LMFDB - Embedded newform 8030.2.a.bd.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 6 x^{13} - 15 x^{12} + 143 x^{11} - 13 x^{10} - 1176 x^{9} + 1018 x^{8} + 4076 x^{7} + \cdots - 54 $ x^14 - 6x^13 - 15x^12 + 143x^11 - 13x^10 - 1176x^9 + 1018x^8 + 4076x^7 - 4865x^6 - 5483x^5 + 7607x^4 + 1210x^3 - 3153x^2 + 878*x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.25086$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.25086 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.25086 q^{6} +4.10088 q^{7} +1.00000 q^{8} +2.06636 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.25086 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.25086 q^{6} +4.10088 q^{7} +1.00000 q^{8} +2.06636 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.25086 q^{12} +4.34795 q^{13} +4.10088 q^{14} -2.25086 q^{15} +1.00000 q^{16} +2.81954 q^{17} +2.06636 q^{18} +1.83413 q^{19} -1.00000 q^{20} +9.23051 q^{21} +1.00000 q^{22} -2.64880 q^{23} +2.25086 q^{24} +1.00000 q^{25} +4.34795 q^{26} -2.10150 q^{27} +4.10088 q^{28} -1.96709 q^{29} -2.25086 q^{30} +8.01521 q^{31} +1.00000 q^{32} +2.25086 q^{33} +2.81954 q^{34} -4.10088 q^{35} +2.06636 q^{36} +4.69506 q^{37} +1.83413 q^{38} +9.78661 q^{39} -1.00000 q^{40} -3.13699 q^{41} +9.23051 q^{42} +5.01613 q^{43} +1.00000 q^{44} -2.06636 q^{45} -2.64880 q^{46} -8.27931 q^{47} +2.25086 q^{48} +9.81725 q^{49} +1.00000 q^{50} +6.34637 q^{51} +4.34795 q^{52} -12.1429 q^{53} -2.10150 q^{54} -1.00000 q^{55} +4.10088 q^{56} +4.12837 q^{57} -1.96709 q^{58} -7.05696 q^{59} -2.25086 q^{60} -10.5482 q^{61} +8.01521 q^{62} +8.47389 q^{63} +1.00000 q^{64} -4.34795 q^{65} +2.25086 q^{66} -13.3878 q^{67} +2.81954 q^{68} -5.96206 q^{69} -4.10088 q^{70} -5.74376 q^{71} +2.06636 q^{72} +1.00000 q^{73} +4.69506 q^{74} +2.25086 q^{75} +1.83413 q^{76} +4.10088 q^{77} +9.78661 q^{78} +6.17086 q^{79} -1.00000 q^{80} -10.9292 q^{81} -3.13699 q^{82} -0.744041 q^{83} +9.23051 q^{84} -2.81954 q^{85} +5.01613 q^{86} -4.42764 q^{87} +1.00000 q^{88} +5.15132 q^{89} -2.06636 q^{90} +17.8304 q^{91} -2.64880 q^{92} +18.0411 q^{93} -8.27931 q^{94} -1.83413 q^{95} +2.25086 q^{96} +3.70449 q^{97} +9.81725 q^{98} +2.06636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) $ 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * 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
$3$	2.25086	1.29953	0.649766	−	0.760134i	$-0.274867\pi$
$3$	2.25086	1.29953	0.649766	+	0.760134i	$0.274867\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.25086	0.918909
$7$	4.10088	1.54999	0.774994	−	0.631968i	$-0.217753\pi$
$7$	4.10088	1.54999	0.774994	+	0.631968i	$0.217753\pi$
$8$	1.00000	0.353553
$9$	2.06636	0.688786
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.25086	0.649766
$13$	4.34795	1.20590	0.602952	−	0.797778i	$-0.293991\pi$
$13$	4.34795	1.20590	0.602952	+	0.797778i	$0.293991\pi$
$14$	4.10088	1.09601
$15$	−2.25086	−0.581169
$16$	1.00000	0.250000
$17$	2.81954	0.683838	0.341919	−	0.939729i	$-0.388923\pi$
$17$	2.81954	0.683838	0.341919	+	0.939729i	$0.388923\pi$
$18$	2.06636	0.487045
$19$	1.83413	0.420778	0.210389	−	0.977618i	$-0.432527\pi$
$19$	1.83413	0.420778	0.210389	+	0.977618i	$0.432527\pi$
$20$	−1.00000	−0.223607
$21$	9.23051	2.01426
$22$	1.00000	0.213201
$23$	−2.64880	−0.552312	−0.276156	−	0.961113i	$-0.589061\pi$
$23$	−2.64880	−0.552312	−0.276156	+	0.961113i	$0.589061\pi$
$24$	2.25086	0.459454
$25$	1.00000	0.200000
$26$	4.34795	0.852703
$27$	−2.10150	−0.404433
$28$	4.10088	0.774994
$29$	−1.96709	−0.365279	−0.182640	−	0.983180i	$-0.558464\pi$
$29$	−1.96709	−0.365279	−0.182640	+	0.983180i	$0.558464\pi$
$30$	−2.25086	−0.410948
$31$	8.01521	1.43957	0.719787	−	0.694195i	$-0.244240\pi$
$31$	8.01521	1.43957	0.719787	+	0.694195i	$0.244240\pi$
$32$	1.00000	0.176777
$33$	2.25086	0.391824
$34$	2.81954	0.483546
$35$	−4.10088	−0.693176
$36$	2.06636	0.344393
$37$	4.69506	0.771862	0.385931	−	0.922528i	$-0.373880\pi$
$37$	4.69506	0.771862	0.385931	+	0.922528i	$0.373880\pi$
$38$	1.83413	0.297535
$39$	9.78661	1.56711
$40$	−1.00000	−0.158114
$41$	−3.13699	−0.489916	−0.244958	−	0.969534i	$-0.578774\pi$
$41$	−3.13699	−0.489916	−0.244958	+	0.969534i	$0.578774\pi$
$42$	9.23051	1.42430
$43$	5.01613	0.764953	0.382477	−	0.923965i	$-0.375071\pi$
$43$	5.01613	0.764953	0.382477	+	0.923965i	$0.375071\pi$
$44$	1.00000	0.150756
$45$	−2.06636	−0.308034
$46$	−2.64880	−0.390544
$47$	−8.27931	−1.20766	−0.603831	−	0.797113i	$-0.706360\pi$
$47$	−8.27931	−1.20766	−0.603831	+	0.797113i	$0.706360\pi$
$48$	2.25086	0.324883
$49$	9.81725	1.40246
$50$	1.00000	0.141421
$51$	6.34637	0.888670
$52$	4.34795	0.602952
$53$	−12.1429	−1.66795	−0.833976	−	0.551800i	$-0.813941\pi$
$53$	−12.1429	−1.66795	−0.833976	+	0.551800i	$0.813941\pi$
$54$	−2.10150	−0.285977
$55$	−1.00000	−0.134840
$56$	4.10088	0.548004
$57$	4.12837	0.546815
$58$	−1.96709	−0.258291
$59$	−7.05696	−0.918739	−0.459369	−	0.888245i	$-0.651925\pi$
$59$	−7.05696	−0.918739	−0.459369	+	0.888245i	$0.651925\pi$
$60$	−2.25086	−0.290584
$61$	−10.5482	−1.35055	−0.675277	−	0.737564i	$-0.735976\pi$
$61$	−10.5482	−1.35055	−0.675277	+	0.737564i	$0.735976\pi$
$62$	8.01521	1.01793
$63$	8.47389	1.06761
$64$	1.00000	0.125000
$65$	−4.34795	−0.539297
$66$	2.25086	0.277061
$67$	−13.3878	−1.63558	−0.817790	−	0.575517i	$-0.804801\pi$
$67$	−13.3878	−1.63558	−0.817790	+	0.575517i	$0.804801\pi$
$68$	2.81954	0.341919
$69$	−5.96206	−0.717748
$70$	−4.10088	−0.490149
$71$	−5.74376	−0.681659	−0.340830	−	0.940125i	$-0.610708\pi$
$71$	−5.74376	−0.681659	−0.340830	+	0.940125i	$0.610708\pi$
$72$	2.06636	0.243523
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	4.69506	0.545789
$75$	2.25086	0.259907
$76$	1.83413	0.210389
$77$	4.10088	0.467339
$78$	9.78661	1.10812
$79$	6.17086	0.694275	0.347138	−	0.937814i	$-0.387154\pi$
$79$	6.17086	0.694275	0.347138	+	0.937814i	$0.387154\pi$
