LMFDB - Embedded newform 4030.2.a.g.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:	$6$
Coefficient field:	6.6.10369693.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 12x^{3} + 5x^{2} - 7x + 1 $ x^6 - 3x^5 - 4x^4 + 12x^3 + 5x^2 - 7*x + 1
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			$2.31687$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.31687 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.31687 q^{6} -4.24970 q^{7} +1.00000 q^{8} -1.26586 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.31687 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.31687 q^{6} -4.24970 q^{7} +1.00000 q^{8} -1.26586 q^{9} +1.00000 q^{10} -1.63555 q^{11} +1.31687 q^{12} -1.00000 q^{13} -4.24970 q^{14} +1.31687 q^{15} +1.00000 q^{16} +5.84178 q^{17} -1.26586 q^{18} -1.36466 q^{19} +1.00000 q^{20} -5.59629 q^{21} -1.63555 q^{22} -8.85279 q^{23} +1.31687 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.61757 q^{27} -4.24970 q^{28} -1.07562 q^{29} +1.31687 q^{30} -1.00000 q^{31} +1.00000 q^{32} -2.15380 q^{33} +5.84178 q^{34} -4.24970 q^{35} -1.26586 q^{36} -0.732230 q^{37} -1.36466 q^{38} -1.31687 q^{39} +1.00000 q^{40} -0.539659 q^{41} -5.59629 q^{42} -6.89347 q^{43} -1.63555 q^{44} -1.26586 q^{45} -8.85279 q^{46} +0.441588 q^{47} +1.31687 q^{48} +11.0599 q^{49} +1.00000 q^{50} +7.69284 q^{51} -1.00000 q^{52} -2.53774 q^{53} -5.61757 q^{54} -1.63555 q^{55} -4.24970 q^{56} -1.79708 q^{57} -1.07562 q^{58} -5.44241 q^{59} +1.31687 q^{60} -2.85872 q^{61} -1.00000 q^{62} +5.37952 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.15380 q^{66} -14.6554 q^{67} +5.84178 q^{68} -11.6579 q^{69} -4.24970 q^{70} -6.52730 q^{71} -1.26586 q^{72} +6.41373 q^{73} -0.732230 q^{74} +1.31687 q^{75} -1.36466 q^{76} +6.95060 q^{77} -1.31687 q^{78} +7.46507 q^{79} +1.00000 q^{80} -3.60002 q^{81} -0.539659 q^{82} -3.14179 q^{83} -5.59629 q^{84} +5.84178 q^{85} -6.89347 q^{86} -1.41645 q^{87} -1.63555 q^{88} +5.44148 q^{89} -1.26586 q^{90} +4.24970 q^{91} -8.85279 q^{92} -1.31687 q^{93} +0.441588 q^{94} -1.36466 q^{95} +1.31687 q^{96} -11.5825 q^{97} +11.0599 q^{98} +2.07038 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 6 q^{5} - 3 q^{6} - 10 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 6 * q^5 - 3 * q^6 - 10 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 6 q^{5} - 3 q^{6} - 10 q^{7} + 6 q^{8} - q^{9} + 6 q^{10} - 10 q^{11} - 3 q^{12} - 6 q^{13} - 10 q^{14} - 3 q^{15} + 6 q^{16} - 4 q^{17} - q^{18} - 7 q^{19} + 6 q^{20} + q^{21} - 10 q^{22} - 3 q^{23} - 3 q^{24} + 6 q^{25} - 6 q^{26} - 3 q^{27} - 10 q^{28} - 4 q^{29} - 3 q^{30} - 6 q^{31} + 6 q^{32} - 4 q^{33} - 4 q^{34} - 10 q^{35} - q^{36} - 2 q^{37} - 7 q^{38} + 3 q^{39} + 6 q^{40} - 10 q^{41} + q^{42} - 15 q^{43} - 10 q^{44} - q^{45} - 3 q^{46} - 24 q^{47} - 3 q^{48} - 2 q^{49} + 6 q^{50} - 3 q^{51} - 6 q^{52} + 2 q^{53} - 3 q^{54} - 10 q^{55} - 10 q^{56} - 23 q^{57} - 4 q^{58} - 25 q^{59} - 3 q^{60} + 9 q^{61} - 6 q^{62} - 9 q^{63} + 6 q^{64} - 6 q^{65} - 4 q^{66} - 26 q^{67} - 4 q^{68} - 2 q^{69} - 10 q^{70} - 38 q^{71} - q^{72} - q^{73} - 2 q^{74} - 3 q^{75} - 7 q^{76} + 9 q^{77} + 3 q^{78} + 6 q^{80} - 18 q^{81} - 10 q^{82} - 18 q^{83} + q^{84} - 4 q^{85} - 15 q^{86} - 7 q^{87} - 10 q^{88} + 4 q^{89} - q^{90} + 10 q^{91} - 3 q^{92} + 3 q^{93} - 24 q^{94} - 7 q^{95} - 3 q^{96} - 21 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 6 * q^5 - 3 * q^6 - 10 * q^7 + 6 * q^8 - q^9 + 6 * q^10 - 10 * q^11 - 3 * q^12 - 6 * q^13 - 10 * q^14 - 3 * q^15 + 6 * q^16 - 4 * q^17 - q^18 - 7 * q^19 + 6 * q^20 + q^21 - 10 * q^22 - 3 * q^23 - 3 * q^24 + 6 * q^25 - 6 * q^26 - 3 * q^27 - 10 * q^28 - 4 * q^29 - 3 * q^30 - 6 * q^31 + 6 * q^32 - 4 * q^33 - 4 * q^34 - 10 * q^35 - q^36 - 2 * q^37 - 7 * q^38 + 3 * q^39 + 6 * q^40 - 10 * q^41 + q^42 - 15 * q^43 - 10 * q^44 - q^45 - 3 * q^46 - 24 * q^47 - 3 * q^48 - 2 * q^49 + 6 * q^50 - 3 * q^51 - 6 * q^52 + 2 * q^53 - 3 * q^54 - 10 * q^55 - 10 * q^56 - 23 * q^57 - 4 * q^58 - 25 * q^59 - 3 * q^60 + 9 * q^61 - 6 * q^62 - 9 * q^63 + 6 * q^64 - 6 * q^65 - 4 * q^66 - 26 * q^67 - 4 * q^68 - 2 * q^69 - 10 * q^70 - 38 * q^71 - q^72 - q^73 - 2 * q^74 - 3 * q^75 - 7 * q^76 + 9 * q^77 + 3 * q^78 + 6 * q^80 - 18 * q^81 - 10 * q^82 - 18 * q^83 + q^84 - 4 * q^85 - 15 * q^86 - 7 * q^87 - 10 * q^88 + 4 * q^89 - q^90 + 10 * q^91 - 3 * q^92 + 3 * q^93 - 24 * q^94 - 7 * q^95 - 3 * q^96 - 21 * q^97 - 2 * q^98 + 3 * 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
$3$	1.31687	0.760294	0.380147	−	0.924926i	$-0.375873\pi$
$3$	1.31687	0.760294	0.380147	+	0.924926i	$0.375873\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.31687	0.537609
$7$	−4.24970	−1.60623	−0.803117	−	0.595821i	$-0.796827\pi$
$7$	−4.24970	−1.60623	−0.803117	+	0.595821i	$0.796827\pi$
$8$	1.00000	0.353553
$9$	−1.26586	−0.421953
$10$	1.00000	0.316228
$11$	−1.63555	−0.493137	−0.246569	−	0.969125i	$-0.579303\pi$
$11$	−1.63555	−0.493137	−0.246569	+	0.969125i	$0.579303\pi$
$12$	1.31687	0.380147
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−4.24970	−1.13578
$15$	1.31687	0.340014
$16$	1.00000	0.250000
$17$	5.84178	1.41684	0.708419	−	0.705792i	$-0.249409\pi$
$17$	5.84178	1.41684	0.708419	+	0.705792i	$0.249409\pi$
$18$	−1.26586	−0.298366
$19$	−1.36466	−0.313075	−0.156538	−	0.987672i	$-0.550033\pi$
$19$	−1.36466	−0.313075	−0.156538	+	0.987672i	$0.550033\pi$
$20$	1.00000	0.223607
$21$	−5.59629	−1.22121
$22$	−1.63555	−0.348701
$23$	−8.85279	−1.84593	−0.922967	−	0.384879i	$-0.874243\pi$
$23$	−8.85279	−1.84593	−0.922967	+	0.384879i	$0.874243\pi$
$24$	1.31687	0.268804
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−5.61757	−1.08110
$28$	−4.24970	−0.803117
$29$	−1.07562	−0.199738	−0.0998692	−	0.995001i	$-0.531842\pi$
$29$	−1.07562	−0.199738	−0.0998692	+	0.995001i	$0.531842\pi$
$30$	1.31687	0.240426
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−2.15380	−0.374929
$34$	5.84178	1.00186
$35$	−4.24970	−0.718330
$36$	−1.26586	−0.210977
$37$	−0.732230	−0.120378	−0.0601889	−	0.998187i	$-0.519170\pi$
$37$	−0.732230	−0.120378	−0.0601889	+	0.998187i	$0.519170\pi$
$38$	−1.36466	−0.221378
