LMFDB - Embedded newform 1183.2.c.j.337.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.17
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.10989i q^{2} +0.955760 q^{3} +0.768150 q^{4} +3.55862i q^{5} +1.06079i q^{6} +1.00000i q^{7} +3.07233i q^{8} -2.08652 q^{9} +O(q^{10})$	\(q+1.10989i q^{2} +0.955760 q^{3} +0.768150 q^{4} +3.55862i q^{5} +1.06079i q^{6} +1.00000i q^{7} +3.07233i q^{8} -2.08652 q^{9} -3.94966 q^{10} -4.00483i q^{11} +0.734167 q^{12} -1.10989 q^{14} +3.40118i q^{15} -1.87364 q^{16} -1.86471 q^{17} -2.31581i q^{18} +6.34660i q^{19} +2.73355i q^{20} +0.955760i q^{21} +4.44491 q^{22} -4.50206 q^{23} +2.93641i q^{24} -7.66376 q^{25} -4.86149 q^{27} +0.768150i q^{28} +8.63110 q^{29} -3.77493 q^{30} +3.22435i q^{31} +4.06514i q^{32} -3.82766i q^{33} -2.06962i q^{34} -3.55862 q^{35} -1.60276 q^{36} +1.83406i q^{37} -7.04401 q^{38} -10.9333 q^{40} -10.3590i q^{41} -1.06079 q^{42} +10.3318 q^{43} -3.07631i q^{44} -7.42514i q^{45} -4.99678i q^{46} -0.832988i q^{47} -1.79075 q^{48} -1.00000 q^{49} -8.50590i q^{50} -1.78221 q^{51} +6.53512 q^{53} -5.39571i q^{54} +14.2517 q^{55} -3.07233 q^{56} +6.06582i q^{57} +9.57955i q^{58} +5.20780i q^{59} +2.61262i q^{60} -1.83794 q^{61} -3.57866 q^{62} -2.08652i q^{63} -8.25913 q^{64} +4.24827 q^{66} -3.05008i q^{67} -1.43238 q^{68} -4.30289 q^{69} -3.94966i q^{70} -14.4391i q^{71} -6.41050i q^{72} +12.9055i q^{73} -2.03559 q^{74} -7.32471 q^{75} +4.87514i q^{76} +4.00483 q^{77} +0.0931919 q^{79} -6.66758i q^{80} +1.61315 q^{81} +11.4973 q^{82} -3.17863i q^{83} +0.734167i q^{84} -6.63578i q^{85} +11.4671i q^{86} +8.24926 q^{87} +12.3042 q^{88} +12.2290i q^{89} +8.24106 q^{90} -3.45826 q^{92} +3.08170i q^{93} +0.924522 q^{94} -22.5851 q^{95} +3.88529i q^{96} +13.1916i q^{97} -1.10989i q^{98} +8.35617i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	$ 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) $ 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.10989i	0.784809i	0.919793	+	0.392404i	$0.128357\pi$
$2$	1.10989i	0.784809i	−0.919793	+	0.392404i	$0.871643\pi$
$3$	0.955760	0.551808	0.275904	−	0.961185i	$-0.411023\pi$
$3$	0.955760	0.551808	0.275904	+	0.961185i	$0.411023\pi$
$4$	0.768150	0.384075
$5$	3.55862i	1.59146i	0.605650	+	0.795731i	$0.292913\pi$
$5$	3.55862i	1.59146i	−0.605650	+	0.795731i	$0.707087\pi$
$6$	1.06079i	0.433064i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	3.07233i	1.08623i
$9$	−2.08652	−0.695508
$10$	−3.94966	−1.24899
$11$	− 4.00483i	− 1.20750i	−0.797173	−	0.603751i	$-0.793672\pi$
$11$	− 4.00483i	− 1.20750i	0.797173	−	0.603751i	$-0.206328\pi$
$12$	0.734167	0.211936
$13$	0	0
$13$	0	0
$14$	−1.10989	−0.296630
$15$	3.40118i	0.878182i
$16$	−1.87364	−0.468411
$17$	−1.86471	−0.452258	−0.226129	−	0.974097i	$-0.572607\pi$
$17$	−1.86471	−0.452258	−0.226129	+	0.974097i	$0.572607\pi$
$18$	− 2.31581i	− 0.545841i
$19$	6.34660i	1.45601i	0.685572	+	0.728005i	$0.259552\pi$
$19$	6.34660i	1.45601i	−0.685572	+	0.728005i	$0.740448\pi$
$20$	2.73355i	0.611241i
$21$	0.955760i	0.208564i
$22$	4.44491	0.947658
$23$	−4.50206	−0.938744	−0.469372	−	0.883001i	$-0.655520\pi$
$23$	−4.50206	−0.938744	−0.469372	+	0.883001i	$0.655520\pi$
$24$	2.93641i	0.599393i
$25$	−7.66376	−1.53275
$26$	0	0
$27$	−4.86149	−0.935595
$28$	0.768150i	0.145167i
$29$	8.63110	1.60275	0.801377	−	0.598159i	$-0.204101\pi$
$29$	8.63110	1.60275	0.801377	+	0.598159i	$0.204101\pi$
$30$	−3.77493	−0.689205
$31$	3.22435i	0.579110i	0.957161	+	0.289555i	$0.0935073\pi$
$31$	3.22435i	0.579110i	−0.957161	+	0.289555i	$0.906493\pi$
$32$	4.06514i	0.718621i
$33$	− 3.82766i	− 0.666309i
$34$	− 2.06962i	− 0.354936i
$35$	−3.55862	−0.601516
$36$	−1.60276	−0.267127
$37$	1.83406i	0.301517i	0.988571	+	0.150758i	$0.0481716\pi$
$37$	1.83406i	0.301517i	−0.988571	+	0.150758i	$0.951828\pi$
$38$	−7.04401	−1.14269
$39$	0	0
$40$	−10.9333	−1.72870
$41$	− 10.3590i	− 1.61780i	−0.587947	−	0.808899i	$-0.700064\pi$
$41$	− 10.3590i	− 1.61780i	0.587947	−	0.808899i	$-0.299936\pi$
$42$	−1.06079	−0.163683
$43$	10.3318	1.57559	0.787793	−	0.615941i	$-0.211224\pi$
$43$	10.3318	1.57559	0.787793	+	0.615941i	$0.211224\pi$
$44$	− 3.07631i	− 0.463771i
$45$	− 7.42514i	− 1.10687i
$46$	− 4.99678i	− 0.736735i
$47$	− 0.832988i	− 0.121504i	−0.998153	−	0.0607519i	$-0.980650\pi$
$47$	− 0.832988i	− 0.121504i	0.998153	−	0.0607519i	$-0.0193498\pi$
$48$	−1.79075	−0.258473
$49$	−1.00000	−0.142857
$50$	− 8.50590i	− 1.20292i
$51$	−1.78221	−0.249560
$52$	0	0
$53$	6.53512	0.897667	0.448834	−	0.893615i	$-0.351840\pi$
$53$	6.53512	0.897667	0.448834	+	0.893615i	$0.351840\pi$
$54$	− 5.39571i	− 0.734263i
$55$	14.2517	1.92169
$56$	−3.07233	−0.410558
$57$	6.06582i	0.803438i
$58$	9.57955i	1.25786i
$59$	5.20780i	0.677997i	0.940787	+	0.338999i	$0.110088\pi$
$59$	5.20780i	0.677997i	−0.940787	+	0.338999i	$0.889912\pi$
$60$	2.61262i	0.337288i
$61$	−1.83794	−0.235324	−0.117662	−	0.993054i	$-0.537540\pi$
$61$	−1.83794	−0.235324	−0.117662	+	0.993054i	$0.537540\pi$
$62$	−3.57866	−0.454491
$63$	− 2.08652i	− 0.262877i
$64$	−8.25913	−1.03239
$65$	0	0
$66$	4.24827	0.522925
$67$	− 3.05008i	− 0.372626i	−0.982490	−	0.186313i	$-0.940346\pi$
$67$	− 3.05008i	− 0.372626i	0.982490	−	0.186313i	$-0.0596539\pi$
$68$	−1.43238	−0.173701
$69$	−4.30289	−0.518007
$70$	− 3.94966i	− 0.472075i
$71$	− 14.4391i	− 1.71361i	−0.515640	−	0.856805i	$-0.672446\pi$
$71$	− 14.4391i	− 1.71361i	0.515640	−	0.856805i	$-0.327554\pi$
$72$	− 6.41050i	− 0.755484i
$73$	12.9055i	1.51047i	0.655454	+	0.755235i	$0.272477\pi$
$73$	12.9055i	1.51047i	−0.655454	+	0.755235i	$0.727523\pi$
$74$	−2.03559	−0.236633
$75$	−7.32471	−0.845785
$76$	4.87514i	0.559217i
$77$	4.00483	0.456393
$78$	0	0
$79$	0.0931919	0.0104849	0.00524245	−	0.999986i	$-0.498331\pi$
$79$	0.0931919	0.0104849	0.00524245	+	0.999986i	$0.498331\pi$
