LMFDB - Embedded newform 8021.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68511 q^{2} +2.15795 q^{3} +5.20984 q^{4} -0.637263 q^{5} -5.79434 q^{6} +0.252834 q^{7} -8.61877 q^{8} +1.65675 q^{9} +O(q^{10})$	\(q-2.68511 q^{2} +2.15795 q^{3} +5.20984 q^{4} -0.637263 q^{5} -5.79434 q^{6} +0.252834 q^{7} -8.61877 q^{8} +1.65675 q^{9} +1.71112 q^{10} +4.55402 q^{11} +11.2426 q^{12} +1.00000 q^{13} -0.678888 q^{14} -1.37518 q^{15} +12.7227 q^{16} -1.91989 q^{17} -4.44857 q^{18} -3.93002 q^{19} -3.32004 q^{20} +0.545603 q^{21} -12.2281 q^{22} -1.52699 q^{23} -18.5989 q^{24} -4.59390 q^{25} -2.68511 q^{26} -2.89866 q^{27} +1.31722 q^{28} -2.58490 q^{29} +3.69252 q^{30} +2.72547 q^{31} -16.9244 q^{32} +9.82735 q^{33} +5.15513 q^{34} -0.161122 q^{35} +8.63142 q^{36} +0.429846 q^{37} +10.5525 q^{38} +2.15795 q^{39} +5.49243 q^{40} +11.4011 q^{41} -1.46501 q^{42} -6.64689 q^{43} +23.7257 q^{44} -1.05579 q^{45} +4.10015 q^{46} -2.00504 q^{47} +27.4550 q^{48} -6.93608 q^{49} +12.3351 q^{50} -4.14304 q^{51} +5.20984 q^{52} +11.7389 q^{53} +7.78323 q^{54} -2.90211 q^{55} -2.17912 q^{56} -8.48078 q^{57} +6.94076 q^{58} -7.88967 q^{59} -7.16448 q^{60} -11.4560 q^{61} -7.31820 q^{62} +0.418884 q^{63} +19.9985 q^{64} -0.637263 q^{65} -26.3875 q^{66} +7.42062 q^{67} -10.0023 q^{68} -3.29518 q^{69} +0.432630 q^{70} -10.2089 q^{71} -14.2792 q^{72} -0.562155 q^{73} -1.15419 q^{74} -9.91340 q^{75} -20.4747 q^{76} +1.15141 q^{77} -5.79434 q^{78} -0.465116 q^{79} -8.10772 q^{80} -11.2254 q^{81} -30.6134 q^{82} +8.48609 q^{83} +2.84250 q^{84} +1.22348 q^{85} +17.8476 q^{86} -5.57809 q^{87} -39.2500 q^{88} -5.07983 q^{89} +2.83491 q^{90} +0.252834 q^{91} -7.95539 q^{92} +5.88143 q^{93} +5.38377 q^{94} +2.50445 q^{95} -36.5220 q^{96} -15.4846 q^{97} +18.6241 q^{98} +7.54489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * 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 $

$2$	−2.68511	−1.89866	−0.949331	−	0.314278i	$-0.898238\pi$
$2$	−2.68511	−1.89866	−0.949331	+	0.314278i	$0.898238\pi$
$3$	2.15795	1.24589	0.622947	−	0.782264i	$-0.285935\pi$
$3$	2.15795	1.24589	0.622947	+	0.782264i	$0.285935\pi$
$4$	5.20984	2.60492
$5$	−0.637263	−0.284993	−0.142496	−	0.989795i	$-0.545513\pi$
$5$	−0.637263	−0.284993	−0.142496	+	0.989795i	$0.545513\pi$
$6$	−5.79434	−2.36553
$7$	0.252834	0.0955622	0.0477811	−	0.998858i	$-0.484785\pi$
$7$	0.252834	0.0955622	0.0477811	+	0.998858i	$0.484785\pi$
$8$	−8.61877	−3.04720
$9$	1.65675	0.552251
$10$	1.71112	0.541105
$11$	4.55402	1.37309	0.686544	−	0.727088i	$-0.259127\pi$
$11$	4.55402	1.37309	0.686544	+	0.727088i	$0.259127\pi$
$12$	11.2426	3.24545
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.678888	−0.181440
$15$	−1.37518	−0.355071
$16$	12.7227	3.18068
$17$	−1.91989	−0.465643	−0.232821	−	0.972520i	$-0.574796\pi$
$17$	−1.91989	−0.465643	−0.232821	+	0.972520i	$0.574796\pi$
$18$	−4.44857	−1.04854
$19$	−3.93002	−0.901608	−0.450804	−	0.892623i	$-0.648863\pi$
$19$	−3.93002	−0.901608	−0.450804	+	0.892623i	$0.648863\pi$
$20$	−3.32004	−0.742383
$21$	0.545603	0.119060
$22$	−12.2281	−2.60703
$23$	−1.52699	−0.318400	−0.159200	−	0.987246i	$-0.550892\pi$
$23$	−1.52699	−0.318400	−0.159200	+	0.987246i	$0.550892\pi$
$24$	−18.5989	−3.79648
$25$	−4.59390	−0.918779
$26$	−2.68511	−0.526594
$27$	−2.89866	−0.557847
$28$	1.31722	0.248932
$29$	−2.58490	−0.480004	−0.240002	−	0.970772i	$-0.577148\pi$
$29$	−2.58490	−0.480004	−0.240002	+	0.970772i	$0.577148\pi$
$30$	3.69252	0.674159
$31$	2.72547	0.489509	0.244754	−	0.969585i	$-0.421293\pi$
$31$	2.72547	0.489509	0.244754	+	0.969585i	$0.421293\pi$
$32$	−16.9244	−2.99184
$33$	9.82735	1.71072
$34$	5.15513	0.884098
$35$	−0.161122	−0.0272345
$36$	8.63142	1.43857
$37$	0.429846	0.0706663	0.0353331	−	0.999376i	$-0.488751\pi$
$37$	0.429846	0.0706663	0.0353331	+	0.999376i	$0.488751\pi$
$38$	10.5525	1.71185
$39$	2.15795	0.345549
$40$	5.49243	0.868429
$41$	11.4011	1.78056	0.890280	−	0.455413i	$-0.150509\pi$
$41$	11.4011	1.78056	0.890280	+	0.455413i	$0.150509\pi$
$42$	−1.46501	−0.226055
$43$	−6.64689	−1.01364	−0.506820	−	0.862052i	$-0.669179\pi$
$43$	−6.64689	−1.01364	−0.506820	+	0.862052i	$0.669179\pi$
$44$	23.7257	3.57678
$45$	−1.05579	−0.157388
$46$	4.10015	0.604535
$47$	−2.00504	−0.292466	−0.146233	−	0.989250i	$-0.546715\pi$
$47$	−2.00504	−0.292466	−0.146233	+	0.989250i	$0.546715\pi$
$48$	27.4550	3.96279
$49$	−6.93608	−0.990868
$50$	12.3351	1.74445
$51$	−4.14304	−0.580141
$52$	5.20984	0.722474
$53$	11.7389	1.61246	0.806229	−	0.591604i	$-0.201505\pi$
$53$	11.7389	1.61246	0.806229	+	0.591604i	$0.201505\pi$
$54$	7.78323	1.05916
$55$	−2.90211	−0.391320
$56$	−2.17912	−0.291197
$57$	−8.48078	−1.12331
$58$	6.94076	0.911366
$59$	−7.88967	−1.02715	−0.513573	−	0.858046i	$-0.671679\pi$
$59$	−7.88967	−1.02715	−0.513573	+	0.858046i	$0.671679\pi$
$60$	−7.16448	−0.924930
$61$	−11.4560	−1.46679	−0.733393	−	0.679805i	$-0.762065\pi$
$61$	−11.4560	−1.46679	−0.733393	+	0.679805i	$0.762065\pi$
$62$	−7.31820	−0.929412
$63$	0.418884	0.0527744
$64$	19.9985	2.49981
$65$	−0.637263	−0.0790428
$66$	−26.3875	−3.24808
$67$	7.42062	0.906573	0.453286	−	0.891365i	$-0.350251\pi$
$67$	7.42062	0.906573	0.453286	+	0.891365i	$0.350251\pi$
$68$	−10.0023	−1.21296
$69$	−3.29518	−0.396693
$70$	0.432630	0.0517092
$71$	−10.2089	−1.21157	−0.605785	−	0.795629i	$-0.707141\pi$
$71$	−10.2089	−1.21157	−0.605785	+	0.795629i	$0.707141\pi$
$72$	−14.2792	−1.68282
$73$	−0.562155	−0.0657952	−0.0328976	−	0.999459i	$-0.510474\pi$
$73$	−0.562155	−0.0657952	−0.0328976	+	0.999459i	$0.510474\pi$
