LMFDB - Embedded newform 4022.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.49263 q^{3} +1.00000 q^{4} -2.25527 q^{5} -1.49263 q^{6} +0.477234 q^{7} +1.00000 q^{8} -0.772062 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.49263 q^{3} +1.00000 q^{4} -2.25527 q^{5} -1.49263 q^{6} +0.477234 q^{7} +1.00000 q^{8} -0.772062 q^{9} -2.25527 q^{10} +5.98267 q^{11} -1.49263 q^{12} +5.51460 q^{13} +0.477234 q^{14} +3.36627 q^{15} +1.00000 q^{16} +0.715926 q^{17} -0.772062 q^{18} -3.01283 q^{19} -2.25527 q^{20} -0.712332 q^{21} +5.98267 q^{22} -6.09699 q^{23} -1.49263 q^{24} +0.0862251 q^{25} +5.51460 q^{26} +5.63029 q^{27} +0.477234 q^{28} +3.57315 q^{29} +3.36627 q^{30} -5.42152 q^{31} +1.00000 q^{32} -8.92990 q^{33} +0.715926 q^{34} -1.07629 q^{35} -0.772062 q^{36} -2.97554 q^{37} -3.01283 q^{38} -8.23124 q^{39} -2.25527 q^{40} +0.265599 q^{41} -0.712332 q^{42} +8.31613 q^{43} +5.98267 q^{44} +1.74121 q^{45} -6.09699 q^{46} -0.0569604 q^{47} -1.49263 q^{48} -6.77225 q^{49} +0.0862251 q^{50} -1.06861 q^{51} +5.51460 q^{52} -1.66606 q^{53} +5.63029 q^{54} -13.4925 q^{55} +0.477234 q^{56} +4.49703 q^{57} +3.57315 q^{58} +14.3518 q^{59} +3.36627 q^{60} +0.938016 q^{61} -5.42152 q^{62} -0.368454 q^{63} +1.00000 q^{64} -12.4369 q^{65} -8.92990 q^{66} +6.50493 q^{67} +0.715926 q^{68} +9.10053 q^{69} -1.07629 q^{70} -6.62638 q^{71} -0.772062 q^{72} -1.37788 q^{73} -2.97554 q^{74} -0.128702 q^{75} -3.01283 q^{76} +2.85513 q^{77} -8.23124 q^{78} -3.74265 q^{79} -2.25527 q^{80} -6.08773 q^{81} +0.265599 q^{82} +4.94367 q^{83} -0.712332 q^{84} -1.61460 q^{85} +8.31613 q^{86} -5.33339 q^{87} +5.98267 q^{88} +18.2998 q^{89} +1.74121 q^{90} +2.63175 q^{91} -6.09699 q^{92} +8.09231 q^{93} -0.0569604 q^{94} +6.79473 q^{95} -1.49263 q^{96} +11.3938 q^{97} -6.77225 q^{98} -4.61900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.49263	−0.861769	−0.430885	−	0.902407i	$-0.641798\pi$
$3$	−1.49263	−0.861769	−0.430885	+	0.902407i	$0.641798\pi$
$4$	1.00000	0.500000
$5$	−2.25527	−1.00859	−0.504293	−	0.863533i	$-0.668247\pi$
$5$	−2.25527	−1.00859	−0.504293	+	0.863533i	$0.668247\pi$
$6$	−1.49263	−0.609363
$7$	0.477234	0.180377	0.0901887	−	0.995925i	$-0.471253\pi$
$7$	0.477234	0.180377	0.0901887	+	0.995925i	$0.471253\pi$
$8$	1.00000	0.353553
$9$	−0.772062	−0.257354
$10$	−2.25527	−0.713178
$11$	5.98267	1.80384	0.901922	−	0.431899i	$-0.142156\pi$
$11$	5.98267	1.80384	0.901922	+	0.431899i	$0.142156\pi$
$12$	−1.49263	−0.430885
$13$	5.51460	1.52947	0.764737	−	0.644342i	$-0.222869\pi$
$13$	5.51460	1.52947	0.764737	+	0.644342i	$0.222869\pi$
$14$	0.477234	0.127546
$15$	3.36627	0.869168
$16$	1.00000	0.250000
$17$	0.715926	0.173638	0.0868188	−	0.996224i	$-0.472330\pi$
$17$	0.715926	0.173638	0.0868188	+	0.996224i	$0.472330\pi$
$18$	−0.772062	−0.181977
$19$	−3.01283	−0.691191	−0.345595	−	0.938384i	$-0.612323\pi$
$19$	−3.01283	−0.691191	−0.345595	+	0.938384i	$0.612323\pi$
$20$	−2.25527	−0.504293
$21$	−0.712332	−0.155444
$22$	5.98267	1.27551
$23$	−6.09699	−1.27131	−0.635655	−	0.771973i	$-0.719270\pi$
$23$	−6.09699	−1.27131	−0.635655	+	0.771973i	$0.719270\pi$
$24$	−1.49263	−0.304681
$25$	0.0862251	0.0172450
$26$	5.51460	1.08150
$27$	5.63029	1.08355
$28$	0.477234	0.0901887
$29$	3.57315	0.663518	0.331759	−	0.943364i	$-0.392358\pi$
$29$	3.57315	0.663518	0.331759	+	0.943364i	$0.392358\pi$
$30$	3.36627	0.614594
$31$	−5.42152	−0.973734	−0.486867	−	0.873476i	$-0.661860\pi$
$31$	−5.42152	−0.973734	−0.486867	+	0.873476i	$0.661860\pi$
$32$	1.00000	0.176777
$33$	−8.92990	−1.55450
$34$	0.715926	0.122780
$35$	−1.07629	−0.181926
$36$	−0.772062	−0.128677
$37$	−2.97554	−0.489176	−0.244588	−	0.969627i	$-0.578653\pi$
$37$	−2.97554	−0.489176	−0.244588	+	0.969627i	$0.578653\pi$
$38$	−3.01283	−0.488746
$39$	−8.23124	−1.31805
$40$	−2.25527	−0.356589
$41$	0.265599	0.0414795	0.0207398	−	0.999785i	$-0.493398\pi$
$41$	0.265599	0.0414795	0.0207398	+	0.999785i	$0.493398\pi$
$42$	−0.712332	−0.109915
$43$	8.31613	1.26820	0.634099	−	0.773252i	$-0.281371\pi$
$43$	8.31613	1.26820	0.634099	+	0.773252i	$0.281371\pi$
$44$	5.98267	0.901922
$45$	1.74121	0.259564
$46$	−6.09699	−0.898952
$47$	−0.0569604	−0.00830853	−0.00415427	−	0.999991i	$-0.501322\pi$
$47$	−0.0569604	−0.00830853	−0.00415427	+	0.999991i	$0.501322\pi$
$48$	−1.49263	−0.215442
$49$	−6.77225	−0.967464
$50$	0.0862251	0.0121941
$51$	−1.06861	−0.149636
$52$	5.51460	0.764737
$53$	−1.66606	−0.228850	−0.114425	−	0.993432i	$-0.536503\pi$
$53$	−1.66606	−0.228850	−0.114425	+	0.993432i	$0.536503\pi$
$54$	5.63029	0.766185
$55$	−13.4925	−1.81933
$56$	0.477234	0.0637730
$57$	4.49703	0.595647
$58$	3.57315	0.469178
$59$	14.3518	1.86844	0.934220	−	0.356698i	$-0.116097\pi$
$59$	14.3518	1.86844	0.934220	+	0.356698i	$0.116097\pi$
$60$	3.36627	0.434584
$61$	0.938016	0.120101	0.0600503	−	0.998195i	$-0.480874\pi$
$61$	0.938016	0.120101	0.0600503	+	0.998195i	$0.480874\pi$
$62$	−5.42152	−0.688534
$63$	−0.368454	−0.0464209
$64$	1.00000	0.125000
$65$	−12.4369	−1.54261
$66$	−8.92990	−1.09920
$67$	6.50493	0.794704	0.397352	−	0.917666i	$-0.369929\pi$
$67$	6.50493	0.794704	0.397352	+	0.917666i	$0.369929\pi$
$68$	0.715926	0.0868188
$69$	9.10053	1.09558
$70$	−1.07629	−0.128641
$71$	−6.62638	−0.786406	−0.393203	−	0.919452i	$-0.628633\pi$
$71$	−6.62638	−0.786406	−0.393203	+	0.919452i	$0.628633\pi$
$72$	−0.772062	−0.0909884
$73$	−1.37788	−0.161269	−0.0806343	−	0.996744i	$-0.525695\pi$
$73$	−1.37788	−0.161269	−0.0806343	+	0.996744i	$0.525695\pi$
$74$	−2.97554	−0.345900
$75$	−0.128702	−0.0148612
$76$	−3.01283	−0.345595
$77$	2.85513	0.325373
