LMFDB - Embedded newform 8022.2.a.w.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 39 x^{11} + 67 x^{10} + 588 x^{9} - 823 x^{8} - 4265 x^{7} + 4419 x^{6} + 14926 x^{5} + \cdots - 984 $ x^13 - 2x^12 - 39x^11 + 67x^10 + 588x^9 - 823x^8 - 4265x^7 + 4419x^6 + 14926x^5 - 9090x^4 - 21330x^3 + 2178x^2 + 5892x - 984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.465864$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.465864 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.465864 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.465864 q^{10} -0.822152 q^{11} +1.00000 q^{12} -5.34040 q^{13} +1.00000 q^{14} -0.465864 q^{15} +1.00000 q^{16} +1.35973 q^{17} -1.00000 q^{18} +5.15118 q^{19} -0.465864 q^{20} -1.00000 q^{21} +0.822152 q^{22} +6.48593 q^{23} -1.00000 q^{24} -4.78297 q^{25} +5.34040 q^{26} +1.00000 q^{27} -1.00000 q^{28} -0.284167 q^{29} +0.465864 q^{30} -2.59883 q^{31} -1.00000 q^{32} -0.822152 q^{33} -1.35973 q^{34} +0.465864 q^{35} +1.00000 q^{36} -9.16359 q^{37} -5.15118 q^{38} -5.34040 q^{39} +0.465864 q^{40} -3.26684 q^{41} +1.00000 q^{42} +8.19647 q^{43} -0.822152 q^{44} -0.465864 q^{45} -6.48593 q^{46} +4.81011 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.78297 q^{50} +1.35973 q^{51} -5.34040 q^{52} +12.9097 q^{53} -1.00000 q^{54} +0.383011 q^{55} +1.00000 q^{56} +5.15118 q^{57} +0.284167 q^{58} -2.88760 q^{59} -0.465864 q^{60} +0.0125659 q^{61} +2.59883 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.48790 q^{65} +0.822152 q^{66} +7.16823 q^{67} +1.35973 q^{68} +6.48593 q^{69} -0.465864 q^{70} -13.6658 q^{71} -1.00000 q^{72} -12.8923 q^{73} +9.16359 q^{74} -4.78297 q^{75} +5.15118 q^{76} +0.822152 q^{77} +5.34040 q^{78} +15.1283 q^{79} -0.465864 q^{80} +1.00000 q^{81} +3.26684 q^{82} -12.8313 q^{83} -1.00000 q^{84} -0.633449 q^{85} -8.19647 q^{86} -0.284167 q^{87} +0.822152 q^{88} +0.320869 q^{89} +0.465864 q^{90} +5.34040 q^{91} +6.48593 q^{92} -2.59883 q^{93} -4.81011 q^{94} -2.39975 q^{95} -1.00000 q^{96} +9.28951 q^{97} -1.00000 q^{98} -0.822152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.465864	−0.208341	−0.104170	−	0.994559i	$-0.533219\pi$
$5$	−0.465864	−0.208341	−0.104170	+	0.994559i	$0.533219\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.465864	0.147319
$11$	−0.822152	−0.247888	−0.123944	−	0.992289i	$-0.539554\pi$
$11$	−0.822152	−0.247888	−0.123944	+	0.992289i	$0.539554\pi$
$12$	1.00000	0.288675
$13$	−5.34040	−1.48116	−0.740580	−	0.671969i	$-0.765449\pi$
$13$	−5.34040	−1.48116	−0.740580	+	0.671969i	$0.765449\pi$
$14$	1.00000	0.267261
$15$	−0.465864	−0.120286
$16$	1.00000	0.250000
$17$	1.35973	0.329783	0.164891	−	0.986312i	$-0.447273\pi$
$17$	1.35973	0.329783	0.164891	+	0.986312i	$0.447273\pi$
$18$	−1.00000	−0.235702
$19$	5.15118	1.18176	0.590880	−	0.806759i	$-0.298780\pi$
$19$	5.15118	1.18176	0.590880	+	0.806759i	$0.298780\pi$
$20$	−0.465864	−0.104170
$21$	−1.00000	−0.218218
$22$	0.822152	0.175283
$23$	6.48593	1.35241	0.676205	−	0.736714i	$-0.263624\pi$
$23$	6.48593	1.35241	0.676205	+	0.736714i	$0.263624\pi$
$24$	−1.00000	−0.204124
$25$	−4.78297	−0.956594
$26$	5.34040	1.04734
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−0.284167	−0.0527685	−0.0263843	−	0.999652i	$-0.508399\pi$
$29$	−0.284167	−0.0527685	−0.0263843	+	0.999652i	$0.508399\pi$
$30$	0.465864	0.0850548
$31$	−2.59883	−0.466764	−0.233382	−	0.972385i	$-0.574979\pi$
$31$	−2.59883	−0.466764	−0.233382	+	0.972385i	$0.574979\pi$
$32$	−1.00000	−0.176777
$33$	−0.822152	−0.143118
$34$	−1.35973	−0.233192
$35$	0.465864	0.0787454
$36$	1.00000	0.166667
$37$	−9.16359	−1.50648	−0.753242	−	0.657743i	$-0.771511\pi$
$37$	−9.16359	−1.50648	−0.753242	+	0.657743i	$0.771511\pi$
$38$	−5.15118	−0.835631
$39$	−5.34040	−0.855148
$40$	0.465864	0.0736596
$41$	−3.26684	−0.510195	−0.255098	−	0.966915i	$-0.582108\pi$
$41$	−3.26684	−0.510195	−0.255098	+	0.966915i	$0.582108\pi$
$42$	1.00000	0.154303
$43$	8.19647	1.24995	0.624975	−	0.780645i	$-0.285109\pi$
$43$	8.19647	1.24995	0.624975	+	0.780645i	$0.285109\pi$
$44$	−0.822152	−0.123944
$45$	−0.465864	−0.0694469
$46$	−6.48593	−0.956298
$47$	4.81011	0.701626	0.350813	−	0.936446i	$-0.385905\pi$
$47$	4.81011	0.701626	0.350813	+	0.936446i	$0.385905\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.78297	0.676414
$51$	1.35973	0.190400
$52$	−5.34040	−0.740580
$53$	12.9097	1.77328	0.886639	−	0.462462i	$-0.153034\pi$
$53$	12.9097	1.77328	0.886639	+	0.462462i	$0.153034\pi$
$54$	−1.00000	−0.136083
$55$	0.383011	0.0516452
$56$	1.00000	0.133631
$57$	5.15118	0.682290
$58$	0.284167	0.0373130
$59$	−2.88760	−0.375934	−0.187967	−	0.982175i	$-0.560190\pi$
$59$	−2.88760	−0.375934	−0.187967	+	0.982175i	$0.560190\pi$
$60$	−0.465864	−0.0601428
$61$	0.0125659	0.00160890	0.000804450	−	1.00000i	$-0.499744\pi$
$61$	0.0125659	0.00160890	0.000804450		1.00000i	$0.499744\pi$
$62$	2.59883	0.330052
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	2.48790	0.308586
$66$	0.822152	0.101200
$67$	7.16823	0.875739	0.437870	−	0.899038i	$-0.355733\pi$
$67$	7.16823	0.875739	0.437870	+	0.899038i	$0.355733\pi$
$68$	1.35973	0.164891
$69$	6.48593	0.780814
$70$	−0.465864	−0.0556814
$71$	−13.6658	−1.62183	−0.810917	−	0.585161i	$-0.801032\pi$
$71$	−13.6658	−1.62183	−0.810917	+	0.585161i	$0.801032\pi$
$72$	−1.00000	−0.117851
$73$	−12.8923	−1.50893	−0.754463	−	0.656342i	$-0.772103\pi$
$73$	−12.8923	−1.50893	−0.754463	+	0.656342i	$0.772103\pi$
$74$	9.16359	1.06525
$75$	−4.78297	−0.552290
$76$	5.15118	0.590880
$77$	0.822152	0.0936929
$78$	5.34040	0.604681