$80$	−1.00000	−0.111803
$81$	−10.9292	−1.21436
$82$	−3.13699	−0.346423
$83$	−0.744041	−0.0816691	−0.0408345	−	0.999166i	$-0.513002\pi$
$83$	−0.744041	−0.0816691	−0.0408345	+	0.999166i	$0.513002\pi$
$84$	9.23051	1.00713
$85$	−2.81954	−0.305822
$86$	5.01613	0.540904
$87$	−4.42764	−0.474692
$88$	1.00000	0.106600
$89$	5.15132	0.546039	0.273019	−	0.962008i	$-0.411978\pi$
$89$	5.15132	0.546039	0.273019	+	0.962008i	$0.411978\pi$
$90$	−2.06636	−0.217813
$91$	17.8304	1.86914
$92$	−2.64880	−0.276156
$93$	18.0411	1.87077
$94$	−8.27931	−0.853945
$95$	−1.83413	−0.188178
$96$	2.25086	0.229727
$97$	3.70449	0.376134	0.188067	−	0.982156i	$-0.439778\pi$
$97$	3.70449	0.376134	0.188067	+	0.982156i	$0.439778\pi$
$98$	9.81725	0.991692
$99$	2.06636	0.207677
$100$	1.00000	0.100000
$101$	−9.73090	−0.968260	−0.484130	−	0.874996i	$-0.660864\pi$
$101$	−9.73090	−0.968260	−0.484130	+	0.874996i	$0.660864\pi$
$102$	6.34637	0.628384
$103$	2.34784	0.231340	0.115670	−	0.993288i	$-0.463099\pi$
$103$	2.34784	0.231340	0.115670	+	0.993288i	$0.463099\pi$
$104$	4.34795	0.426351
$105$	−9.23051	−0.900805
$106$	−12.1429	−1.17942
$107$	−8.46445	−0.818290	−0.409145	−	0.912469i	$-0.634173\pi$
$107$	−8.46445	−0.818290	−0.409145	+	0.912469i	$0.634173\pi$
$108$	−2.10150	−0.202217
$109$	14.8905	1.42625	0.713127	−	0.701034i	$-0.247278\pi$
$109$	14.8905	1.42625	0.713127	+	0.701034i	$0.247278\pi$
$110$	−1.00000	−0.0953463
$111$	10.5679	1.00306
$112$	4.10088	0.387497
$113$	−8.27306	−0.778264	−0.389132	−	0.921182i	$-0.627225\pi$
$113$	−8.27306	−0.778264	−0.389132	+	0.921182i	$0.627225\pi$
$114$	4.12837	0.386657
$115$	2.64880	0.247002
$116$	−1.96709	−0.182640
$117$	8.98441	0.830609
$118$	−7.05696	−0.649646
$119$	11.5626	1.05994
$120$	−2.25086	−0.205474
$121$	1.00000	0.0909091
$122$	−10.5482	−0.954986
$123$	−7.06092	−0.636662
$124$	8.01521	0.719787
$125$	−1.00000	−0.0894427
$126$	8.47389	0.754914
$127$	6.45526	0.572812	0.286406	−	0.958108i	$-0.407539\pi$
$127$	6.45526	0.572812	0.286406	+	0.958108i	$0.407539\pi$
$128$	1.00000	0.0883883
$129$	11.2906	0.994082
$130$	−4.34795	−0.381340
$131$	11.0830	0.968326	0.484163	−	0.874978i	$-0.339124\pi$
$131$	11.0830	0.968326	0.484163	+	0.874978i	$0.339124\pi$
$132$	2.25086	0.195912
$133$	7.52156	0.652202
$134$	−13.3878	−1.15653
$135$	2.10150	0.180868
$136$	2.81954	0.241773
$137$	−3.01810	−0.257854	−0.128927	−	0.991654i	$-0.541153\pi$
$137$	−3.01810	−0.257854	−0.128927	+	0.991654i	$0.541153\pi$
$138$	−5.96206	−0.507524
$139$	1.29572	0.109902	0.0549510	−	0.998489i	$-0.482500\pi$
$139$	1.29572	0.109902	0.0549510	+	0.998489i	$0.482500\pi$
$140$	−4.10088	−0.346588
$141$	−18.6355	−1.56940
$142$	−5.74376	−0.482006
$143$	4.34795	0.363594
$144$	2.06636	0.172196
$145$	1.96709	0.163358
$146$	1.00000	0.0827606
$147$	22.0972	1.82255
$148$	4.69506	0.385931
$149$	10.1404	0.830733	0.415366	−	0.909654i	$-0.363653\pi$
$149$	10.1404	0.830733	0.415366	+	0.909654i	$0.363653\pi$
$150$	2.25086	0.183782
$151$	13.5484	1.10256	0.551278	−	0.834322i	$-0.314140\pi$
$151$	13.5484	1.10256	0.551278	+	0.834322i	$0.314140\pi$
$152$	1.83413	0.148768
$153$	5.82617	0.471018
$154$	4.10088	0.330459
$155$	−8.01521	−0.643797
$156$	9.78661	0.783556
$157$	−2.69977	−0.215465	−0.107733	−	0.994180i	$-0.534359\pi$
$157$	−2.69977	−0.215465	−0.107733	+	0.994180i	$0.534359\pi$
$158$	6.17086	0.490927
$159$	−27.3319	−2.16756
$160$	−1.00000	−0.0790569
$161$	−10.8624	−0.856078
$162$	−10.9292	−0.858682
$163$	6.83134	0.535072	0.267536	−	0.963548i	$-0.413791\pi$
$163$	6.83134	0.535072	0.267536	+	0.963548i	$0.413791\pi$
$164$	−3.13699	−0.244958
$165$	−2.25086	−0.175229
$166$	−0.744041	−0.0577488
$167$	−2.83378	−0.219285	−0.109642	−	0.993971i	$-0.534971\pi$
$167$	−2.83378	−0.219285	−0.109642	+	0.993971i	$0.534971\pi$
$168$	9.23051	0.712149
$169$	5.90465	0.454204
$170$	−2.81954	−0.216249
$171$	3.78997	0.289826
$172$	5.01613	0.382477
$173$	21.1376	1.60707	0.803533	−	0.595261i	$-0.202951\pi$
$173$	21.1376	1.60707	0.803533	+	0.595261i	$0.202951\pi$
$174$	−4.42764	−0.335658
$175$	4.10088	0.309998
$176$	1.00000	0.0753778
$177$	−15.8842	−1.19393
$178$	5.15132	0.386108
$179$	0.284679	0.0212779	0.0106389	−	0.999943i	$-0.496613\pi$
$179$	0.284679	0.0212779	0.0106389	+	0.999943i	$0.496613\pi$
$180$	−2.06636	−0.154017
$181$	−10.7010	−0.795396	−0.397698	−	0.917516i	$-0.630191\pi$
$181$	−10.7010	−0.795396	−0.397698	+	0.917516i	$0.630191\pi$
$182$	17.8304	1.32168
$183$	−23.7424	−1.75509
$184$	−2.64880	−0.195272
$185$	−4.69506	−0.345187
$186$	18.0411	1.32284
$187$	2.81954	0.206185
$188$	−8.27931	−0.603831
$189$	−8.61799	−0.626867
$190$	−1.83413	−0.133062
$191$	−11.5694	−0.837129	−0.418565	−	0.908187i	$-0.637467\pi$
$191$	−11.5694	−0.837129	−0.418565	+	0.908187i	$0.637467\pi$
$192$	2.25086	0.162442
$193$	−0.0894819	−0.00644105	−0.00322053	−	0.999995i	$-0.501025\pi$
$193$	−0.0894819	−0.00644105	−0.00322053	+	0.999995i	$0.501025\pi$
$194$	3.70449	0.265967
$195$	−9.78661	−0.700834
$196$	9.81725	0.701232
$197$	−0.287651	−0.0204943	−0.0102472	−	0.999947i	$-0.503262\pi$
$197$	−0.287651	−0.0204943	−0.0102472	+	0.999947i	$0.503262\pi$
$198$	2.06636	0.146850
$199$	−3.04115	−0.215581	−0.107791	−	0.994174i	$-0.534378\pi$
$199$	−3.04115	−0.215581	−0.107791	+	0.994174i	$0.534378\pi$
$200$	1.00000	0.0707107
$201$	−30.1340	−2.12549
$202$	−9.73090	−0.684664
$203$	−8.06680	−0.566179
$204$	6.34637	0.444335
$205$	3.13699	0.219097
$206$	2.34784	0.163582
$207$	−5.47336	−0.380425
$208$	4.34795	0.301476
$209$	1.83413	0.126869
$210$	−9.23051	−0.636965
$211$	23.9197	1.64670	0.823351	−	0.567533i	$-0.192102\pi$
$211$	23.9197	1.64670	0.823351	+	0.567533i	$0.192102\pi$
$212$	−12.1429	−0.833976
$213$	−12.9284	−0.885839
$214$	−8.46445	−0.578618
$215$	−5.01613	−0.342098
$216$	−2.10150	−0.142989
$217$	32.8694	2.23132
$218$	14.8905	1.00851
