LMFDB - Embedded newform 4022.2.a.c.1.19

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:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.524728 q^{3} +1.00000 q^{4} +0.579848 q^{5} +0.524728 q^{6} +1.74824 q^{7} +1.00000 q^{8} -2.72466 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.524728 q^{3} +1.00000 q^{4} +0.579848 q^{5} +0.524728 q^{6} +1.74824 q^{7} +1.00000 q^{8} -2.72466 q^{9} +0.579848 q^{10} -4.24317 q^{11} +0.524728 q^{12} -1.10363 q^{13} +1.74824 q^{14} +0.304262 q^{15} +1.00000 q^{16} +0.907928 q^{17} -2.72466 q^{18} -4.36173 q^{19} +0.579848 q^{20} +0.917349 q^{21} -4.24317 q^{22} -5.04037 q^{23} +0.524728 q^{24} -4.66378 q^{25} -1.10363 q^{26} -3.00389 q^{27} +1.74824 q^{28} -10.2412 q^{29} +0.304262 q^{30} +7.70378 q^{31} +1.00000 q^{32} -2.22651 q^{33} +0.907928 q^{34} +1.01371 q^{35} -2.72466 q^{36} +1.16291 q^{37} -4.36173 q^{38} -0.579106 q^{39} +0.579848 q^{40} -7.50439 q^{41} +0.917349 q^{42} -7.75223 q^{43} -4.24317 q^{44} -1.57989 q^{45} -5.04037 q^{46} +2.42807 q^{47} +0.524728 q^{48} -3.94367 q^{49} -4.66378 q^{50} +0.476416 q^{51} -1.10363 q^{52} +10.0991 q^{53} -3.00389 q^{54} -2.46039 q^{55} +1.74824 q^{56} -2.28872 q^{57} -10.2412 q^{58} +9.25914 q^{59} +0.304262 q^{60} -3.81983 q^{61} +7.70378 q^{62} -4.76335 q^{63} +1.00000 q^{64} -0.639937 q^{65} -2.22651 q^{66} +5.50662 q^{67} +0.907928 q^{68} -2.64482 q^{69} +1.01371 q^{70} -4.13901 q^{71} -2.72466 q^{72} +2.16475 q^{73} +1.16291 q^{74} -2.44722 q^{75} -4.36173 q^{76} -7.41806 q^{77} -0.579106 q^{78} -3.49154 q^{79} +0.579848 q^{80} +6.59775 q^{81} -7.50439 q^{82} -2.19884 q^{83} +0.917349 q^{84} +0.526460 q^{85} -7.75223 q^{86} -5.37383 q^{87} -4.24317 q^{88} +15.2655 q^{89} -1.57989 q^{90} -1.92941 q^{91} -5.04037 q^{92} +4.04239 q^{93} +2.42807 q^{94} -2.52914 q^{95} +0.524728 q^{96} -6.83419 q^{97} -3.94367 q^{98} +11.5612 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - 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
$3$	0.524728	0.302952	0.151476	−	0.988461i	$-0.451597\pi$
$3$	0.524728	0.302952	0.151476	+	0.988461i	$0.451597\pi$
$4$	1.00000	0.500000
$5$	0.579848	0.259316	0.129658	−	0.991559i	$-0.458612\pi$
$5$	0.579848	0.259316	0.129658	+	0.991559i	$0.458612\pi$
$6$	0.524728	0.214219
$7$	1.74824	0.660771	0.330386	−	0.943846i	$-0.392821\pi$
$7$	1.74824	0.660771	0.330386	+	0.943846i	$0.392821\pi$
$8$	1.00000	0.353553
$9$	−2.72466	−0.908220
$10$	0.579848	0.183364
$11$	−4.24317	−1.27936	−0.639682	−	0.768640i	$-0.720934\pi$
$11$	−4.24317	−1.27936	−0.639682	+	0.768640i	$0.720934\pi$
$12$	0.524728	0.151476
$13$	−1.10363	−0.306092	−0.153046	−	0.988219i	$-0.548908\pi$
$13$	−1.10363	−0.306092	−0.153046	+	0.988219i	$0.548908\pi$
$14$	1.74824	0.467236
$15$	0.304262	0.0785602
$16$	1.00000	0.250000
$17$	0.907928	0.220205	0.110102	−	0.993920i	$-0.464882\pi$
$17$	0.907928	0.220205	0.110102	+	0.993920i	$0.464882\pi$
$18$	−2.72466	−0.642209
$19$	−4.36173	−1.00065	−0.500325	−	0.865838i	$-0.666786\pi$
$19$	−4.36173	−1.00065	−0.500325	+	0.865838i	$0.666786\pi$
$20$	0.579848	0.129658
$21$	0.917349	0.200182
$22$	−4.24317	−0.904646
$23$	−5.04037	−1.05099	−0.525494	−	0.850797i	$-0.676120\pi$
$23$	−5.04037	−1.05099	−0.525494	+	0.850797i	$0.676120\pi$
$24$	0.524728	0.107110
$25$	−4.66378	−0.932755
$26$	−1.10363	−0.216440
$27$	−3.00389	−0.578099
$28$	1.74824	0.330386
$29$	−10.2412	−1.90174	−0.950868	−	0.309597i	$-0.899806\pi$
$29$	−10.2412	−1.90174	−0.950868	+	0.309597i	$0.899806\pi$
$30$	0.304262	0.0555505
$31$	7.70378	1.38364	0.691820	−	0.722070i	$-0.256809\pi$
$31$	7.70378	1.38364	0.691820	+	0.722070i	$0.256809\pi$
$32$	1.00000	0.176777
$33$	−2.22651	−0.387586
$34$	0.907928	0.155708
$35$	1.01371	0.171348
$36$	−2.72466	−0.454110
$37$	1.16291	0.191181	0.0955905	−	0.995421i	$-0.469526\pi$
$37$	1.16291	0.191181	0.0955905	+	0.995421i	$0.469526\pi$
$38$	−4.36173	−0.707566
$39$	−0.579106	−0.0927311
$40$	0.579848	0.0916820
$41$	−7.50439	−1.17199	−0.585994	−	0.810315i	$-0.699296\pi$
$41$	−7.50439	−1.17199	−0.585994	+	0.810315i	$0.699296\pi$
$42$	0.917349	0.141550
$43$	−7.75223	−1.18220	−0.591102	−	0.806597i	$-0.701307\pi$
$43$	−7.75223	−1.18220	−0.591102	+	0.806597i	$0.701307\pi$
$44$	−4.24317	−0.639682
$45$	−1.57989	−0.235516
$46$	−5.04037	−0.743161
$47$	2.42807	0.354170	0.177085	−	0.984196i	$-0.443333\pi$
$47$	2.42807	0.354170	0.177085	+	0.984196i	$0.443333\pi$
$48$	0.524728	0.0757380
$49$	−3.94367	−0.563381
$50$	−4.66378	−0.659558
$51$	0.476416	0.0667115
$52$	−1.10363	−0.153046
$53$	10.0991	1.38721	0.693607	−	0.720353i	$-0.256020\pi$
$53$	10.0991	1.38721	0.693607	+	0.720353i	$0.256020\pi$
$54$	−3.00389	−0.408778
$55$	−2.46039	−0.331759
$56$	1.74824	0.233618
$57$	−2.28872	−0.303149
$58$	−10.2412	−1.34473
$59$	9.25914	1.20544	0.602718	−	0.797954i	$-0.294084\pi$
$59$	9.25914	1.20544	0.602718	+	0.797954i	$0.294084\pi$
$60$	0.304262	0.0392801
$61$	−3.81983	−0.489078	−0.244539	−	0.969639i	$-0.578637\pi$
$61$	−3.81983	−0.489078	−0.244539	+	0.969639i	$0.578637\pi$
$62$	7.70378	0.978381
$63$	−4.76335	−0.600126
$64$	1.00000	0.125000
$65$	−0.639937	−0.0793744
$66$	−2.22651	−0.274064
$67$	5.50662	0.672741	0.336370	−	0.941730i	$-0.390801\pi$
$67$	5.50662	0.672741	0.336370	+	0.941730i	$0.390801\pi$
$68$	0.907928	0.110102
$69$	−2.64482	−0.318399
$70$	1.01371	0.121162
$71$	−4.13901	−0.491210	−0.245605	−	0.969370i	$-0.578987\pi$
$71$	−4.13901	−0.491210	−0.245605	+	0.969370i	$0.578987\pi$
$72$	−2.72466	−0.321104
$73$	2.16475	0.253364	0.126682	−	0.991943i	$-0.459567\pi$
$73$	2.16475	0.253364	0.126682	+	0.991943i	$0.459567\pi$