$79$	15.1283	1.70206	0.851032	−	0.525113i	$-0.175977\pi$
$79$	15.1283	1.70206	0.851032	+	0.525113i	$0.175977\pi$
$80$	−0.465864	−0.0520852
$81$	1.00000	0.111111
$82$	3.26684	0.360763
$83$	−12.8313	−1.40842	−0.704209	−	0.709993i	$-0.748698\pi$
$83$	−12.8313	−1.40842	−0.704209	+	0.709993i	$0.748698\pi$
$84$	−1.00000	−0.109109
$85$	−0.633449	−0.0687072
$86$	−8.19647	−0.883848
$87$	−0.284167	−0.0304659
$88$	0.822152	0.0876417
$89$	0.320869	0.0340120	0.0170060	−	0.999855i	$-0.494587\pi$
$89$	0.320869	0.0340120	0.0170060	+	0.999855i	$0.494587\pi$
$90$	0.465864	0.0491064
$91$	5.34040	0.559826
$92$	6.48593	0.676205
$93$	−2.59883	−0.269486
$94$	−4.81011	−0.496125
$95$	−2.39975	−0.246209
$96$	−1.00000	−0.102062
$97$	9.28951	0.943207	0.471604	−	0.881811i	$-0.343675\pi$
$97$	9.28951	0.943207	0.471604	+	0.881811i	$0.343675\pi$
$98$	−1.00000	−0.101015
$99$	−0.822152	−0.0826293
$100$	−4.78297	−0.478297
$101$	−15.0955	−1.50206	−0.751031	−	0.660267i	$-0.770443\pi$
$101$	−15.0955	−1.50206	−0.751031	+	0.660267i	$0.770443\pi$
$102$	−1.35973	−0.134633
$103$	14.9335	1.47145	0.735723	−	0.677283i	$-0.236843\pi$
$103$	14.9335	1.47145	0.735723	+	0.677283i	$0.236843\pi$
$104$	5.34040	0.523669
$105$	0.465864	0.0454637
$106$	−12.9097	−1.25390
$107$	−7.94788	−0.768351	−0.384175	−	0.923260i	$-0.625514\pi$
$107$	−7.94788	−0.768351	−0.384175	+	0.923260i	$0.625514\pi$
$108$	1.00000	0.0962250
$109$	4.00855	0.383949	0.191975	−	0.981400i	$-0.438511\pi$
$109$	4.00855	0.383949	0.191975	+	0.981400i	$0.438511\pi$
$110$	−0.383011	−0.0365187
$111$	−9.16359	−0.869769
$112$	−1.00000	−0.0944911
$113$	−6.02342	−0.566636	−0.283318	−	0.959026i	$-0.591435\pi$
$113$	−6.02342	−0.566636	−0.283318	+	0.959026i	$0.591435\pi$
$114$	−5.15118	−0.482452
$115$	−3.02156	−0.281762
$116$	−0.284167	−0.0263843
$117$	−5.34040	−0.493720
$118$	2.88760	0.265826
$119$	−1.35973	−0.124646
$120$	0.465864	0.0425274
$121$	−10.3241	−0.938552
$122$	−0.0125659	−0.00113766
$123$	−3.26684	−0.294561
$124$	−2.59883	−0.233382
$125$	4.55753	0.407638
$126$	1.00000	0.0890871
$127$	15.2422	1.35253	0.676263	−	0.736661i	$-0.263598\pi$
$127$	15.2422	1.35253	0.676263	+	0.736661i	$0.263598\pi$
$128$	−1.00000	−0.0883883
$129$	8.19647	0.721659
$130$	−2.48790	−0.218203
$131$	0.926864	0.0809805	0.0404903	−	0.999180i	$-0.487108\pi$
$131$	0.926864	0.0809805	0.0404903	+	0.999180i	$0.487108\pi$
$132$	−0.822152	−0.0715591
$133$	−5.15118	−0.446664
$134$	−7.16823	−0.619241
$135$	−0.465864	−0.0400952
$136$	−1.35973	−0.116596
$137$	−4.69778	−0.401359	−0.200679	−	0.979657i	$-0.564315\pi$
$137$	−4.69778	−0.401359	−0.200679	+	0.979657i	$0.564315\pi$
$138$	−6.48593	−0.552119
$139$	20.0936	1.70432	0.852159	−	0.523283i	$-0.175293\pi$
$139$	20.0936	1.70432	0.852159	+	0.523283i	$0.175293\pi$
$140$	0.465864	0.0393727
$141$	4.81011	0.405084
$142$	13.6658	1.14681
$143$	4.39061	0.367162
$144$	1.00000	0.0833333
$145$	0.132383	0.0109938
$146$	12.8923	1.06697
$147$	1.00000	0.0824786
$148$	−9.16359	−0.753242
$149$	10.3785	0.850243	0.425121	−	0.905136i	$-0.360231\pi$
$149$	10.3785	0.850243	0.425121	+	0.905136i	$0.360231\pi$
$150$	4.78297	0.390528
$151$	12.9710	1.05557	0.527784	−	0.849379i	$-0.323023\pi$
$151$	12.9710	1.05557	0.527784	+	0.849379i	$0.323023\pi$
$152$	−5.15118	−0.417816
$153$	1.35973	0.109928
$154$	−0.822152	−0.0662509
$155$	1.21070	0.0972460
$156$	−5.34040	−0.427574
$157$	−19.6544	−1.56860	−0.784298	−	0.620385i	$-0.786976\pi$
$157$	−19.6544	−1.56860	−0.784298	+	0.620385i	$0.786976\pi$
$158$	−15.1283	−1.20354
$159$	12.9097	1.02380
$160$	0.465864	0.0368298
$161$	−6.48593	−0.511163
$162$	−1.00000	−0.0785674
$163$	12.6512	0.990921	0.495461	−	0.868630i	$-0.334999\pi$
$163$	12.6512	0.990921	0.495461	+	0.868630i	$0.334999\pi$
$164$	−3.26684	−0.255098
$165$	0.383011	0.0298174
$166$	12.8313	0.995902
$167$	2.26663	0.175397	0.0876985	−	0.996147i	$-0.472049\pi$
$167$	2.26663	0.175397	0.0876985	+	0.996147i	$0.472049\pi$
$168$	1.00000	0.0771517
$169$	15.5198	1.19383
$170$	0.633449	0.0485833
$171$	5.15118	0.393920
$172$	8.19647	0.624975
$173$	15.2231	1.15739	0.578695	−	0.815544i	$-0.303562\pi$
$173$	15.2231	1.15739	0.578695	+	0.815544i	$0.303562\pi$
$174$	0.284167	0.0215427
$175$	4.78297	0.361559
$176$	−0.822152	−0.0619720
$177$	−2.88760	−0.217046
$178$	−0.320869	−0.0240501
$179$	3.10074	0.231760	0.115880	−	0.993263i	$-0.463031\pi$
$179$	3.10074	0.231760	0.115880	+	0.993263i	$0.463031\pi$
$180$	−0.465864	−0.0347235
$181$	21.5086	1.59872	0.799362	−	0.600850i	$-0.205171\pi$
$181$	21.5086	1.59872	0.799362	+	0.600850i	$0.205171\pi$
$182$	−5.34040	−0.395856
$183$	0.0125659	0.000928898 0
$184$	−6.48593	−0.478149
$185$	4.26899	0.313862
$186$	2.59883	0.190556
$187$	−1.11790	−0.0817492
$188$	4.81011	0.350813
$189$	−1.00000	−0.0727393
$190$	2.39975	0.174096
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	−4.74460	−0.341524	−0.170762	−	0.985312i	$-0.554623\pi$
$193$	−4.74460	−0.341524	−0.170762	+	0.985312i	$0.554623\pi$
$194$	−9.28951	−0.666948
$195$	2.48790	0.178162
$196$	1.00000	0.0714286
$197$	−11.7739	−0.838859	−0.419429	−	0.907788i	$-0.637770\pi$
$197$	−11.7739	−0.838859	−0.419429	+	0.907788i	$0.637770\pi$
$198$	0.822152	0.0584278
$199$	17.7296	1.25682	0.628408	−	0.777884i	$-0.283707\pi$
$199$	17.7296	1.25682	0.628408	+	0.777884i	$0.283707\pi$
$200$	4.78297	0.338207
$201$	7.16823	0.505608
$202$	15.0955	1.06212
$203$	0.284167	0.0199446
$204$	1.35973	0.0952001
$205$	1.52191	0.106295
$206$	−14.9335	−1.04047
$207$	6.48593	0.450803
$208$	−5.34040	−0.370290
$209$	−4.23505	−0.292944
$210$	−0.465864	−0.0321477