$80$	− 6.66758i	− 0.745458i
$81$	1.61315	0.179239
$82$	11.4973	1.26966
$83$	− 3.17863i	− 0.348900i	−0.984666	−	0.174450i	$-0.944185\pi$
$83$	− 3.17863i	− 0.348900i	0.984666	−	0.174450i	$-0.0558147\pi$
$84$	0.734167i	0.0801042i
$85$	− 6.63578i	− 0.719752i
$86$	11.4671i	1.23653i
$87$	8.24926	0.884413
$88$	12.3042	1.31163
$89$	12.2290i	1.29627i	0.761524	+	0.648137i	$0.224451\pi$
$89$	12.2290i	1.29627i	−0.761524	+	0.648137i	$0.775549\pi$
$90$	8.24106	0.868684
$91$	0	0
$92$	−3.45826	−0.360548
$93$	3.08170i	0.319558i
$94$	0.924522	0.0953572
$95$	−22.5851	−2.31718
$96$	3.88529i	0.396541i
$97$	13.1916i	1.33941i	0.742628	+	0.669704i	$0.233579\pi$
$97$	13.1916i	1.33941i	−0.742628	+	0.669704i	$0.766421\pi$
$98$	− 1.10989i	− 0.112116i
$99$	8.35617i	0.839827i
$100$	−5.88692	−0.588692
$101$	7.73025	0.769188	0.384594	−	0.923086i	$-0.374341\pi$
$101$	7.73025	0.769188	0.384594	+	0.923086i	$0.374341\pi$
$102$	− 1.97806i	− 0.195857i
$103$	0.359154	0.0353885	0.0176943	−	0.999843i	$-0.494367\pi$
$103$	0.359154	0.0353885	0.0176943	+	0.999843i	$0.494367\pi$
$104$	0	0
$105$	−3.40118	−0.331922
$106$	7.25324i	0.704497i
$107$	−3.99044	−0.385770	−0.192885	−	0.981221i	$-0.561784\pi$
$107$	−3.99044	−0.385770	−0.192885	+	0.981221i	$0.561784\pi$
$108$	−3.73436	−0.359339
$109$	9.65395i	0.924681i	0.886702	+	0.462341i	$0.152990\pi$
$109$	9.65395i	0.924681i	−0.886702	+	0.462341i	$0.847010\pi$
$110$	15.8177i	1.50816i
$111$	1.75292i	0.166379i
$112$	− 1.87364i	− 0.177043i
$113$	2.08248	0.195904	0.0979518	−	0.995191i	$-0.468771\pi$
$113$	2.08248	0.195904	0.0979518	+	0.995191i	$0.468771\pi$
$114$	−6.73238	−0.630545
$115$	− 16.0211i	− 1.49398i
$116$	6.62998	0.615578
$117$	0	0
$118$	−5.78007	−0.532098
$119$	− 1.86471i	− 0.170937i
$120$	−10.4496	−0.953911
$121$	−5.03866	−0.458060
$122$	− 2.03991i	− 0.184685i
$123$	− 9.90068i	− 0.892714i
$124$	2.47678i	0.222422i
$125$	− 9.47929i	− 0.847853i
$126$	2.31581	0.206308
$127$	−7.18287	−0.637376	−0.318688	−	0.947860i	$-0.603242\pi$
$127$	−7.18287	−0.637376	−0.318688	+	0.947860i	$0.603242\pi$
$128$	− 1.03643i	− 0.0916084i
$129$	9.87472	0.869421
$130$	0	0
$131$	−1.48085	−0.129383	−0.0646913	−	0.997905i	$-0.520606\pi$
$131$	−1.48085	−0.129383	−0.0646913	+	0.997905i	$0.520606\pi$
$132$	− 2.94022i	− 0.255913i
$133$	−6.34660	−0.550320
$134$	3.38524	0.292440
$135$	− 17.3002i	− 1.48896i
$136$	− 5.72901i	− 0.491258i
$137$	− 4.43864i	− 0.379219i	−0.981860	−	0.189609i	$-0.939278\pi$
$137$	− 4.43864i	− 0.379219i	0.981860	−	0.189609i	$-0.0607222\pi$
$138$	− 4.77572i	− 0.406536i
$139$	17.3529	1.47186	0.735929	−	0.677059i	$-0.236746\pi$
$139$	17.3529	1.47186	0.735929	+	0.677059i	$0.236746\pi$
$140$	−2.73355	−0.231027
$141$	− 0.796136i	− 0.0670468i
$142$	16.0258	1.34486
$143$	0	0
$144$	3.90940	0.325783
$145$	30.7148i	2.55072i
$146$	−14.3236	−1.18543
$147$	−0.955760	−0.0788297
$148$	1.40883i	0.115805i
$149$	− 23.1381i	− 1.89554i	−0.318950	−	0.947771i	$-0.603330\pi$
$149$	− 23.1381i	− 1.89554i	0.318950	−	0.947771i	$-0.396670\pi$
$150$	− 8.12960i	− 0.663779i
$151$	10.8846i	0.885778i	0.896576	+	0.442889i	$0.146047\pi$
$151$	10.8846i	0.885778i	−0.896576	+	0.442889i	$0.853953\pi$
$152$	−19.4989	−1.58157
$153$	3.89076	0.314549
$154$	4.44491i	0.358181i
$155$	−11.4742	−0.921632
$156$	0	0
$157$	14.2555	1.13771	0.568855	−	0.822438i	$-0.307387\pi$
$157$	14.2555	1.13771	0.568855	+	0.822438i	$0.307387\pi$
$158$	0.103432i	0.00822865i
$159$	6.24600	0.495340
$160$	−14.4663	−1.14366
$161$	− 4.50206i	− 0.354812i
$162$	1.79041i	0.140668i
$163$	− 2.01430i	− 0.157772i	−0.996884	−	0.0788861i	$-0.974864\pi$
$163$	− 2.01430i	− 0.157772i	0.996884	−	0.0788861i	$-0.0251364\pi$
$164$	− 7.95724i	− 0.621356i
$165$	13.6212	1.06041
$166$	3.52792	0.273820
$167$	− 18.8978i	− 1.46236i	−0.682187	−	0.731178i	$-0.738971\pi$
$167$	− 18.8978i	− 1.46236i	0.682187	−	0.731178i	$-0.261029\pi$
$168$	−2.93641	−0.226549
$169$	0	0
$170$	7.36497	0.564867
$171$	− 13.2423i	− 1.01267i
$172$	7.93638	0.605143
$173$	12.4146	0.943868	0.471934	−	0.881634i	$-0.343556\pi$
$173$	12.4146	0.943868	0.471934	+	0.881634i	$0.343556\pi$
$174$	9.15575i	0.694095i
$175$	− 7.66376i	− 0.579325i
$176$	7.50363i	0.565607i
$177$	4.97740i	0.374125i
$178$	−13.5728	−1.01733
$179$	9.37393	0.700641	0.350320	−	0.936630i	$-0.386073\pi$
$179$	9.37393	0.700641	0.350320	+	0.936630i	$0.386073\pi$
$180$	− 5.70362i	− 0.425123i
$181$	−5.83547	−0.433747	−0.216873	−	0.976200i	$-0.569586\pi$
$181$	−5.83547	−0.433747	−0.216873	+	0.976200i	$0.569586\pi$
$182$	0	0
$183$	−1.75663	−0.129854
$184$	− 13.8318i	− 1.01970i
$185$	−6.52670	−0.479852
$186$	−3.42034	−0.250792
$187$	7.46784i	0.546102i
$188$	− 0.639860i	− 0.0466666i
$189$	− 4.86149i	− 0.353622i
$190$	− 25.0669i	− 1.81855i
$191$	−16.3051	−1.17980	−0.589899	−	0.807477i	$-0.700833\pi$
$191$	−16.3051	−1.17980	−0.589899	+	0.807477i	$0.700833\pi$
$192$	−7.89375	−0.569682
$193$	21.2251i	1.52782i	0.645323	+	0.763910i	$0.276723\pi$
$193$	21.2251i	1.52782i	−0.645323	+	0.763910i	$0.723277\pi$
$194$	−14.6412	−1.05118
$195$	0	0
$196$	−0.768150	−0.0548679
$197$	16.0798i	1.14564i	0.819683	+	0.572818i	$0.194150\pi$
$197$	16.0798i	1.14564i	−0.819683	+	0.572818i	$0.805850\pi$
$198$	−9.27441	−0.659103
$199$	15.4383	1.09440	0.547198	−	0.837003i	$-0.315695\pi$
$199$	15.4383	1.09440	0.547198	+	0.837003i	$0.315695\pi$
$200$	− 23.5456i	− 1.66493i
$201$	− 2.91514i	− 0.205618i
$202$	8.57970i	0.603666i
$203$	8.63110i	0.605784i
$204$	−1.36901	−0.0958497
$205$	36.8636	2.57466
$206$	0.398621i	0.0277732i
$207$	9.39365	0.652904
$208$	0	0
$209$	25.4170	1.75813
$210$	− 3.77493i	− 0.260495i
$211$	3.45377	0.237767	0.118884	−	0.992908i	$-0.462068\pi$
$211$	3.45377	0.237767	0.118884	+	0.992908i	$0.462068\pi$
$212$	5.01995	0.344772
$213$	− 13.8004i	− 0.945584i
$214$	− 4.42893i	− 0.302756i
