LMFDB - Embedded newform 4030.2.a.r.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1797120146$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 8x^{7} + 39x^{6} + 13x^{5} - 106x^{4} + 9x^{3} + 74x^{2} - 3x - 7 $ x^9 - 4x^8 - 8x^7 + 39x^6 + 13x^5 - 106x^4 + 9x^3 + 74x^2 - 3x - 7
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.78896$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.40140 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40140 q^{6} -1.57433 q^{7} +1.00000 q^{8} -1.03607 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.40140 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40140 q^{6} -1.57433 q^{7} +1.00000 q^{8} -1.03607 q^{9} +1.00000 q^{10} +2.98933 q^{11} +1.40140 q^{12} +1.00000 q^{13} -1.57433 q^{14} +1.40140 q^{15} +1.00000 q^{16} +0.689528 q^{17} -1.03607 q^{18} +6.64866 q^{19} +1.00000 q^{20} -2.20627 q^{21} +2.98933 q^{22} -4.04549 q^{23} +1.40140 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.65616 q^{27} -1.57433 q^{28} +5.90748 q^{29} +1.40140 q^{30} -1.00000 q^{31} +1.00000 q^{32} +4.18926 q^{33} +0.689528 q^{34} -1.57433 q^{35} -1.03607 q^{36} +4.02247 q^{37} +6.64866 q^{38} +1.40140 q^{39} +1.00000 q^{40} -0.671358 q^{41} -2.20627 q^{42} +5.19560 q^{43} +2.98933 q^{44} -1.03607 q^{45} -4.04549 q^{46} +9.40786 q^{47} +1.40140 q^{48} -4.52149 q^{49} +1.00000 q^{50} +0.966306 q^{51} +1.00000 q^{52} +4.54659 q^{53} -5.65616 q^{54} +2.98933 q^{55} -1.57433 q^{56} +9.31746 q^{57} +5.90748 q^{58} +5.23941 q^{59} +1.40140 q^{60} +3.98898 q^{61} -1.00000 q^{62} +1.63111 q^{63} +1.00000 q^{64} +1.00000 q^{65} +4.18926 q^{66} +1.17327 q^{67} +0.689528 q^{68} -5.66937 q^{69} -1.57433 q^{70} -7.19911 q^{71} -1.03607 q^{72} -8.84495 q^{73} +4.02247 q^{74} +1.40140 q^{75} +6.64866 q^{76} -4.70619 q^{77} +1.40140 q^{78} -12.2866 q^{79} +1.00000 q^{80} -4.81836 q^{81} -0.671358 q^{82} -4.78598 q^{83} -2.20627 q^{84} +0.689528 q^{85} +5.19560 q^{86} +8.27876 q^{87} +2.98933 q^{88} -7.93897 q^{89} -1.03607 q^{90} -1.57433 q^{91} -4.04549 q^{92} -1.40140 q^{93} +9.40786 q^{94} +6.64866 q^{95} +1.40140 q^{96} +18.0920 q^{97} -4.52149 q^{98} -3.09715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.40140	0.809101	0.404550	−	0.914516i	$-0.367428\pi$
$3$	1.40140	0.809101	0.404550	+	0.914516i	$0.367428\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.40140	0.572121
$7$	−1.57433	−0.595040	−0.297520	−	0.954716i	$-0.596159\pi$
$7$	−1.57433	−0.595040	−0.297520	+	0.954716i	$0.596159\pi$
$8$	1.00000	0.353553
$9$	−1.03607	−0.345356
$10$	1.00000	0.316228
$11$	2.98933	0.901317	0.450659	−	0.892696i	$-0.351189\pi$
$11$	2.98933	0.901317	0.450659	+	0.892696i	$0.351189\pi$
$12$	1.40140	0.404550
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.57433	−0.420757
$15$	1.40140	0.361841
$16$	1.00000	0.250000
$17$	0.689528	0.167235	0.0836175	−	0.996498i	$-0.473353\pi$
$17$	0.689528	0.167235	0.0836175	+	0.996498i	$0.473353\pi$
$18$	−1.03607	−0.244204
$19$	6.64866	1.52531	0.762654	−	0.646807i	$-0.223896\pi$
$19$	6.64866	1.52531	0.762654	+	0.646807i	$0.223896\pi$
$20$	1.00000	0.223607
$21$	−2.20627	−0.481447
$22$	2.98933	0.637328
$23$	−4.04549	−0.843544	−0.421772	−	0.906702i	$-0.638592\pi$
$23$	−4.04549	−0.843544	−0.421772	+	0.906702i	$0.638592\pi$
$24$	1.40140	0.286060
$25$	1.00000	0.200000
$26$	1.00000	0.196116
$27$	−5.65616	−1.08853
$28$	−1.57433	−0.297520
$29$	5.90748	1.09699	0.548495	−	0.836154i	$-0.315201\pi$
$29$	5.90748	1.09699	0.548495	+	0.836154i	$0.315201\pi$
$30$	1.40140	0.255860
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	4.18926	0.729256
$34$	0.689528	0.118253
$35$	−1.57433	−0.266110
$36$	−1.03607	−0.172678
$37$	4.02247	0.661290	0.330645	−	0.943755i	$-0.392734\pi$
$37$	4.02247	0.661290	0.330645	+	0.943755i	$0.392734\pi$
$38$	6.64866	1.07855
$39$	1.40140	0.224404
$40$	1.00000	0.158114
$41$	−0.671358	−0.104848	−0.0524242	−	0.998625i	$-0.516695\pi$
$41$	−0.671358	−0.104848	−0.0524242	+	0.998625i	$0.516695\pi$
$42$	−2.20627	−0.340435
$43$	5.19560	0.792322	0.396161	−	0.918181i	$-0.370342\pi$
$43$	5.19560	0.792322	0.396161	+	0.918181i	$0.370342\pi$
$44$	2.98933	0.450659
$45$	−1.03607	−0.154448
$46$	−4.04549	−0.596475
$47$	9.40786	1.37228	0.686139	−	0.727471i	$-0.259304\pi$
$47$	9.40786	1.37228	0.686139	+	0.727471i	$0.259304\pi$
$48$	1.40140	0.202275
$49$	−4.52149	−0.645927
$50$	1.00000	0.141421
$51$	0.966306	0.135310
$52$	1.00000	0.138675
$53$	4.54659	0.624522	0.312261	−	0.949996i	$-0.398914\pi$
$53$	4.54659	0.624522	0.312261	+	0.949996i	$0.398914\pi$
$54$	−5.65616	−0.769706
$55$	2.98933	0.403081
$56$	−1.57433	−0.210378
$57$	9.31746	1.23413
$58$	5.90748	0.775690
$59$	5.23941	0.682113	0.341056	−	0.940043i	$-0.389215\pi$
$59$	5.23941	0.682113	0.341056	+	0.940043i	$0.389215\pi$
$60$	1.40140	0.180920
$61$	3.98898	0.510737	0.255368	−	0.966844i	$-0.417803\pi$
$61$	3.98898	0.510737	0.255368	+	0.966844i	$0.417803\pi$
$62$	−1.00000	−0.127000
$63$	1.63111	0.205501
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	4.18926	0.515662
$67$	1.17327	0.143338	0.0716691	−	0.997428i	$-0.477167\pi$
$67$	1.17327	0.143338	0.0716691	+	0.997428i	$0.477167\pi$
$68$	0.689528	0.0836175
$69$	−5.66937	−0.682512
$70$	−1.57433	−0.188168
$71$	−7.19911	−0.854377	−0.427189	−	0.904162i	$-0.640496\pi$
$71$	−7.19911	−0.854377	−0.427189	+	0.904162i	$0.640496\pi$
$72$	−1.03607	−0.122102
$73$	−8.84495	−1.03522	−0.517612	−	0.855616i	$-0.673179\pi$
$73$	−8.84495	−1.03522	−0.517612	+	0.855616i	$0.673179\pi$
$74$	4.02247	0.467602
$75$	1.40140	0.161820
$76$	6.64866	0.762654
$77$	−4.70619	−0.536320
$78$	1.40140	0.158678
$79$	−12.2866	−1.38236	−0.691178	−	0.722685i	$-0.742908\pi$
$79$	−12.2866	−1.38236	−0.691178	+	0.722685i	$0.742908\pi$
$80$	1.00000	0.111803
$81$	−4.81836	−0.535373
$82$	−0.671358	−0.0741391
$83$	−4.78598	−0.525330	−0.262665	−	0.964887i	$-0.584601\pi$
