LMFDB - Embedded newform 4030.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 12x^{5} + 10x^{4} + 26x^{3} - 6x^{2} - 17x - 4 $ x^7 - x^6 - 12x^5 + 10x^4 + 26x^3 - 6x^2 - 17*x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.803589$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.803589 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803589 q^{6} -2.71080 q^{7} -1.00000 q^{8} -2.35424 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.803589 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803589 q^{6} -2.71080 q^{7} -1.00000 q^{8} -2.35424 q^{9} -1.00000 q^{10} +3.99859 q^{11} +0.803589 q^{12} -1.00000 q^{13} +2.71080 q^{14} +0.803589 q^{15} +1.00000 q^{16} +5.09232 q^{17} +2.35424 q^{18} -5.23334 q^{19} +1.00000 q^{20} -2.17837 q^{21} -3.99859 q^{22} +0.963600 q^{23} -0.803589 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.30261 q^{27} -2.71080 q^{28} -3.19320 q^{29} -0.803589 q^{30} +1.00000 q^{31} -1.00000 q^{32} +3.21322 q^{33} -5.09232 q^{34} -2.71080 q^{35} -2.35424 q^{36} -8.00961 q^{37} +5.23334 q^{38} -0.803589 q^{39} -1.00000 q^{40} +0.805382 q^{41} +2.17837 q^{42} -7.99139 q^{43} +3.99859 q^{44} -2.35424 q^{45} -0.963600 q^{46} +2.27051 q^{47} +0.803589 q^{48} +0.348462 q^{49} -1.00000 q^{50} +4.09214 q^{51} -1.00000 q^{52} +10.6981 q^{53} +4.30261 q^{54} +3.99859 q^{55} +2.71080 q^{56} -4.20546 q^{57} +3.19320 q^{58} +10.5592 q^{59} +0.803589 q^{60} -6.54745 q^{61} -1.00000 q^{62} +6.38190 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.21322 q^{66} +0.107922 q^{67} +5.09232 q^{68} +0.774338 q^{69} +2.71080 q^{70} -7.64298 q^{71} +2.35424 q^{72} -8.81462 q^{73} +8.00961 q^{74} +0.803589 q^{75} -5.23334 q^{76} -10.8394 q^{77} +0.803589 q^{78} +0.933724 q^{79} +1.00000 q^{80} +3.60520 q^{81} -0.805382 q^{82} -3.88051 q^{83} -2.17837 q^{84} +5.09232 q^{85} +7.99139 q^{86} -2.56603 q^{87} -3.99859 q^{88} +0.741117 q^{89} +2.35424 q^{90} +2.71080 q^{91} +0.963600 q^{92} +0.803589 q^{93} -2.27051 q^{94} -5.23334 q^{95} -0.803589 q^{96} -14.4685 q^{97} -0.348462 q^{98} -9.41365 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * 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
$3$	0.803589	0.463952	0.231976	−	0.972721i	$-0.425481\pi$
$3$	0.803589	0.463952	0.231976	+	0.972721i	$0.425481\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.803589	−0.328064
$7$	−2.71080	−1.02459	−0.512294	−	0.858810i	$-0.671204\pi$
$7$	−2.71080	−1.02459	−0.512294	+	0.858810i	$0.671204\pi$
$8$	−1.00000	−0.353553
$9$	−2.35424	−0.784748
$10$	−1.00000	−0.316228
$11$	3.99859	1.20562	0.602810	−	0.797885i	$-0.294048\pi$
$11$	3.99859	1.20562	0.602810	+	0.797885i	$0.294048\pi$
$12$	0.803589	0.231976
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.71080	0.724493
$15$	0.803589	0.207486
$16$	1.00000	0.250000
$17$	5.09232	1.23507	0.617535	−	0.786544i	$-0.288132\pi$
$17$	5.09232	1.23507	0.617535	+	0.786544i	$0.288132\pi$
$18$	2.35424	0.554901
$19$	−5.23334	−1.20061	−0.600306	−	0.799771i	$-0.704954\pi$
$19$	−5.23334	−1.20061	−0.600306	+	0.799771i	$0.704954\pi$
$20$	1.00000	0.223607
$21$	−2.17837	−0.475360
$22$	−3.99859	−0.852502
$23$	0.963600	0.200924	0.100462	−	0.994941i	$-0.467968\pi$
$23$	0.963600	0.200924	0.100462	+	0.994941i	$0.467968\pi$
$24$	−0.803589	−0.164032
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−4.30261	−0.828038
$28$	−2.71080	−0.512294
$29$	−3.19320	−0.592963	−0.296482	−	0.955039i	$-0.595813\pi$
$29$	−3.19320	−0.592963	−0.296482	+	0.955039i	$0.595813\pi$
$30$	−0.803589	−0.146715
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	3.21322	0.559350
$34$	−5.09232	−0.873326
$35$	−2.71080	−0.458210
$36$	−2.35424	−0.392374
$37$	−8.00961	−1.31677	−0.658386	−	0.752680i	$-0.728761\pi$
$37$	−8.00961	−1.31677	−0.658386	+	0.752680i	$0.728761\pi$
$38$	5.23334	0.848961
$39$	−0.803589	−0.128677
$40$	−1.00000	−0.158114
$41$	0.805382	0.125780	0.0628898	−	0.998020i	$-0.479968\pi$
$41$	0.805382	0.125780	0.0628898	+	0.998020i	$0.479968\pi$
$42$	2.17837	0.336130
$43$	−7.99139	−1.21868	−0.609338	−	0.792911i	$-0.708565\pi$
$43$	−7.99139	−1.21868	−0.609338	+	0.792911i	$0.708565\pi$
$44$	3.99859	0.602810
$45$	−2.35424	−0.350950
$46$	−0.963600	−0.142075
$47$	2.27051	0.331188	0.165594	−	0.986194i	$-0.447046\pi$
$47$	2.27051	0.331188	0.165594	+	0.986194i	$0.447046\pi$
$48$	0.803589	0.115988
$49$	0.348462	0.0497803
$50$	−1.00000	−0.141421
$51$	4.09214	0.573014
$52$	−1.00000	−0.138675
$53$	10.6981	1.46950	0.734748	−	0.678341i	$-0.237301\pi$
$53$	10.6981	1.46950	0.734748	+	0.678341i	$0.237301\pi$
$54$	4.30261	0.585511
$55$	3.99859	0.539169
$56$	2.71080	0.362247
$57$	−4.20546	−0.557027
$58$	3.19320	0.419288
$59$	10.5592	1.37470	0.687348	−	0.726328i	$-0.258775\pi$
$59$	10.5592	1.37470	0.687348	+	0.726328i	$0.258775\pi$
$60$	0.803589	0.103743
$61$	−6.54745	−0.838315	−0.419157	−	0.907914i	$-0.637674\pi$
$61$	−6.54745	−0.838315	−0.419157	+	0.907914i	$0.637674\pi$
$62$	−1.00000	−0.127000
$63$	6.38190	0.804043
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−3.21322	−0.395520
$67$	0.107922	0.0131847	0.00659236	−	0.999978i	$-0.497902\pi$
$67$	0.107922	0.0131847	0.00659236	+	0.999978i	$0.497902\pi$
$68$	5.09232	0.617535
$69$	0.774338	0.0932194
$70$	2.71080	0.324003
$71$	−7.64298	−0.907054	−0.453527	−	0.891242i	$-0.649835\pi$
$71$	−7.64298	−0.907054	−0.453527	+	0.891242i	$0.649835\pi$
$72$	2.35424	0.277450
$73$	−8.81462	−1.03167	−0.515836	−	0.856687i	$-0.672519\pi$
$73$	−8.81462	−1.03167	−0.515836	+	0.856687i	$0.672519\pi$
$74$	8.00961	0.931099
$75$	0.803589	0.0927905
$76$	−5.23334	−0.600306
$77$	−10.8394	−1.23526
$78$	0.803589	0.0909886
$79$	0.933724	0.105052	0.0525261	−	0.998620i	$-0.483273\pi$
$79$	0.933724	0.105052	0.0525261	+	0.998620i	$0.483273\pi$
$80$	1.00000	0.111803
$81$	3.60520	0.400578
$82$	−0.805382	−0.0889396