$215$	36.7669i	2.50748i
$216$	− 14.9361i	− 1.01628i
$217$	−3.22435	−0.218883
$218$	−10.7148	−0.725698
$219$	12.3345i	0.833490i
$220$	10.9474	0.738075
$221$	0	0
$222$	−1.94554	−0.130576
$223$	− 15.6638i	− 1.04893i	−0.851433	−	0.524464i	$-0.824266\pi$
$223$	− 15.6638i	− 1.04893i	0.851433	−	0.524464i	$-0.175734\pi$
$224$	−4.06514	−0.271613
$225$	15.9906	1.06604
$226$	2.31132i	0.153747i
$227$	8.05474i	0.534612i	0.963612	+	0.267306i	$0.0861335\pi$
$227$	8.05474i	0.534612i	−0.963612	+	0.267306i	$0.913867\pi$
$228$	4.65947i	0.308581i
$229$	− 19.9670i	− 1.31946i	−0.751503	−	0.659730i	$-0.770671\pi$
$229$	− 19.9670i	− 1.31946i	0.751503	−	0.659730i	$-0.229329\pi$
$230$	17.7816	1.17248
$231$	3.82766	0.251841
$232$	26.5176i	1.74097i
$233$	−12.1790	−0.797871	−0.398935	−	0.916979i	$-0.630620\pi$
$233$	−12.1790	−0.797871	−0.398935	+	0.916979i	$0.630620\pi$
$234$	0	0
$235$	2.96428	0.193369
$236$	4.00037i	0.260402i
$237$	0.0890691	0.00578566
$238$	2.06962	0.134153
$239$	− 15.5704i	− 1.00717i	−0.863946	−	0.503584i	$-0.832014\pi$
$239$	− 15.5704i	− 1.00717i	0.863946	−	0.503584i	$-0.167986\pi$
$240$	− 6.37261i	− 0.411350i
$241$	1.30581i	0.0841148i	0.999115	+	0.0420574i	$0.0133912\pi$
$241$	1.30581i	0.0841148i	−0.999115	+	0.0420574i	$0.986609\pi$
$242$	− 5.59235i	− 0.359490i
$243$	16.1263	1.03450
$244$	−1.41182	−0.0903822
$245$	− 3.55862i	− 0.227352i
$246$	10.9886	0.700610
$247$	0	0
$248$	−9.90628	−0.629049
$249$	− 3.03801i	− 0.192526i
$250$	10.5209	0.665402
$251$	20.2852	1.28039	0.640196	−	0.768212i	$-0.278853\pi$
$251$	20.2852	1.28039	0.640196	+	0.768212i	$0.278853\pi$
$252$	− 1.60276i	− 0.100965i
$253$	18.0300i	1.13353i
$254$	− 7.97217i	− 0.500219i
$255$	− 6.34221i	− 0.397165i
$256$	−15.3679	−0.960496
$257$	−17.3450	−1.08195	−0.540977	−	0.841038i	$-0.681945\pi$
$257$	−17.3450	−1.08195	−0.540977	+	0.841038i	$0.681945\pi$
$258$	10.9598i	0.682329i
$259$	−1.83406	−0.113963
$260$	0	0
$261$	−18.0090	−1.11473
$262$	− 1.64358i	− 0.101541i
$263$	−10.8891	−0.671448	−0.335724	−	0.941960i	$-0.608981\pi$
$263$	−10.8891	−0.671448	−0.335724	+	0.941960i	$0.608981\pi$
$264$	11.7598	0.723768
$265$	23.2560i	1.42860i
$266$	− 7.04401i	− 0.431896i
$267$	11.6880i	0.715294i
$268$	− 2.34292i	− 0.143117i
$269$	8.99414	0.548382	0.274191	−	0.961675i	$-0.411590\pi$
$269$	8.99414	0.548382	0.274191	+	0.961675i	$0.411590\pi$
$270$	19.2013	1.16855
$271$	4.94282i	0.300255i	0.988667	+	0.150127i	$0.0479684\pi$
$271$	4.94282i	0.300255i	−0.988667	+	0.150127i	$0.952032\pi$
$272$	3.49380	0.211843
$273$	0	0
$274$	4.92639	0.297614
$275$	30.6920i	1.85080i
$276$	−3.30526	−0.198954
$277$	−19.4610	−1.16930	−0.584650	−	0.811286i	$-0.698768\pi$
$277$	−19.4610	−1.16930	−0.584650	+	0.811286i	$0.698768\pi$
$278$	19.2598i	1.15513i
$279$	− 6.72768i	− 0.402776i
$280$	− 10.9333i	− 0.653387i
$281$	− 20.1468i	− 1.20185i	−0.799304	−	0.600927i	$-0.794798\pi$
$281$	− 20.1468i	− 1.20185i	0.799304	−	0.600927i	$-0.205202\pi$
$282$	0.883621	0.0526189
$283$	22.8282	1.35699	0.678496	−	0.734604i	$-0.262632\pi$
$283$	22.8282	1.35699	0.678496	+	0.734604i	$0.262632\pi$
$284$	− 11.0914i	− 0.658155i
$285$	−21.5859	−1.27864
$286$	0	0
$287$	10.3590	0.611470
$288$	− 8.48200i	− 0.499807i
$289$	−13.5229	−0.795463
$290$	−34.0899	−2.00183
$291$	12.6080i	0.739096i
$292$	9.91334i	0.580134i
$293$	26.5717i	1.55233i	0.630528	+	0.776166i	$0.282838\pi$
$293$	26.5717i	1.55233i	−0.630528	+	0.776166i	$0.717162\pi$
$294$	− 1.06079i	− 0.0618663i
$295$	−18.5326	−1.07901
$296$	−5.63483	−0.327518
$297$	19.4695i	1.12973i
$298$	25.6806	1.48764
$299$	0	0
$300$	−5.62648	−0.324845
$301$	10.3318i	0.595515i
$302$	−12.0807	−0.695167
$303$	7.38826	0.424444
$304$	− 11.8913i	− 0.682011i
$305$	− 6.54053i	− 0.374510i
$306$	4.31830i	0.246861i
$307$	− 7.16833i	− 0.409118i	−0.978854	−	0.204559i	$-0.934424\pi$
$307$	− 7.16833i	− 0.409118i	0.978854	−	0.204559i	$-0.0655761\pi$
$308$	3.07631	0.175289
$309$	0.343265	0.0195277
$310$	− 12.7351i	− 0.723305i
$311$	13.6640	0.774817	0.387408	−	0.921908i	$-0.373370\pi$
$311$	13.6640	0.774817	0.387408	+	0.921908i	$0.373370\pi$
$312$	0	0
$313$	10.5821	0.598137	0.299068	−	0.954232i	$-0.403324\pi$
$313$	10.5821	0.598137	0.299068	+	0.954232i	$0.403324\pi$
$314$	15.8219i	0.892884i
$315$	7.42514	0.418359
$316$	0.0715854	0.00402699
$317$	3.65041i	0.205027i	0.994732	+	0.102514i	$0.0326886\pi$
$317$	3.65041i	0.205027i	−0.994732	+	0.102514i	$0.967311\pi$
$318$	6.93236i	0.388747i
$319$	− 34.5661i	− 1.93533i
$320$	− 29.3911i	− 1.64301i
$321$	−3.81390	−0.212871
$322$	4.99678	0.278459
$323$	− 11.8346i	− 0.658492i
$324$	1.23914	0.0688411
$325$	0	0
$326$	2.23565	0.123821
$327$	9.22686i	0.510247i
$328$	31.8262	1.75731
$329$	0.832988	0.0459241
$330$	15.1180i	0.832216i
$331$	− 21.7576i	− 1.19590i	−0.801532	−	0.597952i	$-0.795981\pi$
$331$	− 21.7576i	− 1.19590i	0.801532	−	0.597952i	$-0.204019\pi$
$332$	− 2.44167i	− 0.134004i
$333$	− 3.82680i	− 0.209707i
$334$	20.9744	1.14767
$335$	10.8541	0.593021
$336$	− 1.79075i	− 0.0976936i
$337$	17.8877	0.974405	0.487202	−	0.873289i	$-0.338017\pi$
$337$	17.8877	0.974405	0.487202	+	0.873289i	$0.338017\pi$
$338$	0	0
$339$	1.99036	0.108101
$340$	− 5.09728i	− 0.276439i
$341$	12.9130	0.699276
$342$	14.6975	0.794749
$343$	− 1.00000i	− 0.0539949i
$344$	31.7428i	1.71145i
$345$	− 15.3123i	− 0.824388i
$346$	13.7789i	0.740756i
$347$	11.2388	0.603331	0.301666	−	0.953414i	$-0.402457\pi$
$347$	11.2388	0.603331	0.301666	+	0.953414i	$0.402457\pi$
$348$	6.33667	0.339681
$349$	− 24.4183i	− 1.30708i	−0.756891	−	0.653542i	$-0.773282\pi$
$349$	− 24.4183i	− 1.30708i	0.756891	−	0.653542i	$-0.226718\pi$
$350$	8.50590	0.454660
$351$	0	0
$352$	16.2802	0.867736
$353$	15.9072i	0.846655i	0.905977	+	0.423327i	$0.139138\pi$
$353$	15.9072i	0.846655i	−0.905977	+	0.423327i	$0.860862\pi$
$354$	−5.52436	−0.293616