$74$	−1.15419	−0.134171
$75$	−9.91340	−1.14470
$76$	−20.4747	−2.34861
$77$	1.15141	0.131215
$78$	−5.79434	−0.656080
$79$	−0.465116	−0.0523296	−0.0261648	−	0.999658i	$-0.508329\pi$
$79$	−0.465116	−0.0523296	−0.0261648	+	0.999658i	$0.508329\pi$
$80$	−8.10772	−0.906470
$81$	−11.2254	−1.24727
$82$	−30.6134	−3.38068
$83$	8.48609	0.931469	0.465735	−	0.884924i	$-0.345790\pi$
$83$	8.48609	0.931469	0.465735	+	0.884924i	$0.345790\pi$
$84$	2.84250	0.310143
$85$	1.22348	0.132705
$86$	17.8476	1.92456
$87$	−5.57809	−0.598034
$88$	−39.2500	−4.18407
$89$	−5.07983	−0.538461	−0.269230	−	0.963076i	$-0.586769\pi$
$89$	−5.07983	−0.538461	−0.269230	+	0.963076i	$0.586769\pi$
$90$	2.83491	0.298826
$91$	0.252834	0.0265042
$92$	−7.95539	−0.829407
$93$	5.88143	0.609876
$94$	5.38377	0.555294
$95$	2.50445	0.256952
$96$	−36.5220	−3.72751
$97$	−15.4846	−1.57223	−0.786113	−	0.618083i	$-0.787910\pi$
$97$	−15.4846	−1.57223	−0.786113	+	0.618083i	$0.787910\pi$
$98$	18.6241	1.88132
$99$	7.54489	0.758290
$100$	−23.9334	−2.39334
$101$	−0.801523	−0.0797545	−0.0398773	−	0.999205i	$-0.512697\pi$
$101$	−0.801523	−0.0797545	−0.0398773	+	0.999205i	$0.512697\pi$
$102$	11.1245	1.10149
$103$	10.9803	1.08192	0.540960	−	0.841048i	$-0.318061\pi$
$103$	10.9803	1.08192	0.540960	+	0.841048i	$0.318061\pi$
$104$	−8.61877	−0.845140
$105$	−0.347693	−0.0339314
$106$	−31.5202	−3.06151
$107$	−3.22955	−0.312212	−0.156106	−	0.987740i	$-0.549894\pi$
$107$	−3.22955	−0.312212	−0.156106	+	0.987740i	$0.549894\pi$
$108$	−15.1015	−1.45315
$109$	−3.99266	−0.382427	−0.191214	−	0.981548i	$-0.561242\pi$
$109$	−3.99266	−0.382427	−0.191214	+	0.981548i	$0.561242\pi$
$110$	7.79249	0.742985
$111$	0.927587	0.0880427
$112$	3.21673	0.303953
$113$	−13.3098	−1.25208	−0.626042	−	0.779790i	$-0.715326\pi$
$113$	−13.3098	−1.25208	−0.626042	+	0.779790i	$0.715326\pi$
$114$	22.7719	2.13278
$115$	0.973097	0.0907418
$116$	−13.4669	−1.25037
$117$	1.65675	0.153167
$118$	21.1846	1.95020
$119$	−0.485414	−0.0444978
$120$	11.8524	1.08197
$121$	9.73907	0.885370
$122$	30.7606	2.78493
$123$	24.6031	2.21839
$124$	14.1993	1.27513
$125$	6.11384	0.546838
$126$	−1.12475	−0.100201
$127$	−20.7432	−1.84066	−0.920330	−	0.391143i	$-0.872080\pi$
$127$	−20.7432	−1.84066	−0.920330	+	0.391143i	$0.872080\pi$
$128$	−19.8494	−1.75445
$129$	−14.3437	−1.26289
$130$	1.71112	0.150076
$131$	−11.2061	−0.979078	−0.489539	−	0.871981i	$-0.662835\pi$
$131$	−11.2061	−0.979078	−0.489539	+	0.871981i	$0.662835\pi$
$132$	51.1989	4.45629
$133$	−0.993641	−0.0861596
$134$	−19.9252	−1.72128
$135$	1.84721	0.158982
$136$	16.5471	1.41890
$137$	17.4810	1.49350	0.746750	−	0.665105i	$-0.231613\pi$
$137$	17.4810	1.49350	0.746750	+	0.665105i	$0.231613\pi$
$138$	8.84793	0.753186
$139$	18.9688	1.60891	0.804456	−	0.594013i	$-0.202457\pi$
$139$	18.9688	1.60891	0.804456	+	0.594013i	$0.202457\pi$
$140$	−0.839418	−0.0709438
$141$	−4.32679	−0.364381
$142$	27.4120	2.30036
$143$	4.55402	0.380826
$144$	21.0784	1.75653
$145$	1.64726	0.136798
$146$	1.50945	0.124923
$147$	−14.9677	−1.23452
$148$	2.23943	0.184080
$149$	−4.23217	−0.346713	−0.173356	−	0.984859i	$-0.555461\pi$
$149$	−4.23217	−0.346713	−0.173356	+	0.984859i	$0.555461\pi$
$150$	26.6186	2.17340
$151$	7.25729	0.590590	0.295295	−	0.955406i	$-0.404582\pi$
$151$	7.25729	0.590590	0.295295	+	0.955406i	$0.404582\pi$
$152$	33.8719	2.74737
$153$	−3.18079	−0.257152
$154$	−3.09167	−0.249134
$155$	−1.73684	−0.139507
$156$	11.2426	0.900126
$157$	−19.5612	−1.56115	−0.780575	−	0.625062i	$-0.785074\pi$
$157$	−19.5612	−1.56115	−0.780575	+	0.625062i	$0.785074\pi$
$158$	1.24889	0.0993563
$159$	25.3319	2.00895
$160$	10.7853	0.852652
$161$	−0.386076	−0.0304270
$162$	30.1415	2.36814
$163$	−20.2291	−1.58446	−0.792232	−	0.610220i	$-0.791081\pi$
$163$	−20.2291	−1.58446	−0.792232	+	0.610220i	$0.791081\pi$
$164$	59.3981	4.63821
$165$	−6.26261	−0.487543
$166$	−22.7861	−1.76855
$167$	−0.575907	−0.0445650	−0.0222825	−	0.999752i	$-0.507093\pi$
$167$	−0.575907	−0.0445650	−0.0222825	+	0.999752i	$0.507093\pi$
$168$	−4.70243	−0.362800
$169$	1.00000	0.0769231
$170$	−3.28518	−0.251961
$171$	−6.51107	−0.497914
$172$	−34.6292	−2.64045
$173$	15.7678	1.19881	0.599404	−	0.800447i	$-0.295404\pi$
$173$	15.7678	1.19881	0.599404	+	0.800447i	$0.295404\pi$
$174$	14.9778	1.13547
$175$	−1.16149	−0.0878006
$176$	57.9394	4.36735
$177$	−17.0255	−1.27972
$178$	13.6399	1.02235
$179$	4.45442	0.332939	0.166469	−	0.986047i	$-0.446763\pi$
$179$	4.45442	0.332939	0.166469	+	0.986047i	$0.446763\pi$
$180$	−5.50048	−0.409982
$181$	−3.61967	−0.269048	−0.134524	−	0.990910i	$-0.542951\pi$
$181$	−3.61967	−0.269048	−0.134524	+	0.990910i	$0.542951\pi$
$182$	−0.678888	−0.0503225
$183$	−24.7214	−1.82746
$184$	13.1608	0.970228
$185$	−0.273925	−0.0201394
$186$	−15.7923	−1.15795
$187$	−8.74323	−0.639368
$188$	−10.4460	−0.761849
$189$	−0.732879	−0.0533091
$190$	−6.72475	−0.487864
$191$	−23.5442	−1.70360	−0.851801	−	0.523866i	$-0.824489\pi$
$191$	−23.5442	−1.70360	−0.851801	+	0.523866i	$0.824489\pi$
$192$	43.1557	3.11450
$193$	25.3909	1.82768	0.913840	−	0.406075i	$-0.133103\pi$
$193$	25.3909	1.82768	0.913840	+	0.406075i	$0.133103\pi$
$194$	41.5780	2.98513
$195$	−1.37518	−0.0984789
$196$	−36.1358	−2.58113
$197$	17.5494	1.25035	0.625173	−	0.780486i	$-0.285028\pi$
$197$	17.5494	1.25035	0.625173	+	0.780486i	$0.285028\pi$
$198$	−20.2589	−1.43974
$199$	−21.1071	−1.49624	−0.748121	−	0.663562i	$-0.769044\pi$
$199$	−21.1071	−1.49624	−0.748121	+	0.663562i	$0.769044\pi$
$200$	39.5937	2.79970