$83$	−3.88051	−0.425942	−0.212971	−	0.977059i	$-0.568314\pi$
$83$	−3.88051	−0.425942	−0.212971	+	0.977059i	$0.568314\pi$
$84$	−2.17837	−0.237680
$85$	5.09232	0.552340
$86$	7.99139	0.861734
$87$	−2.56603	−0.275107
$88$	−3.99859	−0.426251
$89$	0.741117	0.0785582	0.0392791	−	0.999228i	$-0.487494\pi$
$89$	0.741117	0.0785582	0.0392791	+	0.999228i	$0.487494\pi$
$90$	2.35424	0.248159
$91$	2.71080	0.284170
$92$	0.963600	0.100462
$93$	0.803589	0.0833283
$94$	−2.27051	−0.234185
$95$	−5.23334	−0.536930
$96$	−0.803589	−0.0820160
$97$	−14.4685	−1.46905	−0.734526	−	0.678581i	$-0.762595\pi$
$97$	−14.4685	−1.46905	−0.734526	+	0.678581i	$0.762595\pi$
$98$	−0.348462	−0.0352000
$99$	−9.41365	−0.946107
$100$	1.00000	0.100000
$101$	5.37016	0.534351	0.267176	−	0.963648i	$-0.413910\pi$
$101$	5.37016	0.534351	0.267176	+	0.963648i	$0.413910\pi$
$102$	−4.09214	−0.405182
$103$	2.61403	0.257568	0.128784	−	0.991673i	$-0.458893\pi$
$103$	2.61403	0.257568	0.128784	+	0.991673i	$0.458893\pi$
$104$	1.00000	0.0980581
$105$	−2.17837	−0.212587
$106$	−10.6981	−1.03909
$107$	−2.27950	−0.220367	−0.110184	−	0.993911i	$-0.535144\pi$
$107$	−2.27950	−0.220367	−0.110184	+	0.993911i	$0.535144\pi$
$108$	−4.30261	−0.414019
$109$	−1.48948	−0.142667	−0.0713334	−	0.997453i	$-0.522725\pi$
$109$	−1.48948	−0.142667	−0.0713334	+	0.997453i	$0.522725\pi$
$110$	−3.99859	−0.381250
$111$	−6.43644	−0.610920
$112$	−2.71080	−0.256147
$113$	−17.2791	−1.62548	−0.812738	−	0.582629i	$-0.802024\pi$
$113$	−17.2791	−1.62548	−0.812738	+	0.582629i	$0.802024\pi$
$114$	4.20546	0.393877
$115$	0.963600	0.0898561
$116$	−3.19320	−0.296482
$117$	2.35424	0.217650
$118$	−10.5592	−0.972057
$119$	−13.8043	−1.26544
$120$	−0.803589	−0.0733573
$121$	4.98870	0.453518
$122$	6.54745	0.592778
$123$	0.647196	0.0583557
$124$	1.00000	0.0898027
$125$	1.00000	0.0894427
$126$	−6.38190	−0.568545
$127$	−1.76385	−0.156516	−0.0782581	−	0.996933i	$-0.524936\pi$
$127$	−1.76385	−0.156516	−0.0782581	+	0.996933i	$0.524936\pi$
$128$	−1.00000	−0.0883883
$129$	−6.42180	−0.565408
$130$	1.00000	0.0877058
$131$	1.89333	0.165421	0.0827107	−	0.996574i	$-0.473642\pi$
$131$	1.89333	0.165421	0.0827107	+	0.996574i	$0.473642\pi$
$132$	3.21322	0.279675
$133$	14.1866	1.23013
$134$	−0.107922	−0.00932301
$135$	−4.30261	−0.370310
$136$	−5.09232	−0.436663
$137$	−12.3651	−1.05642	−0.528211	−	0.849113i	$-0.677137\pi$
$137$	−12.3651	−1.05642	−0.528211	+	0.849113i	$0.677137\pi$
$138$	−0.774338	−0.0659161
$139$	−4.73495	−0.401613	−0.200807	−	0.979631i	$-0.564356\pi$
$139$	−4.73495	−0.401613	−0.200807	+	0.979631i	$0.564356\pi$
$140$	−2.71080	−0.229105
$141$	1.82456	0.153655
$142$	7.64298	0.641384
$143$	−3.99859	−0.334379
$144$	−2.35424	−0.196187
$145$	−3.19320	−0.265181
$146$	8.81462	0.729503
$147$	0.280020	0.0230957
$148$	−8.00961	−0.658386
$149$	−12.5270	−1.02625	−0.513127	−	0.858313i	$-0.671513\pi$
$149$	−12.5270	−1.02625	−0.513127	+	0.858313i	$0.671513\pi$
$150$	−0.803589	−0.0656128
$151$	10.3733	0.844167	0.422083	−	0.906557i	$-0.361299\pi$
$151$	10.3733	0.844167	0.422083	+	0.906557i	$0.361299\pi$
$152$	5.23334	0.424480
$153$	−11.9886	−0.969218
$154$	10.8394	0.873463
$155$	1.00000	0.0803219
$156$	−0.803589	−0.0643386
$157$	−20.2122	−1.61311	−0.806556	−	0.591157i	$-0.798671\pi$
$157$	−20.2122	−1.61311	−0.806556	+	0.591157i	$0.798671\pi$
$158$	−0.933724	−0.0742831
$159$	8.59687	0.681776
$160$	−1.00000	−0.0790569
$161$	−2.61213	−0.205865
$162$	−3.60520	−0.283251
$163$	−4.18242	−0.327592	−0.163796	−	0.986494i	$-0.552374\pi$
$163$	−4.18242	−0.327592	−0.163796	+	0.986494i	$0.552374\pi$
$164$	0.805382	0.0628898
$165$	3.21322	0.250149
$166$	3.88051	0.301186
$167$	−11.2341	−0.869321	−0.434661	−	0.900594i	$-0.643132\pi$
$167$	−11.2341	−0.869321	−0.434661	+	0.900594i	$0.643132\pi$
$168$	2.17837	0.168065
$169$	1.00000	0.0769231
$170$	−5.09232	−0.390563
$171$	12.3206	0.942178
$172$	−7.99139	−0.609338
$173$	−3.07255	−0.233602	−0.116801	−	0.993155i	$-0.537264\pi$
$173$	−3.07255	−0.233602	−0.116801	+	0.993155i	$0.537264\pi$
$174$	2.56603	0.194530
$175$	−2.71080	−0.204918
$176$	3.99859	0.301405
$177$	8.48529	0.637794
$178$	−0.741117	−0.0555490
$179$	3.03096	0.226545	0.113272	−	0.993564i	$-0.463867\pi$
$179$	3.03096	0.226545	0.113272	+	0.993564i	$0.463867\pi$
$180$	−2.35424	−0.175475
$181$	21.3460	1.58664	0.793319	−	0.608806i	$-0.208351\pi$
$181$	21.3460	1.58664	0.793319	+	0.608806i	$0.208351\pi$
$182$	−2.71080	−0.200938
$183$	−5.26146	−0.388938
$184$	−0.963600	−0.0710375
$185$	−8.00961	−0.588879
$186$	−0.803589	−0.0589220
$187$	20.3621	1.48902
$188$	2.27051	0.165594
$189$	11.6635	0.848398
$190$	5.23334	0.379667
$191$	13.0446	0.943874	0.471937	−	0.881632i	$-0.343555\pi$
$191$	13.0446	0.943874	0.471937	+	0.881632i	$0.343555\pi$
$192$	0.803589	0.0579941
$193$	−9.54455	−0.687032	−0.343516	−	0.939147i	$-0.611618\pi$
$193$	−9.54455	−0.687032	−0.343516	+	0.939147i	$0.611618\pi$
$194$	14.4685	1.03878
$195$	−0.803589	−0.0575462
$196$	0.348462	0.0248901
$197$	−0.453501	−0.0323106	−0.0161553	−	0.999869i	$-0.505143\pi$
$197$	−0.453501	−0.0323106	−0.0161553	+	0.999869i	$0.505143\pi$
$198$	9.41365	0.668999
$199$	−23.8229	−1.68876	−0.844380	−	0.535745i	$-0.820031\pi$
$199$	−23.8229	−1.68876	−0.844380	+	0.535745i	$0.820031\pi$
$200$	−1.00000	−0.0707107
$201$	0.0867246	0.00611708
$202$	−5.37016	−0.377843
$203$	8.65615	0.607543
$204$	4.09214	0.286507
$205$	0.805382	0.0562503
$206$	−2.61403	−0.182128
$207$	−2.26855	−0.157675
$208$	−1.00000	−0.0693375
$209$	−20.9260	−1.44748
$210$	2.17837	0.150322
$211$	−5.24739	−0.361245	−0.180623	−	0.983552i	$-0.557811\pi$
$211$	−5.24739	−0.361245	−0.180623	+	0.983552i	$0.557811\pi$
$212$	10.6981	0.734748
$213$	−6.14181	−0.420830
$214$	2.27950	0.155823
$215$	−7.99139	−0.545008
$216$	4.30261	0.292756
$217$	−2.71080	−0.184021
$218$	1.48948	0.100881
$219$	−7.08333	−0.478647
$220$	3.99859	0.269585