$78$	−8.23124	−0.932005
$79$	−3.74265	−0.421081	−0.210540	−	0.977585i	$-0.567522\pi$
$79$	−3.74265	−0.421081	−0.210540	+	0.977585i	$0.567522\pi$
$80$	−2.25527	−0.252146
$81$	−6.08773	−0.676415
$82$	0.265599	0.0293305
$83$	4.94367	0.542638	0.271319	−	0.962490i	$-0.412540\pi$
$83$	4.94367	0.542638	0.271319	+	0.962490i	$0.412540\pi$
$84$	−0.712332	−0.0777218
$85$	−1.61460	−0.175128
$86$	8.31613	0.896751
$87$	−5.33339	−0.571799
$88$	5.98267	0.637755
$89$	18.2998	1.93977	0.969886	−	0.243561i	$-0.0783155\pi$
$89$	18.2998	1.93977	0.969886	+	0.243561i	$0.0783155\pi$
$90$	1.74121	0.183539
$91$	2.63175	0.275883
$92$	−6.09699	−0.635655
$93$	8.09231	0.839134
$94$	−0.0569604	−0.00587502
$95$	6.79473	0.697125
$96$	−1.49263	−0.152341
$97$	11.3938	1.15687	0.578433	−	0.815730i	$-0.303665\pi$
$97$	11.3938	1.15687	0.578433	+	0.815730i	$0.303665\pi$
$98$	−6.77225	−0.684100
$99$	−4.61900	−0.464227
$100$	0.0862251	0.00862251
$101$	−2.77169	−0.275793	−0.137897	−	0.990447i	$-0.544034\pi$
$101$	−2.77169	−0.275793	−0.137897	+	0.990447i	$0.544034\pi$
$102$	−1.06861	−0.105808
$103$	−0.420079	−0.0413916	−0.0206958	−	0.999786i	$-0.506588\pi$
$103$	−0.420079	−0.0413916	−0.0206958	+	0.999786i	$0.506588\pi$
$104$	5.51460	0.540751
$105$	1.60650	0.156778
$106$	−1.66606	−0.161822
$107$	−9.17732	−0.887205	−0.443603	−	0.896224i	$-0.646300\pi$
$107$	−9.17732	−0.887205	−0.443603	+	0.896224i	$0.646300\pi$
$108$	5.63029	0.541774
$109$	15.9949	1.53204	0.766018	−	0.642820i	$-0.222236\pi$
$109$	15.9949	1.53204	0.766018	+	0.642820i	$0.222236\pi$
$110$	−13.4925	−1.28646
$111$	4.44138	0.421557
$112$	0.477234	0.0450943
$113$	14.7499	1.38755	0.693776	−	0.720190i	$-0.255946\pi$
$113$	14.7499	1.38755	0.693776	+	0.720190i	$0.255946\pi$
$114$	4.49703	0.421186
$115$	13.7503	1.28222
$116$	3.57315	0.331759
$117$	−4.25762	−0.393617
$118$	14.3518	1.32119
$119$	0.341664	0.0313203
$120$	3.36627	0.307297
$121$	24.7924	2.25385
$122$	0.938016	0.0849240
$123$	−0.396440	−0.0357458
$124$	−5.42152	−0.486867
$125$	11.0819	0.991193
$126$	−0.368454	−0.0328245
$127$	−0.987939	−0.0876654	−0.0438327	−	0.999039i	$-0.513957\pi$
$127$	−0.987939	−0.0876654	−0.0438327	+	0.999039i	$0.513957\pi$
$128$	1.00000	0.0883883
$129$	−12.4129	−1.09289
$130$	−12.4369	−1.09079
$131$	7.66846	0.669996	0.334998	−	0.942219i	$-0.391264\pi$
$131$	7.66846	0.669996	0.334998	+	0.942219i	$0.391264\pi$
$132$	−8.92990	−0.777248
$133$	−1.43782	−0.124675
$134$	6.50493	0.561940
$135$	−12.6978	−1.09285
$136$	0.715926	0.0613902
$137$	−12.2763	−1.04884	−0.524419	−	0.851460i	$-0.675718\pi$
$137$	−12.2763	−1.04884	−0.524419	+	0.851460i	$0.675718\pi$
$138$	9.10053	0.774689
$139$	12.7378	1.08041	0.540203	−	0.841535i	$-0.318348\pi$
$139$	12.7378	1.08041	0.540203	+	0.841535i	$0.318348\pi$
$140$	−1.07629	−0.0909630
$141$	0.0850207	0.00716004
$142$	−6.62638	−0.556073
$143$	32.9920	2.75893
$144$	−0.772062	−0.0643385
$145$	−8.05841	−0.669215
$146$	−1.37788	−0.114034
$147$	10.1084	0.833731
$148$	−2.97554	−0.244588
$149$	−16.3164	−1.33669	−0.668344	−	0.743852i	$-0.732997\pi$
$149$	−16.3164	−1.33669	−0.668344	+	0.743852i	$0.732997\pi$
$150$	−0.128702	−0.0105085
$151$	6.17040	0.502140	0.251070	−	0.967969i	$-0.419218\pi$
$151$	6.17040	0.502140	0.251070	+	0.967969i	$0.419218\pi$
$152$	−3.01283	−0.244373
$153$	−0.552740	−0.0446864
$154$	2.85513	0.230073
$155$	12.2270	0.982094
$156$	−8.23124	−0.659027
$157$	−8.79625	−0.702017	−0.351008	−	0.936372i	$-0.614161\pi$
$157$	−8.79625	−0.702017	−0.351008	+	0.936372i	$0.614161\pi$
$158$	−3.74265	−0.297749
$159$	2.48680	0.197216
$160$	−2.25527	−0.178294
$161$	−2.90969	−0.229315
$162$	−6.08773	−0.478297
$163$	−1.20982	−0.0947606	−0.0473803	−	0.998877i	$-0.515087\pi$
$163$	−1.20982	−0.0947606	−0.0473803	+	0.998877i	$0.515087\pi$
$164$	0.265599	0.0207398
$165$	20.1393	1.56784
$166$	4.94367	0.383703
$167$	−2.56306	−0.198335	−0.0991677	−	0.995071i	$-0.531618\pi$
$167$	−2.56306	−0.198335	−0.0991677	+	0.995071i	$0.531618\pi$
$168$	−0.712332	−0.0549576
$169$	17.4108	1.33929
$170$	−1.61460	−0.123834
$171$	2.32609	0.177881
$172$	8.31613	0.634099
$173$	18.0287	1.37070	0.685349	−	0.728215i	$-0.259650\pi$
$173$	18.0287	1.37070	0.685349	+	0.728215i	$0.259650\pi$
$174$	−5.33339	−0.404323
$175$	0.0411495	0.00311061
$176$	5.98267	0.450961
$177$	−21.4218	−1.61016
$178$	18.2998	1.37163
$179$	10.2059	0.762826	0.381413	−	0.924405i	$-0.375438\pi$
$179$	10.2059	0.762826	0.381413	+	0.924405i	$0.375438\pi$
$180$	1.74121	0.129782
$181$	13.5280	1.00553	0.502764	−	0.864424i	$-0.332316\pi$
$181$	13.5280	1.00553	0.502764	+	0.864424i	$0.332316\pi$
$182$	2.63175	0.195078
$183$	−1.40011	−0.103499
$184$	−6.09699	−0.449476
$185$	6.71064	0.493376
$186$	8.09231	0.593357
$187$	4.28315	0.313215
$188$	−0.0569604	−0.00415427
$189$	2.68696	0.195448
$190$	6.79473	0.492942
$191$	−18.4076	−1.33193	−0.665965	−	0.745983i	$-0.731980\pi$
$191$	−18.4076	−1.33193	−0.665965	+	0.745983i	$0.731980\pi$
$192$	−1.49263	−0.107721
$193$	17.3653	1.24998	0.624992	−	0.780631i	$-0.285102\pi$
$193$	17.3653	1.24998	0.624992	+	0.780631i	$0.285102\pi$
$194$	11.3938	0.818027
$195$	18.5636	1.32937
$196$	−6.77225	−0.483732
$197$	−20.1120	−1.43292	−0.716461	−	0.697628i	$-0.754239\pi$
$197$	−20.1120	−1.43292	−0.716461	+	0.697628i	$0.754239\pi$
$198$	−4.61900	−0.328258
$199$	24.6627	1.74829	0.874145	−	0.485666i	$-0.161423\pi$
$199$	24.6627	1.74829	0.874145	+	0.485666i	$0.161423\pi$
$200$	0.0862251	0.00609703
$201$	−9.70944	−0.684851
$202$	−2.77169	−0.195015
$203$	1.70523	0.119684
$204$	−1.06861	−0.0748178
$205$	−0.598995	−0.0418357
