LMFDB - Embedded newform 1183.2.c.j.337.14

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			337.14
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.j.337.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.842530i q^{2} +0.161973 q^{3} +1.29014 q^{4} -3.72786i q^{5} +0.136467i q^{6} -1.00000i q^{7} +2.77204i q^{8} -2.97376 q^{9} +O(q^{10})$	\(q+0.842530i q^{2} +0.161973 q^{3} +1.29014 q^{4} -3.72786i q^{5} +0.136467i q^{6} -1.00000i q^{7} +2.77204i q^{8} -2.97376 q^{9} +3.14083 q^{10} -3.51379i q^{11} +0.208968 q^{12} +0.842530 q^{14} -0.603811i q^{15} +0.244755 q^{16} -7.43189 q^{17} -2.50549i q^{18} -2.67482i q^{19} -4.80947i q^{20} -0.161973i q^{21} +2.96048 q^{22} +2.49854 q^{23} +0.448995i q^{24} -8.89694 q^{25} -0.967586 q^{27} -1.29014i q^{28} +7.30473 q^{29} +0.508729 q^{30} +2.54405i q^{31} +5.75030i q^{32} -0.569138i q^{33} -6.26159i q^{34} -3.72786 q^{35} -3.83658 q^{36} +2.17903i q^{37} +2.25362 q^{38} +10.3338 q^{40} -8.40738i q^{41} +0.136467 q^{42} -11.8923 q^{43} -4.53329i q^{44} +11.0858i q^{45} +2.10510i q^{46} -9.40740i q^{47} +0.0396435 q^{48} -1.00000 q^{49} -7.49594i q^{50} -1.20376 q^{51} -5.84583 q^{53} -0.815220i q^{54} -13.0989 q^{55} +2.77204 q^{56} -0.433247i q^{57} +6.15445i q^{58} -4.25410i q^{59} -0.779003i q^{60} +5.07200 q^{61} -2.14344 q^{62} +2.97376i q^{63} -4.35529 q^{64} +0.479516 q^{66} -1.29175i q^{67} -9.58820 q^{68} +0.404695 q^{69} -3.14083i q^{70} +1.30601i q^{71} -8.24341i q^{72} +4.31232i q^{73} -1.83590 q^{74} -1.44106 q^{75} -3.45090i q^{76} -3.51379 q^{77} +14.2264 q^{79} -0.912411i q^{80} +8.76457 q^{81} +7.08347 q^{82} -9.81167i q^{83} -0.208968i q^{84} +27.7051i q^{85} -10.0196i q^{86} +1.18316 q^{87} +9.74039 q^{88} +4.77241i q^{89} -9.34010 q^{90} +3.22347 q^{92} +0.412067i q^{93} +7.92602 q^{94} -9.97135 q^{95} +0.931391i q^{96} -5.92836i q^{97} -0.842530i q^{98} +10.4492i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.842530i	0.595759i	0.954604	+	0.297879i	$0.0962793\pi$
$2$	0.842530i	0.595759i	−0.954604	+	0.297879i	$0.903721\pi$
$3$	0.161973	0.0935149	0.0467574	−	0.998906i	$-0.485111\pi$
$3$	0.161973	0.0935149	0.0467574	+	0.998906i	$0.485111\pi$
$4$	1.29014	0.645071
$5$	− 3.72786i	− 1.66715i	−0.552406	−	0.833575i	$-0.686290\pi$
$5$	− 3.72786i	− 1.66715i	0.552406	−	0.833575i	$-0.313710\pi$
$6$	0.136467i	0.0557123i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	2.77204i	0.980066i
$9$	−2.97376	−0.991255
$10$	3.14083	0.993219
$11$	− 3.51379i	− 1.05945i	−0.848170	−	0.529724i	$-0.822295\pi$
$11$	− 3.51379i	− 1.05945i	0.848170	−	0.529724i	$-0.177705\pi$
$12$	0.208968	0.0603238
$13$	0	0
$13$	0	0
$14$	0.842530	0.225176
$15$	− 0.603811i	− 0.155903i
$16$	0.244755	0.0611887
$17$	−7.43189	−1.80250	−0.901249	−	0.433301i	$-0.857349\pi$
$17$	−7.43189	−1.80250	−0.901249	+	0.433301i	$0.857349\pi$
$18$	− 2.50549i	− 0.590549i
$19$	− 2.67482i	− 0.613646i	−0.951767	−	0.306823i	$-0.900734\pi$
$19$	− 2.67482i	− 0.613646i	0.951767	−	0.306823i	$-0.0992659\pi$
$20$	− 4.80947i	− 1.07543i
$21$	− 0.161973i	− 0.0353453i
$22$	2.96048	0.631176
$23$	2.49854	0.520982	0.260491	−	0.965476i	$-0.416116\pi$
$23$	2.49854	0.520982	0.260491	+	0.965476i	$0.416116\pi$
$24$	0.448995i	0.0916507i
$25$	−8.89694	−1.77939
$26$	0	0
$27$	−0.967586	−0.186212
$28$	− 1.29014i	− 0.243814i
$29$	7.30473	1.35645	0.678227	−	0.734853i	$-0.262749\pi$
$29$	7.30473	1.35645	0.678227	+	0.734853i	$0.262749\pi$
$30$	0.508729	0.0928808
$31$	2.54405i	0.456925i	0.973553	+	0.228463i	$0.0733699\pi$
$31$	2.54405i	0.456925i	−0.973553	+	0.228463i	$0.926630\pi$
$32$	5.75030i	1.01652i
$33$	− 0.569138i	− 0.0990742i
$34$	− 6.26159i	− 1.07385i
$35$	−3.72786	−0.630123
$36$	−3.83658	−0.639430
$37$	2.17903i	0.358230i	0.983828	+	0.179115i	$0.0573234\pi$
$37$	2.17903i	0.358230i	−0.983828	+	0.179115i	$0.942677\pi$
$38$	2.25362	0.365585
$39$	0	0
$40$	10.3338	1.63392
$41$	− 8.40738i	− 1.31301i	−0.754321	−	0.656506i	$-0.772034\pi$
$41$	− 8.40738i	− 1.31301i	0.754321	−	0.656506i	$-0.227966\pi$
$42$	0.136467	0.0210573
$43$	−11.8923	−1.81356	−0.906780	−	0.421603i	$-0.861467\pi$
$43$	−11.8923	−1.81356	−0.906780	+	0.421603i	$0.861467\pi$
$44$	− 4.53329i	− 0.683420i
$45$	11.0858i	1.65257i
$46$	2.10510i	0.310379i
$47$	− 9.40740i	− 1.37221i	−0.727502	−	0.686105i	$-0.759319\pi$
$47$	− 9.40740i	− 1.37221i	0.727502	−	0.686105i	$-0.240681\pi$
$48$	0.0396435	0.00572205
$49$	−1.00000	−0.142857
$50$	− 7.49594i	− 1.06009i
$51$	−1.20376	−0.168560
$52$	0	0
$53$	−5.84583	−0.802986	−0.401493	−	0.915862i	$-0.631509\pi$
$53$	−5.84583	−0.802986	−0.401493	+	0.915862i	$0.631509\pi$
$54$	− 0.815220i	− 0.110937i
$55$	−13.0989	−1.76626
$56$	2.77204	0.370430
$57$	− 0.433247i	− 0.0573850i
$58$	6.15445i	0.808119i
$59$	− 4.25410i	− 0.553836i	−0.960893	−	0.276918i	$-0.910687\pi$
$59$	− 4.25410i	− 0.553836i	0.960893	−	0.276918i	$-0.0893131\pi$
$60$	− 0.779003i	− 0.100569i
$61$	5.07200	0.649403	0.324701	−	0.945817i	$-0.394736\pi$
$61$	5.07200	0.649403	0.324701	+	0.945817i	$0.394736\pi$
$62$	−2.14344	−0.272217
$63$	2.97376i	0.374659i
$64$	−4.35529	−0.544412
$65$	0	0
$66$	0.479516	0.0590243
$67$	− 1.29175i	− 0.157812i	−0.996882	−	0.0789060i	$-0.974857\pi$
$67$	− 1.29175i	− 0.157812i	0.996882	−	0.0789060i	$-0.0251427\pi$
$68$	−9.58820	−1.16274
$69$	0.404695	0.0487195
$70$	− 3.14083i	− 0.375402i
$71$	1.30601i	0.154995i	0.996993	+	0.0774975i	$0.0246930\pi$
$71$	1.30601i	0.154995i	−0.996993	+	0.0774975i	$0.975307\pi$
$72$	− 8.24341i	− 0.971495i
$73$	4.31232i	0.504719i	0.967634	+	0.252359i	$0.0812065\pi$
$73$	4.31232i	0.504719i	−0.967634	+	0.252359i	$0.918793\pi$
$74$	−1.83590	−0.213419
$75$	−1.44106	−0.166399
$76$	− 3.45090i	− 0.395845i
$77$	−3.51379	−0.400434