$83$	−4.78598	−0.525330	−0.262665	+	0.964887i	$0.584601\pi$
$84$	−2.20627	−0.240724
$85$	0.689528	0.0747898
$86$	5.19560	0.560256
$87$	8.27876	0.887576
$88$	2.98933	0.318664
$89$	−7.93897	−0.841529	−0.420765	−	0.907170i	$-0.638238\pi$
$89$	−7.93897	−0.841529	−0.420765	+	0.907170i	$0.638238\pi$
$90$	−1.03607	−0.109211
$91$	−1.57433	−0.165034
$92$	−4.04549	−0.421772
$93$	−1.40140	−0.145319
$94$	9.40786	0.970347
$95$	6.64866	0.682138
$96$	1.40140	0.143030
$97$	18.0920	1.83696	0.918480	−	0.395468i	$-0.129418\pi$
$97$	18.0920	1.83696	0.918480	+	0.395468i	$0.129418\pi$
$98$	−4.52149	−0.456740
$99$	−3.09715	−0.311275
$100$	1.00000	0.100000
$101$	−0.865190	−0.0860896	−0.0430448	−	0.999073i	$-0.513706\pi$
$101$	−0.865190	−0.0860896	−0.0430448	+	0.999073i	$0.513706\pi$
$102$	0.966306	0.0956786
$103$	12.9389	1.27491	0.637455	−	0.770487i	$-0.279987\pi$
$103$	12.9389	1.27491	0.637455	+	0.770487i	$0.279987\pi$
$104$	1.00000	0.0980581
$105$	−2.20627	−0.215310
$106$	4.54659	0.441604
$107$	15.6869	1.51651	0.758255	−	0.651959i	$-0.226052\pi$
$107$	15.6869	1.51651	0.758255	+	0.651959i	$0.226052\pi$
$108$	−5.65616	−0.544264
$109$	3.06135	0.293224	0.146612	−	0.989194i	$-0.453163\pi$
$109$	3.06135	0.293224	0.146612	+	0.989194i	$0.453163\pi$
$110$	2.98933	0.285022
$111$	5.63710	0.535050
$112$	−1.57433	−0.148760
$113$	−3.22833	−0.303695	−0.151848	−	0.988404i	$-0.548522\pi$
$113$	−3.22833	−0.303695	−0.151848	+	0.988404i	$0.548522\pi$
$114$	9.31746	0.872660
$115$	−4.04549	−0.377244
$116$	5.90748	0.548495
$117$	−1.03607	−0.0957845
$118$	5.23941	0.482326
$119$	−1.08554	−0.0995115
$120$	1.40140	0.127930
$121$	−2.06390	−0.187627
$122$	3.98898	0.361145
$123$	−0.940843	−0.0848330
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	1.63111	0.145311
$127$	−0.751073	−0.0666470	−0.0333235	−	0.999445i	$-0.510609\pi$
$127$	−0.751073	−0.0666470	−0.0333235	+	0.999445i	$0.510609\pi$
$128$	1.00000	0.0883883
$129$	7.28113	0.641068
$130$	1.00000	0.0877058
$131$	−5.35616	−0.467970	−0.233985	−	0.972240i	$-0.575177\pi$
$131$	−5.35616	−0.467970	−0.233985	+	0.972240i	$0.575177\pi$
$132$	4.18926	0.364628
$133$	−10.4672	−0.907619
$134$	1.17327	0.101355
$135$	−5.65616	−0.486805
$136$	0.689528	0.0591265
$137$	16.1337	1.37839	0.689197	−	0.724574i	$-0.257963\pi$
$137$	16.1337	1.37839	0.689197	+	0.724574i	$0.257963\pi$
$138$	−5.66937	−0.482609
$139$	−7.19302	−0.610104	−0.305052	−	0.952336i	$-0.598674\pi$
$139$	−7.19302	−0.610104	−0.305052	+	0.952336i	$0.598674\pi$
$140$	−1.57433	−0.133055
$141$	13.1842	1.11031
$142$	−7.19911	−0.604136
$143$	2.98933	0.249980
$144$	−1.03607	−0.0863390
$145$	5.90748	0.490589
$146$	−8.84495	−0.732013
$147$	−6.33644	−0.522620
$148$	4.02247	0.330645
$149$	−0.237440	−0.0194519	−0.00972593	−	0.999953i	$-0.503096\pi$
$149$	−0.237440	−0.0194519	−0.00972593	+	0.999953i	$0.503096\pi$
$150$	1.40140	0.114424
$151$	14.0173	1.14071	0.570354	−	0.821399i	$-0.306806\pi$
$151$	14.0173	1.14071	0.570354	+	0.821399i	$0.306806\pi$
$152$	6.64866	0.539277
$153$	−0.714397	−0.0577556
$154$	−4.70619	−0.379235
$155$	−1.00000	−0.0803219
$156$	1.40140	0.112202
$157$	−11.8459	−0.945405	−0.472703	−	0.881222i	$-0.656722\pi$
$157$	−11.8459	−0.945405	−0.472703	+	0.881222i	$0.656722\pi$
$158$	−12.2866	−0.977473
$159$	6.37161	0.505301
$160$	1.00000	0.0790569
$161$	6.36893	0.501942
$162$	−4.81836	−0.378566
$163$	−5.51305	−0.431815	−0.215908	−	0.976414i	$-0.569271\pi$
$163$	−5.51305	−0.431815	−0.215908	+	0.976414i	$0.569271\pi$
$164$	−0.671358	−0.0524242
$165$	4.18926	0.326133
$166$	−4.78598	−0.371464
$167$	16.2222	1.25531	0.627657	−	0.778490i	$-0.284014\pi$
$167$	16.2222	1.25531	0.627657	+	0.778490i	$0.284014\pi$
$168$	−2.20627	−0.170217
$169$	1.00000	0.0769231
$170$	0.689528	0.0528844
$171$	−6.88846	−0.526774
$172$	5.19560	0.396161
$173$	−11.3634	−0.863944	−0.431972	−	0.901887i	$-0.642182\pi$
$173$	−11.3634	−0.863944	−0.431972	+	0.901887i	$0.642182\pi$
$174$	8.27876	0.627611
$175$	−1.57433	−0.119008
$176$	2.98933	0.225329
$177$	7.34252	0.551898
$178$	−7.93897	−0.595051
$179$	−18.0993	−1.35281	−0.676403	−	0.736532i	$-0.736462\pi$
$179$	−18.0993	−1.35281	−0.676403	+	0.736532i	$0.736462\pi$
$180$	−1.03607	−0.0772239
$181$	10.1753	0.756323	0.378161	−	0.925740i	$-0.376556\pi$
$181$	10.1753	0.756323	0.378161	+	0.925740i	$0.376556\pi$
$182$	−1.57433	−0.116697
$183$	5.59017	0.413238
$184$	−4.04549	−0.298238
$185$	4.02247	0.295738
$186$	−1.40140	−0.102756
$187$	2.06123	0.150732
$188$	9.40786	0.686139
$189$	8.90465	0.647718
$190$	6.64866	0.482344
$191$	2.94760	0.213281	0.106640	−	0.994298i	$-0.465991\pi$
$191$	2.94760	0.213281	0.106640	+	0.994298i	$0.465991\pi$
$192$	1.40140	0.101138
$193$	−9.36505	−0.674111	−0.337056	−	0.941485i	$-0.609431\pi$
$193$	−9.36505	−0.674111	−0.337056	+	0.941485i	$0.609431\pi$
$194$	18.0920	1.29893
$195$	1.40140	0.100357
$196$	−4.52149	−0.322964
$197$	0.181056	0.0128997	0.00644985	−	0.999979i	$-0.497947\pi$
$197$	0.181056	0.0128997	0.00644985	+	0.999979i	$0.497947\pi$
$198$	−3.09715	−0.220105
$199$	−4.63097	−0.328281	−0.164140	−	0.986437i	$-0.552485\pi$
$199$	−4.63097	−0.328281	−0.164140	+	0.986437i	$0.552485\pi$
$200$	1.00000	0.0707107
$201$	1.64423	0.115975
$202$	−0.865190	−0.0608745
$203$	−9.30030	−0.652753
$204$	0.966306	0.0676550
$205$	−0.671358	−0.0468897
$206$	12.9389	0.901498
$207$	4.19140	0.291323
$208$	1.00000	0.0693375
$209$	19.8750	1.37479
$210$	−2.20627	−0.152247
$211$	−13.3733	−0.920659	−0.460329	−	0.887748i	$-0.652269\pi$
$211$	−13.3733	−0.920659	−0.460329	+	0.887748i	$0.652269\pi$
$212$	4.54659	0.312261
$213$	−10.0889	−0.691277
$214$	15.6869	1.07233
$215$	5.19560	0.354337
$216$	−5.65616	−0.384853
$217$	1.57433	0.106872
$218$	3.06135	0.207341
$219$	−12.3953	−0.837600
$220$	2.98933	0.201541
$221$	0.689528	0.0463826
$222$	5.63710	0.378337
