LMFDB - Embedded newform 4022.2.a.c.1.14

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			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.917670 q^{3} +1.00000 q^{4} -0.382051 q^{5} -0.917670 q^{6} +1.33651 q^{7} +1.00000 q^{8} -2.15788 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.917670 q^{3} +1.00000 q^{4} -0.382051 q^{5} -0.917670 q^{6} +1.33651 q^{7} +1.00000 q^{8} -2.15788 q^{9} -0.382051 q^{10} -2.71697 q^{11} -0.917670 q^{12} -2.03954 q^{13} +1.33651 q^{14} +0.350597 q^{15} +1.00000 q^{16} +0.649187 q^{17} -2.15788 q^{18} +5.96909 q^{19} -0.382051 q^{20} -1.22647 q^{21} -2.71697 q^{22} -0.117098 q^{23} -0.917670 q^{24} -4.85404 q^{25} -2.03954 q^{26} +4.73323 q^{27} +1.33651 q^{28} +2.84114 q^{29} +0.350597 q^{30} +4.22955 q^{31} +1.00000 q^{32} +2.49328 q^{33} +0.649187 q^{34} -0.510614 q^{35} -2.15788 q^{36} -7.56382 q^{37} +5.96909 q^{38} +1.87163 q^{39} -0.382051 q^{40} +5.84531 q^{41} -1.22647 q^{42} -7.38086 q^{43} -2.71697 q^{44} +0.824421 q^{45} -0.117098 q^{46} -11.4672 q^{47} -0.917670 q^{48} -5.21375 q^{49} -4.85404 q^{50} -0.595739 q^{51} -2.03954 q^{52} -10.4574 q^{53} +4.73323 q^{54} +1.03802 q^{55} +1.33651 q^{56} -5.47766 q^{57} +2.84114 q^{58} +9.90556 q^{59} +0.350597 q^{60} +3.45238 q^{61} +4.22955 q^{62} -2.88402 q^{63} +1.00000 q^{64} +0.779210 q^{65} +2.49328 q^{66} -8.39700 q^{67} +0.649187 q^{68} +0.107458 q^{69} -0.510614 q^{70} -3.92922 q^{71} -2.15788 q^{72} -5.49646 q^{73} -7.56382 q^{74} +4.45441 q^{75} +5.96909 q^{76} -3.63125 q^{77} +1.87163 q^{78} -1.67559 q^{79} -0.382051 q^{80} +2.13009 q^{81} +5.84531 q^{82} -16.8711 q^{83} -1.22647 q^{84} -0.248023 q^{85} -7.38086 q^{86} -2.60723 q^{87} -2.71697 q^{88} -7.56775 q^{89} +0.824421 q^{90} -2.72586 q^{91} -0.117098 q^{92} -3.88133 q^{93} -11.4672 q^{94} -2.28050 q^{95} -0.917670 q^{96} -11.0163 q^{97} -5.21375 q^{98} +5.86290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.917670	−0.529817	−0.264909	−	0.964274i	$-0.585342\pi$
$3$	−0.917670	−0.529817	−0.264909	+	0.964274i	$0.585342\pi$
$4$	1.00000	0.500000
$5$	−0.382051	−0.170859	−0.0854293	−	0.996344i	$-0.527226\pi$
$5$	−0.382051	−0.170859	−0.0854293	+	0.996344i	$0.527226\pi$
$6$	−0.917670	−0.374637
$7$	1.33651	0.505152	0.252576	−	0.967577i	$-0.418722\pi$
$7$	1.33651	0.505152	0.252576	+	0.967577i	$0.418722\pi$
$8$	1.00000	0.353553
$9$	−2.15788	−0.719294
$10$	−0.382051	−0.120815
$11$	−2.71697	−0.819197	−0.409598	−	0.912266i	$-0.634331\pi$
$11$	−2.71697	−0.819197	−0.409598	+	0.912266i	$0.634331\pi$
$12$	−0.917670	−0.264909
$13$	−2.03954	−0.565667	−0.282834	−	0.959169i	$-0.591274\pi$
$13$	−2.03954	−0.565667	−0.282834	+	0.959169i	$0.591274\pi$
$14$	1.33651	0.357196
$15$	0.350597	0.0905238
$16$	1.00000	0.250000
$17$	0.649187	0.157451	0.0787255	−	0.996896i	$-0.474915\pi$
$17$	0.649187	0.157451	0.0787255	+	0.996896i	$0.474915\pi$
$18$	−2.15788	−0.508617
$19$	5.96909	1.36940	0.684701	−	0.728824i	$-0.259933\pi$
$19$	5.96909	1.36940	0.684701	+	0.728824i	$0.259933\pi$
$20$	−0.382051	−0.0854293
$21$	−1.22647	−0.267638
$22$	−2.71697	−0.579260
$23$	−0.117098	−0.0244167	−0.0122083	−	0.999925i	$-0.503886\pi$
$23$	−0.117098	−0.0244167	−0.0122083	+	0.999925i	$0.503886\pi$
$24$	−0.917670	−0.187319
$25$	−4.85404	−0.970807
$26$	−2.03954	−0.399987
$27$	4.73323	0.910911
$28$	1.33651	0.252576
$29$	2.84114	0.527587	0.263793	−	0.964579i	$-0.415026\pi$
$29$	2.84114	0.527587	0.263793	+	0.964579i	$0.415026\pi$
$30$	0.350597	0.0640100
$31$	4.22955	0.759649	0.379825	−	0.925059i	$-0.375984\pi$
$31$	4.22955	0.759649	0.379825	+	0.925059i	$0.375984\pi$
$32$	1.00000	0.176777
$33$	2.49328	0.434025
$34$	0.649187	0.111335
$35$	−0.510614	−0.0863095
$36$	−2.15788	−0.359647
$37$	−7.56382	−1.24348	−0.621742	−	0.783222i	$-0.713575\pi$
$37$	−7.56382	−1.24348	−0.621742	+	0.783222i	$0.713575\pi$
$38$	5.96909	0.968314
$39$	1.87163	0.299700
$40$	−0.382051	−0.0604076
$41$	5.84531	0.912884	0.456442	−	0.889753i	$-0.349124\pi$
$41$	5.84531	0.912884	0.456442	+	0.889753i	$0.349124\pi$
$42$	−1.22647	−0.189249
$43$	−7.38086	−1.12557	−0.562785	−	0.826603i	$-0.690270\pi$
$43$	−7.38086	−1.12557	−0.562785	+	0.826603i	$0.690270\pi$
$44$	−2.71697	−0.409598
$45$	0.824421	0.122897
$46$	−0.117098	−0.0172652
$47$	−11.4672	−1.67266	−0.836332	−	0.548223i	$-0.815305\pi$
$47$	−11.4672	−1.67266	−0.836332	+	0.548223i	$0.815305\pi$
$48$	−0.917670	−0.132454
$49$	−5.21375	−0.744822
$50$	−4.85404	−0.686464
$51$	−0.595739	−0.0834202
$52$	−2.03954	−0.282834
$53$	−10.4574	−1.43643	−0.718216	−	0.695820i	$-0.755041\pi$
$53$	−10.4574	−1.43643	−0.718216	+	0.695820i	$0.755041\pi$
$54$	4.73323	0.644112
$55$	1.03802	0.139967
$56$	1.33651	0.178598
$57$	−5.47766	−0.725533
$58$	2.84114	0.373060
$59$	9.90556	1.28959	0.644797	−	0.764354i	$-0.276942\pi$
$59$	9.90556	1.28959	0.644797	+	0.764354i	$0.276942\pi$
$60$	0.350597	0.0452619
$61$	3.45238	0.442032	0.221016	−	0.975270i	$-0.429063\pi$
$61$	3.45238	0.442032	0.221016	+	0.975270i	$0.429063\pi$
$62$	4.22955	0.537153
$63$	−2.88402	−0.363353
$64$	1.00000	0.125000
$65$	0.779210	0.0966491
$66$	2.49328	0.306902
$67$	−8.39700	−1.02586	−0.512928	−	0.858431i	$-0.671439\pi$
$67$	−8.39700	−1.02586	−0.512928	+	0.858431i	$0.671439\pi$
$68$	0.649187	0.0787255
$69$	0.107458	0.0129364
$70$	−0.510614	−0.0610300
$71$	−3.92922	−0.466312	−0.233156	−	0.972439i	$-0.574905\pi$
$71$	−3.92922	−0.466312	−0.233156	+	0.972439i	$0.574905\pi$
$72$	−2.15788	−0.254309
$73$	−5.49646	−0.643312	−0.321656	−	0.946857i	$-0.604239\pi$
$73$	−5.49646	−0.643312	−0.321656	+	0.946857i	$0.604239\pi$
$74$	−7.56382	−0.879277
