pi$
$678$	1.16051	0.0445692
$679$	7.14748	0.274295
$680$	−2.22486	−0.0853193
$681$	4.24944	0.162839
$682$	−5.59573	−0.214272
$683$	−28.6225	−1.09521	−0.547604	−	0.836737i	$-0.684460\pi$
$683$	−28.6225	−1.09521	−0.547604	+	0.836737i	$0.684460\pi$
$684$	−4.55251	−0.174069
$685$	−23.4687	−0.896694
$686$	6.58717	0.251499
$687$	−7.30681	−0.278772
$688$	6.84758	0.261062
$689$	4.16636	0.158726
$690$	−2.50136	−0.0952250
$691$	−9.41860	−0.358300	−0.179150	−	0.983822i	$-0.557335\pi$
$691$	−9.41860	−0.358300	−0.179150	+	0.983822i	$0.557335\pi$
$692$	3.98349	0.151430
$693$	3.20048	0.121576
$694$	11.1277	0.422400
$695$	21.1435	0.802019
$696$	−0.311321	−0.0118006
$697$	−0.428242	−0.0162208
$698$	−16.7748	−0.634936
$699$	7.73596	0.292601
$700$	−3.34914	−0.126585
$701$	−23.4715	−0.886505	−0.443252	−	0.896397i	$-0.646175\pi$
$701$	−23.4715	−0.886505	−0.443252	+	0.896397i	$0.646175\pi$
$702$	2.50978	0.0947255
$703$	2.43018	0.0916562
$704$	2.30625	0.0869200
$705$	−8.71999	−0.328414
$706$	0.786439	0.0295980
$707$	−5.79655	−0.218002
$708$	3.67070	0.137953
$709$	10.1499	0.381189	0.190595	−	0.981669i	$-0.438958\pi$
$709$	10.1499	0.381189	0.190595	+	0.981669i	$0.438958\pi$
$710$	−20.6985	−0.776800
$711$	−47.1392	−1.76786
$712$	6.44517	0.241543
$713$	−5.57443	−0.208764
$714$	−0.0965408	−0.00361295
$715$	10.8123	0.404355
$716$	−2.15491	−0.0805329
$717$	−7.51571	−0.280679
$718$	−6.16111	−0.229931
$719$	−0.640452	−0.0238848	−0.0119424	−	0.999929i	$-0.503801\pi$
$719$	−0.640452	−0.0238848	−0.0119424	+	0.999929i	$0.503801\pi$
$720$	−10.0509	−0.374575
$721$	−8.41361	−0.313339
$722$	−16.5377	−0.615471
$723$	6.13850	0.228293
$724$	−8.42497	−0.313111
$725$	6.93601	0.257597
$726$	1.78544	0.0662640
$727$	−2.57751	−0.0955947	−0.0477973	−	0.998857i	$-0.515220\pi$
$727$	−2.57751	−0.0955947	−0.0477973	+	0.998857i	$0.515220\pi$
$728$	−0.647314	−0.0239911
$729$	−21.8120	−0.807851
$730$	7.28565	0.269654
$731$	−4.39761	−0.162652
$732$	−3.89417	−0.143933
$733$	4.80687	0.177546	0.0887729	−	0.996052i	$-0.471705\pi$
$733$	4.80687	0.177546	0.0887729	+	0.996052i	$0.471705\pi$
$734$	−33.3152	−1.22969
$735$	7.37211	0.271925
$736$	2.29747	0.0846857
$737$	4.53222	0.166946
$738$	−1.93461	−0.0712138
$739$	−19.1414	−0.704128	−0.352064	−	0.935976i	$-0.614520\pi$
$739$	−19.1414	−0.704128	−0.352064	+	0.935976i	$0.614520\pi$
$740$	5.36529	0.197232
$741$	−0.667360	−0.0245161
$742$	−1.47264	−0.0540622
$743$	51.7350	1.89797	0.948986	−	0.315318i	$-0.102111\pi$
$743$	51.7350	1.89797	0.948986	+	0.315318i	$0.102111\pi$
$744$	0.762527	0.0279556
$745$	39.5191	1.44787
$746$	3.27399	0.119869
$747$	27.2516	0.997083
$748$	−1.48110	−0.0541545
$749$	−2.99342	−0.109377
$750$	−2.17938	−0.0795798
$751$	2.63536	0.0961657	0.0480828	−	0.998843i	$-0.484689\pi$
$751$	2.63536	0.0961657	0.0480828	+	0.998843i	$0.484689\pi$
$752$	8.00921	0.292066
$753$	−7.79791	−0.284172