$78$	0	0
$79$	14.2264	1.60060	0.800299	−	0.599601i	$-0.204674\pi$
$79$	14.2264	1.60060	0.800299	+	0.599601i	$0.204674\pi$
$80$	− 0.912411i	− 0.102011i
$81$	8.76457	0.973841
$82$	7.08347	0.782238
$83$	− 9.81167i	− 1.07697i	−0.842635	−	0.538485i	$-0.818997\pi$
$83$	− 9.81167i	− 1.07697i	0.842635	−	0.538485i	$-0.181003\pi$
$84$	− 0.208968i	− 0.0228002i
$85$	27.7051i	3.00504i
$86$	− 10.0196i	− 1.08044i
$87$	1.18316	0.126849
$88$	9.74039	1.03833
$89$	4.77241i	0.505874i	0.967483	+	0.252937i	$0.0813966\pi$
$89$	4.77241i	0.505874i	−0.967483	+	0.252937i	$0.918603\pi$
$90$	−9.34010	−0.984533
$91$	0	0
$92$	3.22347	0.336070
$93$	0.412067i	0.0427293i
$94$	7.92602	0.817506
$95$	−9.97135	−1.02304
$96$	0.931391i	0.0950597i
$97$	− 5.92836i	− 0.601934i	−0.953635	−	0.300967i	$-0.902691\pi$
$97$	− 5.92836i	− 0.601934i	0.953635	−	0.300967i	$-0.0973094\pi$
$98$	− 0.842530i	− 0.0851084i
$99$	10.4492i	1.05018i
$100$	−11.4783	−1.14783
$101$	3.18992	0.317409	0.158705	−	0.987326i	$-0.449268\pi$
$101$	3.18992	0.317409	0.158705	+	0.987326i	$0.449268\pi$
$102$	− 1.01421i	− 0.100421i
$103$	9.80005	0.965627	0.482814	−	0.875723i	$-0.339615\pi$
$103$	9.80005	0.965627	0.482814	+	0.875723i	$0.339615\pi$
$104$	0	0
$105$	−0.603811	−0.0589259
$106$	− 4.92529i	− 0.478386i
$107$	9.03013	0.872975	0.436488	−	0.899710i	$-0.356222\pi$
$107$	9.03013	0.872975	0.436488	+	0.899710i	$0.356222\pi$
$108$	−1.24832	−0.120120
$109$	2.85038i	0.273017i	0.990639	+	0.136508i	$0.0435881\pi$
$109$	2.85038i	0.273017i	−0.990639	+	0.136508i	$0.956412\pi$
$110$	− 11.0362i	− 1.05226i
$111$	0.352943i	0.0334998i
$112$	− 0.244755i	− 0.0231271i
$113$	11.5351	1.08513	0.542566	−	0.840013i	$-0.317453\pi$
$113$	11.5351	1.08513	0.542566	+	0.840013i	$0.317453\pi$
$114$	0.365024	0.0341876
$115$	− 9.31421i	− 0.868554i
$116$	9.42414	0.875009
$117$	0	0
$118$	3.58421	0.329953
$119$	7.43189i	0.681281i
$120$	1.67379	0.152796
$121$	−1.34673	−0.122430
$122$	4.27331i	0.386887i
$123$	− 1.36176i	− 0.122786i
$124$	3.28219i	0.294749i
$125$	14.5273i	1.29936i
$126$	−2.50549	−0.223206
$127$	−0.885393	−0.0785659	−0.0392830	−	0.999228i	$-0.512507\pi$
$127$	−0.885393	−0.0785659	−0.0392830	+	0.999228i	$0.512507\pi$
$128$	7.83114i	0.692181i
$129$	−1.92623	−0.169595
$130$	0	0
$131$	13.3660	1.16779	0.583896	−	0.811829i	$-0.301528\pi$
$131$	13.3660	1.16779	0.583896	+	0.811829i	$0.301528\pi$
$132$	− 0.734269i	− 0.0639099i
$133$	−2.67482	−0.231936
$134$	1.08834	0.0940179
$135$	3.60703i	0.310443i
$136$	− 20.6015i	− 1.76657i
$137$	− 18.2881i	− 1.56246i	−0.624243	−	0.781230i	$-0.714592\pi$
$137$	− 18.2881i	− 1.56246i	0.624243	−	0.781230i	$-0.285408\pi$
$138$	0.340968i	0.0290251i
$139$	3.21091	0.272346	0.136173	−	0.990685i	$-0.456520\pi$
$139$	3.21091	0.272346	0.136173	+	0.990685i	$0.456520\pi$
$140$	−4.80947	−0.406475
$141$	− 1.52374i	− 0.128322i
$142$	−1.10035	−0.0923397
$143$	0	0
$144$	−0.727843	−0.0606536
$145$	− 27.2310i	− 2.26141i
$146$	−3.63326	−0.300691
$147$	−0.161973	−0.0133593
$148$	2.81126i	0.231084i
$149$	− 0.508593i	− 0.0416656i	−0.999783	−	0.0208328i	$-0.993368\pi$
$149$	− 0.508593i	− 0.0416656i	0.999783	−	0.0208328i	$-0.00663176\pi$
$150$	− 1.21414i	− 0.0991339i
$151$	15.4491i	1.25723i	0.777718	+	0.628614i	$0.216377\pi$
$151$	15.4491i	1.25723i	−0.777718	+	0.628614i	$0.783623\pi$
$152$	7.41472	0.601413
$153$	22.1007	1.78674
$154$	− 2.96048i	− 0.238562i
$155$	9.48387	0.761763
$156$	0	0
$157$	−8.63873	−0.689446	−0.344723	−	0.938705i	$-0.612027\pi$
$157$	−8.63873	−0.689446	−0.344723	+	0.938705i	$0.612027\pi$
$158$	11.9862i	0.953570i
$159$	−0.946864	−0.0750912
$160$	21.4363	1.69469
$161$	− 2.49854i	− 0.196913i
$162$	7.38442i	0.580175i
$163$	− 4.33684i	− 0.339688i	−0.985471	−	0.169844i	$-0.945674\pi$
$163$	− 4.33684i	− 0.339688i	0.985471	−	0.169844i	$-0.0543263\pi$
$164$	− 10.8467i	− 0.846986i
$165$	−2.12167	−0.165172
$166$	8.26663	0.641615
$167$	− 11.0384i	− 0.854173i	−0.904211	−	0.427087i	$-0.859540\pi$
$167$	− 11.0384i	− 0.854173i	0.904211	−	0.427087i	$-0.140460\pi$
$168$	0.448995	0.0346407
$169$	0	0
$170$	−23.3423	−1.79028
$171$	7.95428i	0.608279i
$172$	−15.3428	−1.16988
$173$	10.3380	0.785987	0.392994	−	0.919541i	$-0.371439\pi$
$173$	10.3380	0.785987	0.392994	+	0.919541i	$0.371439\pi$
$174$	0.996852i	0.0755712i
$175$	8.89694i	0.672546i
$176$	− 0.860017i	− 0.0648262i
$177$	− 0.689047i	− 0.0517920i
$178$	−4.02090	−0.301379
$179$	−18.0134	−1.34639	−0.673194	−	0.739466i	$-0.735078\pi$
$179$	−18.0134	−1.34639	−0.673194	+	0.739466i	$0.735078\pi$
$180$	14.3022i	1.06603i
$181$	21.3187	1.58460	0.792302	−	0.610129i	$-0.208882\pi$
$181$	21.3187	1.58460	0.792302	+	0.610129i	$0.208882\pi$
$182$	0	0
$183$	0.821524	0.0607288
$184$	6.92606i	0.510596i
$185$	8.12311	0.597223
$186$	−0.347178	−0.0254564
$187$	26.1141i	1.90965i
$188$	− 12.1369i	− 0.885174i
$189$	0.967586i	0.0703815i
$190$	− 8.40117i	− 0.609485i
$191$	5.90224	0.427071	0.213535	−	0.976935i	$-0.431502\pi$
$191$	5.90224	0.427071	0.213535	+	0.976935i	$0.431502\pi$
$192$	−0.705438	−0.0509106
$193$	3.24842i	0.233827i	0.993142	+	0.116913i	$0.0373000\pi$
$193$	3.24842i	0.233827i	−0.993142	+	0.116913i	$0.962700\pi$
$194$	4.99483	0.358608
$195$	0	0
$196$	−1.29014	−0.0921531
$197$	8.99244i	0.640685i	0.947302	+	0.320342i	$0.103798\pi$
$197$	8.99244i	0.640685i	−0.947302	+	0.320342i	$0.896202\pi$
$198$	−8.80376	−0.625656
$199$	−5.58657	−0.396021	−0.198011	−	0.980200i	$-0.563448\pi$
$199$	−5.58657	−0.396021	−0.198011	+	0.980200i	$0.563448\pi$
$200$	− 24.6627i	− 1.74392i
$201$	− 0.209228i	− 0.0147578i
$202$	2.68761i	0.189099i
$203$	− 7.30473i	− 0.512691i
$204$	−1.55303	−0.108734
$205$	−31.3415	−2.18899
$206$	8.25684i	0.575281i
$207$	−7.43007	−0.516426