$355$	51.3834	2.72715
$356$	9.39372i	0.497866i
$357$	− 1.78221i	− 0.0943247i
$358$	10.4040i	0.549869i
$359$	12.4456i	0.656853i	0.944529	+	0.328427i	$0.106518\pi$
$359$	12.4456i	0.656853i	−0.944529	+	0.328427i	$0.893482\pi$
$360$	22.8125	1.20232
$361$	−21.2793	−1.11996
$362$	− 6.47671i	− 0.340408i
$363$	−4.81575	−0.252761
$364$	0	0
$365$	−45.9256	−2.40386
$366$	− 1.94966i	− 0.101910i
$367$	−18.2038	−0.950231	−0.475115	−	0.879923i	$-0.657594\pi$
$367$	−18.2038	−0.950231	−0.475115	+	0.879923i	$0.657594\pi$
$368$	8.43525	0.439718
$369$	21.6142i	1.12519i
$370$	− 7.24390i	− 0.376592i
$371$	6.53512i	0.339286i
$372$	2.36721i	0.122734i
$373$	32.6828	1.69225	0.846126	−	0.532983i	$-0.178929\pi$
$373$	32.6828	1.69225	0.846126	+	0.532983i	$0.178929\pi$
$374$	−8.28846	−0.428586
$375$	− 9.05992i	− 0.467852i
$376$	2.55922	0.131982
$377$	0	0
$378$	5.39571	0.277525
$379$	− 8.81792i	− 0.452946i	−0.974017	−	0.226473i	$-0.927280\pi$
$379$	− 8.81792i	− 0.452946i	0.974017	−	0.226473i	$-0.0727195\pi$
$380$	−17.3488	−0.889973
$381$	−6.86510	−0.351710
$382$	− 18.0969i	− 0.925916i
$383$	2.54364i	0.129974i	0.997886	+	0.0649870i	$0.0207006\pi$
$383$	2.54364i	0.129974i	−0.997886	+	0.0649870i	$0.979299\pi$
$384$	− 0.990579i	− 0.0505502i
$385$	14.2517i	0.726332i
$386$	−23.5575	−1.19905
$387$	−21.5575	−1.09583
$388$	10.1332i	0.514433i
$389$	0.516707	0.0261981	0.0130990	−	0.999914i	$-0.495830\pi$
$389$	0.516707	0.0261981	0.0130990	+	0.999914i	$0.495830\pi$
$390$	0	0
$391$	8.39502	0.424555
$392$	− 3.07233i	− 0.155176i
$393$	−1.41534	−0.0713944
$394$	−17.8467	−0.899104
$395$	0.331634i	0.0166863i
$396$	6.41880i	0.322557i
$397$	− 25.8956i	− 1.29967i	−0.760077	−	0.649833i	$-0.774839\pi$
$397$	− 25.8956i	− 1.29967i	0.760077	−	0.649833i	$-0.225161\pi$
$398$	17.1348i	0.858891i
$399$	−6.06582	−0.303671
$400$	14.3591	0.717957
$401$	− 10.2493i	− 0.511828i	−0.966700	−	0.255914i	$-0.917624\pi$
$401$	− 10.2493i	− 0.511828i	0.966700	−	0.255914i	$-0.0823764\pi$
$402$	3.23548	0.161371
$403$	0	0
$404$	5.93799	0.295426
$405$	5.74057i	0.285251i
$406$	−9.57955	−0.475425
$407$	7.34508	0.364082
$408$	− 5.47556i	− 0.271080i
$409$	− 20.5100i	− 1.01416i	−0.861900	−	0.507078i	$-0.830726\pi$
$409$	− 20.5100i	− 1.01416i	0.861900	−	0.507078i	$-0.169274\pi$
$410$	40.9144i	2.02062i
$411$	− 4.24228i	− 0.209256i
$412$	0.275884	0.0135918
$413$	−5.20780	−0.256259
$414$	10.4259i	0.512405i
$415$	11.3115	0.555261
$416$	0	0
$417$	16.5852	0.812183
$418$	28.2101i	1.37980i
$419$	15.2380	0.744426	0.372213	−	0.928147i	$-0.378599\pi$
$419$	15.2380	0.744426	0.372213	+	0.928147i	$0.378599\pi$
$420$	−2.61262	−0.127483
$421$	26.3846i	1.28590i	0.765906	+	0.642952i	$0.222291\pi$
$421$	26.3846i	1.28590i	−0.765906	+	0.642952i	$0.777709\pi$
$422$	3.83329i	0.186602i
$423$	1.73805i	0.0845068i
$424$	20.0781i	0.975077i
$425$	14.2907	0.693199
$426$	15.3168	0.742103
$427$	− 1.83794i	− 0.0889442i
$428$	−3.06526	−0.148165
$429$	0	0
$430$	−40.8071	−1.96790
$431$	− 37.9100i	− 1.82606i	−0.407889	−	0.913031i	$-0.633735\pi$
$431$	− 37.9100i	− 1.82606i	0.407889	−	0.913031i	$-0.366265\pi$
$432$	9.10871	0.438243
$433$	−8.51058	−0.408993	−0.204496	−	0.978867i	$-0.565556\pi$
$433$	−8.51058	−0.408993	−0.204496	+	0.978867i	$0.565556\pi$
$434$	− 3.57866i	− 0.171781i
$435$	29.3559i	1.40751i
$436$	7.41569i	0.355147i
$437$	− 28.5728i	− 1.36682i
$438$	−13.6899	−0.654130
$439$	−18.6101	−0.888213	−0.444107	−	0.895974i	$-0.646479\pi$
$439$	−18.6101	−0.888213	−0.444107	+	0.895974i	$0.646479\pi$
$440$	43.7859i	2.08741i
$441$	2.08652	0.0993582
$442$	0	0
$443$	26.8582	1.27607	0.638035	−	0.770007i	$-0.279747\pi$
$443$	26.8582	1.27607	0.638035	+	0.770007i	$0.279747\pi$
$444$	1.34650i	0.0639022i
$445$	−43.5184	−2.06297
$446$	17.3851	0.823208
$447$	− 22.1144i	− 1.04598i
$448$	− 8.25913i	− 0.390207i
$449$	15.5278i	0.732804i	0.930457	+	0.366402i	$0.119411\pi$
$449$	15.5278i	0.732804i	−0.930457	+	0.366402i	$0.880589\pi$
$450$	17.7478i	0.836638i
$451$	−41.4859	−1.95349
$452$	1.59966	0.0752418
$453$	10.4031i	0.488780i
$454$	−8.93986	−0.419568
$455$	0	0
$456$	−18.6362	−0.872722
$457$	− 33.5563i	− 1.56970i	−0.619688	−	0.784848i	$-0.712741\pi$
$457$	− 33.5563i	− 1.56970i	0.619688	−	0.784848i	$-0.287259\pi$
$458$	22.1612	1.03552
$459$	9.06527	0.423130
$460$	− 12.3066i	− 0.573799i
$461$	4.34899i	0.202553i	0.994858	+	0.101276i	$0.0322926\pi$
$461$	4.34899i	0.202553i	−0.994858	+	0.101276i	$0.967707\pi$
$462$	4.24827i	0.197647i
$463$	23.2754i	1.08170i	0.841119	+	0.540850i	$0.181897\pi$
$463$	23.2754i	1.08170i	−0.841119	+	0.540850i	$0.818103\pi$
$464$	−16.1716	−0.750748
$465$	−10.9666	−0.508564
$466$	− 13.5173i	− 0.626176i
$467$	−12.2510	−0.566909	−0.283454	−	0.958986i	$-0.591480\pi$
$467$	−12.2510	−0.566909	−0.283454	+	0.958986i	$0.591480\pi$
$468$	0	0
$469$	3.05008	0.140840
$470$	3.29002i	0.151757i
$471$	13.6248	0.627797
$472$	−16.0001	−0.736464
$473$	− 41.3771i	− 1.90252i
$474$	0.0988566i	0.00454063i
$475$	− 48.6388i	− 2.23170i
$476$	− 1.43238i	− 0.0656529i
$477$	−13.6357	−0.624334
$478$	17.2814	0.790434
$479$	− 0.683706i	− 0.0312393i	−0.999878	−	0.0156197i	$-0.995028\pi$
$479$	− 0.683706i	− 0.0312393i	0.999878	−	0.0156197i	$-0.00497209\pi$
$480$	−13.8263	−0.631080
$481$	0	0
$482$	−1.44930	−0.0660140
$483$	− 4.30289i	− 0.195788i
$484$	−3.87045	−0.175930
$485$	−46.9440	−2.13162
$486$	17.8983i	0.811885i
$487$	2.18545i	0.0990323i	0.998773	+	0.0495162i	$0.0157679\pi$
$487$	2.18545i	0.0990323i	−0.998773	+	0.0495162i	$0.984232\pi$
$488$	− 5.64677i	− 0.255617i
$489$	− 1.92519i	− 0.0870601i
$490$	3.94966	0.178428
$491$	−8.81707	−0.397909	−0.198954	−	0.980009i	$-0.563755\pi$
$491$	−8.81707	−0.397909	−0.198954	+	0.980009i	$0.563755\pi$
$492$	− 7.60521i	− 0.342870i
$493$	−16.0945	−0.724859
$494$	0	0
$495$	−29.7364	−1.33655
$496$	− 6.04128i	− 0.271262i
