LMFDB - Embedded newform 1183.2.c.j.337.3

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			337.3
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47725i q^{2} +0.982981 q^{3} -4.13677 q^{4} -1.35413i q^{5} -2.43509i q^{6} +1.00000i q^{7} +5.29330i q^{8} -2.03375 q^{9} +O(q^{10})$	\(q-2.47725i q^{2} +0.982981 q^{3} -4.13677 q^{4} -1.35413i q^{5} -2.43509i q^{6} +1.00000i q^{7} +5.29330i q^{8} -2.03375 q^{9} -3.35452 q^{10} -3.34694i q^{11} -4.06636 q^{12} +2.47725 q^{14} -1.33108i q^{15} +4.83930 q^{16} -0.692094 q^{17} +5.03810i q^{18} -7.45343i q^{19} +5.60172i q^{20} +0.982981i q^{21} -8.29121 q^{22} -8.25231 q^{23} +5.20321i q^{24} +3.16633 q^{25} -4.94808 q^{27} -4.13677i q^{28} +1.07995 q^{29} -3.29742 q^{30} +11.0557i q^{31} -1.40155i q^{32} -3.28998i q^{33} +1.71449i q^{34} +1.35413 q^{35} +8.41314 q^{36} +5.43331i q^{37} -18.4640 q^{38} +7.16781 q^{40} +4.30075i q^{41} +2.43509 q^{42} -4.19825 q^{43} +13.8455i q^{44} +2.75396i q^{45} +20.4430i q^{46} -12.1411i q^{47} +4.75694 q^{48} -1.00000 q^{49} -7.84380i q^{50} -0.680315 q^{51} -4.51915 q^{53} +12.2576i q^{54} -4.53219 q^{55} -5.29330 q^{56} -7.32657i q^{57} -2.67530i q^{58} -1.38180i q^{59} +5.50638i q^{60} -6.49906 q^{61} +27.3877 q^{62} -2.03375i q^{63} +6.20662 q^{64} -8.15010 q^{66} +3.86290i q^{67} +2.86303 q^{68} -8.11186 q^{69} -3.35452i q^{70} -2.65952i q^{71} -10.7652i q^{72} -10.2115i q^{73} +13.4597 q^{74} +3.11245 q^{75} +30.8331i q^{76} +3.34694 q^{77} +1.27930 q^{79} -6.55304i q^{80} +1.23738 q^{81} +10.6540 q^{82} -9.49352i q^{83} -4.06636i q^{84} +0.937185i q^{85} +10.4001i q^{86} +1.06157 q^{87} +17.7164 q^{88} -8.29790i q^{89} +6.82224 q^{90} +34.1379 q^{92} +10.8675i q^{93} -30.0765 q^{94} -10.0929 q^{95} -1.37769i q^{96} +10.2683i q^{97} +2.47725i q^{98} +6.80684i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 2.47725i	− 1.75168i	−0.482602	−	0.875840i	$-0.660308\pi$
$2$	− 2.47725i	− 1.75168i	0.482602	−	0.875840i	$-0.339692\pi$
$3$	0.982981	0.567524	0.283762	−	0.958895i	$-0.408417\pi$
$3$	0.982981	0.567524	0.283762	+	0.958895i	$0.408417\pi$
$4$	−4.13677	−2.06838
$5$	− 1.35413i	− 0.605585i	−0.953057	−	0.302792i	$-0.902081\pi$
$5$	− 1.35413i	− 0.605585i	0.953057	−	0.302792i	$-0.0979189\pi$
$6$	− 2.43509i	− 0.994121i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	5.29330i	1.87146i
$9$	−2.03375	−0.677916
$10$	−3.35452	−1.06079
$11$	− 3.34694i	− 1.00914i	−0.863371	−	0.504570i	$-0.831651\pi$
$11$	− 3.34694i	− 1.00914i	0.863371	−	0.504570i	$-0.168349\pi$
$12$	−4.06636	−1.17386
$13$	0	0
$13$	0	0
$14$	2.47725	0.662073
$15$	− 1.33108i	− 0.343684i
$16$	4.83930	1.20982
$17$	−0.692094	−0.167858	−0.0839288	−	0.996472i	$-0.526747\pi$
$17$	−0.692094	−0.167858	−0.0839288	+	0.996472i	$0.526747\pi$
$18$	5.03810i	1.18749i
$19$	− 7.45343i	− 1.70993i	−0.518683	−	0.854967i	$-0.673578\pi$
$19$	− 7.45343i	− 1.70993i	0.518683	−	0.854967i	$-0.326422\pi$
$20$	5.60172i	1.25258i
$21$	0.982981i	0.214504i
$22$	−8.29121	−1.76769
$23$	−8.25231	−1.72073	−0.860363	−	0.509682i	$-0.829763\pi$
$23$	−8.25231	−1.72073	−0.860363	+	0.509682i	$0.829763\pi$
$24$	5.20321i	1.06210i
$25$	3.16633	0.633267
$26$	0	0
$27$	−4.94808	−0.952258
$28$	− 4.13677i	− 0.781775i
$29$	1.07995	0.200541	0.100271	−	0.994960i	$-0.468029\pi$
$29$	1.07995	0.200541	0.100271	+	0.994960i	$0.468029\pi$
$30$	−3.29742	−0.602025
$31$	11.0557i	1.98566i	0.119537	+	0.992830i	$0.461859\pi$
$31$	11.0557i	1.98566i	−0.119537	+	0.992830i	$0.538141\pi$
$32$	− 1.40155i	− 0.247761i
$33$	− 3.28998i	− 0.572712i
$34$	1.71449i	0.294033i
$35$	1.35413	0.228890
$36$	8.41314	1.40219
$37$	5.43331i	0.893230i	0.894726	+	0.446615i	$0.147371\pi$
$37$	5.43331i	0.893230i	−0.894726	+	0.446615i	$0.852629\pi$
$38$	−18.4640	−2.99526
$39$	0	0
$40$	7.16781	1.13333
$41$	4.30075i	0.671665i	0.941922	+	0.335832i	$0.109018\pi$
$41$	4.30075i	0.671665i	−0.941922	+	0.335832i	$0.890982\pi$
$42$	2.43509	0.375742
$43$	−4.19825	−0.640227	−0.320114	−	0.947379i	$-0.603721\pi$
$43$	−4.19825	−0.640227	−0.320114	+	0.947379i	$0.603721\pi$
$44$	13.8455i	2.08729i
$45$	2.75396i	0.410536i
$46$	20.4430i	3.01416i
$47$	− 12.1411i	− 1.77096i	−0.464676	−	0.885481i	$-0.653829\pi$
$47$	− 12.1411i	− 1.77096i	0.464676	−	0.885481i	$-0.346171\pi$
$48$	4.75694	0.686605
$49$	−1.00000	−0.142857
$50$	− 7.84380i	− 1.10928i
$51$	−0.680315	−0.0952632
$52$	0	0
$53$	−4.51915	−0.620753	−0.310377	−	0.950614i	$-0.600455\pi$
$53$	−4.51915	−0.620753	−0.310377	+	0.950614i	$0.600455\pi$
$54$	12.2576i	1.66805i
$55$	−4.53219	−0.611121
$56$	−5.29330	−0.707347
$57$	− 7.32657i	− 0.970428i
$58$	− 2.67530i	− 0.351284i
$59$	− 1.38180i	− 0.179895i	−0.995947	−	0.0899474i	$-0.971330\pi$
$59$	− 1.38180i	− 0.179895i	0.995947	−	0.0899474i	$-0.0286699\pi$
$60$	5.50638i	0.710870i
$61$	−6.49906	−0.832120	−0.416060	−	0.909337i	$-0.636589\pi$
$61$	−6.49906	−0.832120	−0.416060	+	0.909337i	$0.636589\pi$
$62$	27.3877	3.47824
$63$	− 2.03375i	− 0.256228i
$64$	6.20662	0.775827
$65$	0	0
$66$	−8.15010	−1.00321
$67$	3.86290i	0.471929i	0.971762	+	0.235964i	$0.0758249\pi$
$67$	3.86290i	0.471929i	−0.971762	+	0.235964i	$0.924175\pi$
$68$	2.86303	0.347194
$69$	−8.11186	−0.976553
$70$	− 3.35452i	− 0.400941i
$71$	− 2.65952i	− 0.315627i	−0.987469	−	0.157813i	$-0.949556\pi$
$71$	− 2.65952i	− 0.315627i	0.987469	−	0.157813i	$-0.0504444\pi$
$72$	− 10.7652i	− 1.26870i
$73$	− 10.2115i	− 1.19517i	−0.801806	−	0.597585i	$-0.796127\pi$
$73$	− 10.2115i	− 1.19517i	0.801806	−	0.597585i	$-0.203873\pi$
$74$	13.4597	1.56465
$75$	3.11245	0.359394
$76$	30.8331i	3.53680i
$77$	3.34694	0.381419
$78$	0	0
$79$	1.27930	0.143932	0.0719662	−	0.997407i	$-0.477073\pi$
