LMFDB - Embedded newform 8030.2.a.bd.1.8

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			1.8
Root			$0.454872$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.454872 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.454872 q^{6} -4.57770 q^{7} +1.00000 q^{8} -2.79309 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.454872 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.454872 q^{6} -4.57770 q^{7} +1.00000 q^{8} -2.79309 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.454872 q^{12} +4.27111 q^{13} -4.57770 q^{14} -0.454872 q^{15} +1.00000 q^{16} +0.731710 q^{17} -2.79309 q^{18} -3.54214 q^{19} -1.00000 q^{20} -2.08227 q^{21} +1.00000 q^{22} +6.31807 q^{23} +0.454872 q^{24} +1.00000 q^{25} +4.27111 q^{26} -2.63512 q^{27} -4.57770 q^{28} -6.91536 q^{29} -0.454872 q^{30} -4.01751 q^{31} +1.00000 q^{32} +0.454872 q^{33} +0.731710 q^{34} +4.57770 q^{35} -2.79309 q^{36} +2.67695 q^{37} -3.54214 q^{38} +1.94281 q^{39} -1.00000 q^{40} -10.6731 q^{41} -2.08227 q^{42} -1.24641 q^{43} +1.00000 q^{44} +2.79309 q^{45} +6.31807 q^{46} +2.53680 q^{47} +0.454872 q^{48} +13.9554 q^{49} +1.00000 q^{50} +0.332835 q^{51} +4.27111 q^{52} +3.52262 q^{53} -2.63512 q^{54} -1.00000 q^{55} -4.57770 q^{56} -1.61122 q^{57} -6.91536 q^{58} +1.72070 q^{59} -0.454872 q^{60} +1.30545 q^{61} -4.01751 q^{62} +12.7859 q^{63} +1.00000 q^{64} -4.27111 q^{65} +0.454872 q^{66} +12.5729 q^{67} +0.731710 q^{68} +2.87392 q^{69} +4.57770 q^{70} +9.79672 q^{71} -2.79309 q^{72} +1.00000 q^{73} +2.67695 q^{74} +0.454872 q^{75} -3.54214 q^{76} -4.57770 q^{77} +1.94281 q^{78} -11.9863 q^{79} -1.00000 q^{80} +7.18063 q^{81} -10.6731 q^{82} +3.09844 q^{83} -2.08227 q^{84} -0.731710 q^{85} -1.24641 q^{86} -3.14560 q^{87} +1.00000 q^{88} +8.88742 q^{89} +2.79309 q^{90} -19.5519 q^{91} +6.31807 q^{92} -1.82746 q^{93} +2.53680 q^{94} +3.54214 q^{95} +0.454872 q^{96} +8.47368 q^{97} +13.9554 q^{98} -2.79309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.454872	0.262621	0.131310	−	0.991341i	$-0.458082\pi$
$3$	0.454872	0.262621	0.131310	+	0.991341i	$0.458082\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.454872	0.185701
$7$	−4.57770	−1.73021	−0.865104	−	0.501592i	$-0.832748\pi$
$7$	−4.57770	−1.73021	−0.865104	+	0.501592i	$0.832748\pi$
$8$	1.00000	0.353553
$9$	−2.79309	−0.931030
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.454872	0.131310
$13$	4.27111	1.18459	0.592296	−	0.805720i	$-0.298222\pi$
$13$	4.27111	1.18459	0.592296	+	0.805720i	$0.298222\pi$
$14$	−4.57770	−1.22344
$15$	−0.454872	−0.117448
$16$	1.00000	0.250000
$17$	0.731710	0.177466	0.0887329	−	0.996055i	$-0.471718\pi$
$17$	0.731710	0.177466	0.0887329	+	0.996055i	$0.471718\pi$
$18$	−2.79309	−0.658338
$19$	−3.54214	−0.812622	−0.406311	−	0.913735i	$-0.633185\pi$
$19$	−3.54214	−0.812622	−0.406311	+	0.913735i	$0.633185\pi$
$20$	−1.00000	−0.223607
$21$	−2.08227	−0.454389
$22$	1.00000	0.213201
$23$	6.31807	1.31741	0.658705	−	0.752401i	$-0.271105\pi$
$23$	6.31807	1.31741	0.658705	+	0.752401i	$0.271105\pi$
$24$	0.454872	0.0928504
$25$	1.00000	0.200000
$26$	4.27111	0.837633
$27$	−2.63512	−0.507128
$28$	−4.57770	−0.865104
$29$	−6.91536	−1.28415	−0.642075	−	0.766642i	$-0.721926\pi$
$29$	−6.91536	−1.28415	−0.642075	+	0.766642i	$0.721926\pi$
$30$	−0.454872	−0.0830479
$31$	−4.01751	−0.721567	−0.360783	−	0.932650i	$-0.617491\pi$
$31$	−4.01751	−0.721567	−0.360783	+	0.932650i	$0.617491\pi$
$32$	1.00000	0.176777
$33$	0.454872	0.0791831
$34$	0.731710	0.125487
$35$	4.57770	0.773773
$36$	−2.79309	−0.465515
$37$	2.67695	0.440089	0.220044	−	0.975490i	$-0.429380\pi$
$37$	2.67695	0.440089	0.220044	+	0.975490i	$0.429380\pi$
$38$	−3.54214	−0.574611
$39$	1.94281	0.311098
$40$	−1.00000	−0.158114
$41$	−10.6731	−1.66686	−0.833431	−	0.552624i	$-0.813627\pi$
$41$	−10.6731	−1.66686	−0.833431	+	0.552624i	$0.813627\pi$
$42$	−2.08227	−0.321301
$43$	−1.24641	−0.190075	−0.0950377	−	0.995474i	$-0.530297\pi$
$43$	−1.24641	−0.190075	−0.0950377	+	0.995474i	$0.530297\pi$
$44$	1.00000	0.150756
$45$	2.79309	0.416369
$46$	6.31807	0.931549
$47$	2.53680	0.370030	0.185015	−	0.982736i	$-0.440767\pi$
$47$	2.53680	0.370030	0.185015	+	0.982736i	$0.440767\pi$
$48$	0.454872	0.0656552
$49$	13.9554	1.99362
$50$	1.00000	0.141421
$51$	0.332835	0.0466062
$52$	4.27111	0.592296
$53$	3.52262	0.483869	0.241934	−	0.970293i	$-0.422218\pi$
$53$	3.52262	0.483869	0.241934	+	0.970293i	$0.422218\pi$
$54$	−2.63512	−0.358594
$55$	−1.00000	−0.134840
$56$	−4.57770	−0.611721
$57$	−1.61122	−0.213411
$58$	−6.91536	−0.908031
$59$	1.72070	0.224017	0.112008	−	0.993707i	$-0.464272\pi$
$59$	1.72070	0.224017	0.112008	+	0.993707i	$0.464272\pi$
$60$	−0.454872	−0.0587238
$61$	1.30545	0.167145	0.0835726	−	0.996502i	$-0.473367\pi$
$61$	1.30545	0.167145	0.0835726	+	0.996502i	$0.473367\pi$
$62$	−4.01751	−0.510225
$63$	12.7859	1.61088
$64$	1.00000	0.125000
$65$	−4.27111	−0.529766
$66$	0.454872	0.0559909
$67$	12.5729	1.53602	0.768012	−	0.640435i	$-0.221246\pi$
$67$	12.5729	1.53602	0.768012	+	0.640435i	$0.221246\pi$
$68$	0.731710	0.0887329
$69$	2.87392	0.345979
$70$	4.57770	0.547140
$71$	9.79672	1.16266	0.581328	−	0.813669i	$-0.302533\pi$
$71$	9.79672	1.16266	0.581328	+	0.813669i	$0.302533\pi$
$72$	−2.79309	−0.329169
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	2.67695	0.311190
$75$	0.454872	0.0525241
$76$	−3.54214	−0.406311
$77$	−4.57770	−0.521678
$78$	1.94281	0.219980
$79$	−11.9863	−1.34857	−0.674285	−	0.738471i	$-0.735548\pi$
$79$	−11.9863	−1.34857	−0.674285	+	0.738471i	$0.735548\pi$
$80$	−1.00000	−0.111803