$219$	2.25086	0.152099
$220$	−1.00000	−0.0674200
$221$	12.2592	0.824643
$222$	10.5679	0.709271
$223$	−14.9577	−1.00164	−0.500820	−	0.865551i	$-0.666968\pi$
$223$	−14.9577	−1.00164	−0.500820	+	0.865551i	$0.666968\pi$
$224$	4.10088	0.274002
$225$	2.06636	0.137757
$226$	−8.27306	−0.550316
$227$	4.45850	0.295921	0.147960	−	0.988993i	$-0.452729\pi$
$227$	4.45850	0.295921	0.147960	+	0.988993i	$0.452729\pi$
$228$	4.12837	0.273408
$229$	−23.9432	−1.58221	−0.791107	−	0.611678i	$-0.790495\pi$
$229$	−23.9432	−1.58221	−0.791107	+	0.611678i	$0.790495\pi$
$230$	2.64880	0.174656
$231$	9.23051	0.607323
$232$	−1.96709	−0.129146
$233$	−9.88145	−0.647355	−0.323678	−	0.946167i	$-0.604919\pi$
$233$	−9.88145	−0.647355	−0.323678	+	0.946167i	$0.604919\pi$
$234$	8.98441	0.587330
$235$	8.27931	0.540082
$236$	−7.05696	−0.459369
$237$	13.8897	0.902234
$238$	11.5626	0.749491
$239$	0.350263	0.0226566	0.0113283	−	0.999936i	$-0.496394\pi$
$239$	0.350263	0.0226566	0.0113283	+	0.999936i	$0.496394\pi$
$240$	−2.25086	−0.145292
$241$	12.7341	0.820278	0.410139	−	0.912023i	$-0.365480\pi$
$241$	12.7341	0.820278	0.410139	+	0.912023i	$0.365480\pi$
$242$	1.00000	0.0642824
$243$	−18.2957	−1.17367
$244$	−10.5482	−0.675277
$245$	−9.81725	−0.627201
$246$	−7.06092	−0.450188
$247$	7.97470	0.507418
$248$	8.01521	0.508966
$249$	−1.67473	−0.106132
$250$	−1.00000	−0.0632456
$251$	19.9726	1.26066	0.630329	−	0.776328i	$-0.282920\pi$
$251$	19.9726	1.26066	0.630329	+	0.776328i	$0.282920\pi$
$252$	8.47389	0.533805
$253$	−2.64880	−0.166528
$254$	6.45526	0.405039
$255$	−6.34637	−0.397425
$256$	1.00000	0.0625000
$257$	−8.79498	−0.548616	−0.274308	−	0.961642i	$-0.588449\pi$
$257$	−8.79498	−0.548616	−0.274308	+	0.961642i	$0.588449\pi$
$258$	11.2906	0.702922
$259$	19.2539	1.19638
$260$	−4.34795	−0.269648
$261$	−4.06471	−0.251599
$262$	11.0830	0.684710
$263$	18.2361	1.12448	0.562242	−	0.826973i	$-0.309939\pi$
$263$	18.2361	1.12448	0.562242	+	0.826973i	$0.309939\pi$
$264$	2.25086	0.138531
$265$	12.1429	0.745931
$266$	7.52156	0.461176
$267$	11.5949	0.709596
$268$	−13.3878	−0.817790
$269$	6.19093	0.377468	0.188734	−	0.982028i	$-0.439562\pi$
$269$	6.19093	0.377468	0.188734	+	0.982028i	$0.439562\pi$
$270$	2.10150	0.127893
$271$	−15.3983	−0.935383	−0.467692	−	0.883892i	$-0.654914\pi$
$271$	−15.3983	−0.935383	−0.467692	+	0.883892i	$0.654914\pi$
$272$	2.81954	0.170959
$273$	40.1338	2.42901
$274$	−3.01810	−0.182330
$275$	1.00000	0.0603023
$276$	−5.96206	−0.358874
$277$	−17.3483	−1.04236	−0.521180	−	0.853447i	$-0.674508\pi$
$277$	−17.3483	−1.04236	−0.521180	+	0.853447i	$0.674508\pi$
$278$	1.29572	0.0777124
$279$	16.5623	0.991558
$280$	−4.10088	−0.245075
$281$	−28.9094	−1.72459	−0.862294	−	0.506407i	$-0.830973\pi$
$281$	−28.9094	−1.72459	−0.862294	+	0.506407i	$0.830973\pi$
$282$	−18.6355	−1.10973
$283$	9.48045	0.563554	0.281777	−	0.959480i	$-0.409076\pi$
$283$	9.48045	0.563554	0.281777	+	0.959480i	$0.409076\pi$
$284$	−5.74376	−0.340830
$285$	−4.12837	−0.244543
$286$	4.34795	0.257100
$287$	−12.8644	−0.759364
$288$	2.06636	0.121761
$289$	−9.05022	−0.532366
$290$	1.96709	0.115511
$291$	8.33828	0.488798
$292$	1.00000	0.0585206
$293$	22.8043	1.33224	0.666120	−	0.745844i	$-0.267954\pi$
$293$	22.8043	1.33224	0.666120	+	0.745844i	$0.267954\pi$
$294$	22.0972	1.28874
$295$	7.05696	0.410872
$296$	4.69506	0.272895
$297$	−2.10150	−0.121941
$298$	10.1404	0.587417
$299$	−11.5168	−0.666035
$300$	2.25086	0.129953
$301$	20.5706	1.18567
$302$	13.5484	0.779625
$303$	−21.9029	−1.25829
$304$	1.83413	0.105195
$305$	10.5482	0.603986
$306$	5.82617	0.333060
$307$	11.8661	0.677235	0.338617	−	0.940924i	$-0.390041\pi$
$307$	11.8661	0.677235	0.338617	+	0.940924i	$0.390041\pi$
$308$	4.10088	0.233670
$309$	5.28465	0.300634
$310$	−8.01521	−0.455233
$311$	−26.2429	−1.48810	−0.744048	−	0.668126i	$-0.767097\pi$
$311$	−26.2429	−1.48810	−0.744048	+	0.668126i	$0.767097\pi$
$312$	9.78661	0.554058
$313$	4.09132	0.231255	0.115627	−	0.993293i	$-0.463112\pi$
$313$	4.09132	0.231255	0.115627	+	0.993293i	$0.463112\pi$
$314$	−2.69977	−0.152357
$315$	−8.47389	−0.477450
$316$	6.17086	0.347138
$317$	0.570459	0.0320402	0.0160201	−	0.999872i	$-0.494900\pi$
$317$	0.570459	0.0320402	0.0160201	+	0.999872i	$0.494900\pi$
$318$	−27.3319	−1.53270
$319$	−1.96709	−0.110136
$320$	−1.00000	−0.0559017
$321$	−19.0523	−1.06339
$322$	−10.8624	−0.605338
$323$	5.17140	0.287744
$324$	−10.9292	−0.607180
$325$	4.34795	0.241181
$326$	6.83134	0.378353
$327$	33.5165	1.85347
$328$	−3.13699	−0.173211
$329$	−33.9525	−1.87186
$330$	−2.25086	−0.123906
$331$	−19.2651	−1.05891	−0.529453	−	0.848339i	$-0.677603\pi$
$331$	−19.2651	−1.05891	−0.529453	+	0.848339i	$0.677603\pi$
$332$	−0.744041	−0.0408345
$333$	9.70166	0.531648
$334$	−2.83378	−0.155058
$335$	13.3878	0.731454
$336$	9.23051	0.503565
$337$	−0.0538595	−0.00293391	−0.00146696	−	0.999999i	$-0.500467\pi$
$337$	−0.0538595	−0.00293391	−0.00146696	+	0.999999i	$0.500467\pi$
$338$	5.90465	0.321170
$339$	−18.6215	−1.01138
$340$	−2.81954	−0.152911
$341$	8.01521	0.434048
$342$	3.78997	0.204938
$343$	11.5532	0.623816
$344$	5.01613	0.270452
$345$	5.96206	0.320987
$346$	21.1376	1.13637
$347$	26.6077	1.42838	0.714188	−	0.699954i	$-0.246796\pi$
$347$	26.6077	1.42838	0.714188	+	0.699954i	$0.246796\pi$
$348$	−4.42764	−0.237346
$349$	10.7752	0.576786	0.288393	−	0.957512i	$-0.406879\pi$
$349$	10.7752	0.576786	0.288393	+	0.957512i	$0.406879\pi$
$350$	4.10088	0.219202
$351$	−9.13719	−0.487707
$352$	1.00000	0.0533002
$353$	−3.25680	−0.173342	−0.0866709	−	0.996237i	$-0.527623\pi$
$353$	−3.25680	−0.173342	−0.0866709	+	0.996237i	$0.527623\pi$
$354$	−15.8842	−0.844237
$355$	5.74376	0.304847
$356$	5.15132	0.273019
$357$	26.0257	1.37743
$358$	0.284679	0.0150457
$359$	−32.7291	−1.72738	−0.863689	−	0.504025i	$-0.831852\pi$
$359$	−32.7291	−1.72738	−0.863689	+	0.504025i	$0.831852\pi$