$211$	14.6806	1.01065	0.505327	−	0.862928i	$-0.331372\pi$
$211$	14.6806	1.01065	0.505327	+	0.862928i	$0.331372\pi$
$212$	12.9097	0.886639
$213$	−13.6658	−0.936367
$214$	7.94788	0.543306
$215$	−3.81844	−0.260416
$216$	−1.00000	−0.0680414
$217$	2.59883	0.176420
$218$	−4.00855	−0.271493
$219$	−12.8923	−0.871179
$220$	0.383011	0.0258226
$221$	−7.26149	−0.488461
$222$	9.16359	0.615020
$223$	1.36727	0.0915591	0.0457795	−	0.998952i	$-0.485423\pi$
$223$	1.36727	0.0915591	0.0457795	+	0.998952i	$0.485423\pi$
$224$	1.00000	0.0668153
$225$	−4.78297	−0.318865
$226$	6.02342	0.400672
$227$	12.6765	0.841369	0.420684	−	0.907207i	$-0.361790\pi$
$227$	12.6765	0.841369	0.420684	+	0.907207i	$0.361790\pi$
$228$	5.15118	0.341145
$229$	11.2947	0.746372	0.373186	−	0.927757i	$-0.378265\pi$
$229$	11.2947	0.746372	0.373186	+	0.927757i	$0.378265\pi$
$230$	3.02156	0.199236
$231$	0.822152	0.0540936
$232$	0.284167	0.0186565
$233$	20.9909	1.37516	0.687581	−	0.726108i	$-0.258673\pi$
$233$	20.9909	1.37516	0.687581	+	0.726108i	$0.258673\pi$
$234$	5.34040	0.349113
$235$	−2.24086	−0.146177
$236$	−2.88760	−0.187967
$237$	15.1283	0.982688
$238$	1.35973	0.0881382
$239$	12.8090	0.828544	0.414272	−	0.910153i	$-0.364036\pi$
$239$	12.8090	0.828544	0.414272	+	0.910153i	$0.364036\pi$
$240$	−0.465864	−0.0300714
$241$	−10.5119	−0.677132	−0.338566	−	0.940943i	$-0.609942\pi$
$241$	−10.5119	−0.677132	−0.338566	+	0.940943i	$0.609942\pi$
$242$	10.3241	0.663656
$243$	1.00000	0.0641500
$244$	0.0125659	0.000804450 0
$245$	−0.465864	−0.0297630
$246$	3.26684	0.208286
$247$	−27.5093	−1.75038
$248$	2.59883	0.165026
$249$	−12.8313	−0.813150
$250$	−4.55753	−0.288244
$251$	14.8598	0.937940	0.468970	−	0.883214i	$-0.344625\pi$
$251$	14.8598	0.937940	0.468970	+	0.883214i	$0.344625\pi$
$252$	−1.00000	−0.0629941
$253$	−5.33241	−0.335246
$254$	−15.2422	−0.956380
$255$	−0.633449	−0.0396681
$256$	1.00000	0.0625000
$257$	−8.57369	−0.534812	−0.267406	−	0.963584i	$-0.586166\pi$
$257$	−8.57369	−0.534812	−0.267406	+	0.963584i	$0.586166\pi$
$258$	−8.19647	−0.510290
$259$	9.16359	0.569398
$260$	2.48790	0.154293
$261$	−0.284167	−0.0175895
$262$	−0.926864	−0.0572619
$263$	10.3219	0.636475	0.318237	−	0.948011i	$-0.396909\pi$
$263$	10.3219	0.636475	0.318237	+	0.948011i	$0.396909\pi$
$264$	0.822152	0.0505999
$265$	−6.01415	−0.369446
$266$	5.15118	0.315839
$267$	0.320869	0.0196369
$268$	7.16823	0.437870
$269$	11.8573	0.722949	0.361475	−	0.932382i	$-0.382273\pi$
$269$	11.8573	0.722949	0.361475	+	0.932382i	$0.382273\pi$
$270$	0.465864	0.0283516
$271$	11.4686	0.696668	0.348334	−	0.937371i	$-0.386748\pi$
$271$	11.4686	0.696668	0.348334	+	0.937371i	$0.386748\pi$
$272$	1.35973	0.0824457
$273$	5.34040	0.323215
$274$	4.69778	0.283803
$275$	3.93233	0.237128
$276$	6.48593	0.390407
$277$	23.2143	1.39481	0.697407	−	0.716675i	$-0.254337\pi$
$277$	23.2143	1.39481	0.697407	+	0.716675i	$0.254337\pi$
$278$	−20.0936	−1.20513
$279$	−2.59883	−0.155588
$280$	−0.465864	−0.0278407
$281$	−9.79838	−0.584523	−0.292261	−	0.956339i	$-0.594408\pi$
$281$	−9.79838	−0.584523	−0.292261	+	0.956339i	$0.594408\pi$
$282$	−4.81011	−0.286438
$283$	17.1846	1.02152	0.510761	−	0.859723i	$-0.329364\pi$
$283$	17.1846	1.02152	0.510761	+	0.859723i	$0.329364\pi$
$284$	−13.6658	−0.810917
$285$	−2.39975	−0.142149
$286$	−4.39061	−0.259622
$287$	3.26684	0.192836
$288$	−1.00000	−0.0589256
$289$	−15.1511	−0.891243
$290$	−0.132383	−0.00777382
$291$	9.28951	0.544561
$292$	−12.8923	−0.754463
$293$	24.6712	1.44131	0.720654	−	0.693295i	$-0.243842\pi$
$293$	24.6712	1.44131	0.720654	+	0.693295i	$0.243842\pi$
$294$	−1.00000	−0.0583212
$295$	1.34523	0.0783224
$296$	9.16359	0.532623
$297$	−0.822152	−0.0477061
$298$	−10.3785	−0.601212
$299$	−34.6374	−2.00313
$300$	−4.78297	−0.276145
$301$	−8.19647	−0.472437
$302$	−12.9710	−0.746399
$303$	−15.0955	−0.867216
$304$	5.15118	0.295440
$305$	−0.00585400	−0.000335199 0
$306$	−1.35973	−0.0777306
$307$	−33.7673	−1.92720	−0.963601	−	0.267343i	$-0.913854\pi$
$307$	−33.7673	−1.92720	−0.963601	+	0.267343i	$0.913854\pi$
$308$	0.822152	0.0468464
$309$	14.9335	0.849540
$310$	−1.21070	−0.0687633
$311$	0.812922	0.0460966	0.0230483	−	0.999734i	$-0.492663\pi$
$311$	0.812922	0.0460966	0.0230483	+	0.999734i	$0.492663\pi$
$312$	5.34040	0.302340
$313$	2.16229	0.122220	0.0611099	−	0.998131i	$-0.480536\pi$
$313$	2.16229	0.122220	0.0611099	+	0.998131i	$0.480536\pi$
$314$	19.6544	1.10916
$315$	0.465864	0.0262485
$316$	15.1283	0.851032
$317$	−16.9055	−0.949505	−0.474752	−	0.880119i	$-0.657462\pi$
$317$	−16.9055	−0.949505	−0.474752	+	0.880119i	$0.657462\pi$
$318$	−12.9097	−0.723938
$319$	0.233629	0.0130807
$320$	−0.465864	−0.0260426
$321$	−7.94788	−0.443608
$322$	6.48593	0.361447
$323$	7.00421	0.389725
$324$	1.00000	0.0555556
$325$	25.5430	1.41687
$326$	−12.6512	−0.700687
$327$	4.00855	0.221673
$328$	3.26684	0.180381
$329$	−4.81011	−0.265190
$330$	−0.383011	−0.0210841
$331$	−13.4626	−0.739972	−0.369986	−	0.929037i	$-0.620637\pi$
$331$	−13.4626	−0.739972	−0.369986	+	0.929037i	$0.620637\pi$
$332$	−12.8313	−0.704209
$333$	−9.16359	−0.502162
$334$	−2.26663	−0.124024
$335$	−3.33942	−0.182452
$336$	−1.00000	−0.0545545
$337$	17.9440	0.977472	0.488736	−	0.872432i	$-0.337458\pi$
$337$	17.9440	0.977472	0.488736	+	0.872432i	$0.337458\pi$
$338$	−15.5198	−0.844167
$339$	−6.02342	−0.327147
$340$	−0.633449	−0.0343536
$341$	2.13663	0.115705
$342$	−5.15118	−0.278544
$343$	−1.00000	−0.0539949
$344$	−8.19647	−0.441924
$345$	−3.02156	−0.162675
$346$	−15.2231	−0.818399
$347$	25.7056	1.37995	0.689974	−	0.723834i	$-0.257622\pi$