$39$	−1.31687	−0.210868
$40$	1.00000	0.158114
$41$	−0.539659	−0.0842805	−0.0421403	−	0.999112i	$-0.513418\pi$
$41$	−0.539659	−0.0842805	−0.0421403	+	0.999112i	$0.513418\pi$
$42$	−5.59629	−0.863526
$43$	−6.89347	−1.05125	−0.525623	−	0.850718i	$-0.676168\pi$
$43$	−6.89347	−1.05125	−0.525623	+	0.850718i	$0.676168\pi$
$44$	−1.63555	−0.246569
$45$	−1.26586	−0.188703
$46$	−8.85279	−1.30527
$47$	0.441588	0.0644122	0.0322061	−	0.999481i	$-0.489747\pi$
$47$	0.441588	0.0644122	0.0322061	+	0.999481i	$0.489747\pi$
$48$	1.31687	0.190073
$49$	11.0599	1.57999
$50$	1.00000	0.141421
$51$	7.69284	1.07721
$52$	−1.00000	−0.138675
$53$	−2.53774	−0.348585	−0.174293	−	0.984694i	$-0.555764\pi$
$53$	−2.53774	−0.348585	−0.174293	+	0.984694i	$0.555764\pi$
$54$	−5.61757	−0.764455
$55$	−1.63555	−0.220538
$56$	−4.24970	−0.567890
$57$	−1.79708	−0.238029
$58$	−1.07562	−0.141236
$59$	−5.44241	−0.708541	−0.354270	−	0.935143i	$-0.615271\pi$
$59$	−5.44241	−0.708541	−0.354270	+	0.935143i	$0.615271\pi$
$60$	1.31687	0.170007
$61$	−2.85872	−0.366022	−0.183011	−	0.983111i	$-0.558584\pi$
$61$	−2.85872	−0.366022	−0.183011	+	0.983111i	$0.558584\pi$
$62$	−1.00000	−0.127000
$63$	5.37952	0.677756
$64$	1.00000	0.125000
$65$	−1.00000	−0.124035
$66$	−2.15380	−0.265115
$67$	−14.6554	−1.79044	−0.895221	−	0.445623i	$-0.852982\pi$
$67$	−14.6554	−1.79044	−0.895221	+	0.445623i	$0.852982\pi$
$68$	5.84178	0.708419
$69$	−11.6579	−1.40345
$70$	−4.24970	−0.507936
$71$	−6.52730	−0.774647	−0.387324	−	0.921944i	$-0.626600\pi$
$71$	−6.52730	−0.774647	−0.387324	+	0.921944i	$0.626600\pi$
$72$	−1.26586	−0.149183
$73$	6.41373	0.750670	0.375335	−	0.926889i	$-0.377528\pi$
$73$	6.41373	0.750670	0.375335	+	0.926889i	$0.377528\pi$
$74$	−0.732230	−0.0851200
$75$	1.31687	0.152059
$76$	−1.36466	−0.156538
$77$	6.95060	0.792095
$78$	−1.31687	−0.149106
$79$	7.46507	0.839886	0.419943	−	0.907551i	$-0.362050\pi$
$79$	7.46507	0.839886	0.419943	+	0.907551i	$0.362050\pi$
$80$	1.00000	0.111803
$81$	−3.60002	−0.400002
$82$	−0.539659	−0.0595953
$83$	−3.14179	−0.344857	−0.172428	−	0.985022i	$-0.555161\pi$
$83$	−3.14179	−0.344857	−0.172428	+	0.985022i	$0.555161\pi$
$84$	−5.59629	−0.610605
$85$	5.84178	0.633630
$86$	−6.89347	−0.743342
$87$	−1.41645	−0.151860
$88$	−1.63555	−0.174350
$89$	5.44148	0.576796	0.288398	−	0.957511i	$-0.406877\pi$
$89$	5.44148	0.576796	0.288398	+	0.957511i	$0.406877\pi$
$90$	−1.26586	−0.133433
$91$	4.24970	0.445489
$92$	−8.85279	−0.922967
$93$	−1.31687	−0.136553
$94$	0.441588	0.0455463
$95$	−1.36466	−0.140011
$96$	1.31687	0.134402
$97$	−11.5825	−1.17602	−0.588010	−	0.808853i	$-0.700089\pi$
$97$	−11.5825	−1.17602	−0.588010	+	0.808853i	$0.700089\pi$
$98$	11.0599	1.11722
$99$	2.07038	0.208081
$100$	1.00000	0.100000
$101$	−1.49173	−0.148432	−0.0742161	−	0.997242i	$-0.523645\pi$
$101$	−1.49173	−0.148432	−0.0742161	+	0.997242i	$0.523645\pi$
$102$	7.69284	0.761705
$103$	−0.996574	−0.0981953	−0.0490977	−	0.998794i	$-0.515635\pi$
$103$	−0.996574	−0.0981953	−0.0490977	+	0.998794i	$0.515635\pi$
$104$	−1.00000	−0.0980581
$105$	−5.59629	−0.546142
$106$	−2.53774	−0.246487
$107$	4.23110	0.409036	0.204518	−	0.978863i	$-0.434437\pi$
$107$	4.23110	0.409036	0.204518	+	0.978863i	$0.434437\pi$
$108$	−5.61757	−0.540551
$109$	−0.226427	−0.0216878	−0.0108439	−	0.999941i	$-0.503452\pi$
$109$	−0.226427	−0.0216878	−0.0108439	+	0.999941i	$0.503452\pi$
$110$	−1.63555	−0.155944
$111$	−0.964249	−0.0915225
$112$	−4.24970	−0.401559
$113$	20.4151	1.92049	0.960243	−	0.279164i	$-0.0900573\pi$
$113$	20.4151	1.92049	0.960243	+	0.279164i	$0.0900573\pi$
$114$	−1.79708	−0.168312
$115$	−8.85279	−0.825527
$116$	−1.07562	−0.0998692
$117$	1.26586	0.117029
$118$	−5.44241	−0.501014
$119$	−24.8258	−2.27578
$120$	1.31687	0.120213
$121$	−8.32497	−0.756815
$122$	−2.85872	−0.258817
$123$	−0.710659	−0.0640780
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	5.37952	0.479246
$127$	−7.27571	−0.645615	−0.322807	−	0.946465i	$-0.604627\pi$
$127$	−7.27571	−0.645615	−0.322807	+	0.946465i	$0.604627\pi$
$128$	1.00000	0.0883883
$129$	−9.07779	−0.799255
$130$	−1.00000	−0.0877058
$131$	−12.8456	−1.12233	−0.561164	−	0.827705i	$-0.689646\pi$
$131$	−12.8456	−1.12233	−0.561164	+	0.827705i	$0.689646\pi$
$132$	−2.15380	−0.187465
$133$	5.79940	0.502872
$134$	−14.6554	−1.26603
$135$	−5.61757	−0.483484
$136$	5.84178	0.500928
$137$	6.08125	0.519556	0.259778	−	0.965668i	$-0.416351\pi$
$137$	6.08125	0.519556	0.259778	+	0.965668i	$0.416351\pi$
$138$	−11.6579	−0.992390
$139$	1.30409	0.110612	0.0553058	−	0.998469i	$-0.482387\pi$
$139$	1.30409	0.110612	0.0553058	+	0.998469i	$0.482387\pi$
$140$	−4.24970	−0.359165
$141$	0.581513	0.0489722
$142$	−6.52730	−0.547758
$143$	1.63555	0.136772
$144$	−1.26586	−0.105488
$145$	−1.07562	−0.0893257
$146$	6.41373	0.530804
$147$	14.5645	1.20126
$148$	−0.732230	−0.0601889
$149$	−10.6334	−0.871124	−0.435562	−	0.900159i	$-0.643450\pi$
$149$	−10.6334	−0.871124	−0.435562	+	0.900159i	$0.643450\pi$
$150$	1.31687	0.107522
$151$	11.5419	0.939263	0.469631	−	0.882863i	$-0.344387\pi$
$151$	11.5419	0.939263	0.469631	+	0.882863i	$0.344387\pi$
$152$	−1.36466	−0.110689
$153$	−7.39487	−0.597840
$154$	6.95060	0.560095
$155$	−1.00000	−0.0803219
$156$	−1.31687	−0.105434
$157$	−13.2356	−1.05631	−0.528156	−	0.849147i	$-0.677116\pi$
$157$	−13.2356	−1.05631	−0.528156	+	0.849147i	$0.677116\pi$
$158$	7.46507	0.593889
$159$	−3.34186	−0.265027
$160$	1.00000	0.0790569
$161$	37.6217	2.96500
$162$	−3.60002	−0.282844
$163$	4.33906	0.339861	0.169931	−	0.985456i	$-0.445646\pi$
$163$	4.33906	0.339861	0.169931	+	0.985456i	$0.445646\pi$
$164$	−0.539659	−0.0421403
$165$	−2.15380	−0.167673
$166$	−3.14179	−0.243851
$167$	−15.1311	−1.17088	−0.585439	−	0.810717i	$-0.699078\pi$
$167$	−15.1311	−1.17088	−0.585439	+	0.810717i	$0.699078\pi$
$168$	−5.59629	−0.431763
$169$	1.00000	0.0769231
$170$	5.84178	0.448044
$171$	1.72747	0.132103
$172$	−6.89347	−0.525623
$173$	15.5826	1.18472	0.592362	−	0.805672i	$-0.298196\pi$
$173$	15.5826	1.18472	0.592362	+	0.805672i	$0.298196\pi$
$174$	−1.41645	−0.107381
$175$	−4.24970	−0.321247
$176$	−1.63555	−0.123284
$177$	−7.16693	−0.538699
$178$	5.44148	0.407857