$360$	−2.06636	−0.108907
$361$	−15.6360	−0.822946
$362$	−10.7010	−0.562430
$363$	2.25086	0.118139
$364$	17.8304	0.934569
$365$	−1.00000	−0.0523424
$366$	−23.7424	−1.24104
$367$	−9.57740	−0.499936	−0.249968	−	0.968254i	$-0.580420\pi$
$367$	−9.57740	−0.499936	−0.249968	+	0.968254i	$0.580420\pi$
$368$	−2.64880	−0.138078
$369$	−6.48215	−0.337447
$370$	−4.69506	−0.244084
$371$	−49.7965	−2.58531
$372$	18.0411	0.935387
$373$	−0.0973331	−0.00503972	−0.00251986	−	0.999997i	$-0.500802\pi$
$373$	−0.0973331	−0.00503972	−0.00251986	+	0.999997i	$0.500802\pi$
$374$	2.81954	0.145795
$375$	−2.25086	−0.116234
$376$	−8.27931	−0.426973
$377$	−8.55280	−0.440492
$378$	−8.61799	−0.443262
$379$	−3.36793	−0.172999	−0.0864995	−	0.996252i	$-0.527568\pi$
$379$	−3.36793	−0.172999	−0.0864995	+	0.996252i	$0.527568\pi$
$380$	−1.83413	−0.0940889
$381$	14.5299	0.744388
$382$	−11.5694	−0.591940
$383$	9.96764	0.509323	0.254661	−	0.967030i	$-0.418036\pi$
$383$	9.96764	0.509323	0.254661	+	0.967030i	$0.418036\pi$
$384$	2.25086	0.114864
$385$	−4.10088	−0.209000
$386$	−0.0894819	−0.00455451
$387$	10.3651	0.526889
$388$	3.70449	0.188067
$389$	26.5298	1.34511	0.672557	−	0.740045i	$-0.265196\pi$
$389$	26.5298	1.34511	0.672557	+	0.740045i	$0.265196\pi$
$390$	−9.78661	−0.495564
$391$	−7.46838	−0.377692
$392$	9.81725	0.495846
$393$	24.9462	1.25837
$394$	−0.287651	−0.0144917
$395$	−6.17086	−0.310489
$396$	2.06636	0.103838
$397$	−35.3641	−1.77487	−0.887437	−	0.460929i	$-0.847516\pi$
$397$	−35.3641	−1.77487	−0.887437	+	0.460929i	$0.847516\pi$
$398$	−3.04115	−0.152439
$399$	16.9299	0.847558
$400$	1.00000	0.0500000
$401$	26.0464	1.30070	0.650349	−	0.759636i	$-0.274623\pi$
$401$	26.0464	1.30070	0.650349	+	0.759636i	$0.274623\pi$
$402$	−30.1340	−1.50295
$403$	34.8497	1.73599
$404$	−9.73090	−0.484130
$405$	10.9292	0.543078
$406$	−8.06680	−0.400349
$407$	4.69506	0.232725
$408$	6.34637	0.314192
$409$	9.25939	0.457847	0.228924	−	0.973444i	$-0.426479\pi$
$409$	9.25939	0.457847	0.228924	+	0.973444i	$0.426479\pi$
$410$	3.13699	0.154925
$411$	−6.79332	−0.335090
$412$	2.34784	0.115670
$413$	−28.9398	−1.42403
$414$	−5.47336	−0.269001
$415$	0.744041	0.0365235
$416$	4.34795	0.213176
$417$	2.91649	0.142821
$418$	1.83413	0.0897102
$419$	−4.82684	−0.235806	−0.117903	−	0.993025i	$-0.537617\pi$
$419$	−4.82684	−0.235806	−0.117903	+	0.993025i	$0.537617\pi$
$420$	−9.23051	−0.450403
$421$	7.90933	0.385477	0.192739	−	0.981250i	$-0.438263\pi$
$421$	7.90933	0.385477	0.192739	+	0.981250i	$0.438263\pi$
$422$	23.9197	1.16439
$423$	−17.1080	−0.831820
$424$	−12.1429	−0.589710
$425$	2.81954	0.136768
$426$	−12.9284	−0.626382
$427$	−43.2568	−2.09334
$428$	−8.46445	−0.409145
$429$	9.78661	0.472502
$430$	−5.01613	−0.241899
$431$	−8.22557	−0.396212	−0.198106	−	0.980181i	$-0.563479\pi$
$431$	−8.22557	−0.396212	−0.198106	+	0.980181i	$0.563479\pi$
$432$	−2.10150	−0.101108
$433$	−35.3781	−1.70017	−0.850083	−	0.526649i	$-0.823448\pi$
$433$	−35.3781	−1.70017	−0.850083	+	0.526649i	$0.823448\pi$
$434$	32.8694	1.57778
$435$	4.42764	0.212289
$436$	14.8905	0.713127
$437$	−4.85824	−0.232401
$438$	2.25086	0.107550
$439$	−27.6439	−1.31937	−0.659686	−	0.751542i	$-0.729311\pi$
$439$	−27.6439	−1.31937	−0.659686	+	0.751542i	$0.729311\pi$
$440$	−1.00000	−0.0476731
$441$	20.2860	0.965998
$442$	12.2592	0.583110
$443$	20.7576	0.986225	0.493112	−	0.869966i	$-0.335859\pi$
$443$	20.7576	0.986225	0.493112	+	0.869966i	$0.335859\pi$
$444$	10.5679	0.501530
$445$	−5.15132	−0.244196
$446$	−14.9577	−0.708266
$447$	22.8246	1.07956
$448$	4.10088	0.193749
$449$	24.9172	1.17592	0.587958	−	0.808891i	$-0.299932\pi$
$449$	24.9172	1.17592	0.587958	+	0.808891i	$0.299932\pi$
$450$	2.06636	0.0974090
$451$	−3.13699	−0.147715
$452$	−8.27306	−0.389132
$453$	30.4956	1.43281
$454$	4.45850	0.209248
$455$	−17.8304	−0.835904
$456$	4.12837	0.193328
$457$	15.2073	0.711366	0.355683	−	0.934607i	$-0.384248\pi$
$457$	15.2073	0.711366	0.355683	+	0.934607i	$0.384248\pi$
$458$	−23.9432	−1.11879
$459$	−5.92524	−0.276567
$460$	2.64880	0.123501
$461$	27.7205	1.29107	0.645535	−	0.763730i	$-0.276634\pi$
$461$	27.7205	1.29107	0.645535	+	0.763730i	$0.276634\pi$
$462$	9.23051	0.429442
$463$	−20.7197	−0.962927	−0.481463	−	0.876466i	$-0.659895\pi$
$463$	−20.7197	−0.962927	−0.481463	+	0.876466i	$0.659895\pi$
$464$	−1.96709	−0.0913198
$465$	−18.0411	−0.836635
$466$	−9.88145	−0.457749
$467$	32.3661	1.49773	0.748863	−	0.662725i	$-0.230600\pi$
$467$	32.3661	1.49773	0.748863	+	0.662725i	$0.230600\pi$
$468$	8.98441	0.415305
$469$	−54.9018	−2.53513
$470$	8.27931	0.381896
$471$	−6.07680	−0.280004
$472$	−7.05696	−0.324823
$473$	5.01613	0.230642
$474$	13.8897	0.637976
$475$	1.83413	0.0841557
$476$	11.5626	0.529970
$477$	−25.0915	−1.14886
$478$	0.350263	0.0160206
$479$	10.1845	0.465340	0.232670	−	0.972556i	$-0.425254\pi$
$479$	10.1845	0.465340	0.232670	+	0.972556i	$0.425254\pi$
$480$	−2.25086	−0.102737
$481$	20.4139	0.930792
$482$	12.7341	0.580024
$483$	−24.4497	−1.11250
$484$	1.00000	0.0454545
$485$	−3.70449	−0.168212
$486$	−18.2957	−0.829908
$487$	31.9693	1.44867	0.724333	−	0.689450i	$-0.242148\pi$
$487$	31.9693	1.44867	0.724333	+	0.689450i	$0.242148\pi$
$488$	−10.5482	−0.477493
$489$	15.3764	0.695343
$490$	−9.81725	−0.443498
$491$	−13.5388	−0.610999	−0.305500	−	0.952192i	$-0.598823\pi$
$491$	−13.5388	−0.610999	−0.305500	+	0.952192i	$0.598823\pi$
$492$	−7.06092	−0.318331
$493$	−5.54628	−0.249792
$494$	7.97470	0.358799
$495$	−2.06636	−0.0928759
$496$	8.01521	0.359893
$497$	−23.5545	−1.05656
$498$	−1.67473	−0.0750464
$499$	−7.13430	−0.319375	−0.159688	−	0.987168i	$-0.551049\pi$
$499$	−7.13430	−0.319375	−0.159688	+	0.987168i	$0.551049\pi$
$500$	−1.00000	−0.0447214
$501$	−6.37843	−0.284967
$502$	19.9726	0.891420
$503$	−4.25518	−0.189729	−0.0948646	−	0.995490i	$-0.530242\pi$
$503$	−4.25518	−0.189729	−0.0948646	+	0.995490i	$0.530242\pi$