$347$	25.7056	1.37995	0.689974	+	0.723834i	$0.257622\pi$
$348$	−0.284167	−0.0152330
$349$	−1.02631	−0.0549370	−0.0274685	−	0.999623i	$-0.508745\pi$
$349$	−1.02631	−0.0549370	−0.0274685	+	0.999623i	$0.508745\pi$
$350$	−4.78297	−0.255661
$351$	−5.34040	−0.285049
$352$	0.822152	0.0438208
$353$	−15.1681	−0.807317	−0.403659	−	0.914910i	$-0.632262\pi$
$353$	−15.1681	−0.807317	−0.403659	+	0.914910i	$0.632262\pi$
$354$	2.88760	0.153474
$355$	6.36642	0.337894
$356$	0.320869	0.0170060
$357$	−1.35973	−0.0719645
$358$	−3.10074	−0.163879
$359$	−12.6134	−0.665708	−0.332854	−	0.942978i	$-0.608012\pi$
$359$	−12.6134	−0.665708	−0.332854	+	0.942978i	$0.608012\pi$
$360$	0.465864	0.0245532
$361$	7.53462	0.396559
$362$	−21.5086	−1.13047
$363$	−10.3241	−0.541873
$364$	5.34040	0.279913
$365$	6.00605	0.314371
$366$	−0.0125659	−0.000656830 0
$367$	−4.35982	−0.227581	−0.113790	−	0.993505i	$-0.536299\pi$
$367$	−4.35982	−0.227581	−0.113790	+	0.993505i	$0.536299\pi$
$368$	6.48593	0.338102
$369$	−3.26684	−0.170065
$370$	−4.26899	−0.221934
$371$	−12.9097	−0.670236
$372$	−2.59883	−0.134743
$373$	9.74846	0.504756	0.252378	−	0.967629i	$-0.418787\pi$
$373$	9.74846	0.504756	0.252378	+	0.967629i	$0.418787\pi$
$374$	1.11790	0.0578054
$375$	4.55753	0.235350
$376$	−4.81011	−0.248062
$377$	1.51757	0.0781586
$378$	1.00000	0.0514344
$379$	2.02882	0.104213	0.0521066	−	0.998642i	$-0.483406\pi$
$379$	2.02882	0.104213	0.0521066	+	0.998642i	$0.483406\pi$
$380$	−2.39975	−0.123104
$381$	15.2422	0.780881
$382$	1.00000	0.0511645
$383$	−3.09152	−0.157969	−0.0789847	−	0.996876i	$-0.525168\pi$
$383$	−3.09152	−0.157969	−0.0789847	+	0.996876i	$0.525168\pi$
$384$	−1.00000	−0.0510310
$385$	−0.383011	−0.0195200
$386$	4.74460	0.241494
$387$	8.19647	0.416650
$388$	9.28951	0.471604
$389$	−29.9674	−1.51941	−0.759703	−	0.650270i	$-0.774656\pi$
$389$	−29.9674	−1.51941	−0.759703	+	0.650270i	$0.774656\pi$
$390$	−2.48790	−0.125980
$391$	8.81911	0.446001
$392$	−1.00000	−0.0505076
$393$	0.926864	0.0467541
$394$	11.7739	0.593163
$395$	−7.04772	−0.354610
$396$	−0.822152	−0.0413147
$397$	0.204552	0.0102662	0.00513309	−	0.999987i	$-0.498366\pi$
$397$	0.204552	0.0102662	0.00513309	+	0.999987i	$0.498366\pi$
$398$	−17.7296	−0.888703
$399$	−5.15118	−0.257881
$400$	−4.78297	−0.239149
$401$	16.7083	0.834373	0.417187	−	0.908821i	$-0.363016\pi$
$401$	16.7083	0.834373	0.417187	+	0.908821i	$0.363016\pi$
$402$	−7.16823	−0.357519
$403$	13.8788	0.691352
$404$	−15.0955	−0.751031
$405$	−0.465864	−0.0231490
$406$	−0.284167	−0.0141030
$407$	7.53386	0.373440
$408$	−1.35973	−0.0673166
$409$	15.8433	0.783401	0.391701	−	0.920093i	$-0.371887\pi$
$409$	15.8433	0.783401	0.391701	+	0.920093i	$0.371887\pi$
$410$	−1.52191	−0.0751616
$411$	−4.69778	−0.231724
$412$	14.9335	0.735723
$413$	2.88760	0.142090
$414$	−6.48593	−0.318766
$415$	5.97764	0.293431
$416$	5.34040	0.261834
$417$	20.0936	0.983988
$418$	4.23505	0.207143
$419$	−36.5681	−1.78647	−0.893235	−	0.449591i	$-0.851570\pi$
$419$	−36.5681	−1.78647	−0.893235	+	0.449591i	$0.851570\pi$
$420$	0.465864	0.0227318
$421$	12.0469	0.587131	0.293566	−	0.955939i	$-0.405158\pi$
$421$	12.0469	0.587131	0.293566	+	0.955939i	$0.405158\pi$
$422$	−14.6806	−0.714640
$423$	4.81011	0.233875
$424$	−12.9097	−0.626948
$425$	−6.50355	−0.315468
$426$	13.6658	0.662111
$427$	−0.0125659	−0.000608107 0
$428$	−7.94788	−0.384175
$429$	4.39061	0.211981
$430$	3.81844	0.184142
$431$	22.9347	1.10473	0.552363	−	0.833604i	$-0.313726\pi$
$431$	22.9347	1.10473	0.552363	+	0.833604i	$0.313726\pi$
$432$	1.00000	0.0481125
$433$	4.82014	0.231641	0.115821	−	0.993270i	$-0.463050\pi$
$433$	4.82014	0.231641	0.115821	+	0.993270i	$0.463050\pi$
$434$	−2.59883	−0.124748
$435$	0.132383	0.00634730
$436$	4.00855	0.191975
$437$	33.4102	1.59822
$438$	12.8923	0.616017
$439$	−9.11643	−0.435103	−0.217552	−	0.976049i	$-0.569807\pi$
$439$	−9.11643	−0.435103	−0.217552	+	0.976049i	$0.569807\pi$
$440$	−0.383011	−0.0182593
$441$	1.00000	0.0476190
$442$	7.26149	0.345394
$443$	25.3382	1.20385	0.601927	−	0.798551i	$-0.294400\pi$
$443$	25.3382	1.20385	0.601927	+	0.798551i	$0.294400\pi$
$444$	−9.16359	−0.434885
$445$	−0.149481	−0.00708609
$446$	−1.36727	−0.0647420
$447$	10.3785	0.490888
$448$	−1.00000	−0.0472456
$449$	33.1217	1.56311	0.781555	−	0.623836i	$-0.214427\pi$
$449$	33.1217	1.56311	0.781555	+	0.623836i	$0.214427\pi$
$450$	4.78297	0.225471
$451$	2.68584	0.126471
$452$	−6.02342	−0.283318
$453$	12.9710	0.609433
$454$	−12.6765	−0.594938
$455$	−2.48790	−0.116634
$456$	−5.15118	−0.241226
$457$	26.1601	1.22372	0.611859	−	0.790967i	$-0.290422\pi$
$457$	26.1601	1.22372	0.611859	+	0.790967i	$0.290422\pi$
$458$	−11.2947	−0.527765
$459$	1.35973	0.0634667
$460$	−3.02156	−0.140881
$461$	−7.79693	−0.363139	−0.181570	−	0.983378i	$-0.558118\pi$
$461$	−7.79693	−0.363139	−0.181570	+	0.983378i	$0.558118\pi$
$462$	−0.822152	−0.0382500
$463$	31.7358	1.47489	0.737443	−	0.675410i	$-0.236033\pi$
$463$	31.7358	1.47489	0.737443	+	0.675410i	$0.236033\pi$
$464$	−0.284167	−0.0131921
$465$	1.21070	0.0561450
$466$	−20.9909	−0.972386
$467$	−16.4026	−0.759021	−0.379511	−	0.925187i	$-0.623908\pi$
$467$	−16.4026	−0.759021	−0.379511	+	0.925187i	$0.623908\pi$
$468$	−5.34040	−0.246860
$469$	−7.16823	−0.330998
$470$	2.24086	0.103363
$471$	−19.6544	−0.905629
$472$	2.88760	0.132913
$473$	−6.73874	−0.309848
$474$	−15.1283	−0.694865
$475$	−24.6379	−1.13047
$476$	−1.35973	−0.0623231
$477$	12.9097	0.591093
$478$	−12.8090	−0.585869
$479$	15.0710	0.688611	0.344305	−	0.938858i	$-0.388114\pi$