$223$	−21.3111	−1.42710	−0.713549	−	0.700605i	$-0.752913\pi$
$223$	−21.3111	−1.42710	−0.713549	+	0.700605i	$0.752913\pi$
$224$	−1.57433	−0.105189
$225$	−1.03607	−0.0690712
$226$	−3.22833	−0.214745
$227$	−18.7696	−1.24578	−0.622890	−	0.782309i	$-0.714042\pi$
$227$	−18.7696	−1.24578	−0.622890	+	0.782309i	$0.714042\pi$
$228$	9.31746	0.617064
$229$	12.7888	0.845110	0.422555	−	0.906337i	$-0.361133\pi$
$229$	12.7888	0.845110	0.422555	+	0.906337i	$0.361133\pi$
$230$	−4.04549	−0.266752
$231$	−6.59527	−0.433937
$232$	5.90748	0.387845
$233$	−22.0399	−1.44388	−0.721941	−	0.691955i	$-0.756750\pi$
$233$	−22.0399	−1.44388	−0.721941	+	0.691955i	$0.756750\pi$
$234$	−1.03607	−0.0677299
$235$	9.40786	0.613701
$236$	5.23941	0.341056
$237$	−17.2186	−1.11847
$238$	−1.08554	−0.0703653
$239$	−23.9887	−1.55170	−0.775850	−	0.630917i	$-0.782679\pi$
$239$	−23.9887	−1.55170	−0.775850	+	0.630917i	$0.782679\pi$
$240$	1.40140	0.0904602
$241$	−15.5168	−0.999527	−0.499763	−	0.866162i	$-0.666580\pi$
$241$	−15.5168	−0.999527	−0.499763	+	0.866162i	$0.666580\pi$
$242$	−2.06390	−0.132673
$243$	10.2160	0.655358
$244$	3.98898	0.255368
$245$	−4.52149	−0.288868
$246$	−0.940843	−0.0599860
$247$	6.64866	0.423044
$248$	−1.00000	−0.0635001
$249$	−6.70709	−0.425045
$250$	1.00000	0.0632456
$251$	−3.33443	−0.210467	−0.105234	−	0.994448i	$-0.533559\pi$
$251$	−3.33443	−0.210467	−0.105234	+	0.994448i	$0.533559\pi$
$252$	1.63111	0.102750
$253$	−12.0933	−0.760300
$254$	−0.751073	−0.0471265
$255$	0.966306	0.0605125
$256$	1.00000	0.0625000
$257$	−23.8214	−1.48594	−0.742970	−	0.669324i	$-0.766584\pi$
$257$	−23.8214	−1.48594	−0.742970	+	0.669324i	$0.766584\pi$
$258$	7.28113	0.453304
$259$	−6.33268	−0.393494
$260$	1.00000	0.0620174
$261$	−6.12055	−0.378852
$262$	−5.35616	−0.330905
$263$	14.3324	0.883775	0.441887	−	0.897071i	$-0.354309\pi$
$263$	14.3324	0.883775	0.441887	+	0.897071i	$0.354309\pi$
$264$	4.18926	0.257831
$265$	4.54659	0.279295
$266$	−10.4672	−0.641783
$267$	−11.1257	−0.680882
$268$	1.17327	0.0716691
$269$	11.5162	0.702157	0.351078	−	0.936346i	$-0.385815\pi$
$269$	11.5162	0.702157	0.351078	+	0.936346i	$0.385815\pi$
$270$	−5.65616	−0.344223
$271$	−3.22309	−0.195789	−0.0978944	−	0.995197i	$-0.531211\pi$
$271$	−3.22309	−0.195789	−0.0978944	+	0.995197i	$0.531211\pi$
$272$	0.689528	0.0418088
$273$	−2.20627	−0.133529
$274$	16.1337	0.974672
$275$	2.98933	0.180263
$276$	−5.66937	−0.341256
$277$	−7.39728	−0.444460	−0.222230	−	0.974994i	$-0.571334\pi$
$277$	−7.39728	−0.444460	−0.222230	+	0.974994i	$0.571334\pi$
$278$	−7.19302	−0.431409
$279$	1.03607	0.0620278
$280$	−1.57433	−0.0940841
$281$	7.78652	0.464505	0.232252	−	0.972656i	$-0.425390\pi$
$281$	7.78652	0.464505	0.232252	+	0.972656i	$0.425390\pi$
$282$	13.1842	0.785108
$283$	−17.3600	−1.03195	−0.515973	−	0.856605i	$-0.672570\pi$
$283$	−17.3600	−1.03195	−0.515973	+	0.856605i	$0.672570\pi$
$284$	−7.19911	−0.427189
$285$	9.31746	0.551918
$286$	2.98933	0.176763
$287$	1.05694	0.0623890
$288$	−1.03607	−0.0610509
$289$	−16.5246	−0.972032
$290$	5.90748	0.346899
$291$	25.3541	1.48629
$292$	−8.84495	−0.517612
$293$	9.64550	0.563496	0.281748	−	0.959488i	$-0.409086\pi$
$293$	9.64550	0.563496	0.281748	+	0.959488i	$0.409086\pi$
$294$	−6.33644	−0.369548
$295$	5.23941	0.305050
$296$	4.02247	0.233801
$297$	−16.9081	−0.981110
$298$	−0.237440	−0.0137545
$299$	−4.04549	−0.233957
$300$	1.40140	0.0809101
$301$	−8.17958	−0.471463
$302$	14.0173	0.806603
$303$	−1.21248	−0.0696551
$304$	6.64866	0.381327
$305$	3.98898	0.228408
$306$	−0.714397	−0.0408394
$307$	11.1854	0.638385	0.319193	−	0.947690i	$-0.396588\pi$
$307$	11.1854	0.638385	0.319193	+	0.947690i	$0.396588\pi$
$308$	−4.70619	−0.268160
$309$	18.1327	1.03153
$310$	−1.00000	−0.0567962
$311$	−21.0936	−1.19611	−0.598053	−	0.801456i	$-0.704059\pi$
$311$	−21.0936	−1.19611	−0.598053	+	0.801456i	$0.704059\pi$
$312$	1.40140	0.0793389
$313$	13.1471	0.743118	0.371559	−	0.928409i	$-0.378823\pi$
$313$	13.1471	0.743118	0.371559	+	0.928409i	$0.378823\pi$
$314$	−11.8459	−0.668502
$315$	1.63111	0.0919027
$316$	−12.2866	−0.691178
$317$	−21.6003	−1.21319	−0.606596	−	0.795010i	$-0.707465\pi$
$317$	−21.6003	−1.21319	−0.606596	+	0.795010i	$0.707465\pi$
$318$	6.37161	0.357302
$319$	17.6594	0.988737
$320$	1.00000	0.0559017
$321$	21.9837	1.22701
$322$	6.36893	0.354927
$323$	4.58443	0.255085
$324$	−4.81836	−0.267687
$325$	1.00000	0.0554700
$326$	−5.51305	−0.305340
$327$	4.29018	0.237248
$328$	−0.671358	−0.0370695
$329$	−14.8111	−0.816560
$330$	4.18926	0.230611
$331$	1.40743	0.0773593	0.0386797	−	0.999252i	$-0.487685\pi$
$331$	1.40743	0.0773593	0.0386797	+	0.999252i	$0.487685\pi$
$332$	−4.78598	−0.262665
$333$	−4.16755	−0.228380
$334$	16.2222	0.887641
$335$	1.17327	0.0641028
$336$	−2.20627	−0.120362
$337$	26.9867	1.47006	0.735029	−	0.678035i	$-0.237168\pi$
$337$	26.9867	1.47006	0.735029	+	0.678035i	$0.237168\pi$
$338$	1.00000	0.0543928
$339$	−4.52419	−0.245720
$340$	0.689528	0.0373949
$341$	−2.98933	−0.161881
$342$	−6.88846	−0.372485
$343$	18.1386	0.979393
$344$	5.19560	0.280128
$345$	−5.66937	−0.305229
$346$	−11.3634	−0.610901
$347$	−18.5664	−0.996696	−0.498348	−	0.866977i	$-0.666060\pi$
$347$	−18.5664	−0.996696	−0.498348	+	0.866977i	$0.666060\pi$
$348$	8.27876	0.443788
$349$	−33.1384	−1.77386	−0.886928	−	0.461908i	$-0.847165\pi$
$349$	−33.1384	−1.77386	−0.886928	+	0.461908i	$0.847165\pi$
$350$	−1.57433	−0.0841514
$351$	−5.65616	−0.301903
$352$	2.98933	0.159332
$353$	25.9881	1.38321	0.691603	−	0.722278i	$-0.256905\pi$
$353$	25.9881	1.38321	0.691603	+	0.722278i	$0.256905\pi$
$354$	7.34252	0.390251
$355$	−7.19911	−0.382089
$356$	−7.93897	−0.420765
$357$	−1.52128	−0.0805148
$358$	−18.0993	−0.956578
$359$	6.48864	0.342457	0.171229	−	0.985231i	$-0.445226\pi$
$359$	6.48864	0.342457	0.171229	+	0.985231i	$0.445226\pi$
$360$	−1.03607	−0.0546056
$361$	25.2047	1.32656