$74$	1.16291	0.135185
$75$	−2.44722	−0.282580
$76$	−4.36173	−0.500325
$77$	−7.41806	−0.845367
$78$	−0.579106	−0.0655708
$79$	−3.49154	−0.392829	−0.196415	−	0.980521i	$-0.562930\pi$
$79$	−3.49154	−0.392829	−0.196415	+	0.980521i	$0.562930\pi$
$80$	0.579848	0.0648289
$81$	6.59775	0.733084
$82$	−7.50439	−0.828721
$83$	−2.19884	−0.241355	−0.120677	−	0.992692i	$-0.538507\pi$
$83$	−2.19884	−0.241355	−0.120677	+	0.992692i	$0.538507\pi$
$84$	0.917349	0.100091
$85$	0.526460	0.0571026
$86$	−7.75223	−0.835944
$87$	−5.37383	−0.576135
$88$	−4.24317	−0.452323
$89$	15.2655	1.61814	0.809071	−	0.587711i	$-0.199971\pi$
$89$	15.2655	1.61814	0.809071	+	0.587711i	$0.199971\pi$
$90$	−1.57989	−0.166535
$91$	−1.92941	−0.202257
$92$	−5.04037	−0.525494
$93$	4.04239	0.419176
$94$	2.42807	0.250436
$95$	−2.52914	−0.259484
$96$	0.524728	0.0535549
$97$	−6.83419	−0.693906	−0.346953	−	0.937882i	$-0.612784\pi$
$97$	−6.83419	−0.693906	−0.346953	+	0.937882i	$0.612784\pi$
$98$	−3.94367	−0.398371
$99$	11.5612	1.16194
$100$	−4.66378	−0.466378
$101$	11.5078	1.14507	0.572536	−	0.819880i	$-0.305960\pi$
$101$	11.5078	1.14507	0.572536	+	0.819880i	$0.305960\pi$
$102$	0.476416	0.0471722
$103$	−13.5504	−1.33516	−0.667578	−	0.744540i	$-0.732669\pi$
$103$	−13.5504	−1.33516	−0.667578	+	0.744540i	$0.732669\pi$
$104$	−1.10363	−0.108220
$105$	0.531923	0.0519104
$106$	10.0991	0.980909
$107$	1.45069	0.140244	0.0701218	−	0.997538i	$-0.477661\pi$
$107$	1.45069	0.140244	0.0701218	+	0.997538i	$0.477661\pi$
$108$	−3.00389	−0.289050
$109$	−16.7867	−1.60787	−0.803936	−	0.594716i	$-0.797265\pi$
$109$	−16.7867	−1.60787	−0.803936	+	0.594716i	$0.797265\pi$
$110$	−2.46039	−0.234589
$111$	0.610211	0.0579187
$112$	1.74824	0.165193
$113$	−3.36677	−0.316719	−0.158360	−	0.987382i	$-0.550621\pi$
$113$	−3.36677	−0.316719	−0.158360	+	0.987382i	$0.550621\pi$
$114$	−2.28872	−0.214359
$115$	−2.92264	−0.272538
$116$	−10.2412	−0.950868
$117$	3.00702	0.277999
$118$	9.25914	0.852373
$119$	1.58727	0.145505
$120$	0.304262	0.0277752
$121$	7.00447	0.636770
$122$	−3.81983	−0.345831
$123$	−3.93776	−0.355056
$124$	7.70378	0.691820
$125$	−5.60352	−0.501194
$126$	−4.76335	−0.424353
$127$	8.42595	0.747682	0.373841	−	0.927493i	$-0.378041\pi$
$127$	8.42595	0.747682	0.373841	+	0.927493i	$0.378041\pi$
$128$	1.00000	0.0883883
$129$	−4.06781	−0.358151
$130$	−0.639937	−0.0561262
$131$	10.6228	0.928116	0.464058	−	0.885805i	$-0.346393\pi$
$131$	10.6228	0.928116	0.464058	+	0.885805i	$0.346393\pi$
$132$	−2.22651	−0.193793
$133$	−7.62534	−0.661201
$134$	5.50662	0.475699
$135$	−1.74180	−0.149910
$136$	0.907928	0.0778542
$137$	11.4425	0.977602	0.488801	−	0.872395i	$-0.337434\pi$
$137$	11.4425	0.977602	0.488801	+	0.872395i	$0.337434\pi$
$138$	−2.64482	−0.225142
$139$	3.11849	0.264507	0.132254	−	0.991216i	$-0.457779\pi$
$139$	3.11849	0.264507	0.132254	+	0.991216i	$0.457779\pi$
$140$	1.01371	0.0856742
$141$	1.27408	0.107297
$142$	−4.13901	−0.347338
$143$	4.68288	0.391602
$144$	−2.72466	−0.227055
$145$	−5.93831	−0.493150
$146$	2.16475	0.179156
$147$	−2.06935	−0.170677
$148$	1.16291	0.0955905
$149$	−7.52927	−0.616822	−0.308411	−	0.951253i	$-0.599797\pi$
$149$	−7.52927	−0.616822	−0.308411	+	0.951253i	$0.599797\pi$
$150$	−2.44722	−0.199814
$151$	2.25758	0.183719	0.0918596	−	0.995772i	$-0.470719\pi$
$151$	2.25758	0.183719	0.0918596	+	0.995772i	$0.470719\pi$
$152$	−4.36173	−0.353783
$153$	−2.47380	−0.199995
$154$	−7.41806	−0.597764
$155$	4.46702	0.358800
$156$	−0.579106	−0.0463656
$157$	14.6282	1.16746	0.583729	−	0.811949i	$-0.301593\pi$
$157$	14.6282	1.16746	0.583729	+	0.811949i	$0.301593\pi$
$158$	−3.49154	−0.277772
$159$	5.29927	0.420259
$160$	0.579848	0.0458410
$161$	−8.81175	−0.694463
$162$	6.59775	0.518369
$163$	−19.0197	−1.48974	−0.744868	−	0.667212i	$-0.767488\pi$
$163$	−19.0197	−1.48974	−0.744868	+	0.667212i	$0.767488\pi$
$164$	−7.50439	−0.585994
$165$	−1.29104	−0.100507
$166$	−2.19884	−0.170663
$167$	−1.30550	−0.101023	−0.0505113	−	0.998723i	$-0.516085\pi$
$167$	−1.30550	−0.101023	−0.0505113	+	0.998723i	$0.516085\pi$
$168$	0.917349	0.0707750
$169$	−11.7820	−0.906308
$170$	0.526460	0.0403776
$171$	11.8842	0.908811
$172$	−7.75223	−0.591102
$173$	17.7649	1.35064	0.675320	−	0.737525i	$-0.264005\pi$
$173$	17.7649	1.35064	0.675320	+	0.737525i	$0.264005\pi$
$174$	−5.37383	−0.407389
$175$	−8.15339	−0.616338
$176$	−4.24317	−0.319841
$177$	4.85853	0.365190
$178$	15.2655	1.14420
$179$	10.1556	0.759062	0.379531	−	0.925179i	$-0.376085\pi$
$179$	10.1556	0.759062	0.379531	+	0.925179i	$0.376085\pi$
$180$	−1.57989	−0.117758
$181$	−8.62692	−0.641234	−0.320617	−	0.947209i	$-0.603890\pi$
$181$	−8.62692	−0.641234	−0.320617	+	0.947209i	$0.603890\pi$
$182$	−1.92941	−0.143017
$183$	−2.00437	−0.148167
$184$	−5.04037	−0.371581
$185$	0.674310	0.0495763
$186$	4.04239	0.296402
$187$	−3.85249	−0.281722
$188$	2.42807	0.177085
$189$	−5.25151	−0.381991
$190$	−2.52914	−0.183483
$191$	−19.8025	−1.43286	−0.716429	−	0.697660i	$-0.754224\pi$
$191$	−19.8025	−1.43286	−0.716429	+	0.697660i	$0.754224\pi$
$192$	0.524728	0.0378690
$193$	26.9778	1.94191	0.970953	−	0.239270i	$-0.0769082\pi$
$193$	26.9778	1.94191	0.970953	+	0.239270i	$0.0769082\pi$
$194$	−6.83419	−0.490666
$195$	−0.335793	−0.0240466
$196$	−3.94367	−0.281691
$197$	−0.737518	−0.0525460	−0.0262730	−	0.999655i	$-0.508364\pi$
$197$	−0.737518	−0.0525460	−0.0262730	+	0.999655i	$0.508364\pi$
$198$	11.5612	0.821618
$199$	−12.4212	−0.880518	−0.440259	−	0.897871i	$-0.645113\pi$
$199$	−12.4212	−0.880518	−0.440259	+	0.897871i	$0.645113\pi$
$200$	−4.66378	−0.329779
$201$	2.88948	0.203808