$504$	8.47389	0.377457
$505$	9.73090	0.433019
$506$	−2.64880	−0.117753
$507$	13.2905	0.590253
$508$	6.45526	0.286406
$509$	7.95994	0.352818	0.176409	−	0.984317i	$-0.443552\pi$
$509$	7.95994	0.352818	0.176409	+	0.984317i	$0.443552\pi$
$510$	−6.34637	−0.281022
$511$	4.10088	0.181412
$512$	1.00000	0.0441942
$513$	−3.85442	−0.170177
$514$	−8.79498	−0.387930
$515$	−2.34784	−0.103458
$516$	11.2906	0.497041
$517$	−8.27931	−0.364124
$518$	19.2539	0.845967
$519$	47.5778	2.08843
$520$	−4.34795	−0.190670
$521$	−25.5997	−1.12154	−0.560771	−	0.827971i	$-0.689495\pi$
$521$	−25.5997	−1.12154	−0.560771	+	0.827971i	$0.689495\pi$
$522$	−4.06471	−0.177907
$523$	−16.2454	−0.710362	−0.355181	−	0.934798i	$-0.615581\pi$
$523$	−16.2454	−0.710362	−0.355181	+	0.934798i	$0.615581\pi$
$524$	11.0830	0.484163
$525$	9.23051	0.402852
$526$	18.2361	0.795130
$527$	22.5992	0.984435
$528$	2.25086	0.0979560
$529$	−15.9839	−0.694951
$530$	12.1429	0.527453
$531$	−14.5822	−0.632814
$532$	7.52156	0.326101
$533$	−13.6395	−0.590791
$534$	11.5949	0.501760
$535$	8.46445	0.365950
$536$	−13.3878	−0.578265
$537$	0.640771	0.0276513
$538$	6.19093	0.266910
$539$	9.81725	0.422859
$540$	2.10150	0.0904340
$541$	−2.08968	−0.0898423	−0.0449212	−	0.998991i	$-0.514304\pi$
$541$	−2.08968	−0.0898423	−0.0449212	+	0.998991i	$0.514304\pi$
$542$	−15.3983	−0.661416
$543$	−24.0863	−1.03364
$544$	2.81954	0.120887
$545$	−14.8905	−0.637841
$546$	40.1338	1.71757
$547$	−34.1253	−1.45909	−0.729546	−	0.683932i	$-0.760269\pi$
$547$	−34.1253	−1.45909	−0.729546	+	0.683932i	$0.760269\pi$
$548$	−3.01810	−0.128927
$549$	−21.7963	−0.930243
$550$	1.00000	0.0426401
$551$	−3.60790	−0.153702
$552$	−5.96206	−0.253762
$553$	25.3060	1.07612
$554$	−17.3483	−0.737059
$555$	−10.5679	−0.448582
$556$	1.29572	0.0549510
$557$	−8.09550	−0.343017	−0.171509	−	0.985183i	$-0.554864\pi$
$557$	−8.09550	−0.343017	−0.171509	+	0.985183i	$0.554864\pi$
$558$	16.5623	0.701137
$559$	21.8099	0.922460
$560$	−4.10088	−0.173294
$561$	6.34637	0.267944
$562$	−28.9094	−1.21947
$563$	14.4034	0.607030	0.303515	−	0.952827i	$-0.401840\pi$
$563$	14.4034	0.607030	0.303515	+	0.952827i	$0.401840\pi$
$564$	−18.6355	−0.784698
$565$	8.27306	0.348050
$566$	9.48045	0.398493
$567$	−44.8195	−1.88224
$568$	−5.74376	−0.241003
$569$	36.7132	1.53910	0.769549	−	0.638588i	$-0.220481\pi$
$569$	36.7132	1.53910	0.769549	+	0.638588i	$0.220481\pi$
$570$	−4.12837	−0.172918
$571$	−46.0897	−1.92879	−0.964397	−	0.264459i	$-0.914807\pi$
$571$	−46.0897	−1.92879	−0.964397	+	0.264459i	$0.914807\pi$
$572$	4.34795	0.181797
$573$	−26.0410	−1.08788
$574$	−12.8644	−0.536951
$575$	−2.64880	−0.110462
$576$	2.06636	0.0860982
$577$	43.4762	1.80994	0.904968	−	0.425479i	$-0.139895\pi$
$577$	43.4762	1.80994	0.904968	+	0.425479i	$0.139895\pi$
$578$	−9.05022	−0.376439
$579$	−0.201411	−0.00837036
$580$	1.96709	0.0816789
$581$	−3.05122	−0.126586
$582$	8.33828	0.345633
$583$	−12.1429	−0.502907
$584$	1.00000	0.0413803
$585$	−8.98441	−0.371460
$586$	22.8043	0.942036
$587$	−14.4571	−0.596709	−0.298354	−	0.954455i	$-0.596438\pi$
$587$	−14.4571	−0.596709	−0.298354	+	0.954455i	$0.596438\pi$
$588$	22.0972	0.911275
$589$	14.7009	0.605741
$590$	7.05696	0.290531
$591$	−0.647462	−0.0266330
$592$	4.69506	0.192966
$593$	16.4679	0.676256	0.338128	−	0.941100i	$-0.390206\pi$
$593$	16.4679	0.676256	0.338128	+	0.941100i	$0.390206\pi$
$594$	−2.10150	−0.0862254
$595$	−11.5626	−0.474020
$596$	10.1404	0.415366
$597$	−6.84518	−0.280155
$598$	−11.5168	−0.470958
$599$	24.6606	1.00760	0.503802	−	0.863819i	$-0.331934\pi$
$599$	24.6606	1.00760	0.503802	+	0.863819i	$0.331934\pi$
$600$	2.25086	0.0918909
$601$	−0.652827	−0.0266294	−0.0133147	−	0.999911i	$-0.504238\pi$
$601$	−0.652827	−0.0266294	−0.0133147	+	0.999911i	$0.504238\pi$
$602$	20.5706	0.838395
$603$	−27.6640	−1.12656
$604$	13.5484	0.551278
$605$	−1.00000	−0.0406558
$606$	−21.9029	−0.889743
$607$	5.63190	0.228592	0.114296	−	0.993447i	$-0.463539\pi$
$607$	5.63190	0.228592	0.114296	+	0.993447i	$0.463539\pi$
$608$	1.83413	0.0743838
$609$	−18.1572	−0.735768
$610$	10.5482	0.427083
$611$	−35.9980	−1.45632
$612$	5.82617	0.235509
$613$	33.5130	1.35358	0.676789	−	0.736177i	$-0.263371\pi$
$613$	33.5130	1.35358	0.676789	+	0.736177i	$0.263371\pi$
$614$	11.8661	0.478877
$615$	7.06092	0.284724
$616$	4.10088	0.165229
$617$	−23.7428	−0.955848	−0.477924	−	0.878401i	$-0.658611\pi$
$617$	−23.7428	−0.955848	−0.477924	+	0.878401i	$0.658611\pi$
$618$	5.28465	0.212580
$619$	−20.4438	−0.821704	−0.410852	−	0.911702i	$-0.634769\pi$
$619$	−20.4438	−0.821704	−0.410852	+	0.911702i	$0.634769\pi$
$620$	−8.01521	−0.321898
$621$	5.56644	0.223373
$622$	−26.2429	−1.05224
$623$	21.1250	0.846354
$624$	9.78661	0.391778
$625$	1.00000	0.0400000
$626$	4.09132	0.163522
$627$	4.12837	0.164871
$628$	−2.69977	−0.107733
$629$	13.2379	0.527829
$630$	−8.47389	−0.337608
$631$	−30.9441	−1.23187	−0.615933	−	0.787798i	$-0.711221\pi$
$631$	−30.9441	−1.23187	−0.615933	+	0.787798i	$0.711221\pi$
$632$	6.17086	0.245463
$633$	53.8399	2.13994
$634$	0.570459	0.0226558
$635$	−6.45526	−0.256169
$636$	−27.3319	−1.08378
$637$	42.6849	1.69124
$638$	−1.96709	−0.0778778
$639$	−11.8687	−0.469517
$640$	−1.00000	−0.0395285
$641$	−22.2464	−0.878679	−0.439339	−	0.898321i	$-0.644787\pi$
$641$	−22.2464	−0.878679	−0.439339	+	0.898321i	$0.644787\pi$
$642$	−19.0523	−0.751933
$643$	−2.38971	−0.0942411	−0.0471205	−	0.998889i	$-0.515004\pi$
$643$	−2.38971	−0.0942411	−0.0471205	+	0.998889i	$0.515004\pi$
$644$	−10.8624	−0.428039
$645$	−11.2906	−0.444567
$646$	5.17140	0.203466
$647$	−23.6058	−0.928041	−0.464020	−	0.885824i	$-0.653594\pi$
$647$	−23.6058	−0.928041	−0.464020	+	0.885824i	$0.653594\pi$
$648$	−10.9292	−0.429341
$649$	−7.05696	−0.277010
$650$	4.34795	0.170541
$651$	73.9844	2.89968
$652$	6.83134	0.267536