$497$	14.4391	0.647684
$498$	3.37185	0.151096
$499$	− 16.3801i	− 0.733275i	−0.930364	−	0.366637i	$-0.880509\pi$
$499$	− 16.3801i	− 0.733275i	0.930364	−	0.366637i	$-0.119491\pi$
$500$	− 7.28152i	− 0.325639i
$501$	− 18.0618i	− 0.806940i
$502$	22.5143i	1.00486i
$503$	−11.5765	−0.516168	−0.258084	−	0.966122i	$-0.583091\pi$
$503$	−11.5765	−0.516168	−0.258084	+	0.966122i	$0.583091\pi$
$504$	6.41050	0.285546
$505$	27.5090i	1.22413i
$506$	−20.0112	−0.889608
$507$	0	0
$508$	−5.51752	−0.244800
$509$	− 13.3984i	− 0.593874i	−0.954897	−	0.296937i	$-0.904035\pi$
$509$	− 13.3984i	− 0.593874i	0.954897	−	0.296937i	$-0.0959651\pi$
$510$	7.03914	0.311698
$511$	−12.9055	−0.570904
$512$	− 19.1295i	− 0.845414i
$513$	− 30.8540i	− 1.36224i
$514$	− 19.2510i	− 0.849127i
$515$	1.27809i	0.0563195i
$516$	7.58527	0.333923
$517$	−3.33597	−0.146716
$518$	− 2.03559i	− 0.0894389i
$519$	11.8654	0.520834
$520$	0	0
$521$	38.0891	1.66871	0.834356	−	0.551226i	$-0.185840\pi$
$521$	38.0891	1.66871	0.834356	+	0.551226i	$0.185840\pi$
$522$	− 19.9879i	− 0.874848i
$523$	1.91936	0.0839276	0.0419638	−	0.999119i	$-0.486639\pi$
$523$	1.91936	0.0839276	0.0419638	+	0.999119i	$0.486639\pi$
$524$	−1.13752	−0.0496927
$525$	− 7.32471i	− 0.319677i
$526$	− 12.0856i	− 0.526959i
$527$	− 6.01247i	− 0.261907i
$528$	7.17166i	0.312107i
$529$	−2.73147	−0.118760
$530$	−25.8115	−1.12118
$531$	− 10.8662i	− 0.471552i
$532$	−4.87514	−0.211364
$533$	0	0
$534$	−12.9724	−0.561369
$535$	− 14.2004i	− 0.613938i
$536$	9.37086	0.404760
$537$	8.95923	0.386619
$538$	9.98248i	0.430375i
$539$	4.00483i	0.172500i
$540$	− 13.2892i	− 0.571874i
$541$	− 7.49222i	− 0.322116i	−0.986945	−	0.161058i	$-0.948509\pi$
$541$	− 7.49222i	− 0.322116i	0.986945	−	0.161058i	$-0.0514905\pi$
$542$	−5.48597	−0.235642
$543$	−5.57731	−0.239345
$544$	− 7.58029i	− 0.325002i
$545$	−34.3547	−1.47159
$546$	0	0
$547$	14.7156	0.629192	0.314596	−	0.949226i	$-0.398131\pi$
$547$	14.7156	0.629192	0.314596	+	0.949226i	$0.398131\pi$
$548$	− 3.40955i	− 0.145649i
$549$	3.83491	0.163670
$550$	−34.0647	−1.45252
$551$	54.7781i	2.33363i
$552$	− 13.2199i	− 0.562677i
$553$	0.0931919i	0.00396292i
$554$	− 21.5995i	− 0.917677i
$555$	−6.23796	−0.264787
$556$	13.3297	0.565304
$557$	− 5.45353i	− 0.231073i	−0.993303	−	0.115537i	$-0.963141\pi$
$557$	− 5.45353i	− 0.231073i	0.993303	−	0.115537i	$-0.0368588\pi$
$558$	7.46696	0.316102
$559$	0	0
$560$	6.66758	0.281757
$561$	7.13746i	0.301344i
$562$	22.3606	0.943226
$563$	−36.8364	−1.55247	−0.776235	−	0.630444i	$-0.782873\pi$
$563$	−36.8364	−1.55247	−0.776235	+	0.630444i	$0.782873\pi$
$564$	− 0.611552i	− 0.0257510i
$565$	7.41077i	0.311773i
$566$	25.3367i	1.06498i
$567$	1.61315i	0.0677458i
$568$	44.3619	1.86138
$569$	−15.0251	−0.629885	−0.314942	−	0.949111i	$-0.601985\pi$
$569$	−15.0251	−0.629885	−0.314942	+	0.949111i	$0.601985\pi$
$570$	− 23.9580i	− 1.00349i
$571$	−33.2518	−1.39155	−0.695773	−	0.718262i	$-0.744938\pi$
$571$	−33.2518	−1.39155	−0.695773	+	0.718262i	$0.744938\pi$
$572$	0	0
$573$	−15.5838	−0.651023
$574$	11.4973i	0.479887i
$575$	34.5027	1.43886
$576$	17.2329	0.718036
$577$	− 34.7983i	− 1.44867i	−0.689448	−	0.724335i	$-0.742147\pi$
$577$	− 34.7983i	− 1.44867i	0.689448	−	0.724335i	$-0.257853\pi$
$578$	− 15.0089i	− 0.624286i
$579$	20.2861i	0.843063i
$580$	23.5936i	0.979670i
$581$	3.17863	0.131872
$582$	−13.9935	−0.580049
$583$	− 26.1720i	− 1.08393i
$584$	−39.6499	−1.64072
$585$	0	0
$586$	−29.4915	−1.21828
$587$	19.7267i	0.814210i	0.913381	+	0.407105i	$0.133462\pi$
$587$	19.7267i	0.814210i	−0.913381	+	0.407105i	$0.866538\pi$
$588$	−0.734167	−0.0302766
$589$	−20.4636	−0.843190
$590$	− 20.5690i	− 0.846814i
$591$	15.3684i	0.632171i
$592$	− 3.43637i	− 0.141234i
$593$	7.56122i	0.310502i	0.987875	+	0.155251i	$0.0496186\pi$
$593$	7.56122i	0.310502i	−0.987875	+	0.155251i	$0.950381\pi$
$594$	−21.6089	−0.886624
$595$	6.63578	0.272041
$596$	− 17.7735i	− 0.728031i
$597$	14.7554	0.603896
$598$	0	0
$599$	3.48332	0.142325	0.0711623	−	0.997465i	$-0.477329\pi$
$599$	3.48332	0.142325	0.0711623	+	0.997465i	$0.477329\pi$
$600$	− 22.5040i	− 0.918720i
$601$	−43.3614	−1.76875	−0.884374	−	0.466778i	$-0.845415\pi$
$601$	−43.3614	−1.76875	−0.884374	+	0.466778i	$0.845415\pi$
$602$	−11.4671	−0.467366
$603$	6.36406i	0.259165i
$604$	8.36103i	0.340206i
$605$	− 17.9307i	− 0.728985i
$606$	8.20013i	0.333108i
$607$	−24.5108	−0.994864	−0.497432	−	0.867503i	$-0.665724\pi$
$607$	−24.5108	−0.994864	−0.497432	+	0.867503i	$0.665724\pi$
$608$	−25.7998	−1.04632
$609$	8.24926i	0.334277i
$610$	7.25925	0.293918
$611$	0	0
$612$	2.98869	0.120810
$613$	0.842003i	0.0340082i	0.999855	+	0.0170041i	$0.00541283\pi$
$613$	0.842003i	0.0340082i	−0.999855	+	0.0170041i	$0.994587\pi$
$614$	7.95604	0.321080
$615$	35.2327	1.42072
$616$	12.3042i	0.495749i
$617$	− 11.6951i	− 0.470828i	−0.971895	−	0.235414i	$-0.924355\pi$
$617$	− 11.6951i	− 0.470828i	0.971895	−	0.235414i	$-0.0756446\pi$
$618$	0.380986i	0.0153255i
$619$	30.4915i	1.22556i	0.790254	+	0.612779i	$0.209948\pi$
$619$	30.4915i	1.22556i	−0.790254	+	0.612779i	$0.790052\pi$
$620$	−8.81393	−0.353976
$621$	21.8867	0.878284
$622$	15.1655i	0.608083i
$623$	−12.2290	−0.489945
$624$	0	0
$625$	−4.58563	−0.183425
$626$	11.7450i	0.469423i
$627$	24.2926	0.970153
$628$	10.9503	0.436966
$629$	− 3.41998i	− 0.136363i
$630$	8.24106i	0.328332i
$631$	− 19.0797i	− 0.759552i	−0.925078	−	0.379776i	$-0.876001\pi$
$631$	− 19.0797i	− 0.759552i	0.925078	−	0.379776i	$-0.123999\pi$
$632$	0.286317i	0.0113891i
$633$	3.30097	0.131202
$634$	−4.05154	−0.160907
$635$	− 25.5611i	− 1.01436i
$636$	4.79787	0.190248
$637$	0	0
$638$	38.3644	1.51886
$639$	30.1276i	1.19183i
$640$	3.68826	0.145791
$641$	−26.9166	−1.06314	−0.531571	−	0.847014i	$-0.678398\pi$
$641$	−26.9166	−1.06314	−0.531571	+	0.847014i	$0.678398\pi$