$75$	4.45441	0.514351
$76$	5.96909	0.684701
$77$	−3.63125	−0.413819
$78$	1.87163	0.211920
$79$	−1.67559	−0.188518	−0.0942590	−	0.995548i	$-0.530048\pi$
$79$	−1.67559	−0.188518	−0.0942590	+	0.995548i	$0.530048\pi$
$80$	−0.382051	−0.0427146
$81$	2.13009	0.236677
$82$	5.84531	0.645506
$83$	−16.8711	−1.85185	−0.925923	−	0.377713i	$-0.876710\pi$
$83$	−16.8711	−1.85185	−0.925923	+	0.377713i	$0.876710\pi$
$84$	−1.22647	−0.133819
$85$	−0.248023	−0.0269018
$86$	−7.38086	−0.795898
$87$	−2.60723	−0.279525
$88$	−2.71697	−0.289630
$89$	−7.56775	−0.802180	−0.401090	−	0.916039i	$-0.631369\pi$
$89$	−7.56775	−0.802180	−0.401090	+	0.916039i	$0.631369\pi$
$90$	0.824421	0.0869016
$91$	−2.72586	−0.285748
$92$	−0.117098	−0.0122083
$93$	−3.88133	−0.402475
$94$	−11.4672	−1.18275
$95$	−2.28050	−0.233974
$96$	−0.917670	−0.0936593
$97$	−11.0163	−1.11854	−0.559268	−	0.828987i	$-0.688918\pi$
$97$	−11.0163	−1.11854	−0.559268	+	0.828987i	$0.688918\pi$
$98$	−5.21375	−0.526668
$99$	5.86290	0.589243
$100$	−4.85404	−0.485404
$101$	−4.13873	−0.411819	−0.205909	−	0.978571i	$-0.566015\pi$
$101$	−4.13873	−0.411819	−0.205909	+	0.978571i	$0.566015\pi$
$102$	−0.595739	−0.0589870
$103$	4.35455	0.429067	0.214533	−	0.976717i	$-0.431177\pi$
$103$	4.35455	0.429067	0.214533	+	0.976717i	$0.431177\pi$
$104$	−2.03954	−0.199994
$105$	0.468575	0.0457283
$106$	−10.4574	−1.01571
$107$	−0.432157	−0.0417782	−0.0208891	−	0.999782i	$-0.506650\pi$
$107$	−0.432157	−0.0417782	−0.0208891	+	0.999782i	$0.506650\pi$
$108$	4.73323	0.455456
$109$	−0.872929	−0.0836114	−0.0418057	−	0.999126i	$-0.513311\pi$
$109$	−0.872929	−0.0836114	−0.0418057	+	0.999126i	$0.513311\pi$
$110$	1.03802	0.0989715
$111$	6.94110	0.658820
$112$	1.33651	0.126288
$113$	8.75051	0.823179	0.411589	−	0.911369i	$-0.364974\pi$
$113$	8.75051	0.823179	0.411589	+	0.911369i	$0.364974\pi$
$114$	−5.47766	−0.513029
$115$	0.0447375	0.00417180
$116$	2.84114	0.263793
$117$	4.40109	0.406881
$118$	9.90556	0.911880
$119$	0.867642	0.0795366
$120$	0.350597	0.0320050
$121$	−3.61808	−0.328916
$122$	3.45238	0.312564
$123$	−5.36407	−0.483662
$124$	4.22955	0.379825
$125$	3.76475	0.336729
$126$	−2.88402	−0.256929
$127$	3.23668	0.287209	0.143604	−	0.989635i	$-0.454131\pi$
$127$	3.23668	0.287209	0.143604	+	0.989635i	$0.454131\pi$
$128$	1.00000	0.0883883
$129$	6.77319	0.596347
$130$	0.779210	0.0683412
$131$	22.7115	1.98432	0.992158	−	0.124988i	$-0.0398893\pi$
$131$	22.7115	1.98432	0.992158	+	0.124988i	$0.0398893\pi$
$132$	2.49328	0.217012
$133$	7.97772	0.691756
$134$	−8.39700	−0.725390
$135$	−1.80834	−0.155637
$136$	0.649187	0.0556673
$137$	−17.3328	−1.48084	−0.740422	−	0.672142i	$-0.765374\pi$
$137$	−17.3328	−1.48084	−0.740422	+	0.672142i	$0.765374\pi$
$138$	0.107458	0.00914740
$139$	1.85258	0.157134	0.0785668	−	0.996909i	$-0.474966\pi$
$139$	1.85258	0.157134	0.0785668	+	0.996909i	$0.474966\pi$
$140$	−0.510614	−0.0431548
$141$	10.5231	0.886207
$142$	−3.92922	−0.329733
$143$	5.54137	0.463393
$144$	−2.15788	−0.179823
$145$	−1.08546	−0.0901427
$146$	−5.49646	−0.454890
$147$	4.78450	0.394619
$148$	−7.56382	−0.621742
$149$	−15.2240	−1.24720	−0.623598	−	0.781745i	$-0.714330\pi$
$149$	−15.2240	−1.24720	−0.623598	+	0.781745i	$0.714330\pi$
$150$	4.45441	0.363701
$151$	−5.39614	−0.439132	−0.219566	−	0.975598i	$-0.570464\pi$
$151$	−5.39614	−0.439132	−0.219566	+	0.975598i	$0.570464\pi$
$152$	5.96909	0.484157
$153$	−1.40087	−0.113253
$154$	−3.63125	−0.292614
$155$	−1.61590	−0.129793
$156$	1.87163	0.149850
$157$	−10.6686	−0.851445	−0.425723	−	0.904854i	$-0.639980\pi$
$157$	−10.6686	−0.851445	−0.425723	+	0.904854i	$0.639980\pi$
$158$	−1.67559	−0.133302
$159$	9.59643	0.761046
$160$	−0.382051	−0.0302038
$161$	−0.156503	−0.0123341
$162$	2.13009	0.167356
$163$	−14.8696	−1.16468	−0.582338	−	0.812947i	$-0.697862\pi$
$163$	−14.8696	−1.16468	−0.582338	+	0.812947i	$0.697862\pi$
$164$	5.84531	0.456442
$165$	−0.952562	−0.0741568
$166$	−16.8711	−1.30945
$167$	2.29326	0.177458	0.0887290	−	0.996056i	$-0.471719\pi$
$167$	2.29326	0.177458	0.0887290	+	0.996056i	$0.471719\pi$
$168$	−1.22647	−0.0946244
$169$	−8.84027	−0.680020
$170$	−0.248023	−0.0190225
$171$	−12.8806	−0.985003
$172$	−7.38086	−0.562785
$173$	−6.69038	−0.508660	−0.254330	−	0.967117i	$-0.581855\pi$
$173$	−6.69038	−0.508660	−0.254330	+	0.967117i	$0.581855\pi$
$174$	−2.60723	−0.197654
$175$	−6.48745	−0.490405
$176$	−2.71697	−0.204799
$177$	−9.09004	−0.683249
$178$	−7.56775	−0.567227
$179$	0.235064	0.0175695	0.00878474	−	0.999961i	$-0.497204\pi$
$179$	0.235064	0.0175695	0.00878474	+	0.999961i	$0.497204\pi$
$180$	0.824421	0.0614487
$181$	21.8755	1.62599	0.812996	−	0.582269i	$-0.197835\pi$
$181$	21.8755	1.62599	0.812996	+	0.582269i	$0.197835\pi$
$182$	−2.72586	−0.202054
$183$	−3.16815	−0.234196
$184$	−0.117098	−0.00863259
$185$	2.88977	0.212460
$186$	−3.88133	−0.284593
$187$	−1.76382	−0.128983
$188$	−11.4672	−0.836332
$189$	6.32600	0.460149
$190$	−2.28050	−0.165445
$191$	18.2421	1.31995	0.659977	−	0.751286i	$-0.270566\pi$
$191$	18.2421	1.31995	0.659977	+	0.751286i	$0.270566\pi$
$192$	−0.917670	−0.0662272
$193$	16.1363	1.16152	0.580758	−	0.814076i	$-0.302756\pi$
$193$	16.1363	1.16152	0.580758	+	0.814076i	$0.302756\pi$
$194$	−11.0163	−0.790924
$195$	−0.715058	−0.0512064
$196$	−5.21375	−0.372411
$197$	16.9613	1.20844	0.604220	−	0.796818i	$-0.293485\pi$
$197$	16.9613	1.20844	0.604220	+	0.796818i	$0.293485\pi$
$198$	5.86290	0.416658
$199$	−1.30389	−0.0924301	−0.0462151	−	0.998932i	$-0.514716\pi$
$199$	−1.30389	−0.0924301	−0.0462151	+	0.998932i	$0.514716\pi$
$200$	−4.85404	−0.343232
$201$	7.70568	0.543517
$202$	−4.13873	−0.291200