$81$	7.18063	0.797848
$82$	−10.6731	−1.17865
$83$	3.09844	0.340098	0.170049	−	0.985436i	$-0.445607\pi$
$83$	3.09844	0.340098	0.170049	+	0.985436i	$0.445607\pi$
$84$	−2.08227	−0.227194
$85$	−0.731710	−0.0793651
$86$	−1.24641	−0.134404
$87$	−3.14560	−0.337244
$88$	1.00000	0.106600
$89$	8.88742	0.942065	0.471032	−	0.882116i	$-0.343882\pi$
$89$	8.88742	0.942065	0.471032	+	0.882116i	$0.343882\pi$
$90$	2.79309	0.294418
$91$	−19.5519	−2.04959
$92$	6.31807	0.658705
$93$	−1.82746	−0.189498
$94$	2.53680	0.261651
$95$	3.54214	0.363416
$96$	0.454872	0.0464252
$97$	8.47368	0.860372	0.430186	−	0.902740i	$-0.358448\pi$
$97$	8.47368	0.860372	0.430186	+	0.902740i	$0.358448\pi$
$98$	13.9554	1.40970
$99$	−2.79309	−0.280716
$100$	1.00000	0.100000
$101$	9.97506	0.992556	0.496278	−	0.868164i	$-0.334700\pi$
$101$	9.97506	0.992556	0.496278	+	0.868164i	$0.334700\pi$
$102$	0.332835	0.0329555
$103$	14.9319	1.47128	0.735642	−	0.677370i	$-0.236880\pi$
$103$	14.9319	1.47128	0.735642	+	0.677370i	$0.236880\pi$
$104$	4.27111	0.418817
$105$	2.08227	0.203209
$106$	3.52262	0.342147
$107$	−2.46952	−0.238738	−0.119369	−	0.992850i	$-0.538087\pi$
$107$	−2.46952	−0.238738	−0.119369	+	0.992850i	$0.538087\pi$
$108$	−2.63512	−0.253564
$109$	−1.33743	−0.128102	−0.0640512	−	0.997947i	$-0.520402\pi$
$109$	−1.33743	−0.128102	−0.0640512	+	0.997947i	$0.520402\pi$
$110$	−1.00000	−0.0953463
$111$	1.21767	0.115576
$112$	−4.57770	−0.432552
$113$	8.78779	0.826686	0.413343	−	0.910575i	$-0.364361\pi$
$113$	8.78779	0.826686	0.413343	+	0.910575i	$0.364361\pi$
$114$	−1.61122	−0.150905
$115$	−6.31807	−0.589163
$116$	−6.91536	−0.642075
$117$	−11.9296	−1.10289
$118$	1.72070	0.158404
$119$	−3.34955	−0.307053
$120$	−0.454872	−0.0415240
$121$	1.00000	0.0909091
$122$	1.30545	0.118190
$123$	−4.85491	−0.437752
$124$	−4.01751	−0.360783
$125$	−1.00000	−0.0894427
$126$	12.7859	1.13906
$127$	−7.02605	−0.623461	−0.311731	−	0.950171i	$-0.600909\pi$
$127$	−7.02605	−0.623461	−0.311731	+	0.950171i	$0.600909\pi$
$128$	1.00000	0.0883883
$129$	−0.566957	−0.0499177
$130$	−4.27111	−0.374601
$131$	13.1959	1.15293	0.576465	−	0.817122i	$-0.304432\pi$
$131$	13.1959	1.15293	0.576465	+	0.817122i	$0.304432\pi$
$132$	0.454872	0.0395916
$133$	16.2149	1.40601
$134$	12.5729	1.08613
$135$	2.63512	0.226795
$136$	0.731710	0.0627436
$137$	−11.5757	−0.988980	−0.494490	−	0.869183i	$-0.664645\pi$
$137$	−11.5757	−0.988980	−0.494490	+	0.869183i	$0.664645\pi$
$138$	2.87392	0.244644
$139$	2.74422	0.232762	0.116381	−	0.993205i	$-0.462871\pi$
$139$	2.74422	0.232762	0.116381	+	0.993205i	$0.462871\pi$
$140$	4.57770	0.386886
$141$	1.15392	0.0971776
$142$	9.79672	0.822122
$143$	4.27111	0.357168
$144$	−2.79309	−0.232758
$145$	6.91536	0.574289
$146$	1.00000	0.0827606
$147$	6.34791	0.523567
$148$	2.67695	0.220044
$149$	−9.04073	−0.740645	−0.370323	−	0.928903i	$-0.620753\pi$
$149$	−9.04073	−0.740645	−0.370323	+	0.928903i	$0.620753\pi$
$150$	0.454872	0.0371402
$151$	−8.21234	−0.668311	−0.334155	−	0.942518i	$-0.608451\pi$
$151$	−8.21234	−0.668311	−0.334155	+	0.942518i	$0.608451\pi$
$152$	−3.54214	−0.287305
$153$	−2.04373	−0.165226
$154$	−4.57770	−0.368882
$155$	4.01751	0.322694
$156$	1.94281	0.155549
$157$	−3.13229	−0.249984	−0.124992	−	0.992158i	$-0.539891\pi$
$157$	−3.13229	−0.249984	−0.124992	+	0.992158i	$0.539891\pi$
$158$	−11.9863	−0.953583
$159$	1.60234	0.127074
$160$	−1.00000	−0.0790569
$161$	−28.9223	−2.27939
$162$	7.18063	0.564164
$163$	10.3994	0.814546	0.407273	−	0.913307i	$-0.366480\pi$
$163$	10.3994	0.814546	0.407273	+	0.913307i	$0.366480\pi$
$164$	−10.6731	−0.833431
$165$	−0.454872	−0.0354118
$166$	3.09844	0.240486
$167$	5.32708	0.412222	0.206111	−	0.978529i	$-0.433919\pi$
$167$	5.32708	0.412222	0.206111	+	0.978529i	$0.433919\pi$
$168$	−2.08227	−0.160651
$169$	5.24237	0.403259
$170$	−0.731710	−0.0561196
$171$	9.89351	0.756576
$172$	−1.24641	−0.0950377
$173$	12.8905	0.980044	0.490022	−	0.871710i	$-0.336989\pi$
$173$	12.8905	0.980044	0.490022	+	0.871710i	$0.336989\pi$
$174$	−3.14560	−0.238468
$175$	−4.57770	−0.346042
$176$	1.00000	0.0753778
$177$	0.782701	0.0588314
$178$	8.88742	0.666140
$179$	−0.435529	−0.0325530	−0.0162765	−	0.999868i	$-0.505181\pi$
$179$	−0.435529	−0.0325530	−0.0162765	+	0.999868i	$0.505181\pi$
$180$	2.79309	0.208185
$181$	−1.23791	−0.0920130	−0.0460065	−	0.998941i	$-0.514650\pi$
$181$	−1.23791	−0.0920130	−0.0460065	+	0.998941i	$0.514650\pi$
$182$	−19.5519	−1.44928
$183$	0.593811	0.0438958
$184$	6.31807	0.465775
$185$	−2.67695	−0.196814
$186$	−1.82746	−0.133996
$187$	0.731710	0.0535079
$188$	2.53680	0.185015
$189$	12.0628	0.877438
$190$	3.54214	0.256974
$191$	3.49085	0.252589	0.126294	−	0.991993i	$-0.459692\pi$
$191$	3.49085	0.252589	0.126294	+	0.991993i	$0.459692\pi$
$192$	0.454872	0.0328276
$193$	22.6049	1.62714	0.813570	−	0.581467i	$-0.197521\pi$
$193$	22.6049	1.62714	0.813570	+	0.581467i	$0.197521\pi$
$194$	8.47368	0.608375
$195$	−1.94281	−0.139127
$196$	13.9554	0.996811
$197$	1.93523	0.137880	0.0689398	−	0.997621i	$-0.478038\pi$
$197$	1.93523	0.137880	0.0689398	+	0.997621i	$0.478038\pi$
$198$	−2.79309	−0.198496
$199$	16.3622	1.15988	0.579942	−	0.814658i	$-0.303075\pi$
$199$	16.3622	1.15988	0.579942	+	0.814658i	$0.303075\pi$
$200$	1.00000	0.0707107
$201$	5.71907	0.403392
$202$	9.97506	0.701843
$203$	31.6564	2.22185
$204$	0.332835	0.0233031
$205$	10.6731	0.745443
$206$	14.9319	1.04036
$207$	−17.6470	−1.22655
$208$	4.27111	0.296148
$209$	−3.54214	−0.245015
$210$	2.08227	0.143690
$211$	24.2377	1.66859	0.834296	−	0.551316i	$-0.185874\pi$