$79$	1.27930	0.143932	0.0719662	+	0.997407i	$0.477073\pi$
$80$	− 6.55304i	− 0.732652i
$81$	1.23738	0.137487
$82$	10.6540	1.17654
$83$	− 9.49352i	− 1.04205i	−0.853542	−	0.521024i	$-0.825550\pi$
$83$	− 9.49352i	− 1.04205i	0.853542	−	0.521024i	$-0.174450\pi$
$84$	− 4.06636i	− 0.443676i
$85$	0.937185i	0.101652i
$86$	10.4001i	1.12147i
$87$	1.06157	0.113812
$88$	17.7164	1.88857
$89$	− 8.29790i	− 0.879576i	−0.898102	−	0.439788i	$-0.855054\pi$
$89$	− 8.29790i	− 0.879576i	0.898102	−	0.439788i	$-0.144946\pi$
$90$	6.82224	0.719128
$91$	0	0
$92$	34.1379	3.55912
$93$	10.8675i	1.12691i
$94$	−30.0765	−3.10216
$95$	−10.0929	−1.03551
$96$	− 1.37769i	− 0.140610i
$97$	10.2683i	1.04258i	0.853379	+	0.521292i	$0.174550\pi$
$97$	10.2683i	1.04258i	−0.853379	+	0.521292i	$0.825450\pi$
$98$	2.47725i	0.250240i
$99$	6.80684i	0.684113i
$100$	−13.0984	−1.30984
$101$	−13.0574	−1.29926	−0.649632	−	0.760249i	$-0.725077\pi$
$101$	−13.0574	−1.29926	−0.649632	+	0.760249i	$0.725077\pi$
$102$	1.68531i	0.166871i
$103$	−0.0458921	−0.00452188	−0.00226094	−	0.999997i	$-0.500720\pi$
$103$	−0.0458921	−0.00452188	−0.00226094	+	0.999997i	$0.500720\pi$
$104$	0	0
$105$	1.33108	0.129900
$106$	11.1951i	1.08736i
$107$	5.71462	0.552453	0.276226	−	0.961093i	$-0.410916\pi$
$107$	5.71462	0.552453	0.276226	+	0.961093i	$0.410916\pi$
$108$	20.4690	1.96963
$109$	− 12.6142i	− 1.20822i	−0.796899	−	0.604112i	$-0.793528\pi$
$109$	− 12.6142i	− 1.20822i	0.796899	−	0.604112i	$-0.206472\pi$
$110$	11.2274i	1.07049i
$111$	5.34084i	0.506930i
$112$	4.83930i	0.457271i
$113$	11.4224	1.07453	0.537267	−	0.843412i	$-0.319457\pi$
$113$	11.4224	1.07453	0.537267	+	0.843412i	$0.319457\pi$
$114$	−18.1498	−1.69988
$115$	11.1747i	1.04205i
$116$	−4.46749	−0.414796
$117$	0	0
$118$	−3.42306	−0.315118
$119$	− 0.692094i	− 0.0634442i
$120$	7.04582	0.643193
$121$	−0.202019	−0.0183654
$122$	16.0998i	1.45761i
$123$	4.22756i	0.381186i
$124$	− 45.7348i	− 4.10710i
$125$	− 11.0583i	− 0.989082i
$126$	−5.03810	−0.448830
$127$	−15.1460	−1.34399	−0.671995	−	0.740555i	$-0.734562\pi$
$127$	−15.1460	−1.34399	−0.671995	+	0.740555i	$0.734562\pi$
$128$	− 18.1784i	− 1.60676i
$129$	−4.12680	−0.363344
$130$	0	0
$131$	15.4359	1.34864	0.674321	−	0.738438i	$-0.264436\pi$
$131$	15.4359	1.34864	0.674321	+	0.738438i	$0.264436\pi$
$132$	13.6099i	1.18459i
$133$	7.45343	0.646294
$134$	9.56938	0.826668
$135$	6.70034i	0.576673i
$136$	− 3.66346i	− 0.314139i
$137$	1.45737i	0.124512i	0.998060	+	0.0622558i	$0.0198295\pi$
$137$	1.45737i	0.124512i	−0.998060	+	0.0622558i	$0.980171\pi$
$138$	20.0951i	1.71061i
$139$	1.84411	0.156415	0.0782076	−	0.996937i	$-0.475080\pi$
$139$	1.84411	0.156415	0.0782076	+	0.996937i	$0.475080\pi$
$140$	−5.60172	−0.473431
$141$	− 11.9345i	− 1.00506i
$142$	−6.58829	−0.552877
$143$	0	0
$144$	−9.84192	−0.820160
$145$	− 1.46239i	− 0.121445i
$146$	−25.2965	−2.09355
$147$	−0.982981	−0.0810749
$148$	− 22.4763i	− 1.84754i
$149$	− 20.2755i	− 1.66104i	−0.556992	−	0.830518i	$-0.688045\pi$
$149$	− 20.2755i	− 1.66104i	0.556992	−	0.830518i	$-0.311955\pi$
$150$	− 7.71030i	− 0.629544i
$151$	− 10.1798i	− 0.828422i	−0.910181	−	0.414211i	$-0.864057\pi$
$151$	− 10.1798i	− 0.828422i	0.910181	−	0.414211i	$-0.135943\pi$
$152$	39.4532	3.20008
$153$	1.40755	0.113793
$154$	− 8.29121i	− 0.668125i
$155$	14.9708	1.20249
$156$	0	0
$157$	11.0029	0.878127	0.439064	−	0.898456i	$-0.355310\pi$
$157$	11.0029	0.878127	0.439064	+	0.898456i	$0.355310\pi$
$158$	− 3.16914i	− 0.252124i
$159$	−4.44224	−0.352293
$160$	−1.89787	−0.150040
$161$	− 8.25231i	− 0.650373i
$162$	− 3.06530i	− 0.240833i
$163$	− 25.0175i	− 1.95952i	−0.200164	−	0.979762i	$-0.564148\pi$
$163$	− 25.0175i	− 1.95952i	0.200164	−	0.979762i	$-0.435852\pi$
$164$	− 17.7912i	− 1.38926i
$165$	−4.45506	−0.346826
$166$	−23.5178	−1.82534
$167$	− 8.22613i	− 0.636557i	−0.947997	−	0.318279i	$-0.896895\pi$
$167$	− 8.22613i	− 0.636557i	0.947997	−	0.318279i	$-0.103105\pi$
$168$	−5.20321	−0.401437
$169$	0	0
$170$	2.32164	0.178062
$171$	15.1584i	1.15919i
$172$	17.3672	1.32423
$173$	−9.15205	−0.695818	−0.347909	−	0.937528i	$-0.613108\pi$
$173$	−9.15205	−0.695818	−0.347909	+	0.937528i	$0.613108\pi$
$174$	− 2.62977i	− 0.199362i
$175$	3.16633i	0.239352i
$176$	− 16.1968i	− 1.22088i
$177$	− 1.35828i	− 0.102095i
$178$	−20.5560	−1.54074
$179$	16.9164	1.26439	0.632196	−	0.774809i	$-0.282154\pi$
$179$	16.9164	1.26439	0.632196	+	0.774809i	$0.282154\pi$
$180$	− 11.3925i	− 0.849145i
$181$	3.26162	0.242434	0.121217	−	0.992626i	$-0.461320\pi$
$181$	3.26162	0.242434	0.121217	+	0.992626i	$0.461320\pi$
$182$	0	0
$183$	−6.38845	−0.472248
$184$	− 43.6820i	− 3.22028i
$185$	7.35740	0.540927
$186$	26.9216	1.97399
$187$	2.31640i	0.169392i
$188$	50.2249i	3.66303i
$189$	− 4.94808i	− 0.359920i
$190$	25.0026i	1.81388i
$191$	1.18333	0.0856230	0.0428115	−	0.999083i	$-0.486369\pi$
$191$	1.18333	0.0856230	0.0428115	+	0.999083i	$0.486369\pi$
$192$	6.10098	0.440301
$193$	4.53144i	0.326180i	0.986611	+	0.163090i	$0.0521461\pi$
$193$	4.53144i	0.326180i	−0.986611	+	0.163090i	$0.947854\pi$
$194$	25.4370	1.82627
$195$	0	0
$196$	4.13677	0.295483
$197$	− 12.6500i	− 0.901278i	−0.892706	−	0.450639i	$-0.851196\pi$
$197$	− 12.6500i	− 0.901278i	0.892706	−	0.450639i	$-0.148804\pi$
$198$	16.8622	1.19835
$199$	−21.2820	−1.50864	−0.754320	−	0.656506i	$-0.772033\pi$
$199$	−21.2820	−1.50864	−0.754320	+	0.656506i	$0.772033\pi$
$200$	16.7604i	1.18514i
$201$	3.79716i	0.267831i
$202$	32.3465i	2.27590i
$203$	1.07995i	0.0757975i
$204$	2.81430	0.197041
$205$	5.82377	0.406750
$206$	0.113686i	0.00792089i
$207$	16.7831	1.16651
$208$	0	0
$209$	−24.9462	−1.72556
$210$	− 3.29742i	− 0.227544i