$653$	34.4251	1.34716	0.673580	−	0.739115i	$-0.264756\pi$
$653$	34.4251	1.34716	0.673580	+	0.739115i	$0.264756\pi$
$654$	33.5165	1.31060
$655$	−11.0830	−0.433048
$656$	−3.13699	−0.122479
$657$	2.06636	0.0806163
$658$	−33.9525	−1.32361
$659$	−28.3873	−1.10581	−0.552906	−	0.833244i	$-0.686481\pi$
$659$	−28.3873	−1.10581	−0.552906	+	0.833244i	$0.686481\pi$
$660$	−2.25086	−0.0876145
$661$	32.4955	1.26393	0.631964	−	0.774997i	$-0.282249\pi$
$661$	32.4955	1.26393	0.631964	+	0.774997i	$0.282249\pi$
$662$	−19.2651	−0.748760
$663$	27.5937	1.07165
$664$	−0.744041	−0.0288744
$665$	−7.52156	−0.291673
$666$	9.70166	0.375932
$667$	5.21042	0.201748
$668$	−2.83378	−0.109642
$669$	−33.6676	−1.30166
$670$	13.3878	0.517216
$671$	−10.5482	−0.407207
$672$	9.23051	0.356074
$673$	11.3875	0.438955	0.219478	−	0.975618i	$-0.429565\pi$
$673$	11.3875	0.438955	0.219478	+	0.975618i	$0.429565\pi$
$674$	−0.0538595	−0.00207459
$675$	−2.10150	−0.0808866
$676$	5.90465	0.227102
$677$	29.8991	1.14912	0.574559	−	0.818464i	$-0.305174\pi$
$677$	29.8991	1.14912	0.574559	+	0.818464i	$0.305174\pi$
$678$	−18.6215	−0.715154
$679$	15.1917	0.583003
$680$	−2.81954	−0.108124
$681$	10.0354	0.384559
$682$	8.01521	0.306918
$683$	3.25599	0.124587	0.0622934	−	0.998058i	$-0.480159\pi$
$683$	3.25599	0.124587	0.0622934	+	0.998058i	$0.480159\pi$
$684$	3.78997	0.144913
$685$	3.01810	0.115316
$686$	11.5532	0.441105
$687$	−53.8928	−2.05614
$688$	5.01613	0.191238
$689$	−52.7966	−2.01139
$690$	5.96206	0.226972
$691$	4.10106	0.156012	0.0780058	−	0.996953i	$-0.475145\pi$
$691$	4.10106	0.156012	0.0780058	+	0.996953i	$0.475145\pi$
$692$	21.1376	0.803533
$693$	8.47389	0.321897
$694$	26.6077	1.01001
$695$	−1.29572	−0.0491496
$696$	−4.42764	−0.167829
$697$	−8.84486	−0.335023
$698$	10.7752	0.407849
$699$	−22.2417	−0.841259
$700$	4.10088	0.154999
$701$	43.3003	1.63543	0.817715	−	0.575624i	$-0.195241\pi$
$701$	43.3003	1.63543	0.817715	+	0.575624i	$0.195241\pi$
$702$	−9.13719	−0.344861
$703$	8.61134	0.324783
$704$	1.00000	0.0376889
$705$	18.6355	0.701855
$706$	−3.25680	−0.122571
$707$	−39.9053	−1.50079
$708$	−15.8842	−0.596966
$709$	6.20084	0.232878	0.116439	−	0.993198i	$-0.462852\pi$
$709$	6.20084	0.232878	0.116439	+	0.993198i	$0.462852\pi$
$710$	5.74376	0.215560
$711$	12.7512	0.478207
$712$	5.15132	0.193054
$713$	−21.2307	−0.795094
$714$	26.0257	0.973989
$715$	−4.34795	−0.162604
$716$	0.284679	0.0106389
$717$	0.788392	0.0294430
$718$	−32.7291	−1.22144
$719$	−35.3869	−1.31971	−0.659854	−	0.751394i	$-0.729382\pi$
$719$	−35.3869	−1.31971	−0.659854	+	0.751394i	$0.729382\pi$
$720$	−2.06636	−0.0770086
$721$	9.62823	0.358574
$722$	−15.6360	−0.581910
$723$	28.6627	1.06598
$724$	−10.7010	−0.397698
$725$	−1.96709	−0.0730558
$726$	2.25086	0.0835371
$727$	5.34489	0.198231	0.0991156	−	0.995076i	$-0.468399\pi$
$727$	5.34489	0.198231	0.0991156	+	0.995076i	$0.468399\pi$
$728$	17.8304	0.660840
$729$	−8.39322	−0.310860
$730$	−1.00000	−0.0370117
$731$	14.1432	0.523104
$732$	−23.7424	−0.877545
$733$	30.8171	1.13826	0.569129	−	0.822248i	$-0.307281\pi$
$733$	30.8171	1.13826	0.569129	+	0.822248i	$0.307281\pi$
$734$	−9.57740	−0.353508
$735$	−22.0972	−0.815069
$736$	−2.64880	−0.0976359
$737$	−13.3878	−0.493146
$738$	−6.48215	−0.238611
$739$	−18.3565	−0.675254	−0.337627	−	0.941280i	$-0.609624\pi$
$739$	−18.3565	−0.675254	−0.337627	+	0.941280i	$0.609624\pi$
$740$	−4.69506	−0.172594
$741$	17.9499	0.659407
$742$	−49.7965	−1.82809
$743$	6.46226	0.237077	0.118539	−	0.992949i	$-0.462179\pi$
$743$	6.46226	0.237077	0.118539	+	0.992949i	$0.462179\pi$
$744$	18.0411	0.661418
$745$	−10.1404	−0.371515
$746$	−0.0973331	−0.00356362
$747$	−1.53745	−0.0562525
$748$	2.81954	0.103092
$749$	−34.7117	−1.26834
$750$	−2.25086	−0.0821897
$751$	30.4410	1.11081	0.555405	−	0.831580i	$-0.312563\pi$
$751$	30.4410	1.11081	0.555405	+	0.831580i	$0.312563\pi$
$752$	−8.27931	−0.301915
$753$	44.9554	1.63827
$754$	−8.55280	−0.311475
$755$	−13.5484	−0.493078
$756$	−8.61799	−0.313433
$757$	−43.0935	−1.56626	−0.783129	−	0.621859i	$-0.786378\pi$
$757$	−43.0935	−1.56626	−0.783129	+	0.621859i	$0.786378\pi$
$758$	−3.36793	−0.122329
$759$	−5.96206	−0.216409
$760$	−1.83413	−0.0665309
$761$	−11.9014	−0.431426	−0.215713	−	0.976457i	$-0.569208\pi$
$761$	−11.9014	−0.431426	−0.215713	+	0.976457i	$0.569208\pi$
$762$	14.5299	0.526361
$763$	61.0644	2.21068
$764$	−11.5694	−0.418565
$765$	−5.82617	−0.210646
$766$	9.96764	0.360145
$767$	−30.6833	−1.10791
$768$	2.25086	0.0812208
$769$	−28.8528	−1.04046	−0.520230	−	0.854026i	$-0.674154\pi$
$769$	−28.8528	−1.04046	−0.520230	+	0.854026i	$0.674154\pi$
$770$	−4.10088	−0.147786
$771$	−19.7962	−0.712944
$772$	−0.0894819	−0.00322053
$773$	11.1620	0.401470	0.200735	−	0.979646i	$-0.435667\pi$
$773$	11.1620	0.401470	0.200735	+	0.979646i	$0.435667\pi$
$774$	10.3651	0.372567
$775$	8.01521	0.287915
$776$	3.70449	0.132983
$777$	43.3377	1.55473
$778$	26.5298	0.951140
$779$	−5.75365	−0.206146
$780$	−9.78661	−0.350417
$781$	−5.74376	−0.205528
$782$	−7.46838	−0.267069
$783$	4.13383	0.147731
$784$	9.81725	0.350616
$785$	2.69977	0.0963590
$786$	24.9462	0.889803
$787$	−31.1335	−1.10979	−0.554895	−	0.831921i	$-0.687241\pi$
$787$	−31.1335	−1.10979	−0.554895	+	0.831921i	$0.687241\pi$
$788$	−0.287651	−0.0102472
$789$	41.0467	1.46130
$790$	−6.17086	−0.219549
$791$	−33.9269	−1.20630
$792$	2.06636	0.0734248
$793$	−45.8629	−1.62864
$794$	−35.3641	−1.25503
$795$	27.3319	0.969362
$796$	−3.04115	−0.107791
$797$	−11.8365	−0.419272	−0.209636	−	0.977780i	$-0.567228\pi$
$797$	−11.8365	−0.419272	−0.209636	+	0.977780i	$0.567228\pi$
$798$	16.9299	0.599314
$799$	−23.3438	−0.825844
$800$	1.00000	0.0353553
$801$	10.6445	0.376104
$802$	26.0464	0.919732
$803$	1.00000	0.0352892
$804$	−30.1340	−1.06274
$805$	10.8624	0.382850
$806$	34.8497	1.22753
$807$	13.9349	0.490532
$808$	−9.73090	−0.342332