$362$	10.1753	0.534801
$363$	−2.89236	−0.151809
$364$	−1.57433	−0.0825172
$365$	−8.84495	−0.462966
$366$	5.59017	0.292203
$367$	10.1985	0.532356	0.266178	−	0.963924i	$-0.414239\pi$
$367$	10.1985	0.532356	0.266178	+	0.963924i	$0.414239\pi$
$368$	−4.04549	−0.210886
$369$	0.695572	0.0362100
$370$	4.02247	0.209118
$371$	−7.15782	−0.371616
$372$	−1.40140	−0.0726594
$373$	5.07941	0.263002	0.131501	−	0.991316i	$-0.458020\pi$
$373$	5.07941	0.263002	0.131501	+	0.991316i	$0.458020\pi$
$374$	2.06123	0.106583
$375$	1.40140	0.0723682
$376$	9.40786	0.485173
$377$	5.90748	0.304250
$378$	8.90465	0.458006
$379$	−15.9606	−0.819841	−0.409921	−	0.912121i	$-0.634444\pi$
$379$	−15.9606	−0.819841	−0.409921	+	0.912121i	$0.634444\pi$
$380$	6.64866	0.341069
$381$	−1.05256	−0.0539241
$382$	2.94760	0.150812
$383$	−26.0127	−1.32919	−0.664594	−	0.747205i	$-0.731395\pi$
$383$	−26.0127	−1.32919	−0.664594	+	0.747205i	$0.731395\pi$
$384$	1.40140	0.0715151
$385$	−4.70619	−0.239849
$386$	−9.36505	−0.476669
$387$	−5.38299	−0.273633
$388$	18.0920	0.918480
$389$	−19.2543	−0.976232	−0.488116	−	0.872779i	$-0.662316\pi$
$389$	−19.2543	−0.976232	−0.488116	+	0.872779i	$0.662316\pi$
$390$	1.40140	0.0709628
$391$	−2.78948	−0.141070
$392$	−4.52149	−0.228370
$393$	−7.50615	−0.378635
$394$	0.181056	0.00912147
$395$	−12.2866	−0.618208
$396$	−3.09715	−0.155638
$397$	25.4556	1.27758	0.638790	−	0.769381i	$-0.279435\pi$
$397$	25.4556	1.27758	0.638790	+	0.769381i	$0.279435\pi$
$398$	−4.63097	−0.232130
$399$	−14.6687	−0.734355
$400$	1.00000	0.0500000
$401$	−35.4752	−1.77155	−0.885773	−	0.464118i	$-0.846371\pi$
$401$	−35.4752	−1.77155	−0.885773	+	0.464118i	$0.846371\pi$
$402$	1.64423	0.0820067
$403$	−1.00000	−0.0498135
$404$	−0.865190	−0.0430448
$405$	−4.81836	−0.239426
$406$	−9.30030	−0.461566
$407$	12.0245	0.596032
$408$	0.966306	0.0478393
$409$	−20.1355	−0.995636	−0.497818	−	0.867282i	$-0.665865\pi$
$409$	−20.1355	−0.995636	−0.497818	+	0.867282i	$0.665865\pi$
$410$	−0.671358	−0.0331560
$411$	22.6098	1.11526
$412$	12.9389	0.637455
$413$	−8.24854	−0.405884
$414$	4.19140	0.205996
$415$	−4.78598	−0.234935
$416$	1.00000	0.0490290
$417$	−10.0803	−0.493636
$418$	19.8750	0.972120
$419$	17.1999	0.840272	0.420136	−	0.907461i	$-0.361982\pi$
$419$	17.1999	0.840272	0.420136	+	0.907461i	$0.361982\pi$
$420$	−2.20627	−0.107655
$421$	11.4356	0.557337	0.278669	−	0.960387i	$-0.410107\pi$
$421$	11.4356	0.557337	0.278669	+	0.960387i	$0.410107\pi$
$422$	−13.3733	−0.651004
$423$	−9.74718	−0.473924
$424$	4.54659	0.220802
$425$	0.689528	0.0334470
$426$	−10.0889	−0.488807
$427$	−6.27997	−0.303909
$428$	15.6869	0.758255
$429$	4.18926	0.202259
$430$	5.19560	0.250554
$431$	9.02122	0.434537	0.217268	−	0.976112i	$-0.430285\pi$
$431$	9.02122	0.434537	0.217268	+	0.976112i	$0.430285\pi$
$432$	−5.65616	−0.272132
$433$	−26.4014	−1.26877	−0.634385	−	0.773017i	$-0.718747\pi$
$433$	−26.4014	−1.26877	−0.634385	+	0.773017i	$0.718747\pi$
$434$	1.57433	0.0755701
$435$	8.27876	0.396936
$436$	3.06135	0.146612
$437$	−26.8971	−1.28666
$438$	−12.3953	−0.592273
$439$	4.30409	0.205423	0.102711	−	0.994711i	$-0.467248\pi$
$439$	4.30409	0.205423	0.102711	+	0.994711i	$0.467248\pi$
$440$	2.98933	0.142511
$441$	4.68457	0.223075
$442$	0.689528	0.0327975
$443$	33.2696	1.58069	0.790343	−	0.612665i	$-0.209902\pi$
$443$	33.2696	1.58069	0.790343	+	0.612665i	$0.209902\pi$
$444$	5.63710	0.267525
$445$	−7.93897	−0.376343
$446$	−21.3111	−1.00911
$447$	−0.332749	−0.0157385
$448$	−1.57433	−0.0743800
$449$	−36.0306	−1.70039	−0.850194	−	0.526470i	$-0.823515\pi$
$449$	−36.0306	−1.70039	−0.850194	+	0.526470i	$0.823515\pi$
$450$	−1.03607	−0.0488407
$451$	−2.00691	−0.0945017
$452$	−3.22833	−0.151848
$453$	19.6438	0.922948
$454$	−18.7696	−0.880900
$455$	−1.57433	−0.0738056
$456$	9.31746	0.436330
$457$	5.05528	0.236476	0.118238	−	0.992985i	$-0.462275\pi$
$457$	5.05528	0.236476	0.118238	+	0.992985i	$0.462275\pi$
$458$	12.7888	0.597583
$459$	−3.90008	−0.182040
$460$	−4.04549	−0.188622
$461$	−7.48812	−0.348756	−0.174378	−	0.984679i	$-0.555792\pi$
$461$	−7.48812	−0.348756	−0.174378	+	0.984679i	$0.555792\pi$
$462$	−6.59527	−0.306840
$463$	34.3941	1.59843	0.799215	−	0.601045i	$-0.205249\pi$
$463$	34.3941	1.59843	0.799215	+	0.601045i	$0.205249\pi$
$464$	5.90748	0.274248
$465$	−1.40140	−0.0649885
$466$	−22.0399	−1.02098
$467$	10.2802	0.475713	0.237857	−	0.971300i	$-0.423555\pi$
$467$	10.2802	0.475713	0.237857	+	0.971300i	$0.423555\pi$
$468$	−1.03607	−0.0478923
$469$	−1.84712	−0.0852919
$470$	9.40786	0.433952
$471$	−16.6009	−0.764928
$472$	5.23941	0.241163
$473$	15.5314	0.714133
$474$	−17.2186	−0.790874
$475$	6.64866	0.305061
$476$	−1.08554	−0.0497558
$477$	−4.71058	−0.215682
$478$	−23.9887	−1.09722
$479$	18.8580	0.861645	0.430823	−	0.902437i	$-0.358223\pi$
$479$	18.8580	0.861645	0.430823	+	0.902437i	$0.358223\pi$
$480$	1.40140	0.0639650
$481$	4.02247	0.183409
$482$	−15.5168	−0.706772
$483$	8.92544	0.406122
$484$	−2.06390	−0.0938136
$485$	18.0920	0.821513
$486$	10.2160	0.463408
$487$	11.3420	0.513957	0.256978	−	0.966417i	$-0.417273\pi$
$487$	11.3420	0.513957	0.256978	+	0.966417i	$0.417273\pi$
$488$	3.98898	0.180573
$489$	−7.72601	−0.349382
$490$	−4.52149	−0.204260
$491$	6.14820	0.277465	0.138732	−	0.990330i	$-0.455697\pi$
$491$	6.14820	0.277465	0.138732	+	0.990330i	$0.455697\pi$
$492$	−0.940843	−0.0424165
$493$	4.07337	0.183455
$494$	6.64866	0.299137
$495$	−3.09715	−0.139207
$496$	−1.00000	−0.0449013
$497$	11.3338	0.508389
$498$	−6.70709	−0.300552
$499$	−2.31210	−0.103504	−0.0517519	−	0.998660i	$-0.516481\pi$
$499$	−2.31210	−0.103504	−0.0517519	+	0.998660i	$0.516481\pi$
$500$	1.00000	0.0447214
$501$	22.7339	1.01568
$502$	−3.33443	−0.148823
$503$	−0.136938	−0.00610578	−0.00305289	−	0.999995i	$-0.500972\pi$
$503$	−0.136938	−0.00610578	−0.00305289	+	0.999995i	$0.500972\pi$