$179$	−8.50382	−0.635605	−0.317803	−	0.948157i	$-0.602945\pi$
$179$	−8.50382	−0.635605	−0.317803	+	0.948157i	$0.602945\pi$
$180$	−1.26586	−0.0943517
$181$	−22.8796	−1.70063	−0.850314	−	0.526276i	$-0.823588\pi$
$181$	−22.8796	−1.70063	−0.850314	+	0.526276i	$0.823588\pi$
$182$	4.24970	0.315009
$183$	−3.76456	−0.278284
$184$	−8.85279	−0.652636
$185$	−0.732230	−0.0538346
$186$	−1.31687	−0.0965574
$187$	−9.55453	−0.698696
$188$	0.441588	0.0322061
$189$	23.8730	1.73650
$190$	−1.36466	−0.0990030
$191$	19.9270	1.44187	0.720934	−	0.693003i	$-0.243713\pi$
$191$	19.9270	1.44187	0.720934	+	0.693003i	$0.243713\pi$
$192$	1.31687	0.0950367
$193$	20.4505	1.47206	0.736030	−	0.676949i	$-0.236698\pi$
$193$	20.4505	1.47206	0.736030	+	0.676949i	$0.236698\pi$
$194$	−11.5825	−0.831572
$195$	−1.31687	−0.0943028
$196$	11.0599	0.789995
$197$	−11.9508	−0.851460	−0.425730	−	0.904850i	$-0.639983\pi$
$197$	−11.9508	−0.851460	−0.425730	+	0.904850i	$0.639983\pi$
$198$	2.07038	0.147136
$199$	7.42917	0.526640	0.263320	−	0.964709i	$-0.415182\pi$
$199$	7.42917	0.526640	0.263320	+	0.964709i	$0.415182\pi$
$200$	1.00000	0.0707107
$201$	−19.2992	−1.36126
$202$	−1.49173	−0.104957
$203$	4.57108	0.320827
$204$	7.69284	0.538607
$205$	−0.539659	−0.0376914
$206$	−0.996574	−0.0694346
$207$	11.2064	0.778898
$208$	−1.00000	−0.0693375
$209$	2.23198	0.154389
$210$	−5.59629	−0.386181
$211$	6.15526	0.423745	0.211873	−	0.977297i	$-0.432044\pi$
$211$	6.15526	0.423745	0.211873	+	0.977297i	$0.432044\pi$
$212$	−2.53774	−0.174293
$213$	−8.59558	−0.588960
$214$	4.23110	0.289232
$215$	−6.89347	−0.470131
$216$	−5.61757	−0.382227
$217$	4.24970	0.288488
$218$	−0.226427	−0.0153356
$219$	8.44603	0.570730
$220$	−1.63555	−0.110269
$221$	−5.84178	−0.392960
$222$	−0.964249	−0.0647162
$223$	4.42273	0.296168	0.148084	−	0.988975i	$-0.452689\pi$
$223$	4.42273	0.296168	0.148084	+	0.988975i	$0.452689\pi$
$224$	−4.24970	−0.283945
$225$	−1.26586	−0.0843907
$226$	20.4151	1.35799
$227$	1.26465	0.0839380	0.0419690	−	0.999119i	$-0.486637\pi$
$227$	1.26465	0.0839380	0.0419690	+	0.999119i	$0.486637\pi$
$228$	−1.79708	−0.119015
$229$	−7.15824	−0.473030	−0.236515	−	0.971628i	$-0.576005\pi$
$229$	−7.15824	−0.473030	−0.236515	+	0.971628i	$0.576005\pi$
$230$	−8.85279	−0.583736
$231$	9.15302	0.602225
$232$	−1.07562	−0.0706182
$233$	19.9127	1.30452	0.652262	−	0.757994i	$-0.273820\pi$
$233$	19.9127	1.30452	0.652262	+	0.757994i	$0.273820\pi$
$234$	1.26586	0.0827519
$235$	0.441588	0.0288060
$236$	−5.44241	−0.354270
$237$	9.83050	0.638560
$238$	−24.8258	−1.60922
$239$	22.8344	1.47703	0.738516	−	0.674236i	$-0.235527\pi$
$239$	22.8344	1.47703	0.738516	+	0.674236i	$0.235527\pi$
$240$	1.31687	0.0850034
$241$	6.09812	0.392814	0.196407	−	0.980522i	$-0.437073\pi$
$241$	6.09812	0.392814	0.196407	+	0.980522i	$0.437073\pi$
$242$	−8.32497	−0.535149
$243$	12.1120	0.776983
$244$	−2.85872	−0.183011
$245$	11.0599	0.706593
$246$	−0.710659	−0.0453100
$247$	1.36466	0.0868314
$248$	−1.00000	−0.0635001
$249$	−4.13733	−0.262192
$250$	1.00000	0.0632456
$251$	29.0389	1.83292	0.916459	−	0.400129i	$-0.131035\pi$
$251$	29.0389	1.83292	0.916459	+	0.400129i	$0.131035\pi$
$252$	5.37952	0.338878
$253$	14.4792	0.910299
$254$	−7.27571	−0.456519
$255$	7.69284	0.481745
$256$	1.00000	0.0625000
$257$	8.14669	0.508176	0.254088	−	0.967181i	$-0.418225\pi$
$257$	8.14669	0.508176	0.254088	+	0.967181i	$0.418225\pi$
$258$	−9.07779	−0.565159
$259$	3.11175	0.193355
$260$	−1.00000	−0.0620174
$261$	1.36159	0.0842803
$262$	−12.8456	−0.793605
$263$	6.75253	0.416379	0.208189	−	0.978089i	$-0.433243\pi$
$263$	6.75253	0.416379	0.208189	+	0.978089i	$0.433243\pi$
$264$	−2.15380	−0.132558
$265$	−2.53774	−0.155892
$266$	5.79940	0.355584
$267$	7.16571	0.438535
$268$	−14.6554	−0.895221
$269$	14.7072	0.896714	0.448357	−	0.893855i	$-0.352009\pi$
$269$	14.7072	0.896714	0.448357	+	0.893855i	$0.352009\pi$
$270$	−5.61757	−0.341875
$271$	5.55369	0.337363	0.168681	−	0.985671i	$-0.446049\pi$
$271$	5.55369	0.337363	0.168681	+	0.985671i	$0.446049\pi$
$272$	5.84178	0.354210
$273$	5.59629	0.338703
$274$	6.08125	0.367382
$275$	−1.63555	−0.0986275
$276$	−11.6579	−0.701726
$277$	−19.6416	−1.18015	−0.590075	−	0.807349i	$-0.700902\pi$
$277$	−19.6416	−1.18015	−0.590075	+	0.807349i	$0.700902\pi$
$278$	1.30409	0.0782142
$279$	1.26586	0.0757851
$280$	−4.24970	−0.253968
$281$	5.89827	0.351861	0.175931	−	0.984403i	$-0.443707\pi$
$281$	5.89827	0.351861	0.175931	+	0.984403i	$0.443707\pi$
$282$	0.581513	0.0346286
$283$	−20.4272	−1.21427	−0.607136	−	0.794598i	$-0.707682\pi$
$283$	−20.4272	−1.21427	−0.607136	+	0.794598i	$0.707682\pi$
$284$	−6.52730	−0.387324
$285$	−1.79708	−0.106450
$286$	1.63555	0.0967122
$287$	2.29339	0.135374
$288$	−1.26586	−0.0745915
$289$	17.1263	1.00743
$290$	−1.07562	−0.0631628
$291$	−15.2526	−0.894121
$292$	6.41373	0.375335
$293$	−2.02483	−0.118292	−0.0591460	−	0.998249i	$-0.518838\pi$
$293$	−2.02483	−0.118292	−0.0591460	+	0.998249i	$0.518838\pi$
$294$	14.5645	0.849417
$295$	−5.44241	−0.316869
$296$	−0.732230	−0.0425600
$297$	9.18783	0.533132
$298$	−10.6334	−0.615978
$299$	8.85279	0.511970
$300$	1.31687	0.0760294
$301$	29.2952	1.68855
$302$	11.5419	0.664159
$303$	−1.96440	−0.112852
$304$	−1.36466	−0.0782688
$305$	−2.85872	−0.163690
$306$	−7.39487	−0.422737
$307$	−9.34472	−0.533331	−0.266666	−	0.963789i	$-0.585922\pi$
$307$	−9.34472	−0.533331	−0.266666	+	0.963789i	$0.585922\pi$
$308$	6.95060	0.396047
$309$	−1.31236	−0.0746573
$310$	−1.00000	−0.0567962
$311$	20.7612	1.17726	0.588629	−	0.808403i	$-0.299668\pi$
$311$	20.7612	1.17726	0.588629	+	0.808403i	$0.299668\pi$
$312$	−1.31687	−0.0745529
$313$	22.6328	1.27928	0.639642	−	0.768673i	$-0.279083\pi$
$313$	22.6328	1.27928	0.639642	+	0.768673i	$0.279083\pi$
$314$	−13.2356	−0.746926
$315$	5.37952	0.303102
$316$	7.46507	0.419943
$317$	−15.1836	−0.852798	−0.426399	−	0.904535i	$-0.640218\pi$
$317$	−15.1836	−0.852798	−0.426399	+	0.904535i	$0.640218\pi$
$318$	−3.34186	−0.187402
$319$	1.75924	0.0984985
$320$	1.00000	0.0559017
$321$	5.57179	0.310987
$322$	37.6217	2.09657
$323$	−7.97205	−0.443577
$324$	−3.60002	−0.200001
$325$	−1.00000	−0.0554700
$326$	4.33906	0.240318
$327$	−0.298174	−0.0164891