$202$	11.5078	0.809688
$203$	−17.9040	−1.25661
$204$	0.476416	0.0333558
$205$	−4.35140	−0.303915
$206$	−13.5504	−0.944098
$207$	13.7333	0.954529
$208$	−1.10363	−0.0765229
$209$	18.5076	1.28019
$210$	0.531923	0.0367062
$211$	−23.5187	−1.61909	−0.809546	−	0.587056i	$-0.800287\pi$
$211$	−23.5187	−1.61909	−0.809546	+	0.587056i	$0.800287\pi$
$212$	10.0991	0.693607
$213$	−2.17186	−0.148813
$214$	1.45069	0.0991672
$215$	−4.49511	−0.306564
$216$	−3.00389	−0.204389
$217$	13.4680	0.914269
$218$	−16.7867	−1.13694
$219$	1.13590	0.0767573
$220$	−2.46039	−0.165879
$221$	−1.00202	−0.0674029
$222$	0.610211	0.0409547
$223$	−7.88310	−0.527892	−0.263946	−	0.964538i	$-0.585024\pi$
$223$	−7.88310	−0.527892	−0.263946	+	0.964538i	$0.585024\pi$
$224$	1.74824	0.116809
$225$	12.7072	0.847147
$226$	−3.36677	−0.223954
$227$	23.0428	1.52941	0.764704	−	0.644382i	$-0.222885\pi$
$227$	23.0428	1.52941	0.764704	+	0.644382i	$0.222885\pi$
$228$	−2.28872	−0.151574
$229$	15.7163	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$229$	15.7163	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$230$	−2.92264	−0.192713
$231$	−3.89247	−0.256106
$232$	−10.2412	−0.672365
$233$	−15.8094	−1.03571	−0.517853	−	0.855469i	$-0.673269\pi$
$233$	−15.8094	−1.03571	−0.517853	+	0.855469i	$0.673269\pi$
$234$	3.00702	0.196575
$235$	1.40791	0.0918420
$236$	9.25914	0.602718
$237$	−1.83211	−0.119008
$238$	1.58727	0.102888
$239$	−19.2990	−1.24835	−0.624173	−	0.781286i	$-0.714564\pi$
$239$	−19.2990	−1.24835	−0.624173	+	0.781286i	$0.714564\pi$
$240$	0.304262	0.0196401
$241$	11.0444	0.711431	0.355715	−	0.934594i	$-0.384237\pi$
$241$	11.0444	0.711431	0.355715	+	0.934594i	$0.384237\pi$
$242$	7.00447	0.450264
$243$	12.4737	0.800188
$244$	−3.81983	−0.244539
$245$	−2.28673	−0.146094
$246$	−3.93776	−0.251063
$247$	4.81374	0.306291
$248$	7.70378	0.489190
$249$	−1.15380	−0.0731188
$250$	−5.60352	−0.354398
$251$	0.443319	0.0279820	0.0139910	−	0.999902i	$-0.495546\pi$
$251$	0.443319	0.0279820	0.0139910	+	0.999902i	$0.495546\pi$
$252$	−4.76335	−0.300063
$253$	21.3871	1.34460
$254$	8.42595	0.528691
$255$	0.276248	0.0172993
$256$	1.00000	0.0625000
$257$	27.2469	1.69961	0.849807	−	0.527094i	$-0.176718\pi$
$257$	27.2469	1.69961	0.849807	+	0.527094i	$0.176718\pi$
$258$	−4.06781	−0.253251
$259$	2.03304	0.126327
$260$	−0.639937	−0.0396872
$261$	27.9037	1.72719
$262$	10.6228	0.656277
$263$	10.8589	0.669591	0.334795	−	0.942291i	$-0.391333\pi$
$263$	10.8589	0.669591	0.334795	+	0.942291i	$0.391333\pi$
$264$	−2.22651	−0.137032
$265$	5.85592	0.359727
$266$	−7.62534	−0.467540
$267$	8.01025	0.490220
$268$	5.50662	0.336370
$269$	−12.9728	−0.790966	−0.395483	−	0.918473i	$-0.629423\pi$
$269$	−12.9728	−0.790966	−0.395483	+	0.918473i	$0.629423\pi$
$270$	−1.74180	−0.106003
$271$	13.0312	0.791590	0.395795	−	0.918339i	$-0.370469\pi$
$271$	13.0312	0.791590	0.395795	+	0.918339i	$0.370469\pi$
$272$	0.907928	0.0550512
$273$	−1.01241	−0.0612741
$274$	11.4425	0.691269
$275$	19.7892	1.19333
$276$	−2.64482	−0.159200
$277$	−9.85960	−0.592406	−0.296203	−	0.955125i	$-0.595720\pi$
$277$	−9.85960	−0.592406	−0.296203	+	0.955125i	$0.595720\pi$
$278$	3.11849	0.187035
$279$	−20.9902	−1.25665
$280$	1.01371	0.0605808
$281$	−27.0146	−1.61156	−0.805779	−	0.592217i	$-0.798253\pi$
$281$	−27.0146	−1.61156	−0.805779	+	0.592217i	$0.798253\pi$
$282$	1.27408	0.0758702
$283$	5.04576	0.299939	0.149970	−	0.988691i	$-0.452082\pi$
$283$	5.04576	0.299939	0.149970	+	0.988691i	$0.452082\pi$
$284$	−4.13901	−0.245605
$285$	−1.32711	−0.0786113
$286$	4.68288	0.276905
$287$	−13.1194	−0.774416
$288$	−2.72466	−0.160552
$289$	−16.1757	−0.951510
$290$	−5.93831	−0.348710
$291$	−3.58609	−0.210220
$292$	2.16475	0.126682
$293$	13.5863	0.793721	0.396860	−	0.917879i	$-0.370100\pi$
$293$	13.5863	0.793721	0.396860	+	0.917879i	$0.370100\pi$
$294$	−2.06935	−0.120687
$295$	5.36889	0.312589
$296$	1.16291	0.0675927
$297$	12.7460	0.739599
$298$	−7.52927	−0.436159
$299$	5.56270	0.321699
$300$	−2.44722	−0.141290
$301$	−13.5527	−0.781167
$302$	2.25758	0.129909
$303$	6.03848	0.346902
$304$	−4.36173	−0.250163
$305$	−2.21492	−0.126826
$306$	−2.47380	−0.141417
$307$	29.5812	1.68829	0.844144	−	0.536116i	$-0.180109\pi$
$307$	29.5812	1.68829	0.844144	+	0.536116i	$0.180109\pi$
$308$	−7.41806	−0.422683
$309$	−7.11025	−0.404488
$310$	4.46702	0.253710
$311$	−14.3306	−0.812613	−0.406306	−	0.913737i	$-0.633183\pi$
$311$	−14.3306	−0.812613	−0.406306	+	0.913737i	$0.633183\pi$
$312$	−0.579106	−0.0327854
$313$	−24.3489	−1.37628	−0.688140	−	0.725578i	$-0.741572\pi$
$313$	−24.3489	−1.37628	−0.688140	+	0.725578i	$0.741572\pi$
$314$	14.6282	0.825517
$315$	−2.76202	−0.155622
$316$	−3.49154	−0.196415
$317$	−31.4001	−1.76360	−0.881802	−	0.471620i	$-0.843669\pi$
$317$	−31.4001	−1.76360	−0.881802	+	0.471620i	$0.843669\pi$
$318$	5.29927	0.297168
$319$	43.4550	2.43301
$320$	0.579848	0.0324145
$321$	0.761219	0.0424871
$322$	−8.81175	−0.491060
$323$	−3.96014	−0.220348
$324$	6.59775	0.366542
$325$	5.14708	0.285509
$326$	−19.0197	−1.05340
$327$	−8.80845	−0.487108
$328$	−7.50439	−0.414360
$329$	4.24484	0.234026
$330$	−1.29104	−0.0710692
$331$	−18.1365	−0.996874	−0.498437	−	0.866926i	$-0.666093\pi$
$331$	−18.1365	−0.996874	−0.498437	+	0.866926i	$0.666093\pi$
$332$	−2.19884	−0.120677
$333$	−3.16853	−0.173634
$334$	−1.30550	−0.0714337
$335$	3.19300	0.174452
$336$	0.917349	0.0500455
$337$	−19.2491	−1.04856	−0.524282	−	0.851545i	$-0.675666\pi$
$337$	−19.2491	−1.04856	−0.524282	+	0.851545i	$0.675666\pi$
$338$	−11.7820	−0.640856
$339$	−1.76664	−0.0959507
$340$	0.526460	0.0285513
$341$	−32.6884	−1.77018