$211$	6.82090	0.469570	0.234785	−	0.972047i	$-0.424561\pi$
$211$	6.82090	0.469570	0.234785	+	0.972047i	$0.424561\pi$
$212$	18.6947	1.28396
$213$	− 2.61425i	− 0.179126i
$214$	− 14.1565i	− 0.967720i
$215$	5.68497i	0.387712i
$216$	− 26.1917i	− 1.78212i
$217$	−11.0557	−0.750509
$218$	−31.2486	−2.11642
$219$	− 10.0377i	− 0.678288i
$220$	18.7486	1.26403
$221$	0	0
$222$	13.2306	0.887979
$223$	12.4587i	0.834297i	0.908838	+	0.417148i	$0.136970\pi$
$223$	12.4587i	0.834297i	−0.908838	+	0.417148i	$0.863030\pi$
$224$	1.40155	0.0936448
$225$	−6.43953	−0.429302
$226$	− 28.2962i	− 1.88224i
$227$	− 7.81480i	− 0.518686i	−0.965785	−	0.259343i	$-0.916494\pi$
$227$	− 7.81480i	− 0.518686i	0.965785	−	0.259343i	$-0.0835061\pi$
$228$	30.3083i	2.00722i
$229$	14.9634i	0.988806i	0.869233	+	0.494403i	$0.164613\pi$
$229$	14.9634i	0.988806i	−0.869233	+	0.494403i	$0.835387\pi$
$230$	27.6825	1.82533
$231$	3.28998	0.216465
$232$	5.71649i	0.375306i
$233$	−13.2274	−0.866556	−0.433278	−	0.901260i	$-0.642643\pi$
$233$	−13.2274	−0.866556	−0.433278	+	0.901260i	$0.642643\pi$
$234$	0	0
$235$	−16.4406	−1.07247
$236$	5.71618i	0.372091i
$237$	1.25753	0.0816851
$238$	−1.71449	−0.111134
$239$	7.69420i	0.497697i	0.968542	+	0.248848i	$0.0800521\pi$
$239$	7.69420i	0.497697i	−0.968542	+	0.248848i	$0.919948\pi$
$240$	− 6.44151i	− 0.415798i
$241$	9.00075i	0.579789i	0.957059	+	0.289895i	$0.0936203\pi$
$241$	9.00075i	0.579789i	−0.957059	+	0.289895i	$0.906380\pi$
$242$	0.500452i	0.0321703i
$243$	16.0606	1.03029
$244$	26.8851	1.72114
$245$	1.35413i	0.0865121i
$246$	10.4727	0.667716
$247$	0	0
$248$	−58.5211	−3.71609
$249$	− 9.33194i	− 0.591388i
$250$	−27.3941	−1.73255
$251$	3.21852	0.203151	0.101576	−	0.994828i	$-0.467612\pi$
$251$	3.21852	0.203151	0.101576	+	0.994828i	$0.467612\pi$
$252$	8.41314i	0.529978i
$253$	27.6200i	1.73645i
$254$	37.5204i	2.35424i
$255$	0.921235i	0.0576900i
$256$	−32.6193	−2.03870
$257$	−5.74593	−0.358422	−0.179211	−	0.983811i	$-0.557354\pi$
$257$	−5.74593	−0.358422	−0.179211	+	0.983811i	$0.557354\pi$
$258$	10.2231i	0.636463i
$259$	−5.43331	−0.337609
$260$	0	0
$261$	−2.19634	−0.135950
$262$	− 38.2386i	− 2.36239i
$263$	−4.51679	−0.278517	−0.139259	−	0.990256i	$-0.544472\pi$
$263$	−4.51679	−0.278517	−0.139259	+	0.990256i	$0.544472\pi$
$264$	17.4149	1.07181
$265$	6.11952i	0.375919i
$266$	− 18.4640i	− 1.13210i
$267$	− 8.15668i	− 0.499180i
$268$	− 15.9799i	− 0.976130i
$269$	1.67968	0.102412	0.0512058	−	0.998688i	$-0.483694\pi$
$269$	1.67968	0.102412	0.0512058	+	0.998688i	$0.483694\pi$
$270$	16.5984	1.01015
$271$	16.2674i	0.988174i	0.869412	+	0.494087i	$0.164498\pi$
$271$	16.2674i	0.988174i	−0.869412	+	0.494087i	$0.835502\pi$
$272$	−3.34925	−0.203078
$273$	0	0
$274$	3.61027	0.218104
$275$	− 10.5975i	− 0.639055i
$276$	33.5569	2.01989
$277$	6.96973	0.418770	0.209385	−	0.977833i	$-0.432854\pi$
$277$	6.96973	0.418770	0.209385	+	0.977833i	$0.432854\pi$
$278$	− 4.56831i	− 0.273989i
$279$	− 22.4845i	− 1.34611i
$280$	7.16781i	0.428359i
$281$	− 15.7742i	− 0.941012i	−0.882397	−	0.470506i	$-0.844071\pi$
$281$	− 15.7742i	− 0.941012i	0.882397	−	0.470506i	$-0.155929\pi$
$282$	−29.5647	−1.76055
$283$	27.5891	1.64000	0.820000	−	0.572363i	$-0.193973\pi$
$283$	27.5891	1.64000	0.820000	+	0.572363i	$0.193973\pi$
$284$	11.0018i	0.652837i
$285$	−9.92113	−0.587677
$286$	0	0
$287$	−4.30075	−0.253865
$288$	2.85039i	0.167961i
$289$	−16.5210	−0.971824
$290$	−3.62270	−0.212732
$291$	10.0935i	0.591691i
$292$	42.2427i	2.47207i
$293$	6.96652i	0.406989i	0.979076	+	0.203494i	$0.0652298\pi$
$293$	6.96652i	0.406989i	−0.979076	+	0.203494i	$0.934770\pi$
$294$	2.43509i	0.142017i
$295$	−1.87113	−0.108942
$296$	−28.7601	−1.67165
$297$	16.5609i	0.960963i
$298$	−50.2275	−2.90960
$299$	0	0
$300$	−12.8755	−0.743365
$301$	− 4.19825i	− 0.241983i
$302$	−25.2180	−1.45113
$303$	−12.8352	−0.737364
$304$	− 36.0694i	− 2.06872i
$305$	8.80057i	0.503919i
$306$	− 3.48684i	− 0.199330i
$307$	− 23.3723i	− 1.33393i	−0.745089	−	0.666965i	$-0.767593\pi$
$307$	− 23.3723i	− 1.33393i	0.745089	−	0.666965i	$-0.232407\pi$
$308$	−13.8455	−0.788921
$309$	−0.0451111	−0.00256628
$310$	− 37.0865i	− 2.10637i
$311$	−0.213388	−0.0121001	−0.00605006	−	0.999982i	$-0.501926\pi$
$311$	−0.213388	−0.0121001	−0.00605006	+	0.999982i	$0.501926\pi$
$312$	0	0
$313$	−13.2875	−0.751052	−0.375526	−	0.926812i	$-0.622538\pi$
$313$	−13.2875	−0.751052	−0.375526	+	0.926812i	$0.622538\pi$
$314$	− 27.2569i	− 1.53820i
$315$	−2.75396	−0.155168
$316$	−5.29216	−0.297707
$317$	− 9.25588i	− 0.519862i	−0.965627	−	0.259931i	$-0.916300\pi$
$317$	− 9.25588i	− 0.519862i	0.965627	−	0.259931i	$-0.0836998\pi$
$318$	11.0045i	0.617104i
$319$	− 3.61452i	− 0.202374i
$320$	− 8.40456i	− 0.469829i
$321$	5.61736	0.313530
$322$	−20.4430	−1.13925
$323$	5.15847i	0.287025i
$324$	−5.11876	−0.284375
$325$	0	0
$326$	−61.9747	−3.43246
$327$	− 12.3995i	− 0.685697i
$328$	−22.7652	−1.25700
$329$	12.1411	0.669361
$330$	11.0363i	0.607528i
$331$	− 14.1218i	− 0.776204i	−0.921617	−	0.388102i	$-0.873131\pi$
$331$	− 14.1218i	− 0.776204i	0.921617	−	0.388102i	$-0.126869\pi$
$332$	39.2725i	2.15536i
$333$	− 11.0500i	− 0.605535i
$334$	−20.3782	−1.11504
$335$	5.23087	0.285793
$336$	4.75694i	0.259512i
$337$	−27.8977	−1.51968	−0.759842	−	0.650108i	$-0.774724\pi$
$337$	−27.8977	−1.51968	−0.759842	+	0.650108i	$0.774724\pi$
$338$	0	0
$339$	11.2280	0.609824
$340$	− 3.87691i	− 0.210255i
$341$	37.0027	2.00381
$342$	37.5511	2.03053
$343$	− 1.00000i	− 0.0539949i
$344$	− 22.2226i	− 1.19816i
$345$	10.9845i	0.591386i
$346$	22.6719i	1.21885i
$347$	0.430164	0.0230924	0.0115462	−	0.999933i	$-0.496325\pi$
$347$	0.430164	0.0230924	0.0115462	+	0.999933i	$0.496325\pi$