$208$	0	0
$209$	−9.39876	−0.650126
$210$	− 0.508729i	− 0.0351056i
$211$	−19.2145	−1.32278	−0.661391	−	0.750041i	$-0.730034\pi$
$211$	−19.2145	−1.32278	−0.661391	+	0.750041i	$0.730034\pi$
$212$	−7.54195	−0.517984
$213$	0.211538i	0.0144943i
$214$	7.60815i	0.520083i
$215$	44.3329i	3.02348i
$216$	− 2.68219i	− 0.182500i
$217$	2.54405	0.172701
$218$	−2.40153	−0.162652
$219$	0.698478i	0.0471987i
$220$	−16.8995	−1.13936
$221$	0	0
$222$	−0.297365	−0.0199578
$223$	13.3068i	0.891089i	0.895260	+	0.445545i	$0.146990\pi$
$223$	13.3068i	0.891089i	−0.895260	+	0.445545i	$0.853010\pi$
$224$	5.75030	0.384208
$225$	26.4574	1.76383
$226$	9.71868i	0.646477i
$227$	13.3532i	0.886286i	0.896451	+	0.443143i	$0.146137\pi$
$227$	13.3532i	0.886286i	−0.896451	+	0.443143i	$0.853863\pi$
$228$	− 0.558951i	− 0.0370174i
$229$	10.5744i	0.698773i	0.936979	+	0.349387i	$0.113610\pi$
$229$	10.5744i	0.698773i	−0.936979	+	0.349387i	$0.886390\pi$
$230$	7.84750	0.517449
$231$	−0.569138	−0.0374465
$232$	20.2490i	1.32941i
$233$	−5.25696	−0.344395	−0.172197	−	0.985062i	$-0.555087\pi$
$233$	−5.25696	−0.344395	−0.172197	+	0.985062i	$0.555087\pi$
$234$	0	0
$235$	−35.0695	−2.28768
$236$	− 5.48840i	− 0.357264i
$237$	2.30429	0.149680
$238$	−6.26159	−0.405879
$239$	20.0403i	1.29630i	0.761513	+	0.648149i	$0.224457\pi$
$239$	20.0403i	1.29630i	−0.761513	+	0.648149i	$0.775543\pi$
$240$	− 0.147786i	− 0.00953952i
$241$	− 23.3489i	− 1.50403i	−0.659144	−	0.752017i	$-0.729081\pi$
$241$	− 23.3489i	− 1.50403i	0.659144	−	0.752017i	$-0.270919\pi$
$242$	− 1.13466i	− 0.0729390i
$243$	4.32238	0.277281
$244$	6.54360	0.418911
$245$	3.72786i	0.238164i
$246$	1.14733	0.0731509
$247$	0	0
$248$	−7.05223	−0.447817
$249$	− 1.58922i	− 0.100713i
$250$	−12.2397	−0.774104
$251$	−14.4261	−0.910570	−0.455285	−	0.890346i	$-0.650463\pi$
$251$	−14.4261	−0.910570	−0.455285	+	0.890346i	$0.650463\pi$
$252$	3.83658i	0.241682i
$253$	− 8.77935i	− 0.551953i
$254$	− 0.745970i	− 0.0468063i
$255$	4.48746i	0.281016i
$256$	−15.3086	−0.956785
$257$	−13.0464	−0.813810	−0.406905	−	0.913471i	$-0.633392\pi$
$257$	−13.0464	−0.813810	−0.406905	+	0.913471i	$0.633392\pi$
$258$	− 1.62291i	− 0.101038i
$259$	2.17903	0.135398
$260$	0	0
$261$	−21.7225	−1.34459
$262$	11.2612i	0.695722i
$263$	16.7189	1.03093	0.515464	−	0.856911i	$-0.327619\pi$
$263$	16.7189	1.03093	0.515464	+	0.856911i	$0.327619\pi$
$264$	1.57768	0.0970992
$265$	21.7924i	1.33870i
$266$	− 2.25362i	− 0.138178i
$267$	0.772999i	0.0473068i
$268$	− 1.66654i	− 0.101800i
$269$	6.17733	0.376639	0.188319	−	0.982108i	$-0.439696\pi$
$269$	6.17733	0.376639	0.188319	+	0.982108i	$0.439696\pi$
$270$	−3.03903	−0.184949
$271$	− 30.1026i	− 1.82860i	−0.405036	−	0.914301i	$-0.632741\pi$
$271$	− 30.1026i	− 1.82860i	0.405036	−	0.914301i	$-0.367259\pi$
$272$	−1.81899	−0.110292
$273$	0	0
$274$	15.4083	0.930850
$275$	31.2620i	1.88517i
$276$	0.522114	0.0314276
$277$	6.01177	0.361212	0.180606	−	0.983556i	$-0.442194\pi$
$277$	6.01177	0.361212	0.180606	+	0.983556i	$0.442194\pi$
$278$	2.70529i	0.162252i
$279$	− 7.56541i	− 0.452929i
$280$	− 10.3338i	− 0.617562i
$281$	− 26.4812i	− 1.57974i	−0.613277	−	0.789868i	$-0.710149\pi$
$281$	− 26.4812i	− 1.57974i	0.613277	−	0.789868i	$-0.289851\pi$
$282$	1.28380	0.0764490
$283$	0.200682	0.0119293	0.00596465	−	0.999982i	$-0.498101\pi$
$283$	0.200682	0.0119293	0.00596465	+	0.999982i	$0.498101\pi$
$284$	1.68494i	0.0999829i
$285$	−1.61509	−0.0956694
$286$	0	0
$287$	−8.40738	−0.496272
$288$	− 17.1000i	− 1.00763i
$289$	38.2330	2.24900
$290$	22.9429	1.34726
$291$	− 0.960232i	− 0.0562898i
$292$	5.56351i	0.325580i
$293$	1.96008i	0.114509i	0.998360	+	0.0572544i	$0.0182346\pi$
$293$	1.96008i	0.114509i	−0.998360	+	0.0572544i	$0.981765\pi$
$294$	− 0.136467i	− 0.00795890i
$295$	−15.8587	−0.923328
$296$	−6.04036	−0.351089
$297$	3.39990i	0.197282i
$298$	0.428505	0.0248226
$299$	0	0
$300$	−1.85917	−0.107339
$301$	11.8923i	0.685462i
$302$	−13.0163	−0.749004
$303$	0.516680	0.0296825
$304$	− 0.654674i	− 0.0375482i
$305$	− 18.9077i	− 1.08265i
$306$	18.6205i	1.06446i
$307$	25.1368i	1.43463i	0.696747	+	0.717317i	$0.254630\pi$
$307$	25.1368i	1.43463i	−0.696747	+	0.717317i	$0.745370\pi$
$308$	−4.53329	−0.258308
$309$	1.58734	0.0903005
$310$	7.99045i	0.453827i
$311$	29.5322	1.67462	0.837308	−	0.546731i	$-0.184128\pi$
$311$	29.5322	1.67462	0.837308	+	0.546731i	$0.184128\pi$
$312$	0	0
$313$	6.68905	0.378087	0.189044	−	0.981969i	$-0.439461\pi$
$313$	6.68905	0.378087	0.189044	+	0.981969i	$0.439461\pi$
$314$	− 7.27839i	− 0.410743i
$315$	11.0858	0.624613
$316$	18.3541	1.03250
$317$	− 20.6867i	− 1.16188i	−0.813946	−	0.580941i	$-0.802685\pi$
$317$	− 20.6867i	− 1.16188i	0.813946	−	0.580941i	$-0.197315\pi$
$318$	− 0.797761i	− 0.0447362i
$319$	− 25.6673i	− 1.43709i
$320$	16.2359i	0.907616i
$321$	1.46263	0.0816362
$322$	2.10510	0.117312
$323$	19.8790i	1.10610i
$324$	11.3076	0.628197
$325$	0	0
$326$	3.65392	0.202372
$327$	0.461683i	0.0255311i
$328$	23.3056	1.28684
$329$	−9.40740	−0.518647
$330$	− 1.78757i	− 0.0984024i
$331$	35.4014i	1.94584i	0.231149	+	0.972918i	$0.425752\pi$
$331$	35.4014i	1.94584i	−0.231149	+	0.972918i	$0.574248\pi$
$332$	− 12.6585i	− 0.694723i
$333$	− 6.47992i	− 0.355097i
$334$	9.30014	0.508881
$335$	−4.81545	−0.263096
$336$	− 0.0396435i	− 0.00216273i
$337$	6.69897	0.364916	0.182458	−	0.983214i	$-0.441595\pi$
$337$	6.69897	0.364916	0.182458	+	0.983214i	$0.441595\pi$
$338$	0	0
$339$	1.86837	0.101476
$340$	35.7435i	1.93846i
$341$	8.93927	0.484089
$342$	−6.70172	−0.362388
$343$	1.00000i	0.0539949i
$344$	− 32.9660i	− 1.77741i
$345$	− 1.50865i	− 0.0812228i
$346$	8.71012i	0.468259i
$347$	−7.38059	−0.396211	−0.198105	−	0.980181i	$-0.563479\pi$