$211$	24.2377	1.66859	0.834296	+	0.551316i	$0.185874\pi$
$212$	3.52262	0.241934
$213$	4.45626	0.305338
$214$	−2.46952	−0.168813
$215$	1.24641	0.0850043
$216$	−2.63512	−0.179297
$217$	18.3910	1.24846
$218$	−1.33743	−0.0905820
$219$	0.454872	0.0307374
$220$	−1.00000	−0.0674200
$221$	3.12521	0.210225
$222$	1.21767	0.0817248
$223$	−7.55567	−0.505965	−0.252983	−	0.967471i	$-0.581412\pi$
$223$	−7.55567	−0.505965	−0.252983	+	0.967471i	$0.581412\pi$
$224$	−4.57770	−0.305861
$225$	−2.79309	−0.186206
$226$	8.78779	0.584555
$227$	−13.6439	−0.905580	−0.452790	−	0.891617i	$-0.649571\pi$
$227$	−13.6439	−0.905580	−0.452790	+	0.891617i	$0.649571\pi$
$228$	−1.61122	−0.106706
$229$	19.4021	1.28213	0.641065	−	0.767487i	$-0.278493\pi$
$229$	19.4021	1.28213	0.641065	+	0.767487i	$0.278493\pi$
$230$	−6.31807	−0.416602
$231$	−2.08227	−0.137003
$232$	−6.91536	−0.454015
$233$	9.95812	0.652378	0.326189	−	0.945305i	$-0.394235\pi$
$233$	9.95812	0.652378	0.326189	+	0.945305i	$0.394235\pi$
$234$	−11.9296	−0.779862
$235$	−2.53680	−0.165483
$236$	1.72070	0.112008
$237$	−5.45226	−0.354162
$238$	−3.34955	−0.217119
$239$	2.46068	0.159168	0.0795839	−	0.996828i	$-0.474641\pi$
$239$	2.46068	0.159168	0.0795839	+	0.996828i	$0.474641\pi$
$240$	−0.454872	−0.0293619
$241$	−7.09447	−0.456995	−0.228497	−	0.973545i	$-0.573381\pi$
$241$	−7.09447	−0.456995	−0.228497	+	0.973545i	$0.573381\pi$
$242$	1.00000	0.0642824
$243$	11.1716	0.716660
$244$	1.30545	0.0835726
$245$	−13.9554	−0.891575
$246$	−4.85491	−0.309538
$247$	−15.1289	−0.962626
$248$	−4.01751	−0.255112
$249$	1.40939	0.0893167
$250$	−1.00000	−0.0632456
$251$	16.6039	1.04803	0.524014	−	0.851710i	$-0.324434\pi$
$251$	16.6039	1.04803	0.524014	+	0.851710i	$0.324434\pi$
$252$	12.7859	0.805439
$253$	6.31807	0.397214
$254$	−7.02605	−0.440854
$255$	−0.332835	−0.0208429
$256$	1.00000	0.0625000
$257$	−25.7655	−1.60721	−0.803604	−	0.595165i	$-0.797087\pi$
$257$	−25.7655	−1.60721	−0.803604	+	0.595165i	$0.797087\pi$
$258$	−0.566957	−0.0352972
$259$	−12.2543	−0.761445
$260$	−4.27111	−0.264883
$261$	19.3152	1.19558
$262$	13.1959	0.815245
$263$	16.0639	0.990542	0.495271	−	0.868739i	$-0.335069\pi$
$263$	16.0639	0.990542	0.495271	+	0.868739i	$0.335069\pi$
$264$	0.454872	0.0279955
$265$	−3.52262	−0.216393
$266$	16.2149	0.994196
$267$	4.04264	0.247406
$268$	12.5729	0.768012
$269$	12.5725	0.766560	0.383280	−	0.923632i	$-0.374794\pi$
$269$	12.5725	0.766560	0.383280	+	0.923632i	$0.374794\pi$
$270$	2.63512	0.160368
$271$	−11.8834	−0.721864	−0.360932	−	0.932592i	$-0.617541\pi$
$271$	−11.8834	−0.721864	−0.360932	+	0.932592i	$0.617541\pi$
$272$	0.731710	0.0443664
$273$	−8.89360	−0.538265
$274$	−11.5757	−0.699314
$275$	1.00000	0.0603023
$276$	2.87392	0.172989
$277$	−22.6950	−1.36361	−0.681804	−	0.731535i	$-0.738804\pi$
$277$	−22.6950	−1.36361	−0.681804	+	0.731535i	$0.738804\pi$
$278$	2.74422	0.164587
$279$	11.2213	0.671801
$280$	4.57770	0.273570
$281$	1.22335	0.0729790	0.0364895	−	0.999334i	$-0.488382\pi$
$281$	1.22335	0.0729790	0.0364895	+	0.999334i	$0.488382\pi$
$282$	1.15392	0.0687149
$283$	27.4137	1.62958	0.814788	−	0.579758i	$-0.196853\pi$
$283$	27.4137	1.62958	0.814788	+	0.579758i	$0.196853\pi$
$284$	9.79672	0.581328
$285$	1.61122	0.0954405
$286$	4.27111	0.252556
$287$	48.8584	2.88402
$288$	−2.79309	−0.164584
$289$	−16.4646	−0.968506
$290$	6.91536	0.406084
$291$	3.85444	0.225951
$292$	1.00000	0.0585206
$293$	2.64671	0.154623	0.0773113	−	0.997007i	$-0.475366\pi$
$293$	2.64671	0.154623	0.0773113	+	0.997007i	$0.475366\pi$
$294$	6.34791	0.370217
$295$	−1.72070	−0.100183
$296$	2.67695	0.155595
$297$	−2.63512	−0.152905
$298$	−9.04073	−0.523715
$299$	26.9852	1.56059
$300$	0.454872	0.0262621
$301$	5.70569	0.328870
$302$	−8.21234	−0.472567
$303$	4.53738	0.260666
$304$	−3.54214	−0.203156
$305$	−1.30545	−0.0747496
$306$	−2.04373	−0.116832
$307$	−8.49467	−0.484817	−0.242408	−	0.970174i	$-0.577937\pi$
$307$	−8.49467	−0.484817	−0.242408	+	0.970174i	$0.577937\pi$
$308$	−4.57770	−0.260839
$309$	6.79211	0.386390
$310$	4.01751	0.228179
$311$	12.1329	0.687995	0.343997	−	0.938971i	$-0.388219\pi$
$311$	12.1329	0.687995	0.343997	+	0.938971i	$0.388219\pi$
$312$	1.94281	0.109990
$313$	−24.1157	−1.36310	−0.681549	−	0.731773i	$-0.738693\pi$
$313$	−24.1157	−1.36310	−0.681549	+	0.731773i	$0.738693\pi$
$314$	−3.13229	−0.176765
$315$	−12.7859	−0.720406
$316$	−11.9863	−0.674285
$317$	29.6269	1.66401	0.832005	−	0.554768i	$-0.187193\pi$
$317$	29.6269	1.66401	0.832005	+	0.554768i	$0.187193\pi$
$318$	1.60234	0.0898548
$319$	−6.91536	−0.387186
$320$	−1.00000	−0.0559017
$321$	−1.12332	−0.0626975
$322$	−28.9223	−1.61177
$323$	−2.59182	−0.144213
$324$	7.18063	0.398924
$325$	4.27111	0.236919
$326$	10.3994	0.575971
$327$	−0.608359	−0.0336423
$328$	−10.6731	−0.589325
$329$	−11.6127	−0.640230
$330$	−0.454872	−0.0250399
$331$	1.43579	0.0789181	0.0394590	−	0.999221i	$-0.487437\pi$
$331$	1.43579	0.0789181	0.0394590	+	0.999221i	$0.487437\pi$
$332$	3.09844	0.170049
$333$	−7.47698	−0.409736
$334$	5.32708	0.291485
$335$	−12.5729	−0.686931
$336$	−2.08227	−0.113597
$337$	2.94646	0.160504	0.0802519	−	0.996775i	$-0.474428\pi$
$337$	2.94646	0.160504	0.0802519	+	0.996775i	$0.474428\pi$
$338$	5.24237	0.285147
$339$	3.99732	0.217105
$340$	−0.731710	−0.0396825
$341$	−4.01751	−0.217561
$342$	9.89351	0.534980
$343$	−31.8396	−1.71918
$344$	−1.24641	−0.0672018
$345$	−2.87392	−0.154727
$346$	12.8905	0.692996
$347$	−0.822206	−0.0441383	−0.0220692	−	0.999756i	$-0.507025\pi$
$347$	−0.822206	−0.0441383	−0.0220692	+	0.999756i	$0.507025\pi$
$348$	−3.14560	−0.168622