$201$	16.0133	1.12949
$202$	2.15218	0.151427
$203$	−0.653551	−0.0458703
$204$	−21.5845	−1.51122
$205$	−7.26553	−0.507447
$206$	−29.4833	−2.05420
$207$	−2.52985	−0.175837
$208$	12.7227	0.882161
$209$	−17.8974	−1.23799
$210$	0.933595	0.0644242
$211$	−25.9355	−1.78547	−0.892736	−	0.450580i	$-0.851217\pi$
$211$	−25.9355	−1.78547	−0.892736	+	0.450580i	$0.851217\pi$
$212$	61.1576	4.20032
$213$	−22.0302	−1.50949
$214$	8.67171	0.592786
$215$	4.23582	0.288880
$216$	24.9829	1.69987
$217$	0.689091	0.0467786
$218$	10.7207	0.726100
$219$	−1.21310	−0.0819739
$220$	−15.1195	−1.01936
$221$	−1.91989	−0.129146
$222$	−2.49068	−0.167163
$223$	−25.4858	−1.70666	−0.853328	−	0.521374i	$-0.825420\pi$
$223$	−25.4858	−1.70666	−0.853328	+	0.521374i	$0.825420\pi$
$224$	−4.27906	−0.285907
$225$	−7.61096	−0.507397
$226$	35.7384	2.37728
$227$	5.56747	0.369526	0.184763	−	0.982783i	$-0.440848\pi$
$227$	5.56747	0.369526	0.184763	+	0.982783i	$0.440848\pi$
$228$	−44.1835	−2.92612
$229$	8.43307	0.557273	0.278637	−	0.960397i	$-0.410118\pi$
$229$	8.43307	0.557273	0.278637	+	0.960397i	$0.410118\pi$
$230$	−2.61288	−0.172288
$231$	2.48469	0.163480
$232$	22.2787	1.46267
$233$	27.8546	1.82482	0.912408	−	0.409281i	$-0.134220\pi$
$233$	27.8546	1.82482	0.912408	+	0.409281i	$0.134220\pi$
$234$	−4.44857	−0.290812
$235$	1.27774	0.0833506
$236$	−41.1039	−2.67563
$237$	−1.00370	−0.0651972
$238$	1.30339	0.0844864
$239$	−14.2599	−0.922396	−0.461198	−	0.887297i	$-0.652580\pi$
$239$	−14.2599	−0.922396	−0.461198	+	0.887297i	$0.652580\pi$
$240$	−17.4961	−1.12937
$241$	−12.9284	−0.832790	−0.416395	−	0.909184i	$-0.636707\pi$
$241$	−12.9284	−0.832790	−0.416395	+	0.909184i	$0.636707\pi$
$242$	−26.1505	−1.68102
$243$	−15.5280	−0.996119
$244$	−59.6837	−3.82086
$245$	4.42011	0.282390
$246$	−66.0622	−4.21197
$247$	−3.93002	−0.250061
$248$	−23.4902	−1.49163
$249$	18.3126	1.16051
$250$	−16.4163	−1.03826
$251$	5.43286	0.342919	0.171460	−	0.985191i	$-0.445152\pi$
$251$	5.43286	0.342919	0.171460	+	0.985191i	$0.445152\pi$
$252$	2.18231	0.137473
$253$	−6.95396	−0.437192
$254$	55.6978	3.49479
$255$	2.64020	0.165336
$256$	13.3009	0.831309
$257$	−14.9385	−0.931840	−0.465920	−	0.884827i	$-0.654277\pi$
$257$	−14.9385	−0.931840	−0.465920	+	0.884827i	$0.654277\pi$
$258$	38.5143	2.39780
$259$	0.108680	0.00675303
$260$	−3.32004	−0.205900
$261$	−4.28255	−0.265083
$262$	30.0895	1.85894
$263$	1.77064	0.109182	0.0545912	−	0.998509i	$-0.482614\pi$
$263$	1.77064	0.109182	0.0545912	+	0.998509i	$0.482614\pi$
$264$	−84.6997	−5.21290
$265$	−7.48075	−0.459539
$266$	2.66804	0.163588
$267$	−10.9620	−0.670865
$268$	38.6602	2.36155
$269$	−16.8961	−1.03017	−0.515085	−	0.857139i	$-0.672240\pi$
$269$	−16.8961	−1.03017	−0.515085	+	0.857139i	$0.672240\pi$
$270$	−4.95997	−0.301854
$271$	−4.66233	−0.283216	−0.141608	−	0.989923i	$-0.545227\pi$
$271$	−4.66233	−0.283216	−0.141608	+	0.989923i	$0.545227\pi$
$272$	−24.4262	−1.48106
$273$	0.545603	0.0330214
$274$	−46.9384	−2.83565
$275$	−20.9207	−1.26156
$276$	−17.1673	−1.03335
$277$	16.7136	1.00422	0.502111	−	0.864803i	$-0.332557\pi$
$277$	16.7136	1.00422	0.502111	+	0.864803i	$0.332557\pi$
$278$	−50.9334	−3.05478
$279$	4.51544	0.270332
$280$	1.38867	0.0829890
$281$	4.28293	0.255498	0.127749	−	0.991807i	$-0.459225\pi$
$281$	4.28293	0.255498	0.127749	+	0.991807i	$0.459225\pi$
$282$	11.6179	0.691837
$283$	12.6832	0.753937	0.376968	−	0.926226i	$-0.376967\pi$
$283$	12.6832	0.753937	0.376968	+	0.926226i	$0.376967\pi$
$284$	−53.1865	−3.15604
$285$	5.40449	0.320134
$286$	−12.2281	−0.723060
$287$	2.88260	0.170154
$288$	−28.0395	−1.65225
$289$	−13.3140	−0.783177
$290$	−4.42309	−0.259733
$291$	−33.4151	−1.95883
$292$	−2.92873	−0.171391
$293$	−25.0148	−1.46138	−0.730690	−	0.682710i	$-0.760801\pi$
$293$	−25.0148	−1.46138	−0.730690	+	0.682710i	$0.760801\pi$
$294$	40.1900	2.34393
$295$	5.02779	0.292729
$296$	−3.70475	−0.215334
$297$	−13.2005	−0.765973
$298$	11.3638	0.658290
$299$	−1.52699	−0.0883084
$300$	−51.6472	−2.98185
$301$	−1.68056	−0.0968658
$302$	−19.4866	−1.12133
$303$	−1.72965	−0.0993657
$304$	−50.0005	−2.86772
$305$	7.30047	0.418024
$306$	8.54079	0.488244
$307$	25.1299	1.43424	0.717119	−	0.696951i	$-0.245460\pi$
$307$	25.1299	1.43424	0.717119	+	0.696951i	$0.245460\pi$
$308$	5.99866	0.341805
$309$	23.6950	1.34796
$310$	4.66362	0.264876
$311$	32.8063	1.86027	0.930137	−	0.367212i	$-0.119688\pi$
$311$	32.8063	1.86027	0.930137	+	0.367212i	$0.119688\pi$
$312$	−18.5989	−1.05295
$313$	4.48856	0.253709	0.126854	−	0.991921i	$-0.459512\pi$
$313$	4.48856	0.253709	0.126854	+	0.991921i	$0.459512\pi$
$314$	52.5239	2.96410
$315$	−0.266939	−0.0150403
$316$	−2.42318	−0.136314
$317$	−14.7317	−0.827413	−0.413707	−	0.910410i	$-0.635766\pi$
$317$	−14.7317	−0.827413	−0.413707	+	0.910410i	$0.635766\pi$
$318$	−68.0191	−3.81432
$319$	−11.7717	−0.659088
$320$	−12.7443	−0.712427
$321$	−6.96921	−0.388984
$322$	1.03666	0.0577707
$323$	7.54521	0.419827
$324$	−58.4826	−3.24904
$325$	−4.59390	−0.254823
$326$	54.3174	3.00836
$327$	−8.61596	−0.476463
$328$	−98.2639	−5.42572
$329$	−0.506943	−0.0279487
$330$	16.8158	0.925680
$331$	−12.9388	−0.711179	−0.355590	−	0.934642i	$-0.615720\pi$
$331$	−12.9388	−0.711179	−0.355590	+	0.934642i	$0.615720\pi$
$332$	44.2111	2.42640
$333$	0.712150	0.0390256
$334$	1.54638	0.0846139
$335$	−4.72889	−0.258367
$336$	6.94155	0.378693
$337$	3.70468	0.201807	0.100903	−	0.994896i	$-0.467827\pi$
$337$	3.70468	0.201807	0.100903	+	0.994896i	$0.467827\pi$
$338$	−2.68511	−0.146051
$339$	−28.7220	−1.55996
$340$	6.37412	0.345685