$348$	−4.39146	−0.235407
$349$	27.0848i	1.44982i	0.688844	+	0.724909i	$0.258118\pi$
$349$	27.0848i	1.44982i	−0.688844	+	0.724909i	$0.741882\pi$
$350$	7.84380	0.419269
$351$	0	0
$352$	−4.69089	−0.250025
$353$	27.1110i	1.44297i	0.692430	+	0.721485i	$0.256540\pi$
$353$	27.1110i	1.44297i	−0.692430	+	0.721485i	$0.743460\pi$
$354$	−3.36480	−0.178837
$355$	−3.60133	−0.191139
$356$	34.3265i	1.81930i
$357$	− 0.680315i	− 0.0360061i
$358$	− 41.9062i	− 2.21481i
$359$	22.9394i	1.21070i	0.795961	+	0.605348i	$0.206966\pi$
$359$	22.9394i	1.21070i	−0.795961	+	0.605348i	$0.793034\pi$
$360$	−14.5775	−0.768304
$361$	−36.5536	−1.92387
$362$	− 8.07984i	− 0.424667i
$363$	−0.198581	−0.0104228
$364$	0	0
$365$	−13.8277	−0.723777
$366$	15.8258i	0.827227i
$367$	−0.540610	−0.0282196	−0.0141098	−	0.999900i	$-0.504491\pi$
$367$	−0.540610	−0.0282196	−0.0141098	+	0.999900i	$0.504491\pi$
$368$	−39.9354	−2.08178
$369$	− 8.74665i	− 0.455332i
$370$	− 18.2261i	− 0.947530i
$371$	− 4.51915i	− 0.234623i
$372$	− 44.9564i	− 2.33088i
$373$	4.04819	0.209607	0.104804	−	0.994493i	$-0.466579\pi$
$373$	4.04819	0.209607	0.104804	+	0.994493i	$0.466579\pi$
$374$	5.73830	0.296720
$375$	− 10.8701i	− 0.561328i
$376$	64.2665	3.31429
$377$	0	0
$378$	−12.2576	−0.630464
$379$	− 25.5845i	− 1.31419i	−0.753810	−	0.657093i	$-0.771786\pi$
$379$	− 25.5845i	− 1.31419i	0.753810	−	0.657093i	$-0.228214\pi$
$380$	41.7520	2.14183
$381$	−14.8882	−0.762747
$382$	− 2.93141i	− 0.149984i
$383$	− 10.3550i	− 0.529115i	−0.964370	−	0.264558i	$-0.914774\pi$
$383$	− 10.3550i	− 0.529115i	0.964370	−	0.264558i	$-0.0852259\pi$
$384$	− 17.8690i	− 0.911876i
$385$	− 4.53219i	− 0.230982i
$386$	11.2255	0.571363
$387$	8.53819	0.434020
$388$	− 42.4774i	− 2.15646i
$389$	15.6867	0.795348	0.397674	−	0.917527i	$-0.369817\pi$
$389$	15.6867	0.795348	0.397674	+	0.917527i	$0.369817\pi$
$390$	0	0
$391$	5.71138	0.288837
$392$	− 5.29330i	− 0.267352i
$393$	15.1732	0.765387
$394$	−31.3373	−1.57875
$395$	− 1.73234i	− 0.0871633i
$396$	− 28.1583i	− 1.41501i
$397$	− 17.2121i	− 0.863850i	−0.901909	−	0.431925i	$-0.857834\pi$
$397$	− 17.2121i	− 0.863850i	0.901909	−	0.431925i	$-0.142166\pi$
$398$	52.7208i	2.64266i
$399$	7.32657	0.366787
$400$	15.3228	0.766142
$401$	28.6309i	1.42976i	0.699247	+	0.714881i	$0.253519\pi$
$401$	28.6309i	1.42976i	−0.699247	+	0.714881i	$0.746481\pi$
$402$	9.40651	0.469154
$403$	0	0
$404$	54.0156	2.68738
$405$	− 1.67557i	− 0.0832599i
$406$	2.67530	0.132773
$407$	18.1850	0.901395
$408$	− 3.60111i	− 0.178282i
$409$	− 21.7941i	− 1.07765i	−0.842417	−	0.538826i	$-0.818868\pi$
$409$	− 21.7941i	− 1.07765i	0.842417	−	0.538826i	$-0.181132\pi$
$410$	− 14.4269i	− 0.712496i
$411$	1.43257i	0.0706633i
$412$	0.189845	0.00935299
$413$	1.38180	0.0679939
$414$	− 41.5760i	− 2.04335i
$415$	−12.8554	−0.631049
$416$	0	0
$417$	1.81272	0.0887694
$418$	61.7979i	3.02264i
$419$	−6.96938	−0.340477	−0.170238	−	0.985403i	$-0.554454\pi$
$419$	−6.96938	−0.340477	−0.170238	+	0.985403i	$0.554454\pi$
$420$	−5.50638	−0.268684
$421$	− 8.00034i	− 0.389913i	−0.980812	−	0.194956i	$-0.937543\pi$
$421$	− 8.00034i	− 0.389913i	0.980812	−	0.194956i	$-0.0624565\pi$
$422$	− 16.8971i	− 0.822536i
$423$	24.6920i	1.20056i
$424$	− 23.9212i	− 1.16172i
$425$	−2.19140	−0.106299
$426$	−6.47616	−0.313771
$427$	− 6.49906i	− 0.314512i
$428$	−23.6400	−1.14268
$429$	0	0
$430$	14.0831	0.679147
$431$	− 26.7240i	− 1.28725i	−0.765342	−	0.643624i	$-0.777430\pi$
$431$	− 26.7240i	− 1.28725i	0.765342	−	0.643624i	$-0.222570\pi$
$432$	−23.9452	−1.15207
$433$	25.6499	1.23266	0.616329	−	0.787489i	$-0.288619\pi$
$433$	25.6499	1.23266	0.616329	+	0.787489i	$0.288619\pi$
$434$	27.3877i	1.31465i
$435$	− 1.43750i	− 0.0689228i
$436$	52.1821i	2.49907i
$437$	61.5080i	2.94233i
$438$	−24.8660	−1.18814
$439$	29.7851	1.42156	0.710782	−	0.703413i	$-0.248341\pi$
$439$	29.7851	1.42156	0.710782	+	0.703413i	$0.248341\pi$
$440$	− 23.9903i	− 1.14369i
$441$	2.03375	0.0968452
$442$	0	0
$443$	31.7157	1.50686	0.753429	−	0.657530i	$-0.228399\pi$
$443$	31.7157	1.50686	0.753429	+	0.657530i	$0.228399\pi$
$444$	− 22.0938i	− 1.04852i
$445$	−11.2364	−0.532658
$446$	30.8633	1.46142
$447$	− 19.9304i	− 0.942678i
$448$	6.20662i	0.293235i
$449$	− 25.0667i	− 1.18297i	−0.806316	−	0.591485i	$-0.798542\pi$
$449$	− 25.0667i	− 1.18297i	0.806316	−	0.591485i	$-0.201458\pi$
$450$	15.9523i	0.752000i
$451$	14.3944	0.677804
$452$	−47.2520	−2.22255
$453$	− 10.0066i	− 0.470150i
$454$	−19.3592	−0.908573
$455$	0	0
$456$	38.7818	1.81612
$457$	− 20.3303i	− 0.951011i	−0.879713	−	0.475505i	$-0.842265\pi$
$457$	− 20.3303i	− 0.951011i	0.879713	−	0.475505i	$-0.157735\pi$
$458$	37.0680	1.73207
$459$	3.42454	0.159844
$460$	− 46.2271i	− 2.15535i
$461$	30.1317i	1.40337i	0.712486	+	0.701687i	$0.247569\pi$
$461$	30.1317i	1.40337i	−0.712486	+	0.701687i	$0.752431\pi$
$462$	− 8.15010i	− 0.379177i
$463$	10.7592i	0.500023i	0.968243	+	0.250011i	$0.0804344\pi$
$463$	10.7592i	0.500023i	−0.968243	+	0.250011i	$0.919566\pi$
$464$	5.22619	0.242620
$465$	14.7160	0.682440
$466$	32.7676i	1.51793i
$467$	7.00596	0.324197	0.162099	−	0.986775i	$-0.448174\pi$
$467$	7.00596	0.324197	0.162099	+	0.986775i	$0.448174\pi$
$468$	0	0
$469$	−3.86290	−0.178372
$470$	40.7275i	1.87862i
$471$	10.8156	0.498358
$472$	7.31428	0.336667
$473$	14.0513i	0.646079i
$474$	− 3.11521i	− 0.143086i
$475$	− 23.6000i	− 1.08284i
$476$	2.86303i	0.131227i
$477$	9.19082	0.420819
$478$	19.0605	0.871805
$479$	− 12.4047i	− 0.566787i	−0.959004	−	0.283394i	$-0.908540\pi$
$479$	− 12.4047i	− 0.566787i	0.959004	−	0.283394i	$-0.0914603\pi$
$480$	−1.86557	−0.0851514
$481$	0	0
$482$	22.2971	1.01561
$483$	− 8.11186i	− 0.369102i
$484$	0.835706	0.0379866