$504$	1.63111	0.0726554
$505$	−0.865190	−0.0385004
$506$	−12.0933	−0.537614
$507$	1.40140	0.0622385
$508$	−0.751073	−0.0333235
$509$	20.4454	0.906227	0.453113	−	0.891453i	$-0.350313\pi$
$509$	20.4454	0.906227	0.453113	+	0.891453i	$0.350313\pi$
$510$	0.966306	0.0427888
$511$	13.9249	0.615999
$512$	1.00000	0.0441942
$513$	−37.6059	−1.66034
$514$	−23.8214	−1.05072
$515$	12.9389	0.570157
$516$	7.28113	0.320534
$517$	28.1232	1.23686
$518$	−6.33268	−0.278242
$519$	−15.9247	−0.699018
$520$	1.00000	0.0438529
$521$	7.69784	0.337248	0.168624	−	0.985680i	$-0.446068\pi$
$521$	7.69784	0.337248	0.168624	+	0.985680i	$0.446068\pi$
$522$	−6.12055	−0.267889
$523$	15.4340	0.674881	0.337440	−	0.941347i	$-0.390439\pi$
$523$	15.4340	0.674881	0.337440	+	0.941347i	$0.390439\pi$
$524$	−5.35616	−0.233985
$525$	−2.20627	−0.0962895
$526$	14.3324	0.624923
$527$	−0.689528	−0.0300363
$528$	4.18926	0.182314
$529$	−6.63399	−0.288434
$530$	4.54659	0.197491
$531$	−5.42838	−0.235572
$532$	−10.4672	−0.453809
$533$	−0.671358	−0.0290797
$534$	−11.1257	−0.481456
$535$	15.6869	0.678204
$536$	1.17327	0.0506777
$537$	−25.3644	−1.09456
$538$	11.5162	0.496500
$539$	−13.5162	−0.582186
$540$	−5.65616	−0.243402
$541$	2.44845	0.105267	0.0526336	−	0.998614i	$-0.483238\pi$
$541$	2.44845	0.105267	0.0526336	+	0.998614i	$0.483238\pi$
$542$	−3.22309	−0.138444
$543$	14.2597	0.611941
$544$	0.689528	0.0295633
$545$	3.06135	0.131134
$546$	−2.20627	−0.0944196
$547$	−36.6096	−1.56531	−0.782657	−	0.622454i	$-0.786136\pi$
$547$	−36.6096	−1.56531	−0.782657	+	0.622454i	$0.786136\pi$
$548$	16.1337	0.689197
$549$	−4.13286	−0.176386
$550$	2.98933	0.127466
$551$	39.2768	1.67325
$552$	−5.66937	−0.241304
$553$	19.3432	0.822557
$554$	−7.39728	−0.314280
$555$	5.63710	0.239282
$556$	−7.19302	−0.305052
$557$	−10.8205	−0.458479	−0.229240	−	0.973370i	$-0.573624\pi$
$557$	−10.8205	−0.458479	−0.229240	+	0.973370i	$0.573624\pi$
$558$	1.03607	0.0438602
$559$	5.19560	0.219750
$560$	−1.57433	−0.0665275
$561$	2.88861	0.121957
$562$	7.78652	0.328454
$563$	−22.0305	−0.928474	−0.464237	−	0.885711i	$-0.653671\pi$
$563$	−22.0305	−0.928474	−0.464237	+	0.885711i	$0.653671\pi$
$564$	13.1842	0.555156
$565$	−3.22833	−0.135817
$566$	−17.3600	−0.729696
$567$	7.58568	0.318569
$568$	−7.19911	−0.302068
$569$	17.4234	0.730426	0.365213	−	0.930924i	$-0.380996\pi$
$569$	17.4234	0.730426	0.365213	+	0.930924i	$0.380996\pi$
$570$	9.31746	0.390265
$571$	4.05805	0.169824	0.0849120	−	0.996388i	$-0.472939\pi$
$571$	4.05805	0.169824	0.0849120	+	0.996388i	$0.472939\pi$
$572$	2.98933	0.124990
$573$	4.13077	0.172565
$574$	1.05694	0.0441157
$575$	−4.04549	−0.168709
$576$	−1.03607	−0.0431695
$577$	3.52557	0.146771	0.0733857	−	0.997304i	$-0.476620\pi$
$577$	3.52557	0.146771	0.0733857	+	0.997304i	$0.476620\pi$
$578$	−16.5246	−0.687331
$579$	−13.1242	−0.545424
$580$	5.90748	0.245295
$581$	7.53470	0.312592
$582$	25.3541	1.05096
$583$	13.5913	0.562893
$584$	−8.84495	−0.366007
$585$	−1.03607	−0.0428361
$586$	9.64550	0.398452
$587$	−6.50312	−0.268412	−0.134206	−	0.990953i	$-0.542848\pi$
$587$	−6.50312	−0.268412	−0.134206	+	0.990953i	$0.542848\pi$
$588$	−6.33644	−0.261310
$589$	−6.64866	−0.273953
$590$	5.23941	0.215703
$591$	0.253733	0.0104372
$592$	4.02247	0.165322
$593$	−47.8435	−1.96470	−0.982349	−	0.187059i	$-0.940104\pi$
$593$	−47.8435	−1.96470	−0.982349	+	0.187059i	$0.940104\pi$
$594$	−16.9081	−0.693749
$595$	−1.08554	−0.0445029
$596$	−0.237440	−0.00972593
$597$	−6.48986	−0.265612
$598$	−4.04549	−0.165432
$599$	14.3218	0.585174	0.292587	−	0.956239i	$-0.405484\pi$
$599$	14.3218	0.585174	0.292587	+	0.956239i	$0.405484\pi$
$600$	1.40140	0.0572121
$601$	25.0426	1.02151	0.510755	−	0.859726i	$-0.329366\pi$
$601$	25.0426	1.02151	0.510755	+	0.859726i	$0.329366\pi$
$602$	−8.17958	−0.333375
$603$	−1.21559	−0.0495027
$604$	14.0173	0.570354
$605$	−2.06390	−0.0839095
$606$	−1.21248	−0.0492536
$607$	−5.26605	−0.213743	−0.106871	−	0.994273i	$-0.534083\pi$
$607$	−5.26605	−0.213743	−0.106871	+	0.994273i	$0.534083\pi$
$608$	6.64866	0.269639
$609$	−13.0335	−0.528143
$610$	3.98898	0.161509
$611$	9.40786	0.380601
$612$	−0.714397	−0.0288778
$613$	−26.4768	−1.06939	−0.534693	−	0.845046i	$-0.679573\pi$
$613$	−26.4768	−1.06939	−0.534693	+	0.845046i	$0.679573\pi$
$614$	11.1854	0.451407
$615$	−0.940843	−0.0379385
$616$	−4.70619	−0.189618
$617$	−26.5750	−1.06987	−0.534935	−	0.844893i	$-0.679664\pi$
$617$	−26.5750	−1.06987	−0.534935	+	0.844893i	$0.679664\pi$
$618$	18.1327	0.729403
$619$	−5.24823	−0.210944	−0.105472	−	0.994422i	$-0.533635\pi$
$619$	−5.24823	−0.210944	−0.105472	+	0.994422i	$0.533635\pi$
$620$	−1.00000	−0.0401610
$621$	22.8820	0.918221
$622$	−21.0936	−0.845775
$623$	12.4985	0.500744
$624$	1.40140	0.0561010
$625$	1.00000	0.0400000
$626$	13.1471	0.525464
$627$	27.8530	1.11234
$628$	−11.8459	−0.472703
$629$	2.77360	0.110591
$630$	1.63111	0.0649850
$631$	−9.82185	−0.391002	−0.195501	−	0.980704i	$-0.562633\pi$
$631$	−9.82185	−0.391002	−0.195501	+	0.980704i	$0.562633\pi$
$632$	−12.2866	−0.488737
$633$	−18.7414	−0.744906
$634$	−21.6003	−0.857856
$635$	−0.751073	−0.0298054
$636$	6.37161	0.252651
$637$	−4.52149	−0.179148
$638$	17.6594	0.699142
$639$	7.45877	0.295064
$640$	1.00000	0.0395285
$641$	−4.10249	−0.162038	−0.0810192	−	0.996713i	$-0.525818\pi$
$641$	−4.10249	−0.162038	−0.0810192	+	0.996713i	$0.525818\pi$
$642$	21.9837	0.867626
$643$	−19.7943	−0.780609	−0.390305	−	0.920686i	$-0.627630\pi$
$643$	−19.7943	−0.780609	−0.390305	+	0.920686i	$0.627630\pi$
$644$	6.36893	0.250971
$645$	7.28113	0.286694
$646$	4.58443	0.180372
$647$	19.4818	0.765909	0.382954	−	0.923767i	$-0.374907\pi$
$647$	19.4818	0.765909	0.382954	+	0.923767i	$0.374907\pi$
$648$	−4.81836	−0.189283
$649$	15.6623	0.614800
$650$	1.00000	0.0392232
$651$	2.20627	0.0864705
$652$	−5.51305	−0.215908
$653$	−29.0674	−1.13750	−0.568748	−	0.822512i	$-0.692572\pi$