$479$	15.0710	0.688611	0.344305	+	0.938858i	$0.388114\pi$
$480$	0.465864	0.0212637
$481$	48.9372	2.23134
$482$	10.5119	0.478804
$483$	−6.48593	−0.295120
$484$	−10.3241	−0.469276
$485$	−4.32765	−0.196508
$486$	−1.00000	−0.0453609
$487$	26.6714	1.20860	0.604299	−	0.796758i	$-0.293453\pi$
$487$	26.6714	1.20860	0.604299	+	0.796758i	$0.293453\pi$
$488$	−0.0125659	−0.000568832 0
$489$	12.6512	0.572109
$490$	0.465864	0.0210456
$491$	−28.1207	−1.26907	−0.634535	−	0.772894i	$-0.718809\pi$
$491$	−28.1207	−1.26907	−0.634535	+	0.772894i	$0.718809\pi$
$492$	−3.26684	−0.147281
$493$	−0.386391	−0.0174022
$494$	27.5093	1.23770
$495$	0.383011	0.0172151
$496$	−2.59883	−0.116691
$497$	13.6658	0.612996
$498$	12.8313	0.574984
$499$	−27.9438	−1.25094	−0.625469	−	0.780249i	$-0.715092\pi$
$499$	−27.9438	−1.25094	−0.625469	+	0.780249i	$0.715092\pi$
$500$	4.55753	0.203819
$501$	2.26663	0.101266
$502$	−14.8598	−0.663224
$503$	27.3992	1.22167	0.610835	−	0.791758i	$-0.290834\pi$
$503$	27.3992	1.22167	0.610835	+	0.791758i	$0.290834\pi$
$504$	1.00000	0.0445435
$505$	7.03247	0.312941
$506$	5.33241	0.237055
$507$	15.5198	0.689260
$508$	15.2422	0.676263
$509$	−20.5938	−0.912802	−0.456401	−	0.889774i	$-0.650862\pi$
$509$	−20.5938	−0.912802	−0.456401	+	0.889774i	$0.650862\pi$
$510$	0.633449	0.0280496
$511$	12.8923	0.570321
$512$	−1.00000	−0.0441942
$513$	5.15118	0.227430
$514$	8.57369	0.378169
$515$	−6.95700	−0.306562
$516$	8.19647	0.360830
$517$	−3.95464	−0.173925
$518$	−9.16359	−0.402625
$519$	15.2231	0.668220
$520$	−2.48790	−0.109102
$521$	−37.9299	−1.66174	−0.830870	−	0.556466i	$-0.812157\pi$
$521$	−37.9299	−1.66174	−0.830870	+	0.556466i	$0.812157\pi$
$522$	0.284167	0.0124377
$523$	11.7922	0.515635	0.257818	−	0.966194i	$-0.416997\pi$
$523$	11.7922	0.515635	0.257818	+	0.966194i	$0.416997\pi$
$524$	0.926864	0.0404903
$525$	4.78297	0.208746
$526$	−10.3219	−0.450056
$527$	−3.53371	−0.153931
$528$	−0.822152	−0.0357796
$529$	19.0672	0.829011
$530$	6.01415	0.261238
$531$	−2.88760	−0.125311
$532$	−5.15118	−0.223332
$533$	17.4462	0.755681
$534$	−0.320869	−0.0138854
$535$	3.70263	0.160079
$536$	−7.16823	−0.309621
$537$	3.10074	0.133807
$538$	−11.8573	−0.511202
$539$	−0.822152	−0.0354126
$540$	−0.465864	−0.0200476
$541$	−4.12692	−0.177430	−0.0887150	−	0.996057i	$-0.528276\pi$
$541$	−4.12692	−0.177430	−0.0887150	+	0.996057i	$0.528276\pi$
$542$	−11.4686	−0.492618
$543$	21.5086	0.923023
$544$	−1.35973	−0.0582979
$545$	−1.86744	−0.0799923
$546$	−5.34040	−0.228548
$547$	−39.1163	−1.67249	−0.836245	−	0.548356i	$-0.815254\pi$
$547$	−39.1163	−1.67249	−0.836245	+	0.548356i	$0.815254\pi$
$548$	−4.69778	−0.200679
$549$	0.0125659	0.000536300 0
$550$	−3.93233	−0.167675
$551$	−1.46380	−0.0623598
$552$	−6.48593	−0.276059
$553$	−15.1283	−0.643320
$554$	−23.2143	−0.986283
$555$	4.26899	0.181208
$556$	20.0936	0.852159
$557$	28.5518	1.20978	0.604890	−	0.796309i	$-0.293217\pi$
$557$	28.5518	1.20978	0.604890	+	0.796309i	$0.293217\pi$
$558$	2.59883	0.110017
$559$	−43.7724	−1.85138
$560$	0.465864	0.0196864
$561$	−1.11790	−0.0471979
$562$	9.79838	0.413320
$563$	−2.29480	−0.0967142	−0.0483571	−	0.998830i	$-0.515399\pi$
$563$	−2.29480	−0.0967142	−0.0483571	+	0.998830i	$0.515399\pi$
$564$	4.81011	0.202542
$565$	2.80610	0.118053
$566$	−17.1846	−0.722325
$567$	−1.00000	−0.0419961
$568$	13.6658	0.573405
$569$	2.91494	0.122201	0.0611004	−	0.998132i	$-0.480539\pi$
$569$	2.91494	0.122201	0.0611004	+	0.998132i	$0.480539\pi$
$570$	2.39975	0.100514
$571$	−4.02307	−0.168360	−0.0841802	−	0.996451i	$-0.526827\pi$
$571$	−4.02307	−0.168360	−0.0841802	+	0.996451i	$0.526827\pi$
$572$	4.39061	0.183581
$573$	−1.00000	−0.0417756
$574$	−3.26684	−0.136355
$575$	−31.0220	−1.29371
$576$	1.00000	0.0416667
$577$	17.7723	0.739872	0.369936	−	0.929057i	$-0.379380\pi$
$577$	17.7723	0.739872	0.369936	+	0.929057i	$0.379380\pi$
$578$	15.1511	0.630204
$579$	−4.74460	−0.197179
$580$	0.132383	0.00549692
$581$	12.8313	0.532332
$582$	−9.28951	−0.385063
$583$	−10.6137	−0.439574
$584$	12.8923	0.533486
$585$	2.48790	0.102862
$586$	−24.6712	−1.01916
$587$	−14.3158	−0.590875	−0.295437	−	0.955362i	$-0.595465\pi$
$587$	−14.3158	−0.590875	−0.295437	+	0.955362i	$0.595465\pi$
$588$	1.00000	0.0412393
$589$	−13.3870	−0.551604
$590$	−1.34523	−0.0553823
$591$	−11.7739	−0.484315
$592$	−9.16359	−0.376621
$593$	−18.0466	−0.741087	−0.370543	−	0.928815i	$-0.620829\pi$
$593$	−18.0466	−0.741087	−0.370543	+	0.928815i	$0.620829\pi$
$594$	0.822152	0.0337333
$595$	0.633449	0.0259689
$596$	10.3785	0.425121
$597$	17.7296	0.725623
$598$	34.6374	1.41643
$599$	48.2548	1.97164	0.985818	−	0.167817i	$-0.0536718\pi$
$599$	48.2548	1.97164	0.985818	+	0.167817i	$0.0536718\pi$
$600$	4.78297	0.195264
$601$	−5.41117	−0.220726	−0.110363	−	0.993891i	$-0.535201\pi$
$601$	−5.41117	−0.220726	−0.110363	+	0.993891i	$0.535201\pi$
$602$	8.19647	0.334063
$603$	7.16823	0.291913
$604$	12.9710	0.527784
$605$	4.80961	0.195539
$606$	15.0955	0.613214
$607$	16.6192	0.674553	0.337276	−	0.941406i	$-0.390494\pi$
$607$	16.6192	0.674553	0.337276	+	0.941406i	$0.390494\pi$
$608$	−5.15118	−0.208908
$609$	0.284167	0.0115150
$610$	0.00585400	0.000237022 0
$611$	−25.6879	−1.03922
$612$	1.35973	0.0549638
$613$	−2.31114	−0.0933461	−0.0466731	−	0.998910i	$-0.514862\pi$
$613$	−2.31114	−0.0933461	−0.0466731	+	0.998910i	$0.514862\pi$
$614$	33.7673	1.36274
$615$	1.52191	0.0613692
$616$	−0.822152	−0.0331254
$617$	−28.4887	−1.14691	−0.573457	−	0.819236i	$-0.694398\pi$
$617$	−28.4887	−1.14691	−0.573457	+	0.819236i	$0.694398\pi$
$618$	−14.9335	−0.600715