$349$	−5.74464	−0.307503	−0.153752	−	0.988110i	$-0.549136\pi$
$349$	−5.74464	−0.307503	−0.153752	+	0.988110i	$0.549136\pi$
$350$	−4.57770	−0.244688
$351$	−11.2549	−0.600741
$352$	1.00000	0.0533002
$353$	−8.32572	−0.443133	−0.221567	−	0.975145i	$-0.571117\pi$
$353$	−8.32572	−0.443133	−0.221567	+	0.975145i	$0.571117\pi$
$354$	0.782701	0.0416001
$355$	−9.79672	−0.519956
$356$	8.88742	0.471032
$357$	−1.52362	−0.0806384
$358$	−0.435529	−0.0230184
$359$	5.07434	0.267813	0.133907	−	0.990994i	$-0.457248\pi$
$359$	5.07434	0.267813	0.133907	+	0.990994i	$0.457248\pi$
$360$	2.79309	0.147209
$361$	−6.45326	−0.339645
$362$	−1.23791	−0.0650630
$363$	0.454872	0.0238746
$364$	−19.5519	−1.02480
$365$	−1.00000	−0.0523424
$366$	0.593811	0.0310390
$367$	8.95934	0.467674	0.233837	−	0.972276i	$-0.424872\pi$
$367$	8.95934	0.467674	0.233837	+	0.972276i	$0.424872\pi$
$368$	6.31807	0.329352
$369$	29.8110	1.55190
$370$	−2.67695	−0.139168
$371$	−16.1255	−0.837194
$372$	−1.82746	−0.0947492
$373$	−11.6798	−0.604756	−0.302378	−	0.953188i	$-0.597780\pi$
$373$	−11.6798	−0.604756	−0.302378	+	0.953188i	$0.597780\pi$
$374$	0.731710	0.0378358
$375$	−0.454872	−0.0234895
$376$	2.53680	0.130825
$377$	−29.5362	−1.52119
$378$	12.0628	0.620442
$379$	18.1912	0.934419	0.467209	−	0.884147i	$-0.345259\pi$
$379$	18.1912	0.934419	0.467209	+	0.884147i	$0.345259\pi$
$380$	3.54214	0.181708
$381$	−3.19596	−0.163734
$382$	3.49085	0.178607
$383$	−9.36174	−0.478363	−0.239181	−	0.970975i	$-0.576879\pi$
$383$	−9.36174	−0.478363	−0.239181	+	0.970975i	$0.576879\pi$
$384$	0.454872	0.0232126
$385$	4.57770	0.233301
$386$	22.6049	1.15056
$387$	3.48133	0.176966
$388$	8.47368	0.430186
$389$	−24.9461	−1.26482	−0.632409	−	0.774635i	$-0.717934\pi$
$389$	−24.9461	−1.26482	−0.632409	+	0.774635i	$0.717934\pi$
$390$	−1.94281	−0.0983780
$391$	4.62300	0.233795
$392$	13.9554	0.704852
$393$	6.00244	0.302783
$394$	1.93523	0.0974956
$395$	11.9863	0.603099
$396$	−2.79309	−0.140358
$397$	2.93175	0.147140	0.0735702	−	0.997290i	$-0.476561\pi$
$397$	2.93175	0.147140	0.0735702	+	0.997290i	$0.476561\pi$
$398$	16.3622	0.820162
$399$	7.37569	0.369246
$400$	1.00000	0.0500000
$401$	4.60029	0.229727	0.114864	−	0.993381i	$-0.463357\pi$
$401$	4.60029	0.229727	0.114864	+	0.993381i	$0.463357\pi$
$402$	5.71907	0.285241
$403$	−17.1592	−0.854763
$404$	9.97506	0.496278
$405$	−7.18063	−0.356808
$406$	31.6564	1.57108
$407$	2.67695	0.132692
$408$	0.332835	0.0164778
$409$	30.7353	1.51976	0.759880	−	0.650063i	$-0.225258\pi$
$409$	30.7353	1.51976	0.759880	+	0.650063i	$0.225258\pi$
$410$	10.6731	0.527108
$411$	−5.26547	−0.259726
$412$	14.9319	0.735642
$413$	−7.87687	−0.387596
$414$	−17.6470	−0.867301
$415$	−3.09844	−0.152096
$416$	4.27111	0.209408
$417$	1.24827	0.0611280
$418$	−3.54214	−0.173252
$419$	1.50568	0.0735572	0.0367786	−	0.999323i	$-0.488290\pi$
$419$	1.50568	0.0735572	0.0367786	+	0.999323i	$0.488290\pi$
$420$	2.08227	0.101604
$421$	−25.4270	−1.23924	−0.619618	−	0.784903i	$-0.712713\pi$
$421$	−25.4270	−1.23924	−0.619618	+	0.784903i	$0.712713\pi$
$422$	24.2377	1.17987
$423$	−7.08551	−0.344509
$424$	3.52262	0.171073
$425$	0.731710	0.0354931
$426$	4.45626	0.215906
$427$	−5.97595	−0.289196
$428$	−2.46952	−0.119369
$429$	1.94281	0.0937997
$430$	1.24641	0.0601071
$431$	32.2504	1.55345	0.776724	−	0.629841i	$-0.216880\pi$
$431$	32.2504	1.55345	0.776724	+	0.629841i	$0.216880\pi$
$432$	−2.63512	−0.126782
$433$	−14.6490	−0.703988	−0.351994	−	0.936002i	$-0.614496\pi$
$433$	−14.6490	−0.703988	−0.351994	+	0.936002i	$0.614496\pi$
$434$	18.3910	0.882795
$435$	3.14560	0.150820
$436$	−1.33743	−0.0640512
$437$	−22.3795	−1.07056
$438$	0.454872	0.0217346
$439$	11.4278	0.545417	0.272708	−	0.962097i	$-0.412081\pi$
$439$	11.4278	0.545417	0.272708	+	0.962097i	$0.412081\pi$
$440$	−1.00000	−0.0476731
$441$	−38.9786	−1.85612
$442$	3.12521	0.148651
$443$	17.1812	0.816304	0.408152	−	0.912914i	$-0.366173\pi$
$443$	17.1812	0.816304	0.408152	+	0.912914i	$0.366173\pi$
$444$	1.21767	0.0577882
$445$	−8.88742	−0.421304
$446$	−7.55567	−0.357772
$447$	−4.11238	−0.194509
$448$	−4.57770	−0.216276
$449$	28.2540	1.33339	0.666694	−	0.745331i	$-0.267709\pi$
$449$	28.2540	1.33339	0.666694	+	0.745331i	$0.267709\pi$
$450$	−2.79309	−0.131668
$451$	−10.6731	−0.502578
$452$	8.78779	0.413343
$453$	−3.73557	−0.175512
$454$	−13.6439	−0.640341
$455$	19.5519	0.916606
$456$	−1.61122	−0.0754523
$457$	24.4711	1.14471	0.572355	−	0.820006i	$-0.306030\pi$
$457$	24.4711	1.14471	0.572355	+	0.820006i	$0.306030\pi$
$458$	19.4021	0.906602
$459$	−1.92814	−0.0899979
$460$	−6.31807	−0.294582
$461$	10.0996	0.470387	0.235194	−	0.971949i	$-0.424428\pi$
$461$	10.0996	0.470387	0.235194	+	0.971949i	$0.424428\pi$
$462$	−2.08227	−0.0968760
$463$	−37.7300	−1.75346	−0.876731	−	0.480981i	$-0.840281\pi$
$463$	−37.7300	−1.75346	−0.876731	+	0.480981i	$0.840281\pi$
$464$	−6.91536	−0.321037
$465$	1.82746	0.0847462
$466$	9.95812	0.461301
$467$	−20.9620	−0.970007	−0.485003	−	0.874512i	$-0.661182\pi$
$467$	−20.9620	−0.970007	−0.485003	+	0.874512i	$0.661182\pi$
$468$	−11.9296	−0.551446
$469$	−57.5550	−2.65764
$470$	−2.53680	−0.117014
$471$	−1.42479	−0.0656510
$472$	1.72070	0.0792018
$473$	−1.24641	−0.0573099
$474$	−5.45226	−0.250430
$475$	−3.54214	−0.162524
$476$	−3.34955	−0.153526
$477$	−9.83899	−0.450496
$478$	2.46068	0.112549
$479$	28.1864	1.28787	0.643934	−	0.765081i	$-0.277301\pi$
$479$	28.1864	1.28787	0.643934	+	0.765081i	$0.277301\pi$
$480$	−0.454872	−0.0207620
$481$	11.4336	0.521326
$482$	−7.09447	−0.323144
$483$	−13.1559	−0.598616
$484$	1.00000	0.0454545