$485$	13.9045	0.631373
$486$	− 39.7860i	− 1.80473i
$487$	− 4.21898i	− 0.191180i	−0.995421	−	0.0955900i	$-0.969526\pi$
$487$	− 4.21898i	− 0.191180i	0.995421	−	0.0955900i	$-0.0304738\pi$
$488$	− 34.4015i	− 1.55728i
$489$	− 24.5918i	− 1.11208i
$490$	3.35452	0.151542
$491$	−8.08942	−0.365070	−0.182535	−	0.983199i	$-0.558430\pi$
$491$	−8.08942	−0.365070	−0.182535	+	0.983199i	$0.558430\pi$
$492$	− 17.4884i	− 0.788438i
$493$	−0.747425	−0.0336624
$494$	0	0
$495$	9.21734	0.414289
$496$	53.5018i	2.40230i
$497$	2.65952	0.119296
$498$	−23.1176	−1.03592
$499$	35.5855i	1.59302i	0.604623	+	0.796512i	$0.293324\pi$
$499$	35.5855i	1.59302i	−0.604623	+	0.796512i	$0.706676\pi$
$500$	45.7455i	2.04580i
$501$	− 8.08613i	− 0.361262i
$502$	− 7.97307i	− 0.355856i
$503$	−37.2077	−1.65901	−0.829505	−	0.558500i	$-0.811377\pi$
$503$	−37.2077	−1.65901	−0.829505	+	0.558500i	$0.811377\pi$
$504$	10.7652	0.479522
$505$	17.6815i	0.786815i
$506$	68.4216	3.04171
$507$	0	0
$508$	62.6555	2.77989
$509$	29.2315i	1.29566i	0.761783	+	0.647832i	$0.224324\pi$
$509$	29.2315i	1.29566i	−0.761783	+	0.647832i	$0.775676\pi$
$510$	2.28213	0.101054
$511$	10.2115	0.451732
$512$	44.4492i	1.96440i
$513$	36.8801i	1.62830i
$514$	14.2341i	0.627840i
$515$	0.0621438i	0.00273839i
$516$	17.0716	0.751535
$517$	−40.6356	−1.78715
$518$	13.4597i	0.591383i
$519$	−8.99629	−0.394893
$520$	0	0
$521$	34.1215	1.49489	0.747444	−	0.664324i	$-0.231281\pi$
$521$	34.1215	1.49489	0.747444	+	0.664324i	$0.231281\pi$
$522$	5.44089i	0.238141i
$523$	−13.6495	−0.596850	−0.298425	−	0.954433i	$-0.596461\pi$
$523$	−13.6495	−0.596850	−0.298425	+	0.954433i	$0.596461\pi$
$524$	−63.8548	−2.78951
$525$	3.11245i	0.135838i
$526$	11.1892i	0.487873i
$527$	− 7.65157i	− 0.333308i
$528$	− 15.9212i	− 0.692881i
$529$	45.1006	1.96090
$530$	15.1596	0.658490
$531$	2.81023i	0.121954i
$532$	−30.8331	−1.33678
$533$	0	0
$534$	−20.2061	−0.874404
$535$	− 7.73833i	− 0.334557i
$536$	−20.4475	−0.883198
$537$	16.6285	0.717573
$538$	− 4.16098i	− 0.179392i
$539$	3.34694i	0.144163i
$540$	− 27.7177i	− 1.19278i
$541$	− 9.86414i	− 0.424092i	−0.977260	−	0.212046i	$-0.931987\pi$
$541$	− 9.86414i	− 0.424092i	0.977260	−	0.212046i	$-0.0680127\pi$
$542$	40.2984	1.73096
$543$	3.20611	0.137587
$544$	0.970002i	0.0415885i
$545$	−17.0813	−0.731683
$546$	0	0
$547$	−27.8424	−1.19046	−0.595228	−	0.803557i	$-0.702938\pi$
$547$	−27.8424	−1.19046	−0.595228	+	0.803557i	$0.702938\pi$
$548$	− 6.02880i	− 0.257538i
$549$	13.2175	0.564107
$550$	−26.2527	−1.11942
$551$	− 8.04931i	− 0.342912i
$552$	− 42.9385i	− 1.82758i
$553$	1.27930i	0.0544013i
$554$	− 17.2658i	− 0.733552i
$555$	7.23218	0.306989
$556$	−7.62864	−0.323526
$557$	2.24905i	0.0952954i	0.998864	+	0.0476477i	$0.0151725\pi$
$557$	2.24905i	0.0952954i	−0.998864	+	0.0476477i	$0.984828\pi$
$558$	−55.6997	−2.35796
$559$	0	0
$560$	6.55304	0.276916
$561$	2.27698i	0.0961340i
$562$	−39.0767	−1.64835
$563$	−30.8047	−1.29826	−0.649131	−	0.760676i	$-0.724867\pi$
$563$	−30.8047	−1.29826	−0.649131	+	0.760676i	$0.724867\pi$
$564$	49.3701i	2.07886i
$565$	− 15.4675i	− 0.650721i
$566$	− 68.3450i	− 2.87276i
$567$	1.23738i	0.0519651i
$568$	14.0776	0.590684
$569$	16.0245	0.671783	0.335891	−	0.941901i	$-0.390962\pi$
$569$	16.0245	0.671783	0.335891	+	0.941901i	$0.390962\pi$
$570$	24.5771i	1.02942i
$571$	−8.25263	−0.345362	−0.172681	−	0.984978i	$-0.555243\pi$
$571$	−8.25263	−0.345362	−0.172681	+	0.984978i	$0.555243\pi$
$572$	0	0
$573$	1.16319	0.0485931
$574$	10.6540i	0.444691i
$575$	−26.1296	−1.08968
$576$	−12.6227	−0.525946
$577$	11.8605i	0.493760i	0.969046	+	0.246880i	$0.0794053\pi$
$577$	11.8605i	0.493760i	−0.969046	+	0.246880i	$0.920595\pi$
$578$	40.9267i	1.70232i
$579$	4.45432i	0.185115i
$580$	6.04956i	0.251194i
$581$	9.49352	0.393857
$582$	25.0041	1.03645
$583$	15.1253i	0.626428i
$584$	54.0527	2.23672
$585$	0	0
$586$	17.2578	0.712914
$587$	8.16634i	0.337061i	0.985696	+	0.168531i	$0.0539022\pi$
$587$	8.16634i	0.337061i	−0.985696	+	0.168531i	$0.946098\pi$
$588$	4.06636	0.167694
$589$	82.4027	3.39535
$590$	4.63527i	0.190831i
$591$	− 12.4347i	− 0.511497i
$592$	26.2934i	1.08065i
$593$	21.7045i	0.891296i	0.895208	+	0.445648i	$0.147027\pi$
$593$	21.7045i	0.891296i	−0.895208	+	0.445648i	$0.852973\pi$
$594$	41.0256	1.68330
$595$	−0.937185	−0.0384208
$596$	83.8751i	3.43566i
$597$	−20.9198	−0.856190
$598$	0	0
$599$	−12.5895	−0.514392	−0.257196	−	0.966359i	$-0.582799\pi$
$599$	−12.5895	−0.514392	−0.257196	+	0.966359i	$0.582799\pi$
$600$	16.4751i	0.672594i
$601$	9.71667	0.396351	0.198176	−	0.980167i	$-0.436498\pi$
$601$	9.71667	0.396351	0.198176	+	0.980167i	$0.436498\pi$
$602$	−10.4001	−0.423877
$603$	− 7.85618i	− 0.319928i
$604$	42.1116i	1.71349i
$605$	0.273560i	0.0111218i
$606$	31.7960i	1.29163i
$607$	−19.5676	−0.794223	−0.397111	−	0.917770i	$-0.629987\pi$
$607$	−19.5676	−0.794223	−0.397111	+	0.917770i	$0.629987\pi$
$608$	−10.4463	−0.423654
$609$	1.06157i	0.0430169i
$610$	21.8012	0.882705
$611$	0	0
$612$	−5.82269	−0.235368
$613$	− 1.16145i	− 0.0469105i	−0.999725	−	0.0234552i	$-0.992533\pi$
$613$	− 1.16145i	− 0.0469105i	0.999725	−	0.0234552i	$-0.00746672\pi$
$614$	−57.8991	−2.33662
$615$	5.72466	0.230841
$616$	17.7164i	0.713813i
$617$	− 5.76897i	− 0.232250i	−0.993235	−	0.116125i	$-0.962953\pi$
$617$	− 5.76897i	− 0.232250i	0.993235	−	0.116125i	$-0.0370473\pi$
$618$	0.111751i	0.00449530i
$619$	− 22.1428i	− 0.889995i	−0.895532	−	0.444997i	$-0.853205\pi$
$619$	− 22.1428i	− 0.889995i	0.895532	−	0.444997i	$-0.146795\pi$
$620$	−61.9308	−2.48720
$621$	40.8331	1.63857
$622$	0.528615i	0.0211955i
$623$	8.29790	0.332448
$624$	0	0
$625$	0.857342	0.0342937
$626$	32.9164i	1.31560i