$347$	−7.38059	−0.396211	−0.198105	+	0.980181i	$0.563479\pi$
$348$	1.52645	0.0818264
$349$	15.2129i	0.814326i	0.913355	+	0.407163i	$0.133482\pi$
$349$	15.2129i	0.814326i	−0.913355	+	0.407163i	$0.866518\pi$
$350$	−7.49594	−0.400675
$351$	0	0
$352$	20.2054	1.07695
$353$	12.5476i	0.667843i	0.942601	+	0.333921i	$0.108372\pi$
$353$	12.5476i	0.667843i	−0.942601	+	0.333921i	$0.891628\pi$
$354$	0.580543	0.0308555
$355$	4.86863	0.258400
$356$	6.15709i	0.326325i
$357$	1.20376i	0.0637099i
$358$	− 15.1769i	− 0.802123i
$359$	17.8460i	0.941877i	0.882166	+	0.470939i	$0.156085\pi$
$359$	17.8460i	0.941877i	−0.882166	+	0.470939i	$0.843915\pi$
$360$	−30.7303	−1.61963
$361$	11.8453	0.623439
$362$	17.9616i	0.944042i
$363$	−0.218134	−0.0114491
$364$	0	0
$365$	16.0757	0.841442
$366$	0.692159i	0.0361797i
$367$	−30.9271	−1.61438	−0.807190	−	0.590291i	$-0.799013\pi$
$367$	−30.9271	−1.61438	−0.807190	+	0.590291i	$0.799013\pi$
$368$	0.611529	0.0318782
$369$	25.0016i	1.30153i
$370$	6.84397i	0.355801i
$371$	5.84583i	0.303500i
$372$	0.531625i	0.0275635i
$373$	−28.6520	−1.48354	−0.741772	−	0.670652i	$-0.766014\pi$
$373$	−28.6520	−1.48354	−0.741772	+	0.670652i	$0.766014\pi$
$374$	−22.0019	−1.13769
$375$	2.35302i	0.121509i
$376$	26.0777	1.34486
$377$	0	0
$378$	−0.815220	−0.0419304
$379$	− 4.61700i	− 0.237159i	−0.992945	−	0.118580i	$-0.962166\pi$
$379$	− 4.61700i	− 0.237159i	0.992945	−	0.118580i	$-0.0378341\pi$
$380$	−12.8645	−0.659933
$381$	−0.143409	−0.00734708
$382$	4.97281i	0.254431i
$383$	− 27.7969i	− 1.42036i	−0.704022	−	0.710178i	$-0.748614\pi$
$383$	− 27.7969i	− 1.42036i	0.704022	−	0.710178i	$-0.251386\pi$
$384$	1.26843i	0.0647293i
$385$	13.0989i	0.667583i
$386$	−2.73689	−0.139304
$387$	35.3649	1.79770
$388$	− 7.64844i	− 0.388291i
$389$	−16.8702	−0.855352	−0.427676	−	0.903932i	$-0.640668\pi$
$389$	−16.8702	−0.855352	−0.427676	+	0.903932i	$0.640668\pi$
$390$	0	0
$391$	−18.5689	−0.939069
$392$	− 2.77204i	− 0.140009i
$393$	2.16492	0.109206
$394$	−7.57640	−0.381694
$395$	− 53.0341i	− 2.66844i
$396$	13.4810i	0.677443i
$397$	24.2776i	1.21846i	0.792995	+	0.609228i	$0.208521\pi$
$397$	24.2776i	1.21846i	−0.792995	+	0.609228i	$0.791479\pi$
$398$	− 4.70685i	− 0.235933i
$399$	−0.433247	−0.0216895
$400$	−2.17757	−0.108878
$401$	− 24.0304i	− 1.20002i	−0.799992	−	0.600010i	$-0.795163\pi$
$401$	− 24.0304i	− 1.20002i	0.799992	−	0.600010i	$-0.204837\pi$
$402$	0.176281	0.00879207
$403$	0	0
$404$	4.11546	0.204752
$405$	− 32.6731i	− 1.62354i
$406$	6.15445	0.305440
$407$	7.65665	0.379526
$408$	− 3.33688i	− 0.165200i
$409$	2.04813i	0.101274i	0.998717	+	0.0506368i	$0.0161251\pi$
$409$	2.04813i	0.101274i	−0.998717	+	0.0506368i	$0.983875\pi$
$410$	− 26.4062i	− 1.30411i
$411$	− 2.96218i	− 0.146113i
$412$	12.6435	0.622899
$413$	−4.25410	−0.209331
$414$	− 6.26006i	− 0.307665i
$415$	−36.5765	−1.79547
$416$	0	0
$417$	0.520079	0.0254684
$418$	− 7.91874i	− 0.387318i
$419$	−25.9332	−1.26692	−0.633461	−	0.773775i	$-0.718366\pi$
$419$	−25.9332	−1.26692	−0.633461	+	0.773775i	$0.718366\pi$
$420$	−0.779003	−0.0380114
$421$	− 22.5137i	− 1.09725i	−0.836068	−	0.548626i	$-0.815151\pi$
$421$	− 22.5137i	− 1.09725i	0.836068	−	0.548626i	$-0.184849\pi$
$422$	− 16.1888i	− 0.788059i
$423$	27.9754i	1.36021i
$424$	− 16.2049i	− 0.786979i
$425$	66.1211	3.20735
$426$	−0.178227	−0.00863514
$427$	− 5.07200i	− 0.245451i
$428$	11.6502	0.563131
$429$	0	0
$430$	−37.3518	−1.80126
$431$	2.78073i	0.133943i	0.997755	+	0.0669716i	$0.0213337\pi$
$431$	2.78073i	0.133943i	−0.997755	+	0.0669716i	$0.978666\pi$
$432$	−0.236821	−0.0113941
$433$	−25.5607	−1.22837	−0.614186	−	0.789162i	$-0.710515\pi$
$433$	−25.5607	−1.22837	−0.614186	+	0.789162i	$0.710515\pi$
$434$	2.14344i	0.102888i
$435$	− 4.41067i	− 0.211476i
$436$	3.67740i	0.176115i
$437$	− 6.68314i	− 0.319698i
$438$	−0.588488	−0.0281191
$439$	31.6821	1.51210	0.756052	−	0.654512i	$-0.227126\pi$
$439$	31.6821	1.51210	0.756052	+	0.654512i	$0.227126\pi$
$440$	− 36.3108i	− 1.73105i
$441$	2.97376	0.141608
$442$	0	0
$443$	−17.1943	−0.816928	−0.408464	−	0.912774i	$-0.633935\pi$
$443$	−17.1943	−0.816928	−0.408464	+	0.912774i	$0.633935\pi$
$444$	0.455346i	0.0216098i
$445$	17.7909	0.843368
$446$	−11.2114	−0.530874
$447$	− 0.0823781i	− 0.00389635i
$448$	4.35529i	0.205768i
$449$	− 14.3503i	− 0.677230i	−0.940925	−	0.338615i	$-0.890042\pi$
$449$	− 14.3503i	− 0.677230i	0.940925	−	0.338615i	$-0.109958\pi$
$450$	22.2912i	1.05082i
$451$	−29.5418	−1.39107
$452$	14.8819	0.699988
$453$	2.50232i	0.117569i
$454$	−11.2505	−0.528013
$455$	0	0
$456$	1.20098	0.0562411
$457$	15.0888i	0.705822i	0.935657	+	0.352911i	$0.114808\pi$
$457$	15.0888i	0.705822i	−0.935657	+	0.352911i	$0.885192\pi$
$458$	−8.90921	−0.416300
$459$	7.19100	0.335647
$460$	− 12.0167i	− 0.560280i
$461$	15.8856i	0.739868i	0.929058	+	0.369934i	$0.120620\pi$
$461$	15.8856i	0.739868i	−0.929058	+	0.369934i	$0.879380\pi$
$462$	− 0.479516i	− 0.0223091i
$463$	− 7.03356i	− 0.326877i	−0.986553	−	0.163439i	$-0.947741\pi$
$463$	− 7.03356i	− 0.326877i	0.986553	−	0.163439i	$-0.0522586\pi$
$464$	1.78787	0.0829996
$465$	1.53613	0.0712362
$466$	− 4.42915i	− 0.205176i
$467$	0.621410	0.0287554	0.0143777	−	0.999897i	$-0.495423\pi$
$467$	0.621410	0.0287554	0.0143777	+	0.999897i	$0.495423\pi$
$468$	0	0
$469$	−1.29175	−0.0596473
$470$	− 29.5471i	− 1.36291i
$471$	−1.39924	−0.0644734
$472$	11.7926	0.542796
$473$	41.7871i	1.92137i
$474$	1.94143i	0.0891730i
$475$	23.7977i	1.09191i
$476$	9.58820i	0.439475i
$477$	17.3841	0.795964
$478$	−16.8846	−0.772281
$479$	24.6401i	1.12584i	0.826512	+	0.562919i	$0.190322\pi$
$479$	24.6401i	1.12584i	−0.826512	+	0.562919i	$0.809678\pi$
$480$	3.47210	0.158479
$481$	0	0
$482$	19.6721	0.896041
$483$	− 0.404695i	− 0.0184143i