$203$	3.79720	0.266512
$204$	−0.595739	−0.0417101
$205$	−2.23321	−0.155974
$206$	4.35455	0.303396
$207$	0.252684	0.0175628
$208$	−2.03954	−0.141417
$209$	−16.2178	−1.12181
$210$	0.468575	0.0323348
$211$	−21.0821	−1.45135	−0.725677	−	0.688035i	$-0.758473\pi$
$211$	−21.0821	−1.45135	−0.725677	+	0.688035i	$0.758473\pi$
$212$	−10.4574	−0.718216
$213$	3.60573	0.247060
$214$	−0.432157	−0.0295417
$215$	2.81987	0.192313
$216$	4.73323	0.322056
$217$	5.65282	0.383738
$218$	−0.872929	−0.0591222
$219$	5.04394	0.340838
$220$	1.03802	0.0699834
$221$	−1.32404	−0.0890648
$222$	6.94110	0.465856
$223$	−26.5279	−1.77644	−0.888220	−	0.459418i	$-0.848058\pi$
$223$	−26.5279	−1.77644	−0.888220	+	0.459418i	$0.848058\pi$
$224$	1.33651	0.0892991
$225$	10.4744	0.698296
$226$	8.75051	0.582075
$227$	−7.92416	−0.525945	−0.262972	−	0.964803i	$-0.584703\pi$
$227$	−7.92416	−0.525945	−0.262972	+	0.964803i	$0.584703\pi$
$228$	−5.47766	−0.362767
$229$	8.29498	0.548148	0.274074	−	0.961709i	$-0.411629\pi$
$229$	8.29498	0.548148	0.274074	+	0.961709i	$0.411629\pi$
$230$	0.0447375	0.00294990
$231$	3.33229	0.219248
$232$	2.84114	0.186530
$233$	21.6480	1.41820	0.709102	−	0.705106i	$-0.249100\pi$
$233$	21.6480	1.41820	0.709102	+	0.705106i	$0.249100\pi$
$234$	4.40109	0.287708
$235$	4.38106	0.285789
$236$	9.90556	0.644797
$237$	1.53764	0.0998801
$238$	0.867642	0.0562409
$239$	−1.26741	−0.0819820	−0.0409910	−	0.999160i	$-0.513051\pi$
$239$	−1.26741	−0.0819820	−0.0409910	+	0.999160i	$0.513051\pi$
$240$	0.350597	0.0226310
$241$	1.36282	0.0877867	0.0438934	−	0.999036i	$-0.486024\pi$
$241$	1.36282	0.0877867	0.0438934	+	0.999036i	$0.486024\pi$
$242$	−3.61808	−0.232579
$243$	−16.1544	−1.03631
$244$	3.45238	0.221016
$245$	1.99192	0.127259
$246$	−5.36407	−0.342000
$247$	−12.1742	−0.774626
$248$	4.22955	0.268577
$249$	15.4821	0.981140
$250$	3.76475	0.238104
$251$	21.6989	1.36962	0.684811	−	0.728721i	$-0.259885\pi$
$251$	21.6989	1.36962	0.684811	+	0.728721i	$0.259885\pi$
$252$	−2.88402	−0.181676
$253$	0.318152	0.0200021
$254$	3.23668	0.203087
$255$	0.227603	0.0142531
$256$	1.00000	0.0625000
$257$	−17.9142	−1.11746	−0.558729	−	0.829351i	$-0.688711\pi$
$257$	−17.9142	−1.11746	−0.558729	+	0.829351i	$0.688711\pi$
$258$	6.77319	0.421681
$259$	−10.1091	−0.628149
$260$	0.779210	0.0483246
$261$	−6.13085	−0.379490
$262$	22.7115	1.40312
$263$	3.37235	0.207948	0.103974	−	0.994580i	$-0.466844\pi$
$263$	3.37235	0.207948	0.103974	+	0.994580i	$0.466844\pi$
$264$	2.49328	0.153451
$265$	3.99526	0.245427
$266$	7.97772	0.489146
$267$	6.94470	0.425009
$268$	−8.39700	−0.512928
$269$	−0.619373	−0.0377639	−0.0188819	−	0.999822i	$-0.506011\pi$
$269$	−0.619373	−0.0377639	−0.0188819	+	0.999822i	$0.506011\pi$
$270$	−1.80834	−0.110052
$271$	2.12272	0.128946	0.0644731	−	0.997919i	$-0.479463\pi$
$271$	2.12272	0.128946	0.0644731	+	0.997919i	$0.479463\pi$
$272$	0.649187	0.0393627
$273$	2.50144	0.151394
$274$	−17.3328	−1.04711
$275$	13.1883	0.795282
$276$	0.107458	0.00646819
$277$	−2.99730	−0.180091	−0.0900453	−	0.995938i	$-0.528701\pi$
$277$	−2.99730	−0.180091	−0.0900453	+	0.995938i	$0.528701\pi$
$278$	1.85258	0.111110
$279$	−9.12686	−0.546411
$280$	−0.510614	−0.0305150
$281$	−3.08981	−0.184322	−0.0921612	−	0.995744i	$-0.529378\pi$
$281$	−3.08981	−0.184322	−0.0921612	+	0.995744i	$0.529378\pi$
$282$	10.5231	0.626643
$283$	−15.5101	−0.921979	−0.460990	−	0.887405i	$-0.652505\pi$
$283$	−15.5101	−0.921979	−0.460990	+	0.887405i	$0.652505\pi$
$284$	−3.92922	−0.233156
$285$	2.09275	0.123964
$286$	5.54137	0.327668
$287$	7.81229	0.461145
$288$	−2.15788	−0.127154
$289$	−16.5786	−0.975209
$290$	−1.08546	−0.0637405
$291$	10.1093	0.592619
$292$	−5.49646	−0.321656
$293$	11.4466	0.668715	0.334358	−	0.942446i	$-0.391481\pi$
$293$	11.4466	0.668715	0.334358	+	0.942446i	$0.391481\pi$
$294$	4.78450	0.279038
$295$	−3.78443	−0.220338
$296$	−7.56382	−0.439638
$297$	−12.8601	−0.746216
$298$	−15.2240	−0.881900
$299$	0.238827	0.0138117
$300$	4.45441	0.257175
$301$	−9.86456	−0.568584
$302$	−5.39614	−0.310513
$303$	3.79799	0.218189
$304$	5.96909	0.342351
$305$	−1.31899	−0.0755250
$306$	−1.40087	−0.0800823
$307$	−19.0903	−1.08954	−0.544769	−	0.838586i	$-0.683383\pi$
$307$	−19.0903	−1.08954	−0.544769	+	0.838586i	$0.683383\pi$
$308$	−3.63125	−0.206909
$309$	−3.99604	−0.227327
$310$	−1.61590	−0.0917772
$311$	−13.7990	−0.782469	−0.391234	−	0.920291i	$-0.627952\pi$
$311$	−13.7990	−0.782469	−0.391234	+	0.920291i	$0.627952\pi$
$312$	1.87163	0.105960
$313$	29.6358	1.67511	0.837557	−	0.546351i	$-0.183983\pi$
$313$	29.6358	1.67511	0.837557	+	0.546351i	$0.183983\pi$
$314$	−10.6686	−0.602063
$315$	1.10184	0.0620819
$316$	−1.67559	−0.0942590
$317$	9.47066	0.531925	0.265963	−	0.963983i	$-0.414310\pi$
$317$	9.47066	0.531925	0.265963	+	0.963983i	$0.414310\pi$
$318$	9.59643	0.538141
$319$	−7.71930	−0.432198
$320$	−0.382051	−0.0213573
$321$	0.396578	0.0221348
$322$	−0.156503	−0.00872154
$323$	3.87505	0.215614
$324$	2.13009	0.118339
$325$	9.90002	0.549154
$326$	−14.8696	−0.823550
$327$	0.801061	0.0442988
$328$	5.84531	0.322753
$329$	−15.3260	−0.844950
$330$	−0.952562	−0.0524368
$331$	−16.4528	−0.904328	−0.452164	−	0.891935i	$-0.649348\pi$
$331$	−16.4528	−0.904328	−0.452164	+	0.891935i	$0.649348\pi$
$332$	−16.8711	−0.925923
$333$	16.3218	0.894431
$334$	2.29326	0.125482
$335$	3.20808	0.175276
$336$	−1.22647	−0.0669096
$337$	−5.42559	−0.295551	−0.147775	−	0.989021i	$-0.547211\pi$
$337$	−5.42559	−0.295551	−0.147775	+	0.989021i	$0.547211\pi$
$338$	−8.84027	−0.480847
$339$	−8.03009	−0.436134
$340$	−0.248023	−0.0134509
$341$	−11.4916	−0.622302