$341$	12.4118	0.672139
$342$	17.4830	0.945370
$343$	−3.52351	−0.190252
$344$	57.2880	3.08876
$345$	2.09990	0.113055
$346$	−42.3385	−2.27613
$347$	16.1711	0.868111	0.434056	−	0.900886i	$-0.357082\pi$
$347$	16.1711	0.868111	0.434056	+	0.900886i	$0.357082\pi$
$348$	−29.0609	−1.55783
$349$	−4.87135	−0.260757	−0.130379	−	0.991464i	$-0.541619\pi$
$349$	−4.87135	−0.260757	−0.130379	+	0.991464i	$0.541619\pi$
$350$	3.11874	0.166704
$351$	−2.89866	−0.154719
$352$	−77.0739	−4.10805
$353$	20.0979	1.06970	0.534851	−	0.844946i	$-0.320368\pi$
$353$	20.0979	1.06970	0.534851	+	0.844946i	$0.320368\pi$
$354$	45.7154	2.42975
$355$	6.50573	0.345289
$356$	−26.4651	−1.40265
$357$	−1.04750	−0.0554396
$358$	−11.9606	−0.632139
$359$	−1.68017	−0.0886759	−0.0443379	−	0.999017i	$-0.514118\pi$
$359$	−1.68017	−0.0886759	−0.0443379	+	0.999017i	$0.514118\pi$
$360$	9.09960	0.479591
$361$	−3.55497	−0.187104
$362$	9.71923	0.510831
$363$	21.0164	1.10308
$364$	1.31722	0.0690412
$365$	0.358240	0.0187512
$366$	66.3798	3.46973
$367$	−4.20881	−0.219698	−0.109849	−	0.993948i	$-0.535037\pi$
$367$	−4.20881	−0.219698	−0.109849	+	0.993948i	$0.535037\pi$
$368$	−19.4275	−1.01273
$369$	18.8889	0.983317
$370$	0.735520	0.0382379
$371$	2.96798	0.154090
$372$	30.6413	1.58868
$373$	30.7876	1.59412	0.797060	−	0.603900i	$-0.206387\pi$
$373$	30.7876	1.59412	0.797060	+	0.603900i	$0.206387\pi$
$374$	23.4766	1.21394
$375$	13.1934	0.681302
$376$	17.2810	0.891201
$377$	−2.58490	−0.133129
$378$	1.96786	0.101216
$379$	−24.3052	−1.24848	−0.624238	−	0.781234i	$-0.714590\pi$
$379$	−24.3052	−1.24848	−0.624238	+	0.781234i	$0.714590\pi$
$380$	13.0478	0.669338
$381$	−44.7628	−2.29327
$382$	63.2190	3.23456
$383$	−21.4090	−1.09395	−0.546974	−	0.837150i	$-0.684220\pi$
$383$	−21.4090	−1.09395	−0.546974	+	0.837150i	$0.684220\pi$
$384$	−42.8340	−2.18586
$385$	−0.733751	−0.0373954
$386$	−68.1775	−3.47015
$387$	−11.0123	−0.559784
$388$	−80.6724	−4.09552
$389$	−8.58637	−0.435346	−0.217673	−	0.976022i	$-0.569847\pi$
$389$	−8.58637	−0.435346	−0.217673	+	0.976022i	$0.569847\pi$
$390$	3.69252	0.186978
$391$	2.93167	0.148261
$392$	59.7805	3.01937
$393$	−24.1821	−1.21983
$394$	−47.1222	−2.37398
$395$	0.296401	0.0149136
$396$	39.3076	1.97528
$397$	10.5533	0.529656	0.264828	−	0.964296i	$-0.414685\pi$
$397$	10.5533	0.529656	0.264828	+	0.964296i	$0.414685\pi$
$398$	56.6750	2.84086
$399$	−2.14423	−0.107346
$400$	−58.4468	−2.92234
$401$	9.38792	0.468810	0.234405	−	0.972139i	$-0.424686\pi$
$401$	9.38792	0.468810	0.234405	+	0.972139i	$0.424686\pi$
$402$	−42.9976	−2.14453
$403$	2.72547	0.135765
$404$	−4.17580	−0.207754
$405$	7.15355	0.355463
$406$	1.75486	0.0870922
$407$	1.95753	0.0970310
$408$	35.7079	1.76780
$409$	−15.7919	−0.780861	−0.390431	−	0.920632i	$-0.627674\pi$
$409$	−15.7919	−0.780861	−0.390431	+	0.920632i	$0.627674\pi$
$410$	19.5088	0.963470
$411$	37.7231	1.86074
$412$	57.2055	2.81831
$413$	−1.99477	−0.0981564
$414$	6.79295	0.333855
$415$	−5.40787	−0.265462
$416$	−16.9244	−0.829786
$417$	40.9337	2.00453
$418$	48.0564	2.35052
$419$	−1.07752	−0.0526404	−0.0263202	−	0.999654i	$-0.508379\pi$
$419$	−1.07752	−0.0526404	−0.0263202	+	0.999654i	$0.508379\pi$
$420$	−1.81142	−0.0883884
$421$	−15.5383	−0.757293	−0.378646	−	0.925541i	$-0.623610\pi$
$421$	−15.5383	−0.757293	−0.378646	+	0.925541i	$0.623610\pi$
$422$	69.6397	3.39001
$423$	−3.32187	−0.161515
$424$	−101.175	−4.91347
$425$	8.81979	0.427823
$426$	59.1537	2.86601
$427$	−2.89646	−0.140169
$428$	−16.8254	−0.813288
$429$	9.82735	0.474469
$430$	−11.3736	−0.548486
$431$	28.5437	1.37490	0.687452	−	0.726230i	$-0.258729\pi$
$431$	28.5437	1.37490	0.687452	+	0.726230i	$0.258729\pi$
$432$	−36.8788	−1.77433
$433$	14.1783	0.681366	0.340683	−	0.940178i	$-0.389342\pi$
$433$	14.1783	0.681366	0.340683	+	0.940178i	$0.389342\pi$
$434$	−1.85029	−0.0888167
$435$	3.55471	0.170435
$436$	−20.8011	−0.996191
$437$	6.00111	0.287072
$438$	3.25732	0.155641
$439$	−7.71117	−0.368034	−0.184017	−	0.982923i	$-0.558910\pi$
$439$	−7.71117	−0.368034	−0.184017	+	0.982923i	$0.558910\pi$
$440$	25.0126	1.19243
$441$	−11.4914	−0.547208
$442$	5.15513	0.245205
$443$	14.5757	0.692512	0.346256	−	0.938140i	$-0.387453\pi$
$443$	14.5757	0.692512	0.346256	+	0.938140i	$0.387453\pi$
$444$	4.83258	0.229344
$445$	3.23719	0.153457
$446$	68.4323	3.24036
$447$	−9.13281	−0.431967
$448$	5.05629	0.238887
$449$	18.9524	0.894418	0.447209	−	0.894429i	$-0.352418\pi$
$449$	18.9524	0.894418	0.447209	+	0.894429i	$0.352418\pi$
$450$	20.4363	0.963376
$451$	51.9210	2.44487
$452$	−69.3420	−3.26157
$453$	15.6609	0.735812
$454$	−14.9493	−0.701605
$455$	−0.161122	−0.00755350
$456$	73.0939	3.42294
$457$	−30.6800	−1.43515	−0.717575	−	0.696481i	$-0.754748\pi$
$457$	−30.6800	−1.43515	−0.717575	+	0.696481i	$0.754748\pi$
$458$	−22.6438	−1.05807
$459$	5.56512	0.259757
$460$	5.06968	0.236375
$461$	−32.6936	−1.52269	−0.761347	−	0.648344i	$-0.775462\pi$
$461$	−32.6936	−1.52269	−0.761347	+	0.648344i	$0.775462\pi$
$462$	−6.67167	−0.310394
$463$	−3.92078	−0.182214	−0.0911069	−	0.995841i	$-0.529041\pi$
$463$	−3.92078	−0.182214	−0.0911069	+	0.995841i	$0.529041\pi$
$464$	−32.8870	−1.52674
$465$	−3.74802	−0.173810
$466$	−74.7928	−3.46471
$467$	17.2700	0.799162	0.399581	−	0.916698i	$-0.369156\pi$
$467$	17.2700	0.799162	0.399581	+	0.916698i	$0.369156\pi$
$468$	8.63142	0.398987
$469$	1.87618	0.0866341
$470$	−3.43088	−0.158255
$471$	−42.2120	−1.94503
$472$	67.9992	3.12992
$473$	−30.2700	−1.39182
$474$	2.69504	0.123787
$475$	18.0541	0.828378
$476$	−2.52893	−0.115913