$484$	−1.73748	−0.0789764
$485$	−22.1001	−1.00351
$486$	3.64173i	0.165192i
$487$	20.8751i	0.945941i	0.881078	+	0.472971i	$0.156818\pi$
$487$	20.8751i	0.945941i	−0.881078	+	0.472971i	$0.843182\pi$
$488$	14.0598i	0.636457i
$489$	− 0.702449i	− 0.0317659i
$490$	−3.14083	−0.141888
$491$	2.48344	0.112076	0.0560380	−	0.998429i	$-0.482153\pi$
$491$	2.48344	0.112076	0.0560380	+	0.998429i	$0.482153\pi$
$492$	− 1.75687i	− 0.0792058i
$493$	−54.2879	−2.44501
$494$	0	0
$495$	38.9531	1.75081
$496$	0.622668i	0.0279586i
$497$	1.30601	0.0585826
$498$	1.33897	0.0600005
$499$	0.427604i	0.0191422i	0.999954	+	0.00957109i	$0.00304662\pi$
$499$	0.427604i	0.0191422i	−0.999954	+	0.00957109i	$0.996953\pi$
$500$	18.7422i	0.838178i
$501$	− 1.78791i	− 0.0798779i
$502$	− 12.1545i	− 0.542480i
$503$	36.2684	1.61713	0.808565	−	0.588407i	$-0.200245\pi$
$503$	36.2684	1.61713	0.808565	+	0.588407i	$0.200245\pi$
$504$	−8.24341	−0.367191
$505$	− 11.8916i	− 0.529169i
$506$	7.39687	0.328831
$507$	0	0
$508$	−1.14228	−0.0506806
$509$	− 16.9910i	− 0.753113i	−0.926394	−	0.376557i	$-0.877108\pi$
$509$	− 16.9910i	− 0.753113i	0.926394	−	0.376557i	$-0.122892\pi$
$510$	−3.78082	−0.167418
$511$	4.31232	0.190766
$512$	2.76435i	0.122168i
$513$	2.58812i	0.114268i
$514$	− 10.9920i	− 0.484834i
$515$	− 36.5332i	− 1.60985i
$516$	−2.48511	−0.109401
$517$	−33.0556	−1.45379
$518$	1.83590i	0.0806647i
$519$	1.67448	0.0735015
$520$	0	0
$521$	16.3640	0.716920	0.358460	−	0.933545i	$-0.383302\pi$
$521$	16.3640	0.716920	0.358460	+	0.933545i	$0.383302\pi$
$522$	− 18.3019i	− 0.801052i
$523$	−12.5863	−0.550359	−0.275180	−	0.961393i	$-0.588737\pi$
$523$	−12.5863	−0.550359	−0.275180	+	0.961393i	$0.588737\pi$
$524$	17.2440	0.753309
$525$	1.44106i	0.0628930i
$526$	14.0861i	0.614185i
$527$	− 18.9071i	− 0.823607i
$528$	− 0.139299i	− 0.00606222i
$529$	−16.7573	−0.728578
$530$	−18.3608	−0.797541
$531$	12.6507i	0.548993i
$532$	−3.45090	−0.149615
$533$	0	0
$534$	−0.651275	−0.0281834
$535$	− 33.6631i	− 1.45538i
$536$	3.58078	0.154666
$537$	−2.91768	−0.125907
$538$	5.20459i	0.224386i
$539$	3.51379i	0.151350i
$540$	4.65358i	0.200258i
$541$	− 44.7256i	− 1.92290i	−0.274974	−	0.961452i	$-0.588669\pi$
$541$	− 44.7256i	− 1.92290i	0.274974	−	0.961452i	$-0.411331\pi$
$542$	25.3623	1.08941
$543$	3.45304	0.148184
$544$	− 42.7356i	− 1.83228i
$545$	10.6258	0.455160
$546$	0	0
$547$	23.5754	1.00801	0.504006	−	0.863700i	$-0.331859\pi$
$547$	23.5754	1.00801	0.504006	+	0.863700i	$0.331859\pi$
$548$	− 23.5943i	− 1.00790i
$549$	−15.0829	−0.643724
$550$	−26.3392	−1.12311
$551$	− 19.5388i	− 0.832382i
$552$	1.12183i	0.0477484i
$553$	− 14.2264i	− 0.604969i
$554$	5.06510i	0.215195i
$555$	1.31572	0.0558492
$556$	4.14253	0.175682
$557$	− 19.5362i	− 0.827774i	−0.910328	−	0.413887i	$-0.864171\pi$
$557$	− 19.5362i	− 0.827774i	0.910328	−	0.413887i	$-0.135829\pi$
$558$	6.37409	0.269837
$559$	0	0
$560$	−0.912411	−0.0385564
$561$	4.22977i	0.178581i
$562$	22.3112	0.941142
$563$	−26.1631	−1.10264	−0.551322	−	0.834293i	$-0.685876\pi$
$563$	−26.1631	−1.10264	−0.551322	+	0.834293i	$0.685876\pi$
$564$	− 1.96584i	− 0.0827769i
$565$	− 43.0013i	− 1.80908i
$566$	0.169081i	0.00710698i
$567$	− 8.76457i	− 0.368077i
$568$	−3.62032	−0.151905
$569$	13.5349	0.567412	0.283706	−	0.958911i	$-0.408436\pi$
$569$	13.5349	0.567412	0.283706	+	0.958911i	$0.408436\pi$
$570$	− 1.36076i	− 0.0569959i
$571$	8.45496	0.353829	0.176914	−	0.984226i	$-0.443388\pi$
$571$	8.45496	0.353829	0.176914	+	0.984226i	$0.443388\pi$
$572$	0	0
$573$	0.956001	0.0399375
$574$	− 7.08347i	− 0.295658i
$575$	−22.2294	−0.927029
$576$	12.9516	0.539651
$577$	16.9054i	0.703780i	0.936041	+	0.351890i	$0.114461\pi$
$577$	16.9054i	0.703780i	−0.936041	+	0.351890i	$0.885539\pi$
$578$	32.2125i	1.33986i
$579$	0.526155i	0.0218663i
$580$	− 35.1319i	− 1.45877i
$581$	−9.81167	−0.407057
$582$	0.809025	0.0335351
$583$	20.5410i	0.850722i
$584$	−11.9539	−0.494658
$585$	0	0
$586$	−1.65142	−0.0682197
$587$	10.2055i	0.421227i	0.977569	+	0.210613i	$0.0675461\pi$
$587$	10.2055i	0.421227i	−0.977569	+	0.210613i	$0.932454\pi$
$588$	−0.208968	−0.00861768
$589$	6.80488	0.280390
$590$	− 13.3614i	− 0.550081i
$591$	1.45653i	0.0599136i
$592$	0.533327i	0.0219196i
$593$	3.79490i	0.155838i	0.996960	+	0.0779190i	$0.0248275\pi$
$593$	3.79490i	0.155838i	−0.996960	+	0.0779190i	$0.975172\pi$
$594$	−2.86451	−0.117532
$595$	27.7051	1.13580
$596$	− 0.656158i	− 0.0268773i
$597$	−0.904871	−0.0370339
$598$	0	0
$599$	14.8629	0.607281	0.303640	−	0.952787i	$-0.401798\pi$
$599$	14.8629	0.607281	0.303640	+	0.952787i	$0.401798\pi$
$600$	− 3.99468i	− 0.163082i
$601$	6.70162	0.273365	0.136682	−	0.990615i	$-0.456356\pi$
$601$	6.70162	0.273365	0.136682	+	0.990615i	$0.456356\pi$
$602$	−10.0196	−0.408370
$603$	3.84135i	0.156432i
$604$	19.9315i	0.811001i
$605$	5.02044i	0.204110i
$606$	0.435319i	0.0176836i
$607$	0.0721187	0.00292721	0.00146360	−	0.999999i	$-0.499534\pi$
$607$	0.0721187	0.00292721	0.00146360	+	0.999999i	$0.499534\pi$
$608$	15.3810	0.623783
$609$	− 1.18316i	− 0.0479443i
$610$	15.9303	0.644999
$611$	0	0
$612$	28.5131	1.15257
$613$	− 3.55353i	− 0.143526i	−0.997422	−	0.0717628i	$-0.977138\pi$
$613$	− 3.55353i	− 0.143526i	0.997422	−	0.0717628i	$-0.0228625\pi$
$614$	−21.1785	−0.854695
$615$	−5.07647	−0.204703
$616$	− 9.74039i	− 0.392451i
$617$	− 33.1215i	− 1.33342i	−0.745316	−	0.666711i	$-0.767701\pi$
$617$	− 33.1215i	− 1.33342i	0.745316	−	0.666711i	$-0.232299\pi$
$618$	1.33738i	0.0537973i
$619$	3.55028i	0.142698i	0.997451	+	0.0713489i	$0.0227304\pi$
$619$	3.55028i	0.142698i	−0.997451	+	0.0713489i	$0.977270\pi$
$620$	12.2355	0.491391
$621$	−2.41755	−0.0970130
$622$	24.8817i	0.997667i
$623$	4.77241	0.191202
$624$	0	0
$625$	9.67087	0.386835