$221$	−5.09232	−0.342547
$222$	6.43644	0.431986
$223$	−19.8601	−1.32993	−0.664966	−	0.746874i	$-0.731554\pi$
$223$	−19.8601	−1.32993	−0.664966	+	0.746874i	$0.731554\pi$
$224$	2.71080	0.181123
$225$	−2.35424	−0.156950
$226$	17.2791	1.14939
$227$	−27.0388	−1.79463	−0.897314	−	0.441394i	$-0.854484\pi$
$227$	−27.0388	−1.79463	−0.897314	+	0.441394i	$0.854484\pi$
$228$	−4.20546	−0.278513
$229$	−5.20230	−0.343778	−0.171889	−	0.985116i	$-0.554987\pi$
$229$	−5.20230	−0.343778	−0.171889	+	0.985116i	$0.554987\pi$
$230$	−0.963600	−0.0635379
$231$	−8.71042	−0.573103
$232$	3.19320	0.209644
$233$	2.08010	0.136272	0.0681359	−	0.997676i	$-0.478295\pi$
$233$	2.08010	0.136272	0.0681359	+	0.997676i	$0.478295\pi$
$234$	−2.35424	−0.153902
$235$	2.27051	0.148112
$236$	10.5592	0.687348
$237$	0.750331	0.0487392
$238$	13.8043	0.894799
$239$	−0.929659	−0.0601346	−0.0300673	−	0.999548i	$-0.509572\pi$
$239$	−0.929659	−0.0601346	−0.0300673	+	0.999548i	$0.509572\pi$
$240$	0.803589	0.0518715
$241$	17.8076	1.14709	0.573543	−	0.819175i	$-0.305568\pi$
$241$	17.8076	1.14709	0.573543	+	0.819175i	$0.305568\pi$
$242$	−4.98870	−0.320685
$243$	15.8049	1.01389
$244$	−6.54745	−0.419157
$245$	0.348462	0.0222624
$246$	−0.647196	−0.0412637
$247$	5.23334	0.332990
$248$	−1.00000	−0.0635001
$249$	−3.11834	−0.197617
$250$	−1.00000	−0.0632456
$251$	−3.88286	−0.245084	−0.122542	−	0.992463i	$-0.539105\pi$
$251$	−3.88286	−0.245084	−0.122542	+	0.992463i	$0.539105\pi$
$252$	6.38190	0.402022
$253$	3.85304	0.242238
$254$	1.76385	0.110674
$255$	4.09214	0.256259
$256$	1.00000	0.0625000
$257$	11.4103	0.711753	0.355876	−	0.934533i	$-0.384182\pi$
$257$	11.4103	0.711753	0.355876	+	0.934533i	$0.384182\pi$
$258$	6.42180	0.399804
$259$	21.7125	1.34915
$260$	−1.00000	−0.0620174
$261$	7.51758	0.465327
$262$	−1.89333	−0.116971
$263$	21.5079	1.32623	0.663115	−	0.748517i	$-0.269234\pi$
$263$	21.5079	1.32623	0.663115	+	0.748517i	$0.269234\pi$
$264$	−3.21322	−0.197760
$265$	10.6981	0.657178
$266$	−14.1866	−0.869835
$267$	0.595553	0.0364473
$268$	0.107922	0.00659236
$269$	12.3802	0.754836	0.377418	−	0.926043i	$-0.376812\pi$
$269$	12.3802	0.754836	0.377418	+	0.926043i	$0.376812\pi$
$270$	4.30261	0.261849
$271$	−18.5708	−1.12810	−0.564048	−	0.825742i	$-0.690757\pi$
$271$	−18.5708	−1.12810	−0.564048	+	0.825742i	$0.690757\pi$
$272$	5.09232	0.308767
$273$	2.17837	0.131841
$274$	12.3651	0.747003
$275$	3.99859	0.241124
$276$	0.774338	0.0466097
$277$	10.3226	0.620225	0.310112	−	0.950700i	$-0.399633\pi$
$277$	10.3226	0.620225	0.310112	+	0.950700i	$0.399633\pi$
$278$	4.73495	0.283983
$279$	−2.35424	−0.140945
$280$	2.71080	0.162002
$281$	6.54327	0.390339	0.195169	−	0.980770i	$-0.437474\pi$
$281$	6.54327	0.390339	0.195169	+	0.980770i	$0.437474\pi$
$282$	−1.82456	−0.108651
$283$	1.01445	0.0603029	0.0301514	−	0.999545i	$-0.490401\pi$
$283$	1.01445	0.0603029	0.0301514	+	0.999545i	$0.490401\pi$
$284$	−7.64298	−0.453527
$285$	−4.20546	−0.249110
$286$	3.99859	0.236441
$287$	−2.18323	−0.128872
$288$	2.35424	0.138725
$289$	8.93174	0.525396
$290$	3.19320	0.187511
$291$	−11.6267	−0.681570
$292$	−8.81462	−0.515836
$293$	11.8605	0.692896	0.346448	−	0.938069i	$-0.387388\pi$
$293$	11.8605	0.692896	0.346448	+	0.938069i	$0.387388\pi$
$294$	−0.280020	−0.0163311
$295$	10.5592	0.614783
$296$	8.00961	0.465549
$297$	−17.2044	−0.998299
$298$	12.5270	0.725671
$299$	−0.963600	−0.0557264
$300$	0.803589	0.0463952
$301$	21.6631	1.24864
$302$	−10.3733	−0.596916
$303$	4.31541	0.247914
$304$	−5.23334	−0.300153
$305$	−6.54745	−0.374906
$306$	11.9886	0.685341
$307$	−32.0594	−1.82973	−0.914864	−	0.403762i	$-0.867702\pi$
$307$	−32.0594	−1.82973	−0.914864	+	0.403762i	$0.867702\pi$
$308$	−10.8394	−0.617631
$309$	2.10061	0.119499
$310$	−1.00000	−0.0567962
$311$	17.3953	0.986397	0.493199	−	0.869917i	$-0.335828\pi$
$311$	17.3953	0.986397	0.493199	+	0.869917i	$0.335828\pi$
$312$	0.803589	0.0454943
$313$	−14.5534	−0.822605	−0.411303	−	0.911499i	$-0.634926\pi$
$313$	−14.5534	−0.822605	−0.411303	+	0.911499i	$0.634926\pi$
$314$	20.2122	1.14064
$315$	6.38190	0.359579
$316$	0.933724	0.0525261
$317$	5.18059	0.290971	0.145486	−	0.989360i	$-0.453526\pi$
$317$	5.18059	0.290971	0.145486	+	0.989360i	$0.453526\pi$
$318$	−8.59687	−0.482088
$319$	−12.7683	−0.714888
$320$	1.00000	0.0559017
$321$	−1.83178	−0.102240
$322$	2.61213	0.145568
$323$	−26.6499	−1.48284
$324$	3.60520	0.200289
$325$	−1.00000	−0.0554700
$326$	4.18242	0.231643
$327$	−1.19693	−0.0661906
$328$	−0.805382	−0.0444698
$329$	−6.15491	−0.339331
$330$	−3.21322	−0.176882
$331$	6.27218	0.344750	0.172375	−	0.985031i	$-0.444856\pi$
$331$	6.27218	0.344750	0.172375	+	0.985031i	$0.444856\pi$
$332$	−3.88051	−0.212971
$333$	18.8566	1.03333
$334$	11.2341	0.614703
$335$	0.107922	0.00589639
$336$	−2.17837	−0.118840
$337$	−27.4392	−1.49471	−0.747355	−	0.664425i	$-0.768676\pi$
$337$	−27.4392	−1.49471	−0.747355	+	0.664425i	$0.768676\pi$
$338$	−1.00000	−0.0543928
$339$	−13.8853	−0.754144
$340$	5.09232	0.276170
$341$	3.99859	0.216536
$342$	−12.3206	−0.666220
$343$	18.0310	0.973584
$344$	7.99139	0.430867
$345$	0.774338	0.0416890
$346$	3.07255	0.165181
$347$	−9.06309	−0.486532	−0.243266	−	0.969960i	$-0.578219\pi$
$347$	−9.06309	−0.486532	−0.243266	+	0.969960i	$0.578219\pi$
$348$	−2.56603	−0.137553
$349$	5.49603	0.294196	0.147098	−	0.989122i	$-0.453007\pi$
$349$	5.49603	0.294196	0.147098	+	0.989122i	$0.453007\pi$
$350$	2.71080	0.144899
$351$	4.30261	0.229657
$352$	−3.99859	−0.213125
$353$	−20.6462	−1.09889	−0.549444	−	0.835530i	$-0.685161\pi$
$353$	−20.6462	−1.09889	−0.549444	+	0.835530i	$0.685161\pi$
$354$	−8.48529	−0.450988
$355$	−7.64298	−0.405647
$356$	0.741117	0.0392791
$357$	−11.0930	−0.587103
$358$	−3.03096	−0.160191
$359$	−16.6052	−0.876389	−0.438194	−	0.898880i	$-0.644382\pi$
$359$	−16.6052	−0.876389	−0.438194	+	0.898880i	$0.644382\pi$