$342$	−12.8806	−0.696502
$343$	−16.3238	−0.881400
$344$	−7.38086	−0.397949
$345$	−0.0410543	−0.00221029
$346$	−6.69038	−0.359677
$347$	31.6576	1.69947	0.849734	−	0.527212i	$-0.176763\pi$
$347$	31.6576	1.69947	0.849734	+	0.527212i	$0.176763\pi$
$348$	−2.60723	−0.139762
$349$	6.66547	0.356794	0.178397	−	0.983959i	$-0.442909\pi$
$349$	6.66547	0.356794	0.178397	+	0.983959i	$0.442909\pi$
$350$	−6.48745	−0.346769
$351$	−9.65364	−0.515273
$352$	−2.71697	−0.144815
$353$	−1.83749	−0.0977998	−0.0488999	−	0.998804i	$-0.515572\pi$
$353$	−1.83749	−0.0977998	−0.0488999	+	0.998804i	$0.515572\pi$
$354$	−9.09004	−0.483130
$355$	1.50116	0.0796734
$356$	−7.56775	−0.401090
$357$	−0.796210	−0.0421399
$358$	0.235064	0.0124235
$359$	−29.2625	−1.54441	−0.772207	−	0.635371i	$-0.780847\pi$
$359$	−29.2625	−1.54441	−0.772207	+	0.635371i	$0.780847\pi$
$360$	0.824421	0.0434508
$361$	16.6300	0.875264
$362$	21.8755	1.14975
$363$	3.32020	0.174266
$364$	−2.72586	−0.142874
$365$	2.09993	0.109915
$366$	−3.16815	−0.165602
$367$	7.33069	0.382659	0.191330	−	0.981526i	$-0.438720\pi$
$367$	7.33069	0.382659	0.191330	+	0.981526i	$0.438720\pi$
$368$	−0.117098	−0.00610417
$369$	−12.6135	−0.656632
$370$	2.88977	0.150232
$371$	−13.9764	−0.725616
$372$	−3.88133	−0.201238
$373$	−36.4557	−1.88760	−0.943802	−	0.330512i	$-0.892778\pi$
$373$	−36.4557	−1.88760	−0.943802	+	0.330512i	$0.892778\pi$
$374$	−1.76382	−0.0912050
$375$	−3.45480	−0.178405
$376$	−11.4672	−0.591376
$377$	−5.79463	−0.298439
$378$	6.32600	0.325374
$379$	1.04513	0.0536847	0.0268423	−	0.999640i	$-0.491455\pi$
$379$	1.04513	0.0536847	0.0268423	+	0.999640i	$0.491455\pi$
$380$	−2.28050	−0.116987
$381$	−2.97020	−0.152168
$382$	18.2421	0.933349
$383$	−19.8568	−1.01463	−0.507317	−	0.861760i	$-0.669363\pi$
$383$	−19.8568	−1.01463	−0.507317	+	0.861760i	$0.669363\pi$
$384$	−0.917670	−0.0468297
$385$	1.38732	0.0707045
$386$	16.1363	0.821315
$387$	15.9270	0.809615
$388$	−11.0163	−0.559268
$389$	11.0306	0.559275	0.279638	−	0.960106i	$-0.409786\pi$
$389$	11.0306	0.559275	0.279638	+	0.960106i	$0.409786\pi$
$390$	−0.715058	−0.0362084
$391$	−0.0760186	−0.00384443
$392$	−5.21375	−0.263334
$393$	−20.8417	−1.05133
$394$	16.9613	0.854496
$395$	0.640160	0.0322099
$396$	5.86290	0.294622
$397$	24.5154	1.23039	0.615195	−	0.788375i	$-0.289077\pi$
$397$	24.5154	1.23039	0.615195	+	0.788375i	$0.289077\pi$
$398$	−1.30389	−0.0653580
$399$	−7.32092	−0.366505
$400$	−4.85404	−0.242702
$401$	10.7800	0.538326	0.269163	−	0.963095i	$-0.413253\pi$
$401$	10.7800	0.538326	0.269163	+	0.963095i	$0.413253\pi$
$402$	7.70568	0.384324
$403$	−8.62634	−0.429709
$404$	−4.13873	−0.205909
$405$	−0.813805	−0.0404383
$406$	3.79720	0.188452
$407$	20.5507	1.01866
$408$	−0.595739	−0.0294935
$409$	−3.02755	−0.149703	−0.0748514	−	0.997195i	$-0.523848\pi$
$409$	−3.02755	−0.149703	−0.0748514	+	0.997195i	$0.523848\pi$
$410$	−2.23321	−0.110290
$411$	15.9058	0.784577
$412$	4.35455	0.214533
$413$	13.2388	0.651441
$414$	0.252684	0.0124187
$415$	6.44563	0.316404
$416$	−2.03954	−0.0999968
$417$	−1.70006	−0.0832521
$418$	−16.2178	−0.793240
$419$	−0.993832	−0.0485519	−0.0242759	−	0.999705i	$-0.507728\pi$
$419$	−0.993832	−0.0485519	−0.0242759	+	0.999705i	$0.507728\pi$
$420$	0.468575	0.0228641
$421$	30.9672	1.50925	0.754626	−	0.656156i	$-0.227818\pi$
$421$	30.9672	1.50925	0.754626	+	0.656156i	$0.227818\pi$
$422$	−21.0821	−1.02626
$423$	24.7449	1.20314
$424$	−10.4574	−0.507855
$425$	−3.15118	−0.152855
$426$	3.60573	0.174698
$427$	4.61413	0.223294
$428$	−0.432157	−0.0208891
$429$	−5.08516	−0.245514
$430$	2.81987	0.135986
$431$	3.84809	0.185356	0.0926779	−	0.995696i	$-0.470457\pi$
$431$	3.84809	0.185356	0.0926779	+	0.995696i	$0.470457\pi$
$432$	4.73323	0.227728
$433$	35.1439	1.68891	0.844454	−	0.535629i	$-0.179925\pi$
$433$	35.1439	1.68891	0.844454	+	0.535629i	$0.179925\pi$
$434$	5.65282	0.271344
$435$	0.996096	0.0477592
$436$	−0.872929	−0.0418057
$437$	−0.698969	−0.0334362
$438$	5.04394	0.241009
$439$	−1.37192	−0.0654784	−0.0327392	−	0.999464i	$-0.510423\pi$
$439$	−1.37192	−0.0654784	−0.0327392	+	0.999464i	$0.510423\pi$
$440$	1.03802	0.0494857
$441$	11.2507	0.535745
$442$	−1.32404	−0.0629784
$443$	16.9713	0.806328	0.403164	−	0.915128i	$-0.367910\pi$
$443$	16.9713	0.806328	0.403164	+	0.915128i	$0.367910\pi$
$444$	6.94110	0.329410
$445$	2.89127	0.137059
$446$	−26.5279	−1.25613
$447$	13.9706	0.660786
$448$	1.33651	0.0631440
$449$	4.42525	0.208840	0.104420	−	0.994533i	$-0.466701\pi$
$449$	4.42525	0.208840	0.104420	+	0.994533i	$0.466701\pi$
$450$	10.4744	0.493770
$451$	−15.8815	−0.747832
$452$	8.75051	0.411589
$453$	4.95188	0.232660
$454$	−7.92416	−0.371899
$455$	1.04142	0.0488225
$456$	−5.47766	−0.256515
$457$	20.2956	0.949387	0.474694	−	0.880151i	$-0.342559\pi$
$457$	20.2956	0.949387	0.474694	+	0.880151i	$0.342559\pi$
$458$	8.29498	0.387599
$459$	3.07275	0.143424
$460$	0.0447375	0.00208590
$461$	−28.6596	−1.33481	−0.667404	−	0.744696i	$-0.732595\pi$
$461$	−28.6596	−1.33481	−0.667404	+	0.744696i	$0.732595\pi$
$462$	3.33229	0.155032
$463$	−15.2356	−0.708057	−0.354028	−	0.935235i	$-0.615188\pi$
$463$	−15.2356	−0.708057	−0.354028	+	0.935235i	$0.615188\pi$
$464$	2.84114	0.131897
$465$	1.48287	0.0687663
$466$	21.6480	1.00282
$467$	−32.1018	−1.48549	−0.742747	−	0.669573i	$-0.766477\pi$
$467$	−32.1018	−1.48549	−0.742747	+	0.669573i	$0.766477\pi$
$468$	4.40109	0.203440
$469$	−11.2226	−0.518214
$470$	4.38106	0.202083
$471$	9.79024	0.451111
$472$	9.90556	0.455940
$473$	20.0536	0.922064
$474$	1.53764	0.0706259
$475$	−28.9742	−1.32943
$476$	0.867642	0.0397683
$477$	22.5658	1.03322