$626$	5.63572i	0.225249i
$627$	−1.52234	−0.0607964
$628$	−11.1452	−0.444742
$629$	− 16.1943i	− 0.645709i
$630$	9.34010i	0.372119i
$631$	27.9899i	1.11426i	0.830425	+	0.557131i	$0.188098\pi$
$631$	27.9899i	1.11426i	−0.830425	+	0.557131i	$0.811902\pi$
$632$	39.4363i	1.56869i
$633$	−3.11222	−0.123700
$634$	17.4292	0.692201
$635$	3.30062i	0.130981i
$636$	−1.22159	−0.0484392
$637$	0	0
$638$	21.6255	0.856160
$639$	− 3.88377i	− 0.153640i
$640$	29.1934	1.15397
$641$	−9.33085	−0.368547	−0.184273	−	0.982875i	$-0.558993\pi$
$641$	−9.33085	−0.368547	−0.184273	+	0.982875i	$0.558993\pi$
$642$	1.23231i	0.0486355i
$643$	7.22132i	0.284781i	0.989811	+	0.142390i	$0.0454789\pi$
$643$	7.22132i	0.284781i	−0.989811	+	0.142390i	$0.954521\pi$
$644$	− 3.22347i	− 0.127023i
$645$	7.18071i	0.282740i
$646$	−16.7486	−0.658966
$647$	7.65676	0.301018	0.150509	−	0.988609i	$-0.451909\pi$
$647$	7.65676	0.301018	0.150509	+	0.988609i	$0.451909\pi$
$648$	24.2958i	0.954429i
$649$	−14.9480	−0.586761
$650$	0	0
$651$	0.412067	0.0161502
$652$	− 5.59515i	− 0.219123i
$653$	−11.6265	−0.454979	−0.227490	−	0.973780i	$-0.573052\pi$
$653$	−11.6265	−0.454979	−0.227490	+	0.973780i	$0.573052\pi$
$654$	−0.388982	−0.0152104
$655$	− 49.8265i	− 1.94688i
$656$	− 2.05774i	− 0.0803414i
$657$	− 12.8238i	− 0.500305i
$658$	− 7.92602i	− 0.308988i
$659$	42.8815	1.67043	0.835213	−	0.549927i	$-0.185344\pi$
$659$	42.8815	1.67043	0.835213	+	0.549927i	$0.185344\pi$
$660$	−2.73725	−0.106547
$661$	− 41.0681i	− 1.59736i	−0.601753	−	0.798682i	$-0.705531\pi$
$661$	− 41.0681i	− 1.59736i	0.601753	−	0.798682i	$-0.294469\pi$
$662$	−29.8267	−1.15925
$663$	0	0
$664$	27.1984	1.05550
$665$	9.97135i	0.386672i
$666$	5.45952	0.211552
$667$	18.2512	0.706687
$668$	− 14.2410i	− 0.551003i
$669$	2.15534i	0.0833301i
$670$	− 4.05716i	− 0.156742i
$671$	− 17.8219i	− 0.688009i
$672$	0.931391	0.0359292
$673$	33.2669	1.28234	0.641172	−	0.767397i	$-0.278449\pi$
$673$	33.2669	1.28234	0.641172	+	0.767397i	$0.278449\pi$
$674$	5.64408i	0.217402i
$675$	8.60856	0.331343
$676$	0	0
$677$	36.6928	1.41022	0.705110	−	0.709098i	$-0.250898\pi$
$677$	36.6928	1.41022	0.705110	+	0.709098i	$0.250898\pi$
$678$	1.57416i	0.0604552i
$679$	−5.92836	−0.227510
$680$	−76.7997	−2.94513
$681$	2.16286i	0.0828810i
$682$	7.53160i	0.288400i
$683$	19.0493i	0.728903i	0.931222	+	0.364451i	$0.118743\pi$
$683$	19.0493i	0.728903i	−0.931222	+	0.364451i	$0.881257\pi$
$684$	10.2622i	0.392384i
$685$	−68.1756	−2.60486
$686$	−0.842530	−0.0321680
$687$	1.71276i	0.0653457i
$688$	−2.91070	−0.110969
$689$	0	0
$690$	1.27108	0.0483892
$691$	− 30.5436i	− 1.16193i	−0.813927	−	0.580967i	$-0.802674\pi$
$691$	− 30.5436i	− 1.16193i	0.813927	−	0.580967i	$-0.197326\pi$
$692$	13.3376	0.507018
$693$	10.4492	0.396932
$694$	− 6.21837i	− 0.236046i
$695$	− 11.9698i	− 0.454041i
$696$	3.27979i	0.124320i
$697$	62.4827i	2.36670i
$698$	−12.8173	−0.485142
$699$	−0.851483	−0.0322060
$700$	11.4783i	0.433840i
$701$	−8.37561	−0.316343	−0.158171	−	0.987412i	$-0.550560\pi$
$701$	−8.37561	−0.316343	−0.158171	+	0.987412i	$0.550560\pi$
$702$	0	0
$703$	5.82850	0.219826
$704$	15.3036i	0.576776i
$705$	−5.68029	−0.213932
$706$	−10.5718	−0.397873
$707$	− 3.18992i	− 0.119969i
$708$	− 0.888969i	− 0.0334095i
$709$	8.96509i	0.336691i	0.985728	+	0.168345i	$0.0538424\pi$
$709$	8.96509i	0.336691i	−0.985728	+	0.168345i	$0.946158\pi$
$710$	4.10197i	0.153944i
$711$	−42.3061	−1.58660
$712$	−13.2293	−0.495790
$713$	6.35642i	0.238050i
$714$	−1.01421	−0.0379557
$715$	0	0
$716$	−23.2399	−0.868517
$717$	3.24598i	0.121223i
$718$	−15.0358	−0.561132
$719$	14.3101	0.533678	0.266839	−	0.963741i	$-0.414021\pi$
$719$	14.3101	0.533678	0.266839	+	0.963741i	$0.414021\pi$
$720$	2.71330i	0.101119i
$721$	− 9.80005i	− 0.364973i
$722$	9.98006i	0.371419i
$723$	− 3.78188i	− 0.140650i
$724$	27.5041	1.02218
$725$	−64.9897	−2.41366
$726$	− 0.183784i	− 0.00682088i
$727$	19.0723	0.707354	0.353677	−	0.935368i	$-0.384931\pi$
$727$	19.0723	0.707354	0.353677	+	0.935368i	$0.384931\pi$
$728$	0	0
$729$	−25.5936	−0.947911
$730$	13.5443i	0.501297i
$731$	88.3824	3.26894
$732$	1.05988	0.0391744
$733$	− 26.7063i	− 0.986418i	−0.869911	−	0.493209i	$-0.835824\pi$
$733$	− 26.7063i	− 0.986418i	0.869911	−	0.493209i	$-0.164176\pi$
$734$	− 26.0570i	− 0.961782i
$735$	0.603811i	0.0222719i
$736$	14.3674i	0.529588i
$737$	−4.53893	−0.167194
$738$	−21.0646	−0.775397
$739$	27.5346i	1.01288i	0.862276	+	0.506438i	$0.169038\pi$
$739$	27.5346i	1.01288i	−0.862276	+	0.506438i	$0.830962\pi$
$740$	10.4800	0.385251
$741$	0	0
$742$	−4.92529	−0.180813
$743$	28.8668i	1.05902i	0.848304	+	0.529510i	$0.177624\pi$
$743$	28.8668i	1.05902i	−0.848304	+	0.529510i	$0.822376\pi$
$744$	−1.14227	−0.0418775
$745$	−1.89596	−0.0694628
$746$	− 24.1402i	− 0.883835i
$747$	29.1776i	1.06755i
$748$	33.6910i	1.23186i
$749$	− 9.03013i	− 0.329954i
$750$	−1.98249	−0.0723902
$751$	−6.62174	−0.241631	−0.120815	−	0.992675i	$-0.538551\pi$
$751$	−6.62174	−0.241631	−0.120815	+	0.992675i	$0.538551\pi$
$752$	− 2.30250i	− 0.0839637i
$753$	−2.33664	−0.0851519
$754$	0	0
$755$	57.5920	2.09599
$756$	1.24832i	0.0454011i
$757$	35.9013	1.30485	0.652427	−	0.757852i	$-0.273751\pi$
$757$	35.9013	1.30485	0.652427	+	0.757852i	$0.273751\pi$
$758$	3.88996	0.141290
$759$	− 1.42201i	− 0.0516158i
$760$	− 27.6410i	− 1.00265i
$761$	− 27.2881i	− 0.989191i	−0.869123	−	0.494596i	$-0.835316\pi$
$761$	− 27.2881i	− 0.989191i	0.869123	−	0.494596i	$-0.164684\pi$
$762$	− 0.120827i	− 0.00437709i
$763$	2.85038	0.103191
$764$	7.61473	0.275491
$765$	− 82.3883i	− 2.97876i
$766$	23.4197	0.846190
$767$	0	0
$768$	−2.47957	−0.0894736
$769$	− 20.3268i	− 0.733003i	−0.930418	−	0.366501i	$-0.880556\pi$