$754$	1.34058	0.0488210
$755$	−16.6942	−0.607563
$756$	−0.887103	−0.0322636
$757$	−31.9367	−1.16076	−0.580380	−	0.814346i	$-0.697096\pi$
$757$	−31.9367	−1.16076	−0.580380	+	0.814346i	$0.697096\pi$
$758$	12.2391	0.444543
$759$	−1.66517	−0.0604420
$760$	5.43613	0.197189
$761$	−24.1279	−0.874635	−0.437317	−	0.899307i	$-0.644071\pi$
$761$	−24.1279	−0.874635	−0.437317	+	0.899307i	$0.644071\pi$
$762$	6.62772	0.240097
$763$	6.95445	0.251768
$764$	−27.5604	−0.997102
$765$	6.45483	0.233375
$766$	−6.89651	−0.249181
$767$	−15.8064	−0.570735
$768$	−0.314271	−0.0113403
$769$	−37.5904	−1.35555	−0.677773	−	0.735271i	$-0.737055\pi$
$769$	−37.5904	−1.35555	−0.677773	+	0.735271i	$0.737055\pi$
$770$	−3.82169	−0.137724
$771$	2.95211	0.106317
$772$	10.7597	0.387250
$773$	−50.3371	−1.81050	−0.905250	−	0.424879i	$-0.860317\pi$
$773$	−50.3371	−1.81050	−0.905250	+	0.424879i	$0.860317\pi$
$774$	−19.8664	−0.714084
$775$	−16.9886	−0.610248
$776$	−14.9426	−0.536408
$777$	0.232811	0.00835203
$778$	2.21737	0.0794964
$779$	1.04635	0.0374894
$780$	−1.47338	−0.0527554
$781$	−13.7791	−0.493056
$782$	−1.47546	−0.0527625
$783$	1.83718	0.0656553
$784$	−6.77120	−0.241829
$785$	−70.8440	−2.52853
$786$	−6.43916	−0.229677
$787$	17.6974	0.630843	0.315422	−	0.948952i	$-0.397854\pi$
$787$	17.6974	0.630843	0.315422	+	0.948952i	$0.397854\pi$
$788$	9.14463	0.325764
$789$	−4.54879	−0.161941
$790$	56.2888	2.00266
$791$	1.76633	0.0628035
$792$	−6.69096	−0.237753
$793$	16.7687	0.595473
$794$	24.3756	0.865056
$795$	−3.35193	−0.118881
$796$	8.65745	0.306855
$797$	−31.0046	−1.09824	−0.549119	−	0.835744i	$-0.685037\pi$
$797$	−31.0046	−1.09824	−0.549119	+	0.835744i	$0.685037\pi$
$798$	0.235884	0.00835021
$799$	−5.14363	−0.181968
$800$	7.00174	0.247549
$801$	−18.6989	−0.660695
$802$	−10.6732	−0.376883
$803$	4.85012	0.171157
$804$	−0.617603	−0.0217812
$805$	−3.80713	−0.134184
$806$	−3.28352	−0.115657
$807$	−3.71602	−0.130810
$808$	12.1183	0.426322
$809$	−19.2371	−0.676341	−0.338171	−	0.941085i	$-0.609808\pi$
$809$	−19.2371	−0.676341	−0.338171	+	0.941085i	$0.609808\pi$
$810$	28.1335	0.988511
$811$	−4.83762	−0.169872	−0.0849360	−	0.996386i	$-0.527069\pi$
$811$	−4.83762	−0.169872	−0.0849360	+	0.996386i	$0.527069\pi$
$812$	−0.473839	−0.0166285
$813$	−9.42217	−0.330450
$814$	3.57172	0.125189
$815$	−36.3842	−1.27448
$816$	0.201829	0.00706543
$817$	10.7450	0.375919
$818$	−29.8281	−1.04291
$819$	1.87801	0.0656230
$820$	2.31011	0.0806724
$821$	17.4622	0.609436	0.304718	−	0.952443i	$-0.401438\pi$
$821$	17.4622	0.609436	0.304718	+	0.952443i	$0.401438\pi$
$822$	2.12898	0.0742567
$823$	−0.879489	−0.0306570	−0.0153285	−	0.999883i	$-0.504879\pi$
$823$	−0.879489	−0.0306570	−0.0153285	+	0.999883i	$0.504879\pi$
$824$	17.5896	0.612762
$825$	−5.07477	−0.176681
$826$	5.58690	0.194393
$827$	0.0718560	0.00249868	0.00124934	−	0.999999i	$-0.499602\pi$
$827$	0.0718560	0.00249868	0.00124934	+	0.999999i	$0.499602\pi$