$206$	−0.420079	−0.0292683
$207$	4.70725	0.327177
$208$	5.51460	0.382369
$209$	−18.0248	−1.24680
$210$	1.60650	0.110859
$211$	0.834866	0.0574745	0.0287373	−	0.999587i	$-0.490851\pi$
$211$	0.834866	0.0574745	0.0287373	+	0.999587i	$0.490851\pi$
$212$	−1.66606	−0.114425
$213$	9.89071	0.677700
$214$	−9.17732	−0.627349
$215$	−18.7551	−1.27909
$216$	5.63029	0.383092
$217$	−2.58733	−0.175640
$218$	15.9949	1.08331
$219$	2.05666	0.138976
$220$	−13.4925	−0.909665
$221$	3.94805	0.265574
$222$	4.44138	0.298086
$223$	6.22033	0.416544	0.208272	−	0.978071i	$-0.433216\pi$
$223$	6.22033	0.416544	0.208272	+	0.978071i	$0.433216\pi$
$224$	0.477234	0.0318865
$225$	−0.0665711	−0.00443808
$226$	14.7499	0.981148
$227$	8.80108	0.584148	0.292074	−	0.956396i	$-0.405655\pi$
$227$	8.80108	0.584148	0.292074	+	0.956396i	$0.405655\pi$
$228$	4.49703	0.297823
$229$	19.5464	1.29166	0.645831	−	0.763481i	$-0.276511\pi$
$229$	19.5464	1.29166	0.645831	+	0.763481i	$0.276511\pi$
$230$	13.7503	0.906670
$231$	−4.26165	−0.280396
$232$	3.57315	0.234589
$233$	13.4667	0.882236	0.441118	−	0.897449i	$-0.354582\pi$
$233$	13.4667	0.882236	0.441118	+	0.897449i	$0.354582\pi$
$234$	−4.25762	−0.278329
$235$	0.128461	0.00837987
$236$	14.3518	0.934220
$237$	5.58638	0.362874
$238$	0.341664	0.0221468
$239$	1.29004	0.0834460	0.0417230	−	0.999129i	$-0.486715\pi$
$239$	1.29004	0.0834460	0.0417230	+	0.999129i	$0.486715\pi$
$240$	3.36627	0.217292
$241$	8.70279	0.560596	0.280298	−	0.959913i	$-0.409567\pi$
$241$	8.70279	0.560596	0.280298	+	0.959913i	$0.409567\pi$
$242$	24.7924	1.59371
$243$	−7.80414	−0.500636
$244$	0.938016	0.0600503
$245$	15.2732	0.975770
$246$	−0.396440	−0.0252761
$247$	−16.6145	−1.05716
$248$	−5.42152	−0.344267
$249$	−7.37905	−0.467628
$250$	11.0819	0.700879
$251$	9.05517	0.571557	0.285779	−	0.958296i	$-0.407748\pi$
$251$	9.05517	0.571557	0.285779	+	0.958296i	$0.407748\pi$
$252$	−0.368454	−0.0232104
$253$	−36.4763	−2.29324
$254$	−0.987939	−0.0619888
$255$	2.41000	0.150920
$256$	1.00000	0.0625000
$257$	−9.52349	−0.594059	−0.297030	−	0.954868i	$-0.595996\pi$
$257$	−9.52349	−0.594059	−0.297030	+	0.954868i	$0.595996\pi$
$258$	−12.4129	−0.772792
$259$	−1.42003	−0.0882363
$260$	−12.4369	−0.771303
$261$	−2.75870	−0.170759
$262$	7.66846	0.473759
$263$	−3.71434	−0.229036	−0.114518	−	0.993421i	$-0.536532\pi$
$263$	−3.71434	−0.229036	−0.114518	+	0.993421i	$0.536532\pi$
$264$	−8.92990	−0.549598
$265$	3.75740	0.230815
$266$	−1.43782	−0.0881586
$267$	−27.3147	−1.67163
$268$	6.50493	0.397352
$269$	−8.89703	−0.542461	−0.271231	−	0.962514i	$-0.587431\pi$
$269$	−8.89703	−0.542461	−0.271231	+	0.962514i	$0.587431\pi$
$270$	−12.6978	−0.772763
$271$	−21.3449	−1.29661	−0.648304	−	0.761382i	$-0.724521\pi$
$271$	−21.3449	−1.29661	−0.648304	+	0.761382i	$0.724521\pi$
$272$	0.715926	0.0434094
$273$	−3.92823	−0.237747
$274$	−12.2763	−0.741641
$275$	0.515856	0.0311073
$276$	9.10053	0.547788
$277$	29.2106	1.75510	0.877548	−	0.479489i	$-0.159178\pi$
$277$	29.2106	1.75510	0.877548	+	0.479489i	$0.159178\pi$
$278$	12.7378	0.763962
$279$	4.18575	0.250595
$280$	−1.07629	−0.0643206
$281$	−20.4996	−1.22291	−0.611453	−	0.791281i	$-0.709414\pi$
$281$	−20.4996	−1.22291	−0.611453	+	0.791281i	$0.709414\pi$
$282$	0.0850207	0.00506291
$283$	1.62718	0.0967257	0.0483629	−	0.998830i	$-0.484600\pi$
$283$	1.62718	0.0967257	0.0483629	+	0.998830i	$0.484600\pi$
$284$	−6.62638	−0.393203
$285$	−10.1420	−0.600761
$286$	32.9920	1.95086
$287$	0.126753	0.00748197
$288$	−0.772062	−0.0454942
$289$	−16.4874	−0.969850
$290$	−8.05841	−0.473206
$291$	−17.0067	−0.996950
$292$	−1.37788	−0.0806343
$293$	−15.9123	−0.929604	−0.464802	−	0.885415i	$-0.653874\pi$
$293$	−15.9123	−0.929604	−0.464802	+	0.885415i	$0.653874\pi$
$294$	10.1084	0.589536
$295$	−32.3670	−1.88448
$296$	−2.97554	−0.172950
$297$	33.6842	1.95455
$298$	−16.3164	−0.945182
$299$	−33.6224	−1.94444
$300$	−0.128702	−0.00743061
$301$	3.96873	0.228754
$302$	6.17040	0.355067
$303$	4.13710	0.237670
$304$	−3.01283	−0.172798
$305$	−2.11548	−0.121132
$306$	−0.552740	−0.0315980
$307$	−17.7433	−1.01266	−0.506330	−	0.862340i	$-0.668998\pi$
$307$	−17.7433	−1.01266	−0.506330	+	0.862340i	$0.668998\pi$
$308$	2.85513	0.162686
$309$	0.627021	0.0356700
$310$	12.2270	0.694446
$311$	4.44233	0.251902	0.125951	−	0.992036i	$-0.459802\pi$
$311$	4.44233	0.251902	0.125951	+	0.992036i	$0.459802\pi$
$312$	−8.23124	−0.466002
$313$	−19.6749	−1.11209	−0.556047	−	0.831151i	$-0.687682\pi$
$313$	−19.6749	−1.11209	−0.556047	+	0.831151i	$0.687682\pi$
$314$	−8.79625	−0.496401
$315$	0.830962	0.0468194
$316$	−3.74265	−0.210540
$317$	18.2637	1.02579	0.512897	−	0.858450i	$-0.328572\pi$
$317$	18.2637	1.02579	0.512897	+	0.858450i	$0.328572\pi$
$318$	2.48680	0.139453
$319$	21.3770	1.19688
$320$	−2.25527	−0.126073
$321$	13.6983	0.764566
$322$	−2.90969	−0.162150
$323$	−2.15696	−0.120017
$324$	−6.08773	−0.338207
$325$	0.475497	0.0263758
$326$	−1.20982	−0.0670059
$327$	−23.8745	−1.32026
$328$	0.265599	0.0146652
$329$	−0.0271834	−0.00149867
$330$	20.1393	1.10863
$331$	16.4223	0.902653	0.451327	−	0.892359i	$-0.350951\pi$
$331$	16.4223	0.902653	0.451327	+	0.892359i	$0.350951\pi$
$332$	4.94367	0.271319
$333$	2.29730	0.125891
$334$	−2.56306	−0.140244
$335$	−14.6703	−0.801527
$336$	−0.712332	−0.0388609
$337$	−18.9726	−1.03350	−0.516752	−	0.856135i	$-0.672859\pi$
$337$	−18.9726	−1.03350	−0.516752	+	0.856135i	$0.672859\pi$
$338$	17.4108	0.947023
$339$	−22.0161	−1.19575
$340$	−1.61460	−0.0875642
$341$	−32.4352	−1.75646
$342$	2.32609	0.125781
$343$	−6.57258	−0.354886
$344$	8.31613	0.448375
$345$	−20.5241	−1.10498