$769$	− 20.3268i	− 0.733003i	0.930418	−	0.366501i	$-0.119444\pi$
$770$	−11.0362	−0.397718
$771$	−2.11315	−0.0761033
$772$	4.19093i	0.150835i
$773$	4.74178i	0.170550i	0.996357	+	0.0852750i	$0.0271769\pi$
$773$	4.74178i	0.170550i	−0.996357	+	0.0852750i	$0.972823\pi$
$774$	29.7960i	1.07100i
$775$	− 22.6343i	− 0.813047i
$776$	16.4337	0.589935
$777$	0.352943	0.0126617
$778$	− 14.2136i	− 0.509584i
$779$	−22.4882	−0.805724
$780$	0	0
$781$	4.58905	0.164209
$782$	− 15.6448i	− 0.559459i
$783$	−7.06795	−0.252588
$784$	−0.244755	−0.00874124
$785$	32.2040i	1.14941i
$786$	1.82401i	0.0650604i
$787$	− 31.6106i	− 1.12679i	−0.826186	−	0.563397i	$-0.809494\pi$
$787$	− 31.6106i	− 1.12679i	0.826186	−	0.563397i	$-0.190506\pi$
$788$	11.6015i	0.413287i
$789$	2.70799	0.0964072
$790$	44.6829	1.58974
$791$	− 11.5351i	− 0.410141i
$792$	−28.9656	−1.02925
$793$	0	0
$794$	−20.4546	−0.725906
$795$	3.52978i	0.125188i
$796$	−7.20747	−0.255462
$797$	47.1670	1.67074	0.835370	−	0.549688i	$-0.185253\pi$
$797$	47.1670	1.67074	0.835370	+	0.549688i	$0.185253\pi$
$798$	− 0.365024i	− 0.0129217i
$799$	69.9148i	2.47341i
$800$	− 51.1601i	− 1.80878i
$801$	− 14.1920i	− 0.501450i
$802$	20.2463	0.714923
$803$	15.1526	0.534724
$804$	− 0.269933i	− 0.00951982i
$805$	−9.31421	−0.328283
$806$	0	0
$807$	1.00056	0.0352213
$808$	8.84261i	0.311082i
$809$	−11.6238	−0.408672	−0.204336	−	0.978901i	$-0.565504\pi$
$809$	−11.6238	−0.408672	−0.204336	+	0.978901i	$0.565504\pi$
$810$	27.5281	0.967238
$811$	− 9.29601i	− 0.326427i	−0.986591	−	0.163214i	$-0.947814\pi$
$811$	− 9.29601i	− 0.326427i	0.986591	−	0.163214i	$-0.0521860\pi$
$812$	− 9.42414i	− 0.330722i
$813$	− 4.87579i	− 0.171001i
$814$	6.45096i	0.226106i
$815$	−16.1671	−0.566310
$816$	−0.294626	−0.0103140
$817$	31.8098i	1.11288i
$818$	−1.72561	−0.0603347
$819$	0	0
$820$	−40.4350	−1.41205
$821$	− 44.2153i	− 1.54312i	−0.636154	−	0.771562i	$-0.719476\pi$
$821$	− 44.2153i	− 1.54312i	0.636154	−	0.771562i	$-0.280524\pi$
$822$	2.49572	0.0870483
$823$	−20.1303	−0.701700	−0.350850	−	0.936432i	$-0.614107\pi$
$823$	−20.1303	−0.701700	−0.350850	+	0.936432i	$0.614107\pi$
$824$	27.1662i	0.946378i
$825$	5.06359i	0.176291i
$826$	− 3.58421i	− 0.124710i
$827$	13.4329i	0.467109i	0.972344	+	0.233554i	$0.0750357\pi$
$827$	13.4329i	0.467109i	−0.972344	+	0.233554i	$0.924964\pi$
$828$	−9.58585	−0.333131
$829$	4.62491	0.160630	0.0803148	−	0.996770i	$-0.474407\pi$
$829$	4.62491	0.160630	0.0803148	+	0.996770i	$0.474407\pi$
$830$	− 30.8168i	− 1.06967i
$831$	0.973741	0.0337787
$832$	0	0
$833$	7.43189	0.257500
$834$	0.438182i	0.0151730i
$835$	−41.1494	−1.42403
$836$	−12.1257	−0.419378
$837$	− 2.46159i	− 0.0850849i
$838$	− 21.8495i	− 0.754780i
$839$	− 44.5747i	− 1.53889i	−0.638712	−	0.769446i	$-0.720533\pi$
$839$	− 44.5747i	− 1.53889i	0.638712	−	0.769446i	$-0.279467\pi$
$840$	− 1.67379i	− 0.0577513i
$841$	24.3590	0.839966
$842$	18.9685	0.653698
$843$	− 4.28923i	− 0.147729i
$844$	−24.7895	−0.853289
$845$	0	0
$846$	−23.5701	−0.810357
$847$	1.34673i	0.0462743i
$848$	−1.43079	−0.0491337
$849$	0.0325050	0.00111557
$850$	55.7090i	1.91080i
$851$	5.44439i	0.186631i
$852$	0.272914i	0.00934989i
$853$	− 4.58159i	− 0.156870i	−0.996919	−	0.0784352i	$-0.975008\pi$
$853$	− 4.58159i	− 0.156870i	0.996919	−	0.0784352i	$-0.0249924\pi$
$854$	4.27331	0.146230
$855$	29.6525	1.01409
$856$	25.0319i	0.855573i
$857$	−15.4008	−0.526080	−0.263040	−	0.964785i	$-0.584725\pi$
$857$	−15.4008	−0.526080	−0.263040	+	0.964785i	$0.584725\pi$
$858$	0	0
$859$	−52.8596	−1.80355	−0.901774	−	0.432208i	$-0.857735\pi$
$859$	−52.8596	−1.80355	−0.901774	+	0.432208i	$0.857735\pi$
$860$	57.1958i	1.95036i
$861$	−1.36176	−0.0464088
$862$	−2.34285	−0.0797979
$863$	− 33.2346i	− 1.13132i	−0.824639	−	0.565659i	$-0.808622\pi$
$863$	− 33.2346i	− 1.13132i	0.824639	−	0.565659i	$-0.191378\pi$
$864$	− 5.56391i	− 0.189288i
$865$	− 38.5388i	− 1.31036i
$866$	− 21.5357i	− 0.731813i
$867$	6.19270	0.210315
$868$	3.28219	0.111405
$869$	− 49.9887i	− 1.69575i
$870$	3.71613	0.125988
$871$	0	0
$872$	−7.90138	−0.267574
$873$	17.6296i	0.596670i
$874$	5.63075	0.190463
$875$	14.5273	0.491111
$876$	0.901136i	0.0304466i
$877$	− 24.1314i	− 0.814858i	−0.913237	−	0.407429i	$-0.866425\pi$
$877$	− 24.1314i	− 0.814858i	0.913237	−	0.407429i	$-0.133575\pi$
$878$	26.6931i	0.900849i
$879$	0.317478i	0.0107083i
$880$	−3.20602	−0.108075
$881$	−59.0833	−1.99057	−0.995284	−	0.0970036i	$-0.969074\pi$
$881$	−59.0833	−1.99057	−0.995284	+	0.0970036i	$0.969074\pi$
$882$	2.50549i	0.0843641i
$883$	8.09950	0.272570	0.136285	−	0.990670i	$-0.456484\pi$
$883$	8.09950	0.272570	0.136285	+	0.990670i	$0.456484\pi$
$884$	0	0
$885$	−2.56867	−0.0863449
$886$	− 14.4868i	− 0.486692i
$887$	−34.8540	−1.17028	−0.585142	−	0.810931i	$-0.698961\pi$
$887$	−34.8540	−1.17028	−0.585142	+	0.810931i	$0.698961\pi$
$888$	−0.978373	−0.0328320
$889$	0.885393i	0.0296951i
$890$	14.9893i	0.502444i
$891$	− 30.7969i	− 1.03173i
$892$	17.1677i	0.574816i
$893$	−25.1631	−0.842051
$894$	0.0694061	0.00232129
$895$	67.1516i	2.24463i
$896$	7.83114	0.261620
$897$	0	0
$898$	12.0905	0.403466
$899$	18.5836i	0.619798i
$900$	34.1338	1.13779
$901$	43.4456	1.44738
$902$	− 24.8898i	− 0.828741i
$903$	1.92623i	0.0641009i
$904$	31.9758i	1.06350i
$905$	− 79.4730i	− 2.64177i
$906$	−2.10828	−0.0700430
$907$	−10.2919	−0.341738	−0.170869	−	0.985294i	$-0.554657\pi$
$907$	−10.2919	−0.341738	−0.170869	+	0.985294i	$0.554657\pi$
$908$	17.2276i	0.571718i
$909$	−9.48609	−0.314634
$910$	0	0
$911$	−54.2867	−1.79860	−0.899299	−	0.437334i	$-0.855923\pi$
$911$	−54.2867	−1.79860	−0.899299	+	0.437334i	$0.855923\pi$
$912$	− 0.106039i	− 0.00351131i
$913$	−34.4762	−1.14099
$914$	−12.7127	−0.420500
$915$	− 3.06253i	− 0.101244i