$328$	−0.539659	−0.0297977
$329$	−1.87662	−0.103461
$330$	−2.15380	−0.118563
$331$	−0.137241	−0.00754347	−0.00377173	−	0.999993i	$-0.501201\pi$
$331$	−0.137241	−0.00754347	−0.00377173	+	0.999993i	$0.501201\pi$
$332$	−3.14179	−0.172428
$333$	0.926900	0.0507938
$334$	−15.1311	−0.827935
$335$	−14.6554	−0.800710
$336$	−5.59629	−0.305303
$337$	32.3526	1.76236	0.881180	−	0.472782i	$-0.156750\pi$
$337$	32.3526	1.76236	0.881180	+	0.472782i	$0.156750\pi$
$338$	1.00000	0.0543928
$339$	26.8839	1.46013
$340$	5.84178	0.316815
$341$	1.63555	0.0885701
$342$	1.72747	0.0934110
$343$	−17.2535	−0.931601
$344$	−6.89347	−0.371671
$345$	−11.6579	−0.627643
$346$	15.5826	0.837726
$347$	−23.0916	−1.23962	−0.619810	−	0.784752i	$-0.712790\pi$
$347$	−23.0916	−1.23962	−0.619810	+	0.784752i	$0.712790\pi$
$348$	−1.41645	−0.0759299
$349$	−1.77815	−0.0951822	−0.0475911	−	0.998867i	$-0.515154\pi$
$349$	−1.77815	−0.0951822	−0.0475911	+	0.998867i	$0.515154\pi$
$350$	−4.24970	−0.227156
$351$	5.61757	0.299844
$352$	−1.63555	−0.0871752
$353$	−20.8353	−1.10895	−0.554476	−	0.832200i	$-0.687081\pi$
$353$	−20.8353	−1.10895	−0.554476	+	0.832200i	$0.687081\pi$
$354$	−7.16693	−0.380918
$355$	−6.52730	−0.346433
$356$	5.44148	0.288398
$357$	−32.6923	−1.73026
$358$	−8.50382	−0.449441
$359$	0.855339	0.0451430	0.0225715	−	0.999745i	$-0.492815\pi$
$359$	0.855339	0.0451430	0.0225715	+	0.999745i	$0.492815\pi$
$360$	−1.26586	−0.0667167
$361$	−17.1377	−0.901984
$362$	−22.8796	−1.20252
$363$	−10.9629	−0.575402
$364$	4.24970	0.222745
$365$	6.41373	0.335710
$366$	−3.76456	−0.196777
$367$	−20.9617	−1.09419	−0.547096	−	0.837070i	$-0.684267\pi$
$367$	−20.9617	−1.09419	−0.547096	+	0.837070i	$0.684267\pi$
$368$	−8.85279	−0.461483
$369$	0.683133	0.0355625
$370$	−0.732230	−0.0380668
$371$	10.7846	0.559910
$372$	−1.31687	−0.0682764
$373$	−3.11332	−0.161202	−0.0806009	−	0.996746i	$-0.525684\pi$
$373$	−3.11332	−0.161202	−0.0806009	+	0.996746i	$0.525684\pi$
$374$	−9.55453	−0.494053
$375$	1.31687	0.0680027
$376$	0.441588	0.0227732
$377$	1.07562	0.0553975
$378$	23.8730	1.22789
$379$	6.28867	0.323027	0.161514	−	0.986870i	$-0.448362\pi$
$379$	6.28867	0.323027	0.161514	+	0.986870i	$0.448362\pi$
$380$	−1.36466	−0.0700057
$381$	−9.58114	−0.490857
$382$	19.9270	1.01956
$383$	−25.5880	−1.30748	−0.653742	−	0.756717i	$-0.726802\pi$
$383$	−25.5880	−1.30748	−0.653742	+	0.756717i	$0.726802\pi$
$384$	1.31687	0.0672011
$385$	6.95060	0.354235
$386$	20.4505	1.04090
$387$	8.72618	0.443577
$388$	−11.5825	−0.588010
$389$	22.9613	1.16419	0.582093	−	0.813122i	$-0.302234\pi$
$389$	22.9613	1.16419	0.582093	+	0.813122i	$0.302234\pi$
$390$	−1.31687	−0.0666822
$391$	−51.7160	−2.61539
$392$	11.0599	0.558611
$393$	−16.9160	−0.853299
$394$	−11.9508	−0.602073
$395$	7.46507	0.375608
$396$	2.07038	0.104041
$397$	−35.6969	−1.79157	−0.895787	−	0.444484i	$-0.853387\pi$
$397$	−35.6969	−1.79157	−0.895787	+	0.444484i	$0.853387\pi$
$398$	7.42917	0.372391
$399$	7.63705	0.382331
$400$	1.00000	0.0500000
$401$	−16.1902	−0.808500	−0.404250	−	0.914648i	$-0.632467\pi$
$401$	−16.1902	−0.808500	−0.404250	+	0.914648i	$0.632467\pi$
$402$	−19.2992	−0.962557
$403$	1.00000	0.0498135
$404$	−1.49173	−0.0742161
$405$	−3.60002	−0.178886
$406$	4.57108	0.226859
$407$	1.19760	0.0593628
$408$	7.69284	0.380853
$409$	−8.66847	−0.428628	−0.214314	−	0.976765i	$-0.568752\pi$
$409$	−8.66847	−0.428628	−0.214314	+	0.976765i	$0.568752\pi$
$410$	−0.539659	−0.0266518
$411$	8.00820	0.395015
$412$	−0.996574	−0.0490977
$413$	23.1286	1.13808
$414$	11.2064	0.550764
$415$	−3.14179	−0.154225
$416$	−1.00000	−0.0490290
$417$	1.71731	0.0840973
$418$	2.23198	0.109170
$419$	30.4746	1.48878	0.744392	−	0.667743i	$-0.232739\pi$
$419$	30.4746	1.48878	0.744392	+	0.667743i	$0.232739\pi$
$420$	−5.59629	−0.273071
$421$	−4.68321	−0.228246	−0.114123	−	0.993467i	$-0.536406\pi$
$421$	−4.68321	−0.228246	−0.114123	+	0.993467i	$0.536406\pi$
$422$	6.15526	0.299633
$423$	−0.558989	−0.0271790
$424$	−2.53774	−0.123243
$425$	5.84178	0.283368
$426$	−8.59558	−0.416457
$427$	12.1487	0.587917
$428$	4.23110	0.204518
$429$	2.15380	0.103987
$430$	−6.89347	−0.332433
$431$	−5.27517	−0.254096	−0.127048	−	0.991897i	$-0.540550\pi$
$431$	−5.27517	−0.254096	−0.127048	+	0.991897i	$0.540550\pi$
$432$	−5.61757	−0.270276
$433$	−3.40726	−0.163742	−0.0818712	−	0.996643i	$-0.526090\pi$
$433$	−3.40726	−0.163742	−0.0818712	+	0.996643i	$0.526090\pi$
$434$	4.24970	0.203992
$435$	−1.41645	−0.0679138
$436$	−0.226427	−0.0108439
$437$	12.0811	0.577916
$438$	8.44603	0.403567
$439$	11.6834	0.557619	0.278809	−	0.960346i	$-0.410060\pi$
$439$	11.6834	0.557619	0.278809	+	0.960346i	$0.410060\pi$
$440$	−1.63555	−0.0779719
$441$	−14.0003	−0.666683
$442$	−5.84178	−0.277865
$443$	11.5251	0.547575	0.273787	−	0.961790i	$-0.411724\pi$
$443$	11.5251	0.547575	0.273787	+	0.961790i	$0.411724\pi$
$444$	−0.964249	−0.0457612
$445$	5.44148	0.257951
$446$	4.42273	0.209422
$447$	−14.0028	−0.662310
$448$	−4.24970	−0.200779
$449$	1.44577	0.0682302	0.0341151	−	0.999418i	$-0.489139\pi$
$449$	1.44577	0.0682302	0.0341151	+	0.999418i	$0.489139\pi$
$450$	−1.26586	−0.0596732
$451$	0.882640	0.0415619
$452$	20.4151	0.960243
$453$	15.1991	0.714116
$454$	1.26465	0.0593531
$455$	4.24970	0.199229
$456$	−1.79708	−0.0841560
$457$	15.8896	0.743282	0.371641	−	0.928377i	$-0.378795\pi$
$457$	15.8896	0.743282	0.371641	+	0.928377i	$0.378795\pi$
$458$	−7.15824	−0.334483
$459$	−32.8166	−1.53175
$460$	−8.85279	−0.412763
$461$	−36.2495	−1.68831	−0.844154	−	0.536101i	$-0.819897\pi$
$461$	−36.2495	−1.68831	−0.844154	+	0.536101i	$0.819897\pi$
$462$	9.15302	0.425837
$463$	9.40205	0.436950	0.218475	−	0.975843i	$-0.429892\pi$
$463$	9.40205	0.436950	0.218475	+	0.975843i	$0.429892\pi$
$464$	−1.07562	−0.0499346
$465$	−1.31687	−0.0610683
$466$	19.9127	0.922437
$467$	23.6946	1.09646	0.548229	−	0.836328i	$-0.315302\pi$
$467$	23.6946	1.09646	0.548229	+	0.836328i	$0.315302\pi$
$468$	1.26586	0.0585144
$469$	62.2810	2.87587
$470$	0.441588	0.0203689
$471$	−17.4295	−0.803108
$472$	−5.44241	−0.250507
$473$	11.2746	0.518408
$474$	9.83050	0.451530
$475$	−1.36466	−0.0626150
$476$	−24.8258	−1.13789
$477$	3.21242	0.147087
$478$	22.8344	1.04442