$828$	−6.66549	−0.231642
$829$	33.9561	1.17934	0.589671	−	0.807643i	$-0.299257\pi$
$829$	33.9561	1.17934	0.589671	+	0.807643i	$0.299257\pi$
$830$	−32.5410	−1.12951
$831$	5.77699	0.200402
$832$	1.35328	0.0469166
$833$	4.34856	0.150669
$834$	−1.91805	−0.0664165
$835$	−41.6291	−1.44063
$836$	3.61888	0.125162
$837$	−4.49985	−0.155538
$838$	3.31617	0.114555
$839$	15.8893	0.548558	0.274279	−	0.961650i	$-0.411561\pi$
$839$	15.8893	0.548558	0.274279	+	0.961650i	$0.411561\pi$
$840$	0.520779	0.0179686
$841$	−28.0187	−0.966162
$842$	21.4408	0.738900
$843$	0.0615896	0.00212126
$844$	16.7840	0.577729
$845$	−38.6921	−1.33105
$846$	−23.2366	−0.798891
$847$	2.71749	0.0933742
$848$	3.07871	0.105723
$849$	−5.01053	−0.171961
$850$	−4.49661	−0.154233
$851$	3.55812	0.121971
$852$	1.87767	0.0643281
$853$	−4.49586	−0.153935	−0.0769676	−	0.997034i	$-0.524524\pi$
$853$	−4.49586	−0.153935	−0.0769676	+	0.997034i	$0.524524\pi$
$854$	−5.92703	−0.202819
$855$	−15.7715	−0.539374
$856$	6.25808	0.213897
$857$	−23.4684	−0.801664	−0.400832	−	0.916152i	$-0.631279\pi$
$857$	−23.4684	−0.801664	−0.400832	+	0.916152i	$0.631279\pi$
$858$	−0.980841	−0.0334853
$859$	−23.8758	−0.814632	−0.407316	−	0.913287i	$-0.633535\pi$
$859$	−23.8758	−0.814632	−0.407316	+	0.913287i	$0.633535\pi$
$860$	23.7224	0.808928
$861$	0.100240	0.00341617
$862$	−28.2814	−0.963270
$863$	33.0576	1.12530	0.562648	−	0.826697i	$-0.309783\pi$
$863$	33.0576	1.12530	0.562648	+	0.826697i	$0.309783\pi$
$864$	1.85459	0.0630943
$865$	13.8002	0.469221
$866$	3.18962	0.108388
$867$	5.21299	0.177042
$868$	1.16059	0.0393929
$869$	37.4719	1.27115
$870$	−1.07852	−0.0365654
$871$	2.65946	0.0901123
$872$	−14.5391	−0.492354
$873$	43.3520	1.46724
$874$	3.60510	0.121944
$875$	−3.31708	−0.112138
$876$	−0.660923	−0.0223305
$877$	52.3398	1.76739	0.883695	−	0.468063i	$-0.155048\pi$
$877$	52.3398	1.76739	0.883695	+	0.468063i	$0.155048\pi$
$878$	−36.0339	−1.21608
$879$	9.65134	0.325532
$880$	7.98966	0.269331
$881$	40.4243	1.36193	0.680964	−	0.732317i	$-0.261561\pi$
$881$	40.4243	1.36193	0.680964	+	0.732317i	$0.261561\pi$
$882$	19.6448	0.661476
$883$	−32.1125	−1.08067	−0.540335	−	0.841450i	$-0.681703\pi$
$883$	−32.1125	−1.08067	−0.540335	+	0.841450i	$0.681703\pi$
$884$	−0.869096	−0.0292309
$885$	12.7166	0.427463
$886$	5.59748	0.188051
$887$	11.5697	0.388473	0.194236	−	0.980955i	$-0.437777\pi$
$887$	11.5697	0.388473	0.194236	+	0.980955i	$0.437777\pi$
$888$	−0.486716	−0.0163331
$889$	10.0876	0.338326
$890$	22.3283	0.748448
$891$	18.7287	0.627436
$892$	3.93502	0.131754
$893$	12.5678	0.420564
$894$	−3.58500	−0.119900
$895$	−7.46538	−0.249540
$896$	−0.478329	−0.0159799
$897$	−0.977106	−0.0326246
$898$	−19.0659	−0.636237
$899$	−2.40356	−0.0801632
$900$	−20.3137	−0.677123
$901$	−1.97719	−0.0658698
$902$	1.53786	0.0512050
$903$	1.02936	0.0342550
$904$	−3.69271	−0.122818