$342$	11.8842	0.642626
$343$	−19.1321	−1.03304
$344$	−7.75223	−0.417972
$345$	−1.53359	−0.0825659
$346$	17.7649	0.955047
$347$	28.1876	1.51319	0.756595	−	0.653884i	$-0.226862\pi$
$347$	28.1876	1.51319	0.756595	+	0.653884i	$0.226862\pi$
$348$	−5.37383	−0.288067
$349$	−16.6189	−0.889588	−0.444794	−	0.895633i	$-0.646723\pi$
$349$	−16.6189	−0.889588	−0.444794	+	0.895633i	$0.646723\pi$
$350$	−8.15339	−0.435817
$351$	3.31518	0.176951
$352$	−4.24317	−0.226162
$353$	−21.8164	−1.16117	−0.580585	−	0.814199i	$-0.697176\pi$
$353$	−21.8164	−1.16117	−0.580585	+	0.814199i	$0.697176\pi$
$354$	4.85853	0.258228
$355$	−2.40000	−0.127379
$356$	15.2655	0.809071
$357$	0.832887	0.0440811
$358$	10.1556	0.536738
$359$	−11.8039	−0.622985	−0.311493	−	0.950249i	$-0.600829\pi$
$359$	−11.8039	−0.622985	−0.311493	+	0.950249i	$0.600829\pi$
$360$	−1.57989	−0.0832674
$361$	0.0247128	0.00130068
$362$	−8.62692	−0.453421
$363$	3.67544	0.192911
$364$	−1.92941	−0.101128
$365$	1.25522	0.0657014
$366$	−2.00437	−0.104770
$367$	−37.7917	−1.97271	−0.986354	−	0.164638i	$-0.947354\pi$
$367$	−37.7917	−1.97271	−0.986354	+	0.164638i	$0.947354\pi$
$368$	−5.04037	−0.262747
$369$	20.4469	1.06442
$370$	0.674310	0.0350557
$371$	17.6556	0.916632
$372$	4.04239	0.209588
$373$	9.93160	0.514239	0.257119	−	0.966380i	$-0.417227\pi$
$373$	9.93160	0.514239	0.257119	+	0.966380i	$0.417227\pi$
$374$	−3.85249	−0.199208
$375$	−2.94032	−0.151838
$376$	2.42807	0.125218
$377$	11.3024	0.582106
$378$	−5.25151	−0.270109
$379$	−2.08125	−0.106907	−0.0534534	−	0.998570i	$-0.517023\pi$
$379$	−2.08125	−0.106907	−0.0534534	+	0.998570i	$0.517023\pi$
$380$	−2.52914	−0.129742
$381$	4.42133	0.226512
$382$	−19.8025	−1.01318
$383$	−3.37711	−0.172562	−0.0862810	−	0.996271i	$-0.527498\pi$
$383$	−3.37711	−0.172562	−0.0862810	+	0.996271i	$0.527498\pi$
$384$	0.524728	0.0267774
$385$	−4.30135	−0.219217
$386$	26.9778	1.37313
$387$	21.1222	1.07370
$388$	−6.83419	−0.346953
$389$	0.435883	0.0221002	0.0110501	−	0.999939i	$-0.496483\pi$
$389$	0.435883	0.0221002	0.0110501	+	0.999939i	$0.496483\pi$
$390$	−0.335793	−0.0170035
$391$	−4.57629	−0.231433
$392$	−3.94367	−0.199185
$393$	5.57407	0.281175
$394$	−0.737518	−0.0371556
$395$	−2.02456	−0.101867
$396$	11.5612	0.580972
$397$	−7.38433	−0.370609	−0.185305	−	0.982681i	$-0.559327\pi$
$397$	−7.38433	−0.370609	−0.185305	+	0.982681i	$0.559327\pi$
$398$	−12.4212	−0.622620
$399$	−4.00123	−0.200312
$400$	−4.66378	−0.233189
$401$	−30.0393	−1.50009	−0.750045	−	0.661387i	$-0.769968\pi$
$401$	−30.0393	−1.50009	−0.750045	+	0.661387i	$0.769968\pi$
$402$	2.88948	0.144114
$403$	−8.50212	−0.423521
$404$	11.5078	0.572536
$405$	3.82569	0.190100
$406$	−17.9040	−0.888559
$407$	−4.93442	−0.244590
$408$	0.476416	0.0235861
$409$	−25.0098	−1.23666	−0.618329	−	0.785920i	$-0.712190\pi$
$409$	−25.0098	−1.23666	−0.618329	+	0.785920i	$0.712190\pi$
$410$	−4.35140	−0.214900
$411$	6.00423	0.296167
$412$	−13.5504	−0.667578
$413$	16.1872	0.796518
$414$	13.7333	0.674954
$415$	−1.27499	−0.0625870
$416$	−1.10363	−0.0541099
$417$	1.63636	0.0801330
$418$	18.5076	0.905234
$419$	35.4484	1.73177	0.865885	−	0.500244i	$-0.166756\pi$
$419$	35.4484	1.73177	0.865885	+	0.500244i	$0.166756\pi$
$420$	0.531923	0.0259552
$421$	4.49450	0.219049	0.109524	−	0.993984i	$-0.465067\pi$
$421$	4.49450	0.219049	0.109524	+	0.993984i	$0.465067\pi$
$422$	−23.5187	−1.14487
$423$	−6.61567	−0.321665
$424$	10.0991	0.490454
$425$	−4.23437	−0.205397
$426$	−2.17186	−0.105227
$427$	−6.67796	−0.323169
$428$	1.45069	0.0701218
$429$	2.45724	0.118637
$430$	−4.49511	−0.216774
$431$	−16.5094	−0.795231	−0.397615	−	0.917552i	$-0.630162\pi$
$431$	−16.5094	−0.795231	−0.397615	+	0.917552i	$0.630162\pi$
$432$	−3.00389	−0.144525
$433$	3.74448	0.179948	0.0899741	−	0.995944i	$-0.471322\pi$
$433$	3.74448	0.179948	0.0899741	+	0.995944i	$0.471322\pi$
$434$	13.4680	0.646486
$435$	−3.11600	−0.149401
$436$	−16.7867	−0.803936
$437$	21.9847	1.05167
$438$	1.13590	0.0542756
$439$	−23.9564	−1.14338	−0.571688	−	0.820471i	$-0.693711\pi$
$439$	−23.9564	−1.14338	−0.571688	+	0.820471i	$0.693711\pi$
$440$	−2.46039	−0.117295
$441$	10.7452	0.511674
$442$	−1.00202	−0.0476610
$443$	−38.5346	−1.83083	−0.915416	−	0.402509i	$-0.868138\pi$
$443$	−38.5346	−1.83083	−0.915416	+	0.402509i	$0.868138\pi$
$444$	0.610211	0.0289593
$445$	8.85168	0.419610
$446$	−7.88310	−0.373276
$447$	−3.95082	−0.186867
$448$	1.74824	0.0825964
$449$	−5.34299	−0.252151	−0.126076	−	0.992021i	$-0.540238\pi$
$449$	−5.34299	−0.252151	−0.126076	+	0.992021i	$0.540238\pi$
$450$	12.7072	0.599023
$451$	31.8424	1.49940
$452$	−3.36677	−0.158360
$453$	1.18462	0.0556581
$454$	23.0428	1.08145
$455$	−1.11876	−0.0524483
$456$	−2.28872	−0.107179
$457$	9.37871	0.438717	0.219359	−	0.975644i	$-0.429603\pi$
$457$	9.37871	0.438717	0.219359	+	0.975644i	$0.429603\pi$
$458$	15.7163	0.734372
$459$	−2.72732	−0.127300
$460$	−2.92264	−0.136269
$461$	26.6068	1.23920	0.619601	−	0.784917i	$-0.287295\pi$
$461$	26.6068	1.23920	0.619601	+	0.784917i	$0.287295\pi$
$462$	−3.89247	−0.181094
$463$	25.3046	1.17600	0.588002	−	0.808859i	$-0.299915\pi$
$463$	25.3046	1.17600	0.588002	+	0.808859i	$0.299915\pi$
$464$	−10.2412	−0.475434
$465$	2.34397	0.108699
$466$	−15.8094	−0.732355
$467$	38.7351	1.79245	0.896224	−	0.443602i	$-0.146299\pi$
$467$	38.7351	1.79245	0.896224	+	0.443602i	$0.146299\pi$
$468$	3.00702	0.138999
$469$	9.62687	0.444528
$470$	1.40791	0.0649421
$471$	7.67583	0.353684
$472$	9.25914	0.426186
$473$	32.8940	1.51247
$474$	−1.83211	−0.0841517
$475$	20.3421	0.933362
$476$	1.58727	0.0727526
$477$	−27.5165	−1.25990