$479$	−25.6428	−1.17165	−0.585824	−	0.810438i	$-0.699229\pi$
$479$	−25.6428	−1.17165	−0.585824	+	0.810438i	$0.699229\pi$
$480$	1.31687	0.0601065
$481$	0.732230	0.0333868
$482$	6.09812	0.277762
$483$	49.5428	2.25427
$484$	−8.32497	−0.378408
$485$	−11.5825	−0.525932
$486$	12.1120	0.549410
$487$	−6.36470	−0.288412	−0.144206	−	0.989548i	$-0.546063\pi$
$487$	−6.36470	−0.288412	−0.144206	+	0.989548i	$0.546063\pi$
$488$	−2.85872	−0.129408
$489$	5.71396	0.258394
$490$	11.0599	0.499637
$491$	19.0427	0.859386	0.429693	−	0.902975i	$-0.358622\pi$
$491$	19.0427	0.859386	0.429693	+	0.902975i	$0.358622\pi$
$492$	−0.710659	−0.0320390
$493$	−6.28355	−0.282997
$494$	1.36466	0.0613991
$495$	2.07038	0.0930567
$496$	−1.00000	−0.0449013
$497$	27.7390	1.24427
$498$	−4.13733	−0.185398
$499$	−20.5496	−0.919927	−0.459963	−	0.887938i	$-0.652137\pi$
$499$	−20.5496	−0.919927	−0.459963	+	0.887938i	$0.652137\pi$
$500$	1.00000	0.0447214
$501$	−19.9256	−0.890211
$502$	29.0389	1.29607
$503$	−0.291564	−0.0130002	−0.00650010	−	0.999979i	$-0.502069\pi$
$503$	−0.291564	−0.0130002	−0.00650010	+	0.999979i	$0.502069\pi$
$504$	5.37952	0.239623
$505$	−1.49173	−0.0663809
$506$	14.4792	0.643679
$507$	1.31687	0.0584841
$508$	−7.27571	−0.322807
$509$	−37.3588	−1.65590	−0.827950	−	0.560802i	$-0.810493\pi$
$509$	−37.3588	−1.65590	−0.827950	+	0.560802i	$0.810493\pi$
$510$	7.69284	0.340645
$511$	−27.2564	−1.20575
$512$	1.00000	0.0441942
$513$	7.66609	0.338466
$514$	8.14669	0.359335
$515$	−0.996574	−0.0439143
$516$	−9.07779	−0.399627
$517$	−0.722240	−0.0317641
$518$	3.11175	0.136723
$519$	20.5202	0.900738
$520$	−1.00000	−0.0438529
$521$	4.92065	0.215578	0.107789	−	0.994174i	$-0.465623\pi$
$521$	4.92065	0.215578	0.107789	+	0.994174i	$0.465623\pi$
$522$	1.36159	0.0595952
$523$	−8.56619	−0.374573	−0.187287	−	0.982305i	$-0.559969\pi$
$523$	−8.56619	−0.374573	−0.187287	+	0.982305i	$0.559969\pi$
$524$	−12.8456	−0.561164
$525$	−5.59629	−0.244242
$526$	6.75253	0.294424
$527$	−5.84178	−0.254472
$528$	−2.15380	−0.0937323
$529$	55.3719	2.40747
$530$	−2.53774	−0.110232
$531$	6.88933	0.298971
$532$	5.79940	0.251436
$533$	0.539659	0.0233752
$534$	7.16571	0.310091
$535$	4.23110	0.182926
$536$	−14.6554	−0.633017
$537$	−11.1984	−0.483247
$538$	14.7072	0.634072
$539$	−18.0891	−0.779153
$540$	−5.61757	−0.241742
$541$	15.6057	0.670943	0.335472	−	0.942050i	$-0.391104\pi$
$541$	15.6057	0.670943	0.335472	+	0.942050i	$0.391104\pi$
$542$	5.55369	0.238551
$543$	−30.1294	−1.29298
$544$	5.84178	0.250464
$545$	−0.226427	−0.00969907
$546$	5.59629	0.239499
$547$	9.90466	0.423493	0.211746	−	0.977325i	$-0.432085\pi$
$547$	9.90466	0.423493	0.211746	+	0.977325i	$0.432085\pi$
$548$	6.08125	0.259778
$549$	3.61874	0.154444
$550$	−1.63555	−0.0697402
$551$	1.46786	0.0625331
$552$	−11.6579	−0.496195
$553$	−31.7243	−1.34905
$554$	−19.6416	−0.834492
$555$	−0.964249	−0.0409301
$556$	1.30409	0.0553058
$557$	−22.3730	−0.947976	−0.473988	−	0.880531i	$-0.657186\pi$
$557$	−22.3730	−0.947976	−0.473988	+	0.880531i	$0.657186\pi$
$558$	1.26586	0.0535881
$559$	6.89347	0.291563
$560$	−4.24970	−0.179583
$561$	−12.5820	−0.531214
$562$	5.89827	0.248803
$563$	−27.7549	−1.16973	−0.584865	−	0.811131i	$-0.698852\pi$
$563$	−27.7549	−1.16973	−0.584865	+	0.811131i	$0.698852\pi$
$564$	0.581513	0.0244861
$565$	20.4151	0.858868
$566$	−20.4272	−0.858620
$567$	15.2990	0.642497
$568$	−6.52730	−0.273879
$569$	−29.3630	−1.23096	−0.615480	−	0.788153i	$-0.711038\pi$
$569$	−29.3630	−1.23096	−0.615480	+	0.788153i	$0.711038\pi$
$570$	−1.79708	−0.0752714
$571$	−22.9484	−0.960362	−0.480181	−	0.877169i	$-0.659429\pi$
$571$	−22.9484	−0.960362	−0.480181	+	0.877169i	$0.659429\pi$
$572$	1.63555	0.0683859
$573$	26.2412	1.09624
$574$	2.29339	0.0957241
$575$	−8.85279	−0.369187
$576$	−1.26586	−0.0527442
$577$	−47.0614	−1.95919	−0.979596	−	0.200976i	$-0.935589\pi$
$577$	−47.0614	−1.95919	−0.979596	+	0.200976i	$0.935589\pi$
$578$	17.1263	0.712362
$579$	26.9306	1.11920
$580$	−1.07562	−0.0446629
$581$	13.3517	0.553921
$582$	−15.2526	−0.632239
$583$	4.15060	0.171900
$584$	6.41373	0.265402
$585$	1.26586	0.0523369
$586$	−2.02483	−0.0836450
$587$	12.7130	0.524723	0.262361	−	0.964970i	$-0.415499\pi$
$587$	12.7130	0.524723	0.262361	+	0.964970i	$0.415499\pi$
$588$	14.5645	0.600628
$589$	1.36466	0.0562300
$590$	−5.44241	−0.224060
$591$	−15.7376	−0.647360
$592$	−0.732230	−0.0300944
$593$	38.3439	1.57460	0.787298	−	0.616572i	$-0.211479\pi$
$593$	38.3439	1.57460	0.787298	+	0.616572i	$0.211479\pi$
$594$	9.18783	0.376981
$595$	−24.8258	−1.01776
$596$	−10.6334	−0.435562
$597$	9.78323	0.400401
$598$	8.85279	0.362017
$599$	−1.69246	−0.0691522	−0.0345761	−	0.999402i	$-0.511008\pi$
$599$	−1.69246	−0.0691522	−0.0345761	+	0.999402i	$0.511008\pi$
$600$	1.31687	0.0537609
$601$	−32.0517	−1.30742	−0.653709	−	0.756746i	$-0.726788\pi$
$601$	−32.0517	−1.30742	−0.653709	+	0.756746i	$0.726788\pi$
$602$	29.2952	1.19398
$603$	18.5517	0.755483
$604$	11.5419	0.469631
$605$	−8.32497	−0.338458
$606$	−1.96440	−0.0797985
$607$	−13.1176	−0.532427	−0.266213	−	0.963914i	$-0.585773\pi$
$607$	−13.1176	−0.532427	−0.266213	+	0.963914i	$0.585773\pi$
$608$	−1.36466	−0.0553444
$609$	6.01950	0.243923
$610$	−2.85872	−0.115746
$611$	−0.441588	−0.0178647
$612$	−7.39487	−0.298920
$613$	−22.4350	−0.906141	−0.453070	−	0.891475i	$-0.649671\pi$
$613$	−22.4350	−0.906141	−0.453070	+	0.891475i	$0.649671\pi$
$614$	−9.34472	−0.377122
$615$	−0.710659	−0.0286565
$616$	6.95060	0.280048
$617$	−19.5478	−0.786964	−0.393482	−	0.919332i	$-0.628730\pi$
$617$	−19.5478	−0.786964	−0.393482	+	0.919332i	$0.628730\pi$
$618$	−1.31236	−0.0527907
$619$	20.9883	0.843591	0.421796	−	0.906691i	$-0.361400\pi$
$619$	20.9883	0.843591	0.421796	+	0.906691i	$0.361400\pi$
$620$	−1.00000	−0.0401610
$621$	49.7312	1.99564
$622$	20.7612	0.832447
$623$	−23.1247	−0.926470
$624$	−1.31687	−0.0527169
$625$	1.00000	0.0400000
$626$	22.6328	0.904590
$627$	2.93922	0.117381
$628$	−13.2356	−0.528156
$629$	−4.27752	−0.170556
$630$	5.37952	0.214325
$631$	−47.9128	−1.90738	−0.953688	−	0.300797i	$-0.902747\pi$
$631$	−47.9128	−1.90738	−0.953688	+	0.300797i	$0.902747\pi$
$632$	7.46507	0.296944