$619$	11.7313	0.471519	0.235760	−	0.971811i	$-0.424242\pi$
$619$	11.7313	0.471519	0.235760	+	0.971811i	$0.424242\pi$
$620$	1.21070	0.0486230
$621$	6.48593	0.260271
$622$	−0.812922	−0.0325952
$623$	−0.320869	−0.0128553
$624$	−5.34040	−0.213787
$625$	21.7917	0.871666
$626$	−2.16229	−0.0864225
$627$	−4.23505	−0.169132
$628$	−19.6544	−0.784298
$629$	−12.4600	−0.496813
$630$	−0.465864	−0.0185605
$631$	−31.6348	−1.25936	−0.629681	−	0.776854i	$-0.716814\pi$
$631$	−31.6348	−1.25936	−0.629681	+	0.776854i	$0.716814\pi$
$632$	−15.1283	−0.601771
$633$	14.6806	0.583501
$634$	16.9055	0.671401
$635$	−7.10079	−0.281786
$636$	12.9097	0.511901
$637$	−5.34040	−0.211594
$638$	−0.233629	−0.00924945
$639$	−13.6658	−0.540612
$640$	0.465864	0.0184149
$641$	−13.8503	−0.547056	−0.273528	−	0.961864i	$-0.588191\pi$
$641$	−13.8503	−0.547056	−0.273528	+	0.961864i	$0.588191\pi$
$642$	7.94788	0.313678
$643$	28.6881	1.13135	0.565675	−	0.824628i	$-0.308616\pi$
$643$	28.6881	1.13135	0.565675	+	0.824628i	$0.308616\pi$
$644$	−6.48593	−0.255581
$645$	−3.81844	−0.150351
$646$	−7.00421	−0.275577
$647$	−0.190608	−0.00749356	−0.00374678	−	0.999993i	$-0.501193\pi$
$647$	−0.190608	−0.00749356	−0.00374678	+	0.999993i	$0.501193\pi$
$648$	−1.00000	−0.0392837
$649$	2.37405	0.0931896
$650$	−25.5430	−1.00188
$651$	2.59883	0.101856
$652$	12.6512	0.495461
$653$	34.2590	1.34066	0.670330	−	0.742063i	$-0.266153\pi$
$653$	34.2590	1.34066	0.670330	+	0.742063i	$0.266153\pi$
$654$	−4.00855	−0.156747
$655$	−0.431793	−0.0168715
$656$	−3.26684	−0.127549
$657$	−12.8923	−0.502976
$658$	4.81011	0.187517
$659$	−9.99670	−0.389416	−0.194708	−	0.980861i	$-0.562376\pi$
$659$	−9.99670	−0.389416	−0.194708	+	0.980861i	$0.562376\pi$
$660$	0.383011	0.0149087
$661$	32.5042	1.26427	0.632134	−	0.774859i	$-0.282179\pi$
$661$	32.5042	1.26427	0.632134	+	0.774859i	$0.282179\pi$
$662$	13.4626	0.523239
$663$	−7.26149	−0.282013
$664$	12.8313	0.497951
$665$	2.39975	0.0930582
$666$	9.16359	0.355082
$667$	−1.84309	−0.0713647
$668$	2.26663	0.0876985
$669$	1.36727	0.0528617
$670$	3.33942	0.129013
$671$	−0.0103311	−0.000398827 0
$672$	1.00000	0.0385758
$673$	−30.9109	−1.19153	−0.595763	−	0.803160i	$-0.703150\pi$
$673$	−30.9109	−1.19153	−0.595763	+	0.803160i	$0.703150\pi$
$674$	−17.9440	−0.691177
$675$	−4.78297	−0.184097
$676$	15.5198	0.596916
$677$	18.1845	0.698887	0.349443	−	0.936958i	$-0.386371\pi$
$677$	18.1845	0.698887	0.349443	+	0.936958i	$0.386371\pi$
$678$	6.02342	0.231328
$679$	−9.28951	−0.356499
$680$	0.633449	0.0242917
$681$	12.6765	0.485764
$682$	−2.13663	−0.0818160
$683$	−26.8657	−1.02799	−0.513994	−	0.857794i	$-0.671835\pi$
$683$	−26.8657	−1.02799	−0.513994	+	0.857794i	$0.671835\pi$
$684$	5.15118	0.196960
$685$	2.18853	0.0836193
$686$	1.00000	0.0381802
$687$	11.2947	0.430918
$688$	8.19647	0.312488
$689$	−68.9427	−2.62651
$690$	3.02156	0.115029
$691$	−20.0898	−0.764251	−0.382125	−	0.924110i	$-0.624808\pi$
$691$	−20.0898	−0.764251	−0.382125	+	0.924110i	$0.624808\pi$
$692$	15.2231	0.578695
$693$	0.822152	0.0312310
$694$	−25.7056	−0.975771
$695$	−9.36089	−0.355079
$696$	0.284167	0.0107713
$697$	−4.44203	−0.168254
$698$	1.02631	0.0388463
$699$	20.9909	0.793950
$700$	4.78297	0.180779
$701$	22.2970	0.842148	0.421074	−	0.907026i	$-0.361653\pi$
$701$	22.2970	0.842148	0.421074	+	0.907026i	$0.361653\pi$
$702$	5.34040	0.201560
$703$	−47.2033	−1.78030
$704$	−0.822152	−0.0309860
$705$	−2.24086	−0.0843955
$706$	15.1681	0.570859
$707$	15.0955	0.567726
$708$	−2.88760	−0.108523
$709$	−50.5180	−1.89724	−0.948622	−	0.316411i	$-0.897522\pi$
$709$	−50.5180	−1.89724	−0.948622	+	0.316411i	$0.897522\pi$
$710$	−6.36642	−0.238927
$711$	15.1283	0.567355
$712$	−0.320869	−0.0120251
$713$	−16.8558	−0.631256
$714$	1.35973	0.0508866
$715$	−2.04543	−0.0764947
$716$	3.10074	0.115880
$717$	12.8090	0.478360
$718$	12.6134	0.470727
$719$	15.7969	0.589125	0.294562	−	0.955632i	$-0.404826\pi$
$719$	15.7969	0.589125	0.294562	+	0.955632i	$0.404826\pi$
$720$	−0.465864	−0.0173617
$721$	−14.9335	−0.556154
$722$	−7.53462	−0.280409
$723$	−10.5119	−0.390942
$724$	21.5086	0.799362
$725$	1.35916	0.0504781
$726$	10.3241	0.383162
$727$	−21.1797	−0.785512	−0.392756	−	0.919643i	$-0.628478\pi$
$727$	−21.1797	−0.785512	−0.392756	+	0.919643i	$0.628478\pi$
$728$	−5.34040	−0.197928
$729$	1.00000	0.0370370
$730$	−6.00605	−0.222294
$731$	11.1450	0.412212
$732$	0.0125659	0.000464449 0
$733$	2.94785	0.108881	0.0544407	−	0.998517i	$-0.482662\pi$
$733$	2.94785	0.108881	0.0544407	+	0.998517i	$0.482662\pi$
$734$	4.35982	0.160924
$735$	−0.465864	−0.0171837
$736$	−6.48593	−0.239074
$737$	−5.89338	−0.217085
$738$	3.26684	0.120254
$739$	35.9123	1.32105	0.660527	−	0.750802i	$-0.270333\pi$
$739$	35.9123	1.32105	0.660527	+	0.750802i	$0.270333\pi$
$740$	4.26899	0.156931
$741$	−27.5093	−1.01058
$742$	12.9097	0.473928
$743$	−11.2687	−0.413410	−0.206705	−	0.978403i	$-0.566274\pi$
$743$	−11.2687	−0.413410	−0.206705	+	0.978403i	$0.566274\pi$
$744$	2.59883	0.0952778
$745$	−4.83499	−0.177140
$746$	−9.74846	−0.356916
$747$	−12.8313	−0.469472
$748$	−1.11790	−0.0408746
$749$	7.94788	0.290409
$750$	−4.55753	−0.166418
$751$	−29.1041	−1.06202	−0.531012	−	0.847364i	$-0.678188\pi$
$751$	−29.1041	−1.06202	−0.531012	+	0.847364i	$0.678188\pi$
$752$	4.81011	0.175407
$753$	14.8598	0.541520
$754$	−1.51757	−0.0552665
$755$	−6.04274	−0.219918
$756$	−1.00000	−0.0363696
$757$	−17.0938	−0.621285	−0.310643	−	0.950527i	$-0.600544\pi$
$757$	−17.0938	−0.621285	−0.310643	+	0.950527i	$0.600544\pi$
$758$	−2.02882	−0.0736899
$759$	−5.33241	−0.193554
$760$	2.39975	0.0870480