$916$	13.6424i	0.450759i
$917$	− 13.3660i	− 0.441384i
$918$	6.05863i	0.199965i
$919$	43.4286	1.43258	0.716289	−	0.697803i	$-0.245839\pi$
$919$	43.4286	1.43258	0.716289	+	0.697803i	$0.245839\pi$
$920$	25.8194	0.851240
$921$	4.07147i	0.134160i
$922$	−13.3841	−0.440783
$923$	0	0
$924$	−0.734269	−0.0241557
$925$	− 19.3867i	− 0.637430i
$926$	5.92599	0.194740
$927$	−29.1430	−0.957183
$928$	42.0044i	1.37886i
$929$	30.8380i	1.01176i	0.862603	+	0.505881i	$0.168832\pi$
$929$	30.8380i	1.01176i	−0.862603	+	0.505881i	$0.831168\pi$
$930$	1.29423i	0.0424396i
$931$	2.67482i	0.0876637i
$932$	−6.78223	−0.222159
$933$	4.78340	0.156602
$934$	0.523556i	0.0171313i
$935$	97.3498	3.18368
$936$	0	0
$937$	22.4073	0.732013	0.366007	−	0.930612i	$-0.380725\pi$
$937$	22.4073	0.732013	0.366007	+	0.930612i	$0.380725\pi$
$938$	− 1.08834i	− 0.0355354i
$939$	1.08344	0.0353568
$940$	−45.2446	−1.47572
$941$	12.2484i	0.399287i	0.979869	+	0.199644i	$0.0639784\pi$
$941$	12.2484i	0.399287i	−0.979869	+	0.199644i	$0.936022\pi$
$942$	− 1.17890i	− 0.0384106i
$943$	− 21.0062i	− 0.684055i
$944$	− 1.04121i	− 0.0338885i
$945$	3.60703	0.117337
$946$	−35.2069	−1.14468
$947$	53.1071i	1.72575i	0.505418	+	0.862875i	$0.331338\pi$
$947$	53.1071i	1.72575i	−0.505418	+	0.862875i	$0.668662\pi$
$948$	2.97286	0.0965541
$949$	0	0
$950$	−20.0503	−0.650517
$951$	− 3.35068i	− 0.108653i
$952$	−20.6015	−0.667700
$953$	9.63675	0.312165	0.156082	−	0.987744i	$-0.450113\pi$
$953$	9.63675	0.312165	0.156082	+	0.987744i	$0.450113\pi$
$954$	14.6466i	0.474203i
$955$	− 22.0027i	− 0.711991i
$956$	25.8548i	0.836205i
$957$	− 4.15740i	− 0.134390i
$958$	−20.7601	−0.670727
$959$	−18.2881	−0.590555
$960$	2.62977i	0.0848756i
$961$	24.5278	0.791219
$962$	0	0
$963$	−26.8535	−0.865341
$964$	− 30.1234i	− 0.970209i
$965$	12.1097	0.389824
$966$	0.340968	0.0109705
$967$	12.8720i	0.413937i	0.978348	+	0.206968i	$0.0663597\pi$
$967$	12.8720i	0.413937i	−0.978348	+	0.206968i	$0.933640\pi$
$968$	− 3.73321i	− 0.119990i
$969$	3.21985i	0.103436i
$970$	− 18.6200i	− 0.597853i
$971$	−58.2615	−1.86970	−0.934850	−	0.355042i	$-0.884467\pi$
$971$	−58.2615	−1.86970	−0.934850	+	0.355042i	$0.884467\pi$
$972$	5.57649	0.178866
$973$	− 3.21091i	− 0.102937i
$974$	−17.5879	−0.563553
$975$	0	0
$976$	1.24139	0.0397361
$977$	29.7552i	0.951954i	0.879458	+	0.475977i	$0.157906\pi$
$977$	29.7552i	0.951954i	−0.879458	+	0.475977i	$0.842094\pi$
$978$	0.591835	0.0189248
$979$	16.7692	0.535948
$980$	4.80947i	0.153633i
$981$	− 8.47636i	− 0.270629i
$982$	2.09237i	0.0667703i
$983$	− 11.6376i	− 0.371181i	−0.982627	−	0.185591i	$-0.940580\pi$
$983$	− 11.6376i	− 0.371181i	0.982627	−	0.185591i	$-0.0594198\pi$
$984$	3.77487	0.120338
$985$	33.5226	1.06812
$986$	− 45.7392i	− 1.45663i
$987$	−1.52374	−0.0485012
$988$	0	0
$989$	−29.7134	−0.944832
$990$	32.8192i	1.04306i
$991$	3.02153	0.0959820	0.0479910	−	0.998848i	$-0.484718\pi$
$991$	3.02153	0.0959820	0.0479910	+	0.998848i	$0.484718\pi$
$992$	−14.6291	−0.464473
$993$	5.73405i	0.181965i
$994$	1.10035i	0.0349011i
$995$	20.8259i	0.660227i
$996$	− 2.05032i	− 0.0649670i
$997$	20.0738	0.635742	0.317871	−	0.948134i	$-0.397032\pi$
$997$	20.0738	0.635742	0.317871	+	0.948134i	$0.397032\pi$
$998$	−0.360269	−0.0114041
$999$	− 2.10840i	− 0.0667067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.j.337.14		24
13.5	odd	4		1183.2.a.r.1.7	yes	12
13.8	odd	4		1183.2.a.q.1.6	✓	12
13.12	even	2	inner	1183.2.c.j.337.11		24
91.34	even	4		8281.2.a.cn.1.6		12
91.83	even	4		8281.2.a.cq.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.a.q.1.6	✓	12	13.8	odd	4
1183.2.a.r.1.7	yes	12	13.5	odd	4
1183.2.c.j.337.11		24	13.12	even	2	inner
1183.2.c.j.337.14		24	1.1	even	1	trivial
8281.2.a.cn.1.6		12	91.34	even	4
8281.2.a.cq.1.7		12	91.83	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)

\(f(q)\)	\(=\)	\(q+0.842530i q^{2} +0.161973 q^{3} +1.29014 q^{4} -3.72786i q^{5} +0.136467i q^{6} -1.00000i q^{7} +2.77204i q^{8} -2.97376 q^{9} +O(q^{10})\)	\(q+0.842530i q^{2} +0.161973 q^{3} +1.29014 q^{4} -3.72786i q^{5} +0.136467i q^{6} -1.00000i q^{7} +2.77204i q^{8} -2.97376 q^{9} +3.14083 q^{10} -3.51379i q^{11} +0.208968 q^{12} +0.842530 q^{14} -0.603811i q^{15} +0.244755 q^{16} -7.43189 q^{17} -2.50549i q^{18} -2.67482i q^{19} -4.80947i q^{20} -0.161973i q^{21} +2.96048 q^{22} +2.49854 q^{23} +0.448995i q^{24} -8.89694 q^{25} -0.967586 q^{27} -1.29014i q^{28} +7.30473 q^{29} +0.508729 q^{30} +2.54405i q^{31} +5.75030i q^{32} -0.569138i q^{33} -6.26159i q^{34} -3.72786 q^{35} -3.83658 q^{36} +2.17903i q^{37} +2.25362 q^{38} +10.3338 q^{40} -8.40738i q^{41} +0.136467 q^{42} -11.8923 q^{43} -4.53329i q^{44} +11.0858i q^{45} +2.10510i q^{46} -9.40740i q^{47} +0.0396435 q^{48} -1.00000 q^{49} -7.49594i q^{50} -1.20376 q^{51} -5.84583 q^{53} -0.815220i q^{54} -13.0989 q^{55} +2.77204 q^{56} -0.433247i q^{57} +6.15445i q^{58} -4.25410i q^{59} -0.779003i q^{60} +5.07200 q^{61} -2.14344 q^{62} +2.97376i q^{63} -4.35529 q^{64} +0.479516 q^{66} -1.29175i q^{67} -9.58820 q^{68} +0.404695 q^{69} -3.14083i q^{70} +1.30601i q^{71} -8.24341i q^{72} +4.31232i q^{73} -1.83590 q^{74} -1.44106 q^{75} -3.45090i q^{76} -3.51379 q^{77} +14.2264 q^{79} -0.912411i q^{80} +8.76457 q^{81} +7.08347 q^{82} -9.81167i q^{83} -0.208968i q^{84} +27.7051i q^{85} -10.0196i q^{86} +1.18316 q^{87} +9.74039 q^{88} +4.77241i q^{89} -9.34010 q^{90} +3.22347 q^{92} +0.412067i q^{93} +7.92602 q^{94} -9.97135 q^{95} +0.931391i q^{96} -5.92836i q^{97} -0.842530i q^{98} +10.4492i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{3} - 30 q^{4} + 52 q^{9}+O(q^{10}) \) 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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