$633$	8.10566	0.322171
$634$	−15.1836	−0.603020
$635$	−7.27571	−0.288728
$636$	−3.34186	−0.132514
$637$	−11.0599	−0.438211
$638$	1.75924	0.0696489
$639$	8.26265	0.326865
$640$	1.00000	0.0395285
$641$	−49.8617	−1.96942	−0.984710	−	0.174204i	$-0.944265\pi$
$641$	−49.8617	−1.96942	−0.984710	+	0.174204i	$0.944265\pi$
$642$	5.57179	0.219901
$643$	12.7317	0.502088	0.251044	−	0.967976i	$-0.419226\pi$
$643$	12.7317	0.502088	0.251044	+	0.967976i	$0.419226\pi$
$644$	37.6217	1.48250
$645$	−9.07779	−0.357438
$646$	−7.97205	−0.313656
$647$	−14.2706	−0.561037	−0.280518	−	0.959849i	$-0.590506\pi$
$647$	−14.2706	−0.561037	−0.280518	+	0.959849i	$0.590506\pi$
$648$	−3.60002	−0.141422
$649$	8.90134	0.349408
$650$	−1.00000	−0.0392232
$651$	5.59629	0.219336
$652$	4.33906	0.169931
$653$	8.56611	0.335218	0.167609	−	0.985854i	$-0.446395\pi$
$653$	8.56611	0.335218	0.167609	+	0.985854i	$0.446395\pi$
$654$	−0.298174	−0.0116595
$655$	−12.8456	−0.501920
$656$	−0.539659	−0.0210701
$657$	−8.11889	−0.316748
$658$	−1.87662	−0.0731581
$659$	24.3922	0.950185	0.475093	−	0.879936i	$-0.342415\pi$
$659$	24.3922	0.950185	0.475093	+	0.879936i	$0.342415\pi$
$660$	−2.15380	−0.0838367
$661$	−10.6153	−0.412886	−0.206443	−	0.978459i	$-0.566189\pi$
$661$	−10.6153	−0.412886	−0.206443	+	0.978459i	$0.566189\pi$
$662$	−0.137241	−0.00533404
$663$	−7.69284	−0.298765
$664$	−3.14179	−0.121925
$665$	5.79940	0.224891
$666$	0.926900	0.0359167
$667$	9.52227	0.368704
$668$	−15.1311	−0.585439
$669$	5.82415	0.225175
$670$	−14.6554	−0.566187
$671$	4.67559	0.180499
$672$	−5.59629	−0.215882
$673$	−12.9891	−0.500692	−0.250346	−	0.968156i	$-0.580544\pi$
$673$	−12.9891	−0.500692	−0.250346	+	0.968156i	$0.580544\pi$
$674$	32.3526	1.24618
$675$	−5.61757	−0.216220
$676$	1.00000	0.0384615
$677$	5.64628	0.217004	0.108502	−	0.994096i	$-0.465395\pi$
$677$	5.64628	0.217004	0.108502	+	0.994096i	$0.465395\pi$
$678$	26.8839	1.03247
$679$	49.2220	1.88897
$680$	5.84178	0.224022
$681$	1.66538	0.0638175
$682$	1.63555	0.0626285
$683$	−22.6184	−0.865467	−0.432734	−	0.901522i	$-0.642451\pi$
$683$	−22.6184	−0.865467	−0.432734	+	0.901522i	$0.642451\pi$
$684$	1.72747	0.0660516
$685$	6.08125	0.232352
$686$	−17.2535	−0.658741
$687$	−9.42645	−0.359642
$688$	−6.89347	−0.262811
$689$	2.53774	0.0966801
$690$	−11.6579	−0.443810
$691$	−10.7777	−0.410004	−0.205002	−	0.978762i	$-0.565720\pi$
$691$	−10.7777	−0.410004	−0.205002	+	0.978762i	$0.565720\pi$
$692$	15.5826	0.592362
$693$	−8.79849	−0.334227
$694$	−23.0916	−0.876543
$695$	1.30409	0.0494670
$696$	−1.41645	−0.0536906
$697$	−3.15257	−0.119412
$698$	−1.77815	−0.0673040
$699$	26.2224	0.991821
$700$	−4.24970	−0.160623
$701$	−2.27697	−0.0860000	−0.0430000	−	0.999075i	$-0.513692\pi$
$701$	−2.27697	−0.0860000	−0.0430000	+	0.999075i	$0.513692\pi$
$702$	5.61757	0.212022
$703$	0.999246	0.0376873
$704$	−1.63555	−0.0616422
$705$	0.581513	0.0219010
$706$	−20.8353	−0.784147
$707$	6.33938	0.238417
$708$	−7.16693	−0.269350
$709$	−4.41064	−0.165645	−0.0828225	−	0.996564i	$-0.526393\pi$
$709$	−4.41064	−0.165645	−0.0828225	+	0.996564i	$0.526393\pi$
$710$	−6.52730	−0.244965
$711$	−9.44974	−0.354393
$712$	5.44148	0.203928
$713$	8.85279	0.331540
$714$	−32.6923	−1.22348
$715$	1.63555	0.0611662
$716$	−8.50382	−0.317803
$717$	30.0698	1.12298
$718$	0.855339	0.0319210
$719$	27.6016	1.02936	0.514682	−	0.857381i	$-0.327910\pi$
$719$	27.6016	1.02936	0.514682	+	0.857381i	$0.327910\pi$
$720$	−1.26586	−0.0471758
$721$	4.23514	0.157725
$722$	−17.1377	−0.637799
$723$	8.03041	0.298654
$724$	−22.8796	−0.850314
$725$	−1.07562	−0.0399477
$726$	−10.9629	−0.406871
$727$	29.7170	1.10214	0.551072	−	0.834458i	$-0.314219\pi$
$727$	29.7170	1.10214	0.551072	+	0.834458i	$0.314219\pi$
$728$	4.24970	0.157504
$729$	26.7499	0.990737
$730$	6.41373	0.237383
$731$	−40.2701	−1.48944
$732$	−3.76456	−0.139142
$733$	12.7669	0.471556	0.235778	−	0.971807i	$-0.424236\pi$
$733$	12.7669	0.471556	0.235778	+	0.971807i	$0.424236\pi$
$734$	−20.9617	−0.773711
$735$	14.5645	0.537218
$736$	−8.85279	−0.326318
$737$	23.9697	0.882934
$738$	0.683133	0.0251465
$739$	−14.9878	−0.551335	−0.275667	−	0.961253i	$-0.588899\pi$
$739$	−14.9878	−0.551335	−0.275667	+	0.961253i	$0.588899\pi$
$740$	−0.732230	−0.0269173
$741$	1.79708	0.0660174
$742$	10.7846	0.395916
$743$	−10.6023	−0.388962	−0.194481	−	0.980906i	$-0.562302\pi$
$743$	−10.6023	−0.388962	−0.194481	+	0.980906i	$0.562302\pi$
$744$	−1.31687	−0.0482787
$745$	−10.6334	−0.389578
$746$	−3.11332	−0.113987
$747$	3.97707	0.145513
$748$	−9.55453	−0.349348
$749$	−17.9809	−0.657007
$750$	1.31687	0.0480852
$751$	44.4571	1.62226	0.811131	−	0.584865i	$-0.198853\pi$
$751$	44.4571	1.62226	0.811131	+	0.584865i	$0.198853\pi$
$752$	0.441588	0.0161031
$753$	38.2404	1.39356
$754$	1.07562	0.0391719
$755$	11.5419	0.420051
$756$	23.8730	0.868252
$757$	25.5770	0.929613	0.464807	−	0.885412i	$-0.346124\pi$
$757$	25.5770	0.929613	0.464807	+	0.885412i	$0.346124\pi$
$758$	6.28867	0.228415
$759$	19.0672	0.692095
$760$	−1.36466	−0.0495015
$761$	35.6999	1.29412	0.647060	−	0.762439i	$-0.275998\pi$
$761$	35.6999	1.29412	0.647060	+	0.762439i	$0.275998\pi$
$762$	−9.58114	−0.347088
$763$	0.962246	0.0348357
$764$	19.9270	0.720934
$765$	−7.39487	−0.267362
$766$	−25.5880	−0.924531
$767$	5.44241	0.196514
$768$	1.31687	0.0475184
$769$	21.9419	0.791245	0.395623	−	0.918413i	$-0.370529\pi$
$769$	21.9419	0.791245	0.395623	+	0.918413i	$0.370529\pi$
$770$	6.95060	0.250482
$771$	10.7281	0.386363
$772$	20.4505	0.736030
$773$	31.4192	1.13007	0.565034	−	0.825067i	$-0.308863\pi$
$773$	31.4192	1.13007	0.565034	+	0.825067i	$0.308863\pi$
$774$	8.72618	0.313656
$775$	−1.00000	−0.0359211
$776$	−11.5825	−0.415786
$777$	4.09777	0.147007
$778$	22.9613	0.823204
$779$	0.736452	0.0263861
$780$	−1.31687	−0.0471514
$781$	10.6757	0.382008
$782$	−51.7160	−1.84936
$783$	6.04240	0.215938
$784$	11.0599	0.394998
$785$	−13.2356	−0.472397
$786$	−16.9160	−0.603373
$787$	15.2721	0.544390	0.272195	−	0.962242i	$-0.412250\pi$
$787$	15.2721	0.544390	0.272195	+	0.962242i	$0.412250\pi$
$788$	−11.9508	−0.425730
$789$	8.89219	0.316570
$790$	7.46507	0.265595
$791$	−86.7578	−3.08475
$792$	2.07038	0.0735678