$346$	18.0287	0.969230
$347$	−11.1854	−0.600464	−0.300232	−	0.953866i	$-0.597064\pi$
$347$	−11.1854	−0.600464	−0.300232	+	0.953866i	$0.597064\pi$
$348$	−5.33339	−0.285900
$349$	−3.92140	−0.209908	−0.104954	−	0.994477i	$-0.533469\pi$
$349$	−3.92140	−0.209908	−0.104954	+	0.994477i	$0.533469\pi$
$350$	0.0411495	0.00219953
$351$	31.0488	1.65726
$352$	5.98267	0.318878
$353$	−4.80713	−0.255858	−0.127929	−	0.991783i	$-0.540833\pi$
$353$	−4.80713	−0.255858	−0.127929	+	0.991783i	$0.540833\pi$
$354$	−21.4218	−1.13856
$355$	14.9442	0.793158
$356$	18.2998	0.969886
$357$	−0.509977	−0.0269909
$358$	10.2059	0.539400
$359$	−29.0765	−1.53460	−0.767299	−	0.641289i	$-0.778400\pi$
$359$	−29.0765	−1.53460	−0.767299	+	0.641289i	$0.778400\pi$
$360$	1.74121	0.0917696
$361$	−9.92286	−0.522256
$362$	13.5280	0.711016
$363$	−37.0058	−1.94230
$364$	2.63175	0.137941
$365$	3.10749	0.162653
$366$	−1.40011	−0.0731849
$367$	−6.23316	−0.325368	−0.162684	−	0.986678i	$-0.552015\pi$
$367$	−6.23316	−0.325368	−0.162684	+	0.986678i	$0.552015\pi$
$368$	−6.09699	−0.317827
$369$	−0.205059	−0.0106749
$370$	6.71064	0.348869
$371$	−0.795098	−0.0412794
$372$	8.09231	0.419567
$373$	4.17271	0.216055	0.108027	−	0.994148i	$-0.465547\pi$
$373$	4.17271	0.216055	0.108027	+	0.994148i	$0.465547\pi$
$374$	4.28315	0.221477
$375$	−16.5411	−0.854179
$376$	−0.0569604	−0.00293751
$377$	19.7045	1.01483
$378$	2.68696	0.138202
$379$	16.7009	0.857868	0.428934	−	0.903336i	$-0.358889\pi$
$379$	16.7009	0.857868	0.428934	+	0.903336i	$0.358889\pi$
$380$	6.79473	0.348562
$381$	1.47463	0.0755473
$382$	−18.4076	−0.941817
$383$	32.9637	1.68437	0.842184	−	0.539190i	$-0.181269\pi$
$383$	32.9637	1.68437	0.842184	+	0.539190i	$0.181269\pi$
$384$	−1.49263	−0.0761703
$385$	−6.43908	−0.328166
$386$	17.3653	0.883872
$387$	−6.42057	−0.326376
$388$	11.3938	0.578433
$389$	−23.7640	−1.20488	−0.602441	−	0.798163i	$-0.705805\pi$
$389$	−23.7640	−1.20488	−0.602441	+	0.798163i	$0.705805\pi$
$390$	18.5636	0.940007
$391$	−4.36499	−0.220747
$392$	−6.77225	−0.342050
$393$	−11.4462	−0.577382
$394$	−20.1120	−1.01323
$395$	8.44066	0.424696
$396$	−4.61900	−0.232113
$397$	10.5393	0.528952	0.264476	−	0.964392i	$-0.414801\pi$
$397$	10.5393	0.528952	0.264476	+	0.964392i	$0.414801\pi$
$398$	24.6627	1.23623
$399$	2.14614	0.107441
$400$	0.0862251	0.00431125
$401$	10.7856	0.538606	0.269303	−	0.963055i	$-0.413207\pi$
$401$	10.7856	0.538606	0.269303	+	0.963055i	$0.413207\pi$
$402$	−9.70944	−0.484263
$403$	−29.8975	−1.48930
$404$	−2.77169	−0.137897
$405$	13.7295	0.682222
$406$	1.70523	0.0846291
$407$	−17.8017	−0.882397
$408$	−1.06861	−0.0529041
$409$	11.6006	0.573614	0.286807	−	0.957988i	$-0.407406\pi$
$409$	11.6006	0.573614	0.286807	+	0.957988i	$0.407406\pi$
$410$	−0.598995	−0.0295823
$411$	18.3240	0.903857
$412$	−0.420079	−0.0206958
$413$	6.84914	0.337024
$414$	4.70725	0.231349
$415$	−11.1493	−0.547297
$416$	5.51460	0.270375
$417$	−19.0128	−0.931060
$418$	−18.0248	−0.881621
$419$	4.44229	0.217020	0.108510	−	0.994095i	$-0.465392\pi$
$419$	4.44229	0.217020	0.108510	+	0.994095i	$0.465392\pi$
$420$	1.60650	0.0783891
$421$	−15.2788	−0.744643	−0.372321	−	0.928104i	$-0.621438\pi$
$421$	−15.2788	−0.744643	−0.372321	+	0.928104i	$0.621438\pi$
$422$	0.834866	0.0406406
$423$	0.0439770	0.00213824
$424$	−1.66606	−0.0809109
$425$	0.0617308	0.00299438
$426$	9.89071	0.479207
$427$	0.447653	0.0216634
$428$	−9.17732	−0.443603
$429$	−49.2448	−2.37756
$430$	−18.7551	−0.904450
$431$	14.4590	0.696465	0.348233	−	0.937408i	$-0.386782\pi$
$431$	14.4590	0.696465	0.348233	+	0.937408i	$0.386782\pi$
$432$	5.63029	0.270887
$433$	26.8405	1.28987	0.644937	−	0.764236i	$-0.276884\pi$
$433$	26.8405	1.28987	0.644937	+	0.764236i	$0.276884\pi$
$434$	−2.58733	−0.124196
$435$	12.0282	0.576708
$436$	15.9949	0.766018
$437$	18.3692	0.878717
$438$	2.05666	0.0982711
$439$	12.7900	0.610434	0.305217	−	0.952283i	$-0.401271\pi$
$439$	12.7900	0.610434	0.305217	+	0.952283i	$0.401271\pi$
$440$	−13.4925	−0.643231
$441$	5.22860	0.248981
$442$	3.94805	0.187789
$443$	−3.00736	−0.142884	−0.0714420	−	0.997445i	$-0.522760\pi$
$443$	−3.00736	−0.142884	−0.0714420	+	0.997445i	$0.522760\pi$
$444$	4.44138	0.210778
$445$	−41.2708	−1.95643
$446$	6.22033	0.294541
$447$	24.3543	1.15192
$448$	0.477234	0.0225472
$449$	−20.8138	−0.982264	−0.491132	−	0.871085i	$-0.663417\pi$
$449$	−20.8138	−0.982264	−0.491132	+	0.871085i	$0.663417\pi$
$450$	−0.0665711	−0.00313819
$451$	1.58899	0.0748226
$452$	14.7499	0.693776
$453$	−9.21011	−0.432729
$454$	8.80108	0.413055
$455$	−5.93530	−0.278251
$456$	4.49703	0.210593
$457$	0.713604	0.0333810	0.0166905	−	0.999861i	$-0.494687\pi$
$457$	0.713604	0.0333810	0.0166905	+	0.999861i	$0.494687\pi$
$458$	19.5464	0.913343
$459$	4.03087	0.188145
$460$	13.7503	0.641112
$461$	−16.3313	−0.760626	−0.380313	−	0.924858i	$-0.624184\pi$
$461$	−16.3313	−0.760626	−0.380313	+	0.924858i	$0.624184\pi$
$462$	−4.26165	−0.198270
$463$	39.4871	1.83512	0.917560	−	0.397597i	$-0.130156\pi$
$463$	39.4871	1.83512	0.917560	+	0.397597i	$0.130156\pi$
$464$	3.57315	0.165879
$465$	−18.2503	−0.846338
$466$	13.4667	0.623835
$467$	38.7825	1.79464	0.897319	−	0.441382i	$-0.145512\pi$
$467$	38.7825	1.79464	0.897319	+	0.441382i	$0.145512\pi$
$468$	−4.25762	−0.196808
$469$	3.10437	0.143347
$470$	0.128461	0.00592546
$471$	13.1295	0.604976
$472$	14.3518	0.660593
$473$	49.7527	2.28763
$474$	5.58638	0.256591
$475$	−0.259781	−0.0119196
$476$	0.341664	0.0156601
$477$	1.28630	0.0588956
$478$	1.29004	0.0590053
$479$	3.28088	0.149907	0.0749537	−	0.997187i	$-0.476119\pi$