$478$	−19.2990	−0.882714
$479$	7.26758	0.332064	0.166032	−	0.986120i	$-0.446904\pi$
$479$	7.26758	0.332064	0.166032	+	0.986120i	$0.446904\pi$
$480$	0.304262	0.0138876
$481$	−1.28342	−0.0585189
$482$	11.0444	0.503058
$483$	−4.62378	−0.210389
$484$	7.00447	0.318385
$485$	−3.96279	−0.179941
$486$	12.4737	0.565819
$487$	4.61766	0.209246	0.104623	−	0.994512i	$-0.466636\pi$
$487$	4.61766	0.209246	0.104623	+	0.994512i	$0.466636\pi$
$488$	−3.81983	−0.172915
$489$	−9.98016	−0.451319
$490$	−2.28673	−0.103304
$491$	6.30455	0.284520	0.142260	−	0.989829i	$-0.454563\pi$
$491$	6.30455	0.284520	0.142260	+	0.989829i	$0.454563\pi$
$492$	−3.93776	−0.177528
$493$	−9.29824	−0.418772
$494$	4.81374	0.216580
$495$	6.70373	0.301310
$496$	7.70378	0.345910
$497$	−7.23597	−0.324578
$498$	−1.15380	−0.0517028
$499$	−24.2705	−1.08650	−0.543249	−	0.839571i	$-0.682806\pi$
$499$	−24.2705	−1.08650	−0.543249	+	0.839571i	$0.682806\pi$
$500$	−5.60352	−0.250597
$501$	−0.685032	−0.0306050
$502$	0.443319	0.0197863
$503$	2.43140	0.108411	0.0542054	−	0.998530i	$-0.482737\pi$
$503$	2.43140	0.108411	0.0542054	+	0.998530i	$0.482737\pi$
$504$	−4.76335	−0.212177
$505$	6.67279	0.296935
$506$	21.3871	0.950773
$507$	−6.18235	−0.274568
$508$	8.42595	0.373841
$509$	−12.8200	−0.568237	−0.284119	−	0.958789i	$-0.591701\pi$
$509$	−12.8200	−0.568237	−0.284119	+	0.958789i	$0.591701\pi$
$510$	0.276248	0.0122325
$511$	3.78449	0.167416
$512$	1.00000	0.0441942
$513$	13.1022	0.578475
$514$	27.2469	1.20181
$515$	−7.85714	−0.346227
$516$	−4.06781	−0.179076
$517$	−10.3027	−0.453113
$518$	2.03304	0.0893267
$519$	9.32174	0.409179
$520$	−0.639937	−0.0280631
$521$	9.40642	0.412103	0.206051	−	0.978541i	$-0.433939\pi$
$521$	9.40642	0.412103	0.206051	+	0.978541i	$0.433939\pi$
$522$	27.9037	1.22131
$523$	−7.01366	−0.306686	−0.153343	−	0.988173i	$-0.549004\pi$
$523$	−7.01366	−0.306686	−0.153343	+	0.988173i	$0.549004\pi$
$524$	10.6228	0.464058
$525$	−4.27831	−0.186721
$526$	10.8589	0.473472
$527$	6.99448	0.304684
$528$	−2.22651	−0.0968964
$529$	2.40528	0.104578
$530$	5.85592	0.254365
$531$	−25.2280	−1.09480
$532$	−7.62534	−0.330601
$533$	8.28206	0.358736
$534$	8.01025	0.346638
$535$	0.841180	0.0363674
$536$	5.50662	0.237850
$537$	5.32891	0.229959
$538$	−12.9728	−0.559298
$539$	16.7336	0.720769
$540$	−1.74180	−0.0749551
$541$	14.2576	0.612984	0.306492	−	0.951873i	$-0.400845\pi$
$541$	14.2576	0.612984	0.306492	+	0.951873i	$0.400845\pi$
$542$	13.0312	0.559738
$543$	−4.52679	−0.194263
$544$	0.907928	0.0389271
$545$	−9.73372	−0.416947
$546$	−1.01241	−0.0433273
$547$	−27.1789	−1.16209	−0.581043	−	0.813873i	$-0.697355\pi$
$547$	−27.1789	−1.16209	−0.581043	+	0.813873i	$0.697355\pi$
$548$	11.4425	0.488801
$549$	10.4077	0.444191
$550$	19.7892	0.843814
$551$	44.6692	1.90297
$552$	−2.64482	−0.112571
$553$	−6.10404	−0.259570
$554$	−9.85960	−0.418894
$555$	0.353830	0.0150192
$556$	3.11849	0.132254
$557$	11.9344	0.505675	0.252838	−	0.967509i	$-0.418636\pi$
$557$	11.9344	0.505675	0.252838	+	0.967509i	$0.418636\pi$
$558$	−20.9902	−0.888585
$559$	8.55559	0.361863
$560$	1.01371	0.0428371
$561$	−2.02151	−0.0853482
$562$	−27.0146	−1.13954
$563$	14.4444	0.608761	0.304380	−	0.952551i	$-0.401551\pi$
$563$	14.4444	0.608761	0.304380	+	0.952551i	$0.401551\pi$
$564$	1.27408	0.0536483
$565$	−1.95221	−0.0821303
$566$	5.04576	0.212089
$567$	11.5344	0.484401
$568$	−4.13901	−0.173669
$569$	25.9706	1.08874	0.544372	−	0.838844i	$-0.316768\pi$
$569$	25.9706	1.08874	0.544372	+	0.838844i	$0.316768\pi$
$570$	−1.32711	−0.0555866
$571$	−17.3276	−0.725138	−0.362569	−	0.931957i	$-0.618100\pi$
$571$	−17.3276	−0.725138	−0.362569	+	0.931957i	$0.618100\pi$
$572$	4.68288	0.195801
$573$	−10.3909	−0.434087
$574$	−13.1194	−0.547595
$575$	23.5071	0.980315
$576$	−2.72466	−0.113528
$577$	33.3026	1.38641	0.693203	−	0.720742i	$-0.256199\pi$
$577$	33.3026	1.38641	0.693203	+	0.720742i	$0.256199\pi$
$578$	−16.1757	−0.672819
$579$	14.1560	0.588304
$580$	−5.93831	−0.246575
$581$	−3.84410	−0.159480
$582$	−3.58609	−0.148648
$583$	−42.8521	−1.77475
$584$	2.16475	0.0895779
$585$	1.74361	0.0720894
$586$	13.5863	0.561245
$587$	−12.7872	−0.527782	−0.263891	−	0.964552i	$-0.585006\pi$
$587$	−12.7872	−0.527782	−0.263891	+	0.964552i	$0.585006\pi$
$588$	−2.06935	−0.0853387
$589$	−33.6018	−1.38454
$590$	5.36889	0.221034
$591$	−0.386997	−0.0159189
$592$	1.16291	0.0477953
$593$	37.7716	1.55109	0.775546	−	0.631291i	$-0.217474\pi$
$593$	37.7716	1.55109	0.775546	+	0.631291i	$0.217474\pi$
$594$	12.7460	0.522975
$595$	0.920377	0.0377318
$596$	−7.52927	−0.308411
$597$	−6.51777	−0.266755
$598$	5.56270	0.227476
$599$	−39.3724	−1.60871	−0.804357	−	0.594146i	$-0.797490\pi$
$599$	−39.3724	−1.60871	−0.804357	+	0.594146i	$0.797490\pi$
$600$	−2.44722	−0.0999072
$601$	−27.3220	−1.11449	−0.557244	−	0.830349i	$-0.688141\pi$
$601$	−27.3220	−1.11449	−0.557244	+	0.830349i	$0.688141\pi$
$602$	−13.5527	−0.552368
$603$	−15.0037	−0.610996
$604$	2.25758	0.0918596
$605$	4.06152	0.165124
$606$	6.03848	0.245297
$607$	−18.1635	−0.737234	−0.368617	−	0.929581i	$-0.620169\pi$
$607$	−18.1635	−0.737234	−0.368617	+	0.929581i	$0.620169\pi$
$608$	−4.36173	−0.176892
$609$	−9.39472	−0.380693
$610$	−2.21492	−0.0896794
$611$	−2.67969	−0.108409
$612$	−2.47380	−0.0999973
$613$	23.4303	0.946341	0.473171	−	0.880971i	$-0.343109\pi$
$613$	23.4303	0.946341	0.473171	+	0.880971i	$0.343109\pi$
$614$	29.5812	1.19380
$615$	−2.28330	−0.0920717
$616$	−7.41806	−0.298882
$617$	32.1152	1.29291	0.646454	−	0.762953i	$-0.276251\pi$
$617$	32.1152	1.29291	0.646454	+	0.762953i	$0.276251\pi$
$618$	−7.11025	−0.286016