$478$	−1.26741	−0.0579700
$479$	−22.7128	−1.03777	−0.518886	−	0.854843i	$-0.673653\pi$
$479$	−22.7128	−1.03777	−0.518886	+	0.854843i	$0.673653\pi$
$480$	0.350597	0.0160025
$481$	15.4267	0.703399
$482$	1.36282	0.0620746
$483$	0.143618	0.00653483
$484$	−3.61808	−0.164458
$485$	4.20879	0.191111
$486$	−16.1544	−0.732780
$487$	−42.3708	−1.92000	−0.960002	−	0.279993i	$-0.909668\pi$
$487$	−42.3708	−1.92000	−0.960002	+	0.279993i	$0.909668\pi$
$488$	3.45238	0.156282
$489$	13.6454	0.617065
$490$	1.99192	0.0899858
$491$	30.2630	1.36575	0.682876	−	0.730535i	$-0.260729\pi$
$491$	30.2630	1.36575	0.682876	+	0.730535i	$0.260729\pi$
$492$	−5.36407	−0.241831
$493$	1.84443	0.0830690
$494$	−12.1742	−0.547744
$495$	−2.23993	−0.100677
$496$	4.22955	0.189912
$497$	−5.25142	−0.235559
$498$	15.4821	0.693770
$499$	−15.7860	−0.706677	−0.353338	−	0.935496i	$-0.614954\pi$
$499$	−15.7860	−0.706677	−0.353338	+	0.935496i	$0.614954\pi$
$500$	3.76475	0.168365
$501$	−2.10446	−0.0940204
$502$	21.6989	0.968469
$503$	1.61455	0.0719891	0.0359946	−	0.999352i	$-0.488540\pi$
$503$	1.61455	0.0719891	0.0359946	+	0.999352i	$0.488540\pi$
$504$	−2.88402	−0.128465
$505$	1.58121	0.0703628
$506$	0.318152	0.0141436
$507$	8.11245	0.360287
$508$	3.23668	0.143604
$509$	20.4453	0.906223	0.453112	−	0.891454i	$-0.350314\pi$
$509$	20.4453	0.906223	0.453112	+	0.891454i	$0.350314\pi$
$510$	0.227603	0.0100784
$511$	−7.34605	−0.324970
$512$	1.00000	0.0441942
$513$	28.2531	1.24740
$514$	−17.9142	−0.790161
$515$	−1.66366	−0.0733097
$516$	6.77319	0.298173
$517$	31.1561	1.37024
$518$	−10.1091	−0.444168
$519$	6.13957	0.269497
$520$	0.779210	0.0341706
$521$	18.2123	0.797895	0.398947	−	0.916974i	$-0.369376\pi$
$521$	18.2123	0.797895	0.398947	+	0.916974i	$0.369376\pi$
$522$	−6.13085	−0.268340
$523$	28.0642	1.22716	0.613581	−	0.789631i	$-0.289728\pi$
$523$	28.0642	1.22716	0.613581	+	0.789631i	$0.289728\pi$
$524$	22.7115	0.992158
$525$	5.95334	0.259825
$526$	3.37235	0.147041
$527$	2.74577	0.119607
$528$	2.49328	0.108506
$529$	−22.9863	−0.999404
$530$	3.99526	0.173543
$531$	−21.3750	−0.927596
$532$	7.97772	0.345878
$533$	−11.9218	−0.516389
$534$	6.94470	0.300527
$535$	0.165106	0.00713817
$536$	−8.39700	−0.362695
$537$	−0.215711	−0.00930861
$538$	−0.619373	−0.0267031
$539$	14.1656	0.610156
$540$	−1.80834	−0.0778185
$541$	−21.3709	−0.918806	−0.459403	−	0.888228i	$-0.651937\pi$
$541$	−21.3709	−0.918806	−0.459403	+	0.888228i	$0.651937\pi$
$542$	2.12272	0.0911788
$543$	−20.0745	−0.861479
$544$	0.649187	0.0278337
$545$	0.333504	0.0142857
$546$	2.50144	0.107052
$547$	39.8362	1.70327	0.851637	−	0.524132i	$-0.175610\pi$
$547$	39.8362	1.70327	0.851637	+	0.524132i	$0.175610\pi$
$548$	−17.3328	−0.740422
$549$	−7.44983	−0.317951
$550$	13.1883	0.562350
$551$	16.9590	0.722479
$552$	0.107458	0.00457370
$553$	−2.23943	−0.0952303
$554$	−2.99730	−0.127343
$555$	−2.65186	−0.112565
$556$	1.85258	0.0785668
$557$	21.8372	0.925274	0.462637	−	0.886548i	$-0.346903\pi$
$557$	21.8372	0.925274	0.462637	+	0.886548i	$0.346903\pi$
$558$	−9.12686	−0.386371
$559$	15.0536	0.636698
$560$	−0.510614	−0.0215774
$561$	1.61861	0.0683376
$562$	−3.08981	−0.130336
$563$	27.7266	1.16854	0.584268	−	0.811561i	$-0.301382\pi$
$563$	27.7266	1.16854	0.584268	+	0.811561i	$0.301382\pi$
$564$	10.5231	0.443103
$565$	−3.34314	−0.140647
$566$	−15.5101	−0.651938
$567$	2.84688	0.119558
$568$	−3.92922	−0.164866
$569$	27.7218	1.16216	0.581079	−	0.813847i	$-0.302631\pi$
$569$	27.7218	1.16216	0.581079	+	0.813847i	$0.302631\pi$
$570$	2.09275	0.0876555
$571$	24.5978	1.02938	0.514692	−	0.857375i	$-0.327906\pi$
$571$	24.5978	1.02938	0.514692	+	0.857375i	$0.327906\pi$
$572$	5.54137	0.231697
$573$	−16.7403	−0.699335
$574$	7.81229	0.326079
$575$	0.568399	0.0237039
$576$	−2.15788	−0.0899117
$577$	−18.1827	−0.756957	−0.378478	−	0.925610i	$-0.623553\pi$
$577$	−18.1827	−0.756957	−0.378478	+	0.925610i	$0.623553\pi$
$578$	−16.5786	−0.689577
$579$	−14.8078	−0.615391
$580$	−1.08546	−0.0450714
$581$	−22.5483	−0.935463
$582$	10.1093	0.419045
$583$	28.4124	1.17672
$584$	−5.49646	−0.227445
$585$	−1.68144	−0.0695191
$586$	11.4466	0.472853
$587$	18.5615	0.766117	0.383058	−	0.923724i	$-0.374871\pi$
$587$	18.5615	0.766117	0.383058	+	0.923724i	$0.374871\pi$
$588$	4.78450	0.197310
$589$	25.2465	1.04027
$590$	−3.78443	−0.155803
$591$	−15.5649	−0.640252
$592$	−7.56382	−0.310871
$593$	10.6260	0.436356	0.218178	−	0.975909i	$-0.429989\pi$
$593$	10.6260	0.436356	0.218178	+	0.975909i	$0.429989\pi$
$594$	−12.8601	−0.527654
$595$	−0.331484	−0.0135895
$596$	−15.2240	−0.623598
$597$	1.19654	0.0489711
$598$	0.238827	0.00976635
$599$	22.7739	0.930517	0.465258	−	0.885175i	$-0.345961\pi$
$599$	22.7739	0.930517	0.465258	+	0.885175i	$0.345961\pi$
$600$	4.45441	0.181850
$601$	−1.84730	−0.0753528	−0.0376764	−	0.999290i	$-0.511996\pi$
$601$	−1.84730	−0.0753528	−0.0376764	+	0.999290i	$0.511996\pi$
$602$	−9.86456	−0.402050
$603$	18.1197	0.737892
$604$	−5.39614	−0.219566
$605$	1.38229	0.0561982
$606$	3.79799	0.154283
$607$	24.2040	0.982411	0.491206	−	0.871044i	$-0.336556\pi$
$607$	24.2040	0.982411	0.491206	+	0.871044i	$0.336556\pi$
$608$	5.96909	0.242078
$609$	−3.48458	−0.141202
$610$	−1.31899	−0.0534042
$611$	23.3879	0.946172
$612$	−1.40087	−0.0566267
$613$	39.0415	1.57687	0.788437	−	0.615116i	$-0.210891\pi$
$613$	39.0415	1.57687	0.788437	+	0.615116i	$0.210891\pi$
$614$	−19.0903	−0.770420
$615$	2.04935	0.0826377
$616$	−3.63125	−0.146307
$617$	18.4249	0.741760	0.370880	−	0.928681i	$-0.379056\pi$
$617$	18.4249	0.741760	0.370880	+	0.928681i	$0.379056\pi$
$618$	−3.99604	−0.160744