$905$	−29.1871	−0.970210
$906$	1.51442	0.0503133
$907$	−56.5673	−1.87829	−0.939143	−	0.343526i	$-0.888379\pi$
$907$	−56.5673	−1.87829	−0.939143	+	0.343526i	$0.888379\pi$
$908$	−13.5216	−0.448729
$909$	−35.1581	−1.16612
$910$	−2.24252	−0.0743390
$911$	−3.50065	−0.115982	−0.0579908	−	0.998317i	$-0.518469\pi$
$911$	−3.50065	−0.115982	−0.0579908	+	0.998317i	$0.518469\pi$
$912$	−0.493142	−0.0163296
$913$	−21.6628	−0.716935
$914$	−7.91818	−0.261910
$915$	−13.4908	−0.445991
$916$	23.2500	0.768203
$917$	−9.80059	−0.323644
$918$	−1.19104	−0.0393102
$919$	21.0109	0.693086	0.346543	−	0.938034i	$-0.387355\pi$
$919$	21.0109	0.693086	0.346543	+	0.938034i	$0.387355\pi$
$920$	7.95923	0.262408
$921$	7.29007	0.240216
$922$	−22.7830	−0.750318
$923$	−8.08545	−0.266136
$924$	0.346687	0.0114052
$925$	10.8437	0.356539
$926$	39.3578	1.29338
$927$	−51.0315	−1.67609
$928$	0.990613	0.0325184
$929$	−32.0615	−1.05190	−0.525951	−	0.850515i	$-0.676290\pi$
$929$	−32.0615	−1.05190	−0.525951	+	0.850515i	$0.676290\pi$
$930$	2.64166	0.0866235
$931$	−10.6251	−0.348224
$932$	−24.6156	−0.806309
$933$	7.79851	0.255312
$934$	32.5055	1.06361
$935$	−5.13107	−0.167804
$936$	−3.92619	−0.128331
$937$	23.2440	0.759349	0.379675	−	0.925120i	$-0.376036\pi$
$937$	23.2440	0.759349	0.379675	+	0.925120i	$0.376036\pi$
$938$	−0.940009	−0.0306924
$939$	8.18928	0.267247
$940$	27.7467	0.904999
$941$	18.9976	0.619304	0.309652	−	0.950850i	$-0.399787\pi$
$941$	18.9976	0.619304	0.309652	+	0.950850i	$0.399787\pi$
$942$	6.42666	0.209392
$943$	1.53200	0.0498888
$944$	−11.6800	−0.380153
$945$	−3.07324	−0.0999724
$946$	15.7922	0.513449
$947$	−24.1744	−0.785562	−0.392781	−	0.919632i	$-0.628487\pi$
$947$	−24.1744	−0.785562	−0.392781	+	0.919632i	$0.628487\pi$
$948$	−5.10627	−0.165844
$949$	2.84600	0.0923850
$950$	10.9869	0.356461
$951$	−8.95192	−0.290286
$952$	0.307190	0.00995607
$953$	−53.4304	−1.73078	−0.865390	−	0.501099i	$-0.832929\pi$
$953$	−53.4304	−1.73078	−0.865390	+	0.501099i	$0.832929\pi$
$954$	−8.93206	−0.289186
$955$	−95.4791	−3.08963
$956$	23.9147	0.773458
$957$	−0.717983	−0.0232091
$958$	4.55971	0.147318
$959$	3.24037	0.104637
$960$	−1.08875	−0.0351391
$961$	−25.1129	−0.810093
$962$	2.09585	0.0675728
$963$	−18.1562	−0.585074
$964$	−19.5325	−0.629100
$965$	37.2754	1.19994
$966$	0.345367	0.0111120
$967$	−30.6237	−0.984793	−0.492396	−	0.870371i	$-0.663879\pi$
$967$	−30.6237	−0.984793	−0.492396	+	0.870371i	$0.663879\pi$
$968$	−5.68122	−0.182601
$969$	0.316703	0.0101740
$970$	−51.7664	−1.66212
$971$	41.7741	1.34059	0.670297	−	0.742093i	$-0.266167\pi$
$971$	41.7741	1.34059	0.670297	+	0.742093i	$0.266167\pi$
$972$	−8.11591	−0.260318
$973$	−2.91932	−0.0935892
$974$	31.6498	1.01413
$975$	−2.97782	−0.0953665
$976$	12.3911	0.396630
$977$	−55.4108	−1.77275	−0.886375	−	0.462968i	$-0.846784\pi$
$977$	−55.4108	−1.77275	−0.886375	+	0.462968i	$0.846784\pi$