$642$	− 4.23300i	− 0.167063i
$643$	50.6462i	1.99729i	0.0520237	+	0.998646i	$0.483433\pi$
$643$	50.6462i	1.99729i	−0.0520237	+	0.998646i	$0.516567\pi$
$644$	− 3.45826i	− 0.136274i
$645$	35.1404i	1.38365i
$646$	13.1350	0.516790
$647$	38.2321	1.50306	0.751530	−	0.659699i	$-0.229316\pi$
$647$	38.2321	1.50306	0.751530	+	0.659699i	$0.229316\pi$
$648$	4.95613i	0.194695i
$649$	20.8563	0.818683
$650$	0	0
$651$	−3.08170	−0.120781
$652$	− 1.54729i	− 0.0605964i
$653$	−10.3427	−0.404742	−0.202371	−	0.979309i	$-0.564865\pi$
$653$	−10.3427	−0.404742	−0.202371	+	0.979309i	$0.564865\pi$
$654$	−10.2408	−0.400446
$655$	− 5.26979i	− 0.205908i
$656$	19.4090i	0.757795i
$657$	− 26.9275i	− 1.05054i
$658$	0.924522i	0.0360416i
$659$	12.8844	0.501904	0.250952	−	0.968000i	$-0.419256\pi$
$659$	12.8844	0.501904	0.250952	+	0.968000i	$0.419256\pi$
$660$	10.4631	0.407276
$661$	− 19.1895i	− 0.746385i	−0.927754	−	0.373192i	$-0.878263\pi$
$661$	− 19.1895i	− 0.746385i	0.927754	−	0.373192i	$-0.121737\pi$
$662$	24.1484	0.938555
$663$	0	0
$664$	9.76582	0.378987
$665$	− 22.5851i	− 0.875813i
$666$	4.24731	0.164580
$667$	−38.8577	−1.50458
$668$	− 14.5163i	− 0.561654i
$669$	− 14.9709i	− 0.578807i
$670$	12.0468i	0.465408i
$671$	7.36064i	0.284154i
$672$	−3.88529	−0.149878
$673$	−11.1856	−0.431172	−0.215586	−	0.976485i	$-0.569166\pi$
$673$	−11.1856	−0.431172	−0.215586	+	0.976485i	$0.569166\pi$
$674$	19.8533i	0.764721i
$675$	37.2573	1.43403
$676$	0	0
$677$	−16.4527	−0.632330	−0.316165	−	0.948704i	$-0.602395\pi$
$677$	−16.4527	−0.632330	−0.316165	+	0.948704i	$0.602395\pi$
$678$	2.20907i	0.0848388i
$679$	−13.1916	−0.506248
$680$	20.3873	0.781819
$681$	7.69840i	0.295003i
$682$	14.3319i	0.548798i
$683$	13.5271i	0.517600i	0.965931	+	0.258800i	$0.0833271\pi$
$683$	13.5271i	0.517600i	−0.965931	+	0.258800i	$0.916673\pi$
$684$	− 10.1721i	− 0.388940i
$685$	15.7954	0.603512
$686$	1.10989	0.0423757
$687$	− 19.0837i	− 0.728089i
$688$	−19.3581	−0.738021
$689$	0	0
$690$	16.9950	0.646987
$691$	− 20.5171i	− 0.780507i	−0.920707	−	0.390254i	$-0.872387\pi$
$691$	− 20.5171i	− 0.780507i	0.920707	−	0.390254i	$-0.127613\pi$
$692$	9.53632	0.362516
$693$	−8.35617	−0.317425
$694$	12.4738i	0.473500i
$695$	61.7525i	2.34241i
$696$	25.3445i	0.960680i
$697$	19.3164i	0.731662i
$698$	27.1016	1.02581
$699$	−11.6402	−0.440272
$700$	− 5.88692i	− 0.222505i
$701$	−46.6380	−1.76149	−0.880747	−	0.473587i	$-0.842959\pi$
$701$	−46.6380	−1.76149	−0.880747	+	0.473587i	$0.842959\pi$
$702$	0	0
$703$	−11.6400	−0.439011
$704$	33.0764i	1.24661i
$705$	2.83314	0.106702
$706$	−17.6552	−0.664462
$707$	7.73025i	0.290726i
$708$	3.82339i	0.143692i
$709$	42.2314i	1.58603i	0.609199	+	0.793017i	$0.291491\pi$
$709$	42.2314i	1.58603i	−0.609199	+	0.793017i	$0.708509\pi$
$710$	57.0297i	2.14029i
$711$	−0.194447	−0.00729233
$712$	−37.5716	−1.40806
$713$	− 14.5162i	− 0.543636i
$714$	1.97806	0.0740269
$715$	0	0
$716$	7.20059	0.269099
$717$	− 14.8816i	− 0.555764i
$718$	−13.8132	−0.515504
$719$	−37.9404	−1.41494	−0.707469	−	0.706744i	$-0.750163\pi$
$719$	−37.9404	−1.41494	−0.707469	+	0.706744i	$0.750163\pi$
$720$	13.9121i	0.518472i
$721$	0.359154i	0.0133756i
$722$	− 23.6176i	− 0.878957i
$723$	1.24804i	0.0464152i
$724$	−4.48252	−0.166591
$725$	−66.1466	−2.45662
$726$	− 5.34494i	− 0.198369i
$727$	16.5215	0.612748	0.306374	−	0.951911i	$-0.400884\pi$
$727$	16.5215	0.612748	0.306374	+	0.951911i	$0.400884\pi$
$728$	0	0
$729$	10.5734	0.391607
$730$	− 50.9722i	− 1.88657i
$731$	−19.2658	−0.712571
$732$	−1.34936	−0.0498737
$733$	− 17.6511i	− 0.651957i	−0.945377	−	0.325978i	$-0.894306\pi$
$733$	− 17.6511i	− 0.651957i	0.945377	−	0.325978i	$-0.105694\pi$
$734$	− 20.2042i	− 0.745750i
$735$	− 3.40118i	− 0.125455i
$736$	− 18.3015i	− 0.674601i
$737$	−12.2150	−0.449947
$738$	−23.9893	−0.883060
$739$	− 0.370373i	− 0.0136244i	−0.999977	−	0.00681220i	$-0.997832\pi$
$739$	− 0.370373i	− 0.0136244i	0.999977	−	0.00681220i	$-0.00216841\pi$
$740$	−5.01349	−0.184299
$741$	0	0
$742$	−7.25324	−0.266275
$743$	− 17.5579i	− 0.644137i	−0.946716	−	0.322068i	$-0.895622\pi$
$743$	− 17.5579i	− 0.644137i	0.946716	−	0.322068i	$-0.104378\pi$
$744$	−9.46802	−0.347115
$745$	82.3395	3.01668
$746$	36.2742i	1.32809i
$747$	6.63229i	0.242663i
$748$	5.73642i	0.209744i
$749$	− 3.99044i	− 0.145807i
$750$	10.0555	0.367175
$751$	15.0706	0.549933	0.274967	−	0.961454i	$-0.411333\pi$
$751$	15.0706	0.549933	0.274967	+	0.961454i	$0.411333\pi$
$752$	1.56072i	0.0569137i
$753$	19.3878	0.706530
$754$	0	0
$755$	−38.7342	−1.40968
$756$	− 3.73436i	− 0.135817i
$757$	39.8030	1.44666	0.723332	−	0.690500i	$-0.242609\pi$
$757$	39.8030	1.44666	0.723332	+	0.690500i	$0.242609\pi$
$758$	9.78689	0.355476
$759$	17.2323i	0.625494i
$760$	− 69.3890i	− 2.51700i
$761$	20.7066i	0.750613i	0.926901	+	0.375306i	$0.122462\pi$
$761$	20.7066i	0.750613i	−0.926901	+	0.375306i	$0.877538\pi$
$762$	− 7.61948i	− 0.276025i
$763$	−9.65395	−0.349497
$764$	−12.5248	−0.453131
$765$	13.8457i	0.500593i
$766$	−2.82315	−0.102005
$767$	0	0
$768$	−14.6881	−0.530010
$769$	13.2638i	0.478306i	0.970982	+	0.239153i	$0.0768698\pi$
$769$	13.2638i	0.478306i	−0.970982	+	0.239153i	$0.923130\pi$
$770$	−15.8177	−0.570031
$771$	−16.5777	−0.597031
$772$	16.3041i	0.586798i
$773$	11.6627i	0.419478i	0.977757	+	0.209739i	$0.0672614\pi$
$773$	11.6627i	0.419478i	−0.977757	+	0.209739i	$0.932739\pi$
$774$	− 23.9264i	− 0.860018i
$775$	− 24.7106i	− 0.887632i
$776$	−40.5291	−1.45491
$777$	−1.75292	−0.0628855
$778$	0.573486i	0.0205605i
$779$	65.7442	2.35553
$780$	0	0
$781$	−57.8263	−2.06919
$782$	9.31753i	0.333194i
$783$	−41.9600	−1.49953
$784$	1.87364	0.0669159
$785$	50.7297i	1.81062i
$786$	− 1.57087i	− 0.0560310i
$787$	− 5.00642i	− 0.178460i	−0.996011	−	0.0892298i	$-0.971559\pi$
$787$	− 5.00642i	− 0.178460i	0.996011	−	0.0892298i	$-0.0284405\pi$