$653$	−29.0674	−1.13750	−0.568748	+	0.822512i	$0.692572\pi$
$654$	4.29018	0.167759
$655$	−5.35616	−0.209283
$656$	−0.671358	−0.0262121
$657$	9.16397	0.357520
$658$	−14.8111	−0.577395
$659$	45.2167	1.76139	0.880697	−	0.473680i	$-0.157075\pi$
$659$	45.2167	1.76139	0.880697	+	0.473680i	$0.157075\pi$
$660$	4.18926	0.163067
$661$	−10.4045	−0.404687	−0.202344	−	0.979315i	$-0.564856\pi$
$661$	−10.4045	−0.404687	−0.202344	+	0.979315i	$0.564856\pi$
$662$	1.40743	0.0547013
$663$	0.966306	0.0375282
$664$	−4.78598	−0.185732
$665$	−10.4672	−0.405899
$666$	−4.16755	−0.161489
$667$	−23.8986	−0.925359
$668$	16.2222	0.627657
$669$	−29.8655	−1.15467
$670$	1.17327	0.0453275
$671$	11.9244	0.460336
$672$	−2.20627	−0.0851087
$673$	−13.3884	−0.516085	−0.258042	−	0.966134i	$-0.583077\pi$
$673$	−13.3884	−0.516085	−0.258042	+	0.966134i	$0.583077\pi$
$674$	26.9867	1.03949
$675$	−5.65616	−0.217706
$676$	1.00000	0.0384615
$677$	0.0957854	0.00368133	0.00184067	−	0.999998i	$-0.499414\pi$
$677$	0.0957854	0.00368133	0.00184067	+	0.999998i	$0.499414\pi$
$678$	−4.52419	−0.173750
$679$	−28.4827	−1.09306
$680$	0.689528	0.0264422
$681$	−26.3038	−1.00796
$682$	−2.98933	−0.114467
$683$	17.3039	0.662114	0.331057	−	0.943611i	$-0.392595\pi$
$683$	17.3039	0.662114	0.331057	+	0.943611i	$0.392595\pi$
$684$	−6.88846	−0.263387
$685$	16.1337	0.616437
$686$	18.1386	0.692535
$687$	17.9223	0.683779
$688$	5.19560	0.198080
$689$	4.54659	0.173211
$690$	−5.66937	−0.215829
$691$	14.3494	0.545875	0.272938	−	0.962032i	$-0.412005\pi$
$691$	14.3494	0.545875	0.272938	+	0.962032i	$0.412005\pi$
$692$	−11.3634	−0.431972
$693$	4.87593	0.185221
$694$	−18.5664	−0.704771
$695$	−7.19302	−0.272847
$696$	8.27876	0.313806
$697$	−0.462920	−0.0175343
$698$	−33.1384	−1.25431
$699$	−30.8868	−1.16825
$700$	−1.57433	−0.0595040
$701$	17.0650	0.644535	0.322268	−	0.946649i	$-0.395555\pi$
$701$	17.0650	0.644535	0.322268	+	0.946649i	$0.395555\pi$
$702$	−5.65616	−0.213478
$703$	26.7440	1.00867
$704$	2.98933	0.112665
$705$	13.1842	0.496546
$706$	25.9881	0.978074
$707$	1.36209	0.0512267
$708$	7.34252	0.275949
$709$	−46.3330	−1.74007	−0.870037	−	0.492987i	$-0.835905\pi$
$709$	−46.3330	−1.74007	−0.870037	+	0.492987i	$0.835905\pi$
$710$	−7.19911	−0.270178
$711$	12.7298	0.477405
$712$	−7.93897	−0.297526
$713$	4.04549	0.151505
$714$	−1.52128	−0.0569326
$715$	2.98933	0.111795
$716$	−18.0993	−0.676403
$717$	−33.6179	−1.25548
$718$	6.48864	0.242154
$719$	−24.2827	−0.905592	−0.452796	−	0.891614i	$-0.649573\pi$
$719$	−24.2827	−0.905592	−0.452796	+	0.891614i	$0.649573\pi$
$720$	−1.03607	−0.0386120
$721$	−20.3701	−0.758623
$722$	25.2047	0.938021
$723$	−21.7453	−0.808718
$724$	10.1753	0.378161
$725$	5.90748	0.219398
$726$	−2.89236	−0.107345
$727$	34.0753	1.26378	0.631892	−	0.775057i	$-0.282279\pi$
$727$	34.0753	1.26378	0.631892	+	0.775057i	$0.282279\pi$
$728$	−1.57433	−0.0583485
$729$	28.7718	1.06562
$730$	−8.84495	−0.327366
$731$	3.58251	0.132504
$732$	5.59017	0.206619
$733$	−2.64042	−0.0975260	−0.0487630	−	0.998810i	$-0.515528\pi$
$733$	−2.64042	−0.0975260	−0.0487630	+	0.998810i	$0.515528\pi$
$734$	10.1985	0.376433
$735$	−6.33644	−0.233723
$736$	−4.04549	−0.149119
$737$	3.50730	0.129193
$738$	0.695572	0.0256044
$739$	−5.77282	−0.212356	−0.106178	−	0.994347i	$-0.533861\pi$
$739$	−5.77282	−0.212356	−0.106178	+	0.994347i	$0.533861\pi$
$740$	4.02247	0.147869
$741$	9.31746	0.342285
$742$	−7.15782	−0.262772
$743$	−17.2019	−0.631076	−0.315538	−	0.948913i	$-0.602185\pi$
$743$	−17.2019	−0.631076	−0.315538	+	0.948913i	$0.602185\pi$
$744$	−1.40140	−0.0513780
$745$	−0.237440	−0.00869913
$746$	5.07941	0.185970
$747$	4.95860	0.181426
$748$	2.06123	0.0753659
$749$	−24.6963	−0.902384
$750$	1.40140	0.0511720
$751$	27.9869	1.02126	0.510629	−	0.859801i	$-0.329413\pi$
$751$	27.9869	1.02126	0.510629	+	0.859801i	$0.329413\pi$
$752$	9.40786	0.343069
$753$	−4.67288	−0.170289
$754$	5.90748	0.215138
$755$	14.0173	0.510140
$756$	8.90465	0.323859
$757$	−10.6775	−0.388080	−0.194040	−	0.980994i	$-0.562159\pi$
$757$	−10.6775	−0.388080	−0.194040	+	0.980994i	$0.562159\pi$
$758$	−15.9606	−0.579715
$759$	−16.9476	−0.615160
$760$	6.64866	0.241172
$761$	−5.34614	−0.193797	−0.0968986	−	0.995294i	$-0.530892\pi$
$761$	−5.34614	−0.193797	−0.0968986	+	0.995294i	$0.530892\pi$
$762$	−1.05256	−0.0381301
$763$	−4.81956	−0.174480
$764$	2.94760	0.106640
$765$	−0.714397	−0.0258291
$766$	−26.0127	−0.939877
$767$	5.23941	0.189184
$768$	1.40140	0.0505688
$769$	−27.9513	−1.00795	−0.503975	−	0.863718i	$-0.668130\pi$
$769$	−27.9513	−1.00795	−0.503975	+	0.863718i	$0.668130\pi$
$770$	−4.70619	−0.169599
$771$	−33.3835	−1.20228
$772$	−9.36505	−0.337056
$773$	−27.7993	−0.999872	−0.499936	−	0.866062i	$-0.666643\pi$
$773$	−27.7993	−0.999872	−0.499936	+	0.866062i	$0.666643\pi$
$774$	−5.38299	−0.193488
$775$	−1.00000	−0.0359211
$776$	18.0920	0.649463
$777$	−8.87465	−0.318376
$778$	−19.2543	−0.690300
$779$	−4.46363	−0.159926
$780$	1.40140	0.0501783
$781$	−21.5205	−0.770065
$782$	−2.78948	−0.0997516
$783$	−33.4136	−1.19411
$784$	−4.52149	−0.161482
$785$	−11.8459	−0.422798
$786$	−7.50615	−0.267735
$787$	−0.0498320	−0.00177632	−0.000888160	−	1.00000i	$-0.500283\pi$
$787$	−0.0498320	−0.00177632	−0.000888160		1.00000i	$0.500283\pi$
$788$	0.181056	0.00644985
$789$	20.0855	0.715063
$790$	−12.2866	−0.437139
$791$	5.08245	0.180711
$792$	−3.09715	−0.110052
$793$	3.98898	0.141653
$794$	25.4556	0.903386
$795$	6.37161	0.225978
$796$	−4.63097	−0.164140
$797$	12.0946	0.428414	0.214207	−	0.976788i	$-0.431283\pi$
$797$	12.0946	0.428414	0.214207	+	0.976788i	$0.431283\pi$
$798$	−14.6687	−0.519267
$799$	6.48698	0.229493
$800$	1.00000	0.0353553
$801$	8.22531	0.290627
$802$	−35.4752	−1.25267
$803$	−26.4405	−0.933065
$804$	1.64423	0.0579875
$805$	6.36893	0.224475
$806$	−1.00000	−0.0352235
$807$	16.1389	0.568115