$360$	2.35424	0.124080
$361$	8.38790	0.441468
$362$	−21.3460	−1.12192
$363$	4.00886	0.210411
$364$	2.71080	0.142085
$365$	−8.81462	−0.461378
$366$	5.26146	0.275021
$367$	33.0705	1.72627	0.863133	−	0.504977i	$-0.168499\pi$
$367$	33.0705	1.72627	0.863133	+	0.504977i	$0.168499\pi$
$368$	0.963600	0.0502311
$369$	−1.89607	−0.0987053
$370$	8.00961	0.416400
$371$	−29.0004	−1.50563
$372$	0.803589	0.0416642
$373$	−22.3995	−1.15980	−0.579900	−	0.814688i	$-0.696908\pi$
$373$	−22.3995	−1.15980	−0.579900	+	0.814688i	$0.696908\pi$
$374$	−20.3621	−1.05290
$375$	0.803589	0.0414972
$376$	−2.27051	−0.117093
$377$	3.19320	0.164458
$378$	−11.6635	−0.599908
$379$	−4.08781	−0.209977	−0.104988	−	0.994473i	$-0.533481\pi$
$379$	−4.08781	−0.209977	−0.104988	+	0.994473i	$0.533481\pi$
$380$	−5.23334	−0.268465
$381$	−1.41741	−0.0726161
$382$	−13.0446	−0.667420
$383$	36.3012	1.85491	0.927454	−	0.373938i	$-0.121993\pi$
$383$	36.3012	1.85491	0.927454	+	0.373938i	$0.121993\pi$
$384$	−0.803589	−0.0410080
$385$	−10.8394	−0.552426
$386$	9.54455	0.485805
$387$	18.8137	0.956353
$388$	−14.4685	−0.734526
$389$	−24.9863	−1.26686	−0.633429	−	0.773801i	$-0.718353\pi$
$389$	−24.9863	−1.26686	−0.633429	+	0.773801i	$0.718353\pi$
$390$	0.803589	0.0406913
$391$	4.90696	0.248156
$392$	−0.348462	−0.0176000
$393$	1.52146	0.0767477
$394$	0.453501	0.0228471
$395$	0.933724	0.0469808
$396$	−9.41365	−0.473054
$397$	−3.33665	−0.167462	−0.0837309	−	0.996488i	$-0.526684\pi$
$397$	−3.33665	−0.167462	−0.0837309	+	0.996488i	$0.526684\pi$
$398$	23.8229	1.19413
$399$	11.4002	0.570723
$400$	1.00000	0.0500000
$401$	0.960654	0.0479728	0.0239864	−	0.999712i	$-0.492364\pi$
$401$	0.960654	0.0479728	0.0239864	+	0.999712i	$0.492364\pi$
$402$	−0.0867246	−0.00432543
$403$	−1.00000	−0.0498135
$404$	5.37016	0.267176
$405$	3.60520	0.179144
$406$	−8.65615	−0.429598
$407$	−32.0271	−1.58753
$408$	−4.09214	−0.202591
$409$	−10.5403	−0.521187	−0.260593	−	0.965449i	$-0.583918\pi$
$409$	−10.5403	−0.521187	−0.260593	+	0.965449i	$0.583918\pi$
$410$	−0.805382	−0.0397750
$411$	−9.93647	−0.490130
$412$	2.61403	0.128784
$413$	−28.6240	−1.40850
$414$	2.26855	0.111493
$415$	−3.88051	−0.190487
$416$	1.00000	0.0490290
$417$	−3.80495	−0.186329
$418$	20.9260	1.02352
$419$	−15.0218	−0.733861	−0.366930	−	0.930248i	$-0.619591\pi$
$419$	−15.0218	−0.733861	−0.366930	+	0.930248i	$0.619591\pi$
$420$	−2.17837	−0.106294
$421$	19.1084	0.931284	0.465642	−	0.884973i	$-0.345823\pi$
$421$	19.1084	0.931284	0.465642	+	0.884973i	$0.345823\pi$
$422$	5.24739	0.255439
$423$	−5.34533	−0.259899
$424$	−10.6981	−0.519545
$425$	5.09232	0.247014
$426$	6.14181	0.297572
$427$	17.7489	0.858927
$428$	−2.27950	−0.110184
$429$	−3.21322	−0.155136
$430$	7.99139	0.385379
$431$	−22.7799	−1.09727	−0.548635	−	0.836062i	$-0.684852\pi$
$431$	−22.7799	−1.09727	−0.548635	+	0.836062i	$0.684852\pi$
$432$	−4.30261	−0.207010
$433$	−22.3042	−1.07187	−0.535936	−	0.844259i	$-0.680041\pi$
$433$	−22.3042	−1.07187	−0.535936	+	0.844259i	$0.680041\pi$
$434$	2.71080	0.130123
$435$	−2.56603	−0.123031
$436$	−1.48948	−0.0713334
$437$	−5.04285	−0.241232
$438$	7.08333	0.338455
$439$	−8.71001	−0.415706	−0.207853	−	0.978160i	$-0.566648\pi$
$439$	−8.71001	−0.415706	−0.207853	+	0.978160i	$0.566648\pi$
$440$	−3.99859	−0.190625
$441$	−0.820365	−0.0390650
$442$	5.09232	0.242217
$443$	12.3797	0.588177	0.294088	−	0.955778i	$-0.404984\pi$
$443$	12.3797	0.588177	0.294088	+	0.955778i	$0.404984\pi$
$444$	−6.43644	−0.305460
$445$	0.741117	0.0351323
$446$	19.8601	0.940404
$447$	−10.0666	−0.476133
$448$	−2.71080	−0.128073
$449$	−26.9604	−1.27234	−0.636170	−	0.771549i	$-0.719482\pi$
$449$	−26.9604	−1.27234	−0.636170	+	0.771549i	$0.719482\pi$
$450$	2.35424	0.110980
$451$	3.22039	0.151642
$452$	−17.2791	−0.812738
$453$	8.33587	0.391653
$454$	27.0388	1.26899
$455$	2.71080	0.127084
$456$	4.20546	0.196939
$457$	9.75632	0.456381	0.228191	−	0.973616i	$-0.426719\pi$
$457$	9.75632	0.456381	0.228191	+	0.973616i	$0.426719\pi$
$458$	5.20230	0.243088
$459$	−21.9103	−1.02268
$460$	0.963600	0.0449281
$461$	−15.0606	−0.701443	−0.350721	−	0.936480i	$-0.614064\pi$
$461$	−15.0606	−0.701443	−0.350721	+	0.936480i	$0.614064\pi$
$462$	8.71042	0.405245
$463$	−7.03499	−0.326944	−0.163472	−	0.986548i	$-0.552269\pi$
$463$	−7.03499	−0.326944	−0.163472	+	0.986548i	$0.552269\pi$
$464$	−3.19320	−0.148241
$465$	0.803589	0.0372656
$466$	−2.08010	−0.0963587
$467$	−1.93424	−0.0895058	−0.0447529	−	0.998998i	$-0.514250\pi$
$467$	−1.93424	−0.0895058	−0.0447529	+	0.998998i	$0.514250\pi$
$468$	2.35424	0.108825
$469$	−0.292554	−0.0135089
$470$	−2.27051	−0.104731
$471$	−16.2423	−0.748408
$472$	−10.5592	−0.486028
$473$	−31.9543	−1.46926
$474$	−0.750331	−0.0344638
$475$	−5.23334	−0.240122
$476$	−13.8043	−0.632719
$477$	−25.1859	−1.15318
$478$	0.929659	0.0425216
$479$	8.52767	0.389639	0.194819	−	0.980839i	$-0.437588\pi$
$479$	8.52767	0.389639	0.194819	+	0.980839i	$0.437588\pi$
$480$	−0.803589	−0.0366787
$481$	8.00961	0.365207
$482$	−17.8076	−0.811113
$483$	−2.09908	−0.0955115
$484$	4.98870	0.226759
$485$	−14.4685	−0.656980
$486$	−15.8049	−0.716927
$487$	14.9077	0.675534	0.337767	−	0.941230i	$-0.390328\pi$
$487$	14.9077	0.675534	0.337767	+	0.941230i	$0.390328\pi$
$488$	6.54745	0.296389
$489$	−3.36095	−0.151987
$490$	−0.348462	−0.0157419
$491$	9.58694	0.432652	0.216326	−	0.976321i	$-0.430593\pi$
$491$	9.58694	0.432652	0.216326	+	0.976321i	$0.430593\pi$
$492$	0.647196	0.0291779
$493$	−16.2608	−0.732351
$494$	−5.23334	−0.235459
$495$	−9.41365	−0.423112
$496$	1.00000	0.0449013
$497$	20.7186	0.929357
$498$	3.11834	0.139736
$499$	36.1387	1.61779	0.808896	−	0.587952i	$-0.200065\pi$
$499$	36.1387	1.61779	0.808896	+	0.587952i	$0.200065\pi$
$500$	1.00000	0.0447214
$501$	−9.02761	−0.403324
$502$	3.88286	0.173300
$503$	39.1834	1.74710	0.873551	−	0.486734i	$-0.161812\pi$