$788$	12.3517i	0.440010i
$789$	−10.4073	−0.370511
$790$	−0.368077	−0.0130956
$791$	2.08248i	0.0740446i
$792$	−25.6730	−0.912249
$793$	0	0
$794$	28.7412	1.01999
$795$	22.2271i	0.788315i
$796$	11.8590	0.420330
$797$	−9.95893	−0.352763	−0.176382	−	0.984322i	$-0.556439\pi$
$797$	−9.95893	−0.352763	−0.176382	+	0.984322i	$0.556439\pi$
$798$	− 6.73238i	− 0.238324i
$799$	1.55328i	0.0549511i
$800$	− 31.1542i	− 1.10147i
$801$	− 25.5161i	− 0.901568i
$802$	11.3756	0.401687
$803$	51.6842	1.82389
$804$	− 2.23927i	− 0.0789729i
$805$	16.0211	0.564670
$806$	0	0
$807$	8.59623	0.302602
$808$	23.7499i	0.835519i
$809$	12.0200	0.422601	0.211300	−	0.977421i	$-0.432230\pi$
$809$	12.0200	0.422601	0.211300	+	0.977421i	$0.432230\pi$
$810$	−6.37139	−0.223868
$811$	− 2.91856i	− 0.102484i	−0.998686	−	0.0512422i	$-0.983682\pi$
$811$	− 2.91856i	− 0.102484i	0.998686	−	0.0512422i	$-0.0163180\pi$
$812$	6.62998i	0.232667i
$813$	4.72414i	0.165683i
$814$	8.15221i	0.285735i
$815$	7.16813	0.251089
$816$	3.33923	0.116897
$817$	65.5718i	2.29407i
$818$	22.7638	0.795919
$819$	0	0
$820$	28.3168	0.988865
$821$	− 12.9996i	− 0.453689i	−0.973931	−	0.226844i	$-0.927159\pi$
$821$	− 12.9996i	− 0.453689i	0.973931	−	0.226844i	$-0.0728409\pi$
$822$	4.70845	0.164226
$823$	39.6283	1.38136	0.690678	−	0.723163i	$-0.257312\pi$
$823$	39.6283	1.38136	0.690678	+	0.723163i	$0.257312\pi$
$824$	1.10344i	0.0384402i
$825$	29.3342i	1.02129i
$826$	− 5.78007i	− 0.201114i
$827$	− 31.5319i	− 1.09647i	−0.836323	−	0.548237i	$-0.815299\pi$
$827$	− 31.5319i	− 1.09647i	0.836323	−	0.548237i	$-0.184701\pi$
$828$	7.21574	0.250764
$829$	−36.2352	−1.25850	−0.629251	−	0.777202i	$-0.716638\pi$
$829$	−36.2352	−1.25850	−0.629251	+	0.777202i	$0.716638\pi$
$830$	12.5545i	0.435774i
$831$	−18.6001	−0.645229
$832$	0	0
$833$	1.86471	0.0646083
$834$	18.4078i	0.637408i
$835$	67.2500	2.32728
$836$	19.5241	0.675256
$837$	− 15.6752i	− 0.541813i
$838$	16.9125i	0.584232i
$839$	− 12.0623i	− 0.416438i	−0.978082	−	0.208219i	$-0.933233\pi$
$839$	− 12.0623i	− 0.416438i	0.978082	−	0.208219i	$-0.0667667\pi$
$840$	− 10.4496i	− 0.360545i
$841$	45.4959	1.56882
$842$	−29.2839	−1.00919
$843$	− 19.2555i	− 0.663193i
$844$	2.65301	0.0913204
$845$	0	0
$846$	−1.92904	−0.0663217
$847$	− 5.03866i	− 0.173130i
$848$	−12.2445	−0.420477
$849$	21.8182	0.748800
$850$	15.8610i	0.544029i
$851$	− 8.25702i	− 0.283047i
$852$	− 10.6007i	− 0.363176i
$853$	− 11.7255i	− 0.401475i	−0.979645	−	0.200738i	$-0.935666\pi$
$853$	− 11.7255i	− 0.401475i	0.979645	−	0.200738i	$-0.0643339\pi$
$854$	2.03991	0.0698042
$855$	47.1244	1.61162
$856$	− 12.2600i	− 0.419037i
$857$	−28.0128	−0.956900	−0.478450	−	0.878115i	$-0.658801\pi$
$857$	−28.0128	−0.956900	−0.478450	+	0.878115i	$0.658801\pi$
$858$	0	0
$859$	5.70001	0.194482	0.0972408	−	0.995261i	$-0.468998\pi$
$859$	5.70001	0.194482	0.0972408	+	0.995261i	$0.468998\pi$
$860$	28.2425i	0.963063i
$861$	9.90068	0.337414
$862$	42.0759	1.43311
$863$	− 41.0325i	− 1.39676i	−0.715726	−	0.698381i	$-0.753904\pi$
$863$	− 41.0325i	− 1.39676i	0.715726	−	0.698381i	$-0.246096\pi$
$864$	− 19.7626i	− 0.672339i
$865$	44.1790i	1.50213i
$866$	− 9.44579i	− 0.320981i
$867$	−12.9246	−0.438943
$868$	−2.47678	−0.0840676
$869$	− 0.373218i	− 0.0126605i
$870$	−32.5818	−1.10463
$871$	0	0
$872$	−29.6602	−1.00442
$873$	− 27.5246i	− 0.931568i
$874$	31.7125	1.07269
$875$	9.47929	0.320458
$876$	9.47477i	0.320123i
$877$	− 10.7401i	− 0.362668i	−0.983422	−	0.181334i	$-0.941958\pi$
$877$	− 10.7401i	− 0.362668i	0.983422	−	0.181334i	$-0.0580415\pi$
$878$	− 20.6551i	− 0.697077i
$879$	25.3961i	0.856590i
$880$	−26.7025	−0.900142
$881$	−37.5517	−1.26515	−0.632574	−	0.774500i	$-0.718002\pi$
$881$	−37.5517	−1.26515	−0.632574	+	0.774500i	$0.718002\pi$
$882$	2.31581i	0.0779772i
$883$	−47.1134	−1.58549	−0.792745	−	0.609553i	$-0.791349\pi$
$883$	−47.1134	−1.58549	−0.792745	+	0.609553i	$0.791349\pi$
$884$	0	0
$885$	−17.7127	−0.595405
$886$	29.8095i	1.00147i
$887$	5.06090	0.169928	0.0849642	−	0.996384i	$-0.472922\pi$
$887$	5.06090	0.169928	0.0849642	+	0.996384i	$0.472922\pi$
$888$	−5.38555	−0.180727
$889$	− 7.18287i	− 0.240906i
$890$	− 48.3005i	− 1.61904i
$891$	− 6.46038i	− 0.216431i
$892$	− 12.0322i	− 0.402867i
$893$	5.28664	0.176911
$894$	24.5445	0.820891
$895$	33.3582i	1.11504i
$896$	1.03643	0.0346247
$897$	0	0
$898$	−17.2342	−0.575111
$899$	27.8297i	0.928171i
$900$	12.2832	0.409440
$901$	−12.1861	−0.405977
$902$	− 46.0447i	− 1.53312i
$903$	9.87472i	0.328610i
$904$	6.39809i	0.212797i
$905$	− 20.7662i	− 0.690292i
$906$	−11.5463	−0.383599
$907$	48.6215	1.61445	0.807226	−	0.590243i	$-0.200968\pi$
$907$	48.6215	1.61445	0.807226	+	0.590243i	$0.200968\pi$
$908$	6.18726i	0.205331i
$909$	−16.1293	−0.534976
$910$	0	0
$911$	1.76756	0.0585620	0.0292810	−	0.999571i	$-0.490678\pi$
$911$	1.76756	0.0585620	0.0292810	+	0.999571i	$0.490678\pi$
$912$	− 11.3652i	− 0.376339i
$913$	−12.7299	−0.421297
$914$	37.2437	1.23191
$915$	− 6.25118i	− 0.206658i
$916$	− 15.3377i	− 0.506772i
$917$	− 1.48085i	− 0.0489021i
$918$	10.0614i	0.332076i
$919$	27.4163	0.904380	0.452190	−	0.891922i	$-0.350643\pi$
$919$	27.4163	0.904380	0.452190	+	0.891922i	$0.350643\pi$
$920$	49.2222	1.62281
$921$	− 6.85120i	− 0.225755i
$922$	−4.82689	−0.158965
$923$	0	0
$924$	2.94022	0.0967260
$925$	− 14.0557i	− 0.462150i
$926$	−25.8331	−0.848928
$927$	−0.749383	−0.0246130
$928$	35.0866i	1.15177i
$929$	31.0105i	1.01742i	0.860938	+	0.508710i	$0.169878\pi$
$929$	31.0105i	1.01742i	−0.860938	+	0.508710i	$0.830122\pi$
$930$	− 12.1717i	− 0.399125i
$931$	− 6.34660i	− 0.208001i
$932$	−9.35528	−0.306442
$933$	13.0595	0.427550
$934$	− 13.5972i	− 0.444915i
$935$	−26.5752	−0.869101
$936$	0	0
$937$	−13.5463	−0.442537	−0.221269	−	0.975213i	$-0.571020\pi$
$937$	−13.5463	−0.442537	−0.221269	+	0.975213i	$0.571020\pi$