$978$	3.30062	0.105542
$979$	14.8642	0.475061
$980$	−23.4578	−0.749333
$981$	42.1812	1.34674
$982$	28.6966	0.915746
$983$	17.8232	0.568473	0.284237	−	0.958754i	$-0.408260\pi$
$983$	17.8232	0.568473	0.284237	+	0.958754i	$0.408260\pi$
$984$	−0.209563	−0.00668061
$985$	31.6802	1.00942
$986$	−0.636185	−0.0202603
$987$	1.20398	0.0383232
$988$	2.12352	0.0675581
$989$	15.7321	0.500251
$990$	−23.1799	−0.736704
$991$	30.6932	0.975001	0.487500	−	0.873123i	$-0.337909\pi$
$991$	30.6932	0.975001	0.487500	+	0.873123i	$0.337909\pi$
$992$	−2.42634	−0.0770363
$993$	0.184735	0.00586238
$994$	2.85787	0.0906462
$995$	29.9924	0.950824
$996$	2.95198	0.0935370
$997$	46.1845	1.46268	0.731340	−	0.682013i	$-0.238895\pi$
$997$	46.1845	1.46268	0.731340	+	0.682013i	$0.238895\pi$
$998$	−14.0587	−0.445021
$999$	2.87223	0.0908732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.21	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.21	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.314271 q^{3} +1.00000 q^{4} +3.46435 q^{5} -0.314271 q^{6} -0.478329 q^{7} +1.00000 q^{8} -2.90123 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.314271 q^{3} +1.00000 q^{4} +3.46435 q^{5} -0.314271 q^{6} -0.478329 q^{7} +1.00000 q^{8} -2.90123 q^{9} +3.46435 q^{10} +2.30625 q^{11} -0.314271 q^{12} +1.35328 q^{13} -0.478329 q^{14} -1.08875 q^{15} +1.00000 q^{16} -0.642214 q^{17} -2.90123 q^{18} +1.56916 q^{19} +3.46435 q^{20} +0.150325 q^{21} +2.30625 q^{22} +2.29747 q^{23} -0.314271 q^{24} +7.00174 q^{25} +1.35328 q^{26} +1.85459 q^{27} -0.478329 q^{28} +0.990613 q^{29} -1.08875 q^{30} -2.42634 q^{31} +1.00000 q^{32} -0.724787 q^{33} -0.642214 q^{34} -1.65710 q^{35} -2.90123 q^{36} +1.54871 q^{37} +1.56916 q^{38} -0.425297 q^{39} +3.46435 q^{40} +0.666822 q^{41} +0.150325 q^{42} +6.84758 q^{43} +2.30625 q^{44} -10.0509 q^{45} +2.29747 q^{46} +8.00921 q^{47} -0.314271 q^{48} -6.77120 q^{49} +7.00174 q^{50} +0.201829 q^{51} +1.35328 q^{52} +3.07871 q^{53} +1.85459 q^{54} +7.98966 q^{55} -0.478329 q^{56} -0.493142 q^{57} +0.990613 q^{58} -11.6800 q^{59} -1.08875 q^{60} +12.3911 q^{61} -2.42634 q^{62} +1.38774 q^{63} +1.00000 q^{64} +4.68824 q^{65} -0.724787 q^{66} +1.96519 q^{67} -0.642214 q^{68} -0.722027 q^{69} -1.65710 q^{70} -5.97470 q^{71} -2.90123 q^{72} +2.10303 q^{73} +1.54871 q^{74} -2.20044 q^{75} +1.56916 q^{76} -1.10315 q^{77} -0.425297 q^{78} +16.2480 q^{79} +3.46435 q^{80} +8.12086 q^{81} +0.666822 q^{82} -9.39310 q^{83} +0.150325 q^{84} -2.22486 q^{85} +6.84758 q^{86} -0.311321 q^{87} +2.30625 q^{88} +6.44517 q^{89} -10.0509 q^{90} -0.647314 q^{91} +2.29747 q^{92} +0.762527 q^{93} +8.00921 q^{94} +5.43613 q^{95} -0.314271 q^{96} -14.9426 q^{97} -6.77120 q^{98} -6.69096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 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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