$619$	17.0924	0.687002	0.343501	−	0.939152i	$-0.388387\pi$
$619$	17.0924	0.687002	0.343501	+	0.939152i	$0.388387\pi$
$620$	4.46702	0.179400
$621$	15.1407	0.607576
$622$	−14.3306	−0.574604
$623$	26.6878	1.06922
$624$	−0.579106	−0.0231828
$625$	20.0697	0.802788
$626$	−24.3489	−0.973176
$627$	9.71144	0.387838
$628$	14.6282	0.583729
$629$	1.05584	0.0420990
$630$	−2.76202	−0.110041
$631$	44.1562	1.75783	0.878915	−	0.476978i	$-0.158268\pi$
$631$	44.1562	1.75783	0.878915	+	0.476978i	$0.158268\pi$
$632$	−3.49154	−0.138886
$633$	−12.3409	−0.490507
$634$	−31.4001	−1.24706
$635$	4.88577	0.193886
$636$	5.29927	0.210130
$637$	4.35235	0.172446
$638$	43.4550	1.72040
$639$	11.2774	0.446127
$640$	0.579848	0.0229205
$641$	−14.1301	−0.558104	−0.279052	−	0.960276i	$-0.590020\pi$
$641$	−14.1301	−0.558104	−0.279052	+	0.960276i	$0.590020\pi$
$642$	0.761219	0.0300429
$643$	37.3366	1.47241	0.736205	−	0.676758i	$-0.236616\pi$
$643$	37.3366	1.47241	0.736205	+	0.676758i	$0.236616\pi$
$644$	−8.81175	−0.347232
$645$	−2.35871	−0.0928742
$646$	−3.96014	−0.155810
$647$	−33.3606	−1.31154	−0.655770	−	0.754961i	$-0.727656\pi$
$647$	−33.3606	−1.31154	−0.655770	+	0.754961i	$0.727656\pi$
$648$	6.59775	0.259184
$649$	−39.2881	−1.54219
$650$	5.14708	0.201885
$651$	7.06706	0.276980
$652$	−19.0197	−0.744868
$653$	10.4815	0.410174	0.205087	−	0.978744i	$-0.434252\pi$
$653$	10.4815	0.410174	0.205087	+	0.978744i	$0.434252\pi$
$654$	−8.80845	−0.344437
$655$	6.15959	0.240675
$656$	−7.50439	−0.292997
$657$	−5.89820	−0.230111
$658$	4.24484	0.165481
$659$	−16.4501	−0.640805	−0.320403	−	0.947281i	$-0.603818\pi$
$659$	−16.4501	−0.640805	−0.320403	+	0.947281i	$0.603818\pi$
$660$	−1.29104	−0.0502535
$661$	33.3664	1.29780	0.648901	−	0.760872i	$-0.275229\pi$
$661$	33.3664	1.29780	0.648901	+	0.760872i	$0.275229\pi$
$662$	−18.1365	−0.704897
$663$	−0.525786	−0.0204198
$664$	−2.19884	−0.0853317
$665$	−4.42154	−0.171460
$666$	−3.16853	−0.122778
$667$	51.6192	1.99870
$668$	−1.30550	−0.0505113
$669$	−4.13649	−0.159926
$670$	3.19300	0.123356
$671$	16.2082	0.625709
$672$	0.917349	0.0353875
$673$	34.1976	1.31822	0.659110	−	0.752046i	$-0.270933\pi$
$673$	34.1976	1.31822	0.659110	+	0.752046i	$0.270933\pi$
$674$	−19.2491	−0.741447
$675$	14.0095	0.539225
$676$	−11.7820	−0.453154
$677$	42.4697	1.63224	0.816121	−	0.577881i	$-0.196120\pi$
$677$	42.4697	1.63224	0.816121	+	0.577881i	$0.196120\pi$
$678$	−1.76664	−0.0678474
$679$	−11.9478	−0.458514
$680$	0.526460	0.0201888
$681$	12.0912	0.463337
$682$	−32.6884	−1.25170
$683$	−22.2549	−0.851560	−0.425780	−	0.904827i	$-0.640000\pi$
$683$	−22.2549	−0.851560	−0.425780	+	0.904827i	$0.640000\pi$
$684$	11.8842	0.454405
$685$	6.63493	0.253508
$686$	−19.1321	−0.730468
$687$	8.24676	0.314634
$688$	−7.75223	−0.295551
$689$	−11.1456	−0.424615
$690$	−1.53359	−0.0583829
$691$	4.39965	0.167371	0.0836853	−	0.996492i	$-0.473331\pi$
$691$	4.39965	0.167371	0.0836853	+	0.996492i	$0.473331\pi$
$692$	17.7649	0.675320
$693$	20.2117	0.767779
$694$	28.1876	1.06999
$695$	1.80825	0.0685909
$696$	−5.37383	−0.203694
$697$	−6.81344	−0.258078
$698$	−16.6189	−0.629034
$699$	−8.29563	−0.313769
$700$	−8.15339	−0.308169
$701$	12.6008	0.475925	0.237963	−	0.971274i	$-0.423520\pi$
$701$	12.6008	0.475925	0.237963	+	0.971274i	$0.423520\pi$
$702$	3.31518	0.125124
$703$	−5.07230	−0.191305
$704$	−4.24317	−0.159920
$705$	0.738771	0.0278237
$706$	−21.8164	−0.821072
$707$	20.1184	0.756631
$708$	4.85853	0.182595
$709$	22.9615	0.862339	0.431169	−	0.902271i	$-0.358101\pi$
$709$	22.9615	0.862339	0.431169	+	0.902271i	$0.358101\pi$
$710$	−2.40000	−0.0900703
$711$	9.51327	0.356775
$712$	15.2655	0.572100
$713$	−38.8299	−1.45419
$714$	0.832887	0.0311700
$715$	2.71536	0.101549
$716$	10.1556	0.379531
$717$	−10.1267	−0.378189
$718$	−11.8039	−0.440517
$719$	14.2247	0.530490	0.265245	−	0.964181i	$-0.414547\pi$
$719$	14.2247	0.530490	0.265245	+	0.964181i	$0.414547\pi$
$720$	−1.57989	−0.0588789
$721$	−23.6892	−0.882233
$722$	0.0247128	0.000919717 0
$723$	5.79530	0.215529
$724$	−8.62692	−0.320617
$725$	47.7625	1.77385
$726$	3.67544	0.136408
$727$	−0.451032	−0.0167278	−0.00836392	−	0.999965i	$-0.502662\pi$
$727$	−0.451032	−0.0167278	−0.00836392	+	0.999965i	$0.502662\pi$
$728$	−1.92941	−0.0715085
$729$	−13.2480	−0.490665
$730$	1.25522	0.0464579
$731$	−7.03847	−0.260327
$732$	−2.00437	−0.0740837
$733$	49.6160	1.83261	0.916304	−	0.400483i	$-0.131158\pi$
$733$	49.6160	1.83261	0.916304	+	0.400483i	$0.131158\pi$
$734$	−37.7917	−1.39492
$735$	−1.19991	−0.0442593
$736$	−5.04037	−0.185790
$737$	−23.3655	−0.860679
$738$	20.4469	0.752661
$739$	−26.6773	−0.981339	−0.490669	−	0.871346i	$-0.663248\pi$
$739$	−26.6773	−0.981339	−0.490669	+	0.871346i	$0.663248\pi$
$740$	0.674310	0.0247881
$741$	2.52590	0.0927914
$742$	17.6556	0.648156
$743$	2.06939	0.0759185	0.0379592	−	0.999279i	$-0.487914\pi$
$743$	2.06939	0.0759185	0.0379592	+	0.999279i	$0.487914\pi$
$744$	4.04239	0.148201
$745$	−4.36583	−0.159952
$746$	9.93160	0.363622
$747$	5.99110	0.219203
$748$	−3.85249	−0.140861
$749$	2.53615	0.0926690
$750$	−2.94032	−0.107365
$751$	−6.73841	−0.245888	−0.122944	−	0.992414i	$-0.539234\pi$
$751$	−6.73841	−0.245888	−0.122944	+	0.992414i	$0.539234\pi$
$752$	2.42807	0.0885426
$753$	0.232622	0.00847721
$754$	11.3024	0.411611
$755$	1.30905	0.0476413
$756$	−5.25151	−0.190996
$757$	−36.2973	−1.31925	−0.659623	−	0.751596i	$-0.729284\pi$
$757$	−36.2973	−1.31925	−0.659623	+	0.751596i	$0.729284\pi$
$758$	−2.08125	−0.0755945
$759$	11.2224	0.407348
$760$	−2.52914	−0.0917416
$761$	54.1522	1.96301	0.981507	−	0.191425i	$-0.0613107\pi$