$808$	−0.865190	−0.0304373
$809$	34.2374	1.20372	0.601861	−	0.798601i	$-0.294426\pi$
$809$	34.2374	1.20372	0.601861	+	0.798601i	$0.294426\pi$
$810$	−4.81836	−0.169300
$811$	−19.7380	−0.693094	−0.346547	−	0.938033i	$-0.612646\pi$
$811$	−19.7380	−0.693094	−0.346547	+	0.938033i	$0.612646\pi$
$812$	−9.30030	−0.326377
$813$	−4.51685	−0.158413
$814$	12.0245	0.421458
$815$	−5.51305	−0.193114
$816$	0.966306	0.0338275
$817$	34.5438	1.20853
$818$	−20.1355	−0.704021
$819$	1.63111	0.0569956
$820$	−0.671358	−0.0234448
$821$	−44.5147	−1.55357	−0.776787	−	0.629763i	$-0.783152\pi$
$821$	−44.5147	−1.55357	−0.776787	+	0.629763i	$0.783152\pi$
$822$	22.6098	0.788608
$823$	−8.33652	−0.290593	−0.145296	−	0.989388i	$-0.546414\pi$
$823$	−8.33652	−0.290593	−0.145296	+	0.989388i	$0.546414\pi$
$824$	12.9389	0.450749
$825$	4.18926	0.145851
$826$	−8.24854	−0.287003
$827$	−53.9354	−1.87552	−0.937759	−	0.347287i	$-0.887103\pi$
$827$	−53.9354	−1.87552	−0.937759	+	0.347287i	$0.887103\pi$
$828$	4.19140	0.145661
$829$	−23.7677	−0.825487	−0.412744	−	0.910847i	$-0.635429\pi$
$829$	−23.7677	−0.825487	−0.412744	+	0.910847i	$0.635429\pi$
$830$	−4.78598	−0.166124
$831$	−10.3666	−0.359613
$832$	1.00000	0.0346688
$833$	−3.11769	−0.108022
$834$	−10.0803	−0.349053
$835$	16.2222	0.561393
$836$	19.8750	0.687393
$837$	5.65616	0.195505
$838$	17.1999	0.594162
$839$	6.65958	0.229914	0.114957	−	0.993370i	$-0.463327\pi$
$839$	6.65958	0.229914	0.114957	+	0.993370i	$0.463327\pi$
$840$	−2.20627	−0.0761235
$841$	5.89827	0.203389
$842$	11.4356	0.394097
$843$	10.9121	0.375831
$844$	−13.3733	−0.460329
$845$	1.00000	0.0344010
$846$	−9.74718	−0.335115
$847$	3.24925	0.111646
$848$	4.54659	0.156131
$849$	−24.3284	−0.834948
$850$	0.689528	0.0236506
$851$	−16.2729	−0.557827
$852$	−10.0889	−0.345639
$853$	−36.8989	−1.26339	−0.631696	−	0.775216i	$-0.717641\pi$
$853$	−36.8989	−1.26339	−0.631696	+	0.775216i	$0.717641\pi$
$854$	−6.27997	−0.214896
$855$	−6.88846	−0.235580
$856$	15.6869	0.536167
$857$	43.2801	1.47842	0.739209	−	0.673476i	$-0.235199\pi$
$857$	43.2801	1.47842	0.739209	+	0.673476i	$0.235199\pi$
$858$	4.18926	0.143019
$859$	−20.7068	−0.706508	−0.353254	−	0.935527i	$-0.614925\pi$
$859$	−20.7068	−0.706508	−0.353254	+	0.935527i	$0.614925\pi$
$860$	5.19560	0.177168
$861$	1.48120	0.0504790
$862$	9.02122	0.307264
$863$	36.2711	1.23468	0.617342	−	0.786695i	$-0.288210\pi$
$863$	36.2711	1.23468	0.617342	+	0.786695i	$0.288210\pi$
$864$	−5.65616	−0.192426
$865$	−11.3634	−0.386367
$866$	−26.4014	−0.897156
$867$	−23.1576	−0.786472
$868$	1.57433	0.0534362
$869$	−36.7289	−1.24594
$870$	8.27876	0.280676
$871$	1.17327	0.0397548
$872$	3.06135	0.103670
$873$	−18.7445	−0.634405
$874$	−26.8971	−0.909808
$875$	−1.57433	−0.0532220
$876$	−12.3953	−0.418800
$877$	40.9421	1.38252	0.691259	−	0.722607i	$-0.257057\pi$
$877$	40.9421	1.38252	0.691259	+	0.722607i	$0.257057\pi$
$878$	4.30409	0.145256
$879$	13.5172	0.455925
$880$	2.98933	0.100770
$881$	−20.8101	−0.701109	−0.350554	−	0.936542i	$-0.614007\pi$
$881$	−20.8101	−0.701109	−0.350554	+	0.936542i	$0.614007\pi$
$882$	4.68457	0.157738
$883$	−34.0965	−1.14744	−0.573719	−	0.819052i	$-0.694500\pi$
$883$	−34.0965	−1.14744	−0.573719	+	0.819052i	$0.694500\pi$
$884$	0.689528	0.0231913
$885$	7.34252	0.246816
$886$	33.2696	1.11771
$887$	23.7214	0.796485	0.398243	−	0.917280i	$-0.369620\pi$
$887$	23.7214	0.796485	0.398243	+	0.917280i	$0.369620\pi$
$888$	5.63710	0.189169
$889$	1.18244	0.0396576
$890$	−7.93897	−0.266115
$891$	−14.4037	−0.482541
$892$	−21.3111	−0.713549
$893$	62.5497	2.09314
$894$	−0.332749	−0.0111288
$895$	−18.0993	−0.604993
$896$	−1.57433	−0.0525946
$897$	−5.66937	−0.189295
$898$	−36.0306	−1.20236
$899$	−5.90748	−0.197025
$900$	−1.03607	−0.0345356
$901$	3.13500	0.104442
$902$	−2.00691	−0.0668228
$903$	−11.4629	−0.381461
$904$	−3.22833	−0.107373
$905$	10.1753	0.338238
$906$	19.6438	0.652623
$907$	1.19908	0.0398147	0.0199073	−	0.999802i	$-0.493663\pi$
$907$	1.19908	0.0398147	0.0199073	+	0.999802i	$0.493663\pi$
$908$	−18.7696	−0.622890
$909$	0.896395	0.0297315
$910$	−1.57433	−0.0521885
$911$	46.6421	1.54532	0.772660	−	0.634820i	$-0.218926\pi$
$911$	46.6421	1.54532	0.772660	+	0.634820i	$0.218926\pi$
$912$	9.31746	0.308532
$913$	−14.3069	−0.473489
$914$	5.05528	0.167214
$915$	5.59017	0.184805
$916$	12.7888	0.422555
$917$	8.43236	0.278461
$918$	−3.90008	−0.128722
$919$	1.13508	0.0374429	0.0187214	−	0.999825i	$-0.494040\pi$
$919$	1.13508	0.0374429	0.0187214	+	0.999825i	$0.494040\pi$
$920$	−4.04549	−0.133376
$921$	15.6753	0.516518
$922$	−7.48812	−0.246608
$923$	−7.19911	−0.236962
$924$	−6.59527	−0.216968
$925$	4.02247	0.132258
$926$	34.3941	1.13026
$927$	−13.4056	−0.440298
$928$	5.90748	0.193922
$929$	0.694011	0.0227698	0.0113849	−	0.999935i	$-0.496376\pi$
$929$	0.694011	0.0227698	0.0113849	+	0.999935i	$0.496376\pi$
$930$	−1.40140	−0.0459538
$931$	−30.0619	−0.985238
$932$	−22.0399	−0.721941
$933$	−29.5606	−0.967771
$934$	10.2802	0.336380
$935$	2.06123	0.0674093
$936$	−1.03607	−0.0338649
$937$	37.3808	1.22118	0.610588	−	0.791948i	$-0.290933\pi$
$937$	37.3808	1.22118	0.610588	+	0.791948i	$0.290933\pi$
$938$	−1.84712	−0.0603105
$939$	18.4244	0.601257
$940$	9.40786	0.306851
$941$	37.4844	1.22196	0.610979	−	0.791647i	$-0.290776\pi$
$941$	37.4844	1.22196	0.610979	+	0.791647i	$0.290776\pi$
$942$	−16.6009	−0.540886
$943$	2.71597	0.0884442
$944$	5.23941	0.170528
$945$	8.90465	0.289668
$946$	15.5314	0.504968
$947$	−23.5889	−0.766537	−0.383268	−	0.923637i	$-0.625202\pi$
$947$	−23.5889	−0.766537	−0.383268	+	0.923637i	$0.625202\pi$
$948$	−17.2186	−0.559233
$949$	−8.84495	−0.287119
$950$	6.64866	0.215711
$951$	−30.2707	−0.981594
$952$	−1.08554	−0.0351826
$953$	40.5832	1.31462	0.657309	−	0.753621i	$-0.271695\pi$
$953$	40.5832	1.31462	0.657309	+	0.753621i	$0.271695\pi$
$954$	−4.71058	−0.152511