$619$	5.83094	0.234365	0.117183	−	0.993110i	$-0.462614\pi$
$619$	5.83094	0.234365	0.117183	+	0.993110i	$0.462614\pi$
$620$	−1.61590	−0.0648963
$621$	−0.554253	−0.0222414
$622$	−13.7990	−0.553289
$623$	−10.1144	−0.405223
$624$	1.87163	0.0749251
$625$	22.8319	0.913274
$626$	29.6358	1.18448
$627$	14.8826	0.594355
$628$	−10.6686	−0.425723
$629$	−4.91033	−0.195788
$630$	1.10184	0.0438985
$631$	4.09993	0.163216	0.0816078	−	0.996665i	$-0.473995\pi$
$631$	4.09993	0.163216	0.0816078	+	0.996665i	$0.473995\pi$
$632$	−1.67559	−0.0666512
$633$	19.3465	0.768953
$634$	9.47066	0.376128
$635$	−1.23658	−0.0490721
$636$	9.59643	0.380523
$637$	10.6337	0.421321
$638$	−7.71930	−0.305610
$639$	8.47878	0.335415
$640$	−0.382051	−0.0151019
$641$	11.0065	0.434731	0.217365	−	0.976090i	$-0.430254\pi$
$641$	11.0065	0.434731	0.217365	+	0.976090i	$0.430254\pi$
$642$	0.396578	0.0156517
$643$	−33.1839	−1.30864	−0.654322	−	0.756216i	$-0.727046\pi$
$643$	−33.1839	−1.30864	−0.654322	+	0.756216i	$0.727046\pi$
$644$	−0.156503	−0.00616706
$645$	−2.58771	−0.101891
$646$	3.87505	0.152462
$647$	17.7837	0.699151	0.349576	−	0.936908i	$-0.386326\pi$
$647$	17.7837	0.699151	0.349576	+	0.936908i	$0.386326\pi$
$648$	2.13009	0.0836780
$649$	−26.9131	−1.05643
$650$	9.90002	0.388311
$651$	−5.18742	−0.203311
$652$	−14.8696	−0.582338
$653$	−3.73828	−0.146290	−0.0731451	−	0.997321i	$-0.523304\pi$
$653$	−3.73828	−0.146290	−0.0731451	+	0.997321i	$0.523304\pi$
$654$	0.801061	0.0313240
$655$	−8.67697	−0.339037
$656$	5.84531	0.228221
$657$	11.8607	0.462730
$658$	−15.3260	−0.597470
$659$	−16.8854	−0.657761	−0.328880	−	0.944372i	$-0.606671\pi$
$659$	−16.8854	−0.657761	−0.328880	+	0.944372i	$0.606671\pi$
$660$	−0.952562	−0.0370784
$661$	−9.00464	−0.350240	−0.175120	−	0.984547i	$-0.556031\pi$
$661$	−9.00464	−0.350240	−0.175120	+	0.984547i	$0.556031\pi$
$662$	−16.4528	−0.639457
$663$	1.21504	0.0471881
$664$	−16.8711	−0.654726
$665$	−3.04790	−0.118192
$666$	16.3218	0.632458
$667$	−0.332693	−0.0128819
$668$	2.29326	0.0887290
$669$	24.3439	0.941189
$670$	3.20808	0.123939
$671$	−9.38002	−0.362112
$672$	−1.22647	−0.0473122
$673$	−48.4467	−1.86748	−0.933741	−	0.357949i	$-0.883476\pi$
$673$	−48.4467	−1.86748	−0.933741	+	0.357949i	$0.883476\pi$
$674$	−5.42559	−0.208986
$675$	−22.9753	−0.884320
$676$	−8.84027	−0.340010
$677$	−42.1648	−1.62052	−0.810262	−	0.586068i	$-0.800675\pi$
$677$	−42.1648	−1.62052	−0.810262	+	0.586068i	$0.800675\pi$
$678$	−8.03009	−0.308394
$679$	−14.7234	−0.565030
$680$	−0.248023	−0.00951123
$681$	7.27176	0.278655
$682$	−11.4916	−0.440034
$683$	−37.6267	−1.43975	−0.719873	−	0.694105i	$-0.755800\pi$
$683$	−37.6267	−1.43975	−0.719873	+	0.694105i	$0.755800\pi$
$684$	−12.8806	−0.492501
$685$	6.62203	0.253015
$686$	−16.3238	−0.623244
$687$	−7.61206	−0.290418
$688$	−7.38086	−0.281393
$689$	21.3283	0.812542
$690$	−0.0410543	−0.00156291
$691$	37.0456	1.40928	0.704640	−	0.709565i	$-0.251109\pi$
$691$	37.0456	1.40928	0.704640	+	0.709565i	$0.251109\pi$
$692$	−6.69038	−0.254330
$693$	7.83580	0.297657
$694$	31.6576	1.20170
$695$	−0.707780	−0.0268476
$696$	−2.60723	−0.0988269
$697$	3.79470	0.143734
$698$	6.66547	0.252292
$699$	−19.8657	−0.751389
$700$	−6.48745	−0.245203
$701$	11.0531	0.417470	0.208735	−	0.977972i	$-0.433065\pi$
$701$	11.0531	0.417470	0.208735	+	0.977972i	$0.433065\pi$
$702$	−9.65364	−0.364353
$703$	−45.1491	−1.70283
$704$	−2.71697	−0.102400
$705$	−4.02037	−0.151416
$706$	−1.83749	−0.0691549
$707$	−5.53144	−0.208031
$708$	−9.09004	−0.341624
$709$	−7.97060	−0.299342	−0.149671	−	0.988736i	$-0.547821\pi$
$709$	−7.97060	−0.299342	−0.149671	+	0.988736i	$0.547821\pi$
$710$	1.50116	0.0563376
$711$	3.61571	0.135600
$712$	−7.56775	−0.283614
$713$	−0.495272	−0.0185481
$714$	−0.796210	−0.0297974
$715$	−2.11709	−0.0791747
$716$	0.235064	0.00878474
$717$	1.16306	0.0434355
$718$	−29.2625	−1.09207
$719$	27.0005	1.00695	0.503474	−	0.864011i	$-0.332055\pi$
$719$	27.0005	1.00695	0.503474	+	0.864011i	$0.332055\pi$
$720$	0.824421	0.0307244
$721$	5.81989	0.216744
$722$	16.6300	0.618905
$723$	−1.25062	−0.0465109
$724$	21.8755	0.812996
$725$	−13.7910	−0.512185
$726$	3.32020	0.123224
$727$	3.02866	0.112327	0.0561635	−	0.998422i	$-0.482113\pi$
$727$	3.02866	0.112327	0.0561635	+	0.998422i	$0.482113\pi$
$728$	−2.72586	−0.101027
$729$	8.43416	0.312376
$730$	2.09993	0.0777219
$731$	−4.79155	−0.177222
$732$	−3.16815	−0.117098
$733$	31.3094	1.15644	0.578219	−	0.815882i	$-0.303748\pi$
$733$	31.3094	1.15644	0.578219	+	0.815882i	$0.303748\pi$
$734$	7.33069	0.270581
$735$	−1.82793	−0.0674241
$736$	−0.117098	−0.00431630
$737$	22.8144	0.840379
$738$	−12.6135	−0.464309
$739$	−36.7777	−1.35289	−0.676444	−	0.736494i	$-0.736480\pi$
$739$	−36.7777	−1.35289	−0.676444	+	0.736494i	$0.736480\pi$
$740$	2.88977	0.106230
$741$	11.1719	0.410410
$742$	−13.9764	−0.513088
$743$	−2.88712	−0.105918	−0.0529591	−	0.998597i	$-0.516865\pi$
$743$	−2.88712	−0.105918	−0.0529591	+	0.998597i	$0.516865\pi$
$744$	−3.88133	−0.142297
$745$	5.81633	0.213094
$746$	−36.4557	−1.33474
$747$	36.4059	1.33202
$748$	−1.76382	−0.0644917
$749$	−0.577581	−0.0211043
$750$	−3.45480	−0.126151
$751$	37.2679	1.35993	0.679963	−	0.733246i	$-0.261996\pi$
$751$	37.2679	1.35993	0.679963	+	0.733246i	$0.261996\pi$
$752$	−11.4672	−0.418166
$753$	−19.9124	−0.725650
$754$	−5.79463	−0.211028
$755$	2.06160	0.0750294
$756$	6.32600	0.230074
$757$	37.3633	1.35799	0.678997	−	0.734141i	$-0.262415\pi$
$757$	37.3633	1.35799	0.678997	+	0.734141i	$0.262415\pi$
$758$	1.04513	0.0379608
$759$	−0.291959	−0.0105974
$760$	−2.28050	−0.0827223
$761$	−13.7125	−0.497078	−0.248539	−	0.968622i	$-0.579950\pi$