$479$	3.28088	0.149907	0.0749537	+	0.997187i	$0.476119\pi$
$480$	3.36627	0.153649
$481$	−16.4089	−0.748182
$482$	8.70279	0.396401
$483$	4.34308	0.197617
$484$	24.7924	1.12693
$485$	−25.6960	−1.16680
$486$	−7.80414	−0.354003
$487$	38.9301	1.76409	0.882045	−	0.471166i	$-0.156167\pi$
$487$	38.9301	1.76409	0.882045	+	0.471166i	$0.156167\pi$
$488$	0.938016	0.0424620
$489$	1.80582	0.0816618
$490$	15.2732	0.689974
$491$	15.6682	0.707097	0.353549	−	0.935416i	$-0.384975\pi$
$491$	15.6682	0.707097	0.353549	+	0.935416i	$0.384975\pi$
$492$	−0.396440	−0.0178729
$493$	2.55811	0.115212
$494$	−16.6145	−0.747524
$495$	10.4171	0.468212
$496$	−5.42152	−0.243434
$497$	−3.16233	−0.141850
$498$	−7.37905	−0.330663
$499$	−39.5125	−1.76882	−0.884411	−	0.466710i	$-0.845439\pi$
$499$	−39.5125	−1.76882	−0.884411	+	0.466710i	$0.845439\pi$
$500$	11.0819	0.495596
$501$	3.82569	0.170919
$502$	9.05517	0.404152
$503$	−7.05454	−0.314546	−0.157273	−	0.987555i	$-0.550270\pi$
$503$	−7.05454	−0.314546	−0.157273	+	0.987555i	$0.550270\pi$
$504$	−0.368454	−0.0164123
$505$	6.25090	0.278161
$506$	−36.4763	−1.62157
$507$	−25.9878	−1.15416
$508$	−0.987939	−0.0438327
$509$	0.291601	0.0129250	0.00646250	−	0.999979i	$-0.497943\pi$
$509$	0.291601	0.0129250	0.00646250	+	0.999979i	$0.497943\pi$
$510$	2.41000	0.106717
$511$	−0.657571	−0.0290892
$512$	1.00000	0.0441942
$513$	−16.9631	−0.748939
$514$	−9.52349	−0.420063
$515$	0.947389	0.0417469
$516$	−12.4129	−0.546447
$517$	−0.340776	−0.0149873
$518$	−1.42003	−0.0623925
$519$	−26.9102	−1.18123
$520$	−12.4369	−0.545394
$521$	−23.6544	−1.03632	−0.518158	−	0.855285i	$-0.673382\pi$
$521$	−23.6544	−1.03632	−0.518158	+	0.855285i	$0.673382\pi$
$522$	−2.75870	−0.120745
$523$	36.3157	1.58798	0.793988	−	0.607934i	$-0.208001\pi$
$523$	36.3157	1.58798	0.793988	+	0.607934i	$0.208001\pi$
$524$	7.66846	0.334998
$525$	−0.0614209	−0.00268063
$526$	−3.71434	−0.161953
$527$	−3.88141	−0.169077
$528$	−8.92990	−0.388624
$529$	14.1732	0.616228
$530$	3.75740	0.163211
$531$	−11.0805	−0.480851
$532$	−1.43782	−0.0623376
$533$	1.46467	0.0634419
$534$	−27.3147	−1.18202
$535$	20.6973	0.894822
$536$	6.50493	0.280970
$537$	−15.2336	−0.657380
$538$	−8.89703	−0.383578
$539$	−40.5161	−1.74515
$540$	−12.6978	−0.546426
$541$	−10.3122	−0.443358	−0.221679	−	0.975120i	$-0.571154\pi$
$541$	−10.3122	−0.443358	−0.221679	+	0.975120i	$0.571154\pi$
$542$	−21.3449	−0.916840
$543$	−20.1923	−0.866533
$544$	0.715926	0.0306951
$545$	−36.0728	−1.54519
$546$	−3.92823	−0.168113
$547$	−19.8071	−0.846889	−0.423444	−	0.905922i	$-0.639179\pi$
$547$	−19.8071	−0.846889	−0.423444	+	0.905922i	$0.639179\pi$
$548$	−12.2763	−0.524419
$549$	−0.724207	−0.0309084
$550$	0.515856	0.0219962
$551$	−10.7653	−0.458617
$552$	9.10053	0.387344
$553$	−1.78612	−0.0759534
$554$	29.2106	1.24104
$555$	−10.0165	−0.425176
$556$	12.7378	0.540203
$557$	−35.3374	−1.49729	−0.748647	−	0.662969i	$-0.769296\pi$
$557$	−35.3374	−1.49729	−0.748647	+	0.662969i	$0.769296\pi$
$558$	4.18575	0.177197
$559$	45.8601	1.93968
$560$	−1.07629	−0.0454815
$561$	−6.39315	−0.269919
$562$	−20.4996	−0.864724
$563$	5.69183	0.239882	0.119941	−	0.992781i	$-0.461729\pi$
$563$	5.69183	0.239882	0.119941	+	0.992781i	$0.461729\pi$
$564$	0.0850207	0.00358002
$565$	−33.2649	−1.39947
$566$	1.62718	0.0683954
$567$	−2.90527	−0.122010
$568$	−6.62638	−0.278037
$569$	−9.28232	−0.389135	−0.194568	−	0.980889i	$-0.562330\pi$
$569$	−9.28232	−0.389135	−0.194568	+	0.980889i	$0.562330\pi$
$570$	−10.1420	−0.424802
$571$	−5.71485	−0.239159	−0.119579	−	0.992825i	$-0.538155\pi$
$571$	−5.71485	−0.239159	−0.119579	+	0.992825i	$0.538155\pi$
$572$	32.9920	1.37947
$573$	27.4758	1.14782
$574$	0.126753	0.00529055
$575$	−0.525713	−0.0219237
$576$	−0.772062	−0.0321693
$577$	−4.37989	−0.182337	−0.0911686	−	0.995835i	$-0.529060\pi$
$577$	−4.37989	−0.182337	−0.0911686	+	0.995835i	$0.529060\pi$
$578$	−16.4874	−0.685788
$579$	−25.9200	−1.07720
$580$	−8.05841	−0.334607
$581$	2.35928	0.0978796
$582$	−17.0067	−0.704950
$583$	−9.96747	−0.412810
$584$	−1.37788	−0.0570171
$585$	9.60205	0.396996
$586$	−15.9123	−0.657329
$587$	−16.0036	−0.660540	−0.330270	−	0.943886i	$-0.607140\pi$
$587$	−16.0036	−0.660540	−0.330270	+	0.943886i	$0.607140\pi$
$588$	10.1084	0.416865
$589$	16.3341	0.673036
$590$	−32.3670	−1.33253
$591$	30.0197	1.23485
$592$	−2.97554	−0.122294
$593$	−32.0536	−1.31628	−0.658142	−	0.752894i	$-0.728657\pi$
$593$	−32.0536	−1.31628	−0.658142	+	0.752894i	$0.728657\pi$
$594$	33.6842	1.38208
$595$	−0.770543	−0.0315892
$596$	−16.3164	−0.668344
$597$	−36.8122	−1.50662
$598$	−33.6224	−1.37492
$599$	27.3868	1.11899	0.559497	−	0.828832i	$-0.310994\pi$
$599$	27.3868	1.11899	0.559497	+	0.828832i	$0.310994\pi$
$600$	−0.128702	−0.00525423
$601$	37.0897	1.51292	0.756461	−	0.654039i	$-0.226927\pi$
$601$	37.0897	1.51292	0.756461	+	0.654039i	$0.226927\pi$
$602$	3.96873	0.161754
$603$	−5.02221	−0.204520
$604$	6.17040	0.251070
$605$	−55.9134	−2.27320
$606$	4.13710	0.168058
$607$	−5.61656	−0.227969	−0.113984	−	0.993483i	$-0.536361\pi$
$607$	−5.61656	−0.227969	−0.113984	+	0.993483i	$0.536361\pi$
$608$	−3.01283	−0.122186
$609$	−2.54527	−0.103140
$610$	−2.11548	−0.0856531
$611$	−0.314114	−0.0127077
$612$	−0.552740	−0.0223432
$613$	24.0507	0.971399	0.485700	−	0.874126i	$-0.338565\pi$
$613$	24.0507	0.971399	0.485700	+	0.874126i	$0.338565\pi$
$614$	−17.7433	−0.716059
$615$	0.894077	0.0360527
$616$	2.85513	0.115037
$617$	44.1537	1.77756	0.888780	−	0.458334i	$-0.151554\pi$
$617$	44.1537	1.77756	0.888780	+	0.458334i	$0.151554\pi$
$618$	0.627021	0.0252225
$619$	−26.5739	−1.06809	−0.534047	−	0.845455i	$-0.679329\pi$