$809$	3.56457	0.125324	0.0626618	−	0.998035i	$-0.480041\pi$
$809$	3.56457	0.125324	0.0626618	+	0.998035i	$0.480041\pi$
$810$	10.9292	0.384014
$811$	−16.6180	−0.583537	−0.291769	−	0.956489i	$-0.594244\pi$
$811$	−16.6180	−0.583537	−0.291769	+	0.956489i	$0.594244\pi$
$812$	−8.06680	−0.283089
$813$	−34.6595	−1.21556
$814$	4.69506	0.164562
$815$	−6.83134	−0.239291
$816$	6.34637	0.222167
$817$	9.20024	0.321876
$818$	9.25939	0.323747
$819$	36.8440	1.28744
$820$	3.13699	0.109549
$821$	15.1505	0.528757	0.264379	−	0.964419i	$-0.414833\pi$
$821$	15.1505	0.528757	0.264379	+	0.964419i	$0.414833\pi$
$822$	−6.79332	−0.236944
$823$	−18.9740	−0.661391	−0.330696	−	0.943737i	$-0.607283\pi$
$823$	−18.9740	−0.661391	−0.330696	+	0.943737i	$0.607283\pi$
$824$	2.34784	0.0817909
$825$	2.25086	0.0783648
$826$	−28.9398	−1.00694
$827$	−9.79342	−0.340551	−0.170275	−	0.985397i	$-0.554466\pi$
$827$	−9.79342	−0.340551	−0.170275	+	0.985397i	$0.554466\pi$
$828$	−5.47336	−0.190212
$829$	27.7858	0.965041	0.482520	−	0.875885i	$-0.339721\pi$
$829$	27.7858	0.965041	0.482520	+	0.875885i	$0.339721\pi$
$830$	0.744041	0.0258260
$831$	−39.0486	−1.35458
$832$	4.34795	0.150738
$833$	27.6801	0.959059
$834$	2.91649	0.100990
$835$	2.83378	0.0980670
$836$	1.83413	0.0634347
$837$	−16.8439	−0.582211
$838$	−4.82684	−0.166740
$839$	−4.39703	−0.151802	−0.0759012	−	0.997115i	$-0.524183\pi$
$839$	−4.39703	−0.151802	−0.0759012	+	0.997115i	$0.524183\pi$
$840$	−9.23051	−0.318483
$841$	−25.1306	−0.866571
$842$	7.90933	0.272574
$843$	−65.0709	−2.24116
$844$	23.9197	0.823351
$845$	−5.90465	−0.203126
$846$	−17.1080	−0.588185
$847$	4.10088	0.140908
$848$	−12.1429	−0.416988
$849$	21.3391	0.732357
$850$	2.81954	0.0967093
$851$	−12.4362	−0.426309
$852$	−12.9284	−0.442919
$853$	26.4906	0.907020	0.453510	−	0.891251i	$-0.350172\pi$
$853$	26.4906	0.907020	0.453510	+	0.891251i	$0.350172\pi$
$854$	−43.2568	−1.48022
$855$	−3.78997	−0.129614
$856$	−8.46445	−0.289309
$857$	−22.6163	−0.772559	−0.386279	−	0.922382i	$-0.626240\pi$
$857$	−22.6163	−0.772559	−0.386279	+	0.922382i	$0.626240\pi$
$858$	9.78661	0.334109
$859$	23.2504	0.793295	0.396647	−	0.917971i	$-0.370174\pi$
$859$	23.2504	0.793295	0.396647	+	0.917971i	$0.370174\pi$
$860$	−5.01613	−0.171049
$861$	−28.9560	−0.986819
$862$	−8.22557	−0.280164
$863$	41.7935	1.42267	0.711334	−	0.702854i	$-0.248091\pi$
$863$	41.7935	1.42267	0.711334	+	0.702854i	$0.248091\pi$
$864$	−2.10150	−0.0714943
$865$	−21.1376	−0.718701
$866$	−35.3781	−1.20220
$867$	−20.3707	−0.691827
$868$	32.8694	1.11566
$869$	6.17086	0.209332
$870$	4.42764	0.150111
$871$	−58.2094	−1.97235
$872$	14.8905	0.504257
$873$	7.65480	0.259076
$874$	−4.85824	−0.164332
$875$	−4.10088	−0.138635
$876$	2.25086	0.0760494
$877$	8.76148	0.295854	0.147927	−	0.988998i	$-0.452740\pi$
$877$	8.76148	0.295854	0.147927	+	0.988998i	$0.452740\pi$
$878$	−27.6439	−0.932937
$879$	51.3292	1.73129
$880$	−1.00000	−0.0337100
$881$	0.877391	0.0295600	0.0147800	−	0.999891i	$-0.495295\pi$
$881$	0.877391	0.0295600	0.0147800	+	0.999891i	$0.495295\pi$
$882$	20.2860	0.683064
$883$	13.4636	0.453087	0.226544	−	0.974001i	$-0.427257\pi$
$883$	13.4636	0.453087	0.226544	+	0.974001i	$0.427257\pi$
$884$	12.2592	0.412321
$885$	15.8842	0.533942
$886$	20.7576	0.697366
$887$	−46.3601	−1.55662	−0.778310	−	0.627880i	$-0.783923\pi$
$887$	−46.3601	−1.55662	−0.778310	+	0.627880i	$0.783923\pi$
$888$	10.5679	0.354636
$889$	26.4723	0.887851
$890$	−5.15132	−0.172673
$891$	−10.9292	−0.366143
$892$	−14.9577	−0.500820
$893$	−15.1853	−0.508158
$894$	22.8246	0.763368
$895$	−0.284679	−0.00951576
$896$	4.10088	0.137001
$897$	−25.9227	−0.865535
$898$	24.9172	0.831498
$899$	−15.7666	−0.525846
$900$	2.06636	0.0688786
$901$	−34.2373	−1.14061
$902$	−3.13699	−0.104450
$903$	46.3015	1.54082
$904$	−8.27306	−0.275158
$905$	10.7010	0.355712
$906$	30.4956	1.01315
$907$	−18.3366	−0.608858	−0.304429	−	0.952535i	$-0.598466\pi$
$907$	−18.3366	−0.608858	−0.304429	+	0.952535i	$0.598466\pi$
$908$	4.45850	0.147960
$909$	−20.1075	−0.666924
$910$	−17.8304	−0.591073
$911$	−9.75918	−0.323336	−0.161668	−	0.986845i	$-0.551687\pi$
$911$	−9.75918	−0.323336	−0.161668	+	0.986845i	$0.551687\pi$
$912$	4.12837	0.136704
$913$	−0.744041	−0.0246242
$914$	15.2073	0.503012
$915$	23.7424	0.784900
$916$	−23.9432	−0.791107
$917$	45.4501	1.50089
$918$	−5.92524	−0.195562
$919$	29.3849	0.969318	0.484659	−	0.874703i	$-0.338944\pi$
$919$	29.3849	0.969318	0.484659	+	0.874703i	$0.338944\pi$
$920$	2.64880	0.0873282
$921$	26.7089	0.880089
$922$	27.7205	0.912925
$923$	−24.9736	−0.822015
$924$	9.23051	0.303661
$925$	4.69506	0.154372
$926$	−20.7197	−0.680892
$927$	4.85148	0.159343
$928$	−1.96709	−0.0645729
$929$	−10.3885	−0.340835	−0.170417	−	0.985372i	$-0.554512\pi$
$929$	−10.3885	−0.340835	−0.170417	+	0.985372i	$0.554512\pi$
$930$	−18.0411	−0.591591
$931$	18.0061	0.590127
$932$	−9.88145	−0.323678
$933$	−59.0689	−1.93383
$934$	32.3661	1.05905
$935$	−2.81954	−0.0922087
$936$	8.98441	0.293665
$937$	−35.4124	−1.15687	−0.578437	−	0.815727i	$-0.696337\pi$
$937$	−35.4124	−1.15687	−0.578437	+	0.815727i	$0.696337\pi$
$938$	−54.9018	−1.79261
$939$	9.20897	0.300523
$940$	8.27931	0.270041
$941$	−44.1753	−1.44007	−0.720037	−	0.693936i	$-0.755875\pi$
$941$	−44.1753	−1.44007	−0.720037	+	0.693936i	$0.755875\pi$
$942$	−6.07680	−0.197993
$943$	8.30925	0.270587
$944$	−7.05696	−0.229685
$945$	8.61799	0.280343
$946$	5.01613	0.163089
$947$	−35.2084	−1.14412	−0.572059	−	0.820212i	$-0.693855\pi$
$947$	−35.2084	−1.14412	−0.572059	+	0.820212i	$0.693855\pi$
$948$	13.8897	0.451117
$949$	4.34795	0.141140
$950$	1.83413	0.0595070
$951$	1.28402	0.0416373
$952$	11.5626	0.374746
$953$	37.8591	1.22638	0.613188	−	0.789937i	$-0.289887\pi$
$953$	37.8591	1.22638	0.613188	+	0.789937i	$0.289887\pi$
$954$	−25.0915	−0.812368
$955$	11.5694	0.374376
$956$	0.350263	0.0113283