$485$	−8.47368	−0.384770
$486$	11.1716	0.506755
$487$	24.3233	1.10219	0.551097	−	0.834441i	$-0.314209\pi$
$487$	24.3233	1.10219	0.551097	+	0.834441i	$0.314209\pi$
$488$	1.30545	0.0590948
$489$	4.73041	0.213917
$490$	−13.9554	−0.630439
$491$	−25.3312	−1.14318	−0.571590	−	0.820539i	$-0.693673\pi$
$491$	−25.3312	−1.14318	−0.571590	+	0.820539i	$0.693673\pi$
$492$	−4.85491	−0.218876
$493$	−5.06004	−0.227893
$494$	−15.1289	−0.680679
$495$	2.79309	0.125540
$496$	−4.01751	−0.180392
$497$	−44.8465	−2.01164
$498$	1.40939	0.0631565
$499$	−3.73180	−0.167058	−0.0835291	−	0.996505i	$-0.526619\pi$
$499$	−3.73180	−0.167058	−0.0835291	+	0.996505i	$0.526619\pi$
$500$	−1.00000	−0.0447214
$501$	2.42314	0.108258
$502$	16.6039	0.741067
$503$	−20.6274	−0.919729	−0.459864	−	0.887989i	$-0.652102\pi$
$503$	−20.6274	−0.919729	−0.459864	+	0.887989i	$0.652102\pi$
$504$	12.7859	0.569531
$505$	−9.97506	−0.443885
$506$	6.31807	0.280873
$507$	2.38461	0.105904
$508$	−7.02605	−0.311731
$509$	1.25507	0.0556299	0.0278150	−	0.999613i	$-0.491145\pi$
$509$	1.25507	0.0556299	0.0278150	+	0.999613i	$0.491145\pi$
$510$	−0.332835	−0.0147382
$511$	−4.57770	−0.202506
$512$	1.00000	0.0441942
$513$	9.33395	0.412104
$514$	−25.7655	−1.13647
$515$	−14.9319	−0.657979
$516$	−0.566957	−0.0249589
$517$	2.53680	0.111568
$518$	−12.2543	−0.538423
$519$	5.86352	0.257380
$520$	−4.27111	−0.187301
$521$	34.1663	1.49685	0.748426	−	0.663219i	$-0.230810\pi$
$521$	34.1663	1.49685	0.748426	+	0.663219i	$0.230810\pi$
$522$	19.3152	0.845404
$523$	−1.19603	−0.0522987	−0.0261493	−	0.999658i	$-0.508325\pi$
$523$	−1.19603	−0.0522987	−0.0261493	+	0.999658i	$0.508325\pi$
$524$	13.1959	0.576465
$525$	−2.08227	−0.0908777
$526$	16.0639	0.700419
$527$	−2.93965	−0.128053
$528$	0.454872	0.0197958
$529$	16.9181	0.735568
$530$	−3.52262	−0.153013
$531$	−4.80608	−0.208566
$532$	16.2149	0.703003
$533$	−45.5861	−1.97455
$534$	4.04264	0.174942
$535$	2.46952	0.106767
$536$	12.5729	0.543067
$537$	−0.198110	−0.00854909
$538$	12.5725	0.542040
$539$	13.9554	0.601100
$540$	2.63512	0.113397
$541$	−16.7719	−0.721079	−0.360539	−	0.932744i	$-0.617407\pi$
$541$	−16.7719	−0.721079	−0.360539	+	0.932744i	$0.617407\pi$
$542$	−11.8834	−0.510435
$543$	−0.563090	−0.0241645
$544$	0.731710	0.0313718
$545$	1.33743	0.0572891
$546$	−8.89360	−0.380611
$547$	−12.7811	−0.546481	−0.273240	−	0.961946i	$-0.588095\pi$
$547$	−12.7811	−0.546481	−0.273240	+	0.961946i	$0.588095\pi$
$548$	−11.5757	−0.494490
$549$	−3.64623	−0.155617
$550$	1.00000	0.0426401
$551$	24.4951	1.04353
$552$	2.87392	0.122322
$553$	54.8699	2.33331
$554$	−22.6950	−0.964216
$555$	−1.21767	−0.0516873
$556$	2.74422	0.116381
$557$	−31.5334	−1.33611	−0.668057	−	0.744110i	$-0.732874\pi$
$557$	−31.5334	−1.33611	−0.668057	+	0.744110i	$0.732874\pi$
$558$	11.2213	0.475035
$559$	−5.32355	−0.225162
$560$	4.57770	0.193443
$561$	0.332835	0.0140523
$562$	1.22335	0.0516040
$563$	−21.8616	−0.921357	−0.460679	−	0.887567i	$-0.652394\pi$
$563$	−21.8616	−0.921357	−0.460679	+	0.887567i	$0.652394\pi$
$564$	1.15392	0.0485888
$565$	−8.78779	−0.369705
$566$	27.4137	1.15228
$567$	−32.8708	−1.38044
$568$	9.79672	0.411061
$569$	1.75332	0.0735029	0.0367515	−	0.999324i	$-0.488299\pi$
$569$	1.75332	0.0735029	0.0367515	+	0.999324i	$0.488299\pi$
$570$	1.61122	0.0674866
$571$	1.19968	0.0502051	0.0251025	−	0.999685i	$-0.492009\pi$
$571$	1.19968	0.0502051	0.0251025	+	0.999685i	$0.492009\pi$
$572$	4.27111	0.178584
$573$	1.58789	0.0663351
$574$	48.8584	2.03931
$575$	6.31807	0.263482
$576$	−2.79309	−0.116379
$577$	−11.7537	−0.489315	−0.244657	−	0.969610i	$-0.578675\pi$
$577$	−11.7537	−0.489315	−0.244657	+	0.969610i	$0.578675\pi$
$578$	−16.4646	−0.684837
$579$	10.2824	0.427320
$580$	6.91536	0.287145
$581$	−14.1837	−0.588440
$582$	3.85444	0.159772
$583$	3.52262	0.145892
$584$	1.00000	0.0413803
$585$	11.9296	0.493228
$586$	2.64671	0.109335
$587$	6.48344	0.267600	0.133800	−	0.991008i	$-0.457282\pi$
$587$	6.48344	0.267600	0.133800	+	0.991008i	$0.457282\pi$
$588$	6.34791	0.261783
$589$	14.2306	0.586361
$590$	−1.72070	−0.0708403
$591$	0.880283	0.0362100
$592$	2.67695	0.110022
$593$	−30.3405	−1.24593	−0.622967	−	0.782248i	$-0.714073\pi$
$593$	−30.3405	−1.24593	−0.622967	+	0.782248i	$0.714073\pi$
$594$	−2.63512	−0.108120
$595$	3.34955	0.137318
$596$	−9.04073	−0.370323
$597$	7.44270	0.304609
$598$	26.9852	1.10351
$599$	−17.4079	−0.711267	−0.355633	−	0.934626i	$-0.615735\pi$
$599$	−17.4079	−0.711267	−0.355633	+	0.934626i	$0.615735\pi$
$600$	0.454872	0.0185701
$601$	15.7555	0.642680	0.321340	−	0.946964i	$-0.395867\pi$
$601$	15.7555	0.642680	0.321340	+	0.946964i	$0.395867\pi$
$602$	5.70569	0.232546
$603$	−35.1173	−1.43009
$604$	−8.21234	−0.334155
$605$	−1.00000	−0.0406558
$606$	4.53738	0.184318
$607$	35.4340	1.43822	0.719111	−	0.694895i	$-0.244549\pi$
$607$	35.4340	1.43822	0.719111	+	0.694895i	$0.244549\pi$
$608$	−3.54214	−0.143653
$609$	14.3996	0.583503
$610$	−1.30545	−0.0528560
$611$	10.8350	0.438335
$612$	−2.04373	−0.0826130
$613$	28.4643	1.14966	0.574831	−	0.818272i	$-0.305068\pi$
$613$	28.4643	1.14966	0.574831	+	0.818272i	$0.305068\pi$
$614$	−8.49467	−0.342817
$615$	4.85491	0.195769
$616$	−4.57770	−0.184441
$617$	−17.6367	−0.710028	−0.355014	−	0.934861i	$-0.615524\pi$
$617$	−17.6367	−0.710028	−0.355014	+	0.934861i	$0.615524\pi$
$618$	6.79211	0.273219
$619$	−0.264047	−0.0106129	−0.00530646	−	0.999986i	$-0.501689\pi$
$619$	−0.264047	−0.0106129	−0.00530646	+	0.999986i	$0.501689\pi$
$620$	4.01751	0.161347
$621$	−16.6489	−0.668096
$622$	12.1329	0.486486
$623$	−40.6840	−1.62997