$503$	39.1834	1.74710	0.873551	+	0.486734i	$0.161812\pi$
$504$	−6.38190	−0.284272
$505$	5.37016	0.238969
$506$	−3.85304	−0.171288
$507$	0.803589	0.0356887
$508$	−1.76385	−0.0782581
$509$	−20.4993	−0.908615	−0.454308	−	0.890845i	$-0.650113\pi$
$509$	−20.4993	−0.908615	−0.454308	+	0.890845i	$0.650113\pi$
$510$	−4.09214	−0.181203
$511$	23.8947	1.05704
$512$	−1.00000	−0.0441942
$513$	22.5171	0.994152
$514$	−11.4103	−0.503285
$515$	2.61403	0.115188
$516$	−6.42180	−0.282704
$517$	9.07883	0.399286
$518$	−21.7125	−0.953993
$519$	−2.46907	−0.108380
$520$	1.00000	0.0438529
$521$	9.30511	0.407664	0.203832	−	0.979006i	$-0.434660\pi$
$521$	9.30511	0.407664	0.203832	+	0.979006i	$0.434660\pi$
$522$	−7.51758	−0.329036
$523$	−3.78146	−0.165352	−0.0826758	−	0.996576i	$-0.526347\pi$
$523$	−3.78146	−0.165352	−0.0826758	+	0.996576i	$0.526347\pi$
$524$	1.89333	0.0827107
$525$	−2.17837	−0.0950720
$526$	−21.5079	−0.937787
$527$	5.09232	0.221825
$528$	3.21322	0.139838
$529$	−22.0715	−0.959629
$530$	−10.6981	−0.464695
$531$	−24.8590	−1.07879
$532$	14.1866	0.615066
$533$	−0.805382	−0.0348850
$534$	−0.595553	−0.0257721
$535$	−2.27950	−0.0985512
$536$	−0.107922	−0.00466150
$537$	2.43565	0.105106
$538$	−12.3802	−0.533750
$539$	1.39336	0.0600161
$540$	−4.30261	−0.185155
$541$	−20.6067	−0.885951	−0.442976	−	0.896534i	$-0.646077\pi$
$541$	−20.6067	−0.885951	−0.442976	+	0.896534i	$0.646077\pi$
$542$	18.5708	0.797685
$543$	17.1534	0.736125
$544$	−5.09232	−0.218331
$545$	−1.48948	−0.0638025
$546$	−2.17837	−0.0932258
$547$	27.3784	1.17062	0.585309	−	0.810810i	$-0.300973\pi$
$547$	27.3784	1.17062	0.585309	+	0.810810i	$0.300973\pi$
$548$	−12.3651	−0.528211
$549$	15.4143	0.657866
$550$	−3.99859	−0.170500
$551$	16.7111	0.711919
$552$	−0.774338	−0.0329580
$553$	−2.53114	−0.107635
$554$	−10.3226	−0.438565
$555$	−6.43644	−0.273212
$556$	−4.73495	−0.200807
$557$	2.47505	0.104871	0.0524356	−	0.998624i	$-0.483302\pi$
$557$	2.47505	0.104871	0.0524356	+	0.998624i	$0.483302\pi$
$558$	2.35424	0.0996631
$559$	7.99139	0.338000
$560$	−2.71080	−0.114552
$561$	16.3628	0.690836
$562$	−6.54327	−0.276011
$563$	−35.5515	−1.49832	−0.749158	−	0.662391i	$-0.769542\pi$
$563$	−35.5515	−1.49832	−0.749158	+	0.662391i	$0.769542\pi$
$564$	1.82456	0.0768277
$565$	−17.2791	−0.726935
$566$	−1.01445	−0.0426406
$567$	−9.77299	−0.410427
$568$	7.64298	0.320692
$569$	7.58532	0.317993	0.158997	−	0.987279i	$-0.449174\pi$
$569$	7.58532	0.317993	0.158997	+	0.987279i	$0.449174\pi$
$570$	4.20546	0.176147
$571$	42.4663	1.77716	0.888579	−	0.458724i	$-0.151693\pi$
$571$	42.4663	1.77716	0.888579	+	0.458724i	$0.151693\pi$
$572$	−3.99859	−0.167189
$573$	10.4825	0.437913
$574$	2.18323	0.0911264
$575$	0.963600	0.0401849
$576$	−2.35424	−0.0980935
$577$	13.9574	0.581056	0.290528	−	0.956866i	$-0.406169\pi$
$577$	13.9574	0.581056	0.290528	+	0.956866i	$0.406169\pi$
$578$	−8.93174	−0.371511
$579$	−7.66990	−0.318750
$580$	−3.19320	−0.132591
$581$	10.5193	0.436415
$582$	11.6267	0.481943
$583$	42.7772	1.77165
$584$	8.81462	0.364751
$585$	2.35424	0.0973360
$586$	−11.8605	−0.489951
$587$	−4.06865	−0.167931	−0.0839655	−	0.996469i	$-0.526759\pi$
$587$	−4.06865	−0.167931	−0.0839655	+	0.996469i	$0.526759\pi$
$588$	0.280020	0.0115478
$589$	−5.23334	−0.215636
$590$	−10.5592	−0.434717
$591$	−0.364429	−0.0149906
$592$	−8.00961	−0.329193
$593$	−33.7928	−1.38771	−0.693853	−	0.720117i	$-0.744088\pi$
$593$	−33.7928	−1.38771	−0.693853	+	0.720117i	$0.744088\pi$
$594$	17.2044	0.705904
$595$	−13.8043	−0.565921
$596$	−12.5270	−0.513127
$597$	−19.1438	−0.783504
$598$	0.963600	0.0394045
$599$	−0.251385	−0.0102713	−0.00513567	−	0.999987i	$-0.501635\pi$
$599$	−0.251385	−0.0102713	−0.00513567	+	0.999987i	$0.501635\pi$
$600$	−0.803589	−0.0328064
$601$	10.5745	0.431343	0.215671	−	0.976466i	$-0.430806\pi$
$601$	10.5745	0.431343	0.215671	+	0.976466i	$0.430806\pi$
$602$	−21.6631	−0.882922
$603$	−0.254074	−0.0103467
$604$	10.3733	0.422083
$605$	4.98870	0.202819
$606$	−4.31541	−0.175301
$607$	−32.5208	−1.31998	−0.659989	−	0.751275i	$-0.729439\pi$
$607$	−32.5208	−1.31998	−0.659989	+	0.751275i	$0.729439\pi$
$608$	5.23334	0.212240
$609$	6.95599	0.281871
$610$	6.54745	0.265098
$611$	−2.27051	−0.0918549
$612$	−11.9886	−0.484609
$613$	35.7690	1.44470	0.722349	−	0.691529i	$-0.243063\pi$
$613$	35.7690	1.44470	0.722349	+	0.691529i	$0.243063\pi$
$614$	32.0594	1.29381
$615$	0.647196	0.0260975
$616$	10.8394	0.436731
$617$	10.6593	0.429127	0.214563	−	0.976710i	$-0.431167\pi$
$617$	10.6593	0.429127	0.214563	+	0.976710i	$0.431167\pi$
$618$	−2.10061	−0.0844988
$619$	41.9824	1.68741	0.843707	−	0.536804i	$-0.180368\pi$
$619$	41.9824	1.68741	0.843707	+	0.536804i	$0.180368\pi$
$620$	1.00000	0.0401610
$621$	−4.14600	−0.166373
$622$	−17.3953	−0.697488
$623$	−2.00902	−0.0804898
$624$	−0.803589	−0.0321693
$625$	1.00000	0.0400000
$626$	14.5534	0.581670
$627$	−16.8159	−0.671562
$628$	−20.2122	−0.806556
$629$	−40.7875	−1.62631
$630$	−6.38190	−0.254261
$631$	−18.4895	−0.736057	−0.368029	−	0.929814i	$-0.619967\pi$
$631$	−18.4895	−0.736057	−0.368029	+	0.929814i	$0.619967\pi$
$632$	−0.933724	−0.0371416
$633$	−4.21675	−0.167601
$634$	−5.18059	−0.205748
$635$	−1.76385	−0.0699962
$636$	8.59687	0.340888
$637$	−0.348462	−0.0138066
$638$	12.7683	0.505502
$639$	17.9934	0.711809
$640$	−1.00000	−0.0395285
$641$	25.8566	1.02127	0.510637	−	0.859796i	$-0.329410\pi$
$641$	25.8566	1.02127	0.510637	+	0.859796i	$0.329410\pi$
$642$	1.83178	0.0722946
$643$	11.7633	0.463900	0.231950	−	0.972728i	$-0.425489\pi$
$643$	11.7633	0.463900	0.231950	+	0.972728i	$0.425489\pi$
$644$	−2.61213	−0.102932
$645$	−6.42180	−0.252858
$646$	26.6499	1.04853
$647$	0.765237	0.0300846	0.0150423	−	0.999887i	$-0.495212\pi$
$647$	0.765237	0.0300846	0.0150423	+	0.999887i	$0.495212\pi$
$648$	−3.60520	−0.141626
$649$	42.2220	1.65736
$650$	1.00000	0.0392232