$957$	−4.42764	−0.143125
$958$	10.1845	0.329045
$959$	−12.3769	−0.399671
$960$	−2.25086	−0.0726461
$961$	33.2436	1.07237
$962$	20.4139	0.658169
$963$	−17.4906	−0.563626
$964$	12.7341	0.410139
$965$	0.0894819	0.00288053
$966$	−24.4497	−0.786657
$967$	−14.7072	−0.472950	−0.236475	−	0.971638i	$-0.575992\pi$
$967$	−14.7072	−0.472950	−0.236475	+	0.971638i	$0.575992\pi$
$968$	1.00000	0.0321412
$969$	11.6401	0.373933
$970$	−3.70449	−0.118944
$971$	−37.9135	−1.21670	−0.608350	−	0.793669i	$-0.708168\pi$
$971$	−37.9135	−1.21670	−0.608350	+	0.793669i	$0.708168\pi$
$972$	−18.2957	−0.586834
$973$	5.31362	0.170347
$974$	31.9693	1.02436
$975$	9.78661	0.313422
$976$	−10.5482	−0.337639
$977$	54.1664	1.73294	0.866469	−	0.499231i	$-0.166384\pi$
$977$	54.1664	1.73294	0.866469	+	0.499231i	$0.166384\pi$
$978$	15.3764	0.491682
$979$	5.15132	0.164637
$980$	−9.81725	−0.313601
$981$	30.7692	0.982384
$982$	−13.5388	−0.432042
$983$	−31.2818	−0.997735	−0.498868	−	0.866678i	$-0.666251\pi$
$983$	−31.2818	−0.997735	−0.498868	+	0.866678i	$0.666251\pi$
$984$	−7.06092	−0.225094
$985$	0.287651	0.00916533
$986$	−5.54628	−0.176629
$987$	−76.4222	−2.43254
$988$	7.97470	0.253709
$989$	−13.2867	−0.422493
$990$	−2.06636	−0.0656732
$991$	30.7250	0.976013	0.488007	−	0.872840i	$-0.337724\pi$
$991$	30.7250	0.976013	0.488007	+	0.872840i	$0.337724\pi$
$992$	8.01521	0.254483
$993$	−43.3630	−1.37608
$994$	−23.5545	−0.747104
$995$	3.04115	0.0964108
$996$	−1.67473	−0.0530658
$997$	−60.3559	−1.91149	−0.955746	−	0.294194i	$-0.904949\pi$
$997$	−60.3559	−1.91149	−0.955746	+	0.294194i	$0.904949\pi$
$998$	−7.13430	−0.225832
$999$	−9.86664	−0.312167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.10	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.10	✓	14	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.25086 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.25086 q^{6} +4.10088 q^{7} +1.00000 q^{8} +2.06636 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.25086 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.25086 q^{6} +4.10088 q^{7} +1.00000 q^{8} +2.06636 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.25086 q^{12} +4.34795 q^{13} +4.10088 q^{14} -2.25086 q^{15} +1.00000 q^{16} +2.81954 q^{17} +2.06636 q^{18} +1.83413 q^{19} -1.00000 q^{20} +9.23051 q^{21} +1.00000 q^{22} -2.64880 q^{23} +2.25086 q^{24} +1.00000 q^{25} +4.34795 q^{26} -2.10150 q^{27} +4.10088 q^{28} -1.96709 q^{29} -2.25086 q^{30} +8.01521 q^{31} +1.00000 q^{32} +2.25086 q^{33} +2.81954 q^{34} -4.10088 q^{35} +2.06636 q^{36} +4.69506 q^{37} +1.83413 q^{38} +9.78661 q^{39} -1.00000 q^{40} -3.13699 q^{41} +9.23051 q^{42} +5.01613 q^{43} +1.00000 q^{44} -2.06636 q^{45} -2.64880 q^{46} -8.27931 q^{47} +2.25086 q^{48} +9.81725 q^{49} +1.00000 q^{50} +6.34637 q^{51} +4.34795 q^{52} -12.1429 q^{53} -2.10150 q^{54} -1.00000 q^{55} +4.10088 q^{56} +4.12837 q^{57} -1.96709 q^{58} -7.05696 q^{59} -2.25086 q^{60} -10.5482 q^{61} +8.01521 q^{62} +8.47389 q^{63} +1.00000 q^{64} -4.34795 q^{65} +2.25086 q^{66} -13.3878 q^{67} +2.81954 q^{68} -5.96206 q^{69} -4.10088 q^{70} -5.74376 q^{71} +2.06636 q^{72} +1.00000 q^{73} +4.69506 q^{74} +2.25086 q^{75} +1.83413 q^{76} +4.10088 q^{77} +9.78661 q^{78} +6.17086 q^{79} -1.00000 q^{80} -10.9292 q^{81} -3.13699 q^{82} -0.744041 q^{83} +9.23051 q^{84} -2.81954 q^{85} +5.01613 q^{86} -4.42764 q^{87} +1.00000 q^{88} +5.15132 q^{89} -2.06636 q^{90} +17.8304 q^{91} -2.64880 q^{92} +18.0411 q^{93} -8.27931 q^{94} -1.83413 q^{95} +2.25086 q^{96} +3.70449 q^{97} +9.81725 q^{98} +2.06636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9} - 14 q^{10} + 14 q^{11} + 6 q^{12} + 4 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} + 20 q^{17} + 24 q^{18} - 14 q^{20} + 25 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 14 q^{25} + 4 q^{26} + 21 q^{27} + 4 q^{28} + 7 q^{29} - 6 q^{30} + 8 q^{31} + 14 q^{32} + 6 q^{33} + 20 q^{34} - 4 q^{35} + 24 q^{36} + 17 q^{37} + 7 q^{39} - 14 q^{40} - 14 q^{41} + 25 q^{42} + 12 q^{43} + 14 q^{44} - 24 q^{45} - 4 q^{46} + 28 q^{47} + 6 q^{48} + 20 q^{49} + 14 q^{50} - 13 q^{51} + 4 q^{52} + 13 q^{53} + 21 q^{54} - 14 q^{55} + 4 q^{56} - 23 q^{57} + 7 q^{58} + 36 q^{59} - 6 q^{60} + 25 q^{61} + 8 q^{62} + 45 q^{63} + 14 q^{64} - 4 q^{65} + 6 q^{66} + 20 q^{68} - 7 q^{69} - 4 q^{70} + 17 q^{71} + 24 q^{72} + 14 q^{73} + 17 q^{74} + 6 q^{75} + 4 q^{77} + 7 q^{78} + 10 q^{79} - 14 q^{80} + 58 q^{81} - 14 q^{82} - 6 q^{83} + 25 q^{84} - 20 q^{85} + 12 q^{86} + 44 q^{87} + 14 q^{88} + 36 q^{89} - 24 q^{90} - 15 q^{91} - 4 q^{92} - 2 q^{93} + 28 q^{94} + 6 q^{96} - 19 q^{97} + 20 q^{98} + 24 q^{99}+O(q^{100}) \) 14 * q + 14 * q^2 + 6 * q^3 + 14 * q^4 - 14 * q^5 + 6 * q^6 + 4 * q^7 + 14 * q^8 + 24 * q^9 - 14 * q^10 + 14 * q^11 + 6 * q^12 + 4 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 + 20 * q^17 + 24 * q^18 - 14 * q^20 + 25 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 14 * q^25 + 4 * q^26 + 21 * q^27 + 4 * q^28 + 7 * q^29 - 6 * q^30 + 8 * q^31 + 14 * q^32 + 6 * q^33 + 20 * q^34 - 4 * q^35 + 24 * q^36 + 17 * q^37 + 7 * q^39 - 14 * q^40 - 14 * q^41 + 25 * q^42 + 12 * q^43 + 14 * q^44 - 24 * q^45 - 4 * q^46 + 28 * q^47 + 6 * q^48 + 20 * q^49 + 14 * q^50 - 13 * q^51 + 4 * q^52 + 13 * q^53 + 21 * q^54 - 14 * q^55 + 4 * q^56 - 23 * q^57 + 7 * q^58 + 36 * q^59 - 6 * q^60 + 25 * q^61 + 8 * q^62 + 45 * q^63 + 14 * q^64 - 4 * q^65 + 6 * q^66 + 20 * q^68 - 7 * q^69 - 4 * q^70 + 17 * q^71 + 24 * q^72 + 14 * q^73 + 17 * q^74 + 6 * q^75 + 4 * q^77 + 7 * q^78 + 10 * q^79 - 14 * q^80 + 58 * q^81 - 14 * q^82 - 6 * q^83 + 25 * q^84 - 20 * q^85 + 12 * q^86 + 44 * q^87 + 14 * q^88 + 36 * q^89 - 24 * q^90 - 15 * q^91 - 4 * q^92 - 2 * q^93 + 28 * q^94 + 6 * q^96 - 19 * q^97 + 20 * q^98 + 24 * q^99

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