$477$	19.4484	0.890482
$478$	38.2894	1.75132
$479$	19.0648	0.871091	0.435545	−	0.900167i	$-0.356556\pi$
$479$	19.0648	0.871091	0.435545	+	0.900167i	$0.356556\pi$
$480$	23.2741	1.06231
$481$	0.429846	0.0195993
$482$	34.7142	1.58119
$483$	−0.833133	−0.0379089
$484$	50.7390	2.30632
$485$	9.86779	0.448073
$486$	41.6943	1.89129
$487$	−15.2044	−0.688978	−0.344489	−	0.938790i	$-0.611948\pi$
$487$	−15.2044	−0.688978	−0.344489	+	0.938790i	$0.611948\pi$
$488$	98.7364	4.46959
$489$	−43.6534	−1.97407
$490$	−11.8685	−0.536164
$491$	−21.2021	−0.956839	−0.478419	−	0.878131i	$-0.658790\pi$
$491$	−21.2021	−0.956839	−0.478419	+	0.878131i	$0.658790\pi$
$492$	128.178	5.77872
$493$	4.96274	0.223510
$494$	10.5525	0.474781
$495$	−4.80808	−0.216107
$496$	34.6754	1.55697
$497$	−2.58115	−0.115780
$498$	−49.1713	−2.20342
$499$	36.4875	1.63340	0.816702	−	0.577060i	$-0.195800\pi$
$499$	36.4875	1.63340	0.816702	+	0.577060i	$0.195800\pi$
$500$	31.8521	1.42447
$501$	−1.24278	−0.0555233
$502$	−14.5878	−0.651087
$503$	−31.4716	−1.40325	−0.701624	−	0.712548i	$-0.747541\pi$
$503$	−31.4716	−1.40325	−0.701624	+	0.712548i	$0.747541\pi$
$504$	−3.61026	−0.160814
$505$	0.510781	0.0227295
$506$	18.6722	0.830079
$507$	2.15795	0.0958380
$508$	−108.069	−4.79477
$509$	33.3781	1.47946	0.739728	−	0.672906i	$-0.234954\pi$
$509$	33.3781	1.47946	0.739728	+	0.672906i	$0.234954\pi$
$510$	−7.08925	−0.313917
$511$	−0.142132	−0.00628754
$512$	3.98426	0.176081
$513$	11.3918	0.502959
$514$	40.1117	1.76925
$515$	−6.99734	−0.308340
$516$	−74.7281	−3.28972
$517$	−9.13101	−0.401581
$518$	−0.291817	−0.0128217
$519$	34.0262	1.49359
$520$	5.49243	0.240859
$521$	−12.9677	−0.568126	−0.284063	−	0.958806i	$-0.591682\pi$
$521$	−12.9677	−0.568126	−0.284063	+	0.958806i	$0.591682\pi$
$522$	11.4991	0.503303
$523$	−20.7433	−0.907041	−0.453520	−	0.891246i	$-0.649832\pi$
$523$	−20.7433	−0.907041	−0.453520	+	0.891246i	$0.649832\pi$
$524$	−58.3817	−2.55042
$525$	−2.50644	−0.109390
$526$	−4.75437	−0.207300
$527$	−5.23261	−0.227936
$528$	125.031	5.44125
$529$	−20.6683	−0.898621
$530$	20.0867	0.872509
$531$	−13.0712	−0.567243
$532$	−5.17671	−0.224439
$533$	11.4011	0.493839
$534$	29.4343	1.27375
$535$	2.05807	0.0889783
$536$	−63.9566	−2.76251
$537$	9.61242	0.414807
$538$	45.3678	1.95595
$539$	−31.5870	−1.36055
$540$	9.62365	0.414136
$541$	6.63595	0.285302	0.142651	−	0.989773i	$-0.454437\pi$
$541$	6.63595	0.285302	0.142651	+	0.989773i	$0.454437\pi$
$542$	12.5189	0.537732
$543$	−7.81107	−0.335205
$544$	32.4930	1.39313
$545$	2.54437	0.108989
$546$	−1.46501	−0.0626965
$547$	−32.6258	−1.39498	−0.697490	−	0.716595i	$-0.745700\pi$
$547$	−32.6258	−1.39498	−0.697490	+	0.716595i	$0.745700\pi$
$548$	91.0730	3.89045
$549$	−18.9797	−0.810035
$550$	56.1744	2.39528
$551$	10.1587	0.432775
$552$	28.4004	1.20880
$553$	−0.117597	−0.00500074
$554$	−44.8779	−1.90668
$555$	−0.591117	−0.0250915
$556$	98.8243	4.19108
$557$	−24.3400	−1.03132	−0.515659	−	0.856794i	$-0.672453\pi$
$557$	−24.3400	−1.03132	−0.515659	+	0.856794i	$0.672453\pi$
$558$	−12.1245	−0.513269
$559$	−6.64689	−0.281133
$560$	−2.04991	−0.0866243
$561$	−18.8675	−0.796585
$562$	−11.5002	−0.485105
$563$	15.1593	0.638886	0.319443	−	0.947605i	$-0.396504\pi$
$563$	15.1593	0.638886	0.319443	+	0.947605i	$0.396504\pi$
$564$	−22.5419	−0.949183
$565$	8.48186	0.356835
$566$	−34.0558	−1.43147
$567$	−2.83817	−0.119192
$568$	87.9879	3.69189
$569$	−34.6661	−1.45328	−0.726639	−	0.687019i	$-0.758919\pi$
$569$	−34.6661	−1.45328	−0.726639	+	0.687019i	$0.758919\pi$
$570$	−14.5117	−0.607827
$571$	20.4082	0.854055	0.427027	−	0.904239i	$-0.359561\pi$
$571$	20.4082	0.854055	0.427027	+	0.904239i	$0.359561\pi$
$572$	23.7257	0.992020
$573$	−50.8073	−2.12251
$574$	−7.74010	−0.323066
$575$	7.01485	0.292540
$576$	33.1325	1.38052
$577$	−14.7180	−0.612719	−0.306359	−	0.951916i	$-0.599111\pi$
$577$	−14.7180	−0.612719	−0.306359	+	0.951916i	$0.599111\pi$
$578$	35.7496	1.48699
$579$	54.7924	2.27709
$580$	8.58197	0.356347
$581$	2.14557	0.0890133
$582$	89.7233	3.71915
$583$	53.4590	2.21405
$584$	4.84508	0.200491
$585$	−1.05579	−0.0436515
$586$	67.1676	2.77467
$587$	−35.5664	−1.46798	−0.733991	−	0.679159i	$-0.762344\pi$
$587$	−35.5664	−1.46798	−0.733991	+	0.679159i	$0.762344\pi$
$588$	−77.9793	−3.21581
$589$	−10.7111	−0.441345
$590$	−13.5002	−0.555794
$591$	37.8708	1.55780
$592$	5.46881	0.224767
$593$	26.9348	1.10608	0.553040	−	0.833155i	$-0.313468\pi$
$593$	26.9348	1.10608	0.553040	+	0.833155i	$0.313468\pi$
$594$	35.4450	1.45432
$595$	0.309337	0.0126816
$596$	−22.0489	−0.903158
$597$	−45.5481	−1.86416
$598$	4.10015	0.167668
$599$	10.6388	0.434688	0.217344	−	0.976095i	$-0.430261\pi$
$599$	10.6388	0.434688	0.217344	+	0.976095i	$0.430261\pi$
$600$	85.4414	3.48813
$601$	−16.0831	−0.656042	−0.328021	−	0.944670i	$-0.606382\pi$
$601$	−16.0831	−0.656042	−0.328021	+	0.944670i	$0.606382\pi$
$602$	4.51249	0.183915
$603$	12.2941	0.500656
$604$	37.8093	1.53844
$605$	−6.20635	−0.252324
$606$	4.64430	0.188662
$607$	34.7055	1.40865	0.704327	−	0.709875i	$-0.251249\pi$
$607$	34.7055	1.40865	0.704327	+	0.709875i	$0.251249\pi$
$608$	66.5131	2.69746
$609$	−1.41033	−0.0571495
$610$	−19.6026	−0.793685
$611$	−2.00504	−0.0811154
$612$	−16.5714	−0.669859
$613$	24.7501	0.999646	0.499823	−	0.866128i	$-0.333398\pi$
$613$	24.7501	0.999646	0.499823	+	0.866128i	$0.333398\pi$
$614$	−67.4766	−2.72313
$615$	−15.6787	−0.632225
$616$	−9.92374	−0.399839
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	−63.6236	−2.55932
$619$	16.9804	0.682501	0.341251	−	0.939972i	$-0.389150\pi$