$627$	−24.5216	−0.979299
$628$	−45.5164	−1.81630
$629$	− 3.76036i	− 0.149935i
$630$	6.82224i	0.271805i
$631$	1.53311i	0.0610321i	0.999534	+	0.0305160i	$0.00971506\pi$
$631$	1.53311i	0.0610321i	−0.999534	+	0.0305160i	$0.990285\pi$
$632$	6.77172i	0.269364i
$633$	6.70481	0.266492
$634$	−22.9291	−0.910632
$635$	20.5096i	0.813900i
$636$	18.3765	0.728676
$637$	0	0
$638$	−8.95407	−0.354495
$639$	5.40879i	0.213968i
$640$	−24.6159	−0.973031
$641$	−6.98425	−0.275861	−0.137931	−	0.990442i	$-0.544045\pi$
$641$	−6.98425	−0.275861	−0.137931	+	0.990442i	$0.544045\pi$
$642$	− 13.9156i	− 0.549205i
$643$	− 2.00673i	− 0.0791376i	−0.999217	−	0.0395688i	$-0.987402\pi$
$643$	− 2.00673i	− 0.0791376i	0.999217	−	0.0395688i	$-0.0125984\pi$
$644$	34.1379i	1.34522i
$645$	5.58822i	0.220036i
$646$	12.7788	0.502776
$647$	31.7091	1.24661	0.623306	−	0.781978i	$-0.285789\pi$
$647$	31.7091	1.24661	0.623306	+	0.781978i	$0.285789\pi$
$648$	6.54983i	0.257302i
$649$	−4.62480	−0.181539
$650$	0	0
$651$	−10.8675	−0.425932
$652$	103.492i	4.05305i
$653$	32.9719	1.29029	0.645144	−	0.764061i	$-0.276797\pi$
$653$	32.9719	1.29029	0.645144	+	0.764061i	$0.276797\pi$
$654$	−30.7168	−1.20112
$655$	− 20.9022i	− 0.816717i
$656$	20.8126i	0.812596i
$657$	20.7677i	0.810225i
$658$	− 30.0765i	− 1.17251i
$659$	4.53941	0.176830	0.0884151	−	0.996084i	$-0.471820\pi$
$659$	4.53941	0.176830	0.0884151	+	0.996084i	$0.471820\pi$
$660$	18.4295	0.717368
$661$	3.74518i	0.145671i	0.997344	+	0.0728354i	$0.0232048\pi$
$661$	3.74518i	0.145671i	−0.997344	+	0.0728354i	$0.976795\pi$
$662$	−34.9832	−1.35966
$663$	0	0
$664$	50.2520	1.95016
$665$	− 10.0929i	− 0.391386i
$666$	−27.3736	−1.06070
$667$	−8.91206	−0.345076
$668$	34.0296i	1.31664i
$669$	12.2467i	0.473484i
$670$	− 12.9582i	− 0.500618i
$671$	21.7520i	0.839726i
$672$	1.37769	0.0531457
$673$	12.6511	0.487665	0.243833	−	0.969817i	$-0.421595\pi$
$673$	12.6511	0.487665	0.243833	+	0.969817i	$0.421595\pi$
$674$	69.1095i	2.66200i
$675$	−15.6673	−0.603033
$676$	0	0
$677$	9.61317	0.369464	0.184732	−	0.982789i	$-0.440858\pi$
$677$	9.61317	0.369464	0.184732	+	0.982789i	$0.440858\pi$
$678$	− 27.8147i	− 1.06822i
$679$	−10.2683	−0.394059
$680$	−4.96080	−0.190238
$681$	− 7.68180i	− 0.294367i
$682$	− 91.6650i	− 3.51003i
$683$	− 2.24054i	− 0.0857320i	−0.999081	−	0.0428660i	$-0.986351\pi$
$683$	− 2.24054i	− 0.0857320i	0.999081	−	0.0428660i	$-0.0136489\pi$
$684$	− 62.7067i	− 2.39765i
$685$	1.97347	0.0754023
$686$	−2.47725	−0.0945818
$687$	14.7087i	0.561171i
$688$	−20.3166	−0.774563
$689$	0	0
$690$	27.2114	1.03592
$691$	− 16.7892i	− 0.638693i	−0.947638	−	0.319346i	$-0.896537\pi$
$691$	− 16.7892i	− 0.638693i	0.947638	−	0.319346i	$-0.103463\pi$
$692$	37.8599	1.43922
$693$	−6.80684	−0.258570
$694$	− 1.06562i	− 0.0404505i
$695$	− 2.49716i	− 0.0947227i
$696$	5.61920i	0.212995i
$697$	− 2.97653i	− 0.112744i
$698$	67.0959	2.53962
$699$	−13.0023	−0.491791
$700$	− 13.0984i	− 0.495072i
$701$	50.3596	1.90206	0.951028	−	0.309106i	$-0.100030\pi$
$701$	50.3596	1.90206	0.951028	+	0.309106i	$0.100030\pi$
$702$	0	0
$703$	40.4967	1.52736
$704$	− 20.7732i	− 0.782919i
$705$	−16.1608	−0.608651
$706$	67.1606	2.52762
$707$	− 13.0574i	− 0.491076i
$708$	5.61889i	0.211171i
$709$	10.1451i	0.381006i	0.981687	+	0.190503i	$0.0610119\pi$
$709$	10.1451i	0.381006i	−0.981687	+	0.190503i	$0.938988\pi$
$710$	8.92140i	0.334814i
$711$	−2.60177	−0.0975741
$712$	43.9233	1.64609
$713$	− 91.2349i	− 3.41677i
$714$	−1.68531	−0.0630712
$715$	0	0
$716$	−69.9792	−2.61525
$717$	7.56325i	0.282455i
$718$	56.8266	2.12075
$719$	−5.86968	−0.218902	−0.109451	−	0.993992i	$-0.534909\pi$
$719$	−5.86968	−0.218902	−0.109451	+	0.993992i	$0.534909\pi$
$720$	13.3272i	0.496676i
$721$	− 0.0458921i	− 0.00170911i
$722$	90.5523i	3.37001i
$723$	8.84757i	0.329045i
$724$	−13.4926	−0.501447
$725$	3.41947	0.126996
$726$	0.491935i	0.0182574i
$727$	41.0582	1.52276	0.761382	−	0.648304i	$-0.224521\pi$
$727$	41.0582	1.52276	0.761382	+	0.648304i	$0.224521\pi$
$728$	0	0
$729$	12.0751	0.447225
$730$	34.2547i	1.26783i
$731$	2.90558	0.107467
$732$	26.4275	0.976790
$733$	19.8655i	0.733748i	0.930271	+	0.366874i	$0.119572\pi$
$733$	19.8655i	0.733748i	−0.930271	+	0.366874i	$0.880428\pi$
$734$	1.33923i	0.0494317i
$735$	1.33108i	0.0490977i
$736$	11.5660i	0.426328i
$737$	12.9289	0.476243
$738$	−21.6676	−0.797597
$739$	− 32.3664i	− 1.19062i	−0.803497	−	0.595309i	$-0.797030\pi$
$739$	− 32.3664i	− 1.19062i	0.803497	−	0.595309i	$-0.202970\pi$
$740$	−30.4358	−1.11884
$741$	0	0
$742$	−11.1951	−0.410984
$743$	− 46.4032i	− 1.70237i	−0.524866	−	0.851185i	$-0.675885\pi$
$743$	− 46.4032i	− 1.70237i	0.524866	−	0.851185i	$-0.324115\pi$
$744$	−57.5251	−2.10897
$745$	−27.4557	−1.00590
$746$	− 10.0284i	− 0.367165i
$747$	19.3074i	0.706422i
$748$	− 9.58240i	− 0.350367i
$749$	5.71462i	0.208808i
$750$	−26.9279	−0.983267
$751$	33.2309	1.21261	0.606306	−	0.795232i	$-0.292651\pi$
$751$	33.2309	1.21261	0.606306	+	0.795232i	$0.292651\pi$
$752$	− 58.7544i	− 2.14255i
$753$	3.16374	0.115293
$754$	0	0
$755$	−13.7848	−0.501680
$756$	20.4690i	0.744452i
$757$	22.3961	0.814001	0.407001	−	0.913428i	$-0.366575\pi$
$757$	22.3961	0.814001	0.407001	+	0.913428i	$0.366575\pi$
$758$	−63.3791	−2.30203
$759$	27.1499i	0.985480i
$760$	− 53.4248i	− 1.93792i
$761$	37.9167i	1.37448i	0.726430	+	0.687240i	$0.241178\pi$
$761$	37.9167i	1.37448i	−0.726430	+	0.687240i	$0.758822\pi$
$762$	36.8819i	1.33609i
$763$	12.6142	0.456666
$764$	−4.89518	−0.177101
$765$	− 1.90600i	− 0.0689115i
$766$	−25.6519	−0.926841
$767$	0	0
$768$	−32.0641	−1.15701
$769$	5.88438i	0.212196i	0.994356	+	0.106098i	$0.0338358\pi$
$769$	5.88438i	0.212196i	−0.994356	+	0.106098i	$0.966164\pi$