$761$	13.2244	0.479386	0.239693	−	0.970849i	$-0.422953\pi$
$761$	13.2244	0.479386	0.239693	+	0.970849i	$0.422953\pi$
$762$	−15.2422	−0.552166
$763$	−4.00855	−0.145119
$764$	−1.00000	−0.0361787
$765$	−0.633449	−0.0229024
$766$	3.09152	0.111701
$767$	15.4209	0.556818
$768$	1.00000	0.0360844
$769$	−31.9463	−1.15201	−0.576006	−	0.817445i	$-0.695390\pi$
$769$	−31.9463	−1.15201	−0.576006	+	0.817445i	$0.695390\pi$
$770$	0.383011	0.0138028
$771$	−8.57369	−0.308774
$772$	−4.74460	−0.170762
$773$	23.2370	0.835777	0.417888	−	0.908498i	$-0.362770\pi$
$773$	23.2370	0.835777	0.417888	+	0.908498i	$0.362770\pi$
$774$	−8.19647	−0.294616
$775$	12.4301	0.446504
$776$	−9.28951	−0.333474
$777$	9.16359	0.328742
$778$	29.9674	1.07438
$779$	−16.8281	−0.602929
$780$	2.48790	0.0890811
$781$	11.2354	0.402033
$782$	−8.81911	−0.315371
$783$	−0.284167	−0.0101553
$784$	1.00000	0.0357143
$785$	9.15630	0.326802
$786$	−0.926864	−0.0330602
$787$	45.9559	1.63815	0.819075	−	0.573687i	$-0.194487\pi$
$787$	45.9559	1.63815	0.819075	+	0.573687i	$0.194487\pi$
$788$	−11.7739	−0.419429
$789$	10.3219	0.367469
$790$	7.04772	0.250747
$791$	6.02342	0.214168
$792$	0.822152	0.0292139
$793$	−0.0671069	−0.00238304
$794$	−0.204552	−0.00725929
$795$	−6.01415	−0.213300
$796$	17.7296	0.628408
$797$	−7.80763	−0.276561	−0.138280	−	0.990393i	$-0.544157\pi$
$797$	−7.80763	−0.276561	−0.138280	+	0.990393i	$0.544157\pi$
$798$	5.15118	0.182350
$799$	6.54044	0.231384
$800$	4.78297	0.169104
$801$	0.320869	0.0113373
$802$	−16.7083	−0.589991
$803$	10.5994	0.374045
$804$	7.16823	0.252804
$805$	3.02156	0.106496
$806$	−13.8788	−0.488860
$807$	11.8573	0.417395
$808$	15.0955	0.531059
$809$	44.7910	1.57477	0.787385	−	0.616462i	$-0.211435\pi$
$809$	44.7910	1.57477	0.787385	+	0.616462i	$0.211435\pi$
$810$	0.465864	0.0163688
$811$	3.88957	0.136581	0.0682907	−	0.997665i	$-0.478245\pi$
$811$	3.88957	0.136581	0.0682907	+	0.997665i	$0.478245\pi$
$812$	0.284167	0.00997232
$813$	11.4686	0.402221
$814$	−7.53386	−0.264062
$815$	−5.89376	−0.206449
$816$	1.35973	0.0476001
$817$	42.2215	1.47714
$818$	−15.8433	−0.553948
$819$	5.34040	0.186609
$820$	1.52191	0.0531473
$821$	−5.48334	−0.191370	−0.0956850	−	0.995412i	$-0.530504\pi$
$821$	−5.48334	−0.191370	−0.0956850	+	0.995412i	$0.530504\pi$
$822$	4.69778	0.163854
$823$	47.3893	1.65189	0.825944	−	0.563753i	$-0.190643\pi$
$823$	47.3893	1.65189	0.825944	+	0.563753i	$0.190643\pi$
$824$	−14.9335	−0.520235
$825$	3.93233	0.136906
$826$	−2.88760	−0.100473
$827$	31.1115	1.08185	0.540926	−	0.841070i	$-0.318074\pi$
$827$	31.1115	1.08185	0.540926	+	0.841070i	$0.318074\pi$
$828$	6.48593	0.225402
$829$	46.9176	1.62951	0.814757	−	0.579802i	$-0.196870\pi$
$829$	46.9176	1.62951	0.814757	+	0.579802i	$0.196870\pi$
$830$	−5.97764	−0.207487
$831$	23.2143	0.805297
$832$	−5.34040	−0.185145
$833$	1.35973	0.0471118
$834$	−20.0936	−0.695785
$835$	−1.05594	−0.0365424
$836$	−4.23505	−0.146472
$837$	−2.59883	−0.0898288
$838$	36.5681	1.26322
$839$	−50.4269	−1.74093	−0.870465	−	0.492230i	$-0.836182\pi$
$839$	−50.4269	−1.74093	−0.870465	+	0.492230i	$0.836182\pi$
$840$	−0.465864	−0.0160738
$841$	−28.9192	−0.997215
$842$	−12.0469	−0.415165
$843$	−9.79838	−0.337474
$844$	14.6806	0.505327
$845$	−7.23013	−0.248724
$846$	−4.81011	−0.165375
$847$	10.3241	0.354739
$848$	12.9097	0.443319
$849$	17.1846	0.589776
$850$	6.50355	0.223070
$851$	−59.4344	−2.03738
$852$	−13.6658	−0.468183
$853$	10.6644	0.365143	0.182571	−	0.983193i	$-0.441558\pi$
$853$	10.6644	0.365143	0.182571	+	0.983193i	$0.441558\pi$
$854$	0.0125659	0.000429996 0
$855$	−2.39975	−0.0820697
$856$	7.94788	0.271653
$857$	−50.2386	−1.71612	−0.858058	−	0.513553i	$-0.828329\pi$
$857$	−50.2386	−1.71612	−0.858058	+	0.513553i	$0.828329\pi$
$858$	−4.39061	−0.149893
$859$	58.4740	1.99511	0.997554	−	0.0698958i	$-0.0222667\pi$
$859$	58.4740	1.99511	0.997554	+	0.0698958i	$0.0222667\pi$
$860$	−3.81844	−0.130208
$861$	3.26684	0.111334
$862$	−22.9347	−0.781159
$863$	27.1072	0.922739	0.461370	−	0.887208i	$-0.347358\pi$
$863$	27.1072	0.922739	0.461370	+	0.887208i	$0.347358\pi$
$864$	−1.00000	−0.0340207
$865$	−7.09190	−0.241132
$866$	−4.82014	−0.163795
$867$	−15.1511	−0.514560
$868$	2.59883	0.0882101
$869$	−12.4377	−0.421922
$870$	−0.132383	−0.00448822
$871$	−38.2812	−1.29711
$872$	−4.00855	−0.135747
$873$	9.28951	0.314402
$874$	−33.4102	−1.13012
$875$	−4.55753	−0.154073
$876$	−12.8923	−0.435590
$877$	−4.34980	−0.146882	−0.0734412	−	0.997300i	$-0.523398\pi$
$877$	−4.34980	−0.146882	−0.0734412	+	0.997300i	$0.523398\pi$
$878$	9.11643	0.307665
$879$	24.6712	0.832139
$880$	0.383011	0.0129113
$881$	−10.6976	−0.360412	−0.180206	−	0.983629i	$-0.557676\pi$
$881$	−10.6976	−0.360412	−0.180206	+	0.983629i	$0.557676\pi$
$882$	−1.00000	−0.0336718
$883$	−0.723538	−0.0243490	−0.0121745	−	0.999926i	$-0.503875\pi$
$883$	−0.723538	−0.0243490	−0.0121745	+	0.999926i	$0.503875\pi$
$884$	−7.26149	−0.244230
$885$	1.34523	0.0452195
$886$	−25.3382	−0.851254
$887$	16.8644	0.566250	0.283125	−	0.959083i	$-0.408629\pi$
$887$	16.8644	0.566250	0.283125	+	0.959083i	$0.408629\pi$
$888$	9.16359	0.307510
$889$	−15.2422	−0.511207
$890$	0.149481	0.00501062
$891$	−0.822152	−0.0275431
$892$	1.36727	0.0457795
$893$	24.7777	0.829154
$894$	−10.3785	−0.347110
$895$	−1.44452	−0.0482850
$896$	1.00000	0.0334077
$897$	−34.6374	−1.15651
$898$	−33.1217	−1.10529
$899$	0.738503	0.0246305
$900$	−4.78297	−0.159432
$901$	17.5536	0.584797
$902$	−2.68584	−0.0894288
$903$	−8.19647	−0.272762
$904$	6.02342	0.200336
$905$	−10.0201	−0.333079
$906$	−12.9710	−0.430934