$955$	2.94760	0.0953820
$956$	−23.9887	−0.775850
$957$	24.7479	0.799988
$958$	18.8580	0.609275
$959$	−25.3997	−0.820200
$960$	1.40140	0.0452301
$961$	1.00000	0.0322581
$962$	4.02247	0.129690
$963$	−16.2527	−0.523735
$964$	−15.5168	−0.499763
$965$	−9.36505	−0.301472
$966$	8.92544	0.287171
$967$	56.8235	1.82732	0.913661	−	0.406477i	$-0.133243\pi$
$967$	56.8235	1.82732	0.913661	+	0.406477i	$0.133243\pi$
$968$	−2.06390	−0.0663363
$969$	6.42464	0.206389
$970$	18.0920	0.580898
$971$	−45.2448	−1.45198	−0.725988	−	0.687708i	$-0.758617\pi$
$971$	−45.2448	−1.45198	−0.725988	+	0.687708i	$0.758617\pi$
$972$	10.2160	0.327679
$973$	11.3242	0.363036
$974$	11.3420	0.363422
$975$	1.40140	0.0448808
$976$	3.98898	0.127684
$977$	19.5088	0.624141	0.312071	−	0.950059i	$-0.398977\pi$
$977$	19.5088	0.624141	0.312071	+	0.950059i	$0.398977\pi$
$978$	−7.72601	−0.247051
$979$	−23.7322	−0.758485
$980$	−4.52149	−0.144434
$981$	−3.17176	−0.101267
$982$	6.14820	0.196197
$983$	9.06195	0.289031	0.144516	−	0.989503i	$-0.453838\pi$
$983$	9.06195	0.289031	0.144516	+	0.989503i	$0.453838\pi$
$984$	−0.940843	−0.0299930
$985$	0.181056	0.00576893
$986$	4.07337	0.129722
$987$	−20.7563	−0.660679
$988$	6.64866	0.211522
$989$	−21.0188	−0.668358
$990$	−3.09715	−0.0984339
$991$	−36.3157	−1.15361	−0.576803	−	0.816883i	$-0.695700\pi$
$991$	−36.3157	−1.15361	−0.576803	+	0.816883i	$0.695700\pi$
$992$	−1.00000	−0.0317500
$993$	1.97238	0.0625915
$994$	11.3338	0.359485
$995$	−4.63097	−0.146812
$996$	−6.70709	−0.212522
$997$	27.3840	0.867259	0.433630	−	0.901091i	$-0.357233\pi$
$997$	27.3840	0.867259	0.433630	+	0.901091i	$0.357233\pi$
$998$	−2.31210	−0.0731883
$999$	−22.7517	−0.719833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.r.1.6	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.r.1.6	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.40140 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40140 q^{6} -1.57433 q^{7} +1.00000 q^{8} -1.03607 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.40140 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40140 q^{6} -1.57433 q^{7} +1.00000 q^{8} -1.03607 q^{9} +1.00000 q^{10} +2.98933 q^{11} +1.40140 q^{12} +1.00000 q^{13} -1.57433 q^{14} +1.40140 q^{15} +1.00000 q^{16} +0.689528 q^{17} -1.03607 q^{18} +6.64866 q^{19} +1.00000 q^{20} -2.20627 q^{21} +2.98933 q^{22} -4.04549 q^{23} +1.40140 q^{24} +1.00000 q^{25} +1.00000 q^{26} -5.65616 q^{27} -1.57433 q^{28} +5.90748 q^{29} +1.40140 q^{30} -1.00000 q^{31} +1.00000 q^{32} +4.18926 q^{33} +0.689528 q^{34} -1.57433 q^{35} -1.03607 q^{36} +4.02247 q^{37} +6.64866 q^{38} +1.40140 q^{39} +1.00000 q^{40} -0.671358 q^{41} -2.20627 q^{42} +5.19560 q^{43} +2.98933 q^{44} -1.03607 q^{45} -4.04549 q^{46} +9.40786 q^{47} +1.40140 q^{48} -4.52149 q^{49} +1.00000 q^{50} +0.966306 q^{51} +1.00000 q^{52} +4.54659 q^{53} -5.65616 q^{54} +2.98933 q^{55} -1.57433 q^{56} +9.31746 q^{57} +5.90748 q^{58} +5.23941 q^{59} +1.40140 q^{60} +3.98898 q^{61} -1.00000 q^{62} +1.63111 q^{63} +1.00000 q^{64} +1.00000 q^{65} +4.18926 q^{66} +1.17327 q^{67} +0.689528 q^{68} -5.66937 q^{69} -1.57433 q^{70} -7.19911 q^{71} -1.03607 q^{72} -8.84495 q^{73} +4.02247 q^{74} +1.40140 q^{75} +6.64866 q^{76} -4.70619 q^{77} +1.40140 q^{78} -12.2866 q^{79} +1.00000 q^{80} -4.81836 q^{81} -0.671358 q^{82} -4.78598 q^{83} -2.20627 q^{84} +0.689528 q^{85} +5.19560 q^{86} +8.27876 q^{87} +2.98933 q^{88} -7.93897 q^{89} -1.03607 q^{90} -1.57433 q^{91} -4.04549 q^{92} -1.40140 q^{93} +9.40786 q^{94} +6.64866 q^{95} +1.40140 q^{96} +18.0920 q^{97} -4.52149 q^{98} -3.09715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} + 3 q^{6} + 9 q^{7} + 9 q^{8} + 14 q^{9} + 9 q^{10} + 10 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} + 3 q^{15} + 9 q^{16} + q^{17} + 14 q^{18} + 10 q^{19} + 9 q^{20} + 3 q^{21} + 10 q^{22} + 8 q^{23} + 3 q^{24} + 9 q^{25} + 9 q^{26} + 15 q^{27} + 9 q^{28} + 9 q^{29} + 3 q^{30} - 9 q^{31} + 9 q^{32} + 4 q^{33} + q^{34} + 9 q^{35} + 14 q^{36} - 3 q^{37} + 10 q^{38} + 3 q^{39} + 9 q^{40} + 3 q^{42} + 7 q^{43} + 10 q^{44} + 14 q^{45} + 8 q^{46} + 7 q^{47} + 3 q^{48} + 8 q^{49} + 9 q^{50} - 3 q^{51} + 9 q^{52} + 8 q^{53} + 15 q^{54} + 10 q^{55} + 9 q^{56} - 7 q^{57} + 9 q^{58} + 2 q^{59} + 3 q^{60} - 2 q^{61} - 9 q^{62} + 10 q^{63} + 9 q^{64} + 9 q^{65} + 4 q^{66} + 18 q^{67} + q^{68} - 16 q^{69} + 9 q^{70} + 14 q^{71} + 14 q^{72} + q^{73} - 3 q^{74} + 3 q^{75} + 10 q^{76} - 5 q^{77} + 3 q^{78} + 6 q^{79} + 9 q^{80} + q^{81} + 7 q^{83} + 3 q^{84} + q^{85} + 7 q^{86} + 11 q^{87} + 10 q^{88} - 19 q^{89} + 14 q^{90} + 9 q^{91} + 8 q^{92} - 3 q^{93} + 7 q^{94} + 10 q^{95} + 3 q^{96} - 6 q^{97} + 8 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 + 3 * q^6 + 9 * q^7 + 9 * q^8 + 14 * q^9 + 9 * q^10 + 10 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 + 3 * q^15 + 9 * q^16 + q^17 + 14 * q^18 + 10 * q^19 + 9 * q^20 + 3 * q^21 + 10 * q^22 + 8 * q^23 + 3 * q^24 + 9 * q^25 + 9 * q^26 + 15 * q^27 + 9 * q^28 + 9 * q^29 + 3 * q^30 - 9 * q^31 + 9 * q^32 + 4 * q^33 + q^34 + 9 * q^35 + 14 * q^36 - 3 * q^37 + 10 * q^38 + 3 * q^39 + 9 * q^40 + 3 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 + 8 * q^46 + 7 * q^47 + 3 * q^48 + 8 * q^49 + 9 * q^50 - 3 * q^51 + 9 * q^52 + 8 * q^53 + 15 * q^54 + 10 * q^55 + 9 * q^56 - 7 * q^57 + 9 * q^58 + 2 * q^59 + 3 * q^60 - 2 * q^61 - 9 * q^62 + 10 * q^63 + 9 * q^64 + 9 * q^65 + 4 * q^66 + 18 * q^67 + q^68 - 16 * q^69 + 9 * q^70 + 14 * q^71 + 14 * q^72 + q^73 - 3 * q^74 + 3 * q^75 + 10 * q^76 - 5 * q^77 + 3 * q^78 + 6 * q^79 + 9 * q^80 + q^81 + 7 * q^83 + 3 * q^84 + q^85 + 7 * q^86 + 11 * q^87 + 10 * q^88 - 19 * q^89 + 14 * q^90 + 9 * q^91 + 8 * q^92 - 3 * q^93 + 7 * q^94 + 10 * q^95 + 3 * q^96 - 6 * q^97 + 8 * q^98 - 5 * q^99

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