$619$	16.9804	0.682501	0.341251	+	0.939972i	$0.389150\pi$
$620$	−9.04866	−0.363403
$621$	4.42624	0.177619
$622$	−88.0886	−3.53203
$623$	−1.28435	−0.0514565
$624$	27.4550	1.09908
$625$	19.0734	0.762934
$626$	−12.0523	−0.481707
$627$	−38.6216	−1.54240
$628$	−101.910	−4.06667
$629$	−0.825259	−0.0329052
$630$	0.716762	0.0285565
$631$	33.4061	1.32987	0.664937	−	0.746899i	$-0.268458\pi$
$631$	33.4061	1.32987	0.664937	+	0.746899i	$0.268458\pi$
$632$	4.00873	0.159459
$633$	−55.9675	−2.22451
$634$	39.5562	1.57098
$635$	13.2189	0.524575
$636$	131.975	5.23315
$637$	−6.93608	−0.274817
$638$	31.6083	1.25139
$639$	−16.9136	−0.669091
$640$	12.6493	0.500007
$641$	−21.4721	−0.848097	−0.424049	−	0.905639i	$-0.639391\pi$
$641$	−21.4721	−0.848097	−0.424049	+	0.905639i	$0.639391\pi$
$642$	18.7131	0.738548
$643$	38.3323	1.51168	0.755838	−	0.654758i	$-0.227230\pi$
$643$	38.3323	1.51168	0.755838	+	0.654758i	$0.227230\pi$
$644$	−2.01139	−0.0792599
$645$	9.14069	0.359914
$646$	−20.2597	−0.797109
$647$	44.3485	1.74352	0.871760	−	0.489933i	$-0.162979\pi$
$647$	44.3485	1.74352	0.871760	+	0.489933i	$0.162979\pi$
$648$	96.7494	3.80068
$649$	−35.9297	−1.41036
$650$	12.3351	0.483824
$651$	1.48703	0.0582811
$652$	−105.390	−4.12740
$653$	−31.7692	−1.24322	−0.621612	−	0.783325i	$-0.713522\pi$
$653$	−31.7692	−1.24322	−0.621612	+	0.783325i	$0.713522\pi$
$654$	23.1348	0.904643
$655$	7.14121	0.279030
$656$	145.054	5.66339
$657$	−0.931352	−0.0363355
$658$	1.36120	0.0530651
$659$	−10.9221	−0.425465	−0.212733	−	0.977110i	$-0.568236\pi$
$659$	−10.9221	−0.425465	−0.212733	+	0.977110i	$0.568236\pi$
$660$	−32.6272	−1.27001
$661$	−20.0191	−0.778653	−0.389326	−	0.921100i	$-0.627292\pi$
$661$	−20.0191	−0.778653	−0.389326	+	0.921100i	$0.627292\pi$
$662$	34.7421	1.35029
$663$	−4.14304	−0.160902
$664$	−73.1397	−2.83837
$665$	0.633211	0.0245549
$666$	−1.91220	−0.0740964
$667$	3.94713	0.152834
$668$	−3.00038	−0.116088
$669$	−54.9972	−2.12631
$670$	12.6976	0.490551
$671$	−52.1707	−2.01403
$672$	−9.23400	−0.356209
$673$	−22.8913	−0.882393	−0.441197	−	0.897410i	$-0.645446\pi$
$673$	−22.8913	−0.882393	−0.441197	+	0.897410i	$0.645446\pi$
$674$	−9.94748	−0.383163
$675$	13.3161	0.512538
$676$	5.20984	0.200378
$677$	−3.16942	−0.121811	−0.0609054	−	0.998144i	$-0.519399\pi$
$677$	−3.16942	−0.121811	−0.0609054	+	0.998144i	$0.519399\pi$
$678$	77.1217	2.96184
$679$	−3.91504	−0.150245
$680$	−10.5449	−0.404377
$681$	12.0143	0.460390
$682$	−33.3272	−1.27616
$683$	−26.8125	−1.02595	−0.512976	−	0.858403i	$-0.671457\pi$
$683$	−26.8125	−1.02595	−0.512976	+	0.858403i	$0.671457\pi$
$684$	−33.9216	−1.29702
$685$	−11.1400	−0.425637
$686$	9.46103	0.361224
$687$	18.1982	0.694303
$688$	−84.5664	−3.22406
$689$	11.7389	0.447215
$690$	−5.63846	−0.214653
$691$	−20.2934	−0.771996	−0.385998	−	0.922500i	$-0.626143\pi$
$691$	−20.2934	−0.771996	−0.385998	+	0.922500i	$0.626143\pi$
$692$	82.1479	3.12279
$693$	1.90760	0.0724639
$694$	−43.4213	−1.64825
$695$	−12.0881	−0.458528
$696$	48.0763	1.82233
$697$	−21.8890	−0.829104
$698$	13.0801	0.495090
$699$	60.1089	2.27353
$700$	−6.05118	−0.228713
$701$	22.9408	0.866461	0.433230	−	0.901283i	$-0.357374\pi$
$701$	22.9408	0.866461	0.433230	+	0.901283i	$0.357374\pi$
$702$	7.78323	0.293759
$703$	−1.68930	−0.0637133
$704$	91.0734	3.43246
$705$	2.75730	0.103846
$706$	−53.9651	−2.03100
$707$	−0.202652	−0.00762152
$708$	−88.7001	−3.33355
$709$	15.3694	0.577209	0.288604	−	0.957448i	$-0.406809\pi$
$709$	15.3694	0.577209	0.288604	+	0.957448i	$0.406809\pi$
$710$	−17.4686	−0.655586
$711$	−0.770583	−0.0288991
$712$	43.7819	1.64080
$713$	−4.16178	−0.155860
$714$	2.81266	0.105261
$715$	−2.90211	−0.108533
$716$	23.2068	0.867279
$717$	−30.7722	−1.14921
$718$	4.51144	0.168365
$719$	−29.7668	−1.11011	−0.555056	−	0.831813i	$-0.687303\pi$
$719$	−29.7668	−1.11011	−0.555056	+	0.831813i	$0.687303\pi$
$720$	−13.4325	−0.500600
$721$	2.77619	0.103391
$722$	9.54551	0.355247
$723$	−27.8988	−1.03757
$724$	−18.8579	−0.700848
$725$	11.8748	0.441018
$726$	−56.4315	−2.09437
$727$	−11.0946	−0.411476	−0.205738	−	0.978607i	$-0.565960\pi$
$727$	−11.0946	−0.411476	−0.205738	+	0.978607i	$0.565960\pi$
$728$	−2.17912	−0.0807635
$729$	0.167720	0.00621186
$730$	−0.961916	−0.0356021
$731$	12.7613	0.471994
$732$	−128.795	−4.76038
$733$	−5.47722	−0.202306	−0.101153	−	0.994871i	$-0.532253\pi$
$733$	−5.47722	−0.202306	−0.101153	+	0.994871i	$0.532253\pi$
$734$	11.3011	0.417133
$735$	9.53837	0.351828
$736$	25.8434	0.952602
$737$	33.7936	1.24480
$738$	−50.7188	−1.86699
$739$	−35.8175	−1.31757	−0.658783	−	0.752333i	$-0.728929\pi$
$739$	−35.8175	−1.31757	−0.658783	+	0.752333i	$0.728929\pi$
$740$	−1.42711	−0.0524614
$741$	−8.48078	−0.311549
$742$	−7.96937	−0.292565
$743$	−53.5347	−1.96400	−0.981999	−	0.188884i	$-0.939513\pi$
$743$	−53.5347	−1.96400	−0.981999	+	0.188884i	$0.939513\pi$
$744$	−50.6907	−1.85841
$745$	2.69700	0.0988106
$746$	−82.6681	−3.02670
$747$	14.0594	0.514405
$748$	−45.5508	−1.66550
$749$	−0.816540	−0.0298357
$750$	−35.4257	−1.29356
$751$	53.8796	1.96609	0.983047	−	0.183354i	$-0.0586955\pi$
$751$	53.8796	1.96609	0.983047	+	0.183354i	$0.0586955\pi$
$752$	−25.5096	−0.930239
$753$	11.7238	0.427241
$754$	6.94076	0.252767
$755$	−4.62480	−0.168314
$756$	−3.81818	−0.138866
$757$	37.4055	1.35953	0.679764	−	0.733431i	$-0.262082\pi$
$757$	37.4055	1.35953	0.679764	+	0.733431i	$0.262082\pi$
$758$	65.2623	2.37043
$759$	−15.0063	−0.544694
$760$	−21.5853	−0.782982
$761$	13.6350	0.494268	0.247134	−	0.968981i	$-0.420511\pi$