$761$	−13.7125	−0.497078	−0.248539	+	0.968622i	$0.579950\pi$
$762$	−2.97020	−0.107599
$763$	−1.16668	−0.0422365
$764$	18.2421	0.659977
$765$	0.535203	0.0193503
$766$	−19.8568	−0.717454
$767$	−20.2028	−0.729481
$768$	−0.917670	−0.0331136
$769$	−8.25670	−0.297744	−0.148872	−	0.988856i	$-0.547564\pi$
$769$	−8.25670	−0.297744	−0.148872	+	0.988856i	$0.547564\pi$
$770$	1.38732	0.0499956
$771$	16.4393	0.592048
$772$	16.1363	0.580758
$773$	−4.81136	−0.173053	−0.0865263	−	0.996250i	$-0.527577\pi$
$773$	−4.81136	−0.173053	−0.0865263	+	0.996250i	$0.527577\pi$
$774$	15.9270	0.572485
$775$	−20.5304	−0.737473
$776$	−11.0163	−0.395462
$777$	9.27682	0.332804
$778$	11.0306	0.395467
$779$	34.8912	1.25011
$780$	−0.715058	−0.0256032
$781$	10.6756	0.382002
$782$	−0.0760186	−0.00271842
$783$	13.4478	0.480585
$784$	−5.21375	−0.186205
$785$	4.07595	0.145477
$786$	−20.8417	−0.743399
$787$	18.1320	0.646336	0.323168	−	0.946342i	$-0.395252\pi$
$787$	18.1320	0.646336	0.323168	+	0.946342i	$0.395252\pi$
$788$	16.9613	0.604220
$789$	−3.09470	−0.110174
$790$	0.640160	0.0227759
$791$	11.6951	0.415830
$792$	5.86290	0.208329
$793$	−7.04128	−0.250043
$794$	24.5154	0.870018
$795$	−3.66633	−0.130031
$796$	−1.30389	−0.0462151
$797$	10.3806	0.367700	0.183850	−	0.982954i	$-0.441144\pi$
$797$	10.3806	0.367700	0.183850	+	0.982954i	$0.441144\pi$
$798$	−7.32092	−0.259158
$799$	−7.44436	−0.263363
$800$	−4.85404	−0.171616
$801$	16.3303	0.577003
$802$	10.7800	0.380654
$803$	14.9337	0.526999
$804$	7.70568	0.271758
$805$	0.0597920	0.00210739
$806$	−8.62634	−0.303850
$807$	0.568381	0.0200079
$808$	−4.13873	−0.145600
$809$	−19.1617	−0.673690	−0.336845	−	0.941560i	$-0.609360\pi$
$809$	−19.1617	−0.673690	−0.336845	+	0.941560i	$0.609360\pi$
$810$	−0.813805	−0.0285942
$811$	−3.34439	−0.117437	−0.0587187	−	0.998275i	$-0.518702\pi$
$811$	−3.34439	−0.117437	−0.0587187	+	0.998275i	$0.518702\pi$
$812$	3.79720	0.133256
$813$	−1.94796	−0.0683180
$814$	20.5507	0.720301
$815$	5.68094	0.198995
$816$	−0.595739	−0.0208551
$817$	−44.0570	−1.54136
$818$	−3.02755	−0.105856
$819$	5.88209	0.205537
$820$	−2.23321	−0.0779870
$821$	26.4673	0.923716	0.461858	−	0.886954i	$-0.347183\pi$
$821$	26.4673	0.923716	0.461858	+	0.886954i	$0.347183\pi$
$822$	15.9058	0.554779
$823$	−19.5400	−0.681123	−0.340561	−	0.940222i	$-0.610617\pi$
$823$	−19.5400	−0.681123	−0.340561	+	0.940222i	$0.610617\pi$
$824$	4.35455	0.151698
$825$	−12.1025	−0.421354
$826$	13.2388	0.460638
$827$	48.1934	1.67585	0.837925	−	0.545786i	$-0.183769\pi$
$827$	48.1934	1.67585	0.837925	+	0.545786i	$0.183769\pi$
$828$	0.252684	0.00878138
$829$	20.3593	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$829$	20.3593	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$830$	6.44563	0.223731
$831$	2.75054	0.0954151
$832$	−2.03954	−0.0707084
$833$	−3.38470	−0.117273
$834$	−1.70006	−0.0588681
$835$	−0.876144	−0.0303202
$836$	−16.2178	−0.560905
$837$	20.0194	0.691973
$838$	−0.993832	−0.0343314
$839$	−26.4790	−0.914157	−0.457078	−	0.889426i	$-0.651104\pi$
$839$	−26.4790	−0.914157	−0.457078	+	0.889426i	$0.651104\pi$
$840$	0.468575	0.0161674
$841$	−20.9279	−0.721652
$842$	30.9672	1.06720
$843$	2.83542	0.0976572
$844$	−21.0821	−0.725677
$845$	3.37743	0.116187
$846$	24.7449	0.850746
$847$	−4.83559	−0.166153
$848$	−10.4574	−0.359108
$849$	14.2332	0.488481
$850$	−3.15118	−0.108084
$851$	0.885710	0.0303618
$852$	3.60573	0.123530
$853$	−21.9378	−0.751135	−0.375568	−	0.926795i	$-0.622552\pi$
$853$	−21.9378	−0.751135	−0.375568	+	0.926795i	$0.622552\pi$
$854$	4.61413	0.157892
$855$	4.92104	0.168296
$856$	−0.432157	−0.0147708
$857$	39.4769	1.34851	0.674253	−	0.738500i	$-0.264466\pi$
$857$	39.4769	1.34851	0.674253	+	0.738500i	$0.264466\pi$
$858$	−5.08516	−0.173604
$859$	−14.3703	−0.490309	−0.245154	−	0.969484i	$-0.578839\pi$
$859$	−14.3703	−0.490309	−0.245154	+	0.969484i	$0.578839\pi$
$860$	2.81987	0.0961566
$861$	−7.16911	−0.244323
$862$	3.84809	0.131066
$863$	12.6421	0.430341	0.215171	−	0.976576i	$-0.430969\pi$
$863$	12.6421	0.430341	0.215171	+	0.976576i	$0.430969\pi$
$864$	4.73323	0.161028
$865$	2.55607	0.0869090
$866$	35.1439	1.19424
$867$	15.2137	0.516683
$868$	5.65282	0.191869
$869$	4.55251	0.154433
$870$	0.996096	0.0337708
$871$	17.1260	0.580294
$872$	−0.872929	−0.0295611
$873$	23.7719	0.804555
$874$	−0.698969	−0.0236430
$875$	5.03161	0.170099
$876$	5.04394	0.170419
$877$	−33.1294	−1.11870	−0.559350	−	0.828931i	$-0.688949\pi$
$877$	−33.1294	−1.11870	−0.559350	+	0.828931i	$0.688949\pi$
$878$	−1.37192	−0.0463002
$879$	−10.5042	−0.354297
$880$	1.03802	0.0349917
$881$	34.5164	1.16289	0.581443	−	0.813587i	$-0.302488\pi$
$881$	34.5164	1.16289	0.581443	+	0.813587i	$0.302488\pi$
$882$	11.2507	0.378829
$883$	8.89271	0.299264	0.149632	−	0.988742i	$-0.452191\pi$
$883$	8.89271	0.299264	0.149632	+	0.988742i	$0.452191\pi$
$884$	−1.32404	−0.0445324
$885$	3.47286	0.116739
$886$	16.9713	0.570160
$887$	−56.4382	−1.89501	−0.947505	−	0.319741i	$-0.896404\pi$
$887$	−56.4382	−1.89501	−0.947505	+	0.319741i	$0.896404\pi$
$888$	6.94110	0.232928
$889$	4.32584	0.145084
$890$	2.89127	0.0969156
$891$	−5.78740	−0.193885
$892$	−26.5279	−0.888220
$893$	−68.4488	−2.29055
$894$	13.9706	0.467246
$895$	−0.0898064	−0.00300190
$896$	1.33651	0.0446495
$897$	−0.219164	−0.00731768
$898$	4.42525	0.147673
$899$	12.0167	0.400781
$900$	10.4744	0.349148
$901$	−6.78879	−0.226167
$902$	−15.8815	−0.528797
$903$	9.05242	0.301246
$904$	8.75051	0.291038
$905$	−8.35756	−0.277815
$906$	4.95188	0.164515
$907$	−5.01820	−0.166626	−0.0833132	−	0.996523i	$-0.526550\pi$