$651$	−2.17837	−0.0853772
$652$	−4.18242	−0.163796
$653$	39.1548	1.53225	0.766123	−	0.642695i	$-0.222184\pi$
$653$	39.1548	1.53225	0.766123	+	0.642695i	$0.222184\pi$
$654$	1.19693	0.0468038
$655$	1.89333	0.0739787
$656$	0.805382	0.0314449
$657$	20.7518	0.809603
$658$	6.15491	0.239943
$659$	14.7354	0.574010	0.287005	−	0.957929i	$-0.407340\pi$
$659$	14.7354	0.574010	0.287005	+	0.957929i	$0.407340\pi$
$660$	3.21322	0.125074
$661$	2.89787	0.112714	0.0563571	−	0.998411i	$-0.482051\pi$
$661$	2.89787	0.112714	0.0563571	+	0.998411i	$0.482051\pi$
$662$	−6.27218	−0.243775
$663$	−4.09214	−0.158925
$664$	3.88051	0.150593
$665$	14.1866	0.550132
$666$	−18.8566	−0.730678
$667$	−3.07697	−0.119141
$668$	−11.2341	−0.434661
$669$	−15.9594	−0.617025
$670$	−0.107922	−0.00416938
$671$	−26.1805	−1.01069
$672$	2.17837	0.0840326
$673$	−14.0790	−0.542707	−0.271353	−	0.962480i	$-0.587471\pi$
$673$	−14.0790	−0.542707	−0.271353	+	0.962480i	$0.587471\pi$
$674$	27.4392	1.05692
$675$	−4.30261	−0.165608
$676$	1.00000	0.0384615
$677$	−26.6351	−1.02367	−0.511836	−	0.859083i	$-0.671034\pi$
$677$	−26.6351	−1.02367	−0.511836	+	0.859083i	$0.671034\pi$
$678$	13.8853	0.533260
$679$	39.2212	1.50517
$680$	−5.09232	−0.195282
$681$	−21.7281	−0.832622
$682$	−3.99859	−0.153114
$683$	−20.6791	−0.791263	−0.395631	−	0.918409i	$-0.629474\pi$
$683$	−20.6791	−0.791263	−0.395631	+	0.918409i	$0.629474\pi$
$684$	12.3206	0.471089
$685$	−12.3651	−0.472446
$686$	−18.0310	−0.688428
$687$	−4.18051	−0.159496
$688$	−7.99139	−0.304669
$689$	−10.6981	−0.407565
$690$	−0.774338	−0.0294786
$691$	4.11671	0.156607	0.0783036	−	0.996930i	$-0.475050\pi$
$691$	4.11671	0.156607	0.0783036	+	0.996930i	$0.475050\pi$
$692$	−3.07255	−0.116801
$693$	25.5186	0.969370
$694$	9.06309	0.344030
$695$	−4.73495	−0.179607
$696$	2.56603	0.0972649
$697$	4.10126	0.155346
$698$	−5.49603	−0.208028
$699$	1.67155	0.0632237
$700$	−2.71080	−0.102459
$701$	6.21914	0.234894	0.117447	−	0.993079i	$-0.462529\pi$
$701$	6.21914	0.234894	0.117447	+	0.993079i	$0.462529\pi$
$702$	−4.30261	−0.162392
$703$	41.9171	1.58093
$704$	3.99859	0.150702
$705$	1.82456	0.0687168
$706$	20.6462	0.777031
$707$	−14.5575	−0.547490
$708$	8.48529	0.318897
$709$	3.55404	0.133475	0.0667374	−	0.997771i	$-0.478741\pi$
$709$	3.55404	0.133475	0.0667374	+	0.997771i	$0.478741\pi$
$710$	7.64298	0.286836
$711$	−2.19822	−0.0824395
$712$	−0.741117	−0.0277745
$713$	0.963600	0.0360871
$714$	11.0930	0.415144
$715$	−3.99859	−0.149539
$716$	3.03096	0.113272
$717$	−0.747064	−0.0278996
$718$	16.6052	0.619700
$719$	−14.1255	−0.526794	−0.263397	−	0.964688i	$-0.584843\pi$
$719$	−14.1255	−0.526794	−0.263397	+	0.964688i	$0.584843\pi$
$720$	−2.35424	−0.0877375
$721$	−7.08613	−0.263901
$722$	−8.38790	−0.312165
$723$	14.3100	0.532194
$724$	21.3460	0.793319
$725$	−3.19320	−0.118593
$726$	−4.00886	−0.148783
$727$	18.6470	0.691581	0.345790	−	0.938312i	$-0.387611\pi$
$727$	18.6470	0.691581	0.345790	+	0.938312i	$0.387611\pi$
$728$	−2.71080	−0.100469
$729$	1.88508	0.0698178
$730$	8.81462	0.326244
$731$	−40.6947	−1.50515
$732$	−5.26146	−0.194469
$733$	−43.0285	−1.58929	−0.794646	−	0.607073i	$-0.792344\pi$
$733$	−43.0285	−1.58929	−0.794646	+	0.607073i	$0.792344\pi$
$734$	−33.0705	−1.22065
$735$	0.280020	0.0103287
$736$	−0.963600	−0.0355188
$737$	0.431534	0.0158958
$738$	1.89607	0.0697952
$739$	33.6225	1.23682	0.618412	−	0.785854i	$-0.287776\pi$
$739$	33.6225	1.23682	0.618412	+	0.785854i	$0.287776\pi$
$740$	−8.00961	−0.294439
$741$	4.20546	0.154491
$742$	29.0004	1.06464
$743$	26.1694	0.960061	0.480031	−	0.877252i	$-0.340625\pi$
$743$	26.1694	0.960061	0.480031	+	0.877252i	$0.340625\pi$
$744$	−0.803589	−0.0294610
$745$	−12.5270	−0.458954
$746$	22.3995	0.820102
$747$	9.13568	0.334257
$748$	20.3621	0.744512
$749$	6.17927	0.225786
$750$	−0.803589	−0.0293429
$751$	26.6882	0.973867	0.486934	−	0.873439i	$-0.338115\pi$
$751$	26.6882	0.973867	0.486934	+	0.873439i	$0.338115\pi$
$752$	2.27051	0.0827969
$753$	−3.12022	−0.113707
$754$	−3.19320	−0.116290
$755$	10.3733	0.377523
$756$	11.6635	0.424199
$757$	13.0824	0.475486	0.237743	−	0.971328i	$-0.423592\pi$
$757$	13.0824	0.475486	0.237743	+	0.971328i	$0.423592\pi$
$758$	4.08781	0.148476
$759$	3.09626	0.112387
$760$	5.23334	0.189833
$761$	−27.3034	−0.989748	−0.494874	−	0.868965i	$-0.664786\pi$
$761$	−27.3034	−0.989748	−0.494874	+	0.868965i	$0.664786\pi$
$762$	1.41741	0.0513474
$763$	4.03770	0.146175
$764$	13.0446	0.471937
$765$	−11.9886	−0.433448
$766$	−36.3012	−1.31162
$767$	−10.5592	−0.381272
$768$	0.803589	0.0289970
$769$	27.7528	1.00079	0.500396	−	0.865797i	$-0.333188\pi$
$769$	27.7528	1.00079	0.500396	+	0.865797i	$0.333188\pi$
$770$	10.8394	0.390624
$771$	9.16917	0.330220
$772$	−9.54455	−0.343516
$773$	−13.5474	−0.487267	−0.243633	−	0.969867i	$-0.578339\pi$
$773$	−13.5474	−0.487267	−0.243633	+	0.969867i	$0.578339\pi$
$774$	−18.8137	−0.676244
$775$	1.00000	0.0359211
$776$	14.4685	0.519388
$777$	17.4479	0.625941
$778$	24.9863	0.895804
$779$	−4.21484	−0.151012
$780$	−0.803589	−0.0287731
$781$	−30.5611	−1.09356
$782$	−4.90696	−0.175473
$783$	13.7391	0.490996
$784$	0.348462	0.0124451
$785$	−20.2122	−0.721406
$786$	−1.52146	−0.0542688
$787$	7.75055	0.276277	0.138139	−	0.990413i	$-0.455888\pi$
$787$	7.75055	0.276277	0.138139	+	0.990413i	$0.455888\pi$
$788$	−0.453501	−0.0161553
$789$	17.2835	0.615308
$790$	−0.933724	−0.0332204
$791$	46.8401	1.66544
$792$	9.41365	0.334499
$793$	6.54745	0.232507
$794$	3.33665	0.118413
$795$	8.59687	0.304899
$796$	−23.8229	−0.844380
$797$	34.0730	1.20693	0.603463	−	0.797391i	$-0.293787\pi$
$797$	34.0730	1.20693	0.603463	+	0.797391i	$0.293787\pi$
$798$	−11.4002	−0.403562
$799$	11.5622	0.409040
$800$	−1.00000	−0.0353553
$801$	−1.74477	−0.0616484
$802$	−0.960654	−0.0339219
$803$	−35.2460	−1.24380
$804$	0.0867246	0.00305854
$805$	−2.61213	−0.0920655