$761$	13.6350	0.494268	0.247134	+	0.968981i	$0.420511\pi$
$762$	120.193	4.35414
$763$	−1.00948	−0.0365456
$764$	−122.662	−4.43774
$765$	2.02700	0.0732864
$766$	57.4855	2.07704
$767$	−7.88967	−0.284879
$768$	28.7028	1.03572
$769$	−7.98128	−0.287812	−0.143906	−	0.989591i	$-0.545966\pi$
$769$	−7.98128	−0.287812	−0.143906	+	0.989591i	$0.545966\pi$
$770$	1.97021	0.0710013
$771$	−32.2366	−1.16097
$772$	132.283	4.76095
$773$	7.63243	0.274519	0.137260	−	0.990535i	$-0.456171\pi$
$773$	7.63243	0.274519	0.137260	+	0.990535i	$0.456171\pi$
$774$	29.5692	1.06284
$775$	−12.5205	−0.449751
$776$	133.459	4.79088
$777$	0.234526	0.00841356
$778$	23.0554	0.826575
$779$	−44.8067	−1.60537
$780$	−7.16448	−0.256529
$781$	−46.4913	−1.66359
$782$	−7.87186	−0.281497
$783$	7.49275	0.267769
$784$	−88.2457	−3.15163
$785$	12.4656	0.444917
$786$	64.9318	2.31604
$787$	18.0823	0.644565	0.322283	−	0.946643i	$-0.395550\pi$
$787$	18.0823	0.644565	0.322283	+	0.946643i	$0.395550\pi$
$788$	91.4297	3.25705
$789$	3.82095	0.136030
$790$	−0.795871	−0.0283158
$791$	−3.36518	−0.119652
$792$	−65.0277	−2.31066
$793$	−11.4560	−0.406813
$794$	−28.3369	−1.00564
$795$	−16.1431	−0.572537
$796$	−109.965	−3.89759
$797$	−24.9505	−0.883792	−0.441896	−	0.897066i	$-0.645694\pi$
$797$	−24.9505	−0.883792	−0.441896	+	0.897066i	$0.645694\pi$
$798$	5.75750	0.203813
$799$	3.84947	0.136184
$800$	77.7488	2.74884
$801$	−8.41603	−0.297366
$802$	−25.2076	−0.890112
$803$	−2.56006	−0.0903426
$804$	83.4268	2.94224
$805$	0.246032	0.00867149
$806$	−7.31820	−0.257773
$807$	−36.4609	−1.28348
$808$	6.90815	0.243028
$809$	−43.8061	−1.54014	−0.770070	−	0.637960i	$-0.779779\pi$
$809$	−43.8061	−1.54014	−0.770070	+	0.637960i	$0.779779\pi$
$810$	−19.2081	−0.674904
$811$	13.3163	0.467597	0.233799	−	0.972285i	$-0.424884\pi$
$811$	13.3163	0.467597	0.233799	+	0.972285i	$0.424884\pi$
$812$	−3.40489	−0.119488
$813$	−10.0611	−0.352858
$814$	−5.25618	−0.184229
$815$	12.8913	0.451561
$816$	−52.7107	−1.84524
$817$	26.1224	0.913906
$818$	42.4032	1.48259
$819$	0.418884	0.0146370
$820$	−37.8522	−1.32186
$821$	13.3908	0.467341	0.233670	−	0.972316i	$-0.424926\pi$
$821$	13.3908	0.467341	0.233670	+	0.972316i	$0.424926\pi$
$822$	−101.291	−3.53292
$823$	10.5889	0.369105	0.184552	−	0.982823i	$-0.440916\pi$
$823$	10.5889	0.369105	0.184552	+	0.982823i	$0.440916\pi$
$824$	−94.6367	−3.29683
$825$	−45.1458	−1.57178
$826$	5.35620	0.186366
$827$	51.8160	1.80182	0.900910	−	0.434005i	$-0.142900\pi$
$827$	51.8160	1.80182	0.900910	+	0.434005i	$0.142900\pi$
$828$	−13.1801	−0.458041
$829$	−13.2274	−0.459405	−0.229703	−	0.973261i	$-0.573775\pi$
$829$	−13.2274	−0.459405	−0.229703	+	0.973261i	$0.573775\pi$
$830$	14.5208	0.504023
$831$	36.0671	1.25115
$832$	19.9985	0.693322
$833$	13.3165	0.461390
$834$	−109.912	−3.80593
$835$	0.367004	0.0127007
$836$	−93.2423	−3.22485
$837$	−7.90021	−0.273071
$838$	2.89327	0.0999463
$839$	42.7362	1.47542	0.737709	−	0.675119i	$-0.235908\pi$
$839$	42.7362	1.47542	0.737709	+	0.675119i	$0.235908\pi$
$840$	2.99669	0.103395
$841$	−22.3183	−0.769596
$842$	41.7222	1.43784
$843$	9.24236	0.318324
$844$	−135.120	−4.65101
$845$	−0.637263	−0.0219225
$846$	8.91959	0.306662
$847$	2.46237	0.0846079
$848$	149.350	5.12871
$849$	27.3697	0.939325
$850$	−23.6821	−0.812291
$851$	−0.656373	−0.0225002
$852$	−114.774	−3.93209
$853$	3.59980	0.123255	0.0616274	−	0.998099i	$-0.480371\pi$
$853$	3.59980	0.123255	0.0616274	+	0.998099i	$0.480371\pi$
$854$	7.77732	0.266134
$855$	4.14927	0.141902
$856$	27.8348	0.951372
$857$	−11.1873	−0.382151	−0.191076	−	0.981575i	$-0.561198\pi$
$857$	−11.1873	−0.382151	−0.191076	+	0.981575i	$0.561198\pi$
$858$	−26.3875	−0.900856
$859$	−51.6410	−1.76197	−0.880984	−	0.473146i	$-0.843118\pi$
$859$	−51.6410	−1.76197	−0.880984	+	0.473146i	$0.843118\pi$
$860$	22.0679	0.752509
$861$	6.22050	0.211994
$862$	−76.6432	−2.61048
$863$	32.9340	1.12109	0.560544	−	0.828125i	$-0.310592\pi$
$863$	32.9340	1.12109	0.560544	+	0.828125i	$0.310592\pi$
$864$	49.0580	1.66899
$865$	−10.0483	−0.341651
$866$	−38.0704	−1.29368
$867$	−28.7310	−0.975755
$868$	3.59005	0.121854
$869$	−2.11815	−0.0718532
$870$	−9.54481	−0.323599
$871$	7.42062	0.251438
$872$	34.4118	1.16533
$873$	−25.6542	−0.868264
$874$	−16.1137	−0.545053
$875$	1.54579	0.0522571
$876$	−6.32006	−0.213535
$877$	−36.3204	−1.22645	−0.613227	−	0.789907i	$-0.710129\pi$
$877$	−36.3204	−1.22645	−0.613227	+	0.789907i	$0.710129\pi$
$878$	20.7054	0.698772
$879$	−53.9807	−1.82072
$880$	−36.9227	−1.24466
$881$	32.1854	1.08435	0.542176	−	0.840265i	$-0.317601\pi$
$881$	32.1854	1.08435	0.542176	+	0.840265i	$0.317601\pi$
$882$	30.8556	1.03896
$883$	−25.2868	−0.850969	−0.425485	−	0.904966i	$-0.639896\pi$
$883$	−25.2868	−0.850969	−0.425485	+	0.904966i	$0.639896\pi$
$884$	−10.0023	−0.336415
$885$	10.8497	0.364710
$886$	−39.1374	−1.31485
$887$	30.0427	1.00874	0.504368	−	0.863489i	$-0.331726\pi$
$887$	30.0427	1.00874	0.504368	+	0.863489i	$0.331726\pi$
$888$	−7.99466	−0.268283
$889$	−5.24458	−0.175898
$890$	−8.69222	−0.291364
$891$	−51.1208	−1.71261
$892$	−132.777	−4.44570
$893$	7.87986	0.263689
$894$	24.5226	0.820160
$895$	−2.83864	−0.0948852
$896$	−5.01860	−0.167660
$897$	−3.29518	−0.110023
$898$	−50.8893	−1.69820
$899$	−7.04508	−0.234966
$900$	−39.6518	−1.32173
$901$	−22.5374	−0.750829
$902$	−139.414	−4.64197
$903$	−3.62656	−0.120684
$904$	114.714	3.81534
$905$	2.30668	0.0766767
$906$	−42.0512	−1.39706
$907$	14.2583	0.473438	0.236719	−	0.971578i	$-0.423928\pi$
$907$	14.2583	0.473438	0.236719	+	0.971578i	$0.423928\pi$