$761$	54.1522	1.96301	0.981507	+	0.191425i	$0.0613107\pi$
$762$	4.42133	0.160168
$763$	−29.3471	−1.06244
$764$	−19.8025	−0.716429
$765$	−1.43442	−0.0518617
$766$	−3.37711	−0.122020
$767$	−10.2187	−0.368974
$768$	0.524728	0.0189345
$769$	−4.21453	−0.151980	−0.0759899	−	0.997109i	$-0.524212\pi$
$769$	−4.21453	−0.151980	−0.0759899	+	0.997109i	$0.524212\pi$
$770$	−4.30135	−0.155010
$771$	14.2972	0.514902
$772$	26.9778	0.970953
$773$	1.84907	0.0665064	0.0332532	−	0.999447i	$-0.489413\pi$
$773$	1.84907	0.0665064	0.0332532	+	0.999447i	$0.489413\pi$
$774$	21.1222	0.759222
$775$	−35.9287	−1.29060
$776$	−6.83419	−0.245333
$777$	1.06679	0.0382710
$778$	0.435883	0.0156272
$779$	32.7321	1.17275
$780$	−0.335793	−0.0120233
$781$	17.5625	0.628436
$782$	−4.57629	−0.163648
$783$	30.7633	1.09939
$784$	−3.94367	−0.140845
$785$	8.48213	0.302740
$786$	5.57407	0.198820
$787$	−13.5333	−0.482408	−0.241204	−	0.970474i	$-0.577542\pi$
$787$	−13.5333	−0.482408	−0.241204	+	0.970474i	$0.577542\pi$
$788$	−0.737518	−0.0262730
$789$	5.69799	0.202854
$790$	−2.02456	−0.0720307
$791$	−5.88591	−0.209279
$792$	11.5612	0.410809
$793$	4.21567	0.149703
$794$	−7.38433	−0.262060
$795$	3.07277	0.108980
$796$	−12.4212	−0.440259
$797$	14.1358	0.500716	0.250358	−	0.968153i	$-0.419452\pi$
$797$	14.1358	0.500716	0.250358	+	0.968153i	$0.419452\pi$
$798$	−4.00123	−0.141642
$799$	2.20451	0.0779901
$800$	−4.66378	−0.164889
$801$	−41.5934	−1.46963
$802$	−30.0393	−1.06072
$803$	−9.18538	−0.324145
$804$	2.88948	0.101904
$805$	−5.10947	−0.180085
$806$	−8.50212	−0.299474
$807$	−6.80720	−0.239625
$808$	11.5078	0.404844
$809$	−33.1148	−1.16426	−0.582128	−	0.813097i	$-0.697780\pi$
$809$	−33.1148	−1.16426	−0.582128	+	0.813097i	$0.697780\pi$
$810$	3.82569	0.134421
$811$	−24.6147	−0.864338	−0.432169	−	0.901793i	$-0.642252\pi$
$811$	−24.6147	−0.864338	−0.432169	+	0.901793i	$0.642252\pi$
$812$	−17.9040	−0.628306
$813$	6.83785	0.239814
$814$	−4.93442	−0.172951
$815$	−11.0285	−0.386312
$816$	0.476416	0.0166779
$817$	33.8132	1.18297
$818$	−25.0098	−0.874449
$819$	5.25698	0.183694
$820$	−4.35140	−0.151957
$821$	0.918011	0.0320388	0.0160194	−	0.999872i	$-0.494901\pi$
$821$	0.918011	0.0320388	0.0160194	+	0.999872i	$0.494901\pi$
$822$	6.00423	0.209421
$823$	−30.2958	−1.05605	−0.528023	−	0.849230i	$-0.677067\pi$
$823$	−30.2958	−1.05605	−0.528023	+	0.849230i	$0.677067\pi$
$824$	−13.5504	−0.472049
$825$	10.3839	0.361523
$826$	16.1872	0.563224
$827$	−3.77313	−0.131204	−0.0656022	−	0.997846i	$-0.520897\pi$
$827$	−3.77313	−0.131204	−0.0656022	+	0.997846i	$0.520897\pi$
$828$	13.7333	0.477265
$829$	−45.0545	−1.56481	−0.782403	−	0.622772i	$-0.786006\pi$
$829$	−45.0545	−1.56481	−0.782403	+	0.622772i	$0.786006\pi$
$830$	−1.27499	−0.0442557
$831$	−5.17361	−0.179471
$832$	−1.10363	−0.0382615
$833$	−3.58057	−0.124059
$834$	1.63636	0.0566626
$835$	−0.756991	−0.0261967
$836$	18.5076	0.640097
$837$	−23.1413	−0.799881
$838$	35.4484	1.22455
$839$	−22.1547	−0.764864	−0.382432	−	0.923984i	$-0.624913\pi$
$839$	−22.1547	−0.764864	−0.382432	+	0.923984i	$0.624913\pi$
$840$	0.531923	0.0183531
$841$	75.8814	2.61660
$842$	4.49450	0.154891
$843$	−14.1753	−0.488225
$844$	−23.5187	−0.809546
$845$	−6.83177	−0.235020
$846$	−6.61567	−0.227451
$847$	12.2455	0.420759
$848$	10.0991	0.346804
$849$	2.64765	0.0908672
$850$	−4.23437	−0.145238
$851$	−5.86149	−0.200929
$852$	−2.17186	−0.0744066
$853$	12.8890	0.441311	0.220655	−	0.975352i	$-0.429180\pi$
$853$	12.8890	0.441311	0.220655	+	0.975352i	$0.429180\pi$
$854$	−6.67796	−0.228515
$855$	6.89105	0.235669
$856$	1.45069	0.0495836
$857$	31.3615	1.07129	0.535644	−	0.844444i	$-0.320069\pi$
$857$	31.3615	1.07129	0.535644	+	0.844444i	$0.320069\pi$
$858$	2.45724	0.0838889
$859$	−12.7738	−0.435837	−0.217919	−	0.975967i	$-0.569927\pi$
$859$	−12.7738	−0.435837	−0.217919	+	0.975967i	$0.569927\pi$
$860$	−4.49511	−0.153282
$861$	−6.88414	−0.234611
$862$	−16.5094	−0.562313
$863$	57.3228	1.95129	0.975646	−	0.219352i	$-0.0703944\pi$
$863$	57.3228	1.95129	0.975646	+	0.219352i	$0.0703944\pi$
$864$	−3.00389	−0.102194
$865$	10.3009	0.350242
$866$	3.74448	0.127243
$867$	−8.48783	−0.288262
$868$	13.4680	0.457135
$869$	14.8152	0.502571
$870$	−3.11600	−0.105642
$871$	−6.07727	−0.205920
$872$	−16.7867	−0.568469
$873$	18.6208	0.630220
$874$	21.9847	0.743645
$875$	−9.79628	−0.331175
$876$	1.13590	0.0383786
$877$	−1.00474	−0.0339276	−0.0169638	−	0.999856i	$-0.505400\pi$
$877$	−1.00474	−0.0339276	−0.0169638	+	0.999856i	$0.505400\pi$
$878$	−23.9564	−0.808489
$879$	7.12912	0.240459
$880$	−2.46039	−0.0829397
$881$	−43.3265	−1.45971	−0.729853	−	0.683604i	$-0.760412\pi$
$881$	−43.3265	−1.45971	−0.729853	+	0.683604i	$0.760412\pi$
$882$	10.7452	0.361808
$883$	−27.9397	−0.940245	−0.470123	−	0.882601i	$-0.655790\pi$
$883$	−27.9397	−0.940245	−0.470123	+	0.882601i	$0.655790\pi$
$884$	−1.00202	−0.0337015
$885$	2.81721	0.0946994
$886$	−38.5346	−1.29459
$887$	−29.1669	−0.979330	−0.489665	−	0.871911i	$-0.662881\pi$
$887$	−29.1669	−0.979330	−0.489665	+	0.871911i	$0.662881\pi$
$888$	0.610211	0.0204773
$889$	14.7306	0.494047
$890$	8.85168	0.296709
$891$	−27.9954	−0.937880
$892$	−7.88310	−0.263946
$893$	−10.5906	−0.354401
$894$	−3.95082	−0.132135
$895$	5.88868	0.196837
$896$	1.74824	0.0584045
$897$	2.91890	0.0974594
$898$	−5.34299	−0.178298
$899$	−78.8956	−2.63132
$900$	12.7072	0.423574
$901$	9.16923	0.305471
$902$	31.8424	1.06023
$903$	−7.11150	−0.236656
$904$	−3.36677	−0.111977
$905$	−5.00230	−0.166282
$906$	1.18462	0.0393562
$907$	−37.2353	−1.23638	−0.618188	−	0.786030i	$-0.712133\pi$