$624$	1.94281	0.0777746
$625$	1.00000	0.0400000
$626$	−24.1157	−0.963856
$627$	−1.61122	−0.0643459
$628$	−3.13229	−0.124992
$629$	1.95875	0.0781006
$630$	−12.7859	−0.509404
$631$	−24.5336	−0.976668	−0.488334	−	0.872657i	$-0.662395\pi$
$631$	−24.5336	−0.976668	−0.488334	+	0.872657i	$0.662395\pi$
$632$	−11.9863	−0.476791
$633$	11.0251	0.438207
$634$	29.6269	1.17663
$635$	7.02605	0.278820
$636$	1.60234	0.0635369
$637$	59.6049	2.36163
$638$	−6.91536	−0.273782
$639$	−27.3631	−1.08247
$640$	−1.00000	−0.0395285
$641$	−24.7203	−0.976393	−0.488197	−	0.872734i	$-0.662345\pi$
$641$	−24.7203	−0.976393	−0.488197	+	0.872734i	$0.662345\pi$
$642$	−1.12332	−0.0443338
$643$	−32.8078	−1.29381	−0.646907	−	0.762569i	$-0.723938\pi$
$643$	−32.8078	−1.29381	−0.646907	+	0.762569i	$0.723938\pi$
$644$	−28.9223	−1.13970
$645$	0.566957	0.0223239
$646$	−2.59182	−0.101974
$647$	17.4577	0.686334	0.343167	−	0.939274i	$-0.388500\pi$
$647$	17.4577	0.686334	0.343167	+	0.939274i	$0.388500\pi$
$648$	7.18063	0.282082
$649$	1.72070	0.0675436
$650$	4.27111	0.167527
$651$	8.36555	0.327872
$652$	10.3994	0.407273
$653$	−20.6007	−0.806168	−0.403084	−	0.915163i	$-0.632062\pi$
$653$	−20.6007	−0.806168	−0.403084	+	0.915163i	$0.632062\pi$
$654$	−0.608359	−0.0237887
$655$	−13.1959	−0.515606
$656$	−10.6731	−0.416715
$657$	−2.79309	−0.108969
$658$	−11.6127	−0.452711
$659$	−12.3497	−0.481078	−0.240539	−	0.970639i	$-0.577324\pi$
$659$	−12.3497	−0.481078	−0.240539	+	0.970639i	$0.577324\pi$
$660$	−0.454872	−0.0177059
$661$	−11.1444	−0.433466	−0.216733	−	0.976231i	$-0.569540\pi$
$661$	−11.1444	−0.433466	−0.216733	+	0.976231i	$0.569540\pi$
$662$	1.43579	0.0558035
$663$	1.42157	0.0552093
$664$	3.09844	0.120243
$665$	−16.2149	−0.628785
$666$	−7.47698	−0.289727
$667$	−43.6917	−1.69175
$668$	5.32708	0.206111
$669$	−3.43687	−0.132877
$670$	−12.5729	−0.485734
$671$	1.30545	0.0503962
$672$	−2.08227	−0.0803253
$673$	11.1796	0.430944	0.215472	−	0.976510i	$-0.430871\pi$
$673$	11.1796	0.430944	0.215472	+	0.976510i	$0.430871\pi$
$674$	2.94646	0.113493
$675$	−2.63512	−0.101426
$676$	5.24237	0.201630
$677$	11.1218	0.427445	0.213722	−	0.976894i	$-0.431441\pi$
$677$	11.1218	0.427445	0.213722	+	0.976894i	$0.431441\pi$
$678$	3.99732	0.153516
$679$	−38.7900	−1.48862
$680$	−0.731710	−0.0280598
$681$	−6.20625	−0.237824
$682$	−4.01751	−0.153839
$683$	−38.4934	−1.47291	−0.736455	−	0.676486i	$-0.763502\pi$
$683$	−38.4934	−1.47291	−0.736455	+	0.676486i	$0.763502\pi$
$684$	9.89351	0.378288
$685$	11.5757	0.442285
$686$	−31.8396	−1.21564
$687$	8.82550	0.336714
$688$	−1.24641	−0.0475189
$689$	15.0455	0.573187
$690$	−2.87392	−0.109408
$691$	−22.8712	−0.870063	−0.435032	−	0.900415i	$-0.643263\pi$
$691$	−22.8712	−0.870063	−0.435032	+	0.900415i	$0.643263\pi$
$692$	12.8905	0.490022
$693$	12.7859	0.485698
$694$	−0.822206	−0.0312105
$695$	−2.74422	−0.104094
$696$	−3.14560	−0.119234
$697$	−7.80963	−0.295811
$698$	−5.74464	−0.217438
$699$	4.52967	0.171328
$700$	−4.57770	−0.173021
$701$	8.95957	0.338398	0.169199	−	0.985582i	$-0.445882\pi$
$701$	8.95957	0.338398	0.169199	+	0.985582i	$0.445882\pi$
$702$	−11.2549	−0.424788
$703$	−9.48214	−0.357626
$704$	1.00000	0.0376889
$705$	−1.15392	−0.0434591
$706$	−8.32572	−0.313343
$707$	−45.6629	−1.71733
$708$	0.782701	0.0294157
$709$	−41.5616	−1.56088	−0.780440	−	0.625231i	$-0.785005\pi$
$709$	−41.5616	−1.56088	−0.780440	+	0.625231i	$0.785005\pi$
$710$	−9.79672	−0.367664
$711$	33.4790	1.25556
$712$	8.88742	0.333070
$713$	−25.3830	−0.950599
$714$	−1.52362	−0.0570200
$715$	−4.27111	−0.159730
$716$	−0.435529	−0.0162765
$717$	1.11929	0.0418008
$718$	5.07434	0.189373
$719$	21.4358	0.799420	0.399710	−	0.916642i	$-0.369111\pi$
$719$	21.4358	0.799420	0.399710	+	0.916642i	$0.369111\pi$
$720$	2.79309	0.104092
$721$	−68.3538	−2.54563
$722$	−6.45326	−0.240166
$723$	−3.22708	−0.120016
$724$	−1.23791	−0.0460065
$725$	−6.91536	−0.256830
$726$	0.454872	0.0168819
$727$	−9.63680	−0.357409	−0.178705	−	0.983903i	$-0.557191\pi$
$727$	−9.63680	−0.357409	−0.178705	+	0.983903i	$0.557191\pi$
$728$	−19.5519	−0.724640
$729$	−16.4602	−0.609638
$730$	−1.00000	−0.0370117
$731$	−0.912009	−0.0337319
$732$	0.593811	0.0219479
$733$	−21.7986	−0.805148	−0.402574	−	0.915387i	$-0.631884\pi$
$733$	−21.7986	−0.805148	−0.402574	+	0.915387i	$0.631884\pi$
$734$	8.95934	0.330695
$735$	−6.34791	−0.234146
$736$	6.31807	0.232887
$737$	12.5729	0.463129
$738$	29.8110	1.09736
$739$	−40.4118	−1.48657	−0.743285	−	0.668974i	$-0.766734\pi$
$739$	−40.4118	−1.48657	−0.743285	+	0.668974i	$0.766734\pi$
$740$	−2.67695	−0.0984068
$741$	−6.88170	−0.252805
$742$	−16.1255	−0.591985
$743$	−17.9881	−0.659918	−0.329959	−	0.943995i	$-0.607035\pi$
$743$	−17.9881	−0.659918	−0.329959	+	0.943995i	$0.607035\pi$
$744$	−1.82746	−0.0669978
$745$	9.04073	0.331227
$746$	−11.6798	−0.427627
$747$	−8.65422	−0.316642
$748$	0.731710	0.0267540
$749$	11.3047	0.413066
$750$	−0.454872	−0.0166096
$751$	37.9296	1.38407	0.692036	−	0.721863i	$-0.256714\pi$
$751$	37.9296	1.38407	0.692036	+	0.721863i	$0.256714\pi$
$752$	2.53680	0.0925076
$753$	7.55265	0.275234
$754$	−29.5362	−1.07565
$755$	8.21234	0.298878
$756$	12.0628	0.438719
$757$	−45.6944	−1.66079	−0.830396	−	0.557173i	$-0.811886\pi$
$757$	−45.6944	−1.66079	−0.830396	+	0.557173i	$0.811886\pi$
$758$	18.1912	0.660734
$759$	2.87392	0.104317
$760$	3.54214	0.128487
$761$	−5.22552	−0.189425	−0.0947125	−	0.995505i	$-0.530193\pi$
$761$	−5.22552	−0.189425	−0.0947125	+	0.995505i	$0.530193\pi$
$762$	−3.19596	−0.115777
$763$	6.12235	0.221644
$764$	3.49085	0.126294
$765$	2.04373	0.0738913