$908$	29.0056	0.962585
$909$	−1.32793	−0.0440446
$910$	0.432630	0.0143416
$911$	−43.9046	−1.45463	−0.727313	−	0.686306i	$-0.759231\pi$
$911$	−43.9046	−1.45463	−0.727313	+	0.686306i	$0.759231\pi$
$912$	−107.899	−3.57288
$913$	38.6458	1.27899
$914$	82.3793	2.72486
$915$	15.7541	0.520813
$916$	43.9349	1.45165
$917$	−2.83327	−0.0935629
$918$	−14.9430	−0.493191
$919$	−14.3638	−0.473819	−0.236910	−	0.971532i	$-0.576135\pi$
$919$	−14.3638	−0.473819	−0.236910	+	0.971532i	$0.576135\pi$
$920$	−8.38690	−0.276508
$921$	54.2290	1.78691
$922$	87.7861	2.89108
$923$	−10.2089	−0.336029
$924$	12.9448	0.425853
$925$	−1.97467	−0.0649267
$926$	10.5277	0.345963
$927$	18.1917	0.597492
$928$	43.7479	1.43609
$929$	28.0348	0.919792	0.459896	−	0.887973i	$-0.347887\pi$
$929$	28.0348	0.919792	0.459896	+	0.887973i	$0.347887\pi$
$930$	10.0639	0.330007
$931$	27.2589	0.893374
$932$	145.118	4.75350
$933$	70.7944	2.31770
$934$	−46.3720	−1.51734
$935$	5.57174	0.182215
$936$	−14.2792	−0.466730
$937$	18.1258	0.592145	0.296072	−	0.955165i	$-0.404323\pi$
$937$	18.1258	0.592145	0.296072	+	0.955165i	$0.404323\pi$
$938$	−5.03777	−0.164489
$939$	9.68610	0.316094
$940$	6.65682	0.217122
$941$	−4.51163	−0.147075	−0.0735375	−	0.997292i	$-0.523429\pi$
$941$	−4.51163	−0.147075	−0.0735375	+	0.997292i	$0.523429\pi$
$942$	113.344	3.69295
$943$	−17.4095	−0.566931
$944$	−100.378	−3.26702
$945$	0.467037	0.0151927
$946$	81.2785	2.64259
$947$	−20.4014	−0.662956	−0.331478	−	0.943463i	$-0.607547\pi$
$947$	−20.4014	−0.662956	−0.331478	+	0.943463i	$0.607547\pi$
$948$	−5.22910	−0.169833
$949$	−0.562155	−0.0182483
$950$	−48.4773	−1.57281
$951$	−31.7902	−1.03087
$952$	4.18367	0.135594
$953$	4.65147	0.150676	0.0753379	−	0.997158i	$-0.475996\pi$
$953$	4.65147	0.150676	0.0753379	+	0.997158i	$0.475996\pi$
$954$	−52.2212	−1.69072
$955$	15.0039	0.485514
$956$	−74.2917	−2.40276
$957$	−25.4027	−0.821154
$958$	−51.1910	−1.65391
$959$	4.41978	0.142722
$960$	−27.5016	−0.887609
$961$	−23.5718	−0.760381
$962$	−1.15419	−0.0372125
$963$	−5.35057	−0.172420
$964$	−67.3547	−2.16935
$965$	−16.1807	−0.520876
$966$	2.23706	0.0719761
$967$	−22.9756	−0.738845	−0.369423	−	0.929262i	$-0.620444\pi$
$967$	−22.9756	−0.738845	−0.369423	+	0.929262i	$0.620444\pi$
$968$	−83.9388	−2.69790
$969$	16.2822	0.523060
$970$	−26.4961	−0.850740
$971$	−45.1797	−1.44988	−0.724942	−	0.688810i	$-0.758134\pi$
$971$	−45.1797	−1.44988	−0.724942	+	0.688810i	$0.758134\pi$
$972$	−80.8981	−2.59481
$973$	4.79595	0.153751
$974$	40.8256	1.30814
$975$	−9.91340	−0.317483
$976$	−145.751	−4.66537
$977$	−42.7083	−1.36636	−0.683179	−	0.730251i	$-0.739403\pi$
$977$	−42.7083	−1.36636	−0.683179	+	0.730251i	$0.739403\pi$
$978$	117.214	3.74810
$979$	−23.1336	−0.739354
$980$	23.0280	0.735603
$981$	−6.61485	−0.211196
$982$	56.9301	1.81671
$983$	−40.3841	−1.28805	−0.644027	−	0.765003i	$-0.722737\pi$
$983$	−40.3841	−1.28805	−0.644027	+	0.765003i	$0.722737\pi$
$984$	−212.049	−6.75987
$985$	−11.1836	−0.356340
$986$	−13.3255	−0.424371
$987$	−1.09396	−0.0348211
$988$	−20.4747	−0.651388
$989$	10.1498	0.322743
$990$	12.9102	0.410314
$991$	60.0372	1.90714	0.953572	−	0.301166i	$-0.0973759\pi$
$991$	60.0372	1.90714	0.953572	+	0.301166i	$0.0973759\pi$
$992$	−46.1269	−1.46453
$993$	−27.9212	−0.886054
$994$	6.93067	0.219828
$995$	13.4508	0.426418
$996$	95.4055	3.02304
$997$	−16.7106	−0.529231	−0.264616	−	0.964354i	$-0.585245\pi$
$997$	−16.7106	−0.529231	−0.264616	+	0.964354i	$0.585245\pi$
$998$	−97.9730	−3.10128
$999$	−1.24598	−0.0394210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.2	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.2	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68511 q^{2} +2.15795 q^{3} +5.20984 q^{4} -0.637263 q^{5} -5.79434 q^{6} +0.252834 q^{7} -8.61877 q^{8} +1.65675 q^{9} +O(q^{10})\)	\(q-2.68511 q^{2} +2.15795 q^{3} +5.20984 q^{4} -0.637263 q^{5} -5.79434 q^{6} +0.252834 q^{7} -8.61877 q^{8} +1.65675 q^{9} +1.71112 q^{10} +4.55402 q^{11} +11.2426 q^{12} +1.00000 q^{13} -0.678888 q^{14} -1.37518 q^{15} +12.7227 q^{16} -1.91989 q^{17} -4.44857 q^{18} -3.93002 q^{19} -3.32004 q^{20} +0.545603 q^{21} -12.2281 q^{22} -1.52699 q^{23} -18.5989 q^{24} -4.59390 q^{25} -2.68511 q^{26} -2.89866 q^{27} +1.31722 q^{28} -2.58490 q^{29} +3.69252 q^{30} +2.72547 q^{31} -16.9244 q^{32} +9.82735 q^{33} +5.15513 q^{34} -0.161122 q^{35} +8.63142 q^{36} +0.429846 q^{37} +10.5525 q^{38} +2.15795 q^{39} +5.49243 q^{40} +11.4011 q^{41} -1.46501 q^{42} -6.64689 q^{43} +23.7257 q^{44} -1.05579 q^{45} +4.10015 q^{46} -2.00504 q^{47} +27.4550 q^{48} -6.93608 q^{49} +12.3351 q^{50} -4.14304 q^{51} +5.20984 q^{52} +11.7389 q^{53} +7.78323 q^{54} -2.90211 q^{55} -2.17912 q^{56} -8.48078 q^{57} +6.94076 q^{58} -7.88967 q^{59} -7.16448 q^{60} -11.4560 q^{61} -7.31820 q^{62} +0.418884 q^{63} +19.9985 q^{64} -0.637263 q^{65} -26.3875 q^{66} +7.42062 q^{67} -10.0023 q^{68} -3.29518 q^{69} +0.432630 q^{70} -10.2089 q^{71} -14.2792 q^{72} -0.562155 q^{73} -1.15419 q^{74} -9.91340 q^{75} -20.4747 q^{76} +1.15141 q^{77} -5.79434 q^{78} -0.465116 q^{79} -8.10772 q^{80} -11.2254 q^{81} -30.6134 q^{82} +8.48609 q^{83} +2.84250 q^{84} +1.22348 q^{85} +17.8476 q^{86} -5.57809 q^{87} -39.2500 q^{88} -5.07983 q^{89} +2.83491 q^{90} +0.252834 q^{91} -7.95539 q^{92} +5.88143 q^{93} +5.38377 q^{94} +2.50445 q^{95} -36.5220 q^{96} -15.4846 q^{97} +18.6241 q^{98} +7.54489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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