$770$	−11.2274	−0.404606
$771$	−5.64814	−0.203413
$772$	− 18.7455i	− 0.674665i
$773$	18.1883i	0.654188i	0.944992	+	0.327094i	$0.106069\pi$
$773$	18.1883i	0.654188i	−0.944992	+	0.327094i	$0.893931\pi$
$774$	− 21.1512i	− 0.760265i
$775$	35.0060i	1.25745i
$776$	−54.3530	−1.95116
$777$	−5.34084	−0.191601
$778$	− 38.8599i	− 1.39320i
$779$	32.0553	1.14850
$780$	0	0
$781$	−8.90125	−0.318512
$782$	− 14.1485i	− 0.505949i
$783$	−5.34367	−0.190967
$784$	−4.83930	−0.172832
$785$	− 14.8994i	− 0.531781i
$786$	− 37.5878i	− 1.34071i
$787$	− 8.90957i	− 0.317592i	−0.987311	−	0.158796i	$-0.949239\pi$
$787$	− 8.90957i	− 0.317592i	0.987311	−	0.158796i	$-0.0507612\pi$
$788$	52.3302i	1.86419i
$789$	−4.43992	−0.158065
$790$	−4.29143	−0.152682
$791$	11.4224i	0.406135i
$792$	−36.0307	−1.28029
$793$	0	0
$794$	−42.6387	−1.51319
$795$	6.01537i	0.213343i
$796$	88.0386	3.12045
$797$	−47.3677	−1.67785	−0.838925	−	0.544248i	$-0.816815\pi$
$797$	−47.3677	−1.67785	−0.838925	+	0.544248i	$0.816815\pi$
$798$	− 18.1498i	− 0.642494i
$799$	8.40279i	0.297269i
$800$	− 4.43776i	− 0.156899i
$801$	16.8758i	0.596279i
$802$	70.9260	2.50448
$803$	−34.1774	−1.20609
$804$	− 15.7080i	− 0.553977i
$805$	−11.1747	−0.393856
$806$	0	0
$807$	1.65109	0.0581211
$808$	− 69.1170i	− 2.43153i
$809$	49.5112	1.74072	0.870361	−	0.492414i	$-0.163885\pi$
$809$	49.5112	1.74072	0.870361	+	0.492414i	$0.163885\pi$
$810$	−4.15081	−0.145845
$811$	41.3191i	1.45091i	0.688269	+	0.725456i	$0.258371\pi$
$811$	41.3191i	1.45091i	−0.688269	+	0.725456i	$0.741629\pi$
$812$	− 4.46749i	− 0.156778i
$813$	15.9905i	0.560813i
$814$	− 45.0487i	− 1.57896i
$815$	−33.8770	−1.18666
$816$	−3.29225	−0.115252
$817$	31.2914i	1.09475i
$818$	−53.9895	−1.88770
$819$	0	0
$820$	−24.0916	−0.841315
$821$	18.1127i	0.632137i	0.948736	+	0.316068i	$0.102363\pi$
$821$	18.1127i	0.632137i	−0.948736	+	0.316068i	$0.897637\pi$
$822$	3.54883	0.123780
$823$	50.6779	1.76652	0.883261	−	0.468882i	$-0.155343\pi$
$823$	50.6779	1.76652	0.883261	+	0.468882i	$0.155343\pi$
$824$	− 0.242921i	− 0.00846255i
$825$	− 10.4172i	− 0.362679i
$826$	− 3.42306i	− 0.119103i
$827$	4.24466i	0.147601i	0.997273	+	0.0738007i	$0.0235129\pi$
$827$	4.24466i	0.147601i	−0.997273	+	0.0738007i	$0.976487\pi$
$828$	−69.4278	−2.41278
$829$	−31.8934	−1.10770	−0.553852	−	0.832615i	$-0.686842\pi$
$829$	−31.8934	−1.10770	−0.553852	+	0.832615i	$0.686842\pi$
$830$	31.8462i	1.10540i
$831$	6.85111	0.237662
$832$	0	0
$833$	0.692094	0.0239796
$834$	− 4.49056i	− 0.155496i
$835$	−11.1392	−0.385490
$836$	103.197	3.56913
$837$	− 54.7044i	− 1.89086i
$838$	17.2649i	0.596406i
$839$	− 43.0363i	− 1.48578i	−0.669414	−	0.742889i	$-0.733455\pi$
$839$	− 43.0363i	− 1.48578i	0.669414	−	0.742889i	$-0.266545\pi$
$840$	7.04582i	0.243104i
$841$	−27.8337	−0.959783
$842$	−19.8188	−0.683002
$843$	− 15.5058i	− 0.534047i
$844$	−28.2165	−0.971250
$845$	0	0
$846$	61.1681	2.10300
$847$	− 0.202019i	− 0.00694146i
$848$	−21.8695	−0.751003
$849$	27.1195	0.930740
$850$	5.42865i	0.186201i
$851$	− 44.8373i	− 1.53700i
$852$	10.8146i	0.370501i
$853$	19.3374i	0.662101i	0.943613	+	0.331050i	$0.107403\pi$
$853$	19.3374i	0.662101i	−0.943613	+	0.331050i	$0.892597\pi$
$854$	−16.0998	−0.550924
$855$	20.5264	0.701989
$856$	30.2492i	1.03390i
$857$	−46.1320	−1.57584	−0.787920	−	0.615778i	$-0.788842\pi$
$857$	−46.1320	−1.57584	−0.787920	+	0.615778i	$0.788842\pi$
$858$	0	0
$859$	0.0356597	0.00121669	0.000608347	−	1.00000i	$-0.499806\pi$
$859$	0.0356597	0.00121669	0.000608347		1.00000i	$0.499806\pi$
$860$	− 23.5174i	− 0.801937i
$861$	−4.22756	−0.144075
$862$	−66.2019	−2.25485
$863$	53.6734i	1.82707i	0.406765	+	0.913533i	$0.366657\pi$
$863$	53.6734i	1.82707i	−0.406765	+	0.913533i	$0.633343\pi$
$864$	6.93496i	0.235932i
$865$	12.3931i	0.421377i
$866$	− 63.5413i	− 2.15922i
$867$	−16.2398	−0.551534
$868$	45.7348	1.55234
$869$	− 4.28174i	− 0.145248i
$870$	−3.56105	−0.120731
$871$	0	0
$872$	66.7709	2.26115
$873$	− 20.8830i	− 0.706784i
$874$	152.371	5.15401
$875$	11.0583	0.373838
$876$	41.5238i	1.40296i
$877$	− 31.8812i	− 1.07655i	−0.842769	−	0.538275i	$-0.819076\pi$
$877$	− 31.8812i	− 1.07655i	0.842769	−	0.538275i	$-0.180924\pi$
$878$	− 73.7850i	− 2.49012i
$879$	6.84796i	0.230976i
$880$	−21.9326	−0.739349
$881$	−40.5926	−1.36760	−0.683799	−	0.729670i	$-0.739674\pi$
$881$	−40.5926	−1.36760	−0.683799	+	0.729670i	$0.739674\pi$
$882$	− 5.03810i	− 0.169642i
$883$	7.42994	0.250037	0.125019	−	0.992154i	$-0.460101\pi$
$883$	7.42994	0.250037	0.125019	+	0.992154i	$0.460101\pi$
$884$	0	0
$885$	−1.83929	−0.0618270
$886$	− 78.5676i	− 2.63953i
$887$	−31.6297	−1.06202	−0.531010	−	0.847365i	$-0.678187\pi$
$887$	−31.6297	−1.06202	−0.531010	+	0.847365i	$0.678187\pi$
$888$	−28.2707	−0.948701
$889$	− 15.1460i	− 0.507981i
$890$	27.8354i	0.933046i
$891$	− 4.14144i	− 0.138744i
$892$	− 51.5388i	− 1.72565i
$893$	−90.4928	−3.02823
$894$	−49.3727	−1.65127
$895$	− 22.9070i	− 0.765697i
$896$	18.1784	0.607299
$897$	0	0
$898$	−62.0964	−2.07218
$899$	11.9396i	0.398207i
$900$	26.6388	0.887961
$901$	3.12768	0.104198
$902$	− 35.6584i	− 1.18730i
$903$	− 4.12680i	− 0.137331i
$904$	60.4625i	2.01095i
$905$	− 4.41665i	− 0.146815i
$906$	−24.7888	−0.823552
$907$	−30.4198	−1.01007	−0.505037	−	0.863098i	$-0.668521\pi$
$907$	−30.4198	−1.01007	−0.505037	+	0.863098i	$0.668521\pi$
$908$	32.3280i	1.07284i
$909$	26.5556	0.880792
$910$	0	0
$911$	−3.61427	−0.119746	−0.0598731	−	0.998206i	$-0.519070\pi$
$911$	−3.61427	−0.119746	−0.0598731	+	0.998206i	$0.519070\pi$
$912$	− 35.4555i	− 1.17405i
$913$	−31.7742	−1.05157
$914$	−50.3632	−1.66587
$915$	8.65079i	0.285986i
$916$	− 61.8999i	− 2.04523i