$806$	1.00000	0.0352235
$807$	9.94863	0.350208
$808$	−5.37016	−0.188922
$809$	−6.59259	−0.231783	−0.115892	−	0.993262i	$-0.536972\pi$
$809$	−6.59259	−0.231783	−0.115892	+	0.993262i	$0.536972\pi$
$810$	−3.60520	−0.126674
$811$	−19.7374	−0.693075	−0.346537	−	0.938036i	$-0.612643\pi$
$811$	−19.7374	−0.693075	−0.346537	+	0.938036i	$0.612643\pi$
$812$	8.65615	0.303771
$813$	−14.9233	−0.523383
$814$	32.0271	1.12255
$815$	−4.18242	−0.146504
$816$	4.09214	0.143253
$817$	41.8217	1.46316
$818$	10.5403	0.368535
$819$	−6.38190	−0.223002
$820$	0.805382	0.0281252
$821$	2.43380	0.0849401	0.0424700	−	0.999098i	$-0.486477\pi$
$821$	2.43380	0.0849401	0.0424700	+	0.999098i	$0.486477\pi$
$822$	9.93647	0.346574
$823$	37.4764	1.30634	0.653172	−	0.757209i	$-0.273438\pi$
$823$	37.4764	1.30634	0.653172	+	0.757209i	$0.273438\pi$
$824$	−2.61403	−0.0910641
$825$	3.21322	0.111870
$826$	28.6240	0.995958
$827$	−52.0583	−1.81025	−0.905123	−	0.425150i	$-0.860221\pi$
$827$	−52.0583	−1.81025	−0.905123	+	0.425150i	$0.860221\pi$
$828$	−2.26855	−0.0788375
$829$	45.8127	1.59114	0.795571	−	0.605860i	$-0.207171\pi$
$829$	45.8127	1.59114	0.795571	+	0.605860i	$0.207171\pi$
$830$	3.88051	0.134695
$831$	8.29513	0.287755
$832$	−1.00000	−0.0346688
$833$	1.77448	0.0614821
$834$	3.80495	0.131755
$835$	−11.2341	−0.388772
$836$	−20.9260	−0.723740
$837$	−4.30261	−0.148720
$838$	15.0218	0.518918
$839$	10.0810	0.348036	0.174018	−	0.984742i	$-0.444325\pi$
$839$	10.0810	0.348036	0.174018	+	0.984742i	$0.444325\pi$
$840$	2.17837	0.0751610
$841$	−18.8034	−0.648395
$842$	−19.1084	−0.658517
$843$	5.25810	0.181099
$844$	−5.24739	−0.180623
$845$	1.00000	0.0344010
$846$	5.34533	0.183776
$847$	−13.5234	−0.464669
$848$	10.6981	0.367374
$849$	0.815203	0.0279777
$850$	−5.09232	−0.174665
$851$	−7.71806	−0.264572
$852$	−6.14181	−0.210415
$853$	−39.2968	−1.34550	−0.672748	−	0.739872i	$-0.734886\pi$
$853$	−39.2968	−1.34550	−0.672748	+	0.739872i	$0.734886\pi$
$854$	−17.7489	−0.607353
$855$	12.3206	0.421355
$856$	2.27950	0.0779116
$857$	−40.8180	−1.39432	−0.697158	−	0.716918i	$-0.745552\pi$
$857$	−40.8180	−1.39432	−0.697158	+	0.716918i	$0.745552\pi$
$858$	3.21322	0.109698
$859$	53.0512	1.81008	0.905042	−	0.425323i	$-0.139839\pi$
$859$	53.0512	1.81008	0.905042	+	0.425323i	$0.139839\pi$
$860$	−7.99139	−0.272504
$861$	−1.75442	−0.0597906
$862$	22.7799	0.775887
$863$	5.11568	0.174140	0.0870700	−	0.996202i	$-0.472250\pi$
$863$	5.11568	0.174140	0.0870700	+	0.996202i	$0.472250\pi$
$864$	4.30261	0.146378
$865$	−3.07255	−0.104470
$866$	22.3042	0.757928
$867$	7.17745	0.243759
$868$	−2.71080	−0.0920107
$869$	3.73358	0.126653
$870$	2.56603	0.0869964
$871$	−0.107922	−0.00365678
$872$	1.48948	0.0504403
$873$	34.0623	1.15284
$874$	5.04285	0.170577
$875$	−2.71080	−0.0916419
$876$	−7.08333	−0.239324
$877$	2.88776	0.0975127	0.0487563	−	0.998811i	$-0.484474\pi$
$877$	2.88776	0.0975127	0.0487563	+	0.998811i	$0.484474\pi$
$878$	8.71001	0.293948
$879$	9.53094	0.321471
$880$	3.99859	0.134792
$881$	37.4989	1.26337	0.631685	−	0.775225i	$-0.282364\pi$
$881$	37.4989	1.26337	0.631685	+	0.775225i	$0.282364\pi$
$882$	0.820365	0.0276231
$883$	−20.4166	−0.687072	−0.343536	−	0.939139i	$-0.611625\pi$
$883$	−20.4166	−0.687072	−0.343536	+	0.939139i	$0.611625\pi$
$884$	−5.09232	−0.171273
$885$	8.48529	0.285230
$886$	−12.3797	−0.415904
$887$	52.8462	1.77440	0.887201	−	0.461382i	$-0.152646\pi$
$887$	52.8462	1.77440	0.887201	+	0.461382i	$0.152646\pi$
$888$	6.43644	0.215993
$889$	4.78145	0.160365
$890$	−0.741117	−0.0248423
$891$	14.4157	0.482944
$892$	−19.8601	−0.664966
$893$	−11.8824	−0.397628
$894$	10.0666	0.336677
$895$	3.03096	0.101314
$896$	2.71080	0.0905616
$897$	−0.774338	−0.0258544
$898$	26.9604	0.899680
$899$	−3.19320	−0.106499
$900$	−2.35424	−0.0784748
$901$	54.4781	1.81493
$902$	−3.22039	−0.107227
$903$	17.4082	0.579310
$904$	17.2791	0.574693
$905$	21.3460	0.709566
$906$	−8.33587	−0.276941
$907$	−29.0507	−0.964613	−0.482306	−	0.876003i	$-0.660201\pi$
$907$	−29.0507	−0.964613	−0.482306	+	0.876003i	$0.660201\pi$
$908$	−27.0388	−0.897314
$909$	−12.6427	−0.419331
$910$	−2.71080	−0.0898623
$911$	48.6856	1.61302	0.806512	−	0.591217i	$-0.201352\pi$
$911$	48.6856	1.61302	0.806512	+	0.591217i	$0.201352\pi$
$912$	−4.20546	−0.139257
$913$	−15.5166	−0.513524
$914$	−9.75632	−0.322710
$915$	−5.26146	−0.173938
$916$	−5.20230	−0.171889
$917$	−5.13246	−0.169489
$918$	21.9103	0.723147
$919$	6.83872	0.225588	0.112794	−	0.993618i	$-0.464020\pi$
$919$	6.83872	0.225588	0.112794	+	0.993618i	$0.464020\pi$
$920$	−0.963600	−0.0317689
$921$	−25.7626	−0.848907
$922$	15.0606	0.495995
$923$	7.64298	0.251572
$924$	−8.71042	−0.286552
$925$	−8.00961	−0.263355
$926$	7.03499	0.231184
$927$	−6.15407	−0.202126
$928$	3.19320	0.104822
$929$	48.1746	1.58056	0.790279	−	0.612747i	$-0.209936\pi$
$929$	48.1746	1.58056	0.790279	+	0.612747i	$0.209936\pi$
$930$	−0.803589	−0.0263507
$931$	−1.82362	−0.0597668
$932$	2.08010	0.0681359
$933$	13.9787	0.457641
$934$	1.93424	0.0632902
$935$	20.3621	0.665912
$936$	−2.35424	−0.0769509
$937$	−45.3989	−1.48312	−0.741559	−	0.670888i	$-0.765913\pi$
$937$	−45.3989	−1.48312	−0.741559	+	0.670888i	$0.765913\pi$
$938$	0.292554	0.00955224
$939$	−11.6949	−0.381650
$940$	2.27051	0.0740558
$941$	43.5170	1.41861	0.709307	−	0.704900i	$-0.249008\pi$
$941$	43.5170	1.41861	0.709307	+	0.704900i	$0.249008\pi$
$942$	16.2423	0.529204
$943$	0.776066	0.0252722
$944$	10.5592	0.343674
$945$	11.6635	0.379415
$946$	31.9543	1.03892
$947$	−46.1498	−1.49967	−0.749834	−	0.661626i	$-0.769867\pi$
$947$	−46.1498	−1.49967	−0.749834	+	0.661626i	$0.769867\pi$
$948$	0.750331	0.0243696
$949$	8.81462	0.286135
$950$	5.23334	0.169792
$951$	4.16307	0.134997
$952$	13.8043	0.447400
$953$	36.7390	1.19009	0.595047	−	0.803691i	$-0.297134\pi$
$953$	36.7390	1.19009	0.595047	+	0.803691i	$0.297134\pi$
$954$	25.1859	0.815424