$619$	−26.5739	−1.06809	−0.534047	+	0.845455i	$0.679329\pi$
$620$	12.2270	0.491047
$621$	−34.3278	−1.37753
$622$	4.44233	0.178121
$623$	8.73326	0.349891
$624$	−8.23124	−0.329513
$625$	−25.4237	−1.01695
$626$	−19.6749	−0.786369
$627$	26.9043	1.07445
$628$	−8.79625	−0.351008
$629$	−2.13027	−0.0849393
$630$	0.830962	0.0331063
$631$	33.9233	1.35047	0.675234	−	0.737604i	$-0.264043\pi$
$631$	33.9233	1.35047	0.675234	+	0.737604i	$0.264043\pi$
$632$	−3.74265	−0.148874
$633$	−1.24614	−0.0495298
$634$	18.2637	0.725346
$635$	2.22807	0.0884181
$636$	2.48680	0.0986081
$637$	−37.3462	−1.47971
$638$	21.3770	0.846324
$639$	5.11598	0.202385
$640$	−2.25527	−0.0891472
$641$	−29.2632	−1.15583	−0.577914	−	0.816098i	$-0.696133\pi$
$641$	−29.2632	−1.15583	−0.577914	+	0.816098i	$0.696133\pi$
$642$	13.6983	0.540630
$643$	−2.74238	−0.108149	−0.0540744	−	0.998537i	$-0.517221\pi$
$643$	−2.74238	−0.108149	−0.0540744	+	0.998537i	$0.517221\pi$
$644$	−2.90969	−0.114658
$645$	27.9943	1.10228
$646$	−2.15696	−0.0848646
$647$	4.20910	0.165477	0.0827384	−	0.996571i	$-0.473633\pi$
$647$	4.20910	0.165477	0.0827384	+	0.996571i	$0.473633\pi$
$648$	−6.08773	−0.239149
$649$	85.8619	3.37037
$650$	0.475497	0.0186505
$651$	3.86192	0.151361
$652$	−1.20982	−0.0473803
$653$	6.05706	0.237031	0.118516	−	0.992952i	$-0.462186\pi$
$653$	6.05706	0.237031	0.118516	+	0.992952i	$0.462186\pi$
$654$	−23.8745	−0.933565
$655$	−17.2944	−0.675749
$656$	0.265599	0.0103699
$657$	1.06381	0.0415032
$658$	−0.0271834	−0.00105972
$659$	39.3171	1.53158	0.765788	−	0.643094i	$-0.222349\pi$
$659$	39.3171	1.53158	0.765788	+	0.643094i	$0.222349\pi$
$660$	20.1393	0.783922
$661$	−1.20938	−0.0470393	−0.0235196	−	0.999723i	$-0.507487\pi$
$661$	−1.20938	−0.0470393	−0.0235196	+	0.999723i	$0.507487\pi$
$662$	16.4223	0.638272
$663$	−5.89296	−0.228864
$664$	4.94367	0.191851
$665$	3.24267	0.125746
$666$	2.29730	0.0890187
$667$	−21.7855	−0.843537
$668$	−2.56306	−0.0991677
$669$	−9.28464	−0.358965
$670$	−14.6703	−0.566765
$671$	5.61184	0.216643
$672$	−0.712332	−0.0274788
$673$	−20.5029	−0.790327	−0.395163	−	0.918611i	$-0.629312\pi$
$673$	−20.5029	−0.790327	−0.395163	+	0.918611i	$0.629312\pi$
$674$	−18.9726	−0.730797
$675$	0.485472	0.0186858
$676$	17.4108	0.669646
$677$	−37.3643	−1.43603	−0.718013	−	0.696030i	$-0.754948\pi$
$677$	−37.3643	−1.43603	−0.718013	+	0.696030i	$0.754948\pi$
$678$	−22.0161	−0.845523
$679$	5.43750	0.208672
$680$	−1.61460	−0.0619172
$681$	−13.1367	−0.503401
$682$	−32.4352	−1.24201
$683$	34.1957	1.30846	0.654232	−	0.756294i	$-0.272992\pi$
$683$	34.1957	1.30846	0.654232	+	0.756294i	$0.272992\pi$
$684$	2.32609	0.0889404
$685$	27.6864	1.05784
$686$	−6.57258	−0.250942
$687$	−29.1755	−1.11311
$688$	8.31613	0.317049
$689$	−9.18763	−0.350021
$690$	−20.5241	−0.781340
$691$	−6.60024	−0.251085	−0.125543	−	0.992088i	$-0.540067\pi$
$691$	−6.60024	−0.251085	−0.125543	+	0.992088i	$0.540067\pi$
$692$	18.0287	0.685349
$693$	−2.20434	−0.0837360
$694$	−11.1854	−0.424592
$695$	−28.7271	−1.08968
$696$	−5.33339	−0.202162
$697$	0.190149	0.00720240
$698$	−3.92140	−0.148427
$699$	−20.1008	−0.760284
$700$	0.0411495	0.00155530
$701$	6.53265	0.246735	0.123367	−	0.992361i	$-0.460631\pi$
$701$	6.53265	0.246735	0.123367	+	0.992361i	$0.460631\pi$
$702$	31.0488	1.17186
$703$	8.96480	0.338114
$704$	5.98267	0.225480
$705$	−0.191744	−0.00722151
$706$	−4.80713	−0.180919
$707$	−1.32274	−0.0497469
$708$	−21.4218	−0.805082
$709$	5.33497	0.200359	0.100180	−	0.994969i	$-0.468058\pi$
$709$	5.33497	0.200359	0.100180	+	0.994969i	$0.468058\pi$
$710$	14.9442	0.560847
$711$	2.88956	0.108367
$712$	18.2998	0.685813
$713$	33.0549	1.23792
$714$	−0.509977	−0.0190854
$715$	−74.4058	−2.78262
$716$	10.2059	0.381413
$717$	−1.92556	−0.0719112
$718$	−29.0765	−1.08513
$719$	2.11226	0.0787740	0.0393870	−	0.999224i	$-0.487459\pi$
$719$	2.11226	0.0787740	0.0393870	+	0.999224i	$0.487459\pi$
$720$	1.74121	0.0648909
$721$	−0.200476	−0.00746610
$722$	−9.92286	−0.369291
$723$	−12.9900	−0.483104
$724$	13.5280	0.502764
$725$	0.308095	0.0114424
$726$	−37.0058	−1.37341
$727$	34.1140	1.26522	0.632609	−	0.774472i	$-0.281984\pi$
$727$	34.1140	1.26522	0.632609	+	0.774472i	$0.281984\pi$
$728$	2.63175	0.0975392
$729$	29.9119	1.10785
$730$	3.10749	0.115013
$731$	5.95373	0.220207
$732$	−1.40011	−0.0517495
$733$	5.17657	0.191201	0.0956004	−	0.995420i	$-0.469523\pi$
$733$	5.17657	0.191201	0.0956004	+	0.995420i	$0.469523\pi$
$734$	−6.23316	−0.230070
$735$	−22.7972	−0.840889
$736$	−6.09699	−0.224738
$737$	38.9169	1.43352
$738$	−0.205059	−0.00754831
$739$	1.12306	0.0413126	0.0206563	−	0.999787i	$-0.493424\pi$
$739$	1.12306	0.0413126	0.0206563	+	0.999787i	$0.493424\pi$
$740$	6.71064	0.246688
$741$	24.7993	0.911026
$742$	−0.795098	−0.0291890
$743$	16.3021	0.598066	0.299033	−	0.954243i	$-0.403336\pi$
$743$	16.3021	0.598066	0.299033	+	0.954243i	$0.403336\pi$
$744$	8.09231	0.296679
$745$	36.7978	1.34817
$746$	4.17271	0.152774
$747$	−3.81682	−0.139650
$748$	4.28315	0.156608
$749$	−4.37973	−0.160032
$750$	−16.5411	−0.603996
$751$	−8.45572	−0.308554	−0.154277	−	0.988028i	$-0.549305\pi$
$751$	−8.45572	−0.308554	−0.154277	+	0.988028i	$0.549305\pi$
$752$	−0.0569604	−0.00207713
$753$	−13.5160	−0.492550
$754$	19.7045	0.717596
$755$	−13.9159	−0.506451
$756$	2.68696	0.0977238
$757$	19.2574	0.699924	0.349962	−	0.936764i	$-0.386195\pi$
$757$	19.2574	0.699924	0.349962	+	0.936764i	$0.386195\pi$
$758$	16.7009	0.606604
$759$	54.4455	1.97625
$760$	6.79473	0.246471
$761$	−37.3061	−1.35235	−0.676173	−	0.736743i	$-0.736363\pi$