$917$	15.4359i	0.509739i
$918$	− 8.48343i	− 0.279995i
$919$	−23.5740	−0.777635	−0.388817	−	0.921315i	$-0.627116\pi$
$919$	−23.5740	−0.777635	−0.388817	+	0.921315i	$0.627116\pi$
$920$	−59.1510	−1.95015
$921$	− 22.9746i	− 0.757037i
$922$	74.6437	2.45826
$923$	0	0
$924$	−13.6099	−0.447732
$925$	17.2037i	0.565653i
$926$	26.6532	0.875880
$927$	0.0933330	0.00306546
$928$	− 1.51360i	− 0.0496862i
$929$	− 12.9440i	− 0.424678i	−0.977196	−	0.212339i	$-0.931892\pi$
$929$	− 12.9440i	− 0.424678i	0.977196	−	0.212339i	$-0.0681081\pi$
$930$	− 36.4553i	− 1.19542i
$931$	7.45343i	0.244276i
$932$	54.7187	1.79237
$933$	−0.209756	−0.00686711
$934$	− 17.3555i	− 0.567890i
$935$	3.13670	0.102581
$936$	0	0
$937$	3.98151	0.130070	0.0650352	−	0.997883i	$-0.479284\pi$
$937$	3.98151	0.130070	0.0650352	+	0.997883i	$0.479284\pi$
$938$	9.56938i	0.312451i
$939$	−13.0613	−0.426240
$940$	68.0110	2.21827
$941$	8.25663i	0.269158i	0.990903	+	0.134579i	$0.0429683\pi$
$941$	8.25663i	0.269158i	−0.990903	+	0.134579i	$0.957032\pi$
$942$	− 26.7930i	− 0.872965i
$943$	− 35.4911i	− 1.15575i
$944$	− 6.68694i	− 0.217641i
$945$	−6.70034	−0.217962
$946$	34.8086	1.13172
$947$	25.6597i	0.833828i	0.908946	+	0.416914i	$0.136888\pi$
$947$	25.6597i	0.833828i	−0.908946	+	0.416914i	$0.863112\pi$
$948$	−5.20209	−0.168956
$949$	0	0
$950$	−58.4632	−1.89680
$951$	− 9.09835i	− 0.295034i
$952$	3.66346	0.118734
$953$	−5.32962	−0.172643	−0.0863217	−	0.996267i	$-0.527511\pi$
$953$	−5.32962	−0.172643	−0.0863217	+	0.996267i	$0.527511\pi$
$954$	− 22.7680i	− 0.737140i
$955$	− 1.60239i	− 0.0518520i
$956$	− 31.8291i	− 1.02943i
$957$	− 3.55301i	− 0.114852i
$958$	−30.7297	−0.992830
$959$	−1.45737	−0.0470609
$960$	− 8.26152i	− 0.266639i
$961$	−91.2281	−2.94284
$962$	0	0
$963$	−11.6221	−0.374517
$964$	− 37.2340i	− 1.19923i
$965$	6.13615	0.197530
$966$	−20.0951	−0.646549
$967$	− 2.30160i	− 0.0740145i	−0.999315	−	0.0370073i	$-0.988218\pi$
$967$	− 2.30160i	− 0.0740145i	0.999315	−	0.0370073i	$-0.0117825\pi$
$968$	− 1.06935i	− 0.0343702i
$969$	5.07068i	0.162894i
$970$	− 34.4450i	− 1.10596i
$971$	28.9098	0.927760	0.463880	−	0.885898i	$-0.346457\pi$
$971$	28.9098	0.927760	0.463880	+	0.885898i	$0.346457\pi$
$972$	−66.4388	−2.13102
$973$	1.84411i	0.0591194i
$974$	−10.4515	−0.334886
$975$	0	0
$976$	−31.4509	−1.00672
$977$	13.9475i	0.446221i	0.974793	+	0.223111i	$0.0716211\pi$
$977$	13.9475i	0.446221i	−0.974793	+	0.223111i	$0.928379\pi$
$978$	−60.9199	−1.94800
$979$	−27.7726	−0.887616
$980$	− 5.60172i	− 0.178940i
$981$	25.6542i	0.819075i
$982$	20.0395i	0.639487i
$983$	− 21.0575i	− 0.671630i	−0.941928	−	0.335815i	$-0.890988\pi$
$983$	− 21.0575i	− 0.671630i	0.941928	−	0.335815i	$-0.109012\pi$
$984$	−22.3777	−0.713376
$985$	−17.1298	−0.545800
$986$	1.85156i	0.0589657i
$987$	11.9345	0.379878
$988$	0	0
$989$	34.6453	1.10166
$990$	− 22.8337i	− 0.725701i
$991$	−29.0676	−0.923364	−0.461682	−	0.887046i	$-0.652754\pi$
$991$	−29.0676	−0.923364	−0.461682	+	0.887046i	$0.652754\pi$
$992$	15.4951	0.491968
$993$	− 13.8814i	− 0.440514i
$994$	− 6.58829i	− 0.208968i
$995$	28.8186i	0.913610i
$996$	38.6041i	1.22322i
$997$	−17.2046	−0.544875	−0.272437	−	0.962174i	$-0.587830\pi$
$997$	−17.2046	−0.544875	−0.272437	+	0.962174i	$0.587830\pi$
$998$	88.1541	2.79047
$999$	− 26.8844i	− 0.850586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.3		24
13.5	odd	4		1183.2.a.q.1.2	✓	12
13.8	odd	4		1183.2.a.r.1.11	yes	12
13.12	even	2	inner	1183.2.c.j.337.22		24
91.34	even	4		8281.2.a.cq.1.11		12
91.83	even	4		8281.2.a.cn.1.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.2	✓	12	13.5	odd	4
1183.2.a.r.1.11	yes	12	13.8	odd	4
1183.2.c.j.337.3		24	1.1	even	1	trivial
1183.2.c.j.337.22		24	13.12	even	2	inner
8281.2.a.cn.1.2		12	91.83	even	4
8281.2.a.cq.1.11		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)

\(f(q)\)	\(=\)	\(q-2.47725i q^{2} +0.982981 q^{3} -4.13677 q^{4} -1.35413i q^{5} -2.43509i q^{6} +1.00000i q^{7} +5.29330i q^{8} -2.03375 q^{9} +O(q^{10})\)	\(q-2.47725i q^{2} +0.982981 q^{3} -4.13677 q^{4} -1.35413i q^{5} -2.43509i q^{6} +1.00000i q^{7} +5.29330i q^{8} -2.03375 q^{9} -3.35452 q^{10} -3.34694i q^{11} -4.06636 q^{12} +2.47725 q^{14} -1.33108i q^{15} +4.83930 q^{16} -0.692094 q^{17} +5.03810i q^{18} -7.45343i q^{19} +5.60172i q^{20} +0.982981i q^{21} -8.29121 q^{22} -8.25231 q^{23} +5.20321i q^{24} +3.16633 q^{25} -4.94808 q^{27} -4.13677i q^{28} +1.07995 q^{29} -3.29742 q^{30} +11.0557i q^{31} -1.40155i q^{32} -3.28998i q^{33} +1.71449i q^{34} +1.35413 q^{35} +8.41314 q^{36} +5.43331i q^{37} -18.4640 q^{38} +7.16781 q^{40} +4.30075i q^{41} +2.43509 q^{42} -4.19825 q^{43} +13.8455i q^{44} +2.75396i q^{45} +20.4430i q^{46} -12.1411i q^{47} +4.75694 q^{48} -1.00000 q^{49} -7.84380i q^{50} -0.680315 q^{51} -4.51915 q^{53} +12.2576i q^{54} -4.53219 q^{55} -5.29330 q^{56} -7.32657i q^{57} -2.67530i q^{58} -1.38180i q^{59} +5.50638i q^{60} -6.49906 q^{61} +27.3877 q^{62} -2.03375i q^{63} +6.20662 q^{64} -8.15010 q^{66} +3.86290i q^{67} +2.86303 q^{68} -8.11186 q^{69} -3.35452i q^{70} -2.65952i q^{71} -10.7652i q^{72} -10.2115i q^{73} +13.4597 q^{74} +3.11245 q^{75} +30.8331i q^{76} +3.34694 q^{77} +1.27930 q^{79} -6.55304i q^{80} +1.23738 q^{81} +10.6540 q^{82} -9.49352i q^{83} -4.06636i q^{84} +0.937185i q^{85} +10.4001i q^{86} +1.06157 q^{87} +17.7164 q^{88} -8.29790i q^{89} +6.82224 q^{90} +34.1379 q^{92} +10.8675i q^{93} -30.0765 q^{94} -10.0929 q^{95} -1.37769i q^{96} +10.2683i q^{97} +2.47725i q^{98} +6.80684i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 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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