$793$	2.85872	0.101516
$794$	−35.6969	−1.26683
$795$	−3.34186	−0.118524
$796$	7.42917	0.263320
$797$	−22.9610	−0.813321	−0.406660	−	0.913579i	$-0.633307\pi$
$797$	−22.9610	−0.813321	−0.406660	+	0.913579i	$0.633307\pi$
$798$	7.63705	0.270349
$799$	2.57966	0.0912618
$800$	1.00000	0.0353553
$801$	−6.88816	−0.243381
$802$	−16.1902	−0.571696
$803$	−10.4900	−0.370184
$804$	−19.2992	−0.680631
$805$	37.6217	1.32599
$806$	1.00000	0.0352235
$807$	19.3674	0.681766
$808$	−1.49173	−0.0524787
$809$	−25.8934	−0.910363	−0.455181	−	0.890399i	$-0.650426\pi$
$809$	−25.8934	−0.910363	−0.455181	+	0.890399i	$0.650426\pi$
$810$	−3.60002	−0.126492
$811$	36.6235	1.28603	0.643013	−	0.765855i	$-0.277684\pi$
$811$	36.6235	1.28603	0.643013	+	0.765855i	$0.277684\pi$
$812$	4.57108	0.160413
$813$	7.31347	0.256495
$814$	1.19760	0.0419758
$815$	4.33906	0.151991
$816$	7.69284	0.269303
$817$	9.40727	0.329119
$818$	−8.66847	−0.303086
$819$	−5.37952	−0.187976
$820$	−0.539659	−0.0188457
$821$	−10.6509	−0.371719	−0.185859	−	0.982576i	$-0.559507\pi$
$821$	−10.6509	−0.371719	−0.185859	+	0.982576i	$0.559507\pi$
$822$	8.00820	0.279318
$823$	−17.7429	−0.618479	−0.309239	−	0.950984i	$-0.600074\pi$
$823$	−17.7429	−0.618479	−0.309239	+	0.950984i	$0.600074\pi$
$824$	−0.996574	−0.0347173
$825$	−2.15380	−0.0749859
$826$	23.1286	0.804746
$827$	5.18310	0.180234	0.0901171	−	0.995931i	$-0.471276\pi$
$827$	5.18310	0.180234	0.0901171	+	0.995931i	$0.471276\pi$
$828$	11.2064	0.389449
$829$	26.1239	0.907320	0.453660	−	0.891175i	$-0.350118\pi$
$829$	26.1239	0.907320	0.453660	+	0.891175i	$0.350118\pi$
$830$	−3.14179	−0.109053
$831$	−25.8654	−0.897260
$832$	−1.00000	−0.0346688
$833$	64.6097	2.23859
$834$	1.71731	0.0594657
$835$	−15.1311	−0.523632
$836$	2.23198	0.0771945
$837$	5.61757	0.194172
$838$	30.4746	1.05273
$839$	4.81426	0.166207	0.0831033	−	0.996541i	$-0.473517\pi$
$839$	4.81426	0.166207	0.0831033	+	0.996541i	$0.473517\pi$
$840$	−5.59629	−0.193090
$841$	−27.8430	−0.960105
$842$	−4.68321	−0.161394
$843$	7.76724	0.267518
$844$	6.15526	0.211873
$845$	1.00000	0.0344010
$846$	−0.558989	−0.0192184
$847$	35.3786	1.21562
$848$	−2.53774	−0.0871463
$849$	−26.8999	−0.923203
$850$	5.84178	0.200371
$851$	6.48227	0.222209
$852$	−8.59558	−0.294480
$853$	−11.9418	−0.408879	−0.204439	−	0.978879i	$-0.565537\pi$
$853$	−11.9418	−0.408879	−0.204439	+	0.978879i	$0.565537\pi$
$854$	12.1487	0.415720
$855$	1.72747	0.0590783
$856$	4.23110	0.144616
$857$	−36.3955	−1.24325	−0.621623	−	0.783316i	$-0.713527\pi$
$857$	−36.3955	−1.24325	−0.621623	+	0.783316i	$0.713527\pi$
$858$	2.15380	0.0735297
$859$	−6.89472	−0.235245	−0.117622	−	0.993058i	$-0.537527\pi$
$859$	−6.89472	−0.235245	−0.117622	+	0.993058i	$0.537527\pi$
$860$	−6.89347	−0.235066
$861$	3.02009	0.102924
$862$	−5.27517	−0.179673
$863$	51.2032	1.74298	0.871489	−	0.490414i	$-0.163155\pi$
$863$	51.2032	1.74298	0.871489	+	0.490414i	$0.163155\pi$
$864$	−5.61757	−0.191114
$865$	15.5826	0.529825
$866$	−3.40726	−0.115783
$867$	22.5531	0.765944
$868$	4.24970	0.144244
$869$	−12.2095	−0.414179
$870$	−1.41645	−0.0480223
$871$	14.6554	0.496579
$872$	−0.226427	−0.00766779
$873$	14.6618	0.496226
$874$	12.0811	0.408648
$875$	−4.24970	−0.143666
$876$	8.44603	0.285365
$877$	−24.1459	−0.815350	−0.407675	−	0.913127i	$-0.633660\pi$
$877$	−24.1459	−0.815350	−0.407675	+	0.913127i	$0.633660\pi$
$878$	11.6834	0.394296
$879$	−2.66643	−0.0899366
$880$	−1.63555	−0.0551344
$881$	43.6759	1.47148	0.735740	−	0.677264i	$-0.236835\pi$
$881$	43.6759	1.47148	0.735740	+	0.677264i	$0.236835\pi$
$882$	−14.0003	−0.471416
$883$	17.6594	0.594286	0.297143	−	0.954833i	$-0.403966\pi$
$883$	17.6594	0.594286	0.297143	+	0.954833i	$0.403966\pi$
$884$	−5.84178	−0.196480
$885$	−7.16693	−0.240914
$886$	11.5251	0.387194
$887$	−30.5114	−1.02447	−0.512236	−	0.858845i	$-0.671183\pi$
$887$	−30.5114	−1.02447	−0.512236	+	0.858845i	$0.671183\pi$
$888$	−0.964249	−0.0323581
$889$	30.9196	1.03701
$890$	5.44148	0.182399
$891$	5.88801	0.197256
$892$	4.42273	0.148084
$893$	−0.602619	−0.0201659
$894$	−14.0028	−0.468324
$895$	−8.50382	−0.284251
$896$	−4.24970	−0.141972
$897$	11.6579	0.389248
$898$	1.44577	0.0482461
$899$	1.07562	0.0358741
$900$	−1.26586	−0.0421953
$901$	−14.8249	−0.493889
$902$	0.882640	0.0293887
$903$	38.5779	1.28379
$904$	20.4151	0.678995
$905$	−22.8796	−0.760544
$906$	15.1991	0.504956
$907$	−37.0395	−1.22988	−0.614939	−	0.788575i	$-0.710819\pi$
$907$	−37.0395	−1.22988	−0.614939	+	0.788575i	$0.710819\pi$
$908$	1.26465	0.0419690
$909$	1.88832	0.0626315
$910$	4.24970	0.140876
$911$	−56.5255	−1.87277	−0.936386	−	0.350972i	$-0.885851\pi$
$911$	−56.5255	−1.87277	−0.936386	+	0.350972i	$0.885851\pi$
$912$	−1.79708	−0.0595073
$913$	5.13857	0.170062
$914$	15.8896	0.525580
$915$	−3.76456	−0.124452
$916$	−7.15824	−0.236515
$917$	54.5900	1.80272
$918$	−32.8166	−1.08311
$919$	−17.7815	−0.586559	−0.293280	−	0.956027i	$-0.594747\pi$
$919$	−17.7815	−0.586559	−0.293280	+	0.956027i	$0.594747\pi$
$920$	−8.85279	−0.291868
$921$	−12.3058	−0.405488
$922$	−36.2495	−1.19381
$923$	6.52730	0.214849
$924$	9.15302	0.301112
$925$	−0.732230	−0.0240756
$926$	9.40205	0.308970
$927$	1.26152	0.0414339
$928$	−1.07562	−0.0353091
$929$	−29.8942	−0.980796	−0.490398	−	0.871499i	$-0.663149\pi$
$929$	−29.8942	−0.980796	−0.490398	+	0.871499i	$0.663149\pi$
$930$	−1.31687	−0.0431818
$931$	−15.0931	−0.494656
$932$	19.9127	0.652262
$933$	27.3397	0.895062
$934$	23.6946	0.775312
$935$	−9.55453	−0.312466
$936$	1.26586	0.0413759
$937$	−40.2854	−1.31607	−0.658034	−	0.752988i	$-0.728612\pi$
$937$	−40.2854	−1.31607	−0.658034	+	0.752988i	$0.728612\pi$
$938$	62.2810	2.03355
$939$	29.8044	0.972631
$940$	0.441588	0.0144030
$941$	28.8611	0.940844	0.470422	−	0.882442i	$-0.344102\pi$
$941$	28.8611	0.940844	0.470422	+	0.882442i	$0.344102\pi$
$942$	−17.4295	−0.567883
$943$	4.77748	0.155576
$944$	−5.44241	−0.177135
$945$	23.8730	0.776588
$946$	11.2746	0.366570
$947$	39.6657	1.28896	0.644481	−	0.764620i	$-0.277073\pi$
$947$	39.6657	1.28896	0.644481	+	0.764620i	$0.277073\pi$
$948$	9.83050	0.319280
$949$	−6.41373	−0.208198
$950$	−1.36466	−0.0442755
$951$	−19.9948	−0.648377
$952$	−24.8258	−0.804608