$761$	−37.3061	−1.35235	−0.676173	+	0.736743i	$0.736363\pi$
$762$	1.47463	0.0534200
$763$	7.63331	0.276344
$764$	−18.4076	−0.665965
$765$	1.24658	0.0450700
$766$	32.9637	1.19103
$767$	79.1442	2.85773
$768$	−1.49263	−0.0538606
$769$	−39.3795	−1.42006	−0.710031	−	0.704171i	$-0.751319\pi$
$769$	−39.3795	−1.42006	−0.710031	+	0.704171i	$0.751319\pi$
$770$	−6.43908	−0.232048
$771$	14.2150	0.511942
$772$	17.3653	0.624992
$773$	−10.8324	−0.389616	−0.194808	−	0.980841i	$-0.562408\pi$
$773$	−10.8324	−0.389616	−0.194808	+	0.980841i	$0.562408\pi$
$774$	−6.42057	−0.230783
$775$	−0.467471	−0.0167921
$776$	11.3938	0.409014
$777$	2.11957	0.0760393
$778$	−23.7640	−0.851981
$779$	−0.800203	−0.0286703
$780$	18.5636	0.664685
$781$	−39.6434	−1.41855
$782$	−4.36499	−0.156092
$783$	20.1179	0.718954
$784$	−6.77225	−0.241866
$785$	19.8379	0.708044
$786$	−11.4462	−0.408271
$787$	39.8079	1.41900	0.709499	−	0.704707i	$-0.248921\pi$
$787$	39.8079	1.41900	0.709499	+	0.704707i	$0.248921\pi$
$788$	−20.1120	−0.716461
$789$	5.54413	0.197376
$790$	8.44066	0.300305
$791$	7.03914	0.250283
$792$	−4.61900	−0.164129
$793$	5.17278	0.183691
$794$	10.5393	0.374025
$795$	−5.60840	−0.198909
$796$	24.6627	0.874145
$797$	−27.7297	−0.982235	−0.491117	−	0.871093i	$-0.663411\pi$
$797$	−27.7297	−0.982235	−0.491117	+	0.871093i	$0.663411\pi$
$798$	2.14614	0.0759724
$799$	−0.0407795	−0.00144267
$800$	0.0862251	0.00304852
$801$	−14.1286	−0.499208
$802$	10.7856	0.380852
$803$	−8.24341	−0.290903
$804$	−9.70944	−0.342425
$805$	6.56212	0.231284
$806$	−29.8975	−1.05310
$807$	13.2799	0.467476
$808$	−2.77169	−0.0975077
$809$	−45.7413	−1.60818	−0.804090	−	0.594508i	$-0.797347\pi$
$809$	−45.7413	−1.60818	−0.804090	+	0.594508i	$0.797347\pi$
$810$	13.7295	0.482404
$811$	8.28025	0.290759	0.145379	−	0.989376i	$-0.453560\pi$
$811$	8.28025	0.290759	0.145379	+	0.989376i	$0.453560\pi$
$812$	1.70523	0.0598418
$813$	31.8599	1.11738
$814$	−17.8017	−0.623949
$815$	2.72847	0.0955742
$816$	−1.06861	−0.0374089
$817$	−25.0551	−0.876566
$818$	11.6006	0.405606
$819$	−2.03188	−0.0709995
$820$	−0.598995	−0.0209178
$821$	−54.4226	−1.89936	−0.949680	−	0.313220i	$-0.898592\pi$
$821$	−54.4226	−1.89936	−0.949680	+	0.313220i	$0.898592\pi$
$822$	18.3240	0.639123
$823$	−16.9949	−0.592406	−0.296203	−	0.955125i	$-0.595721\pi$
$823$	−16.9949	−0.592406	−0.296203	+	0.955125i	$0.595721\pi$
$824$	−0.420079	−0.0146341
$825$	−0.769981	−0.0268073
$826$	6.84914	0.238312
$827$	0.229881	0.00799374	0.00399687	−	0.999992i	$-0.498728\pi$
$827$	0.229881	0.00799374	0.00399687	+	0.999992i	$0.498728\pi$
$828$	4.70725	0.163588
$829$	−9.88521	−0.343327	−0.171664	−	0.985156i	$-0.554914\pi$
$829$	−9.88521	−0.343327	−0.171664	+	0.985156i	$0.554914\pi$
$830$	−11.1493	−0.386997
$831$	−43.6006	−1.51249
$832$	5.51460	0.191184
$833$	−4.84843	−0.167988
$834$	−19.0128	−0.658359
$835$	5.78038	0.200038
$836$	−18.0248	−0.623400
$837$	−30.5247	−1.05509
$838$	4.44229	0.153457
$839$	−35.9571	−1.24138	−0.620689	−	0.784057i	$-0.713147\pi$
$839$	−35.9571	−1.24138	−0.620689	+	0.784057i	$0.713147\pi$
$840$	1.60650	0.0554295
$841$	−16.2326	−0.559744
$842$	−15.2788	−0.526542
$843$	30.5983	1.05386
$844$	0.834866	0.0287373
$845$	−39.2660	−1.35079
$846$	0.0439770	0.00151196
$847$	11.8318	0.406544
$848$	−1.66606	−0.0572126
$849$	−2.42877	−0.0833552
$850$	0.0617308	0.00211735
$851$	18.1418	0.621894
$852$	9.89071	0.338850
$853$	−26.6965	−0.914072	−0.457036	−	0.889448i	$-0.651089\pi$
$853$	−26.6965	−0.914072	−0.457036	+	0.889448i	$0.651089\pi$
$854$	0.447653	0.0153184
$855$	−5.24596	−0.179408
$856$	−9.17732	−0.313674
$857$	−20.7021	−0.707170	−0.353585	−	0.935402i	$-0.615038\pi$
$857$	−20.7021	−0.707170	−0.353585	+	0.935402i	$0.615038\pi$
$858$	−49.2448	−1.68119
$859$	48.9607	1.67052	0.835258	−	0.549858i	$-0.185318\pi$
$859$	48.9607	1.67052	0.835258	+	0.549858i	$0.185318\pi$
$860$	−18.7551	−0.639543
$861$	−0.189194	−0.00644773
$862$	14.4590	0.492475
$863$	−37.6150	−1.28043	−0.640214	−	0.768197i	$-0.721154\pi$
$863$	−37.6150	−1.28043	−0.640214	+	0.768197i	$0.721154\pi$
$864$	5.63029	0.191546
$865$	−40.6596	−1.38247
$866$	26.8405	0.912078
$867$	24.6096	0.835787
$868$	−2.58733	−0.0878198
$869$	−22.3910	−0.759563
$870$	12.0282	0.407794
$871$	35.8721	1.21548
$872$	15.9949	0.541656
$873$	−8.79672	−0.297724
$874$	18.3692	0.621347
$875$	5.28864	0.178789
$876$	2.05666	0.0694882
$877$	−42.9451	−1.45015	−0.725076	−	0.688669i	$-0.758195\pi$
$877$	−42.9451	−1.45015	−0.725076	+	0.688669i	$0.758195\pi$
$878$	12.7900	0.431642
$879$	23.7511	0.801104
$880$	−13.4925	−0.454833
$881$	−55.1992	−1.85971	−0.929854	−	0.367930i	$-0.880067\pi$
$881$	−55.1992	−1.85971	−0.929854	+	0.367930i	$0.880067\pi$
$882$	5.22860	0.176056
$883$	−6.90921	−0.232514	−0.116257	−	0.993219i	$-0.537090\pi$
$883$	−6.90921	−0.232514	−0.116257	+	0.993219i	$0.537090\pi$
$884$	3.94805	0.132787
$885$	48.3119	1.62399
$886$	−3.00736	−0.101034
$887$	35.7490	1.20033	0.600167	−	0.799875i	$-0.295101\pi$
$887$	35.7490	1.20033	0.600167	+	0.799875i	$0.295101\pi$
$888$	4.44138	0.149043
$889$	−0.471478	−0.0158129
$890$	−41.2708	−1.38340
$891$	−36.4209	−1.22015
$892$	6.22033	0.208272
$893$	0.171612	0.00574278
$894$	24.3543	0.814528
$895$	−23.0171	−0.769376
$896$	0.477234	0.0159433
$897$	50.1858	1.67565
$898$	−20.8138	−0.694565
$899$	−19.3719	−0.646090
$900$	−0.0665711	−0.00221904
$901$	−1.19277	−0.0397370
$902$	1.58899	0.0529076
$903$	−5.92384	−0.197133
$904$	14.7499	0.490574
$905$	−30.5092	−1.01416
$906$	−9.21011	−0.305985
$907$	−37.1925	−1.23496	−0.617478	−	0.786588i	$-0.711845\pi$