$955$	13.0446	0.422113
$956$	−0.929659	−0.0300673
$957$	−10.2605	−0.331674
$958$	−8.52767	−0.275516
$959$	33.5194	1.08240
$960$	0.803589	0.0259357
$961$	1.00000	0.0322581
$962$	−8.00961	−0.258240
$963$	5.36649	0.172933
$964$	17.8076	0.573543
$965$	−9.54455	−0.307250
$966$	2.09908	0.0675368
$967$	4.52998	0.145674	0.0728371	−	0.997344i	$-0.476795\pi$
$967$	4.52998	0.145674	0.0728371	+	0.997344i	$0.476795\pi$
$968$	−4.98870	−0.160343
$969$	−21.4156	−0.687967
$970$	14.4685	0.464555
$971$	22.0502	0.707625	0.353813	−	0.935316i	$-0.384885\pi$
$971$	22.0502	0.707625	0.353813	+	0.935316i	$0.384885\pi$
$972$	15.8049	0.506944
$973$	12.8355	0.411488
$974$	−14.9077	−0.477675
$975$	−0.803589	−0.0257355
$976$	−6.54745	−0.209579
$977$	9.61977	0.307764	0.153882	−	0.988089i	$-0.450822\pi$
$977$	9.61977	0.307764	0.153882	+	0.988089i	$0.450822\pi$
$978$	3.36095	0.107471
$979$	2.96342	0.0947113
$980$	0.348462	0.0111312
$981$	3.50661	0.111957
$982$	−9.58694	−0.305931
$983$	0.842876	0.0268836	0.0134418	−	0.999910i	$-0.495721\pi$
$983$	0.842876	0.0268836	0.0134418	+	0.999910i	$0.495721\pi$
$984$	−0.647196	−0.0206319
$985$	−0.453501	−0.0144498
$986$	16.2608	0.517850
$987$	−4.94602	−0.157433
$988$	5.23334	0.166495
$989$	−7.70050	−0.244862
$990$	9.41365	0.299185
$991$	−20.2964	−0.644736	−0.322368	−	0.946614i	$-0.604479\pi$
$991$	−20.2964	−0.644736	−0.322368	+	0.946614i	$0.604479\pi$
$992$	−1.00000	−0.0317500
$993$	5.04026	0.159948
$994$	−20.7186	−0.657155
$995$	−23.8229	−0.755236
$996$	−3.11834	−0.0988084
$997$	19.4898	0.617250	0.308625	−	0.951184i	$-0.400131\pi$
$997$	19.4898	0.617250	0.308625	+	0.951184i	$0.400131\pi$
$998$	−36.1387	−1.14395
$999$	34.4623	1.09034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.h.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.h.1.5	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.803589 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803589 q^{6} -2.71080 q^{7} -1.00000 q^{8} -2.35424 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.803589 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.803589 q^{6} -2.71080 q^{7} -1.00000 q^{8} -2.35424 q^{9} -1.00000 q^{10} +3.99859 q^{11} +0.803589 q^{12} -1.00000 q^{13} +2.71080 q^{14} +0.803589 q^{15} +1.00000 q^{16} +5.09232 q^{17} +2.35424 q^{18} -5.23334 q^{19} +1.00000 q^{20} -2.17837 q^{21} -3.99859 q^{22} +0.963600 q^{23} -0.803589 q^{24} +1.00000 q^{25} +1.00000 q^{26} -4.30261 q^{27} -2.71080 q^{28} -3.19320 q^{29} -0.803589 q^{30} +1.00000 q^{31} -1.00000 q^{32} +3.21322 q^{33} -5.09232 q^{34} -2.71080 q^{35} -2.35424 q^{36} -8.00961 q^{37} +5.23334 q^{38} -0.803589 q^{39} -1.00000 q^{40} +0.805382 q^{41} +2.17837 q^{42} -7.99139 q^{43} +3.99859 q^{44} -2.35424 q^{45} -0.963600 q^{46} +2.27051 q^{47} +0.803589 q^{48} +0.348462 q^{49} -1.00000 q^{50} +4.09214 q^{51} -1.00000 q^{52} +10.6981 q^{53} +4.30261 q^{54} +3.99859 q^{55} +2.71080 q^{56} -4.20546 q^{57} +3.19320 q^{58} +10.5592 q^{59} +0.803589 q^{60} -6.54745 q^{61} -1.00000 q^{62} +6.38190 q^{63} +1.00000 q^{64} -1.00000 q^{65} -3.21322 q^{66} +0.107922 q^{67} +5.09232 q^{68} +0.774338 q^{69} +2.71080 q^{70} -7.64298 q^{71} +2.35424 q^{72} -8.81462 q^{73} +8.00961 q^{74} +0.803589 q^{75} -5.23334 q^{76} -10.8394 q^{77} +0.803589 q^{78} +0.933724 q^{79} +1.00000 q^{80} +3.60520 q^{81} -0.805382 q^{82} -3.88051 q^{83} -2.17837 q^{84} +5.09232 q^{85} +7.99139 q^{86} -2.56603 q^{87} -3.99859 q^{88} +0.741117 q^{89} +2.35424 q^{90} +2.71080 q^{91} +0.963600 q^{92} +0.803589 q^{93} -2.27051 q^{94} -5.23334 q^{95} -0.803589 q^{96} -14.4685 q^{97} -0.348462 q^{98} -9.41365 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9	\( 7 q - 7 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + q^{6} - 4 q^{7} - 7 q^{8} + 4 q^{9} - 7 q^{10} - 2 q^{11} - q^{12} - 7 q^{13} + 4 q^{14} - q^{15} + 7 q^{16} - 8 q^{17} - 4 q^{18} + q^{19} + 7 q^{20} - 11 q^{21} + 2 q^{22} - 5 q^{23} + q^{24} + 7 q^{25} + 7 q^{26} - q^{27} - 4 q^{28} - 4 q^{29} + q^{30} + 7 q^{31} - 7 q^{32} - 4 q^{33} + 8 q^{34} - 4 q^{35} + 4 q^{36} - 2 q^{37} - q^{38} + q^{39} - 7 q^{40} - 6 q^{41} + 11 q^{42} - 5 q^{43} - 2 q^{44} + 4 q^{45} + 5 q^{46} - 18 q^{47} - q^{48} - 9 q^{49} - 7 q^{50} - q^{51} - 7 q^{52} - 12 q^{53} + q^{54} - 2 q^{55} + 4 q^{56} - 31 q^{57} + 4 q^{58} + 3 q^{59} - q^{60} - 7 q^{61} - 7 q^{62} - 19 q^{63} + 7 q^{64} - 7 q^{65} + 4 q^{66} + 6 q^{67} - 8 q^{68} - 10 q^{69} + 4 q^{70} + 4 q^{71} - 4 q^{72} - 31 q^{73} + 2 q^{74} - q^{75} + q^{76} - 25 q^{77} - q^{78} - 2 q^{79} + 7 q^{80} + 31 q^{81} + 6 q^{82} - 40 q^{83} - 11 q^{84} - 8 q^{85} + 5 q^{86} - 5 q^{87} + 2 q^{88} - 4 q^{90} + 4 q^{91} - 5 q^{92} - q^{93} + 18 q^{94} + q^{95} + q^{96} - 21 q^{97} + 9 q^{98} - 23 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + q^6 - 4 * q^7 - 7 * q^8 + 4 * q^9 - 7 * q^10 - 2 * q^11 - q^12 - 7 * q^13 + 4 * q^14 - q^15 + 7 * q^16 - 8 * q^17 - 4 * q^18 + q^19 + 7 * q^20 - 11 * q^21 + 2 * q^22 - 5 * q^23 + q^24 + 7 * q^25 + 7 * q^26 - q^27 - 4 * q^28 - 4 * q^29 + q^30 + 7 * q^31 - 7 * q^32 - 4 * q^33 + 8 * q^34 - 4 * q^35 + 4 * q^36 - 2 * q^37 - q^38 + q^39 - 7 * q^40 - 6 * q^41 + 11 * q^42 - 5 * q^43 - 2 * q^44 + 4 * q^45 + 5 * q^46 - 18 * q^47 - q^48 - 9 * q^49 - 7 * q^50 - q^51 - 7 * q^52 - 12 * q^53 + q^54 - 2 * q^55 + 4 * q^56 - 31 * q^57 + 4 * q^58 + 3 * q^59 - q^60 - 7 * q^61 - 7 * q^62 - 19 * q^63 + 7 * q^64 - 7 * q^65 + 4 * q^66 + 6 * q^67 - 8 * q^68 - 10 * q^69 + 4 * q^70 + 4 * q^71 - 4 * q^72 - 31 * q^73 + 2 * q^74 - q^75 + q^76 - 25 * q^77 - q^78 - 2 * q^79 + 7 * q^80 + 31 * q^81 + 6 * q^82 - 40 * q^83 - 11 * q^84 - 8 * q^85 + 5 * q^86 - 5 * q^87 + 2 * q^88 - 4 * q^90 + 4 * q^91 - 5 * q^92 - q^93 + 18 * q^94 + q^95 + q^96 - 21 * q^97 + 9 * q^98 - 23 * q^99

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