$938$	3.38524i	0.110532i
$939$	10.1140	0.330057
$940$	2.27702	0.0742681
$941$	27.1579i	0.885321i	0.896689	+	0.442661i	$0.145965\pi$
$941$	27.1579i	0.885321i	−0.896689	+	0.442661i	$0.854035\pi$
$942$	15.1220i	0.492701i
$943$	46.6367i	1.51870i
$944$	− 9.75756i	− 0.317581i
$945$	17.3002	0.562775
$946$	45.9239	1.49312
$947$	30.1736i	0.980511i	0.871579	+	0.490256i	$0.163097\pi$
$947$	30.1736i	0.980511i	−0.871579	+	0.490256i	$0.836903\pi$
$948$	0.0684184	0.00222213
$949$	0	0
$950$	53.9835	1.75146
$951$	3.48892i	0.113136i
$952$	5.72901	0.185678
$953$	−13.0194	−0.421738	−0.210869	−	0.977514i	$-0.567629\pi$
$953$	−13.0194	−0.421738	−0.210869	+	0.977514i	$0.567629\pi$
$954$	− 15.1341i	− 0.489983i
$955$	− 58.0237i	− 1.87760i
$956$	− 11.9604i	− 0.386828i
$957$	− 33.0369i	− 1.06793i
$958$	0.758836	0.0245169
$959$	4.43864	0.143331
$960$	− 28.0908i	− 0.906627i
$961$	20.6036	0.664632
$962$	0	0
$963$	8.32614	0.268306
$964$	1.00306i	0.0323064i
$965$	−75.5322	−2.43147
$966$	4.77572	0.153656
$967$	− 49.5415i	− 1.59315i	−0.604542	−	0.796573i	$-0.706644\pi$
$967$	− 49.5415i	− 1.59315i	0.604542	−	0.796573i	$-0.293356\pi$
$968$	− 15.4805i	− 0.497561i
$969$	− 11.3110i	− 0.363361i
$970$	− 52.1025i	− 1.67291i
$971$	−34.3718	−1.10304	−0.551522	−	0.834160i	$-0.685953\pi$
$971$	−34.3718	−1.10304	−0.551522	+	0.834160i	$0.685953\pi$
$972$	12.3874	0.397326
$973$	17.3529i	0.556310i
$974$	−2.42561	−0.0777214
$975$	0	0
$976$	3.44365	0.110228
$977$	− 10.8964i	− 0.348607i	−0.984692	−	0.174303i	$-0.944233\pi$
$977$	− 10.8964i	− 0.348607i	0.984692	−	0.174303i	$-0.0557674\pi$
$978$	2.13674	0.0683255
$979$	48.9751	1.56525
$980$	− 2.73355i	− 0.0873202i
$981$	− 20.1432i	− 0.643123i
$982$	− 9.78595i	− 0.312282i
$983$	− 17.8803i	− 0.570293i	−0.958484	−	0.285146i	$-0.907958\pi$
$983$	− 17.8803i	− 0.570293i	0.958484	−	0.285146i	$-0.0920422\pi$
$984$	30.4182	0.969697
$985$	−57.2217	−1.82323
$986$	− 17.8631i	− 0.568876i
$987$	0.796136	0.0253413
$988$	0	0
$989$	−46.5144	−1.47907
$990$	− 33.0041i	− 1.04894i
$991$	−43.2925	−1.37523	−0.687616	−	0.726074i	$-0.741343\pi$
$991$	−43.2925	−1.37523	−0.687616	+	0.726074i	$0.741343\pi$
$992$	−13.1074	−0.416161
$993$	− 20.7950i	− 0.659909i
$994$	16.0258i	0.508308i
$995$	54.9392i	1.74169i
$996$	− 2.33365i	− 0.0739444i
$997$	25.7004	0.813940	0.406970	−	0.913442i	$-0.366585\pi$
$997$	25.7004	0.813940	0.406970	+	0.913442i	$0.366585\pi$
$998$	18.1801	0.575480
$999$	− 8.91625i	− 0.282098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.17		24
13.5	odd	4		1183.2.a.q.1.9	✓	12
13.8	odd	4		1183.2.a.r.1.4	yes	12
13.12	even	2	inner	1183.2.c.j.337.8		24
91.34	even	4		8281.2.a.cq.1.4		12
91.83	even	4		8281.2.a.cn.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.9	✓	12	13.5	odd	4
1183.2.a.r.1.4	yes	12	13.8	odd	4
1183.2.c.j.337.8		24	13.12	even	2	inner
1183.2.c.j.337.17		24	1.1	even	1	trivial
8281.2.a.cn.1.9		12	91.83	even	4
8281.2.a.cq.1.4		12	91.34	even	4

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.10989i q^{2} +0.955760 q^{3} +0.768150 q^{4} +3.55862i q^{5} +1.06079i q^{6} +1.00000i q^{7} +3.07233i q^{8} -2.08652 q^{9} +O(q^{10})\)	\(q+1.10989i q^{2} +0.955760 q^{3} +0.768150 q^{4} +3.55862i q^{5} +1.06079i q^{6} +1.00000i q^{7} +3.07233i q^{8} -2.08652 q^{9} -3.94966 q^{10} -4.00483i q^{11} +0.734167 q^{12} -1.10989 q^{14} +3.40118i q^{15} -1.87364 q^{16} -1.86471 q^{17} -2.31581i q^{18} +6.34660i q^{19} +2.73355i q^{20} +0.955760i q^{21} +4.44491 q^{22} -4.50206 q^{23} +2.93641i q^{24} -7.66376 q^{25} -4.86149 q^{27} +0.768150i q^{28} +8.63110 q^{29} -3.77493 q^{30} +3.22435i q^{31} +4.06514i q^{32} -3.82766i q^{33} -2.06962i q^{34} -3.55862 q^{35} -1.60276 q^{36} +1.83406i q^{37} -7.04401 q^{38} -10.9333 q^{40} -10.3590i q^{41} -1.06079 q^{42} +10.3318 q^{43} -3.07631i q^{44} -7.42514i q^{45} -4.99678i q^{46} -0.832988i q^{47} -1.79075 q^{48} -1.00000 q^{49} -8.50590i q^{50} -1.78221 q^{51} +6.53512 q^{53} -5.39571i q^{54} +14.2517 q^{55} -3.07233 q^{56} +6.06582i q^{57} +9.57955i q^{58} +5.20780i q^{59} +2.61262i q^{60} -1.83794 q^{61} -3.57866 q^{62} -2.08652i q^{63} -8.25913 q^{64} +4.24827 q^{66} -3.05008i q^{67} -1.43238 q^{68} -4.30289 q^{69} -3.94966i q^{70} -14.4391i q^{71} -6.41050i q^{72} +12.9055i q^{73} -2.03559 q^{74} -7.32471 q^{75} +4.87514i q^{76} +4.00483 q^{77} +0.0931919 q^{79} -6.66758i q^{80} +1.61315 q^{81} +11.4973 q^{82} -3.17863i q^{83} +0.734167i q^{84} -6.63578i q^{85} +11.4671i q^{86} +8.24926 q^{87} +12.3042 q^{88} +12.2290i q^{89} +8.24106 q^{90} -3.45826 q^{92} +3.08170i q^{93} +0.924522 q^{94} -22.5851 q^{95} +3.88529i q^{96} +13.1916i q^{97} -1.10989i q^{98} +8.35617i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9} + 12 q^{10} - 26 q^{12} + 6 q^{14} + 26 q^{16} - 62 q^{17} - 8 q^{22} - 36 q^{23} - 64 q^{25} + 64 q^{27} + 30 q^{29} + 20 q^{30} - 8 q^{35} - 98 q^{36} - 90 q^{38} - 40 q^{40} + 4 q^{42} + 44 q^{43} + 22 q^{48} - 24 q^{49} - 36 q^{51} + 106 q^{53} - 52 q^{55} - 24 q^{56} + 44 q^{61} - 38 q^{62} - 4 q^{64} - 68 q^{66} + 68 q^{68} - 6 q^{69} - 80 q^{74} - 30 q^{75} - 24 q^{77} + 4 q^{79} + 72 q^{81} + 64 q^{82} + 54 q^{87} + 96 q^{88} + 52 q^{90} + 104 q^{92} - 88 q^{94} - 58 q^{95}+O(q^{100}) \) 24 * q + 16 * q^3 - 30 * q^4 + 52 * q^9 + 12 * q^10 - 26 * q^12 + 6 * q^14 + 26 * q^16 - 62 * q^17 - 8 * q^22 - 36 * q^23 - 64 * q^25 + 64 * q^27 + 30 * q^29 + 20 * q^30 - 8 * q^35 - 98 * q^36 - 90 * q^38 - 40 * q^40 + 4 * q^42 + 44 * q^43 + 22 * q^48 - 24 * q^49 - 36 * q^51 + 106 * q^53 - 52 * q^55 - 24 * q^56 + 44 * q^61 - 38 * q^62 - 4 * q^64 - 68 * q^66 + 68 * q^68 - 6 * q^69 - 80 * q^74 - 30 * q^75 - 24 * q^77 + 4 * q^79 + 72 * q^81 + 64 * q^82 + 54 * q^87 + 96 * q^88 + 52 * q^90 + 104 * q^92 - 88 * q^94 - 58 * q^95

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