$766$	−9.36174	−0.338253
$767$	7.34932	0.265368
$768$	0.454872	0.0164138
$769$	−35.3320	−1.27411	−0.637053	−	0.770820i	$-0.719847\pi$
$769$	−35.3320	−1.27411	−0.637053	+	0.770820i	$0.719847\pi$
$770$	4.57770	0.164969
$771$	−11.7200	−0.422086
$772$	22.6049	0.813570
$773$	40.3370	1.45082	0.725410	−	0.688317i	$-0.241650\pi$
$773$	40.3370	1.45082	0.725410	+	0.688317i	$0.241650\pi$
$774$	3.48133	0.125134
$775$	−4.01751	−0.144313
$776$	8.47368	0.304187
$777$	−5.57414	−0.199971
$778$	−24.9461	−0.894361
$779$	37.8057	1.35453
$780$	−1.94281	−0.0695637
$781$	9.79672	0.350554
$782$	4.62300	0.165318
$783$	18.2228	0.651229
$784$	13.9554	0.498406
$785$	3.13229	0.111796
$786$	6.00244	0.214100
$787$	3.98497	0.142049	0.0710245	−	0.997475i	$-0.477373\pi$
$787$	3.98497	0.142049	0.0710245	+	0.997475i	$0.477373\pi$
$788$	1.93523	0.0689398
$789$	7.30702	0.260137
$790$	11.9863	0.426455
$791$	−40.2279	−1.43034
$792$	−2.79309	−0.0992482
$793$	5.57570	0.197999
$794$	2.93175	0.104044
$795$	−1.60234	−0.0568292
$796$	16.3622	0.579942
$797$	13.6160	0.482305	0.241153	−	0.970487i	$-0.422475\pi$
$797$	13.6160	0.482305	0.241153	+	0.970487i	$0.422475\pi$
$798$	7.37569	0.261096
$799$	1.85620	0.0656677
$800$	1.00000	0.0353553
$801$	−24.8234	−0.877091
$802$	4.60029	0.162442
$803$	1.00000	0.0352892
$804$	5.71907	0.201696
$805$	28.9223	1.01938
$806$	−17.1592	−0.604408
$807$	5.71889	0.201315
$808$	9.97506	0.350922
$809$	−0.492519	−0.0173160	−0.00865802	−	0.999963i	$-0.502756\pi$
$809$	−0.492519	−0.0173160	−0.00865802	+	0.999963i	$0.502756\pi$
$810$	−7.18063	−0.252302
$811$	3.65880	0.128478	0.0642390	−	0.997935i	$-0.479538\pi$
$811$	3.65880	0.128478	0.0642390	+	0.997935i	$0.479538\pi$
$812$	31.6564	1.11092
$813$	−5.40542	−0.189576
$814$	2.67695	0.0938272
$815$	−10.3994	−0.364276
$816$	0.332835	0.0116515
$817$	4.41495	0.154460
$818$	30.7353	1.07463
$819$	54.6101	1.90823
$820$	10.6731	0.372722
$821$	−7.33959	−0.256154	−0.128077	−	0.991764i	$-0.540880\pi$
$821$	−7.33959	−0.256154	−0.128077	+	0.991764i	$0.540880\pi$
$822$	−5.26547	−0.183654
$823$	26.8034	0.934307	0.467154	−	0.884176i	$-0.345279\pi$
$823$	26.8034	0.934307	0.467154	+	0.884176i	$0.345279\pi$
$824$	14.9319	0.520178
$825$	0.454872	0.0158366
$826$	−7.87687	−0.274071
$827$	−30.3312	−1.05472	−0.527360	−	0.849642i	$-0.676818\pi$
$827$	−30.3312	−1.05472	−0.527360	+	0.849642i	$0.676818\pi$
$828$	−17.6470	−0.613274
$829$	29.3102	1.01799	0.508993	−	0.860771i	$-0.330018\pi$
$829$	29.3102	1.01799	0.508993	+	0.860771i	$0.330018\pi$
$830$	−3.09844	−0.107548
$831$	−10.3233	−0.358112
$832$	4.27111	0.148074
$833$	10.2113	0.353800
$834$	1.24827	0.0432240
$835$	−5.32708	−0.184351
$836$	−3.54214	−0.122507
$837$	10.5866	0.365927
$838$	1.50568	0.0520128
$839$	55.6761	1.92215	0.961077	−	0.276281i	$-0.0891020\pi$
$839$	55.6761	1.92215	0.961077	+	0.276281i	$0.0891020\pi$
$840$	2.08227	0.0718451
$841$	18.8222	0.649040
$842$	−25.4270	−0.876272
$843$	0.556469	0.0191658
$844$	24.2377	0.834296
$845$	−5.24237	−0.180343
$846$	−7.08551	−0.243605
$847$	−4.57770	−0.157292
$848$	3.52262	0.120967
$849$	12.4697	0.427961
$850$	0.731710	0.0250974
$851$	16.9132	0.579777
$852$	4.45626	0.152669
$853$	−4.30535	−0.147412	−0.0737061	−	0.997280i	$-0.523483\pi$
$853$	−4.30535	−0.147412	−0.0737061	+	0.997280i	$0.523483\pi$
$854$	−5.97595	−0.204493
$855$	−9.89351	−0.338351
$856$	−2.46952	−0.0844066
$857$	−19.6775	−0.672169	−0.336085	−	0.941832i	$-0.609103\pi$
$857$	−19.6775	−0.672169	−0.336085	+	0.941832i	$0.609103\pi$
$858$	1.94281	0.0663264
$859$	16.7991	0.573176	0.286588	−	0.958054i	$-0.407479\pi$
$859$	16.7991	0.573176	0.286588	+	0.958054i	$0.407479\pi$
$860$	1.24641	0.0425022
$861$	22.2243	0.757403
$862$	32.2504	1.09845
$863$	7.78133	0.264880	0.132440	−	0.991191i	$-0.457719\pi$
$863$	7.78133	0.264880	0.132440	+	0.991191i	$0.457719\pi$
$864$	−2.63512	−0.0896485
$865$	−12.8905	−0.438289
$866$	−14.6490	−0.497794
$867$	−7.48929	−0.254350
$868$	18.3910	0.624231
$869$	−11.9863	−0.406609
$870$	3.14560	0.106646
$871$	53.7003	1.81956
$872$	−1.33743	−0.0452910
$873$	−23.6678	−0.801032
$874$	−22.3795	−0.756998
$875$	4.57770	0.154755
$876$	0.454872	0.0153687
$877$	29.3750	0.991923	0.495962	−	0.868344i	$-0.334816\pi$
$877$	29.3750	0.991923	0.495962	+	0.868344i	$0.334816\pi$
$878$	11.4278	0.385668
$879$	1.20392	0.0406071
$880$	−1.00000	−0.0337100
$881$	−54.7691	−1.84522	−0.922609	−	0.385736i	$-0.873948\pi$
$881$	−54.7691	−1.84522	−0.922609	+	0.385736i	$0.873948\pi$
$882$	−38.9786	−1.31248
$883$	24.5387	0.825792	0.412896	−	0.910778i	$-0.364517\pi$
$883$	24.5387	0.825792	0.412896	+	0.910778i	$0.364517\pi$
$884$	3.12521	0.105112
$885$	−0.782701	−0.0263102
$886$	17.1812	0.577214
$887$	26.5428	0.891221	0.445610	−	0.895227i	$-0.352987\pi$
$887$	26.5428	0.891221	0.445610	+	0.895227i	$0.352987\pi$
$888$	1.21767	0.0408624
$889$	32.1632	1.07872
$890$	−8.88742	−0.297907
$891$	7.18063	0.240560
$892$	−7.55567	−0.252983
$893$	−8.98570	−0.300695
$894$	−4.11238	−0.137538
$895$	0.435529	0.0145581
$896$	−4.57770	−0.152930
$897$	12.2748	0.409844
$898$	28.2540	0.942848
$899$	27.7825	0.926600
$900$	−2.79309	−0.0931030
$901$	2.57753	0.0858701
$902$	−10.6731	−0.355376
$903$	2.59536	0.0863681
$904$	8.78779	0.292278
$905$	1.23791	0.0411495
$906$	−3.73557	−0.124106
$907$	41.6386	1.38259	0.691293	−	0.722574i	$-0.257041\pi$
$907$	41.6386	1.38259	0.691293	+	0.722574i	$0.257041\pi$
$908$	−13.6439	−0.452790
$909$	−27.8613	−0.924100
$910$	19.5519	0.648138
$911$	56.6775	1.87781	0.938905	−	0.344176i	$-0.111842\pi$
$911$	56.6775	1.87781	0.938905	+	0.344176i	$0.111842\pi$