$907$	17.6619	0.586452	0.293226	−	0.956043i	$-0.405271\pi$
$907$	17.6619	0.586452	0.293226	+	0.956043i	$0.405271\pi$
$908$	12.6765	0.420684
$909$	−15.0955	−0.500688
$910$	2.48790	0.0824730
$911$	−42.1349	−1.39599	−0.697996	−	0.716102i	$-0.745925\pi$
$911$	−42.1349	−1.39599	−0.697996	+	0.716102i	$0.745925\pi$
$912$	5.15118	0.170572
$913$	10.5493	0.349130
$914$	−26.1601	−0.865299
$915$	−0.00585400	−0.000193527 0
$916$	11.2947	0.373186
$917$	−0.926864	−0.0306078
$918$	−1.35973	−0.0448778
$919$	−36.5042	−1.20416	−0.602082	−	0.798434i	$-0.705662\pi$
$919$	−36.5042	−1.20416	−0.602082	+	0.798434i	$0.705662\pi$
$920$	3.02156	0.0996179
$921$	−33.7673	−1.11267
$922$	7.79693	0.256778
$923$	72.9809	2.40220
$924$	0.822152	0.0270468
$925$	43.8292	1.44109
$926$	−31.7358	−1.04290
$927$	14.9335	0.490482
$928$	0.284167	0.00932825
$929$	−9.13731	−0.299785	−0.149893	−	0.988702i	$-0.547893\pi$
$929$	−9.13731	−0.299785	−0.149893	+	0.988702i	$0.547893\pi$
$930$	−1.21070	−0.0397005
$931$	5.15118	0.168823
$932$	20.9909	0.687581
$933$	0.812922	0.0266139
$934$	16.4026	0.536709
$935$	0.520791	0.0170317
$936$	5.34040	0.174556
$937$	31.8314	1.03989	0.519943	−	0.854201i	$-0.325953\pi$
$937$	31.8314	1.03989	0.519943	+	0.854201i	$0.325953\pi$
$938$	7.16823	0.234051
$939$	2.16229	0.0705637
$940$	−2.24086	−0.0730887
$941$	−9.70901	−0.316505	−0.158252	−	0.987399i	$-0.550586\pi$
$941$	−9.70901	−0.316505	−0.158252	+	0.987399i	$0.550586\pi$
$942$	19.6544	0.640376
$943$	−21.1885	−0.689993
$944$	−2.88760	−0.0939835
$945$	0.465864	0.0151546
$946$	6.73874	0.219095
$947$	46.1389	1.49931	0.749657	−	0.661827i	$-0.230219\pi$
$947$	46.1389	1.49931	0.749657	+	0.661827i	$0.230219\pi$
$948$	15.1283	0.491344
$949$	68.8498	2.23496
$950$	24.6379	0.799360
$951$	−16.9055	−0.548197
$952$	1.35973	0.0440691
$953$	−14.0193	−0.454129	−0.227065	−	0.973880i	$-0.572913\pi$
$953$	−14.0193	−0.454129	−0.227065	+	0.973880i	$0.572913\pi$
$954$	−12.9097	−0.417966
$955$	0.465864	0.0150750
$956$	12.8090	0.414272
$957$	0.233629	0.00755214
$958$	−15.0710	−0.486921
$959$	4.69778	0.151699
$960$	−0.465864	−0.0150357
$961$	−24.2461	−0.782131
$962$	−48.9372	−1.57780
$963$	−7.94788	−0.256117
$964$	−10.5119	−0.338566
$965$	2.21034	0.0711533
$966$	6.48593	0.208681
$967$	23.7856	0.764895	0.382447	−	0.923977i	$-0.375081\pi$
$967$	23.7856	0.764895	0.382447	+	0.923977i	$0.375081\pi$
$968$	10.3241	0.331828
$969$	7.00421	0.225008
$970$	4.32765	0.138952
$971$	−30.9571	−0.993460	−0.496730	−	0.867905i	$-0.665466\pi$
$971$	−30.9571	−0.993460	−0.496730	+	0.867905i	$0.665466\pi$
$972$	1.00000	0.0320750
$973$	−20.0936	−0.644171
$974$	−26.6714	−0.854607
$975$	25.5430	0.818029
$976$	0.0125659	0.000402225 0
$977$	−47.6323	−1.52389	−0.761947	−	0.647639i	$-0.775756\pi$
$977$	−47.6323	−1.52389	−0.761947	+	0.647639i	$0.775756\pi$
$978$	−12.6512	−0.404542
$979$	−0.263803	−0.00843118
$980$	−0.465864	−0.0148815
$981$	4.00855	0.127983
$982$	28.1207	0.897369
$983$	−44.3741	−1.41531	−0.707656	−	0.706557i	$-0.750248\pi$
$983$	−44.3741	−1.41531	−0.707656	+	0.706557i	$0.750248\pi$
$984$	3.26684	0.104143
$985$	5.48506	0.174768
$986$	0.386391	0.0123052
$987$	−4.81011	−0.153107
$988$	−27.5093	−0.875188
$989$	53.1617	1.69044
$990$	−0.383011	−0.0121729
$991$	32.9433	1.04648	0.523239	−	0.852186i	$-0.324723\pi$
$991$	32.9433	1.04648	0.523239	+	0.852186i	$0.324723\pi$
$992$	2.59883	0.0825130
$993$	−13.4626	−0.427223
$994$	−13.6658	−0.433454
$995$	−8.25957	−0.261846
$996$	−12.8313	−0.406575
$997$	28.6967	0.908833	0.454417	−	0.890789i	$-0.349848\pi$
$997$	28.6967	0.908833	0.454417	+	0.890789i	$0.349848\pi$
$998$	27.9438	0.884546
$999$	−9.16359	−0.289923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.w.1.6	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.w.1.6	✓	13	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.465864 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.465864 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.465864 q^{10} -0.822152 q^{11} +1.00000 q^{12} -5.34040 q^{13} +1.00000 q^{14} -0.465864 q^{15} +1.00000 q^{16} +1.35973 q^{17} -1.00000 q^{18} +5.15118 q^{19} -0.465864 q^{20} -1.00000 q^{21} +0.822152 q^{22} +6.48593 q^{23} -1.00000 q^{24} -4.78297 q^{25} +5.34040 q^{26} +1.00000 q^{27} -1.00000 q^{28} -0.284167 q^{29} +0.465864 q^{30} -2.59883 q^{31} -1.00000 q^{32} -0.822152 q^{33} -1.35973 q^{34} +0.465864 q^{35} +1.00000 q^{36} -9.16359 q^{37} -5.15118 q^{38} -5.34040 q^{39} +0.465864 q^{40} -3.26684 q^{41} +1.00000 q^{42} +8.19647 q^{43} -0.822152 q^{44} -0.465864 q^{45} -6.48593 q^{46} +4.81011 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.78297 q^{50} +1.35973 q^{51} -5.34040 q^{52} +12.9097 q^{53} -1.00000 q^{54} +0.383011 q^{55} +1.00000 q^{56} +5.15118 q^{57} +0.284167 q^{58} -2.88760 q^{59} -0.465864 q^{60} +0.0125659 q^{61} +2.59883 q^{62} -1.00000 q^{63} +1.00000 q^{64} +2.48790 q^{65} +0.822152 q^{66} +7.16823 q^{67} +1.35973 q^{68} +6.48593 q^{69} -0.465864 q^{70} -13.6658 q^{71} -1.00000 q^{72} -12.8923 q^{73} +9.16359 q^{74} -4.78297 q^{75} +5.15118 q^{76} +0.822152 q^{77} +5.34040 q^{78} +15.1283 q^{79} -0.465864 q^{80} +1.00000 q^{81} +3.26684 q^{82} -12.8313 q^{83} -1.00000 q^{84} -0.633449 q^{85} -8.19647 q^{86} -0.284167 q^{87} +0.822152 q^{88} +0.320869 q^{89} +0.465864 q^{90} +5.34040 q^{91} +6.48593 q^{92} -2.59883 q^{93} -4.81011 q^{94} -2.39975 q^{95} -1.00000 q^{96} +9.28951 q^{97} -1.00000 q^{98} -0.822152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - q^99

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