$953$	10.3302	0.334627	0.167313	−	0.985904i	$-0.446491\pi$
$953$	10.3302	0.334627	0.167313	+	0.985904i	$0.446491\pi$
$954$	3.21242	0.104006
$955$	19.9270	0.644823
$956$	22.8344	0.738516
$957$	2.31668	0.0748878
$958$	−25.6428	−0.828481
$959$	−25.8435	−0.834529
$960$	1.31687	0.0425017
$961$	1.00000	0.0322581
$962$	0.732230	0.0236080
$963$	−5.35598	−0.172594
$964$	6.09812	0.196407
$965$	20.4505	0.658325
$966$	49.5428	1.59401
$967$	36.1221	1.16161	0.580805	−	0.814043i	$-0.302738\pi$
$967$	36.1221	1.16161	0.580805	+	0.814043i	$0.302738\pi$
$968$	−8.32497	−0.267575
$969$	−10.4981	−0.337249
$970$	−11.5825	−0.371890
$971$	6.43955	0.206655	0.103327	−	0.994647i	$-0.467051\pi$
$971$	6.43955	0.206655	0.103327	+	0.994647i	$0.467051\pi$
$972$	12.1120	0.388492
$973$	−5.54199	−0.177668
$974$	−6.36470	−0.203938
$975$	−1.31687	−0.0421735
$976$	−2.85872	−0.0915055
$977$	−3.08551	−0.0987141	−0.0493570	−	0.998781i	$-0.515717\pi$
$977$	−3.08551	−0.0987141	−0.0493570	+	0.998781i	$0.515717\pi$
$978$	5.71396	0.182712
$979$	−8.89983	−0.284440
$980$	11.0599	0.353297
$981$	0.286625	0.00915123
$982$	19.0427	0.607678
$983$	−14.2207	−0.453569	−0.226784	−	0.973945i	$-0.572821\pi$
$983$	−14.2207	−0.453569	−0.226784	+	0.973945i	$0.572821\pi$
$984$	−0.710659	−0.0226550
$985$	−11.9508	−0.380785
$986$	−6.28355	−0.200109
$987$	−2.47125	−0.0786609
$988$	1.36466	0.0434157
$989$	61.0265	1.94053
$990$	2.07038	0.0658010
$991$	62.6965	1.99162	0.995810	−	0.0914478i	$-0.0291495\pi$
$991$	62.6965	1.99162	0.995810	+	0.0914478i	$0.0291495\pi$
$992$	−1.00000	−0.0317500
$993$	−0.180729	−0.00573525
$994$	27.7390	0.879829
$995$	7.42917	0.235521
$996$	−4.13733	−0.131096
$997$	−35.5398	−1.12556	−0.562779	−	0.826607i	$-0.690268\pi$
$997$	−35.5398	−1.12556	−0.562779	+	0.826607i	$0.690268\pi$
$998$	−20.5496	−0.650486
$999$	4.11335	0.130141

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.g.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.g.1.5	✓	6	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.31687 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.31687 q^{6} -4.24970 q^{7} +1.00000 q^{8} -1.26586 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.31687 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.31687 q^{6} -4.24970 q^{7} +1.00000 q^{8} -1.26586 q^{9} +1.00000 q^{10} -1.63555 q^{11} +1.31687 q^{12} -1.00000 q^{13} -4.24970 q^{14} +1.31687 q^{15} +1.00000 q^{16} +5.84178 q^{17} -1.26586 q^{18} -1.36466 q^{19} +1.00000 q^{20} -5.59629 q^{21} -1.63555 q^{22} -8.85279 q^{23} +1.31687 q^{24} +1.00000 q^{25} -1.00000 q^{26} -5.61757 q^{27} -4.24970 q^{28} -1.07562 q^{29} +1.31687 q^{30} -1.00000 q^{31} +1.00000 q^{32} -2.15380 q^{33} +5.84178 q^{34} -4.24970 q^{35} -1.26586 q^{36} -0.732230 q^{37} -1.36466 q^{38} -1.31687 q^{39} +1.00000 q^{40} -0.539659 q^{41} -5.59629 q^{42} -6.89347 q^{43} -1.63555 q^{44} -1.26586 q^{45} -8.85279 q^{46} +0.441588 q^{47} +1.31687 q^{48} +11.0599 q^{49} +1.00000 q^{50} +7.69284 q^{51} -1.00000 q^{52} -2.53774 q^{53} -5.61757 q^{54} -1.63555 q^{55} -4.24970 q^{56} -1.79708 q^{57} -1.07562 q^{58} -5.44241 q^{59} +1.31687 q^{60} -2.85872 q^{61} -1.00000 q^{62} +5.37952 q^{63} +1.00000 q^{64} -1.00000 q^{65} -2.15380 q^{66} -14.6554 q^{67} +5.84178 q^{68} -11.6579 q^{69} -4.24970 q^{70} -6.52730 q^{71} -1.26586 q^{72} +6.41373 q^{73} -0.732230 q^{74} +1.31687 q^{75} -1.36466 q^{76} +6.95060 q^{77} -1.31687 q^{78} +7.46507 q^{79} +1.00000 q^{80} -3.60002 q^{81} -0.539659 q^{82} -3.14179 q^{83} -5.59629 q^{84} +5.84178 q^{85} -6.89347 q^{86} -1.41645 q^{87} -1.63555 q^{88} +5.44148 q^{89} -1.26586 q^{90} +4.24970 q^{91} -8.85279 q^{92} -1.31687 q^{93} +0.441588 q^{94} -1.36466 q^{95} +1.31687 q^{96} -11.5825 q^{97} +11.0599 q^{98} +2.07038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 6 q^{5} - 3 q^{6} - 10 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 6 * q^5 - 3 * q^6 - 10 * q^7 + 6 * q^8 - q^9	\( 6 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 6 q^{5} - 3 q^{6} - 10 q^{7} + 6 q^{8} - q^{9} + 6 q^{10} - 10 q^{11} - 3 q^{12} - 6 q^{13} - 10 q^{14} - 3 q^{15} + 6 q^{16} - 4 q^{17} - q^{18} - 7 q^{19} + 6 q^{20} + q^{21} - 10 q^{22} - 3 q^{23} - 3 q^{24} + 6 q^{25} - 6 q^{26} - 3 q^{27} - 10 q^{28} - 4 q^{29} - 3 q^{30} - 6 q^{31} + 6 q^{32} - 4 q^{33} - 4 q^{34} - 10 q^{35} - q^{36} - 2 q^{37} - 7 q^{38} + 3 q^{39} + 6 q^{40} - 10 q^{41} + q^{42} - 15 q^{43} - 10 q^{44} - q^{45} - 3 q^{46} - 24 q^{47} - 3 q^{48} - 2 q^{49} + 6 q^{50} - 3 q^{51} - 6 q^{52} + 2 q^{53} - 3 q^{54} - 10 q^{55} - 10 q^{56} - 23 q^{57} - 4 q^{58} - 25 q^{59} - 3 q^{60} + 9 q^{61} - 6 q^{62} - 9 q^{63} + 6 q^{64} - 6 q^{65} - 4 q^{66} - 26 q^{67} - 4 q^{68} - 2 q^{69} - 10 q^{70} - 38 q^{71} - q^{72} - q^{73} - 2 q^{74} - 3 q^{75} - 7 q^{76} + 9 q^{77} + 3 q^{78} + 6 q^{80} - 18 q^{81} - 10 q^{82} - 18 q^{83} + q^{84} - 4 q^{85} - 15 q^{86} - 7 q^{87} - 10 q^{88} + 4 q^{89} - q^{90} + 10 q^{91} - 3 q^{92} + 3 q^{93} - 24 q^{94} - 7 q^{95} - 3 q^{96} - 21 q^{97} - 2 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 6 * q^5 - 3 * q^6 - 10 * q^7 + 6 * q^8 - q^9 + 6 * q^10 - 10 * q^11 - 3 * q^12 - 6 * q^13 - 10 * q^14 - 3 * q^15 + 6 * q^16 - 4 * q^17 - q^18 - 7 * q^19 + 6 * q^20 + q^21 - 10 * q^22 - 3 * q^23 - 3 * q^24 + 6 * q^25 - 6 * q^26 - 3 * q^27 - 10 * q^28 - 4 * q^29 - 3 * q^30 - 6 * q^31 + 6 * q^32 - 4 * q^33 - 4 * q^34 - 10 * q^35 - q^36 - 2 * q^37 - 7 * q^38 + 3 * q^39 + 6 * q^40 - 10 * q^41 + q^42 - 15 * q^43 - 10 * q^44 - q^45 - 3 * q^46 - 24 * q^47 - 3 * q^48 - 2 * q^49 + 6 * q^50 - 3 * q^51 - 6 * q^52 + 2 * q^53 - 3 * q^54 - 10 * q^55 - 10 * q^56 - 23 * q^57 - 4 * q^58 - 25 * q^59 - 3 * q^60 + 9 * q^61 - 6 * q^62 - 9 * q^63 + 6 * q^64 - 6 * q^65 - 4 * q^66 - 26 * q^67 - 4 * q^68 - 2 * q^69 - 10 * q^70 - 38 * q^71 - q^72 - q^73 - 2 * q^74 - 3 * q^75 - 7 * q^76 + 9 * q^77 + 3 * q^78 + 6 * q^80 - 18 * q^81 - 10 * q^82 - 18 * q^83 + q^84 - 4 * q^85 - 15 * q^86 - 7 * q^87 - 10 * q^88 + 4 * q^89 - q^90 + 10 * q^91 - 3 * q^92 + 3 * q^93 - 24 * q^94 - 7 * q^95 - 3 * q^96 - 21 * q^97 - 2 * q^98 + 3 * q^99

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