$912$	−1.61122	−0.0533528
$913$	3.09844	0.102543
$914$	24.4711	0.809433
$915$	−0.593811	−0.0196308
$916$	19.4021	0.641065
$917$	−60.4068	−1.99481
$918$	−1.92814	−0.0636381
$919$	43.6250	1.43906	0.719528	−	0.694464i	$-0.244358\pi$
$919$	43.6250	1.43906	0.719528	+	0.694464i	$0.244358\pi$
$920$	−6.31807	−0.208301
$921$	−3.86399	−0.127323
$922$	10.0996	0.332614
$923$	41.8429	1.37727
$924$	−2.08227	−0.0685017
$925$	2.67695	0.0880177
$926$	−37.7300	−1.23989
$927$	−41.7062	−1.36981
$928$	−6.91536	−0.227008
$929$	−43.2170	−1.41790	−0.708952	−	0.705257i	$-0.750832\pi$
$929$	−43.2170	−1.41790	−0.708952	+	0.705257i	$0.750832\pi$
$930$	1.82746	0.0599246
$931$	−49.4318	−1.62006
$932$	9.95812	0.326189
$933$	5.51893	0.180682
$934$	−20.9620	−0.685898
$935$	−0.731710	−0.0239295
$936$	−11.9296	−0.389931
$937$	19.1434	0.625388	0.312694	−	0.949854i	$-0.398769\pi$
$937$	19.1434	0.625388	0.312694	+	0.949854i	$0.398769\pi$
$938$	−57.5550	−1.87924
$939$	−10.9695	−0.357978
$940$	−2.53680	−0.0827413
$941$	−17.1787	−0.560011	−0.280005	−	0.959998i	$-0.590336\pi$
$941$	−17.1787	−0.560011	−0.280005	+	0.959998i	$0.590336\pi$
$942$	−1.42479	−0.0464223
$943$	−67.4336	−2.19594
$944$	1.72070	0.0560042
$945$	−12.0628	−0.392402
$946$	−1.24641	−0.0405242
$947$	−26.9032	−0.874235	−0.437118	−	0.899404i	$-0.644001\pi$
$947$	−26.9032	−0.874235	−0.437118	+	0.899404i	$0.644001\pi$
$948$	−5.45226	−0.177081
$949$	4.27111	0.138646
$950$	−3.54214	−0.114922
$951$	13.4764	0.437003
$952$	−3.34955	−0.108560
$953$	43.6719	1.41467	0.707335	−	0.706878i	$-0.249897\pi$
$953$	43.6719	1.41467	0.707335	+	0.706878i	$0.249897\pi$
$954$	−9.83899	−0.318549
$955$	−3.49085	−0.112961
$956$	2.46068	0.0795839
$957$	−3.14560	−0.101683
$958$	28.1864	0.910661
$959$	52.9902	1.71114
$960$	−0.454872	−0.0146809
$961$	−14.8596	−0.479341
$962$	11.4336	0.368633
$963$	6.89760	0.222272
$964$	−7.09447	−0.228497
$965$	−22.6049	−0.727679
$966$	−13.1559	−0.423285
$967$	3.89976	0.125408	0.0627039	−	0.998032i	$-0.480028\pi$
$967$	3.89976	0.125408	0.0627039	+	0.998032i	$0.480028\pi$
$968$	1.00000	0.0321412
$969$	−1.17895	−0.0378732
$970$	−8.47368	−0.272073
$971$	1.13157	0.0363139	0.0181569	−	0.999835i	$-0.494220\pi$
$971$	1.13157	0.0363139	0.0181569	+	0.999835i	$0.494220\pi$
$972$	11.1716	0.358330
$973$	−12.5622	−0.402726
$974$	24.3233	0.779369
$975$	1.94281	0.0622197
$976$	1.30545	0.0417863
$977$	15.5695	0.498111	0.249056	−	0.968489i	$-0.419880\pi$
$977$	15.5695	0.498111	0.249056	+	0.968489i	$0.419880\pi$
$978$	4.73041	0.151262
$979$	8.88742	0.284043
$980$	−13.9554	−0.445788
$981$	3.73556	0.119267
$982$	−25.3312	−0.808350
$983$	−27.3231	−0.871471	−0.435736	−	0.900075i	$-0.643512\pi$
$983$	−27.3231	−0.871471	−0.435736	+	0.900075i	$0.643512\pi$
$984$	−4.85491	−0.154769
$985$	−1.93523	−0.0616616
$986$	−5.06004	−0.161144
$987$	−5.28230	−0.168138
$988$	−15.1289	−0.481313
$989$	−7.87490	−0.250407
$990$	2.79309	0.0887703
$991$	−1.47888	−0.0469783	−0.0234892	−	0.999724i	$-0.507478\pi$
$991$	−1.47888	−0.0469783	−0.0234892	+	0.999724i	$0.507478\pi$
$992$	−4.01751	−0.127556
$993$	0.653101	0.0207255
$994$	−44.8465	−1.42244
$995$	−16.3622	−0.518716
$996$	1.40939	0.0446584
$997$	−53.5423	−1.69570	−0.847851	−	0.530235i	$-0.822104\pi$
$997$	−53.5423	−1.69570	−0.847851	+	0.530235i	$0.822104\pi$
$998$	−3.73180	−0.118128
$999$	−7.05409	−0.223181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bd.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bd.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.454872 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.454872 q^{6} -4.57770 q^{7} +1.00000 q^{8} -2.79309 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.454872 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.454872 q^{6} -4.57770 q^{7} +1.00000 q^{8} -2.79309 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.454872 q^{12} +4.27111 q^{13} -4.57770 q^{14} -0.454872 q^{15} +1.00000 q^{16} +0.731710 q^{17} -2.79309 q^{18} -3.54214 q^{19} -1.00000 q^{20} -2.08227 q^{21} +1.00000 q^{22} +6.31807 q^{23} +0.454872 q^{24} +1.00000 q^{25} +4.27111 q^{26} -2.63512 q^{27} -4.57770 q^{28} -6.91536 q^{29} -0.454872 q^{30} -4.01751 q^{31} +1.00000 q^{32} +0.454872 q^{33} +0.731710 q^{34} +4.57770 q^{35} -2.79309 q^{36} +2.67695 q^{37} -3.54214 q^{38} +1.94281 q^{39} -1.00000 q^{40} -10.6731 q^{41} -2.08227 q^{42} -1.24641 q^{43} +1.00000 q^{44} +2.79309 q^{45} +6.31807 q^{46} +2.53680 q^{47} +0.454872 q^{48} +13.9554 q^{49} +1.00000 q^{50} +0.332835 q^{51} +4.27111 q^{52} +3.52262 q^{53} -2.63512 q^{54} -1.00000 q^{55} -4.57770 q^{56} -1.61122 q^{57} -6.91536 q^{58} +1.72070 q^{59} -0.454872 q^{60} +1.30545 q^{61} -4.01751 q^{62} +12.7859 q^{63} +1.00000 q^{64} -4.27111 q^{65} +0.454872 q^{66} +12.5729 q^{67} +0.731710 q^{68} +2.87392 q^{69} +4.57770 q^{70} +9.79672 q^{71} -2.79309 q^{72} +1.00000 q^{73} +2.67695 q^{74} +0.454872 q^{75} -3.54214 q^{76} -4.57770 q^{77} +1.94281 q^{78} -11.9863 q^{79} -1.00000 q^{80} +7.18063 q^{81} -10.6731 q^{82} +3.09844 q^{83} -2.08227 q^{84} -0.731710 q^{85} -1.24641 q^{86} -3.14560 q^{87} +1.00000 q^{88} +8.88742 q^{89} +2.79309 q^{90} -19.5519 q^{91} +6.31807 q^{92} -1.82746 q^{93} +2.53680 q^{94} +3.54214 q^{95} +0.454872 q^{96} +8.47368 q^{97} +13.9554 q^{98} -2.79309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{2} + 6 q^{3} + 14 q^{4} - 14 q^{5} + 6 q^{6} + 4 q^{7} + 14 q^{8} + 24 q^{9}+O(q^{10}) \) 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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