$907$	−37.2353	−1.23638	−0.618188	+	0.786030i	$0.712133\pi$
$908$	23.0428	0.764704
$909$	−31.3549	−1.03998
$910$	−1.11876	−0.0370866
$911$	−19.0463	−0.631034	−0.315517	−	0.948920i	$-0.602178\pi$
$911$	−19.0463	−0.631034	−0.315517	+	0.948920i	$0.602178\pi$
$912$	−2.28872	−0.0757872
$913$	9.33007	0.308780
$914$	9.37871	0.310220
$915$	−1.16223	−0.0384221
$916$	15.7163	0.519280
$917$	18.5711	0.613272
$918$	−2.72732	−0.0900149
$919$	5.88448	0.194111	0.0970556	−	0.995279i	$-0.469058\pi$
$919$	5.88448	0.194111	0.0970556	+	0.995279i	$0.469058\pi$
$920$	−2.92264	−0.0963567
$921$	15.5221	0.511470
$922$	26.6068	0.876248
$923$	4.56794	0.150355
$924$	−3.89247	−0.128053
$925$	−5.42355	−0.178325
$926$	25.3046	0.831561
$927$	36.9201	1.21262
$928$	−10.2412	−0.336183
$929$	1.84754	0.0606159	0.0303080	−	0.999541i	$-0.490351\pi$
$929$	1.84754	0.0606159	0.0303080	+	0.999541i	$0.490351\pi$
$930$	2.34397	0.0768618
$931$	17.2012	0.563747
$932$	−15.8094	−0.517853
$933$	−7.51966	−0.246183
$934$	38.7351	1.26745
$935$	−2.23386	−0.0730550
$936$	3.00702	0.0982874
$937$	−34.6431	−1.13174	−0.565870	−	0.824494i	$-0.691460\pi$
$937$	−34.6431	−1.13174	−0.565870	+	0.824494i	$0.691460\pi$
$938$	9.62687	0.314329
$939$	−12.7765	−0.416947
$940$	1.40791	0.0459210
$941$	−54.7222	−1.78389	−0.891947	−	0.452140i	$-0.850661\pi$
$941$	−54.7222	−1.78389	−0.891947	+	0.452140i	$0.850661\pi$
$942$	7.67583	0.250092
$943$	37.8248	1.23175
$944$	9.25914	0.301359
$945$	−3.04508	−0.0990564
$946$	32.8940	1.06948
$947$	−18.6067	−0.604637	−0.302319	−	0.953207i	$-0.597761\pi$
$947$	−18.6067	−0.604637	−0.302319	+	0.953207i	$0.597761\pi$
$948$	−1.83211	−0.0595042
$949$	−2.38908	−0.0775528
$950$	20.3421	0.659986
$951$	−16.4765	−0.534287
$952$	1.58727	0.0514438
$953$	7.53800	0.244180	0.122090	−	0.992519i	$-0.461040\pi$
$953$	7.53800	0.244180	0.122090	+	0.992519i	$0.461040\pi$
$954$	−27.5165	−0.890881
$955$	−11.4824	−0.371562
$956$	−19.2990	−0.624173
$957$	22.8020	0.737086
$958$	7.26758	0.234805
$959$	20.0043	0.645972
$960$	0.304262	0.00982003
$961$	28.3482	0.914458
$962$	−1.28342	−0.0413791
$963$	−3.95264	−0.127372
$964$	11.0444	0.355715
$965$	15.6430	0.503567
$966$	−4.62378	−0.148768
$967$	54.2198	1.74359	0.871796	−	0.489869i	$-0.162955\pi$
$967$	54.2198	1.74359	0.871796	+	0.489869i	$0.162955\pi$
$968$	7.00447	0.225132
$969$	−2.07800	−0.0667549
$970$	−3.96279	−0.127237
$971$	−34.6730	−1.11271	−0.556355	−	0.830945i	$-0.687801\pi$
$971$	−34.6730	−1.11271	−0.556355	+	0.830945i	$0.687801\pi$
$972$	12.4737	0.400094
$973$	5.45187	0.174779
$974$	4.61766	0.147959
$975$	2.70082	0.0864954
$976$	−3.81983	−0.122270
$977$	9.32413	0.298305	0.149153	−	0.988814i	$-0.452345\pi$
$977$	9.32413	0.298305	0.149153	+	0.988814i	$0.452345\pi$
$978$	−9.98016	−0.319130
$979$	−64.7742	−2.07019
$980$	−2.28673	−0.0730468
$981$	45.7380	1.46030
$982$	6.30455	0.201186
$983$	−32.7800	−1.04552	−0.522759	−	0.852480i	$-0.675097\pi$
$983$	−32.7800	−1.04552	−0.522759	+	0.852480i	$0.675097\pi$
$984$	−3.93776	−0.125531
$985$	−0.427648	−0.0136260
$986$	−9.29824	−0.296116
$987$	2.22739	0.0708986
$988$	4.81374	0.153145
$989$	39.0741	1.24248
$990$	6.70373	0.213058
$991$	21.9102	0.696000	0.348000	−	0.937495i	$-0.386861\pi$
$991$	21.9102	0.696000	0.348000	+	0.937495i	$0.386861\pi$
$992$	7.70378	0.244595
$993$	−9.51676	−0.302005
$994$	−7.23597	−0.229511
$995$	−7.20242	−0.228332
$996$	−1.15380	−0.0365594
$997$	37.0735	1.17413	0.587065	−	0.809540i	$-0.300283\pi$
$997$	37.0735	1.17413	0.587065	+	0.809540i	$0.300283\pi$
$998$	−24.2705	−0.768270
$999$	−3.49325	−0.110522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.19	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.19	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.524728 q^{3} +1.00000 q^{4} +0.579848 q^{5} +0.524728 q^{6} +1.74824 q^{7} +1.00000 q^{8} -2.72466 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.524728 q^{3} +1.00000 q^{4} +0.579848 q^{5} +0.524728 q^{6} +1.74824 q^{7} +1.00000 q^{8} -2.72466 q^{9} +0.579848 q^{10} -4.24317 q^{11} +0.524728 q^{12} -1.10363 q^{13} +1.74824 q^{14} +0.304262 q^{15} +1.00000 q^{16} +0.907928 q^{17} -2.72466 q^{18} -4.36173 q^{19} +0.579848 q^{20} +0.917349 q^{21} -4.24317 q^{22} -5.04037 q^{23} +0.524728 q^{24} -4.66378 q^{25} -1.10363 q^{26} -3.00389 q^{27} +1.74824 q^{28} -10.2412 q^{29} +0.304262 q^{30} +7.70378 q^{31} +1.00000 q^{32} -2.22651 q^{33} +0.907928 q^{34} +1.01371 q^{35} -2.72466 q^{36} +1.16291 q^{37} -4.36173 q^{38} -0.579106 q^{39} +0.579848 q^{40} -7.50439 q^{41} +0.917349 q^{42} -7.75223 q^{43} -4.24317 q^{44} -1.57989 q^{45} -5.04037 q^{46} +2.42807 q^{47} +0.524728 q^{48} -3.94367 q^{49} -4.66378 q^{50} +0.476416 q^{51} -1.10363 q^{52} +10.0991 q^{53} -3.00389 q^{54} -2.46039 q^{55} +1.74824 q^{56} -2.28872 q^{57} -10.2412 q^{58} +9.25914 q^{59} +0.304262 q^{60} -3.81983 q^{61} +7.70378 q^{62} -4.76335 q^{63} +1.00000 q^{64} -0.639937 q^{65} -2.22651 q^{66} +5.50662 q^{67} +0.907928 q^{68} -2.64482 q^{69} +1.01371 q^{70} -4.13901 q^{71} -2.72466 q^{72} +2.16475 q^{73} +1.16291 q^{74} -2.44722 q^{75} -4.36173 q^{76} -7.41806 q^{77} -0.579106 q^{78} -3.49154 q^{79} +0.579848 q^{80} +6.59775 q^{81} -7.50439 q^{82} -2.19884 q^{83} +0.917349 q^{84} +0.526460 q^{85} -7.75223 q^{86} -5.37383 q^{87} -4.24317 q^{88} +15.2655 q^{89} -1.57989 q^{90} -1.92941 q^{91} -5.04037 q^{92} +4.04239 q^{93} +2.42807 q^{94} -2.52914 q^{95} +0.524728 q^{96} -6.83419 q^{97} -3.94367 q^{98} +11.5612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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