$907$	−5.01820	−0.166626	−0.0833132	+	0.996523i	$0.526550\pi$
$908$	−7.92416	−0.262972
$909$	8.93088	0.296219
$910$	1.04142	0.0345227
$911$	6.77054	0.224318	0.112159	−	0.993690i	$-0.464223\pi$
$911$	6.77054	0.224318	0.112159	+	0.993690i	$0.464223\pi$
$912$	−5.47766	−0.181383
$913$	45.8383	1.51703
$914$	20.2956	0.671318
$915$	1.21040	0.0400145
$916$	8.29498	0.274074
$917$	30.3541	1.00238
$918$	3.07275	0.101416
$919$	14.2271	0.469310	0.234655	−	0.972079i	$-0.424604\pi$
$919$	14.2271	0.469310	0.234655	+	0.972079i	$0.424604\pi$
$920$	0.0447375	0.00147495
$921$	17.5186	0.577256
$922$	−28.6596	−0.943852
$923$	8.01381	0.263778
$924$	3.33229	0.109624
$925$	36.7151	1.20718
$926$	−15.2356	−0.500672
$927$	−9.39660	−0.308625
$928$	2.84114	0.0932651
$929$	−36.5393	−1.19882	−0.599409	−	0.800443i	$-0.704597\pi$
$929$	−36.5393	−1.19882	−0.599409	+	0.800443i	$0.704597\pi$
$930$	1.48287	0.0486251
$931$	−31.1213	−1.01996
$932$	21.6480	0.709102
$933$	12.6629	0.414565
$934$	−32.1018	−1.05040
$935$	0.673870	0.0220379
$936$	4.40109	0.143854
$937$	−39.2742	−1.28303	−0.641517	−	0.767109i	$-0.721694\pi$
$937$	−39.2742	−1.28303	−0.641517	+	0.767109i	$0.721694\pi$
$938$	−11.2226	−0.366432
$939$	−27.1959	−0.887504
$940$	4.38106	0.142895
$941$	−49.1021	−1.60068	−0.800341	−	0.599545i	$-0.795348\pi$
$941$	−49.1021	−1.60068	−0.800341	+	0.599545i	$0.795348\pi$
$942$	9.79024	0.318983
$943$	−0.684475	−0.0222896
$944$	9.90556	0.322398
$945$	−2.41686	−0.0786203
$946$	20.0536	0.651997
$947$	21.4326	0.696465	0.348232	−	0.937408i	$-0.386782\pi$
$947$	21.4326	0.696465	0.348232	+	0.937408i	$0.386782\pi$
$948$	1.53764	0.0499401
$949$	11.2103	0.363901
$950$	−28.9742	−0.940046
$951$	−8.69094	−0.281823
$952$	0.867642	0.0281204
$953$	−2.38006	−0.0770978	−0.0385489	−	0.999257i	$-0.512274\pi$
$953$	−2.38006	−0.0770978	−0.0385489	+	0.999257i	$0.512274\pi$
$954$	22.5658	0.730594
$955$	−6.96943	−0.225525
$956$	−1.26741	−0.0409910
$957$	7.08377	0.228986
$958$	−22.7128	−0.733816
$959$	−23.1654	−0.748051
$960$	0.350597	0.0113155
$961$	−13.1109	−0.422933
$962$	15.4267	0.497378
$963$	0.932544	0.0300508
$964$	1.36282	0.0438934
$965$	−6.16489	−0.198455
$966$	0.143618	0.00462082
$967$	−2.44829	−0.0787317	−0.0393659	−	0.999225i	$-0.512534\pi$
$967$	−2.44829	−0.0787317	−0.0393659	+	0.999225i	$0.512534\pi$
$968$	−3.61808	−0.116289
$969$	−3.55602	−0.114236
$970$	4.20879	0.135136
$971$	−50.9089	−1.63375	−0.816873	−	0.576818i	$-0.804294\pi$
$971$	−50.9089	−1.63375	−0.816873	+	0.576818i	$0.804294\pi$
$972$	−16.1544	−0.518154
$973$	2.47598	0.0793764
$974$	−42.3708	−1.35765
$975$	−9.08495	−0.290951
$976$	3.45238	0.110508
$977$	4.43124	0.141768	0.0708840	−	0.997485i	$-0.477418\pi$
$977$	4.43124	0.141768	0.0708840	+	0.997485i	$0.477418\pi$
$978$	13.6454	0.436331
$979$	20.5614	0.657144
$980$	1.99192	0.0636296
$981$	1.88368	0.0601412
$982$	30.2630	0.965732
$983$	26.8651	0.856863	0.428431	−	0.903574i	$-0.359066\pi$
$983$	26.8651	0.856863	0.428431	+	0.903574i	$0.359066\pi$
$984$	−5.36407	−0.171000
$985$	−6.48007	−0.206472
$986$	1.84443	0.0587387
$987$	14.0642	0.447669
$988$	−12.1742	−0.387313
$989$	0.864285	0.0274827
$990$	−2.23993	−0.0711896
$991$	−0.630346	−0.0200236	−0.0100118	−	0.999950i	$-0.503187\pi$
$991$	−0.630346	−0.0200236	−0.0100118	+	0.999950i	$0.503187\pi$
$992$	4.22955	0.134288
$993$	15.0983	0.479129
$994$	−5.25142	−0.166565
$995$	0.498152	0.0157925
$996$	15.4821	0.490570
$997$	−33.3304	−1.05558	−0.527792	−	0.849374i	$-0.676980\pi$
$997$	−33.3304	−1.05558	−0.527792	+	0.849374i	$0.676980\pi$
$998$	−15.7860	−0.499696
$999$	−35.8014	−1.13270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.14	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.917670 q^{3} +1.00000 q^{4} -0.382051 q^{5} -0.917670 q^{6} +1.33651 q^{7} +1.00000 q^{8} -2.15788 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.917670 q^{3} +1.00000 q^{4} -0.382051 q^{5} -0.917670 q^{6} +1.33651 q^{7} +1.00000 q^{8} -2.15788 q^{9} -0.382051 q^{10} -2.71697 q^{11} -0.917670 q^{12} -2.03954 q^{13} +1.33651 q^{14} +0.350597 q^{15} +1.00000 q^{16} +0.649187 q^{17} -2.15788 q^{18} +5.96909 q^{19} -0.382051 q^{20} -1.22647 q^{21} -2.71697 q^{22} -0.117098 q^{23} -0.917670 q^{24} -4.85404 q^{25} -2.03954 q^{26} +4.73323 q^{27} +1.33651 q^{28} +2.84114 q^{29} +0.350597 q^{30} +4.22955 q^{31} +1.00000 q^{32} +2.49328 q^{33} +0.649187 q^{34} -0.510614 q^{35} -2.15788 q^{36} -7.56382 q^{37} +5.96909 q^{38} +1.87163 q^{39} -0.382051 q^{40} +5.84531 q^{41} -1.22647 q^{42} -7.38086 q^{43} -2.71697 q^{44} +0.824421 q^{45} -0.117098 q^{46} -11.4672 q^{47} -0.917670 q^{48} -5.21375 q^{49} -4.85404 q^{50} -0.595739 q^{51} -2.03954 q^{52} -10.4574 q^{53} +4.73323 q^{54} +1.03802 q^{55} +1.33651 q^{56} -5.47766 q^{57} +2.84114 q^{58} +9.90556 q^{59} +0.350597 q^{60} +3.45238 q^{61} +4.22955 q^{62} -2.88402 q^{63} +1.00000 q^{64} +0.779210 q^{65} +2.49328 q^{66} -8.39700 q^{67} +0.649187 q^{68} +0.107458 q^{69} -0.510614 q^{70} -3.92922 q^{71} -2.15788 q^{72} -5.49646 q^{73} -7.56382 q^{74} +4.45441 q^{75} +5.96909 q^{76} -3.63125 q^{77} +1.87163 q^{78} -1.67559 q^{79} -0.382051 q^{80} +2.13009 q^{81} +5.84531 q^{82} -16.8711 q^{83} -1.22647 q^{84} -0.248023 q^{85} -7.38086 q^{86} -2.60723 q^{87} -2.71697 q^{88} -7.56775 q^{89} +0.824421 q^{90} -2.72586 q^{91} -0.117098 q^{92} -3.88133 q^{93} -11.4672 q^{94} -2.28050 q^{95} -0.917670 q^{96} -11.0163 q^{97} -5.21375 q^{98} +5.86290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 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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