$907$	−37.1925	−1.23496	−0.617478	+	0.786588i	$0.711845\pi$
$908$	8.80108	0.292074
$909$	2.13992	0.0709766
$910$	−5.93530	−0.196753
$911$	7.52800	0.249414	0.124707	−	0.992194i	$-0.460201\pi$
$911$	7.52800	0.249414	0.124707	+	0.992194i	$0.460201\pi$
$912$	4.49703	0.148912
$913$	29.5763	0.978834
$914$	0.713604	0.0236039
$915$	3.15762	0.104388
$916$	19.5464	0.645831
$917$	3.65965	0.120852
$918$	4.03087	0.133038
$919$	−7.37799	−0.243377	−0.121689	−	0.992568i	$-0.538831\pi$
$919$	−7.37799	−0.243377	−0.121689	+	0.992568i	$0.538831\pi$
$920$	13.7503	0.453335
$921$	26.4841	0.872680
$922$	−16.3313	−0.537844
$923$	−36.5418	−1.20279
$924$	−4.26165	−0.140198
$925$	−0.256566	−0.00843584
$926$	39.4871	1.29763
$927$	0.324327	0.0106523
$928$	3.57315	0.117295
$929$	−24.4255	−0.801376	−0.400688	−	0.916215i	$-0.631229\pi$
$929$	−24.4255	−0.801376	−0.400688	+	0.916215i	$0.631229\pi$
$930$	−18.2503	−0.598452
$931$	20.4036	0.668702
$932$	13.4667	0.441118
$933$	−6.63075	−0.217081
$934$	38.7825	1.26900
$935$	−9.65965	−0.315904
$936$	−4.25762	−0.139165
$937$	−1.73992	−0.0568406	−0.0284203	−	0.999596i	$-0.509048\pi$
$937$	−1.73992	−0.0568406	−0.0284203	+	0.999596i	$0.509048\pi$
$938$	3.10437	0.101361
$939$	29.3674	0.958367
$940$	0.128461	0.00418993
$941$	−10.4540	−0.340791	−0.170396	−	0.985376i	$-0.554505\pi$
$941$	−10.4540	−0.340791	−0.170396	+	0.985376i	$0.554505\pi$
$942$	13.1295	0.427783
$943$	−1.61935	−0.0527333
$944$	14.3518	0.467110
$945$	−6.05981	−0.197126
$946$	49.7527	1.61760
$947$	−10.9300	−0.355177	−0.177588	−	0.984105i	$-0.556830\pi$
$947$	−10.9300	−0.355177	−0.177588	+	0.984105i	$0.556830\pi$
$948$	5.58638	0.181437
$949$	−7.59846	−0.246656
$950$	−0.259781	−0.00842842
$951$	−27.2610	−0.883998
$952$	0.341664	0.0110734
$953$	18.0937	0.586111	0.293056	−	0.956095i	$-0.405328\pi$
$953$	18.0937	0.586111	0.293056	+	0.956095i	$0.405328\pi$
$954$	1.28630	0.0416455
$955$	41.5141	1.34337
$956$	1.29004	0.0417230
$957$	−31.9079	−1.03144
$958$	3.28088	0.106001
$959$	−5.85868	−0.189187
$960$	3.36627	0.108646
$961$	−1.60710	−0.0518418
$962$	−16.4089	−0.529045
$963$	7.08547	0.228326
$964$	8.70279	0.280298
$965$	−39.1634	−1.26072
$966$	4.34308	0.139736
$967$	11.5196	0.370447	0.185223	−	0.982696i	$-0.440699\pi$
$967$	11.5196	0.370447	0.185223	+	0.982696i	$0.440699\pi$
$968$	24.7924	0.796857
$969$	3.21954	0.103427
$970$	−25.6960	−0.825050
$971$	−15.8268	−0.507907	−0.253953	−	0.967216i	$-0.581731\pi$
$971$	−15.8268	−0.507907	−0.253953	+	0.967216i	$0.581731\pi$
$972$	−7.80414	−0.250318
$973$	6.07890	0.194881
$974$	38.9301	1.24740
$975$	−0.709739	−0.0227299
$976$	0.938016	0.0300252
$977$	−29.0850	−0.930512	−0.465256	−	0.885176i	$-0.654038\pi$
$977$	−29.0850	−0.930512	−0.465256	+	0.885176i	$0.654038\pi$
$978$	1.80582	0.0577436
$979$	109.482	3.49904
$980$	15.2732	0.487885
$981$	−12.3491	−0.394276
$982$	15.6682	0.499993
$983$	41.6962	1.32990	0.664950	−	0.746887i	$-0.268453\pi$
$983$	41.6962	1.32990	0.664950	+	0.746887i	$0.268453\pi$
$984$	−0.396440	−0.0126380
$985$	45.3579	1.44522
$986$	2.55811	0.0814669
$987$	0.0405747	0.00129151
$988$	−16.6145	−0.528579
$989$	−50.7033	−1.61227
$990$	10.4171	0.331076
$991$	20.3310	0.645835	0.322918	−	0.946427i	$-0.395336\pi$
$991$	20.3310	0.645835	0.322918	+	0.946427i	$0.395336\pi$
$992$	−5.42152	−0.172134
$993$	−24.5124	−0.777879
$994$	−3.16233	−0.100303
$995$	−55.6208	−1.76330
$996$	−7.37905	−0.233814
$997$	−40.0377	−1.26801	−0.634004	−	0.773330i	$-0.718590\pi$
$997$	−40.0377	−1.26801	−0.634004	+	0.773330i	$0.718590\pi$
$998$	−39.5125	−1.25075
$999$	−16.7531	−0.530046

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.13	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.13	✓	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.49263 q^{3} +1.00000 q^{4} -2.25527 q^{5} -1.49263 q^{6} +0.477234 q^{7} +1.00000 q^{8} -0.772062 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.49263 q^{3} +1.00000 q^{4} -2.25527 q^{5} -1.49263 q^{6} +0.477234 q^{7} +1.00000 q^{8} -0.772062 q^{9} -2.25527 q^{10} +5.98267 q^{11} -1.49263 q^{12} +5.51460 q^{13} +0.477234 q^{14} +3.36627 q^{15} +1.00000 q^{16} +0.715926 q^{17} -0.772062 q^{18} -3.01283 q^{19} -2.25527 q^{20} -0.712332 q^{21} +5.98267 q^{22} -6.09699 q^{23} -1.49263 q^{24} +0.0862251 q^{25} +5.51460 q^{26} +5.63029 q^{27} +0.477234 q^{28} +3.57315 q^{29} +3.36627 q^{30} -5.42152 q^{31} +1.00000 q^{32} -8.92990 q^{33} +0.715926 q^{34} -1.07629 q^{35} -0.772062 q^{36} -2.97554 q^{37} -3.01283 q^{38} -8.23124 q^{39} -2.25527 q^{40} +0.265599 q^{41} -0.712332 q^{42} +8.31613 q^{43} +5.98267 q^{44} +1.74121 q^{45} -6.09699 q^{46} -0.0569604 q^{47} -1.49263 q^{48} -6.77225 q^{49} +0.0862251 q^{50} -1.06861 q^{51} +5.51460 q^{52} -1.66606 q^{53} +5.63029 q^{54} -13.4925 q^{55} +0.477234 q^{56} +4.49703 q^{57} +3.57315 q^{58} +14.3518 q^{59} +3.36627 q^{60} +0.938016 q^{61} -5.42152 q^{62} -0.368454 q^{63} +1.00000 q^{64} -12.4369 q^{65} -8.92990 q^{66} +6.50493 q^{67} +0.715926 q^{68} +9.10053 q^{69} -1.07629 q^{70} -6.62638 q^{71} -0.772062 q^{72} -1.37788 q^{73} -2.97554 q^{74} -0.128702 q^{75} -3.01283 q^{76} +2.85513 q^{77} -8.23124 q^{78} -3.74265 q^{79} -2.25527 q^{80} -6.08773 q^{81} +0.265599 q^{82} +4.94367 q^{83} -0.712332 q^{84} -1.61460 q^{85} +8.31613 q^{86} -5.33339 q^{87} +5.98267 q^{88} +18.2998 q^{89} +1.74121 q^{90} +2.63175 q^{91} -6.09699 q^{92} +8.09231 q^{93} -0.0569604 q^{94} +6.79473 q^{95} -1.49263 q^{96} +11.3938 q^{97} -6.77225 q^{98} -4.61900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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